Tax rate and tax base competition for foreign direct investment

Abstract

This paper examines empirically whether governments behave strategically when setting corporate tax rates and tax bases, and—if so—how they react to changes in other countries’ tax rates and bases. Specifically, we estimate the slopes of tax policy reaction functions and examine how marginal changes in trade costs and GDP affect tax policies in the Nash equilibrium. The estimated slopes and comparative static effects can be rationalized in a model in which governments compete for foreign direct investment (FDI). Using estimated policy reaction functions, we demonstrate that observed changes in corporate tax systems are consistent with tougher competition for FDI following regional trade integration.

Appendix

1.1 Proofs

1.1.1 Proof of Lemma 1

We derive the EMTR for $H$; the derivation of $F$’s EMTR is equivalent. The after-tax profit generated by a firm located in $H$ and selling its output in both $H$ and $F$ is given by (7). The profit-maximizing output choices are

$$\begin{aligned} Q_{H}=\frac{n\left( 1-\alpha c\right) }{2},\text { and }Q_{F}=\frac{\left( 1-\alpha c-s\right) }{2}, \end{aligned}$$

which implies a maximized after-tax profit equal to

$$\begin{aligned} \hat{\Pi }_{H}=\left( 1-\tau \right) \frac{n\left( 1-\alpha c\right) ^{2}+\left( 1-\alpha c-s\right) ^{2}}{4}. \end{aligned}$$

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The tax revenue accruing to $H$ from such a firm is equal to

$$\begin{aligned} \tau \frac{n\left( 1-\alpha c\right) ^{2}+\left( 1-\alpha c-s\right) ^{2}}{4} -\frac{(1-\alpha )c\left( n\left( 1-\alpha c\right) +\left( 1-\alpha c-s\right) \right) }{2}, \end{aligned}$$

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where the second term adjusts for the fact that for $\alpha \ne 1$ there is an implicit subsidy/tax on the firm’s output.

Now it is straightforward to compute the social welfare country $H$ derives from the presence of domestic and multinational firms. In the case of domestic firms, the profit tax is simply redistributed to the local owners and thus does not affect welfare. The welfare associated with a good produced by a domestic firm is hence independent of $\tau$ and thus equal to the sum of consumer surplus (the first term) and profit adjusted for the implicit tax/subsidy (the last two terms):

$$\begin{aligned}&W_{H}(\alpha )=\frac{n\left( 1-\alpha c\right) ^{2}}{8}+\frac{n\left( 1-\alpha c\right) ^{2}+\left( 1-\alpha c-s\right) ^{2}}{4}\\&\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad -\frac{(1-\alpha )c\left( n\left( 1-\alpha c\right) +\left( 1-\alpha c-s\right) \right) }{2}. \end{aligned}$$

In the case of a good produced by a multinational, social welfare equals the sum of consumer surplus and tax revenue:

$$\begin{aligned}&W_{H}(\alpha ,\tau )=\frac{n\left( 1-\alpha c\right) ^{2}}{8}+\tau \frac{ n\left( 1-\alpha c\right) ^{2}+\left( 1-\alpha c-s\right) ^{2}}{4}\\&\qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad \qquad -\frac{(1-\alpha )c\left( n\left( 1-\alpha c\right) +\left( 1-\alpha c-s\right) \right) }{2}. \end{aligned}$$

In setting $\tau$, the government has to take into account the multinational’s participation constraint (8). Since this constraint has to be binding at the optimum, we can use it to eliminate $\tau$ in the welfare function. This yields as social welfare:

$$\begin{aligned} W_{H}(\alpha )-\left( 1-\tau ^{*}\right) \frac{\left( 1-\alpha ^{*}c\right) ^{2}+n\left( 1-\alpha ^{*}c-s\right) ^{2}}{4}. \end{aligned}$$

