# Do Financial Frictions Amplify Fiscal Policy? Evidence

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- **Document type:** Agency decision

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Do Financial Frictions Amplify Fiscal Policy? Evidence
from Business Investment Stimulus∗
Eric Zwick
Harvard University

James Mahon
Harvard University

zwick@fas.harvard.edu

jmahon@fas.harvard.edu

November 25, 2013

Abstract
We estimate the causal effect of temporary tax incentives on equipment investment
using a difference-in-differences design and policy shifts in accelerated depreciation. Analyzing data for over 120,000 US firms from 1993 to 2010, we present three findings. First,
bonus depreciation raised investment by 18.5 percent on average between 2001 and 2004
and 31.2 percent between 2008 and 2010. Second, financially constrained firms respond
more than unconstrained firms. And third, firms respond strongly when the policy generates immediate cash flows, but do not respond at all when the policy only benefits them
in the future. The results provide an estimate of the discount rate firms apply to future
cash flows: constrained firms act as if $1 next year is worth 38 cents today. The estimated
discount rate is too high to match the predictions of a frictionless model, nor can it be
explained entirely by costly external finance, unless firms also neglect financial constraints
binding in the future.

JOB MARKET PAPER

∗

Zwick thanks Raj Chetty, David Laibson, Josh Lerner, David Scharfstein and Andrei Shleifer for extensive
advice and support. We thank Gary Chamberlain, George Contos, Ian Dew-Becker, Fritz Foley, Paul GoldsmithPinkham, Robin Greenwood, Sam Hanson, Ron Hodge, John Kitchen, Pat Langetieg, Day Manoli, Isaac Sorkin,
Larry Summers, Adi Sunderam, Nick Turner, Danny Yagan and seminar and conference participants at Harvard,
the IRS, Oxford, the US Treasury and Washington University in Saint Louis for comments, ideas, and help with
data. We are grateful to our colleagues in the US Treasury Office of Tax Analysis and the IRS Office of Research,
Analysis and Statistics—especially Curtis Carlson, John Guyton, Barry Johnson, Jay Mackie, Rosemary Marcuss
and Mark Mazur—for making this work possible. The views expressed here are ours and do not necessarily
reflect those of the US Treasury Office of Tax Analysis, nor the IRS Office of Research, Analysis and Statistics.
Zwick thanks the Harvard Business School Doctoral Office for financial support.

1

1

Introduction

Going back to Hall and Jorgenson (1967), public and macroeconomists have asked how taxes
affect investment. The answer is central to the design of countercyclical fiscal policy, since
policymakers often use tax-based investment incentives to spur growth in times of economic
weakness. Such policies typically coincide with disruptions in capital markets, so it is natural
to ask how taxes affect investment in the presence of financial frictions. However, the standard
theoretical and empirical treatments assume perfect capital markets.1 This paper uses recent
episodes of investment stimulus to study whether the effect of taxes on investment accords
with the standard, frictionless model. We find that, in ignoring financial frictions, the standard
analysis overlooks a crucial driver of firm responses to tax policy.
The policy we study, “bonus” depreciation, accelerates the schedule for when firms can
deduct from taxable income the cost of investment purchases. Bonus alters the timing of deductions but not their amount, so the economic incentive created by bonus works because
future deductions are worth less than current deductions. That is, bonus works because of
discounting: firms judge the benefits of bonus by the present discounted value of deductions
over time.2 Speeding up the timing of deductions reduces short term taxes, but at the expense
of higher taxes in the future. With a reasonable risk-adjusted discount rate, bonus depreciation generates a modest subsidy, so the frictionless model predicts a small effect of bonus on
investment.3 But in the presence of financial frictions, firms sharply discount future deductions. Thus financial frictions make bonus more appealing, since the difference in today’s tax
benefits dwarfs the present value comparison that matters in theory.
We study two episodes of bonus depreciation using a standard difference-in-differences
methodology to estimate the effect of these policies. We present three empirical findings. First,
1

Key theoretical studies include Hall and Jorgenson (1967), Tobin (1969), Hayashi (1982), Abel and Eberly
(1994), and Caballero and Engel (1999). Abel (1990) presents a unifying synthesis of the early theoretical
literature. Key empirical work includes Summers (1981), Auerbach and Hassett (1992), Cummins, Hassett and
Hubbard (1994), Chirinko, Fazzari and Meyer (1999), Desai and Goolsbee (2004), Cooper and Haltiwanger
(2006), and House and Shapiro (2008). Edgerton (2010) relaxes the frictionless assumption but, in contrast to
our study, finds mixed results.
2
Summers (1987) states this most clearly: “It is only because of discounting that depreciation schedules affect
investment decisions. . . ”
3
Consider a firm making a $100 investment in computer equipment, which the IRS assigns a depreciation life
of five years. Under the normal schedule, a firm can only deduct from taxable income $20 in the year of the
purchase and must spread the remaining $80 over the next five years. Assuming a seven percent risk-adjusted
discount rate, the difference in present values for even full expensing—i.e., 100 percent bonus, which lets the
firm deduct $100 in the purchase year—implies a subsidy of less than four percent.

2

bonus depreciation has a substantial effect on investment, much larger than past estimates and
much stronger than the conventional wisdom predicts. Estimates of how tax changes affect
investment vary, but the consensus prediction is that bonus depreciation has a small positive
effect.4 In contrast, we find that bonus depreciation raised eligible investment by 18.5 percent
on average between 2001 and 2004 and 31.2 percent between 2008 and 2010. We estimate
a user cost elasticity of approximately 1.6, outside the range of estimates of 0.5 to 1 surveyed
by Hassett and Hubbard (2002) and more than double the consensus point estimate.5
The first part of the paper details this finding and a litany of robustness tests. The research
design compares firms at the same point in time whose benefits from bonus differ. Our strategy exploits technological differences between firms in narrowly defined industries. Firms in
industries with most of their investment in short duration categories act as the “control group”
because bonus only modestly alters their depreciation schedule. This natural experiment separates the effect of bonus from other economic shocks happening at the same time. If the
parallel trends assumption holds—if investment growth for short and long duration industries
would have been similar absent the policy—then the experimental design is valid.
The key threat to this design is that time-varying industry shocks may coincide with bonus.
This risk is limited for four reasons. First, graphical inspection of parallel trends indicates
smooth pretrends and a clear, steady break for short and long duration firms during both the
2001 to 2004 and 2008 to 2010 bonus periods. The effects are the same size in both periods,
though different industries suffered in each recession. Second, the estimates are stable across
many specifications and after including firm-level cash flow controls, industry Q, and flexible industry trends. Allowing industry-level co-movement with the macroeconomy actually
increases our estimates. Third, the estimates pass a placebo test: the effect of bonus on ineligible investment is indistinguishable from zero. Last, for firms making eligible investments,
bonus take-up rates (i.e., do firms fill in the bonus box on the tax form?) are indeed higher in
long duration industries. For these reasons, spurious factors are unlikely to explain the large
4

Cummins, Hassett and Hubbard (1994) study many corporate tax reforms and public company investment
data and conclude that tax policy has a strong effect on investment. Using similar data and a different empirical
methodology, Chirinko, Fazzari and Meyer (1999) argue that tax policy has a small effect on investment and that
Cummins, Hassett and Hubbard (1994) misinterpret their results. Hassett and Hubbard (2002) survey empirical
work and conclude that the range of estimates for the user cost elasticity has narrowed to between -0.5 and -1.
Surveying this and more recent work, Bond and Van Reenen (2007) decide “it is perhaps a little too early to agree
with Hassett and Hubbard (2002) that there is a new ‘consensus’ on the size and robustness of this effect.”
5
In Section 5, we collect estimates from past studies of tax reforms. The average user cost elasticity across
these studies is 0.69.

3

effect of bonus.
Firms respond to bonus depreciation as if they apply implausibly high discount rates to
investment decisions. This finding is inconsistent with a frictionless model of firm behavior.
In the second part of the paper, we explore alternative models that generate high effective
discount rates by adding financial frictions.6 One alternative is costly external finance, which
raises the total discount rate firms apply to evaluate projects. Another alternative is managerial
myopia, which raises effective discount rates by sharply discounting the future relative to the
present. Both models prove useful in explaining our findings.
Our second empirical finding is that, consistent with the costly external finance story, financial constraints amplify the effects of investment stimulus. Nearly all prior empirical tests
of financial constraints use public firm data, which is problematic because public firms have
the best collateral, the strongest banking relationships and broad access to equity and bond
markets.7 In contrast, we work with an analysis sample of more than 120,000 public and private companies drawn from two million corporate tax returns. Half the firms in our sample are
smaller than the smallest firms in Compustat.8 Our baseline estimate therefore averages over
substantial heterogeneity in firm type, including many firms likely to face financial constraints.
The largest firms in our sample, those most like the firms in past studies, yield estimates in
line with the Hassett and Hubbard (2002) range. In contrast, small and medium-sized firms,
previously unstudied, show much stronger responses. Building on the differential response by
firm size, we perform a split sample analysis using several markers of ex ante financial constraints. In addition to small firms, non-dividend payers and firms with low cash holdings are
1.5 to 2.6 times more responsive than their unconstrained counterparts. Moreover, we find
that firms respond by borrowing and cutting dividends. These facts do not match the frictionless model of investment behavior, in which firms divided by financial constraint markers do
not respond differently to bonus.
Firms with tax losses must wait to realize the benefits of tax breaks. Because many firms
6

We use the term financial frictions as an umbrella term over a class of models that generate high effective
discount rates. Some of these—such as managerial myopia and agency theory—are not about external finance
per se, but refer instead to organizational frictions. These theories have not crossed from the finance literature
into standard public and macroeconomics treatments.
7
Kaplan and Zingales (1997) find that very few of Fazzari, Hubbard and Petersen’s (1988a) most constrained
firms appear constrained by other measures.
8
When aggregated, these small firms account for a large amount of economic activity. According to Census
tabulations in 2007 (http://www.census.gov/econ/susb/data/susb2007.html), firms with less than
$100 million in receipts (around the 80th percentile in our data) account for more than half of total employment
and one third of total receipts.

4

in our sample are in a tax loss position when a policy shock occurs, we can ask whether firms
value future cash windfalls, namely, the larger deductions bonus depreciation provides them
in later years. Our third empirical finding is that, consistent with the managerial myopia
story, firms only respond to investment incentives when the policy immediately generates cash
flows. This finding holds even though firms can carry forward unused deductions to offset
future taxes, and it cannot be explained by differences in growth opportunities. Furthermore,
this fact contradicts a simple model of costly external finance, because firms neglect how the
policy affects borrowing in the future.
To confirm the myopia story, we study a second component of the depreciation schedule. Firms making small investment outlays face a permanent kink in the tax schedule, which
creates a discontinuous change in marginal investment incentives. This sharp change in incentives induces substantial investment bunching, with many firms electing amounts within just
a few hundred dollars of the kink. And when legislation raises the kink, the bunching pattern
follows. Consistent with myopia, bunching strongly depends on a firm’s current tax status:
firms just in positive tax position are far more likely to bunch than firms on the other side of
the discontinuity. For a different group of firms and a different depreciation policy, we again
find that firms ignore future tax benefits.
These facts do not match the predictions of a frictionless model, which cannot account for
the large baseline response, the differential response for constrained firms or the nonresponse
for nontaxable firms. The facts point instead toward models in which costly finance matters
and current benefits outweigh future benefits. We use an investment model to clarify these
findings. The model incorporates costly external finance and managerial myopia into a general
model in which the frictionless model of Hayashi (1982) is a special case. These alternative
theories make predictions about the discount rate firms apply to future cash flows. The model
shows how to combine reduced form estimates to distinguish the frictionless benchmark from
costly external finance and managerial myopia.
The general model yields a set of theoretical moments—one comparing constrained and
unconstrained firms and one comparing taxable and nontaxable firms—which we can combine
with our empirical findings to measure financial frictions. With these comparisons we can
estimate the shadow cost of external funds and an implied present versus future discount
factor. We estimate the shadow cost of external funds to be between $0.63 and $1.61 per
dollar and an implied discount factor of 0.84. Combining these results, financially constrained
5

firms act as if $1 next year is worth just 38 cents today, yielding a total discount rate of 97
percent. Thus accounting for the effect of bonus depreciation on investment requires a major
role for financial frictions.
The logic of the general model is simple. The optimal investment decision trades off the
after-tax future benefits of the marginal dollar of investment against its price and the marginal
external finance cost, less the marginal benefit due to depreciation deductions. Deductions
reduce the marginal cost of investment both through their net present value and through
relaxing the external finance constraint. By returning more cash in earlier years, bonus depreciation makes investment a better tax shield; by raising the value of cash back, financial
constraints amplify this effect. There are two differences between taxable and nontaxable
firms. First, if a firm owes no taxes in period zero, depreciation deductions only relax future
financial constraints. Second, because the deductions must wait, the effect of bonus on current
investment operates exclusively through discounted expectations of future benefits. If future
benefits don’t matter, neither does bonus.
Our paper sits at the intersection of several strands in the economics and finance literatures. Most directly, the paper relates to studies of the effect of taxes on business investment.9
The paper also relates to the literature on financial constraints.10 Our findings imply that
incorporating financial frictions adds much explanatory power to neoclassical investment theory.11 In the literature on salience and taxation, our study offers an example of a strong tax
policy effect on economic behavior.12
The outline of the paper is as follows. Section 2 describes the paper’s methodological approach and how it relates to past studies. Section 3 formalizes intuition about how bonus
works and develops a set of testable hypotheses, which guide the empirical analysis. Section 4
describes the corporate tax data, variable construction and sample selection process. Section
9

