in the wide (narrow) band. Clearly, then, the productivity impact of temperature shocks greater than half a degree must be inferred by extrapolation out of our sample. Yet, most climate change scenarios for India over the next 30 years predict two and a half times this much warming.

With this caveat in mind, we proceed to the panel estimates in Table 4. The first two columns report annual weather shock impacts on gross revenue per hectare controlling for, respectively, a linear year trend (quadratic and cubic terms were not significant) and for year dummies. There is no compelling reason to choose one of these specifications over the other a priori, since macro shocks affecting land productivity are unlikely to be correlated with weather (recall that, by construction, our gross revenue measure is invariant to intertemporal crop price movements). Be that as it may, the estimates show that a 1<sup>_◦_</sup> C increase in annual temperature reduces gross productivity per hectare by 24 percent with a year trend and by 31 percent with year dummies.

Working with year dummies, we next disaggregate temperature and rainfall into their seasonal averages (or totals in the case of rainfall). Since kharif and rabi season temperature shocks are much less intercorrelated than the corresponding seasonal temperature normals, it should be easier to distinguish seasonal temperature effects with panel data than with cross-sectional data. In the event, we find that higher kharif temperatures reduce annual productivity by nearly twice as much as higher rabi temperatures (column 3 of Table 4). Together with the fact that the value of kharif output is typically double that of rabi output, this result implies that the temperature sensitivity of kharif and rabi production are roughly equal.<sup>23</sup> Our evidence also shows that rabi precipitation, relatively minor as it is, has no significant productivity impact, hence its exclusion from all subsequent specifications. Quadratic terms, shown in column 4, are also not significant for seasonal temperature, but there are diminishing marginal returns to kharif season precipitation.

Results in column 5 of Table 4 allow for interactions of seasonal weather variables with the proportion area irrigated in the district.<sup>24</sup> Consonant with the cross-sectional findings, the

> 23Denoting gross annual revenue by _Y_ , revenue per hectare by _y_ , and temperature by _T_ , one can show that

where subscripts denote kharif ( _K_ ) and rabi ( _R_ ) specific values of the relevant variable. Our estimate of _YK/YR_ comes from the 59th round of the NSS, which gives gross revenue by season at the household level for the 2002-03 crop-year. Since the left-hand side is around two, as is _YK/YR_ , _d_ log( _yK_ ) _/dTK_ must be close to _d_ log( _yR_ ) _/dTR._

> 24This variable is calculated from the 59th round of the NSS, as these data have the most complete district-wise coverage and are measured at the midpoint of the relevant period. The correlation between this irrigation ratio and a corresponding one calculated from Ministry of Agriculture data on the subset of districts for which the latter is available is about 0.8.

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