metadata: authors: 0: author: Li,Yue-000316086
1: author: Rama,Martin G.
2: author: Zhao,Qinghua
count: India
docna: 0: docna: States Diverge, Cities Converge : Drivers of
            Local Growth Catch-up in India
docty: Policy Research Working Paper
subtopic: Labor & Employment Law,Employment and Unemployment,Social Development & Poverty,Business Cycles and Stabilization Policies,Plastics & Rubber Industry,Construction Industry,Common Carriers Industry,Pulp & Paper Industry,Food & Beverage Industry,General Manufacturing,Textiles, Apparel & Leather Industry
teratopic: Law and Development,Social Protections and Labor,Poverty Reduction,Macroeconomics and Economic Growth,Industry
abstracts: cdata!: This paper takes a fresh look at growth
            convergence in India, combining insights from macroeconomics
            and urban economics. It departs from the existing literature
            in three ways. First, the paper assesses growth patterns
            across districts and across places below the district level
            instead of taking the state as the unit of analysis. Second,
            it relies on household expenditures per capita, instead of
            gross domestic product per capita, to measure living
            standards. And third, it uses a Bayesian model averaging
            approach to identify the key drivers of local growth,
            instead of the classical econometric approach. The paper
            finds absolute convergence in living standards across
            districts and places below the district level, with
            locations in the gray area between rural and urban growing
            fastest. In assessing conditional convergence, it finds that
            geography is a strong predictor of local growth, but
            population density is not. Market access, electrification
            and transport infrastructure matter, but irrigation and
            housing investments do not. The quality of state-level
            governance has a significant impact on local growth, but
            variations in city governance are only mildly relevant. The
            share of medium and large firms plays a role, but the
            sectoral structure of economic activity does not. And the
            coverage of primary education is an important predictor of
            subsequent growth, but not that of other levels of
            education. Strong convergence at the local level can be
            reconciled with lack of convergence at the state level if
            low-income states fail to generate enough locations with the
            "right" characteristics.
geo_reg_key: 517198,517191,517212
repnme: repnme: States Diverge, Cities Converge : Drivers
            of Local Growth Catch-up in India
display_title: States Diverge, Cities Converge :
            Drivers of Local Growth Catch-up in India
listing_relative_url: /research/2018/12/30659424/states-diverge-cities-converge-drivers-local-growth-catch-up-india
topicv3: Social Inclusion m1326031 421,Manufacturing Sectors m1326521 1281,Population, Aging and Health m1327736 640,Self-Employment m1504000 2698,Working Age Population m1504053 2749
publishtoextweb_dt: 2018-12-03T00:00:00Z
historic_topic: Law and Development,Social Protections and Labor,Poverty Reduction,Macroeconomics and Economic Growth,Industry
no_of_pages: 40
author_keys: 0: author_key: 95769
1: author_key: 123591
model_extractions: WPS8660 Policy Research Working Paper 8660 States Diverge, Cities Converge Drivers of Local Growth Catch-up in India _Yue Li Martin Rama Qinghua Zhao_ South Asia Region Office of the Chief Economist December 2018
Policy Research Working Paper 8660

# **Abstract**

This paper takes a fresh look at growth convergence in India, combining insights from macroeconomics and urban economics. It departs from the existing literature in three ways. First, the paper assesses growth patterns across districts and across places below the district level instead of taking the state as the unit of analysis. Second, it relies on household expenditures per capita, instead of gross domestic product per capita, to measure living standards. And third, it uses a Bayesian model averaging approach to identify the key drivers of local growth, instead of the classical econometric approach. The paper finds absolute convergence in living standards across districts and places below the district level, with locations in the gray area between rural and urban growing fastest. In assessing conditional convergence, it finds that geography is a strong predictor of local growth, but population density is not. Market access, electrification and transport infrastructure matter, but irrigation and housing investments do not. The quality of state-level governance has a significant impact on local growth, but variations in city governance are only mildly relevant. The share of medium and large firms plays a role, but the sectoral structure of economic activity does not. And the coverage of primary education is an important predictor of subsequent growth, but not that of other levels of education. Strong convergence at the local level can be reconciled with lack of convergence at the state level if low-income states fail to generate enough locations with the “right” characteristics.

This paper is a product of the Office of the Chief Economist, South Asia Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/research. The authors may be contacted at yli7@worldbank.org.

_The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._ Produced by the Research Support Team
States Diverge, Cities Converge: Drivers of Local Growth Catch‐up in India Yue Li, Martin Rama and Qinghua Zhao Keywords: city growth, convergence, determinants of city growth, Bayesian model averaging JEL classification: R1, R11; O1, O18, O11 Yue Li and Martin Rama are with the World Bank’s Office of the Chief Economist for South Asia; Qinghua Zhao is with its Development Research Group. The corresponding author is Yue Li (yli7@worldbank.org).

The authors gratefully acknowledge the skillful research assistance provided by Virgilio Galdo, María Florencia Pinto and Jiarui Wang, and the useful comments and suggestions received from Urmila Chatterjee, Gaurav Datt, Gilles Duranton, Chetan Ghate, Denis Medvedev, Rinku Murgai and Stephen Wright.

This research was funded by the World Bank and the Australian Partnership for South Asia Trust Fund. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
# 1. Introduction

India’s growth performance over the past three decades has been nothing short of spectacular. Between 1985 and 2017, gross domestic product (GDP) per capita grew on average 4.5 percent a year (World Bank 2018). As a result, India is catching up with more advanced economies, defying the claim that the world suffers from “divergence, big time” (Pritchett 1997). Growth patterns at the subnational level are less encouraging, however. Income disparities within India are wide, to the point of justifying a distinction between high‐ and low‐income states. And a key question is thus whether poorer locations are catching up with the richer ones as the country experiences rapid growth.

The consensus among economists is that within itself India is characterized by “divergence, big time.” Datt and Ravallion (2002) found that the states that were richer in the 1980s grew faster in the 1990s. Kumar and Subramanian (2012) documented not only a continuation of state‐level divergence in the 2000s, but also an increase in its magnitude. In the most positive assessment, Ghate and Wright (2013) concluded that there was no clear evidence in favor of absolute convergence or absolute divergence across states from the 1980s to the 2000s. A recent Economic Survey by the government of India featured this debate, showing the sharp contrast between growth divergence in India and growth convergence within China and other large federations (Ministry of Finance 2017).

However, the same Economic Survey also pointed to new evidence that nonmonetary measures of well‐ being are improving across the board and especially in low‐income states. The Survey also reported an increase in cross‐state transactions and cross‐state migration, two trends that could support convergence (Ministry of Finance 2017). Unlike previous research, a recent study using the intensity of nighttime light to proxy for income found evidence of convergence across Indian states, districts, and cities (Tewari and Godfrey 2016).

In this paper, we take a fresh look into the Indian convergence debate building on both the growth and the urban economics literatures. But we depart from previous studies in three important ways:

- We assess growth patterns across districts and across places below the district level. Some Indian states are bigger than all but a few countries in the world. Taking the state as the spatial unit of analysis can hide substantial heterogeneity in local growth patterns.

- We rely on household consumption expenditure per capita to measure living standards. This indicator, estimated on the basis of household expenditure surveys, provides greater spatial granularity than GDP per capita, while still being highly correlated with it.

- We use a Bayesian model averaging approach to identify the best predictors of local economic growth. Compared to the classical econometric approach, this allows us to better address the uncertainty on the true model of the economy resulting from the many potential predictors.

