In recent years, the link between public capital and private sector production has been a subject of considerable debate among policy makers and researchers.
Journal of Economic Dynamics and Control 22 (1998) 91 l-935
ELSEVIER
Optimal fiscal policy, public capital, and the productivity slowdown Steven P. Cassou”, Kevin J. Lansingb,* aDepartment of Economics, Kansas State University, Manhattan, KS, 66506, USA bResearch Department, Federal Reserve Bank of Cleveland, P. 0. Box 6387, Cleveland, OH 44101-1387, USA
Received 11 July 1995; accepted 23 May 1997
Abstract
This paper develops a quantitative theoretical model for the optimal provision of public capital. We show that the ratio of public to private capital in the US economy since 1925 evolves in a manner that is broadly consistent with an optimal transition path derived from a simple growth model. The model is used to quantify the conditions under which an increase in the stock of public capital is desirable and to investigate the degree to which nonoptimal fiscal policies can account for the US productivity Elsevier Science B.V. All rights reserved. JEL classification:
slowdown.
@ 1998
E62; H40; H54; 041; El 3
Keywords: Fiscal policy; Infrastructure; Growth; Public investment
1. Introduction years, the link between public capital and private sector production has been a subject of considerable debate among policy makers and researchers. Although the idea that public capital may represent an important productive input is not new (see, Arrow and Kurz, 1970), the empirical work of Aschauer (1989, In recent
* Corresponding author. For helpful comments, we would like to thank David Altig, Costas Azariadis, Michael Dotsey, Timothy Fuerst, Gary Hansen, Gregory Huffman, Per Kmsell, B. Ravikumar, Peter Rupert, Randall Wright, Mark Wynne, and two anonymous referees. The views in this paper are those of the authors and not necessarily those of the Federal Reserve Bank of Cleveland or of the Board of Governors of the Federal Reserve System. 0165-1889/98/%19.00 0 1998 Elsevier Science B.V. All rights reserved PflSO165-1889(97)00083-3
912
S. P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Control 22 (1998) 911-935
1993) and Munnell (1990) stimulated renewed interest in this area because their results implied the existence of very high rates of return to public infrastructure investment. They also claimed that the observed decline in the rate of public capital accumulation during the 1970s and 1980s contributed significantly to the slowdown in the growth rate of US labor productivity over the same period. Subsequent studies have added to the debate by attempting to confirm (or refute) the productive effects of public capital using increasingly sophisticated empirical methods. ’ Up to this point, however, little attention has been given to addressing these issues from a theoretical perspective. In this paper, we develop a quantitative theoretical model for the optimal provision of public capital. We show that the ratio of public to private capital in the US economy since 1925 evolves in a manner that is broadly consistent with an optimal transition path derived from a simple growth model. Moreover, we are able to quantify the conditions under which an increase in the stock of public capital is justified in terms of maximizing the utility of a representative household. We find that even when the output elasticity of public capital is as high as 0.10, an increase in public capital from the vicinity of current levels is not called for. Finally, we show that a nonoptimal public investment policy of the type that might be interpreted as reflecting US experience over the last 30 years can account for only a small portion of the productivity slowdown that began in the early 1970s. In contrast, we show that the trend of increasing tax rates in the US economy offers a better explanation for the productivity slowdown within the context of our model. However, we find that this result is sensitive to the choice of certain parameter values - in particular, the elasticity of household labor supply. To perform our analysis, we embed a version of the empirical public capital model used by Aschauer (1989), Munnell ( 1990), and others into a general equilibrium framework with an optimizing government. * Our model is similar to the one used by Glomm and Ravikumar (1994), but differs in three fundamental
’ For example, Aaron (1990), Tatom (1991). and Holtz-Eakin (1994) have shown that empirical methods which incorporate omitted variables, adjustments for nonstationarities, or more disaggregated data find that the output elasticity of public capital is not statistically different from zero. In contrast, Lynde and Richmond (1992), Finn (1993), and Ai and Cassou (1995) show that empirical techniques which properly handle reverse causality concerns continue to support large contributions to output from public capital. 2 Other papers that explore optimal fiscal policy in the context of dynamic general equilibrium models include Kydland and Prescott (1980), Lucas and Stokey (1983), Judd (1985), Charnley (1986) Lucas (1990), Zhu (1992, 1995), Jones et al. (1993, 1997), Bull (1993), Chari et al. (1994), Cassou (1995), Milesi-Ferrctti and Roubini (199.5), and Coleman (1996). Research on optimal fiscal policy that focuses on the spending side of the government budget constraint (as we do here) includes Barre (1990), Glomm and Ravikumar (1994), Corsetti and Roubini (1996), Turnovsky (1996), Judd ( 1997), and Lansing (1997).
S. P. Cassou, K. J. Lansing I Journal of Economic
Dynamics
and Control 22 (1998)
9If-93s
9 13
respects. First, labor supply is endogenous. This opens up an important channel through which fiscal policy can affect the growth rate of productivity. Second, both private and public capital stocks are long-lasting. This allows our model to capture the lengthy transitional dynamics of an economy moving toward its balanced growth path. Third, the relevant stock of public capital for production is defined as a per capita (or per firm) quantity. This ensures that there are no scale effects associated with the number of firms. The model is used to explore optimal transition dynamics and to quantify the effects of nonoptimal fiscal policies on productivity growth. We also investigate the sensitivity of our results to alternative economic environments. The remainder of this paper is organized as follows. Section 2 presents the model. Section 3 describes the transition dynamics implied by optimal fiscal policy. Section 4 describes how we obtain parameter values to carry out our quantitative exercises. Section 5 presents the quantitative exercises, and Section 6 concludes.
2. The model The model economy consists of a private sector that operates in competitive markets and a benevolent government that solves a dynamic version of the Ramsey (1927) optimal tax problem. The private sector is typical of macroeconomic models with agents behaving optimally, taking government policy as given. In formulating its policy, the government takes into account the rational responses of the private sector. The model includes what we consider to be the important elements: long-lived capital, endogenous labor supply, and productive public expenditures. We specify functional forms and the menu of available policy instruments in such a way as to obtain closed-form expressions for the decision rules of all agents. The ability to obtain a solution which is globally valid is important for our analysis because we will be investigating transition dynamics that can take the economy far away from its balanced growth path. Moreover, a closed-form solution allows us to readily identify the key model parameters that are important for determining the quantitative impacts of fiscal policy on productivity growth.
2.1.
