A structured approach to testing the stability of
individual preferences∗
Nicolás Salamanca†
November 2013
Abstract
The stability of preferences is central to economic analysis but is difficult to test
empirically. I develop a simple model which can be used as a framework to test
it. The model captures four important features related to the stability of preferences: (1) Systematic variation (i.e., as predicted by observables) in preference
changes, (2) autoregressive variation, (3) severity of idiosyncratic shocks (i.e., preference changes unexplained by other factors), and (4) measurement error. I use
this model to test the stability of risk aversion, patience, and conscientiousness in a
Dutch panel dataset. The results show that: (1) observable characteristics predict
little of the change in any of the preferences; (2) patience and conscientiousness can
be considered as time-invariant while risk aversion cannot; (3) idiosyncratic shocks
to patience are more severe than shocks to risk aversion and conscientiousness; and
(4) there is substantial error in the measurement of all preferences, but especially
of risk aversion. I find evidence of heterogeneity in stability across gender, family composition and marital status. There is also some evidence that controlling
for unobserved individual heterogeneity explains most of autoregressive variation
in the studied preferences. Implications of these findings for economic analysis are
discussed.
JEL classification: D01; D03; C18
Keywords: Economic preferences; personality traits; measurement error; autoregressive process
∗
The core ideas of this paper were partly developed in my master thesis “The Stability of Personality
Traits and Economic Preference Parameters,” and I owe thanks to Denis de Crombrugghe and Bart
Golsteyn for supervising it. I have also received helpful comments from Thomas Dohmen, Jan Feld, Dan
Hamermesh, Simon Georges-Kot, Andries de Grip, Paul Smeets, Maria Zumbül, and participants in an
internal seminar at Maastricht University. In this paper use is made of data of the DNB Household
Survey.
†
Research Center for Education and the Labour Market (ROA), Maastricht University, 6211 LM,
Maastricht, The Netherlands. Tel.: +31 43 388 3647; fax: +31 43 388 4914. e-mail address:
[email protected]
I.
Introduction
Economists and social psychologists generally assume that economic preferences and personality traits are stable. This stability assumption matters tremendously for economic
analysis since it simplifies models and makes them tractable. Yet time variation of economic preferences and in personality traits is easy to imagine. For example, as people
age their ideas of how much risk they like to take will probably change. Also, abrupt
situational changes such as the death of a loved one could render people more neurotic or
less open to experiences.
In some sense the stability assumption has held up over the years because it is convenient. Another reason for the assumption to go unchallenged is that it is difficult to test
it. The concept of stability itself has several interpretations (over time, rank-order, with
respect to life events) and finding parameters that directly reflect them is not straightforward. In addition, most measures of preferences and personality are plagued with
measurement error and thus it is difficult to tell whether changes in expressed preferences
over time are a result of measurement error or of actual changes in preferences. There are
remarkably few economic studies that attempt to test the stability of preferences. There
are more psychology studies that question whether personality traits are stable, but their
attempts to test for stability suffer from the same difficulties. In essence, these economists
and psychologists are asking the same question: Are preferences and personality traits
stable? This paper provides a structured framework to answer to this question.
I develop a model to determine the stability of economic preferences and personality
traits, which I will simply refer to jointly as preferences. The model has parameters
that capture several key features related to preferences and preference stability. First,
systematic variation (i.e., as predicted by observables) in the changes of preferences is
captured by a drift term. The drift parameters will therefore contain information on how
1
preference correlate to other observables. Second, variation over time in latent preferences
is modeled as a simple autoregressive process with an idiosyncratic error term. The
autoregressive parameter captures how preferences evolve for each person over time on
average. Third, the variance of the idiosyncratic shock captures another facet of stability:
How large are the deviations of preferences from their conditional mean. Finally, the
model also incorporates measurement error in stated preferences.
Using data from the DNB Household Survey, I illustrate the use of this model by
testing the stability of two key economic preferences, risk aversion and patience, and one
important personality trait, conscientiousness. The model’s estimates provides various
insights. First, the socioeconomic characteristics in the drift term are relatively unimportant or predicting changes in all three preferences. Second, the autoregressive parameters
show that all three constructs change slowly over time. Statistical tests of these parameters suggest that patience and conscientiousness can be considered as conditionally
time-invariant while risk aversion cannot. Third, the variance of the idiosyncratic shocks
to patience is larger than those to risk aversion and conscientiousness, which suggests that
patience is less stable in the sense that is more likely to be farther away from its conditional mean at any one point in time. Finally, the model estimates suggest that there is
substantial error in the measurement of all three preferences, but that measurement error
is most severe for risk aversion. Comparing the estimates across subgroups defined by
gender, marital status and having a child suggests that there is some heterogeneity in the
stability of preferences. Estimating the model using dynamic panel data methods suggest
individual unobserved heterogeneity captures most of the time-dependence in preferences.
These results have important implication for empirical analyses of preferences. First
of all, preference measures can go “stale”. Assuming stability in preferences could lead to
wrong inferences when they are not measured simultaneously with the decisions they are
supposed to explain. Second, the result that risk preferences vary over time has important
2
implications for asset pricing models and for the design of investment products that try to
match investment strategies to individual risk preferences, such as individual investment
accounts and certain pension arrangements. Finally, the empirical findings in this paper
and a more widespread application of its model could improve preference measurement
by guiding survey design to less noisy preference measures.
The positive variance of idiosyncratic shocks in patience also has an important implication: Stability over time is not the whole story. Preferences that seem to be completely
time-stable could also suffer from large shocks. This means that for preferences with a
large idiosyncratic variance, such as patience, there is a larger chance that the actual
preference level is far away from the conditional level. Taken together, the results in this
paper suggest that, unless thoroughly controlling for individual unobserved heterogeneity, assuming stability in preferences can lead to wrong inferences. They also underscore
the importance of accounting for measurement error in preferences, especially in settings
where the dynamics of preferences and errors might play a role.
There are few studies in economics that deal with the stability of economic preferences
(Borghans et al., 2008). Most of the existing literature studies correlations between various observable characteristics and measures of risk preferences (e.g., Barsky et al., 1997;
Harrison et al., 2007; Dohmen et al., 2011), time preferences (e.g., Green et al., 1994;
Harrison et al., 2002; Read and Read, 2004), or personality traits (e.g., Nyhus and Pons,
2005; Löckenhoff et al., 2009; Terracciano et al., 2010).1 Only recently here have been
studies that explicitly look at the reasons why preferences can change. Malmendier and
Nagel (2011) show that past experienced stock returns affect a person’s current risk aver1
In a way, psychologists have been thinking about personality trait stability in a more structured way
than economists have been thinking about the stability of economic preferences. First, they have long
acknowledged at least four different types of stability in personality traits: intra-individual consistency,
ipsative consistency, mean level consistency, and rank-order consistency (see e.g., Block and Robins
(1993)). Second, they have thought about different models of personality formation (see e.g., Roberts
et al. (2006)). Third, they have studied it longer (since at least Schaie and Parham (1976)). Empirically,
they typically research the relation between changes in personality and other observable characteristics.
In economics, this approach is only recently becoming popular.
3
sion. Hoffmann et al. (2013) and Guiso et al. (2013) find similar relation triggered by the
financial crisis of 2007. Sahm (2012) also shows that age and macroeconomic conditions
also correlate with risk aversion, but that persistent differences across individuals account
for the majority of the variation. Krupka and Stephens (2010) use microeconomic panel
data to show that changes in expressed individual time preference are correlated with the
business cycle and other socioeconomic changes. Meier and Sprenger (2010), also using
panel data, sustains that time preferences are unchanging.2
A few studies have looked at the stability of preferences in a more structured way.3
Becker and Mulligan (1997) develop a theoretical foundation for “endogenous” (and thus
possibly time-varying) time preferences and they show some macroeconomic evidence
consistent with their hypothesis. More recently Cobb-Clark and Schurer (2013) look
at the stability of locus of control, another personality trait that has been extensively
researched in economics. They consider locus of control as stable but measured with
error and find no evidence suggesting its instability.4 This paper is closest to my work in
the sense that I ask a similar question. My framework, however, takes a more structural
approach and can be used to test the stability of any type of preference, allowing for
more flexibility than in Becker and Mulligan (1997). I also show how to estimate various
structural parameters that provide an unambiguous and straightforward way of testing
for the stability of preferences. Finally, I test the stability of risk aversion and patience
which are the cornerstone of economic analysis. These findings provide a strong baseline
to determine how stable economic preferences really are in other data.
