The Tax Structure-Economic Growth Puzzle Revisited K. Peren Arin

Tolga Omay

Mehmet A. Ulubasoglu

Zayed University, College of Cankaya University, Department of Deakin University, Department of Business, Abu Dhabi, UAE Banking, Ankara, Turkey Economics, Melbourne, Australia [email protected] [email protected] [email protected]

August 2015 Abstract

Previous literature, using different tax measures, sample countries, estimation methodologies and model specifications, has generated mixed evidence on the effects of tax structure on economic growth. We investigate whether two major tax instruments, namely, labor income taxes and corporate taxes, affect the long-run economic growth by using use both statutory and average tax rates for a sample of 19 OECD countries over the 1981-2005 period. We also contribute to the literature by using a newly developed Panel Smooth Transition (PSTR) model that controls for non-linearities in the tax structureeconomic growth relationship. Our findings suggest that while taxes on corporate income are distortionary for growth in both high- and low-growth regimes, taxes on labor income are harmful only during high-growth regime. Our results shed important light on some inconsistencies in the previous literature. JEL Classification: 023, H30

1

1

Introduction

A corpus of literature has advanced compelling but contradicting arguments to explain the role of fiscal policy in economic growth. The neoclassical growth model (Solow, 1956; Swan, 1956) predicts no long-run effect of government policy on the rate of economic growth. As, in this framework, economic growth depends largely on the accumulation of physical and human capital, any given tax structure that generates an equilibrium labor ratio can but have transitory effects. However, in endogenous growth paradigm, some of the fiscal policy instruments are harmful for growth (Barro, 1991; Lucas, 1990). For example, distortionary tax instruments (labor and corporate taxes) can adversely affect the saving and investment decisions on physical and/or human capital. On the other hand, three different arguments exist in the literature pointing to the inconclusive effects of income taxes on human capital: positive (e.g., Heckman (1976)); nil or minimal (e.g., Boskin (1975)); and negative (e.g., King and Rebelo (1990); Lucas (1990)). Recent contributions have provided various channels through which tax policy can affect economic growth in a theoretical endogenous growth framework. For example, Cullen and Gordon (2002) list several alternate ways through which taxes can possibly affect entrepreneurial activity. Empirical evidence on the effects of fiscal policy on growth is also quite mixed. Many cross-country studies, such as Easterly and Rebelo (2002) and Mendoza et al. (1997), find that long-run growth rates do not respond to taxation. In contrast, using timeseries data over 100 years from the United States and the United Kingdom, Kocherlakota and Yi (1997) find that when both a tax and a public capital variable are included in a regression, evidence indicates strong direct effect of fiscal policy on long-run endogenous growth. In a more recent context, adopting pooled cross-sectional data for 23 OECD countries, Widmalm (2001) finds a negative effect of income tax on growth. Kneller et al. (1999) and Lee and Gordon (2005) are two key studies in the literature that put forward more nuanced effects of taxes on economic growth. In their seminal paper, Kneller et al. (1999), using a panel of 22 OECD countries, contend that while distortionary taxation (labor and corporate taxes) reduces economic growth, non-distortionary 2