Our results reveal that there is growth divergence at the state level, but strong convergence when districts or places below district level are considered. This finding runs against the growth divergence consensus but is in line with more indirect evidence provided by nonmonetary indicators of well‐being and by nighttime light intensity. Growth is fastest in the midrange between purely rural places and major urban centers. But the best‐performing locations do equally well in high‐ and low‐income states. It is just that there are not many top performers among the latter.
Our findings on the drivers of local growth are not fully aligned with previous research either. We show that geography matters, as the urban economics literature claims, but population density does not and variations in city governance are only mildly relevant. Market access, the availability of electricity and transport infrastructure are very important, which is consistent with the emphasis on openness and investment in the growth literature. But we do not find evidence that the sectoral structure of economic activity – such as the share of manufacturing – plays a role. On human capital, the coverage of primary education is important, but that of tertiary education less so. Remarkably, all the indicators of social inclusion considered are strongly correlated with local growth. On governance, finally, high crime rates are detrimental to grow, as are state‐level distortions to labor and land markets.

# 2. Previous research

At the global level, the first studies on convergence were part of the growth literature that emerged in the 1990s. These studies differed in the way convergence was defined, in their unit of observation, and in their statistical approach. Regarding the definition, an important distinction was usually made between absolute and conditional convergence. Absolute convergence analyses focus on whether administrative units with a low initial income per capita grow faster than those with a high initial income per capita. Conditional convergence analyses also control for other factors that could affect the speed of growth, in addition to the initial level of income per capita.

The administrative unit considered by the first studies in the growth literature was the nation state (Barro 1991; Baumol 1986). Back then there was consensus that the world was experiencing both absolute divergence and conditional convergence. However, the second wave of studies found that at the subnational level regions sufficiently integrated with each other experienced both absolute and conditional convergence. Examples included the 48 states of the United States during 1880–2000, the 47 prefectures of Japan during 1930–90, and the 90 regions of eight European countries during 1950–90 (Barro and Sala‐i‐Martin 1992; Barro et al. 1991; Sala‐i‐Martin 1996). Subsequent studies confirmed this finding for Australasia, Canada, Ireland and Sweden.

As for the statistical model, the earliest studies in this growth literature considered GDP per capita measured in comparable purchasing power as the performance indicator, and the investment rate and secondary school enrollment as the key drivers of growth. But the number of potentially relevant indicators included in the specification burgeoned over just a few years, reaching a point where degrees of freedom became scarce. Not surprisingly, there was substantial uncertainty about which potential drivers of growth mattered the most.

Meanwhile, the urban economics literature had been exploring the determinants of city growth focusing on one particular set of potential drivers at a time. Glaeser, Scheinkman and Shleifer (1995) broke with this tradition by adapting the cross‐country regression model to the analysis of growth across U.S. metropolitan areas in 1960–90. The performance indicators were city population and the city wage rate, with schooling, unemployment and the employment share of manufacturing identified as robust drivers of urban growth. Other studies involving multiple indicators were conducted by da Mata et al. (2007) for Brazilian cities in 1970–2000 and by Duranton (2016) for Colombian cities in 1993–2010. The results of these other studies suggested that geography, road connectivity, educational attainment and economic specialization were important drivers of subsequent city growth.

2
Most convergence studies for India followed the tradition of the growth literature and used the state as the unit of observation. Indeed, there was ample consensus that imbalances among states are wide. For example, Goa has a GDP per capita comparable to that of Mexico, whereas Bihar’s GDP per capita is closer to that of Benin. Large subnational gaps in living standards, including both monetary and nonmonetary dimensions of well‐being, had also been documented in multiple studies.

The literature on this topic up to 2007 has been summarized by Kalra and Sodsriwiboon (2010). With the addition of more recent publications, there have been 20 studies of subnational convergence in India (table 1). These studies used different methodologies, including cross‐sectional regression, panel regression and distributional analysis. Bajpai and Sachs (1996), Rao, Shand and Kalirajan (1999), and Kumar and Subramanian (2012) split the sample into various time periods, which led to multiple results. Kochhar et al. (2006) also reported multiple results because they used different estimation methods.

Of the 26 results from these 20 studies, 17 support absolute divergence, 2 are inconclusive, and 7 favor absolute convergence. The evidence in favor of absolute divergence is strongest at the state level, and especially in the 1980s and 1990s. Thus, Datt and Ravallion (2002) reported absolute divergence across states in the 1990s, except for the richest two. Rodrik and Subramanian (2004) found that states were  diverging at an annual rate of about 1.2 percent a year during that same period a result they saw as a striking case of “divergence, big time.” Findings were more mixed for the 2000s, but on balance the evidence suggested that absolute divergence remained the norm. Kumar and Subramanian (2012) even reported an increase in the magnitude of divergence from the 1990s to the 2000s. The Ministry of Finance (2017) expanded the analysis to 2004 for income and to 2011 for expenditure, confirming that there was continuing divergence across states. Using income as the performance indicator, Das (2012) also reported strong divergence across states in 1980–2005. However, Ghate and Wright (2013) found no clear evidence to support either absolute convergence or absolute divergence across major states in 1987–2004. In addition to assessing the correlation between initial income per capita and growth directly, they conducted millions of convergence regressions controlling for other factors potentially affecting growth and found that the coefficient on initial income per capita was symmetrically distributed around zero.

Because few studies considered higher levels of spatial disaggregation, the results at the district or below‐district level appear to be inconclusive. Das, Ghate and Robertson (2015) found that richer districts in 2001 grew slightly faster during the period 2001–08. When using expenditure as the performance indicator, Das (2012) also found evidence of divergence across the rural areas of states but reported convergence across their urban areas. This finding is consistent with the evidence presented by Tewari and Godfrey (2016) using nighttime light intensity as the performance indicator, which showed absolute convergence across states, districts and cities.

Studies also differ in the list of potential drivers of local performance they consider when assessing conditional convergence. At the global level, the selection of these potential drivers was initially influenced by the growth literature, focusing on indicators such as trade openness or infrastructure. However, over time some indicators explored by the urban economics literature – such as population density– have been incorporated as well. Also, while the growth literature focuses on key drivers at the country or state level, the urban economics literature considers drivers defined at a much more granular level.

3
**Table 1: A summary of the literature on growth convergence within India**

||**Find**|**ing**|**Dependent**|**Spatial level**|**Time**|
|---|---|---|---|---|---|
|**Study**|**Absolute**|**Conditional**|**Variable**|**(no.)**|**Period**|
|Cashin and Sahay (1996)|Convergence|Convergence|Income|State (20)|1961–91|
|Bajpai and Sachs (1996)|Convergence|Convergence|Income|State (19)|1961–71|
||Divergence|Divergence|Income|State (19)|1971–95|
|Rao, Shand and Kalirajan (1999)|Divergence|Divergence|Income|State (14)|1961–91|
|Nagaraj, Varoudakis and<br>Veganzones (2000)|Divergence|Convergence|Income|State (17)|1971–91|
|Aiyar (2001)|Divergence|Convergence|Income|State (19)|1971–95|
|Sachs, Bajpai and Ramiah(2002)|Divergence||Income|State (14)|1976–95|
|Datt and Ravallion (2002)|Divergence||Income|State (12)|1992–2000|
|Bandyopadhyay (2012)|Divergence||Income|State (17)|1965–97|
|Rodrik and Subramanian (2004)|Divergence||Income|State (20)|1980–99|
|Baddeley, McNay and Cassen<br>(2006)|Divergence||Income|State (15)|1970–97|
|Kochhar et al. (2006)|Inconclusive||Income|State (14)|1961–2000|
|Purfield (2006)|Convergence|Convergence|Income|State (15)|1976–2005|
|Misra (2007)|Divergence|Convergence|Income|State (14)|1976–2001|
|Kalra and Sodsriwiboon (2010)|Divergence||Income|State (15)|1960–2003|
||Divergence||Income|State (14)|1980–2005|
|Das (2012)|Divergence||Rural expenditure|State (14)|1980–2005|
||Convergence||Urban expenditure|State (14)|1980–2005|
|Kumar and Subramanian (2012)|Divergence||Income|State (21)|1993–2009|
||Divergence||Income|State (21)|2001–09|
|Ghate and Wright (2013)|Inconclusive|Inconclusive|Income|State (15)|1987–2004|
|Tripathi (2013)||Inconclusive|Income|City (52)|2001‐2005|
|Nayyar (2014)|Divergence|Convergence|Expenditure|State (17)|1994–2012|
|Das, Ghate and Robertson (2015)|Divergence|Convergence|Income|District (575)|2001–08|
||Convergence||Nighttime light<br>intensity|State (33)|1992–2013|
|Tewari and Godfrey (2016)|Convergence||Nighttime light<br>intensity|District (618)|1992–2013|
||Convergence||Nighttime light<br>intensity|City (479)|1996–2011|

_Source_ : Authors, building on Kalra and Sodsriwiboon (2010).