The modern empirical literature begins with Hall and Jorgenson (1967). Recent studies include Desai and
Goolsbee (2004), Edgerton (2010) and Yagan (2013).
10
Fazzari, Hubbard and Petersen (1988a) argue that, if firms more likely to be financially constrained respond
more strongly to cash flow shocks, then financial constraints are responsible. Subsequent studies make this
argument while identifying quasi-experimental variation in cash flows or credit supply (Lamont, 1997; Rauh,
2006; Chaney, Sraer and Thesmar, 2012). We apply this insight to the case of bonus depreciation, which creates
a shock to the amount of cash firms need to perform their desired investment.
11
Hayashi (1982) derives the workhorse neoclassical model. Stein (2003) surveys models in which financial
frictions influence investment decisions.
12
Our evidence is consistent with the strong behavioral response to and salience of the Earned Income Tax
Credit (Chetty, Friedman and Saez, 2013). It stands, for instance, in contrast to evidence that individuals react
incompletely to obscure taxes (Chetty, Looney and Kroft, 2009) and that business investment does not react to
changes in the dividend tax (Yagan, 2013).

6

5 describes the main empirical strategy for studying bonus depreciation, the identification
assumptions and presents results. Section 6 uses split sample tests by markers of financial
constraints and by tax position to show financial frictions can account for the large baseline
effect of bonus. Section 7 develops a set of theoretical moments and combines the empirical
results to test between models and estimate implied discount rates. Section 8 studies substitution margins and external finance responses to bonus. There, we use our heterogeneous size
results to estimate the aggregate investment effect. Section 9 discusses policy implications and
avenues for future research.

2

Conceptual Framework and Related Literature

Consider a firm buying $1 million worth of computers. The firm owes corporate taxes on
income net of business expenses. For expenses on nondurable items such as wages and advertising, the firm can immediately deduct the full cost of these items on its tax return. Thus, an
extra dollar of spending on wages reduces the firm’s taxable income by a dollar and reduces
the firm’s tax bill by the tax rate.13 But for investment expenses the rules differ.
Usually, the firm follows the regular depreciation schedule in the top panel of Table 1.
The first year deduction is $200 thousand, which provides an after-tax benefit of $70 thousand. Over the next five years, the firm deducts the remaining $800 thousand. The total
undiscounted deduction is the $1 million spent and the total undiscounted tax benefit is $350
thousand. With bonus depreciation the situation changes. Assume fifty percent bonus. The
firm can now deduct a $500 thousand bonus before following the normal schedule for the
remaining amount, so the total first year deduction rises to $600 thousand. Each subsequent
deduction falls by half.
The total amount deducted over time does not change. However, the accelerated schedule
does raise the present value of these deductions. Applying a seven percent discount rate yields
$311 thousand for the present value of cash back in normal times. Bonus raises this present
value by $20 thousand, just two percent of the original purchase price. This small present
13

The exact benefit depends on the marginal tax rate, which in turn depends on tax rate progressivity and the
level of other expenses relative to taxable income. See, e.g., Graham (1996, 2000) for a method tracing out the
marginal tax benefit curve. The policies we study will increase the use of investment as a tax shield regardless
of where the firm is on this marginal benefit curve. Except when current and all future taxes are zero, bonus
increases the marginal tax benefit of investment.

7

Table 1: Regular and Bonus Depreciation Schedules for Five Year Items
Normal Depreciation
Year

0

1

2

3

4

5

Total

Deductions (000s)
Tax Benefit (τ = 35%)

200
70

320
112

192
67.2

115
40.3

115
40.3

58
20.2

1000
350

Bonus Depreciation (50%)
Year

0

1

2

3

4

5

Total

Deductions (000s)
Tax Benefit (τ = 35%)

600
210

160
56

96
33.6

57.5
20.2

57.5
20.2

29
10

1000
350

Notes: This table displays year-by-year deductions and tax benefits for a $1 million investment in computers,
a five year item, depreciable according to the Modified Accelerated Cost Recovery System (MACRS). The top
schedule applies during normal times. It reflects a half-year convention for the purchase year and a 200 percent
declining balance method (2X straight line until straight line is greater). The bottom schedule applies when 50
percent bonus depreciation is available. See IRS publication 946 for the recovery periods and schedules applying
to other class lives.

value payoff is why some authors conclude that bonus provides little stimulus for short-lived
items (Desai and Goolsbee, 2004).14
In a frictionless model, a firm will judge the benefits of bonus by comparing these present
value payoffs.15 Note however the large difference in the initial deduction, which translates
into $140 thousand of savings in the investment year. Such a difference will matter if firms
must borrow to meet current expenses and external finance is costly. Or it will matter if
managers display myopia. The same high discount rate that causes myopic managers to underinvest in long-term, low-visibility activities will cause them to overinvest in short term,
cash flow generating activities. One such short term activity might be using bonus to reduce
current taxes at the expense of higher future taxes. Below, we find that bonus caused a large
increase in eligible investment and financial frictions—whether due to costly external finance
or to managerial myopia—offer the best explanation.
14

See also Steuerle (2008), Knittel (2007) and House and Shapiro (2008). In his comment on Desai and
Goolsbee (2004), Kevin Hassett argues that the temporary nature of these policies increases the stimulus through
intertemporal shifting, and that the authors’ results are consistent with a large response; see also Cohen, Hansen
and Hassett (2002). The intertemporal shifting story cannot explain our heterogeneity results and predicts
aggregate patterns which we do not observe.
15
This is true whether the policy is temporary or permanent. If temporary, the firm will also take account of
future present value payoffs, as in Auerbach and Hassett (1992). In their setup, expected future tax increases
(e.g., expiration of temporary stimulus) reduce the current user cost and generate larger current stimulus. Still,
the full discounted stream of deductions determines the effect size.

8

To show the effect of bonus depreciation on investment, we adopt the same methodological
approach as Cummins, Hassett and Hubbard (1994), in which technology differences between
firms imply that investment tax breaks benefit some more than others.16 Like Cummins, Hassett and Hubbard (1994) and Edgerton (2010), we proxy for the firm-level benefit of bonus
depreciation with an industry measure of policy benefits. Unlike these studies, our measure
derives directly from tax data, reducing measurement error. From tax returns filed between
1993 and 2000, we compute average industry shares of eligible investment in each of the 3-,
5-, 7-, 10-, 15- and 20-year class lives. Applying these shares to a class-specific measure of
the present discounted value of deductions yields an industry-level value of deductions per
investment dollar. Bonus depreciation causes this present value to increase for all firms, but
the size of the benefit varies across industries. This allows a continuous treatment, differencein-differences experimental design.17
Our data improve on past studies by including two periods of bonus depreciation; a granular breakdown of eligible investment; a large sample of small, private firms; and better tax
variables. Except for House and Shapiro (2008), earlier studies pool the effects of different
tax reforms, which include depreciation changes, tax rate changes and rule changes regarding
corporate form. We focus on one specific policy, bonus depreciation, and carefully dissect how
firms respond. As a result, we can provide a new estimate of how much taxes affect investment
that also tells us which models match the results.
House and Shapiro (2008) study the first episode of bonus depreciation using aggregate
investment data. Their design compares residuals from a prediction model for investment in
short duration (e.g., computers) and long duration (e.g., blast furnaces) categories. One risk
here is that a misspecified prediction model will lead to measurement error in their residuals. Firm level data enable a cleaner research design. We compare firm investment growth
rates, so that our first difference does not depend on an estimated model. Their design also
suffers from the problem that only a few industries account for most long duration eligible
investment. Thus, the design assigns a few industries to the “treatment group” and a larger
number of dissimilar industries to the “control group.” More, the long duration categories
16
See also Cummins, Hassett and Hubbard (1996), Desai and Goolsbee (2004), House and Shapiro (2008) and
Edgerton (2010).
17
It is possible to apply the same strategy at the firm level. This approach does not alter our findings. We
present results for the industry level design to make our results as comparable to these other studies as possible.
In addition, cross-firm variation in investment composition is low within four-digit NAICS industries, so the
industry level design captures most of the quasi-experimental variation.

9

account for a small share of total eligible investment, so that their approach can only yield
an aggregate predicted effect under strong extrapolation assumptions across investment categories. Despite the same long duration/short duration logic, our experiment produces a more
balanced division of firms that relies less on outlying industries.
With this natural experiment, we show that investment responds strongly to bonus depreciation. We then run a series of split sample tests by ex ante indicators for financial constraints,
applying a standard methodology for documenting financial constraints going back to Eisner
(1978) and Fazzari, Hubbard and Petersen (1988a). Suppose firms differ in how easily they
can finance new investments. After sorting firms along this dimension, if constrained firms
respond more to cash flow shocks, then we should reject the perfect capital markets model in
favor of a model with financial constraints. Fazzari, Hubbard and Petersen (1988a) make and
test this argument and find that financial constraints matter.
Subsequent studies ask if Fazzari, Hubbard and Petersen (1988a)’s outcome measure, the
investment-cash flow sensitivity, offers a reliable test. In a static model with a general cost
function, this measure does not increase monotonically with external finance costs (Kaplan
and Zingales, 1997). In more general models, even when financing constraints are absent,
investment responds to cash flow (Gomes, 2001; Alti, 2003) and small, growing firms can display higher sensitivities than big, stable firms (Abel and Eberly, 2011). This motivates taking
the split sample approach to settings with plausibly exogenous shocks to cash flows (Lamont, 1997; Rauh, 2006). or credit supply (Chaney, Sraer and Thesmar, 2012).18 We follow
these latter studies and use depreciation changes as a plausibly exogenous financial constraint
shock.19 Unlike past studies, our instrument also changes the relative price of investment. We
use this feature and an investment model to estimate the shadow price of internal funds from
the difference between constrained and unconstrained firm elasticities.20
The tax code allows us to ask a related question about financial frictions: what do firms
do with future cash windfalls? Cummins, Hassett and Hubbard (1995) and Edgerton (2010)
note that tax losses will reduce the incentive of firms to respond to tax changes. The former
study uses a sample of sixty loss firms to conclude that losses reduce the effect of tax breaks
on investment. The latter maps financial accounting data to a tax account and finds mixed
18

Others study cash management policies directly (Almeida, Campello and Weisbach, 2004).
See the conclusion of Fazzari, Hubbard and Petersen (1988a) and Fazzari, Hubbard and Petersen (1988b) for
a discussion of how taxes might affect investment in the presence of financial constraints. They focus on average
tax rates more generally and do not perform an empirical analysis along these lines.
20
This is a similar exercise to Koijen and Yogo’s (2012) study of insurance companies.
19

10

evidence that losses matter.21 With our data, we can precisely measure whether a firm’s current
tax position means that the next dollar of investment affects this year’s tax bill. For tax loss
firms, the effect of bonus operates only through expected future payoffs. Our sample of loss
firms includes almost two hundred thousand loss year observations.
Our first split sample analysis compares financially constrained firms to unconstrained
firms, revealing that constrained firms respond more strongly to bonus. Our second split
sample analysis shows that currently taxable firms respond strongly while nontaxable firms
do not respond at all. These findings reveal how much the data depart from a frictionless
benchmark model. The next section introduces the theoretical framework we use to make this
point.

