Decomposing Consumption Inequality: The
Contribution of Income Dispersion and Taxation∗
Estelle Dauchy†
Nathan Seegert‡
July 2014
Keywords: Automatic stabilizers, personal income taxation, income risk, consumption, inequality
JEL: D12, D31, D91, H24, E21
Abstract
This paper examines the contributions of tax policy, the income distribution, and
behavioral responses to the link between income and consumption inequality. We use
income from the Panel Study of Income Dynamics in conjunction with consumption
from the Consumer Expenditure Survey as complementary indicators of inequality. We
document the increase in income dispersion in the 1980s and 1990s are due to increases
in both permanent and transitory income shocks. Further, we find an increase in the
link between income and consumption inequality due to changes in tax policy, partially
mitigated by changes in the income distribution and household behavioral responses.
∗
We are grateful to Alexey Khazanov for excellent research assistance, Alan Feenberg of the National
Bureau of Economic Research for his help compiling certain CEX years, and we thank Byron Lutz and
Ramen Molley of the Federal Reserve Board for very valuable comments, as well as seminar participants at
the New Economic School in Moscow, Drexel University in Philadelphia for their helpful comments. Potential
errors are entirely those of the authors.
†
New Economic School, Novaya ulitsa 100, Skolkovo village, Moscow, 143025, Russian Federation,
[email protected].
‡
University of Utah, 1655 East Campus Center Drive, Salt Lake City, Utah, 84108,
[email protected].
1
I
Introduction
Income and consumption inequality in the U.S. have both increased in the past three decades
and these topics have recently received substantial attention (Moffitt and Gottschalk, 2011;
Blundell et al., 2008; Krueger and Perri, 2006).1 However, the underlying mechanisms that
link these processes are poorly understood. The relationship between income and consumption inequality depends on the persistence of the underlying income shocks and the degree of
insurance that buffers consumption from these income shocks (consumption insurance). An
important determinant of consumption insurance is fiscal policy, particularly in the form of
“automatic stabilizers.” Understanding the link between income and consumption inequality is important for policy makers trying to decrease inequality with minimal distortions to
income mobility and the economy as a whole.
We directly estimate the degree of consumption insurance jointly with the covariance
structure of the income process using income and consumption panel data. First, we show
that an important explanation for the increase in consumption inequality in the U.S. is due
to decreases in the degree of consumption insurance. Further, we decompose the decrease in
consumption insurance and find that changes in federal tax policy, the income distribution,
and behavioral changes all have important explanatory power for the change in consumption
insurance. Between 1968 and 2010, changes in federal tax policies decreased the degree of
consumption insurance, but changes in the income distribution and offsetting behavioral
responses mitigated some of this effect.
Our analysis proceeds in three steps. First, the variance of income is separated into
its permanent and transitory components. Second, we estimate the degree of consumption
insurance across different time periods. Finally, we decompose the changes in the degree of
consumption insurance using micro-simulation methods. Toward our goal of analyzing the
variation in the degree of consumption insurance across time, we create a panel series of
income and consumption combining information from the Panel Study of Income Dynamics
(PSID) and the Consumer Expenditure Survey (CEX) using imputation methods pioneered
by Skinner (1987); Blundell et al. (2004); Kniesner and Ziliak (2002). The resulting panel
data consists of data from 1968 to 2010 substantially extending the sample period of previous
studies (e.g. Blundell et al. (2008)). To extend our analysis beyond 1999, when the PSID
began reporting biannually, we construct additional moment conditions based on the two1
For a discussion of the different measurement methods and findings on the inequality of income and
consumption in the United States see (Debacker et al., 2013).
2
year growth of income and consumption. These additional moments are used in a diagonallyweighted minimum distance estimation of the variance of permanent and transitory income
and the degree of consumption insurance.
The results reveal considerable changes over time in the importance of the variance of
permanent and transitory income in explaining increases in the variance of income documented by Krueger and Perri (2006). Studies by Heathcote et al. (2010) and Gottschalk
and Moffitt (2009) suggest an important role for increases in transitory income in explaining
the increase in income inequality. In contrast, studies by Kopczuk et al. (2010) using Social
Security earnings data and Primiceri and Van Rens (2009) using repeated cross sections from
the Consumer Expenditure Survey suggest the increase in income inequality is due to the
permanent component of income. We find that both the permanent and transitory components contributed to the increase in the variance of income in the 1980s, though to different
extents across years, consistent with the evidence presented by Blundell et al. (2008). We
document a large increase in the variance of income in the 1990s and find that it remained
elevated through the 2000s. The initial increase is due to an increase in the permanent
component of income, while the elevated levels in the 2000s are due to a series of spikes in
the variance of transitory income.
The degree to which these income shocks are transferred to consumption has substantially
changed over the last forty years. This suggests that changes in consumption insurance may
have an important role in explaining the substantial rise in the level of consumption inequality
in the U.S. that has recently been documented by Attanasio et al. (2012) and Aguiar and
Bils (2011). We estimate the degree of consumption insurance for five separate time periods
roughly corresponding to different federal tax regimes, namely 1968-1980, 1981-1986, 19871992, 1993-2002, and 2003-2010. We find that the degree of consumption insurance decreased
substantially in the first half of our sample and subsequently increased. The net result across
the last forty years is a decrease in the degree of consumption insurance from permanent
income shocks but an increase in insurance from transitory income shocks.
Over this time period, changes in fiscal stabilization due to tax policy and the income
distribution are isolated using the National Bureau of Economic Research’s Taxsim software to run different simulations. We measure changes in stabilization due to tax policy
changes by simulating the percentage of an income shock the tax code absorbs holding the
income distribution fixed. Similarly, changes in stabilization due to changes in the income
distribution are measured by simulating the percentage of an income shock the tax code
3
absorbs holding the tax policy fixed. These simulations suggest that over this time period
tax policy changes have decreased stabilization while changes in the income distribution have
increased stabilization. These measures of stabilization are used to quantify the changes in
consumption insurance due to changes in tax policy, the income distribution, and behavioral
responses.
The empirical evidence presented in this paper has its origins in a large and important
literature looking at income and consumption inequality (Moffitt and Gottschalk, 2011, 2002;
Debacker et al., 2013; Meghir and Pistaferri, 2004a; Autor et al., 2008; Blundell et al., 2008;
Heathcote et al., 2010; Kopczuk et al., 2010) as well as in a growing empirical literature
analyzing the impact of fiscal policy on consumption insurance (Hoynes and Luttmer, 2011;
Seegert, 2012; Grant et al., 2010; Kniesner and Ziliak, 2002). The empirical evidence demonstrates the ability of fiscal policy to provide consumption insurance to households. This is
particularly relevant for policymakers because the variance of income has remained elevated
since its increase in the 1990s.2
The paper is structured as follows. Section II provides a detailed description of the theory
and the empirical approaches. Section III describes the data and the imputation strategy, as
well as the micro-simulation of income stocks. Section IV presents the results, and section
V concludes.
II
Model of Income and Consumption Dynamics
The main contribution of the model is to understand the mechanisms that insure consumption against income shocks. We setup a simple life-cycle consumption smoothing model that
describes the relationship between consumption and income shocks, heavily drawing from
Blundell et al.(2003; 2008). Then we derive a series of moment conditions that link the model
to the data. We then extend this model to allows us to consider how insurance parameters
are influenced by policy and market stabilizers. We finally describe how policy and market
stabilizers can be constructed from a micro-simulation approach.
2
Despite the usefulness of automatic stabilizers in providing consumption insurance, policymakers have
increasingly relied on discretionary policy to smooth consumption (Feldstein, 2009; Souleles et al., 2006;
Solow, 2005; Auerbach and Gale, 2009; Auerbach, 2009; Dauchy and Balding, 2013).
4
A
Dynamic Life-Cycle Model of Consumption
The unit of analysis is the household, defined as stable prime-age couples with or without
children. Because the focus is to study consumption insurance from market income shocks
and the smoothing effects of tax policy, we do not model life-cycle income shocks that stem
from changes in family composition, such as divorce, widowhood, or separation.3 We further
assume that the two main sources of uncertainty are changes in market income and changes
in government insurance, where income includes before-tax earnings and cash transfers (such
as food stamps and welfare payments). Household i maximizes the present discounted value
of its future consumption, as follows
max Et
∞
X
(1 + δ)−j u(Ci,t+j , Zi,t+j ),
(1)
j=0
where Ci,t+j is the consumption of household i in period t + j, Zi,t is a set of deterministic
factors including both observable and unobservable taste shifts, and δ is a subjective discount
rate. Households are subject to an inter-temporal budget constraint and an end of life
condition for assets, where individuals have access to a risk-free bond with real return rt+j
described by
Ai,t+j+1 = (1 + rt+j )(Ai,t+j + Yi,t+j − Ci,t+j ),
Ai,T = 0,
(2)
(3)
where Ai,t is the real value of assets at the beginning of period t, and Yi,t is household income.
The income process is subject to permanent and transitory shocks and the variance of
each shock is allowed to vary across years,4
0
log(Yi,t ) = Zi,t
ϕt + Pi,t + νi,t ,
(4)
where Zi,t represents the deterministic component of income which is known in year t and
allowed to shift over time.5 Consistent with previous studeis using the PSID the permanent
3
We further defend in Section III why this assumption does not limit our findings.
Carroll (2009) and Blundell and Pistaferri (2003) show evidence that simulations based on reasonable
values for equation (4) accurately reflect the income process in the PSID.
5
In the empirical approach, deterministic factors include several demographic variables such as education,
family size, age, number of kids, region, labor market experience, and ethnicity. We also allow for those
characteristics to vary across groups based on education, age, income, and cohorts by including group fixed
4
5
component Pi,t is assumed to be a martingale and the transitory component νi,t is a meanreverting MA(q) process, described by,
Pi,t = Pi,t−1 + ζi,t ,
q
X
νi,t =
θj εi,t−j ,
(5)
(6)
j=0
where ζi,t is serially uncorrelated.6 Although we determine the order q empirically, as in
Blundell et al. (2008), we start with a simple model where εi,t are serially uncorrelated, and
assume that θ0 = 1. We estimate the model in two steps. First, we isolate the unexplained
0
component of income growth yi,t = log(Yi,t ) − Zi,t
ϕt . We then estimate income growth,
represented by
∆yi,t = ζi,t + ∆νi,t .
(7)
A commonly used utility function in the literature on precautionary savings is a CRRA
function (Carroll (1994); Abowd and Card (1989)) which we define as u(C, Z) = (C 1−γ /1 −
0
γ)eZ ϑ . The Euler equation that results from maximizing (1) under constraints (2) and (3)
can be linearized using a Taylor expansion of consumption as follows
∆ci,t ∼
= ξi,t + πi,t ζi,t + γt,L πi,t εi,t ,
7
(8)
0
ϑ0t −ϕi,t is the unexplained (residual) change in consumption
where ∆ci,t = ∆logCi,t −∆logZi,t
and πi,t is the share of future labor income in current human and financial wealth. The slope
of the consumption path, ϕt , depends on a common retirement age L, is derived from the
approximation of consumption, and can be viewed as an age-increasing annuitization factor.8
Innovations in consumption are given by the random term, ξi,t , which is independent from
income shocks and also captures measurement error in consumption.9
effects.
6
Many empirical studies show that this is an accurate representation of the income process. See e.g.,
MaCurdy (1982); Abowd and Card (1989); Moffitt and Gottschalk (2011); Meghir and Pistaferri (2004b).
7
See Blundell et al. (2013) and appendix B in Blundell et al. (2008) for a detailed derivation of the
approximation of consumption and income using a similar utility function.
8
For exposition convenience, we also assume that the transitory income component is i.i.d (q = 1) and
θ0 ≡ 1. Meghir and Pistaferri (2004b) show that this equation can be easily extended to MA(q) transitory
shock processes of higher order.
9
See Blundell and Preston (1998) for a derivation of γt,L in the case of a CCRA utility function. Carroll
(2009) simulates a buffer-stock model that directly explains changes in πi,t . In particular, an increase in
the permanent shock may temporarily increase the amount of precautionary savings because it reduces the
6
For individuals many years from retirement age, it is commonly assumed that the present
value of financial assets is small relative to the remaining value of labor income, implying
πi,t ≈ 1, which means that no part of permanent income shocks is self-insured.10 A tractable
version of (8) can be written as
∆ci,t = φi,t ζi,t + ψi,t εi,t + ξi,t .
(9)
Equation (9) allows both permanent and transitory shocks to have an impact on consumption with loading factors φi,t and ψi,t , which are defined as partial insurance parameters
that capture one minus the degree of consumption insurance. Although we expect the intermediate case where φi,t ∈ (0, 1) and ψi,t ∈ (0, 1), this equation allows the two polar cases of
no insurance (φi,t = ψi,t = 1) as predicted by the permanent income hypothesis (with only
self-insurance through savings) or full insurance (φi,t = ψi,t = 0) as predicted by models of
complete markets.11 The lower the loading factors, the larger the degree of insurance.
Before delving into details on parameter identification under the model presented above
it is useful to take a step back and consider more carefully what direct estimations of these
parameters should capture. Estimating φi,t < πi,t and ψi,t < γt,L πi,t would provide evidence
of “excess-smoothing” over and above self-insurance through asset accumulation, and justify that individuals should insure relatively more against transitory shocks than against
permanent income shocks. This “excess-smoothing” of consumption to income shocks has
alternatively been explained by the macroeconomic literature as resulting from imperfect
markets either due to the existence of private information, or to limited contract enforcements. Under these models, households engage in more precautionary saving (insure more)
ratio of assets to permanent income rather than increasing precautionary savings. The term ξi,t has also
been characterized as an innovation to higher moments of the income process. For example Caballero (1990)
presents a stochastic model in which ξi,t captures revisions to the variance forecast of consumption growth
as a response to income shocks, which contrasts with effects that occur to the mean of consumption growth
and which are captured by ζi,t and εi,t .
10
Carroll (2009) estimates values of πi,t between 0.85 and 0.95, and Blundell et al. (2013) find an average
of 0.8 and evidence of smaller values as age increase (from 0.85 at age 30 to 0.78 at age 50) using panel data
for Britain. Below, we discuss results that allow estimates of insurance loading factors to vary by age and
cohorts. Although, we find some evidence that insurance factors tends to be smaller for earlier cohorts and
older age groups, implying that πi is smaller than one (and therefore insurance is larger) for these groups,
we do not find find a significant difference across groups.
11
Traditional life-cycle models with forward-looking consumers imply that the marginal propensity to
consume out of permanent income shocks should be equal to one. However, extensive macro-economic
and micro-economic empirical literature has shown evidence of “excess-smoothness” or excess sensitivity in
consumption response to predicted income shocks, implying that the basic intuition from the PIH is not
correct. See, among others, Hall (1978), Deaton (1991), Hall and Mishkin (1982).
7
than with a single, non-contingent bond, but less than with complete markets. In turn,
these models allow the relationship between income shocks and consumption to depend on
the degree of persistence of income shocks (Alvarez and Jermann, 2000). Other explanations
of the excess-smoothness of consumption in response to perfectly anticipated permanent income shocks has been attributed to the severity of informational problems, such as moral
hazard (Attanasio and Pavoni, 2011).
The income process presented in (4) assumes that permanent and transitory shocks constitute new information to agents. Instead, if advance information about future income
shocks was available to consumers, consumption growth should not directly react to current
income shocks because agents would already have internalized them in previous periods.
Advance information would lead the econometrician to underestimate the impact of income
shocks on consumption volatility, however the empirical evidence suggests advance information does not seem to be a concern in our sample.12
B
Linking The Model and Data: Moment Conditions
This subsection derives a series of moment conditions that allow us to estimate the variance
of permanent and transitory income shocks, the partial insurance parameters, and other
model parameters such as the serial correlation of the transitory shocks. The first set of
covariance restrictions are derived from one-year differences as in Hall and Mishkin (1982)
and Blundell et al. (2008). The second set of covariance restrictions are derived from twoyear differences, which allow us to extend our analysis to the years in which the PSID is
reported biannually.
We derive one-year difference covariance restrictions using equations (7) and (9). The
restrictions due to the covariance of income across different leads is given by,



 var(ζt ) + var(∆νt )
cov(∆yt , ∆yt+s ) =
−cov(νt , νt+s )


 0
if s = 0
if 0 < |s| ≤ q + 1 ,
(10)
if |s| > q + 1
where cov(., .) and var(.) denote the cross-sectional covariance and variance, respectively,
and can be easily computed from observed data on households. If q = 0 and ν is serially
uncorrelated (νt = εt ) then var(∆νt ) = 2var(∆εt ). In this case, and ignoring issues of
12
See section IV.
8
measurement error, two years of data are enough to compute the moments of the income
process shown in (10).13
The consumption growth restriction from equation (9) leads to the restrictions
cov(∆ct , ∆ct+s ) = φ2t var(ζt ) + ψt2 var(εt ) + var(ξt ),
(11)
for s = 0, and zero otherwise (because consumption follows a martingale process). Finally,
the covariance between income and consumption at various lags is
(
cov(∆yt+s , ∆ct ) =
φt var(ζt ) + ψt var(∆νt )
if s = 0
ψt cov(εt , ∆νt+s )
if s > 0
.
(12)
In particular, if ν is serially uncorrelated (νt = εi,t ) then cov(∆yt+s , ∆ct ) = −ψt var(εt )
for s = 1, and 0 if s > 1.14 Equations (10), (11), and (12) define eight types of moment
conditions using the covariance of one-year differences in income and consumption.
One complication of using PSID data after 1999 is that the data are only reported
biannually, meaning the moment conditions based on one-year differences can not be used.
To extend our analysis to years after 1999 we construct moment conditions based on the
covariances of two-year differences in income and consumption which can be derived from
the model as,
˜ t = ζt + ζt−1 + ∆v
˜ t , and
∆y
˜ t = φζt + φζt−1 + ψεt + ψεt−1 + ξt + ξt−1 ,
∆c
˜ t defines the two-year difference in variable x.
where ∆x
The first set of moment conditions are based on the covariance of the two-year growth in
13
Meghir and Pistaferri (2004b) show that with a more general model where transitory shocks have MA(q)
with q ≥ 1, q + 1 years of observations are necessary to estimate the parameters of the income process. If
measurement error is added to the model, they show that q + 4 years of observations are required. Since
our empirical approach uses more than 40 years of income data from the PSID, this limitation is satisfied.
Although classical measurement error could be captured by the innovations in the MA process, previous work
suggests that measurement error in earnings are serially correlated Bound and Krueger (1991). Ludvigson
and Paxson (2001) show that the the Taylor expansion traditionally used to linearize inter-temporal changes
in consumption and income can also lead to approximation error, which would inflate existing measurement
error in observed values. They further discuss the extent to which instrumental variables’ techniques can
correct some of the approximation bias.
14
As shown, for instance, in Abowd and Card (1989), and further discussed in the empirical methodology,
consumption and income are likely to be contaminated with measurement error. With independent errors,
the model above still fully identifies ψt , while with dependent errors only a lower bound for ψt is identifiable
(Blundell et al., 2008).
9
income with different leads,

˜


 var(ζt ) + var(ζt−1 ) + var(∆vt )
˜ t , ∆y
˜ t+s ) =
˜ t , ∆v
˜ t+1 )
cov(∆y
var(ζt ) + cov(∆v


 cov(∆v
˜ , ∆v
˜
)
t
t+2
if s = 0
if s = 1 ,
if s = 2
where cov(., .) and var(.) denote the cross-sectional covariance and variance, respectively.
The second set of moment conditions are based on the covariance of the two-year growth in
consumption with different leads,

2
2
2
2


 φ var(ζt ) + φ var(ζt−1 ) + ψ var(εt ) + ψ var(εt−1 ) + 2var(ξ)
˜ t , ∆c
˜ t+s ) =
cov(∆c
φ2 var(ζt ) + ψ 2 var(εt ) + var(ξ)


 0
if s = 0
if s = 1 .
if s > 1
Finally, the covariance between the two-year growth in income and consumption at various
lags provides the third set of moments,

˜
˜


 φvar(ζt ) + φvar(ζt−1 ) + ψcov(εt , ∆vt ) + ψcov(εt−1 , ∆vt )
˜ t+s , ∆c
˜ t) =
˜ t+1 ) + ψcov(εt−1 , ∆v
˜ t+1 )
cov(∆y
φvar(ζt ) + ψcov(εt , ∆v


 ψcov(ε , ∆v
˜
˜
) + ψcov(ε , ∆v
)
t
t+2
t−1
t+2
if s = 0
if s = 1 .
if s = 2
These moment conditions based on two-year differences of income and consumption are used
throughout our sample period, not only for the years after 1999. The combined number
of moments from one-year and two-year differences across years is 477 which are used to
estimate 167 parameters.15
C
Micro-Simulations: Policy, Market, and Behavioral Effects
A contribution of this paper is to link the methods that directly estimate partial insurance
using consumption data with methods that use micro-simulations to investigate the mechanisms that constitute the partial insurance parameters. This subsection begins with the
partial insurance parameters estimated directly with consumption data using methods em15
More details, on deriving each of these moment conditions is given in Appendix Appendix B:. The
standard errors are calculated following Gary Chamberlain’s (1984) method. The computation requires the
variance-covariance matrix of the moments, the weights used in the estimation (in this case the diagonal
matrix of the inverse of the variance-covariance matrix), and the Jacobian matrix evaluated at the estimated
parameters.
10
ployed by the macro-economic literature (McKay and Reis, 2013; Christiano and G. Harrison,
1999).16 We then extend this model with measures of policy and market stabilizers which we
construct using micro-simulation methods employed by the public finance literature (Dolls
et al., 2012; Auerbach and Feenberg, 2000; Pechman, 1973).17 This model extension allows
us to decompose and isolate the changes in insurance into the parts due to changes in policy
stabilization, market stabilization, and behavioral responses.
