metadata: authors: 0: author: Gunter,Samara
1: author: Riera-Crichton,Daniel
2: author: Vegh Gramont,Carlos Alberto
3: author: Vuletin,Guillermo Javier
count: World
docna: 0: docna: Non-Linear Effects of Tax Changes on Output
            : The Role of the Initial Level of Taxation
docty: Policy Research Working Paper
subtopic: Public Finance Decentralization and
            Poverty Reduction,Economic Adjustment and Lending,Public Sector Economics,Tax Law,Tax Policy,Macro-Fiscal Policy,Tax Administration,Taxation & Subsidies,Labor Markets,Mining & Extractive Industry (Non-Energy),International Trade and Trade Rules
teratopic: Law and Development,Public Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Industry,International Economics and Trade
abstracts: cdata!: This paper estimates the effect of
            worldwide tax changes on output following the narrative
            approach developed for the United States by Romer and Romer
            (2010). The analysis uses a novel dataset on value-added
            taxes for 51 countries (21 industrial and 30 developing) for
            the period 1970-2014 to identify 96 tax changes. It then
            uses contemporaneous economic records to classify such
            changes as endogenous or exogenous to current (or
            prospective) economic conditions. In line with theoretical
            distortionary and disincentive-based arguments, and using
            only exogenous tax changes, the main finding is that the
            effect of tax changes on output is highly non-linear. The
            tax multiplier is essentially zero under relatively
            low/moderate initial tax rate levels and more negative as
            the initial tax rate and the size of the change in the tax
            rate increase. Based on a global sample, these novel
            non-linear findings suggest that the recent consensus
            pointing to large negative tax multipliers in industrial
            countries, particularly in Europe (e.g., Alesina, Favero,
            and Giavazzi, 2015), (i) is not a robust empirical
            regularity, and (ii) is mainly driven by high initial tax
            rates in these countries. The paper also shows that the bias
            introduced by misidentification of tax shocks critically
            depends on the procyclical or countercyclical nature of
            endogenous tax changes. The relevance of the arguments is
            evaluated both for the novel global sample and for Romer and
            Romer's U.S. dataset.
repnme: repnme: Non-Linear Effects of Tax Changes on Output
            : The Role of the Initial Level of Taxation
display_title: Non-Linear Effects of Tax Changes on
            Output : The Role of the Initial Level of Taxation
listing_relative_url: /research/2018/12/30675185/non-linear-effects-tax-changes-output-role-initial-level-taxation
topicv3: Trade m1326924 698,Taxation m1327615 1121,Tax Policy m1327616 983,Tin m1503520 2938
publishtoextweb_dt: 2018-12-07T00:00:00Z
historic_topic: Law and Development,Public Sector Development,Macroeconomics and Economic Growth,Social Protections and Labor,Industry,International Economics and Trade
no_of_pages: 50
author_keys: 0: author_key: 1239900
1: author_key: 1172435
2: author_key: 743651
model_extractions: WPS8668 Policy Research Working Paper 8668 Non-Linear Effects of Tax Changes on Output The Role of the Initial Level of Taxation _Samara Gunter Daniel Riera-Crichton Carlos Vegh Guillermo Vuletin_ Latin America and the Caribbean Region Office of the Chief Economist December 2018
Policy Research Working Paper 8668

# **Abstract**

This paper estimates the effect of worldwide tax changes on output following the narrative approach developed for the United States by Romer and Romer (2010). The analysis uses a novel dataset on value-added taxes for 51 countries (21 industrial and 30 developing) for the period 1970–2014 to identify 96 tax changes. It then uses contemporaneous economic records to classify such changes as endogenous or exogenous to current (or prospective) economic conditions. In line with theoretical distortionary and disincentive-based arguments, and using only exogenous tax changes, the main finding is that the effect of tax changes on output is highly non-linear. The tax multiplier is essentially zero under relatively low/moderate initial tax rate levels and more negative as the initial tax rate and the size of the change in the tax rate increase. Based on a global sample, these novel non-linear findings suggest that the recent consensus pointing to large negative tax multipliers in industrial countries, particularly in Europe (e.g., Alesina, Favero, and Giavazzi, 2015), (i) is not a robust empirical regularity, and (ii) is mainly driven by high initial tax rates in these countries. The paper also shows that the bias introduced by misidentification of tax shocks critically depends on the procyclical or countercyclical nature of endogenous tax changes. The relevance of the arguments is evaluated both for the novel global sample and for Romer and Romer’s U.S. dataset.

This paper is a product of the Office of the Chief Economist, Latin America and the Caribbean Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/ research. The authors may be contacted at gvuletin@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
# Non-linear e¤ects of tax changes on output: The role of the initial level of taxation<sup>�</sup>

Samara Gunter Daniel Riera-Crichton Colby College World Bank Carlos Vegh Guillermo Vuletin World Bank World Bank JEL Classi...cation: E32, E62. Keywords: tax multiplier, tax policy, tax rate, value-added tax, non-linear, narrative.

�This pap er was previously circulated under the title “Non-linear distortion-based e¤ects of tax changes on output: A worldwide narrative approach.” We would like to thank sem inar participants at the International M onetary Fund, Inter-Am erican D evelopm ent Bank, World Bank, Federal Reserve Board, Europ ean Stability M echanism , Central Bank of Argentina, Central Bank of Chile, Central Bank of Spain, UN Econom ic Com m ission for Latin Am erica and the Caribb ean, G eorge Washington University, Johns Hopkins University, W illiam s College, D avidson College, Universidad Nacional de La Plata, Sao Paulo School of Econom ics-G etulio Vargas Foundation, Escola Sup erior d’Adm inistració i D irecció d’Em preses (ESAD E), Institute of Education and Research (INSPER), International M acro Workshop-RID G E, Latin Am erican and Caribb ean Econom ic Association (LACEA), Annual Sym p osium of the Spanish Econom ic Association, and XLIV M eeting of the Network of Central Banks and Finance M inistries-ID B for m any helpful com m ents and suggesttions. We would also like to thank Alb erto Alesina, Silvia Albrizio, Leop oldo Avellan, Frank Bohn, Fernando Broner, Eduardo Cavallo, Javier G arcia-Cicco, Aitor Erce, D avide Furceri, Vitor G aspar, Alejandro Izquierdo, Herm an Kam il, G raciela Kam insky, Aart K raay, G erardo Licandro, Alessandro Notarpietro, Peter M ontiel, Eduardo M oron, Ilan Noy, Pablo O ttonello, Peter Pedroni, Javier Perez, Rob erto Ram os, D avid Robinson, D iego Saravia, O lena Staveley-O ’Carroll, Jay Shambaugh, Ham ilton Taveras, Teresa Ter-M inassian, and M artin Urib e for helpful discussions, the IM F Archives sta¤ m emb ers for their hospitality during our rep eated visits, and José Andrée Cam arena Fonseca, D iego Friedheim , Pablo Hernando-Kam insky, Luis M orano, Q i Sun, and Siyang Xu for excellent research assistance.
# 1 Introduction

After the 2007-2008 Global Financial Crisis, ...scal multipliers –the e¤ects of ...scal policy on aggregate output – have taken center stage in the policy world. Motivated early on by the policy focus on ...scal stimulus (to counter the economic recession that followed the crisis) and, more recently, by ...scal consolidation (due to increasing concerns about debt sustainability) studies estimating government spending multipliers and, to a lesser extent, tax multipliers have ‡ourished.

The main challenge and point of contention among researchers has been how to address the possible endogeneity of ...scal policy or, put di¤erently, how to identify exogenous ...scal policy shocks (i.e., changes in ...scal policy variables that are not directly or indirectly related to output changes). On the taxation front, which is the focus of this paper, there is an emerging consensus in the literature that the so-called narrative approach developed by Romer and Romer (2010) (henceforth RR) in their study of the United States is better suited to identifying exogenous tax policy shocks than the traditional approach pioneered by Blanchard and Perotti (2002) (hereafter BP). The BP approach imposes short-term restrictions in the context of structural vector autoregressions (SVAR). While changes in tax policy are allowed to contemporaneously a¤ect output, it is assumed that it takes the government at least one quarter to respond to developments in the state of the economy. While appealing at ...rst sight, this timing identifying strategy has been criticized on the basis that most changes in ...scal policy, including tax changes, are actually anticipated by agents (e.g., Ramey and Shapiro, 1998; Leeper, Walker, and Yang, 2008; Ramey, 2011; Auerbach and Gorodnichenko, 2012a; and Riera-Crichton, Vegh, and Vuletin, 2016). Moreover, and especially for large and sudden falls in output, it is not obvious that within-the-quarter economic developments do not a¤ect tax policy. For example, during episodes of natural disasters, it is often the case that governments quickly respond by increasing or reducing taxes. The earthquakes in Ecuador (2016), Japan (2011), India (2001), and California (1989) are clear examples of the unsuitability of the BP timing assumption as tax responses occurred within 26, 47, 6, and 18 days following the earthquakes, respectively.<sup>1</sup> See, Chahrour, Schmitt-Grohe, and Uribe (2012) for a model-based evaluation of the implications of using SVAR vis-à-vis the narrative approach relying on a DSGE model.

In contrast, RR use narrative records, from Congressional reports to presidential speeches, to identify the principal motivation behind all major postwar tax policy actions in the U.S. The analysis of contemporaneous records enables RR to separate legislated tax changes into those enacted for reasons related to current or prospective economic conditions (i.e., endogenous to the business cycle) from those taken for reasons exogenous to the business cycle, including those motivated by long-run growth considerations (e.g., by a belief that lower taxes will raise output in the long run) and inherited de...citdriven tax changes (which re‡ect past economic conditions and budgetary decisions, not current or

> 1 See Appendix 1 for more details about the nature of these earthquakes, e¤ects on GDP, as well as the tax policy responses.

2
prospective ones). With this classi...cation of tax changes in hand, RR analyze the behavior of output following exogenous tax changes. RR ...nd that (i) tax hikes (cuts) lead to contractions (expansions) in economic activity, and (ii) misidenti...cation of tax shocks (i.e., when using all tax changes à la BP) tends to underestimate the negative e¤ect of tax changes on output. Interestingly, RR also ...nd that the e¤ect of tax changes on output varies depending upon the motivation for the exogenous tax change. While the tax multiplier associated with long-run growth considerations is negative (and virtually identical to that of a generic exogenous tax change), the multipliers of de...cit-driven tax changes are essentially zero. For this reason, RR cautiously suggest that “tax increases to reduce an inherited de...cit may be less costly than other tax increases.” Since RR’s seminal work, several other studies have used the narrative approach for individual or multi-country analyses (in all cases, focusing solely on industrial economies, and mostly on industrial European countries). These studies ...nd large negative tax multipliers, ranging between �2 and �5.<sup>2</sup> This recent consensus pointing to large negative tax multipliers, especially in industrial European countries, naturally entails important policy prescriptions. For example, as part of a more comprehensive series of papers focusing on spending and tax multipliers, Alesina, Favero, and Giavazzi (2015) point that “policies based upon spending cuts are much less costly in terms of short run output losses than tax based adjustments.” A natural question is whether large negative tax multipliers are a robust empirical regularity and, if not, whether there are some underlying forces behind the observed di¤erence in tax multipliers across countries or groups of countries. In order to answer this highly relevant academic and policy question, one would ideally need to conduct a study using a more global sample including industrial and, particularly, developing countries. To the best of our knowledge, there is no such a study. The main reason is surely the lack of data on legislated tax changes in developing countries, which is needed to capture the behavior of a tax policy instrument (i.e., a variable that is under the direct control of policymakers).<sup>3</sup> Furthermore, unlike the BP approach, the RR narrative approach poses a major challenge in terms of the sheer time needed to gather contemporaneous economic records to identify the motivation behind each tax change.