The remainder of the paper is organized as follows. Section 2 develops the model of
time-varying preferences and shows how to estimate its parameters. Section 3 estimates
2
The correlates of preferences and personality traits and how they are affected by life events are
investigated in a similar way by Salamanca (2010).
3
There are some preference formation models adapting classical economic investment models to preferences and skills (e.g., Cunha and Heckman, 2007; Borghans et al., 2008).
4
A shorter companion paper, Cobb-Clark and Schurer (2012), performs a similar analysis for all the
Big Five, including conscientiousness.
4
the model for risk aversion, patience and conscientiousness, and provides several specification checks and ancillary evidence supporting the identification strategy. Section 4
concludes.
II.
Model
Let me abstract from any one specific individual preference and describe the model for a
preference P . Let person i’s measured level of this preference at time t be written as Pit .
Also, let Pit∗ be the latent individual preference. I model the individual preference process
in these terms via the following two equations:
Pit = Pit∗ + εit
(1)
∗
Pit∗ = g(Xit ) + αPi,t−1
+ ηit
(2)
Equation (1) defines the observed preference Pit as the sum of the latent preference
Pit∗ and a measurement error term εit . This measurement error is assumed to be classical
(i.e., heteroscedastic, independent of Pit∗ and serially uncorrelated) although other error
structures (such as autocorrelated measurement error) can also be accommodated.
Equation (2) defines the evolution of the latent preference Pit∗ as an AR(1) autoregressive process with a drift g(Xit ), which depends on the vector of individual characteristics
Xit . For simplicity, I assume g(Xit ) is linear in parameters, although none of the result
and intuitions depend on this assumption.5 The drift allows preferences to tend towards
an “equilibrium” level which can be correlated with observable characteristics. The economic interpretation of the drift could be the level to which preferences tend once their
5
More complicated autoregressive preference structures, such as an AR(2) process, can also be accommodated. However, they complicates the extraction of formulas for the variances and do not add to the
model empirically. In an AR(2) model, both autoregressive coefficients are insignificant.
5
autocorrelation has been accounted for.6 The error term ηit represents the idiosyncratic
shocks to the latent preference Pit∗ .
The three sets of model parameters that provide useful information about the preference process are g(Xit ), α, and the variances of ηit and εit . The drift parameters (the
coefficients estimates of Xit ) will be informative as to what affects the conditional level
to which preferences tend. The autoregressive parameter, α, shows the intra-individual
consistency of Pit∗ ; how close are the current latent preferences to the past latent preferences. The variance of ηit , the idiosyncratic shocks, contains information on how severe
are variations in latent preferences, which is another important facet of stability. The
variance of εit will quantify the measurement error in preferences.
To estimate these parameters, begin by replacing (1) in (2) to obtain:
Pit = g(Xit ) + αPi,t−1 + ηit + εit − αεi,t−1 .
(3)
Estimates of g(Xit ) and α can be directly obtained from (3). However, an ordinary least
squares regression will not work since Pi,t−1 and εi,t−1 are correlated. To obtain consistent
estimates of the parameters, I use the moment conditions E[Pij (Pit −g(Xit )−αPi,t−1 )] = 0
for j = 0, . . . , t − 2 in a Generalized Method of Moments (GMM) estimation. These are
the moment conditions implied in an instrumental variable (IV) approach. Instrumenting
for Pi,t−1 is a key step in this process to obtain consistent estimates of both α and g(Xit ).7
To derive expressions for the variance of ηit and εit it will be simpler to work with the
6
The presence of the drift makes it simpler to see that time-varying preferences under this process
will tend to a non-zero level. However, it is not needed; one could simply write the model in terms of
de-drifted preferences. Carroll and Samwick (1997) take this approach when calculating the variance of
permanent income. If the drift is correlated with the lagged preferences, however, de-drifting the process
without including lagged preferences as an additional explanatory variable will result in biased estimates
of the drift parameters.
7
More complicated autoregressive structures require adding further lags of Pit to the regression, and
so the instruments have to be adjusted accordingly. However, the lag choice for the instruments does
not seem to matter empirically; in unreported analysis I observed that choosing more distant lags as
instruments does not affect the main results.
6
de-drifted preference, P̃it∗ , which is Pit∗ net of the drift g(Xit ). Taking the k th difference of
P̃it and replacing recursively yields:
∗
P̃i,t+k − P̃it = P̃i,t+k
+ εi,t+k − P̃it∗ − εit
∗
= αP̃i,t+k−1
+ ηi,t+k + εi,t+k − P̃it∗ − εit
..
.
k
= (α −
1)P̃it∗
+
k
X
αj ηi,t+k−j + εi,t+k − εit .
j=0
Replacing P̃it∗ and rearranging terms, results in:
k
P̃i,t+k − P̃it = (α − 1)P̃it +
k
X
αj ηi,t+k−j − αk εit + εi,t+k ,
j=0
which simplifies to
k
P̃i,t+k − (α )P̃it =
k
X
αj ηi,t+k−j − αk εit + εi,t+k
(4)
j=0
= ϑi,t+k .
In Equation (4), ϑi,t+k represents the collection of all the error and noise terms. The
left-hand side of (4) is expressed completely in terms of observable measures of P̃i,t and the
parameter α, for which I have a consistent estimator. Therefore, I can obtain estimates
of ϑi,t+k for every k as long as there is data for periods t and t + k.
To calculate the variances of εt and ηt I simply take the variance on both sides of
Equation (4):
7
2
σϑ,k
k
X
= V ar(
αj ηi,t+k−j − αk εit + εi,t+k )
j=0
= ση2
k
X
(5)
α2j + σε2 (α2k + 1).
j=0
Equation (5) shows how the variances an be obtained as the solutions to a two-unknown
equation system. This procedure is an extension of the technique used to identify the
variance of permanent income of Carroll and Samwick (1997). I can identify ση2 and σε2 by
taking two different k–lengths. For example, for k = 1, 2, the two equations to be solved
are:
2
σϑ,1
= (α2 + 1)(ση2 + σε2 )
2
σϑ,2
=
2
X
α2j ση2 + (α4 + 1)σε2
j=0
An efficient estimator of ση2 and σε2 can be constructed by combining the information of
all k–lengths in a linear regression and obtaining the variances as regression parameters (of
course constraining them to be positive). Once this is done, I will have consistent estimates
of g(Xit ), α, and both variances. Importantly, the noise-to-signal ratio (Cameron, 2005, p.
903) can also be estimated from σε2 . Since Pit can be standardized to have unit variance,
the noise-to-signal ratio can be estimated as s = σε2 /(1−σε2 ), which is a comparable metric
of the amount of measurement error in preferences.
8
III.
The stability of risk tolerance, patience, and conscientiousness
A.
General stability
I estimate this model using data from the Dutch National Bank Household Survey (DHS).
The DHS is a yearly panel survey that has been running on a representative sample of
Dutch households since 1993. In the survey, every household member over the age of
16 answers a number of questions about the household organization, education, work
situation and labor income, assets and liabilities, health, and economic and psychological
concepts. The DHS is also used in e.g., Guiso et al. (2008), Kapteyn and Teppa (2011)
and Salamanca et al. (2013). On average, about 2,000 households (4,500 people) are
interviewed each year, and each household stays in the panel for about seven and a half
years on average.
