# **Appendix C: Further robustness checks and heterogeneity analysis**

# **_C1. Robustness checks_**

In this section, we explore the robustness of our results in a number of different ways. We start with the results of panel model and long difference model presented in Tables 1 and 2 and show that our results are broadly consistent when using alternative model specifications. First, we estimate several alternate specifications to assuage the reader of misspecification concerns. These are presented in Tables A1 and A2 (Appendix A). Our panel model with fixed effects represents a substantial improvement over the standard cross-sectional regression, but it may also be subject to bias if there are unobservable, time-varying differences across countries or regions. We show that our estimates are insensitive to the inclusion of country (region) specific time trends (Columns 1 and 2, Table A1). Another concern is related to misspecification of the functional form of temperature. Therefore, from Columns (3) to (7) of Table A1, we employ different functional forms of temperature including controlling for temperature change, quadratic term and cubic term of temperature, and an interaction term between temperature and temperature change. Results of these exercises strengthen our main findings.

Similarly, we also apply different variants of the long differences model and present the results in Table A2. We first check whether our results remain robust when using different choices of window length (i.e., 4-year and 5-year period). The results in Columns (1) and (2) show that our findings are not sensitive to the alternative windows. In Column (3), we add a number of time-invariant covariates at the regional level including cumulative oil gas, distance to coast, distance to river, and altitude. Finally, we include an interaction term between temperature and temperature change in Column (4). In overall, the results are qualitatively similar to our main finding.

Second, we replicate the results in Figure 2 but using alternative thresholds to define hot and cold days. In Panel A of Figure A1 (Appendix A), we present the results of the temperature bin approach using the 2-degree bin, while Panels B and C show the results using the 4-degree bin and 5-degree bin, respectively. We find that when our definition of hot and cold days is less (or more) demanding, the implied effects on income inequality remain consistent.

Third, we present the results using alternative measures of poverty and income inequality at the subnational level. In Table A3 (Appendix A), we employ the multidimensional poverty indicators, which complement the traditional measure by capturing the acute deprivations in different aspects including monetary, education, electricity, sanitation, and drinking water. Similarly, we plot in Figure A2 (Appendix A) the effects of temperature using alternative measures of income including (i) the 90/10 ratio, (ii) the 80/20 ratio, and (iii) the Palma ratio. This helps address potential concern of using Gini and Theil indices as they are more sensitive to changes in the middle-income group. In overall, the results reaffirm the negative effects of higher temperature on poverty and income inequality.

Fourth, we provide further tests in Table A4 (Appendix A) to ensure that our results are not sensitive to the choice of temperature measures. We do so by using (i) log of temperature (Column 1); (ii) temperature measured in degrees Fahrenheit (Column 2); (iii) the temperature data at 0.5<sup>◦</sup> resolution from the Climate Research Unit of the University of East Anglia (CRU) (Column 3); (iv) the number of days that temperature is above 28<sup>o</sup> C (Column 4);<sup>15</sup> (v) dropping regions with temperature being above that level (Column 5); and (vi) temperature shock, defined as the difference between actual temperature and long-term temperature being greater (less) than 2 (-2) standard deviations (Column 6). The results show little change from the baseline specification.

> 15 We choose the temperature at 28oC as this is the most common temperature in our sample (see Figure B3, Appendix B).

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