2. On the relationship between constraints on the executive and tax revenues

How do countries learn to tax? Recent political economy explanations have argued that the presence of political institutions placing limits on the executive power is a key long-term factor explaining fiscal capacity.Footnote ⁵ This argument suggests that greater constraints on the executive power have a positive effect, because they provide stronger incentives for incumbent groups to invest in tax systems. In particular, as Besley and Persson (Reference Besley and Persson2011) also argue, ‘constraints on the executive will diminish the concern that the government is run in the interests of a narrow group’ (Bardhan, Reference Bardhan2016: 871). Such mechanisms may include ‘various kinds of checks and balances including constitutional constraints on executive power, separation of powers, electoral rules, independent judiciary, free media and other accountability mechanisms for the state leadership’ (Bardhan, Reference Bardhan2016: 871). Similarly, according to Dincecco (Reference Dincecco2017: 21–22), the presence of ‘an institutional player within the national government that has the formal political authority to regularly monitor state finances’ is an essential mechanism for effective statehood. In parliamentary democracies, such a role will be played by an effective parliament, one which the political leader cannot form, control or disband at will. Here, an effective parliament can ‘regularly oversee the state's budget, including authority over taxation, the right to audit previous government spending, and the right to veto new expenditures’ (Dincecco, Reference Dincecco2017: 22). In autocracies, such checks and balances on the executive may be weaker. However, as Besley and Kudamatsu (Reference Besley, Kudamatsu and Helpman2008) point out, even in autocracies, there may be constraints placed on the autocrat by government insiders – the ‘selectorate’ (Bueno de Mesquita et al., Reference Bueno de Mesquita, Smith, Siverson and Morrow2003) – whose power does not depend on the current executive and who can remove poorly performing executives, if necessary. Thus, limits on executive power promote a common interest environment and may translate into new and more sophisticated forms of taxation and more effective revenue authorities (e.g. Besley and Persson, Reference Besley and Persson2009).Footnote ⁶ The empirical literature, although still rather thin, has hitherto largely supported the hypothesis that constraints on the executive have a long-run positive impact on fiscal capacity and, in turn, on the amount of revenues collected.Footnote ⁷ It is questionable, however, whether one can separate the forces that lead from political institutions to the development of the tax system from those that lead from taxation to institutional change. In an authoritative survey on taxation and development, Besley and Persson (Reference Besley, Persson, Auerbach, Chetty, Feldstein and Saez2013: 106) note: ‘States that raise significant revenues will find themselves facing strong demands for accountability and representation, creating a two-way relationship between political development and the growth of the tax system. Little is yet known about this relationship. But it seems far from coincidental that states that are able to appropriate nearly half of national income in the form of taxation have also evolved strong political institutions, particularly those that constrain the use of such resources’.

The foregoing quote implies that one aspect requiring systematic analysis is the dynamics of the relationship between constraints on the executive and tax revenues: whether they co-evolve in the long run. A separate literature, mainly based on the European experience, has argued that central to how tax systems develop is also the bargaining process between the state and the citizenry. Citizens enter a fiscal contract with the state, which involves an exchange of tax revenues for goods and services as they have more control over its action (Bräutigam et al., Reference Bräutigam, Fjeldstad and Moore2008; Levi, Reference Levi1988; Moore, Reference Moore2007; Ross, Reference Ross2004; Tilly, Reference Tilly1992). This implies that there may be a feedback effect from tax revenues to political institutions placing limits on the executive power. As an increase in the amount of revenues levied comes with greater demand for scrutiny over the government actions, one can hypothesise also that increased tax revenues could in turn reinforce executive constraints, as taxpayers will demand greater accountability from the ruler.Footnote ⁸ This ultimately suggests that there may be a long-run relationship between executive constraints and tax revenues such that they are cointegrated. Existing empirical literature has not investigated this proposition yet. Some empirical literature on the structural determinants of tax revenues has looked at the effect of political representation (Aidt and Jensen, Reference Aidt and Jensen2009; Andersson, Reference Andersson2018; Cheibub, Reference Cheibub1998; Timmons, Reference Timmons2010) or elite competition (Beramendi et al., Reference Beramendi, Dincecco and Rogers2018) on taxation. Others study the effect of taxation on regime type (Dom, Reference Dom2018; Ross, Reference Ross2004). Some of these studies have used historical macro data (Albers et al., Reference Albers, Gerven and Suesse2020; Andersson, Reference Andersson2018; Beramendi et al., Reference Beramendi, Dincecco and Rogers2018). Nonetheless, no study explicitly focuses on constraints on the executive or, above all, on the dynamic aspects of its relationship with taxation.