I estimate the model separately for risk aversion, patience, and conscientiousness (a
personality trait belonging to the Big Five, a prominent personality inventory in psychology; see Goldberg (1993)). The DHS measures these three preferences by asking the
respondents to rate their agreement with several statements for each preference on discrete
scales. Risk aversion is measured through 6 items asked between 1994 and 2011. The
items are mainly about financial risk attitudes and behavior so the index should be interpreted as measuring financial risk aversion. Patience is measured through 10 items asked
between 1996 and 2007 and they capture trade-offs between present and future rewards
and pains, and general future-oriented thinking. Conscientiousness is measured through
10 items asked between 2004 and 2011 aimed at capturing a thorough and diligent personality.8 These measures of risk aversion and patience have been behaviorally validated
8
The DHS also contains measures of the other Big Five (Openness, Extraversion, Agreeableness and
9
in several studies such as Warneryd (1996), Borghans and Golsteyn (2006), Kapteyn and
Teppa (2011), and Salamanca et al. (2013), and the items for conscientiousness have been
obtained from the International Personality Item Pool, a popular repository of personality
measures. Tables 1, 2 and 3, provide details and summary statistics on the individual
items constituting each preference index, together with information on the variables in
Xit : Income, financial wealth, age, gender, marital status and family composition. They
show that there is significant variation in the scores of the individual items composing
the indices and, in the case of Table 1, that there is negative skewness in most of the risk
aversion items. They also show that all three estimation samples are very similar in terms
of the observables in Xit , suggesting that there is no systematic selectivity in observables
across samples.
I construct an index for each preference by reversing the items that measure the
trait negatively and then adding up the trait’s individual item scores.9 Figures 1 to 3
show the distribution of the constructed preference indices and figures 4 to 6 show the
distribution of their one-year changes. The figures show there is substantial heterogeneity
in all indices. This indicates that the underlying preferences are potentially time-varying,
although part of the one-year change variability could be due to measurement error. The
figures also show that, with the exception of risk aversion, the preference indices seen
normally distributed.10 For all the subsequent analyses I standardize the indices so they
have zero mean and a standard deviation of unity over their respective estimation samples
to simplify the interpretation of the results. The interpretation of the autoregressive
Neuroticism), as well as measures on economic locus of control (Rotter, 1966; Furnham, 1986). However,
the other Big five traits are only measured in 2005 and 2009 and economic locus of control is measured
in 2005-2007 and 2009.
9
Taking the first eigenvector as the index for each construct yields near identical results; the correlations between the sum index and the first eigenvector is above 0.99 for all constructs.
10
The right-censored shape of the distribution of risk aversion shows that there is a non-negligible
amount of people (about 5 percent of the estimation sample) that would prefer not taking any financial
risk. These people’s risk attitudes could be modeled in a different setting (e.g., a discrete choice model).
The main results do not change substantially if I exclude non-risk-takers from the analyses.
10
coefficient does not change because of this, but the effect of observables on preferences
and the variances of the error terms are now more easily compared across preference
measures.
Table 4 shows the estimates of g(Xit ), α, ση2 , σε2 and the noise-to-signal ratio (s) for
risk aversion, patience, and conscientiousness in Columns (1), (2), and (3), respectively.
For these estimations g(Xit ) is linear in Xit , which includes log-income, log-wealth, age,
and dummies for zero reported income and financial wealth, for women, for having a child,
and for being married.11 I use Pi,t−2 , Pi,t−3 and Pi,t−4 as instruments for Pi,t−1 .
The top panel of Table 4 shows the drift coefficient estimates of Xit . Note that the
coefficients here should be interpreted as the marginal effect of Xit given the preference
level in the previous period. Thus, they reflect the way that Xit relate to the evolution
of Pit on top of what its autoregressive process predicts.12 The main message is that,
after accounting for the autocorrelation in preferences, the drift variables are mostly
uncorrelated with the evolution of preferences. These findings are similar to what CobbClark and Schurer (2013) and Cobb-Clark and Schurer (2012) find for various personality
traits, including conscientiousness. The exception is the negative relation between risk
aversion and wealth. People who report having no wealth are particularly risk-averse, and
risk aversion also decreases as wealth increases. The coefficient of the zero-wealth dummy
can be explained if some risk-averse people believe that reporting their assets in a survey
entails some risk in terms of data misuse or a violation of their privacy. However, this
might truly be a wealth effect on risk aversion since those who report no wealth also report
significantly lower income, are less likely to report positive income, and are more likely to
be married and women. The positive coefficient on log-wealth suggests increasing relative
or absolute risk aversion, although economically the effect is tiny. The changes in patience
11
Below I also show non-parametric estimations of the relation between these preferences and income,
wealth and age.
12
Because of this, the coefficients are closer to the effect of Xit on the changes of Pit rather that its
level.
11
and conscientiousness are only very weakly predicted by the observable characteristics.
The second panel of Table 4 shows the estimates of α, the autoregressive parameter.
The estimates can essentially be interpreted as the stability of preferences over time.
This estimate is already clean of the attenuation caused by measurement error, which is
substantial. To make this more evident, note that the analogous estimates via Generalized
Least Squares (GLS)—which do not correct for measurement error—are between 0.623
for patience and 0.761 for conscientiousness. The downward bias is evident.13
Once measurement error is accounted for, it is clear that risk aversion, patience, and
conscientiousness change very slowly over time. All three coefficients are close to unity
(which would imply perfect stability over time), yet their standard errors are very small.
However, the null of α = 1 is rejected in the case of risk aversion (p = 0.010), which can be
interpreted as evidence that risk aversion is not completely stable. This same hypothesis
cannot be rejected for patience (p = 0.382) or conscientiousness (p = 0.243).
Testing α = 1 is similar to the common unit root test of Phillips and Perron (1988).
The similarity suggests that, under the unit root hypothesis, α could have a distribution
that degenerates too fast as N tends to infinity.14 Measurement error further complicates
matters. However, one could construct a test in the form of the (augmented) Dickey-Fuller,
regressing the first differences of Pit on Pi,t−1 . Measurement error remains an issue, so
to obtain a consistent estimate of the coefficient of Pi,t−1 it is necessary to instrument
it using further lags of Pit , mirroring the procedure above. The t-statistic of Pi,t−1 , now
that measurement error has been accounted for, should reflect regression to the mean or
persistence in Pit depending on whether Pit has a unit root or not. Such a test reaches
the same conclusions as described above: stationarity is rejected for risk aversion but not
for either patience or conscientiousness.15
13
See Table A.1 for the complete estimation.
The estimator of α is (super-)consistent, making all the other statistics derived from it valid.
15
The test statistic is calculated as β̂/s.e.(β̂) from the regression ∆Pit = βPi,t−1 + eit where Pi,t−1 is
instrumented with the second to fourth lags of Pit and ∆ = 1 − L stands as the first difference operator.
14
12
The third panel of Table 4 shows the results of three specification tests for the IV GMM
regressions: An endogeneity test for the lagged preference; an F-test for the instruments
in the first stage; and an overidentification test. The tests present very strong evidence
in favor of the use of IV in all regressions, and show that the instruments function well.
The last panel of Table 4 shows the estimates of the variances of the idiosyncratic
shocks to preferences (η) and the measurement error (ε). These estimates are obtained
via an auxiliary non-linear least squares regression, as explained above. The variance of η
is substantially larger for patience than for risk aversion and conscientiousness, suggesting
that patience could be relatively less stable. This instability is driven by the fact that
shocks to latent patience are more severe. It is, thus, a different type of instability different
as the one captured by α. An α estimate close to unity means that preferences will be, on
average, very similar to what they were in the previous period. A larger ση2 , on the other
hand, means that the deviations of preferences from their conditional value (based on past
preferences and the drift terms) are larger. In essence, α will capture how preferences
evolve on average and ση2 will capture how large the deviations from that average (net of
measurement error) will be.
