A more rigorous OLS regression analysis yields a statistically significant estimate of 1.5 for coefficient β<sup>�</sup> in equation (1), which links the initial expenditure per capita and the subsequent growth rate (table 4). This estimate means that a state whose household expenditure per capita in 2004 was 10 percentage points higher than the average experienced an annual growth rate that was about 0.15 percentage points higher than the average.

**Table 4: Absolute convergence in expenditure per capita, 2004–11**

||**State l**|**evel**||**District level**|||**Place level**||
|---|---|---|---|---|---|---|---|---|
|Sample|Largest 21<br>states|All 31<br>states|Largest 21<br>states|All 31<br>states|25<br>quantiles|Largest 21<br>states|All 31<br>states|25<br>quantiles|
|Log of 2004<br>expenditure per<br>capita|1.479*<br>(0.798)|–1.686<br>(1.866)|–2.574***<br>(0.540)|–2.537***<br>(0.513)|–2.472***<br>(–0.661)|–4.886***<br>(0.386)|–4.747***<br>(0.373)|–4.740***<br>(–0.503)|
|Constant|–6.469<br>(5.625)|15.161<br>(12.893)|21.233***<br>(3.685)|20.915***<br>(3.507)|20.468***<br>(–4.528)|37.203***<br>(2.644)|36.195***<br>(2.558)|36.149***<br>(–3.453)|
|No. of observations|21|31|512|561|25|1,218|1,315|25|
|R<sup>2</sup>|0.102|0.074|0.054|0.051|0.421|0.136|0.128|0.848|
|Adjusted R<sup>2</sup>|0.055|0.042|0.052|0.049|0.396|0.136|0.127|0.842|

_Note_ : Standard errors are in parentheses.

Significance levels: * = 0.1, ** = 0.05 and *** = 0.01.

Even if we expand the sample to 31 states, we find no evidence to support absolute convergence in living standards across states. The estimated coefficient β<sup>�</sup> becomes negative, but it is statistically insignificant. The change in the sign of the relationship is primarily driven by the three small richer states that grew relatively slowly.

A valid question is whether the conclusion would have been the same had GDP per capita been used to measure living standards, instead of household expenditure per capita. To answer this question, we repeat the analysis for the growth of GDP per capita across states over 2004‐2011, using official data from MOSPI (2015). But again, we find no evidence of convergence across states. For the largest 21 states, the estimate of the convergence coefficient β<sup>�</sup> is 1.1, very close to the one estimated using household expenditure per capita. Moreover, the coefficient based on GDP per capita is statistically insignificant, which is consistent with previous studies.

In sharp contrast, we find strong evidence of absolute convergence of living standards when the district rather than the state is the unit of observation. The results are not sensitive to the choice of the sample, which is also in contrast to the results of the state‐level analysis. For both large states and all states, the estimate of β<sup>�</sup> is significantly negative (between –2.6 and –2.5). Therefore, a district whose household expenditure per capita in 2004 was 10 percent higher than the average experienced an annual growth rate 0.25 to 0.26 percentage points lower than the average.

The speed of absolute convergence is twice as fast when considering place instead of district as the unit of observation. The estimate of β<sup>�</sup> remains significant and negative, regardless of the choice of sample. Based on these more granular estimates, a place whose household expenditure per capita in 2004 was 18