Capital Taxes When Firms Face Real and Financial Frictions
Jason DeBacker
October 13, 2008
1
Introduction
Taxes on capital take many forms. Most common are taxation of capital gains, corporate
profits, and dividends payments. The choice of tax instrument can affect corporate investment policy and so, even if a government finds it optimal to tax capital, it still must choose
among these tax instruments. Beyond taxes, investment policy is also affect by the real and
financial frictions that firms face when undertaking investment. In the following analysis, I
study how real and financial frictions interact with tax policy in an economy with heterogenous firms. My study has three main parts. First, I undertake some comparative statics,
understanding how tax policy affects investment decisions when firms face various frictions.
Second, I estimate several models of real and financial frictions and find the model that
best fits the data on the dynamics of firms. Finally, I use the estimated model to evaluate
the long run impact of several changes in tax policy.
This paper relates to three well-established literatures. Firm dynamics have an extensive literature in both economics and finance. Economists have largely focused on the role
of real frictions in explaining investment behavior (e.g. Cooper and Haltiwanger (2006))
whereas finance has tended towards the use of financial frictions to explain the behavior of
firms (e.g. Hennessy and Whited (2005)). There has been strikingly little overlap between
these two strands ( Cooley and Quadrini (2001), Cooper and Ejarque (2003) and Bayraktar,
Sakellaris and Vermeulen (2005)). The typical finance paper takes financial frictions seriously, but typically assumes the real frictions are quadratic in nature to support Q theory
based regressions. Economists often ignore financial frictions, but allow for more flexible
specifications of real costs of adjustment. I will try to span these two literatures, allowing
for real and financial frictions to affect firm dynamics. Allowing for both real and financial frictions is potentially important in the evaluation of tax policy. For example, with
the quadratic costs of adjustment that are typically used in the finance literature, firms’
investment is less elastic with respect to current cash flows, so tax policy will not have a
large effect on aggregate investment. The economics literature that cites the importance of
non-convexitites in capital accumulation decisions (e.g. Cooper and Haltiwanger (2006)),
on the other hand, finds that cash flow can be very important in investment behavior (e.g.
Miao (2008)). Similarly, financial frictions can increase the importance of cash flow because
external financing is more expensive.
The following also related to the long public finance and macroeconomics literature on
the aggregate effects of capital taxation. Important in public finance literature are the two
views on dividend taxation. The “traditional view” is that the marginal source of funds
for investment is new equity and the returns are used to pay dividends. This means that
dividend taxes are going to affect investment decisions since a dividend tax cut will lower
1
the user cost of capital and thus raise investment. The “new” view suggests that firms use
internal funds to finance investment and so don’t issue new equity. In this view, dividend
taxes do not influence the investment decisions of firms. Poterba and Summers (1985)
analyze dividend taxation in a dynamic model and find support for the traditional view.
However, the empirical results have been mixed, as Desai and Goolsbee (2004) find support
for the new view. The model in this paper will next both views. Depending on the firm’s
capital stock and productivity, its marginal source of funds may be internal or external.
In what follows, I first show adjustment costs interact with tax policy using calibrated
models. Following this exercise, I will estimate the nature and size of the adjustment costs
that firms face- both real costs and financial frictions. Using the estimated model, I will then
conduct several policy experiments. The policy experiments will include the tax changes
brought forth by the Jobs and Growth Tax Relief Reconciliation Act (JGTRRA), which
changes the rates of dividend and capital gains taxes.
The paper is organized as follows.
2
Investment Behavior
Non-convex adjustment costs result in investment “bursts” as firms try to spread the fixed
costs of adjusting their capital stock over a large investment. Such burst are apparent in
Figure 1, which shows the investment rate ( ki ) for firms in the Compustat North America
files over the 1988-2007 period. Over 25% of the observations have an investment rate
higher than 30%.
0
.02
Fraction
.04
.06
Distribution of Investment Rates
0
.2
.4
Investment Rate
.6
.8
Source: Compustat
Figure 1: PDF of Investment
3
Model
Following Gourio and Miao (2008), I will present a general equilibrium framework with
which to analyze tax policy. Gourio and Miao (2008) show that the effects of dividend
taxation are very different in the GE model versus a PE model. Below, I outline each part
of the economy.
2
3.1
Households
Households hold shares in firms and a risk free bond. They supply labor (inelastically
perhaps). Households are not heterogenous. The presence of a rise free bond helps to price
the shares.