3

Hypothesis Development

To direct our empirical analysis, we develop a simple model of investment in the presence
of depreciation incentives, financial constraints and heterogeneous tax positions. We modify the neoclassical investment model with adjustment costs (Abel, 1982; Hayashi, 1982) by
introducing an external finance wedge and managerial myopia. The model yields a formal hypothesis corresponding to our baseline investment design: investment increases due to bonus
depreciation and increases more for industries doing longer lived investment. We develop two
further hypotheses corresponding to split sample tests. First, investment responds more when
firms face an external finance wedge. Second, investment responds less when firms are in tax
loss positions. Here, we focus on the intuition of the model and the mapping from theory to
empirical objects and tests. We use a simple one shot static investment model with a reduced
form credit wedge, in the spirit of Stein (2003).22 Appendix A derives the hypotheses in an
infinite horizon setting with adjustment costs and a dynamic leverage constraint.
21

Recent work documents large differences between “book” and tax accounts, which introduces the risk of
measurement error into such a mapping (see, e.g., Mills, Newberry and Trautman (2002). Edgerton (2010) is
very careful with this procedure, but acknowledges that “[one] cannot rule out, however, the possibility that
difficulties in measuring firms’ taxable status drive the relative unimportance of taxable status observed in the
Compustat data.”
22
This wedge is a reduced form model of a set of capital market frictions, which might reflect, e.g., costly
monitoring problems or adverse selection (Stein, 2003).

11

3.1

Model Setup

Consider a firm making a one shot investment decision. The firm begins with initial profits π0
and chooses a level of investment I to determine the capital stock and hence future profits.23
Future profits are given by π(I), taxed at the proportional corporate tax rate τ. The firm
discounts future flows at risk-adjusted rate r.
The tax code permits the firm to write off the cost of investment over time. The value
of these deductions depends on the tax rate and how the schedule interacts with the firm’s
discount rate. We collapse the stream of future depreciation deductions owed for investment:
z 0 (β) = D0 + β

T
X

1

(1 + r) t
t=1

Dt ,

(3.1)

where D t is the allowable deduction per dollar of investment in period t (e.g., D1 = .32 in the
normal schedule in Table 1) and T is the class life of investment (e.g., T = 5 in Table 1). z 0 (β)
measures the present discounted value of one dollar of investment deductions before tax. If
the firm can immediately deduct the full dollar, then z 0 equals one. Because of discounting,
z 0 is lower for longer lived items (i.e., items with greater T ), which forms the core of our
identification strategy.
In general, the stream of future deductions depends on future tax rates and discount rates.
Our empirical analysis assumes the effective tax rate does not change over time, except when
the firm is nontaxable.24 For discount rates, we begin by assuming a risk-adjusted rate of seven
percent to compute z 0 in the data, which enables comparison to past work. We then relax
this assumption in Section 7 when we estimate an implied discount rate. β is an additional
discount term between zero and one, which reflects the possibility of myopia.25 We use our
heterogeneity analysis to identify this term separately.26
23

Normalize the price of investment to one.
We use the top statutory tax rate in the set of specifications requiring a tax rate. This is an upper bound on
the more realistic effective marginal tax rate. In reality bonus would thus cause a smaller change in the tax term
than we impute, tending to bias our estimates downward.
25
The myopia model is closer to Akerlof (1991) and Laibson (1997) than it is to the model of managerial
myopia in Stein (1989). Stein’s (1989) model of managerial myopia specifically refers to the incentive to boost
current earnings as a way of signaling high quality to the stock market. We use the term to reflect any motive to
boost current earnings and neglect projects with long term payoffs and short term costs.
26
There may at first appear an inconsistency in this setup, because we do not apply β to future profits. This
is merely for notational convenience. In our analysis, we assume that β explicitly applies to depreciation deductions, which have both a present and future component. In the case of profits, which only arrive in the future,
we assume π incorporates β implicitly. Our analysis does not rely on measures of future profitability, which we
24

12

Bonus depreciation, the policy we study in our empirical analysis, allows the firm to deduct
a per dollar bonus, θ , at the time of the investment and then depreciate the remaining 1 − θ
according to the normal schedule:
z(β) = θ + (1 − θ )z 0 (β)

(3.2)

At different points in time, Congress has set θ equal to 0, 0.3, 0.5 or 1. We use these policy
shocks to identify the effect of bonus depreciation on investment. Industries differ by average
z 0 prior to bonus, providing the basis for identification in a difference-in-differences setup with
continuous treatment.
We further generalize z by incorporating a nontaxable state. When the next dollar of
investment does not affect this year’s tax bill, then the firm must carry forward the deductions
to future years.27 Our general z reflects this case:
z(β, γ) = γz(β) + (1 − γ)βφz(1),

(3.3)

where γ ∈ {0, 1} is an indicator for current tax state and φ is a discounter that reflects both
the expected arrival time of the taxable state and the discount rate applied to the future and
subsequent periods when the firm switches. Note that for the nontaxable firm, β applies to
all future deductions. Even when β equals one, φ is less than one, so the value of these
deductions are lower when the firm is nontaxable. We measure φ in the data and apply our
split sample results to determine whether we can justify these findings in a model without
myopia.
External finance matters for all investment exceeding current cash flow. During the investment period, the firm faces an external finance wedge that is linear in expenses net of cash
flows, that is,


c(I) = λ (1 − τz)I − (1 − τ)π0 ,

(3.4)

where λ can be thought of as the shadow price on a borrowing constraint that may or may not
bind now or in the future. Thus, a dollar of cash inside the firm is worth 1 + λ.28 We include
assume bonus does not affect in the infinite horizon.
27
This assumes that “carrybacks”—in which firms apply unused deductions this year against past tax bills—
have been exhausted or ignored. Carryback take-up rates are surprisingly low.
28
Note that because we have assumed a linear external finance function, there will be no direct effect of
cash flows on investment, that is, the investment-cash flow sensitivity is zero. This is not true in the general

13

z in the net expense term and not just the first year deduction, to capture the influence of depreciation deductions on future taxes and thus future borrowing.29 While bonus depreciation
relaxes the current constraint through reducing this year’s tax bill, it does so at the expense of
higher future taxes. The net effect is to reduce the present discounted borrowing costs for the
firm. However, if myopia plays a role (that is, for low β), then only the current year change
will matter. The two models thus yield different predictions for constrained, nontaxable firms:
constrained, myopic firms respond much less to bonus when nontaxable than do constrained,
farsighted firms. This is the feature we use to distinguish costly external finance from myopia
models, which are otherwise observationally equivalent.

3.2

Optimal Investment

We derive a condition for optimal investment. Though the problem occurs over time, we can
write it as a static one shot investment problem by discounting future flows to the present.
Discarding elements not involving investment, the firm’s objective is

max
I

(1 − τ)π(I)
1+r

− (1 − τz)I − λ(1 − τz)I


(3.5)

Here, we assume π is weakly concave, which ensures that the problem yields a unique interior
solution.
The first order condition for optimal investment is
(1 − τ)π0 (I ∗ ) = (1 + r)(1 + λ)(1 − τz).

(3.6)

Intuitively, the investment decision trades off the after-tax future benefits of the marginal
dollar of investment against its price (normalized to one) and the marginal external finance
cost, less the marginal benefit due to depreciation deductions. Deductions lower the hurdle
rate for investment both through their net present value and through relaxing the external
model, because the dynamic constraint makes the effective external finance function convex. Nevertheless, this
simplifying assumption is not worrisome. Because each dollar of investment can only generate at most 35 cents
of cash back, these policies cannot operate mainly through a direct cash windfall channel.
29
As modeled the constraint is closer to a long run credit constraint than it is to a liquidity constraint, which
would depend on current cash balances only. Recovering a β close to zero might imply that this distinction is
important. Note also that we do not include future profits in the external finance function. This is merely for
notational convenience and to fit the simple model more closely into the adjustment cost framework in the full
model.

14

finance constraint. With costly external finance, optimal investment is strictly lower than in
the frictionless case or when inside cash can cover all investment expenses (i.e., when λ = 0).

3.3

Testable Hypotheses

We derive three testable hypotheses from the model. The first concerns the average effect
of bonus depreciation on investment, while the latter two concern heterogeneous effects by
the presence of costly external finance and by tax position. Bonus depreciation increases
the present value of deductions, reducing the price of investment. Thus bonus depreciation
should increase investment. Each hypothesis builds on the comparative static with respect to
the bonus parameter θ . In the appendix, we show that investment is increasing in θ .
Hypothesis 1. Investment responds more strongly to bonus depreciation for industries with more
investment in longer lived eligible items. That is, ∂ 2 I/∂ θ ∂ z 0 < 0.
Bonus depreciation works through increasing θ . Hypothesis one concerns the basic effect
of this policy on investment. The more delayed the normal depreciation schedule is, the more
generous bonus will be. Longer lived items like telephone lines and heavy manufacturing
equipment have a more delayed baseline schedule than short lived items like computers (i.e.,
0
0
zLong
< zShort
). Thus, industries that buy more long lived equipment see a larger relative price

cut when bonus happens.
Our second hypothesis concerns how the investment response varies with costly external
finance.
Hypothesis 2. Investment responds more strongly to bonus depreciation for financially constrained firms. That is, ∂ 2 I/∂ θ ∂ λ > 0.
For financially constrained firms, bonus depreciation both reduces the price of investment
and reduces how much they have to borrow. The effective price change is thus larger for
constrained firms. We use several proxies for ex ante financial constraints—firm size, dividend
payment activity and liquid asset positions—to test for a difference in elasticities between
constrained and unconstrained firms. If financial constraints are unimportant, then we should
not find a consistent, systematic difference in elasticities for groups of firms based on these
proxies. We can use the difference in coefficients between constrained and unconstrained firms

15

to ask what the implied external finance spread. We formalize and implement this intuition in
Section 7.
Our third hypothesis concerns how the investment response varies with the firm’s current
tax position.
Hypothesis 3. Investment responds more strongly to bonus depreciation for firms with currentyear taxable income. That is, ∂ I/∂ θ |γ=1 − ∂ I/∂ θ |γ=0 > 0.
Hypothesis three emerges in any model with some positive discounting, since future benefits are worth less than immediate benefits. The main value of the comparison between taxable
and nontaxable groups derives from the calibration it offers. We can calibrate the expected
arrival of the taxable state for nontaxable firms and ask whether the difference between elasticities for taxable and nontaxable firms requires some myopia (i.e., β < 1).

4

Business Tax Data

The analysis in this paper uses the most complete dataset yet applied to study business investment incentives.30 The data include detailed information on equipment and structures
investment, offering a finer breakdown than previously available for a broad class of industries. The sample includes many small, private firms and all of the largest US firms, which
enables the heterogeneity analysis we use to document financial constraints. Because the data
come from corporate tax returns, we can separate firms based on whether the next dollar of
investment affects this year’s taxes. This allows a split sample analysis that can distinguish
the myopia model from a simple model of costly external finance. In this section, we describe
where these data come from and the analysis sample, as well as how we map the theory into
empirical objects.

4.1

Sampling Process

Each year, the Statistics of Income (SOI) division of the IRS Research, Analysis and Statistics
unit produces a stratified sample of approximately 100,000 unaudited corporate tax returns.31
30

Yagan (2013) uses these data to study the 2003 dividend tax cut. Kitchen and Knittel (2011) use these data
to describe general patterns in bonus and Section 179 take-up.
31
Details come from http://www.irs.gov/pub/irs-soi/08cosec3ccr.pdf.