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Hence the optimal $\alpha$, denoted by $\bar{\alpha }$, is the same for domestic and multinational firms. Maximization of $W_{H}(\alpha )$ with respect to $\alpha$ gives:

$$\begin{aligned} \bar{\alpha }=\frac{\left( 2c-n+2cn\right) }{\left( n+2\right) c}. \end{aligned}$$

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1.1.2 Proof of Proposition 1

The equilibrium tax rate for $H$ is given by

$$\begin{aligned} \bar{\tau }(c,n,s)&=\frac{1}{2}\frac{\mathcal {A}s^{2}+\mathcal {B}s+\mathcal {C}}{\left( 2n+1\right) \mathcal {D}},\text { where} \\ \mathcal {A}&=\left( 2n+1\right) \left( 3-2n\right) \left( n+2\right) ^{2},\\ \mathcal {B}&=4\left( 2n+1\right) \left( n+2\right) \left( n^{2}-n-3\right) \left( 1-c\right) , \\ \mathcal {C}&=4\left( 3n^{2}+4n-1\right) \left( n+1\right) ^{2}\left( 1-c\right) ^{2}, \\ \mathcal {D}&=\left( n+2\right) ^{2}s^{2}-4\left( n+2\right) \left( n+1\right) \left( 1-c\right) s+4\left( n+1\right) ^{3}\left( 1-c\right) ^{2}. \end{aligned}$$

The equilibrium tax rate for $F$ is

$$\begin{aligned} \bar{\tau }^{*}(c,n,s)&= \frac{1}{2}\frac{\mathcal {E}s^{2}-\mathcal {F}s+ \mathcal {G}}{\left( n+2\right) ^{2}\mathcal {H}},\text { where} \\ \mathcal {E}&= \left( n+2\right) ^{2}\left( 2n+1\right) ^{2}, \\ \mathcal {F}&= 4\left( 2n+1\right) \left( n+2\right) \left( 5n+3n^{2}+1\right) \left( 1-c\right) , \\ \mathcal {G}&= 4\left( 8n+5n^{2}+5\right) \left( n+1\right) ^{2}\left( 1-c\right) ^{2}, \\ \mathcal {H}&= n\left( 2n+1\right) ^{2}s^{2}-4n\left( n+1\right) \left( 2n+1\right) \left( 1-c\right) s+4\left( n+1\right) ^{3}\left( 1-c\right) ^{2}. \end{aligned}$$

Taking the derivatives with respect to $s$, we have

$$\begin{aligned} \frac{\partial \bar{\tau }}{\partial s}&= \frac{2\left( 1-c\right) (n+2)}{2n+1}\frac{\mathcal {I}s^{2}-\mathcal {J}s+\mathcal {K}}{\mathcal {D}^{2}}, \\ \frac{\partial \bar{\tau }^{*}}{\partial s}&= \frac{2\left( 2n+1\right) ^{2}\left( 1-c\right) }{\left( n+2\right) ^{2}}\frac{\mathcal {L}s^{2}- \mathcal {M}s+\mathcal {N}}{\mathcal {H}^{2}},\text { where} \\ \mathcal {I}&= n^{2}\left( n+2\right) ^{2}\left( 2n+1\right) , \\ \mathcal {J}&= 2\left( n-1\right) \left( n+2\right) \left( 4n^{2}+7n+4\right) \left( n+1\right) ^{2}\left( 1-c\right) , \\ \mathcal {K}&= 4\left( 2n^{3}+2n^{2}-3n-4\right) \left( n+1\right) ^{3}\left( 1-c\right) ^{2}, \\ \mathcal {L}&= n\left( 2n+1\right) \left( n+2\right) \left( 2n^{2}+2n-1\right) , \\ \mathcal {M}&= 2\left( n-1\right) \left( 4n^{2}+7n+4\right) \left( n+1\right) ^{2}\left( 1-c\right) , \\ \mathcal {N}&= 4\left( n^{2}-2n-2\right) \left( n+1\right) ^{3}\left( 1-c\right) ^{2}. \end{aligned}$$