The priuate sector
The private sector consists of a large but fixed number of households. Each household is the owner of a single firm that produces output y, according to the technology (1)
914
S. P. Cassou. K. J. Lansing1 Journal of Economic Dynamics and Control 22 (1998)
911-935
where A0 > 0, 8i > 0 for i = 1,2,3, and 131+ 02 + 8s = 1. 3 With this technology, there are three factors of production: the per capita stock of private capital kl, the per capita labor supply II, and the per capita stock of public capital kg,. Specifying kg, as a per capita quantity ensures that there are no scale effects associated with the number of firms. 4 The firm chooses k, and It, but takes kg, as exogenously supplied by the government. Output is also affected by hl, which is an index of knowledge outside the firm’s control that augments the productive capacity of labor. Following Arrow (1962) and Romer (1986), we assume that the mechanism for knowledge accumulation is learning by doing. This means that knowledge grows proportionally to, and as a by-product of, accumulated private investment and research activities. This idea can be captured by the specification h, = Et, where i;, is the average capital stock across firms. The assumption that firms view h, as outside their control requires that there be a sufficiently large number of firms so that no single firm has an impact on Et. Furthermore, because all firms are identical, & = k, in equilibrium. We therefore impose the condition ht=Et=k,
(2)
after firms choose their optimal labor and capital input levels. 5 It is assumed that firms operate in competitive markets and maximize profits. The firm’s decision problem can be summarized as
where r, denotes the real rental rate on private capital and w, is the real wage. Since 0i + 0, + e3 = 1, the firm earns an economic profit equal to the difference between the value of output and payments made to the private sector inputs. Our assumptions about firm ownership imply that all households receive equal amounts of total profits. 6 We assume that these profits are distributed to households as dividends and taxed as ordinary income. The market clearing prices for
3 Empirical research by Aschauer (1989), Munnell (1990), and Ai and Cassou (1995) finds support for a technology specification with 0t + 02 + 83 = 1. 4 See Barre and Sala-i-Martin (1992). Our setup can be viewed as incorporating an implicit congestion effect associated with the number of firms (which is equal to the number of households here). See Glomm and Ravikumar (1994) and Judd (1997) for models in which an explicit congestion effect is linked to the size of the private sector inputs. s The technology specification, the equilibrium condition h, = 6 = k,, and the condition 01 + 62 + 8s = 1, imply constant returns to scale in the two reproducible factors k, and kr,. Consequently, the model exhibits endogenous growth. Kocherlakota and Yi (1996, 1997) find evidence in US data supporting endogenous growth models that incorporate public capital. 6 It is possible to allow for different numbers of households and fhms. However, as long as ownership of firms is uniform across households, each household will realize exactly the same level of profits as here.
S. P. Cassou, K.J. Lansing I Journal of Economic Dynamics and Conrrol22
private capital and labor inputs and the resulting
(1998)
91 l-935
9 15
firm profits 7r1 are given by
rt = 01 y&l,
(4)
wt = e2Yrilr,
(5)
n, = (1 - 8, - &)yt.
(6)
The infinitely imize
lived representative
household
chooses
{c,, It, it, k,+1}:,
to max-
(7) I==0
subject to
ct + it = (1 - rt)(w,Z, + rtk, + TLC,), k,+l =A, k’-‘i6 *, t
h
given,
(8) (9)
where p E (0,1), is the household discount factor, cf is private consumption, it is private investment, and r! is the income tax rate. The household takes government tax policy zl, knowledge accumulation ht, and dividends rc( as determined outside of its control. The utility function can be interpreted as the reduced form of one that incorporates home production. ’ The presence of hl in both (1) and (7) implies that productivity in the market and productivity in the home increase at the same rate. As a result, labor supply 1, remains stationary along the model’s balanced growth path. The parameters B>O and y > 1 affect the supply of market labor, where l/(y - 1) is the intertemporal elasticity of substitution in labor supply. As y becomes large, 1, approaches 1.0 and the model reduces to one with a fixed supply of labor. Investment adds to the stock of private capital according to the law of motion (9), where Ai >O and 6 E (0, l] are parameters that govern the relationship between new investment and next period’s capital stock. When Ai = 1 and 6 = 1, capital depreciates fully after one period, as in Glomm and Ravikumar (1994). When 0 < 6 < 1, capital is long lasting. This nonlinear specification facilitates closed-form decision rules and can be viewed as reflecting adjustment costs as in Lucas and Prescott ( 1971). *
‘See
Greenwood
et al. (1995).
*This specification has been used in applied work by Hercowitz and Sampson (1991) and Kocherlakotfl and Yi (1997), among others. Our setup differs from the standard one given by k,+r = (l-6)& +i,, where 6 is the linear depreciation rate. Eq. (4) might also be viewed as capturing the behavior of an aggregate stock that is measured by adding up di%rent types of capital (structures, equipment, consumer durables, etc.) which each display different depreciation characteristics.
916 S. P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Control 22 (1998)
911-935
Using standard techniques, it can be shown that the household’s optimal decision rules are given by ct = (1 - ao)(l - r*)y,, 4 = a0(1
-
7th,
(10)
(11) (12)
where a0 = pStIr/[ 1 - /I( 1 - S)]. W e can interpret a0 as the marginal propensity to save out of after-tax income. Notice that government fiscal policy affects the equilibrium allocations in two ways: (1) through the tax rate zt, and (2) through the ratio kgl/k,.9 2.2. The public sector The government chooses an optimal program of taxes and expenditures to maximize the discounted utility of the representative household. In addition to public investment, government expenditures include purchases of other goods and services, gr, which do not contribute to either production or household utility. The per capita quantity of nonproductive expenditures is assumed to increase in fixed proportion to per capita output, such that gr = &J+, where CJ~ 1 0. We further assume that the policymaker views gr as exogenous. This specification is a simple way of ensuring that gr continues to represent a significant fraction of output as the economy grows. ‘O In per capita terms, the government’s budget constraint is
(13) where iet represents public investment. Our assumption of a period-by-period balanced budget facilitates a closed-form solution to the government’s decision problem. ’ *
g The derivation of the household decision rules and other analytical results in the paper are contained in a technical appendix that is available from the authors upon request.
to
Alternatively, we could endogenize public consumption by an additively separable argument Dlngr in the household utility function (7), where D 2 0. In this case, we obtain a similar result - that the optimal ratio g,/yr is constant for all t. I1The balanced budget assumption has also been used by Barre (1990) and Glomm and Ravikumar (1994), among others. We believe that this setup may represent a closer approximation to actual constraints than one which allows the government to borrow or lend large amounts. For example, Zhu (1992), Jones et al. (1993), and Coleman (1996) show that models with no limits on debt imply that the optimal fiscal policy involves a large budget surplus in early periods financed by heavy capital taxation. The government becomes a net lender to the public, which provides a source of revenue that facilitates lower distortionaty taxes in the future. It is doubtful, however, that confiscatory taxes of this kind are politically feasible. See Coleman (1996) for further analysis of this issue.