Is the existence and nature of a long-run relationship different for different forms of taxation? The dynamic relationship between constraints on the executive and taxation may be different for different taxes because constraints on the executive, by supporting the emergence of fiscal capacity, may also have an effect on the composition of tax revenues. Investments in fiscal capacity bring greater organisational ability on the part of revenue authorities, so that states can ‘earn’ taxes: for example, states can increasingly substitute revenues from taxing land or its produce and taxes on the movement of goods (via customs on external borders and various types of taxes on internal sales and excises, such as salt, tobacco) with revenues from taxes levied on accounting categories (e.g. income, profits, value added), which require greater organisational effort. This should result in a transition from taxes with a narrow base to broad-based taxation over time. Indeed, Besley and Persson (Reference Besley, Persson, Auerbach, Chetty, Feldstein and Saez2013: 56–63) show that one of the stylised facts on taxation and development is that more advanced economies tend to rely much more on broad-based taxes compared to less developed ones: this is the result of changes in the composition of revenues from trade taxes and excises towards labour income and other broad bases.Footnote ⁹ Since broad-based taxes are consensual, they require a fiscal bargain between the state and the citizens, where compliance with taxation is exchanged for institutionalised influence over the mode of taxation and the use of revenues. Hence, broad-based taxes are more likely to have a feedback effect into executive constraints rather than narrow-based taxation, so that a long-run relationship may be more likely to exist for direct taxes, such as on income, rather than trade taxes and excises.

How general is the proposition that there is a long-run dynamic relationship between executive constraints and taxation? The dynamics of the relationship between constraints on the executive and taxation may be different in different contexts because the effect of constraints on the executive on government revenues, and how fiscal bargaining develops over time, may depend on country-specific factors, such as culture and history. First, the amount and composition of revenues collected depend on the level of tax morale (Luttmer and Singhal, Reference Luttmer and Singhal2014), a culturally driven aspect of tax compliance (Andriani et al., Reference Andriani, Bruno, Douarin and Stepien-Baig2021). Second, colonial heritage matters: colonial governors appointed on the basis of patron-and-client ties may be less willing to invest in fiscal capacity or enter a fiscal bargain with the citizens (Xu, Reference Xu2019). Third, a civic culture based on reciprocal obligations facilitates, and sustains over time, a fiscal bargain that does not develop if such culture is lacking (Besley, Reference Besley2019). Fourth, taxation preferences in different countries may reflect different preferences for redistribution (Alesina and Angeletos, Reference Alesina and Angeletos2005). Further arguments include how the structure of the economy, such as the reliance on natural resources rents, aid and the prevalence of agriculture, may adversely affect the emergence of tax systems and their functioning (see Moore, Reference Moore2007). This ultimately suggests that the dynamic relationship between constraints on the executive and tax revenues may be heterogeneous across countries, because it is subject to country-specific cultural, economic and political history. This may contribute to explaining why certain countries have seen a full transition from a domain to a tax state and others have not.

In the next sections, we produce evidence on cointegration between executive constraints and taxation, testing whether a long-run relationship exists for different taxes and in different contexts.

