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Working Paper 9406
OPTIMAL FISCAL POLICY WHEN
PUBLIC CAPITAL IS PRODUCTIVE:'
A BUSINESS-CYCLE PERSPECTIVE
by Kevin J. Lansing
Kevin J. Lansing is an economist at the Federal
Reserve Bank of Cleveland. For helpful comments
and suggestions, the author thanks Chuck Carlstrom,
Rajeev Dhawan, Eric Engen, Jang-Ting Guo, Gary
Hansen, Axel Leijonhufvud, Michael Wallerstein, and
seminar participants at UCLA and the University of
California. Riverside.
Working papers of the Federal Reserve Bank of
Cleveland are preliminary materials circulated to
stimulate discussion and critical comment. The
views stated herein are those of the author and
not necessarily those of the Federal Reserve Bank
of Cleveland or of the Board of Governors of the
Federal Reserve System.
April 1994
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Abstract
Recent empirical evidence suggests that the stock of public-sector capital may be an
important input to private production.
This paper examines the business-cycle
implications of productive public capital in a two-sector, dynamic general-equilibrium
model with endogenous fiscal policy. In the model, public capital is a direct input to the
neoclassical production technology, and public consumption goods provide direct utility to
households. The production of public and private goods takes place in separate sectors.
At the optimum level of public capital, the rate of return on public investment is found to
be less than that on private investment. In simulations, public investment and public
consumption are procyclical, and the capital tax is more variable than the labor tax,
features also observed in annual U.S. data. The introduction of stochastic shocks to
households' preference for public consumption helps the model to match certain features
of the data, namely, the high variability and low correlation of public expenditures relative
to their private-sector counterparts over the business cycle.
-
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1. Introduction
A growing body of research incorporates public capital into neoclassical growth models.'
Furthermore, in recent years, business-cycle research has begun to address the effects of government
fiscal policy on aggregate fluctuations. For example, Braun (1989) and McGrattan (1991) study the
effects of distortionary taxation on business cycles, Aiyagari, Christiano, and Eichenbaum (1992) and
Christiano and Eichenbaum (1992) examine the impact of time-varying public consumption expenditures,
and Braun and McGrattan (1993) study wartime fluctuations in a model with government-owned (but
privately operated) capital. Baxter and King (1993) discuss the temporary and long-run effects of
changes in public consumption, public investment, and tax rates. A common feature of all these papers
is that government policy is viewed as exogenous. In contrast, this paper undertakes the study of fiscal
policy and business cycles in a model that endogenizes a l l variables of interest. I then subject the model
to the same kind of quantitative comparisons with U.S. data that have been widely used in the real
business-cycle literature.
The framework for the analysis is a two-sector, dynamic general-equilibrium model with an
infinitely lived, representative househoId. The government solves a dynamic version of the Rarnsey
(1927) optimal tax probIem in which the endogenous policy variables are public investment, public
consumption, and tax rates on labor and capital income (for simplicity, a period-by-period balanced
budget is assumed). A distinction is made between the production of private and public goods. Privatesector firms produce private goods, which households purchase using after-tax income. The government
sector produces non-rival public goods. Public investment goods augment the stock of public capital,
while public consumption goods provide direct utility to households. Public capital is a direct input to
the constant-returns-to-scale production technologies in both sectors, as are sector-specific quantities of
private capital and labor. The government does not assess fees for the use of public goods; rather, it
levies distortionary taxes to finance their production.
In equilibrium, the rate of return on public investment (as measured by the marginal product of
' ~ e c e n tmodels of endogenous growth with public capital include Barro (1990). Jones, Manuelli, and Rossi (1992), Barro and
Sala-i-Martin (1992). and Glomm and Ravikumar (1993). Arrow and Kun. (1970) provide a comprehensive study of the existence
and stability properties of equilibrium in a neoclassical growth model with public capital. Pestieau and Possen (1978) study optimal
redistributive fiscal policy in a model with public capital and exogenous savings.
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public capital) is found to be less than the rate of return on private investment. This result is due to the
impact of distortionary capital taxation and the higher depreciation rate assumed for private versus public
capital. Both effects reduce the steady-state level of private capital and hence raise its marginal product.
A primary finding is that optimal fiscal policy displays procyclical behavior for public
investment and public consumption, in agreement with annual U.S. data. The presence of public capital
in the constant-returns-to-scale production function causes private firms to realize positive profits after
private factors are paid their marginal products. This, in turn, causes the optimal steady-state tax on
capital to be positive. Essentially, the govemment uses the tax on private capital to collect a user fee
for the productive services of public capital. Furthermore, in simulations, the optimal capital tax
fluctuates over time to absorb budget shocks, while the optimal labor tax remains relatively stable. This
characteristic can also be observed in estimates of average marginal tax rates for the U.S. e ~ o n o m y . ~
An important feature of the model is the introduction
of stochastic shocks to household
-
preferences for public consumption. These shocks are intended to represent unforeseen events that affect
household demand for public goods, such as national defense, police protection, or disaster relief
services. Specific examples might include the collapse of the Soviet Union (which reduced desired levels
of U.S. defense spending) and the 1994 Los Angeles earthquake (which, so far, has resulted in more than
$8 billion in federal disaster relief appropriations). The preference shocks cause adjustments along two
margins: the mix of production between the private and government sectors, and the choice between
public investment and public consumption. As a result, the shocks help the model to match certain
features of U.S. data, namely, the high variability and low correlation of public expenditures relative to
their private-sector counterparts over the business cycle. This result is similar to other examples in the
business-cycle literature wherein a stochastic term in the household utility function can improve model
performance, as demonstrated recently by Christiano and Eichenbaum (1992) and Bencivenga (1992).'
The remainder of this paper is organized as follows. Section 2 provides some facts about public
ones, Manuem, and Rossi (1993) provide a formal treatment of the effect of profits on the optimal steady-statecapital tax. The
optimality of a statecontingent capital tax to absorb budget shocks is shown by Judd (1989) and Chari, Christiano. and Kehoe (1993).
3~lemming(1987) develops a model with shocks to the demand for public goods in a small open economy with exogenous wages
and interest rates, and obtains procyclical government expenditures.
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capital and public expenditures in the postwar U.S. economy. Sections 3 and 4 describe the model and
the solution method. Section 5 describes the choice of parameter values. Section 6 presents quantitative
results from steady-state analysis and dynamic simulations, and section 7 concludes.