S.P. Cassou. K. J. Lansing1 Journal of Economic Dynamics and Control 22 (1998)
Public investment contributes to the stock of public following law of motion, which is analogous to (9) k gt+l =A, ki,‘i,d,,
k,a given.
capital
911-935
according
917
to the
(14)
The government chooses {7,, i,,, kg*+,, cI, 11,it, k,+l}~‘O to maximize (7) subject to (9)-( 14). In Ramsey problems of this type, it is typical to assume that the government can commit to a sequence of policy variables announced at t = 0. The commitment assumption is not needed here, however, because none of the private sector decisions at time t depend on expected future policy variables. Thus, the government cannot surprise agents by deviating from its originally announced plan. ‘* Standard techniques yield the following optimal policy rules: lgf = a1.J+,
(15)
7f = Ql + 4,
(16)
where ai = @&/[l - p( 1 - S)]. Notice that the tax rate is constant over time and can be decomposed into two parts, one associated with public investment igt and the other associated with nonproductive expenditures gr.
3. Transition
dynamics
The model’s tractable nature allows us to obtain closed-form expressions describing the optimal transition path for an economy with initial conditions that lie off the balanced growth path. To characterize the transition dynamics, we begin by computing the optimal ratio of public to private capital, R*, when the economy is in balanced growth. The intuition for the transitional changes is straightforward. If the current value of Rt = k,,/k, is less than the balanced growth ratio R*, then optimal policy calls for an increase in Rt over time until R* is reached. On the other hand, if R, is greater than R*, then a decline in RI over time is consistent with optimal fiscal policy. To derive an expression for R*, we combine the household and government decision rules with the laws of motion for the two capital stocks (9) and (14). Because there are two state variables, kl and kgl, the decision rules must be solved jointly to obtain the equations that govern the optimal transition path leading to R’.
‘* Our choice of functional forms - logarithmic utility and Cobb-Douglas technologies for output and capital accumulation - yield exactly offsetting income and substitution effects. As a result, the investment decision does not depend on the future return to capital. See Chang (1988) for other examples of preference and technology combinations that exhibit this property.
918
S.P. Cassou. K.J. LansingI Journal of Economic Dynamics and Control 22 (1998) 911-935
Substituting the optimal decision rules ( 1 1), ( 12), and ( 16), and the production equations (1) and (2), into (9) yields
k([~Y(el+82)-6821/(Y-82))+1-6ksYesl(Y-82)
x
I
(17)
CP
Eq. (17) is the equilibrium law of motion for private capital when there is optimal behavior on the part of households, firms, and the government. Similarly, ( 15), (16), (12), (1 ), and (2) can be substituted into (14) to yield the equilibrium law of motion for public capital:
k[sY(el+ez)-~e2ii(Y-e2)k[~Ye3i(Y--2)i+~ -6
x
I
(18)
61
Dividing (18) by (17) yields k -=gt+1 k 1+1
(19)
The above equation tells us that along the balanced growth path, that is, when = k,,/k,, we have R* = at/[ac(l - at - &)I, which is constant. Making use of the expressions for a~, al, and (16) yields R* = O,/[& (1 - r)], where r is the constant tax rate. An expression for the economy’s long run per capita growth rate p can be obtained by substituting kg, = R’k, into (17) and then taking logarithms to obtain: I3
k,,+l/k,+l
p=ln+i =ln* +-
=lnYt+l= et
I
hJ
( ,[ Y-
02
In (1 -al
In
y
=
~~/~y-fwA~u~ (!g’Y]
In
Yt el
- c#I)‘-~, $
,
()I
where the second term captures the influence of optimal fiscal policy on the growth rate.
I3 To derive this result, we make use of the expression 01 + 65 + 03 = 1. Consequently, necessary condition for balanced growth in the model.
this is a
S. P. Cassou, K.J. Lansing1 Journal of Economic Dynamics and Control 22 (1998)
911-935
919
4. Calibration To investigate the quantitative implications of our model, we assigned values parameters based on empirically observed features of the US economy. For parameters that are important for the results, such as 03, 6, and y, a range of values will be examined. Our use of a CobbDouglas production technology captures the fact that labor’s share of output in US data has remained relatively constant over time. Empirical estimates of 02 are influenced by the way in which certain types of income are apportioned between labor and capital. For example, proprietor’s income, indirect business taxes, and imputed services from consumer durables may affect estimates of &. We choose Q2 = 0.60 based on empirical work by Christiano (1988) Ai and Cassou (1995), and others. This is close to values commonly used in the literature. For example, Ring et al. (1988) specify labor’s share as 0.58. The range of direct empirical estimates of 0s at the aggregate national level is quite large. Aschauer (1989) and Munnell (1990) estimate values of 0.39 and 0.34, respectively. Finn (1993) estimates a value of 0.16 for highway public capital. Aaron (1990) and Tatom (1991) argue that removing the effects of trends and taking account of possible missing explanatory variables, such as oil-prices, can yield point estimates for 0s that are not statistically different from zero. Since & is important for determining R*, we attempt to remain objective by considering a range of values. l4 The parameter 6 in Eqs. (9) and (14) is the elasticity of next period’s capital stock with respect to new investment. Using this nonlinear specification, Hercowitz and Sampson (1991) report a point estimate of 6 = 0.34, with a standard deviation of 0.26, based on annual US data from 1954 to 1987. Given the imprecise nature of the estimate, we explore a range of values for 6. We investigate values up to 1.0, which coincides with the value implicitly used by Glomm and Ravikumar (1994). In our experiments, we find that 6 = 0.10 provides a reasonable fit of the US time series of R, = k,,/k, from 1925 to 1992. ” The value 4 = 0.17 implies that government spending on nonproductive goods and services is 17% of output, consistent with the postwar US average. Following
to
I4 See Sturm et al. (1997) for an extensive effects of public capital.
review of the empirical
evidence regarding
the productive
Is The capital stock data are in 1987 dollars from Fixed Reproducible Tangible Wealth in the United States, US Department of Commerce (1993). The series for k,, is defined as govemmentowned equipment and nonresidential structures, excluding military components. The series for kr is defined as privately owned equipment and nonresidential structures. The ‘capital input’ measure of the net stock (which is an estimate of the remaining productive services available) was used for all capital data.
