metadata: authors: 0: author: Abreha,Kaleb Girma
1: author: Amaral Ornelas,Rafael
2: author: Zaourak,Gabriel Roberto
count: Brazil
docna: 0: docna: Regional Convergence in Brazil
docty: Policy Research Working Paper
theme: Inclusive Growth,Mitigation,Job Creation,Gender,Human Development and Gender,Data Development and Capacity Building,Economic Policy,Economic Growth and Planning,Fiscal Policy,Environment and Natural Resource Management,Private Sector Development,Public Sector Management,Climate change,Jobs,Adaptation,Data production, accessibility and use,Tax policy
abstracts: cdata!: This paper examines whether labor
            productivity converged across Brazil&#x2019;s states
            (&#x201c;departments&#x201d;) between 2002 and 2018.
            The results show strong evidence of unconditional
            convergence in which states with lower levels of initial
            labor productivity experienced substantially faster labor
            productivity growth. The convergence rate was faster over
            2002&#x2013;10 compared to 2010&#x2013;18 period and
            particularly strong in agriculture, extractives, and
            manufacturing. These findings of the regional convergence
            are robust to controlling for state and industry fixed
            effects, states&#x2019; initial poverty rates, human
            capital, tax collection per capita, and infrastructure.
            Given the high disparity in labor productivity across
            Brazil&#x2019;s states, such regional convergence has
            the potential to raise aggregate productivity and per capita income.
display_title: Regional Convergence in Brazil
listing_relative_url: /research/2024/09/34389399/regional-convergence-brazil
topicv3: Private Sector Development m1326060 1921,Economic Growth m1326241 471,Macroeconomic and Structural Policies
            m1327380 439,Jobs m1503931 2670
publishtoextweb_dt: 2024-09-10T00:00:00Z
dois: 10.1596/1813-9450-10904
no_of_pages: 32
author_keys: 0: author_key: 1656162
1: author_key: 1547219
2: author_key: 1594959
model_extractions: Policy Research Working Paper 10904 Regional Convergence in Brazil _Kaleb Abreha Rafael Ornelas Gabriel Zaourak_ Macroeconomics, Trade and Investment Global Practice September 2024
Policy Research Working Paper 10904

# **Abstract**

This paper examines whether labor productivity converged across Brazil’s states (“departments”) between 2002 and 2018. The results show strong evidence of unconditional convergence in which states with lower levels of initial labor productivity experienced substantially faster labor productivity growth. The convergence rate was faster over 2002–10 compared to 2010–18 period and particularly strong in agriculture, extractives, and manufacturing. These findings of the regional convergence are robust to controlling for state and industry fixed effects, states’ initial poverty rates, human capital, tax collection per capita, and infrastructure. Given the high disparity in labor productivity across Brazil’s states, such regional convergence has the potential to raise aggregate productivity and per capita income.

This paper is a product of the Macroeconomics, Trade and Investment Global Practice. 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/prwp. The authors may be contacted at gzaourak@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
# **Regional Convergence in Brazil**<sup>∗</sup>

Kaleb Abreha Rafael Ornelas Gabriel Zaourak

**JEL Classification:** O11, O47, O54, R11, R12

**Keywords:** Regional inequality, regional convergence, labor productivity, Brazil

> ∗ The World Bank, 1818 H Street, NW Washington, DC 20433, USA. Corresponding email addresses: gzaourak@worldbank.org (G. Zaourak), kaleb.abreha@gmail.com (K. Abreha), and ramaralornelas@worldbankgroup.org (R. Ornelas). The views expressed herein are solely our own and should not be attributed to the World Bank, its executive directors, the countries they represent, the Mosbacher Institute, the Bush School, or Texas A&M University. All errors and omissions are ours.
# **1 Introduction**

Evidence shows a substantial and widening gap in per capita income across countries although income distribution became roughly stable in the early 2000s (Hall and Jones 1999; Jones 2016). Jones (2016, p. 37-38) reports that “the poorest countries in 1960 such as Ethiopia were only about 32 times poorer than the United States. By 2011, there are many countries with relative incomes below this level, and both Niger and the Central African Republic were more than 64 times poorer than the United States.” Relatedly, regional inequalities are as equivalently high and ubiquitous as in cross-country cases, especially among low-income countries. Gennaioli et al. (2014) find considerable regional disparities within countries for a large sample of 107 countries in 2005. Comparing the per capita income of the richest to the poorest regions, they find an average ratio of 4.41. This ratio is 3.77 for Africa, 5.63 for Asia, 3.74 for Europe, 4.60 for North America, and 5.61 for South America. These results on regional inequalities hold even after excluding extremely poor and rich regions: the average standard deviation of per capita income in the 20 poorest countries is 1.64 times larger than the average dispersion of per capita income in the 20 richest countries (Gennaioli et al. 2014).<sup>1</sup> Against this backdrop of significant spatial (across countries and regions) per capita income gaps, a large body of research has tested for evidence of convergence and the drivers of economic growth. In this respect, the convergence hypothesis states that the distribution of per capita income across countries converges in the long run, and hence, it will be independent of countries’ initial conditions. Under the Solow-Swan growth model, capital exhibits diminishing returns, which leads to the reallocation of capital to low-income countries. These countries will then experience faster economic growth and eventually catch up with their high-income counterparts.

