The estimation of reaction functions under tax competition

Raffaele Miniaci; Paolo M. Panteghini; Giulia Rivolta

doi:10.1515/ger-2020-0137

Article

The estimation of reaction functions under tax competition

Raffaele Miniaci , Paolo M. Panteghini and Giulia Rivolta

Published/Copyright: December 10, 2021

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From the journal German Economic Review Volume 23 Issue 2

Abstract

Most of the empirical literature on tax competition has been using panel models in which each country’s tax rate responds to a weighted average of other countries’ tax rates, where weights are given. This approach imposes the reaction functions to be such that all tax rates are either strategic complements or strategic substitutes for all the countries. Moreover, it also requires that the intensity of the reactions of the countries to be proportional to the same set of given weights. Since no theoretical model relies on such restrictive assumptions, we regain flexibility in the empirical analysis by using Vector Autoregressive (VAR) models, where the sign and intensity of countries’ reactions may be heterogeneous. Using a Monte Carlo exercise, we show that if the objects of interest are the reactions to shocks in the tax rates of the other countries and there is no a priori knowledge of the structure of the economy, it can be convenient to opt for a VAR rather than a panel setup. A Bayesian VAR model on real data shows that strategic complementarity between some countries may co-exist with strategic substitutability between other countries, a finding with potential policy implications on the debate on tax competition.

Keywords: Tax competition; VAR models; reaction functions; strategic interactions

Appendix A Monte Carlo Exercise: Artificial dataset

Figure A1

Artificial datasets.

Appendix B Monte Carlo Exercise: Estimated matrices

This section reports the average matrices of reduced-form coefficients and errors’ variance-covariances computed across the Monte Carlo simulations. The subscripts P and V specify the matrices from the panel and VAR model respectively.

When the time-series dimension of the dataset is 30 observation, the matrices are as follows:

D ˆ 1 , P 30 = 0.1156 − 0.4488 − 0.2948 0.8643 0.1335 0.1335 0.1335 0.1335 0.1182 0.1182 0.1182 0.1182 − 0.0046 − 0.0756 0.3851 0.0339 − 0.0695 − 0.0304 0.1399 0.5431 Σ ˆ 1 , P 30 = 0.4557 0.7896 0.7652 0.6869 0.7896 1.9173 1.5275 1.2164 0.7652 1.5275 1.6837 1.1168 0.6869 1.2164 1.1168 1.0748 D ˆ 1 , V 30 = 0.0476 − 0.6069 − 0.3969 0.7403 − 0.0703 − 0.5386 − 0.2810 − 0.3306 0.0697 0.1548 0.0854 0.0716 0.0697 0.0662 0.1056 0.0339 0.16 0.3276 0.2123 0.3432 Σ ˆ 1 , V 30 = 0.4278 0.7589 0.733751 0.6499 0.7589 1.8483 1.4767 1.1642 0.7338 1.4767 1.6148 1.0682 0.6499 1.1642 1.0682 1.0151 D ˆ 2 , P 30 = 0.0625 − 0.5252 − 0.2529 0.9472 − 0.0441 − 0.0441 − 0.0441 − 0.0441 − 0.0945 − 0.0945 − 0.0945 − 0.0945 0.033 0.0662 0.1056 0.0339 0.16 0.3276 0.2123 0.3432 Σ ˆ 2 , P 30 = 0.4572 0.7957 0.7640 0.6869 0.7957 1.9354 1.5174 1.2185 0.764 1.5174 1.7093 1.1219 0.6869 1.2185 1.1219 1.0789 D ˆ 2 , V 30 = 0.0897 − 0.5187 − 0.3088 0.8009 − 0.0941 − 0.1196 − 0.0826 − 0.1421 − 0.0036 0.0304 − 0.0359 − 0.0563 − 0.0164 − 0.0176 − 0.1454 − 0.0741 − 0.0314 0.0235 0.001 0.1062 Σ ˆ 2 , V 30 = 0.4302 0.7606 0.7371 0.6536 0.7606 1.854 1.4817 1.1667 0.7371 1.4817 1.624 1.0728 0.6536 1.1667 1.0728 1.0208