920
S. P. Cassou, K. J. Lansing 1Journal o$ Economic Dynamics and Control 22 (I 998) 91 I-935
Greenwood et al. (1988), we set y = 1.60, which implies that the intertemporal elasticity of substitution in labor supply l/(y - 1) is equal to 1.7. As noted by these authors, this value lies about midway in the range of the empirical elasticity estimates. Later, in our sensitivity analysis, we will investigate the effects of a less elastic labor supply. Given the values for 02, 6, 4, and y noted above, we simultaneously pick the remaining six parameters 81, 83, B, Ao, Al, and j3 as follows. First, recall that 81 and 03 are not independent because we must satisfy the necessary condition for balanced growth. We therefore define 81 = 1 - 02 - 83, and choose the remaining five parameters so that the model’s balanced growth path displays five characteristics identified from long-run US data. The first characteristic is the ratio of public to private capital R*. We identify two values that are of particular interest. One is R* = 0.60, which is slightly higher than the maximum value observed in the postwar US economy. The other is R* = 0.44, which coincides with the value observed- at the end of our data sample in 1992. The second characteristic is labor supply. Given a time endowment normalized to one, we choose I= 0.30, which implies that households spend about one-third of their discretionary time in market work. The third characteristic is the private sector capital-to-output ratio. We choose k,/y, = 1.25, which coincides with the postwar US average for privately owned equipment and nonresidential structures (see footnote 15). The fourth and fifth characteristics are the growth rate of labor productivity (which equals the growth rate of per capita output) and the after-tax real interest rate. We choose a growth rate of ,u = 2.77%, which coincides with the US average from 1947 to 1969. Our decision to calibrate to this 23-year subsample of US data is motivated by our interest in examining the degree to which nonoptimal fiscal policies can account for a productivity slowdown of the magnitude observed in the US economy during the early 1970s. Finally, we choose an interest rate of 6.9% based on the value estimated by Cooley and Prescott (1995) using data from the US National Income and Product Accounts. I6 Table 1 summarizes the parameter values we obtain using the above methodology. When R’ = 0.60, the optimal tax rate in the model turns out to be approximately 0.26, and the ratio of private investment to output is 0.15. When R’ = 0.44, the corresponding values are 0.24 and 0.16, ”
I6 The after-tax interest rate i is defined by introducing privately issued real bonds (which exist in zero net supply) into the household budget constaint. The first-order condition for bonds gives i= exp(p - In/?) - 1. ” If consumer durables are included in the definition of k~, then the ratio of public to private capital in 1992 is 0.37. Choosing R’ =0.37 in the calibration yields 81 =0.312 and 4 =0.088.
S. P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Control 22 (1998) 91 I-935 Table I Parameter
92 I
values Values
Parameter
R’ = 0.60
R* = 0.44
0.277 0.600 0.123 0.100 0.170 I.600 1S28 I .755
0.300 0.600 0.100 0.200 0.170 1.600 1.562 1.789 1.260 0.962
1.273 0.962
5. Policy evaluation 5.1. The historical transition path In this section, we examine how well our model can account for the evolution of the stock of public capital relative to private capital in the US economy over the last 70 or so years. Fig. 1 shows the US time series of RI = k,,/k, over the period 1925-1992. The series, which is plotted as a dashed line in the figure, grew at a rapid pace throughout the 1930s before experiencing a temporary acceleration during World War II. After the war, the ratio declined for a few years and then settled into a long, slow growth period that peaked in the mid-1960s. Over the last 30 years, the ratio has displayed a generally declining trend. For comparison, Fig. 1 plots the optimal transition paths implied by our model for three different parameter settings. In general, the model predicts a rapid initial growth in the ratio of public to private capital, followed by a leveling off as the economy converges to the balanced growth ratio R”. Although the US data do not display this monotonicity, the model’s optimal transition path leading to R* = 0.60 (with 6 = 0.10) is generally consistent with the data up until about the mid-1960s particularly if one views the war years as being influenced by a temporary shock. In contrast, the optimal transition path leading to R* = 0.44 lies below the US data for most of the sample period. Fig. 1 also includes an optimal transition path for the case of 6 = 1.0. As a comparative statics exercise, all other parameters were maintained at the values shown in the second column of Table 1. Looking to the far right of the figure, we see that 6 has a quantitatively small impact on the balanced growth ratio R *. I8 Although 6 has little effect on R*, it strongly influences the length of time
I8 It can be shown that aR*/i% > 0.
922 S. P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Conrrol22
(1998)
911-935
.¶ d A' - 0.62. 6 1 /
1.0
\ \ /p
_.---..__
R' - 0.60. d - 0.10 '_
\
\
.
U.S. ratio k.,Jk, '.
.
R* - 0.44. 6 - 0.10
2
1925 1930 1955 1940
1945
1950
1955
1960
1965
1970
1975
1960
,965
,990
I
1995
rear
Fig. 1. Model versus Historical Transition Path.
needed for the transition. As one would expect, higher values of 6 lead to more rapid transitions. When 6 = 1.0, the transition occurs in a single jump after the initial period. In the policy analysis that follows, we restrict our attention to the case of 6 = 0.10, since this yields a reasonable transition path in comparison to US data. 5.2. Optimal policy and the decline in public capital In recent years, many policymakers and researchers have voiced concern that the decline in the ratio of public to private capital over the last 30 years is evidence that the United States has been underinvesting in public capital. I9 However, Fig. 1 shows that this conclusion does not necessarily follow. In particular, a declining ratio of public to private capital can be consistent with optimal fiscal policy, even when public capital contributes in a significant way to private output. When R* = 0.44, the optimal transition path in Fig. 1 lies below the US time series of R,= k,,/k, over the postwar period. Thus, a decline in the US ratio over this period could be interpreted as bringing the economy closer to the optimal balanced growth ratio R*. To explore the robustness of this result, consider Fig. 2, which shows the effect of varying 193on R*.For each point in Fig. 2, we recalibrate the remaining parameters to match the long-run characteristics of US data described in Section 4.
I9 See, for example, Economic Report of the President, 1994, p. 43.