Finally, the bottom panel of Table 4 also reports the noise-to-signal ratio s = σε2 /(1 −
σε2 ) for every preference. Clearly there is some variation in s across constructs. The results
indicate that risk aversion is relatively noisier than patience and conscientiousness, the
latter measured with the least noise. This suggests that regressions where this index of
risk aversion is used will show attenuated coefficients; comparatively more attenuated
than patience of conscientiousness. Using a different method to estimate the noise-tosignal ratio, Salamanca et al. (2013) illustrate this attenuation in explaining individual
The test statistics are compared to the Dickey Fuller critical values. The tests reject the presence of a
drift and a constant for all preferences, and they continue to reject after being augmented with lags of
∆Pit . The presence of additional covariates does not change the results. An IV unit root test constructed
after Lee and Schmidt (1994) yields very similar results.
13
portfolio choice and show how biased inference can be due to this problem.16
B.
Specification checks and heterogeneity across subgroups
In estimating g(Xit ) above, the linearity assumption on Xit should be carefully considered
since, other than for simplicity, there is no reason why we should assume a linear relation
between preferences and the continuous characteristics in Xit . In particular, the age
evolution of risk aversion and its relation to income and wealth deserve a closer look.
To better investigate these non-linearities, Figures 7, 8, and 9 present non-parametric
fits of risk aversion on age, log-income, and log-wealth.17 All three graphs show that risk
aversion does not change much across age, income, or wealth, respectively. In particular,
Figure 9 suggests that the positive wealth coefficients on risk aversion in Table 4 come
mainly from the observations with extremely low reported wealth, but that otherwise the
risk-aversion-wealth relationship is rather flat. If these observations are excluded from
the analysis, the wealth effect disappears whereas the other estimates remain virtually
unchanged.
Another way in which this model can be helpful is by revealing heterogeneity in preference stability across individuals. Estimating α, g(Xit ), ση2 , and σε2 for each individual
in our sample is unfeasible. However, we can assess the stability of preferences across
subgroups by estimating all parameters for different subgroups based on observable characteristics and comparing the estimates. Tables 5, 6 and 7 do this for women versus men,
people with children versus no children, and married/cohabiting versus single people,
16
Cobb-Clark and Schurer (2013) show that the noise-to-signal ratio can also be estimated via structural
equations systems. However, those methods usually impose strong distributional assumptions on the
underlying preference and its covariance with other variables. Some of the distributional assumptions
often imposed, like normality, may not hold for some preferences (see Figure 1). The method used here
makes no assumptions about the distribution of preferences, and moreover it can be adapted to account
for persistence in the measurement error terms and for more complex autoregressive structures.
17
These figures are produced via a first-degree local polynomial smoothing of Pit net of the effect of
the other variables in g(Xit ) and of α̂Pi,t−1 .
14
respectively.
The results show little variation in the estimated g(Xit ) across all groups. Most of
this variation comes from the wealth and income variables, which are likely not well
captured by the linear form of the model. In terms of the α estimates, there is also little
variation across subgroups for risk aversion and conscientiousness. However, for patience
the estimates are spread across a relatively wide range, from as low as 0.898 for single
people to as high as 1.014 for married/cohabiting people. All autoregressive coefficients
are precisely estimated, but for some of them we can not reject the null that they are
equal to one. This suggests that for these subgroups we can consider their preferences as
effectively unchanging over time.
Tables 5, 6 and 7 also indicate that there is some heterogeneity in the variance of η
and the noise-to-signal ratio across subgroups. However, a proper comparison is difficult
to make since for many of the subgroups the variation in ηit is actually estimated as zero.
This happens because the non-linear least squares algorithm reached a boundary in its
optimization process, and unfortunately the boundary estimates cannot be interpreted.
The fact that the zero boundary is reached for ση2 and not for σε2 , however, is likely a sign
that the variance of idiosyncratic shocks to preferences is extremely low compared to the
noise for these subgroups.
C.
Variance-based evidence of stability
With all the evidence suggesting that the time stability of preferences is fairly high, Can
we just assume preferences are stable? The tests of α = 1 and the variance estimates of
ηit in section IV.A would suggest that we should not. As ancillary evidence, one can look
at the structure of the variance of changes in preferences.
If preferences are truly stable but measured with error, then Pit = Pi∗ +εit .18 Assuming
18
When other researchers write about stable preferences, this is the model they usually have in mind.
15
that εit behaves as regular measurement error, the variance of Pit − Pi,t−k should remain
constant for all k. Under the alternative hypothesis that preferences evolve according to
equations (1) and (2), the variance of Pit − Pi,t−k can be written as:
∗
V ar(Pit − Pi,t−k ) = V ar(Pit∗ + εit − Pi,t−k
− εi,t−k )
∗
∗
− εi,t−k )
+ αηit + εit − Pi,t−k
= V ar(αPi,t−1
..
.
∗
= V ar((αk − 1)Pi,t−k
+
k
X
αj ηi,t−j + εit − εi,t−k )
j=0
= (αk − 1)2 σP2 ∗ +
k
X
α2j ση2 + 2σε2 ,
j=0
which is monotonically increasing in k for k ≥ 1 and the parameters as estimated in Table
4. Simply put, if preferences are autoregressive, then the variance of increasingly lagged
differences should be increasing in the lags.
Figures 10, 11, and 12 show the variance of up to five k-length differences in risk
aversion, patience, and conscientiousness, respectively. Around each variance estimate
there are percentile-based 95% confidence intervals bootstrapped with 1,000 replications
each. One the one hand, Figure 10 shows that the variance of the differences in risk
aversion increases with k just as it should if risk aversion followed an autoregressive
process. On the other hand, in Figure 12 the constant-variance hypothesis clearly cannot
be rejected. The evidence in these three figures is consistent with the fact that α = 1 is
rejected for risk aversion but not for conscientiousness. Figure 12 shows that the variance
of patience increases between k = 2 and k = 3 but otherwise remains stable. In this case
the figure is not unambiguously consistent with the stability hypothesis.
In fact, this model is explicitly written in Cobb-Clark and Schurer (2013).
16
D.
Tests for stability that account for unobserved heterogeneity
The estimations so far have not exploited the panel structure of the data to its full extent.
A straightforward extension is to use panel data models that explicitly take into account
unobserved heterogeneity via individual-specific intercepts. In this context, individualspecific intercepts are particularly attractive because they have a clear economic interpretation: They are the individual level to which preference Pit conditionally tends to.
However, they also will capture every other time-invariant individual factor that might
affect preference levels, and in the case of preferences the effect of these unobserved factors
can explain a large part of the variation (see Sahm (2012)).
One needs to be careful when jointly dealing with unobserved heterogeneity and measurement error in these dynamic panel data models. The panel data extension of the
model can be written as a simple extension of Equation 3:
Pit = γi + g panel (Xit ) + αpanel Pi,t−1 + ηit + εit − αpanel εi,t−1 ,
(3’ )
where γi represents the unobserved individual heterogeneity, which is allowed to be correlated to g(Xit ) and Pi,t−1 . Because of the dynamic nature of the model, the natural
estimator is Arellano and Bond (1991). This estimator works by first eliminating the
unobserved individual heterogeneity using first differences, and then obtaining unbiased
parameter estimates from those first differences by using lags of preferences as instruments. The estimator thus also accounts for measurement error since instrumenting the
lagged differences of Pit affects measurement error in the same way as above. The complication introduced by the measurement error means that we can only use the third and
longer lags as GMM instruments in the first difference equation.