One important advantage of panel data over cross-sectional data is that it allows for the
direct estimation of the partial insurance parameters φt and ψt .18 Meghir and Pistaferri
(2004b) show that with an MA(q) process for transitory shocks and possible measurement
error in consumption, the model summarized by equations (10), (11), and (12) can be fully
identified with at least q + 4 years of panel data.19
In this paper, the ability to estimate the partial insurance parameters φt and ψt is critical
because our aim is to disentangle changes in partial insurance due to changes in tax policy, the
income distribution, and behavioral responses. In the following example we use the simple
case of serially uncorrelated transitory shocks to illustrate how the partial insurance relies
on tax policy, the income distribution, and behavioral responses. Equation (12) implies that
a simple regression of cov(∆yt+1 , ∆ct ) is informative about the size of the transitory income
shock (i.e., ψvar(ε)).20 In other words, scaling cov(∆yt+1 , ∆ct ) by cov(∆yt , ∆yt+1 ) = var(ε)
directly identifies the partial insurance parameter ψt , of transitory income shocks.
To illustrate the model’s implication that the parameters of interest are derived from
the variance-covariance structure of changes in income and consumption, we start with the
minimum distance estimator suggested by Blundell et al. (2008), where the left-hand-side
16
See section III for details on the imputation approach to construct a panel data on consumption.
Papers relying on a micro-simulation approach (Dolls et al., 2012; Auerbach and Feenberg, 2000; Pechman, 1973) generally have to make strong assumptions about the nature of the transmission of income shocks
to household consumption. They generally arbitrarily assume that income shocks only affect the behavior of
a given proportion of liquidity constrained consumers. Auerbach and Feenberg (2000) and Pechman (1973)
use a micro-simulation approach with cross-sections of household tax data to calculate the size of automatic
stabilizers in the United States. Dolls et al. (2012) further compare recent changes in automatic stabilizers
in the United States and Europe. They assume that automatic stabilizers smooth consumption of liquidity
constrained households, and use proxies for the proportion of households who are liquidity constrained.
18
Panel data also allows for serial correlation of transitory shocks and measurement error in income and
consumption. By contrast, cross sectional data require the assumption of serially uncorrelated transitory
shocks and do not permit full identification of the parameters of interest. For example, Blundell and Preston
(1998) assume that φt = 1 and ψt = 0.
19
Total consumption is imputed into the PSID based on CEX data, which automatically implies measurement error in our measures of consumption.
20
See and Blundell and Pistaferri (2003) and appendix B in Blundell et al. (2008) for details.
17
11
variable of equation (13) is the scaled value of cov(∆yt+1 , ∆ct )
ψt = cov(∆yt+1 , ∆ct ) = αt + t ,
(13)
where ∆y and ∆c are unexplained residual income and consumption resulting from preliminary regressions of the log of income and the log consumption on household deterministic
factors (including demographics and cohort effects). A regression of equation (13) on a
constant directly identifies the partial insurance parameter ψt .
In this paper we take this estimation a step further by decomposing the partial insurance
parameters as a function of tax policy, the income distribution, and household behavior. To
M
, and
do this we rewrite equation (13) in terms of insurance 1 − ψi,t and include market, Si,t
P
, effects21
policy, Si,t
M
P
1 − ψi,t = αt + βt Γ(Si,t
, Si,t
) + i,t ,
(14)
where Γ is a function of these effects, β captures the relationship between these effects and
the partial insurance ψi,t , and i,t is an i.i.d. error term.22 Totally differentiating equation
(14) gives
M
P
M
P
d(1 − ψi,t ) = βt Γ0M dSi,t
+ βt Γ0P dSi,t
+ Γ(Si,t
, Si,t
)dβt .
(15)
The first term on the right-hand-side of equation (15) captures changes in insurance due
to changes in the income distribution. The second term captures changes in insurance due
to changes in tax policy and the third term captures changes in insurance due to the ways
households respond to these policies.23
D
Measuring Policy Stabilizers
The effectiveness of tax policy to stabilize consumption, relative to income, may change over
time due to changes in policy, changes in the income distribution, and changes in households’
reactions to these policies. For example, changes in the federal income tax rate has a direct
21
M
P
The market and policy effects Si,t
and Si,t
are constructed using the National Bureau of Economic
Research’s Taxsim software. Details are given in section D.
22
In the empirical part, we allow measurement error in consumption and income as well as heterogeneity
in unobserved idiosyncratic factors. Equation (14) also allows for additional controls to be included in the
regression such as the variance of permanent or temporary income shocks, more details are given in the
appendix.
23
In the empirical part, we allow for heterogeneity in behavioral effects by introducing groups fixed effects.
12
effect on the level of automatic stabilization provided in the tax code. We define these
changes as “policy effects.” The average level of automatic stabilization provided in the tax
code may also vary with changes in the income distribution. For example, the progressivity of
the federal income tax provides different levels of stabilization for different levels of income.
Therefore, if the income distribution changes such that more households have incomes in
places where the federal income tax provides more stabilization then the average level of
stabilization increases, even though tax policy remained constant. We define these changes
as “market effects.” Finally, changes in households’ responses to automatic stabilizers also
affects their effectiveness. For example, consider a household who receives a negative income
shock such that they receive a larger tax rebate at the end of the year. If the propensity to
smooth their negative income shock using their tax rebate (or their expected rebate) changes
over time then we may observe changes in the effectiveness of the automatic stabilizers even
in the absence of policy or market changes. We define these changes as “behavioral effects.”24
To disentangle the policy and market effects, we use traditional measures of automatic
stabilizers obtained from changes in tax liability, or disposable income, that follow changes
in market income. For example, if Y D denotes disposable income, the stabilization effect
due to the tax system can be written as
Si,t = 1 −
∆Yi,tD
∆Ti,t
=
,
∆Yi,t
∆Yi,t
(16)
where the ∆Yi,tD /∆Yi,t captures the extent to which the tax system dampens changes in
disposable income that result from changes in market income. At one extreme, if policy
stabilizers completely absorb shocks to market income, this term will be exactly zero and
Si,t = 1. At the other extreme, in the absence of stabilization effect (such as in a system
with no taxation), changes in disposable income are equal to changes in market income and
Si,t = 0.
In equation (16), ∆Ti,t is the change in tax liability that results from an income shock.
For example, if the tax system consisted solely of a flat marginal tax rate, τ , the tax structure
would insure τ percent of disposable income against income shocks (Si,t = τ ). Clearly, the
actual tax code is more complicated, which is why we use micro-simulations based on NBER’s
TaxSim program.25
24
For more details on the origin and definition of “automatic stabilizers,” or “built-in-flexibility”, see for
instance Musgrave and Miller (1948); Cohen (1959); Smith (1963).
25
Butrica and Burkhauser (1997) provide a methodology for calculating tax liability based on TaxSim
13
To estimate equation (15), we separately calculate changes in tax liability caused by
changes in the tax policy and income distribution. For this, we apply household income data
obtained from the PSID to the NBER’s TaxSim software from 1967 to 2010.
P
To calculate Si,t
we use NBER’s Taxsim to simulate the federal tax liability for each
household and year for two separate levels of income. First, the federal tax liability is
simulated for each year holding the household’s income fixed to their income in a base year,
here 1980, but allowing tax policy to be what it was in the given year, f itaxi,y1980 ,τt .26 Second,
the federal tax liability is simulated for each year holding the household’s income fixed to
1.1 times their income in the base year, simulating a 10 percent shock in their income, again
27
Then the policy
allowing tax policy to be what it was in the given year, f itaxci,y1980
c
,τt .
stabilization is constructed as the difference in these simulated tax liabilities,
P
Si,t
=
f itaxi,y1980 ,τt − f itaxci,y1980
c
,τt
c
yi,1980 − yi,1980
(17)
divided by the size of the simulated income shock, here ten percent of a household’s 1980
income. As this measure allows for policy changes but not income or behavioral changes it
isolates the changes in stabilization due solely to tax policy.
M
we similarly use NBER’s Taxsim to simulate the federal tax liability for
To calculate Si,t
each household and year for two separate levels of income. First, the federal tax liability is
simulated for each year using each household’s reported income in that year but using the
tax code that existed in the base year 1980, f itaxi,yt ,τ1980 . Second, the federal tax liability
is simulated for each year using each household’s reported income in the previous year but
using the tax code that existed in the base year 1980, f itaxi,yt−1 ,τ1980 . Then the market
stabilization is constructed as the difference in these simulated tax liabilities,
M
Si,t
=
f itaxi,yt ,τ1980 − f itaxi,yt−1 ,τ1980
∆yi,t
(18)
divided by the size of the household’s actual income shock between the two years. This
measure allows the household’s income to change every year but calculates their federal tax
and PSID data.
26
Although our benchmark base year is 1980, we use alternative base years to evaluate the sensitivity of
the choice of base years (see Appendix C. 2 for a discussion on the sensitivity of market and policy effects to
the choice of base year). The Economic Recovery Tax Act of 1981 marks the first year when federal income
tax schedules started to be indexed for inflation.
27
household’s income in 1980 is imputed for household’s that do not report income in 1980.
14
liability as if the tax policy had not changed since the base year 1980, isolating the changes
in stabilization due solely to changes in income. Changes in the average market stabilization
are therefore due to changes in the income distribution.
The following section reports the constructed measures of policy and market stabilization
across years and income quartile.
III
Data
Our goal is to evaluate the degree to which consumption is insured from income shocks, and
specifically the ability of fiscal policy to attenuate the dispersion of consumption relative to
income dispersion. To do this we need a long panel database covering household income and
consumption. We construct panel data on consumption and combine them with PSID data
on income using the imputation approach developed by Skinner (1987) and extensively used
since then (Blundell et al., 2004, 2008).28 One advantage of this imputation method is that it
allows demand to change over time with respect to changes in socioeconomic characteristics
and changes in relative prices because it is built upon a standard food demand function. The
demand model allows food and total expenditures to be jointly endogenous and measured
with error. Finally, this method produces, with the assumption of normality of food demand,
a measure of nondurable consumption in the PSID. As in Blundell et al. (2008), we start
from a standard demand function for food based on consumption items that are available in
both surveys.29
One innovation of our paper is that we expand the sample years to include the years 1967
through 2010. This allows us to compare the imputed values of nondurable consumption
produced through this method with data on nondurable consumption collected in the PSID
from 1999 to 2008. We also matched the CEX data from 1972-73 to those post 1980, enabling
us to expand the imputation method back to the 1970s.30 Furthermore, we explicitly model
28
Skinner (1987) imputes total consumption in the PSID using the estimated coefficients of a regression
of total consumption on a series of consumption items (food, utilities, vehicles, etc.) that are present in both
the PSID and the CEX. The regression is estimated with CEX data. Ziliak and Kniesner (2005) and Ziliak
(1998) impute consumption on the basis of income and the first difference of wealth (defined as the difference
between income and savings obtained from the Federal Reserve Board’s Survey of Consumer Finances).
29
More details on the underlying data used for the imputation are given in the appendix.
30
Food consumption was not collected in the PSID in 1967, 1972, 1987, 1988, and 1993. For these years,
we also impute food consumption. We construct a demand function for food expenses and estimate it using
PSID data on income and several demographics from 1967 to 2010. In this imputation, we allow income to
be endogenous, and include a cubic trend.
15
the variation in consumption due to demand shifters (such as socioeconomic characteristics,
income variation, and price variation) and fiscal policies with the later being an innovation
of this paper.
Before presenting the model, we briefly describe the data and sample selection. We start
with an unbalanced panel from the PSID using data from 1967 to 2010. To focus on income
risk, rather than variation in consumption due to divorce, widowhood, or other household
breaking-up factors, we restrict our sample to households with continuously married couples
(excluding 64.2 percent of households, with or without children), headed by a male of age 30
to 65 (excluding 29.7 percent of households).31 Excluding families headed by single parents is
done to ensure we are identifying consumption shocks stemming from income shocks rather
than changes in family composition. Even among low income households we do not feel
that this is an important limitation since, for example, the percentage of single and joint
households receiving the EITC are similar.32 An important contribution of our paper is
that we allow the effect of fiscal policy to be heterogeneous with respect to income groups,
allowing different income groups to have differential access to external smoothing mechanisms
in addition to self-insurance, through savings or borrowing and family networks. To this end
we use the two available samples of households in the PSID: the representative sample of
the US population and the low-income sample (SEO).33
In this sample we create 12 cohorts, each defined as being born in a given half decade
starting in 1920 and ending in 1980, eliminating 27.9 percent of the sample. Income outliers,
defined as households with income growth above 500 percent, below -80 percent, or with a
level of income below $100 in a given year, are eliminated (25.5 percent). To avoid family
composition and education changes in the sample we eliminate those younger than 30 (35.8
31
Families that report changes in head are excluded, further excluding 16.8 percent of the sample. Also,
the PSID public files do not report marital status from 1993-1996. To account for this, individuals are
assigned the marital status they had in 1992 and 1997 if these two years have the same values and dropped
otherwise.
32
This sample selection also makes our paper comparable to previous studies imputing consumption from
the PSID (Blundel et al., 2008). We recognize that certain tax and non-tax benefits such as the EITC
have largely benefited low-income single households. For instance in 2003, 76 percent of EITC recipients
were single headed households. Yet, within low-income groups, the proportion of single and joint household
receiving the EITC are similar. For instance in 2003, about 0.02 percent of both single-headed and joint
taxpayers with less than $40,000 of AGI received the EITC (authors’ calculations using data from the Joint
Committee on Taxation and SOI/IRS tax statistics). Finally, we define income groups based on 1980 income
distribution, implying that intergenerational mobility likely moved low-income families in and out of the
EITC over the period.
33
The PSID’s representative sample of the US population covers 61 percent of the 1967 sample and and
the low-income sample (SEO) covers 39 percent of the 1967 sample.
16
percent). To avoid changes due to retirement we drop those older than 65 (11.0 percent). We
eliminate households with missing report on race (0.6 percent) and region (6.0 percent).34
Starting with 23,107 families and 243,539 observations the final sample is composed of 4,139
households (17.9 percent) and 42,582 observations (17.5 percent). This sample selection is
followed to the extent possible in the CEX.
To further ensure accuracy of the demand equation, we compare food consumption and
other covariates obtained from the PSID (representative and SEO samples) and the CEX, as
well as a measure of food consumption obtained from national aggregates in NIPA accounts.
Table 1 shows the summary statistics of these variables in selected years. To account for the
discrepancy between food expenses in the two databases, we apply an annual weight to PSID
observations calculated as the difference in logs of annual averages between NIPA and PSID
measures. Because this weight is uniformly applied to all observations, its only effect is to
adjust the sample mean. The means of food consumption are quite close in the PSID and
CEX. As expected, since the purpose of the CEX is to follow household consumption, food
consumption is less volatile in the CEX. In all other categories the demographics look very
similar between the representative subsample of the PSID and the CEX. This is important
for the imputation to correctly predict consumption for households in the PSID using data
from the CEX.
A
Imputation of Nondurable Expenditures
The imputation method relies on measures of food and nondurable consumption. Food
consumption is constructed as the sum of food at home and food away from home, reported
in both the PSID and CEX. In the CEX data nondurable consumption is constructed as the
sum of food, alcohol, tobacco, services, heating fuel, public and private transport (including
gasoline), personal care, clothing, and footwear, as proposed by Attanasio and Weber (1995).
The PSID had limited consumption variables until additional questions were added in 1999
and 2005.35 These additional consumption data permit us to construct a PSID-based proxy
34
The PSID public files do not report state for years 1993-1996. To account for this, individuals are
assigned the state where they lived in 1992 and 1997 if those are the same and dropped otherwise (3.8
percent).
35
Consumption variables from 1999 include health care expenses (e.g. hospital, doctor, and prescription
expenses), housing expenses (e.g. mortgage payments, rent, property taxes, and home owner’s insurance),
utilities, vehicle expenses (e.g. loan payments, down payments, repairs, car insurance, and gasoline costs),
transportation expenses (e.g. taxi, bus, and train), education expenses, and adult care expenses. Additional
consumption variables added in 2005 include cell phone, internet, and cable expenses, recreation and vacation
17
Table 1: Comparison of Means (Variance)–PSID and CEX
1973
PSID(S) PSID(R)
Age
Family Size
No. of Kids
White
Food expenditures
Non-durable consumption (Imputed)
HS dropout
At least some college
Midwest
South
West
Husband working
Wife working
Observations
45.71
(9.573)
5.351
(2.571)
2.663
(2.210)
0.302
(0.460)
2,764
(1,286)
4,527
(2,701)
0.629
(0.484)
0.147
(0.355)
0.111
(0.314)
0.622
(0.486)
0.138
(0.345)
0.902
(0.298)
0.538
(0.499)
407
47.40
(10.02)
3.713
(1.629)
1.339
(1.500)
0.896
(0.305)
2,767
(1,138)
5,057
(2,395)
0.320
(0.467)
0.356
(0.479)
0.309
(0.462)
0.302
(0.459)
0.154
(0.362)
0.929
(0.257)
0.524
(0.500)
693
1990
2010
CEX
PSID(S)
PSID(R)
CEX
PSID(S)
PSID(R)
CEX
46.30
(10.20)
3.909
(1.765)
1.490
(1.594)
0.927
(0.260)
2,393
(973.8)
5,240
(2,903)
0.337
(0.473)
0.325
(0.469)
0.283
(0.451)
0.298
(0.458)
0.211
(0.408)
0.916
(0.277)
0.515
(0.500)
4,283
42.68
(9.523)
3.671
(1.363)
1.322
(1.243)
0.436
(0.496)
5,033
(2,440)
13,884
(9,405)
0.238
(0.426)
0.414
(0.493)
0.137
(0.344)
0.610
(0.488)
0.126
(0.332)
0.887
(0.317)
0.775
(0.418)
621
44.94
(10.02)
3.382
(1.206)
1.100
(1.184)
0.934
(0.248)
6,034
(2,718)
16,798
(10,519)
0.135
(0.342)
0.557
(0.497)
0.303
(0.460)
0.295
(0.456)
0.168
(0.374)
0.924
(0.266)
0.804
(0.397)
851
45.98
(9.879)
3.609
(1.444)
1.163
(1.272)
0.875
(0.330)
6,171
(2,939)
19,017
(9,626)
0.151
(0.358)
0.565
(0.496)
0.265
(0.442)
0.272
(0.445)
0.238
(0.426)
0.912
(0.284)
0.729
(0.444)
1,301
46.99
(9.991)
3.433
(1.352)
1.029
(1.269)
0.0250
(0.156)
6,648
(4,701)
24,605
(29,254)
0.133
(0.341)
0.483
(0.501)
0.0958
(0.295)
0.792
(0.407)
0.0458
(0.210)
0.821
(0.384)
0.796
(0.404)
240
46.61
(10.55)
3.296
(1.323)
1.045
(1.245)
0.884
(0.321)
8,870
(4,911)
31,207
(37,988)
0.0846
(0.278)
0.650
(0.477)
0.292
(0.455)
0.302
(0.459)
0.225
(0.418)
0.886
(0.318)
0.780
(0.415)
981
48.46
(10.15)
3.453
(1.449)
1.050
(1.241)
0.847
(0.360)
9,264
(4,526)
29,056
(17,279)
0.117
(0.321)
0.623
(0.485)
0.251
(0.434)
0.333
(0.472)
0.233
(0.423)
0.875
(0.331)
0.675
(0.468)
1,767
Notes: R = Representative PSID households (drawn from the national survey only); S = Total PSID households (from both the representative
survey and the SEO); CEX = Consumer Expenditure Survey. Standard errors are in parentheses.
18
for nondurable expenditures, which we compare with the imputed values of nondurables to
provide some external validity to the imputation method.
Our baseline measure of consumption is nondurable consumption but to test the durability of our findings we also consider three broader measures that alternatively include
semi-durables, services from durable goods, or both. Our second measure of consumption,
which we call “total consumption” includes the first measure of nondurable goods as well as
semi-durables such as luxury goods (e.g., jewelry, boats, etc), art, vehicles and parts, home
furniture and appliances, electronics. Total consumption also includes education and health
expenses. Our third and fourth measures for consumption respectively expand the first two
measures with a proxy for durable goods’ services. We call these measures “NondurablesPlus” and “Total consumption-Plus.” To obtain services from durable goods, we use an
external additional CEX database over the same period and for the same sets of households,
and apply a methodology similar to Johnson et al. (2005) and Slesnick (1994) to calculate
the rental equivalent value of owned homes and owned vehicles.36
The imputation method uses pooled cross section data from the CEX in 1972 and 1973,
and from 1980 to 2008, and the following demand equation (following Blundell et al. (2008)’s
notation) for food, f , expressed in logs:
0
fi,t = Wi,t
µ + p0t θ + β(Di,t )ci,t + ei,t ,
(19)
for each household i in period t with demographics, W , and relative price, p. Demand
shifters controlling for nondurable expenditure are given by c, expressed in logs, and the
budget elasticity β is allowed to vary with observed household characteristics, D. Finally,
we allow for unobserved heterogeneity in the measurement error in food expenditures given
by e.
Table 2 reports the results for this specification in which we instrument for total expenditures to account for its measurement error. Instruments for total expenditures include the
average hourly wage of the husband and wife by year, number of kids, and education. External instruments include several demographics such as age, ethnicity, region, family size, and
cohorts. This specification passes the test of over-identifying restrictions as the test fails to
reject the null hypothesis that the instrumental variables are uncorrelated with the residuals
expenses, furnishing, clothing, home repair, and charitable giving.
36
See appendix A. 1 for details on the construction of proxies for the rental values of owned homes and
vehicles.