The speed of convergence, however, depends on several factors, including geography, institutions, policy, and technological progress. In addition, although spatial (across countries and regions) convergence occurs, initial differences in per capita income and productivity persist because of agglomeration economies. These small differences compound over time to render high inequalities. For instance, if all regions in Brazil have the same steady-state per capita income, a region that

> 1 Price differences across the regions partly explain the regional disparities observed. However, it is unlikely for the price differences to fully explain the significant regional variations in nominal incomes. The regional variations also depend on how regions are weighted in these computations given differences in regions’ resource endowments, population sizes and age structures, and employment rates.

2
is currently one standard deviation below steady-state income will require about 23 years to close the gap at a convergence rate of 2 percent per year (Gennaioli et al. 2014).

In this paper, we investigate whether labor productivity converged across Brazil’s states (“departments”) between 2002 and 2018. During the sample period, our findings show strong evidence of unconditional regional convergence in which states with lower initial levels of labor productivity experienced substantially faster labor productivity growth. Additionally, the convergence rate is faster for the period 2002-10 compared with the 2010-18 period. The convergence rate is particularly strong in agriculture, extractives, and manufacturing. These findings also hold when controlling state and industry fixed effects as well as states’ initial poverty rate, human capital, per capita tax collection, and infrastructure.

This paper is related to the literature on convergence, especially regional convergence. It is related to Gennaioli et al. (2014), who show that regional convergence is relatively faster than crosscountry convergence but generally slower than expected using a large sample of countries, including Brazil. We complement their findings by focusing on labor productivity (rather than per capita income) and using a matched employer-employee dataset. Unlike Azzoni and Castro (2023) who provide evidence of stronger convergence across states of Brazil only during periods of economic crisis (2008 and 2014) and show that periods of better aggregate growth are linked with increasing regional dispersion, our results generally show evidence of regional convergence between 2002 and 2018. Our results also contribute to country case studies on regional inequality that account for the sectoral dimension (e.g., Kinfemichael and Morshed 2019a; Iacovone et al. 2015).

The rest of this paper is organized as follows. Section 2 provides a brief survey of the evidence on the patterns and drivers of convergence from cross-country and country case studies. Section 3 presents the main data sources and summary statistics on labor productivity, poverty rate, and geographic concentration of different sectors. It then introduces the test used to detect if there is any form of regional convergence. Section 4 discusses the results, and section 5 concludes.

3
# **2 Literature review**

A common approach to testing the convergence hypothesis is the _β_ -convergence that relies on whether poorer countries grow faster. It can be tested by using country-level cross-sectional or panel data: where _y_ represents per capita income in country _i_ and time _t_ ,<sup>2</sup> _τ >_ 0, and _ε_ is an error term. Empirically, testing for convergence entails conducting a test of the null hypothesis _β_ = 0 against the alternative _β <_ 0 (Johnson and Papageorgiou 2020). This test presumes that initial per capita income contains sufficient information to capture countries’ initial conditions. If the null hypothesis is rejected, this provides support to the _β_ -convergence hypothesis. Specifically, it implies the occurrence of unconditional convergence in that there is no effect of initial conditions in the long run.

However, several studies show that initial per capita income is not a sufficient statistic to determine convergence, and therefore, other factors such as geography, human capital, and institutions need to be accounted for in characterizing income growth.<sup>3</sup> This is called conditional convergence and can be tested as in equation 1 after introducing controls ( _Ci,t−τ_ ) and country fixed effects ( _λi_ ): Another approach to testing for convergence is the _σ_ -convergence depending on whether crosscountry dispersion in per capita income falls over time. That is, between two different points in time _t_ and _t_ + _τ_ where _τ >_ 0, the presence of _σ_ -convergence yields _σt_<sup>2</sup><sup>_>σ_</sup> _t_<sup>2</sup> + _τ_<sup>,where</sup><sup>_σ_2isthecross-</sup> country dispersion in per capita income. It is important to note that _β_ -convergence is a necessary but not sufficient condition for _σ_ -convergence.<sup>4</sup> Empirically, testing for convergence is commonly done using linear models (as in equations (1) and (2)). Studies have also used non-linear models to allow for possibilities of club convergences and divergence. Johnson and Papageorgiou (2020) categorize these models into those clustering the data

> 2 Although the specification in equation 1 is based on per capita income, it can be generalized to productivity or any other economic development indicators.