Households solve:
max
{Ct }∞
t=0
∞
X
β t U (Ct )
(3.1)
t=0
subject to:
Ct +bt+1 +
Z
Pt θt+1 dµt =
Z
[(1−τd )dt +Pt0 −τg (Pt0 −Pt−1 )]θt dµt+(1+(1−τi )rt )bt +(1−τi )wt L̄+Tt
(3.2)
3.2
Firms
Firms choose equity issuance and dividends to maximize firm value. Firms buy capital and
hire labor. Firms face idiosyncratic shocks to productivity, which means that a decrease in
a tax on dividends can help out by improving the allocative efficiency of investment.
The firm’s problem is represented by the following Bellman Equation:
V (k, z) = max
′
k ,d,s
1
1 − τd
d−s+
E ′ V (k′ , z ′ )
1 − τg
1 + r(1 − τi )/(1 − τg ) z |z
(3.3)
Subject to the following constraints:
k′ + (1 − δ)k +
ψ(k′ − (1 − δ)k)2
+ d = (1 − τc )π(k, z, w) + τc δk + s
2k
(3.4)
d≥0
(3.5)
s≥s
¯
(3.6)
π(k, z, w) = max{F (k, l, z) − wl}
(3.7)
Where the profit function is given by:
l≥0
3.3
Government
Governments run a balanced budget transferring tax revenues from taxes on income, capital
gains, dividends, and corporate profits.
The Government Budget Constraint is:
T = τc
Z
(π(k, z; w)−δk)µ(dk, dz)+τd
Z
d(k, z; w)µ(dk, dz)+τi wL̄−τg
Z
s(k, z; w)µ(dk, dz)
(3.8)
3
Table 1: Common Parameters
Parameter
δ
β
αk
αl
ρ
σz
Value
0.095
0.971
0.611
0.351
0.797
0.211
The for households to purchase shares, the expected return on a share on holding equity
must be the same as the return on holding risk free bonds. This is the no arbitrage condition
that determines the asset market equilibrium.
The after tax return on a bond is (1 − τi )r. The expected return on equity is given by:
Rt =
1
0
Et [(1 − taud )dt+1 + (1 − taug )(Pt+1
− Pt )]
Pt
(3.9)
Asset pricing equilibrium implies that (1 − τi )r = Rt .
I’ll want to analyze the long run effects and so look at the steady state.
Equilibrium: Stationary Recursive Competitive Equilibrium:
• Stationary dist of firms.
• Firms max given prices.
• HH max given prices.
• Goods market clears.
• Labor market clears.
Using a GE framework is important because of the feedback of wages dampens the
effect of tax policy. E.g. lower dividend taxes increases the capital stock and so increase the
marginal product of labor and thus the wage. The higher wage means lowers the marginal
product of capital.
FIGURE: Show policy function- esp one that show different financing regimes.
4
Effects of Tax policy When Frictions are Present
Figures: show have investment change of 1% decrease in the dividend tax rate, cap gains
tax rate, and corporate profits when change parameters of frictions (real quad costs, real
fixed costs, financing fixed cost, financing variable cost).
5
Data
I use annual firm level data from Compustat. All the variables are readily available from
this dataset.
I drop financial and regulated firms (SIC codes 4900-4999 and 6000-6999) and those with
missing values for the important variables (dividends, equity issued, capital, earnings). I
4
Table 2: Tax Changes
Model
Decrease τc by 1%
∆C
∆I
∆T
∆I
Decrease τd by 1%
∆C
∆T
Decrease τg by 1%
∆C
∆I
No Cost
ψ
ψ, φ0
ψ, φ0 , φ1
ψ, F
ψ, F , φ0
ψ, F , φ0 , φ1
also drop firms with less than one million dollars of capital and those with less than two
million dollars in assets to avoid rounding errors.
I have about 80,000 firm-year observations for the 1988-2002 period. I use this period
to calculate all the moments that I estimate the model with.
Summary Stats...
Say something about how dividends issued change after tax changes...
Figure 5 shows the fractions of firms in the various financing regimes before and after the
2003 tax cuts. As Chetty and Saez (2005) find, dividend issuance increases. Also notable,
us increase in equity issuance. The two of these together mean that less firms are liquidity
constrained.