19
(p-value of 18.7 percent).37
The estimates in Table 2 generally have the expected sign and magnitude. The price
elasticity is -0.93 and the budget elasticity is 0.54 where we reject the null hypothesis that
this elasticity has remained constant over the period (p-value less than 0.001 percent). The
estimates show that the budget elasticity decreases in the 1980s (as in Blundell et al., 2008)
and continues to decrease in the years afterwards. The elasticity of food to total consumption
was at the largest in the 1970s.38 We run similar regressions for the three broader measures
of consumption–total consumption, and measures that include services from durables. As
the results are consistent, for exposition purposes we report these results in Appendix A. 5.39
These estimates allow us to invert the demand function and impute nondurable consumption
for all households in the PSID.40
The imputed values of nondurable consumption are provided in appendix A. 3 and further compared with reported nondurable consumption for the years in which nondurable
consumption was collected in the PSID (post-1999). Imputed statistics of nondurable consumption over time are also compared to nondurable personal expenditures per person obtained from NIPA accounts.41
As shown in Figure 1, averages of imputed measures of nondurable consumption (in
logs) are closely related to both the CEX and NIPA averages over time, and lie consistently
between the two series. Variances of imputed consumption and CEX consumption are also
close throughout the period.
37
We also include a test for the power of external instrument, which passes as its p-value is close to 1.
The larger budget elasticity during the 1970s can be recovered by adding the coefficient on the interaction
between ln c and y7273 (the dummy for 1972-73). Using a smaller estimation period, Blundell et al. (2008)
find a larger budget elasticity of 0.85. However, we believe that our estimates are reliable because if we limit
the estimation period to 1980-92, we recover a larger budget elasticity. Moreover, several of our interactions
of total consumption and demographics are also slightly different in magnitude. The price elasticity of food
over the 40 years is very close Blundell et al. (2008)’s estimate over 12 years.
39
Tables A.2, A.3, and A.4 provide the same estimates using three broader measures of consumption.
These specifications produce similar estimates. The budget elasticity and price elasticity for total consumption are 0.68 and -1.44 respectively. The budget elasticity of nondurables and total consumption that include
services from durables is larger (around 0.75).
40
We also impute in the PSID the three broader measures of consumption by inverting the specifications
presented in Appendix A. 5.
41
See Table A.1 of appendix A. 3.
38
20
Table 2: THE DEMAND FOR FOOD IN THE CEX-NONDURABLES
Variable
ln c
Estimate
0.539***
0.103
ln c x HS dropout
0.0803***
0.021
ln c x HS graduate
0.206***
0.043
ln c x one child
-0.0300***
0.008
ln c x two children
-0.0501***
0.009
ln c x three children +
-0.0750***
0.010
ln c x 1980
0.130*
0.071
ln c x 1981
0.106*
0.062
ln c x 1982
0.0915
0.061
ln c x 1983
0.0845
0.058
ln c x 1984
0.0774
0.055
ln c x 1985
0.0703
0.050
ln c x 1986
0.0677
0.050
ln c x 1987
0.0621
0.042
ln c x 1988
0.0592
0.037
ln c x 1989
0.0496
0.030
ln c x 1990
0.0388*
0.023
Number of observations
51,269
Test of overidentifying restrictions
Test time consistency of income elasticity
Variable
ln c x 1991
ln c x 1992
ln c x 1993
ln c x 1994
ln c x 1996
ln c x 1997
ln c x 1998
ln c x 1999
ln c x 2000
ln c x 2001
ln c x 2002
ln c x 2003
ln c x 2004
ln c x 2005
ln c x 2006
ln c x 2007
ln c x 2008
R-squared
Estimate
0.0196
0.016
0.0145
0.015
0.00811
0.012
0.00350
0.007
-0.00998***
0.003
-0.0118*
0.006
-0.0143
0.010
-0.0199
0.012
-0.0276**
0.013
-0.0311*
0.018
-0.0351*
0.021
-0.0392*
0.023
-0.0446*
0.025
-0.0527**
0.026
-0.0567*
0.030
-0.0554*
0.033
-0.0641*
0.036
0.502
Variable
ln c x 2009
Estimate
-0.0617
0.047
ln c x 2010
-0.0706*
0.040
ln c x 2011
-0.0808**
0.039
ln c x y7273
0.267*
0.142
Age
0.0419***
0.005
Age2
-0.000381***
5.56e
pf ood
-0.925***
0.303
palcohol+tobacco
1.505
1.728
pf uel+utils
-0.135
1.409
ptransports
0.836
2.498
HS dropout
-0.725***
0.202
HS graduate
-1.940***
0.417
Northeast
0.00723
0.004
Midwest
-0.0251***
0.008
South
-0.0106
0.010
Born 1975-79
0.107*
0.064
Born 1970-74
0.0854
0.059
Variable
Born 1965-69
Born 1960-64
Born 1955-59
Born 1950-54
Born 1945-49
Born 1940-44
Born 1935-40
Born 1930-34
Born 1925-29
Born 1920-24
One Child
Two children
Three children+
Family Size
White
Constant
Estimate
0.0690
0.053
0.0414
0.048
0.0109
0.042
-0.00158
0.037
-0.00295
0.032
-0.0285
0.029
-0.0224
0.024
-0.0122
0.018
-0.0247
0.015
-0.0309**
(0.0120)
0.326***
(0.0847)
0.545***
(0.0885)
0.775***
(0.108)
0.0513***
(0.00698)
0.101***
(0.0101)
1.016
(0.860)
30.18
(d.f. 27; χ2 p-value 30.6%)
97.83
(d.f. 28; χ2 p-value 0.0001%)
Notes: This table reports IV estimates of the demand equation for (the logarithm of) food spending in the CEX. We use family composition-educationyear specific average of the log of the husband and wife’s hourly wages as instruments for the log of total nondurable expenditure and its interactions
with year, education, and kids dummies. Standard errors are in parentheses. *** Significant at the 1 percent level. ** Significant at the 5 percent
level. * Significant at the 10 percent level.
21
.35
.8
.31
.33
.9
10.2
.27
.23
.6
.25
CEX
.7
PSID
.29
10
9.8
.19
.5
.21
9.6
10
20
08
20
06
20
04
20
02
20
00
20
19
10
20
08
20
06
20
04
20
02
20
20
00
98
9.4
98
19
Variance log(nd)
PSID
CEX
PSID
PSID (imputed)
NIPA
CEX
(b) Variance of ln(c), 2000-2010
CEX
PSID (imputed)
NIPA
CEX
.18
PSID (imputed)
(c) Mean of ln(c), by sample
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
7.5
.2
.14
8
.3
.16
8.5
.4
PSID
9
.5
9.5
.2
.6
10
.7
.22
(a) Mean of ln(c), 2000-2010
PSID (imputed)
CEX
(d) Variance of ln(c), by sample
Figure 1: Mean and Variance of Log Nondurable Expenditures
Notes: See Table A.1 notes for an explanation of the NIPA average and nondurable consumption
imputation (PSID imp.).
B
Federal Income Taxes
Instead of using reported tax liability in the years when it is reported, we directly simulate tax
liability from NBER’s TaxSim software for all years. This choice was made for consistency
purposes because NBER’s TaxSim is able to simulate federal tax liability for all years covered
in our sample, while tax liability is not consistently reported every year in the PSID.42
As described in equation (15), to separate the effects on the insurance parameters due to
42
See Appendix A. 4 for a detailed description of federal income tax calculation and evidence that these
simulations are close to PSID reported taxes.
22
changes in tax policy (“policy effect”) and income distribution (“market effect”), we create
two variables that capture these changes independently of each other (see section D). To
calculate the policy and market effect we follow equations (17) and (18). For the policy
effect, we simulate an income shock of 10 percent every year, holding households’ incomes
constant (using 1980 as the base year), and allowing the tax code to change every year.
For the policy effect we hold the tax code constant using the same base year and allow
households’ incomes to change as observed.43
Figure 2 shows the changes in market and policy stabilization over time and by income
group. These two stabilization parameters describe the percentage of an income shock that
is absorbed by the tax code. The larger the stabilization parameter the larger the percent of
an income shock that the tax schedule absorbs. Both stabilization measures show that the
tax code insures most high income taxpayers.
Although the market stabilization parameter increases for all groups, the gaps between
groups rapidly expands until the early 1980s, with a larger increase for the top quartile.
After 1980, the gap diminishes to become relatively stable after the mid 1990s. The market
stabilization becomes almost constant over time in the years that follow, for all income
groups.44 This implies that changes in income distribution have had a slightly increasing
pressure on the tax code to provide more insurance on average.
The policy stabilization parameter experiences a decreasing trend with the largest decrease in the 1980s, implying that tax policy changes have reduced the average amount of
insurance provided by the tax code. This decrease in the insurance provided by the tax code
affected all income groups similarly until the mid-1990s, and stabilized afterwards except for
the bottom group, for which it continued to decrease. The top two quartiles experienced an
increase in insurance from changes in the tax code after 2003, which incidentally is consistent
with the start of the Bush tax cuts.
This suggests that up to the mid 1990s the total stabilization from market and policy
changes has evolved in opposite directions. However, after that period, both stabilizers
increased for the top income groups, but decreased for the lowest income group. The estimation of equation (15) uses these measures of policy and market stabilization to quantify
their affects on the estimated changes in insurance against income shocks.
43
See appendix C. 1 for a detailed description of the market and policy effects.
The width of the trends in the market insurance parameters across income groups depends on the choice
of the base year, but the same pattern is observed for alternative base years.
44
23
.6
.4
.5
.2
.4
0
.3
-.2
.2
Q2
Q3
top
bottom
(a) Market Stabilization: Holding Policy Fixed
Q2
Q3
top
(b) Policy Stabilization: Holding Income Fixed
Figure 2: Percent Change in Tax Liability, by Quartile of Income
IV
Empirical Evidence
This section reports the estimates of the autocovariance of income and consumption growth
in section A, the variance of permanent and transitory income in section B, and the partial
insurance parameters in section C. The estimates of the autocovariance of income and consumption comprise the moment conditions derived in section II B. These moment conditions
are then used to separate the variance of income into its permanent and transitory components, reported in section B, and estimate the transmission of income shocks to consumption
shocks summarized by the partial insurance parameters reported in section C. Finally, the
estimates of insurance are decomposed to quantify the effects of changes in policy stabilization, market stabilization, and behavioral responses on the changes in insurance from 1968
to 2010.
A
The Autocovariance of Income and Consumption Growth
Through a series of figures this section reports the autocovariance of income and consumption
growth used in the moment conditions. All estimates and their standard errors are reported
in Tables D.1, D.2, and D.3 in the appendix. Trends in the autocovariance of income and
consumption growth are linear combinations of the permanent and transitory components of
the variance of income and the partial insurance loading factors. For example, the covariance
between current consumption growth and income growth one period ahead, cov(∆ct , ∆yt+1 ),
24
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
-.4
.1
1967
bottom
combines the variance of transitory income shocks and the partial insurance of transitory
income shocks, described in equation (12). In the extreme case of full insurance against
transitory income shocks the covariance between current consumption growth and future
income growth would be zero.
The variance of consumption and income growth are depicted in Figure 3, which shows
the variance of the standard one-year difference and the two-year difference we use to extend
our analysis to the years in which the PSID is reported biannually. The trends of the oneand two-year differences are very similar for the years when both series are available. The
variance of consumption growth increases in the mid 1970s, early 1980s and 1990s, and experiences a much faster increase in the 2000s. Changes in the variance of consumption growth
are associated with changes in the variance of income shocks and changes in households’
insurance from income shocks.45
The variance of consumption increases more in the 1980s than the variance of income,
which suggests that the increase in the dispersion of consumption is due to decreases in the
insurance from income shocks. The variance of income growth increases in the 1990s and
remains high through the 2000s at about 165 percent its level in the 1980s. This suggests the
variance of permanent or transitory income shocks increased, the insurance to these income
shocks decreased, or some combination.
Figure 4 reports the covariance of consumption and income growth, using either current
or lagged consumption. The covariances constructed with one- and two-year differences have
similar trends. The contemporary covariance increases in the 1980s and then decreases in the
1990s but remained higher in the 2000s than it had been in the 1970s. This suggests insurance
against combined permanent and transitory income shocks decreased in the 1980s and slightly
increased in the 1990s but remained lower than the amount of insurance households had in
the 1970s.
45
The variance of consumption also captures the heterogeneity in household’s responses to income shocks
and the measurement error from the imputation.
25
.2
.15
.6
.1
.4
2003
2007
2011
2003
2007
2011
1999
1995
1991
1987
1983
1979
1975
1971
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
.05
.2
0
1967
Consumption
Standard
Income
Two-yr
Standard
Consumption
Two-yr
Income
Figure 3: Variance of Consumption and Income Growth—1967 to 2010
Standard
Two-yr
Standard
Current Income and Consumption
1999
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
0
-.03
-.02
.02
-.01
0
.04
.01
.06
.02
Notes: Estimates, with standard errors, are reported in Tables D.2 and D.1.
Two-yr
Current Income, Lagged Consumption
Figure 4: Covariances Between Income and Consumption Growth, 1967-2010
Notes: Estimates, with standard errors, are reported in Table D.3.
The autocovariances graphed in Figures 3 and 4 are graphed separately by income quartiles in Figures 5, 6, and 7.46 The variance of income growth for the lowest income quartile
is consistently larger than the other quartiles throughout the period and about 50 percent
larger than the upper quartiles until the early 1990s, depicted in Figure 5. In the 1990s
the variance of income growth for the top income quartile rapidly increases to reach levels
similar to the bottom quartile’s, while the two middle quartiles experience slightly smaller
46
A household’s income quartile is assigned using their 1980 income in order to hold the composition of
individuals within a quartile constant throughout the period.
26
increases in their variance of income growth.
Figure 7 graphs the contemporary covariance of consumption and income growth into
quartiles of income. The increase in the contemporary covariance in the 1980s observed in
the whole sample is least pronounced for the third income quartile. In the 2000s the top
three income quartiles remain constant or slightly decrease while the bottom income quartile
increases. This graphical evidence suggests that households’ insurance from income shocks
decreased in the 1980s for all income quartiles and decreased again in the late 1990s and
.3
.25
.2
.15
.1
.05
1999
2003
2007
2011
2003
2007
2011
Two-yr
.25
.2
.15
.1
.05
Two-yr
Standard
Q3
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
0
Standard
1991
1987
1983
1979
1975
1971
1967
0
.05
.1
.15
.2
.25
.3
Q2
.3
Q1 (Bottom)
1995
1991
Standard
1999
Two-yr
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
0
Standard
1995
1991
1987
1983
1979
1975
1971
1967
0
.05
.1
.15
.2
.25
.3
2000s for the bottom income quartile.
Two-yr
Q4 (Top)
Figure 5: Variance of Income Growth, by Quartile of Income
Notes: Estimates, with standard errors, are reported in Table D.2.
27
Standard
Two-yr
Q3
28
Standard
Notes: Estimates, with standard errors, are reported in Table D.1.
2003
2007
2011
2007
2011
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
2003
.8
.8
Q2
1999
.6
.6
Two-yr
1999
.4
.4
Standard
1995
.2
.2
Q1 (Bottom)
1991
0
0
Two-yr
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
Standard
Two-yr
Q4 (Top)
Figure 6: Variance of Consumption Growth, by Quartile of Income
0
0
.2
.2
.4
.4
.6
.6
.8
.8
.09
.07
.09
.05
.07
.03
.05
.01
.03
-.01
.01
-.03
-.01
1999
2003
2007
2011
2003
2007
2011
Two-yr
Q2
Two-yr
Standard
Q3
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
-.05
Standard
1991
1987
1983
1979
1975
1971
1967
-.05
-.03
-.03
-.01
-.01
.01
.01
.03
.03
.05
.05
.07
.07
.09
.09
Q1 (Bottom)
1995
1991
Standard
1999
Two-yr
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
-.05
-.03
-.05
1967
Standard
Two-yr
Q4 (Top)
Figure 7: Contemporary Covariances of Consumption and Income Growth, by Quartiles of
Income
Notes: Estimates, with standard errors, are reported in Table D.3.
The evidence in Figures 3 and 4 suggest income shocks increased and households’ insurance against income shocks changed during this period. The next subsections separate
the permanent and transitory components of income shocks, estimates households’ insurance
from these shocks, and decomposes changes in insurance into those due to changes in tax
policy, the income distribution, and household behavior.
29
B
The Variance of Permanent and Transitory Income Shocks
This section investigates how the variance of permanent and transitory income shocks have
changed over time. Our panel data allows us to estimate the permanent and transitory
variances of income shocks for the years 1968 through 2010, a time span of 43 years, extending
the analysis of many similar studies.47 Figure 8 graphs the five-year moving average of the
diagonally weighted minimum distance (DWMD) estimates of the variance of the permanent
and transitory income shocks, estimated separately by year.48 All estimates, with standard
errors, are reported in Tables D.4 and D.5 in the appendix.
The permanent component of the variance of income shocks experiences two periods of
growth, one in the early 1980s and one in the late 1990s, as depicted in Figure 8. The
variance of permanent income shocks more than doubles in the early 1980s and more than
triples in the late 1990s. After these both periods of growth the variance of permanent
income shocks decreases and levels out.
Figure 8 reveals three general trends for the variance of transitory income shocks. First,
the variance of transitory income shocks decreases from around 0.03 in the 1970s to 0.01 in the
late 1990s. Second, the variance of transitory income has a strong cyclical pattern roughly
following the business cycle, corroborating the evidence found by Moffitt and Gottschalk
(2011) and Blundell et al. (2008). Third, in the 2000s the variance of transitory income
shocks increases sharply due to spikes in 2001 (0.052), 2007 (0.138), and 2009 (0.721).49
The diagonally weighted minimum distance estimates decompose the variance of income,
depicted in Figure 3, into its permanent and transitory components, reported in Figure 8.
Figure 8 demonstrates the initial increase in the cross-sectional variance of income is due
to an increase in permanent income shocks while the high levels in the 2000s are due to an
increase in the variance of transitory income shocks. Previous studies have highlighted the
increase in the variance of permanent income shocks in the early 1980s, noting a stabilization
47
Blundell et al. (2008) use consumption and income data to separate income into its permanent and
transitory components from 1979 to 1993. Debacker et al. (2013) use confidential data on tax returns from
1987 to 2009 to study whether the rise in inequality in male labor and total household earnings are due
to persistent or transitory income shocks. They find that most of the increase in earnings’ inequality over
the period was due to permanent income shocks, while transitory shocks also played a role to increase total
household income inequality. Moffitt and Gottschalk (2011) use the PSID from 1970 to 2004 to estimate the
trends in the transitory variance of male earnings in the U.S.
48
Figure 8 uses five-year moving averages to focus on observed general trends. The trends are robust to
smoothing with three-year or nine-year moving averages, as depicted in the appendix. Extreme outliers are
scaled for expositional ease. All estimates are reported in Table D.5 in the appendix.
49
Figure 8 scales the spike in 2009 for expositional reasons. All estimates are reported in Table D.5 in
the appendix.
30
or decrease thereafter (Blundell et al., 2008). We find a similar pattern for the 1980s and
Variance Smoothed 5 Year Moving Average
0
.02
.04
.08
.06
provide a larger context that includes large changes in the 1990s and 2000s.
1970
1980
1990
year
2000
2010
Variance Permanent Income Shock
Variance Transitory Income Shock
Figure 8: Variance Permanent and Transitory Income Shocks
Notes: Estimates, with standard errors, are reported in Tables D.4 and D.5.
Figure 9 depicts the changes in the five-year moving average of the variance of permanent
and transitory income shocks by income quartiles. The full estimates by income quartiles
are given in Table D.4 in the appendix.50 The trends in the variance of permanent income
shocks are largely shared by all income groups. In the 1980s the bottom income quartile has
a larger variance of permanent income shocks than the other income quartiles but all income
groups experience an increase in the 1990s. After the increase in the variance of permanent
income shocks the top two income quartiles experience larger decreases than the bottom two
income quartiles which remain elevated through the 2000s.
The general trends in the variance of transitory income shocks are also shared by all four
income quartiles. However, the cyclical trend in the whole sample is more pronounced for
the bottom income quartile. The sharp increase in the variance of transitory income shocks
in the late 2000s occurs for all income groups but at slightly different times and much more
pronounced for the bottom three income quartiles, especially the second income quartile.
50
The appendix also reports estimates of the permanent and transitory variance of income by education
and age groups.
31
Variance Permanent Income Shock
0
.02
.04
.06
Variance Permanent Income Shock
0
.02
.06
.08
.04
1970
1980
1990
year
2000
2010
Bottom Income Quartile (Smoothed)
Q2 Income Quartile (Smoothed)
Q3 Income Quartile (Smoothed)
Top Income Quartile (Smoothed)
1970
1980
1990
year
2000
2010
Bottom Income Quartile (Smoothed)
Q2 Income Quartile (Smoothed)
Q3 Income Quartile (Smoothed)
Top Income Quartile (Smoothed)
Permanent Income
Transitory Income
Figure 9: Variance Income Shocks By Income Quartile
Notes: Estimates, with standard errors, are reported in Tables D.4 and D.5.
C
Partial Insurance: the Transmission of Income Shocks to Consumption
The previous section separates the variance of income into its transitory and permanent
components. This section investigates changes in households’ ability to insure against these
income shocks by allowing the partial insurance parameters to vary across time periods. We
further investigate differences in partial insurance parameters across income quartiles and
the appendix discusses the differences across education and age groups.