> 3 See, for example, Durlauf and Johnson (1995), Fiaschi et al. (2019), and Tan (2010).

> 4 Using U.S. county-level data on real per capita income, Young et al. (2008) show that _β_ -convergence does not necessarily imply _σ_ -convergence.

4
into groups of countries, models having smoothly varying parameters, and models characterizing the cross-country per capita income distribution (not just a few moments). On the other hand, a large number of studies that apply linear or non-linear models use primarily cross-sectional or panel data of countries. However, recent papers have started using time-series methods. Consistent with results from non-linear models, which strongly reject unconditional convergence in favor of club convergence, results based on time-series methods mostly find evidence in support of club convergence (Johnson and Papageorgiou 2020).

# **_Cross-country convergence_**

In one of the recent studies, Bakker et al. (2020) find no support for unconditional convergence and show that differences in human capital and total factor productivity (TFP)—not the capitallabor ratio—drive cross-country differences in GDP per capita in a sample of emerging economies in Europe and Asia and advanced countries between 1996 and 2017. Their findings are in line with the occurrence of conditional convergence. Unlike the rapid rate of convergence in emerging Asia ad and Europe, their findings uncover weaker growth performance and a lack of convergence in Latin America although most of the countries in the region experienced less macroeconomic volatility and favorable terms of trade by comparison. Similarly, Kollias et al. (2021) document the absence of labor productivity convergence in Latin America between 1970 and 2014. In fact, they find countries’ productivity contracted, including the ineffectiveness of the structural reforms of the 1990s.

Additionally, Barrios et al. (2019) find no evidence of overall convergence but evidence of club convergence among a sample of 17 Latin American countries during 1990-2014, which does not necessarily depend on economic ties or geographical proximity.<sup>5</sup> Applying the same method to a larger set of 63 countries during 1960-2011, Tebaldi (2016) also finds evidence against overall convergence in TFP but that supports club convergence and show that initial conditions (TFP, institutional quality, and economic openness) matter for TFP growth. Similarly, Borsi and Metiu (2015) show a long-run difference between new and old EU members and a lack of overall convergence between 1970 and 2010, but find evidence of club convergence depending on geographic region, and not necessarily related to EU membership.

> 5 Barrios et al. (2019) apply Phillips and Sul’s (2007) method, which characterizes the transition path of individual countries and tests if they have a common growth path. Recent methods do not require a prior grouping of countries; clusters of countries would emerge endogenously (Beylunioglu et al. 2020; Phillips and Sul 2007).

5
# **_Sectoral convergence_**

Given the patterns of cross-country convergence are reflections of and shaped by countries’ sectoral composition, it is insightful to investigate sectoral convergence. Using data on more than 100 countries, Rodrik (2013) shows strong evidence of unconditional convergence in manufacturing labor productivity, as well as _σ_ -convergence for a sub-sample of countries. However, there is no aggregate convergence because of a rather small share of formal manufacturing employment and the slow pace of industrialization in low-income countries. In addition, Kinfemichael and Morshed (2019a), using 95 countries, find evidence of unconditional convergence for aggregate labor productivity, primarily driven by the fast convergence in services. Kinfemichael (2019) also reports similar results.

By contrast, Herrendorf et al. (2022), based on a new dataset for low-income countries during 1990-2018, uncover that cross-country differences in productivity gaps (with high-income countries) are larger in manufacturing than in the aggregate, and no observed tendency for productivity to converge in manufacturing. They also find a positive correlation between manufacturing labor productivity growth and aggregate and other sectors’ labor productivity growth, suggesting weak growth of manufacturing employment is not necessarily the force behind the lack of convergence in lowincome countries. The seemingly sharp contrast findings between Rodrik (2013) and Herrendorf et al. (2022) are partly attributed to the role and size of the informal sector in developing countries. Rodrik (2013)’s findings in support of unconditional convergence are based on data on larger establishments in the formal manufacturing sector.<sup>6</sup> When the sample coverage extends to small and informal establishments and workers, which are highly prevalent in developing countries, as in Herrendorf et al. (2022), the data does not reveal unconditional convergence in manufacturing.

An earlier study by Wong (2006) decomposes the pattern of _β_ -convergence into within- and between-sector contributions and show that both the within-sector growth and between-sector reallocations. Among the OECD countries during 1970-1990, Wong (2006) shows sizable contributions of productivity growth in agriculture and services to aggregate convergence, but limited role of labor reallocation and productivity growth in manufacturing. Relatedly, Dieppe and Matsuoka (2021) apply the same technique on a larger sample of advanced and developing countries and more recent years<sup>7</sup> and show that both the within-sector growth and between-sector reallocations

> 6 Rodrik (2013) clearly indicates the context in which to interpret the findings; they apply to formal manufacturing.