_Note: Income_ refers to either GDP per capita or gross value added per capita. _Expenditure_ refers to average household expenditure per capita. Nighttime light intensity is measured per unit of surface.

4
This broadening of the set of potential drivers of local performance, and the increasing granularity of their measurement, can also be found in studies specific to India. With so many possible indicators, it is convenient to regroup the findings of previous studies into nine major “buckets”. Each of them corresponds to a defensible conceptualization of an important mechanism underlying economic growth, and researchers may have different priors on which of these mechanisms matter the most. Each of them may also be captured through multiple, often highly correlated indicators.

The buckets we consider are:

1. _Geography_ . Fundamental differences in climate and topography give rise to location advantages, which have been identified as an important force shaping the size and productivity of cities (Behrens and Robert‐Nicoud 2015; Glaeser 2012). Precipitation and temperature are among the most common indicators of climate, whereas elevation is often considered in relation to topography.

2. _Urbanization._ A number of city outcomes and characteristics are potentially correlated with local growth. City outcomes include the share of the unit of analysis that is administratively urban, its population size and its population density; city characteristics relate mainly to governance and finance (Duranton 2015, 2016; Glaeser, Scheinkman and Shleifer 1995; Rosenthal and Strange 2004).

3. _Market access._ The easiness to reach dynamic centers supports a stronger demand for final products and better access to inputs (Fujita, Krugman and Venables 1999; Krugman and Venables 1995; Redding and Venables 2004). Market access is often measured as nearby economic activity weighted by distance or travel time, or through proximity to large cities or ports.

4. _Infrastructure._ Closely linked to the previous bucket, infrastructure plays a central role both in the neoclassical growth theory and in the new growth literature (Barro 1991; Solow 1956, 1957). The broader urban economics literature also emphasizes the importance of connectivity and access to housing on local growth (Donaldson 2018; Glaeser 2008, 2012).

5. _Economic structure_ . The growth literature stresses structural transformation – from agriculture to manufacturing and services – as a source of productivity gains. The urban economics literature focuses on economic diversification and specialization (Glaeser and others 1992, Duranton 2016) and on the distribution of firms by size (Glaeser, Kerr and Kerr 2015; Rosenthal and Strange 2010).

6. _Employment structure_ . The urban economics literature finds that labor pooling is an important channel through which local economies become more productive (Glaeser, Scheinkman and Shleifer 1995; Rosenthal and Strange 2004). In a developing country context, the shares of self‐employment and wage employment may provide a snapshot of the local employment structure (World Bank 2012).

7. _Human capital._ In the so‐called endogenous growth literature, human capital is the ultimate driver of economic dynamism (Romer 1986). In the urban economics literature human capital contributes to city growth too, through knowledge spillovers (Moretti 2004a, b). Typical indicators include enrollment rates or educational attainment, from primary to tertiary level.

8. _Social inclusion._ Discrimination against population groups, as well as the barriers that prevent them from accessing markets and services, ought to be detrimental to growth. But which groups and which barriers should be the focus of analysis is less clear. Lack of access to finance and insufficient access to education and jobs by women are relatively obvious candidates.

5
# **Table 2: Drivers of local growth in the literature and results in India’s case**

|**Bucket**|**Indicator**|**Results**<br> <br>||
|---|---|---|---|
|||**Significantly negative**<br>**Small or inconclusive**|**Significantly positive**|
||Temperature|Sridhar (2010)<br>Tripathi (2013)||
|**Geography**|Precipitation|Ghate and Wright (2013)||
||Elevation|Considered in the literature but not in India|’s case|
||Urbanization rate|Tripathi (2013)|Ghate and Wright (2013)<br>Das, Ghate and Robertson (2015)|
||Population size or growth|Ghate and Wright (2013)|Tripathi (2013)<br>Abhishek, Jenamani and Mahanty<br>(2017)|
|**Urbanization**|Population density|Tripathi (2013)||
||State capital|Tripathi (2013)|Abhishek, Jenamani and Mahanty<br>(2017)|
||Governance quality|Cidd i th litt bt t i Idi|’|
||Revenue, expenditure or debt|onsere n e eraure u no n n|s case|
||Nearby economic activity|Das, Ghate and Robertson (2015)||
|**Market access**|Distance to large cities|Sridhar (2010)<br>Das, Ghate and Robertson (2015)<br>Abhishek, Jenamani and Mahanty<br>(2017)<br>Tripathi (2013)||
||Landlocked|Ghate and Wright (2013)||
||Riverbank or seaport city|Tripathi (2013)||

(Continued) 6
# **Table 2: Drivers of local growth in the literature and results in India’s case (continued)**

|**Bucket**|**Indicator**|**Results**||
|---|---|---|---|
|||**Significantly negative**<br>**Small or inconclusive**|**Significantly positive**|
||Access to electricity||Das, Ghate and Robertson (2015)|
||Electricity losses|Purfield (2006)<br>Kalra and Sodsriwiboon (2010)||
||Access to roads or road density|Abhishek, Jenamani and Mahanty<br>(2017)<br>Purfield (2006)<br>Sridhar (2010)<br>Das, Ghate and Robertson (2015)||
||Railways stations or railways density|Considered in the literature but not in India’|case|
||Transportation costs|||
|**Infrastructure**|Telephone lines||Kalra and Sodsriwiboon (2010)|
||Irrigated land|Das, Ghate and Robertson (2015)||
||Housing supply|Considered in the literature but not in India’|s case|
||Private investment|Baddeley, McNay and Cassen (2006)|Rao, Shand and Kalirajan (1999)<br>Aiyar (2001)<br>Purfield (2006)<br>Kalra and Sodsriwiboon (2010)|
||Development expenditure|Ghate and Wright (2013)<br>Tripathi (2013)|Rao, Shand and Kalirajan (1999)<br>Baddeley, McNay and Cassen (2006)<br>Kalra and Sodsriwiboon (2010)|
||Agricultural productivity||Baddeley, McNay and Cassen (2006)|
||Share of agriculture|Bajpai and Sachs (1996)<br>Purfield (2006)<br>Ghate and Wright (2013)<br>Baddeley, McNay and Cassen (2006)||
|**Economic**<br>**structure**|Share of manufacturing or industry|Purfield (2006)<br>Ghate and Wright (2013)|Sridhar (2010)|
||Share of services||Kalra and Sodsriwiboon (2010)|
||Diversification index|||
||Specialization index|Considered in the literature but not in India’|s case|
||Mineral production capacity|||

(Continued) 7
# **Table 2: Drivers of local growth in the literature and results in India’s case (continued)**

|**Bucket**|**Indicator**|**Results**<br> <br>||
|---|---|---|---|
|||**Significantly negative**<br>**Small or inconclusive**|**Significantly positive**|
||Share of small, medium or large firms|Considered in the literature but not in India’|s case|
||Employment rate|Baddeley, McNay and Cassen (2006)||
|**Employment**|Private sector employment share|Kalra and Sodsriwiboon (2010)||
|**structure**|Unemployment rate|||
||Self‐employment share|Considered in the literature but not in India’|s case|
||Wage‐employment share|||
||Birth rate|Kalra and Sodsriwiboon (2010)||
||Literacy rate|Purfield (2006)<br>Kalra and Sodsriwiboon (2010)<br>Das, Ghate and Robertson (2015)<br>Tripathi (2013)|Aiyar (2001)<br>Sridhar (2010)<br>Ghate and Wright (2013)|
|**Human capital**|Primary education|Tripathi (2013)<br>Abhishek, Jenamani and Mahanty<br>(2017)|Sridhar (2010)|
||Secondary education|Tripathi (2013)|Baddeley, McNay and Cassen (2006)|
||Tertiary education|idd i h li b i di’||
||Years of schooling|Consere n te terature ut not n Ina|case|
||Access to finance|Das, Ghate and Robertson (2015)||
||Land inequality|Considered in the literature but not in India’|s case|
||Female educational disadvantage|Purfield (2006)|Baddeley, McNay and Cassen (2006)|
|**Social inclusion**|Rural income inequality||Baddeley, McNay and Cassen (2006)|
||Urban income inequality|Baddeley, McNay and Cassen (2006)||
||Overall income inequality|Considered in the literature but not in India’|case|
||Social heterogeneity or segregation|||