3. Data

Empirical research on fiscal development often faces a trade-off: choosing between a dataset with substantial cross-sectional (number of countries) and short-time dimensions and a dataset with a long temporal dimension (number of years observed) and relatively few countries. In our case, studying the dynamic relationship between executive constraints and taxation means documenting long-run phenomena that originate from institutional changes, and hence are best observed with measures spanning many decades. Consequently, our analysis focuses on measures that have substantial time series variation, for as many countries as possible. In particular, we use historical data on central government tax revenues covering the period from 1800 to 2012 obtained from the Financing the State dataset (Andersson and Brambor, Reference Andersson and Brambor2019), which includes 31 countries: all countries from South America, North America and Western European countries with a population of more than one million, plus Australia, Japan, Mexico and New Zealand.Footnote ¹⁰ This dataset provides a rich set of comparable taxation measures and has the crucial advantage of providing the longest temporal coverage. The first measure we select is the ratio of central government total tax to GDP, as it measures the extent to which a state is financed by taxes. We investigate also if the dynamic relationship between constraints on the executive and taxation may be different for different taxes and, in particular, on differences between broad- and narrow-based taxes. We exploit, for this purpose, various measures on tax composition. We use the share of total taxes collected from direct and indirect taxation. Such variables broadly map into the narrow- and broad-based taxes categorisation, but they do not perfectly reflect it.Footnote ¹¹ Hence, we focus also on the share of specific taxes, as they may more neatly reflect this categorisation. We select measures of income, consumption and trade taxes as a share of total central tax revenues. Income tax is a prime example of broad-based taxation. Instead, trade revenues are an example of narrow-based taxes. Finally, consumption taxes are a significant share of total revenues, hence it should be considered, but they may capture both narrow- and broad-based taxes.

To measure political institutions that constrain the power of the executive – expressing to what extent they provide institutionalised checks and balances – we resort to the V-Dem dataset (Coppedge et al., Reference Coppedge, Gerring, Knutsen, Lindberg, Teorell, Altman, Bernhard, Fish, Glynn, Hicken, Luhrmann, Marquardt, McMann, Paxton, Pemstein, Seim, Sigman, Skaaning, Staton, Wilson, Cornell, Alizada, Gastaldi, Gjerløw, Hindle, Ilchenko, Maxwell, Mechkova, Medzihorsky, von Römer, Sundström, Tzelgov, Wang, Wig and Ziblatt2020). Apart from being methodologically innovative and covering over 200 years for a global sample of countries, it provides a more granular measure of executive constraints. Checks and balances can operate through the legislative and judicial branches. The former works through parliamentary systems, which institutionally oversee and audit the state budget, and the latter through independent judicial systems enforcing the rule of law. The V-Dem dataset provides variables measuring each aspect. The Judicial Constraints on the executive index (v2x_jucon) addresses the following question: ‘To what extent does the executive respect the constitution and comply with court rulings, and to what extent is the judiciary able to act in an independent fashion?’. The Legislative Constraints on the executive index (v2xlg_legcon) addresses the question: ‘To what extent are the legislature and government agencies, e.g. controller general, general prosecutor or ombudsman, capable of questioning, investigating and exercising oversight over the executive?’. We use such measures individually or combined in a single index, labelled Executive Constraints, which is the arithmetic mean of the legislative and judicial constraints. The variables range from 0 to 100: lower values indicating lower constraints on the power of the executive (hence more executive discretion) and vice versa.Footnote ¹²

Figure 1, where variables are averaged over the entire period, offers a visualisation of the long-run relationship between taxation and executive constraints. One apparent fact is that countries with greater constraints on the executive tend to have higher central tax-to-GDP ratios, implying that executive constraints are associated with greater reliance of states on taxation. Second, more effective constraints on the executive tend to shift the composition of tax revenues. Countries with greater constraints on the executive tend to collect a greater share of direct taxes. Vice versa, there is a weak, negative correlation between executive constraints and the share of indirect taxes.Footnote ¹³ While Figure 1 does not lend itself to causal interpretation, it points to the fact that countries placing greater checks and balances on the executive power tend to transition from revenues from narrow tax bases (such as on trade and excises) to more broad-based taxation (such as on income).