> 7 Their results are based on sectoral data for 91 countries over 1995-2018, including a longer horizon (between 1975 and 2018) for a sub-sample of 60 countries.

6
have contributed significantly toward convergence in aggregate labor productivity. Interestingly, productivity growth in agriculture was the main driver of aggregate convergence. Nevertheless, agricultural productivity in low-income countries still markedly lags and is weakly converging relative to advanced countries. As for manufacturing, they find evidence in support of unconditional convergence consistent with Rodrik (2013) albeit with a slower convergence rate. In line with Bakker et al. (2020), their findings also imply addressing barriers to sectoral reallocation through human capital development, good governance, and a favorable business environment would boost productivity growth and accelerate convergence.

# **_Regional convergence_**

Studies have also examined the patterns of regional inequalities and convergence within countries. Gennaioli et al. (2014), based on regional data from 83 countries, show that rich countries experienced faster regional convergence than poor countries, mainly attributed to better capital markets in the former and limited factor mobility in the latter. Their results further show that the pace of convergence across regions within countries is relatively faster than the one observed across countries.Yet, the regional convergence rate is generally slow, as indicated by lower resource mobility. This is despite regions being more likely to exhibit homogeneity in technology, productivity, and institutions compared to countries.

Examining the determinants of regional growth, Gennaioli et al. (2014) show that geography (e.g., resource endowment, temperature, proximity to the ocean) and human capital (e.g., educational attainment) are important factors but not culture (e.g., ethnic heterogeneity, trust) and institutions (e.g., business environment) factors. More importantly, they highlight the crucial role of human capital through the mechanisms of worker education, entrepreneurial/managerial education, and externalities while noting the ease with which firms, workers, and entrepreneurs move across regions than countries.

Coming to country-specific studies, Kinfemichael and Morshed (2019b) argue that the slowdown of labor productivity convergence in recent years in the United States is possibly due to factors such as the decline in cross-state migration, increase in housing costs in major cities, and strengthening of agglomeration economies. During the period 2000-2012 for Peru, Iacovone et al. (2015) report evidence of labor productivity cross-region convergence in manufacturing and mining sectors, but 7
there is no strong evidence of convergence in agriculture and services. More importantly, their results show that the rate of convergence in manufacturing and mining has been strong enough to lead aggregate convergence across regions, albeit at a slower pace because of high employment shares of agriculture and services.<sup>8</sup> In the case of Brazil, Azzoni and Castro (2023) examined regional disparities from 2002 to 2019. Their findings indicate a general increase in _σ_ -convergence in per capita income across regions. Moreover, periods of economic crisis, such as the Great Recession of 2008 and the economic crisis of 2014, were linked to more pronounced convergence. The study also reveals evidence of conditional convergence in regional per capita income and wages (serving as a proxy for labor productivity) during these crisis periods.

Overall, this observed (or lack thereof) convergence and its speed call for further evidence that accounts for the drivers of factor accumulation, sectoral composition, technology diffusion, and production externalities within and across regions and countries.

# **3 Empirical approach**

## **3.1 Data**

Given data availability, we focus on the period from 2002 to 2018. The main dataset comes from the Relação Anual de Informações Sociais (RAIS), which is a matched employer-employee dataset put together by the Ministry of Labor and Employment (Ministério do Trabalho e Emprego). RAIS covers all registered firms and formal employees in which a firm is identified by its registration number (CNPJ) and a worker by its identification number (PIS). Most importantly, both the PIS and CNPJ do not change over time, even when a worker stops to work in the formal sector. These unique features allow us to track workers and firms over time. The dataset contains detailed information on firms’ geographic location, economic classification (CNAE 5-digit), employment size, and personnel records such as monthly wage, age, gender, and education, among others.<sup>9</sup> This dataset is used to compute the key variable of interest: labor productivity at the sectoral and industry levels.

Another data source is derived from the Pesquisa Nacional por Amostra de Domicílios (PNAD).

> 8 They also report lack of convergence in poverty rates across regions because of limited labor mobility toward converging sectors and high employment of the poor in sectors exhibiting weak convergence.

> 9 National Classification of Economic Activities (CANE) is Brazil’s system of economic activity classification in the production and dissemination of economic statistics.

8
This data is gathered through surveys conducted with individuals from 27 states ( ’departments’), covering aspects such as education, employment, income, and housing characteristics, among others.<sup>10</sup> We primarily utilize this dataset to calculate the baseline poverty rate for each state, defined as the proportion of the population earning an income below half of the minimum wage.