(Continued) 8
**Table 2: Drivers of local growth in the literature and results in India’s case (continued)**

|**Bucket**|**Indicator**|**Results**<br> <br>||
|---|---|---|---|
|||**Significantly negative**<br>**Small or inconclusive**|**Significantly positive**|
||Crime rate|Rao, Shand and Kalirajan (1999)|Baddeley, McNay and Cassen (2006)|
|**Governance**|Labor rigidity|Ghate and Wright (2013)<br>Purfield (2006)||
||Land market distortions|Sridhar (2010)||

_Source:_ Authors.

9
9. _Governance._ Multiple aspects of governance – from political regime to social capital or the control corruption – could be relevant, making this a broad bucket. The quality of governance also influences economic policies that have strong implications for local growth, such as labor and land regulations (Besley and Burgess 2004).

A few empirical regularities have emerged in India in relation to these buckets (Table 2). For example, geography does not seem to be particularly relevant for local growth, although only a limited number of indicators have been considered in practice. Urbanization, on the other hand, appears to be associated with stronger local performance, and the same is true of market access. Almost all studies consider indicators of infrastructure or investment and they are generally found to matter, but their significance varies. Studies are parsimonious – and generally inconclusive – in relation to economic structure, and none of them focuses on the employment structure. Most studies include human capital indicators such as literacy rate or school enrollment rate, but the results are mixed. As for social inclusion, in the Indian case it would make sense to concentrate on lower castes and tribal groups, but this is a dimension not considered by existing studies. Similarly, few governance indicators have been considered in the Indian case, and their results are inconclusive.

# 3. Methodology

While existing studies provide interesting clues on the contribution to Indian local growth of each of the nine buckets considered, their results cannot be interpreted literally because the empirical approach used in these studies raises important methodological questions.

The specifications most commonly used to assess growth convergence are and Equation (1) is used to assess absolute convergence and equation whereas equation (2) deals with conditional convergence.

In these equations g�,�,��� is the annual growth rate of the living standards indicator in place l between t and t�T , y�,� represents the level of the living standards indicator in l at t , X�,� is a vector of _K_ other factors that potentially affect growth in place l , and ∅ is a vector of coefficients φ capturing the impact of individual factors x . The superscripts a and c differentiate the absolute and conditional convergence models. When β<sup>�</sup> �0 , there is absolute convergence and when β<sup>�</sup> �0 , there is absolute divergence. When β<sup>�</sup> �0 that is, when other factors are controlled forthere is conditional convergence.

The potential drivers of growth X�,� are generally assessed at or before t . This may not be enough to ensure that they are fully exogenous. Except for indicators related to geography (altitude, precipitation and the like), the factors included in X�,� could be influenced by the anticipation of future growth in location l . However, the chosen time structure at least attenuates the risk of endogeneity.

An important methodological challenge faced by this framework is the large number of variables ( _K_ ) that could potentially have an impact on local living standards. The estimated impact φ of each of these 10
indicators on the growth rate could vary depending on which other indicators are retained for the analysis. But there is inherent uncertainty regarding the true model of the economy. Standard approaches generally ignore this uncertainty by enlisting a combination of indicators that yields a good fit, and then proceeding as if the associated model was correct. As a consequence, more precision is assigned to the inference than is warranted by the data (Draper 1995; Moral‐Benito 2013; Steel 2017). An also standard alternative, if the number of degrees of freedom allows it, is to include all possible indicators, and then let the results speak by themselves. However, this may lead to the inclusion of indicators that do not belong in the true model of the economy and bias the estimated coefficients.

One way to address model uncertainty is to run the analysis multiple times, including all the possible combinations of indicators, and retain as robust only those indicators that remain significant in all circumstances, regardless of the other indicators considered. However, this approach faces computational constraints because the number of potential combinations increases exponentially with the number of potential drivers of growth. For example, if there were 30 indicators a total of 1.07 billion (=2^30) regressions could be run.

A practical alternative to make this approach tractable is to impose restrictions on the model. Sala‐i‐ Martin (1997), with their “two million regressions” method, constrained equation (2) to a maximum of seven X�,� variables: three of them fixed based on previous literature and four of them flexible. This method reduces the number of possible regressions substantially, and the same logic could be applied using our nine buckets. However, the method can be criticized for the arbitrariness of the restrictions it imposes on equation (2).

The Bayesian model averaging approach represents a substantial methodological improvement to address model uncertainty and assess the robustness of indicators. In practice, this approach amounts to estimating a randomly selected subset of regressions. The selected regressions are drawn based on priors regarding the probability of each indicator to belong in the real model of the economy. Priors are adjusted along the way, based on the fit of the various regressions. Posterior statistics on the estimated impact of each of the indicators are derived as part of this process.

The principle behind this approach had been outlined long ago by Leamer (1978). But computational capacities were for long a roadblock to its implementation. The development of practical methods by Raftery (1995) considerably moved the agenda forward. The early applications, such as Fernandez, Ley, and Steel (2001), showed the potential of this approach for the study of economic growth. However, the Bayesian approach has seldom been applied to understanding city or local growth by the urban economics literature (Leon‐Gonzalez and Montolio 2015; Rockey and Temple 2016 are exceptions).

We take a step toward filling in this gap by implementing the Bayesian model averaging method to districts and places below the district level in India. We do so using the Bayesian Averaging of Classical Estimates method, or BACE, proposed by Sala‐i‐Martin, Doppelhofer and Miller (2004).

The BACE method applies “diffuse priors” in the form of probabilities that a particular indicator belongs in the true model. Let M� denote model j , defined as a subset of the _K_ indicators that contains k� of them, and let P�M�� be the prior probability attached to model M� derived from the priors on indicators. BACE runs equation (2) repeatedly, randomly drawing each time a subset of the K potential indicators based on prior probabilities P�M�� .

11
Jj P(M,|Z) ~ <u>OK ; —k;/2 : —N/2</u> 2", P(M,)N-Ki i

Jj Jj I(x € Mi) 7) 2k P(xlZ) =) i=1P(MiIZ) «10 € Mi) EWld)? = ~~20: * P(M;|Z)«I(x € M;)~~ auP(M,|Z) * I(x € XM;)

i i 7) Var(g|z) ~~=r~~ K ~~¥ar(or i) * P(OMIz) * 1G € Mi) + XE~~ K oA ~~— E(@IZ))? * P(MIZ) * 1 € M~~ 2e, P(M;IZ) «I(x € M,)

Var(9; i)
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
location premiums as an alternative performance indicator. The location premium is computed as the fraction of local expenditure per capita that cannot be accounted for by observable household characteristics, following Li and Rama (2015b). The growth rate of the location premium provides a good proxy of local productivity growth.

We consider three types of locations: states, districts and places. The latter result from a breakdown of the district into up to four types of agglomerations: small rural (fewer than 5,000 inhabitants), large rural, small urban (fewer than one million inhabitants) and large urban. The methodology to process this disaggregation, developed by Chatterjee et al. (2015), exploits the fact that NSS 2004–05 and NSS 2011– 12 follow a stratified multistage sampling design. Each district of a state or union territory is stratified into rural and urban areas. Within each stratum, first‐stage units are ordered by their population and then further stratified into small rural, large rural, small urban and large urban places.

