# **4. Robustness Tests, Anticipation Effects and Heterogeneity**

# **4.1 Robustness Tests**

This section presents an additional set of results to investigate whether our main results (presented in Table 1) are robust to additional controls or ways of identifying outliers, and also compares to the literature. The result tables are in Online Appendix 4.

**Alternative treatment of outliers and influential observations.** This subsection tests the robustness of our findings to alternative assumptions about winsorizing growth data and excluding influential observations. Online Appendix Table A4.1 Column 1-6 starts this analysis by re-estimating Table 1 including both influential observations (EE2011 and HR2016 in country-level regressions) and not winsorizing any growth data. Even in this case, we find little evidence of large multipliers (>1), with the exception of IV country-level results for CEE countries, which are now very large (2.36) and significant at 5%. This large and significant coefficient is due to the inclusion of one influential observation (specifically Croatia 2016); in Column 8 we remove both influential observations, and the CEE multiplier becomes insignificant (because the first stage is now weak). Including influential observations and not winsorizing also makes multipliers for OLS CEE (subnational) and All Europe (country level) insignificant at the 5% level (they were significant in Table 1). The insignificance of the former is due to the larger standard errors/smaller coefficient with winsorized data, and the insignificance of the latter is due mostly due to the inclusion of influential observation Estonia 2011 (excluding influential observations makes the latter significant in column 7).

An alternative approach is to winsorize at a different level. In our default results, we winsorized at the 90% level for the more-volatile NUTS2 data, and at the 98% level for the country-level data. Reversing this in Online Appendix Table A4.2 so NUTS2 data are winsorized at 98%, and country-level data are winsorized at 90%, generates broadly similar results (few multipliers above one). While a more aggressive winsorizing level (lower percentage) often leads to marginally larger estimates with slightly smaller standard errors, results are still similar to our baseline, even winsorizing at the 80% level (Online Appendix Table A4.3).

**Alternative Controls.** Our default specification is parsimonious; it only includes lagged GDP growth as a control (in addition to time and region fixed effects). In this section we show that our results are robust to a range of controls used in the literature. First, we add the change in the institutional index (also used by Durand and Espinoza 2021).<sup>54</sup> Results are almost identical to those in Table 1 (not reported). A second possible control is population growth, as much of the literature seeks to explain per capita GDP growth rather than aggregate GDP growth (as we do in Equation 1). Adding population growth (sourced from Eurostat) has almost no effect on the results; significance at the 5% is the same as in the baseline results, and most estimates are almost identical (not reported).

> 54 To get the institutional index, we use data from the International Country Risk Guide (ICRG). In particular, we construct an index of institutional quality as an average of subindices of government effectiveness, the rule of law, regulatory quality, and control of corruption, where each subindex is first normalized to be between zero and one.

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