Tax uncertainty and investment: a cross-country empirical examination.

Edmiston, Kelly D.

I. INTRODUCTION

Spanning a period of nearly 100 years of economic research, a substantial body of literature has developed with the goal of explaining the behavior of investment over time. (1) Although many of these studies have considered the implications of tax policy for investment in an uncertain world, most have also implicitly assumed that the tax policy itself does not contribute to the uncertainty. The problem is that tax policy can be very uncertain in many cases, (2) and to date we know little about the consequences, especially from an empirical standpoint. More generally, empirical evaluations of uncertainty and investment are very limited compared with the development of theoretical analyses (Calcagnini and Saltari 2000), and the case of tax uncertainty is no exception.

This article sets out to fill part of the intellectual void by empirically investigating the impact of volatility in effective tax rates on investment in a cross-section of countries, namely, the 15 countries of the European Union (EU), the United States, and Japan. In doing so, I first estimate tax rate volatility using an ARCH specification with data on effective capital tax rates. I then provide panel regression results, using the system generalized method of moments (GMM-Sys) estimator of Arellano and Bover (1995) (see also Blundell and Bond 1998), which suggest that the volatility of effective tax rates on capital have a significant negative impact on investment per worker in these countries.

The remainder of the article proceeds as follows. Section II briefly reviews the existing literature on tax policy uncertainty and investment as well as existing empirical studies of uncertainty (in general) and investment. Section III develops the empirical model I employ to estimate the relationship between tax volatility and investment. Section IV then presents an analysis of effective tax rates in the EU countries, the United States, and Japan, followed by a discussion of the data and econometric issues in section V, and an examination of the effects of tax rate volatility on investment in section VI. Section VII provides concluding remarks.

II. THEORETICAL FOUNDATIONS

Tax Policy Uncertainty and Investment

Although most of the voluminous literature on tax policy and investment under uncertainty ignores observed randomness in tax policy, a recent set of literature has begun to explore these issues in some detail, mostly through simulation. (3) The basic premise underlying these studies is that because output price uncertainty tends to retard investment (Pindyck 1988), (4) tax uncertainty might be expected to harm investment as well (Hassett and Metcalf 1999). Further credence to a negative relationship between tax uncertainty and investment is given by the business community's mantra that "they cannot make plans if they don't have confidence in the tax structure" (Bizer and Judd 1989, 223). These simulation studies, however, demonstrate that the impact of tax uncertainty depends crucially on the source and nature of the uncertainty. Contrary perhaps to conventional wisdom, in some cases increased uncertainty can be shown to have positive effects on investment, growth, or welfare.

Bizer and Judd (1989) simulate the economic effects of introducing random tax policy in a dynamic general equilibrium model. They find that if random tax rates or credits are serially correlated, the target capital stock falls when taxes are high and rises when taxes are low. Their more interesting case considers independently and identically distributed random tax shocks. In this case the authors find that randomness in investment tax credits generates large fluctuations in investment, which have the effect of reducing both utility and production (because both are concave functions) as well revenue. (5) They find that variance in future tax rates, however, is not important for long-term investments and in fact raises nontrivial mounts of revenue at a welfare cost that is never more than the cost associated with raising an equivalent amount of revenue with a permanent increase in a deterministic tax rate.

Dotsey (1990) also considers a stochastic growth model in which tax rates themselves are the outcome of some stochastic process and derives results that are complementary to those of Bizer and Judd (1989). In cases where tax rates are independently and identically distributed, certainty equivalence is shown to be obtained, and thus the fraction of output devoted to investment and the time path of consumption and the capital stock are invariant to tax realizations. In the case where tax rates are persistent, however, the property of certainty equivalence no longer holds. Specifically, when tax rates are assumed to follow a two-state Markov process with transition probabilities ([[pi].sub.0],[[pi].sub.1]) given by [[pi].sub.0] + [[pi].sub.1] > 1 (they are persistent), a greater fraction of output will be invested in the low-tax state because the low-tax state implies a greater likelihood that taxes will be low in the future.

Hassett and Metcalf (1999) undertake a similar analysis and, like Bizer and Judd (1989) and Dotsey (1990), find that the stochastic process underlying realized tax rates is crucial to understanding the links between tax policy and investment. Specifically, they find that when tax policy uncertainty leads to capital costs following a continuous time random walk in logs, increasing uncertainty delays investment. On the contrary, they find that when tax policy follows a jump-diffusion process, such as the Poisson (which is likely in the case of investment tax credits), increasing uncertainty actually speeds up investment.

Despite the theoretical work that suggests uncertain tax policy to be an important determinant of investment, there has been surprisingly little empirical work. What has been done does not directly investigate the impact on investment, but instead tends to look at the impact of random tax policy on economic growth. (6) An empirical investigation of uncertain tax policy and investment is thus crucial to a full understanding of the interplay between taxes and investment, especially given ambiguities in the limited theoretical literature.

Empirical Studies of (Nontax) Uncertainty and Investment

Although this study is the first to empirically assess the impact of uncertainty in tax policy on investment, there exists a fairly substantial body of literature that empirically examines the impact of other forms of uncertainty on investment. These studies are remarkably varied in the specific measures of uncertainty, the nature of the data (aggregate and disaggregated), and methodology, but there appears to be a general consensus that uncertainty deters investment. The literature is surveyed in some detail in Carruth et al. (2000b).

Most relevant for this study is the literature that incorporates some form of macroeconomic uncertainty in analyses of aggregate data. The general approach is to derive uncertainty estimates as predictions from univariate time series models, often of the ARMA or ARCH-GARCH type, and to employ the estimates as proxies for uncertainty in models of investment. In a study of manufacturing investment in the United Kingdom, Driver and Moreton (1991) find elasticities of investment with respect to output and inflation of -0.08 and -0.05, respectively. Ferderer (1993) finds that a one-standard-deviation increase in risk premium, as computed from interest rate term structure, results in a decline of equipment expenditures of between 0.241 and 0.254 standard deviations. Calcagnini and Saltari (2000) find a significant negative relationship between demand volatility and investment in Italy but do not find a significant relationship between interest rate volatility and investment there. Episcopos (1995) finds that fixed investment is inversely related to the uncertainty of prices, interest rates, consumption, the index of leading indicators, and an index of stock prices. Finally, Price (1995, 1996) finds a significant (and very large) relationship between volatility in manufacturing output and investment. Compared to the case of output volatility having been zero (an unlikely counterfactual admitted by the author), long-run estimates from Price (1996) suggest that uncertainty reduced investment in the UK manufacturing sector by a substantial 59.6%.