S. P. Cassou. K.J. LansinglJournal
of Economic Dynamics and Control 22 (1998)
e3 = 0.100
0.00
0.02
0.04
0.06
0.06
1
I
I
I
0.10
Fig. 2. R’ versus Output Elasticity
0.12
0.14
0.16
911-935
923
0.16
of public capital
As public capital becomes more productive (0s increases), the optimal ratio R* increases rapidly. If 0s E [O,O.lO], then R’ 5 0.44 and the model implies that an increase in the US ratio of public-to-private capital from the vicinity of current levels is not called for. On the other hand, when 03 > 0.10, Fig. 2 shows that R’ >0.44 and the model implies that the current US ratio of public-to-private capital is too low. It is important to recognize that our analysis does not resolve the debate over whether the US economy is underinvested in public capital because the optimal ratio R* depends crucially on the size of 93, which is the subject of much uncertainty. However, our model identifies some middle ground that neither side of the public capital debate seems to have formally recognized. Proponents of expanding public investment tend to make their case using empirical evidence that shows 03 >O. This result, together with the observation that the ratio of public to private capital has been declining over time, is often cited as evidence of nonoptimal fiscal policy. In contrast, opponents of expanding public investment tend to make their case by testing Ho: 03 = 0. Our analysis shows that this condition is much stronger than is needed to establish that the data do not call for an increase in public investment. Even with 0s as high as 0.10, our model suggests that the decline in the US ratio of public-to-private capital over the last 30 years is no cause for concern. The above argument is made even stronger by the fact that empirical estimates of 83 tend to be very imprecise. For example, Firm (1993) estimates the output
924
S. P. Cassou. K. J. Lansing I Journal of Economic Dynamics and Control 22 (1998) 911-935
elasticity of public highway capital to be 0.16. However, the 95% confidence interval for this estimate ranges from a low of 0.001 to a high of 0.32. Thus, even for relatively large point estimates of 03, the data do not necessarily imply that the ‘true’ value of 193would call for an increase in public investment. 5.3. Public capital and the productivity slowdown The debate on the productive effects of public capital is often linked to discussions regarding the slowdown in the growth rate of US labor productivity that began in the early 1970s. Some researchers argue that underinvestment in public capital is at least partially responsible for the slowdown.20 In this section, we take up this issue by examining how nonoptimal fiscal policies can affect the growth rate of labor productivity within the context of our model. For our first experiment, we investigate the consequences of a nonoptimal public investment policy. In the previous section, we pointed out that the observed decline in the US ratio of public to private capital can be reconciled with optimal fiscal policy when 0s E [O,O.lO]. However, if the optimal transition path is more appropriately described by the trajectory leading to R* = 0.60 in Fig. 1, then the recent decline in the US ratio would not be optimal. For this experiment, we take the latter view and adopt the parameter values that are consistent with R* =0.60. Next, as an input to the model, we construct an exogenous series for public investment igt such that the model’s resulting time path for the ratio Rt=kgl/k, coincides with the ratio observed in the US economy from 1947 to 1992. The constructed series for Rt is shown as a crossed line in Fig. 3a, while the solid line shows the optimal transition path computed earlier in Fig. 1. Since the constructed R, lies below the optimal transition path leading to R* =0.60 and tends to move further away over time, we interpret this experiment as capturing the type of nonoptimal public investment policy that is often cited as a possible cause of the US productivity slowdown. For this experiment, we isolate the effect of a declining public capital ratio on productivity by holding the tax rate constant at the optimal level implied by (16). The level of nonproductive government expenditures g, is then determined ‘as a residual such that the government’s budget constraint (13) is satisfied each period 21 Finally, we assume that the private sector reacts optimally to government policy, according to the decision rules (lo), ( 1 1 ), and ( 12). Fig. 3b displays the results of this experiment. The crossed line shows labor productivity in the model with the nonoptimal public investment policy described
*OSee, for example, Aschauer (1993) and Munnell (1990). Using state-level manufacturing data, Morrison and Schwartz (1996) cite evidence that shortfalls in inCastructure investment may have hindered productivity growth, particularly in the South and West. *l The optimal tax rate T* is computed from (16) using &=0.123, 6=0.10, b=O.962, and +=0.17. Nonproductive expenditures are then given by gr = T*J+ - isr. Since gr is determined as a residual for this experiment, the ratio gr/yr is no longer constant.
S. P. Cassou, K.J. Lansing I Journal of Economic Dynamics and Control 22 (1998)
911-935
925
r:;l-:l-----.: -1 r
1952
1957
1962
1967
1972
,977
1982
1987
1992
1977
1982
1987
1992
1997
YeOr
z
1947
1952
1957
,962
1967
1972 YeOr
(b)
Fig. 3. Productivity
experiment:
Suboptimal
public investment
policy.
above. The solid line shows labor productivity when public investment policy is optimal, that is, when R, follows the optimal trajectory leading to R* =0.60. The dashed line shows US labor productivity from 1947 to 1992.** In comparison
*‘We define US labor productivity labor hours (LHOURS).
as real output
(Citibase
series GNPQ)
divided
by aggregate
926
S. P. Cassou, K. J. Lansing 1Journal of Economic Dynamics and Control 22 (1998) 91 I-935
to the optimal policy case, the nonoptimal policy produces a mild slowdown in productivity growth. Notice, however, that this slowdown is much less pronounced than the one observed for the US economy. This experiment shows that a nonoptimal public investment policy of the type that might be interpreted as reflecting US experience over the last 30 years can account for only a small portion of the productivity slowdown, suggesting that other explanations for the slowdown should be considered. One alternative, which can be investigated using the same methodology, represents another type of nonoptimal fiscal policy, namely, increasing tax rates. For the second experiment, we introduce an exogenous sequence of tax rates rr that coincides with an average tax rate series defined for the US economy.23 In our model, it is important to recognize that an increasing tax rate can be beneficial if it moves the economy toward the optimal fiscal policy defined by r’ and R*.24 However, since the US tax rate series displays an increasing trend that eventually causes it to exceed T*, we interpret the trend as nonoptimal. To isolate the impact of rising tax rates on productivity, we construct an exogenous series for public investment ig, such that the model’s resulting time path for the ratio R, =k,,/k, follows the optimal trajectory leading to R* =0.60. As before, the private sector reacts optimally and gt is determined as a residual such that the government budget constraint is satisfied each period. The results of the second experiment are displayed in Figs. 4a and b. Fig. 4b shows that a policy of nonoptimal tax rates can also generate a productivity slowdown. The slowdown is much more severe than in the first experiment, however. The key difference between the two exercises is that in the first experiment, the government misallocates resources between igl and gt, while tax revenue as a fraction of total output remains constant. In the second experiment, the share of total resources claimed by the government increases over time.25 Fig. 4b shows that labor productivity in the model displays an abrupt change in trend around 1970 that is strikingly similar to the trend shift in US labor productivity that occurred around the same time. In the model, the cause of this
23We computed the average tax rate series for the US economy by dividing total federal, state, and local government receipts for each year (Citibase series GGFR+GGSR+GGFSIN+GGSSIN) by GDP. This approach yields an average tax rate that is roughly consistent with the model’s use of a production tax to finance all government expenditures. The resulting tax rate series displays an upward trend that is very similar to the one observed for the average marginal tax rate on labor income estimated by Barre and Sahasakul (1986). 24This feature suggests a possible explanation for why the sharp increase in US average income tax rates in the early 1940s did not produce a noticeable drop in the growth rate of per capita real output, as documented by Stokey and Rebel0 (1995). “To the extent that some of these resources may be returned to US households in the form of transfers and used to finance investment in private capital, the second experiment may overstate the growth-reducing effects of increasing taxes. However, if such transfers are largely consumed, then these effects would not be overstated.