16

Stratification occurs by form type,32 total assets, and proceeds. Each sample year includes returns with accounting periods ending between July of that year and the following June. When
necessary, we recode the tax year to align with the implementation of the policies studied in
this paper. In 2008, the sample represented about 1.8 percent of the total population of 6.4
million C and S corporation returns.
SOI uses these samples to generate annual publications documenting income characteristics. The BEA uses them to finalize national income statistics. In addition, the Treasury’s Office
of Tax Analysis (OTA) uses the sample to perform policy analysis and revenue estimation. To
enable these aggregate statistics, SOI carefully reports sampling weights which reflect each
observation’s sampling frequency. Our aggregate estimates incorporate these weights. Any
corporation selected into the sample in a given year will be selected again the next year, providing it continues to fall in a stratum with the same or higher sampling rate. Shrinking firms
are resampled at a lower rate, which introduces sampling attrition. We address this attrition
in several ways, including a nonparametric reweighting procedure for figures and through
assessing the robustness of our results in a balanced panel.

4.2

Analysis Samples, Variable Definitions and Summary Statistics

We create a panel by linking the cross sectional SOI study files using firm identifiers.33 The raw
dataset has 1.84 million rows covering the years from 1993 to 2010. There are 355 thousand
distinct firms in this dataset, 19,711 firms with returns in each year of the sample and 62,478
firms with at least 10 years of returns. Beginning with the sample of firms with valid data
for each of the main data items analyzed, we keep firm-years satisfying the following criteria:
(a) having non-zero total deductions or non-zero total income34 and (b) having an attached
investment form.35 In addition, we exclude partial year returns, which occur when a firm
32

For example, C corporations file form 1120 and S corporations file form 1120S. Other form types include
real estate investment trusts, regulated investment companies, foreign corporations, life insurance companies,
and property and casualty insurance companies. Sampling frequencies reflect the distribution of these types in
the population. We focus on 1120 and 1120S, which cover the bulk of business activity in industries making
equipment investments.
33
We thank OTA staff for providing the data crosswalk.
34
Knittel et al. (2011) use a similar “de minimus” test to select business entities that engage in “substantial”
business activity.
35
Form 4562 is the tax form that corporations attach to their return to claim depreciation deductions on new
and past investments. An entity that claims no depreciation deductions need not attach form 4562. It is likely
that these firms do not engage in investment activity, and so their exclusion should not affect the interpretation
of results.

17

closes or changes its fiscal year. To analyze bonus depreciation, we exclude firms potentially
affected by Section 179, a small firm investment incentive which we analyze separately. Our
main bonus analysis sample consists of all firms with average eligible investment greater than
$100,000 during years of positive investment.36 This sample consists of 820,769 observations
for 128,151 distinct firms.
This section describes the economic concepts underlying the variables we study. Eligible
investment, our main variable of interest, includes expenditures for all equipment investment
put in place during the current year for which bonus and Section 179 incentives apply.37
We conduct separate analyses for intensive and extensive margin responses. The intensive
margin variable is the logarithm of eligible investment. The extensive margin variable is an
indicator for positive eligible investment. We aggregate this indicator at the industry level and
transform it into a log odds ratio38 for our empirical analyses. In some specifications, we use
an alternative measure of investment, which is eligible investment divided by lagged capital
stock. Capital stock is the reported book value of all tangible, depreciable assets. Sales equals
operating revenue and assets equals total book assets. Total debt equals the sum of non-equity
liabilities excluding trade credit. Liquid assets equals cash and other liquid securities. Payroll
equals non-officer wage compensation. Rents equals lease and rental expenses. Interest
equals interest payments.
Our main policy variable of interest, zN,t , is the present discounted value of one dollar of
deductions for eligible investment. In each non-bonus year, we compute the share of eligible
investment a firm reports in each category.39 We use these shares and the present value of
one dollar of eligible investment for each category to construct a weighted average, firm-level
z. Category z’s come from applying a seven percent discount rate to the pertinent deduction
36

The relevant threshold for Section 179 was $25,000 until 2003, when it increased to $100,000. In 2008, it
increased to $250,000 and then to $500,000 in 2010. Using alternative thresholds in the range from $50,000 to
$500,000 does not alter the results.
37
Section 179 and bonus rules differ slightly, in that Section 179 also applies to used equipment purchases,
while bonus only applies to new equipment. The form does not require firms to list used purchases separately.
p
38
I.e., we use log( 1−p ) as our measure of the extensive margin.
39
Specifically, 3-, 5-, 7-, 10-, 15-, and 20-year Modified Accelerated Cost Recovery System (MACRS) property
and listed property.

18

schedule, while assuming a six-month convention for the purchase year.4041 We compute zN at
the four-digit NAICS industry level as the simple average of the firm-level z’s across non-bonus
years prior to 2001. In bonus years, we adjust z by the size of the bonus. If θ is the additional
expense allowed per dollar of investment (e.g., θ = .3 for 2001), then zN ,t|θt = θ t +(1−θ t )×zN .
The interaction between the time series variation in θ and the cross sectional variation in zN
delivers the identifying variation we use to test our three hypotheses.
Table 3 collects summary statistics for the sample in our bonus depreciation analysis. The
average observation has $6.8 million in eligible investment, $180 million in sales and $27
million in payroll. The size distribution of corporations is skewed, with median eligible investment of just $370 thousand and median revenues of $26 million. The average net present
value of depreciation allowances, zN ,t , is 0.88 in non-bonus years, implying that eligible investment deductions for a dollar of investment are worth eighty-eight cents to the average
firm. zN ,t increases to an average of 0.94 during bonus years. Cross sectional differences in
zN ,t are similar in magnitude to the change induced by bonus, with zN ,t varying from 0.87 at
the tenth percentile to 0.94 at the ninetieth. The first year deduction, θN ,t , increases from an
average of 0.18 in non-bonus years to 0.58 in bonus years.
The difference in z’s over time of just six cents per dollar before tax translates into a
benefit of just over two cents after tax, which is why some authors claim the effect of bonus
on investment should be small. However, if the discount rate firms apply to future deductions
includes a large external finance wedge or myopia, then this two cent difference can increase
to as much as the forty cent difference in average θ ’s.
It is helpful to give a sense of the groups being compared, because our identification will
be based on assuming that industry-by-year shocks are not confounding the trends between
industry groups. The ten most common three-digit industries (NAICS code) in the bottom
three zN deciles are: motor vehicle and parts dealers (441), food manufacturing (311), real
estate (531), telecommunications (517), fabricated metal product manufacturing (332), food
services and drinking places (722), transportation equipment manufacturing (336), oil and
gas extraction (211), nondurable goods wholesalers (424), and primary metal manufacturing
40

The category deduction schedules are available in IRS publication 946. We use a seven percent rate as
a frictionless benchmark that is likely larger than the rate firms should be using, which will tend to bias our
results downward. Summers (1987) argues that firms should apply a discount rate close to the risk-free rate
for depreciation deductions. Seven percent is the largest discount rate House and Shapiro (2008) apply when
computing the value of bonus depreciation.
41
The six-month convention is applied because on average the property is in place for only half of the first year.

19

(331). In the top three deciles are: professional, scientific and technical services (541), specialty trade contractors (238), computer and electronic product manufacturing (334), durable
goods wholesalers (423), construction of buildings (236), heavy and civil engineering construction and land subdivision (237), truck transportation (484), rental and leasing services
(532), nondepository credit intermediation (522), and administrative and support service
(561). Neither group of industries appears to be skewed toward a spurious relative boom
in the low z group. The telecommunications industry suffered unusually during the early
bonus period as did real estate in the later period. Both industries are in the group for which
we observe a larger investment response due to bonus.

5

The Effect of Bonus Depreciation on Investment

We begin with a test of Hypothesis 1, which predicts that investment responds more strongly
to bonus depreciation for industries with more investment in longer lived eligible items.
Because bonus depreciation encourages investment by shifting later deductions forward in
time, industries that invest more heavily in longer lived eligible items receive a more generous
subsidy (Cummins, Hassett and Hubbard, 1994; House and Shapiro, 2008). Industries investing mainly in short-lived items provide a control group. This cross sectional variation in policy
intensity allows us to identify the causal effect of bonus depreciation on investment.
In both bonus periods we study, we estimate large responses to bonus depreciation, which
imply a significant effect on aggregate equipment investment. The estimates are similar in both
periods. We assess the key risk of this design—that time-varying industry shocks confound our
estimates—using a variety of specifications, a placebo test and differences in policy salience
across space.

5.1

Policy Background

House and Shapiro (2008) provide a detailed discussion of the baseline depreciation schedule42 and legislative history of the first round of bonus depreciation. Kitchen and Knittel
(2011) provide a brief legislative history of the second round.43 Appendix B summarizes the
relevant legislation.
42
43

Known as the Modified Accelerated Cost Recovery System, or MACRS.
See also the Treasury’s “Report to The Congress on Depreciation Recovery Periods and Methods” (2000).

20

In 2001, firms buying qualified investments44 were allowed to immediately write off 30
percent of the cost of these investments. The bonus increased to 50 percent in 2003 and
expired at the end of 2004. In 2008, 50 percent bonus depreciation was reinstated. In subsequent years it was extended to 100 percent bonus for tax years ending between September
2010 and December 2011.45 The policies applied to equipment investment and excluded most
structures.46
The policies were intended as economic stimulus. In the words of Congress, “increasing
and extending the additional first-year depreciation will accelerate purchases of equipment,
promote capital investment, modernization, and growth, and will help to spur an economic
recovery” (Committee on Ways & Means, 2003, p. 23). To avoid encouraging firms to delay
investment until the policy came online, legislators announced that the policy would apply
retroactively to include the time when the policy was under debate. Although the first bonus
legislation passed in early 2002, firms anticipating policy passage would have begun responding in the fourth quarter of 2001. We therefore include firm-years with the tax year ending
within the legislated window in our treatment window.
Whether firms perceived the policy as temporary or permanent is a subject of debate.
The initial bill branded the policy as temporary stimulus, slating it to expire at the end of
2004, which it did. For this reason, House and Shapiro (2008) assume firms treat the policy
as temporary. In contrast, Desai and Goolsbee (2004) cite survey evidence indicating that
many firms expected the provisions to continue, and our empirical analysis in Section 8 offers
little evidence of intertemporal shifting.47 Expecting the policy to be temporary is critical
to House and Shapiro (2008), because their exercise relies upon how policies approximated
as instantaneous interact with the duration of investment goods approximated as infinitely
lived. Our design relies much less on this assumption. In our model, credit constraints and
myopia amplify the effects of both temporary and permanent policies. And our cross sectional
44

Depreciable tangible personal property with class life of twenty years or less, purchased for use in the active
conduct of a trade or business. Used equipment was excluded.
45
In the first bonus period, property had to be put in place after September 10, 2001 and before January 1,
2005. The start date for the second bonus period was December 31, 2007 and the end date was December 31,
2011.
46
These provisions coincided with an increase in the Section 179 allowance for small investments from $24,000
to $100,000 in 2003, from $125,000 to $250,000 in 2008, and from $250,000 to $500,000 in 2010. In our main
sample, we exclude firms with mean eligible investment greater than $100,000. Altering this threshold does not
change our results.
47
Note that when production functions exhibit constant returns to scale, the effect of temporary and permanent
policies on investment will be the same (Abel, 1982).

21

identification relies much less on the response of the longest lived investment goods.

5.2

Empirical Setup

Bonus depreciation provides a temporary reduction in the price and a temporary increase in
the first year deduction for eligible investment goods. Eligible items are classified for deduction profiles over time based on their useful life. Identification builds upon the idea that some
industries benefited more from these cuts by virtue of having longer duration investment patterns, that is, by having more investment in longer class life categories. This cross-sectional
variation permits a within-year comparison of investment growth for firms in different industries. The policy variation is at the industry-by-year level, so the key identifying assumption
is that the policies are independent of other industry-by-year shocks. Several robustness tests
validate this assumption.
The regression framework implements the standard difference-in-differences (DD) specification given by
f (I i t , Ki,t−1 ) = αi + β g(zN ,t ) + γX i t + δ t + "i t

(5.1)

where zN ,t is measured at the four-digit NAICS industry level and increases temporarily during
the bonus years. The specific additive form we adopt in (5.1) for the unobserved firm-level
components, αi , can only be valid for a particular class of investment functions. For example,
if valid in levels, the design cannot be valid in logs. The investment data summarized in Table
3 is highly skewed with a mean of $6.8 million and a median of just $368 thousand. Thus, a
multiplicative unobserved effect (that is, I i = Ai I ∗ (z)) is the most likely empirical model for
investment levels. This delivers an additive model in logarithms, which is the approach we
pursue below. Because approximately eight percent of our observations for eligible investment
are equal to zero, we supplement the intensive margin logs approach with a log odds model
for the extensive margin. We measure the log odds ratio as log(P[I > 0]/(1 − P[I > 0])) at
the four-digit industry level.48
Studies often use an alternative empirical specification for f (I, K), where investment is
scaled by lagged assets or lagged capital stock. We prefer log investment for four reasons.
First, small firms are not always required to disclose balance sheet information, so requiring
48
An alternative specification, with the odds ratio replaced by P[I > 0], works as well. However, the logs odds
ratio has better statistical properties (e.g., a more symmetric distribution).