# **3.2 Convergence test**

Using the RAIS dataset, we compute labor productivity for each sector and subsector in each state as follows: where _i_ represents a state, _j_ a sector or an industry, and _t_ a time period. We use the following four sectors: agriculture, extractives, manufacturing, and services. Each industry in the CNAE classifications (2-digit) is grouped into one of these sectors.<sup>11</sup> We define labor productivity using the wage bill because data value-added are available only at the sector level. However, this will not be an issue given that the wage bill is a good proxy for labor productivity. Then, we test for the _β_ -convergence across states using the estimating equation: where _τ >_ 0 and _εi,j,t_ is an error term. We consider 8-year and 16-year windows. If data rejects the null hypothesis _β_ = 0 against the alternative _β <_ 0, it shows evidence of unconditional regional convergence. Alternatively, we test for conditional convergence by controlling the state ( _si_ ) and industry ( _λj_ ) fixed effects, and for states’ initial period poverty rate, indicators of human capital, per capita tax collection, and infrastructure access: We also run equations 3 and 4 regression at the aggregate levels; that is, all the sectors combined.

> 10 See the list of states in Appendix A.

> 11 See the list of sectors and industries within the CNAE classification in Appendix A.

9
# **4 Results**

## **4.1 Unconditional convergence**

Considering all the sectors in the aggregate, Figure 1 plots the average annualized growth rates in labor productivity during 2002-10 and 2010-18 against the initial labor productivity levels in 2002 and 2010, respectively. The pattern clearly shows evidence of the unconditional convergence of productivity across regions. States with initial lower productivity levels in 2002 experienced higher growth rates annually, catching up with the leading states. The convergence rate is particularly faster for the 2002-10 period compared with the 2010-18 period. Furthermore, all the sectors have experienced unconditional productivity convergence with the regional convergence pattern looking stronger in non-agriculture sectors (Figure 2). We see that initial levels of labor productivity are relatively lower in agriculture compared with the other sectors.

Considering industry-level labor productivity within each sector, the coefficient estimates in Table 1 provide strong support for unconditional convergence across regions.<sup>12</sup> Looking at the entire sample period (2002-18) and in the aggregate, the estimate is negative (-0.023) and statistically significant, representing a coverage rate of about 2.3 percent. The estimates for individual sectors are also negative and significant; entire sample period (2002-18), the estimates are -0.023, -0.031 (agriculture), -0.030 (extractives), -0.028 (manufacturing), and -0.020 (services). These results imply that states with lower levels of labor productivity in 2002, on average, experienced faster productivity growth over the sample period. This regional convergence holds when considering both the regional economies and disaggregated by sectors.

> 12 In the appendix, we report the estimation results based on labor productivity computed at different levels of aggregations. Except for agriculture and services, regression results at broader levels of aggregation are comparable to estimates at the industry levels within each of the four sectors. The aggregation level seems to have an influence on the significance and size of the estimate. These features suggest substantial variation in productivity growth across industries within these sectors. Some industries may have experienced rapid growth but their shares in the sectoral economy are probably small.

10
<!-- Start of picture text --> aTotal Aggregation - Labor Productivity 002-2010)<br>eo<br>mL<br>a A<br>[efaBa) wleemee-“ “ |<br>a a<br>bya - oea<br>Ho = gt [a<br>: - ated a—<br>q -—r<br>Hl tk<br>Ga 65 Log of Latergz Productihy7 Ir 2002 TZ Te<br><!-- End of picture text -->

<!-- Start of picture text --> Labor Productivity - Agriculture<br>3<br>@aAP AM<br>£3 @Pl eco<br>& ; ese @Es eto eT<br>3ssiy IER@BA @RJ ergeBR @DFgc<br>ao] @RS<br>gi ece PB @PA<br>&5e_ @AL ems<br>ePE @RN esc<br>5.4 5.6 5.8 6 6.2<br>Log of Labor Productivity in 2002<br><!-- End of picture text --> <!-- Start of picture text --> A Labor Productivity- Manufacturing<br>eo<br>cc eco<br># |<br>= - badd<br>a See ee<br>fq ao<br>= al —<br>H a ae<br>Hs aFh<br>: ° me—<— ye<br>gee tial<br>ac ae<br>a aFn<br>55 q 65 T<br>Logof Labor Produciudby irr 2000<br><!-- End of picture text -->

<!-- Start of picture text --> Total Aggregationon- Labor Productivity 2010-2015)<br>S| aco<br>[2]a_payee 7os“— wn “_ -<br>i —, __<br>bya -wane eesc ee |e<br>| — ogee” Cal ——__<br>| a a _<br>Pind<br>5<br>as Log of Later Produciul7 yin 200 1S<br><!-- End of picture text -->