taxation (indirect and consumption taxes) does not1 . Kneller et al. (1999) use the average tax rates (which is defined as tax revenues as a percentage of income) as a measure of tax policy. They also argue that studies focusing exclusively on one side of the budget and ignoring the other side suffer from substantial bias in the estimates. Following their footsteps, we also consistently control for the expenditure side of the budget in our analysis. On the other hand, Lee and Gordon (2005) demonstrate, using a cross-section dataset for 70 countries over the 1970-1997 period, that top marginal corporate tax rate (or, statutory rate) exerts a significant and negative effect on economic growth. They argue that as entrepreneurial activity is an important engine for growth, progressive taxation of corporate income discourages risk-taking, and therefore, has substantial negative effects on growth. Interestingly, they do not find a significant effect of income taxes on growth. The difference in the results of Kneller et al. (1999) and Lee and Gordon (2005) can be due to either the identification of tax shocks (average vs. statutory rates) or, sample size (22 vs 70 countries), or different model specifications. There is an additional important factor in the tax structure-economic growth relationship that has become increasingly important but been ignored by previous studies: non-linearities. The main idea behind non-linearities in the tax structure-growth relationship is that heterogeneous tax effects of growth may arise due to differential impacts under recessionary versus boom periods, or critical thresholds in certain variables such as the government budget deficit, economic growth, or the tax rate. A recent line of literature has documented the prominent role of non-linearities in determining the course of the fiscal policy-economic growth association, see Adam and Bevan (2005) and Arin et al. (2013). We contribute to the tax structure-economic growth literature in two major respects. First, we empirically investigate the effects of both average and top statutory tax rates, for both labor as well as corporate taxes, using a panel of 19 OECD countries over the period 1981 to 2005. In this vein, we not only to compare and contrast the effects of different 1

Further, productive government expenditure enhances growth, while non- productive expenditure does not.

3

taxes and tax brackets on economic growth, but also to shed light on the differing findings of Lee and Gordon (2005) and Kneller et al. (1999). Second, we study the non-linear effects of different taxes (as well as different tax measures) on economic growth. To this end we propose a new methodology, namely, the panel smooth transition method with common correlated effects (a la Pesaran (2006)), which is a variant of the class of panel smooth transition methodologies recently developed in the literature (see, among others, González et al. (2005), and Omay and Kan (2010)). The panel smooth transition method (hereafter, PSTR) models, unlike simple threshold and Markov-Switching models, do not use abrupt changes in coefficients and allow for modelling different types of nonlinear and asymmetric dynamics depending on the type of the transition function (Teräsvirta and Anderson, 1992; Granger and Teräsvirta, 1993). Our results demonstrate that while the statutory taxes on corporate income adversely affect economic growth in both high- and low-growth regimes, statutory taxes on labor income are harmful only during the high-growth regime. Importantly we find that the distortionary effect of corporate taxes is more sizeable, given the stronger statistical significance levels and larger coefficient magnitudes associated with this effect. We also obtain largely similar results when we measure the tax policy with average tax rates: average corporate taxes are negatively related to economic growth in both high- and low-growth regimes, while average labor taxes are harmful during only high-growth regime. However, the magnitude of the estimated effects with average tax rates are smaller compared to the above findings with statutory rates. Our results imply that corporate tax cuts may be more reliable policy instruments that can be used to stimulate the economy especially during low-growth/recessionary periods. Our findings shed strong light on the existing puzzle on tax policy-economic growth relationship, given the fact that we not only control for non-linearities in the data, but also use both average and statutory tax rates to find out which taxes do really matter for growth. We also control for unobserved heterogeneity at country and time levels by taking full advantage of our data set. The aforementioned contributions address two very important inconsistencies which plagued the previous literature: whether it is statutory

4

(i.e., top marginal) or average taxes that matter, and whether it is corporate or labor taxes that affect the course of economic growth. The remainder of this paper is organized as follows: Section 2 discusses the data, Section 3 explains the PSTR approach utilized, section 4 presents the empirical results, section 5 discusses some robustness checks performed and section 6 concludes.

2

Data

Our data have been obtained from a number of sources. The dependent variable is the percentage growth rate of output per worker (∆yit ), which is provided by the World Development Indicators (WDI). The main explanatory variables of interest are the tax measures. Statutory or top tax rates for corporate and labor taxes (top_corptaxit and top_inctaxit, , respectively) are obtained from the World Tax Database (http://www.bus. umich.edu/otpr/otpr/default.asp) We were also engaged in extensive communications with the Finance Ministries in the OECD countries to confirm the data in the above database, as well as to find some of the missing data. The average tax rates are defined as the share of tax revenues of the respective tax group in the GDP (corptaxit and labtaxit , respectively), and obtained from the OECD National Economic Outlook database. As Kneller et al. (1999) show the importance of controlling for the expenditure side while investigating the effects of the revenue side in empirical studies, we also adopt the natural log of government disbursements in GDP (Git ), in each and every regression, which was also obtained from OECD Economic Outlook database. We use a number of control variables in the estimation in conjunction with the CobbDouglas production function approach used in the neoclassical growth models. Human capital is measured by natural logarithm of secondary school completion rate (HCit ) and provided by Barro and Lee (2010). The effects of population growth (P opit ) are measured by the natural logarithm of labor force growth rate (provided by WDI)2 . Finally, we also control for the effects of saving and investment (Iit ) by including the natural logarithm 2

