assume a specific functional form for environmental income, other or total income, we use a quadratic function, which may be justified by a second-order Taylor approximation.

In the previous section we had argued that households respond in two ways to climate and weather, respectively. In a first step, they choose income activities and crop portfolios according to their climatebased weather expectations. In a second step, they redirect some production factors after weather realization. We measure the former impact on income by including _climate means_ in our regression framework. To account for the latter effect we include as weather deviations from the mean in our survey year _weather anomalies_ . The impact of a positive deviation from the mean temperature or precipitation on agriculture depends on the regional climate. We therefore allow the effect of a positive and a negative shock to differ between hot or wet and cool or dry climates (see Section 2), hence using interaction terms in the estimation part (Section 5).<sup>6</sup> In this specification, the coefficients of the climate means capture the effect of expected weather on expected income. With caution, they can be interpreted as the effect of climate change with adaptation (Dell et al. 2014). The point estimates for the deviations from mean climates capture the effects of climate shocks on income. They can be interpreted as the effect of weather shocks on income with _ex post_ coping but no _ex ante_ adaptation. The coefficients on the interaction terms capture the effects that a deviation from the mean may have different effects on income, depending on the mean. For instance, more rain in humid climates likely means something different than more rain in dry climates.

Unlike some studies that analyzed the effect of floods on income (e.g. Bui et al. 2014) we have no problem with spatial endogeneity. Our weather anomalies are standardized by the standard deviation of weather in a specific location. Therefore they reflect an unusual large deviation of weather from the mean and all villages face similar probabilities of weather anomaly as a result.

Next, we want to address the question of which controls to include. Any controls that the household has at its command could potentially bias the climate results, as they can be employed according to weather expectations or realizations, and may thus themselves be functions of weather (Welch et al. 2010). Further, to the extent that income is a function of climate, and capital is related to accumulated income, then capital will be a function of climate as well. Including capital endowments might therefore potentially pick up a large share of the climate effect on sector income. On the other hand, households’ accumulated assets (including human capital) are co-determined by many factors that are independent of climate, and have thus also in our previous analyses proved to be important contextual factors in explaining household income differences in the PEN data (Angelsen et al. 2014). Furthermore, comparing estimations both with and without capital/asset controls may allow us to distinguish some _ex ante_ adaptive strategies of are an affine transformation of the crop yields. This is because the affine transformation of a quadratic function is quadratic function. This result allows for a wide range of profit specifications involving fixed and proportional costs.

> 6 If the response of income to weather can be approximated by a quadratic function of mean annual temperature (temp) and total annual precipitation (prec), then this is equivalent to regressing income on climate means in linear and squared from, deviation from the climate means in linear and squared form, and the linear interaction terms between climate means and deviation from the climate means. We drop the squared terms for the temperature and precipitation anomalies, as few values exceed unity and the differences between the linear and squared term are small).

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