These derivatives are continuous in $s$ and at $s=0$ are equal to

$$\begin{aligned} \frac{\partial \bar{\tau }}{\partial s}&= \frac{1}{2}\frac{\left( 2n^{3}+2n^{2}-3n-4\right) \left( n+2\right) }{\left( 1-c\right) \left( n+1\right) ^{3}\left( 2n+1\right) }, \\ \frac{\partial \bar{\tau }^{*}}{\partial s}&= \frac{1}{2}\frac{\left( 2n+1\right) ^{2}\left( n^{2}-2n-2\right) }{\left( 1-c\right) \left( n+1\right) ^{3}\left( n+2\right) ^{2}}. \end{aligned}$$

For $n$ sufficiently big, both derivatives are positive in the neighborhood of $s=0$.

The equilibrium depreciation allowances are

$$\begin{aligned} \bar{\delta }(c,n,s)&= \frac{\mathcal {O}s^{2}-\mathcal {P}s+\mathcal {Q}}{ c\left( n+2\right) \left( \mathcal {A}s^{2}+\mathcal {B}s+\mathcal {C}\right) }\\ \bar{\delta }^{*}(c,n,s)&= \frac{\mathcal {R}s^{2}-\mathcal {S}s+\mathcal {T}}{c\left( \mathcal {E}s^{2}-\mathcal {F}s+\mathcal {G}\right) }\text {, where}\\ \mathcal {O}&= \left( 2n+1\right) \left( n+2\right) ^{2}\left( \left( 2-4c\right) n^{2}-n+6c\right) , \\ \mathcal {P}&= 4\left( n+2\right) \left( 2n+1\right) \left( 1-c\right) \left( \left( 1-2c\right) (n^{3}+n^{2})-\left( 1-6c\right) n+6c\right) , \\ \mathcal {Q}&= 4\left( n+1\right) ^{2}\left( 1-c\right) ^{2}\left( \left( 2c+1\right) n^{3}+\left( 8c+2\right) n^{2}+\left( 4c+3\right) n-2c\right) ,\\ \mathcal {R}&= \left( 2n+1\right) \left( n+2\right) ^{2}\left( 2c+2n-1\right) , \\ \mathcal {S}&= 4\left( n+2\right) \left( 2n+1\right) \left( 1-c\right) \left( \left( 2c+1\right) n^{2}+\left( 4c+1\right) n-\left( 1-2c\right) \right) , \\ \mathcal {T}&= 4\left( n+1\right) ^{2}\left( 1-c\right) ^{2}\left( 2c+2n+4cn^{2}+6cn+n^{2}+3\right) . \end{aligned}$$

The derivatives with respect to $s$ are continuous in $s$ and, evaluated at $s=0$, are equal to

$$\begin{aligned} \frac{\partial \bar{\delta }}{\partial s}&= \left( -2\right) \frac{\left( 2n^{3}+2n^{2}-3n-4\right) \left( 2n+1\right) n}{\left( 3n^{2}+4n-1\right) ^{2}\left( n+1\right) c}, \\ \frac{\partial \bar{\delta }^{*}}{\partial s}&= \left( -2\right) \frac{ \left( n+2\right) ^{2}\left( n^{2}-2n-2\right) \left( 2n+1\right) }{\left( 5n^{2}+8n+5\right) ^{2}\left( n+1\right) c}. \end{aligned}$$

Both derivatives are negative in the neighborhood of $s=0$ for sufficiently large $n$.

