آشتی SVAR و برآوردهای روایی ضرایب مالیاتی

Existing empirical estimates of US nationwide tax multipliers vary from close to zero to very large. Using narrative measures as proxies for structural shocks to total tax revenues in an SVAR, we estimate tax multipliers at the higher end of the range: around two on impact and up to three after 6 quarters. We show that earlier findings of lower multipliers can be explained by an output elasticity of tax revenues assumption that is contradicted by empirical evidence or by failure to account for measurement error in narrative series of tax shocks.

The empirical literature on the dynamic output effects of unanticipated changes in tax policy does not speak with one voice. Although most studies agree that tax increases are contractionary, there is considerable disagreement regarding the size of the effect on economic activity. Estimates of tax multipliers for the United States vary from close to zero to almost four, a range that is sufficiently wide that the literature provides only limited guidance for theory and economic policy. The broad range of estimates reflects numerous differences in methodology, including identification assumptions, model specifications, as well as sample coverage. In this paper, we use a new approach to estimate tax multipliers associated with shocks to total federal tax revenues. Our estimates imply tax multipliers of around two on impact and up to three after one-and-a-half years. Importantly, we provide a reconciliation of our estimates with previous findings in the literature. The main challenge to measuring the aggregate effects of changes in tax policy is endogeneity of fiscal policy instruments. One strand of the literature has identified tax shocks by imposing short run restrictions in structural vector autoregressions (SVARs). In a seminal contribution, Blanchard and Perotti (2002) make assumptions on policy lags and calibrate certain parameters to identify structural innovations to taxes and government spending. Mountford and Uhlig (2009) use economic theory to derive sign restrictions on VAR impulse responses. Another part of the literature instead assumes that some exogenous changes in tax policy are observable. In a leading example, Romer and Romer (2009) construct comprehensive narrative measures of legislated changes in federal tax liabilities in the United States for the postwar period. A number of studies estimate the output effects of tax changes as the response to innovations in one of these narrative measures.1 Unfortunately, the estimated output effects of tax shocks vary significantly both within the SVAR and narrative approaches. Blanchard and Perotti (2002) find tax multipliers that are small on impact and never exceed unity thereafter. The sign restriction approach of Mountford and Uhlig (2009) yields maximum multipliers of more than three for horizons of several years after a deficit-financed tax cut. Caldara and Kamps (2012) investigate closely the source of the difference between both these SVAR estimates and show analytically that the identified tax multiplier is increasing in the output elasticity of tax revenues as long as this elasticity does not become too large. They point out that the divergence in the estimates of Blanchard and Perotti (2002) and Mountford and Uhlig (2009) mostly reflects different ex ante assumptions about the value of the output elasticity of tax revenues. They propose instead to formulate a prior based on information from available studies and obtain tax multiplier estimates that properly reflect the uncertainty surrounding the output elasticity of tax revenues. The key finding of Caldara and Kamps (2012) is that tax multipliers in the mid range are most probable and also that they are likely to be smaller than government spending multipliers. Using the narrative approach, Romer and Romer (2010) find output increases of more than three percent approximately two years after a one percentage point cut in tax liabilities to GDP. Eliminating tax changes that are likely to be anticipated because of long implementation lags, Mertens and Ravn (2012) find maximally two percent increases in output following a one percentage point cut in tax liabilities to GDP. Favero and Giavazzi (2012) instead find output effects of Romer and Romer (2010) shocks that are similar to the much lower estimates of Blanchard and Perotti (2002). Charhour et al. (2012) investigate a claim made by Favero and Giavazzi (2012) that alternative assumptions regarding model specifications explain the differences between the Blanchard and Perotti (2002) and Romer and Romer (2010) estimates. They conclude that a reconciliation of the results must instead lie with identification assumptions and/or sampling uncertainty. Finally, Perotti (2012) produces a refined measure of Romer and Romer's (2009) tax changes and finds output tax multipliers that are larger across various specifications than those in Blanchard and Perotti (2002). We adopt a new approach to the estimation of tax multipliers, described in Mertens and Ravn (2012) and Stock and Watson (2012), that integrates narrative identification into the standard SVAR framework.2 The key identifying assumptions are that the narrative measures correlate with tax shocks but are orthogonal to other structural shocks. The narrative tax changes are treated as proxy measures of latent structural tax shocks, which is why we refer to it as the ‘proxy SVAR’ approach. The main idea is to complement the usual VAR residual covariance restrictions with moment restrictions on the proxy to achieve identification. An application to US post WWII data yields estimates of tax multipliers that are large, robust and relatively precisely estimated. At medium forecast horizons, our results support tax multipliers at the higher end of the range, such as those of Mountford and Uhlig (2009) and Romer and Romer (2010). However, we find tax multipliers that are larger than these studies also in the short run. The proxy SVAR allows us to elicit the underlying differences between the estimates produced by alternative identification schemes. Unlike the Blanchard and Perotti (2002) or Caldara and Kamps (2012) SVARs, the proxy SVAR does not require direct assumptions or priors for the key structural elasticities but instead estimates them. Because the specification in both SVARs are identical in every other respect, the discrepancy between results can be traced to the values of those structural elasticities. In close analogy with Caldara and Kamps (2012), the answer lies exclusively with the output elasticity of tax revenues. The proxy SVAR estimates this elasticity to be high and rejects at the 95% level the lower cyclical elasticities calculated by international organizations on which Blanchard and Perotti (2002) rely. We provide several criticisms of the conventional cyclical adjustment procedures and argue that alternative methods available in the literature, while small in number, all point to high output elasticities, and therefore large tax multipliers. Our methodology also has an advantage over existing narrative approaches because it is robust to various types of measurement error. We discuss several reasons why some error in measurement is hard to avoid when constructing the narrative measures of tax shocks, including those that concern Perotti (2012). The proxy SVAR yields estimates of the statistical reliability of the narrative series, which measures the squared correlation between the narrative measures and the estimated structural shocks. This statistic allows for an evaluation of the quality of different available tax shock measures. We find for instance that it is important to correct for anticipated tax changes. Another issue in the calculation of the output effects of tax changes is the scaling of shocks. As in Blanchard and Perotti (2002) or Mountford and Uhlig (2009), we scale the tax shocks by their impact on tax revenues to obtain tax multipliers. Standard applications of the narrative approach instead scale the tax shocks in terms of their projected impact on tax liabilities. We quantify the measurement error bias present in the existing narrative specifications through simulations. We find that measurement error explains the differences across the narrative estimates and is the reason for the low tax multipliers estimated by Favero and Giavazzi (2012). The key objective of this paper is to understand the dispersion of estimated tax multipliers associated with unanticipated shocks to total revenues. In doing so, we abstract from other issues relevant to the empirical characterization of the aggregate effects of tax policy shocks. For instance, we focus exclusively on unanticipated tax changes. Other studies have looked at shocks to expectations of future tax policy, e.g. Mountford and Uhlig (2009), Mertens and Ravn (2012), Leeper et al. (2011) or Kueng (2011). As in most previous work, there is no attempt to define more narrowly which of the many tax instruments is adjusted, as is done in Barro and Redlick (2011) or Mertens and Ravn (2012). Finally, we restrict attention to linear models that do not allow for time-varying effects such as in Auerbach and Gorodnichenko (2012). Nonetheless, the identification and measurement issues we raise are also highly relevant for extensions in any of these directions.

