conditions over time or other time‐variant household factors. The model regresses the household specific difference of the income in one specific year from the mean in years with observations using the difference of weather conditions in one year from their means in all observed years.<sup>7</sup> By taking differences, all time‐invariant commune and household‐fixed effects are taken out eliminating any omitted variable bias caused by time‐invariant factors.

To take advantage of the full data set and test the robustness of the results, additional models are fitted based on the _Pooled_ data set, which estimate the determinants of income differences between households. First an Ordinary Least Squares model (OLS) is fitted that controls for observable commune characteristics in _Z_ ( _Pooled OLS_ ). These commune controls include long‐term rain and temperature levels and variability calculated from the CRU data and other location‐specific factors (e.g. altitude, slope, soil conditions, tree cover, distance from city and roads) calculated from other geo‐spatial data sets.<sup>8</sup> Whereas the set of commune controls reduces omitted variable bias caused by time‐invariant commune characteristics, it is unlikely to eliminate it. To further reduce this bias, a fixed‐effects linear model is fitted by including a dummy for each commune in _Z_ ( _Pooled FE_ ). This specification can control for commune‐ fixed effects, but not for unobservable household‐fixed effects.<sup>9</sup> Where unobserved household‐factors are correlated with weather deviation (e.g. cultural preferences or risk aversion), they can also lead to omitted variable bias, which can only be reduced through the _Panel FE_ model.

These regression models are estimated for various sub‐samples to disentangle differences between socioeconomic groups and climate zones. To identify weather impacts on different income activities, the regression models are also applied to the household sub‐sample participating in the respective income activity.<sup>10</sup> Each model is calculated separately for each of the five sets of weather variables specified in section 4. Robust standard errors are estimated by clustering at the commune‐level in order to account for spatial correlation. The natural logarithm of the outcome variables is used in the regression to

> 7 For households with observations for only two years, this approach corresponds to regressing the difference in incomes between the two years on the difference in weather conditions.

> 8 The advantage of using observed time‐invariant commune factors is that they allow estimating their impact on income differences, which is not possible in a fixed effects model using the Pooled Cross‐section or Panel data set. 9 The effects of other observable, time‐invariant commune factors cannot be estimated.

> 10 In the _Panel FE_ model, only those households are included that have reported the respective income activity in both years. Although it would also be interesting to analyze how weather variability affects the choice to take‐up a new activity or to drop an existing activity, the limited number of households with such changes does not allow for a meaningful analysis. For the _Pooled_ data set selection models were tested, as the factors that drive participation in an activity can be very different from those that determine income levels. Such selection biases can be corrected by a Heckman selection model using limited information maximum likelihood (LIML) or full information maximum likelihood (FIML) estimators (Heckman, 1979). Yet such estimators are not robust when the model is not correctly specified or subject to collinearity (Puhani, 2000).  The levels of collinearity found in this data when estimating selection models for the different incomes exceed critical levels as defined in other work (Leung and Yu, 1996). This collinearity is possibly caused be the lack of sufficient exclusion restrictions, i.e. variables that determine income levels but not participation in the income activity. In the presence of such collinearity problems OLS for the sub‐ samples without correction of election biases provide more robust estimates (Puhani, 2000).

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