ways. One of them, mimicking the traditional literature on growth convergence across countries, assumes that all k� indicators in a bucket have the same prior inclusion probability 1⁄k� . This helps to reduce the sensitivity of results (Rockey and Temple 2016). The other way is totally agnostic, and therefore each of the K indicators considered has an inclusion probability equal to 1⁄K . This other way is used as a robustness check.

Because our study covers hundreds or even thousands of localities, degrees of freedom are much less of a constraint than in the growth literature on which most studies of convergence have been based (Levine and Renelt 1992). The large number of observations also increases the stability of the estimated coefficients, which in the cross‐country literature have proven sensitive to small changes in the data (Ciccone and Jarociński 2010).

We also improve over the previous literature on the computational front. Until recently, computational constraints prevented the full implementation of this kind of analysis. For example, Sala‐i‐Martin, Doppelhofer and Miller (2004) ran 100,000 regressions at a time, at which point they replaced the prior probabilities with the estimated posterior probabilities and start again, until the process converged and probabilities stabilized. A compact algorithm developed for this paper allows us to run one billion regressions on an ordinary laptop computer in a few hours. The C++ code is available on request.

# 4. Data

We use household consumption expenditure per capita as the living standards indicator. Data are from the Household Consumer Expenditure modules of the 61st and 68th rounds of National Sample Surveys of India, hereafter identified as NSS 2004–05 and NSS 2011–12. These surveys were conducted between July 2004 and June 2005 and between July 2011 and June 2012, respectively (NSSO 2005, 2012). They report household consumption information on an itemized form. We use monthly consumption based on the mixed recall period and divide by household size to compute the monthly nominal household expenditure per capita.

To account for spatial price variations, we deflate the resulting nominal expenditure by a year‐specific subnational deflator that differs across state and between rural and urban areas. To allow for comparability across years, we further deflate the resulting expenditures by the nationwide consumer price index.

One caveat of using household‐level surveys is their vulnerability to low response rates among the rich and to underreporting of expenditures among those who respond (Ravallion 2003). As a result, survey‐ based consumption aggregates for nationally representative samples typically fall short of private consumption as measured by national accounts. With the underestimation being larger in better‐off locations, the convergence coefficient ( β<sup>�</sup> or β<sup>�</sup> ) could be biased in the direction of greater apparent convergence. However, the discrepancy between levels of consumption as measured by India’s NSS and national accounts has stabilized since the late 2000s, which mitigates the risk of bias for the period under consideration in this paper (2004 to 2011).

When using living standards as performance indicator to study drivers of growth, the finding can be biased by self‐selection and sorting. Households are heterogeneous in their mixture of skills, energy and entrepreneurship, and the most productive often drawn to more productive places (Combes, Duranton and Gobillon 2008; Combes et al. 2010). To account for this possibility, we consider the growth in 13