2. The Data
The stock of public-sector capital in the United States is about one-third the size of the private
capital stock. The largest single category of public capital comprises what is known as the economy's
core infrastructure, namely, highways, streets, airports, transit systems, utilities, and the like. State and
local governments own about two-thirds of the nation's public capital, while the federal government
owns the stock of military capital, which represents about one-fifth of the total. A number of empirical
studies (Ratner [1983], Aschauer [1989a], Munnell [1990, 19921, and Lynde and Richmond [1992])
suggest that public capital may be an important input to private production. The primary evidence for
the public capital hypothesis can be seen in figure 1, which plots U.S. labor productivity versus the stock
of public capital from 1947 to 1992.4 The well-documented slowdown in the growth trend of U.S.
productivity that began in the early 1970s coincides with a similar decrease in the growth trend of public
capital. This observation is the basis for many claims regarding the productive effects of public capital.
The association of these trends does not prove, however, the existence of a causal link running from
public capital to output. Indeed, a number of studies cite evidence that disputes the public capital
hypothesis. These include Tatom (1991), using aggregate U.S. data, Hulten and Schwab (1993). using
regional data, and Holtz-Eakin (1992), using state-level data. Eberts (1990) provides evidence that
causation between public capital and output runs in both directions, using metropolitan-level data.'
Theoretically, public capital could act as either a substitute or a complement to private capital
in production. For example, public investment might "crowd out" private investment if firms rely
increasingly on public capital for productive purposes rather than expanding their own capacity. On the
4
In figure 1, output is real GNP in 1987 dollars from Citibase. Public capital is government-owned equipment, structures, and
residential capital (with and without military capital) in 1987 dollars from Fixed Reproducible Tangible Wealth in the United States.
U.S. Department of Commerce (1993). All series have been divided by the total labor hour series, LHOURS,in Citibase.
'see Munnell (1992) and Aschauer (1993) for a summary and critique of the various empirical studies on this topic.
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other hand, public investment may raise the profitability of private capital, thus stimulating private
investment. Aschauer (l989b) and Lynde and Richmond (1992) present empirical evidence (using postwar U.S.data) suggesting that the complementary effect dominates, although both effects appear to be
operating. Furthermore, the empirical studies that find support for the public capital hypothesis are
consistent with a Cobb-Douglas aggregate production function that exhibits constant returns to scale in
labor, private capital, and public capital.
Figure 2 compares trends in U.S.private and public investment, while figure 3 compares the
analogous consumption trends. During the postwar period, private investment avenged 21 percent of
GNP, while public investment (including military) averaged 4.5 percent. The corresponding averages for
The non-trivial size of the
private and public consumption are 56 percent and 17 percent, re~pectively.~
government sector relative to the private economy motivates a model in which government policy is not
only included, but is endogenized in a full general-equilibrium framework
Figures 4 and 5 depict the business-cycle movements of the annual investment and consumption
series from 1947 to 1992, where cyclical components have been extracted by detrending each series with
the Hodrick-Prescott filter? Note that public investment and public consumption both tend to move
procyclically. In figure 4a, the correlation coefficient between total public investment and real GNP is
0.59. If military investment is excluded, the correlation is 0.56. In the private sector, the correlation
between investment and real GNP is 0.69. Even though both types of investment are procyclical, figure
4b shows that the contemporaneous correlation between private and public investment is quite low,
ranging only from 0.04 to 0.25, with the higher value obtained when military investment is excluded.
The standard deviation of total public investment is about 1.7 times larger than that of private
investment, mostly due to large increases in military investment that occurred during the Korean and
Vietnam Wars. Excluding military investment, the standard deviations of public and private investment
'In figure 2, the first series for private investment is fixed investment + consumer durables expenditures + residential investment,
from Fixed Reproducible Tangible Wedfhin fhe United Sfutes, U.S. Department of Commerce (1993). The second series is gross
private investment (GPIQ), from Citibase. In figure 3, private consumption is expenditures on nondurables and services
(GCNQ+ GCDQ), from Citibase. Public consumption is government purchases of goods and services (GGEQ) from Citibase, minus
public investment (this avoids double counting). All series are annualized and expressed in 1987 dollars.
' S e e Rescott (1986). The smoothing parameter for the filter was set at A=100, since all data are at annual frequency.
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are about equal. For the consumption series (figure 5), the correlations with real GNP are 0.6 1 for public
consumption and 0.71 for private consumption.' The contemporaneous correlation between the two
consumption series is 0.16. The standard deviation of public consumption is about five times larger than
the standard deviation of private consumption. The temporary spikes observed in the U.S. series for
public investment and public consumption provide a justification for incorporating shocks to the demand
for public goods in the model.
3. The Model
The model economy consists of many identical, infinitely lived households, identical private
fm,and the government. Public and private goods are produced in separate sectors, each using a
technology that exhibits constant returns to scale in the three productive inputs: labor, private capital,
and public capital. The form of the technology implies that private firms earn an economic profit equal
to the difference between the value of output and payments to private factor inputs. As owners of the
firms,households receive net profits in the form of dividends, but consider them to be outside their
control, similar to wages and interest rates. The govemment finances production of public goods by
levying distortionary taxes on households and fm.It is assumed that profits are initially taxed at the
firm level, then distributed as dividends and taxed again at the household level. This formulation is
intended to capture the double taxation of corporate dividends in the U.S. economy. Furthermore, I
assume that the government can distinguish between labor and capital income, but cannot distinguish
between the different categories of capital income, such as profits, dividends, and interest. Consequently,
there are only two types of distortionary taxes in the model: a labor tax and a capital tax.9
'At quarterly frequency, the public consumption series (GGEQ from Citibase) displays much weaker procyclical behavior. From
1947:IQ to 1992:IVQ, the comelation with real GNP is 0.33. For the public investment series, data are available only at annual
frequency. Because government budgets are enacted into law annually, the annual correlations would appear to be more relevant for
a model with endogenous public expenditures.
9 ~ an model with profits, Jones, Manuelli, and Rossi (1993) show that a restriction on the menu of tax instruments is needed for
optirnality of a positive tax on capital in the steady state. Guo and Lansing (1994) demonstrate that the structure of dividend taxation
(double versus single) can affect the stability of the steady state in a one-sector version of this model.
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3.1 The Households' Problem
Households maximize a discounted stream of within-period utility functions over consumption
and leisure, subject to a sequence of budget constraints. The decision problem can be summarized as
where H, = h,,
+
(1)
h,,
subject to
c,
+x,5
(l-~,,)w,H,+ ( I - ~ , , ) ( r , K , + f t , +7,,8K,
)
-.
k , +,
VI+l
=:
(1-6 )k,, +x,,,
= PvV,
+
5,+1
9
0<6 < l ,
k,,, k2, given
O < p v < l , 5,-iid(O,o:),
v, given.