Research employing disaggregated (firm-level) data also generally finds a negative relationship between uncertainty and investment. Driver et al. (1996) find elasticities of investment with respect to market share volatility of between -0.05 and -0.15 in 5 of 12 industries examined (the relationship was statistically insignificant in the remaining industries). Campa (1993) finds a negative relationship between exchange rate volatility and inbound foreign direct investment (FDI) to the United States from Japan, Germany, and the United Kingdom, with the strongest relationship being found for Japan and for projects with greater sunk costs. Huizinga (1993) finds a negative relationship between volatility in wages and material prices and investment but a positive relationship with uncertainty in output prices. Ghousal and Loungani (1996), on the other hand, find a negative relationship between output price volatility and investment. Finally, Leahy and Whited (1996) find that a 10% increase in the variance of firms' daily stock returns over a year leads to a 1.7% decline in the rate of investment (investment over capital stock), for an implied elasticity of -0.17. The addition of a standard proxy for marginal q (Tobin's q) eliminates the significance of the variance, however, as predicted by the authors. (7)

III. AN EMPIRICAL MODEL OF INVESTMENT WITH TAX VOLATILITY

Consider a model where capital (K) can be employed, along with labor (L), to produce F(K, L) units of output forever, which can be sold at price [p.sub.t], where [p.sub.t] is after-tax return and is stochastic and [F.sub.K] > 0.

Following Hassett and Metcalf (1999), [p.sub.t] is assumed to follow geometric Brownian motion (GBM): d[p.sub.t] = [[mu].sub.p][p.sub.t]dt + [[sigma].sub.p] [p.sub.t]d[z.sub.p]. In deriving the empirical model, I also assume that the price of capital also evolves according to GBM: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], although a more realistic scenario, in the case of investment tax credits, might model capital prices as evolving according to a jump-diffusion process. Hassett and Metcalf (1999) consider, for example, the case of an investment tax credit [[pi].sub.t] [member of] {[[pi].sub.0], [[pi].sub.1]}, which reduces the price of capital to [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. The use of effective tax rates in the empirical analysis allows for a very general accounting of uncertainty in tax rates, however, including that which would arise from investment tax credits. The conceptual model presented here is intended to illustrate the way tax uncertainty can affect investment decisions and highlight the ambiguity of the effects in even a simple theoretical framework. (8) Randomness in tax policy is assumed to affect investment decisions through volatility in output price and the price of capital.

Given randomness in output and capital prices, the firm's objective is to maximize the expected value of the stream of discounted profits, net of the cost of investment:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where the firm chooses the optimal size of the project ([K.sup.*]) and time to invest ([T.sup.*]), [w.sub.s] is the wage rate at time s, and [rho] is the relevant discount factor.

Linear homogeneity in prices implies that V(p, [p.sub.K]) = [p.sub.K] V(p/[p.sub.K]). Because both prices evolve according to GBM, then p/[p.sub.K] evolves according to GBM as well, with trend [alpha] = [[mu].sub.p] - [[mu].sub.K] - [[sigma].sup.2.sub.K] - v [[sigma].sub.p][[sigma].sub.K], where v is the correlation between the Weiner processes for p and [p.sub.K], and volatility [[sigma].sup.2.sub.0] = [[sigma].sup.2.sub.p] + [[sigma].sup.2.sub.K] + 2v[[sigma].sub.p][[sigma].sub.K]. A differential equation in one variable can be obtained from this reduced model and solved to yield the following investment conditions (Hassett and Metcalf 1994; see also Dixit and Pindyck 1994):

(2) pF(K,L)/([rho] - [[mu].sub.p]) [is greater than or equal to] ([beta]/[beta] - 1)[p.sub.K]K

(3) p[F.sub.K](K, L)/([rho] - [[mu].sub.p]) = [p.sub.K],

where

(4) [beta] = 0.5[[sigma].sup.2.sub.0]

-[alpha][square root of ((0.5[[sigma].sup.2.sub.0] - [alpha]) + 2([rho] - [[mu].sub.K])[[sigma].sup.2.sub.0]/[[sigma].sup.2.sub.0]).

That is, expected revenue must exceed the cost of the capital, adjusted by a mark-up factor ([beta]/[beta] - 1), which accounts for the loss of the option to invest in the future (2); once the firm has made the investment decision, it should choose the level of investment that will equate marginal revenue and marginal cost (3). Hassett and Metcalf (1994, 1999) demonstrate that in the case just outlined, the required hurdle price ratio (p/[p.sub.K]) increases as the variance of the capital price increases (because the expected value of the project declines), which should delay investment. But an increasing variance in capital prices increases the likelihood that capital costs will fall sharply in a short period of time, and thus the required hurdle price will be reached in a shorter time. They go on to document through simulations that the overall effect of tax uncertainty on investment depends on the form of the stochastic process generating realized tax rates, which echoes the work of Dotsey (1990) and Bizer and Judd (1989). The empirical reality of the link between tax uncertainty and investment thus remains a mystery to be explored in econometric work.

From (2) and (3), a more general form of the optimal capital stock can be expressed as

(5) [K.sup.*] = [phi] ([rho], w, p , [p.sub.K], [beta]).