Table 3 reports the partial insurance parameters that determine the transmission of income shocks to consumption, described by equation (9). A large partial insurance parameter
implies a large fraction of a household’s income shocks transfer to their consumption. Panel
A reports the partial insurance parameters for permanent income shocks across five time periods, roughly corresponding to different federal income tax regimes; 1968-1980, 1981-1986,
1987-1992, 1993-2002, and 2003-2010. Column 1 shows that the partial insurance parameter
for the permanent income shock increased from 1968 to 2010, meaning that insurance from
permanent income shocks decreased over this time period. Consumption insurance experienced a large decrease in the 1980s and subsequent increases in 1993-2002 and 2003-2010.
Insurance against transitory income shocks also experienced a decrease until the middle of
the period but increased over the full time period due to a large increase since the late 1980s,
as reported in the Panel B of Table 3. Focusing on the permanent income shock, we find
32
Table 3: ESTIMATES PARTIAL INSURANCE
Income Quartiles
Years
Whole Sample Bottom
Q2
Q3
Panel A: Partial Insurance Permanent Shock φ
1968 - 1980
0.008
0.061
0.038
0.106
(0.023)
(0.054) (0.031) (0.143)
1981 - 1986
0.043
1.061
0.08
0.464
(0.058)
(0.108) (0.048) (0.186)
1987 - 1992
0.882
0.766
0.648
0.446
(0.096)
(0.089) (0.056) (0.182)
1993 - 2002
0.055
0.164
0.181
0.011
(0.012)
(0.046) (0.025) (0.024)
2003 - 2010
0.129
0.487
0.010
-0.073
(0.023)
(0.021) (0.026) (0.183)
Panel B: Partial Insurance Transitory Shock ψ
1968 - 1980
0.141
0.151
0.810
0.153
(0.021)
(0.113) (0.038) (0.040)
1981 - 1986
0.581
-0.252
1.351
0.799
(0.086)
(0.134) (0.030) (0.109)
1987 - 1992
1.111
0.036
0.614
1.065
(0.089)
(0.032) (0.091) (0.211)
1993 - 2002
0.437
0.351
0.538
-0.008
(0.059)
(0.117) (0.086) (0.053)
2003 - 2010
7.4E-05
0.041
-0.109 -0.020
(0.148)
(0.078) (0.025) (0.067)
Top
0.037
(0.018)
0.129
(0.057)
1.731
(0.310)
0.044
(0.020)
0.583
(0.010)
0.656
(0.030)
1.079
(0.053)
-0.211
(0.485)
0.343
(0.170)
0.005
(0.254)
Notes: This table reports diagonally weighted minimum distance (DWMD)
estimates of the partial insurance parameters. Panel A reports the partial
insurance parameters for permanent income shocks and Panel B reports the
partial insurance parameters for the transitory income shocks. The partial
insurance parameters for the whole sample are reported in column 1 and
columns 2-5 report the estimates for each income quartile. Standard errors
are calculated using the method proposed by Gary Chamberlain (1984) and
are reported in parentheses.
that in the most recent period (2003-2010), a ten percent change in income translates into a
1.29 percent change in consumption.
Columns 2-5 of Table 3 report the partial insurance parameters separately for each income
quartile. Each quartile roughly follows the same pattern as the whole sample, with a decrease
in insurance in the first half of the sample and a subsequent increase. Over the full time
period the bottom and top quartiles experienced a substantial decrease in insurance. This
implies that part of the increase in the variance of consumption growth, particularly for the
bottom and top income quartiles, is due to a decrease in insurance.
To investigate the decrease in insurance to permanent income shocks over this time period
we quantify the effects of changes in tax policy, the income distribution, and households’
behavioral responses by decomposing the decrease in insurance according to equation (15).
The results of this decomposition are reported in Table 4 with further details described in
33
appendix D. 4. For convenience Table 4 reports changes in insurance (rather than loading
parameters) between tax regimes. The decomposition controls for the variance of permanent
and transitory income shocks, which accounts for the differences between Table 3 and 4.
Panel A decomposes the 0.183 decrease in insurance between tax regimes 1968-1980 and
2003-2010. Insurance against permanent income shocks would have decreased by 0.888 if
influenced solely by changes in tax regimes quantified by the policy effect. Insurance did not
decrease to this extent because changes in the income distribution, quantified by the market
effect, and changes in behavioral responses mitigated some of this effect. Specifically, Table
4 reports that changes in the income distribution led the tax code on average to increase
insurance by 0.273 and that households’ responses to the tax code also dampened the variance
of consumption, increasing insurance by 0.432. These results suggest over the past forty years
changes in tax regimes had a large negative impact on the level of households’ insurance
to permanent income shocks but that changes in the income distribution and households’
behavioral responses mitigated some of the effect.
Panels B and C separately decompose changes in consumption insurance from permanent
income shocks for the first and second halves of the period. During the first half of the period,
insurance decreased by 0.790. The decomposition demonstrates that this decrease is due to
both tax policy changes and changes in behavioral responses, while changes in the income
distribution had a mitigating effect, although only enough to offset about one fifth of the
overall decrease in insurance. In contrast, insurance increased by 0.664 in the second half of
the period. This increase is due to changes in behavioral responses and to a continued effect
from changes in the income distribution, while changes in tax policy still had a negative,
but smaller effect. The estimates in Panels B and C suggest that the effect from tax policy
changes on insurance is concentrated in the first half of the sample (1968-1992), changes
in the income distribution increased insurance throughout the period, and changes in how
households interacted with the tax code decreased insurance in the first half of the period,
but increased it afterwards.
The general trends of insurance mechanisms described so far for the whole sample are
decomposed by income quartiles in columns 2-5 of Table 4. Over the whole period, the
lowest income quartile experienced the largest decrease in insurance. The top quartile also
experienced a larger than average decrease in insurance, while insurance for the middle two
quartiles did not significantly change. The mechanisms that explain this overall decrease in
insurance differed for the top and bottom quartiles. For both quartiles changes in tax policy
34
Table 4: DECOMPOSITION PARTIAL INSURANCE OF PERMANENT INCOME SHOCKS
Whole Sample
Panel A: Difference 1968-1980 and 2003-2010
-0.183
(0.0004)
P
Policy Effect βt Γ0P dSi,t
-0.888
(0.0006)
M
0.273
Market Effect βt Γ0M dSi,t
(0.0007)
P
M
)dβt
0.432
, Si,t
Behavioral Effect Γ(Si,t
(0.0012)
Panel B: Difference 1968-1980 and 1986-1992
-0.790
(0.0006)
P
Policy Effect βt Γ0P dSi,t
-0.411
(0.0003)
M
0.206
Market Effect βt Γ0M dSi,t
(0.0005)
M
P
)dβt
-0.585
Behavioral Effect Γ(Si,t
, Si,t
(0.0009)
Panel C: Difference 1986-1992 and 2003-2010
0.664
(0.0015)
P
0
-0.084
Policy Effect βt ΓP dSi,t
(0.009)
M
Market Effect βt Γ0M dSi,t
0.133
(0.0002)
M
P
Behavioral Effect Γ(Si,t
, Si,t
)dβt
0.615
(0.0077)
Bottom
-1.207
(0.0064)
-1.312
(0.0035)
0.985
(0.0035)
-0.88
(0.0078)
-0.754
(0.0009)
-0.309
(0.0009)
0.567
(0.0021)
-1.012
(0.0029)
0.306
(0.0021)
0.017
(0.0055)
0.147
(0.0018)
0.142
(0.0056)
Income Quartiles
Q2
Q3
-0.039
0.408
(0.0908) (1.0163)
-0.586
-0.545
(0.0005) (0.0004)
0.438
0.256
(0.0009) (0.0004)
0.109
0.697
(0.0909) (1.0163)
-0.487
0.523
(0.0014) (0.0013)
-0.320
-0.392
(0.0002) (0.0002)
0.31
0.221
(0.0007) (0.0004)
-0.477
0.694
(0.0017) (0.0014)
0.451
-0.326
(0.0226) (0.2096)
-0.270
0.040
(0.1143) (0.7296)
0.149
0.089
(0.0176) (0.0729)
0.572
-0.455
(0.1111) (0.5956)
Top
-0.329
(0.1215)
-0.51
(0.0003)
0.129
(0.0003)
0.052
(0.1215)
-1.188
(0.0017)
-0.380
(0.0002)
0.122
(0.0002)
-0.930
(0.0018)
0.669
(0.0599)
-0.025
(0.1068)
0.008
(0.0021)
0.686
(0.1673)
Notes: This table reports the decomposition of the change in partial insurance (equal to 1 minus the partial insurance
parameter for permanent income shocks. Panel A decomposes the change in partial insurance from period 19681980 to 2002-2010. Panels B and C decompose this change into two smaller time periods to take into account the
numerous tax reforms in this time period, notably the tax reform act of 1986. The decomposition is performed on
the whole sample (column 1) and each income quartile (column 2 - column 5). Bootstrapped standard errors are
reported in parenthesis. The decomposition includes a control for the variance of permanent income shocks. For
more details and alternative methods of estimating the decomposition see appendix D. 4. The decomposition for
the partial insurance parameter for transitory income shocks is reported in Table D.12 in the appendix.
had a negative effect on their level of insurance. This effect is mitigated to some extent by
changes in the income distribution for the bottom income quartile and changes in behavioral
responses for the top income quartile.
V
Conclusion
The dispersion of income is only one piece to understanding the growing income inequality.
We use current income in conjunction with current expenditures as complementary indicators
of the dispersion of lifetime welfare or inequality-the phenomenon of interest. The dispersion
of income increased in the 1980s and again in the 1990s however, this need not lead to an
increase in the dispersion of consumption or lifetime welfare. For example, when transitory
income shocks explain most of the increase in the dispersion of income and individuals are
able to smooth consumption from these shocks, the effect on consumption dispersion may be
negligible. Likewise, when permanent income shocks contribute more to the increase in the
35
dispersion of income, then public policy towards, for example, more progressive taxation may
substantially dampen the impact on the dispersion of consumption. Therefore, changes in
the dispersion of lifetime welfare depends on the causes of the increase in income dispersion,
whether due to permanent or transitory income shocks, and the degree to which income
dispersion translates into consumption dispersion.
The evidence presented in this paper suggests that inequality increased in the 1980s and
again in the 1990s due to increases in both permanent and transitory income shocks as well
as an increase in the degree to which income shocks translate into shocks in consumption.
The mechanisms underlying the transmission of income shocks to consumption inequality
changed along several dimensions including tax policy, market conditions, and household
responses to market and policy changes. This paper presents a model of insurance that
decomposes the transmission of income shocks to consumption inequality into these three
mechanisms. With a focus on the role of the U.S. federal income tax, this paper empirically
evaluates how changes in tax policy, the income distribution, and behavioral responses of
housheholds have affected the role of teh federal income tax system to dampen the dispersion
of consumption relative to income.
Changes in tax policy that occurred in the 1980s decreased the ability of the federal
income tax to insure consumers from income shocks, although changes in the income distribution and households’ behavioral responses mitigated some of this effect. Changes in tax
policy since the 1990s played no significant role in changing the ability of the tax code to
smooth consumption from income shocks, but households responded to policy changes and
increasing income inequality by finding other insurance mechanisms. The overall evidence
suggests that changes in tax policy contributed to the increase in inequality in the last four
decades. Further research is needed to investigate the effects of other public policies on consumption inequality, specifically changes occurring at the state level. This paper suggests
that the mechanisms by which different policies affect inequality and the magnitudes of their
associated impacts are heterogenous. To effectively design and efficiently manage the level
of inequality, pubic policy needs a detailed understanding of how these market and policy
mechanisms operate.
36
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41
APPENDIX FOR ONLINE PUBLICATION
Appendix A:
A. 1
Data
Consumer Expenditure Survey
Consumption data are obtained from the Consumer Expenditure Survey (CEX) for all available years including 1972, 1973, and from 1980 to 2010. To collect information on nondurable consumption, semi-durables (including education and health services), and durables
(e.g., jewelry, vehicles), we use monthly expenditure files (MTAB) for each quarter. To obtain
socio-economic and income information, we use member files and family files (MEMB and
FMLY). We also calculate the value of service flows from two important consumer durables:
own-occupied housing and owned vehicles. For the value of the service flow from vehicles, we
use two additional CEX surveys: “inventory and purchases of owned vehicles” and “vehicle
make/model code titles” (the detailed calculation of the service flow from vehicles is provided
below). CEX surveys from 1980 onwards have a consistent format. However in the 1972-73
surveys, Universal Classification Codes (UCC) are different from those in 1980 and after.
We carefully match our definition of consumption variables between these two formats. To
construct non-durable and durable consumption, we use Blundell et al. (2008)’s definition.51
All stata programs to construct CEX consumption variables are provided in the attached
folder called “CEX programs”, which includes: readmemb.do, readfmly.do, readmtab.do, cexall.do, and cexall plus.do.
Python programs are used to obtain consumption data in 1972 and 1973, and to calculate vehicle data for all available years are named: Script1972.py, Script1973.py, and
vehicles [year].py.
A. 1.1
Service Flow of Owner-Occupied Housing
To calculate the value of the service flow from owner-occupied housing, we use the definition provided by the Bureau of Labor Statistics.52 Housing includes expenses associated
with owning or renting a home or apartment, including rental payments, mortgage interest
and charges, property taxes, contracted repairs and maintenance, insurance, and utilities,
both for owner-occupied housing and for vacation homes (rental payments are not provided
in years 1972 and 1973). Certain expenditures for other lodging and household operations
are not included because they already appear in the definition of non-durable consumption.
These include owner occupied housing and vacation home insurances, parking owned, property management costs, and own repair equipment. Expenditures for principal payments on
existing mortgages are excluded. The data are directly obtained from CEX expenditures files.
51
52
Our programs to construct variables are available on demand.
See Johnson et al. (2005).
42
A. 1.2
Service Flow of Owned Vehicles
To calculate the value of the service flow from cars and trucks, we follow the methodology
used by Danziger et al. (1984), Slesnick (1994), and Johnson et al. (2005). We define the
service flow of cars and trucks as the annual change in the value of vehicles. For this, we
need the purchase price of a vehicle (P0 ) and its age (a). The service flow of vehicles in year
t is given by:
St = (r + d).(1 − d)a .P0 ,
(A.1)
where r is the interest rate and d is the depreciation rate (we assume that r = .05 and
d = .1).
We collect data on vehicles for all households surveyed in the CEX. The CEX does not
collect vehicles information in 5 survey years: 1980-1983, and 1992. The survey provides
information on the age, the model type, the brand, the year acquired, the status of the car
(“old” or “new”), the trade-in allowance, and the amount paid for the vehicle after trade-in
and transmission. However, the purchase price is only provided for vehicles purchased at
most 12 months before the interview year (i.e., years t and t − 1 of a given survey year). We
impute the value of vehicles purchased before t − 1 as the average price of comparable cars,
after inflation and depreciation. For this we group cars in each year of the CEX survey into
bins that depend on detailed car characteristic and calculate their average price based on
the price of recently purchased cars, adjusting for inflation.53
Vehicles are grouped into bins for each year, by type, brand, old-new status, and year
acquired to construct an average purchase price, for recently purchased cars, by group and
year as the sum of the trade-in amount and the amount paid after the trade-in. The service
flow value for vehicles purchased in earlier years is obtained from equation (A.1).
A. 2
Panel Survey of Income Dynamics
The Panel Study of Income Dynamics started collecting information on roughly 3,000 households representing the US population as a whole starting in 1968. Families and their children
as they move out of the house have been followed since that time. There was a large recontact effort initiated in 1992 for households that had previously attrited. Starting with the
1999 wave the PSID switched to a biennial interview, rather than annual. For robustness,
and to investigate possible heterogeneity in results by income we also use the the Census
Bureau’s Survey of Economic Opportunities, or SEO sample which is a sample of roughly
2,000 low-income families.
The questions the PSID ask vary from year to year but a core group of socioeconomic
characteristics of households are almost always asked, including questions about income and
food spending. Questions about income are retrospective in nature, thus answers in 1985
refer to income in 1984. The timing of other variables is not always as clear. For instance
survey questions on food have been interpreted both as retrospective and contemporaneous
(Hall and Mishkin (1982) and Altonji and Siow (1987)). Interviews are typically conducted
53
We use a $3 average inflation per year, based on the Consumer Price Index for All Urban Consumers:
New vehicles (CUUR0000SETA01) provided by The Federal Reserve Bank of St. Louis.
43
in March and participants are asked how much is spent on food in an average week, thus
the confusion of whether participants’ answers best represents the amount spent in calendar
year t or t-1. We assume the answers are retrospective.
Household data are obtained from the Panel Study of Income Dynamics for the years
1967 to 2010. To collect information on household demographics (e.g. age, sex, race), income
(including wages of husband and wife and hours worked), family composition (including
number of kids and marital status), and consumption expenditures (e.g. food at home and
out and insurance and vehicle payments) we use the PSID family files.54 To construct a
panel from the individual year family files we use the individual files from the PSID. We
restrict attention to head of households. Together the unbalanced panel consists of 37 years,
24,960 different households, and 252,467 observations.
To focus on income risk rather than variation in consumption due to changes in family
composition the focus is restricted in several ways. First, households with breaks in years
or that only appear once are dropped (44,394 and 3,776 observations respectively). Second, households are dropped if they experience a family composition change (e.g. head of
household changes or wife left) or where females are household heads (53,454 and 50,864
observations respectively). Third, households are dropped if they are missing demographic
information on race, education, or state of residence (639, 1,419, and 9,457 observations
respectively). The sample is also restricted to households with heads aged between thirty
and sixty-five without changes in marital status (30,004 and 4,342 observations respectively).
Finally, households with extreme income growth (more than 500 percent or loss of more than
80 percent) are dropped (5,280 observations). The final panel consists of 48,847 observations
with 4,670 different households across 37 years around 20 percent of the full data sample.
All stata programs to construct PSID household variables are provided in the attached
folder called “PSID do files”, which includes: PSIDFamilyFiles.do, PSIDIndividualFile.do,
and SampleSelection.do.
A. 3
Comparison of CEX and PSID Data and Imputations
Table A.1 compares the imputed values of nondurable consumption with reported nondurable
consumption in the PSID for the years in which nondurable consumption was collected
in the PSID (post-1999). The first three rows demonstrate the closeness in fit between
food expenditures reported in the PSID and the CEX. The measures of average nondurable
consumption are also compared to a nondurable personal expenditures per person obtained
from NIPA accounts. The imputed value is around 1 percent or less different than both
the PSID and the CEX values, as shown in Table A.1. In addition, imputed and PSID
reported nondurable expenditures exhibit similar trends and variation, as shown in Figure
1.55 Finally, the imputed PSID values of consumption lie between the PSID and the NIPA
values (where, as was the case for food expenses, the NIPA trend lies consistently below
54
The full list and exact variable identification in the PSID are given in the do file, PSIDFamilyFiles.do.
The large changes in the variance of total spending in the PSID from 1998 to 2002 is not surprising,
as the 1999 and 2001 questionnaires were slightly different from those used in later years. Moreover several
expenditure items were added to PSID waves in 2004 and after (Li et al., 2010).
55
44
the PSID and CEX trends). These descriptive statistics are supportive of the ability of
the imputation method to capture nondurable expenditures, although this evidence includes
only the last decade of the four-decade period covered in this paper.56
56
Li et al. (2010) also compare the sum of all expenditures reported in the PSID (as opposed to nondurable
consumption, which includes durable goods such as imputed housing and vehicles) with the CEX from 1999 to
2003. Combining all PSID categories, annual spending totals $25,961, 2 percent greater than CEX spending.
Estimates for 1999 and 2003 are similar, with PSID total spending 4 percent smaller than CEX spending
in 1999 and 1 percent larger in 2003. As reported by the CEX in 2001, spending on categories included in
the PSID totals $25,340, which accounts for 72 percent of total spending across all CEX categories. This
spending gap falls largely into five categories not measured in the 1999, 2001 or 2003 PSID waves: home
repairs and maintenance, household furnishing and equipment, clothing and apparel, trips and vacations,
and recreation and entertainment. PSID added questions covering these spending items in the 2005 and
subsequent waves.
45
46
PSID
10.17
(0.811)
8.35
10.24
NIPA
9.84
8.12
9.98
NIPA
9.59
CEX PSID (imp.)
10.22
10.11
(0.193)
(0.654)
10.32
10.22
(0.171)
(0.495)
9.9
10.54
10.45
(0.633) (0.266)
(0.576)
10.62
10.52
(0.239)
(0.52)
8.98
9.07
8.97
(8.977) (0.193)
(0.245)
1097
1781
1006
PSID
10.13
(0.79)
2008
CEX PSID (imp.)
9.98
9.96
(0.192)
(0.503)
10.09
10.06
(0.175)
(0.406)
9.87
10.37
10.35
(0.768) (0.283)
(0.457)
10.45
10.43
(0.262)
(0.421)
8.87
8.8
8.76
(8.868) (0.19)
(0.212)
831
1939
782
PSID
10.07
(0.91)
2002
8.42
10.29
NIPA
9.9
8.16
10.04
NIPA
9.64
CEX PSID (imp.)
10.17
10.11
(0.202)
(0.618)
10.26
10.2
(0.179)
(0.463)
9.99
10.46
10.42
(0.546) (0.279)
(0.562)
10.55
10.49
(0.251)
(0.498)
9.04
9.03
8.98
(9.045) (0.219)
(0.225)
(981
1767
922
PSID
10.15
(0.619)
2010
CEX PSID (imp.)
10.02
10.05
(0.217)
(0.66)
10.12
10.14
(0.179)
(0.52)
9.92
10.38
10.42
(0.696) (0.332)
(0.593)
10.47
10.49
(0.287)
(0.544)
8.94
8.85
8.84
(8.943) (0.194)
(0.265)
918
1241
865
PSID
10.13
(0.841)
2004
8.42
10.29
NIPA
9.9
8.26
10.14
NIPA
9.73
Notes: Average nondurable consumption in NIPA is the difference of the logs of nondurable personal expenditures and mid period population. Nondurable personal
expenditures include nondurables, housing goods, utilities, transportation and communication services, personal services (food & accommodation, household care, etc.)
and professional services (Table 2.4.5—Personal Consumption Expenditures by Type of Product). P SID and CEX are the observed PSID and CEX averages, respectively.