--
(5)
In the above equations, subscripts 1 and 2 refer to the private and government sectors,
respectively. Households supply labor and capital to both sectors. The term c, represents private
consumption goods. Households are endowed with one unit of time each period and work a total of H,
hours during period t. Household preferences include a separable term representing the utility provided
by public consumption goods g, . Furthermore, these preferences are subjected to serially correlated
exogenous shocks v, that are revealed to agents at the beginning of period t. Examples of public
consumption goods that might affect household utility are national defense, police protection, and
government provision of food and housing during natural disasters. Public goods are assumed to be noncongestable and free of specific user charges. They are also nontradeable, i.e., no market exists wherein
households may buy or sell public goods.
Households maximize the utility function in (1) over c, ,h,, ,and h, ,but view g, as outside their
control. The logarithmic form of the within-period utility function has been chosen for tractability and
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for comparability with previous business-cycle literature. The separability in c, and g,implies that public
consumption does not affect the marginal utility of private consumption, an assumption supported by
parameter estimates in McGrattan, Rogerson, and Wright (1993). The symbol El is the expectation
operator conditional on information available at time t, and P is the constant household discount factor.
The fact that utility is linear in hours worked reflects "indivisible labor," as described by
Rogerson (1988) and Hansen (1985). This means that all variation in economywide hours worked is due
to variations in the number of employed workers, as opposed to variations in hours per worker. In a
decentralized economy, these authors show that the utility function in (1) can be supported by a lottery
that randomly assigns workers to employment or unemployment each period, with the firm (or the
government employer) providing full unemployment insurance. Wage contracts call for households to
be paid based on their expected (rather than actual) number of hours worked. Real business-cycle models
with indivisible labor are better able to match some key characteristics of aggregate labor market data.
Specifically, U.S. data display a large volatility of hours worked relative to labor productivity and a
weakly positive or even slightly negative correlation between hours and productivity.I0
Equation (2) represents the period budget constraint of the household. The t e r n XI and K,
represent total private investment and total private capital, respectively. Private capital is assumed to be
"sector specific" in the sense that total capital cannot be reallocated freely between sectors at the start
of each period, but instead must be reallocated via the investment process. This feature is reflected in
the separate laws of motion for k,, and k,,equations (3) and (4). The distribution of capital across
sectors is relevant for household decisions in this model because, in equilibrium, the government's statecontingent policy rules are functions of both k,, and k,. All private capital is assumed to depreciate at
the constant rate 6 . In equilibrium, the after-tax returns to labor and capital are equalized across sectors.
Households derive income by supplying labor and capital to both sectors at rental rates w, and
r, , and pay taxes on labor and capital income at rates z, and z,, respectively. An additional source of
income is the f m ' net profits
ft,,
which are distributed to households as dividends and are taxed at
the same rate a s interest income. The term zh6K, represents the depreciation allowance built into the
'Osee Hansen (1985). Christiano and Eichenbaum (1992), and Hansen and Wright (1992).
7
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U.S. tax code. Households view tax rates, wages, interest rates, and dividends as determined outside their
control. The household decision variables c,, h,,, h,, k,,, , and k,+, are all known at time t.
3.2 Household Optimality
The Lagrangian for the households' problem is defined as
1l =
E,Cp 1 {lnc, - A HI + exp(v,)B lng, +
1-0
The household first-order .conditions with respect to the indicated variables and the associated
transversality conditions are
-
The government uses these equilibrium conditions to recover the appropriate tax rates, 7, and
7,.
that support the household equilibrium allocations in a decentralized economy. Note that the first-
order conditions for hi,and
k+,yield the same equation for i=l, 2. This implies that if the before-tax
prices w, and r, are the same across sectors (as assumed here), the government will announce 7, and
7,
to also be the same across sectors. If w, and r, were allowed to differ across sectors, the government
would announce sector-specific tax rates in order to maintain the equilibrium condition of equal afer-tax
returns across sectors.
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3 3 Production Environment
Private-Sector Production
Private-sector output y, is produced by identical firms that seek to maximize after-tax profits by
using a technology that exhibits constant returns to scale in the three inputs, h,,, k,, , and kt,where k,,
is the stock of public capital. Private-sector output consists of private consumption goods c, and private
investment goods x,, and h . The firm's profits are taxed at rate ,z
The production technology is
subjected to serially correlated exogenous shocks z, that are revealed to agents at the beginning of period
t. These shocks generate equilibrium business-cycle fluctuations in the modeL Since the focus here is
on the (detrended) business-cycle movements of variables, the model abstracts from exogenous technical
progress. Private-sector production can be summarized as
subject to
Zr+l
= P r 1'
+
El+,
O<p,<l,
E,-iid(o,o,?),
z, given.
The private f i ' s fmt-order conditions are"
The f i ' s after-tax profits, distributed to households in the form of dividends, are
"There is no need to distinguish between variables under the household's control and variables representing per capita quantities
here, as is necessary when solving directly for a decentralized, competitive equilibrium. As noted by Lucas and Stokey (1983), the
solution to the government's decision problem yields a set of policies that dictate household equilibrium allocations. These allocations
determine the equilibrium prices r, and w,. Thus. prices are not outside the government's control as they are for households.
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Government-Sector Production
Government-sector output y,, involves the employment of workers, the rental of private capital
(for example, office buildings), and the use of public capital (such as infrastructure and governmentowned facilities or equipment). The government-sector technology exhibits constant returns to scale in
the inputs ha, k, , and kc,. Public capital is assumed to be "noncongestable" in the sense that the same
capital stock is used as an input to both private- and government-sector production.12 Government-sector
output consists of public consumption goods g, and public investment goods x,,. Since there is no formal
market for public goods, there is no requirement for the government to maximize any notion of "profit."
However, following Uzawa (1966), I assume that the government employs labor and private capital in
such a way as to minimize external production costs. This assumption permits the definition of a shadow
price of public goods relative to private goods P,13 Technology shocks are assumed to be the same for
both sectors, but are uncorrelated with preference shocks. Government-sector production is described as
follows:
subject to
yGl = up(r, ) k,:' h,:'
%+I
= PZZt+&,+I
&?I' O < $ i < l ,
O<pz<l,
@I
+ $ 2 + $ 3=
E,-iid(0,o:),
z0 given.
I2~xperimentswith diiferent versions of the model indicate that the results are not substantially changed if public capital is
assumed to be fully congestable, i.e., if separate stocks of public capital k , ,and h,, are employed in the two sectors.
I31n a standard two-sector growth model, the sectors are typically identified with consumption and investment goods, and a formal
market exists for both goods. Here, there is no formal market for goods produced in the government sector. This setup shares some
features of a home production model in which the two sectors are identified with market and nonmarket (home-produced) goods. See
Benhabib, Rogerson, and Wright (1991), Greenwood and Hercowitz (1991), and McGrattan, Rogerson, and Wright (1993) for home
production models in a businesscycle framework.