A burgeoning empirical literature on the aggregate effects of changes in tax policy has produced a range of estimates of the effects on economic activity sufficiently broad that one might question the value of the findings. In this paper, we analyze the underlying reasons for the disagreement among the various methodologies. We do this by an application of a structural vector autoregression in which tax shocks are identified by proxies based on narrative tax shock measures. Our proxy SVAR estimates large tax multipliers in US data with relatively high precision. A comparison with the popular (Blanchard and Perotti, 2002) approach reveals a fundamental conflict in the cyclical adjustment of tax revenues. The narrative identification method clearly implies that the output elasticity of tax revenues is significantly greater than calculated by international organizations. Differences with earlier narrative studies can be explained by measurement error, which our proxy SVAR identifies in the data. The evidence in this paper is supportive for tax multipliers that are at the higher end of the range, such as those of Mountford and Uhlig (2009) and Romer and Romer (2010), and rejects the lower estimates of for instance Blanchard and Perotti (2002) and Favero and Giavazzi (2012). Unlike all these studies, however, we also find large output effects of tax changes in the short run. There are several directions for future research. Our analysis raises concerns with the cyclical adjustment procedures of government and international institutions and calls for alternative, structural, approaches to the estimation of the output elasticity of tax revenues. This is important since this elasticity is a vital ingredient of policy evaluations, budget forecasting, and other empirical work, e.g. on fiscal consolidations by Alesina and Ardagna (2010). In focusing attention on cyclical adjustment and measurement error, we followed the common practice of studying the effects of shocks to total revenues in linear models. Other aspects of the empirical study of tax policy shocks, such as the dependence on the type of the tax instrument being adjusted or the possible time-varying nature of tax multipliers can be incorporated. Given that narrative measures of policy shocks become increasingly available, our analysis can be repeated in the future for other countries as well as for other types of shocks. Finally, our analysis is also informative about features that can improve the explanatory and predictive power of theoretical models of fiscal policy. These features are likely to include large tax multipliers and high output elasticities of tax revenues.