S.P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Conlrol22
-
Optimal
-
Observed
47
I952
70x
Rate
lrom
(1998)
911-935
927
Model
IncreosinQ Tax Fate
1957
1967
1962
1972
1977
1982
1987
1992
1
1982
1987
1992
1997
YeOr
x
7947
-
U.S. Produclivity
1947-1992
-
Modal
Productivity
w/
Optimal
-
Model
Productivity
w/
lncrcasinp
1952
(957
lax
Rote lox
1962
Rate
1967
/
1972
1977
YeOr
(b) Fig. 4. Productivity
experiment:
Suboptimal
tax policy.
trend shift can be traced to the period of sharply increasing average tax rates in the late 1960s and early 1970s (see Fig. 4a). This experiment shows that the existence of a productivity slowdown need not imply that public investment policy is nonoptimal.
928
S. P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Control 22 (I 998) 91 I-935
Table 2 Results of fiscal policy
experiments Growth rate of labor productivity 1947-1969 (%) 1970-1992
Experiment Suboptimal public investment Suboptimal tax policy Joint suboptimal policy US economy
policy
2.65 2.67 2.57 2.77
(%)
2.30 1.16 0.66 0.62
As a final experiment, we introduce both types of nonoptimal fiscal policy into the model. The results of this exercise are shown in Figs. 5a and b. As one might expect, the productivity slowdown in the model becomes even more severe. This occurs because an increasing fraction of total resources are now being devoted to nonproductive public expenditures gl. Interestingly, the simulated productivity trend from the model provides a very close match to the US productivity trend. Table 2 provides a quantitative comparison of the productivity effects in each of the three experiments. To summarize, our experiments show that a nonoptimal public investment policy does not, by itself, provide a convincing explanation for the US productivity slowdown. However, it may have been a contributing factor, together with other factors, such as the trend of increasing tax rates. As a caveat to the interpretation of our tax rate experiment, we note that the empirical evidence regarding the links between tax policy and growth appears to be inconclusive.26 We also note that many alternative hypotheses have been put forth to help explain the US productivity slowdown. Some of these include: (1) a return to ‘normal’ productivity growth from the unsustainably high growth rates experienced after the Great Depression and World War II; (2) changes in demographic factors that have tended to reduce the quality of the labor force; (3) a fall-off in the rate of research and development spending; (4) increased costs of complying with government regulations; (5) increases in energy costs due to oil price shocks; (6) difficulties in measuring service-sector productivity; (7) temporary inefficiencies linked to the adoption of new technologies; and (8) aging of the capital stock.27
26 See Engen and Skinner
(1996)
for a review and analysis
of the empirical
evidence.
27 See Griliches (1988), Mtmnell (1990), Tatom (1991), Gordon (1996), Greenwood (1997), Wolff (1996) and the references cited therein for a more detailed discussion native hypotheses.
and Yorukoglu of these alter-
S. P. Cassou. K. J. Lansing I Journal of Economic Dynamics and Control 22 (1998)
_
Optimal
-
Obssrvad
-
Optimal
-
Observed
” Q ,947
1952
Rotio
from
Declining lax
Rate
91 l-935
929
Model Roti0
from
Increasing
Model
Tar Rote
1957
1962
1967
(a)
1972
1977
1982
1987
1992
1
,977
1982
1987
1992
1
YeOr
-
2 1947
Uodel
1852
Productivity
1957
w/
Obaawsd
Policy
1962
Fig. 5. Productivity
5.4. Alternative
1967
1972 YeOr
(b)
experiment:
Joint suboptimal
policy.
environments
As in all studies, it is useful to consider how our results might change in alternative economic environments. In what follows, we discuss the sensitivity of our results to parameter values and choices regarding the specification of utility
930
S. P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Control 22 (I 998) 91 I-935
and technology. Where appropriate, we cite other research that addresses similar questions in the context of endogenous growth models. To investigate the influence of parameter values on the outcome of our productivity experiments, it is useful to formulate an expression for labor productivity y,/ll that allows for nonoptimal fiscal policy. By combining (1 ), (2), and (12) and making the substitution kg, =Rlkt, we obtain Yf I,=
(A,-,Rf’ )“- ’
[(l - r,)(h)]‘-e2
ll(Y-e2) k I,
(21)
YE
which shows that the level of labor productivity at time t depends on RI, q, and k,. Hence, the growth rate of productivity in our model depends on the trends in the fiscal variables as well as the growth rate of the private capital stock. An expression for the growth rate of k, can be obtained by combining ( 1), (2), (ll), (12), and kgr=Rlk,, to yield
(22) Eq. (22) captures the possibility of nonoptimal fiscal policy and represents the growth rate of k, even when the economy is not in balanced growth. Together, Eqs. (21) and (22) show that the results of our productivity experiments are likely to be influenced by a number of parameters, including y, 62, 133,and 6. Since we have already considered the effects of varying 0, and 6 in the analyses of Sections 5.1 and 5.2, the discussion below concentrates on the effects of varying y and e2. With y= 1.6, the joint suboptimal policy reported earlier in Table 2 causes equilibrium labor hours to drop by about 13% over the course of the 45 period simulation (from 0.30 to 0.26). To explore the effects of a relatively inelastic labor supply, we set y =6 such that the intertemporal elasticity in labor supply l/(y - 1) is equal to 0.2. This value is at the low end of the empirical elasticity estimates.” The remaining parameters were then recalibrated to match the longrun characteristics of US data, as described in Section 4. Table 3 summarizes the results of the policy experiments when labor supply is less elastic. From Table 3, we see that the growth-reducing effects of nonoptimal fiscal policies are significantly smaller with y=6. The joint suboptimal policy now reduces labor hours by only 3.3% (from 0.30 to 0.29). Eqs. (21) and (22) imply that higher values of y tend to restrict the channels through which the policy variables rt and Rt can affect productivity growth. In particular, an increase in y
28 See Mulligan
(1995)
for a review of the various
empirical
studies.