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The government's cost minimization condition yields an expression for the shadow price of
public goods relative to private goods.14 Also, since households earn income in both sectors, it is
necessary to define what is meant by GNP. Here, GNP is defined as income and profits generated in
the private sector (y,), plus income earned in the government sector (w,h,+ r, k,). The expressions are
akzl
ah,,
Combining (16) with the private firm's profit maximization conditions (1 1) yields the following
constraint imposed on the government's choice of policy:
3.4 The Government's Problem
The government chooses an optimal program of public expenditures and tax rates to maximize
the discounted utility of the household. The vector !PI= {xc,, g, , T,,;,T~ ) summarizes government policy
implemented at time t. The problem is a dynamic version of the classic Rarnsey case, involving a
Stackelberg game between the government and households. To avoid time-consistency problems, I
assume that the government can commit to a set of state-contingent policy rules announced at time zero.
Also, to make the problem interesting, lump-sum taxes are ruled out. Otherwise, the government would
elect to finance all future expenditures with an initial levy on private-sector assets. To simplify the
formulation, I further assume that the government adheres to a period-by-period balanced budget
l 4 ~ h shadow
e
price is the L a p n g e multiplier on the production constraint in the cost minimization problem. Equivalently, the
expression for PC, can be obtained from the following shadow profit maximization problem for a hypothetical competitive f m that
produces public goods: max (PC,yGl- r, k, - w, h, ). The (unobservable) profits earned by such a fum are (1 - $, - & ) PGlyGl.
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constraint, i.e., government debt is ruled out.15 With these assumptions, the government's problem is
subject to
(i)
household first-order conditions and budget constraint,
(ii)
private -fm profit maximization conditions,
(iii)
government-sector cost minimization condition,
(vii)
lim Eo P'A,, k,,+, = 0.
I+="
Constraints (i) and (ii) summarize rational maximizing behavior on the part of private agents and
constitute "irnplementability" constraints imposed on the government's choice of policy. Constraint (iii)
is the cost minimization assumption for the government's use of private-sectorinputs, i.e., equation (18).
Constraint (iv) is the government budget constraint, where outlays on the left side consist of payments
to labor and capital employed in the government sector. The last term on the right side of (iv) reflects
the double taxation of firm dividends. Constraint (v) is the resource constraint governing the production
of public goods. Constraint (vi) is the law of motion for public capital, where
is gross public
investment and 6, is the depreciation rate of public capital. Finally, (vi) is a transversality condition on
the accumulation of public capital, where 1C;,is the marginal utility of public consumption g, .
The summation of the household budget constraint (2) and the government budget constraint
(19. iv) yields the following resource constraint for the private sector. Because the private-sector resource
15~dding
government debt to the model introduces complications that I wish to avoid here. Specifically, equilibrium for a model
with debt and capital imposes an ex ante arbitrage condition on the expected returns from government bonds and private capital. The
steady-state level of debt is thus indeterminate (see Charnley [1985]). Furthennore, in a stochastic environment, the government can
vary the ex post combination of the capital tax and the bond interest rate in many different ways to raise needed revenue, yet still
satisfy ex ante arbitrage (see Zhu [I9921 and Chari, Christiano, and Kehoe [1991]). One method of resolving these complications is
to assume an exogenous ratio of steady-state debt to GNP and to restrict the government's ability to set the ex post bond interest rate
independently (see Lansing [1993a]).
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constraint and the govemment budget constraint are not independent equations, (20) will be used in place
of (19. iv) in the recursive version of the problem16
4. Solution of the Model
The government's problem under commitment can be solved using the unique recursive
algorithm developed by Kydland and Prescott (1980). A recursive structure is obtained by defining the
household lagged shadow price A,., to be a "pseudo-state variable." Including this price in the state
vector provides a link to the past by which the policymaker at time t considers the fact that household
decisions in earlier periods depend on current policy by means of expectations. This is the mechanism
Appendix A describes
by which the commitment problem can be solved using dynamic pr~grarnming.'~
the procedure for formulating the recursive version of (19) and numerically solving the dynamic
programming problem.
5. Calibration of the.Model
To explore the quantitative predictions of the model, as many parameters as possible are assigned
values in advance based on empirically observed features of postwar U.S. data Parameter choices are
also guided by the desire to obtain steady-state values for key model variables that are consistent with
long-run averages in the U.S. economy. Table 1 summarizes the choice of parameter values and is
followed by a brief description of how they were selected.
16.4n alternative formulation for the two resource constraints would be y, = c, +x,, ++,+xG, and yG,= g,. This implies that public
consumption goods g, are produced in the govemment sector but that public investment goods x, are purchased from the private sector
using tax revenue. Experiments with this version of the model yielded less successful results (the correlation between public and
private investment was too high). See Lansing (1993b) for further variations on the present model, including a one-sector model with
adjustment costs for public investment and a two-sector model with sector-specific technology shocks.
17seeLansing (1993a) for a more detailed discussion of this method.
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Table 1: Parameter Set
Agent
Parameters and Values
Households
-
Firms
9 , = 0.30
9, = 0.62
9, = 0.08
6 = 0.07
Government
I$, = 0.30
I$, = 0.62
I$, = 0.08
6, = 0.04
p, = 0.85
~
a, = 0.02
The time period in the model is taken to be one year. This is consistent with the frequency of
available data on public investment and tax rates. The discount factor of P=0.962 implies an annual rate
of time preference equal to 4 percent. The parameter A in the household utility function is chosen such
that total hours worked is close to 0.3. This is in line with time-use studies, such as Juster and Stafford
-
(1991). which indicate that households spend approximately one-third of their discretionary time in
market work.'' The value of B is chosen to yield a steady-state value of gIGNP near 0.18, the average
ratio for the U.S. economy from 1947 to 1992. In computing this average, public consumption was
estimated by subtracting public investment from an annualized series for government purchases of goods
and services (GGEQfrom Citibase). This was done to reduce double counting, since the series does not
distinguish between government consumption and investment goods.
The exponents in the Cobb-Douglas production functions are chosen to be the same for both
sectors. This is because estimates of private- versus government-sector output elasticities are not
available. With these values, however, the shares of GNP in the model received by total private capital
and total labor are close to levels estimated for the U.S. economy (see Christian0 [1988]). Furthermore,
these values yield a steady-state ratio of public investment to GNP near 0.045, consistent with the U.S.
average (including military) from 1947 to 1992.19 With constant returns to scale in all inputs, the value
''~otal hours worked is H=h,+h, . The sector-specific values are h,=0.23 and h,=0.07. These values imply that employment in
the private sector is about three times larger than in the government sector.
l9l'he range of empirical estimates for 0, is quite large. Aschauer (1989a) and Munnell (1990) estimate values of 0,=0.39
and 0.34, respectively. Tatom (1991) estimates values in the range of 0 to 0.13, and Holtz-Eakin (1992) estimates a value of 0,=0
using state-level data. See Munnell (1992) and Aschauer (1993) for a summary and critique of the empirical findings.