The results of estimating (3’ ), presented in Table 8, show that once the fixed un17
observed individual heterogeneity is taken into account, the autoregressive process of
preferences disappears. This is not surprising, since in the case of preferences individual
fixed effects are likely to capture many characteristics that are strongly associated with
preference evolution. The estimates have a caveat, though: They are quite sensitive to
the model specification and the choice of instruments for both the difference and the level
equation. In the case of conscientiousness, a sign of this lack of robustness is the failure to find a model specification that does not fail to reject Sargan test’s null while at
the same time showing an appropriate autocorrelation structure of the residuals (i.e., no
autocorrelation of order 2 and above). Another problem is that the α parameter leads
to nonsensical estimations of the variances of ε and η. Overall, it is quite possible that
unobserved individual heterogeneity accounts for a large part of the autocorrelation in
preferences, but the evidence presented here should only be interpreted with caution.
E.
The severity of the bias
Even though some preferences might not be completely stable, an important question to
answer is: So what? I could be that results do not change meaningfully if we assume
preferences are stable. I argue that they do, and to do so I take the example of risk
aversion, which is shown to be time-varying above.
The evidence shown above on time-varying risk preferences validates the concerns of
some researchers that inferring risk preferences from “stale” choices can be misleading.
This concern is explicitly expressed in Einav et al. (2012) but applies to the studies that
elicit risk preferences using either (hypothetical) lottery choices (e.g., Barsky et al., 1997;
Andersen et al., 2008; Dohmen et al., 2011) or observed choices (e.g., Cutler and Glaeser,
2005; Einav et al., 2012). Under the assumption of stable risk preferences, one could be
tempted to correlate an inferred risk preferences at one point to outcomes observed earlier
or later in time. However, since risk preferences do change and since that change can be
18
different for various subgroups, extrapolating preferences is inappropriate and could result
in bias.
To illustrate the severity of the bias, I simulate a relation between risk aversion rt and
and outcome yt and then I check what would happen if I use increasingly stale measures
of the preference (e.g., rt−1 , rt−2 , . . .) to predict the outcome. The data generating process
∗
(DGP) can be described as follows: yt = rt + et with rt = rt∗ + ηt and rt∗ = αrt−1
+ εt .
The preferences in the DGP evolve as in equations (2) and (3) and the DGP postulates
a one-to-one contemporaneous relation between yt and rt . The parameters in the model
were calibrated based on the results in Table 4 for risk aversion.19
Figure 13 shows the coefficients and one-standard-deviation bands of regressing yt on
rt−k for k = 0, . . . , 9. The coefficients are calculated via both OLS and IV methods (in
the IV regressions, rt−k−1 is used as an instrument for rt−k ). The figure clearly shows that
when regressing the outcome on the contemporaneous measure (k = 0) of yt both OLS and
IV estimate a coefficient indistinguishable from the true value of unity (IV is obviously
less efficient). However, as increasingly stale measures of the preference are used, the
coefficient estimated decreases. The decrease is most severe for the OLS method since the
bias comes from both the staleness of preferences and measurement error. However, the
IV estimates, which are not affected by measurement error, also show a steep decline as
preference measures become stale. In the extreme case of using a decade-old risk aversion
measure to predict the outcome, the results would suggest that the IV estimate would be
biased by about 20 percent and the OLS by almost 50 percent. The figure also indicates
that, with the parameters calibrated as they are in this simulation, measurement error
is the more serious problem, although the cost of not accounting for preference stability
should not be overlooked.
19
The simulation was done 1,000 times for N = 3, 000 individuals over K = 10 periods under the
following parametrization: α = 0.971; et ∼ N (0, 1); ηt ∼ N (0, 0.244); εt ∼ N (0, 0.031); and r0 ∼
N (0, 0.708).
19
F.
Implications for asset pricing and consumer finance
Time-varying risk aversion could also affect well-established results in areas of finance
such as asset pricing. The great majority of Capital Asset Pricing Models (CAPM)
spurred by Sharpe (1964) and Lintner (1965) assume that the risk preference parameter
is stable over time. Based on this assumption, they derive theoretical macroeconomic
implications that they proceed to test empirically as to provide indirect evidence for their
models. For example, Li (2007) argues that there is a one-to-one relation between the
Sharpe ratio of stock market returns and the volatility of log surplus consumption. Other
models make similar predictions. However, these predictions are usually dependent on
the constant risk aversion assumption, and by letting risk aversion change over time the
models would change substantially. Moreover, since observables do not explain preferences
well conditional on lagged preferences (their incremental R2 is less than 0.01), this problem
cannot be solved by simply adding correlates or allowing risk aversion to be endogenous.
It is also not clear that analyzing the decisions of a representative agent is even valid in
this case.
Finally, time-varying risk aversion could make some of the recently introduced retail
investment products less beneficial for consumers. Many banks and financial institutions
now offer to help their customers invest in financial instruments by advising them and/or
directly managing their investment accounts. To do so they elicit the risk tolerance of their
customers once they open their investment accounts and the subsequently allocate the
customers’ funds into different mixes of equity, fixed income, and other instruments. In
principle, access to equity instruments improves a person’s financial situation (especially
if using diversified instruments) because it allows him or her to benefit from the equity
premium. However, if the customers’ risk aversion changes over time, then the banks’
strategy will be sub-optimal in the sense that it will not match the customers’ preferences.
20
The results presented above suggest that (occasionally) reassessing the customers’ risk
profiles could lead to better asset allocations for them.
IV.
Conclusions
In this paper I develop and estimate a model of time-varying preferences to determine
their stability. The model adds to existing work on preference and personality stability by
parameterizing four important features of preferences: their predictable change correlated
with observables, their autoregressive structure, the variance of their idiosyncratic shocks,
and their measurement error. These parameters provide a comprehensive view of different
aspects of the stability of preferences and the noise in their measures. The estimation of
this model not only provides the first formal statistical test for the stability of preferences,
it also provides metrics for different types of stability that should be considered separately
in many applications.
I illustrate how the model parameters can be estimated and interpreted using measures
of risk aversion, patience, and conscientiousness from the Dutch national bank Household
Survey. There are several important findings. First, observable characteristics only weakly
predict changes in all studied preferences. Second, patience and conscientiousness can be
treated as time-invariant but risk aversion does change, albeit slowly, over time. Third,
idiosyncratic shocks to patience are more severe than shocks to risk aversion and conscientiousness, making it less stable in the sense that deviations from its conditional mean
are larger. Fourth, all preferences are measured with substantial error, but risk aversion
is measured with more noise than patience and conscientiousness. Fifth, for patience
there is heterogeneity by gender, family compositions and marital status in terms of the
autoregressive parameter, and there might be substantial heterogeneity in terms of idiosyncratic variance and measurement error for all preferences. Finally, controlling for
21
individual unobserved heterogeneity makes the autoregressive parameters insignificant,
although these results lack robustness. These results align with the general findings in
the literature suggesting that both economic preferences and personality traits are stable.
However, they improve on existing studies by formally testing whether these preferences
are stable, by considering and measuring various facets of stability simultaneously, and
by measuring the extent and influence of measurement error in these tests.
The empirical results indicate that the (often implicit) treatment of risk aversion as
time-constant and measured with error can result in biased estimates of its relation to
economic outcomes. However, since risk aversion only changes slowly over time, assuming
time-stability over short periods is unlikely to make a substantial difference. But even
then, properly accounting for the autocorrelation structure in risk aversion could bring
modeling improvements, especially if there are also regressors that are themselves determined by lagged risk aversion. For studies that observe individuals over long periods
of time, using stale measures of risk aversion could still lead to large biases. This is of
particular importance for financial institutions such as pension funds and retail investment providers that try to match their investment strategies to the preferences of their
stakeholders. In addition, it is also important to know that studied preferences are likely
to react slowly to shocks that could change them (i.e., individual changes such as divorce
or widespread phenomena such as the financial crisis). Finally, it is paramount to rigorously account for measurement error in all preference measures which is, as I have shown,
substantial. This is especially important when investigating preference stability.