In an effort to directly highlight the role of tax uncertainty and tax rates on investment, I decompose after-tax output and capital prices. Let q and [q.sub.K] represent before-tax prices, respectively, and let [tau] = [[[tau].sub.K] [[tau].sub.F]] represent the vector of effective tax rates on capital ([[tau.sub.K]) and output ([[tau].sub.F]). Because the specific way tax rate volatility, which is used to measure uncertainty, enters the optimal capital stock function is unknown (because the underlying stochastic process is unknown), and following typical practice in the literature (see, e.g., Driver and Moreton 1991), I express [K.sup.*] as a function of the tax rate volatilities directly, rather than through [beta]. Letting [sigma] = [[sigma].sub.K] [[sigma].sub.F]] represent volatility in effective tax rates on capital ([[sigma].sub.K]) and output ([[sigma].sub.F]), the optimal capital stock is then rewritten as

(6) [K.sup.*] = [phi]([rho], w, q, [q.sub.K], [tau], [sigma]).

The interest in this article is to explore the effects of aggregate uncertainty on aggregate investment. Following the empirical work of Caballero and Pindyck (1996) and the simulation set-up of Hassett and Metcalf (1999), I build on the firm-level investment decision to consider the aggregate economy as a continuum of single project firms. Based in part on the work of Caballero et al. (1995), Hassett and Metcalf (1999, 385) state that "modeling either a single firm with variable (but irreversible) capital stock [as in Pindyck 1988] or a continuum of single project firms in an industry setting [as in Caballero and Pindyck 1996] will not lead to qualitatively different conclusions." Further, Bernanke (1983) makes arguments for why uncertainty may be important specifically in the aggregate (see also Temple et al. 2001). For the purpose of the empirical analysis, I also assume that the production function is homogeneous of degree one (that is, F(K, L)/L = F(K/L) = F(k)) and express key variables in per-worker values. Aggregate gross investment per worker at date t ([i.sub.t]) is then given by

(7) [i.sub.t] = [k.sup.*.sub.t]([rho], w, q, [q.sub.K], [tau], [sigma]) - [k.sub.t-1].

IV. MODELING VOLATILITY IN EFFECTIVE TAX RATES

In constructing a tax rate series for estimating the impact of tax volatility on investment, it is important to be able to capture not only changes in statutory rates but also changes in other factors that may substantially alter tax liabilities, such as investment tax credits and other incentives, exemptions, deductions, and/ or tax bracket creep. This means that the relevant tax measure is an effective tax rate that incorporates all of the factors affecting tax liabilities.

Traditional measures of average effective tax rates, which in many cases have used gross domestic product (GDP) as the base, are easily computed from aggregate macroeconomic data but provide only very rough estimates of actual tax distortions. At the same time, traditional measures of marginal effective tax rates (King 1977; King and Fullerton 1984) often are much more precise but are not tractable for constructing a long time series of tax rates over several countries, as required for this analysis. Fortunately, work by Mendoza et al. (1994) and more recent work by Devereux et al. (2002) provides suitable effective tax rate calculations for this study. This section discusses the calculations that underlie both alternatives (estimates from both sources are used in the empirical analysis that follows).

Measuring Effective Tax Rates on Capital Income

Mendoza et al. (1994) provides a method for computing effective tax rates using readily available data from national accounts and revenue statistics that does a good job of reflecting the distortions faced by a representative agent in a general equilibrium framework (Razin and Sadka 1993). Moreover, despite differences in levels, tax rates calculated in this manner have been shown to be "within the range of [empirical] marginal tax rate estimates and [to] display very similar trends" (Mendoza et al. 1994, 299). (9)

Using a simple general equilibrium representative agent framework, Mendoza et al. derive the following expression for the effective tax rate on capital (KETR):

(8) KETR = [-q.sub.k][y.sub.k] - ([-p.sub.k][y.sub.k])/ [-q.sub.k][y.sub.k],

where q is the (pretax) producer price, p is the (posttax) consumer price, y is net output. (10) In some models used in the empirical analysis, I also use their measure of the effective tax rate on consumption (CETR), as a proxy for taxes on output. The formula is given by

(9) CETR = [p.sub.c][y.sub.c] - [q.sub.c][y.sub.c]/[q.sub.c][y.sub.c].

The numerators represent the difference between pretax and posttax valuations of capital and consumption, which can be approximated by tax revenues derived from capital and consumption; the denominator is consumption or the income derived from capital, which are measures of the tax base.

Mendoza and colleagues show that all of the data necessary for calculating the effective tax rates given in (8)-(9) are available in the OECD's Revenue Statistics and National Accounts: Volume II, Detailed Tables. Tax rates calculated in this manner are provided in Mendoza et al. (1994) and updated for G7 countries in Mendoza and Tesar (1998).

Several researchers have since set out to improve on the Mendoza et al. (1994) methodology while continuing to calculate effective tax rates roughly in the manner just outlined. I use estimates of effective tax rates on net capital income (depreciation excluded in the tax base) and consumption provided by the Directorate General for Economic and Financial Affairs for the European Union (ECFIN) (2000). These measures of effective tax rates are analyzed and compared with other measures of effective tax rates (specifically Mendoza et al. 1994 and Carey and Tchilinguirian 2000) in Martinez-Mongay (2000).

The approach of Devereux et al. (2002) is conceptually similar to (but different from) the well-known approach of King and Fullerton (1984). The marginal effective tax rate (METR) calculation is based on the difference between the pretax and posttax required rates of return and is given by (11)

(10) METR = ([??] - r)/[??],

where [??] is the value of p (financial return) for which the after-tax net present value (NPV) of investment is just equal to zero, thus satisfying

(11) 0 = [(p + [delta])(1 - T) - (r + [delta])(1 - A)]/1 + r,

where [delta] is depreciation, r is the discount rate, A is the NPV of tax allowances generated by one unit of capital, and T is the tax rate applied to the total return (p + [delta]).

The calculation of the average effective tax rate (AETR) is based on the NPV of tax payments (for a given p) expressed as a proportion of the NPV of pretax capital income:

(12) AETR = p/1 + r.

Additional details are available in Devereux et al. (2002) or Devereux and Griffith (2003).

Data on Effective Tax Rates in the EU, United States, and Japan

Table 1 shows descriptive statistics for effective tax rates on capital income and consumption calculated using the method of Mendoza et al. (1994) (KETR and CETR, respectively) for the period 1970-2001, as well as METR, AETR, and statutory tax rate calculations of Devereux et al. (2002) for the period 1982-2002, for the 15 countries of the EU, the United States, and Japan.