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of 8, (=I- 8, - 8,) affects the steady-state level of
firm
profits. These profits in turn affect the steady-
state level of 2,. because the government uses the tax on private capital to collect an indirect user fee
for the productive services of public capital. In the model, the steady-state ratio of profits to GNP is
0.06, and the resulting steady-state tax on capital is 0.27.
The private capital depreciation n t e of m.07
is based on the value estimated in Braun and
McGrattan (1993) and is consistent with values commonly used in the real business-cycle literature.
Together with the values of
P and 8,. this depreciation rate implies a steady-state ratio of private capital
to GNP of 2.62 and a ratio of private investment to GNP of 0.18. The corresponding averages for the
U.S. economy from 1947 to 1992 are 2.58 and 0.21. The public capital depreciation rate of 6 ~ 0 . 0 4was
estimated by regressing the linear law of motion on annual data for kc, and x,,
.
The process governing technology shocks was estimated using annual data from 1947 to 1992.
The series for z, was constructed by computing the changes in output not accounted for by changes in
the three productive inputs.20The estimated parameters, pp0.85 and 0,=0.02, represent values close
to those estimated by other authors, such as Benhabib and Jovanovic (1991). In the simulations, the
estimated value of a, yields a standard deviation of output in the neighborhood of 2.5 percent, a value
very close to the U.S. avenge of 2.46 percent over this period. The standard deviation of the preference
shocks o5was chosen to match the relative variability of public versus private consumption in U.S.
data. Over this period, the standard deviation of g, is about fives times larger than the standard deviation
of c , . Due to the lack of any direct observations on the preference shock, the persistence parameter p,
is set equal to 0.85, the same value used for the technology shock. This choice reflects a belief that
shocks that affect household demand for public consumption (such as wars or crime trends) tend to be
highly correlated from one year to the next."
,O~heproduction function residual was measured as zI= LnGNP, - 0 . 3 0 M I- 0.621nHr- 0 . 0 8 M G , .The private capital stock K,is
defied as futed private capital + stock of consumer durables + residential capital from Fixed Reproducible Tangible Wedth in the
United States, U.S. Department of Commerce (1993). Real GNP and the labor input (HI= LHOURS) are from Citibase. The public
capital series includes military capital and is described in footnote 4.
21~lemming
(1987) discusses the effect of changing the serial correlation properties of preference shocks.
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6. Quantitative Properties of the Model
6.1 Steady-State Results
Table 2 shows the model's steady-state values versus the corresponding U.S. averages from 1947
to 1992. For the U.S. data, two values are shown for the average values of x,IGNP and k,IGNP. The
first includes military items and the second excludes these items. Two values are also shown for the
average marginal tax rates
7,
and
7,.
The first is computed using tax rate estimates in Barro and
Sahasakul(1986) and Jorgenson and Sullivan (1981). The second uses tax rate estimates in McGrattan,
Rogerson, and Wright (1993). For the most part, the choice of parameters yields steady-state values that
are close to long-run averages in the U.S. economy. Under constant returns, the value of 8, (= 1-8, -8,)
controls the level of firm profits. It is interesting that a relatively small value of 8, (which implies a
ratio of profits to GNP of 0.06) is sufficient to induce an optimal capital tax of 7, = 0.27.
Table 2 does not report U.S. values for the rates of return on private versus public investment:
r, r,, , and r,, . Empirical estimates of these rates span a wide range and are very sensitive to the level
of data aggregation and the statistical techniques employed (see Aschauer [I9931 and Holtz-Eakin
[1993]). In the model, the rate of return on public investment (in both sectors) is less than the rate of
return on private investment. This is due to the impact of distortionary taxation on firm profits and the
higher depreciation rate of private capital in the calibration (6>6,). Both effects tend to reduce the
steady-state level of private capital and hence raise its marginal product.
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Table 2: Model Steady State versus U.S. Averages
Variable
-
Modela
U.S. Economyb
0.136
0.159
xG IGNP
X IGNP
g IGNP
c IGNP
K IGNP
kc IGNP
RevenuelGNP from
RevenuelGNP from T,
0.068
0.067
.................................................................................................................................................................................................................................................
a~heseare steady-state values based on the parameters in table 1. For variables in the government sector, xG , g, and kc,
the shadow price of public goods (PC=0.903 from equation 1161)was used to convert quantities into equivalent units of private goods.
b ~ othe
r U.S. economy, investment, consumption. and capital averages are for 1947 to 1992. Data sources are described
in footnotes 4, 6, and 20. The average labor tax rates (T,) are from B m and Sahasakul (1986)for 1947-83and from McGrattan,
Rogerson, and Wright (1993)for 1947-87.The average capital tax rates (zk)are from Jorgenson and Sullivan (1981,table 11) for
1947-80and from McGrattan, Rogerson, and Wright (1993)for 1947-87.Average tax revenue data are from various issues of Revenue
Statistics of OECD Member Countries, 1965-1990, table 61. Labor tax revenue is defined to include federal and state individual
income taxes and Social Security taxes. Capital tax revenue is defined to include federal and state corporate taxes, capital gains taxes.
and property taxes.
6.2 Dynamic Simulation
6.2.1 Optimal Policy Rules
The (approximate) solution to the government's problem yields the following set of log-linear
optimal policy rules, which are valid in the neighborhood of the deterministic steady state. The optimal
decision rules for private investment and private consumption have also been included for comparison.
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Table 3: Optimal Policy Rules
Constant
I
V,
In (kit 1
In ( k , 1
In ( k ~1,
In (4.11
The optimal behavior of public versus private expenditures over the business cycle can be
inferred by examining the coefficients on the technology shock z, in the policy rules. For k,and g,,
these coefficients are both positive, implying procyclical behavior. The coefficients on v, indicate optimal
responses to shifts in the demand for public consumption goods. As expected, g, responds more strongly
to preference shocks than does c,, accounting for the higher variability of g, relative to c, in the model.
The preference shocks affect the optimal trade-off between production in the two sectors as we1 as the
optimal mix between public investment and public consumption. This feature is reflected by the
coefficients on v, in the investment rules. A positive value of v, stimulates private investment in the
government sector x,in order to increase production of g, . As a result, x,, and x,, both decline. In this
way, preference shocks lower the contemporaneous correlation between public investment and total
private investment XI (=x,, +x,) and improve the model's comparison with U.S.data.