1.1.3 Proof of Proposition 2

At $s=0$, we obtain

$$\begin{aligned} \frac{\partial (\bar{\tau }-\bar{\tau }^{*})}{\partial s}&= \frac{\left( 58n+39n^{2}+6n^{3}+2n^{4}+30\right) \left( n-1\right) }{2\left( 1-c\right) \left( n+1\right) ^{2}\left( n+2\right) ^{2}\left( 2n+1\right) }>0, \\ \frac{\partial (\bar{\delta }-\bar{\delta }^{*})}{\partial s}&= \frac{ \left( -2\right) \left( 2n+1\right) \left( n-1\right) \mathcal {Z}}{\left( 8n+5n^{2}+5\right) ^{2}\left( 4n+3n^{2}-1\right) ^{2}c}<0, \\ \text {where}\quad \mathcal {Z}&\equiv \left( 148n+429n^{2}+492n^{3}+350n^{4}+168n^{5}+41n^{6}-8\right) \end{aligned}$$

1.1.4 Proof of Proposition 3

At $s=0$ and assuming that $n$ is sufficiently big, we obtain the following signs for the derivatives:

$$\begin{aligned} \frac{\partial \bar{\tau }}{\partial n}&= \frac{1}{2}\frac{\left( 10n+n^{2}+7\right) }{\left( 2n+1\right) ^{2}\left( n+1\right) ^{2}}>0, \\ \frac{\partial \bar{\tau }^{*}}{\partial n}&= \left( -\frac{1}{2}\right) \frac{\left( 3n+6n^{2}+5n^{3}+4\right) }{\left( n+2\right) ^{3}\left( n+1\right) ^{2}}<0, \\ \frac{\partial \bar{\delta }}{\partial n}&= 2\frac{\left( 1-c\right) \left( 2n^{4}-11n^{2}-2n^{3}-4n-3\right) }{\left( 4n+3n^{2}-1\right) ^{2}\left( n+2\right) ^{2}c}>0, \\ \frac{\partial \bar{\delta }^{*}}{\partial n}&= \left( -2\right) \frac{ \left( 1-c\right) \left( 10n+n^{2}+7\right) }{\left( 8n+5n^{2}+5\right) ^{2}c }<0. \end{aligned}$$

1.1.5 Proof of Proposition 4

For $s=0$ and $n$ sufficiently big, we obtain $\frac{\partial \bar{\tau }}{ \partial c}=0$, $\frac{\partial \bar{\tau }^{*}}{\partial c}=0$, and

$$\begin{aligned} \frac{\partial \bar{\delta }}{\partial c}&= -\frac{\left( 2n+n^{2}+3\right) n }{\left( 3n^{2}+4n-1\right) \left( n+2\right) c^{2}}<0 \\ \frac{\partial \bar{\delta }^{*}}{\partial c}&= -\frac{\left( 2n+n^{2}+3\right) }{\left( 8n+5n^{2}+5\right) c^{2}}<0. \end{aligned}$$

For $n=1$ (symmetric countries) and $s>0$, we find that

$$\begin{aligned} \frac{\partial \bar{\tau }}{\partial c}=\frac{\left( -6\right) \left( 32\left( 1-c\right) ^{2}-9s^{2}\right) s}{\left( 24cs-24s-64c+32c^{2}+9s^{2}+32\right) ^{2}}<0\text { for }s\text { close to zero,} \end{aligned}$$

and

$$\begin{aligned} \frac{\partial \bar{\delta }}{\partial c}=\left( -\frac{1}{3}\right) \frac{ \mathcal {K}}{\left( 8-8c-3s\right) ^{2}\left( 4-4c-3s\right) ^{2}c^{2}}<0, \end{aligned}$$

for $s$ can $c$ small enough, where

$$\begin{aligned} \mathcal {K}&= 3840cs-1536s-4096c+6144c^{2}-4096 c^{3}+1024c^{4}+1008s^{2} \\&-\,432s^{3}+81s^{4}-2016cs^{2}-2304c^{2}s+648cs^{3}-768c^{3}s+768c^{4}s \\&+1008c^{2}s^{2}-216c^{2}s^{3}+1024. \end{aligned}$$

1.2 Data sources

The data used in the present analysis fall into three categories: ones on statutory corporate tax rates and depreciation allowances (the dependent variables of our empirical analysis); explanatory variables which are supposed to measure country size ($n$), production costs ($c$), and trade costs ($s$) in the theoretical analysis; and variables which measure the relative independence of tax parameters across countries as a function not only of unilateral $n$, $c$, and $s$, but also of bilateral integration among the economies—we will use “natural” bilateral trade flows and, in the sensitivity analysis, stocks of bilateral foreign direct investment as measures thereof. Let us summarize in this subsection of the appendix which variables we use and which sources they come from.