There is fairly substantial variation between the effective tax rate on net income from capital, as calculated using the Mendoza method (KETR), which averaged 44.3% over the 1970-2001 period for these countries, and the average and marginal effective tax rates of Devereux et al. (AETR and METR), which averaged 35.0% and 26.4%, respectively, over the 1982-2002 period. The statutory tax rates for these countries, again over the period 1982-2002 and reported by Devereux et al., averaged 40.8%.

Modeling Tax Rate Volatility

To build a model for examining this volatility, I first conceptually separate the series into its deterministic and stochastic components:

(13) [[tau].sub.j,t] = [g.sub.j](*) + [[theta].sub.j,t],

where [[tau].sub.j,t] is the effective tax rate on capital (or consumption in one case), [g.sub.j](*) is the deterministic component, and [[theta].sub.j,t] is the stochastic component. I assume that firms' expectations of future tax rates are in some sense adaptive, an assumption supported by existing literature (Schmalensee 1976; Swenson 1997). (12) Firms observe the mean tax rate ([alpha]) and its trend ([beta]) such that

(14) E([[tau].sub.j,t]) = [[alpha].sub.j] + [[beta].sub.j]t.

Tax rate volatility is then defined as a function of the deviation of the effective tax rate from this trend, which is identical to an error in expectations:

(15) [v.sub.j,t] = [phi][[[tau].sub.j,t] - [[alpha].sub.j] + [[beta].sub.j]t] = [phi][[[tau].sub.j,t] - E([[tau].sub.j,t])].

It is important to note that although there are a multitude off actors that jointly determine the pattern of effective tax rates in any one country, such as political stability, overall fiscal health, and the macroeconomic environment, among others, my specific interest in measuring volatility is get a measure of the deviation of the effective tax rate series away from its trend, not to develop and estimate an accurate model of the effective tax rates series. That is, there are a host of potentially significant explanatory variables that do not appear in (15), but their absence is intentional. I posit that these explanatory factors, other than trend, are themselves random occurrences, and therefore take seriously Lucas's (1976) advocation that policy should be modeled as the outcome of a stochastic process (see Dotsey 1990).

A common approach to measuring uncertainty in empirical investment models is to use an ARCH-GARCH model on the individual time series to estimate a forecast of volatility (Episcopos 1995; Huizinga 1993; Price 1995 1996; Carruth et al. 2000a). (13) This is the procedure followed here. Other measures of uncertainty are discussed in Pagan and Ullah (1988). The specific specification employed here is a first-order ARCH model where

(16) [[tau].sub.j,t] = [[alpha].sub.j] + [[beta].sub.j]t + [v.sub.j,t]

(17) [v.sub.j,t] = [u.sub.j,t] [square root of ([h.sub.j,t])]

(18) [u.sub.j,t] ~ IID(0, 1),

and [h.sub.j,t] evolves according to

(19) [h.sub.j,t] = [[delta].sub.0] + [[delta].sub.1][v.sup.2.sub.j,t-1],

with nonnegativity constraints [[delta].sub.0] > 0, [[delta].sub.1] [is greater than or equal to] 0.

Results from the ARCH(1) models, estimated by maximum likelihood, are presented in Table 2, and mean tax rate volatilities are presented in Table 3. The mean volatility for KETR is considerably higher across countries than is the mean volatility estimated for METR, AETR, and the statutory tax rate. Average KETR volatility ranges from a low of 7.2 for the United States to a high of 1,413.1 for Japan. By contrast, the average volatility for METR ranges from a low of 0.3 for the United States to a high of 153.0 for Italy. Average volatility for AETR ranges from 0.7 (Spain) to 54.2 (Italy), and the average volatility for the statutory tax rates ranges from 0.0 (Ireland) to 57.4 (United States). (14) Average volatility in effective tax rates on consumption range from 0.7 (United States) to 20.0 (Sweden). Given the longer time series available for KETR, as well as the more pronounced variability, most specifications of the investment model below use KETR as the relevant tax rate. However, the model is also estimated using METR, AETR, and the statutory tax rate for comparison.

V. DATA AND EMPIRICAL ISSUES

A panel data set of the 15 EU countries, the United States, and Japan over 28 years (1970-98) was used to estimate the model given in (7). (15) The use of panel data provides several advantages. In addition to exploiting variation both within countries over time and across countries within a specific time period, the use of panel data is likely to reduce simultaneity problems associated with the effects of uncertainty on saving and "spurious correlation between investment and uncertainty arising from the relationship between uncertainty and the business cycle" (Leahy and Whited 1996, 67).

Following the typical formulation of investment models in the empirical literature, I allow for investment per worker to adjust with lags (see Nickell 1978) and estimate the model in log-linear form, giving the estimating equation:

(20) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The variable [y.sub.j,t-1] is real GDP per worker and serves as a proxy for the period t - 1 level of capital stock per worker, the data for which was unavailable. Descriptions and sample statistics for the remaining explanatory variables are provided in Table 4. The error components [[mu].sub.i] and [[lambda].sub.t] capture country-specific and time-specific fixed effects, respectively, and the remaining error [[epsilon].sub.j,t] ~ N(0,[v.sup.2]).

Data on investment per worker was calculated from data on the investment share of GDP and GDP per worker provided in the Penn World Tables Mark VI. Data on output and capital prices, proxied by inflation and a capital price index, were taken directly from the Penn World Tables. A proxy for wages (w) was calculated by dividing average employee compensation from the OECD National Accounts by GDP. Finally, data on the volatility of effective tax rates were derived from the estimates described.

The empirical specification in (20) is estimated using GMM-Sys described in Arellano and Bover (1995) and Blundell and Bond (1998). The econometric issues addressed by this method include the presence of lagged dependent variables as explanatory variables, which are correlated with the fixed effects error components, and potential endogeneity of remaining explanatory variables.

For simplicity in the exposition, assume that (20) is a first-order autoregression, ignore the time-specific effects, and let a matrix [X.sub.j,t] contain the remaining explanatory variables. As a first step, the GMM-Sys procedure takes first differences to eliminate the country-specific effect:

(21) [DELTA][i.sub.j,t] = [beta][DELTA][i.sub.j,t-1] + [alpha]'[X.sub.j,t] + ([epsilon].sub.j,t] - [[epsilon].sub.j,t-1]).