In particular, we add +0.07 to the population growth rate as a measure of depreciation rate. This also avoids negative numbers within the logarithms.

5

of investment as a percentage of GDP, also from WDI. The following countries are included in our sample: Australia, Austria, Belgium, Canada, Germany, Denmark, Finland, France, Ireland, Italy, Japan, the Netherlands, Norway, New Zealand, Portugal, Spain, Sweden, UK and the USA. The time period covered in the study is 1981 to 2005. This panel yields 475 observations with few missing values. Table 1 presents summary statistics for all variables.

3

Methodology

Panel Smooth Transition Regression (PSTR) allows for a small number of extreme regimes where transitions in-between are smooth. Let us first consider the simplest case with two extreme regimes:

∆yit = µi + β0 xit + β1 xit F (sit ; γ, c) + uit

(1)

for i = 1, . . . , N , and t = 1, . . . , T , where N and T denote the cross-section and time dimensions of the panel, respectively. The dependent variable ∆yit is a scalar and denotes growth rates of output per worker for the 19 countries in our sample. In this study, the independent variable k-dimensional vector xit of time-varying exogenous variables are selected to be fiscal variables of interest, investment (Iit ), population (P opit ), (corpit ), and, human capital (Hcit ). µi represents the fixed individual effects, and finally uit are the errors. Transition function F (sit ; γ, c) is a continuous function of observable variable sit . It is normalized to lie between 0 and 1, which denote the two extreme values for regression coefficients (González et al., 2005). Granger and Teräsvirta (1993) considered the following logistic and exponential transition function for the time series STR models, where

F (sit ; γ, c) =

1 1 + exp(−γi (sit − cl )/σsit )

is the logistic function, and

6

(2)

F (sit ; γ, c) = (1 − exp(−γE (sit − cE )2 /σsit )

(3)

is the exponential function These functions yield, respectively, the Logistic Smooth Transition Regression (LSTR) and Exponential Smooth Transition Regression (ESTR) models, where the slope parameters γ determine how rapid the transition is and the vector of location parameter c decides where the transition occur. In cases where logistic function is used, the low and high values of sit correspond to the two extreme regimes. Given that γ → ∞, the logistic transition function F (sit ; γ, c) turns into an indicator function of I[A], which takes a value of 1 when event A occurs and 0 otherwise. Hence, the PSTR model reduces to Hansen (1999)’s two-regime panel threshold model. However for exponential, F (sit ; γ, c) takes a value of 2 ). In that case, if γ → ∞, F (sit ; γ, c) 1 for both low and high sit, minimizing at ( c1 +c 2

reduces to a three-regime threshold model. Indeed given γ → ∞, the transition function F (sit ; γ, c) will boil down to a homogenous or linear fixed effects panel regression for any kind transition function3 . Once the transition variable and form of the transition function are selected, the PSTAR models can be estimated by using non-linear least squares. The optimization algorithm can be disburdened by using good starting values. Hence, a convenient way to obtain reasonable starting values for the Non-linear Least Squares (NNLS) is to perform a two-dimensional grid search over γ and c, and select those estimates that minimize the panel sum of squared residuals4 . We should also note that endogeneity is not an issue here: Fouquau (2008) apply IV estimation technique to PSTAR model; they conclude that PSTAR estimation technique limits the potential endogeneity bias, since for each level of threshold variable there is “particular” value of the estimated FH regression parameter. 3