Information on tax codes is primarily taken from the following online sources of the International Bureau of Fiscal Documentation (IBFD): Asia-Pacific—Taxation & Investment; Central/Eastern Europe—Taxation & Investment; Corporate Taxation in Europe; Global Tax Surveys; and Tax News Service.

In addition, the information on tax law from a number of printed publications has been used:

• Arthur Anderson, 1992–1996. A tax guide to Europe, London: Arthur Andersen.

• Baker&McKenzie, 1999. Survey of the effective tax burden in the European Union, Amsterdam.

• Commission of the European Communities, 1992. Report of the committee of independent experts on company taxation, Brussels and Luxembourg.

• Commission of the European Communities, 2001. Towards an internal market without tax obstacles. A strategy for providing companies with a consolidated corporate tax base for their EU-wide activities, COM (2001) 582 final, Brussels.

• Coopers & Lybrand, 1991–1998. International tax summaries : a guide for planning and decisions, Chichester: John Wiley & Sons.

• Ernst&Young, 2003. Company taxation in the new EU Member states survey of the tax regimes and effective tax burdens for multinational investors, Frankfurt am Main.

• Ernst&Young, 1998–2003. Worldwide Corporate Tax Guide, Frankfurt am Main.

• IBFD, 1994–1999. Central and East European Tax Directory, Amsterdam.

• IBFD, 1990–2005. European Tax Handbook, Amsterdam.

• IBFD, 1990–2001. Steuerberaterhandbuch Europa, Bonn: Stollfuss.

• IBFD, 1990–1994. Taxation in European Socialist Countries, Amsterdam.

• Matthew Bender, 1990–2003. Foreign tax and trade briefs : international withholding tax treaty guide, New York: LexisNexis.

• Nexia International, 1992–2003. The international Handbook of Corporate and Personal Taxation, London: LexisNexis.

• OECD, 1991. Taxing Profits in a Global Economy: Domestic and International Issues, Paris: Organisation for Economic Co-operation and Development.

• PriceWaterhouseCoopers, 1999. Spectre: Study of potential of effective corporate tax rates in Europe, Report commissioned by the Ministry of Finance in the Netherlands, Amsterdam.

• PriceWaterhouseCoopers, 1990–2004. Corporate taxes: worldwide summaries, Hoboken: Wiley.

• Yoo, K.-Y., 2003. Corporate taxation of foreign direct investment income 1991–2001, OECD Economics Department Working Paper No. 365, Paris: Organisation for Economic Co-operation and Development.

These sources provide information about the number of years for which depreciations can be claimed (i.e., the “depreciation rate”), the depreciation system (i.e., whether there depreciation follows a straight line or a declining balance schedule), and on (general) investment incentives (e.g., on the existence of extra first-year allowances in Australia, Poland, or Spain). Otherwise, the computation of the net present value of depreciation allowances follows King and Fullerton (1984) and Devereux and Griffith (1998). In line with those authors, we use the most generous option of depreciation in case that the model firm has several opportunities to choose from. The data used here are a (balanced) subset of the ones in Egger et al. (2009).

1.2.1 Measures of Nash-equilibrium-shifting variables $n$, $c$, and $s$

In Tables 1, 2, and 3, we associate country size ($n$) mainly with log real GDP, production costs ($c$) mainly with log GDP-per-capita, and trade costs ($s$) mainly with a trade cost index. For instance, this is the case throughout Tables 1 and 2. The source of the data on real GDP and GDP per capita is the World Bank’s World Development Indicators 2008. The trade cost index is published by the World Economic Forum and has kindly been provided by Keith Maskus.