By construction the lagged difference in investment per worker is correlated with the error term and must be instrumented. Likewise given potential endogenity of variables in [X.sub.j,t]. Under the conditions that the error term is not serially correlated and that the lagged variables of the explanatory variables are uncorrelated with future error terms (they are weakly exogenous), Arellano and Bond (1991) propose the following moment conditions:

(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Arellano and Borer (1995) propose estimating the regression in differences jointly with a regression in levels in an effort to address issues with the GMM difference estimator (see also Blundell and Bond 1998). Specifically, the cross-country dimension of the data is lost by first-differencing but retained with the regression in levels. Further, persistence in the lagged dependent and explanatory variables makes lagged levels of these variables weak instruments for the regression in levels. Simulations in Blundell and Bond (1998) reveal large finite sample bias and poor precision in the GMM difference estimator. Provided that there is no correlation between the lagged differences of the explanatory variables and the country-specific error component, lagged differences of the explanatory variables are valid as instruments for the regression in levels, giving the moment conditions:

(23) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The system is given by the stacked regressions in differences and levels with moment conditions given by (22) and (23). Results from Sargan tests of the validity of the instruments (see Blundell and Bond 1998) and first-and second-order serial correlation are reported for each estimation (the GMM-Sys estimator requires the absence of second-order serial correlation, but first-order serial correlation is expected because the equations are estimated in differences).

VI. RESULTS

Table 5 presents panel estimation results of (20). Models 1 and 2 utilize KETR as the relevant tax rate on capital, whereas models 3-5 use the AETR, METR, and statutory tax rates of Devereux et al. (2002), respectively. Model 2 differs from the other models in that the effective tax rate on consumption (CETR), a proxy for output taxes, is included in the regression. Sargan and serial correlation tests suggest that the models are appropriately specified.

Regression results suggest that volatility in effective tax rates on capital has a significant negative impact on investment per worker. Elasticity estimates for volatility in KETR are relatively small at -0.029, but significant at the 95% confidence level (99% in model 1). Thus, a doubling of volatility in KETR is expected to lead to a 2.9% decline in investment per worker. For the average country in the average year, this amounts to a decrease in investment per worker of approximately US$8,065. Using estimates from Devereux et al. (2002), elasticities were significantly smaller at -0.016 for AETR, -0.012 for the statutory tax rate, and statistically zero for METR. Approximately 55% of observations are lost when employing the Devereux et al. tax rates, and other critical determinants of investment expenditure, such as real interest rates and wages, were also found to be statistically insignificant in these models. Taken together, the estimates suggest that volatility in effective tax rates on capital have a statistically significant negative effect on investment per worker in these countries, although the magnitude of the elasticities is relatively small. The results do compare quite well with the empirical estimates of other forms of uncertainty on investment, such as those of Driver and Moreton (1991), which ranged between -0.05 and -0.08; Driver et al. (1996), which ranged from -0.05 to -0.15; and Leahy and Whited (1996), which was -0.17. Model 2 also considers volatility in effective tax rates on output (as proxied by taxes on consumption). The effect of capital tax volatility on investment is unchanged from model 1, but output tax volatility is not found to be statistically significant.

In an effort to ensure that the model is capturing the effects of volatility in effective tax rates on capital, as distinct from the effects of levels of tax rates, alternative formulations of model 1 are presented in Table 6. The first column of results is simply a reproduction of model 1's results. The second column (model 6) shows results when the deviation of the capital tax rate from its trend is added to the model, and the third column (model 7) shows results where the lagged value of the capital tax rate is included in the model. The coefficients on capital tax volatility in models 6 and 7 are slightly lower but statistically no different than those reported for model 1. The deviation of the capital tax rate from its trend is statistically zero, whereas the lagged value of the capital tax rate is negative and marginally significant.

Elasticities of KETR itself ranged from -0.186 to -0.201, which are somewhat lower than are typically estimated. For example, empirical estimates of the tax elasticity of U.S. inbound or outbound FDI suggest a consensus elasticity figure of -0.6 (Hines 1999). The elasticity of the statutory tax rate is more in line with expectations at -0.428. METR and AETR do not appear to affect investment per worker in these countries.

Other parameter estimates were relatively stable, and for the most part had the expected signs, although the lack of degrees of freedom in the Devereux et al. (2002) models lead to more statistically insignificant results.

Real GDP per worker is positive and significant in all specifications, with elasticities ranging from 1.4 to 2.2. The wage proxy is negatively related to investment per worker in the Mendoza models (1-2, 6-7) with an elasticity of approximately -1.0 but was found to be insignificant in the Devereux specifications (3-5). Firms are expected to respond favorably to output prices and unfavorably to input prices. Elasticities for the capital price index in the Mendoza models are negative as expected but statistically insignificant. Contrary to expectations, the capital price index elasticities in the Devereux models are positive and significant, ranging in magnitude from 0.9 to 1.5. The GDP price index, which may proxy for perceived output prices (in the new classical sense) is positive and significant across the Mendoza specifications, with elasticities ranging between 1.8 and 2.0, but statistically insignificant in the Devereux specifications (and negative). Finally, the real interest rate is shown to be negatively related to investment per worker, again reflecting input cost, with relatively small elasticities ranging between -0.05 and -0.09 (or zero in models 3 and 4).

Overall the regression equations did a good job of explaining variation in investment per worker across countries and over time, with [R.sup.2]s that ranged between 0.75 and 0.83. In all specifications the fixed effects were found to be jointly significant at the 99%, confidence level.

VII. CONCLUSION

The government sector seems very inclined to believe that tax policy plays a crucial role in investment decisions, despite some evidence to the contrary (Hassett and Hubbard 1997). This means that policy makers can be expected to tinker continually with the tax code in an effort to stimulate investment, be it adjusting rates, altering depreciation schedules, or offering a portfolio of tax incentives, many of which are temporary. As a result, effective tax rates on capital, which account for investment tax incentives as well as statutory rates, can be expected to be quite volatile over time. Observations of realized effective capital tax rates have been shown to bear this out, even in the relatively stable countries of the EU, the United States, and Japan. Further analysis suggests that this volatility deters investment. Even if tax policy were shown to stimulate investment, and the literature is far from consensus on this point, policy makers would do well to establish some permanence in the tax code.