The optimal response of tax rates to shocks is governed by the shock's impact on the
govemrnent budget. In general, technology shocks alter the size of the tax base, affecting revenues, while
preference shocks alter the level of required outlays. The government responds by adjusting the capital
tax in an offsetting-manner. This can be observed by examining the coefficients on z, and v, in the
decision rule for 7,.
The magnitude of these coefficients is the largest of any policy variable. A
positive technology shock causes a large decrease in 7,. A positive z, causes GNP and household
income (the tax base) to rise, allowing the use of a lower tax on capital even though public expenditures
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x,, and g, increase. In contrast, a positive preference shock v, calls for an increase in 7
, to finance a
higher level of outlays. Absorbing shocks in this way is efficient because capital is completely inelastic
within a given period, unlike labor supply.22 The shock-absorbing feature of 7, allows the government
to maintain relatively stable tax rates on labor income, reminiscent of the tax-rate-smoothing hypothesis
of Barro (1979). Finally, notice that tax rates (and household allocations) depend on the distribution of
private capital across sectors, as reflected by the coefficients on In (k,,) and In (k,)in the policy rules.
6.2.2 Policy Simulations
Figures 6 and 7 plot simulated public and private expenditures from the model and highlight the
effect of preference shocks. Comparing these figures to those for the U.S. economy (figures 4b and 5b)
reveals that preference shocks improve the model's performance. Without these shocks, x,, and XI are
too highly correlated (figure 6a) and g, does not show enough variability relative to c, (figure 7a). In
figure 6a, the series for public and private investment diverge only slightly, due to the lower depreciation
rate of public capital in the calibration.
Figures 8 and 9 plot simulated tax rates from the model versus estimates of average marginal
tax rates for the U.S. economy. As noted earlier, the model predicts that the capital tax should be more
variable than the labor tax. An eyeball comparison of the U.S. tax rate series seems to bear this out.
Tables 4-7 provide a more quantitative comparison of the model with postwar U.S. data."
2 2 ~ eBohn
e (1988). Judd (1989), and Chari. Christiano, and Kehoe (1993) for related examples of optimal shock-absorbingpolicy.
" ~ i ~ u r e 8s and 9 display the tax rate series before detrending. For quantitative comparisons (tables 6 and 7), detrending is
necessary because the U.S. labor tax displays a distinct upward trend, while the U.S. capital tax displays a downward trend. These
trends have no counterpart in the model. The trend in T, is possibly linked to the phenomenon of "bracket creep," which existed
before tax schedules were indexed for inflation in 1985. Regarding the trend in T,. Auerbach and Poterba (1988) argue that the
downward trend is due to increasingly generous investment tax credits and accelerated depreciation schedules.
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Table 4a: Business-Cycle Statistics for the Model'
Cross-Correlation of GNP with Variable at r+i
S t d Dev.
Variable
r-2
1-1
I
I+ 1
r+2
GNP
2.48
0.03
0.38
1.00
0.38
0.03
XG
15.61
0.09
0.39
0.55
0.23
0.02
X
9.83
-0.14
0.19
0.96
0.44
0.13
g
3.28
0.12
0.25
0.43
0.09
-0.08
c
0.57
0.54
0.70
0.63
0.00
-0.30
H
1.32
-0.24
0.08
0.86
0.45
0.20
GNPIH
1.51
0.26
0.56
0.89
0.23
-0.12
astatistics are mean values over 100 simulations, each 46 periods long. Before computing statistics, all series were logged
and detrended using the Hodrick-Prescott filter with a smoothing parameter of 100. GNP= y + rk, + wh, , X=x,+x, and H = h, + h,.
.
Table 4b: Business-Cycle Statistics for U.S. Economy, 1947 to 1992'
Cross-Correlation of GNP with Variable at r+i
S t d Dev.
Variable
1-2
I- 1
r
r+ 1
r+2
GNP
2.46
0.05
0.56
1.00
0.56
0.05
GNPIH(est)
1.07
-0.25
-0.10
0.4 1
0.80
0.60
'Data sources for GNP, investment, and consumption are described in footnotes 4, 6, and 20. Public investment includes
military items. Private investment is futed investment + consumer durables expenditures + residential investment. All series have been
annualized, logged, and detrended as in the model. H(hh) represents total labor hours from the household s w e y (LHOURS) in
Citibase. H(est) represents total labor hours from the establishment survey (LPMHU) in Citibase.
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Table 5: Com~arisonof Selected Statistics
Statistic
corn (H.GNPIH)
Model
0.53
U.S. Economya
0.16 / 4.02
a ~ othe
r labor market statistics, the two numbers refer to the household and establishment surveys, respectively. See the notes
to table 4b.
The summary statistics in tables 4 and 5 reveal that the model performs reasonably well in
capturing the correlation structure and relative standard deviations of the aggregate variables, but is less
successful in matching the absolute standard deviations of the investment and consumption series. In
agreement with the data, the model predicts that private expenditures are more strongly procyclical than
public expenditures. Although the model standard deviations for x, and X are much higher than in the
data (table 4), the relative magnitudes (table 5) are about right. The model standard deviations could be
reduced by introducing adjustment costs for both types of investment (see Lansing [1993b]). The
standard deviations for the consumption series, g and c, display the opposite problem, i.e., the model
series are less variable than the corresponding U.S. series. Once again, however, the relative variability
in table 5 is close to the U.S. value. The two problems are no doubt linked; the excessive volatility of
investment in the model allows for very smooth consumption.
In the labor market, the model predicts a lower standard deviation for total hours H than is
observed in the U.S. data. Consequently, the model's variability of hours relative to labor productivity
(table 5) is too low. This occurs despite the assumption of indivisible labor, which operates to increase
the variability of H. Also, the correlation between hours and productivity in the model is higher than
in the data. For these two statistics, the model does not do as well as other real business-cycle models
that treat government policy as exogenous (see Christian0 and Eichenbaum [1992], McGrattan [1991],
and Braun [1989]). Although not shown in table 5, the contemporaneous correlation between hours
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.
worked in the two sectors, corr(h, h,), averaged 0.37 in the simulations. This is consistent with
conventional wisdom regarding the comovement of employment in different sectors over the business
cycle.24
Tables 6 and 7 provide a closer examination of the behavior of policy variables. The model does
well in matching the standard deviations and serial correlation of the tax rates (table 6), but is less
successful regarding the cross-correlations with other policy variables (tables 7a and 7b). The model's
prediction that the capital tax should display larger variability than the labor tax is generally confirmed
by the data. The capital tax series estimated by Jorgenson and Sullivan (1981) has a much higher
standard deviation than the series estimated by McGrattan, Rogerson, and Wright (1993). The values are
16.38 percent and 4.82 percent, respectively. The Jorgenson and Sullivan series is an estimate of the
effective corporate tax rate, while the McGrattan, Rogerson, and Wright series also includes taxes paid
by individuals on capital gains and dividends. The correlation between these two series (after detrending)
is 0.45. The correlation between the two estimates of the U.S. labor tax is 0.84.