For more detailed discussion, see González et al. (2005), and Omay and Kan (2010) In order to solve a possible cross-section dependency, following Pesaran (2006)), we made use of cross-sectional averages to provide valid inference for stationary panel regressions with multifactor error structure. 4

7

4

Results

All the asymptotic theory for the Smooth Transition Autoregressive (STR) models (as well as the PSTR extensions) are for stationary regressors. Therefore, we start our empirical analysis with non-linear panel unit root tests to determine the stochastic properties of our dataset. The test results for the Ucar-Omay test (2009- UO, hereafter) are presented in Table 2. As can be seen, the UO test rejects the null hypothesis of unit root at 1 % and 5 % significance levels for all series. From the non-linear panel unit root test, we can conclude that the all variables in our study are I(0). Next, we apply the LMF test of linearity (homogeneity), as mentioned in the methodology section, using lagged GDP growth as the transition variable. Restricting coefficients of some variables to be constant in the PSTR model has no effect on the distribution theory (?). For this purpose, LMF tests thus applied suggest strong non-linearity, see Table 3. The first lag of growth was chosen as the transition variable, given its high significance level. In the presence of cross-sectionally correlated error terms, traditional OLS-based estimations are inefficient (Pesaran, 2006). Therefore, we adopt the Nonlinear Static Pool Common Correlated Effect (NPCCE) estimation. Table 4 reports the unbiased estimates of PSTR model. Before proceeding with our results, it is important to note that the threshold growth rate to distinguish between low-growth and high-growth regime seems to be around 1.5 %; more specifically, 1.2 % for Model 1, and 1.8 % for Model 2.

4.1

Top Tax Rates: Corporate and Labor

Our results show that, consistent with the majority of the previous literature, taxation is harmful for economic growth. In particular, using the top statutory tax rate a la Lee and Gordon (2005), we find that corporate taxes are distortionary for growth in high-growth and low-growth periods (Model 1). More specifically, a one-percentage point increase in the top corporate tax rate decreases growth by 0.58 percent in low-growth regimes and 0.73 percent in high-growth regimes. Importantly, our coefficient estimates are much larger than those reported by Lee and Gordon (2005). The discrepancy between the magnitudes of the coefficients may be pointing out the importance of non-linear relationship between 8

economic growth and the fiscal variables. Another explanation for this discrepancy could be the difference in sample countries- as our sample includes the OECD countries only. On the other hand, our results show that labor taxes are distortionary for growth only during high-growth periods (Model 1). Our coefficient estimate shows that a onepercentage point increase in the top-labor tax rate decreases growth by 0.27 percent. This result is quite different than Lee and Gordon (2005), who report no significant effect of labor tax on economic growth.

4.2

Average Taxes: Corporate and Labor

We next use the average tax rate for corporate and labor to measure the fiscal policy a la Kneller et al. (1999). Our estimations point to largely similar results as above. In particular, we find that a one-percentage point increase in average corporate tax rate decreases the growth rate by 0.12 percent in low-growth regimes and 0.07 percent in high-growth regimes (Model 2). Though the magnitude of coefficients are smaller in this case, our result provides further evidence that corporate taxes are harmful for economic growth in both states of the world. However, it is evident that the distortionary effects of taxation may be better identified through statutory rates, given the larger magnitude of estimated coefficients. Interestingly, while the magnitude of the effect is larger in the high-growth regime if we identify corporate tax shocks through top rate, the magnitude of the effect is larger in the low-growth regime if we identify corporate tax shocks through average rate. Proceeding to average labor taxes, we find that labor taxes exert a significant effect on growth only on high-growth regime (Model 2). In particular, our coefficient estimate shows that a one-percentage point increase in average labor tax rate decreases economic growth by 0.07 percent. Importantly, these estimates are lower than those reported by Kneller et al. (1999). This particular result is not surprising as Kneller et al. (1999) use average rate for distortionary taxes which include both income and corporate taxes, while we look into those two groups separately. The estimated sign of the coefficients of our control variables (i.e. physical invest-

9

ment, human capital, population growth, and government expenditure) are intuitive in both models, although most of them are estimated to be statistically insignificant. This is probably because most of the OECD countries already operate at their steady-state levels, and therefore, additional factor accumulation in physical capital, human capital and labor do not raise the economic growth rate further. An exception to these findings is the coefficient for government expenditures, which is negative and significant – a result consistent with the “Non-Keynesian Effects” of fiscal policy (Alesina et al., 2002).