PSID (imp.) represents the measures of consumption imputed in the PSID using the CEX-based demand equation, and NIPA weights (as described in table ??’s footnote).
Four measures of consumption are imputed, as described in the text and in appendix A. 5.
CEX PSID (imp)
10.12
10.16
(0.2)
(0.687)
Non-&semi-durable expenses
10.23
10.25
(0.176)
(0.529)
Nondurable & durable expenses
9.96
10.46
10.51
(0.676) (0.283)
(0.598)
Total expenses
10.55
10.58
(0.253)
(0.548)
Food expenses
8.96
8.92
8.91
(8.963) (0.208)
(0.255)
Observations
1002
1948
942
Nondurable expenses
2006
CEX PSID (imp)
9.94
9.89
(0.2)
(0.519)
Non-&semi-durable expenses
10.04
9.99
(0.18)
(0.419)
Nondurable & durable expenses
9.76
10.31
10.27
(0.536) (0.283)
(0.444)
Total expenses
10.4
10.34
(0.254)
(0.411)
Food expenses
8.84
8.76
8.73
(8.843) (0.187)
(0.22)
Observations
775
1873
735
Nondurable expenses
PSID
9.93
(0.64)
2000
Table A.1: Consumption Comparison PSID-CEX-Imputation
A. 4
Federal Income Tax
From 1970 to 1991 the PSID asked respondents their total household federal income tax.
Other studies, notably Blundell, Pistaferri, and Preston (2008), supplement this data by
simulating federal tax liability using the National Bureau of Economic Research’s TaxSim
software with information obtained from the PSID such as wages, other income, marital
status, and number of children.
For consistency purposes, we directly simulate tax liability from NBER’s TaxSim software
for all years. NBER’s TaxSim is able to simulate federal tax liability after tax credits and
refunds, for all years covered in our sample.57 Figure A.1 graphs the average federal tax
liability from the PSID and NBER’s TaxSim program. Some of the difference is a result
of deductions. On the one hand TaxSim assumes that individuals take all deductions for
which they are eligible, regardless of what the household actually takes. On the other
hand, data covered by the PSID may not include enough information, in which case TaxSim
would not account for all possible deductions that a household could take. To test whether
TaxSim systematically under or over simulates federal tax liability for a given characteristic,
relative to the PSID, we regress the difference between the PSID and TaxSim on year and
state dummies, marital status, number of children, age of husband and wife, labor income of
husband and wife, other income, and rent. We find that only husband’s labor income (p-value
4 percent), other income (p-value < 0.01 percent), husband’s age (p-value 4 percent), and
years 1990, 1991, 1992 were statistically significant. The coefficients suggest that, relative
to the PSID, for an additional $100 of husband’s labor income TaxSim under reports federal
tax liability by $5, for an additional $100 of other income TaxSim under reports $14 of
tax liability, and for an additional year of husband’s age TaxSim under reports $113 of tax
liability. Despite these limitations we feel that TaxSim estimates are sufficient to capture
the insurance imbedded in the tax system, which is the main focus of this paper.
57
NBER’s Taxsim program is able to estimate federal tax liability from 1960 to 2013 and state tax
liability from 1977 to 2011. Blundell et al. (2008) use the PSID reported federal tax liability from 1980
to 1991 and use NBER’s TaxSim program to simulate federal tax liability in 1992 and 1993, the last year
covered in their study. Because we extend the data from 1993 to 2010 simply replicating their strategy to
measure taxation would imply the use of NBER’s TaxSim program for half of the years covered by our data
(1992-2010).
47
PSID
A. 5
1989
1988
1987
1986
1985
1984
1983
1982
1981
1980
1979
1978
3000
4000
5000
6000
7000
Figure A.1: Mean Federal Tax Liability—Taxsim-PSID
Taxsim
Demand for Food in CEX—Alternative Measures of Total
Consumption
As explained in section III this paper evaluates the ability of the tax system to insure
consumption against permanent and transitory shocks and how this relationship changed
over time. To do this we investigate four measures of consumption, following Blundell et
al. (2008). The first includes nondurable goods and services (G&S). The second adds semidurables G&S to the first measure. The third and fourth expands the first two measures
with the service flow of durable goods (see appendix A. 1 for details about the construction
of the proxy for services of durable goods). These measures can be summarized as follows:
1. Nondurables: includes total food and beverages consumption (incl. food stamps), insurance, housing maintenance costs (equipment, contractors), lodging (including vacation), utilities, personal services (e.g., nursing, housekeeping),clothing, transportation
expenditures, rentals, memberships, etc.
2. Total consumption = Nondurables & semi-durables such as luxury goods (e.g., jewelry, boats, etc), art, vehicles and parts, home furniture and appliances, electronics +
Education and health expenses.
3. Nondurables-Plus= Nondurables + Service flow of owned vehicles and homes.
4. Total consumption-Plus = Total consumption + Service flow of owned vehicles and
homes.
We impute consumption in the PSID from a CEX-based estimation of the demand equation
for food. This methodology allows for measurement error in total consumption measures
by instrumenting consumption. Only the results for the first measure (nondurables) are
presented in section III. Tables A.2, A.3, and A.4 below present the results of these specifications for the three broader measures of consumption. Tests of over-identifying restrictions
and of the strength of excluded instruments are presented in the bottom of each table, and
are all passed.
48
Table A.2: THE DEMAND FOR FOOD IN THE CEX-TOTAL CONSUMPTION
Variable
ln c
Estimate
0.648***
0.121
ln c x HS dropout
0.0440*
0.025
ln c x HS graduate
0.144***
0.049
ln c x one child
-0.0353***
0.010
ln c x two children
-0.0542***
0.009
ln c x three children +
-0.0827***
0.011
ln c x 1980
0.145*
0.082
ln c x 1981
0.134*
0.072
ln c x 1982
0.110
0.071
ln c x 1983
0.0930
0.069
ln c x 1984
0.0913
0.065
ln c x 1985
0.0832
0.059
ln c x 1986
0.0502
0.058
ln c x 1987
0.0509
0.050
ln c x 1988
0.0503
0.043
ln c x 1989
0.0461
0.035
ln c x 1990
0.0424
0.027
Number of observations
51,268
Test of overidentifying restrictions
Test time consistency of income elasticity
Variable
ln c x 1991
ln c x 1992
ln c x 1993
ln c x 1994
ln c x 1996
ln c x 1997
ln c x 1998
ln c x 1999
ln c x 2000
ln c x 2001
ln c x 2002
ln c x 2003
ln c x 2004
ln c x 2005
ln c x 2006
ln c x 2007
ln c x 2008
R-squared
Estimate
0.00198
0.019
-0.00756
0.017
-0.00925
0.013
-0.00487
0.008
-0.00895**
0.003
-0.0183***
0.006
-0.0322***
0.011
-0.0375***
0.013
-0.0362**
0.015
-0.0566***
0.019
-0.0655***
0.022
-0.0727***
0.024
-0.0745***
0.026
-0.0737***
0.026
-0.0777***
0.029
-0.0790**
0.032
-0.0852**
0.035
0.388
Variable
ln c x 2009
ln c x 2010
ln c x 2011
ln c x y7273
Age
Age2
pf ood
palcohol+tobacco
pf uel+utils
ptransports
HS dropout
HS graduate
Northeast
Midwest
South
Born 1975-79
Born 1970-74
Estimate
-0.123***
0.047
-0.103**
0.039
-0.0802**
0.040
0.174
0.159
0.0414***
0.006
-0.000382***
5.95e
-1.055***
0.323
4.635**
2.008
1.319
1.590
-3.786
2.961
-0.432*
0.251
-1.452***
0.489
0.0220***
0.004
-0.0353***
0.007
-0.0201**
0.009
0.0690
0.071
0.0431
0.066
Variable
Born 1965-69
Estimate
0.0321
0.060
Born 1960-64
0.00840
0.054
Born 1955-59
-0.0172
0.047
Born 1950-54
-0.0298
0.042
Born 1945-49
-0.0314
0.037
Born 1940-44
-0.0595*
0.034
Born 1935-40
-0.0436
0.028
Born 1930-34
-0.0311
0.022
Born 1925-29
-0.0441**
0.018
Born 1920-24
-0.0377***
(0.0140)
One Child
0.393***
(0.0999)
Two children
0.625***
(0.102)
Three children+ 0.929***
(0.129)
Family Size
0.0403***
(0.00907)
White
0.0591***
(0.0164)
Constant
-0.208
(1.074)
23.07
(d.f. 27; χ2 p-value 68.13%)
70.14
(d.f. 28; χ2 p-value 0.0001%)
Notes: This table reports IV estimates of the demand equation for (the logarithm of) food spending in the CEX. We use family composition-educationyear specific average of the log of the husband and wife’s hourly wages as instruments for the log of total nondurable expenditure and its interactions
with year, education, and kids dummies. Standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
49
Table A.3: THE DEMAND FOR FOOD IN THE CEX-NONDURABLES & SERVICES FROM DURABLES
Variable
ln c
Estimate
0.641***
0.105
ln c x HS dropout
0.0519***
0.019
ln c x HS graduate
0.148***
0.040
ln c x one child
-0.0385***
0.008
ln c x two children
-0.0587***
0.009
ln c x three children +
-0.0828***
0.011
ln c x 1980
0.0557
0.072
ln c x 1981
0.0472
0.064
ln c x 1984
0.0273
0.057
ln c x 1985
0.0252
0.052
ln c x 1986
0.0181
0.051
ln c x 1987
0.0175
0.044
ln c x 1988
0.0198
0.037
ln c x 1989
0.0177
0.031
ln c x 1990
0.0148
0.024
ln c x 1991
0.00248
0.017
Number of observations
41,031
Test of overidentifying restrictions
Test time consistency of income elasticity
Variable
ln c x 1993
Estimate
-0.00145
0.012
ln c x 1994 -0.00200
0.007
ln c x 1996 -0.00660*
0.003
ln c x 1997 -0.00774
0.006
ln c x 1998 -0.0119
0.011
ln c x 1999 -0.0143
0.013
ln c x 2000 -0.0153
0.014
ln c x 2001 -0.0221
0.019
ln c x 2002 -0.0250
0.022
ln c x 2003 -0.0275
0.024
ln c x 2004 -0.0287
0.026
ln c x 2006 -0.0327
0.027
ln c x 2006 -0.0338
0.031
ln c x 2007 -0.0307
0.034
ln c x 2008 -0.0345
0.037
ln c x 2009 -0.0422
0.049
R-squared
0.501
Variable
ln c x 2010
ln c x y7273
Age
Age2
pf ood
palcohol+tobacco
pf uel+utils
ptransports
HS dropout
HS graduate
Northeast
Midwest
South
Born 1975-79
Born 1970-74
Born 1965-69
Estimate
-0.0396
0.041
0.0970
0.140
0.0429***
0.005
-0.000390***
5.54e
-0.631**
0.314
0.999
1.879
0.399
1.546
-0.836
2.670
-0.471**
0.189
-1.413***
0.391
0.00592
0.005
-0.0192**
0.008
-0.00741
0.010
0.111
0.070
0.0895
0.065
0.0638
0.059
Variable
Born 1960-64
Estimate
0.0361
0.053
Born 1955-59
0.00668
0.046
Born 1950-54
-0.00353
0.041
Born 1945-49
-0.00305
0.036
Born 1940-44
-0.0303
0.031
Born 1935-40
-0.0214
0.025
Born 1930-34
-0.00626
0.020
Born 1925-29
-0.0125
0.015
Born 1920-24
-0.0221*
0.012
One Child
0.410***
0.087
Two children
0.628***
0.092
Three children+ 0.851***
0.114
Family Size
0.0548***
0.006
White
0.104***
0.009
Constant
0.486
(0.895)
24.47
(d.f. 25; χ2 p-value 49.3%)
84.1
(d.f. 26; χ2 p-value 0.0001%)
Notes: This table reports IV estimates of the demand equation for (the logarithm of) food spending in the CEX. We use family composition-educationyear specific average of the log of the husband and wife’s hourly wages as instruments for the log of total nondurable expenditure and its interactions
with year, education, and kids dummies. Standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
50
Table A.4: THE DEMAND FOR FOOD IN THE CEX-TOTAL CONSUMPTION & SERVICES FROM DURABLES
Variable
ln c
Estimate
0.699***
0.119
ln c x HS dropout
0.0165
0.023
ln c x HS graduate
0.0923**
0.046
ln c x one child
-0.0421***
0.010
ln c x two children
-0.0605***
0.010
ln c x three children +
-0.0856***
0.012
ln c x 1980
0.0597
0.083
ln c x 1981
0.0606
0.073
ln c x 1984
0.0245
0.067
ln c x 1985
0.0225
0.061
ln c x 1986
-0.00980
0.061
ln c x 1987
-0.00205
0.051
ln c x 1988
0.00394
0.044
ln c x 1989
0.00851
0.036
ln c x 1990
0.0133
0.028
ln c x 1991
-0.0157
0.020
Number of observations
41,030
Test of overidentifying restrictions
Test time consistency of income elasticity
Variable
ln c x 1993
ln c x 1994
ln c x 1996
ln c x 1997
ln c x 1998
ln c x 1999
ln c x 2000
ln c x 2001
ln c x 2002
ln c x 2003
ln c x 2004
ln c x 2006
ln c x 2006
ln c x 2007
ln c x 2008
ln c x 2009
R-squared
Estimate
-0.0193
0.014
-0.0107
0.008
-0.00549
0.003
-0.0133*
0.006
-0.0270**
0.012
-0.0276*
0.014
-0.0213
0.015
-0.0472**
0.019
-0.0513**
0.023
-0.0628**
0.025
-0.0577**
0.026
-0.0560**
0.026
-0.0597**
0.030
-0.0586*
0.032
-0.0621*
0.036
-0.106**
0.049
0.397
Variable
ln c x 2010
ln c x y7273
Age
Age2
pf ood
palcohol+tobacco
pf uel+utils
ptransports
HS dropout
HS graduate
Northeast
Midwest
South
Born 1975-79
Born 1970-74
Born 1965-69
Estimate
-0.0750*
0.040
0.00909
0.161
0.0445***
0.005
-0.000411***
5.72e
-0.777**
0.333
3.516*
2.086
2.334
1.756
-5.427*
3.148
-0.161
0.231
-0.937**
0.460
0.0188***
0.005
-0.0323***
0.007
-0.0198**
0.009
0.0936
0.078
0.0608
0.072
0.0437
0.065
Variable
Born 1960-64
Born 1955-59
Born 1950-54
Born 1945-49
Born 1940-44
Born 1935-40
Born 1930-34
Born 1925-29
Born 1920-24
One Child
Two children
Three children+
Family Size
White
Constant
Estimate
0.0214
0.058
-0.00916
0.051
-0.0185
0.045
-0.0203
0.040
-0.0489
0.035
-0.0322
0.028
-0.0185
0.022
-0.0276
0.018
-0.0271*
0.014
0.464***
0.102
0.686***
0.106
0.947***
0.133
0.0471***
0.008
0.0728***
0.013
-0.186
(1.045)
19.92
(d.f. 25; χ2 p-value 75.1%)
64.8
(d.f. 26; χ2 p-value 0.0001%)
Notes: This table reports IV estimates of the demand equation for (the logarithm of) food spending in the CEX. We use family composition-educationyear specific average of the log of the husband and wife’s hourly wages as instruments for the log of total nondurable expenditure and its interactions
with year, education, and kids dummies. Standard errors are in parentheses. *** p<0.01, ** p<0.05, * p<0.1.
51
Table B.1: LIST OF SETS OF VARIABLES
Variable
var(ζ)
var(ε)
var(uc )
var(uy )
var(ξ)
ψ
φ
θ
Description
Variance of permanent shock to income
Variance of transitory shock to income
Variance of measurement error of consumption
Variance of measurement error of income
Variance of heterogeneous shocks to consumption
Partial insurance parameter temporary shock to income
Partial insurance parameter permanent shock to income
Serial correlation factor MA(1) process
Appendix B:
Number of Variables
36
45
37
37
1
5
5
1
Moment Conditions
This paper dramatically extends the number of moments previous studies have used to estimate similar models. First, compared with Blundell et al. (2008) the set of years is expanded
to 1968 to 2010, in contrast with the range 1980 to 1992 which is the range considered by
Blundell et al. (2008). Second, an additional set of moments are used. These moments include the variance and covariance of two year differences in income and consumption. These
additions more than double the number of moments used to estimate the model while only
slightly increasing the number of variables to be estimated.
There are eight sets of variables that are estimated: the variances of the permanent shock
to income, of the transitory shock to income, of the measurement error in consumption, of
the measurement error in income, and of the temporary shock to consumption, as well as
the partial insurance parameters on the permanent and transitory shocks to income, and the
serial correlation factor in the moving average process of income temporary shocks. In total
there are 167 variables estimated across these eight sets.
To estimate the eight sets of variables there are eight sets of moment conditions. The
first two sets consist of the variance of the growth in income and growth in consumption.
The second two sets consist of the covariance of the growth in income in year t and the
growth in income in year t + 1 and the growth in consumption in year t and the growth in
consumption in year t + 1. The next set is the covariance of the growth in income in year
t and the growth in income in year t + 2. The final sets consist of the covariance of the
growth in consumption in year t and the growth in income, in years t, t + 1, and t + 2. Each
of these sets consist of two subsets of moment conditions. The first defines the growth in
income and consumption as the difference from year t and t − 1. The second subset defines
the growth in income and consumption as the difference from year t and t − 2. In total there
are 477 moment conditions of which only 225 are from defining the growth in income and
consumption as one year apart. To distinguish the moment conditions, those that define the
growth as one year differences are denoted by ∆ and those that define the growth as two
˜
year differences are denoted by ∆.
var(∆yt ) = var(ζt ) + (θ − 1)2 var(εt−1 ) + var(εt ) + θ2 var(εt−2 )
(B.1a)
˜ t ) = var(ζt ) + var(ζt−1 ) + var(εt ) + (θ2 )var(εt−1 ) + var(εt−2 ) + θ2 var(εt−3 ) (B.1b)
var(∆y
52
var(∆ct ) = φ2 var(ζt ) + ψ 2 var(εt ) + var(ξt )
˜ t ) = φ2 var(ζt ) + φ2 var(ζt−1 ) + ψ 2 var(εt ) + ψ 2 var(εt−1 ) + 2var(ξt )
var(∆c
(B.2a)
(B.2b)
cov(∆yt , ∆yt+1 ) = (θ − 1)var(εt ) − θ(θ − 1)var(εt−1 ) − var(uyt )
˜ t , ∆y
˜ t+1 ) = var(ζt ) + θvar(εt ) − θvar(εt−1 ) + θvar(εt−2 )
cov(∆y
(B.3b)
cov(∆ct , ∆ct+1 ) = −var(uct )
(B.4a)
˜ t , ∆c
˜ t+1 ) = φ2 var(ζt ) + ψ 2 var(εt ) + var(ξt )
cov(∆c
(B.4b)
cov(∆yt , ∆yt+2 ) = −θvar(εt )
(B.5a)
˜ t , ∆y
˜ t+2 ) = −var(εt ) − θ2 var(εt−1 ) − var(uyt )
cov(∆y
(B.5b)
cov(∆ct , ∆yt ) = φvar(ζt ) + ψvar(εt )
(B.6a)
˜ t , ∆y
˜ t ) = φvar(ζt ) + φvar(ζt−1 ) + ψvar(εt ) + ψθvar(εt−1 )
cov(∆c
(B.6b)
cov(∆ct , ∆yt+1 ) = ψ(θ − 1)var(εt )
˜ t , ∆y
˜ t+1 ) = φvar(ζt ) + ψθvar(εt ) − ψvar(εt−1 )
cov(∆c
(B.7a)
cov(∆ct , ∆yt+2 ) = −ψθvar(εt )
˜ t , ∆y
˜ t+2 ) = −ψvar(εt ) − ψθvar(εt−1 )
cov(∆c
(B.3a)
(B.7b)
(B.8a)
(B.8b)
Most variables appear in numerous moment conditions. The Table B.3 indexes which equations each variable enters. Sometimes the variable enters in a lagged value as well and is
denoted by (t-1) for one lag and (t-2) for two lags. Only the largest lag is depicted.
Appendix C:
C. 1
Policy and Market Effects
Construction
As described in equation (15), we decompose changes in insurance from income shocks into
three parts: those due to changes in the distribution of income (or market effects), those due
to due to changes in tax policy (or policy effects), and insurance changes due to individuals’
behavioral response to policy or market effects (behavioral effects). Tax policy provides
insurance by absorbing part of the income shocks, helping households smooth consumption
relative to income shocks. For example consider a household with gross income of $70,000
half of the time and $30,000 the other half of the time. Without taxation this household’s
income can differ by $40,000 year over year. Now assume that there exists a progressive tax
schedule such that the average tax rate is 25 percent at $70,000 and 15 percent at $30,000.