This model contributes to a large literature in economics and psychology that relies on
measures of (the stability of) economic preferences and personality traits. The application of this model can provide evidence supporting the stability assumption for a number
of other preferences or point out the cases where it is unlikely to hold. Moreover, many
of these preferences have alternative and competing measures and measurement models,
22
and the reasons for choosing one over another are often empirically unfounded. I provide
a metric for the measurement error in competing models that can be used as an assessment tool for choosing between them. The conclusions of these assessments can help to
determine which preference measures are should be included in surveys, and provide a
basis to reassess some of the evidence that relates preferences to economic behavior.
23
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28
Table 1: Summary statistics of the estimation sample for risk aversion (n=3,451)
Percentile
th
50th
90th
95th
3
6
7
7
1
1
5
7
7
1.39
3
4
6
7
7
6.02
5.43
1.43
1.61
3
2
4
3
7
6
7
7
7
7
5.57
1.50
3
3
6
7
7
Sum of scores of risk aversion
32.28
6.24
22
24
33
41
42
Gross Income (1,000 euros)
Total wealth (1,000 Euro)
Age
1 if zero reported income
1 if zero reported wealth
1 if female
1 if has a child
1 if married
31.46
59.04
56.40
0.09
0.07
0.38
0.29
0.73
Variable
Mean
S.D.
5
(a) I think it is more important to have safe investments and guaranteed returns, than to take a risk to have a chance to get the
highest possible returns
(b) I would never consider investments in shares because I find this
too risky
(c) If I think an investment will be profitable, I am prepared to
borrow money to make this investment (reversed)
(d) I want to be certain that my investments are safe
(e) I get more and more convinced that I should take greater financial risks to improve my financial position (reversed)
(f ) I am prepared to take the risk to lose money, when there is also
a chance to gain money (reversed)
5.24
1.74
1
4.56
2.09
5.47
th
10
20.40 0.00 1.14 31.05
123.85 0.00 0.50 25.19
13.36
34
38
57
0.29
0
0
0
0.26
0
0
0
0.49
0
0
0
0.45
0
0
0
0.44
0
0
1
57.29 67.34
131.50 217.59
74
78
0
1
0
1
1
1
1
1
1
1
The six risk aversion statements have the following common heading: “The following statements concern saving and taking risks. Please
indicate for each statement to what extent you agree or disagree. Please indicate on a scale from 1 to 7 to what extent you agree with the
following statements, where 1 indicates ‘totally disagree’. and 7 indicates ‘totally agree’.” The statements and the rest of the variables are
observed yearly in the 1998-2011 period.
29
Table 2: Summary statistics of the estimation sample for patience (n=1,159)
Percentile
th
50th
90th
95th
2
4
6
6
1
1
2
2
4
3
6
5
6
6
1.39
2
3
5
7
7
4.18
1.36
2
2
4
6
6
4.28
1.55
2
2
4
6
7
4.22
1.57
2
2
4
6
7
4.77
1.40
2
3
5
7
7
4.13
1.48
2
2
4
6
7
4.21
1.46
2
2
4
6
7
Sum of scores of patience
41.99
8.32
28
31
42
53
56
Gross Income (1,000 euros)
Total wealth (1,000 Euro)
Age
1 if zero reported income
1 if zero reported wealth
1 if female
1 if has a child
1 if married
30.16
59.23
55.12
0.10
0.07
0.40
0.31
0.75
Variable
Mean
S.D.
5
(a) I think about how things can change in the future, and try to
influence those things in my everyday life.
(b) I often work on things that will only pay off in a couple of years.
(c) I am only concerned about the present, because I trust that
things will work themselves out in the future (reversed)
(d) With everything I do, I am only concerned about the immediate
consequences (say a period of a couple of days or weeks) (reversed)
(e) I am ready to sacrifice my well-being in the present to achieve
certain results in the future
(f ) I think it is important to take warnings about negative consequences of my acts seriously, even if these negative consequences
would only occur in the distant future
(g) I think it is more important to work on things that have important consequences in the future, than to work on things that have
immediate but less important consequences
(h) In general, I ignore warnings about future problems because
I think these problems will be solved before they get critical (reversed)
(i) I think there is no need to sacrifice things now for problems that
lie in the future, because it will always be possible to solve these
future problems later (reversed)
(j) I only respond to urgent problems, trusting that problems that
come up later can be solved in a later stage (reversed)
4.18
1.39
2
3.66
3.40
1.48
1.43
4.96
th
10
20.32 0.00 0.00 30.00
121.92 0.00 0.44 23.76
13.01
34
37
55
0.30
0
0
0
0.26
0
0
0
0.49
0
0
0
0.46
0
0
0
0.43
0
0
1
55.67 66.18
145.67 250.94
73
77
1
1
0
1
1
1
1
1
1
1
The ten patience statements have the following common heading: “To what extent do you agree or disagree with the following statements. If
you really don’t know, type 0 (zero).’ Right below they show a numbered scale from 1 (labeled ‘totally disagree’) to 7 (labeled ‘totally agree’).
The statements and the rest of the variables are observed yearly in the 2000-2007 period.
30
Table 3: Summary statistics of the estimation sample for Conscientiousness (n=2,352)
Percentile
Variable
th
Mean
S.D.
5
(a) I do chores right away
(b) I’ll leave my things lying around (reversed)
(c) I live my life according to schedules
(d) I neglect my obligations (reversed)
(e) I have an eye for details
(f ) I am accurate in my work
(g) I forget to put things back where they belong (reversed)
(h) I am always well prepared
(i) I often make a mess of things (reversed)
(j) I like order
3.34
2.75
3.75
4.02
3.60
3.88
3.66
4.23
3.80
4.30
1.04
1.12
0.90
0.83
0.79
0.90
1.16
0.97
1.08
0.85
2
1
2
3
2
2
2
2
2
3
Sum of scores of Conscientiousness
37.33
5.93
28
Gross Income (1,000 euros)
Total wealth (1,000 Euro)
Age
1 if zero reported income
1 if zero reported wealth
1 if female
1 if has a child
1 if married
30.21
59.71
57.27
0.10
0.08
0.42
0.29
0.70
th
50th
90th
95th
2
1
3
3
3
3
2
3
2
3
3
3
4
4
4
4
4
5
4
5
5
4
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
5
30
38
45
46
10
20.46 0.00 0.00 30.00
149.13 0.00 0.33 24.29
13.70
34
38
58
0.30
0
0
0
0.27
0
0
0
0.49
0
0
0
0.45
0
0
0
0.46
0
0
1
56.26 66.04
130.51 207.66
75
78
1
1
0
1
1
1
1
1
1
1
The ten Conscientiousness statements have the following common heading: “For the following statements on human behavior, please choose
the statement which applies most to you. Describe yourself as you are, not as how you want to be. Describe yourself in comparison to other
people you know of the same sex and of about the same age. Where 1 means ‘very inaccurate’ and 5 means ‘very accurate’.” The statements
and the rest of the variables are observed yearly in the 2008-2011 period.
31
Table 4: The stability of risk tolerance, patience, and Conscientiousness in the DHS
Dependent variable =
(1)
Risk aversion
(2)
Patience
(3)
Conscientiousness
0.015
(0.016)
0.015∗∗
(0.007)
0.000
(0.001)
0.134
(0.162)
0.250∗∗∗
(0.087)
0.012
(0.022)
−0.009
(0.024)
0.014
(0.022)
−0.030
(0.028)
−0.001
(0.014)
0.003
(0.002)
−0.273
(0.281)
−0.070
(0.165)
−0.020
(0.046)
0.033
(0.051)
−0.083∗
(0.044)
−0.012
(0.018)
−0.012∗
(0.007)
0.000
(0.001)
−0.150
(0.184)
−0.158∗
(0.086)
0.014
(0.023)
0.026
(0.027)
−0.004
(0.023)
g(Xit )
Log(income)
Log(wealth)
Age
1 if zero reported income
1 if zero reported wealth
1 if female
1 if has children
1 if married
α
Endogeneity test
p=
F-test of first stage instruments
p=
Overidentifying restristions test
p=
Observations
R-squared
ση2
σε2
Noise-to-signal ratio (s)
0.971∗∗∗
(0.011)
0.978∗∗∗
(0.026)
0.985∗∗∗
(0.013)
265.119
[0.001]
1,708.680
[0.001]
0.379
[0.827]
111.296
[0.001]
325.434
[0.001]
1.486
[0.475]
109.205
[0.001]
1,216.590
[0.001]
1.111
[0.573]
3,451
0.464
1,159
0.294
2,352
0.544
0.031
(0.008)
0.244
(0.011)
0.323
(0.019)
0.196
(0.068)
0.218
(0.089)
0.279
(0.146)
0.029
(0.016)
0.194
(0.017)
0.241
(0.027)
Standard errors clustered at the individual level in parentheses and p-values in square brackets. Standard
errors of α coefficients should be interpreted with care since they could be biased downwards. The regressions
report IV coefficients, instrumenting the first lag of the dependent variable with its lags 2 to 4. The
constant is not reported in the table. Endogeneity tests are based on the difference-in-Sargan statistic.