<!-- Start of picture text --> Labor Productivity - Extractyes<br>F ani.<br>eel<br>4<br>i =<br>Fz= aa ee Sal “=<br>~ _<br>g4 i<br>i ar reae 4c:ae— rr<br>a ai eH aFo.ai—ie<br>5 6 7 a<br>Log of Labor Prodceciul kt In 200<br><!-- End of picture text --> <!-- Start of picture text --> A Labor Productivity- Senices<br>ett<br>mg -<br>ra aco<br>s_<br>PF ords,, -<br>a |e 7 we<br>a a er<br>= | Paine re<br>H bate an<br>5: = - a,a .<br>a “— a<br>a a 7 ae<br>' ao<br>ae 6 L o f azLaborg ProduciudT by irr 2000 TZ Ta<br><!-- End of picture text -->
Table 2 compares the patterns of regional convergence in the first and second halves of the sample period and shows that the convergence coefficient is negative and significant in the two sub-periods as well as all the sectors. The sizes of the estimates are also systematically larger in the 2002-10 period compared with the estimates in 2010-18. In the 2002-10 period, the estimates are -0.038 (all sectors), -0.079 (agriculture), vs -0.059 (extractives), -0.041 (manufacturing), and -0.035 (services). The corresponding estimates in 2010-18 are -0.019, -0.020, -0.021, -0.030, and -0.017. The convergence rate is especially low for services.

Table 1: Growth of Aggregate and Sectoral Labor Productivity 2002-18 (Labor Productivity Computed at the Industry Level)

||All Sectors|Agriculture|Extractives|Manufacturing|Services|
|---|---|---|---|---|---|
||(1)|(2)|(3)|(4)|(5)|
|Initial labor productivity (log)|-0.023<sup>_∗∗∗_</sup>|-0.031<sup>_∗∗∗_</sup>|-0.030<sup>_∗∗∗_</sup>|-0.028<sup>_∗∗∗_</sup>|-0.020<sup>_∗∗∗_</sup>|
||(0.0011)|(0.0076)|(0.0053)|(0.0020)|(0.0012)|
|Constant|0.153<sup>_∗∗∗_</sup>|0.201<sup>_∗∗∗_</sup>|0.210<sup>_∗∗∗_</sup>|0.186<sup>_∗∗∗_</sup>|0.137<sup>_∗∗∗_</sup>|
||(0.0069)|(0.0447)|(0.0353)|(0.0124)|(0.0073)|
|Industry FEs|No|No|No|No|No|
|State FEs|No|No|No|No|No|
|Obs.|2,266|81|112|625|1,448|
|R<sup>2</sup>|0.294|0.228|0.291|0.440|0.255|

*** Source: World Bank staff using RAIS. Note: Robust standard errors in parentheses. _p <_ 0 _._ 01, ** _p <_ 0 _._ 05, * _p <_ 0 _._ 1.

# **4.2 Conditional convergence**

A multiplicity of factors influences the pace of regional convergence in productivity. Some are geographic (e.g., resource endowment, sea access), institutional (e.g., regulatory capacity, market distortions), and policy. To this end, the regional convergence regressions are now estimated after controlling for industry fixed effects (the levels and productivity growth rates inherently differ due to differences in production and market structure) and state fixed effects (to capture the effect of mostly geographic factors on regional development). In addition, these regression account for states’ initial level of development (approximated by poverty rates) and determinants of development (e.g., population size and age composition, labor market features, and infrastructure).

Table 3 presents tests for the presence of regional conditional convergence. Column (1) shows that including the industry and state fixed effects accelerates productivity growth and promotes re12
||ices<br>2010-18|(10)|-0.017_∗∗∗_<br>(0.0020)|0.116_∗∗∗_|(0.0127)|No<br>No|1,440|0.093||
|---|---|---|---|---|---|---|---|---|---|
||Serv<br>2002-10|(9)|-0.035_∗∗∗_<br>(0.0022)|0.228_∗∗∗_|(0.0139)|No<br>No|1,463|0.200|.|
|evel)|acturing<br>2010-18|(8)|-0.030_∗∗∗_<br>(0.0035)|0.195_∗∗∗_|(0.0220)|No<br>No|622|0.191|_._05, *_p <_0_._1|
|industry l|Manuf<br>2002-10|(7)|-0.041_∗∗∗_<br>(0.0032)|0.265_∗∗∗_|(0.0200)|No<br>No|637|0.305|01, **_p <_0|
|-18 (at the|ctives<br>2010-18|(6)|-0.021_∗∗_<br>(0.0098)|0.154_∗∗_|(0.0660)|No<br>No|107|0.059|es. ***_p <_0_._|
|versus 2010|Extra<br>2002-10|(5)|-0.059_∗∗∗_<br>(0.0094)|0.408_∗∗∗_|(0.0625)|No<br>No|113|0.321|in parenthes|
|y 2002-10|lture<br>2010-18|(4)|-0.020_∗_<br>(0.0117)|0.136_∗_|(0.0714)|No<br>No|80|0.046|ard errors|
|it|cu||||||||d|
|productiv|Agri<br>2002-10|(3)|-0.079_∗∗∗_<br>(0.0152)|0.486_∗∗∗_|(0.0895)|No<br>No|80|0.350|Robust stan|
|ctoral labor|ectors<br>2010-18|(2)|-0.019_∗∗∗_<br>(0.0019)|0.131_∗∗∗_|(0.0121)|No<br>No|2,247|0.099|RAIS. Note:|
|Table 2: Growth of se|All s<br>2002-10|(1)|tial labor productivity (log)<br>-0.038_∗∗∗_<br>(0.0020)|nstant<br>0.253_∗∗∗_|(0.0126)|ustry FEs<br>No<br>te FEs<br>No|s.<br>2,293|0.237|Source: World Bank staf using|
||||Ini|Co||Ind<br>Sta|Ob|R2||

