than an ad-hoc and ex-post taxonomy. Let me briefly sketch the procedure of identifying convergence clubs.<sup>6</sup> First, sort the districts decreasingly according to their yields in the last third fraction of the time sample. The second step is to identify a core group of districts. To do this, the -test statistic from the regression for all highest yield districts in step 1 are obtained. The subsequent step is to kk tt tt add districts to the core conditional on preserving convergence. The core group size is chosen by log tt maximizing subject to kk∈[2, NN]≥−1.65 . If no such exists, there is no evidence of club convergence. Conditional on existence of , the third step is to sieve districts for club membership. Let kk<sup>∗</sup> and ∗ kk kk denote the set of districts in the core group and its complement respectively. Taking a district from tt tt kk<sup>∗</sup> cc∗ kk<sup>∗</sup> kk one at a time and adding it to the core group, run the kk<sup>∗</sup> regression again. Filter the districts for whom GG GGcc kk the -test statistic exceeds 0.<sup>7</sup> Starting with the district with the highest -statistic, keep adding districts GG one at a time to the group till the -statistic for each subsequent enlarged group exceeds the log tt asymptotic tt 5% critical value of −1.65 . The fourth step follows the recursion of the above three steps with tt kk<sup>∗</sup> GG tt the left-over districts not getting included in the most recent club. The final step is to merge the identified clubs, if possible. The process follows iteratively beginning with the first two clubs. For example, test for convergence among members of club 1 and 2. If the test shows convergence, then merge them together and test for convergence between the merged club and club 3. Else, proceed to test convergence between club 2 and 3.<sup>8</sup> The next section discusses the data that I use to test convergence. log tt

# **3   Data**

The data for the analysis come from Bihar Economic Surveys (BES) (Government of Bihar, 2010– 2019). Since 2010, the BESs started reporting both the annual production and the gross area under cultivation of many crops at the district level. The annual surveys jointly provide data for agricultural production in 13 periods. The first period for which the data are available is 2005-06. Utilizing the two series, I construct the district-wise crop yields. Hereafter, I refer to the production period overlapping two calendar years by the initial year for the sake of exposition (for example, the year 2007 represents the production period 2007-08). There are 38 districts in the state. Barring Arwal, the surveys have no gaps in data. Hence, I drop Arwal from my analysis. There are three major agro-climatic zones (ACZ) in Bihar - northwest alluvial plain (NW), northeast alluvial plain (NE), and south alluvial plain (South). The Himalayan rivers feed the northern zones which are flood prone whereas the southern zone is adversely affected by the onslaught of droughts. Figure 1 shows the districts and their ACZ classification.

The district-wise data on production and cultivated area for the three major crops – rice, wheat and maize, are available starting in 2005. In recent years, the surveys have also started reporting such figures for other crops like pulses, oilseeds, sugarcane etc. Nonetheless, the three cereal crops account for the bulk of the area under cultivation. The gross area under cultivation dedicated to rice, wheat or

> 6Refer to Phillips and Sul (2007) and Phillips and Sul (2009) for details on the clustering procedure.

> 7It is possible to aim for more clubs by increasing the threshold for -test statistic. I restrict my choice of the critical value to 0 in order to target the most conservative number of convergence clubs. 8 The club identification follows a slightly different algorithm relative to Phillips and Sul (2007, 2009). Specifically, I tt follow the revision suggested in Schnurbus, Haupt and Meier (2017) which makes the manual interventions in the former procedure redundant. The analysis makes use of STATA's psecta package (Du, 2018).

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