22

reported assets would reduce our sample frame. Second, and related to the first reason,
requiring two consecutive years of data for a firm-year reduces our sample by fifteen percent.
Third, there is some concern that balance sheet data on tax accounts are not reported correctly
for consolidated companies due to failure to net out subsidiary elements.49 Measurement error
in the scaling variable introduces non-additive measurement error into the dependent variable.
Last, with multiple types of capital, the scaling variable might not remove the unobserved
firm effect from the model. This is especially a concern because we cannot measure a firm’s
stock of eligible capital and because firms vary in the share of total investments made in
eligible categories.50 While we prefer the log investment model for these reasons, we also
report results using investment scaled by lagged capital stock, which allows comparison to
past studies.

5.3

Graphical Evidence

Figure 1 presents a visual implementation of this research design. To allow a comparison
that matches a regression analysis with fixed effects and firm-level covariates, we construct
residuals from a two-step regression procedure. First, we nonparametrically reweight (i.e.,
Dinardo, Fortin and Lemieux (1996) reweight) the group-by-year distribution within ten size
bins based on assets crossed with ten size bins based on sales.51 This procedure addresses
sampling frame changes over time, which cause instability in the aggregate distribution.52
In the second step, we run cross sectional regressions each year of the outcome variable on
an indicator for treatment group—either long duration or short duration—and a rich set of
controls, including ten-piece splines in assets, sales, profit margin and age. We plot the residual
group means from these regressions.53
We compare mean investment in calendar time for the top and bottom three deciles of
the investment duration distribution.54 Long duration industries show growth well above that
of the short duration industries, with this difference only appearing in the bonus years. The
49

Mills, Newberry and Trautman (2002) analyze balance sheet accounting in tax data and document difficulties
in reconciling these accounts with book accounts.
50
Abel (1990) notes that this issue and other violations of linear homogeneity can lead to spurious conclusions
(e.g., a reversed investment-Q relationship.
51
The bins are set based on the size distribution in 2000.
52
During the period we study, the size of the sample frame changed twice due to budgetary constraints.
53
To align the first year of each series and ease comparison of trends, we subtract from each dot the group
mean in the first year and add back the pooled mean from the first year. All means are count weighted.
54
Deciles are computed at the industry level.

23

difference between the slopes of these two lines in any year gives the difference-in-differences
estimate between these groups in that year. The other years provide placebo tests of the
natural experiment and indicate no false positives.
Figure 2 provides another way of visualizing this relationship. For each firm, we compute
the difference in average eligible investment between when bonus was in place—treatment
years—and an equal length period prior to bonus—control years.55 We group these observations into equally sized bins based on zN ,t in non-bonus years, our proxy for treatment intensity. The average level of investment growth is negative in both periods, which is not surprising
because the motivation for these policies is prevailing economic weakness. Despite this weakness, temporary investment incentives clearly influence equipment investment. Firms doing
more eligible investment in short duration equipment categories receive the smallest benefit
from bonus depreciation and display the largest contraction in investment when these policies
are active. The upward sloping relationship is clear and present in both samples.

5.4

Statistical Results and Economic Magnitudes

Table 4 presents regressions of the form in (5.1), where f (I i t , Ki,t−1 ) equals log(I i t ) in the
intensive margin model, log(PN [I i t > 0]/(1− PN [I i t > 0])) in the extensive margin model, and
I i t /Ki,t−1 in the user cost model; and g(zN ,t ) equals zN ,t in the intensive and extensive margin
models and (1 − τzN ,t )/(1 − τ) in the user cost model.56 The baseline specification includes
year and firm fixed effects. Standard errors are clustered at the firm level in the intensive
margin and user cost models.57 Because log odds ratios are computed at the industry level,
standard errors in the extensive margin model are clustered at the industry level.
The first column reports an intensive margin semi-elasticity of investment with respect
to z of 3.7, an extensive margin semi-elasticity of 3.8 and a user cost elasticity of −1.6. The
average change in zN ,t was 4.7 cents during the early bonus period and 8 cents during the later
Unless otherwise specified, investment is measured by log(I e ) where I e denotes eligible investment expense.
This allows convenient interpretation of differences as approximate percent changes. We study the extensive
margin in separate specifications.
56
τ is set to 35 percent, the top statutory tax rate for all firms.
57
This is consistent with recent work (e.g., Desai and Goolsbee (2004), Edgerton (2010), Yagan (2013)) and
enables us to compare our confidence bands to past estimates. The implicit assumption that errors within industries are independent is strong, for the same reason that Bertrand, Duflo and Mullainathan (2004) criticize
papers that cluster at the individual level when studying state policy changes. Our results in this section are
robust to industry clustering, as are the tax splits in the next section. In the financial constraint splits regressions,
we discuss which inferences are robust to this more conservative structure. We are not aware of other studies
that restrict inference in this way and still show that taxes affect investment.
55

24

period, implying average investment increases of 18.5(= 3.79 × 4.7) and 31.4(= 3.79 × 8) log
points, respectively. These predictions should not be confused with the aggregate effect of the
policy, because they are based on equal-weighted regressions which include many small firms.
They only provide an informative aggregate prediction under the strong assumption that the
semi-elasticity is independent of firm size. We relax this assumption to produce an aggregate
estimate in section 8.
In the second column, including a control for contemporaneous cash flow scaled by lagged
capital does not alter the estimates. Columns three and four show a similar semi-elasticity
for both the early and late episodes. Column five controls for fourth order polynomials in
each of assets, sales, profit margin and firm age, as well as industry average Q measured from
Compustat at the four-digit level. Column six adds quadratic time trends interacted with twodigit NAICS industry dummies, which causes the estimated semi-elasticity to increase.58 These
alternative control sets do not challenge our main finding: the investment response to bonus
depreciation is robust across many specifications.
Appendix Table A.2 collects from other studies estimates that we can compare to our user
cost model. Like our study, each one uses tax reforms crossed with industry characteristics to
estimate the effect of taxes on investment. The average user cost elasticity across these studies
is 0.69, which falls within Hassett and Hubbard (2002)’s consensus range of 0.5 to 1, but is
less than half our estimate of 1.60.
In an investment model, the elasticity of investment with respect to the net of tax rate,
1 − τz, equals the price elasticity and interest rate elasticity.59 Our empirical model delivers an
elasticity of 7.2. We are not aware of easily comparable estimates for prices or interest rates.
Thus by several accounts, bonus depreciation has a substantial effect on investment, much
larger than past estimates and much stronger than the conventional wisdom predicts. We
further investigate the robustness of this fact and then turn to potential explanations in Section
6.
58

We can replace the quadratic time trends with increasingly nonlinear trends or two digit industry-by-time
fixed effects. We can also replace the time trends with two-digit industry interacted with log GDP or GDP
growth. In each case, the estimates increase. This suggests that omitted industry-level factors bias our estimates
downward. Consistent with this story, Dew-Becker (2012) shows that long duration investment falls more during
recessions than short duration investment.
59
Appendix A provides a derivation.

25

5.5

Additional Robustness and Policy Salience

The calendar time plot in Figure 1 provides several visual placebo tests through inspection
of the parallel trends assumption in non-bonus years. Because bonus depreciation excludes
very long lived items (i.e., structures), we can use ineligible investment as an alternative intratemporal placebo test.60 The first two columns of Table 5 present two specifications of the
intensive margin model, which replace eligible investment with structures investment. The
first specification is the baseline model, and the second includes two-digit industry dummies
interacted with quadratic time trends. We cannot distinguish the structures investment response from zero. Thus, the results pass this placebo test.
Another concern with our results is that they may merely reflect a reporting response, with
much less actual investment taking place. The third and fourth columns of Table 5 provide
a reality check. We replace our measure of investment derived from Form 4562 with net
investment, which is the difference in logarithms of the capital stock between year t and year
t − 1. Both the baseline and industry trend regressions confirm our gross investment results
with net investment responding strongly as well.
Columns five and six of Table 5 offer a sanity check of our findings. Here, the dependent
variable is an indicator for whether the firm reports depreciation expense in the specific form
item applicable to bonus. Effectively, this is a test for bonus depreciation take-up. The table
indicates that the probability of taking up bonus is strongly increasing in the strength of the
incentive.
We present direct evidence that firms take the tax code into account when making investment decisions. With respect to equipment investment, they pay special attention to the depreciation schedule and the nonlinear incentives it creates. These nonlinear budget sets should
induce bunching of firms at rate kinks. Consistent with this logic, we find sharp bunching at
depreciation kink points. This evidence supports our claim that temporary bonus depreciation
incentives were also salient.
To show policy salience, we study a component of the depreciation schedule, Section 179,
which applies mainly to smaller firms. Under Section 179, taxpayers may elect to expense
60

This placebo test is valid if structures are neither complements nor substitutes for equipment, an assumption
that is unlikely to hold. Still, the structures test is useful, since observing a structures response equal in magnitude
or larger than the equipment response would be a cause for concern that time-varying industry shocks drive our
results.

26

qualifying investment up to a specified limit. With the exception of used equipment,61 all
investment eligible for Section 179 expensing is eligible for bonus depreciation. Focusing on
Section 179 thus serves as an out of sample test of policy salience that remains closely linked
to the bonus incentives at the core of the paper.
For a given tax year, there is a maximum deduction and a threshold over which Section
179 expensing is phased out dollar for dollar. Thus, Section 179 resembles bonus depreciation with a one hundred percent first year deduction. Appendix Table A.1 summarizes the
changes in Section 179 depreciation rules over the past twenty years. The kink and phase-out
regions have increased incrementally since 1993, with larger jumps in 2003 (from $24,000 to
$100,000), 2008 (from $125,000 to $250,000) and 2010 (from $250,000 to $500,000).
We exploit the kink induced by the Section 179 schedule at the maximum deduction level
of investment. When the tax schedule contains kinks and the underlying distribution of types is
relatively smooth, the empirical distribution should display excess mass at these kinks (Hausman, 1981; Saez, 2010). Figure 4 shows how dramatic the bunching behavior of eligible
investment is in our setting. These figures plot frequencies of observations in our dataset for
eligible investment grouped in $250 bins. Each plot represents a year or group of years with
the same maximum deduction, demarcated here by a vertical line. The bunching within $250
of the kink tracks the policy shifts in the schedule exactly and reflects a density five to fifteen
times larger than the counterfactual distribution nearby.62
In general, evidence of bunching at kink points reflects a mix of reporting and real responses.63 The bunching evidence is informative in either case because these are both behavioral responses, which show whether firms understand and respond to the schedule. In
the next section, we study managerial myopia by comparing bunching activity across different
groups of firms. This test does not depend on whether the response is real or reported.
We can interact the bunching evidence with the basic regression model identifying the re61

Used equipment accounts for approximately six percent of equipment investment (Kitchen and Knittel, 2011).
Excess mass ratios are computed using the algorithm and code in Chetty et al. (2011).
63
See Saez (2010) for a discussion of this point. The bonus difference-in-differences (DD) design is less vulnerable to misreporting. In that design, we can confirm the response by looking at other outcomes. In addition,
the DD estimator is much less sensitive to misreporting by a small fraction of total investment. Moreover, the
sample contains many firms who use external auditors, for whom misreporting investment entails substantial risk
and little benefit. Last, our conversations with tax preparers and corporate tax officers suggest that misreporting
investment is an inferior way to avoid taxes. This is because investment purchases are typically easily verifiable,
require receipts when audited, and usually reduce current taxable income by just a fraction of each dollar claimed
as spent. In the case of investment expenses depreciated over multiple years, the audit risk of misreporting is
also extended over the entire depreciation schedule.
62