The correlation coefficients in the model match the signs in U.S. data for the majority of the
cases in table 7. However, the model predicts signs opposite to those in the data for the correlation
between x, and g and the correlation between
2,
and
2,.
The predicted negative correlation between
x, and g (-0.36) reflects the impact of preference shocks on the optimal mix between public investment
and public consumption. Without preference shocks, the correlation between x, and g in the model is
strongly positive (0.74) and close to the U.S. value (0.85). In this case, however, model performance
suffers in other areas, such as the relative variability of g and c. The predicted negative correlation
between
2,
and
2,
is also counter to U.S. data. The U.S data display a positive correlation, which
suggests that there may be rigidities in the U.S. tax code (not accounted for in the model) that link the
movement of tax rates over the business cycle.
24~na model version with different technology shocks in the two sectors, the comelation between h, and h, is negative (and hence
counterfactual), as employment always flows into the most productive sector. This is also a characteristic of home production models
that specify sector-specific technology shocks for the home and market sectors. See Benhabib, Rogerson, and Wright (1991).
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Table 6: Comparison of Tax Rate Statistics (detrended)
-
Model'
U.S
Economvb
U.S.
Economv'
3.82
5.65
3.65
(-1)
0.41
0.43
0.55
corr (-2)
0.05
-0.19
-0.09
-
Mean
Std. Dev. (%)
COIT
'=hr
-0.16
-0.67
-0.54
corr (-3)
..................................................................................................................................................................................................................................
Mean
0.268
0.299
0.568
-0.18
-0.24
-0.27
Std. Dev. (%)
COrr (-1)
'=kt
corr (-2)
corr (-3)
a ~ o d estatistics
l
are means over 100 simulations, each 46 periods long. The tax rate series were detrended using the
Hodrick-Prescott filter with a smoothing parameter of 100. The tax rate series were not logged before detrending.
b~, is from B m and Sahasakul(1986), 1947-83, and T
, is from Jorgenson and Sullivan (1981, table 11). 1947-80.
,
T
' and T
, are from McGrattan, Rogerson, and Wright (1993), 1947-87.
Table 7a: Contemporaneous Correlation in Model'
g
XG
XG
1.00
-0.36
=r,
=ri
0.82
-0.62
X
c
GNP
0.49
0.39
0.55
c
GNP
Table 7b: Contemporaneous Correlation in U.S. Economy'
-
XG
.
g
=A
Tk
X
asterisk indicates that the correlation coefficient has the same sign as in the model. For the tax rate correlations. the
top and bottom numbers in each cell are correlations using U.S. data described in footnotes b and c, respectively, of table 6. All
variables have been detrended as in the model.
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7. Concluding Remarks
The recent controversy surrounding the productive effects of public capital has focused on
questions related to long-run growth. In contrast, this paper is concerned with the optimal behavior of
public investment and other key elements of fiscal policy over the business cycle. While a number of
researchers have incorporated fiscal policy into real business-cycle models, the government policymaker
is generally treated as exogenous. This paper employs a two-sector real business-cycle model, augmented
with preference shocks, to endogenize the choice of fiscal policy over time.
I subjected the model to comparisons with postwar U.S. data on public investment, public
consumption, and tax rates and obtained reasonable success in capturing the observed behavior of the
various time series. At the optimal level of public capital, the rate of return on public investment is less
than the rate of return on private investment. The model predicts procyclical behavior for public
investment and public consumption, in contrast to the Keynesian view of countercyclical fiscal policy.
It also predicts a positive tax on capital that should be more variable than the labor tax. The model
disagrees with the data, most notably, in predicting negative correlations between public investment and
public consumption and between the capital tax and the labor tax.
A natural extension of this work would be to incorporate heterogeneity, since it is highly
probable that key elements of fiscal policy, such as the capital tax, are driven by distributional
considerations (see Lansing [1993a]). Further research is also needed to address the many empirical
questions suggested by this work, including formal tests of model predictions and direct estimation of
parameter values. In addition, much work remains to be done in modeling the institutional structure of
the tax code and endogenizing the choice of tax instruments, topics that have been emphasized by
Slemrod (1990).
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APPENDIX A
A.l Recursive Formulation of the Government's Problem
To formulate the recursive version of (19), we first substitute the household first-order conditions
from (7) into the household budget constraint (2), the private-sector resource constraint (20), and the
utility function U(-)to eliminate z,, z,, and c, .' In addition, g, can be eliminated using the
government-sector resource constraint (19.v). The vector of state variables for the govemment's problem
is s, ={z,, v, , k,, , k, , k,, , h ,.,). In the transformed problem, the government's decision variables are h , ,
h,, , h,, k,,,, , k,,
, and
kc+,
. Using primes (') to denote next-period quantities, the recursive version
of the government's problem is shown in (A.l).
The Bellman equation in (A.1) summarizes the recursive nature of the problem. The first
constraint is the household budget after substituting in the first-order conditions. The symbol u represents
a composite error term that arises due to the presence of E, in the first-order condition for h,,.The next
constraint is the private-sector resource constraint. The government-sector resource constraint has been
substituted into U(.).The remaining constraints define the cost minimization condition, the production
technologies, the rental rate on private capital, and the laws of motion for the two exogenous shocks.
The dynamic programming problem applies for all t > 0. The problem at t=O must be considered
separately, as shown by Kydland and Prescott (1980), Lucas and Stokey (1983), and Chamley (1986).
At t=O, the stock of private capital is fixed. Optimal policy thus implies a high initial tax on capital to
take full advantage of this nondistortionary source of revenue. I assume that this form of lump-sum
taxation is insufficient to finance the entire stream of future expenditures. The analysis here will focus
on policy in stationary stochastic equilibrium, i.e., when t is very large. The linear-quadratic
approximation method used to solve (A.1) is accurate only in the neighborhood of the deterministic
steady state. Consequently, I do not solve the t=O problem or compute the transition path to the
stationary equilibrium.
' ~ u to
e the presence of the expectation operator in the fmt-order conditions for ki,, (i=1,2), the substitution is accomplished
using the expression E ,., f , (-1= f, (-1 - u,, where f , ( - ) is a function of random variables and u, is the forecast error. The
assumption of rational expectations implies E ,.,u, = 0.