2 Relying on the narrative approach for ...scal consolidation episodes and using a multi-country analysis, Alesina, Favero, and Giavazzi (2015) ...nd, for a sample of 17 industrial countries, a tax multiplier of about �2 (after two years of the tax shock). Using a similar identi...cation strategy, yet based on value-added tax rate changes, Riera-Crichton, Vegh, and Vuletin (2016) ...nd for a sample of 14 industrial countries a tax multiplier of about �3:5 (after one year of the tax shock). Relying on the narrative approach for country-speci...c studies, RR, Cloyne (2013), Hayo and Uhl (2013), Gil, Marti, Morris, Perez, and Ramos (2017), and Pereira and Wemans (2013) ...nd a tax multiplier of about �2:7, �2, �2:4, �2, and �1:7 (after two years of the tax shock) for the U.S, U.K, Germany, Portugal, and Spain, respectively. Also relying on a narrative approach, Pereira and Wemans (2013) and Gil, Marti, Morris, Perez, and Ramos (2017) ...nd for Portugal and Spain even more negative tax multiplier for indirect taxation of about �2:7 and �5 (after two years of the tax shock), respectively.

> 3 As discussed in RR and Mertens and Ravn (2014) for the case of the U.S. and Riera-Crichton, Vegh, and Vuletin (2016) for a sample of 14 industrial countries, cyclically-adjusted changes in tax revenues are often used as a proxy for discretionary changes in tax policy. While appealing in principle, the use of cyclically-adjusted revenues su¤ers from serious measurement error because it implicitly attributes any change in revenues not associated with the estimated change in the tax base to policymakers’discretionary behavior. As a result – and as shown in Riera-Crichton, Vegh, and Vuletin (2016) –tax multipliers estimated with cyclically-adjusted revenues yield misleading results.

3
This paper takes on this challenge by focusing on 51 countries (21 industrial and 30 developing) for the period 1970-2014. Given the lack of readily-available data on average marginal individual and/or corporate income tax rates on a global scale, we focus our e¤orts on building a new series for quarterly standard value-added tax rates (henceforth VAT rates). We believe that this signi...cant e¤ort in collecting VAT rates is crucial for any study analyzing tax policy in Europe as well as in the developing world, where indirect/value-added taxation is the main tax revenue instrument.<sup>4</sup> VAT rates were obtained from various primary sources including countries’revenue agencies, national libraries, books, newspapers, tax law experts, and research and policy papers. We identify a total of 96 VAT rate changes in 35 countries (18 industrial and 17 developing). As sources for the narrative analysis, we use contemporaneous International Monetary Fund (IMF) documents, OECD Economic Surveys, and news articles to gather evidence on policymakers’intentions and primary motivation behind each VAT rate change.

While closely following RR’s identi...cation strategy, we also incorporate some new elements that arise due both the global nature of our sample of countries and the speci...c tax measure used. In particular, we allow endogenous tax changes to include countercyclical tax changes (as in RR) as well as procyclical tax changes. While the latter type of policy behavior is not found by RR in the U.S., it is of critical importance in the developing world as well as in many other industrial countries (particularly industrial European countries after the 2007-2008 Global Financial Crisis). When focusing on exogenous tax changes motivated by inherited ...scal factors, we consider inherited de...cit-driven tax changes (as in RR) as well as inherited debt-driven tax changes. Since, over the last 60 years, the U.S. has not faced sustainability problems regarding the public debt, RR do not concern themselves with the latter case. As our analysis will show, however, this distinction has important implications in terms of the size of the tax multipliers in our sample.

Relying on our novel worldwide narrative approach, we ...nd that, for the entire global sample, the tax multiplier reaches �1:7 after two years of the tax shock. This ...gure is, compared to the range of estimated tax multipliers depicted before, among the least negative ones. Interestingly, when splitting the sample into industrial European economies and the rest of countries, we ...nd tax multipliers of �3:6 and �1:2, respectively. While the tax multiplier in industrial European economies is quite negative and statistically signi...cant (in line with recent studies), it is about 3 times smaller (in absolute value) and borderline statistically signi...cant for the rest of countries.

Motivated by this large di¤erence in tax multipliers, the paper’s main empirical contribution consists in evaluating the role of tax distortions and disincentives in generating non-linear e¤ects of tax changes on output. Many di¤erent kinds of non-linearities have been found in the estimation of spending multipliers in recent years. In most cases, the non-linear e¤ect of spending on output has been asso-

> 4 When analyzing the impact of speci...c taxes, Barro and Redlick (2011) focus on the e¤ect of individual income and social-security payroll taxes in the U.S. Mertens and Ravn (2013) analyze the e¤ect of individual and corporate income taxes in the U.S. Riera-Crichton, Vegh, and Vuletin (2016) focus on the impact of VAT in 14 industrial countries.

4
ciated with the macroeconomic context in which spending decisions have taken place. Building upon di¤erent macroeconomic theoretical frameworks, recent empirical ...ndings have shown that spending multipliers tend to be larger under ...xed exchange-rate regimes (Ilzetzki, Mendoza, and Vegh, 2013), under low debt (Ilzetzki, Mendoza, and Vegh, 2013; Huidrom, Kose, and Ohnsorge, 2016), and in recessions (Auerbach and Gorodnichenko, 2012a,b; Riera-Crichton, Vegh, and Vuletin, 2015). Rather than focusing on the aforementioned macroeconomic-based non-linear e¤ects, our paper focuses on the non-linear e¤ects of tax changes on output generated by distortionary and disincentive-based arguments.<sup>5</sup> Based on di¤erent types of macroeconomic models (which in turn rely on di¤erent mechanisms), the output e¤ect of tax changes is expected to be small at low initial levels of taxation but exponentially larger when initial tax levels are high. Therefore, the distortions and disincentives imposed by taxation on economic activity are directly, and non-linearly, related to the level of tax rates. By the same token, for a given level of initial tax rates, larger tax rate changes have larger tax multipliers. These theoretical results are present, for example, in Jaimovich and Rebelo (2017) (hereafter JR) who show that such a non-linear mechanism may operate through heterogeneity in entrepreneurial ability and its disincentives to innovate and invest. We also propose an alternative explanation for such a non-linear e¤ect, based on the role played by informality. For this purpose, we use a simple reduced-formed solution type of model, where both the formal and informal sectors have identical production functions. The existence of VAT (which is imposed only on the “formal”good, and not on the “informal”one) generates, in and of itself, an initial distortion in which workers are incentivized to work in the informal sector more than under the absence of such a tax. Therefore, the marginal productivity of formal workers is, in equilibrium, larger than that of informal ones. Under this situation, an increase in the VAT rate simply increases the initial distortion, raising the share of informality, and reducing total output. Moreover, larger increases in the share of informality and more profound falls in output are observed when the tax increase is implemented in a context of higher initial VAT rates. Naturally, while we exempli...ed the mechanism using an increase in the VAT rate, the same results hold for a reduction in the VAT rate.<sup>6;7</sup> In line with theoretical distortionary and disincentive-based arguments, we ...nd, using our novel worldwide narrative, that the e¤ect of tax changes on output is indeed highly non-linear. Our empirical

> 5 As we will discuss later in Sections 5.6 and 6, macroeconomic-based non-linear e¤ects are not behind the non-linear e¤ects associated with distortionary and disincentive-based type of arguments.

> 6 See Appendix 2 for details on the model. If the production functions of the formal and informal sectors allowed larger productivity in the formal sector than in the informal one (as it is frequently assumed based on ...rm level data evidence) and/or if there existed a segmentation in the labor market where formal workers were paid more than informal ones (as empirical evidence strongly suggests), the proposed mechanism as well as the output and informality implications would be further ampli...ed.

> 7 While di¤erent in the nature of the object under analysis (output versus tax burden), JR and our simple model based on the role played by the informal sector, also relate to a well-established public ...nance literature (e.g., Harberger, 1964a,b; Browning, 1975; Feldstein, 1995) which argues that the excess burden of taxation, or deadweight loss, associated with taxation is small at low tax rates, increases with higher tax rates, until, eventually, “a tax [is] imposed at so high rate that it eliminates the taxed activity.”(Hines, 2007, p. 1).

5
...ndings show that the tax multiplier is essentially zero under relatively low/moderate initial tax rate levels and more negative as the initial tax rate and the size of the change in the tax rate increase. Based on a global sample, these novel non-linear ...ndings suggest that the large negative tax multipliers, especially in industrial Europe, are not a universal empirical regularity but are instead mainly driven by high initial tax rates for these countries. Moreover, for an important part of the world, especially in developing countries, where tax multipliers are virtually zero or slightly negative, the implied policy prescription could be the opposite of that of Alesina, Favero, and Giavazzi (2015).

The paper proceeds as follows. Section 2 outlines the conceptual framework that motivates our narrative analysis, which closely follows that of RR. However, unlike RR, we highlight the critical role of procyclical/countercyclical ...scal policy in determining the sign of the bias of the estimator of the e¤ects of tax changes on output. Section 3 discusses our sample and data sources. Section 4 proceeds to identify the motivation behind all tax changes in our sample. We ...rst discuss some general considerations and then classify all tax changes into endogenous and exogenous and, within each category, into various subcategories that will prove critical for the remainder of the study. We then turn to the econometric analysis. Section 5 ...rst introduces our basic linear speci...cation and then discusses our basic results, the biases introduced by misidenti...cation of tax shocks, the role of expectations, and the mechanisms involved. We also show that while the tax multiplier in industrial European economies is quite negative and statistically signi...cant (in line with recent studies), it is about 3 times smaller (in absolute value) and borderline statistically signi...cant for the rest of countries. Section 6 shows, in line with theoretical distortionary and disincentive-based arguments, the existence of strong non-linear e¤ects of tax changes on output. In particular, tax multipliers are essentially zero under relatively low/moderate initial tax rate levels and more negative as the initial tax rate and the size of the change in the tax rate increase. We also show that these non-linear e¤ects are critical in explaining (i) the linear ...ndings of Section 5 when estimating the tax multiplier for industrial Europe and the rest of countries, and (ii) the VAT or indirect tax multipliers calculated on country-speci...c studies using di¤erent empirical strategies. We also show further evidence that these non-linear e¤ects are powerful in explaining (i) the di¤erent e¤ect of tax changes on output observed depending upon the motivation of the exogenous tax change (e.g., like the one identi...ed by RR when comparing the output e¤ect of long-run growth versus inherited de...cit-driven tax changes), (ii) the perceived (survey-based) extent to which taxes reduce the incentive to work and invest, and (iii) policymakers’tax plans to deal with the current need for increasing economic activity and addressing ...scal de...cits. We also show that the same non-linear arguments are present in RR’s sample. Section 7 provides some ...nal thoughts.