Now the household’s income net of taxes is about $56,300 half of the time and about $25,900
half of the time reducing the uncertainty from year to year to $30,400. In this example the
government absorbs 24 percent of the uncertainty.58
58
Here we apply the progressivity of the actual 2009 tax schedules for singles, but we disregard exemption
amounts. Though the government absorbs 24 percent of the shock they do so at a cost of $9,600, the
53
Table B.2: NUMBER OF MOMENT CONDITIONS BY SET
Equation
1a
1b
2a
2b
3a
3b
4a
4b
5a
5b
6a
6b
7a
7b
8a
8b
Moment Condition
var(∆yt )
˜ t)
var(∆y
var(∆ct )
˜ t)
var(∆c
cov(∆yt ,∆yt+1 )
˜ t ,∆y
˜ t+1 )
cov(∆y
cov(∆ct ,∆ct+1 )
˜ t ,∆c
˜ t+1 )
cov(∆c
cov(∆yt ,∆yt+2 )
˜ t ,∆y
˜ t+2 )
cov(∆y
cov(∆ct ,∆yt )
˜ t ,∆y
˜ t)
cov(∆c
cov(∆ct ,∆yt+1 )
˜ t ,∆y
˜ t+1 )
cov(∆c
cov(∆ct ,∆yt+2 )
˜ t ,∆y
˜ t+2 )
cov(∆c
Range of Years
1968 - 1996
1969 - 2010
1968 - 1996
1969 - 2010
1968 - 1995
1969 - 1995
1968 - 1995
1969 - 1995
1968 - 1994
1969 - 2006
1968 - 1996
1969 - 2010
1968 - 1995
1969 - 1995
1968 - 1994
1969 - 2006
Total Years
29
35
29
35
28
27
28
27
27
33
29
35
28
27
27
33
Table B.3: INDEX OF VARIABLE EQUATION
APPEARANCES
Variable Equations Appear In
var(ζ) 1a, 1b (t-1), 2a, 2b (t-1), 3b, 4b, 6a, 6b (t-1), 7b
var(ε) 1a (t-2), 1b (t - 3), 2a, 2b (t-1), 3a (t-1), 3b (t-2),
4b, 5a, 5b, 6a, 6b (t-1), 7a, 7b (t-1), 8a, 8b (t -1)
c
var(u ) 4a
var(uy ) 3a, 5b
var(ξ) 2a, 2b, 4b
ψ
2a, 2b, 4b, 6a, 6b, 7a, 8a, 8b
φ
2a, 2b, 4b, 6a, 6b, 7b
θ
1a, 1b, 3a, 3b, 5a, 5b, 6b, 7a, 7b, 8a, 8b
54
From the previous example we can identify two mechanical ways in which the insurance
from taxation may change over time. First, assume that this tax system changes such that
the average tax rate is now 10 percent at $30,000 and 30 percent at $70,000 (while all other
parameters of the 2009 tax schedule are the same, for illustration purposes). In this case, the
government absorbs 28 percent of the uncertainty. This is because both the average and the
marginal tax rates of this household have increased from the first to the second tax system.
Second, consider the case where tax policy is the same as the actual 2009 tax system changes
but the income distribution changes such that now the household makes $90,000 half of the
time and $50,000 the other half of the time. With the same tax code the average tax rates
are roughly 21 percent at $90,000 and 17.5 percent at $50,000. In this case the government
absorbs 25.6 percent of the shock. This simple example illustrates how changes in the tax
system or changes in the distribution of income can alter the degree to which the tax system
is structurally able to shelter households’ disposable income from income shocks.59
To separate the effects on the insurance parameters due to changes in policy and changes
due to the income distribution, we create two variables that capture these changes independently of each other (see section D in main paper). Both of these variables determine the
percentage of income shock that is absorbed by the tax code, as illustrated in the previous
examples.
C. 2
Sensitivity to Base Year
To construct income quartiles and the policy and market effects, we use 1980 as the base year
for income distribution, tax policy, or income. To evaluate the sensitivity of these effects to
the choice of the base year, we use 1995 as an alternative base year to fix tax policy in the case
of the market effect, or to fix income levels in the case of the policy effect. To keep the left
hand side of the decomposition equation (15) constant in either cases, we also hold income
quartiles constant (i.e., we use 1980 as the base year for income distribution). In other words,
a household in the lowest income quartile based on 1980 income distribution remains in the
lowest quartile when we use 1995 as the base year for policy and market effects, even if the
same family moved to an upper quartile by 1995. The results of the decomposition described
in equation (15) by quartiles of income and decades are very similar to our benchmark case.
Figures C.1 and C.2 illustrate the sensitivity to the base year of our measurements of policy
and market stabilization, respectively.
Appendix D:
Additional Empirical Evidence
This appendix supplements the figures and tables reported in the paper and provides additional durability to the estimates.
difference in the average net of taxes income.
59
Similar to this simple example, our analysis evaluates the size of each effect the policy and the market
effects based on observed data on income and tax policy, holding either policy constant or market income
constant (we also account for inflation when we hold policy and market effects constant).
55
.6
.5
.6
.4
.4
.3
.2
.2
0
.1
-.2
Q2
Q3
top
bottom
(a) Base Year for Income = 1980
Q2
Q3
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
-.4
1967
bottom
top
(b) Base Year for Income = 1995
.3
bottom
Q2
Q3
top
bottom
(a) Base Year for Tax Policy = 1980
Q2
Q3
top
(b) Base Year for Tax Policy = 1995
Figure C.2: Market (Income) Effects (% Change in Tax), Holding Tax Policy Constant, by
Quartile of Income
D. 1
The Autocovariance of Income and Consumption Growth
This section reports the autocovariance of income and consumption growth in Tables D.1,
D.2, and D.3 supplementing the Figures 3 and 4 reported in the paper.
Table D.1 reports the autocovariance of consumption growth for one and two periods
ahead. Column 1 shows that the variance of consumption growth increases until the mid
1980s decreases until the 1990s where it increases for the first few years before decreasing
56
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
2011
2007
2003
1999
1995
1991
1987
1983
1979
1975
1971
1967
-.2
.1
-.1
.2
0
.3
.1
.4
.2
.5
Figure C.1: Tax Policy Effects (% Change in Tax), Holding Income Constant, by Quartile
of Income
Table D.1: CONSUMPTION GROWTH AUTOCOVARIANCE MATRIX
Year
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
(1)
(2)
(3)
var(∆ct ) cov(∆ct ,∆ct+1 ) cov(∆ct ,∆ct+2 ) Year
0.034
-0.057**
0.028*
1982
(0.033)
(0.022)
(0.015)
0.119***
-0.063***
0.003
1985
(0.034)
(0.023)
(0.015)
0.120***
-0.046**
0.008
1986
(0.034)
(0.023)
(0.016)
0.131***
-0.069***
-0.013
1987
(0.035)
(0.024)
(0.016)
0.065*
0.023
0.002
1988
(0.035)
(0.024)
(0.016)
0.063*
-0.068***
0.023
1989
(0.036)
(0.024)
(0.016)
0.140***
-0.069***
-0.015
1990
(0.036)
(0.024)
(0.016)
0.160***
-0.064***
-0.002
1991
(0.036)
(0.024)
(0.016)
0.296***
-0.171***
-0.016
1992
(0.036)
(0.024)
(0.016)
0.250***
-0.061**
0.009
1993
(0.036)
(0.024)
(0.016)
0.180***
-0.080***
-0.013
1994
(0.035)
(0.024)
(0.016)
0.170***
-0.069***
-0.006
1995
(0.035)
(0.023)
(0.016)
0.219***
-0.125***
0.012
1996
(0.034)
(0.023)
(0.015)
0.249***
-0.121***
0.02
(0.034)
(0.023)
(0.015)
0.085***
-0.024***
-0.007
(0.009)
(0.006)
(0.005)
(1)
(2)
var(∆ct ) cov(∆ct ,∆ct+1 )
0.249***
-0.106***
(0.034)
(0.023)
0.387***
-0.177***
(0.033)
(0.022)
0.327***
-0.151***
(0.033)
(0.022)
0.200***
-0.032
(0.032)
(0.022)
0.04
-0.004
(0.032)
(0.021)
0.190***
-0.158***
(0.032)
(0.021)
0.341***
-0.113***
(0.032)
(0.021)
0.309***
-0.132***
(0.032)
(0.022)
0.294***
-0.120***
(0.033)
(0.022)
0.119***
0.007
(0.032)
(0.022)
0.121***
-0.111***
(0.034)
(0.023)
0.243***
-0.093***
(0.034)
(0.023)
0.199***
(0.035)
(3)
cov(∆ct ,∆ct+2 )
-0.009
(0.015)
0.046***
(0.015)
-0.002
(0.015)
0.001
(0.014)
-0.002
(0.014)
0.014
(0.014)
-0.003
(0.014)
0.030**
(0.015)
0.02
(0.015)
0.02
(0.015)
0.022
(0.015)
Notes: This table reports the variance autocovariance matrix for consumption growth. See the main text for
details of how these estimates are used to in later estimates. Standard errors are in parentheses. *** Significant
at the 1 percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level.
again. The level of the variance of consumption growth is a combination of the variance
associated with income, the heterogeneity in household’s responses to income shocks, and
the measurement error from the imputation. Column 2 shows the covariance of current
period consumption with one-period-ahead consumption, which is informative about the
variance of the measurement error. Finally, Column 3 shows the second-order consumption
growth autocovariance, which is not used as a moment condition and is economically small
and rarely statistically significant.
Table D.2 reports the autocovariance of income growth for one and two periods ahead.
The first column reports the variance of income growth which increases from 1968 to 1987
and then levels off or decreases before starting to increase again in 1992.60 The second
column reports the first-order income growth autocovariance, which increases in magnitude
throughout the sample but most dramatically in the 1990s. Finally, the third column is
informative about the serial correlation of the transitory income shock. Given that the
estimates are statistically significant for a few years we allow for a MA(1) serial correlation
in the transitory component (vi,t = εi,t + θεi,t−1 ).
60
The PSID converted the questionnaire to an electronic form and income was machine imputed post
1992.
57
Table D.2: INCOME GROWTH AUTOCOVARIANCE MATRIX
Year
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
(1)
(2)
var(∆yt ) cov(∆yt ,∆yt+1 )
0.112***
-0.037***
(0.009)
(0.006)
0.083***
-0.031***
(0.009)
(0.006)
0.089***
-0.031***
(0.009)
(0.006)
0.086***
-0.033***
(0.009)
(0.006)
0.088***
-0.032***
(0.009)
(0.006)
0.084***
-0.025***
(0.009)
(0.006)
0.071***
-0.021***
(0.01)
(0.006)
0.083***
-0.027***
(0.01)
(0.006)
0.091***
-0.032***
(0.009)
(0.006)
0.095***
-0.032***
(0.01)
(0.006)
0.087***
-0.025***
(0.009)
(0.006)
0.086***
-0.031***
(0.009)
(0.006)
0.090***
-0.023***
(0.009)
(0.006)
0.082***
-0.030***
(0.009)
(0.006)
0.085***
-0.024***
(0.009)
(0.006)
(3)
cov(∆yt ,∆yt+2 )
0.003
(0.005)
0.002
(0.005)
-0.002
(0.005)
-0.002
(0.005)
-0.002
(0.005)
-0.003
(0.005)
-0.006
(0.005)
-0.014***
(0.005)
-0.005
(0.005)
-0.008
(0.005)
0.003
(0.005)
0.004
(0.005)
0.0001
(0.005)
-0.009**
(0.005)
-0.007
(0.005)
Year
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
(1)
(2)
var(∆yt ) cov(∆yt ,∆yt+1 )
0.087***
-0.027***
(0.009)
(0.006)
0.090***
-0.033***
(0.009)
(0.006)
0.091***
-0.028***
(0.009)
(0.006)
0.094***
-0.030***
(0.009)
(0.006)
0.109***
-0.046***
(0.009)
(0.006)
0.098***
-0.027***
(0.008)
(0.006)
0.089***
-0.034***
(0.008)
(0.006)
0.094***
-0.037***
(0.008)
(0.006)
0.086***
-0.033***
(0.008)
(0.006)
0.120***
-0.065***
(0.009)
(0.006)
0.147***
-0.053***
(0.009)
(0.006)
0.127***
-0.046***
(0.009)
(0.006)
0.120***
-0.059***
(0.009)
(0.006)
0.175***
(0.009)
(3)
cov(∆yt ,∆yt+2 )
-0.007
(0.005)
0.0001
(0.005)
-0.009*
(0.005)
-0.007
(0.005)
0.002
(0.004)
-0.004
(0.004)
-0.002
(0.004)
0.0001
(0.004)
0.003
(0.005)
-0.009*
(0.005)
0.003
(0.005)
-0.007
(0.005)
Notes: This table reports the variance autocovariance matrix for income growth. See the main text for details of
how these estimates are used to in later estimates. Standard errors are in parentheses. *** Significant at the 1
percent level. ** Significant at the 5 percent level. * Significant at the 10 percent level.
58
Table D.3 reports the covariance of income and consumption in the same period, with a
lag, and with a lead. The contemporaneous covariance, reported in column (1), is informative
about the transmission of income shocks to consumption. The covariance increases dramatically in the early 1980s but declines from then through the mid 1990s. This trend suggests
insurance decreased in the early 1980s, after which it increased. Column (2) reports current
period income with one-period-ahead consumption growth, which is informative about the
importance of liquidity constraints. These estimates are close to zero and rarely statistically
significant suggesting a limited role for liquidity constraints. The covariance between current
consumption growth and one-period-ahead income growth, reported in column (3), is informative about the insurance of transitory income shocks. The estimates experience slight
increases in the early 1980s and 1990s before dropping again. This suggest insurance from
transitory income shocks decreased in the 1980s and then increased in the late 1990s and
2000s. The last four lines of Table D.3 report the p-values of joint significance tests of autocovariances between current consumption and future income shocks, E(∆ct , ∆yt+j ) (j > 0),
which inform about advance information: if consumers had access to information about future income shocks, our estimates of the insurance parameters would be biased downward
because consumers would previously have internalized this information. This said, as these
tests are generally insignificant, we believe that advance information is not a significant issue
in the period covered by our sample.
D. 2
The Variance of Permanent and Transitory Income Shocks
This appendix reports the estimates of the permanent and transitory income shocks for the
full sample, income quartile, education group, and age group. The estimates are summarized
in a series of figures that graph the variance of permanent and transitory income shocks.
The whole sample and income quartile estimates are graphed in the paper in Figures 8 and
9. The estimates by age and education group are graphed in the appendix in Figures D.3
and D.4. All of these figures graph the five year moving average of the estimates reported
in Tables D.4 through D.9. To demonstrate the trends using the five year moving average
are robust to different moving averages the estimates of the whole sample are graphed using
three year and nine year moving averages in Figures D.1 and D.2.
Figures D.1 and D.2 graph the variance of permanent and transitory income using three
and nine year moving averages as opposed to the baseline five year moving average used in
the paper. As expected the nine year moving average graph is smoother than the five or three
but the general points are robust. First, the variance of transitory income has a decreasing
trend from 1968 through 2000 with a cyclical trend that is most pronounced in the three year
moving average figure and least pronounced in the nine year moving average figure. Second,
there is an increase in the variance of permanent income in the late 1970s early 1980s that is
most pronounced in the three year moving average figure and least pronounced in the nine
year moving average figure. Finally, there are large increases in the variance of permanent
income shocks in the 1990s and large increases in the variance of transitory income shocks
in the 2000s.
59
Table D.3: CONSUMPTION-INCOME GROWTH COVARIANCE MATRIX
(1)
cov(∆ct ,∆yt )
0.018**
(0.007)
1969
0.011
(0.007)
1970
0.017**
(0.007)
1971
0.01
(0.007)
1972
0.011
(0.007)
1973
0.018**
(0.007)
1974
0.005
(0.008)
1975
0.006
(0.008)
1976
0.014*
(0.008)
1977
0.018**
(0.008)
1978
0.01
(0.007)
1979
0.003
(0.007)
1980
0.012
(0.007)
1981
0.021***
(0.007)
1982
0.023***
(0.007)
Test cov(∆yt+1 , ∆ct )
Test cov(∆yt+2 , ∆ct )
Test cov(∆yt+3 , ∆ct )
Test cov(∆yt+4 , ∆ct )
Year
1968
(2)
cov(∆ct+1 ,∆yt )
-0.011*
(0.006)
0.0001
(0.006)
-0.004
(0.007)
-0.002
(0.007)
-0.009
(0.007)
-0.011
(0.007)
0.0001
(0.007)
-0.009
(0.007)
-0.012*
(0.007)
-0.012*
(0.007)
-0.004
(0.007)
-0.002
(0.007)
0.002
(0.007)
-0.013*
(0.007)
0.006
(0.006)
= 0 for all t
= 0 for all t
= 0 for all t
= 0 for all t
(3)
cov(∆ct ,∆yt+1 )
-0.006
(0.007)
-0.004
(0.007)
-0.005
(0.007)
0.004
(0.007)
-0.005
(0.007)
-0.001
(0.007)
0.007
(0.007)
0.002
(0.007)
0.005
(0.007)
0.001
(0.007)
-0.002
(0.007)
0.005
(0.007)
-0.011*
(0.007)
-0.005
(0.007)
-0.009
(0.007)
Year
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
(1)
cov(∆ct ,∆yt )
0.029***
(0.007)
0.030***
(0.007)
0.026***
(0.007)
0.028***
(0.007)
0.045***
(0.007)
0.037***
(0.007)
0.032***
(0.007)
0.01
(0.007)
0.018***
(0.007)
0.024***
(0.007)
0.035***
(0.007)
0.021***
(0.007)
0.011
(0.007)
0.009
(0.007)
(2)
cov(∆ct+1 ,∆yt )
-0.009
(0.006)
-0.014**
(0.006)
-0.009
(0.006)
-0.005
(0.006)
-0.023***
(0.006)
-0.013**
(0.006)
-0.002
(0.006)
0.004
(0.006)
-0.012*
(0.006)
-0.006
(0.006)
-0.012*
(0.006)
0.002
(0.006)
-0.002
(0.007)
(3)
cov(∆ct ,∆yt+1 )
-0.007
(0.007)
-0.001
(0.007)
-0.009
(0.007)
-0.008
(0.007)
-0.011
(0.006)
-0.009
(0.006)
0.002
(0.006)
0.01
(0.006)
-0.018***
(0.007)
-0.001
(0.007)
-0.008
(0.007)
0.001
(0.007)
-0.006
(0.007)
p-value
p-value
p-value
p-value
60.3%
0.97%
32.7%
96.5%
Notes: This table reports the variance autocovariance matrix for consumption-income growth. See the main text for details
of how these estimates are used to in later estimates. Standard errors are in parentheses. *** Significant at the 1 percent
level. ** Significant at the 5 percent level. * Significant at the 10 percent level.
60
0
Variance 3 Year Moving Average
.02
.04
.06
.08
.1
Variance Smoothed 5 Year Moving Average
0
.02
.08
.04
.06
Figure D.1: Variance Income Shocks Robust Moving Average Window (3 Year)
1970
1980
1990
year
2000
2010
1970
1980
Variance Permanent Income Shock
Variance Transitory Income Shock
1990
year
2000
2010
Variance Permanent Income Shock
Variance Transitory Income Shock
0
Variance 9 Year Moving Average
.02
.04
.06
Variance Smoothed 5 Year Moving Average
0
.02
.08
.04
.06
.08
5 Year Moving Average
3 Year Moving Average
Figure D.2: Variance Income Shocks Robust Moving Average Window (9 Year)
1970
1980
1990
year
2000
2010
1970
Variance Permanent Income Shock
Variance Transitory Income Shock
1980
1990
year
2000
2010
Variance Permanent Income Shock
Variance Transitory Income Shock
5 Year Moving Average
9 Year Moving Average
In all of these graphs the variance of transitory income in 2009 is an extreme outlier and
has been scaled to fit the graph. The variance of transitory income reported in Table D.5
experiences three spikes. The first in 2001 has a value of 0.0526 up from 0.0004 in 2000.
The second in 2007 has a value of 0.1380 up from 0.0073 in 2006. The third and largest in
2009 has a value of 0.7210 up from 0.0034 in 2008 and an order of magnitude larger than
the spike in 2001. Therefore, the value in 2009 is scaled down for expositional reasons such
that the trends in the previous time periods are not overwhelmed by the spike in 2009.
Table D.4 reports the estimates of the variance of permanent income shocks for each year
up to 1996 and the sum of conjoining years up to 2009 and 2010. The variance of permanent
income shocks after 1996 is only identified as the sum of two conjoining years. The variance
of permanent income shocks after 1996 are not identified yearly because only the two-year
difference moment conditions, every other year, are used to estimate the variance in later
years and the variance of permanent income shocks for two conjoining years enter the twoyear difference moment conditions in exactly the same way. For the graphs the variance of
permanent income shocks in year t is assumed to be one-half of the estimated value equal to
the variance in year t plus t + 1 or t − 1. This convention has limited impact on the figures
as they graph the five year moving average. However, the estimates empirically do not need
to be split evenly between the two years and could cause some small changes in the figures
if the values are very different.