27

sponse to bonus. The design of the test generates control and treatment groups from the notion
that firms differ in their tax code knowhow.64 We compute geographic proxies of investment
schedule sophistication through measuring the local propensity to bunch at the Section 179
kink point. We use the low information areas as cross-sectional counterfactuals for the high
information areas. We then separately estimate the baseline model for each group, effectively
providing a difference-in-difference-in-differences estimate of the bonus response.
We group firms by two-digit ZIP code, which is the lowest level of aggregation that permits
a reliable measure of bunching. For each ZIP-2, we pool all years and compute the fraction
of firms within $10,000 of the kink who bunch within $250 of it. This provides the sorting
variable. In this design, more bunching in a region indicates more awareness of the tax code
for that region. So, we should expect the growth in investment during bonus periods to be
increasing in the level of bunching. Columns seven and eight of Table 5 show that indeed the
high bunching areas display a stronger response to bonus than do the low bunching areas.65
To recapitulate, bonus depreciation has a large effect on investment, and spurious timevarying industry factors cannot explain this fact. Such factors would cause parallel trends to
fail in the years prior to bonus. They would lead to different estimates in recessions marked
by weakness in different industries. They would lead ineligible investment to expand. They
would attenuate the estimated effect when regressions include flexible industry-by-time controls. And they would lead to a similar response across geographies where firms pay more and
less attention to the depreciation schedule. The facts do not match these predictions. Section
6, which presents heterogeneous effects by firm size, further contradicts the omitted industry
factor story.
These investment responses directly correspond to take-up of depreciation incentives—
bonus take-up rates rise with the policy’s generosity and many firms sharply bunch around the
Section 179 kink point—in contrast to recent work on partial salience of sales taxes (Chetty,
Looney and Kroft, 2009) and the nonresponse of investment to dividend tax changes (Yagan,
2013). Net investment responds to bonus depreciation as well, even though the reported
balance sheet items do not affect taxable income. Section 8 shows that debt issuance increases
because of bonus depreciation and that payroll and dividend payments—which are double
64

This test follows the design of Chetty, Friedman and Saez (2013), who use geographic differences in individual bunching at a kink in the Earned Income Tax Credit schedule to study the labor supply response to
taxes.
65
Specifically, we compare the top and bottom three deciles of local bunching.

28

reported—respond as well. Thus the observed response is a policy response that does not
reflect a mere reporting response, but rather reflects real economic actions.

6

Explaining the Large Response with Financial Frictions

The large response of investment to bonus depreciation is not consistent with a frictionless
model of firm behavior: the magnitudes imply implausibly high discount rates. In this section,
we explore alternative models that generate high effective discount rates.
One alternative is costly external finance, which raises the total discount rate firms apply to
evaluate projects. Our rich data environment enables us to study how the investment response
to tax incentives interacts with costly external finance. We perform a series of split sample
tests, using several common markers of ex ante financial constraints.66 Consistent with this
story, firms more likely to depend on costly external finance—small firms, non-dividend payers
and firms with low levels of cash—respond more strongly to bonus. Split sample analysis by
size also leads to a more accurate prediction for the aggregate policy response.
Another alternative model is managerial myopia, which raises effective discount rates by
sharply discounting the future relative to the present. Consistent with this story, firms only
respond to investment incentives when the policy immediately generates after-tax cash flows.
For firms with positive taxable income before depreciation, expanding investment reduces this
year’s tax bill and brings extra cash into firm coffers today. Firms without this immediate
incentive can still carry forward the deductions incurred but must wait to receive the tax
benefits.67 We present evidence that, for both Section 179 and bonus depreciation, this latter
incentive is weak, and differences in growth opportunities cannot explain this fact.

6.1

Heterogeneous Responses by Ex Ante Credit Constraints

We divide the sample along several markers of ex ante credit constraints used elsewhere in
the literature. Even for private unlisted firms, we can still measure size, payout frequency
66

See Fazzari, Hubbard and Petersen (1988a) for an early application of this methodology and Almeida,
Campello and Weisbach (2004) and Chaney, Sraer and Thesmar (2012) for recent examples.
67
In the code, current loss firms have the option to “carry back” losses against past taxable income. The IRS
then credits the firm with a tax refund. Our logic assumes that firms have limited loss carryback opportunities
because, in the data, we find low take-up rates of carrybacks. Furthermore, carrybacks create a bias against our
finding a difference between taxable and nontaxable firms, because carrybacks create immediate incentives for
the nontaxable group.

29

and proxies for balance sheet strength. Figure 3 plots elasticities and confidence bands from
regressions run for each of ten deciles based on average sales.68 We plot both the intensive
margin elasticities and the user cost elasticities. The smallest firms in the sample show the
largest response to bonus, regardless of the specification. The user cost estimates help us
reconcile our findings with those in past studies. Larger firms show user cost elasticities in line
with the findings surveyed in Hassett and Hubbard (2002). It is only the smaller firms, for
whom data were previously unavailable, that yield estimates outside the consensus range.
Table 6 presents a statistical test of the difference in elasticities across three markers of ex
ante constraints. For the sales regressions, we split the sample into deciles based on average
sales and compare the bottom three to the top three deciles.69 The average semi-elasticity for
small firms is twice that for large firms and statistically significantly different with a p-value of
0.03.70 The second two columns present separate estimates for firms who paid a dividend in
any of the three years prior to the first round of bonus depreciation.71 Here, the non-paying
firms are significantly more responsive.
Our third sample split is based on whether firms enter the bonus period with relatively
low levels of liquid assets. We run a regression of liquid assets on a ten-piece linear spline
in total assets plus fixed effects for four-digit industry, time, and corporate form. We sort
firm-year observations based on the residuals from this regression lagged by one year, and
then report in the last two columns of Table 6 separate estimates for the top and bottom three
deciles. These are reported in the last two columns of Table 6. The results using this marker
of liquidity parallel those in the size and dividend tests, with the low liquidity firms yielding
an estimate of 7.2 as compared to 2.8 for the high liquidity firms.
These constraint markers are imperfect.72 First, they do not directly measure the external
finance cost faced by new firms. This concern would tend to bias any differences existing
between groups toward zero, and thus against the results we present. A second concern with
sample splitting is that the splitting criteria are correlated with the investment error term and
68

Specifically, we use average sales from the three years before each bonus period. We use as many of these
six years as are available for each firm.
69
When we measure size with total assets or payroll, the size results are unchanged.
70
Cross equation tests are based on seemingly unrelated regressions with a variance-covariance matrix clustered at the firm level.
71
We only use the first round of bonus for the dividend split. The dividend tax cut of 2003, which had a strong
effect on corporate payouts (Yagan, 2013), may have influenced the stability of this marker for the later period.
72
Criticism of split sample markers dates back to Poterba’s comments in Fazzari, Hubbard and Petersen (1988a).
See Farre-Mensa and Ljungqvist (2013) for a more recent assessment of their value in samples of public and
private companies.

30

so may bias the estimated coefficient of interest (Bond and Van Reenen, 2007). This issue
is important for investment-cash flow sensitivity tests because cash flow is likely correlated
with other components of the investment error term. Because our setting features plausibly
exogenous policy variation at the industry level, this concern is less important here. The key
assumption we make is that interacting our splitting criterion, measured prior to the policy
change, with the policy variable and the year effects enables a valid difference-in-differences
design for each group.

6.2

Heterogeneous Responses by Tax Position

The Section 179 bunching environment presents an elegant setting to document the immediacy of investment responses to tax policy. The simple idea is to separate firms based on
whether their investment decisions will fully offset current year taxable income, or whether
deductions will have to be carried forward to future years. We choose net income before depreciation expense as our sorting variable. Firms for which this variable is positive have an
immediate incentive to invest and reduce their current tax bill. If firms for which this variable
is negative show an attenuated investment response and these groups are sufficiently similar,
we can infer that the immediate benefit accounts for this difference.
The panels of Figure 5 starkly confirm our intuition. In panel (a), we pool all years in the
sample, recenter eligible investment around the year’s respective kink, and split the sample
according to a firm’s taxable status. Firms in the left graph have positive net income before
depreciation and firms in the right graph have negative net income before depreciation. For
firms below the kink on the left, a dollar of Section 179 spending reduces taxable income by
a dollar in the current year. Retiming investment from the beginning of next fiscal year to the
end of the current fiscal year can have a large and immediate effect on the firm’s tax liability.
For firms below the kink on the right, the incentive is weaker because the deduction only adds
to current year losses, deferring recognition of this deduction until future profitable years. As
the figure demonstrates, firms with the immediate incentive to bunch do so dramatically, while
firms with the weaker, forward-looking incentive do not bunch at all.
One objection to the taxable versus nontaxable split is that nontaxable firms have poor
growth opportunities and so are not comparable to taxable firms. We address this objection
in two ways. First, we restrict the sample to firms very near the zero net income before

31

depreciation threshold to see whether the difference persists when we exclude firms with large
losses. Panel (a) of Figure 6 plots bunch ratios for taxable and nontaxable firms, estimated
within a narrow bandwidth of the tax status threshold. The difference in bunching appears
almost immediately away from zero, with the confidence bands separating after we include
firms within $50 thousand dollars of the threshold. For loss firms, the observed pattern cannot
be distinguished from a smooth distribution, even for firms very close to positive tax position.
The bunching difference for nontaxable firms is not driven by firms making very large losses.
Table 7 replicates the tax status split idea in the context of bonus depreciation. We modify
the intensive margin model from Table 4 by interacting all variables with a taxable indicator
based on whether net income before depreciation is positive or negative.73 According to these
regressions and consistent with bunching results, the positive effect of bonus depreciation on
investment is concentrated exclusively among taxable firms. The semi-elasticity is statistically
indistinguishable from zero for nontaxable firms, while it is 3.8 for taxable firms. In panel (b)
of Figure 6, we repeat the narrow bandwidth test for bonus depreciation. The figure plots the
coefficients on the interaction of taxable and nontaxable status with the policy variable. The
difference in coefficients in Table 7 emerges within $50 thousand of the tax status threshold,
and these coefficients are statistically distinguishable within $100 thousand of the threshold.
Here as well, the results are not driven by differences for firms far from positive tax positions.
To address the concern about nontaxable firms, Panel (b) of Figure 5 uses differences
within the group of taxable firms. This plot shows again that bunching is due to tax planning with regard to the immediate potential benefit. Here, we divide profitable firms by their
stock of loss carryforwards in the previous year. Each dot in this plot represents a bunching
histogram where the y-axis measures the degree of bunching using the excess mass estimator
in Chetty et al. (2011). The groups are sorted according to the ratio of lagged loss carryforward stock to current year net income before depreciation, which proxies for the availability
of alternative tax shields. The scatter clearly indicates a negative relationship between the
presence of this alternative tax shield and the extent of eligible investment manipulation.
We confirm this pattern in the bonus setting. Column (7) of Table 7 focuses on the group
of taxable firms with non-zero stocks of lagged loss carryforwards. We split this group into
three subgroups based on the size of their carryforward stock. Firms with large stocks of loss
73

That is, we interact z, any controls, and the time fixed effects with the taxable indicator. We do not interact
the firm effects with the taxable indicator.

32

carryforwards display a semi-elasticity with respect to z of 2 compared to a semi-elasticity of
5.7 for firms with low loss carryforward stocks.
The finding for nontaxable firms contradicts a simple model of costly external finance,
because firms neglect how the policy affects borrowing in the future. On the other hand, firms
cannot be too myopic because the investment decision itself only pays off in the future. Thus
for myopia to be the explanation, firms must use different accounts to think about investment
decisions and the tax implications. Moreover, the myopia story needs complexity to explain
the finding for financially constrained firms—are small firms, non-dividend payers and firms
with low levels of cash more myopic? While plausible, there is no evidence of this.
The facts presented in this section—the stronger response for financially constrained firms
and the nonresponse for nontaxable firms—do not match the predictions of a frictionless
model. The facts point instead toward models in which costly external finance matters and
current benefits outweigh future benefits, with neither alternative being obviously redundant.
In the next section, we use an investment model and the estimates to calibrate a parameter
for each alternative model.