.01
.02
.03
Ratio
.04
.05
.06
Equity−Capital Ratio
Ratio
.04 .045 .05 .055 .06 .065 .07 .075 .08
Dividend−Capital Ratio
1988
1990
1992
1994
1996
1998
Year
2000
2002
2004
2006
2008
1988
Source: Computstat
1990
1992
1994
1996
1998
Year
2000
2002
2004
2006
2008
Source: Computstat
(a) Dividend-Capital Ratio
(b) Equity Issuance - Capital Ratio
Earnings−Capital Ratio
.25
.15
.3
.16
.17
.35
Ratio
Ratio
.4
.18
.19
.45
.2
.5
Investment−Capital Ratio
1988
1990
1992
1994
1996
1998
Year
2000
2002
2004
2006
2008
1988
Source: Computstat
1990
1992
1994
1996
1998
Year
2000
2002
2004
2006
2008
Source: Computstat
(c) Investment - Capital Ratio
(d) Earnings - Capital Ratio
Figure 2: Aggregate Corporate Investment and Financing Behavior.
Figure 5 shows the number of firms in different financing regimes. In the equity issuance regime, the marginal source of funds is new equity (corresponding to the traditional
view) in the dividend distribution regime, the marginal source of funds is retained earnings
5
∆T
Table 3: Data Moments
Variable
Corr Investment and Profit Shocks
Serial Corr Investment Rate
Serial Corr New Equity Issues
a1
a2
a3
a4
Compustat Value
0.244
0.555
0.155
0.277
0.009
2.491
-0.012
Std. Error
(0.001)
(0.003)
(0.003)
(0.044)
(0.001)
(0.036)
(0.000)
(corresponding tot he new view).
Dividend Distribution Regime
.15
.2
.34 .36 .38
Fraction of Firms
.25
.3
.35
Fraction of Firms
.4 .42 .44 .46 .48
.5
.4
Equity Issuance Regime
1988
1990
1992
1994
1996
1998
Year
2000
2002
2004
2006
2008
1988
Source: Computstat
1990
1992
1994
1996
1998
Year
2000
2002
2004
2006
2008
Source: Computstat
(a) Equity Issuance Regime
(b) Dividend Distribution Regime
.22
.24
Fraction of Firms
.26 .28
.3
.32
.34
.36
Liquidity Constrained Regime
1988
1990
1992
1994
1996
1998
Year
2000
2002
2004
2006
2008
Source: Computstat
(c) Liquidity Constrained Regime
Figure 3: Financing Regimes.
6
6.1
Estimation
Estimation of the Profit Function and Productivity Process
Profit functions imply linear regression models and are estimated by OLS with time and
firm fixed effects.
Assuming that F (k, l, z) = zkαk lαl then corporate profits are given by π(k, z; w) =
1
αl
(1 − αl )(zkαk ) 1−αl ( αwl ) 1−αl . Taking the natural log of the profit function one can form the
following:
ln(πi,t ) = α0 + α1 ln(ki,t ) + α2 ηi,t
6
(6.1)
Table 4: Parameters Estimated Outside SMM
Parameter
αk
ρ
σz
Value
0.297
0.761
0.312
Std Error
(0.001)
(0.003)
(0.001)
Table 5: Calibrated Parameters
Parameter
β
δ
αl
Value
0.971
0.095
0.65
The error term, ηit has a common component, bt and a firm-specific component, ei t.
Thus ηi,t = bt + ei,t . Then the log profits function becomes:
ln(πi,t ) = α0 + α1 ln(ki,t ) + b̃t + ẽi,t
(6.2)
αk
Running the regression specified by Equation 6.2 identifies the parameter α1 = (1−α
.
l)
I set αl equal to 0.65, following Gourio and Miao (2008). Thus I find that αk = 0.297.
To find the AR(1) process that is technology, I fit an AR(1) to zit = (1 − αl )ẽi,t :
zi,t = ρzi,t−1 + σui,t
(6.3)
I find that ρ̂=0.761 and σ̂=0.312.
The rate of time preference and the rate of depreciation are calibrated. β = 0.971, δ =
0.095.
Taxes are set to the statutory rate or are set for at a rate for some representative
household.
subsubsectionStructural Estimation
After the estimating the profit function and the process for the idiosyncratic productivity
shocks, I use a simulated method of moments procedure (SMM) to identify the parameters
of the cost functions.
The parameters Θ = (ψ, F, φ0 , φ1 ) are estimated using a simulated method of moments
(SMM) approach as described in McFadden (1989). The choice of SMM is because estimation based off the Euler equations cannot be done with non-convex costs of adjustment and
because firms transition between financing regimes, another non-continuity in the decision
rules.