As for the potential drivers of local growth, we construct 30 indicators to measure the potential drivers of growth identified above, making sure that there are several of them for each of the nine conceptual buckets. To construct these indicators, we draw primarily from the Spatial Database for South Asia compiled by the World Bank (Li et al. 2015). The detailed metadata is available on request.

Of these 30 indicators considered, 27 are measured at the district level and three at the state level:

1. _Geography_ (3). We capture climate through temperature and precipitation.  To reduce the impact of short‐term fluctuations we use averages in the preceding decade. We capture topography through the average altitude of each location.

2. _Infrastructure_ (4). Indicators cover electricity, connectivity, irrigation and housing. The connectivity measure is the density of railway and metro stations. Data on road density, based on Open Street Maps (a crowdsourcing platform) is also available, but it is too recent to be reliable.

3. _Market access_ (2). We compute the weighted average of economic activity across all neighboring districts, discounted by distance, for up to 400 kilometers. We do so using GDP and nighttime light intensity as alternative measures of district‐level economic activity.

4. _Economic structure_ (7). We include traditional measures on the sectoral composition of the economy (except for agriculture, to avoid collinearity), a measure of output diversification, an indicator on mineral production capacity, and two measures of the distribution of firms by size.

5. _Employment structure_ (2). Because the employment or unemployment rate is not very relevant in India’s case, we use the shares of self‐employment and wage employment relative to the working‐ age population to provide a snapshot of the local employment structure.

6. _Urbanization_ (2). To mitigate biases that may arise from the administrative definition of urban areas, we use population density instead of population size to measure city size. We use the population share of the state capital in a district to proxy for city governance.

7. _Human capital_ (3). We use three measures of educational attainment – primary, secondary and tertiary – in line with the city growth literature. By differentiating between the three levels of education we allow nonlinearity in the impact of schooling on local growth.

8. _Social inclusion_ (4). We consider the fraction of households with a bank account, the gap in secondary educational attainment between men and women, the shares of scheduled castes, and the share of scheduled tribes in the total population.

14
**Table 3: Summary statistics for the sample of large states**

|**Performance**|**Indicator**|**Number of**<br>**observations**|**Mean**|**Standard**<br>**deviation**|
|---|---|---|---|---|
||Annual growth of household expenditure per capita, district (percent)|512|11.48|3.02|
|Annual rowth rate|Annual growth of household expenditure per capita, place (percent)|1,218|11.26|3.88|
|g|Annual growth of location premium, district (percent)|512|9.83|2.54|
||Annual growth of location premium, place (percent)|1,218|9.96|2.54|
||Initial household expenditure per capita, district (2004 Rs per month)|512|959|261|
|Iitil f|Initial household expenditure per capita, place (2004 Rs per month)|1,218|1,017|316|
|na perormance|Initial location premium, district (2004 Rs per month, log)|512|7.12|0.20|
||Initial location premium, place (2004 Rs per month, log)|1,218|7.16|0.18|
|**Bucket**|**Indicator**|**Number of**<br>**observations**|**Mean**|**Standard**<br>**deviation**|
||Temperature (°C)|512|10.0|1.0|
|Geography|Precipitation (mm)|512|36.0|19.0|
||Elevation (m)|512|125|158|
|Urbanization|Population density (no. per km<sup>2</sup>)|512|200|557|
||Population share of state capital (share of total population)|512|0.02|0.09|
|Market access|Market access, nearby GDP weighted by distance (index)|512|4.22|2.35|
||Market access, nearby nighttime light weighted by distance (index)|512|0.45|0.04|
||Access to electricity (share of total households)|512|0.52|0.28|
|Infrastructure|Railway station density (no. per 1,000 km<sup>2</sup>)|512|1.66|6.87|
||Land with irrigation systems (share of total area)|512|0.28|0.26|
||Share of housing in good condition (share)|512|0.47|0.15|

(Continued) 15
**Table 3: Summary statistics for the sample of large states (continued)**

|**Performance**|**Indicator**|**Number of**<br>**observations**|**Mean**|**Standard**<br>**deviation**|
|---|---|---|---|---|
||Share of manufacturing (share of working‐age population)|512|0.06|0.05|
||Share of other industries (share of working‐age population)|512|0.04|0.03|
||Share of services (share of working‐age population)|512|0.13|0.06|
|Economic structure|Share of medium‐size firms (share of firms)|512|0.0055|0.0033|
||Share of large firms (share of firms)|512|0.0008|0.0011|
||Diversification index (index)|512|16.0|6.0|
||Mineral production capacity (million metric tons per year)|512|58.0|482.0|
|Elt tt|Share of self‐employed (share of working‐age population)|512|0.40|0.13|
|mpoymen srucure|Share of wage workers (share of working‐age population)|512|0.27|0.11|
||Primary education (share of working‐age population)|512|0.17|0.07|
|Human capital|Secondary education (share of working‐age population)|512|0.04|0.03|
||Tertiary education (share of working‐age population)|512|0.01|0.01|
||Access to finance (share of total households)|512|0.33|0.14|
|Sil ili|Gender gap in secondary education (percentage point difference)|512|0.03|0.02|
|oca ncuson|Share of scheduled castes (share of total households)|512|0.13|0.23|
||Share of scheduled tribes (share of total households)|512|0.19|0.11|
||Crime rate (incidence per million people)|512|47.0|34.0|
|Governance|Labor regulation index (index)|512|0.03|1.20|
||Land reform index (index)|512|4.51|3.03|

_Source:_ Authors, based on Li et al. (2015).

_Note:_ The 21 largest states or union territories are Andhra Pradesh, Assam, Bihar, Chhattisgarh, Delhi, Gujarat, Haryana, Himachal Pradesh, Jammu & Kashmir, Jharkhand, Karnataka, Kerala, Madhya Pradesh, Maharashtra, Orissa, Punjab, Rajasthan, Tamil Nadu, Uttar Pradesh, Uttaranchal and West Bengal. km<sup>2</sup> = square kilometer; m = meter; mm = millimeter; Rs = Indian rupees 16
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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
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It is true that the number of households surveyed becomes smaller when the level of spatial disaggregation goes from state to district and further to place and, as a result, the standard errors of the estimated expenditure per capita become greater. This type of measurement error could bias our estimates in the direction of greater apparent convergence. For example, if the expenditure per capita in a place is overestimated in the initial year, this base effect is likely to lead to an underestimation of the annual growth rate in subsequent years, which could be misconstrued as convergence.

To mitigate the impact of measurement error, we divide both districts and places into 25 quantiles, based on their initial expenditure per capita. We then estimate the mean initial expenditure per capita and the mean annual growth rate for each quantile. These means should not suffer from a serious measurement error because there are many districts and places in each quantile. As we rerun equation (1) on these 25 observations, the estimates of coefficient β<sup>�</sup> barely change compared to the corresponding regressions at the district and the place level (figure 2). This suggests that the finding on rapid absolute convergence at the place level is not driven by measurement error.

The conclusion that India has experienced rapid convergence holds when considering location premium as the performance indicator instead of household expenditure per capita. The estimates of coefficient β<sup>�</sup> at the place level are similar to those obtained when using household expenditure per capita. But interestingly, districts converge as fast as places when focusing on the location premium (table 5). These results imply that self‐selection and the sorting of households across spatial units do not significantly affect the observed convergence pattern. Other forces are at play and result in productivity growing faster in poorer locations in India during the second half of the 2000s.

