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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