SMM estimation has the following algorithm. Given the parameters of the profit function
and productivity process and a vector Θ, the dynamic programming problem (DPP) of the
firms is solved. The solution to the DPP is a set of policy functions determining the
firm’s optimal choice of investment, dividend distribution and equity issuance given their
productivity and capital stock. The policy functions are used to solve for the stationary
distribution of firms over capital and productivity. From the stationary distribution, I
calculate a set of moments. Call the vector of simulated moments Ψs (Θ).
The estimate, Θ̂, is the vector of parameters that minimizes the weighted distance
between Ψs (Θ) and the vector of moments from the data, Ψd . Formally, Θ̂ solves:
£(Θ) = minΘ [Ψd − Ψs (Θ)]′ W [Ψd − Ψs (Θ)]
7
(6.4)
Table 6: Data Versus Model Moments
Model
Data
No Cost
ψ
ψ, φ0
ψ, φ0 , φ1
ψ, F
ψ, F , φ0
ψ, F , φ0 , φ1
Corr Investment and Profit Shocks
0.244
Serial Corr Investment Rate
0.555
Serial Corr New Equity Issues
0.155
Where W is the optimal weighting matrix , calculated as the inverse of the variancecovariance matrix of the moments, following Gourieroux, Monfort and Renault (1993). The
variance-covariance matrix is found by bootstrapping the moments from the data. Using
the SMM procedure with the optimal weighting matrix ensures consistent and efficient
estimates of Θ.
6.1.1
Moments and Identification
Identification of the real frictions, ψ, F and the financial frictions, φ0 , φ1 is achieved by
use of the following moments: the serial correlation of investment rates, the correlation
between the investment rate and productivity, the serial correlation of equity issuance, and
the coefficients a1 , a2 , a3 , a4 from the following regression:
Regression of investment rate on profits and equity issuance:
πit
πit
sit
sit
iit
= a0 + a1
+ a2
+ a3
+ a4
+ δt + ǫit
kit
kit
kit
kit
kit
(6.5)
The serial correlation of investment rates, helps to pin down both the size and nature of
the real costs of adjustment. If the costs of adjustment are quadratic, firms will try to spread
investment out over several periods, leading to a higher serial correlation of the investment
rate. On the other hand, if non-convexities are present, firms will make large investments
in a single period, leading to a low serial correlation. If the correlation between investment
and productivity is high, this means that the quadratic costs of adjustment are low or that
there are non-convexities in the costs of adjusting capital. The serial correlation of equity
issuance is important in identifying the fixed costs involved in issuing equity. Finally, the
regression coefficients further identify the costs parameters. a1 and a2 help to identify the
real costs, while a3 and a4 help to identify the financial frictions.
7
Results of Estimation
8
Policy Experiments
Change of JGTRRA.
Graph of transition to steady state for capital stock, consump, etc
Table with changes to investment and consumption in the long run from the div tax
change
Proposed changed by Obama and McCain. McCain- lower max corporate profit tax
from 35% to 25%. Obama- increase max capital gains tax from 15% to 20%.
8
a1
0.277
a
0.0
Table 7: Parameter Estimates from SMM
Model
No Cost
ψ
ψ, φ0
ψ, φ0 , φ1
ψ, F
ψ, F , φ0
ψ, F , φ0 , φ1
ψ
0
F
0
0
0
0
φ0
0
0
φ1
0
0
0
0
0
0
Table 8: 2003 Dividend Tax Cuts
Aggregate Variable
Investment
Capital
Consumption
Tax Revenue
Pre-2003
τg = 0.20, taud = 0.25
Post-2003
τg = 0.15, τ d = 0.15
Table 9: McCain and Obama Plans
Aggregate Variable
Investment
Capital
Consumption
Tax Revenue
Baseline (Post-2003)
τg = 0.15, τ d = 0.15, τc = 0.34
9
McCain
τg = 0.15, τ d = 0.15, τc = 0.25
Obama
τg = 0.25, τ d = 0.15, τc = 0.34
9
Long Run Costs of Various Tax Policy
MCPF with div, cap gains, corp profits. Revenue equal change better than div tax cut?
Elasticity of investment to various taxes.
Table with % changes in I, C, for change in various taxes
10
Conclusion
References
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10