When the time-series dimension of the dataset is 100 observation, the matrices are as follows:

D ˆ 1 , P 100 = 0.1036 − 0.4628 − 0.3137 0.8281 0.1671 0.1671 0.1671 0.1671 0.1405 0.1405 0.1405 0.1405 0.033 0.0662 0.1056 0.0339 0.16 0.3276 0.2123 0.3432 Σ ˆ 1 , P 100 = 0.4421 0.7885 0.7565 0.6697 0.7885 1.9165 1.5421 1.205 0.7565 1.5421 1.6713 1.101 0.6697 1.205 1.101 1.0442 D ˆ 1 , V 100 = 0.0663 − 0.5441 − 0.3929 0.7653 0.1 − 0.1308 − 0.0824 − 0.0874 0.0415 0.1446 0.0249 0.0395 0.0511 0.0689 0.1811 0.0528 0.0949 0.1553 0.1443 0.251 Σ ˆ 1 , V 100 = 0.4344 0.7797 0.747 0.6595 0.7797 1.8955 1.5246 1.1909 0.747 1.5246 1.6489 1.0868 0.6595 1.1909 1.0868 1.0281 D ˆ 2 , P 100 = 0.0566 − 0.5364 − 0.2666 0.9192 − 0.0169 − 0.0169 − 0.0169 − 0.0169 − 0.0896 − 0.0896 − 0.0896 − 0.0896 0.033 0.0662 0.1056 0.0339 0.16 0.3276 0.2123 0.3432 Σ ˆ 2 , P 100 = 0.443 0.7908 0.753 0.6686 0.7908 1.93 1.5269 1.2028 0.753 1.5269 1.6883 1.1038 0.6686 1.2028 1.1038 1.0458 D ˆ 2 , V 100 = 0.0669 − 0.5142 − 0.3709 0.7646 − 0.1011 − 0.0398 − 0.1386 − 0.1776 − 0.0212 0.0344 − 0.0654 − 0.0752 0.009 − 0.0024 − 0.0893 − 0.0367 − 0.0179 − 0.0084 0.0514 0.1329 Σ ˆ 2 , V 100 = 0.435 0.7801 0.7474 0.6603 0.7801 1.8981 1.5254 1.1914 0.7474 1.5254 1.6494 1.0873 0.6603 1.1914 1.0873 1.0292

Appendix C Results from the estimation of VAR models

Figure C1

IRFs of VAR model for tax rates, FDI inflows and GDP.

Figure C1 shows the IRFs to a shock in the EATR of the country in the heading of the subfigure on the tax rates of the four countries. In this VAR model, the order of the variables is: tax rates, FDI inflows and GDP. The blue line is the average response and the red dotted lines are the 90 % credible sets.

Figure C2

IRFs of VAR model for FDI inflows, tax rates and GDP.

Figure C2 shows the IRFs to a shock in the EATR of the country in the heading of the subfigure on the tax rates of the four countries. In this VAR model, the order of the variables is: FDI inflows, tax rates, and GDP. The blue line is the average response and the red dotted lines are the 90 % credible sets.

Figure C3

IRFs of VAR model for FDI inflows, GDP and tax rates.

Figure C3 shows the IRFs to a shock in the EATR of the country in the heading of the subfigure on the tax rates of the four countries. In this VAR model, the order of the variables is: FDI inflows, GDP, and tax rates. The blue line is the average response and the red dotted lines are the 90 % credible sets.

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Published Online: 2021-12-10

Published in Print: 2022-05-31

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https://doi.org/10.1515/ger-2020-0137

Keywords for this article

Tax competition; VAR models; reaction functions; strategic interactions