6
# 2 Conceptual framework

This section outlines the conceptual framework that motivates our narrative analysis, which closely follows that of RR. However, unlike RR, we highlight the critical role of procyclical/countercyclical tax policy in determining the sign of the bias of the estimator of the e¤ects of tax changes on output. We ...rst lay out the basic set-up and then illustrate the possible biases.

## 2.1 Basic set-up

To ...x ideas, let us use the simplest speci...cation capturing how tax changes a¤ect real GDP: where yt is the logarithm of real GDP (and �yt is thus the real GDP growth rate, expressed as the di¤erence in logarithms), �t<sup>all</sup> t represents all legislated tax rate changes expressed in percentage points, and "t is the stochastic error, with zero mean and variance �<sup>2</sup> "<sup>.</sup> Tax changes can be broken down into two types: where �t<sup>endog</sup> t (endog stands for endogenous) are changes in tax rates enacted as a result of (i) current or prospective output growth di¤ering from normal and/or (ii) other factors likely to a¤ect output growth in the near future. In contrast, �t<sup>exog</sup> t (where exog stands for exogenous) are changes in tax rates driven by reasons unrelated to developments likely to a¤ect output in the near term. Therefore, while �t<sup>exog</sup> t are orthogonal to "t (i.e., cov(�t<sup>exog</sup> t ; "t) = 0), �t<sup>endog</sup> t are not (i.e., cov(�t<sup>endog</sup> t ; "t) 6= 0). As indicated by RR, examples of exogenous tax changes would be a cut in taxes (i) based on the belief that lower marginal rates will increase long-run growth or (ii) with the hope that lower revenues will eventually shrink the size of the government.

Let us now focus on endogenous tax changes. Without loss of generality, we can write �t<sup>endog</sup> t as where � 7 0 captures how endogenous tax changes respond to output shocks caused by factors other than taxes such as government spending, monetary policy, and terms-of-trade shocks, among many others. For example, suppose that a negative terms-of-trade shock reduces output (i.e., "t < 0). Policymakers may decide to reduce taxes to ...ght o¤ such a recession (i.e., �> 0), or they may be “forced”(due to the ensuing fall in ...scal revenues) to increase taxes (i.e., �< 0).<sup>8</sup> More generally, countercyclical tax policies (aimed at smoothing out the business cycle) imply �> 0; procyclical tax policies (which in principle tend to amplify output volatility) are captured by �< 0; and acyclical

> 8 We should note that these endogenous tax changes are triggered by lower cyclical tax revenues and thus are not the result of inherited ...scal problems. This important distinction will be discussed in detail in Section 4.

7
tax policies (re‡ecting, on average, a non-systematic reaction of taxes to cyclical ‡uctuations) imply � = 0.

## 2.2 Biases in tax multipliers

Using equations (1)-(3), it is straightforward to show that there would be no bias if only exogenous tax changes were used to estimate (1). Formally, if we used �t<sup>exog</sup> t (and not �t<sup>endog</sup> t ) to identify tax changes in equation (2), the bias associated with the OLS coe¢ cient �<sup>[exog</sup> (where �<sup>[exog</sup> refers to the estimator for � in regression (1) when solely using �t<sup>exog</sup> t ) would be given by In contrast, if both �t<sup>exog</sup> t and �t<sup>endog</sup> t were used to identify tax changes as captured in equation (2), it is easy to show that the sign of the bias would depend on the sign of �: What would happen if �< 0? Recall that �< 0 implies that endogenous tax changes are procyclical. Then, Bias of �<<sup>b</sup> 0, or E �b < �. To ...x ideas, suppose that �< 0 (indicating that higher taxes h i b reduce output). Then, E � would be even more negative. Why would that be the case? Suppose h i that there is a tax hike enacted in response to a decline in tax revenues triggered by a fall in output. If such a tax change was wrongly included in the estimation sample, such observation would be taken as evidence of a larger contractionary e¤ect of tax increases on output (while it was actually the fall in output what caused the tax increase!).

What if �> 0? When �> 0, endogenous tax changes are countercyclical. Hence, Bias of �><sup>b</sup> 0, or b b E � > �. Suppose that �< 0; then E � would be less negative (or even positive). Intuitively, the h i h i wrong inclusion of countercyclical tax changes (i.e., taxes increases during good times or tax reductions in bad times) would lead to an underestimation of the true e¤ect of tax changes on output. Only in the case in which � = 0 (re‡ecting, on average, a non-systematic response of taxes to output ‡uctuations) would there be no bias.

# 3 Narrative analysis: Sample and sources

As the conceptual framework makes clear, we need to identify the motivation behind each tax change (i.e., whether it was exogenous to the business cycle or not). To this e¤ect, we ...rst need to identify the size and timing of legislated tax changes, in terms of their announcement and implementation. As in RR, we proxy the announcement of tax rate changes by using the time of approval of the corresponding 8
tax law. This section ...rst discusses our sample and data sources and then proceeds to identify the motivation behind each tax change.

# 3.1 Sample

Our sample comprises 51 countries (21 industrial and 30 developing) for the period 1970-2014. Given the lack of readily-available data on average marginal individual and/or corporate income tax rates on a global scale, we focus our e¤orts on creating a new series for quarterly standard VAT rates, building on Vegh and Vuletin (2015) and Riera-Crichton, Vegh, and Vuletin (2016).<sup>9</sup> We believe that this signi...cant e¤ort in collecting VAT rates is crucial for any study analyzing tax policy in the developing world as well as in Europe, where indirect/value-added taxation is one of the main tax revenue instruments.<sup>10</sup> Due to data availability, we use the standard VAT rate as a proxy for overall VAT policy. Such an approach could, in principle, raise concerns due to the omission of reduced VAT rates and/or exempted goods for some countries, as well as possible changes over time in the goods covered by the di¤erent rates. While data limitations prevent us from assessing the practical relevance of this concern for our whole sample of 51 countries, Vegh and Vuletin (2015) show, for a subset of 9 industrial countries, that these concerns are not warranted. First, the standard rate typically applies to most goods while reduced tax rates (if present at all) typically apply to a small subset of particular goods, including some food categories and child/elderly care. The average share of transactions covered by the standard VAT rate is about 75 percent of the total tax base. Second, the standard and average reduced VAT rates tend to be highly and positively correlated over time. In 80 percent of the countries, this correlation is larger than 0.5 and statistically signi...cant at the one percent level. Third, the share of transactions covered by di¤erent statutory tax rates does not vary much over time in any given country. As a result, the standard VAT rate explains about 85 percent of the observed variability of the e¤ective VAT rate (computed as the average of the di¤erent VAT rates weighted by their share in transactions as a percentage of the taxable base).<sup>11</sup>

# 3.2 Sources

The VAT rates were obtained from various primary sources, including countries’ revenue agencies, national libraries, books, newspapers, tax law experts, and research and policy papers. In most cases,

> 9 Vegh and Vuletin (2015) build a novel annual dataset of tax rates for 62 countries for the period 1960-2013 that comprises corporate income, highest personal income, and standard VAT rates. Riera-Crichton, Vegh, and Vuletin (2016) build a new quarterly standard VAT rate series for 14 industrial countries for the period 1980-2009.

> 10 Indirect (value-added) taxes represent, on average, 43 (28) percent of total tax revenues in industrial countries and 47 (32) percent in the developing world.

> 11 While the use of standard VAT rates is a good proxy for overall VAT tax policy, our narrative analysis will take into account the fact that, in some cases, changes in the standard VAT rate are intended to compensate for changes in the VAT base and/or VAT reduced rates.

9
we were able to gather the complete time series of the VAT rate since its introduction. However, since our study focuses on the output implications of tax changes, we only use those tax changes for which we have real GDP data collected on a quarterly basis (as opposed to interpolated data). As discussed in detail in Ilzetzki, Mendoza, and Vegh (2013), relying on interpolated quarterly data creates serious problems associated with measurement error. The coverage, which varies across countries, starts as early as 1970:Q1 and ends as late as 2014:Q4 (see column 1 in Table 1 for country-speci...c coverage). As sources for the narrative analysis, we use contemporaneous International Monetary Fund (IMF) documents, OECD Economic Surveys, and news articles to gather evidence on policymakers’intentions and primary motivations for VAT rate changes. IMF documents include Sta¤Reports and Background Material for Article IV Consultations, as well as additional IMF country reports and publications such as Recent Economic Developments, Selected Issues, and Public Information Notices. IMF documents published prior to 1997 are available in digitalized hard copies at the IMF Archives in Washington, D.C., whereas documents from 1997 and onward are available at the IMF website. News articles were obtained from global media including BBC, Bloomberg News, EU Business, Financial Times, International Herald Tribune, Los Angeles Times, New York Times, Reuters, The Daily Mirror, The Daily Telegraph, The Guardian, The Independent, The Times, Wall Street Journal, and Xinhua News Agency as well as from individual countries’media outlets such as Mmegi (Botswana), National Post (Canada), The Globe and Mail (Canada), Prague Daily Monitor (Czech Republic), Intellinews-Czech Republic Today (Czech Republic), Irish Times (Ireland), The Belfast News Letter (Ireland), Sunday Business Post-Cork (Ireland), Baltic News Service (Latvia), The Southland Times (New Zealand), Sunday Star-Times (New Zealand), and El Pais (Spain).

# 4 Tax changes: Identifying motivation

This section explains the actual identi...cation of tax changes. We ...rst discuss some general considerations and then classify all the tax changes in our sample into endogenous and exogenous. Then, within each category, we further classify each change into various subcategories that will prove critical for the remainder of the analysis.

## 4.1 Identi...cation strategy

We identify a total of 96 VAT rate changes in 35 countries (18 industrial and 17 developing). Given the time coverage of these 35 countries, there is, on average, a VAT rate change every 11 years with an average change (in absolute value) of 1.9 percentage points. The remaining 16 economies in our sample of 51 countries show no VAT rate change. Out of those 96 VAT rate changes, 60 occurred in industrial countries and 36 in developing ones.