Overidentifying restrictions tests are based on Hansen’s J statistic. ση2 and σε2 and the noise-to-signal ratio
are calculated via non-linear least squares as described on the main text using information from 4 lags and
netting out the dependent variable from g(Xit ) as estimated in this table. *** p<0.01, ** p<0.05, * p<0.1
32
Table 5: The stability of risk aversion in subgroups of the DHS
Subgroup =
(1)
Women
(2)
Men
(3)
With children
(4)
With no children
(5)
Married
(6)
Single
0.021
(0.018)
0.015∗
(0.008)
0.000
(0.001)
0.203
(0.181)
0.232∗∗
(0.097)
0.019
(0.031)
−0.011
(0.029)
−0.011
(0.039)
0.015
(0.016)
0.000
(0.001)
−0.206
(0.469)
0.438∗
(0.233)
0.007
(0.035)
0.006
(0.054)
g(Xit )
Log(income)
Log(wealth)
Age
1 if zero reported income
1 if zero reported wealth
−0.014
(0.022)
0.027∗∗
(0.011)
−0.001
(0.001)
−0.159
(0.223)
0.398∗∗∗
(0.123)
0.064∗∗∗
(0.023)
0.004
(0.010)
0.002
(0.001)
0.790∗∗∗
(0.258)
0.042
(0.156)
1 if female
1 if has children
1 if married
α
Observations
R-squared
ση2
σε2
Noise-to-signal ratio (s)
−0.011
(0.037)
0.001
(0.039)
0.948∗∗∗
(0.021)
−0.011
(0.031)
0.012
(0.027)
0.978∗∗∗
(0.014)
−0.007
(0.031)
0.011
(0.013)
0.001
(0.002)
−0.093
(0.323)
0.185
(0.161)
0.008
(0.046)
0.026
(0.018)
0.016∗
(0.009)
0.000
(0.001)
0.239
(0.186)
0.280∗∗∗
(0.105)
0.015
(0.026)
−0.003
(0.049)
0.020
(0.024)
0.985∗∗∗
(0.024)
0.965∗∗∗
(0.013)
0.973∗∗∗
(0.013)
0.968∗∗∗
(0.026)
1,319
0.254
2,132
0.522
1,008
0.401
2,443
0.482
2,516
0.485
935
0.399
0
0.281
(0.011)
0.391
(0.021)
0.030
(0.007)
0.239
(0.011)
0.315
(0.020)
0.032
(0.016)
0.247
(0.025)
0.328
(0.044)
0.009
(0.015)
0.257
(0.022)
0.347
(0.041)
0.024
(0.009)
0.250
(0.014)
0.334
(0.024)
0
0.245
(0.009)
0.325
(0.016)
Standard errors clustered at the individual level in parentheses. Standard errors of α coefficients should be interpreted with care since they could
be biased downwards. The regressions report IV coefficients, instrumenting the first lag of the dependent variable with its lags 2 to 4 to obtain the
α coefficient. The constant is not reported in the table. ση2 and σε2 are calculated via non-linear least squares as described on the main text using
information from 4 lags and netting out the dependent variable from g(Xit ) as estimated in this table. *** p<0.01, ** p<0.05, * p<0.1
33
Table 6: The stability of patience in subgroups of the DHS
Subgroup =
(1)
Women
(2)
Men
(3)
With children
(4)
With no children
(5)
Married
(6)
Single
−0.084∗∗
(0.037)
0.002
(0.021)
0.006
(0.004)
−0.719∗∗
(0.355)
−0.046
(0.239)
−0.008
(0.049)
−0.006
(0.018)
−0.000
(0.002)
−0.019
(0.527)
−0.107
(0.210)
−0.058∗
(0.035)
0.004
(0.020)
0.003
(0.004)
−0.371
(0.337)
0.019
(0.235)
−0.126∗
(0.074)
−0.027
(0.038)
−0.008
(0.018)
0.003
(0.002)
−0.335
(0.397)
−0.161
(0.221)
0.009
(0.056)
0.061
(0.094)
−0.257∗∗∗
(0.081)
−0.023
(0.057)
0.032
(0.049)
−0.062∗
(0.033)
−0.011
(0.016)
0.003
(0.002)
−0.554∗
(0.319)
−0.138
(0.198)
−0.121∗∗
(0.056)
0.050
(0.064)
−0.004
(0.067)
0.025
(0.021)
0.001
(0.003)
0.075
(0.709)
0.070
(0.322)
0.165∗∗
(0.066)
−0.069
(0.091)
−0.024
(0.090)
−0.085∗
(0.050)
g(Xit )
Log(income)
Log(wealth)
Age
1 if zero reported income
1 if zero reported wealth
1 if female
1 if has children
1 if married
α
Observations
R-squared
ση2
σε2
Noise-to-signal ratio (s)
1.001∗∗∗
(0.051)
0.962∗∗∗
(0.029)
0.999∗∗∗
(0.047)
0.972∗∗∗
(0.030)
1.014∗∗∗
(0.033)
0.898∗∗∗
(0.039)
460
0.251
699
0.327
365
0.194
794
0.324
868
0.199
291
0.532
0
0.276
(0.049)
0.382
(0.094)
0.232
(0.065)
0.198
(0.099)
0.246
(0.154)
0.190
(0.083)
0.142
(0.138)
0.165
(0.188)
0.169
(0.060)
0.274
(0.094)
0.377
(0.178)
0.128
(0.066)
0.324
(0.112)
0.478
(0.245)
0
0.215
(0.028)
0.272
(0.046)
Standard errors clustered at the individual level in parentheses. Standard errors of α coefficients should be interpreted with care since they could
be biased downwards. The regressions report IV coefficients, instrumenting the first lag of the dependent variable with its lags 2 to 4 to obtain the
α coefficient. The constant is not reported in the table. ση2 and σε2 are calculated via non-linear least squares as described on the main text using
information from 4 lags and netting out the dependent variable from g(Xit ) as estimated in this table. *** p<0.01, ** p<0.05, * p<0.1
34
Table 7: The stability of Conscientiousness in subgroups of the DHS
Subgroup =
(1)
Women
(2)
Men
(3)
With children
(4)
With no children
(5)
Married
(6)
Single
−0.017
(0.020)
−0.016∗
(0.010)
0.002
(0.001)
−0.219
(0.209)
−0.226∗∗
(0.110)
0.024
(0.034)
−0.007
(0.010)
−0.000
(0.001)
0.351
(0.371)
−0.038
(0.169)
−0.029
(0.022)
−0.014
(0.011)
0.002
(0.002)
−0.309
(0.223)
−0.128
(0.156)
−0.060
(0.043)
−0.008
(0.026)
−0.011
(0.009)
0.000
(0.001)
−0.111
(0.280)
−0.151
(0.107)
0.038
(0.029)
0.005
(0.036)
0.028
(0.036)
0.051
(0.038)
−0.027
(0.032)
−0.020
(0.021)
−0.009
(0.008)
0.001
(0.001)
−0.227
(0.212)
−0.130
(0.098)
0.024
(0.035)
0.055∗
(0.033)
0.019
(0.039)
−0.021
(0.013)
−0.000
(0.001)
0.076
(0.465)
−0.251
(0.206)
−0.008
(0.034)
−0.013
(0.054)
0.016
(0.047)
−0.011
(0.027)
g(Xit )
Log(income)
Log(wealth)
Age
1 if zero reported income
1 if zero reported wealth
1 if female
1 if has children
1 if married
α
Observations
R-squared
ση2
σε2
Noise-to-signal ratio (s)
0.980∗∗∗
(0.017)
0.992∗∗∗
(0.019)
0.993∗∗∗
(0.024)
0.982∗∗∗
(0.016)
0.996∗∗∗
(0.018)
0.963∗∗∗
(0.018)
997
0.612
1,355
0.485
679
0.583
1,673
0.532
1,645
0.523
707
0.569
0.046
(0.029)
0.171
(0.030)
0.207