Figure 1. Total tax revenues, direct and indirect tax shares, and executive constraints.

Notes: the Y-axis, from left to right, reports: the Total central government tax revenues as a share of GDP, the Share of total central government tax revenue from direct taxes, the Share of total tax revenue from indirect taxes. See Andersson and Brambor (Reference Andersson and Brambor2019) for details.

How do the variables behave over time? Focussing on direct taxes, Figure 2 reports the time series plots for selected countries. We observe a marked increase in central government revenues from direct taxes. For most European states, they increased sharply during the 19th and especially the 20th centuries. Most evident in this respect was the United Kingdom, where the share of direct revenues increased nearly threefold between the early 19th century and late 20th century. This pattern is common to most current advanced economies (e.g. Australia, Belgium, Canada, Finland, Germany, Italy, Norway, Spain, United States). Outside the group of advanced economies, many countries showed comparable increases. Argentina, Brazil, Chile and Mexico have seen a marked increase in the share of direct revenues. In Peru, Ecuador, Bolivia, Colombia, Uruguay and Venezuela, there has been more limited (or no) increase and substantial volatility. Notably, the countries experiencing a long-run increase in the share of direct tax revenues include many resource-rich economies.

Figure 2. Share of direct taxes and executive constraints, 1800–2012.

Notes: the left-hand side vertical axis variable is the Share of total central government tax revenue from direct taxes. The right-hand side vertical axis variable is Executive Constraints.

We also observe that constraints on the executive and taxation tend to move together: changes in executive constraints are followed by changes in direct tax shares, and vice versa. Both variables are trended (formal unit roots test, presented in the appendix, confirm non-stationarity). This is most evident in the current group of advanced economies, and it is also observable in Brazil, Chile and Mexico. Instead, it is less clear in Peru, Ecuador, Bolivia, Uruguay and Venezuela, where there seems to be significant volatility in both variables. Figure 2 ultimately suggests that fiscal and political development experiences vary to a significant extent across countries. Indeed, the historical literature recognises that the path to fiscal development can be heterogeneous because it is subject to country-specific circumstances (e.g. Yun-Casalilla and O'Brien, Reference Yun-Casalilla and O'Brien2011). However, it also recognises that political motives, as shaped by institutions, are intertwined with the evolution of the tax system. Steinmo (Reference Steinmo2018) offers evidence, based on historical case studies, that fiscal capacity and tax compliance co-evolve. Sweden is an example of virtuous cycle where effective administrative institutions increased trust in the state among the taxpayers so that they would be willing to accept higher taxes (Nistotskaya and D'Arcy, Reference Nistotskaya, D'Arcy and Steinmo2018). Italy may be understood as partial exception to this (see D'Attoma Reference D'Attoma and Steinmo2018, for a historical illustration). Even the status of resource-rich economy, where the presence of a significant natural resources sector can weaken the incentive to invest in tax systems, may not necessarily limit fiscal development (see Peres-Cajías, Reference Peres-Cajías, Badia-Miró, Pinilla and Willebald2015, for a case study on Bolivia; for a historical comparison of public finance in Bolivia, Chile, Peru, Norway and Sweden, see Peres-Cajías et al., Reference Peres-Cajías, Torregrosa-Hetland and Ducoing2020).