10
<!-- Start of picture text --> All tax rate changes<br>Total number Endogenous Exogenous<br>periodCountry and VAT cate —_——_SH Oe<br>coverage changes GoP-driven offsetting Long-run growth Inherited fiscal factors<br>Procyclical Countercyclical Other tax Within VAT Spending Deficit-driven Debt-driven<br>Argentina<br>(1993:Q2- 2013:Q1) + (April 1985, 3 pp.)<br>Australia* °<br>(2000:03 - 2014:03)<br>Austria* °<br>(1984:02- 2014:01)<br>(1983:Q2Belgium=- 2014:02) 3 (January 1994, 1 pp.) (January{April 1992, 1996,0.5 0.5pp.) pp.)<br>(2002:03-2013:04)Botswana 1 (April 2010, 2 pp.)<br>Bulgaria °<br>(asso. 201402) tuuly 2006, -1 pp.)<br>(1991:01-2014:03) 2 (January 2008, -1 pp.)<br>(1991:02-2014:03)Chile 1 (October 2003, 1 pp.)<br>China<br>(1994:01-2014:03)<br>(1995:02-2014:02)Czech Republic 3 (January 2010, 1 pp.) (May 2004, -3 pp.) (January 2013, 1 pp.)<br>(1980:04-2014:02)Denmark* 1 (January 1992, 3 pp.)<br>(1992:02-2014:02)Ecuador 3 (November 1999, 2 pp.) (September 2001, -2 pp.) (May 2001, 2 pp.)<br>Egypt<br>(2004:02-2014:02)<br>(1992:03-2014:02)El Salvador 1 (July 1995, 3 pp.)<br>(1994:03-2014:02)Finland* 2 (July 2010, 1 pp.) (anuary 2013, 1 pp.)<br>France* 3 (April 2000, -1 pp.) (July 1982, 1 pp.) (August 1995, 2 pp.)<br>(1977:02-2014:02)<br>(1983:04-2014:03)Germany* 3 (anuary 1993, 1 pp.) (January(april 1998, 1 2007, pp.)3 pp.)<br>Greece* 3 (March 2010, 2 pp.) (April 2005, 1 pp.)<br>(1995:Q2-2014:Q2) (July 2010, 2 pp.)<br>(1995:02-2014:02)Hungary 3 (September(January 2006, 2009,-5 pp.)5 pp.) (January 2012,2 pp.)<br>India<br>(2005:02-2014:03)<br>(1997:02-2014:02)Ireland* 5 (December(March 202 0 2, 108, 0.5 PP.)pp.) (ssuary 2010, -0.5 pp.) (January 2001, -1 pp.) (January 2012, 2 pp.)<br>(August 1988, 1 pp.)<br>ttaly* (January 1981, 1 pp.) (October 1997, 1 pp.)<br>(1981:01-2014:02) 6 (August 1982, 3 pp.) (November 2011, 1 pp.)<br>(October 2013, 1 pp.)<br>Jamaica<br>(2010:01-2014:01)<br>(1989:01-2014:03)Japan* 1 (April 1997, 2 pp.)<br>Korea, Rep.<br>(1977:01-2014:03)<br>(1995:Q2-2014:Q1)Latvia 3 (January 2009, 3 pp.) (July 2012, -1 pp.) (January 2011, 1 pp.)<br><!-- End of picture text -->
<!-- Start of picture text --> All tax rate changes<br>Country and Tot‘otVAT a ll number atenumb FeEndogenous —— Exogenous<br>period coverage changesby GDP-driven Offsetting Long-run growth Inherited fiscal factors<br>Procyclical Countercyclical Other tax Within VAT Spending Deficit-driven Debt-driven<br>Lithuania > (January 2009, 1 pp.)<br>(1994:02-2014:02) (September 2009, 2 pp.)<br>Luxembourg*<br>(1995:02-2014:Q1)<br>Malta<br>(2004:02-2014:02)<br>Mauritius<br>(2002:02-2010:03)<br>Miexico March 1995, 5 pp.]<br>(1983:02-2014:02) 3 (January(Mord 2010, 1pp)pp.) (November 1991, -5 pp.)<br>(1986:Q2-2014:03)Netherlands* 4 (January 2001,11.5 pp.)| (January(October1989, 1992,-1.5-1 pp.)pp.) (October 2012, » 2 pp.).]<br>{asse:o8-2004:02)New Zealand* 2 (October 2010, 2.5 pp.) (July 1989, 2.5 pp.)<br>Norway* (January 1993, 2 pp.)<br>(1970:Q2-2014:Q2) 4 (anuary 1995, 1 pp.)| (January 2005, 1 pp.) (anuary 2001, 1 pp.)5<br>Paraguay<br>(1994:02-2014:02)<br>Philippines<br>(2006:02-2014:Q2)<br>(a995:02-2014:02)Poland 1 (January 2011, 1 pp.)<br>(June 2002, 2 pp.)<br>Portugal* 6 (July 2010, 1 pp.) (July 2008, -1 pp.) (January 1995, 1 pp.) (July 2005, 2 pp.)<br>(1992:03-2014:02) (January 2011, 2 pp.)<br>Romania<br>(1998:Q2-2014:Q2) 2 (July Y 2010,> 5 PP. pp.) (Januaryv 2000, 1-3 -3 PP. pp.)<br>Russia<br>(2004:02-2014:02)<br>Singapore<br>(2007:04-2014:03)<br>(asososlovak Republimunes) 3 (anuary 2004, -1 pp.) (January 2003,-3 pp.) (January 2011, 1 pp.)<br>(1999:Q3-2014:Q1)Slovenia + (anuary 2002, 1 pp.)<br>(1991:04-2014:02)South Africa 1 (Apr(April 1993,4 pp) p .<br>Spain* (July 2010, 2 pp.)<br>(1992:04-2014:Q2) 3 (September 2012, 3 pp.) (anuary 1995, 1 pp.)<br>(assoc rounca) 4 (July 1990, 1.54 pp.) (anuary 1983, 1.95 pp.) (November 1981, -1.95 pp.) September 1980, 2.83 pp.)<br>Switzerland* Ganuary 1999, 1 pp.)<br>(21995:01-2014:02)1995:01-2014: 3 (January(January 2011, 0.4 2001, 0.1 pp.)pp.)<br>(1993:Q2-2014:Q2)Thailand 2 (August8 1997,73 3 PP. pp.) (AprilP 1999, V3 -3 PP p .)<br>(1975:Q1-2014:02)United Kingdom* 5 Uijanualv 2010,|,2.52.5pp p .) pp.) (D(December 2008,ber 2008,-2.5-2.5 pp. pp. pp.) (April(une 1991, 1979, 2.57 pp.) pp.) Uianualv 2011, , 2.52.5 pp p . pp.)<br>las7s022011:08)us 5 (une 1984, 2 pp.) (May 1995, 1 pp.) (anuary 2007,-1 pp.) (October 1987,1 pp.) (April 1990, 1 pp.)<br>Venezuela<br>(2011:@1-2013:a)<br><!-- End of picture text -->

<!-- Start of picture text --> countercyclical<br>GDP-driven (7)<br>(33)<br>procyclical<br>endogenous (26)<br>(52)<br>offsetting<br>tax changes (19)<br>(96)<br>long-run growth<br>(9)<br>exogenous<br>(44) deficit-driven<br>inherited fiscal factors (14)<br>(35)<br>debt-driven<br>(21)<br><!-- End of picture text -->
# 4.2 Endogenous tax changes

As illustrated in Figure 1, we classify endogenous tax changes into two categories: (i) GDP-driven tax changes and (ii) o¤setting tax changes.

- GDP-driven tax changes are those enacted by policymakers in response to deviations of (contemporaneous or prospective) output from trend. Clearly, such changes present a problem of reverse causality since we are trying to quantify the e¤ect of tax changes on output.<sup>12</sup> In turn, GDP-driven tax changes may be countercyclical or procyclical:

- Countercyclical tax changes: Tax changes aimed at stabilizing output around trend, which implies either cutting taxes in recessions or increasing taxes during booms. In our sample, the most common countercyclical tax change is a tax cut in response to a current or prospective recession with the aim of stimulating economic activity.<sup>13</sup> A clear example would be Thailand in 1999. After increasing the VAT rate from 7 percent to 10 percent during the Asian crisis in the summer of 1997, Thai authorities attempted to revive domestic demand by reducing the VAT rate back to 7 percent in March 1999. The IMF supported the stimulus package. “The package is an important step in facilitating economic recovery,”said Reza Moghadam, the IMF representative in Thailand at the time.

- While less common, there are also cases in our sample in which tax rates were increased to restrain domestic demand and cool o¤ economic activity. An example would be the tax hike implemented in Sweden in 1990 (with the VAT rate changing from 23.5 to 25 percent) that was intended to relieve pressure from very tight labor markets and wage increases.

- Procyclical tax changes: Tax hikes (cuts) enacted in response to a current or prospective recession (boom).<sup>14</sup> The natural question is, of course, why would policymakers pursue a tax policy that would tend to amplify the underlying business cycle? In fact, procyclical tax policy falls under the more general phenomenon of procyclical ...scal policy (which would also include increasing government spending in booms and reducing it in recessions) that has been explored in detail in the literature. The most common explanations for such procyclical behavior have revolved around (i) political economy pressures that induce policymakers to loosen ...scal policy during booms and (ii) limited access to international credit markets in bad times, which forces policymakers to tighten ...scal policy.<sup>15</sup> While

> 12 Of the 33 GDP-driven tax changes in our sample, 17 occurred in industrial countries and 16 in developing ones.

> 13 In line with the ...ndings in Vegh and Vuletin (2015), most countercyclical tax policy is to be found in industrial countries (5 out of 7 countercyclical tax changes in our sample occurred in industrial countries).

> 14 We identi...ed 26 procyclical tax changes (12 in industrial countries and 14 in developing ones).

> 15 See, among others, Gavin and Perotti, 1997; Tornell and Lane, 1999; Kaminsky, Reinhart, and Vegh, 2004; Talvi and Vegh, 2005; Alesina, Campante and Tabellini, 2008; Frankel, Vegh, and Vuletin, 2013; Vegh and Vuletin, 2015; and Avellan and Vuletin, 2015.

13
procyclical ...scal policies have been most common in developing countries, it has also been observed in several Eurozone countries since the Global Financial Crisis of 2007-2008.

The most common procyclical tax change is a tax hike enacted in response to a current (or prospective) recession which has dramatically reduced tax revenues. In e¤ect, particularly when large and/or sudden contractions in economic activity are involved, the increase in the ...scal de...cit that results from a sharp fall in tax revenues often leads to an unsustainable public debt. In such circumstances, it is not uncommon for countries to face a sharp increase in borrowing costs or even lose access to international credit markets altogether, which leaves policymakers with no choice (other than defaulting) but to raise taxes.