**Table 5: Absolute convergence in location premiums, 2004–11**

|||**District level**|||**Place level**||
|---|---|---|---|---|---|---|
|Sample|Largest 21<br>states|All 31<br>states|25<br>quantiles|Largest 21<br>states|All 31<br>states|25<br>quantiles|
|2004 location premium|–4.170***<br>(0.561)|–4.362***<br>(0.534)|–4.130***<br>(0.495)|–4.698***<br>(0.386)|–4.804***<br>(0.366)|–4.876***<br>(–0.361)|
|Constant|39.603***<br>(3.996)|40.935***<br>(3.810)|39.321***<br>(3.505)|43.583***<br>(2.760)|44.340***<br>(2.620)|44.859***<br>(–2.581)|
|No. of observations|512|561|25|1,218|1,315|25|
|R<sup>2</sup>|0.1112|0.1169|0.7121|0.1159|0.1189|0.8773|
|Adjusted R<sup>2</sup>|0.1094|0.1154|0.6995|0.1151|0.1182|0.8719|

_Note_ : Standard errors are in parentheses.

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

# 6. Why do states diverge?

  The finding that districts and places converge and quite rapidly is more encouraging than the prevailing “divergence, big time” consensus. But it also begs the question: if locations at lower levels of spatial disaggregation converge, why is it that states do not?

20
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We illustrate this point by considering the annual growth rate of the fastest‐growing district in each state. There is no clear correlation between the growth rate of the state and the growth rate of its fastest‐growing district (figure 3). On average, all states have star districts that grow on a par with peers in other states. But there is a positive correlation between the growth rate of the states and their shares of fast‐growing districts. States with a higher share of fast‐growing districts also tend to grow faster overall. Low‐income states perform more poorly because they do not generate enough of the fast‐ growing districts.

A simple regression analysis corroborates this result: the state‐level growth rate is significantly and positively correlated with the share of fast‐growing districts, but it is not correlated with the speed of the fastest‐growing district (table 6). The results are robust to changes in the definition of the fast‐ growing district, such as considering the 75th percentile in the distribution of growth rates across districts as the relevant threshold. They are also robust to the inclusion of a measure of the share of rich districts in a state, with a rich district defined as one whose initial expenditure per capita is above the median value across all districts. Finally, the results also remain the same if the sample is expanded from large states to all states.

**Table 6: Fast‐growing districts and growth of expenditure per capita across states, 2004–11**

|||**Largest states**|||**All states**||
|---|---|---|---|---|---|---|
|Share of fast‐growing districts<br>(above median value)|4.397***<br>(0.649)||4.443***<br>(0.751)|3.930***<br>(0.402)||3.825***<br>(0.425)|
|Share of fast‐growing districts<br>(above 75th percentile)||5.364***<br>(1.292)|||5.865***<br>(0.984)||
|Growth rate of fastest‐growing<br>district (maximum)|0.054<br>(0.038)|–0.002<br>(0.053)|0.052<br>(0.042)|0.048<br>(0.032)|0.034<br>(0.046)|0.061<br>(0.035)|
|Share of rich districts<br>(above median value)|||–0.064<br>(0.476)|||0.283<br>(0.345)|
|Constant|0.944*<br>(0.526)|2.455***<br>(0.561)|0.973<br>(0.583)|1.235***<br>(0.291)|1.855***<br>(0.387)|1.013**<br>(0.399)|
|No. of observations|20|20|20|28|28|28|
|R<sup>2</sup>|0.733|0.510|0.734|0.826|0.654|0.831|
|Adjusted R<sup>2</sup>|0.702|0.453|0.684|0.812|0.627|0.810|

_Note_ : Standard errors are in parentheses.

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

The conclusion is the same when we conduct the analysis at the place level instead of the district level, and when we use location premium as the performance indicator instead of expenditure per capita. The association between the state growth rate and the share of fast‐growing locations is largest when conducting the analysis at the place level with expenditure per capita as the performance indicator. It is smallest when looking at the district level and focusing on the location premium. But in all cases the association between the growth rate of the state and that of its fastest‐growing location is statistically insignificant. The empirical analyses underlying these findings are available on request.

22
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because it attenuates the bias introduced by self‐selection and sorting. We restrict the sample to the 21 largest states following the literature. Each of the 30 potential drivers of local growth we constructed belongs to one of the nine conceptual buckets considered: geography, urbanization, market access, infrastructure, economic structure, employment structure, human capital, social inclusion, and governance. We assume that the true model of the economy includes the initial performance of the location and one indicator from each of these nine buckets.

To implement BACE we first draw one million random combinations of indicators from the nine buckets plus the initial performance indicator. We run a standard OLS regression for each model and use the one million results to compute posterior probabilities of inclusion. We then replace our initial priors by the posterior probabilities estimated using the BACE approach and repeat the process. We continue doing so until both the probability of including each indicator and its posterior conditional mean coefficient converge, which seldom takes more than seven iterations.

The mean of the posterior conditional coefficients is computed on the basis of equation (5). It can be viewed as the impact of the corresponding indicators on subsequent growth at the local level (table 7, column 1). In this respect, the interpretation is the same as for the standard φ� coefficients of an OLS regression. The dispersion of these posterior conditional coefficients, in turn, indicates the significance of the estimated impacts: the highest the dispersion, the lowest the significance.

The posterior conditional inclusion probability for each indicator, computed following equation (4), captures the weighted average of the goodness of fit across models (table 7, column 2). A positive difference between the posterior and the prior inclusion probabilities reinforces the belief that the indicator belongs in the true model of the economy (column 3). This metric provides a _first criterion_ for determining which indicators to retain as part of the true model. Nine of the 31 indicators – including among them the initial performance of the location – meet this first criterion (table 7, first section).

The posterior standard deviation for each coefficient conditional on the inclusion of the indicator, computed following equation (6), is comparable to the estimated standard deviation in classical econometrics (column 4). In the spirit of classical econometrics, we also calculate the ratio between the posterior conditional mean coefficient and the posterior conditional standard deviation. This ratio is akin to a t‐statistic (column 5). The posterior conditional t‐statistic can also be computed with weights defined as in equation (3), as the weighted average of t‐statistics across regression models (column 6).

These two standard deviation measures are highly consistent and provide a _second criterion_ to assess the significance of indicators. In classical terms, a coefficient would be 5 percent significant in a one‐ sided test if the absolute value of the t‐statistic was greater than 1.66 for a sample size of 100 or more. Applying the 1.66 cutoff to both measures on t‐statistics, we identify 12 indicators as significant (table 7, second section). Not surprisingly, the nine indicators selected based on the first criterion are part of this set of 12 indicators.

Not all estimates of a specific coefficient have the same sign as the posterior conditional mean of the coefficient. For each individual regression, the posterior density of the coefficient is the same as in the classical regression model. In that model, a coefficient is significant at the 5 percent level if the probability of the true coefficient having the same sign as the estimated coefficient is 95 percent. Based on the posterior density it is thus possible to assess how likely the signs coincide (column 7).

24
# **Table 7: Baseline results from Bayesian Averaging of Classical Estimates**