4. Empirical strategy

We model the bi-variate long-run relationship between taxation and executive constraints accounting for the possibility that the dynamic relationship between the two may be different in different contexts. Hence, for i = 1, 2,…, N countries over the time period t = 1, 2,…, T, we specify a multi-factor error structure of the form:

(1)$${\rm ta}{\rm x}_{it} = \beta _i^{\prime} {\rm C}{\rm V}_{it} + u_{it}\quad \quad u_{it} = \alpha _i + \lambda _i^{\prime} f_t + \varepsilon _{it}$$

where tax_it represents the log of the tax shares while CV_it represents the log of the executive constraints variables. A fundamental aspect of the model is allowing the vector of parameter coefficients (β _i) to differ across countries. This is necessary because, for the arguments presented in section 2 and considering that countries included in our sample are a mixture of developed and developing countries, the long-run dynamic relationship between tax shares and constraints may not be the same across countries.

Equation (1) also incorporates unobserved heterogeneity, modelled through country-specific fixed effects (α _i) and a constellation of unobserved, time-varying common factors (f _t), with factor loadings that can differ across countries (λ _i). The country-specific heterogeneity in α _i may reflect time-invariant characteristics: social and cultural norms, political history – as argued in section 2 – and geography (including natural resource endowment, country size and location). The common factors address the presence of strong cross-section dependence, which is a form of unobserved, time-varying heterogeneity distinct from weaker forms of dependence (e.g. spatial correlation). Ultimately, strong cross-section dependence may be a source of endogeneity, leading to biased and inconsistent estimates (see Kapetanios et al., Reference Kapetanios, Pesaran and Yamagata2011). The common factors can be represented by a combination of a limited number of ‘strong’ factors and an unlimited number of ‘weak’ factors (Chudik et al., Reference Chudik, Pesaran and Tosetti2011). The former represents global effects, which affect all countries irrespective of their location, (initial) level of development and polity, while the latter represents local spillover effects, which may occur through geographic proximity, as well as social or economic interaction. External conflicts (regional or global), economic integration (e.g. trade agreement), structural adjustment programmes, financial crises (regional or global) and commodity price shocks are examples of common factors that may be at the origin of cross-section dependence and can affect both taxation and executive constraints. The impacts of these shocks and countries' abilities to respond differ across countries. Test results, presented in the appendix, point to pervasive cross-section dependence, thus justifying the inclusion of f _t in equation (1).

Given the length of the sample period, persistence in the data raises further econometric issues. Tax revenues (and the associated tax shares) and political institutions display considerable inertia over time. For example, constitutional changes, which enact increased (or reduced) institutionalised checks and balances on the power of the executive, evolve slowly over time. This calls for a distinction between short-run and long-run impacts. A dynamic specification is thus preferable, with at least two clear advantages over its static counterpart. First, it allows for a distinction between short-run and long-run effects. Additionally, the error correction term (ρ _i) can be used as a supporting test for cointegration between taxation and constraints on the executive, while the error correction and long-run coefficients (β _i) can be used to test for the direction of long-run causality between variables. Second, a dynamic specification following an error correction model (ECM) easily encapsulates the feedback effects postulated by our primary hypothesis: increased accountability brought about by increased taxation (with the effect possibly stronger for direct tax shares). Thus, we employ an ECM specification of the form:

(2)$${\rm \Delta ta}{\rm x}_{it} = \alpha _i + \rho _i( {{\rm ta}{\rm x}_{it-1}-\beta_i^{{\rm CV}} {\rm C}{\rm V}_{it-1}-\lambda_if_{t-1}} ) + \gamma _i^{{\rm CV}} {\rm \Delta C}{\rm V}_{it} + \gamma _i^F {\rm \Delta }f_t + \mu _{it}$$

where $\beta _i^{{\rm CV}}$ in equation (2) represents the long-run equilibrium relationship between taxation and executive constraints in the model, $\gamma _i^{{\rm CV}}$ represents the short-run relationship and ρ _i is the error correction term indicating the speed of convergence of the economy to its long-run equilibrium. The expression in parentheses represents the potential cointegrating relationship we seek to investigate. Unobserved common factors are included in the long-run relation, which implies we will investigate an equilibrium relationship between tax shares, executive constraints and the unobservables (Banerjee and Carríon-i-Silvestre, Reference Banerjee and Carrion-i-Silvestre2017; Eberhardt and Presbitero, Reference Eberhardt and Presbitero2015; Eberhardt and Teal, Reference Eberhardt and Teal2013).