In practice, typical examples of procyclical tax changes have taken place as a direct result of sudden economic crises, including the increases (i) from 10 percent to 15 percent in Mexico (March 10, 1995) as a consequence of the Tequila crisis, (ii) from 18 percent to 21 percent in Argentina (March 16, 1995) as a consequence of the contagion e¤ects of the Tequila crisis, (iii) from 7 percent to 10 percent in Thailand (August 5, 1997) as a consequence of the Asian ...nancial crisis, (iv) from 10 percent to 12 percent in Ecuador (October 26, 1999) after the 1998-1999 Ecuadorean economic crisis, as well as (v) several tax hikes in Europe (Czech Republic, Finland, Greece, Hungary, Ireland, Latvia, Lithuania, Portugal, Romania, Spain, and the United Kingdom), during the 2008-2010 period, following the Global Financial Crisis.

While less frequent, procyclical tax changes also include tax cuts made during buoyant economic times, when ...scal revenues are higher than normal due to the increase in the tax base (be it income or consumption). In such circumstances, policymakers may be subject to powerful political pressures to reduce taxes. A good example would be the VAT rate cut passed by France (March 1, 2000), when a stronger-than-expected ...scal position led to a reduction in the VAT rate from 20.6 percent to 19.6 percent.

We should note that, as Figure 1 indicates, procyclical tax changes are much more prevalent than countercyclical ones, with close to 80 percent (or 26 out of 33) of GDP-driven tax changes being procyclical. Moreover, procyclical tax changes are more common in the developing world than in industrial countries: while about 70 percent (or 12 out of 17) of GDP-driven tax changes are procyclical in industrial countries, this ...gure increases to close to 90 percent (or 14 out of 16) in developing economies.

- O¤setting tax changes are those intended to o¤set other factor(s) that would likely move output growth away from normal. More speci...cally, they involve standard VAT rate changes intended to o¤set the e¤ect of changes in (i) government spending, (ii) other non-VAT taxes or (iii) the VAT base and/or VAT reduced rates.<sup>16</sup> Since these tax changes are, though indirectly, responding

> 16 We include possible changes in other non-VAT taxes as well as changes in the VAT base and/or VAT reduced rates because the main tax series used in this study is the standard (as opposed to the e¤ective) VAT rate.

14
to changes in GDP, we have again a problem of reverse causality. As indicated in Figure 1, we identify 19 o¤setting changes (13 in industrial countries and 6 in developing ones). The proportion of o¤setting tax changes is roughly the same in industrial and developing countries, with 22 percent (or 13 out of 60) of total tax changes in industrial and 17 percent (or 6 out of 36) in developing countries.

In line with the discussion in RR, contemporaneous IMF, OECD, and news articles often explicitly identify policymakers’intentions in this regard. However, even when that link was not made explicit, it is appropriate to classify these type of changes as endogenous. Speci...cally, we found the following cases:

- In 4 cases, VAT rates were raised because government spending was increased. For example, after twelve years of armed con‡ict in El Salvador that ended in 1992, the new government of President Armando Calderon Sol increased the VAT rate from 10 percent to 13 percent on July 1, 1995 to help ...nance a “National Reconstruction Plan which will provide for the rehabilitation of damaged infrastructure [during the civil war] and the reintroduction of di¤erent segments of society into the economic mainstream,”as stated by Mr. Fernandez, the IMF o¢ cial at the time. In the same vein, Norway increased the VAT rate from 23 percent to 24 percent on January 1, 2001 to ensure no budgetary implications of an increase in spending on health and education.

- In 11 cases, VAT rates were raised because other non-VAT taxes were reduced. In most cases, these VAT hikes were implemented to o¤set reductions in personal, corporate, and labor taxes aimed at increasing competitiveness and labor supply. For example, on June 18, 1979, the government of recently-elected Prime Minister Margaret Thatcher increased the VAT rate by 7 percentage points (from 8 percent to 15 percent) as part of a major tax reform intended to partially o¤set the impact of large cuts to marginal income tax rates.

- In 4 cases, the VAT rate was reduced because the VAT base was broadened and/or VAT reduced rates were increased or eliminated. For example, on May 1, 2004, the Czech Republic reduced the standard VAT rate from 22 to 19 percent and shifted over 25 percent of the consumption basket of goods and services from the reduced to the standard VAT rate.

# 4.3 Exogenous tax changes

Following RR’s identi...cation strategy, exogenous tax changes are those not made in response to (i) current or prospective output di¤erent from normal or (ii) other factors likely to a¤ect output contemporaneously or in the near future. In other words, exogenous tax changes do not present a problem of reverse causality because, according to the historical narrative, they should be uncorrelated 15
with contemporaneous output or output in the near future. Such tax changes would thus be legitimate right-hand variables in a regression of output on tax changes. In fact, as a check on the accuracy of our historical narrative, we will show in Section 5 that exogenous tax changes are not Granger-caused by GDP ‡uctuations. We identify a total of 44 exogenous tax changes (30 in industrial countries and 14 in developing ones).

In turn, exogenous tax changes are classi...ed into those motivated by long-run growth considerations or enacted in response to inherited ...scal factors:

- Long-run growth. As indicated by RR, this type of tax change responds to the belief that a tax cut will raise output in the long run by unleashing supply-side forces related to labor, capital, or, more generally, a more e¢ cient use of resources. Such tax change is thus aimed at raising long-run growth, as opposed to responding to cyclical output ‡uctuations.

- In total, we ...nd 9 tax changes motivated by long-run growth considerations, representing 20 percent of exogenous tax changes. For example, Canada’s economy was operating close to potential and performing strongly during the mid-2000s. Yet, both in 2006 and in 2008, the government reduced the VAT rate by 1 percentage point each time to promote long-term growth according to several news articles and IMF’s assessments.

- Inherited ...scal factors. These are tax changes that respond to either (i) ...scal de...cits inherited from the past and thus determined by past actions (as opposed to ...scal de...cits caused by current or prospective conditions) or (ii) a stock of public debt that is viewed as unsustainable if current de...cits persist.<sup>17</sup> The critical point is that in neither case the change in the tax rate responds to the current (or prospective) state of the economy but rather to past actions that may have caused a ...scal de...cit to be viewed as too large or a stock of public debt that has come to be seen as unsustainable. Such tax changes are thus exogenous to the current state of the business cycle.<sup>18</sup> In general, the identi...cation of this type of tax changes is clear from the used sources. In the rare cases where di¤erent sources disagree, we err on the safe side and exclude potentially legitimate observations.

- In our sample, a clear example of tax changes motivated by inherited ...scal de...cits can be found in Switzerland in 1999 and 2001, when VAT rates increased from 6.5 to 7.5 percent and from 7.5 to 7.6 percent, respectively. After running primary budget surpluses for much of the 1980s, a prolonged period of economic stagnation during 1991-1996 (with average GDP growth rates of only 1 percent) caused the primary de...cit to steadily increase, reaching about 2 percent of

> 17 Since, over the last 60 years, the U.S. has not faced sustaninability problems regarding the public debt, RR do not concern themselves with the latter case.

> 18 Occasionally, ...scal packages aimed at dealing with inherited ...scal factors include not only tax increases but also cuts in government spending. To this e¤ect, government spending will be used as a control in our empirical speci...cations. If we also included changes in corporate tax rates and/or the highest personal income tax rate, results would not be a¤ected. Unfortunately, as discussed before, we do not have the average marginal personal tax rate. Results are not shown for brevity’s sake.

16
GDP in 1997 and 1998. While low by international standards, the rapid growth in the ...scal de...cit during the ...rst half of the 1990s caused concern among the public. In June 1998, voters approved a constitutional amendment requiring the federal government to balance the budget by 2001. Annual de...cit ceilings were imposed and an additional, more stringent constitutional amendment was planned for 2001. The VAT tax increases of 1999 and 2001 were thus a response to such legal/constitutional demands. Clearly, these tax changes responded to what was viewed as a large inherited ...scal de...cit rather than to current economic conditions.

Examples of tax changes caused by inherited public debt can be found in Belgium in 1992 and 1996, when the VAT rate increased by 0.5 percentage points each time. According to the IMF Sta¤ Report SM/92/206 for the 1992 Article IV Consultation for Belgium “[i]n the late 1970s and early 1980s, a combination of domestic political developments, attempts to cushion the e¤ects of the oil price shocks, and international recession led to double-digit ...scal de...cits (as ratios to GNP) and massive increases in government debt. The general government de...cit (excluding net lending) peaked at over 13 percent of GNP in 1981. Despite a steady reduction in the de...cit, the debt ratio rose for most of the decade, and general government debt net of shortterm ...nancial assets reached 124 percent of GNP in 1988.[...] Policy since the mid-1980s has been guided by the goal of ...rst stabilizing and then reducing the public debt ratio.[...] However, after stabilizing in 1990, it rose once again to 124 percent of GNP in 1991.[...] The agreement reached in December 1991 at Maastricht on economic and monetary union (EMU) among EC countries requires countries proceeding to the third stage of EMU to have general government ...scal de...cits that do not exceed 3 percent of GDP, unless due to temporary and exceptional circumstances, and general government debt ratios that are at most 60 percent of GDP, or else declining at a satisfactory pace.” Other examples of tax changes triggered by inherited public debt are those that took place in Europe (Hungary, Ireland, Italy, Netherlands, Poland, Portugal, and the United Kingdom) as a result of debt sustainability concerns, particularly during the 2011-2014 period. Unlike the tax hikes enacted during the early stages of the Global Financial Crisis, which were triggered by a large and sudden fall in economic activity, these more recent tax hikes were mainly motivated by debt-sustainability concerns driven by past economic conditions and budgetary decisions, rather than by current developments.

# 5 Linear estimations

Having identi...ed and classi...ed all the tax changes in our sample, we can now proceed to the econometric analysis. This section ...rst introduces our basic linear speci...cation and then discusses our basic results, the biases introduced by misidenti...cation, the role of expectations, and the mechanisms involved. Then, we also show that while the tax multiplier in industrial European economies is 17
quite negative and statistically signi...cant (in line with recent studies), it is about 3 times smaller (in absolute value) and borderline statistically signi...cant for the rest of countries.

# 5.1 Basic speci...cation

As has been the norm in the literature, this section estimates the linear e¤ect of tax changes on output. We proceed in two steps. First, we estimate the e¤ect of tax rate changes on economic growth using the single-equation approach proposed by Jorda (2005) and Stock and Watson (2007), which is based on linear “local projections”(LP). Second, we derive an expression for the tax multiplier as a function of our estimated regression coe¢ cient.

The use of LP provides several advantages over the traditional SVAR methodology pioneered by BP. Speci...cally, LP (i) can be estimated by single-regression techniques (least-squares dummy variables, LSDV, in our case), (ii) are more robust to potential misspeci...cations, and (iii) can easily accommodate highly non-linear and ‡exible speci...cations that may be impractical in a multivariate SVAR context (a feature that will prove crucial later in the paper).