||||**Posterior**<br>**conditional**<br>**mean**<br>**coefficient**|**Posterior**<br>**inclusion**<br>**probability**|**Posterior**<br>**inclusion**<br>**probability**<br>**minus prior**<br>**inclusion**<br>**probability**|**Posterior**<br>**conditional**<br>**standard**<br>**deviation**|**Posterior**<br>**conditional mean**<br>**coefficient/**<br>**posterior**<br>**conditional**<br>**standard**<br>**deviation**|**Posterior**<br>**conditional t‐**<br>**statistic**|**Certainty of**<br>**coefficient**<br>**sign, in**<br>**probability**|
|---|---|---|---|---|---|---|---|---|---|
|**Criterion**|**Rank**|**Indicator**|**(1)**|**(2)**|**(3)**|**(4)**|**(5)**|**(6)**|**(7)**|
||1|Initial location premium|–0.489|1.000|0.000|0.048|–10.193|–10.203|1.000|
||2|Access to electricity|0.257|0.976|0.726|0.065|3.982|4.126|1.000|
||3|Market access, lights|0.211|0.899|0.399|0.061|3.482|3.561|1.000|
||4|Share of medium‐size firms|0.140|0.496|0.353|0.058|2.432|2.451|1.000|
|First|5|Share of scheduled tribes|–0.131|0.488|0.238|0.053|–2.464|–2.494|1.000|
||6|Elevation|–0.129|0.447|0.114|0.054|–2.398|–2.421|1.000|
||7|Crime rate|–0.114|0.369|0.036|0.052|–2.175|–2.160|1.000|
||8|Access to finance|0.113|0.264|0.014|0.056|2.024|2.028|1.000|
||9|Labor regulation index|–0.110|0.457|0.124|0.047|–2.312|–2.308|1.000|
|d|10|Primary education|0.108|0.226|–0.107|0.056|1.935|1.957|1.000|
|econ|11|Railway station density|0.104|0.222|–0.028|0.052|2.021|2.089|1.000|
|S|12|Market access, GDP|0.100|0.111|–0.389|0.057|1.763|1.968|0.965|
||13|Land reform index|0.105|0.144|–0.189|0.065|1.633|1.607|0.973|
||14|Precipitation|–0.089|0.117|–0.216|0.056|–1.590|–1.651|0.998|
||15|Tertiary education|–0.072|0.143|–0.190|0.049|–1.484|–1.482|1.000|
|d|16|Diversification index|0.069|0.098|–0.045|0.053|1.287|1.292|1.000|
|Thir|17|Share of large firms|0.066|0.091|–0.052|0.053|1.248|1.336|0.955|
||18|Gender gap in secondary education|–0.054|0.083|–0.167|0.046|–1.171|–1.169|1.000|
||19|Population share of state capital|0.049|0.068|–0.433|0.048|1.019|1.023|0.999|
||20|Share of scheduled castes|–0.043|0.055|–0.195|0.051|–0.851|–0.843|0.978|
||21|Mineral production capacity|–0.021|0.038|–0.105|0.045|–0.472|–0.471|0.990|

(Continued) 25
**Table 7: Baseline results from Bayesian Averaging of Classical Estimates (continued)**

||||**Posterior**<br>**conditional**<br>**mean**<br>**coefficient**|**Posterior**<br>**inclusion**<br>**probability**|**Posterior**<br>**inclusion**<br>**probability**<br>**minus prior**<br>**inclusion**<br>**probability**|**Posterior**<br>**conditional**<br>**standard**<br>**deviation**|**Posterior**<br>**conditional mean**<br>**coefficient/**<br>**posterior**<br>**conditional**<br>**standard deviation**|**Posterior**<br>**conditional**<br>**t‐statistic**|<br>**Certainty of**<br>**coefficient**<br>**sign, in**<br>**probability**|
|---|---|---|---|---|---|---|---|---|---|
|**Criterion**|**Rank**|**Indicator**|**(1)**|**(2)**|**(3)**|**(4)**|**(5)**|**(6)**|**(7)**|
||22|Share of self‐employed|0.040|0.054|–0.446|0.055|0.737|0.721|0.932|
||23|Share of housing in good condition|0.030|0.071|–0.179|0.066|0.449|0.393|0.625|
||24|Secondary education|0.024|0.044|–0.290|0.059|0.414|0.427|0.701|
|ed|25|Share of wage workers|0.018|0.036|–0.464|0.059|0.306|0.298|0.773|
|tain|26|Population density|0.018|0.045|–0.455|0.060|0.296|0.383|0.611|
|ot re|27|Share of other industries|0.013|0.035|–0.108|0.046|0.291|0.291|0.894|
|N|28|Share of manufacturing|0.003|0.034|–0.109|0.049|0.071|0.074|0.578|
||29|Land with irrigation systems|0.002|0.037|–0.214|0.059|0.030|0.038|0.456|
||30|Temperature|0.002|0.055|–0.278|0.055|0.028|0.113|0.502|
||31|Share of services|–0.001|0.037|–0.106|0.059|–0.019|–0.011|0.569|

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The likelihood that that the signs of the coefficients coincide with their posterior conditional mean provides us with a _third criterion_ to identify the indicators that belong in the true model. Based on this third criterion, 21 indicators are retained as statistically significant. They include the 12 indicators that are significant based on the previous two criteria (table 7, third section).

Even by this least restrictive third criterion, the BACE approach allows us to discard at least one‐third of the indicators that economic theory or previous studies would have picked up as top candidates to drive growth at the local level. In addition, if we rely on the two stricter criteria, we would discard almost half of the indicators. This method enables us to be selective about what matters.

To facilitate the interpretation of the baseline results, we multiply the posterior conditional means of the coefficients for the 21 significant indicators by the standard deviation of the growth rate of the location premiums. This multiplication yields the estimated difference in growth rates between two locations that would be identical in all respects, except that they would differ by one standard deviation in the value of the indicator of interest (figure 5).

Based on this transformation, the most relevant difference between two locations is the initial level of  their location premium an indicator that is significant according to all three criteria. This result reinforces the conclusion that India is experiencing convergence, big time. It also confirms the validity of our prior in restricting to the models always including the initial performance.

The second most important set of indicators is related to infrastructure and includes electricity and connectivity. Access to electricity is identified as significant according to all three criteria, and density of railway stations is identified as significant by two. The importance of infrastructure is consistent with the findings of the literature on convergence within India. However, our results also allow differentiating between infrastructure services. In sharp contrast to the results on electricity and connectivity, we do not find evidence that investments in housing and irrigation have a significant impact on local growth. This calls for a differentiated approach to infrastructure investments.

Market access also appears to be an important predictor of growth. Average market access is identified as a significant driver by all three criteria when it is computed based on nighttime light intensity and by two criteria when it is computed based on GDP. This result confirms that distance matters, and “distance to what” especially so.

Although economic structure has an impact on subsequent economic growth, it is not the sectoral structure that makes a difference but rather firm dynamics and entrepreneurship. In sharp contrast with previous studies, our results do not support retaining the shares of manufacturing, other industries or services as robust predictors of subsequent growth.

Instead, we find locations with a larger faction of medium‐size and large firms grow faster, as do places with a more diversified economic structure. The indicator on the share of medium‐size firms meets all three criteria. The share of large firms, the diversification index and mineral production capacity are all significant by the third criterion. But their impacts are more modest. These findings cast doubts on the idea that specific sectors drive growth and suggest that more attention should be paid to firm dynamics and entrepreneurship.

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Inclusion seems to be a solid correlate of faster growth. A one standard deviation increase in the share of schedule tribes is associated with a 0.33 percentage point decrease in subsequent growth. One standard deviation increase in the share of households with access to finance is associated with 0.29 percentage points of additional growth. The gender gap in secondary education and the share of scheduled castes are also significant by the third criterion, but their estimated impacts are much smaller. The finding that social inclusion is good for growth should not come as a surprise, but it marks a departure from previous studies on convergence within India, where inclusion is mostly absent.

Geography‐related factors also appear to be important for growth. Elevation is negatively associated with growth and is significant by all three criteria. The measure on precipitation adversely affects growth and is identified as significant by one criterion. However, our results suggest that temperature does not have a significant impact, perhaps because the specification in equation (2) is linear, whereas the literature on climate suggests the relationship between temperature and growth can be nonlinear.

Governance indicators measured at the state level are robust predictors of subsequent growth at the local level. The crime rate and the labor regulation index are significant indicators according to all three criteria. The land reform index is significant according to the sign certainty probability criterion. The crime rate, which can be interpreted as a measure of law and order, has a large impact. The impact is similar for the labor rigidity index, but much smaller for the land reform indicator. Overall, these results confirm the role of federalism in India, and the prominence of policies and regulations at the state level.

Human capital also matters for growth, but the impact is not uniform across the attainment of all education levels. Completion of a primary education is found to be significantly related to subsequent growth by two of the criteria. However, secondary education is insignificant, and tertiary education is found to be insignificant by two of the criteria.