5

Robustness Tests

In this section we continue our analysis by checking diagnostics of our benchmark model. More specifically, we investigate any possible remaining issues related to non-linearity and parameter constancy by conducting additional econometric tests. The results of the misspecification test reported in Table 5 suggest that the two-regime model is adequate. All of the models pass the proposed misspecification tests (?). The estimated values of the location (threshold) parameter c and transition parameter gamma and the graph of the estimated transition function as a function of ∆yit−1 provide useful information about the features of the transition itself and the interpretation of the models. Figure 1 shows the transition function for both models. As can be seen from the figure, our Model 1 behaves like a regular threshold model, whereas Model 2 exhibits a moderate transition speed, which implies smooth transition between the two regimes. Both figures, however, are consistent with the high significance of threshold variable in our regressions. Figure 2 presents the threshold value (the blue horizontal line) as well as the values for the growth rate that stay in low and high regimes. The lower panel, on the other hand, exhibits how the transition function behaves over the time domain. In addition, we also re-estimate our model with two changes simultaneously5 . First we estimate the model without the control variables, with the exception of government expenditures. As Kneller et al. (1999) argued that the regression models that do not con5

We also performed robustness checks where we introduced one check at a time, and results were qualitatively similar. They are available upon request.

10

trol for both the spending and the revenue side are misspecified, we kept the government expenditure variable in the regression alongside our tax variables. On the other hand, in the presence of cross-sectionally correlated error terms, traditional OLS-based estimation are inefficient and invalidates much inferential theory of panel data models which we mentioned before. By using the same methodology of Omay and Kan (2010) we propose a nonlinear version of CCE estimator for mean-group estimator which leads to a nonlinear CCEMG estimator that solves the cross-section dependency in PSTAR models. The results are presented in Table 6. Our results are qualitatively similar, although now, top corporate tax rate has a negative and significant sign only during low-growth regime, and average tax rate on labor income has a negative and significant sign only in the high-growth regime.

6

Concluding Remarks

Since the financial and economic crisis of 2008, a popular question among both academics and policymakers has been on the effectiveness of fiscal policy in stimulating the economic activity in both the short-run and the medium-run. Accordingly, an accurate understanding of whether some taxes are better than others for improved economic performance has become a crucial policy problem. The previous literature has not much assisted in this vein because it has documented conflicting results. For example, Kneller et al. (1999), using average tax rates, find that taxes on both corporate and personal income are harmful, while Lee and Gordon (2005), by using statutory rates, contend that only corporate taxes are distortionary for growth. More recent work, particularly by Adam and Bevan (2005) and Arin et al. (2013), has shown that controlling for the non-linearities in the tax structure-growth nexus is important to paint an accurate picture of the said relationship. By using a rich data set on statutory and average tax rates and utilizing an advanced panel non-linear estimation technique, this paper attempts to shed some light on the tax rate-economic growth puzzle. Our results are partly supportive of both Kneller et al. (1999) and Lee and Gordon (2005). We find that corporate taxes are distortionary re11

gardless of whether the growth regime is a high-regime or a low-regime, while taxes on labor income are distortionary only during the low-growth regimes. In terms of the sign of the effects, both corporate and labor taxes have analogous effects in the high-growth regime. However, the magnitude of the effect is larger for the corporate taxes. According to OECD estimates, Tax-to-GDP ratios fell in a majority of OECD countries between 2007 and 2011 while the share of tax revenue from income and profits decreased by 2.5 percentage points. Bearing this in mind6 , our findings suggests that governments might choose to rely more on corporate taxes to stimulate the economy. On the other hand, it can also be argued that governments might opt for increasing labor taxes and avoid corporate taxes during low-growth periods, especially when trying to consolidate their budgets7 . Obviously the political viability of this suggestion is an open question. Needless to say, further avenues of research include identifying the more specific channels through which different tax groups affect economic growth in different regimes.