In our basic linear speci...cation, the cumulative response of output growth at the horizon h is estimated based on the following regression where subscripts i and t denote country and time, respectively, �i is the country ...xed e¤ect, T and T<sup>2</sup> are the linear and quadratic trends, y and g are the logarithm of real GDP and real government spending, respectively, �y and �g measure the respective growth rates (expressed as the di¤erence in logarithms), tax rate changes (�t<sup>exog</sup> and �t<sup>all</sup> ) are expressed in percentage points, and � is the error term.<sup>19</sup> Unlike the SVAR speci...cation, the estimated coe¢ cients contained in the polynomial lags �h(L), h(L), and �h(L) are not used directly to build the impulse response function (IRF) values but only serve as controls, “cleaning”the �h coe¢ cients from the dynamic e¤ects of output and the e¤ects of past changes in government spending and tax rates.<sup>20;21</sup> For this reason, the tax rate changes

> 19 In all of our regression analyses, we use robust Driscoll and Kraay (1998) standard errors to correct for potential heteroskedasticity, autocorrelation in the lags, and error correlation across panels. Given concerns about the non-normal distribution of tax rate changes (which are zero most of the time) and small sample considerations, standard errors are computed using bootstrap techniques. In particular, standard errors are calculated from the average of 10,000 draws of the coe¢ cient vector from a multivariate normal distribution with mean and variance-covariance matrix equal to the point estimates and variance-covariance matrix of the regression coe¢ cients.

> 20 We use four lags (i.e., L = 4). The selection of four lags balances the need to account for a su¢ ciently long structure of lags in order to study the e¤ect of tax changes on output as well as to preserve most of our tax rate changes. Unfortunately, as we move towards longer lag structures, we are forced to drop some data points. Having said that, our results for the case of eight and twelve lags remain almost the same as in the four-quarter speci...cation. Figures showing the multipliers for the eight- and twelve-lag estimations are not shown for the sake of brevity.

> 21 We control for government spending for the reasons discussed in Section 4. However, not doing so does not a¤ect

18
serving as controls include all tax rate changes (i.e., �t<sup>all</sup> ). In contrast, the tax rate changes used to identify the e¤ect on output have to be exogenous in nature (i.e., �t<sup>exog</sup> ). It is important to note that, in this LP approach, each step in the cumulative IRF is obtained from a di¤erent individual equation. De...ning �yi;t+h as the accumulated output growth from t � 1 to t + h (i.e., �yi;t+h � yi;t+h � yi;t�1), the cumulative IRF values are obtained directly from the �h estimated coe¢ cients at each time horizon h. Therefore, each coe¢ cient �h represents the step in the cumulative IRF at a forward time h and is read as the accumulated response of output growth to a one percentage point increase in the tax rate.

While conceptually appropriate, a drawback of using tax rate changes as the independent variable in equation (6) is that the estimated coe¢ cients �h do not correspond to the usual tax multiplier discussed in the literature, which measures the e¤ect of a $1 change in tax revenues on the level of GDP. In other words, the coe¢ cients �h link the change in GDP to the change in the tax rate and not in the tax revenue. Following Barro and Redlick (2011, pp. 80-81), the tax multiplier at time horizon h is then computed exploiting the typical relationship between tax revenues and the tax rate<sup>22</sup> where I captures the relationship between real VAT revenue and real output, e measures the relationship between I and the VAT rate t, and �h captures how permanent is the initial tax shock at time horizon h.<sup>23</sup> Using a ...rst-order approximation of (7), the standard error of the tax multiplier can be written as where �<sup>SE</sup> h is the standard error of coe¢ cient �h. We now proceed to use this methodology to estimate the size of the tax multiplier, which will be reported, as is typical in the literature, with one-standard-error bands.

# 5.2 Basic results

Using speci...cation (6) as well as equations (7)-(8), Figure 2 shows the estimated tax multipliers at di¤erent time horizons when using exogenous legislated tax rate changes (Panel A) and all legislated

> our results. As also discussed in Section 4, if we also included changes in corporate tax rates and/or the highest personal income tax rate, results would not be a¤ected. Unfortunately, as discussed before, we do not have the average marginal personal tax rate. Results are not shown for brevity’s sake.

> 22 See Appendix 3 for the derivation of the next two expressions.

> 23 See Appendix 3 for details. We use the sample average values of e (39 percent) and of I (6.2 percent) for our tax multiplier calculations. While there is some variation across countries, the variability is fairly small. The standard deviations of e and I are 8 and 1.8 percent, respectively. The estimated �h for di¤erent time horizons h ranges between 0.99 (for �1) to 0.91 (for �8). Out of the 44 exogenous cases (i) in only 5 cases there is a tax change within two-year period and (ii) there is no tax change within one-year period. This latter evidence coupled with close to one values of �h points that most VAT rate changes are, by and large, of permanent nature.

19
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same in tax changes for industrial European and the rest of countries.<sup>30</sup> While, in principle, we cannot rule out other plausible considerations, we show in the next section that this need not be the case and that a simpler explanation could simply rely on non-linear distortionary and disincentive-based e¤ects of tax rates on output.

# 6 The non-linear e¤ect of tax changes on output

As discussed in the Introduction, and based on di¤erent types of macroeconomic models, the output e¤ect of tax changes is expected to be small at low initial levels of taxation but exponentially larger (in absolute value) when initial tax levels are high. Therefore, the distortions and disincentives imposed by taxation on economic activity are directly, and non-linearly, related to the level of tax rates. By the same token, for a given level of initial tax rates, larger tax rate changes have larger tax multipliers.

In this section, we ...rst show that these non-linear theoretical arguments are actually present empirically, and then that they can also explain (i) the linear ...ndings of Section 5 when estimating the tax multiplier for industrial Europe and the rest of countries, and (ii) the VAT or indirect tax multipliers calculated on country-speci...c studies using di¤erent empirical strategies. We also show further evidence that these non-linear e¤ects are powerful in explaining (i) the di¤erent e¤ect of tax changes on output observed depending upon the motivation of the exogenous tax change (e.g., like the one identi...ed by RR when comparing the output e¤ect of long-run growth versus inherited de...cit-driven tax changes), (ii) the perceived (survey-based) extent to which taxes reduce the incentive to work and invest, and (iii) policymakers’tax plans to deal with the current need for increasing economic activity and addressing ...scal de...cits. We also show that the same non-linear arguments are present in RR’s sample.

## 6.1 Multipliers for di¤erent levels of initial tax rates

We will ...rst evaluate how the e¤ect of tax rate changes on output depends upon the initial level of the tax rate. For this purpose, we modify our linear speci...cation (6) as follows:

> 30 Results are not shown for the sake of brevity.

27
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where �t<sup>exog+</sup> and �t<sup>exog�</sup> refer to positive (i.e., increases) and negative (i.e., reductions) exogenous tax changes, respectively. Unlike linear speci...cation (6) and non-linear speci...cation (10), speci...cation (11) includes non-linear terms of the tax changes themselves.<sup>33</sup> In particular, we include quadratic and cubic terms.<sup>34;35</sup> Raising tax changes to the power of an even number (quadratic in our case), combined with the fact that some tax changes are positive while others are negative, poses a challenge that was not present in speci...cations (6) or (10). Since raising any tax change to the power of two always delivers a positive number, any proposed speci...cation should di¤erentiate increases in tax changes from reductions. Not doing so would imply, in terms of this quadratic term, that both increases and reductions in tax rates have the same e¤ect on output. This is naturally not a concern when focusing on the linear term associated with the tax change (i.e., �1�t<sup>exog</sup> ) or when raising tax changes to the power of an odd number (e.g., �3 (�t<sup>exog</sup> )<sup>3</sup> ). In these cases, the sign of the tax change would be maintained. Obviously, this would not be an issue if the empirical speci...cation under consideration dealt with the non-linear e¤ect of a variable expressed in levels (as opposed to its change). To deal with this challenge in a manner that allows us to use the entire set of exogenous tax changes, speci...cation (11) constrains the quadratic coe¢ cient associated with �t<sup>exog�</sup> to be that of �t<sup>exog+</sup> with the opposite sign.<sup>36;37</sup> Panel B in Figure 10 shows the estimated tax multipliers after two years, evaluated at alternative initial tax rate levels and sizes of tax changes. The results clearly support our previous ...ndings. Blue color area in Panel B represents a statistically zero tax multiplier. We can see that the most negative multipliers occur for high levels of both the initial tax rate and the size of the tax rate change. In other words, the fall (increase) of output associated with increasing (reducing) revenues by $1 (i) tends to be zero for low levels of initial tax rates and when small tax changes are involved and (ii)

> 33 In speci...cation (10), the non-linear e¤ect of tax changes is the result of interacting tax changes with the initial tax rate levels. Tax changes themselves (i.e., term �1�t<sup>exog</sup> ) as well as tax changes interacting with the initial tax rate levels (i.e., term � ��t<sup>exog</sup> � t<sup>all�</sup> ) both entered in a linear way.

> 34 Since theory does not point to a speci...c non-linear form, nested models’tests (using F-tests) support the selection of a cubed speci...cation. Comparing linear (i.e., restricted) and squared (i.e., unrestricted) models, both o¤er the same predicting power at all time horizons (in our case h). While a cubed speci...cation is more powerful than a squared or linear one at most time horizons, adding a term of exogenous tax changes to the fourth power does not yield additional explanatory power (particularly after a year of the tax shock). Hence, for parsimonious considerations, a cubed speci...cation is used. Similar tax multipliers are obtained if terms to the fourth power are also included. Results are not shown for the sake of brevity.

> 35 In this non-linear speci...cation, the tax multiplier de...ned in expression (7) becomes Tax multiplier (h) = ['h] = [e � �h + 'h � I], where 'h � �1h + �2h � �t<sup>exog�</sup> + �3h (�t<sup>exog�</sup> )<sup>2</sup> + �1h � t<sup>all�</sup> + �2h ��t<sup>exog�</sup> � t<sup>all��</sup> + �3h �(�t<sup>exog�</sup> )<sup>2</sup> � t<sup>all��</sup> . The terms �t<sup>exog�</sup> and t<sup>all�</sup> represent the change in the tax rate (expressed positively for convenience) and the initial tax rate level, respectively, at which the multiplier is evaluated. Similarly, the standard error of the tax multiplier de...ned in expression (8) becomes Tax multiplierSE (h) = �e � �h � '<sup>SE</sup> h � = �(e � �h + 'h � I)<sup>2�</sup> , where '<sup>SE</sup> h is the standard error of 'h.