(0.044)
0.021
(0.009)
0.209
(0.010)
0.265
(0.016)
0.066
(0.027)
0.130
(0.029)
0.150
(0.039)
0.018
(0.011)
0.217
(0.012)
0.276
(0.019)
0
0.197
(0.002)
0.246
(0.004)
0.054
(0.036)
0.220
(0.036)
0.282
(0.060)
Standard errors clustered at the individual level in parentheses. Standard errors of α coefficients should be interpreted with care since they could
be biased downwards. The regressions report IV coefficients, instrumenting the first lag of the dependent variable with its lags 2 to 4 to obtain the
α coefficient. The constant is not reported in the table. ση2 and σε2 are calculated via non-linear least squares as described on the main text using
information from 4 lags and netting out the dependent variable from g(Xit ) as estimated in this table. *** p<0.01, ** p<0.05, * p<0.1
35
Table 8: Dynamic panel data estimation of the stability of risk aversion, patience, and Conscientiousness
Dependent variable =
(1)
Risk aversion
(2)
Patience
(3)
Conscientiousness
0.017
(0.037)
0.029∗
(0.017)
0.138
(0.341)
0.209
(0.178)
0.057
(0.101)
0.005
(0.110)
−0.114
(0.069)
−0.035
(0.030)
−1.024∗
(0.617)
−0.240
(0.301)
−0.061
(0.134)
−0.619∗∗
(0.287)
−0.001
(0.033)
0.017
(0.013)
0.031
(0.298)
0.166
(0.129)
0.087
(0.085)
−0.033
(0.061)
g(Xit )
Log(income)
Log(wealth)
1 if zero reported income
1 if zero reported wealth
1 if has children
1 if married
α
−0.084
(0.084)
−0.215
(0.163)
−0.526∗
(0.283)
Overidentifying restrictions:
Autocorrelation test:
Order 1
Order 2
Order 3
Order 4
[0.115]
[0.341]
[0.238]
[0.001]
[0.849]
[0.325]
[0.255]
[0.043]
[0.556]
[0.222]
[0.486]
[0.817]
[0.041]
[0.590]
-
Observations
Individuals
3,277
1,060
1,079
525
2,236
840
Standard errors clustered at the individual level in parentheses and p-values in square brackets. The
regressions reports dynamic panel data estimates obtained via Arellano/Bond. The GMM instruments
include lags three and four of the dependent variable, and levels and differences of the exogenous
variables for the difference equation. Overidentifying restrictions are based on the Sargan test with the
null that the restrictions are valid. The tests are based on regressions without robust standard errors.
Autocorrelation tests are the usual Arellano/Bond. *** p<0.01, ** p<0.05, * p<0.1
36
0
.02
Fraction
.04
.06
.08
Figure 1: Distribution of risk aversion in the DHS
0
10
20
Risk aversion
30
40
0
.02
Fraction
.04
.06
.08
Figure 2: Distribution of patience in the DHS
0
20
40
Patience
37
60
80
0
.02
Fraction
.04
.06
.08
Figure 3: Distribution of conscientiousness in the DHS
10
20
30
Conscientiousness
40
50
0
.05
Fraction
.1
.15
Figure 4: Distribution of one-year changes in risk aversion in the DHS
−40
−20
0
∆Risk aversion
38
20
40
0
.02
Fraction
.04
.06
.08
Figure 5: Distribution of one-year changes in patience in the DHS
−40
−20
0
∆Patience
20
40
0
.05
Fraction
.1
.15
Figure 6: Distribution of one-year changes in conscientiousness in the DHS
−40
−20
0
∆Conscientiousness
39
20
40
−.2
Risk tolerance net of g(Xi)
0
.2
.4
.6
Figure 7: Non-parametric fit of risk aversion on age
20
40
60
80
Age
−1.5
−1
Risk tolerance net of g(Xi)
−.5
0
.5
1
Figure 8: Non-parametric fit of risk aversion on log-income
−2
0
2
Log(income)
40
4
6
−2
Risk tolerance net of g(Xi)
−1
0
1
Figure 9: Non-parametric fit of risk aversion on log-wealth
−5
0
5
10
Log(wealth)
.6
Variance of risk aversion differences
.65
.7
.75
.8
.85
Figure 10: Variance of differences in risk aversion over several periods
1
2
3
k
Var(Pit−Pi,t−k)
41
4
95% CI
5
.65
Variance of patience differences
.7
.75
.8
.85
.9
Figure 11: Variance of differences in patience over several periods
1
2
3
k
Var(Pit−Pi,t−k)
4
5
95% CI
.5
.55
.6
.65
Figure 12: Variance of differences in conscientiousness over several periods
1
2
3
k
Var(Pit−Pi,t−k)
42
4
95% CI
5
.5
Coefficient of preference on y
.6
.7
.8
.9
1
Figure 13: Effect of lagged measure of simulated preferences pt−k on outcome yt
0
1
2
3
4
5
6
Lags of preference measure (k)
OLS
43
IV
7
8
9
Appendix
44
Table A.1: The biased stability estimates of risk tolerance, patience, and Conscientiousness
under GLS
Dependent variable =
(1)
Risk aversion
(2)
Patience
(3)
Conscientiousness
−0.014
(0.034)
0.039∗∗
(0.016)
0.000
(0.002)
−0.194
(0.334)
0.274
(0.177)
0.001
(0.055)
0.032
(0.056)
−0.078
(0.054)
0.005
(0.019)
−0.004
(0.008)
0.001
(0.001)
0.050
(0.193)
−0.098
(0.091)
0.065∗∗
(0.028)
0.017
(0.031)
0.054∗
(0.028)
g(Xit )
Log(income)
Log(wealth)
Age
1 if zero reported income
1 if zero reported wealth
1 if female
1 if has children
1 if married
α
Observations
R-squared
ση2
σε2
Noise-to-signal ratio (s)
−0.000
(0.017)
0.001
(0.008)
0.003∗∗∗
(0.001)
−0.002
(0.176)
0.119
(0.090)
0.130∗∗∗
(0.028)
−0.032
(0.032)
0.016
(0.027)
0.698∗∗∗
(0.015)
0.623∗∗∗
(0.032)
0.761∗∗∗
(0.019)
3,451
0.533
1,159
0.420
2,352
0.593
0.545
(0.063)
0.119
(0.039)
0.135
(0.050)
1.599
(0.161)
0
0
-
0.297
(0.033)
0.127
(0.022)
0.145
(0.028)
Standard errors clustered at the individual level in parentheses. Standard errors of α coefficients
should be interpreted with care since they could be biased downwards. The regressions report GLS
coefficients. The constant is not reported in the table. ση2 and σε2 and the noise-to-signal ratio
are calculated via non-linear least squares as described on the main text using information from 4
lags and netting out the dependent variable from g(Xit ) as estimated in this table. *** p<0.01, **
p<0.05, * p<0.1
45