one crop might fail for another. Finally, it is in this context that I test whether the divergence in yields is associated with the allocation of agricultural credit. The results are inconsistent with the credit allocation hypothesis. The key takeaway is that there are limits to following an umbrella policy in which the supply of credit solves all problems. Credit might not be enough when there are structural snags in the availability of more direct agricultural inputs.

The points above summarize the analysis’s three critical policy implications. Let me conclude by raising one final point that I mentioned in the introduction. The convergence tests make use of crop yields, which are only a partial measure of productivity. As such, there is no guarantee that the convergence findings will extend to multi-factor measures of productivity. Of course, lack of data on inputs is the limiting reason why the analysis relies on yields, and hence, a formal test of such concerns remains elusive. But can adjustment be made using the relationship between TFPs and yields observed elsewhere? To make progress, I use TFP measures from Avila and Emerson (2010). The estimates from the study help in adjusting the district yields in Bihar to obtain quantitative guidance on how findings might change if TFPs are used instead of the partial measure.

Before I outline the adjustment, let's first consider why the convergence tests may yield different outcomes for the two productivity measures. One option is to ascertain the relationship between yields and TFPs, and a positive association might seem sufficient to conclude that the convergence tests are robust to the choice of measure. Though reasonable, such reasoning does not suffice. Instead, what matters is whether the _bias_ present in yield (as a proxy for TFP) is systematically correlated with yield or not.

To see this, reflect on the divergence outcome and suppose that as a proxy for TFP growth, yield growth always overestimates it. If the difference between the two rates is uncorrelated with the latter, then the convergence results from one should be a reasonable first-order approximation for the other. On the other hand, divergence obtained using yields may come under threat if the difference becomes systematically correlated. Of interest is the case where the excess of yield growth over TFP growth (bias) is positively correlated with the former. In other words, differences in TFP growth across districts will be smaller than the variations in yield growth. Hence, the divergence in yields may not hold for the multifactor measure if the across district variations reduce sufficiently after adjusting for the bias.

Now let me get back to the case of Bihar. The strategy to correct the bias in district yields is to exploit the yield-TFP relationship from Avila and Emerson (2010). The study calculates annual TFP growth rates for several developing countries using output and input<sup>10</sup> data for two 20-year periods – 1961-1980 and 1981-2001. As it also provides the growth rates of output and inputs separately, it is possible to back out yield growth. Figure 6 plots the bias against the estimates of yield growth and confirms the positive association between the two variables. The coefficient of correlation is modest but also highly significant. Furthermore, note that the bias often lies in the negative zone. Yield growth not only overestimates TFP growth by a larger amount when the former is higher but also underestimates the latter when lower. Hence, in addition to exerting a larger downward force in districts with higher yield growth, a move towards the TFP measure also apply an upward push in the lagging ones, further putting the divergence result under threat.

> 10 Inputs include land, labor, fertilizer, seeds, tractors and combine harvesters.

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