Following Pesaran (Reference Pesaran2006), we employ the common correlated effects mean group (CCEMG) estimator which uses (weighted) cross-section averages of the dependent $( \overline {{\rm tax}} _t)$ and independent variables $( \overline {{\rm CV}} _t)$ constructed to filter out unobserved common factors f and omitted elements of the cointegrating relationship. The estimator thus augments the country-specific OLS regressions with cross-sectional averages. Chudik and Pesaran (Reference Chudik and Pesaran2015) extend the standard Pesaran (Reference Pesaran2006) approach to accommodate dynamics (feedback) from weakly exogenous regressors and find the standard CCEMG is subject to small sample bias in such contexts. The empirical strategy they propose to curb this bias is based on the inclusion of lags of cross-section averages:

(3)$$\eqalign{{\rm \Delta ta}{\rm x}_{it} & = \pi _{0i} + \pi _i^{{\rm EC}} {\rm ta}{\rm x}_{it-1} + \pi _i^{{\rm CV}} {\rm C}{\rm V}_{it-1} + \Phi _i^{{\rm CV}} \Delta {\rm C}{\rm V}_{it} + \pi _{1i}^{{\rm CA}} \overline {{\rm tax}} _t + \pi _{2i}^{{\rm CA}} \overline {{\rm tax}} _{t-1} \cr & \quad + \pi _{3i}^{{\rm CA}} \overline {{\rm CV}} _{t-1} + \pi _{4i}^{{\rm CA}} \overline {\Delta {\rm CV}} _t + \Sigma _{l = 1}^p \pi _{5i}^{{\rm CA}} \overline {\Delta {\rm tax}} _{t-p} + \Sigma _{l = 1}^p \pi _{6i}^{{\rm CA}} \overline {\Delta {\rm CV}} _{t-p} + \varepsilon _{it}} $$

and/or the inclusion of cross-section averages of one or more further covariates (other than the constraints variables) that may help to identify the unobserved factors. Further details on this are in the appendix.

4.1 Co-integration and causality

The main hypothesis is a direct test for bivariate cointegration between constraints on the executive and taxation. A suitable test, one which allows for greater flexibility in cross-sectional dependence, is provided by Gengenbach et al. (Reference Gengenbach, Urbain and Westerlund2009). The test is based on a conditional ECM of the form:

(4)$$\eqalign{{\rm \Delta ta}{\rm x}_{it} = \alpha _i{\rm ta}{\rm x}_{it-1} + \gamma _{1i}^{\prime} {\rm C}{\rm V}_{it-1} + \gamma _{2i}^{\prime} f_{it-1} + \mathop \sum \limits_{s = 0}^{\,p_i} \pi _{1is}^{\prime} {\rm \Delta C}{\rm V}_{it-s} + \mathop \sum \limits_{s = 1}^{\,p_i} \pi _{2is}^{\prime} {\rm \Delta ta}{\rm x}_{it-s} + \mathop \sum \limits_{s = 0}^{\,p_i} \pi _{3is}^{\prime} {\rm \Delta }f_{it-s} + \varepsilon _{it}}$$

The procedure in equation (4) is based on the CCEMG (Pesaran, Reference Pesaran2006) whereby common factors f are approximated by cross-section averages, including cross-section averages of lagged Δtax_it and ΔCV_it, depending on the lag-length p _i. The test is for a null hypothesis of no error correction (hence no cointegration) against an alternative of error correction (cointegration). The test statistic $\bar{\tau }^\ast$ is the average of the t-ratios for $\hat{\alpha }_i$, from country regressions. The individual t-ratios, as well as their averages, have non-standard distributions under the null hypothesis so Gengenbach et al. (Reference Gengenbach, Urbain and Westerlund2009) provide simulated critical values. The test is run for each CCEMG model with different deterministic terms (neither intercept nor trend, intercept, intercept and trend). Finding cointegration between tax shares and political institutions is important, as it will imply no important non-stationary variable has been omitted: any omitted non-stationary variable that is meant to be part of the cointegrating relationship will now be part of the error term, producing non-stationary residuals and failure to detect cointegration (Herzer, Reference Herzer2020).