6

http://www.oecd-ilibrary.org/taxation/the-tax-policy-landscape-five-years-afterthe-crisis_5k40l4dxk0hk-en?crawler=true 7 The effect of a tax increase on the success probability of the budget consolidation is another question, which is beyond the scope of this paper.

12

References Adam, C. S. and D. L. Bevan (2005). Fiscal deficit and growth in developing countries. Journal of Public Economics 89 (4), 571–597. Alesina, A., S. Ardagna, R. Perotti, and F. Schiantarelli (2002). Fiscal policy, profits and investment. American Economic Review 92 (3), 571–589. Arin, P. K., M. Berlemann, F. Koray, and T. Kuhlenkasper (2013). Non-linear growth effects of taxation: A semi parametric approach using marginal tax rates. Journal of Applied Econometrics 28 (5), 883–899. Barro, R. J. (1991). Economic growth in a cross-section of countries. Quarterly Journal of Economics 106 (2), 407–443. Boskin, M. J. (1975). Notes on the tax treatment of human capital. In Conference on Tax Research, Washington. Department of Treasury. Cullen, J. B. and R. H. Gordon (2002). Taxes and entrepreneurial activity: Theory and evidence for the u.s. Working Paper 9015, NBER. Easterly, W. and S. Rebelo (2002). Fiscal policy and economic growth: An empirical investigation. Working Paper 4499, NBER. Fouquau, J. (2008). Threshold effects in okun’s law: a panel data analysis. Economics Bulletin 5 (33), 1–14. González, A., T. Teräsvirta, and D. van Dijk (2005). Panel smooth transition regression models. Working paper, Stockholm School of Economics. Granger, C. W. J. and T. Teräsvirta (1993). Modelling Non-Linear Economic Relationships. Oxford: Oxford University Press. Hall, R. E. and D. W. Jorgenson (1967). Tax policy and investment behavior. American Economic Review 57 (3), 391–414.

13

Hansen, B. (1999). Threshold effects in non-dynamic panels: Estimation, testing, and inference. Journal of Econometrics 93 (2), 345–368. Heckman, J. J. (1976). A life-cycle model of earnings, learning, and consumption. Journal of Political Economy 84 (4), 11–44. King, R. G. and S. Rebelo (1990). Public policy and economic growth: Developing neoclasical implications. Journal of Political Economy 98 (5), 126–150. Kneller, R., M. F. Bleaney, and N. Gemmel (1999). Fiscal policy and economic growth: Evidence from oecd countries. Journal of Public Economics 74 (2), 171–190. Kocherlakota, N. R. and K.-M. Yi (1997). Is there endogenous long-run growth? evidence from the united states and the united kingdom. Journal of Money, Credit and Banking 29 (2), 235–267. Lee, Y. and R. H. Gordon (2005). Tax structure and economic growth. Journal of Public Economics 89 (5-6), 1027–1043. Lucas, R. (1990). Supply side economics: An analytical review. Oxford Economics Papers 42 (2), 293–316. Mendoza, E. G., G. M. Milesi-Feretti, and P. Asea (1997). On the effectiveness of tax policy in altering long-run growth: Harberger’s superneutrality conjecture. Journal of Public Economics 66 (1), 99–126. Omay, T. and E. O. Kan (2010). Re-examining the threshold effects in the inflationgrowth nexus with cross-sectionally dependent non-linear panel: Evidence from six industrialized economies. Economic Modelling 27 (5), 996–1005. Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74 (4), 967–1012. Solow, R. M. (1956). A contribution to the theory of economic growth. Quarterly Journal of Economics 71 (1), 65–94.