As for urbanization, we find weak evidence to support the influence of city governance and little evidence for city size as measured by population density. The measure on the population share of the state capital is positive and significant by the sign certainty probability criterion. However, the magnitude of its impact is small. One possible interpretation of this result is that differences in city governance are small in India, as most local urban bodies are characterized by limited autonomy, resources and capacity. As for population density, it is insignificant by all three criteria, contradicting the conventional wisdom in urban economics.

Last but not least, we find little evidence to support the importance of employment structure. Wage employment and self‐employment are insignificantly related to subsequent growth by all criteria. This lack of evidence could be attributed to the fact that types of jobs in a location are intermediate outcomes shaped by factors such as infrastructure, market access, economic structure and governance. Once these factors are adequately taken into account, the impact of the types of jobs available becomes negligible.

# 8. Robustness

The results just described could be affected by the computational solution adopted to implement the BACE approach. One question is whether the number of instances in which prior probabilities are replaced by posterior probabilities makes a difference. Sala‐i‐Martin, Doppelhofer and Miller (2004) enacted this replacement every 100,000 regressions. We increased the threshold to one million 29
regressions, but we still had to do a half‐dozen replacements of prior probabilities by estimated posterior probabilities. To check whether this sequential approach affects the results, we run one billion random regressions instead of one million. But we find that the results are almost identical (table 8). Thus, we are confident that our baseline results are not biased by our computational choice.

**Table 8: Pairwise correlation coefficients between baseline and alternative results**

**a. Conditional posterior means**

||**Baseline**|**1 billion**<br>**regressions**|**Alternative**<br>**prior**|**29**<br>**indicators**|**All states**|**OLS, all**<br>**variables**|**OLS, 30**<br>**indicators**|
|---|---|---|---|---|---|---|---|
|1 billion regressions|1.0000|1||||||
|Alternative prior|0.9967|0.9966|1|||||
|29 indicators|0.9943|0.9941|0.997|1||||
|All states|0.9804|0.9802|0.9791|0.9774|1|||
|OLS, all variables|0.9580|0.9585|0.9431|0.9488|0.9352|1||
|OLS, 30 indicators|0.9643|0.9646|0.9495|0.9579|0.9447|0.9976|1|
|Place‐level regressions|0.9223|0.9225|0.9214|0.9300|0.9460|0.8863|0.8798|
|||**b. Posteri**|**or inclusion**|**probabilit**|**ies**|||
||**Baseline**|**1 billion**<br>**regressions**|**Alternative**<br>**prior**|**29**<br>**indicators**|**All states**|**OLS, all**<br>**variables**|**OLS, 30**<br>**indicators**|
|1 billion regressions|0.9998|1||||||
|Alternative prior|0.9805|0.9782|1|||||
|29 indicators|0.9801|0.9783|0.9908|1||||
|All states|0.9109|0.9093|0.8784|0.8528|1|||
|Place‐level regressions|0.5861|0.5953|0.5308|0.5598|0.6154|||

_Note:_ OLS = ordinary least squares.

Another potentially sensitive choice concerns the prior probabilities used to run the BACE approach. In the analyses above we assumed that the true model of the economy included the initial performance, and one indicator from each of the buckets. It was reassuring that the initial performance indicator and at least one indicator from eight of the nine buckets was retained as significant. However, it could well be that the posterior probabilities were not independent of our choice of priors. To check whether this is so, we assume that the true model of the economy continues to contain 10 explanatory variables, but that any of our 31 indicators – including the initial performance of the location – has the same chance of belonging in the true model. Again, the results are highly consistent.

The sample chosen for the analysis could affect the results as well. Our sample includes the 21 largest states. To assess whether this choice matters, we expand the sample to all 31 states for which we have a reasonable amount of data. A challenge in doing so is that two state‐level indicators (labor regulation index and land reform index) are not available for the additional 10 states. To ensure that the comparison is meaningful, we proceed in two steps. First, we exclude these two state‐level indicators 30
and rerun the baseline analysis for the largest states. We find that the results from using 29 indicators are highly consistent with the baseline. The estimated impact of some of the indicators changes, but neither the direction nor the significance of the impacts is affected.

As a second step, we expand the sample to all states and conduct the analysis with the available 29 indicators. We then compare the results of using 29 indicators based on all states with the baseline results. The two sets of results are highly consistent. The assessment of the significance of the share of other industries is affected (it becomes positively and significantly related to growth by the sign certainty probability criterion), but the direction and significance of other indicators remain the same.

One relevant question is how the result from the BACE approach compares to that of an OLS regression including all 31 indicators. To answer this question, we first standardize these indicators so that the coefficient estimates are comparable among indicators and with the posterior conditional mean coefficients of the baseline results. Also, because the two measures on market access not only belong in one bucket but also are proxies of the same concept, we exclude the one based on GDP. We then run the growth regression on the 30 standardized indicators.

On the surface, the difference between BACE and OLS seems to be minor. Both identify 11 indicators as statistically significant, and the correlation between the posterior conditional mean coefficients and the OLS coefficients is generally high. However, the assessment of railway station density, share of self‐ employed, and the land regulation index differs substantively between the two approaches. Railway station density becomes one of the least significant indicators according to the OLS estimates, whereas the share of self‐employed becomes significant, and the land reform index becomes one of the most relevant indicators. This finding confirms that the estimates are sensitive to model specification. And BACE remains the more reliable approach, as it explicitly addresses model uncertainty.

Finally, the baseline results are based on district‐level analysis, and so a relevant question is whether the conclusions would hold if the analysis were conducted at the place level. One limitation of this comparison is that we can only calculate a few of the indicators at this level of spatial disaggregation. Among them are the indicators for sectoral composition of economic activity, employment structure, human capital and social inclusion. For other potential drivers of growth that could well vary across places, we can only use the district‐level indicators as proxies.

Despite this limitation, the results remain roughly consistent. However, the correlation between posterior inclusion probabilities declines compared with that for previous robustness tests. The results on the overall significance of the indicators change only for six indicators, but the magnitude of the impacts often differs between estimates at the district level and at the place level. This suggests that for a more thorough analysis at the place level we would need to expand the availability of indicators capturing initial local conditions.

# 9. Conclusion

In contrast with the growth divergence consensus, in this paper we find that Indian living standards strongly converged across districts and places below the district level between 2004 and 2011. A district whose household expenditure per capita in 2004 was 10 percentage points lower than the average district experienced an annual growth rate that was about 0.25 percentage points above the average.

31
This result holds when restricting the analysis to the largest states, which suggests that it is not driven by smaller places with potentially larger measurement errors.

Importantly, there is also convergence in location premiums. These premiums are the spatial differences in household expenditures per capita after controlling for the observable characteristics of the  households living in those locations their demographics, educational attainment, and assets. By controlling for household characteristics, location premiums can be interpreted as an indicator of local productivity. The observed convergence in location premiums implies that there is more than self‐ selection of households at play.

On the drivers of local growth, some of our results confirm the findings of previous research while others contradict the conventional wisdom. Geography matters, as urban economics would have predicted, with both elevation and rainfall having significant impacts on growth. But population density does not and variations in city governance are only mildly relevant. Market access, the availability of electricity and connectivity are strong drivers of growth, whereas irrigation and housing investments are not. We do not find evidence that the sectoral structure of economic activity – such as the share of manufacturing – plays a role, but locations with a bigger share of large firms perform substantially better. On human capital, the attainment of primary education is important, but that of tertiary  education less so. Importantly, all of the indicators of inclusion considered higher access to finance,  lower gender gaps in educational attainment and greater social homogeneity are strongly correlated with local growth. As for governance, law and order at the state level matters, as do state‐level labor and land regulations.

Growth is fastest in the midrange between purely rural places and major urban centers. Divergence at the state level most likely stems from low‐income states not generating enough of fast‐growing locations. The governance results in the analysis of the drivers of growth help make sense of this finding. With state‐level governance more relevant than city governance, low‐income states may fail to create the conditions for the emergence of more vibrant cities.

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