An appealing feature of cointegration is that it allows testing the direction of long-run causality between variables. This is of particular interest here since we have hypothesised in section 2 that executive constraints and taxation may reinforce each other. If there exists a co-integrating relationship between tax shares and executive constraints, the Granger representation theorem (Granger, Reference Granger1988) states that long-run causality must run in at least one direction (equivalent to at least one variable adjusting to maintain an equilibrium relation) and the variables can be represented in the form of a dynamic ECM. For the pair of cointegrated variables CV_it and tax_it, we estimate:

(5)$$\Delta {\rm ta}{\rm x}_{it} = \rho _{1i} + \theta _{1i}\hat{e}_{it-1} + \mathop \sum \limits_{\,j = 1}^K \lambda _{11ij}{\rm \Delta ta}{\rm x}_{it-j} + \mathop \sum \limits_{\,j = 1}^K \lambda _{12ij}{\rm \Delta C}{\rm V}_{it-j} + \epsilon _{it}^{{\rm tax}} \;$$

(6)$$\Delta {\rm C}{\rm V}_{it} = \rho _{2i} + \theta _{2i}\hat{e}_{it-1} + \mathop \sum \limits_{\,j = 1}^K \lambda _{21ij}{\rm \Delta C}{\rm V}_{it-j} + \mathop \sum \limits_{\,j = 1}^K \lambda _{22ij}{\rm \Delta ta}{\rm x}_{it-j} + \epsilon _{it}^{{\rm CV}} $$

where $\hat{e}_{it-1}$ is the error correction term $\hat{e} = {\rm tax}-\hat{\beta }_i{\rm CV}-\hat{d}$ constructed using the cointegrating relationship between the variables (d represents deterministic terms obtained after estimating equations (5) and (6)). Equations (5) and (6) also include cross-section averages of the non-error terms in the weak exogeneity regressions. The lagged differences capture the short-run dynamics while the error correction term represents how far the variables are from the equilibrium relationship: with the error correction mechanism then indicating the speed of adjustment following a deviation from the long-run equilibrium (Canning and Pedroni, Reference Canning and Pedroni2008). Each variable may react to its lagged differences, as well as lagged differences of other variables in the co-integrating relationship. The Granger representation theorem implies that at least one of the adjustment coefficients θ _1i, θ _2i, must be non-zero if a cointegrating (equilibrium) relationship between the variables is to hold (Canning and Pedroni, Reference Canning and Pedroni2008). If θ _1i ≠ 0, then CV _it has a long-run causal impact on tax_it and, if θ _2i ≠ 0, then tax_it has a long-run causal impact on CV_it. If both θ _1i and θ _2i are non-zero, then CV_it and tax_it determine each other jointly.

The ECM regressions are estimated at the country-level and empirical estimates of θ _i are investigated using standard t-ratios, given that all the variables in the ECM regressions (5) and (6) are stationary (Canning and Pedroni, Reference Canning and Pedroni2008; Eberhardt and Presbitero, Reference Eberhardt and Presbitero2015). Following Canning and Pedroni (Reference Canning and Pedroni2008), we present the group-mean statistic (GM hereafter), which averages the θ _i from individual country estimations of equations (5) and (6), and the test for the null of ‘no long-run causal impact’ is computed from the averaged t-ratio from country regressions $( \bar{t}_{\theta _2} = N^{{-}1}\sum\nolimits_{i = 1}^N {t_{\theta _2}} )$. The GM statistic follows a standard normal distribution.