14

Swan, T. W. (1956). Economic growth and capital accumulation. Economic Record 32 (3), 334–361. Teräsvirta, T. and H. M. Anderson (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of Applied Econometrics 7 (S), 119–136. Ucar, N. and T. Omay (2009). Testing for unit root in nonlinear heterogeneous panels. Economics Letters 104 (1), 5–8. Widmalm, F. (2001). Tax structure and growth: Are some taxes better than the others? Public Choice 107 (3-4), 199–219.

15

Table 1: Summary Statistics Variable Names

Mean

Median

Standard Error

Variance

Se of Sample Mean

Max Value

Min Value

Growth top_corptaxit top_inctaxit average corptaxit average labtaxit Git HCit P opit Init

1.612 3.664 3.779 0.985 3.117 3.791 2.893 1.769 3.07

1.734 3.663 3.871 1.023 3.16 3.831 2.909 1.754 3.063

2.014 0.243 0.375 0.398 0.257 0.201 0.536 0.187 0.159

4.057 0.059 0.141 0.158 0.066 0.04 0.287 0.035 0.025

0.094 0.011 0.017 0.018 0.012 0.009 0.027 0.008 0.007

8.207 4.127 4.43 1.818 3.588 4.213 3.837 2.792 3.582

-6.946 2.484 1.945 0.018 2.537 3.266 1.581 0.074 2.715

16

Table 2: Non-linear panel unit root test Ucar-Omay (UO) Intercept HCit P opit Init Git top_corptaxit top_inctaxit average corptaxit

-3.148(0.004) -4.253(0.002) -2.219(0.019) -2.855(0.000) -1.735(0.120) -1.013(0.574) -1.890(0.140) -2.294(0.008)

average_labtaxit

Intercept and trend HCit -2.127(0.003) P opit -2.137(0.008) Init -2.583(0.000) Git -2.832(0.000) top_corptaxit -2.137(0.008) top_inctaxit -1.812(0.025) average corptaxit -2.821(0.071) average_labtaxit -2.714(0.098) Notes: t-bar statistic was computed by bootstrapping with 2000 replications p-values in parantheses.

17

Table 3: Linearity Test Dependent Variable: Growth rate State Variable

Model 1

Model 2

Lag 1

20.688 0.000 11.452 (0.000) 9.767 (0.000) 11.59 (0.000) 10.605 (0.000)

16.439 0.000 11.004 (0.000) 7.518 (0.000) 7.183 (0.000) 8.116 (0.000)

Lag 2 Lag 3 Lag 4 Lag 5

18

Table 4: Estimation results of two-regime PSTR models with Pool Common Correlated Effect -1 -2 Dependent variable Low Growth Periods HCit HCit Init Git top_corptaxit top_inctaxit

∆yit

∆yit

-0.058 (-0.132) -1.675 (-1.498) 1.166 -1.151 -3.129* (-2.755) -0.582*** (-1.673) 0.148 -1.424

-0.059 (-0.702) -0.006 (-1.054) 0.112 -1.339 -0.078 (-0.262)

average corptaxit

-0.122* (-2.553) -0.174 (-0.883)

average labtaxit

High Growth Periods HCit HCit Init Git top_corptaxit top_inctaxit

0.271 -0.847 0.881 -0.689 -0.714 (-0.645) -2.268* (-2.669) -0.733** (-1.946) -0.276* (-2.268)

average corptaxit average labtaxit Threshold

1.203* -33.799

Gamma

-0.198 (-0.221) -0.006 (-0.493) 0.152* -2.433 -0.056 (-0.839)

-0.067*** (-1.649) -0.069* (-2.185) 1.818* -21.158

98.014 10.143 -1.012 -1.234 (*) %1 significance level, (**) %5 significance level, (***)%10 significance level. ** The values in the parentheses are t values.