In the sensitivity analysis (Table 3), we use log population instead of log real GDP as an alternative measure for $n$, log manufacturing wages per worker instead of log GDP per capita to measure production costs $c$, and log unilateral cost–insurance–freight/free-on-board (c.i.f./f.o.b.) ratios of goods trade flows as a measure of trade costs ($s$). These variables are taken from the following sources. Population is based on figures in the World Bank’s World Development Indicators. Average wages per worker in manufacturing stem from United Nations Industrial Development Organization’s Industrial Statistics Database. To calculate unilateral c.i.f./f.o.b. ratios, we use bilateral aggregate goods trade data from the United Nations’ World Trade Database. More specifically, we take all countries’ imports from a given economy and divide them by this country’s exports into all economies in our sample in a given year. Theoretically, this ratio should be larger than unity and the deviation from unity should measure unilateral trade costs in a given year with the covered countries. It is well known that c.i.f./f.o.b. ratios are not a perfect measure of trade costs, since they are prone to measurement error. However, Limão and Venables (2001) illustrated that they are at least systematically correlated with (for most countries unobserved) true trade costs.

1.2.2 Measures of the strength of interdependence between domestic and foreign tax rates

In Tables 1, 2, and 3, we pursue a variety of approaches to weight foreign countries’ tax parameters, i.e., to parameterize the channel and the decay of tax competition in some metric. Since economic integration is a key factor determining tax competition in our theoretical analysis, our benchmark results in Table 1 are based upon “natural” goods-trade-weighted tax parameters. For this, we take bilateral exports among all countries in our sample for the years 1982–2000 from United Nations’ World Trade Database. How we then proceed to obtain “natural” bilateral (export plus import) trade weights is described in the last subsection of this Appendix.

Alternatively, we use inverse bilateral distances between all countries (Table 2), contiguity-based weights (Table 3) and “natural” bilateral stock-of-foreign-direct-investment-based weights (Table 3). Bilateral distance and a bilateral contiguity indicator is taken from the Geographical Database published by the Centre d’Etudes Prospectives et d’Informations Internationales (CEPII). Bilateral stocks of outward FDI are taken from the FDI online database of the United Nations Conference on Trade and Development (UNCTAD). As for “natural” bilateral trade weights, the last subsection of this Appendix describes how we obtain “natural” bilateral (outward plus inward) FDI stock weights.

1.3 Descriptive statistics

Table 6 summarizes the averages and standard deviations for the key variables in our analysis: statutory corporate tax rates and depreciation allowances as the two endogenous variables and measures of market size (GDP), production costs (GDP/capita), and trade costs.

Table 6 Descriptive statistics

Summary statistics on other variables used in the sensitivity analysis in Table 3 are available from the authors upon request.