As a first attempt to empirically examine the effects of random tax policy on investment, this study offers a substantial body of new information on the relationship between taxes and investment. Much work remains to be done, however. In particular, the empirical evidence presented in section VI would be more convincing with additional studies over a wider range of countries over longer periods of time. For example, in an empirical study of the effects of uncertainty in the marginal profitability of capital on investment, Pindyck and Solimano (1993) suggest that the relationship is much stronger for less-developed countries than for OECD countries. This will require much better data collection and compilation than is currently available.

ABBREVIATIONS

FDI: Foreign Direct Investment GBM: Geometric Brownian Motion GDP: Gross Domestic Product GMM: Generalized Method of Moments NPV: Net Present Value

TABLE 1
Effective Tax Rates: Means and Standard Deviations

 Mendoza
 (1970-2001) Devereux (1982-2002)

 KETR CETR METR AETR Statutory
 Mean Mean Mean Mean Mean
Country (SD) (SD) (SD) (SD) (SD)

Austria 50.5 33.2 27.2 38.7 45.1
 (15.1) (2.6) (4.6) (8.7) (12.4)
Belgium 48.0 23.8 26.9 35.4 41.7
 (6.7) (2.3) (1.9) (2.2) (2.3)
Denmark 62.4 39.7
 (8.0) (3.6)
Finland 46.3 31.2 26.6 34.8 40.6
 (18.1) (3.1) (11.3) (13.3) (14.2)
France 37.5 30.3 21.7 33.0 40.7
 (7.8) (1.3) (3.2) (5.1) (5.9)
Germany (unified) 33.5 21.3 38.7 50.5 57.8
 (3.7) (1.2) (5.1) (5.7) (6.0)
Greece 16.9 21.4 31.0 36.7 41.2
 (6.1) (2.3) (1.8) (2.0) (2.0)
Ireland 34.0 27.7 4.5 7.5 10.0
 (8.1) (3.0) (3.2) (1.4)
Italy 38.2 19.9 24.7 38.0 46.5
 (8.9) (4.5) (9.3) (5.9) (4.7)
Japan 69.7 14.6 40.8 46.3 50.5
 (16.7) (1.0) (4.6) (4.7) (4.8)
Luxembourg 63.6 23.0
 (22.1) (6.9)
Netherlands 50.4 20.3 26.9 33.3 38.2
 (8.1) (1.9) (4.0) (4.4) (4.7)
Portugal 19.1 24.1 30.7 38.0 43.5
 (8.7) (5.0) (11.3) (8.9) (7.3)
Spain 25.8 15.5 25.5 30.8 35.0
 (4.5) (3.9) (2.5) (1.4) (1.0)
Sweden 49.4 32.7 26.2 34.7 40.7
 (7.8) (3.9) (11.6) (13.5) (14.2)
United Kingdom 67.5 22.5 19.2 29.2 35.6
 (11.7) (1.9) (7.3) (2.8) (6.3)
United States 34.7 11.3 23.1 34.2 41.6
 (3.0) (1.2) (0.8) (3.1) (4.7)

Notes. Devereux et al. (2002) do not provide calculations for Denmark
and Luxembourg. The statutory tax rate in Ireland did not change over
the 1982-2002 period.

TABLE 2
ARCH Results: Mendoza, Effective Tax Rate on Net Capital Income

 Parameter Estimates

Country Intercept Time Trend ARCH(0)

Austria 58.856 *** -0.414 *** 6.160
 (2.965) (0.132) (6.554)
Belgium 43.458 *** 0.272 *** 3.087
 (1.462) (0.069) (2.161)
Denmark 59.913 *** 0.028 3.333
 (1.252) (0.061) (3.544)
Finland 33.151 *** 0.512 *** 0.006
 (0.590) (0.020) (0.016)
France 24.471 *** 0.481 *** 1.576
 (0.670) (0.033) (2.816)
Germany Excluded
 (insufficient time series
 following reunification)
Greece 9.727 *** 0.321 *** 0.912
 (0.739) (0.041) (1.584)
Ireland 43.196 *** -0.507 *** 3.710 *
 (0.957) (0.083) (2.052)
Italy 24.775 *** 0.767 *** 5.130
 (1.030) (0.061) (3.501)
Japan 105.963 *** -1.880 *** 1.05E-8 ***
 (1.019) (0.062) (5.8E-14)
Luxembourg 83.951 *** -0.892 *** 61.366 **
 (4.422) (0.270) (30.439)
Netherlands 54.311 *** -0.247 49.051 ***
 (2.721) (0.213) (14.327)
Portugal 8.143 *** 0.770 *** 3.235
 (1.214) (0.060) (2.867)
Spain 18.551 *** 0.372 *** 1.292
 (0.629) (0.036) (0.876)
Sweden 37.342 *** 0.679 *** 15.755 **
 (2.374) (0.127) (6.362)
United Kingdom 63.844 *** -0.090 26.083
 (2.508) (0.162) (22.912)
United States 39.504 *** -0.294 *** 2.146 **
 (0.679) (0.045) (1.001)

 Parameter
 Estimates

 Regression
 ARCH(1) [R.sup.2] (OLS)

Austria 1.884 *** 0.006
 (0.564)
Belgium 1.170 ** 0.207
 (0.497)
Denmark 1.791 *** 0.041
 (0.621)
Finland 4.536 *** 0.120
 (0.893)
France 1.290 ** 0.052
 (0.549)
Germany Excluded
 (insufficient time
 series following
 reunification)
Greece 1.389 ** 0.713
 (0.696)
Ireland 1.445 ** 0.357
 (0.588)
Italy 0.902 0.781
 (0.558)
Japan 2.721 *** 0.070
 (0.670)
Luxembourg 1.062 *** 0.006
 (0.386)
Netherlands 0.172 0.087
 (0.344)
Portugal 0.874 0.761
 (0.654)
Spain 0.985 ** 0.699
 (0.457)
Sweden 0.464 0.535
 (0.472)
United Kingdom 1.092 * 0.008
 (0.595)
United States 0.757 0.283
 (0.808)

Notes: Standard errors in parentheses. All models estimated using
maximum likelihood. and ***, **, and * denote statistical
significance at the 1%, 5%, and 10% levels, respectively.