7

Discount Rates and the Shadow Cost of Funds

Taken together, our empirical findings emphasize a financial frictions channel for how investment incentives work. In this section, we use a standard investment model to quantify the
importance of this channel. Specifically, we ask what is the marginal value of cash, λ, implied
by our financial constraint split sample analysis, and what is the discount term, β, implied by
our tax status split sample analysis. The answers combine to tell us what discount rates firms
apply when making investment decisions.
In Appendix A, we derive the comparative static for investment with respect to the bonus
depreciation term θ :
I · " I,θ ≡

∂I
∂θ

=

(1 + λ)p I ∂ z
ψI I

∂θ

> 0,

(7.1)

where " I,θ is the semi-elasticity of investment with respect to θ , p I is the price of investment,
ψ I I is the second derivative of the adjustment cost function, and z is defined as in (3.3). In
the Appendix, we state assumptions under which I · ψ I I will be equal across groups.74 Under
74

That is, we assume linear homogeneity of the marginal adjustment cost function. Nearly all studies in the
literature make this assumption, which is necessary for example for marginal q to equal average Q.

33

these assumptions, we can derive two empirical moments that combine our estimates for
constrained and unconstrained firms and for taxable and nontaxable firms and yield simple
formulas for λ and β.
The first empirical moment we use compares the estimated response with respect to bonus
for constrained and unconstrained firms. Assuming constrained firms face shadow price λC
and unconstrained firms face shadow price λU , we take the ratio of comparative statics:
C
" I,z
U
" I,z

≡ m1 =

∂ I/∂ θ |λC
∂ I/∂ θ |λU

=

1 + λC
1 + λU

=1+

∆λ
1 + λU

,

(7.2)

which reveals an implied credit spread between constrained and unconstrained firms. Table 2
presents m1 for each pair of estimates in Table 6. λ is the shadow price of relaxing the firm’s
Table 2: Calibrated Moments
Shadow Cost of Funds Calibration
m1
λC |λU =0

Mean Sales

Dividend Payers

Lagged Cash

Average

1.95
0.95

1.63
0.63

2.61
1.61

2.06
1.06

p

φ

r

β

.5
.1

.88
.59

.07
.07

0.84
0.92

Discount Factor Calibration
High φ
Low φ

Notes: This table computes empirical estimates for m1 and m2 , as defined in the text. m1 reveals an implied
credit spread between constrained and unconstrained firms. m2 reveals the discount factor firms apply to all
future cash flows relative to current flows.

borrowing constraint. An alternative interpretation is that every after-tax dollar inside the firm
is worth 1 + λ dollars outside the firm. Our estimates reveal that, for financially constrained
firms, a dollar inside the firm is worth $2.06 on average outside the firm.
Is this estimate reasonable? There are not many existing benchmarks. Faulkender and
Wang (2006) attempt a calculation with a very different methodology, but that ultimately
arrives at a similar conclusion. They estimate the value of changes in cash in excess return
regressions, while attempting to control for a host of omitted factors. They find that for low
payout firms and for small firms the value of a dollar of after-tax cash is worth $1.67 and
$1.62, respectively. For these firms’ unconstrained counterparts, a dollar is only worth $1.07
34

and $1.12. The spreads in their study are comparable to ours, especially considering their
exercise operates within a group of firms we consider to be relatively unconstrained.75
We define a second empirical moment that compares taxable and nontaxable firms:
γ=0

" I,z

∂ I/∂ θ |γ=0

" I,z

∂ I/∂ θ |γ=1

≡ m2 =
γ=1

= βφ

1 − z t0 (1)
1 − z t0 (β)

,

(7.3)

where φ is a discounter that reflects the average arrival of the taxable status event for nontaxable firms. We proxy for φ by assuming a fixed transition probability p for nontaxable
firms and an infinite horizon for carryforward realization.76 This implies φ = p/(p + r).77
We calibrate the transition probability using the probability that an actually nontaxable firm
transitions into tax status in the next period. In our data, this probability is approximately
0.5.78 The sample we compare restricts the nontaxable group to include only firms that are
nearly taxable, so this p offers a conservative estimate of φ. We compute the implied β for
this p and for an extreme p equal to 0.1.
Note the external finance wedge falls out of this expression. This is true as long as average
shadow costs are the same across taxable and nontaxable groups. To maintain this assumption, we use our loss carryforward group estimates to calibrate m2 . That is, we estimate
semi-elasticities within the group of taxable firms sorted according to their past stocks of alternative tax shields. For firms with large loss carryforward stocks relative to current income,
the marginal dollar of investment is unlikely to affect this year’s tax bill. At the same time, we
have less reason to believe these firms face substantially worse growth opportunities or tighter
financial constraints. This biases our estimates of β toward the neoclassical benchmark of β
equal to one.
Applying the estimates from the last column of Table 7 yields a value for m2 of 0.35(=
(5.68 − 3.7)/5.68). For p = 0.5, this maps to an implied discount factor (β) of 0.84. Ignoring
for the moment the other discount terms, β equal to 0.84 implies a discount rate of approxi75

Similarly, Koijen and Yogo (2012) find that a relaxed borrowing constraint for life insurers is worth $2.32
per dollar of inside capital.
76
The actual expiration period for carryforwards is twenty years.
77
That is, the expected arrival is p/(1 + r) + (1 − p)p(1 + r)−2 + (1 − p)2 p(1 + r)−3 + · · · = p/(1 + r) · [1/(1 −
(1 − p)/(1 + r))] = p/(p + r).
78
Auerbach and Poterba (1987) note more persistence of nontaxable positions than we do. Our measure is
based on net income before depreciation, in order to capture the state of having the next dollar of investment
affect this year’s tax bill. Their measure is based on whether firms exhaust their carryforward stocks. Below, we
assess the robustness of our results to varying φ.

35

mately 17 percent. We are not aware of studies that attempt to measure discount factors such
as this for firms. Prior studies on individual decision making have found similar magnitudes
for short term discount rates in both lab and field experiments.79
The discounting implied by β says that one dollar next year is worth 84 cents, before
taking into account risk or the shadow cost of funds. If we then apply the assumed risk
adjusted rate of 7 percent and the estimated shadow cost of funds of 1.06, we find that a
dollar next year is worth approximately 38 cents today for the credit constrained firms in our
sample. This substantial discount is not surprising, given the starkness of the reduced form
empirical results: nontaxable firms seem to ignore the future benefits and small, financially
constrained firms seem to value highly the immediate cash back due to bonus depreciation. In
the model, we use costly external finance and myopia to describe the deviations from a rational
benchmark we observe, but the exercise performed here provides just one of several plausible
calibrations of this basic fact. In general, models of firm behavior that do not generate high
discount rates are unlikely to fit the data for most firms.

8

Substitution Margins, External Finance and Aggregation

We ask whether increased investment involves substitution away from payroll or equipment
rentals, how firms finance their additional investment, and whether the increased investment
reflects intertemporal substitution or new investment. Studying external finance responses
helps us understand how firms paid for new investments. Understanding substitution margins
is critical for assessing the macroeconomic impact of these policies. We then apply the findings from our heterogeneity analysis to estimate the predicted aggregate investment effect of
bonus.

8.1

Substitution and External Finance

We find little evidence of substitution away from leasing or payroll. In contrast, these policies coincide with within-firm payroll growth, suggesting a new margin—complementarity
between capital and labor—through which investment incentives affect employment. Regard79

Laibson D. Repetto and Tobacman (2007) estimate short term discount rates of 40 percent in the context of
individual saving decisions. In a more general model, they estimate a short run discount rate of 15 percent and
a long run rate of 3 percent.

36

ing external finance, firms appear to fund new investments through a mix of debt issuance,
despite tightened credit conditions, and reduced payouts. We also document limited intertemporal shifting, as high past incentives only weakly predict low future investment. The payroll
and finance effects offer more evidence that the investment effects do not reflect misreporting,
but rather reflect a real response.
Table 8 presents estimates of the intratemporal and intertemporal substitution margins.
These regressions follow the baseline specification in equation 5.1, with a different left hand
side variable. For rents, payroll and debt, we focus on flows80 as outcomes that match investment (i.e., capital stock flows) most closely. For payouts, we study the logarithm of dividend
payments and an indicator for whether dividends are non-zero, which separates the intensive
and extensive margins.
How flexible is the rent-versus-own margin for equipment investment? This is a crucial
question for assessing the real effect of these stimulus policies. If firms simply shift away from
leasing to take advantage of the tax benefits of buying, then the aggregate impact of these
policies will be minimal. In their tax returns, firms separately report rental payments for computing net income. Unfortunately, this item does not permit decomposition into equipment
and structures leasing. Given this limitation, we can still ask what effect bonus depreciation
had on changes in rental payments. The first column of Table 8 shows that growth in rental
payments did not slow due to bonus, but rather increased somewhat. Thus, we do not find
evidence of substitution away from equipment leasing. The second column of Table 8 reports
the effect of bonus on growth in non-officer payrolls. Again, we find no evidence of substitution, but rather coincident growth of payroll. Finding limited substitution in both leasing and
employment makes it more likely that bonus incentives caused more output.
While increased depreciation deductions do allow firms to reduce their tax bills and keep
more cash inside the firm, they must still raise adequate financing to make the purchases in the
first place. This point is especially critical if, as the data suggest, firms thought to be in tight
financial positions respond more. Here, we test whether bonus incentives affect net issuance of
debt and payout policy. Columns three through five of Table 8 provide some insight. Increased
equipment investment appears to coincide with significantly expanded borrowing and reduced
payouts both on the extensive and intensive margins.
We assess the extent of intertemporal substitution using a model that includes both con80

Namely, differences in logs.

37

temporaneous z and lagged z. Our data often do not include the fiscal year month, so it is
possible that we are marking some years as t when they should be t − 1 or t + 1. For most of
our tests, this issue introduces an attenuation but no systematic bias. However, when testing
for intertemporal substitution, we want to be sure that lagged z measures past policy changes.
Thus, column (6) of Table 8 includes regressions with twice lagged z added to the baseline
bonus model. The coefficient on lagged z is negative but not distinguishable from zero and
including lagged z does not alter the coefficient on contemporaneous z. This implies limited
intertemporal shifting of investment.81

8.2

Estimating the Aggregate Response to Bonus

We can use these cross sectional designs to produce aggregate estimates of the effect of bonus
depreciation on equipment investment. While not the central question of this study, the answer
to this question is of interest to policymakers. Two caveats should be noted. First, the cross
sectional variation in the policy variable of interest (z) is smaller than the its time series
variation. Aggregate predictions will therefore depend on an extrapolation of the estimating
equations outside the support of the data we use to identify the policy semi-elasticity. Caution
should be taken in relying upon these estimates.
A second concern is that our preferred empirical specification, which estimates the effect
of bonus in percentage changes, does not permit a direct prediction in levels. We address this
through supplementing our baseline specification with a conditional fixed effects Poisson estimation of the policy semi-elasticity. The Poisson model allows us to preserve the assumption of
multiplicative firm-level unobserved effects, while modeling directly the level of investment.
Gross investment is bounded below by zero and exhibits considerable skewness, so permits a
natural analogy to count probability models such as the Poisson.
We run our baseline regression and generate both a predicted log investment and a predicted counterfactual log investment under the assumption that bonus does not occur. We
81

The argument in House and Shapiro (2008) still holds even if intertemporal shifting is limited, because it
remains true that investment would be higher during bonus periods. These results only imply that the temporarily
high investment does not significantly alter the investment decision (through, e.g., affecting future marginal
products). See Abel (1982) for an analysis of temporary incentives and discussion of when intertemporal shifting
should occur.