S. P. Cassou. K. J. Lansing I Journal of Economic Dynamics and Control 22 (I 998) 91 l-935
Table 3 Fiscal policy
experiments
93 I
with less elastic labor supply Growth rate of labor productivity 1970-1992 1947-1969 (%)
Experiment Suboptimal public investment Suboptimal tax policy Joint suboptimal policy
policy
2.71 2.64 2.56
(%)
2.37 1.64 1.21
will reduce the magnitude of the derivatives a( y,/l,)/ar,, a( yt/lt)/aR,, ap~Jaz,, and apkl/aRt. 29 These results strengthen our conclusion that a suboptimal public investment policy cannot fully explain the US productivity slowdown. The explanatory power of rising US tax rates is also diminished, however. The latter finding is consistent with results of Stokey and Rebel0 (1995) who show that the growth-reducing effects of distortionary taxation are sensitive to assumptions about the elasticity of household labor supply. Stokey and Rebel0 (1995) also show that production function substitution elasticities are relatively unimportant in determining the growth effects of flat-rate taxes. However, our specification, unlike theirs, implies that households underinvest in human capital because of the learning by doing externality. Our specification tends to magnify the growth effects of fiscal policies that affect investment incentives. To investigate the influence of the learning by doing externality on our results, we set 02 = 0.10 to substantially reduce its importance in production. Once again, the remaining parameters were recalibrated to match the long-run characteristics of US data, with y = 1.6. In the resulting calibration, we obtained 81 = 0.648 and 8s = 0.252, which imply R” = 0.60. The suboptimal public investment experiment was carried out in exactly the same way as before. However, the suboptimal tax experiment required a modification to account for the higher value of 83. With 0s = 0.252, the optimal tax rate r* from Eq. (16) equals 0.35. To maintain comparability with our earlier experiment, we shifted up the observed US tax series by the amount 0.35 - 0.26 = 0.09, so that at each date the shifted tax rate exceeds the new r* by exactly the same distance as before. Table 4 summarizes the results of the experiments. From Table 4, we see that reducing the externality does not dramatically overturn our results in comparison to those in Table 2. For the tax experiment, we find that the crucial feature is the degree to which the actual tax rate exceeds
29 Formally, this can be shown by examining the signs of the second derivatives a/dy la(y,/r,)/api 1 and a/dy la~,,/apil, where 1 1 represents absolute value and pi={rr,RI}. It can be shown that all of these second derivatives are negative, implying that an increase in y will reduce the impact of the policy variables q and RI on the level of productivity and its growth rate.
932
S. P. Cassou, K. J. Lansing I Journal of Economic Dynamics and Control 22 (I 998) 911-935
Table 4 Fiscal policy
experiments
with reduced
Growth Rate of Labor Productivity 1947-1969 (%) 1970-1992
Experiment Suboptimal public investment Suboptimal tax policy Joint suboptimal policy
externality
policy
2.60 2.86 2.72
(%)
2.11 1.57 0.88
the optimal tax rate z*. Thus, we believe our results are reasonably robust to alternative formulations of the human capital technology. This issue is discussed further below when we consider the implications of the human capital technology on the form of the leisure specification. Some other features of our model are (1) taxes are levied on gross income from capital, (2) the coefficient of relative risk aversion for household utility is at the low end of the empirical estimates, and (3) leisure activity has a home production or ‘quality time’ interpretation. Some common alternatives include (1) taxes levied on income net of depreciation, (2) higher risk aversion, and (3) leisure defined as ‘raw time’, i.e., unadjusted for the level of human capital. Stokey and Rebel0 (1995) show that the quantitative effects of taxes on growth are sensitive to assumptions about the tax treatment of depreciation. Our specification does not include a depreciation allowance. This setup magnifies the effect of rising tax rates on growth, and thereby helps our model to account for the US productivity slowdown. Jones et al. (1993) show that higher levels of risk aversion - implying more curvature in utility - reduce the impact of nonoptimal tax rates on growth. This suggests that our use of a logarithmic utility function also helps rising tax rates account for the US productivity slowdown. Milesi-Ferretti and Roubini (1995) present a systematic study of how the human capital technology interacts with the leisure specification to determine the links between factor income taxes and growth. They consider three different specifications of the leisure activity: ‘raw time’, ‘quality time’, and ‘home production’. Factor income taxes are shown to be growth reducing in all three cases if physical capital is an input to the production of human capital. Since this production condition is trivially satisfied in our learning by doing formulation (h, = E, = I$), we expect that our quantitative results would not be substantially changed by an alternative leisure setup, such as raw time. 3o
3o The relevant results are summarized by Milesi-Fetritti and Roubini (1995) in Propositions 1 and 2 of their paper. when physical capital is not used to produce human capital, they show that factor income taxes have no effect on the balanced growth rate in the ‘quality time’ and ‘home production’ cases, but continue to be growth-reducing in the ‘raw time’ specification.
S.P. Cassou, K.J. Lansing/ Journal of Economic Dynamics and Conlrol22
(1998)
911-935
933
6. Conclusion This paper showed that optimal transition dynamics in a simple growth model can account for much of the behavior of the stock of public capital in the US economy over the last 70 years. Moreover, we showed that the observed decline in the US ratio of public to private capital since the mid-1960s might be interpreted as a movement toward the optimal balanced growth ratio, even for public capital output elasticities as high as 0.10. Finally, we found that a nonoptimal public investment policy of the type consistent with US data does not have much impact on the growth rate of labor productivity in our model, suggesting that other explanations for the US productivity slowdown should be considered. We find that one such explanation, the trend of increasing tax rates in the postwar US economy, can produce a large productivity slowdown in our model.
References Aaron, H.J., 1990. Discussion of Why is Infrastructure Important?. In: Munnell, A.H. (Ed.), Is There a Shortfall in Public Capital Investment?, Proceedings of a conference sponsored by the Federal Reserve Bank of Boston. Ai, C., Cassou, S.P., 1995. A normative analysis of public capital. Applied Economics 27, 1201-1209. Arrow, K.J., 1962. The economic implications of learning by doing. Review of Economic Studies 29, 155-173. Arrow, K.J., Km-z, M., 1970. Public Investment, The Rate of Return, and Optimal Fiscal Policy. Johns Hopkins Press, Baltimore. Aschauer, D.A., 1989. Is public expenditure productive?. Journal of Monctory Econoniic~ 23. 177-200. Aschauer, D.A., 1993. Public capital and economic growth. Jerome Levy Economics Institute. Public Policy Brief No. 4. Barro, R.J., 1990. Government spending in a simple model of endogenous growth. Journal of Political Economy 98, SlO3-125. Barre, R.J., Sahasakul, C., 1986. Average marginal tax rates from social security and the individual income tax. Journal of Business 59, 555-566. Barro, R.J., Sala-i-Martin, X., 1992. Public finance in models of economic growth. Review of Economic Studies 89, 645-661. Bull, N., 1993. When all the optimal dynamic taxes are zero. Federal Reserve Board Working paper No. 137. Cassou, S.P., 1995. Optimal tax rules in a dynamic stochastic economy with capital. Journal of Economic Dynamics and Control 19, I 165-l 197. Charnley, C.P., 1986. Optimal taxation of income in general-equilibrium with infinite lives. Econometrica 54, 607-622. Chang, F.-R., 1988. The inverse optimal problem: a dynamic programming approach. Econometrica 56, 147-I 72. Chari, V.V., Christiano, L.J., Kehoe, P.J., 1994. Optimal fiscal policy in a business cycle model. Journal of Political Economy 102, 617-652. Christiano, L.J., 1988. Why does inventory investment fluctuate so much? Journal of Monetary Economics 2 I, 247-280. Coleman, W.J.B., 1996. Tax Rates and Welfare. Duke University, unpublished manuscript.