61
Table D.4: ESTIMATES VARIANCE PERMANENT INCOME SHOCK
Year
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Baseline
0.0026
(0.0689)
0.0025
(0.0772)
0.0225
(0.0009)
2.0E-05
(0.0009)
0.0034
(0.0007)
0.0146
(0.0009)
0.0011
(0.001)
0.0317
(0.0015)
0.0055
(0.0028)
0.0010
(0.0037)
0.0038
(0.0031)
0.0002
(0.002)
0.0231
(0.0014)
0.0298
(0.0015)
0.0117
(0.0018)
0.0234
(0.0018)
0.0002
(0.0022)
0.0026
(0.0020)
Bottom
0.0393
(0.0665)
0.0100
(0.0282)
0.0218
(0.0029)
0.0086
(0.0012)
0.0186
(0.0028)
0.0021
(0.0026)
0.0308
(0.0019)
0.0080
(0.0024)
0.0104
(0.0051)
0.0406
(0.005)
0.0104
(0.0064)
3.0E-05
(0.0062)
0.0467
(0.0052)
0.0378
(0.0074)
0.0170
(0.0049)
0.0354
(0.0059)
0.0011
(0.0041)
0.0598
(0.0084)
Q2
0.0649
(0.0765)
0.0045
(0.0282)
0.0146
(0.0016)
0.0201
(0.0015)
0.0194
(0.0013)
0.0039
(0.0013)
0.0006
(0.0015)
0.0324
(0.002)
0.0005
(0.0014)
0.0160
(0.0018)
0.0380
(0.0023)
0.0044
(0.0025)
0.0256
(0.002)
0.0361
(0.003)
0.0176
(0.0018)
0.0312
(0.0016)
0.0003
(0.0033)
0.0157
(0.0025)
Q3
0.0002
(0.0068)
0.0299
(0.0423)
0.0012
(0.0016)
0.0060
(0.0015)
0.0006
(0.0016)
0.0135
(0.0029)
0.0087
(0.0022)
0.0246
(0.0023)
0.0040
(0.0015)
0.0051
(0.0038)
0.0107
(0.0027)
0.0002
(0.0027)
0.0077
(0.0031)
0.0071
(0.0032)
0.0114
(0.0028)
0.0000
(0.0019)
0.0080
(0.0032)
1.2E-06
(0.0023)
Top
Year
Baseline Bottom
Q2
Q3
Top
0.0016
1986
0.0200
0.0314
0.0188
0.0109
0.0188
(0.0146)
(0.0025) (0.0033) (0.0046) (0.002) (0.0041)
0.0000
1987
0.0164
0.0186
0.0133
0.0024
0.0456
(0.0243)
(0.0017) (0.0058) (0.0036) (0.0012) (0.0056)
0.0533
1988
0.0034
0.0351
0.0279
0.0007
0.0094
(0.0016)
(0.0029) (0.0037) (0.0083) (0.001) (0.0077)
0.0209
1989
0.0232
0.0314
0.0228
0.0021
0.0189
(0.002)
(0.0023) (0.012) (0.0058) (0.0009) (0.0026)
0.0297
1990
0.0084
0.0342
0.0017
0.0063
0.0012
(0.0014)
(0.0021) (0.0106) (0.0097) (0.0016) (0.002)
0.0193
1991
0.0057
0.0002
0.0052
0.0016
0.0081
(0.0012)
(0.0015) (0.0076) (0.0035) (0.0009) (0.0034)
0.0002
1992
0.0248
0.0186
0.0127
0.0052
0.0088
(0.0014)
(0.0016) (0.0105) (0.0027) (0.0013) (0.0033)
0.0178
1993
0.0114
0.0117
0.0123
0.0180
0.0097
(0.0012)
(0.0013) (0.0059) (0.0037) (0.0013) (0.0043)
0.0002
1994
0.0162
0.0460
0.0321
0.0227
0.0120
(0.0012)
(0.0012) (0.0039) (0.0027) (0.0017) (0.0055)
0.0002
1995
0.0132
0.0324
0.0000
0.0229
0.0159
(0.0011)
(0.0017) (0.0038) (0.0041) (0.0031) (0.0047)
0.0147
1996
0.1226
0.0880
0.1013
0.0966
0.1129
(0.0013)
(0.0023) (0.0046) (0.0061) (0.0054) (0.0059)
0.0016 1997 + 1998 0.1200
0.1362
0.0983
0.1138
0.1293
(0.0021)
(0.0336) (0.0397) (0.0169) (0.2925) (0.116)
0.0147 1999 + 2000 0.1173
0.1212
0.1097
0.0919
0.1038
(0.0016)
(0.0364) (0.0383) (0.0249) (0.339) (0.0796)
0.0109 2001 + 2002 0.1325
0.1509
0.0854
0.1188
0.1435
(0.0014)
(0.0454) (0.0437) (0.0219) (0.5298) (0.141)
0.0080 2003 + 2004 0.0100
0.1228
0.1513
0.0200
0.0170
(0.0017)
(0.0163) (0.0083) (0.0165) (0.0611) (0.0106)
0.0002 2005 + 2006 0.0041
0.0815
0.0933
0.0169
3.0E-05
(0.0022)
(0.0153) (0.0081) (0.5045) (0.0673) (0.0142)
0.0004 2007 + 2008 0.0601
0.0616
0.0995
0.0063
0.0299
(0.0029)
(0.0432) (0.0037) (0.3027) (0.0482) (0.0142)
0.0173 2009 + 2010 0.0046
0.0701
0.0248
0.0074
0.0097
(0.0056)
(0.1782) (0.0068) (0.1009) (0.0881) (0.0034)
θ
0.2146
0.1647
0.4123
0.2417
0.4457
(Serial correl. trans. shock)
(0.0101) (0.0195) (0.0301) (0.0208) (0.1427)
σξ2
0.0132
0.0081
0.0034
0.0103
0.0105
(Variance unobs. slope heterog.) (0.0007) (0.0014) (0.0016) (0.0009) (0.0008)
Notes: This table reports diagonally weighted minimum distance estimates of the variance of the permanent shock. Standard errors
in parentheses. The first specification is for the whole sample. The following four specifications correspond to income quartile groups
defined in 1980.
62
Table D.5: ESTIMATES OF THE VARIANCE OF TRANSITORY INCOME SHOCKS
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
Baseline
0.0011
(0.358)
0.004
(0.0037)
0.0069
(0.0022)
0.0011
(0.0028)
0.0432
(0.0031)
0.0511
(0.0034)
0.0356
(0.0029)
0.0242
(0.0031)
0.0096
(0.0064)
0.042
(0.0124)
0.0573
(0.0093)
0.0257
(0.0044)
2.6E-07
(0.0054)
0.0133
(0.0046)
0.0101
(0.0043)
0.028
(0.0081)
0.0283
(0.0066)
0.0381
(0.0074)
0.0317
(0.0059)
0.0378
(0.0047)
0.0092
(0.0011)
0.0075
(0.002)
Bottom
0.0213
(0.169)
0.0583
(0.0118)
0.0363
(0.0113)
0.0464
(0.0202)
0.0031
(0.0051)
0.0003
(0.005)
0.0406
(0.0224)
0.0181
(0.0093)
0.0016
(0.0103)
0.0432
(0.0434)
0.0684
(0.0242)
0.0371
(0.0216)
1.6E-08
(0.0243)
0.0218
(0.022)
0.002
(0.0098)
0.0046
(0.0116)
0.0058
(0.0082)
0.0022
(0.0088)
0.0593
(0.0196)
0.0391
(0.0143)
0.0007
(0.0174)
0.0001
(0.0248)
Q2
0.0037
(0.0677)
0.0005
(0.0026)
0.0006
(0.001)
0.0104
(0.0015)
0.0125
(0.0011)
0.0078
(0.0014)
0.0100
(0.0017)
0.0088
(0.0012)
0.0072
(0.0014)
0.0036
(0.0017)
0.0299
(0.0032)
0.0039
(0.0024)
4.6E-06
(0.003)
0.0045
(0.0025)
1.8E-05
(0.0013)
0.0159
(0.0019)
0.0117
(0.0008)
0.027
(0.0067)
0.0023
(0.0014)
0.0191
(0.0035)
0.0021
(0.0066)
0.0167
(0.0094)
Q3
0.0168
(0.174)
0.0087
(0.0033)
0.0098
(0.0041)
2.0E-07
(0.0052)
0.0219
(0.0042)
0.0253
(0.0018)
0.0172
(0.0084)
0.0089
(0.0064)
0.0002
(0.0084)
0.0529
(0.0076)
0.0417
(0.0087)
0.0168
(0.0074)
0.0002
(0.006)
0.0118
(0.0087)
0.0037
(0.0043)
0.0001
(0.0042)
0.0219
(0.0059)
0.0014
(0.004)
0.0139
(0.0041)
0.0025
(0.0022)
0.0056
(0.0017)
0.0075
(0.0018)
Top
0.002
(0.0054)
0.0004
(0.0002)
0.0002
(0.0002)
0.0004
(0.0003)
0.0012
(0.0003)
0.0014
(0.0002)
0.0017
(0.0002)
0.002
(0.0002)
0.0018
(0.0002)
0.0007
(0.0003)
0.0019
(0.0002)
0.0001
(0.0001)
1.5E-08
(0.0002)
0.0007
(0.0002)
0.0015
(0.0002)
0.0018
(0.0003)
0.0005
(0.0004)
0.0009
(0.0003)
0.0003
(0.001)
6.7E-07
(0.0001)
0.0006
(0.0003)
0.0008
(0.0023)
Year Baseline
1989 0.0087
(0.0011)
1990 0.0007
(0.0026)
1991 0.0174
(0.0026)
1992 0.0028
(0.0027)
1993 0.0523
(0.0052)
1994 0.0145
(0.0021)
1995 0.0099
(0.004)
1996 0.0012
(0.0026)
1997 2.3E-08
(0.0159)
1998 0.0035
(0.0012)
1999 6.8E-09
(0.0153)
2000 0.0004
(0.0013)
2001 0.0526
(0.0209)
2002 9.0E-08
(0.0015)
2003 0.0177
(0.0003)
2004 0.0044
(0.0009)
2005 4.7E-07
(0.0004)
2006 0.0073
(0.0008)
2007 0.1380
(0.0012)
2008 0.0034
(0.0251)
2009 0.7210
(0.0035)
2010 3.0E-08
(0.0771)
Bottom
0.0272
(0.0561)
0.0097
(0.0496)
0.0085
(0.0313)
0.1011
(0.0195)
0.056
(0.0146)
0.0048
(0.0053)
0.0297
(0.0161)
0.0023
(0.0100)
4.4E-08
(0.0459)
0.0041
(0.0026)
1.9E-06
(0.0518)
0.0001
(0.0020)
0.009
(0.0391)
5.5E-07
(0.0022)
0.0021
(0.3059)
0.0029
(0.0082)
0.0001
(0.045)
0.0225
(0.0018)
0.0407
(0.0001)
0.0023
(0.0228)
0.0008
(0.0003)
1.0E-06
(0.0265)
Q2
0.0053
(0.0043)
0.0075
(0.007)
0.0025
(0.005)
0.0023
(0.0030)
0.0321
(0.0032)
0.0002
(0.0034)
0.016
(0.0086)
0.0004
(0.0040)
2.9E-08
(0.0204)
0.0011
(0.0042)
2.3E-07
(0.0162)
0.0001
(0.0037)
0.0424
(0.0240)
1.7E-05
(0.0051)
0.0061
(0.1069)
0.0037
(0.0178)
2.3E-07
(0.1368)
1.3E-05
(0.023)
0.0212
(0.0401)
0.0001
(0.0344)
0.1149
(0.0175)
2.6E-09
(0.0262)
Q3
0.0012
(0.0008)
0.0064
(0.0022)
0.0065
(0.0023)
0.0104
(0.0020)
0.0102
(0.005)
0.0011
(0.0059)
0.0242
(0.0153)
0.0004
(0.2166)
6.0E-09
(1.4082)
0.0012
(0.0826)
2.4E-07
(1.3648)
0.0001
(0.0800)
0.0011
(1.8393)
1.2E-07
(0.1076)
0.0057
(0.2049)
0.0334
(0.0123)
0.0033
(0.5920)
0.0113
(0.0340)
0.0015
(0.0283)
0.0063
(0.1600)
0.0324
(0.0081)
4.4E-08
(0.2419)
Top
0.0015
(0.0018)
0.0018
(0.0005)
0.0033
(0.0003)
0.0051
(0.0008)
0.0011
(0.0006)
0.0006
(0.0004)
5.1E-06
(0.0009)
0.0045
(0.0069)
2.6E-08
(0.0008)
0.0005
(0.0154)
3.9E-07
(0.0004)
0.0009
(0.0081)
0.0008
(0.0006)
2.3E-07
(0.0113)
0.0021
(0.0300)
0.0048
(0.5955)
1.0E-05
(0.0526)
0.0082
(1.0445)
0.0055
(0.0085)
0.0002
(0.0005)
0.0005
(0.0083)
8.5E-08
(0.0004)
Notes: This table reports diagonally weighted minimum distance estimates of the variance of the permanent shock. Standard
errors in parentheses. The first specification is for the whole sample. The following four specifications correspond to income
quartile groups defined in 1980.
63
0
0
Variance Transitory Income Shock
Five Year Moving Average
.2
.4
.6
.8
1
Variance Permanent Income Shock
Five Year Moving Average
.05
.15
.1
Figure D.3 and Tables D.6 and D.7 report the estimates of the variance of permanent and
transitory income shocks by age group. All age groups experience increases in the variance
of permanent income shocks during the early 1980s and the late 1990s. The variance of
permanent income shocks are similar for all age groups until the 1990s where those between
the ages of forty and fifty-five initially experienced a decrease, household heads fifty-five or
older experience a larger increase in the late 1990s, and individuals forty years or younger
experienced smaller variance of permanent income in the 2000s. Table D.7 report age groups
differ in the spikes in the variance of transitory income shocks they experience. Individuals
forty years or younger experience a large spike in 2007 and a smaller spike in 2009. Individuals
fifty-five or older experience a small spike in 2003 and a very large spike in 2007. Individuals
between forty and fifty-five experience large spikes in 2001, 2003, 2007, and 2009.
Figure D.4 and Tables D.8 and D.9 report the estimates of the variance of permanent
and transitory income shocks by education group. All education groups experience increases
in the variance of permanent income shocks in the early 1980s and late 1990s. Individuals
with the least education experience a larger increase in their variance of permanent income
shocks in the 1980s than other education groups but in the late 1990s experienced a smaller
increase than other education groups. Individuals that graduated high school but did not
attend any college did not experience the cyclical pattern or spikes in transitory income the
other education groups experienced. The spikes in the variance of transitory income shocks
in the 2000s seem to be concentrated by education group. Individuals that dropped out of
high school experienced spikes in 2003 and 2007 while individuals with at least some college
experienced spikes in 2001 and 2009.
Figure D.3: Variance Income Shocks By Age Group
1970
1980
1990
year
2000
2010
Age =< 40
40 < Age < 55
Age >= 55
1970
1980
1990
year
Age =< 40
40 < Age < 55
Age >= 55
Permanent Income
Transitory Income
64
2000
2010
Table D.6: ESTIMATES VARIANCE PERMANENT INCOME SHOCK: AGE GROUPS
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Whole Sample
0.003
(0.069)
0.002
(0.077)
0.022
(0.001)
2.0E-05
(0.001)
0.003
(0.001)
0.015
(0.001)
0.001
(0.001)
0.032
(0.002)
0.006
(0.003)
0.001
(0.004)
0.004
(0.003)
2.0E-04
(0.002)
0.023
(0.001)
0.030
(0.002)
0.012
(0.002)
0.023
(0.002)
0.000
(0.002)
0.003
(0.002)
Age < 40
7.9E-05
(0.054)
2.0E-04
(0.061)
0.036
(0.000)
6.2E-09
(0.001)
0.001
(0.000)
0.016
(0.001)
3.4E-06
(0.001)
0.028
(0.005)
0.001
(0.007)
1.7E-05
(0.012)
2.7E-06
(0.008)
5.4E-07
(0.007)
0.032
(0.003)
0.022
(0.003)
1.2E-04
(0.004)
0.029
(0.002)
2.4E-07
(0.001)
3.4E-09
(0.002)
40 < Age < 55
0.001
(0.002)
0.001
(0.002)
0.020
(0.001)
0.000
(0.001)
0.001
(0.001)
0.019
(0.001)
4.6E-05
(0.001)
0.028
(0.002)
0.004
(0.002)
2.4E-04
(0.001)
0.003
(0.001)
1.2E-06
(0.002)
0.019
(0.003)
0.026
(0.002)
0.006
(0.002)
0.026
(0.004)
1.4E-07
(0.007)
2.4E-04
(0.007)
Age > 55
2.3E-05
(0.794)
1.1E-05
(0.034)
0.035
(0.001)
1.6E-08
(0.001)
5.6E-05
(0.001)
2.7E-04
(0.002)
8.6E-07
(0.000)
0.013
(0.002)
0.001
(0.002)
1.4E-05
(0.001)
0.012
(0.002)
3.5E-07
(0.001)
0.036
(0.002)
0.025
(0.003)
7.9E-05
(0.004)
0.035
(0.002)
7.7E-07
(0.001)
2.8E-05
(0.002)
Year
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1998
2000
2002
2004
2006
2008
2010
Whole Sample
0.020
(0.002)
0.016
(0.002)
0.003
(0.003)
0.023
(0.002)
0.008
(0.002)
0.006
(0.002)
0.025
(0.002)
0.011
(0.001)
0.016
(0.001)
0.013
(0.002)
0.123
(0.002)
0.120
(0.034)
0.117
(0.036)
0.132
(0.045)
0.010
(0.016)
0.004
(0.015)
0.060
(0.043)
0.005
(0.178)
Age <40
0.005
(0.003)
0.023
(0.002)
0.001
(0.003)
0.016
(0.003)
0.016
(0.003)
4.1E-07
(0.003)
0.026
(0.002)
0.018
(0.001)
0.060
(0.001)
0.014
(0.002)
0.071
(0.004)
0.127
(0.015)
0.107
(0.015)
0.091
(0.012)
1.9E-04
(0.003)
7.7E-06
(0.004)
0.001
(0.958)
0.001
(0.028)
40 < Age < 55
0.042
(0.002)
0.016
(0.001)
0.001
(0.001)
0.019
(0.001)
0.003
(0.000)
4.2E-04
(0.001)
0.004
(0.000)
0.001
(0.001)
0.004
(0.001)
0.006
(0.001)
0.117
(0.002)
0.119
(0.010)
0.101
(0.010)
0.128
(0.013)
0.012
(0.004)
0.007
(0.003)
0.078
(0.004)
0.003
(0.004)
Age > 55
0.009
(0.003)
0.042
(0.001)
0.001
(0.002)
0.022
(0.002)
0.006
(0.002)
4.3E-04
(0.002)
0.057
(0.001)
0.003
(0.002)
0.069
(0.001)
0.001
(0.002)
0.212
(0.004)
0.188
(0.068)
0.194
(0.109)
0.176
(0.108)
0.001
(0.008)
8.7E-05
(0.004)
0.082
(0.553)
6.8E-05
(0.004)
Notes: This table reports diagonally weighted minimum distance estimates of the variance of the permanent shock. Standard errors in
parentheses. The first specification is for the whole sample. The following three specifications correspond to age groups.
0
0
Variance Transitory Income Shock
Five Year Moving Average
.05
.1
.15
Variance Permanent Income Shock
Five Year Moving Average
.02
.04
.06
.08
Figure D.4: Variance Income Shocks By Education Group
1970
1980
1990
year
2000
2010
HS Dropout
HS Graduate
Atleast Some College
1970
1980
1990
year
HS Dropout
HS Graduate
Atleast Some College
Permanent Income
Transitory Income
65
2000
2010
Table D.7: ESTIMATES OF THE VARIANCE OF TRANSITORY INCOME SHOCKS: AGE GROUPS
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
Whole Sample
0.0011
(0.358)
0.004
(0.004)
0.0069
(0.002)
0.0011
(0.003)
0.0432
(0.003)
0.0511
(0.003)
0.0356
(0.003)
0.0242
(0.003)
0.0096
(0.006)
0.042
(0.012)
0.0573
(0.009)
0.0257
(0.004)
2.5E-07
(0.005)
0.0133
(0.005)
0.0101
(0.004)
0.028
(0.008)
0.0283
(0.007)
0.0381
(0.007)
0.0317
(0.006)
0.0378
(0.005)
0.0092
(0.001)
0.0075
(0.002)
Age < 40
3.4E-07
(0.202)
4.6E-04
(0.001)
1.7E-05
(0.002)
7.2E-06
(0.003)
0.0333
(0.002)
0.0284
(0.000)
0.0209
(0.001)
0.0269
(0.003)
0.0372
(0.016)
0.0417
(0.023)
0.043
(0.024)
0.0235
(0.003)
4.7E-15
(0.003)
0.018
(0.004)
1.6E-04
(0.005)
0.0307
(0.005)
0.0073
(0.003)
0.0064
(0.004)
0.0287
(0.010)
0.049
(0.010)
0.017
(0.002)
0.0274
(0.003)
40 < Age < 55
3.6E-06
(0.009)
5.4E-05
(0.003)
0.0088
(0.002)
1.2E-04
(0.001)
0.0312
(0.002)
0.0339
(0.003)
0.0223
(0.003)
0.0219
(0.005)
0.0033
(0.004)
0.0532
(0.004)
0.0618
(0.004)
0.0469
(0.006)
3.6E-12
(0.004)
0.0255
(0.006)
1.8E-05
(0.007)
0.0455
(0.009)
0.0391
(0.012)
0.0597
(0.014)
0.0285
(0.013)
0.0335
(0.009)
1.1E-04
(0.001)
0.0153
(0.002)
Age > 55
3.8E-12
(0.424)
2.5E-05
(0.010)
2.0E-05
(0.005)
4.3E-06
(0.007)
0.0652
(0.041)
0.1085
(0.063)
0.0972
(0.065)
0.0312
(0.017)
6.6E-04
(0.005)
0.0582
(0.046)
0.0633
(0.005)
0.014
(0.010)
2.9E-13
(0.025)
8.4E-05
(0.014)
2.3E-04
(0.001)
0.039
(0.004)
0.0528
(0.004)
0.0638
(0.016)
0.0305
(0.005)
0.0545
(0.004)
1.5E-04
(0.008)
0.0012
(0.009)
Year
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Whole Sample
0.0087
(0.001)
7.3E-04
(0.003)
0.0174
(0.003)
0.0028
(0.003)
0.0523
(0.005)
0.0145
(0.002)
0.0099
(0.004)
0.0012
(0.003)
2.3E-08
(0.016)
0.0035
(0.001)
6.7E-09
(0.015)
3.8E-04
(0.001)
0.0526
(0.021)
9.0E-08
(0.002)
0.0177
(0.000)
0.0044
(0.001)
4.7E-07
(0.000)
0.0073
(0.001)
0.138
(0.001)
0.0034
(0.025)
0.721
(0.004)
3.0E-08
(0.077)
Age <40
0.0031
(0.002)
2.8E-06
(0.005)
0.0038
(0.002)
2.5E-04
(0.001)
0.0648
(0.003)
0.0046
(0.003)
0.0055
(0.009)
2.2E-04
(0.008)
7.9E-16
(0.015)
3.0E-05
(0.002)
9.5E-16
(0.035)
6.8E-07
(0.003)
8.1E-08
(0.019)
1.2E-16
(0.002)
3.1E-04
(0.095)
6.6E-04
(0.009)
3.2E-12
(0.020)
1.9E-04
(0.002)
1.243
(0.044)
5.8E-04
(0.476)
0.0365
(0.042)
3.1E-13
(0.462)
40 < Age < 55
0.0054
(0.002)
1.6E-06
(0.002)
0.0207
(0.004)
2.3E-04
(0.001)
0.0569
(0.003)
0.0173
(0.002)
0.015
(0.003)
1.5E-05
(0.002)
5.7E-14
(0.010)
2.7E-04
(0.001)
1.0E-14
(0.010)
1.3E-05
(0.001)
0.0921
(0.016)
6.6E-15
(0.001)
0.4971
(0.006)
9.8E-04
(0.003)
1.1E-11
(4.032)
1.7E-04
(0.208)
0.7351
(0.000)
7.5E-04
(0.007)
0.7273
(0.000)
1.9E-14
(0.008)
Age > 55
0.0022
(0.021)
1.3E-05
(0.018)
0.024
(0.016)
2.8E-08
(0.018)
0.0595
(0.017)
0.0079
(0.009)
9.1E-04
(0.014)
2.1E-06
(0.012)
2.4E-14
(0.130)
0.0016
(0.001)
3.0E-15
(0.125)
1.1E-06
(0.002)
0.0018
(0.188)
6.2E-13
(0.002)
0.0283
(0.001)
4.4E-04
(0.001)
5.3E-12
(0.000)
6.0E-04
(0.001)
4.0928
(0.002)
1.9E-04
(0.258)
0.0013
(0.002)
1.8E-14
(0.259)
Notes: This table reports diagonally weighted minimum distance estimates of the variance of the permanent shock. Standard errors in
parentheses. The first specification is for the whole sample. The following four specifications correspond to age groups.