> 36 If we allowed the quadratic coe¢ cient associated with �texog � to di¤er from that associated with �texog +, we could not reject the null hypothesis that both coe¢ cients are statistically the same (but with di¤erent signs) at any horizon level. If we allowed all coe¢ cients (linear, quadratic, and cubed) associated with �t<sup>exog�</sup> to di¤er from those associated with �t<sup>exog+</sup> , we could not reject the null hypothesis that all coe¢ cients associated with positive and negative changes are statistically the same at any time horizon (in the case of the linear and cubed coe¢ cients with the same sign and in the case of the quadratic coe¢ cients with opposite signs). Results of these tests are not shown for the sake of brevity.

> 37 Similar results would be obtained if the quadratic terms were excluded from speci...cation (11). Results are not shown for the sake of brevity.

30
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||Industrial<br>european|Rest of<br>.<br>countries|.<br>Difference|
|---|---|---|---|
||(1)|(2)|(1) - (2)|
|Initial tax rate|20|18|28|
|Sizeoftaxchange|1|1|0|
<!-- Start of picture text --> Industrial Europe Rest of countries<br>2 foe ENE: Pe<br>as fccfissereieietesesciche<br>& fs:<br>33<br>36<br>-4<br>GLinear estimator<br>Non-linear estimator (median value)<br><!-- End of picture text --> <!-- Start of picture text --> Peru changed Peru changed Dominican Rep. Colombia Portugal Spain changed<br>its VAT rate its VAT rate changedits VAT changed its VAT changed its VAT _its VAT rate 5<br>from 18% to from 19% to rate from 16% rate from 16% to rate 5S times times during<br>19% in 2003. 18% in 2011. to 18% in 2013. 19% in 2017. during the 1996- the 1986-2015<br>—______ _ _ 2012 period. period.<br>2 Qe * . 3 x<br>R 4 R 4 q Ff Rg 2<br>. =<25 a&s& =s a& B£é >Rg a¢ go:sg ao$2 Rx ooBuyfs<br>@ S 8 S 8 8 ¢ § = gs a §:<br>= = 2 a ir S £ a £ aed c§ & £8<br>2 2 3 2 3 & & ® 23 ¢ 23<br>= ] 56 8 sg g 2 s 2 £ ge 33 2f<br>£&2 a5 35 25 3}OS ez fo5 &es6 &$s6 =6 65<br>x<br>oO<br>vi]<br>So<br>-5<br>-6<br>GB Linear estimator from external source<br>f Non-linear estimator<br><!-- End of picture text -->
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<!-- Start of picture text --> 7.0<br>5.0<br>5 3.0<br>2 =e<br>-1.0<br>-3.0 . oe<br>Using deficit-driven tax changes<br>—5.0<br>0 2 4 6 8 10 12 14 16 18 20<br>Quarter<br><!-- End of picture text -->
<!-- Start of picture text --> 2<br>Bo 0 eee — a<br>2 ‘<br>2 ‘<br>83— -4 ‘ NS<br>6<br>8<br>0 1 2 3 4 5 6 7 8<br>Quarter<br><!-- End of picture text --> <!-- Start of picture text --> 4<br>@<br>— 4<br>6<br>01 2 3 4 5 6 7 8<br>Quarter<br><!-- End of picture text --> <!-- Start of picture text --> 2<br>an) — ot cossssseee<br>2 TT eeeete<br>2 teen<br>8<br>3€ -4<br>76<br>8<br>0 1 2 3 4 5 6 7 8<br>Quarter<br><!-- End of picture text --> <!-- Start of picture text --> 4<br>@ ae<br>— 4 aa oe<br>6<br>0 1 2 3 4 5 6 7 8<br>Quarter<br><!-- End of picture text -->
||Long-run growth|Inherited fiscal<br>factors|Difference|
|---|---|---|---|
||(1)|(2)|(1) - (2)|
|Initial tax rate|21|19|2**|
|Sizeoftaxchange|1|1|0|

||Debt-driven|Deticit-driven|Difference|
|---|---|---|---|
||(1)|(2)|(1) - (2)|
|Initial tax rate|19|18.5|0.5|
|Sizeoftaxchange|2|1|1**|
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Panels A and B in Figure 18 show the relationship between the VAT rate and the perceived e¤ect of taxes on incentives to work and invest, respectively, for a sample of 123 countries for the year 2014.<sup>42</sup> Supporting our previous ...ndings, the relationship is highly non-linear. While the perceived e¤ect of taxes on the incentives to work and invest barely changes as VAT rates increase at low/moderate levels (approximately until the VAT rate reaches 14 percent), it falls rapidly for high levels of VAT rates.

# 6.6 Non-linearities in action IV: It works in empirics, but does it work in policy?

In the recent past, two of the most pressing policy challenges faced by governments around the world have been (i) how to regain the lost economic growth of the 2000s and (ii) how to deal with larger and more persistent ...scal de...cits (161 out of 191 countries had ...scal de...cits in 2017 and 120 governments have plans for ...scal adjustment in 2018).<sup>43;44</sup> In this section, we evaluate the extent to which our nonlinear ...ndings are, in a broad sense, actually being taken into account by countries’...scal authorities when dealing with these key challenges. If the tax multiplier is essentially zero for countries with relatively low/moderate initial tax rate levels, then their governments could contemplate conducting ...scal adjustments by raising tax rates and, consequently, revenues. By the same token, it would prove ine¤ective to reduce the VAT rate to increase economic activity. In contrast, if the tax multiplier is largely negative for countries with high initial tax rate levels, it would prove quite costly to mobilize revenues by increasing the VAT rate and quite bene...cial to reduce such a rate to boost economic activity. Figure 19 shows the relationship between the VAT rate (as of November 2017) and the expected change in cyclically-adjusted revenues (as a percentage of GDP) between 2017 and 2018 (�CAR).<sup>45</sup> The evidence is quite striking in that countries’...scal authorities with low rates are, indeed, planning to boost revenues as part of their adjustment e¤orts, while countries with high tax rates are not only not planning to substantially increase revenues, but also trying to reduce such a burden. In fact, the expected change in cyclically-adjusted revenues (as a percentage of GDP) is (i) 0.4 percentage points (statistically signi...cant at the 1 percent level) for countries with VAT rates between 6 and 13 percent (with 83 percent of these countries planning increases in �CAR), (ii) -0.15 percentage points (statistically not signi...cant) for countries with VAT rates between 14 and 18 percent (with 45 percent of these countries planning increases in �CAR), and (iii) -0.52 percentage points (statistically signi...cant at the 1 percent level) for countries with VAT rates between 19 and 27 percent (with 76 percent of these countries planning decreases in �CAR). Figure 20 shows the same regularity when

> 42 Figure 18 does not include 19 countries that, in spite of having Global Competitiveness Index data, lack a VAT scheme.

> 43 For these purposes, a ...scal adjustment plan is identi...ed as a situation where the overall ...scal balance (being it de...cit or surplus) is expected to increase from 2017 to 2018.

> 44 While the number of countries planning to conduct ...scal adjustment in 2018 represent about 63 percent (or 120 out of 191) of the total number of countries, their economies represent about 86 percent of global output.

> 45 It is worth noting that the correlation between the VAT rate (as of November 2017) and the revenue (as a pecentage of GDP) for 2017 is 0.62 (statistically signi...cant at the 1 percent level).

38
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# 7 Final thoughts

This paper has estimated tax multipliers for a large group of countries following the narrative approach. Speci...cally, based on a novel dataset on VAT rates in 51 countries (20 industrial and 31 developing) and contemporaneous economic records and sources, we have identi...ed 96 tax rate changes and classi...ed them into endogenous and exogenous to current (or prospective) economic conditions. The analysis has made clear the critical importance of relying on a narrative approach as opposed to the much more common (due to its considerable ease of implementation) Blanchard-Perotti approach. In terms of the bias, the Blanchard-Perrotti approach tends to overestimate the size of the tax multiplier in our global sample due to the numerous tax changes that have responded procyclically to the business cycle. In contrast, the true e¤ect of tax changes on output would be underestimated in advanced economies like the U.S. which typically follow countercyclical tax policies by increasing (cutting) taxes in good (bad) times.

When properly identi...ed, we show, as in RR, that the tax multiplier is negative, indicating that tax hikes reduce economic activity and tax cuts boost output. Why? Because increases (decreases) in the VAT rate reduce (increase) the incentives to consume, invest, and work. However, we found –both for our global sample and for RR’s U.S. dataset –that such “average”multiplier hides important nonlinearities. In line with theoretical models, which are based on distortionary and disincentive-based type of arguments, we ...nd that the tax multiplier is essentially zero under relatively low/moderate initial tax rate levels but markedly negative when initial tax levels are high. By the same token, for a given initial tax rate, larger changes in the tax rate have larger tax multipliers. These ...ndings have important policy implications given that the initial level of taxes varies greatly across countries and thus so will the potential output e¤ects of changing tax rates.

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# Appendices

# 1 Responses of tax policy to several recent earthquakes

Ecuador 2016: On April 16, 2016, Ecuador su¤ered a severe earthquake (with a magnitude of 7.8). According to contemporaneous estimates, GDP was expected to fall about 1 percent as a consequence of the disaster, and reconstruction costs were estimated to be about 3 to 4 percent of GDP. On April 20, President Correa announced an increase of 2 percentage points in the VAT rate (from 12% to 14%). Congress approved the VAT increase on May 12 and it was implemented on June 1. The time elapsed between the natural disaster and the approval (implementation) of the tax change was 26 (46) days.

Japan 2011: On March 11, 2011, Japan su¤ered a “triple disaster”(earthquake-tsunami-nuclear meltdown), with an earthquake magnitude of 9.0. According to contemporaneous reports, the economic damages were estimated to be about 6 to 7 percent of GDP. The earthquake hit Japan’s north-east section, responsible for 6% to 8% of the country’s total production. On April 27, several “special” national tax laws were promulgated and became e¤ective immediately. Also, an expected cut of 5 percentage points of the Japanese corporate tax rate (announced on December 2010 by the Prime Minister) was deferred as consequence of the earthquake. Therefore, the time elapsed between the natural disaster and the approval and implementation of tax changes was of 47 days.

India 2001: On January 26, 2001, India su¤ered a severe earthquake (with a magnitude of 7.7). According to contemporaneous reports, the economic damage was estimated to be about 0.8 percent of GDP. On February 1, the Cabinet imposed a nationwide 2 percent surcharge on both income and corporate taxes in order to help ...nance the reconstruction of the a¤ected areas. Therefore, the time elapsed between the natural disaster and the tax change approval was 6 days.

California 1989: On October 17, 1989, California su¤ered a severe earthquake (with a magnitude of 6.9). According to contemporaneous reports, the economic damage was estimated to be about 1 percent of California’s GDP. The Governor called for a Special Session to address the needs for earthquake relief to be held on November 2. On November 4, a package of legislation was approved including a one-year 0.25% surcharge to the State’s sales tax. The tax increase became e¤ective on December 1. Therefore, the time elapsed between the natural disaster and the approval (implementation) of the tax change was 18 (45) days.