934
S.P. Cassou, K J. Lansing1 Journal of Economic Dynamics and Control 22 (1998)
911-935
Cooley, T.F., Prescott, E.C., 1995. Economic growth and business cycles. In: Cooley, T.F. (Ed.), Frontiers of Business Cycle Research. Princeton University Press, Princeton, NJ. Corsetti, G., Roubini, N., 1996. Optimal government spending and taxation in endogenous growth models. National Bureau of Economic Research, Working paper 5851. Engen, E.M., Skinner, J., 1996. Taxation and economic growth. National Bureau of Economic Research, Working paper 5826. Finn, M., 1993. Is all government capital productive?. Federal Reserve Bank of Richmond. Economic Quarterly 79, 53-80. Glomm, G., Ravikumar, B., 1994. Public investment in infrastructure in a simple growth model. Journal of Economic Dynamics and Control 18, 1173-l 187. Gordon, R., 1996. Problems in the measurement and performance of service-sector productivity in the united states. National Bureau of Economic Research, Working paper No. 5519. Greenwood, J., Hercowitz, Z., HufTman, G.W., 1988. Investment, capacity utilization, and the real business cycle. American Economic Review 78, 402-417. Greenwood, J., Rogerson, R., Wright, R., 1995. Household production in real business cycle theory. In: Cooley, T.F. (Ed.), Frontiers of Business Cycle Research. Princeton University Press, Princeton, NJ. Greenwood, J., Yorukoglu, M., 1997. 1974, Carnegie-Rochester Conference Series on Public Policy, forthcoming. Griliches, Z., 1988. Productivity puzzles and R&D: another non-explanation. Journal of Economic Perspectives 2, 9-2 1. Hercowitz, Z., Sampson, M., 1991. Output growth, the real wage, and employment fluctuations. American Economic Review 81, 1215-1237. Holtz-Eakin, D., 1994. Public-sector capital and the productivity puzzle. Review of Economics and Statistics 76, 12-2 1. Jones, L.E., Manuelli, R., Rossi, P.E., 1997. On the optimal taxation of capital income. Journal of Economic Theory 73, 93-117. Jones, L.E., Manuelli, R., Rossi, P.E., 1993. Optimal taxation in models of endogenous growth. Journal of Political Economy 101, 485 -5 17. Judd, K.L., 1985. Redistributive taxation in a simple perfect foresight model. Journal of Public Economics 28, 59-83. Judd, K.L., 1997. Optimal taxation and spending in general competitive growth models. Journal of Public Economics, forthcoming. King, R.G., Plosser, C.I., Rebelo, ST., 1988. Production, growth and business cycles 1. the basic neoclassical model. Journal of Monetary Economics 21, 195-232. Koeherlakota, N.R., Yi, K.-M., 1996. A simple time series test of endogenous vs. exogenous growth models: an application to the United States. Review of Economics and Statistics 58, 126-134. Kocherlakota, N.R., Yi, K.-M., 1997. Is there endogenous long run growth? Evidence from the US and UK. Journal of Money Credit and Banking 29, 235-262. Kydland, F.E., Prescott, E.C., 1980. Dynamic optimal taxation, rational expectations, and optimal control. Journal of Economic Dynamics and Control 2, 79-91. Lansing, K.J., 1997. Optimal fiscal policy in a business cycle model with public capital. Canadian Journal of Economics, forthcoming. Lucas, R.E., Jr., 1990. Supply side economics: an analytical review. Oxford Economic Papers 42, 293-316. Lucas, R.E., Jr., Prescott, E.C., 1971. Investment under uncertainty. Econometrica 39, 659-681. Lucas, R.E., Jr., Stokey, N.L., 1983. Optimal fiscal and monetary policy in an economy without capital. Journal of Monetary Economics 12, 55-94. Lynde, C., Richmond, J., 1992. The role of public capital in production. Review of Economics and Statistics 74, 37-44. Morrison, C.J., Schwartz, A.E., 1996. State infrastructure and productive performance. American Economic Review 86, 1095 -1111.
S.P. Cussou. K.J. LansinglJournal
of Economic Dynamics and Control 22 (1998)
911-935
935
Milesi-Ferretti, G.M., Roubini, N., 1995. Growth effects of income and consumption taxes: positive and normative analysis. National Bureau of Economic Research, Working paper 5317. Mulligan, C.B., 1995. The lntertemporal Substitution of Work-What Does the Evidence Say? University of Chicago, unpublished manuscript. Munnell, A.H., 1990. Why has productivity growth declined?: productivity and public investment. New England Economic Review, 3-22. Ramsey, F.P., 1927. A contribution to the theory of taxation. Economic Journal 37, 47-61. Romer, P., 1986. Increasing returns and long-run growth. Journal of Political Economy 94, 1002-1037. Stokey, N.L., Rebelo, S., 1995. Growth effects of flat-rate taxes. Journal of Political Economy 103, 519-550. Sturm, J.-E., Kaper, G.H., de Haan, J., 1997. Modeling government investment and economic growth on a macro level: a review. In: Brakman, S., van Ees, H., Kuipers, S.K. (Eds.), Market Behavior and Macroeconomic Modeling. Macmillan/St. Martin’s Press, London. Tatom, J.A., 1991. Public capital and private sector performance. Federal Reserve Bank of St. Louis Review, 3-15. Tumovsky, S.J., 1996. Optimal tax, debt, and expenditure policies in a growing economy. Journal of Public Economics 60, 21-44. Wolff, E.N., 1996. The productivity slowdown: the culprit at last? follow-up on Hulten and WoltT. American Economic Review 86, 1239-1252. Zhu, X., 1992. Optimal fiscal policy in a stochastic growth model. Journal of Economic Theory 58, 250-289. Zhu, X., 1995. Endogenous Capital Utilization, Investor’s Effort, and Optimal Fiscal Policy. Journal of Monetary Economics 36, 655-677.