66
Table D.8: ESTIMATES VARIANCE PERMANENT INCOME SHOCK: EDUCATION GROUPS
Year
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
Whole Sample
0.003
(0.069)
0.002
(0.077)
0.022
(0.001)
2.00E-05
(0.001)
0.003
(0.001)
0.015
(0.001)
0.001
(0.001)
0.032
(0.002)
0.006
(0.003)
0.001
(0.004)
0.004
(0.003)
2.00E-04
(0.002)
0.023
(0.001)
0.030
(0.002)
0.012
(0.002)
0.023
(0.002)
0.000
(0.002)
0.003
(0.002)
HS Dropout HS Graduate At least some college
0.009
0.045
4.0E-04
(1.246)
(0.609)
(0.028)
0.006
0.000
0.003
(0.075)
(0.071)
(0.017)
0.005
0.002
0.019
(0.002)
(0.002)
(0.001)
0.017
0.018
3.3E-08
(0.001)
(0.001)
(0.001)
0.001
0.006
7.9E-07
(0.001)
(0.002)
(0.001)
0.016
0.001
0.008
(0.001)
(0.001)
(0.001)
3.6E-04
6.3E-05
1.1E-05
(0.001)
(0.002)
(0.001)
0.025
0.008
0.029
(0.001)
(0.002)
(0.003)
4.7E-04
9.6E-05
3.1E-04
(0.002)
(0.002)
(0.003)
0.001
0.012
2.4E-07
(0.002)
(0.002)
(0.004)
0.003
0.001
4.1E-05
(0.002)
(0.003)
(0.003)
0.001
2.3E-05
1.2E-06
(0.002)
(0.003)
(0.001)
0.025
0.004
0.030
(0.001)
(0.004)
(0.001)
0.042
0.026
0.025
(0.002)
(0.003)
(0.002)
0.003
0.001
0.018
(0.002)
(0.003)
(0.002)
0.056
0.013
0.029
(0.001)
(0.002)
(0.001)
0.001
7.7E-05
1.0E-10
(0.001)
(0.007)
(0.002)
0.037
0.017
2.2E-04
(0.001)
(0.008)
(0.001)
Year
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1998
2000
2002
2004
2006
2008
2010
Whole Sample
0.02
(0.002)
0.016
(0.002)
0.003
(0.003)
0.023
(0.002)
0.008
(0.002)
0.006
(0.002)
0.025
(0.002)
0.011
(0.001)
0.016
(0.001)
0.013
(0.002)
0.123
(0.002)
0.12
(0.034)
0.117
(0.036)
0.132
(0.045)
0.01
(0.016)
0.004
(0.015)
0.06
(0.043)
0.005
(0.178)
HS Dropout
0.014
(0.001)
0.010
(0.001)
0.023
(0.001)
0.012
(0.001)
0.007
(0.001)
0.000
(0.001)
0.043
(0.002)
0.002
(0.002)
0.068
(0.002)
0.000
(0.002)
0.133
(0.003)
0.076
(0.547)
0.098
(0.616)
0.057
(0.748)
3.3E-05
(0.001)
1.0E-04
(0.001)
0.071
(0.003)
0.009
(0.001)
HS Graduate
0.019
(0.009)
0.004
(0.005)
1.7E-04
(0.003)
1.7E-04
(0.002)
1.3E-04
(0.001)
0.001
(0.003)
0.005
(0.002)
0.009
(0.002)
0.049
(0.003)
0.003
(0.002)
0.108
(0.003)
0.154
(0.103)
0.103
(0.102)
0.097
(0.108)
0.004
(0.056)
0.018
(0.06)
0.071
(0.016)
3.4E-08
(0.036)
At least some college
0.027
(0.001)
0.032
(0.002)
0.004
(0.001)
0.028
(0.002)
0.018
(0.001)
1.1E-06
(0.001)
0.011
(0.001)
3.1E-06
(0.001)
0.016
(0.001)
0.004
(0.001)
0.119
(0.002)
0.131
(0.016)
0.136
(0.017)
0.126
(0.02)
0.001
(0.018)
3.4E-04
(0.022)
0.094
(0.245)
3.4E-07
(1.605)
Notes: This table reports diagonally weighted minimum distance estimates of the variance of the permanent shock. Standard errors in parentheses. The first
specification is for the whole sample. The following three specifications correspond to education groups.
Table D.9: ESTIMATES OF THE VARIANCE OF TRANSITORY INCOME SHOCKS: EDUCATION
Year
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
Whole Sample
0.001
(0.358)
0.004
(0.004)
0.007
(0.002)
0.001
(0.003)
0.043
(0.003)
0.051
(0.003)
0.036
(0.003)
0.024
(0.003)
0.01
(0.006)
0.042
(0.012)
0.057
(0.009)
0.026
(0.004)
1.0E-04
(0.005)
0.013
(0.005)
0.010
(0.004)
0.028
(0.008)
0.028
(0.007)
0.038
(0.007)
0.032
(0.006)
0.038
(0.005)
0.009
(0.001)
0.008
(0.002)
HS Dropout HS Graduate At least some college
1.0E-04
0.002
1.0E-04
(0.684)
(0.02)
(0.095)
0.068
0.002
0.001
(0.008)
(0.0001)
(0.005)
0.034
0.0001
0.0001
(0.003)
(0.0001)
(0.002)
0.055
0.004
0.0001
(0.006)
(0.001)
(0.002)
0.039
0.002
0.027
(0.003)
(0.001)
(0.002)
0.041
0.002
0.038
(0.006)
(0.0001)
(0.003)
0.053
0.001
0.028
(0.005)
(0.0001)
(0.002)
0.0001
0.003
0.03
(0.007)
(0.001)
(0.003)
0.006
0.003
0.001
(0.012)
(0.0001)
(0.012)
0.002
0.002
0.068
(0.006)
(0.001)
(0.014)
0.067
0.001
0.037
(0.011)
(0.001)
(0.005)
0.043
0.004
0.01
(0.013)
(0.001)
(0.003)
0.0001
0.0001
1.0E-04
(0.012)
(0.0001)
(0.004)
0.035
0.002
0.001
(0.012)
(0.001)
(0.005)
0.006
0.002
0.001
(0.001)
(0.001)
(0.004)
0.005
0.004
0.026
(0.002)
(0.001)
(0.006)
0.008
0.003
0.014
(0.001)
(0.001)
(0.004)
0.008
0.003
0.009
(0.002)
(0.002)
(0.005)
0.0001
0.003
0.034
(0.001)
(0.002)
(0.006)
0.002
0.003
0.045
(0.001)
(0.001)
(0.003)
0.041
0.001
0.003
(0.008)
(1.0E-04)
(1.0E-04)
0.041
0.0001
0.002
(0.011)
(1.0E-04)
(1.0E-04)
Year
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
Whole Sample
0.009
(0.001)
0.001
(0.003)
0.017
(0.003)
0.003
(0.003)
0.052
(0.005)
0.015
(0.002)
0.01
(0.004)
0.001
(0.003)
1.0E-04
(0.016)
0.004
(0.001)
1.0E-04
(0.015)
1.0E-04
(0.001)
0.053
(0.021)
1.0E-04
(0.002)
0.018
(0.0001)
0.004
(0.001)
1.0E-04
(0.0001)
0.007
(0.001)
0.138
(0.001)
0.003
(0.025)
0.721
(0.004)
1.0E-04
(0.077)
HS Dropout
0.013
(0.004)
0.017
(0.005)
0.038
(0.012)
0.064
(0.013)
0.077
(0.022)
0.03
(0.006)
0.016
(0.009)
0.001
(0.01)
0.0001
(0.035)
0.0001
(0.001)
1.0E-04
(0.04)
0.005
(0.001)
0.001
(0.059)
1.0E-04
(0.001)
0.027
(0.013)
0.006
(0.001)
1.0E-04
(0.928)
0.0001
(0.011)
0.011
(0.003)
0.025
(0.283)
0.0001
(0.003)
1.0E-04
(0.282)
HS Graduate
0.001
(0.001)
0.003
(0.001)
0.0001
(0.001)
0.003
(0.001)
0.004
(0.001)
0.003
(1.0E-04)
1.0E-04
(0.001)
1.0E-04
(0.019)
1.0E-04
(0.002)
1.0E-04
(0.028)
1.0E-04
(0.002)
0.0001
(0.031)
0.001
(0.003)
1.0E-04
(0.04)
0.002
(0.003)
0.009
(0.041)
1.0E-04
(0.004)
0.005
(0.054)
0.005
(0.015)
0.001
(0.028)
0.001
(0.018)
1.0E-04
(0.038)
At least some college
0.001
(1.0E-04)
1.0E-04
(1.0E-04)
0.001
(1.0E-04)
1.0E-04
(1.0E-04)
0.076
(0.005)
0.02
(0.002)
0.003
(0.004)
0.001
(0.003)
1.0E-04
(0.023)
1.0E-04
(0.001)
1.0E-04
(0.02)
1.0E-04
(0.001)
0.117
(0.029)
1.0E-04
(0.001)
0.001
(0.011)
0.001
(0.001)
1.0E-04
(0.066)
0.003
(0.002)
1.0E-04
(0.004)
0.001
(0.115)
1.826
(0.024)
1.0E-04
(0.689)
Notes: This table reports diagonally weighted minimum distance estimates of the variance of the permanent shock. Standard errors in parentheses. The first
specification is for the whole sample. The following four specifications correspond to education groups.
67
D. 3
Partial Insurance
This appendix reports the partial insurance parameters by age and education group. Table
D.10 reports the general trend found in the whole sample that insurance initially decreased
and then increased is robust across age groups. Individuals fifty-five and older typically have
the most insurance from both permanent and transitory income shocks, which is consistent
with their ability to self-insure out of accumulated assets. Interestingly, individuals between
forty and fifty-five do not always have more insurance than individuals forty or younger.
Table D.11 reports the partial insurance parameters by education group. The partial
insurance parameter for permanent income shocks is not consistently statistically significant
for high school dropouts or high school graduates. Individuals with at least some college
experience a similar trend in the partial insurance to permanent income as found with the
whole sample. All education groups report similar trends in their partial insurance from
transitory income shocks as found with the whole sample. The trend is most pronounce for
individuals with at least some college and least pronounced for individuals that dropped out
of high school.
D. 4
Decomposition
Changes in insurance to income shocks may be due to several factors. First, the period from
1968 to 2010 features several large tax policy changes, notably the tax reform act of 1986,
the Revenue Reconciliation Act of 1993 and the Jobs and Growth Tax Relief Reconciliation
Act of 2003.61 These tax policy changes may have changed the extent of automatic (or
structural) stabilization from tax policy. Second, changes towards more unequal income
distribution may have changed the effectiveness of existing automatic stabilizers. Third,
given the increase in the variance of permanent income shocks reported in Table D.4, one
would expect an increase in insurance due to behavioral responses of risk averse (or inequality
averse) individuals.
To quantify the specific contribution of these effects on the insurance to income shocks,
we decompose the change in insurance using the definition of insurance described by equation
(14). A positive sign means an increase in insurance. The difference in insurance against
permanent income shocks can be explained by one of three mechanisms: policy changes,
market changes, or behavioral changes. By taking the difference across two period of this
equation and rearranging this difference, we can quantify these effects using our DWMD
estimates in the following way,
61
Auerbach (2009) refers to the countercyclical tax packages in the 2000s, and especially during the
financial crisis, as a period of “revival of tax policy activism,” referring to 1980s.
68
Table D.10: ESTIMATES PARTIAL INSURANCE
Year
Whole Sample
Age < 40
Panel A: Partial Insurance Permanent Shock φ
1968 - 1980
0.008
0.012
(0.023)
(0.045)
1981 - 1986
0.043
0.884
(0.058)
(0.056)
1987 - 1992
0.882
0.86
(0.096)
(0.065)
1993 - 2002
0.055
0.234
(0.012)
(0.025)
2003 - 2010
0.129
-0.642
(0.023)
(0.003)
Panel B: Partial Insurance Transitory Shock ψ
1968 - 1980
0.141
0.218
(0.021)
(0.017)
1981 - 1986
0.581
0.406
(0.086)
(0.09)
1987 - 1992
1.111
0.807
(0.089)
(0.021)
1993 - 2002
0.437
0.246
(0.059)
(0.037)
2003 - 2010
7.4E-05
1.0E-04
(0.148)
(1.628)
40 < Age < 55 Age > 55
0.262
(0.037)
0.756
(0.012)
3.086
(0.046)
0.157
(0.01)
0.474
(0.003)
0.001
(0.041)
0.43
(0.015)
0.492
(0.01)
0.038
(0.014)
0.472
(0.175)
0.156
(0.012)
0.088
(0.008)
1.079
(0.205)
0.491
(0.032)
-0.001
(0.009)
0.149
(0.108)
0.321
(0.033)
0.004
(0.041)
0.155
(0.052)
1.0E-04
(0.832)
Notes: This table reports diagonally weighted minimum distance (DWMD) estimates
of the partial insurance parameters. Panel A reports the partial insurance parameters
for permanent income shocks and Panel B reports the partial insurance parameters for
the transitory income shocks. The partial insurance parameters for the whole sample
are reported in column 1 and columns 2-4 report the estimates for each age group.
Standard errors are calculated using the method proposed by Gary Chamberlain (1984)
and are reported in parentheses.
69
Table D.11: ESTIMATES PARTIAL INSURANCE
Year
Whole Sample
HS dropout
HS graduate
Panel A: Partial Insurance Permanent Shock φ
1968 - 1980
0.008
-0.001
0.009
(0.023)
(0.034)
(0.136)
1981 - 1986
0.043
-0.011
0.114
(0.058)
(0.022)
(0.092)
1987 - 1992
0.882
-0.161
-0.102
(0.096)
(0.059)
(0.573)
1993 - 2002
0.055
0.003
-0.021
(0.012)
(0.019)
(0.013)
2003 - 2010
0.129
2.182
0.043
(0.023)
(0.020)
(0.016)
Panel B: Partial Insurance Transitory Shock ψ
1968 - 1980
0.141
0.132
0.818
(0.021)
(0.012)
(0.226)
1981 - 1986
0.581
1.655
1.304
(0.086)
(0.016)
(0.099)
1987 - 1992
1.111
0.350
2.165
(0.089)
(0.071)
(0.202)
1993 - 2002
0.437
0.228
0.061
(0.059)
(0.066)
(0.062)
2003 - 2010
7.4E-05
-0.009
0.045
(0.148)
(0.139)
(0.018)
At least some college
-0.023
(0.024)
0.597
(0.026)
1.127
(0.146)
0.116
(0.011)
0.111
(0.282)
0.161
(0.009)
-0.014
(0.010)
4.062
(0.003)
0.329
(0.033)
1.0E-04
(0.526)
Notes: This table reports diagonally weighted minimum distance (DWMD) estimates of the
partial insurance parameters. Panel A reports the partial insurance parameters for permanent
income shocks and Panel B reports the partial insurance parameters for the transitory income
shocks. The partial insurance parameters for the whole sample are reported in column 1 and
columns 2-4 report the estimates for each education group. Standard errors are calculated using
the method proposed by Gary Chamberlain (1984) and are reported in parentheses.
70
∆(1 − φ) = φM,2 S2M + φP,2 S2P − φM,1 S1M − φP,1 S1P
+ φM,1 S2M + φP,1 S2P − φM,1 S2M − φP,1 S2P
=
φP,1 (S2P
|
S1P ) + φM,1 (S2M
S1M ) + S2M (φM,2
|
|
−
{z
}
∆ Policy
−
{z
}
∆ Market
(D.1)
S2P (φP,2
− φM,1 ) +
{z
∆ Beh.
− φP,1 ),
}
which reframes equation (15) in terms of the partial insurance parameters. This decomposition also allows for additional control variables to be included. In the baseline results
the variance of permanent and transitory income shocks are used as control variables and
the results are robust to excluding them and also including dummy variables for income,
age, and education group.
The decomposition for the insurance of transitory income shocks is reported in Table
D.12. Over the full sample the insurance to transitory income shocks increased slightly by
0.086, however this is a result of a substantial decrease in insurance (−0.917) in the first
half of the sample and a slightly larger increase in insurance (1.048) in the later half of
the sample. Similar to the results for the permanent income shock tax policy decreased
the insurance over the full sample and both subperiods with the larger decrease occurring
in the first half of the sample. Changes in the income distribution increased the insurance
similarly in both subperiods. Behavioral changes increased insurance over the full period
but decreased insurance in the first half of the sample and increased insurance in the later
half. All of these findings are consistent with the evidence from the permanent income shock
decomposition reported in Table 4.
71
Table D.12: DECOMPOSITION PARTIAL INSURANCE OF TRANSITORY INCOME SHOCKS
Whole Sample
Panel A: Difference 1968-1980 and 2003-2010
0.086
(0.01)
Policy Effect φP ∆S P
-0.769
(0.012)
Market Effect φM ∆S M
0.236
(0.015)
Behavioral Effect S P ∆φP + S M ∆φM
0.619
(0.025)
Panel B: Difference 1968-1980 and 1986-1992
-0.917
(0.008)
Policy Effect φP ∆S P
-0.356
(0.005)
Market Effect φM ∆S M
0.178
(0.011)
Behavioral Effect S P ∆φP + S M ∆φM
-0.739
(0.017)
Panel C: Difference 1986-1992 and 2003-2010
1.048
(0.085)
Policy Effect φP ∆S P
-0.097
(0.56)
Market Effect φM ∆S M
0.153
(0.004)
Behavioral Effect S P ∆φP + S M ∆φM
0.992
(0.476)
Income
Bottom
Q2
-0.631
0.692
(0.193) (3.759)
-1.186
-0.116
(0.067) (0.002)
0.891
0.087
(0.067) (0.004)
-0.336
0.721
(0.212) (3.758)
0.089
0.016
(0.039) (0.046)
-0.279
-0.063
(0.017) (0.001)
0.512
0.061
(0.04) (0.003)
-0.144
0.018
(0.066) (0.046)
-0.022
0.829
(0.088) (0.94)
0.032
-0.303
(0.156) (4.869)
0.275
0.167
(0.06)
(0.75)
-0.328
0.965
(0.176) (4.707)
Quartiles
Q3
0.389
(1.892)
-0.517
(0.008)
0.242
(0.01)
0.664
(1.891)
-0.896
(0.006)
-0.372
(0.004)
0.209
(0.009)
-0.734
(0.013)
1.086
(0.506)
0.038
(1.262)
0.085
(0.149)
0.963
(0.907)
Top
0.653
(8.465)
-0.182
(0.003)
0.046
(0.002)
0.79
(8.466)
0.482
(0.034)
-0.136
(0.002)
0.044
(0.002)
0.574
(0.035)
0.197
(3.538)
-0.06
(6.415)
0.018
(0.193)
0.238
(10.103)
Notes: This table reports the decomposition of the change in the partial insurance parameter for transitory
income shocks. Panel A decomposes the change in partial insurance parameter between the time period 19681980 and 2002-2010. Panels B and C decompose this change into two smaller time changes to take into account
the numerous tax reforms in this time period, notably the tax reform act of 1986. The decomposition is performed
on the whole sample (column 1) and each income quartile (column 2 - column 5). Bootstrapped standard errors
are reported in parenthesis.
72