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V(s) = max E ,
k;. k;, k;.
h,. h,.
where
S =
9
+
B [v(sf)ls])
I z , V, kl, k2, kc, h - , )
U ( - ) = ln(1b) - A(hl + h,)
+
exp(v)B h [ y , -k,'
+(I-6,)k,]
subject to
A
A-1
-(hl
+h,) +-(kl
h
PA
Y
1
+
k2) +(I-0,-0,)y
-h - klf - k,'
+
r -6
/-(k;+k;)
-h
+U
=0
(1-6)(kl +k2) = 0
Arrow and Kurz (1970) prove the existence of a unique, stationary equilibrium in a one-sector
economy similar to the one developed here. Uzawa (1966) proves existence and uniqueness in a twosector model with a production tax, but excludes public capital. Although I do not prove existence and
uniqueness, analogy to these other models suggests that the model possesses a unique, stationary
equilibrium The computational algorithm (described below) always converged to the same value
function regardless of the initial starting point. Equilibrium is defined as a value function V(s) and an
associated set of stationary decision rules that satisfy (A. 1). The decision rules dictate a set of household
allocations and prices at time t that can be implemented by means of the government's chosen policy.
The government's explicit policy rules for tax rates and public expenditures are recovered by substituting
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FIG 1: U.S. LABOR PRODUCTIVITY vs PUBLIC CAPITAL
- - Public Capitol (talal) p r Lobor nour
+
- Public Capitol (ercl.
military) p n Lobar Hour
FIG 2: U.S. PRIVATE vs PUBLIC INVESTMENT
0
E
C
80,
\ "
US
x'
1047
1952
1917
1982
1987
1972
1 077
lM2
1W7
lW2
1
W
1
W
1992
Year
FIG 3: U.S. PRIVATE vs PUBLIC CONSUMPTION
a
n
0
2.
..
-Private Consumption (Nondurobla.+Sonic.o)
- - Public Conrumption (Coads+Semcea l e u Investment)
a
n
.
!2.
rr-
E;s.
;
z
"8.
2
a
0
8 .
.
_---
1947
C
C
_
1962
_
_
_
_
_
_
_
1951
_
_
-
-
-
-
-
C
_
_
_
_
_
_
_
_
_
_
_
_
-
-
-
-
-
-
-
-
-
-
-
1981
190
1972
year
Sources: U.S. Department of Commerce and Citibase.
$On
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FIG 40: U.S. SERIES OF PUBLIC INVESTMENT AND GNP (Logged/Deirended)
--
Real GNP
Public Investment ootol)
Public Invedment (Excluding Military)
Year
FIG 4b: U.S. SERIES OF PRIVATE & PUBLIC INVESTMENT (Logged/Detrended)
-Privote Invedment (Fi~ed+Duroblea+ReaidmPal)
- - Public Investment Ootal)
- Public Investment (Excluding Military)
-
Year
Sources: U.S. Department of Commerce and Citibase.
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FIG 50: U.S. SERIES OF PUBLIC CONSUMPTION AND GNP (~ogged/Detrended)
-
--
-0.1 2
1947
1952
Rsal CNP
Public Consumption (Coodm+krvicas lass Invmmtmant)
1957
1962
1967
1972
1977
1982
1987
Year
FIG 5b: U.S. SERIES OF PRIVATE & PUBLIC CONSUMPTION (~ogged/Detrended)
--
Private Consumption (Dvrobles+krvices)
Public Consumption (Goods+Senices leas Invmtment)
Source: Ci tibase.
1992
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FIG 60: SIMULATED PRIVATE & PUBLIC INVESTMENT
- No Preference Shocks
- Privde Innrtmant
- Public Inveatmsnt
X
Xg
Year
FIG 6b: SIMULATED PRIVATE & PUBLIC INVESTMENT
-
w/
Preference Shocks
0.30
X
Xg
-0.30
1
6
- Private Investment
- Public lnvsstmont
11
16
21
26
Year
Source: Author's calculations.
31
36
41
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F I G 70: S I M U L A T E D P R I V A T E & P U B L I C C O N S U M P T I O N
-
N o Preference Shocks
0.10
0.08
-
0.06
-
0.04
-
P
I-
\
.->
0 -0.02
-
I
-
0
-0.04
-
-0.06
-
-0.08
-
0
-0.10
1
c
9
6
- Prirotc Consurnption
- Public
Consurnption
11
16
21
26
31
36
41
46
Year
FIG 7b: SIMULATED PRIVATE & PUBLIC CONSUMPTION
0.10
0.08
-
0.06
-
-
w/
I
I
26
31
Preference Shocks
I
m
0'
-0.04
-
' II
I
-0.06
-0.08
-0.10
'
'I
-
c
1
9
6
- Private Consumption
- Public Conmumption
11
16
21
Year
Source: Author's calculations.
36
41
46
clevelandfed.org/research/workpaper/index.cfm
FIG &: U.S. SERIES FOR LABOR TAX (Barra & Soharakul-19116)
U.S. SERIES FOR CAPITAL TAX (Jorprnson & Sullivan-1981)
FIG 90:
0.40
0.S
0.35
.
0.45
.
.
+ 0.30
Z
D
2
m
I-
'
I 0.15
c'
.
0.15
0"?047
'
0.10
-r,
lei1
- Tan Rats on Lobar Income
1857
1082
inn
tkrz
r,
ion
t i n
iw
iwz
O.D9047
1152
- Tax Rala on Copilal lncame
1*57
ion
Year
- 1993)
FIG 9b:
ion
lea
in7
U.S. SERIES FOR CAPITAL TAX (McCraltan e l al.
o
FIG Bb:
1871
U.S. SERIES FOR LABOR TAX (UcCrallan at al.
-
'
0.15
0'1q047
-r, - Tax Rate on Labar lncoma
1052
1957
1062
1187
1172
o.s
1177
lM2
lW7
1 [-
0.59647
lW2
T,
10%
- Tax Rat.
1057
an Capital Income
1101
ion
Year
FIG I c :
SIMULATED SERIES FOR LABOR TAX
- w/
Prefarencr Shocks
FIG 9c:
0.50
0.45
0.30
1072
1
inn
im
im
1A2
Year
0.40
0.35
1993)
1
0:80
0.40
i n 2
year
-
SIMULATED SERIES FOR UPlTAL TAX
- w/
Preference Shoclu
'
'
.
. DD
2
C
0.15
'
L-D
1 0.18
0.15
O.l01
.
c'
0.10
-r, - Tax Rata an Labor Incoma
0
11
18
I
21
.
'
O.w .
31
3I
41
year
Sources: As noted and author's calculations.
41
o'W1
- - Tax Rate an Copilal lncama
T,
I
11
18
I
21
Ymr
31
;I
;
I
48
@FedFRASER