1.4 IV-2SLS GMM estimator

For the definition of the IV-2SLS GMM estimator and its heteroskedasticity and spatial as well as serial autocorrelation-consistent (SHAC) estimator of the variance–covariance matrix in the spirit of Driscoll and Kraay (1998), it will be useful to introduce some further notation. Recall that we indicate countries by $i=1,...,N$ and time periods by $t=1,...,T$. For convenience, let us use the running index $\ell =\tau ,\delta$ to refer to the two Eqs. (13) and (14), respectively. Furthermore, define the $N\times (K+2)$ matrix $\mathbf {Z}_{t}=[\mathbf {W}$ $\mathbf {\tau }_{t},\mathbf {W}$ $\mathbf {\delta }_{t},\mathbf {X}_{t}]$ and refer to the $NT\times (K+2)$ stacked version of this matrix (covering all years) as $\mathbf {Z}$. IV-2SLS potentially involves sets of instruments which differ across equations. Define the number of instruments in equation $\ell$ as $P_{\ell }\ge K+2$ and collect the instruments for equation $\ell$ and all years into the $NT\times P_{\ell }$ matrix $\mathbf {D}_{\ell }$.¹⁹ Then, we may define the projection $\hat{\mathbf {Z}}_{\ell }=\mathbf {D}_{\ell }( \mathbf {D}_{\ell }^{\prime }\mathbf {D}_{\ell })^{-1}\mathbf {D}_{\ell }^{\prime }\mathbf {Z}_{\ell }$. Later on, we will refer to one row of $\hat{ \mathbf {Z}}_{\ell }$ by the $1\times (K+2)$ vector $\hat{\mathbf {z}}_{\ell it}$. Finally, collect the IV-2SLS parameters for equation $\ell$ into the $(K+2)\times 1$ vector $\mathbf {\theta }_{\ell }$. Let us refer to the (inefficient) estimate of the $(K+2)\times (K+2)$ variance–covariance matrix of the parameters as $\hat{\mathbf {V}}_{\ell }=(\mathbf {Z}_{\ell }^{\prime } \mathbf {D}_{\ell }\mathbf {D}_{\ell }^{\prime }\mathbf {Z}_{\ell })^{-1}$.

Driscoll and Kraay (1998) suggest averaging the moment conditions to obtain $\mathbf {h}_{t}(\varvec{\theta }_{\ell })=\frac{1}{N}\sum _{i=1}^{N}\mathbf {h} _{it}(\varvec{\theta }_{\ell })$. Let us use the notation $\mathbf {h}_{\ell t}=\mathbf {h}_{t}(\varvec{\theta }_{\ell })$ and refer to one row of $\mathbf {D}_{\ell }$ by $\mathbf {d}_{\ell it}$ to write

$$\begin{aligned} \mathbf {h}_{\ell t}=\frac{1}{N}\sum _{i=1}^{N}\mathbf {d}_{\ell it}\mathbf {u} _{\ell it};\qquad \mathbf {h}_{\ell t^{\prime }}=\frac{1}{N} \sum _{i=1}^{N}\mathbf {d}_{\ell it^{\prime }}\mathbf {u}_{\ell it^{\prime }} \end{aligned}$$

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with $t,t^{\prime }=1,...,T$. Furthermore, let us define the matrix

$$\begin{aligned} \mathbf {S}_{\ell T}=\frac{1}{T}\sum _{t=1}^{T}\sum _{t^{\prime }=1}^{T}E[ \mathbf {h}_{\ell t}\mathbf {h}_{\ell t^{\prime }}^{\prime }] \end{aligned}$$

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and note that $E[\mathbf {h}_{\ell t}\mathbf {h}_{\ell t^{\prime }}^{\prime }]= \frac{1}{N^{2}}\sum _{i=1}^{N}\mathbf {d}_{\ell it}\mathbf {d}_{\ell it^{\prime }}^{\prime }E[u_{\ell it}u_{\ell it^{\prime }}]$.

A HAC estimator of the variance–covariance matrix with IV-2SLS in the spirit of Driscoll and Kraay (1998) is then defined as

$$\begin{aligned} \hat{\mathbf {V}}_{HHC}=(\mathbf {Z}^{\prime }\mathbf {D}_{\ell }\hat{\mathbf {S} }_{\ell T}^{-1}\mathbf {D}_{\ell }^{\prime }\mathbf {Z})^{-1}. \end{aligned}$$

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Driscoll and Kraay (1998) prove that such a Newey and West (1987)-type estimator of the variance–covariance matrix relies on fairly weak assumptions.

