tween annual temperature and precipitation (see Model III in Table 2). Figure 3 displays the resulting distribution of temperature effects on land values, based on a 1<sup>_◦_</sup> C increase, evaluated at the sample proportion of plots irrigated in each district. The wide range of impacts mirrors, of course, the huge spatial variation in rainfall. At the left tail of precipitation distribution are districts in the arid northwest of India (in the states of Rajastan, Haryana, and Punjab), with temperature-productivity effects exceeding _−_ 18 percent in magnitude. At the right tail, a mere seven very wet districts are predicted to slightly benefit from higher temperatures, although extrapolations this far out along the rainfall distribution should probably be taken with a pinch of salt.

# **4.3 Agricultural output and weather shocks**

Panel data covering the production of the 20 most important crops in terms of cultivated area are available for nearly 500 districts from 1999 to 2005 (though not always continuously).<sup>21</sup> We aggregate crop-wise output using state-level prices averaged over the period 2001-03 and divide by area cultivated with these crops to get gross revenue per hectare. Annual cultivation cost data are not available at the district level, so we cannot calculate net revenue, the empirical counterpart of _π_ . However, since the sensitivity of gross revenue to bad weather shocks, in general, _overestimates_ the corresponding weather sensitivity of net revenue,<sup>22</sup> our results should still provide an upper bound on long-run damages. Table 3 reports descriptive statistics for the panel data.

How much intertemporal weather variation is available to identify productivity impacts of climate change? Consider the residuals from regressions of annual average temperature and total annual rainfall on district dummies and either (1) a linear year trend or (2) year dummies. Figure 4 plots temperature against precipitation residuals for both specifications of year effects and shows a strong negative correlation; wetter than average years in a particular district, not surprisingly, tend to be cooler than average as well. Also, while most intertemporal rainfall variation falls within a generous plus or minus 500 mm/year band around the mean, temperature variation is relatively confined. With year dummies removed, almost all residual variation in temperature, 99 percent to be precise, lies inside a _±_ 0 _._ 5<sup>_◦_</sup> C range, whereas around 84 percent lies within _±_ 0 _._ 25<sup>_◦_</sup> C. Residuals are a bit more dispersed for the more restrictive linear time trend specification, with 97.5 (75) percent lying

> 21The crops are rice, wheat, jowar, bajra, cotton, maize, groundnut, sugarcane, urad, ragi, barley, gram, arhar, moong, rapeseed/mustard, potato, coconut, sunflower, soyabean, and sesamum. These constitute around 90% of cultivated area over this period.

> 22Using our earlier notation, we have _py/a_ = _π_ + _wh/a_ , and by the envelope theorem, _d_ ( _py/a_ ) _/dξ_ = _dπ/dξ_ + ( _dw/dξ_ ) _h/a_ . If _ξ_ is, say, temperature, and a positive temperature shock depresses production and wages, then _d_ ( _py/a_ ) _/dξ < dπ/dξ._

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