TABLE 3 Mean Tax Rate Volatility Estimates

 Mendoza
 (1970-2001) Devereux (1982-2002)

Country KETR CETR METR AETR Statutory

Austria 484.6 3.4 20.1 8.9 33.8
Belgium 45.0 6.3 1.7 2.3 2.3
Denmark 124.4 7.1
Finland 1,413.1 11.4 34.9 40.0 46.6
France 119.5 1.8 11.2 36.4 32.3
Germany Insufficient time series available
Greece 23.8 2.7 1.0 1.1 1.2
Ireland 65.2 7.6 6.4 1.3 0.0
Italy 21.1 7.1 153.0 54.2 51.7
Japan 1244.0 0.8 15.5 17.2 18.1
Luxembourg 715.1 4.0
Netherlands 59.5 2.0 7.2 8.8 9.6
Portugal 21.8 7.0 67.1 15.1 17.2
Spain 8.5 4.0 1.3 0.7 0.9
Sweden 29.3 20.0 22.7 30.1 33.3
United Kingdom 203.3 6.2 107.8 2.2 55.5
United States 7.2 0.7 0.3 25.2 57.4

Notes. Estimates are predicted volatility and are derived from the
maximum likelihood ARCH estimates presented in Table 2. Ireland's
statutory tax rate did not change over the relevant period.

TABLE 4
Data Description, Sources, and Statistics

Variable Source Mean (SD)

Real investment per worker Penn World Tables Mark VI $278,100
 ($405,929)
Real GDP per worker Penn World Tables Mark VI $36,879
 ($10,469)
Capital price index Penn World Tables Mark VI 88.5
 (relative to U.S.) (20.3)
GDP price index (relative Penn World Tables Mark VI 97.2
 to U.S.) (25.1)
Real wage Author's calculation using 7.2
 data from OECD National (9.4)
 Accounts and Penn World
 Tables Mark VI
Interest rate International Monetary 8.5
 Fund, International (4.5)
 Financial Statistics
Capital tax rate (KETR) European Commission (2000) 44.3
 (20.0)
Capital tax volatility Estimated 306.2
 (KETR) (1,828.9)
Capital tax rate (METR) Devereux et al. (2002) 26.4
 (10.4)
Capital tax volatility Estimated 29.4
 (METR) (93.3)
Capital tax rate (AETR) Devereux et al. (2002) 35.0
 (11.1)
Capital tax volatility Estimated 17.3
 (AETR) (32.2)
Capital tax rate Devereux et al. (2002) 40.8
 (Statutory) (12.1)
Capital tax volatility Estimated 26.4
 (Statutory) (58.5)
Consumption tax rate (CETR) European Commission (2000) 24.0
 (8.0)
Consumption tax volatility Estimated 5.8
 (CETR) (11.6)

TABLE 5
GMM-Sys Dynamic Panel Data Estimation: Basic Results

Variable Model

 3 Devereux
Tax Rate 1 Mendoza 2 Mendoza AETR

Investment per worker (t-1) 0.846 *** 0.759 *** 0.516 ***
 (0.078) (0.093) (0.097)
Investment per worker (t-2) -0.084 -0.037 -0.227 ***
 (0.070) (0.067) (0.069)
Investment per worker (t-3) 0.198 ***
 -0.046
Real GDP per worker 1.852 *** 2.169 *** 1.608 **
 (0.491) (0.617) (0.645)
Capital price index -0.297 -0.476 1.220 **
 (0.322) (0.431) (0.510)
GDP price index 1.787 *** 2.048 ** -0.353
 (0.455) (0.886) (1.005)
Wage -1.045 *** -1.073 ** -0.135
 (0.395) (0.469) (0.548)
Interest rate -0.076 ** -0.087 ** -0.049 *
 (0.037) (0.042) (0.026)
Capital tax rate -0.201 * -0.186 ** 0.036
 (0.113) (0.091) (0.104)
Capital tax volatility -0.029 *** -0.029 ** -0.016 **
 (0.008) (0.012) (0.007)
Consumption tax rate -0.285
 (0.424)
Consumption tax volatility 0.004
 (0.009)
Sargan (p-value) 0.329 0.970 0.074
AR(1) test (p-value) 0.007 0.009 0.077
AR(2) test (p-value) 0.519 0.308 0.435
Number of observations 431 431 195

Variable Model

 4 Devereux 5 Devereux
Tax Rate METR Statutory

Investment per worker (t-1) 0.563 *** 0.625 ***
 (0.099) (131)
Investment per worker (t-2) -0.236 *** -0.243 ***
 (0.090) (0.093)
Investment per worker (t-3) 0.203 *** 0.201 ***
 -0.053 -0.045
Real GDP per worker 1.768 * 1.424 **
 (0.962) (0.444)
Capital price index 1.497 ** 0.861 **
 (0.647) (0.416)
GDP price index -0.438 0.261
 (1.086) (0.823)
Wage -0.410 -0.195
 (0.745) (0.549)
Interest rate -0.031 0.007
 (0.021) (0.030)
Capital tax rate -0.023 -0.428 **
 (0.026) (0.193)
Capital tax volatility 0.006 -0.012 **
 (0.007) (0.005)
Consumption tax rate

Consumption tax volatility

Sargan (p-value) 0.994 0.442
AR(1) test (p-value) 0.006 0.012
AR(2) test (p-value) 0.376 0.414
Number of observations 195 181

Notes:: Heteroscedasticity robust standard errors in parentheses.
All models estimated using the GMM-Sys estimator of Blundell and
Bond (1998) in differences on DPD for Ox (Doornik et al. 2002). All
variables transformed by natural logarithm. The null hypothesis of
the Sargan test is that the instruments used are not correlated with
the residuals (see Arellano and Bond 1991, Blundell and Bond 1998 for
details). The null hypotheses of the AR(1) and AR(2) tests are the
absence of first- and second-order serial correlation in the
residuals, respectively. The estimator employed requires the absence
of second-order serial correlation (first-order serial correlation
is expected because the equations are estimated in differences).
***, **, and * denote statistical significance at the 1%, 5%, and 10%
levels, respectively.

