Chapter 7: Statistical Analysis
1. Econometric Specification of the 2SLS Model
Tax competition results in strategic interaction between the governments of countries trying to attract mobile tax bases and preventing domestic capital from fleeing. Econometrically these tactical considerations are captured by modelling the decision on the domestic tax rate as reaction function to the mean of all foreign tax rates or a substantially weighted sum thereof and specific domestic variables:
( , , ),
cjt R c jt Xjt j j
τ = τ − ≠ − (21)
with τcjt being the capital tax rate of country j at time t. τc,−jt denotes a vector of capital tax burdens of all other countries –j at time t and Xjt
describes a vector of domestic variables affecting tax decisions of country j.
The reaction function can be rewritten into an estimation equation to allow the statistical analysis of the empirical model:
W X
τ =β τ+ γ ε+ or cjt j, j c, jt jt jt
j j
τ β ω τ− − X γ ε
≠−
=
∑
+ + (22)where τc,−jt on the right hand side stands for the spatial lag of the dependent variable and ωj,-j denotes a weighting matrix representing the strength with which capital tax rates in a specific foreign jurisdiction impact the domestic choice. εjt represents the classical identically and independently distributed disturbance term of linear models. W is a NT*NT block-diagonal spatial-weighting matrix with elements ωj,−j, thus ω τj,−j c,−jt characterises the weighted spatial lag. The diagonal elements of the off-diagonal T*T blocks in W depict the single weights ωj,−j that reflect the degree of connection from country j to -j. The spatial autoregression coefficient beta reflects the impact of the outcomes in the other (j ≠ -j) spatial units, as weighted by
, j j
ω − , on the outcome in j. Hence, beta gauges the overall strength of the spatial dependence whereas the ωj,−jdescribe the relative magnitudes of the diffusion paths or the path of spatial dependence between the countries (Franzese and Hays 2007). The matrix ω τj,−j c,−jt just gives the entire set of these vector inner-products for all countries -j.
Some researchers just use arbitrarily weighted spatial lags which in this case would mean that a country’s response to other countries’ capital tax rates is given by the average foreign capital tax burden:
, , ,
Equation (22) depicts the theoretical result that domestic taxation is a function of domestic political, institutional and economic constraints as well as tax rates implemented in competitor countries. The weighted spatial lag corresponds to the effects of the global economy. To isolate the domestic effects, I include government consumption as percentage of GDP, the strength of societal equality needs and the share of multinationals in the domestic economy – capturing de facto capital mobility – into the right hand side of the regression model.60
The inclusion of weighted spatial lags leads to endogeneity bias and therefore an inconsistent estimation of included domestic variables. This problem can be dealt with by instrumenting the spatial lag with suitable exogenous variables. To do so I implement a two stage least squares (2SLS) instrumental variable approach, where in the first step the weighted spatial lag Wτ is regressed on X – the included exogenous variables and WX – the excluded exogenous instrumental variables. In the second step the fitted values Wlτ from the first stage are used as instruments for Wτ.61
Instrumental variable estimation implies regressing the weighted linear combination of the τ’s from the right hand side variables of equation (22) on Xj and on the same linear combination of all X-j’s. Thus, the instruments used in the first step to produce fitted values of the weighted spatial lag are
60 An obvious extension would be to incorporate interaction terms between the spatial tax lag and the most important domestic variables. Yet, since I treat the weighted spatial lag as endogenous applying an instrumental estimation this would raise severe estimation problems: The interaction effects and the tax rate of adjacent economies are highly correlated.
61 For details on this procedure see Wooldridge (2002) and Baum et al. (2003).
the domestic control variables included into the final regression model as well as a weighted average of these variables for all other countries WX.
This involves that if we employ a spatial tax lag weighted by FDI, the average of exogenous instrumental variables X-j must also be weighted by FDI. Or if we weight taxes abroad by distance the X-j have to be weighted by distance as well.
Within the set of instruments for each regression model, I only use those instrumental variables which pass both the Hansen-Sargan test for over-identification62 and the redundancy test for instruments (Hall and Peixe 2000). Additionally, the validity of the instruments used in the first stage regression is tested with an Anderson-Rubin F-test for the (joint) significance of the excluded instruments (See Dufour 2003 for details.). In order to decide whether the spatial lags are really endogenous I employ the Wu-Hausman F test (Davidson and MacKinnon 1993) and the Durbin-Wu-Hausman Chi-sqared test (Baum et al. 2003). Both tests suggest that arbitrarily and FDI weighted spatial tax lags are indeed endogenous in most of the regression models and that the implementation of an instrumental equation eliminates potential endogeneity problems.
Another problem occurs as the Wooldridge test (Wooldridge 2002) for serial correlation in the idiosyncratic errors of a linear panel data model reveals that the estimation suffers from arbitrary serial correlation.
Moreover, the Pagan and Hall (1983) test of heteroskedasticity for instrumental variables estimation as well as the Breusch-Pagan (1979) and Cook-Weisberg (1983) tests for heteroskedasticity in linear regressions
62 For further discussion, see e.g., Hayashi (2000, 227-228, 407, and 417) and Baum et al.
(2003).
indicate that we face arbitrary heteroskedasticity in both stages of the estimation model.63 To control for theses problems I implement heteroscedastic and autocorrelation consistent (HAC) Newey-West type (Newey and West 1987) standard errors and variance-covariance estimates.
Doing so accounts for the increased inefficiency of the estimation caused by spatially and/or timely correlated observations of the residuals.
The proposed specification of the econometric model takes the set-up of the theoretical model and its empirical implications seriously and accounts for a variety of problems in the data structure. Therefore, the statistical estimation should provide reliable empirical results adding to our understanding of the domestic political processes of tax policy making.