13
|ices|(10)|-0.021_∗∗∗_|(0.0012)|-0.001_∗∗∗_<br>0.147_∗∗∗_|(0.0078)|No|No|1,448|0.264|
|---|---|---|---|---|---|---|---|---|---|
|Serv|(9)|-0.045_∗∗∗_|(0.0025)|-||Yes|Yes|1,448|0.706|
|cturing|(8)|-0.031_∗∗∗_|(0.0022)|-0.001_∗∗∗_<br>(0.0002)<br>0.208_∗∗∗_|(0.0143)|No|No|625|0.467|
|Manufa|(7)|-0.042_∗∗∗_|(0.0031)|-||Yes|Yes|625|0.634|
|ctives|(6)|-0.031_∗∗∗_|(0.0056)|-0.001<br>(0.0010)<br>0.227_∗∗∗_|(0.0405)|No|No|112|0.301|
|Extra|(5)|-0.035_∗∗∗_|(0.0075)|-||Yes|Yes|112|0.580|
|lture|(4)|-0.044_∗∗∗_|(0.0076)|-0.001_∗∗∗_<br>(0.0004)<br>0.286_∗∗∗_|(0.0460)|No|No|81|0.341|
|Agricu|(3)|-0.042_∗∗∗_|(0.0099)|-||Yes|Yes|81|0.817|
|ll|(2)|-0.024_∗∗∗_|(0.0012)|-0.001_∗∗∗_<br>(0.0001)<br>0.165_∗∗∗_|(0.0075)|No|No|2,266|0.306|
|A|(1)|(log)<br>-0.040_∗∗∗_|(0.0019)|-||Yes|Yes|2,266|0.624|
|||Initial labor productivity||Initial poverty rate<br>Constant||Industry Fes|<br>State Fes|Obs.|R2|

14
|ices|(8)|-0.018_∗∗∗_<br>(0.0021)|-0.001_∗∗∗_|(0.0002)|0.133_∗∗∗_<br>(0.0143)|No|No|1,440|0.108||
|---|---|---|---|---|---|---|---|---|---|---|
|Serv|(7)|-0.035_∗∗∗_<br>(0.0022)|-0.0004|(0.0002)|0.235_∗∗∗_<br>(0.0147)|No|No|1,463|0.201|_<_0_._1.|
|cturing|(6)|-0.034_∗∗∗_<br>(0.0041)|-0.001_∗∗∗_|(0.0003)|0.233_∗∗∗_<br>(0.0279)|No|No|620|0.216|*_p <_0_._05, *_p_|
|Manufa|(5)|-0.043_∗∗∗_<br>(0.0035)|-0.001_∗∗∗_|(0.0003)|0.288_∗∗∗_<br>(0.0227)|No|No|637|0.315|. ***_p <_0_._01, *|
|tives|(4)|-0.022_∗∗_<br>(0.0098)|-0.001|(0.0015)|0.163_∗∗_<br>(0.0653)|No|No|107|0.061|in parentheses|
|Extrac|(3)|-0.060_∗∗∗_<br>(0.0101)|-0.001|(0.0018)|0.416_∗∗∗_<br>(0.0748)|No|No|113|0.322|standard errors|
|lture|(2)|-0.037_∗∗∗_<br>(0.0124)|-0.002_∗∗∗_|(0.0005)|0.259_∗∗∗_<br>(0.0774)|No|No|80|0.188|. Note: Robust|
|Agricu|(1)|-0.095_∗∗∗_<br>(0.0156)|-0.002_∗∗_|(0.0007)|0.597_∗∗∗_<br>(0.0927)|No|No|80|0.390|staf using RAIS|
|||tial labor productivity (log)|tial poverty rate||nstant|dustry FEs|te FEs|s.||Source: World Bank|
|||Ini|Ini||Co|In|Sta|Ob|R2||