19

Table 5: Misspecification test Models Remaining Heterogeneity (Non-linearity) Transition Variable used ∆yit−1 ∆yit−2 ∆yit−3 ∆yit−4 ∆yit−5 Parameter Constancy Transition Variable used m=1

Model 1

Model 2

1.105 -0.268 1.213 -0.119 1.015 -0.45 1.032 -0.412 0.802 -0.887

1.179 -0.163 1.238 -0.103 0.999 -0.489 0.804 -0.88 0.893 -0.725

Time 0.556 -0.999

Values in the parenthesis are p values

20

0.818 -0.865

Model 1

Model 2

Figure 1: The Transition functions for model 1 and 2

21

Figure 2: Transition Function with respect to time and threshold value for the first model

22

Table 6: Estimation results of two-regime PSTR models with Pool Common Correlated Effect -1 -2 Dependent variable Low Growth Periods top_corptaxit top_inctaxit

∆yit -0.480*** (-1.860) -0.517 (-0.861)

average corptaxit average labtaxit government

-0.694*** (-1.684)

High Growth Periods top_corptaxit top_inctaxit

average labtaxit

Threshold

-0.019 (-0.075) 1.803 -1.473 -4.271* (-3.545)

0.454 -0.711 -0.116 (-0.316)

average corptaxit

government

∆yit

0.544 -0.934 1.138 * -226.5

Gamma

-0.037 (-0.121) -2.933** (-2.316) -0.747* (-3.369) 1.371 * -28.788

90.289 5.004 -0.099 -1.001 (*) %1 significance level, (**) %5 significance level, (***)%10 significance level. ** The values in the parentheses are t values.

23

Appendix Non-linear model with single factor:

yit = µi + β 0 xit + F (sit , γ, c)β˜0 xit + uit

(4)

where

F (sit , γ, c) =

1 1+

e−γ(si t−c)

,

uit = φi ft + εi,t , xit = δi f˜t + νit Notice here that ft and f˜t are different factor variables that effect dependent, independent and state dependent variables, respectively. Now suppose that uit and xit specifications are plugged into original yit equation. Thus, we have:

yit = µi β 0 δi f˜t + F (sit , γ, c)β˜0 δi f˜t + βνit + F (sit , γ, c)β˜0 νit + φft + εit

(5)

N

P f˜t can be removed by usig proxy variable, x¯t where x¯t = N −1 xit which can be obtained i=1

through taking average of xit : x¯t = δ¯f˜t + ν¯t which implies that f˜t =

x ¯t −¯ νt . δ¯

Substitute this

into (5) then we have:

0

yit = µi +β δi



   x¯t − ν¯t x¯t − ν¯t 0 ˜ +F (sit , γ, c)β δi +βνit +F (sit , γ, c)β˜0 νit +φft +εit (6) δ¯ δ¯

In order to remove the factor ft from equation (6), we first take the averages of the above equation then obtain ft appropriately, that is:     x¯t − ν¯t ¯t − ν¯t ¯ 0¯ x ¯ ¯ ˜ ¯ t + ε¯t ¯ y¯t = µ ¯ + βδ + F (.)β δ + β¯ν¯ + F¯ (.)β¯˜ν¯t + φf δ¯ δ¯ then, with some algebra, y¯t can be written as: 24

(7)

¯ t + ε¯t y¯t = µ ¯ + β¯x¯t + F¯ (.)β˜¯0 x¯t + phif

(8)

 1 ¯ 0 0 ¯ ˜ ¯ y¯t − µ ¯ − β x¯t − F (.)β x¯t − ε¯t ft = φ

(9)

Hence ft is:

we obtain ft from equation (9) and substitute in equation (4): i φi h yit = µi β 0 xit + F (.)β˜0 xit + ¯ y¯t − α ¯ − β¯x¯t − F¯ (.)β¯˜0 x¯t − ε¯ φ again with relevant algebra, we obtain the auxiliary regression

yit = µ ˜i + β 0 xit + F (.)β˜0 xit + a¯ yt + b¯ xt + F¯ (.)c¯ xt + ηit ¯, b = where µ ˜=µ ˜ − φφ¯ µ

φβ¯ , φ¯

a = φφ¯ , c =

¯ φβ˜ , ¯ φ

and ηit = εit − φφ¯ ε¯t .

25

(10)