38

compute the counterfactual level of investment using the formula,
Û) − log(I)),
Ø
I C F = I × exp(log(I
CF

(8.1)

and then aggregate these counterfactuals using the SOI sample weights. For the stimulus
period from 2008 to 2010, aggregate eligible investment averaged $378 billion per year. This
method yields an average difference relative to the counterfactual level of $108 billion per
year.
This prediction relies on the assumption that the policy response is the same across all
firms. We can relax this assumption and estimate separate elasticities for each of three size
groups based on average sales. To give a sense of how these groups compare in the aggregate,
in 2005, the bottom, middle and top third have mean investment of $216 thousand, $699
thousand and $12.1 million, respectively. The bottom, middle and top third have aggregate
investment of $53.1 billion, $33.4 billion and $244 billion, respectively. In 2004, the bottom
third declared $12 billion in bonus deductions, the middle third declared $10.8 billion and the
top third declared $86.3 billion. Estimating separate coefficients for each group reduces the
average aggregate response to $95 billion. On average, the smallest, middle and largest third
respectively account for 12 percent, 9 percent and 79 percent of this response.
To incorporate both the intensive and extensive margins into one model, while preserving
the multiplicative identification assumption, we use a Poisson model with conditional fixed
effects. The model enables direct estimation of the policy effect in levels, affording a more
accurate aggregate prediction in levels. The Poisson model yields an aggregate prediction that
because of bonus investment increased $55 billion on average between 2008 and 2010.

9

Conclusion

This paper combines methods from public and applied economics with insights from finance to
answer a first order macroeconomic question: how do taxes affect investment behavior in the
presence of financial frictions? We find that firms respond strongly to incentives that directly
target investment decisions. Our heterogeneity results—that the investment response is larger
for financially constrained firms, but only when the benefit is immediate—show that financial
frictions are critical for understanding investment behavior.

39

The results point toward a set of models in which costly external finance matters and firms
place more weight on current benefits than they would in a frictionless model. Whether the
high implied discount rate reflects an external finance wedge, managerial myopia, agency
considerations or a mix of these is an important question for future research. Further study of
the external finance mechanism would be valuable. A deeper study of the employment effects
of these policies is of direct interest to macroeconomic modelers.
A related question for future research concerns the effects of tax planning. How do tax
preparers affect the decision to take up these policies? More generally, do firms focus on
minimizing current taxes at the possible expense of future payoffs? The answer to these
questions might shed light on the role of agency problems and firm learning about optimal
management practices.
The empirical results imply that policies which target investment directly and yield immediate payoffs are most likely to influence investment activity. Policies that target financial
constraints, such as direct loans, might have a similar effect if conditional on the investment
decision. In comparison to studies of consumer durable goods, we find less evidence of intertemporal shifting, but more work on this question is needed. Data from the period following
the recent stimulus, once available, will be very useful.

40

A

Investment with Adjustment Costs and a Borrowing Constraint

We develop an infinite horizon, non-stochastic investment model, deriving the testable hypotheses in Section 3 and the empirical moments for calibration in Section 7. The model nests
the standard neoclassical investment model with adjustment costs (Hayashi, 1982), a model
with credit constraints and a model with managerial myopia.

A.1

General Setup

We begin with a discrete time version of Hayashi (1982). Firm value, V0 , is given by an infinite
series of discounted net receipts, R t . The discount rate, r t , is risk-adjusted and possibly time
varying. The expression for firm value is
V0 =

∞
X

1

t=0

t
(1 + rs )
Πs=0

Rt .

(A.1)

Net receipts in each period reflect net revenues after taxes, investment costs, adjustment costs
and depreciation deductions for current and past investments:
∞
X




R t = 1 − τ t π t − 1 − k t p I,t I t − ψ t (I t , K t ) + τ t
D t−x (x)p I,t−x I t−x ,

(A.2)

x=0

where τ t is the corporate tax rate, π t is pretax profits, p I,t is the price of investment goods,
k t is the investment tax credit, I t is investment, ψ t is adjustment costs and D t−x (x) is the
depreciation deduction for capital of age x, based on the schedule from time t − x. Pretax
profits are π t , which equals gross revenues, p t F t (K t , Nt ), with capital, K t , and labor, Nt , inputs,
less the cost of labor inputs. Net revenues are thus given by
π t = p t F t (K t , Nt ) − w t Nt .

(A.3)

Firms are price takers so output prices, p t , and wages, w t , are exogenous. F t is weakly concave.
The firm maximizes (A.1) subject to a capital accumulation law of motion:
K t+1 = K t − δK t + I t ,
41

(A.4)

where δ is the rate of economic depreciation. The adjustment cost function is convex and
reflects after-tax resource losses due to production disruptions and installation.82
It is useful to have an expression for the stream of future depreciation deductions owed for
investment in time t:
z t0 (β) = τ t D0 + β

∞
X

1

x
Πs=1
(1 + r t+s )
x=1

τ t+x D t (x).

(A.5)

z t0 (β) reflects the present discounted value of one dollar of investment deductions after tax.83
If the firm can immediately deduct the full dollar, then z t0 equals τ t . In general, the stream
of future deductions will depend on future tax rates and interest rates. β is an additional
discount term between zero and one, which reflects the possibility of myopia. We use our
heterogeneity analysis to identify this term separately.
Bonus depreciation, the policy we study in our empirical analysis, allows the firm to deduct
a per dollar bonus, θ t , at the time of the investment and then depreciate the remaining 1 − θ t
according to the normal schedule:
z t (β) = τ t θ t + (1 − θ t )z t0 (β)

(A.6)

At different points in time, Congress set θ t equal to 0.3, 0.5 or 1. We use these policy shocks
to identify the effect of bonus depreciation on investment.
We further generalize z t by incorporating a nontaxable state. When the next dollar of
investment does not affect this year’s tax bill, then the firm must carry forward the deductions
to future years. Our general z t reflects this case:
z t (β, γ) = γz t (β) + (1 − γ)βφz t (1),

(A.7)

where γ ∈ {0, 1} is an indicator for current tax state and φ is a discounter that reflects both
82

Hayashi (1982) models adjustment costs through influencing the law of motion in (A.4), rather than as a
net receipts flow. Abel (1982) models adjustment costs through augmenting pretax profits in (A.3). There is no
strong a priori argument for one versus the other. We adopt this notation to simplify the borrowing constraint in
our calibration exercise. Intuitively, it means adjustment costs are not verifiable and thus the firm cannot borrow
to offset them. It makes sense to further assume that such costs would not be deductable as well. The hypotheses
we derive do not depend on the assumption.
83
In the main text, we define z without incorporating the tax rates, in order to isolate the direct effect of
bonus. Here, we define z with tax rates because it matches Hayashi (1982)’s notation and highlights the general
dependence of the term on future tax rates.

42

the expected arrival time and the discount rate, r T , applied to the future period when the firm
switches. Note that for the nontaxable firm, β will apply to all future deductions.84
Hayashi (1982) considers the case with β and γ equal to one. We consider this case first.
Define z t ≡ z t (1, 1). We can rewrite the objective in (A.1) as
V0 =

∞
X

1

t=0

t
Πs=0
(1 + rs )

”
—
(1 − τ t )π t − ψ t (I t , K t ) − (1 − k t − z t )p I,t I t + A0 ,

(A.8)

where A0 is the present value of depreciation deductions on past investments.85 We assume r
is fixed over time and that k equals zero, since the investment tax credit is not active during
our sample frame. We isolate the terms where period t investment enters and rewrite the
relevant part of the problem:


max −ψ(I, K) − (1 − z)p I I +
I

q t+1 I
1+r


,

(A.9)

where q t+1 is the multiplier on the law of motion for capital.
We write the first order condition for investment as


q t+1 = (1 + r) ψ I + (1 − z)p I ,

(A.10)

which emphasizes that optimal investment equates the marginal product of capital, q t+1 , with
the hurdle rate (1 + r) applied to the marginal costs of investment. These costs include adjustment costs and the price of investment less the value of investment as a tax shield. q t+1 is
the marginal value of a unit of capital, which accumulates over many future periods. We can
apply the envelope condition and differentiate V0 (K t ) = max I V0 (K t , I) to show that
qt =

∞
X

1

s=t

Πsv=t (1 + r v + δ)

”
—
(1 − τs )πK,s − ψK,s ,

(A.11)

which says that q t includes the present discounted value of future after-tax marginal products
84

This formula is not exactly correct because additional periods will lead to additional accumulated losses for
subsequent deductions. The firm will deduct these at an accelerated rate relative to the schedule in z t (1). This
formulation simplifies the algebra and biases our empirical findings toward the neoclassical benchmark.
85
The A0 term is important for Hayashi (1982) because it influences the average value of the firm and one
purpose of his study is to show when average Q and marginal q are equal. A0 does not affect the investment
decision problem.

43

for capital, accounting for the rate of economic depreciation.86 In a two period model without
adjustment costs, we could rewrite (A.10) as
r=



1−τ



πK,t+1

1−z

pI

− 1,

(A.12)

which shows that the general condition is just a dynamic statement of the simple idea that
optimal investment should equate returns and the risk-adjusted discount rate.87
We augment the problem to introduce the possibility of imperfect capital markets, which
leads to a generalized version of (A.10). Firms face a credit limit on gross borrowing, B t ,
which accumulates according to
B t+1 = B t + (1 − τ t )π t − (1 − z t )p I,t I t .

(A.13)

Firms must borrow to cover tax obligations and investment outlays, to the extent these exceed
current cash flows. Note that z t and not just τθ t enters here. This is because future borrowing
constraints also matter.
From Summers (1981) to Edgerton (2010), modern empirical studies of investment apply
a parameterized version of (A.10), typically under the conditions shown in Hayashi (1982) to
yield marginal q equal to average Q.88 The financial constraint augmented first order condition
is


q t+1 = (1 + r) ψ I + (1 + λ)(1 − z)p I ,

(A.14)

where λ ≥ 0 is the shadow price associated with the borrowing constraint (A.13).89 The
shadow price on the borrowing constraint works in this model much like a discount rate. To
see this, note that without adjustment costs and in the one shot model we can rewrite (A.12)
as
r +λ=



1−τ
1−z



πK,t+1
pI

− 1,

(A.15)

where we have assumed for illustration that rλ is small. The hurdle rate for an investment
86

Note that capital also has an effect on future adjustment costs.
Also, note that with immediate expensing, z = τ and so taxes do not affect investment. This also holds in
certain versions of the more general model. See Abel (1982).
88
These assumptions include making firms price takers in all markets and linear homogeneity for production
(i.e., constant returns to scale) and adjustment
costs.
n
o
87

89

q

I

t+1
The general version of (A.9) is max I −ψ(I, K) − (1 − z)p I I + 1+r
− λ(1 − z)p I I .

44

project reflects both the discount rate and the borrowing spread. In our empirical analysis, we
assume that firms use the same r but may differ in λ, in order to back out an implied λ spread
between constrained and unconstrained firms.90

A.2

Testable Hypotheses

We can derive the three testable hypotheses outlined in Section 3. Each hypothesis results
from defining optimal investment in (A.14) as a function of an exogenous parameter, a, and
then implicitly differentiating. The general condition is
ψI I

∂I
∂a

+

∂q
∂a

= (1 + λ)p I

∂z
∂a

,

(A.16)

where z includes nontaxable states and possibly myopia, as in (A.7) and q now satisfies the
general version of (A.11):
qt =

∞
X

1

s=t

Πsv=t (1 + r v + δ)

”
—
(1 + λs )(1 − τs )πK,s − ψK,s .

(A.17)

The only difference between (A.11) and (A.17) is that increasing capital leads to higher future
after-tax profits, which relax future credit constraints.
We consider comparative statics with respect to θ , z t0 , λ, and γ. Except for λ, none of
these terms directly affect q. They only affect q through investment’s effect on future capital.
We assume this latter effect is negligible. While nontrivial, this assumption is justified for two
reasons. First, while the policies we study have a substantial temporary effect on investment,
the change in investment is small relative to the existing capital stock. Thus, the long run
marginal product of capital, which q measures, is likely unaffected.91 The second reason
is that nearly all empirical studies of investment incentives assume that production exhibits
constant returns to scale and linear homogeneity in adjustment costs, which leads to constant
q as a function of capital.92
90

When thinking about the discount rates firms apply to depreciation tax shields, this assumption feels appropriate. In general, our estimated λ spread will also include discount rate differences.
91
This is the assumption House and Shapiro (2008) make to replace short run approximat

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Source: Frix Law Library, https://www.frixlaw.com/law-library/documents/agency%3Airs%3A7724897d45a99ecf. Public record. Not legal advice.