TABLE 6
Results: GMM-Sys Dynamic Panel Data Estimation: Extended Results

 Model

Variable Tax
 Rate 1 Mendoza 6 Mendoza 7 Mendoza

Investment per worker 0.846 *** 0.764 *** 0.773 ***
 (t-1) (0.078) (0.087) (0.072)
Investment per worker -0.084 -0.068 -0.025
 (t-2) (0.070) (0.069) (0.060)
Real GDP per worker 1.852 *** 2.038 *** 1.957 ***
 (0.491) (0.569) (0.481)
Capital price index -0.297 -0.420 -0.427
 (0.322) (0.333) (0.322)
GDP price index 1.787 *** 1.715 *** 1.985 ***
 (0.455) (0.458) (0.554)
Wage -1.045 *** -0.790 *** -1.061 **
 (0.395) (0.301) (0.425)
Interest rate -0.076 ** -0.075 -0.072 *
 (0.037) (0.046) (0.039)
Capital tax rate (r) -0.201 * -0.443 -0.132
 (0.113) (0.392) (0.086)
Capital tax rate (t-1) -0.136 *
 (0.076)
Capital tax rate (dev- 0.006
 iation from trend) (0.007)
Tax volatility -0.029 *** -0.023 ** -0.026 ***
 (0.008) (0.011) (0.009)
Sargan(p-value) 0.329 0.981 0.794
AR(1) test (P-value) 0.007 0.003 0.006
AR(2) test (p-value) 0.519 0.718 0.669
Number of observations 431 431 431

Notes. Heteroscedasticity robust standard errors in parentheses. All
models estimated using the GMM-Sys estimator of Blundell and Bond
(1998) in differences on DPD for Ox (Doornik et al. 2002). All
variables transformed by natural logarithm except for Tax rate
(deriation from trend). The null hypothesis of the Sargan test is
that the instruments used are not correlated with the residuals
(see Arellano and Bond 1990, Blundell and Bond 1998 for details).
The null hypotheses of the AR(1) and AR(2) tests are the absence of
first- and second-order serial correlation in the residuals,
respectively. The estimator employed requires the absence of
second-order serial correlation (first-order serial correlation
is expected because the equations are estimated in differences). ***,
**, and * denote statistical significance at the 1%, 5%G, and 10%
levels, respectively.

(1.) Hassett and Hubbard (1997) provide an extensive review of the literature on tax policy and investment.

(2.) For a review of post-World War II tax changes, see Cummins et al. (1994). See also Auerbach and Hines (1988).

(3.) This is not to say there has been no work in the area of tax uncertainty. A substantial body of literature has investigated the impact of randomness in tax policy on consumer behavior, work effort, and/or welfare. These include (but are not limited to) Alm (1988), Engen and Gale (1997), Judd (1998), McGrattan (1994), and Alvarez et al. (1998), as well as several papers in Aaron and Gale (1996). Auerbach and Hines (1988) were perhaps the first to consider the impact of tax changes on investment, but they did not explicitly incorporate the volatility of tax rates and considered policy changes that are anticipated. See also Alvarez et al. (1998).

(4.) Note that earlier work by Hartman (1972) and Abel (1983) suggests that uncertainty about future prices would lead to an increase in the firm's optimal capital stock if the production function is linearly homogeneous. In their models investment is reversible and thus has zero opportunity cost, whereas Pindyck considers the (more realistic) case of irreversible investment. See Pindyck (1988, 970n.) for more details.

(5.) The explanation for this result is that firms will adjust the timing of their investment to make expanded use of the subsidy when it is relatively large.

(6.) See, in particular, Skinner (1988). Ramey and Ramey (1995) consider the relationship between volatility and growth via an investment "conduit" (and find no empirically important relationship) but do not directly consider the role of tax uncertainty.

(7.) Ferderer (1993) finds a significant relationship independent of marginal q.

(8.) The existence of investment tax credits, or some type of uncertainty not considered here for that matter, would make the theoretical relationship between tax uncertainty and investment even more unclear. The innovation that comes from the empirical analysis is that no specific stochastic process for taxes is imposed.

(9.) For other studies employing this methodology, see Mendoza et al. (1997) and Mendoza and Tesar (1998).

(10.) The variables [y.sub.k] and [y.sub.l] represent the utilization of inputs. As elements of a net output vector, [bar.y], they are thus negatively valued.

(11.) This discussion follows the outline in Box 1 of Devereux et al. (2002).

(12.) In his experimental study of expectations formation of tax credits, Swenson (1997) found that none conformed to rational expectations, 44% conformed to adaptive expectations, 40% conformed to naive expectations (a Martingale-type rule), and 16% conformed to no model.

(13.) See Leahy and Whited (1996) and Carruth et al. (2000b) for a general discussion of the use of ARCH-GARCH models to estimate proxies for uncertainty in the empirical investment literature. For discussion of the ARCH framework, as employed in this article, see Engle (1982).

(14.) Ireland's statutory tax rate was a constant 10% over the representative period.

(15.) Although data on effective tax rates is available from 1970 to 2001, the Penn World Tables Mark VI (see Summers and Heston 1991), from which much of the data was extracted, provides data only through 1998.

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KELLY D. EDMISTON, I would like to thank Jim Skinner for very helpful comments on an earlier draft and to acknowledge useful comments and suggestions from Jim Alm, Neven Valev, seminar participants at Georgia State University and the University of Tennessee, and an anonymous referee.

Edmiston: Assistant Professor of Economics, Andrew Young School of Policy Studies, Georgia State University, University Plaza, Atlanta, GA 30303-3083. Phone 1-404-651-3519, Fax 1-404-651-2737, E-mail edmiston@gsu.edu