# 2 Model

What follows is a simple general equilibrium reduced-formed-solution type of model which explains the non-linear e¤ects of VAT on output based on distortionary and disincentive-based arguments originated by the presence of informality. The representative agent (RA) maximizes by selecting the consumption of formal and informal goods, subject to the budget constraint The variables w, L, p, t, and T are wages, total worked hours (which are assumed as given), relative price of the informal good in terms of the formal one, VAT rate (which is only paid by the formal 43
good), and government’s lump sum rebate (to avoid wealth e¤ects of taxation).

There are two types of representative ...rms (RF), one in the formal sector (RFformal) and the other one in the informal sector (RFinformal). RFformal and RFinformal maximize pro...ts by selecting Lformal and Linformal, respectively. For simplicity, we assume that both RFformal and RFinformal have identical production functions: yformal = (Lformal)<sup>�</sup> and yinformal = (Linformal)<sup>�</sup> , where �< 1 to have decreasing marginal returns. The government collects VAT to ...nance the lump sum rebate (i.e., cformalt = T ). In equilibrium, naturally, the goods and labor markets need to clear. Solving the RA and RF problems, we obtain<sup>46</sup> Therefore, note that for any t > 0, it is easy to show that where � captures the total output e¤ect of a change in t. In other words, for example, for a given increase in t, the increase in output in the informal sector (as ...rms hire more in this sector given that now it is less costly to produce informal goods relative to formal ones) would be smaller (in absolute terms) than the fall in output of the formal sector. Why? Because the existence of VAT taxation generates, in and of itself, an initial distortion in which workers are incentivized to work in the informal sector more than in the absence of such a tax. Therefore, the marginal productivity of formal workers is, in equilibrium, larger than that of informal ones. Under this situation, an increase in the VAT rate simply increases the initial distortion, reducing output of the formal sector (more productive in equilibrium) by a larger margin (in absolute terms) than the increase in output of the informal sector (less productive in equilibrium). These last e¤ects, in turn, obviously increase the share of informality (i.e., increases yinformal<sup>�=y</sup> formal<sup>�).Naturally,whileweexempli...edthemechanismusinganincreasein</sup> the VAT rate, the same results hold if a reduction in the VAT rate was used instead.

We now show that this e¤ect is non-linear, in particular more (less) intense when starting with higher (lower) initial VAT rate levels. It is easy to show that �(t = thigh) < �(t = tlow) < 0, where thigh > tlow > 0. In other words, as the initial VAT rate starts at a higher level, and consequently at a larger initial distortion, the increase in the VAT rate operates generating a larger fall in output (and an increase in the share of informality) under a high initial VAT rate than under a low initial VAT rate. Moreover, it is easy to show that �(t = 0) = 0. This last result further shows that for truly low levels of VAT rate (mathematically speaking t = 0), our distortionary and disincentive-based arguments virtually vanish.

The proposed mechanism as well as the output and informality implications would be further ampli...ed

> 46 Derivations are not shown for brevity. Only most relevant endogenous variables are presented, also for the sake of brevity.

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if (i) the production functions of the formal and informal sectors allowed larger productivity in the formal sector than in the informal one (i.e., yformal = (Lformal)<sup>�form al</sup> , yinformal = (Linformal)<sup>�inform al</sup> , and �informal < �formal < 1), as it is frequently assumed based on ...rm level data evidence, and/or (ii) if there existed a segmentation in the labor market where formal workers were paid more than informal ones (i.e., �formal = yformal � wLformal", where 1 > " > 0), as empirical evidence strongly suggests.

# 3 Computation of tax multiplier and standard error

The derivation of equation (7) is as follows. Recall that the multiplier for time horizon h is typically de...ned as �Yh=�Rh, where R is the real VAT revenue, Y is the real output, �Yh � Yt+h � Yt, and �Rh � Rt+h � Rt. Notice that �Yh=�Rh = (�Yh=Y )= (�Rh=Y ). From equation (6), �Yh=Y = �h�t. Therefore, �Yh=�Rh = �h�t= (�Rh=Y ). Since R � I � Y , then �Rh � Y � �Ih + I � �Yh. Further, given that e � I=t is taken as a constant, then �Ih = e � �th. Hence, �Yh=�Rh = �h�t= (e � �th + I � �h � �t). Since �th � �h � �t, then �Yh=�Rh = �h= (e � �h + �h � I).

The derivation of equation (8) is as follows. From (7), Tax multiplier = f (x), where f (x) = x=(e � �h + x � I). Using a ...rst-order approximation, it follows that the Tax multiplier evaluated around a equals f (x) � f (a) + f<sup>0</sup> (a) (x � a) = f (a) + f<sup>0</sup> (x) x � f<sup>0</sup> (x) a. Hence, the variance of the Tax multiplier equals V ar [f (x)] � 0 + [f<sup>0</sup> (x)]<sup>2</sup> V ar(x) � 0 = [f<sup>0</sup> (x)]<sup>2</sup> V ar(x). Evaluating f (x) at �h, V ar [Tax multiplier (h)] = [f<sup>0</sup> (�h)]<sup>2</sup> V ar [�h]. Hence, Tax multiplierSE (h) = f<sup>0</sup> (�h) � �<sup>SE</sup> h<sup>.</sup> Using (7), it follows that Tax multiplierSE (h) = [(e � �h)= (e � �h + �h � I)<sup>2</sup> ] � �<sup>SE</sup> h<sup>.</sup>

# 4 External estimates of VAT/indirect taxation multipliers

Regarding Peru: Estimates of Peru’s Fiscal Council, 2018, “Cambios en la tasa del impuesto general a las ventas (IGV) y su efecto en la recaudación ...scal y actividad económica”reports the GDP growth response after one year of the VAT rate changes of 2003 (from 18% to 19%) and 2011 (from 19% to 18%). We use Peru’s (i) average VAT revenue (as a percentage of GDP) for the period 1990-2010 from OECD (which equals 5%) and (ii) ratio of VAT revenue (as a percentage of GDP) to the tax rate (which equals 0.28) and equation (8) to calculate the associated tax multiplier values.

Regarding Dominican Republic: Hamilton Taveras, 2017, “Shocks de información y efectos de una reforma tributaria en la Republica Dominicana: Un enfoque a partir de los modelos DSGE Bayesianos” reports the GDP growth response after one year of the VAT rate change using a Bayesian DSGE model calibrated for the period 2007-2015. During such a period, Dominican Republic changed its VAT rate only once, from 16% to 18% in 2013. We use Dominican Republic’s (i) average VAT revenue (as a percentage of GDP) for the period (which equals 2.9%) and (ii) ratio of VAT revenue (as a percentage of GDP) to the tax rate (which equals 0.2) and equation (8) to calculate the associated multiplier value.

Regarding Colombia: Bancolombia, 2016, “Análisis especial: El proyecto de reforma tributaria y sus efectos macroeconómicos”reports the GDP growth e¤ect after one year of the VAT rate change from 16% to 19% in 2017. We use Colombia’s (i) average VAT revenue (as a percentage of GDP) for the period 1990-2010 from OECD (which equals 4%) and (ii) ratio of VAT revenue (as a percentage of GDP) to the tax rate (which equals 0.31) and equation (8) to calculate the associated multiplier value.

Regarding Portugal: Pereira and Wemans, 2013, “Output e¤ects of a measure of tax shocks based on changes in legislation for Portugal” use the narrative approach covering the period 1996-2012 to 45
estimate the tax multipliers of indirect and direct taxation. For indirect taxation, the authors ...nd a multiplier of -2.3 after one year of the tax shock. Since such a multiplier is based on tax changes identi...ed for the 1996 to 2012 period, we report as our non-linear estimate, the median non-linear estimate for VAT rate changes in such a period, which involves (i) a tax increase from 17% to 19% in 2002, (ii) a tax increase from 19% to 21% in 2005, (iii) a tax decrease from 21% to 20% in 2008, (iv) a tax increase from 20% to 21% in 2010, and (v) a tax increase from 21% to 23% in 2012.

Regarding Spain: Gil, Marti, Morris, Perez, and Ramos, 2017, “Output e¤ects of tax changes: Narrative evidence from Spain”use the narrative approach covering the period 1986-2015 to estimate the e¤ect of indirect and direct taxation. For indirect taxation, the authors ...nd a multiplier of -5 after two years of the tax shock. Since such a multiplier is based on tax changes identi...ed for the 1986 to 2015 period, we report as our non-linear estimate, the median non-linear estimate for VAT rate changes in such a period, which involves (i) a tax increase from 12% to 13% in 1992, (ii) a tax increase from 13% to 15% in 1993, (iii) a tax increase from 15% to 16% in 1995, (iv) a tax increase from 16% to 18% in 2010, and (v) a tax increase from 18% to 21% in 2012. x and xx refer to the e¤ect after one and two years of the tax shock, respectively.

# 5 Can non-linear distortion-based arguments explain the e¤ects of di¤erent exogenous tax changes when using RR’s sample?

In Section 6.4, we explained the e¤ects of di¤erent exogenous tax changes based on non-linear arguments using our global sample and narrative strategy. This appendix analyzes whether the same type of non-linear arguments is present in RR’s U.S. dataset and the extent to which they can explain the di¤erent response of output to tax changes motivated by long-run growth considerations relative to de...cit-driven ones. In order to maintain the comparability with RR’s study, we use their speci...cation and econometric strategy. In particular, RR’s basic speci...cation is as follows: where y is the logarithm of real GDP (and thus �y measures the real GDP growth rate) and �t<sup>exog</sup> is RR’s measure of legislated tax change.

First, we proceed as in Subsections 6.1 and 6.2 and evaluate whether the e¤ect of tax changes on output depends upon the initial tax level and the size of the tax change. Using the same type of interaction strategy proposed in speci...cations (10) and (11), Panels A and B in Figure A1 show similar ...ndings to those obtained before using a global sample. This evidence further supports that the output e¤ect of tax increases is, as theoretically argued, highly non-linear and becomes more negative with the initial tax level and size of the tax change.

Second, we analyze whether the di¤erences in the initial tax levels and/or the respective size of the tax changes across long-run growth and inherited de...cit-driven tax changes may help explain the di¤erences in tax multipliers identi...ed by RR and reported in Section 6.4. Table A1 and Figure A2 are equivalent to Table 3 and Figure 13 from Section 6.4. Table A1 and Figure A2 also support that a key reason why RR’s tax changes driven by long-run growth motivations have a more negative e¤ect on output than that of inherited de...cit-driven ones lies on the larger initial tax rates observed for the former group.

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||Long-run growth|=Detficit-driven|Difference|
|---|---|---|---|
||(1)|(2)|(1) - (2)|
|Initial tax level|23.7|23.3|0.4**|
|Sizeoftaxchange|0.34|0.22|0.12|
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