1.5 “Natural” trade and foreign direct investment-based weights matrices in the empirical model

In Table 1, we use “natural” trade and in Table 3 “natural” foreign direct investment as weights to compute competitor countries’ statutory tax rates and depreciation allowances. They are derived from cross-sectional empirical models using average bilateral exports and stocks of outward foreign direct investment, respectively, as the dependent variable for the period 1982–2000 for all pairings among the 43 countries in our analysis. Apart from exporter (parent country) and importer (host country) fixed effects, the empirical models include the following explanatory variables of exports or outward foreign direct investment: log bilateral distance, common border between exporter and importer, and a free trade area indicator (as reported to the World Trade Organization).

Since both trade flows and stocks of foreign direct investment take zero values, we follow Santos Silva and Tenreyro (2006) and estimate the equations by a Poisson pseudo-maximum-likelihood routine. In Table 7, we summarize the coefficient estimates for the model determining “natural” bilateral trade flows which are used to weight foreign statutory corporate tax rates and depreciation allowances for each year in Table 1. The associated model predictions are then used to compute predicted (“natural”) exports plus imports and outward plus inward stocks of FDI, respectively, for each country pair. This results in two matrices whose elements are divided by the corresponding row sums and diagonal elements are set to zero to obtain a matrix $\mathbf {W}$ which is used to weight a country’s competitors’ tax parameters.

Table 7 Poisson pseudo-maximum likelihood regression to predict bilateral trade flows (the dependent variable is nominal bilateral exports in U.S. dollars)

The estimation results for bilateral FDI stocks which are used as an alternative weighting scheme in the sensitivity analysis at the bottom of Table 4 are available from the authors upon request.

1.6 Further regression results

In this part of the Appendix, we summarize the results from three further specification which—as in Table 1—employ spatial weights that are based on natural trade weights. We summarize the corresponding parameter estimates in Tables 8 and 9, where for ease of presentation we list separately the results pertaining to tax rates and those pertaining to depreciation allowances. In the tables, we refer to the specifications as an Alternative specification, an Augmented specification A, and an Augmented specification B. The Alternative specification eliminates the trade cost variable but includes the dependency ratio (the fraction of the population of a country that is younger than 15 years or older than 65 years) and the urbanization rate (the fraction of the population that lives in metropolitan areas)—both from the World Bank’s World Development Indicators—together with fixed time effects and a time-lagged right-hand side variable (not instrumented due to the sufficiently long time series for a small-enough bias). Notice that also other authors such as Devereux et al. (2008) and Davies and Voget (2010) estimated models with time effects and a lagged-dependent variable. However, the effects become hard to interpret, especially, when simulations of counterfactual equilibria are at stake (since some variables may be fixed in estimation but not exogenous to counterfactual shocks in fundamentals). The Augmented specification A excludes a time lag but, apart from the regressors as in Table 1, includes fixed time effects as well as the dependency and urbanization ratios. Finally, Augmented specification B is similar to Augmented specification A but additionally includes a time-lag of the left-hand side variable.

Table 8 Modified reaction function estimation for corporate tax rates (potential-trade-based third-country weights)

Table 9 Modified reaction function estimation for depreciation allowances (potential-trade-based third-country weights)

The results of the dynamic specifications (including a time lag of the left-hand side variable) exhibit smaller point estimates of the spatial lags of the tax instruments and also the Nash equilibrium shifters than in Table 1. However, notice that the coefficients are not directly comparable to Table 1, not only because trade costs are excluded in Tables 8 and 9, but also because the parameters reflect short-run parameters in Alternative specification of Tables 8 and 9 (and also in Augmented specification B). Market size takes on the wrong sign, which makes us suspicious about the exclusion of the (Table 1 highly relevant) trade cost variable. However, except for market size, the earlier findings are not qualitatively affected from excluding fixed time effects or adjustment costs. Furthermore, including the dependency ratio, the urbanization ratio, and fixed time effects in the specification as of Table 1 has little qualitative bearing for the effects of interest to this paper, as can be seen from the results for Augmented specification A. This is also not changed drastically when including the lagged-dependent variable in Augmented specification B on top of the ones used in Augmented specification A.