15
gional convergence. This result also holds when examining the regional convergence in the major sectors separately. We also see in column (2) that states with an initial high prevalence of poverty rate have experienced relatively higher productivity; this effect is considerably stronger in the agricultural sector suggesting the prevalence of poverty in agriculture-intensive regions. Note that the convergence rate in the services sector is about half when initial poverty is accounted for relative to the estimates when the industry and state fixed effects are included. A feature worth mentioning is the fact that after conditioning on departmental poverty rates or fixed effects, convergence appears to be significant and faster when the data is disaggregated by industries. This suggests that productivity convergence would have been even faster if industries were more “similar”.

Table 5: Growth of aggregate labor productivity, 2002-18

||(1)|(2)|(3)|(4)|(5)|(6)|
|---|---|---|---|---|---|---|
|Initial<br>labor<br>productivity|-0.024<sup>_∗∗∗_</sup>|-0.024<sup>_∗∗∗_</sup>|-0.023<sup>_∗∗∗_</sup>|-0.024<sup>_∗∗∗_</sup>|-0.023<sup>_∗∗∗_</sup>|-0.024<sup>_∗∗∗_</sup>|
|(log)|(0.0012)|(0.0012)|(0.0012)|(0.0012)|(0.0011)|(0.0012)|
|Initial poverty rate|-0.0006<sup>_∗∗∗_</sup><br>(0.0001)||||||
|Initial years of schooling (tot.||0.003<sup>_∗∗∗_</sup>|||||
|pop.)||(0.0007)|||||
|Initial working age popula-|||0.000||||
|tion (% of tot. pop.)|||(0.0002)||||
|Initial government tax col-||||0.004<sup>_∗∗∗_</sup>|||
|lected per capita (log)||||(0.0009)|||
|Initial HHs with access to|||||0.0002<sup>_∗∗_</sup>||
|electricity network (% total<br>HHs)|||||(0.0000)||
|Initial HHs with landline or||||||0.0002<sup>_∗∗∗_</sup>|
|mobile telephone (% of total<br>HHs)||||||(0.0000)|
|Constant|0.165<sup>_∗∗∗_</sup>|0.144<sup>_∗∗∗_</sup>|0.151<sup>_∗∗∗_</sup>|0.138<sup>_∗∗∗_</sup>|0.136<sup>_∗∗∗_</sup>|0.152<sup>_∗∗∗_</sup>|
||(0.0075)|(0.0068)|(0.0115)|(0.0071)|(0.0100)|(0.0068)|
|Industry FEs|No|No|No|No|No|No|
|<br>State FEs|No|No|No|No|No|No|
|Obs.|2,266|2,266|2,266|2,266|2,266|2,266|
|R<sup>2</sup>|0.306|0.301|0.294|0.301|0.296|0.302|

footnote: World Bank staff using RAIS. Note: Robust standard errors parentheses.<sup>_∗∗∗_</sup> _p <_ 0 _._ 01,<sup>_∗∗_</sup> _p <_ 0 _._ 05,<sup>_∗_</sup> _p <_ 0 _._ 1.

16
As in the case of unconditional convergence results, the convergence rate is markedly higher for the 2002-10 period than for the 2010-18 period. This is particularly evident for agriculture and extractives (Table 4). Furthermore, Table 5 introduces additional state controls in the convergence regressions. We see that there is a strong and significant convergence in productivity across the states, including identical sizes of the coefficient estimates. It is found that productivity growth is higher in states with better human capital development (measured by years of schooling in the state’s population, stronger institutional capacity (approximated by per capita tax collection), and better infrastructure access (electricity and telephone connection). However, the share of the working population does not have an impact.

# **5 Conclusion**

Testing for regional convergence in productivity across Brazil’s states between 2002 and 2018, the findings provide evidence supporting unconditional convergence in which states with lower levels of initial labor productivity experienced substantially faster labor productivity growth. Additionally, the convergence rate is faster for the period 2002-10 compared with the 2010-18 period and particularly strong in agriculture, extractives, and manufacturing. These findings on regional convergence are robust to controlling for state and industry fixed effects, states’ initial poverty rate, human capital, tax collection per capita, and infrastructure.

Given the high disparity in labor productivity across Brazil’s states, such regional convergence has the potential to raise aggregate productivity and per capita income. However, the extent to which regional convergence promotes aggregate productivity critically depends on the reallocation of factor inputs and output shares toward sectors and industries with higher levels of productivity and faster speeds of convergence.

17