Convergence of labor productivity across the US states

Economic Modelling xxx (2018) 1–11

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Convergence of labor productivity across the US states Bisrat Kinfemichael a, A.K.M. Mahbub Morshed b, * a b

School of Management, New York Institute of Technology, New York, NY 10023, USA Department of Economics, Southern Illinois University, Carbondale, IL 62901, USA

A R T I C L E I N F O

A B S T R A C T

JEL codes: O40 O47 R11

Most studies of labor productivity convergence among US states base their analyses on state-level GDP per worker. Such aggregated analysis may hide important information about the role of sectors, and changes in the sectoral composition of these economies, in explaining economy-wide convergence results. Using highly disaggregated data for the period 1987–2015 from the US Bureau of Economic Analysis, we examine sectoral unconditional convergence in labor productivity in the US states. Our results demonstrate a general slowing down in the rate of convergence of labor productivity in the latter years of this period. The sectoral analysis also indicates that manufacturing was the primary driver of convergence during the 1987–1997 period, which had the highest rate of convergence; the role of this sector, however, has diminished in recent years. Several factors—such as the decline in interstate migration, rising housing costs in major cities, agglomeration, and structural changes in the US economy that have reduced the role of manufacturing—may have contributed to the rise in the labor productivity differential among US states.

Keywords: Unconditional convergence Labor productivity Aggregation bias U.S. states

1. Introduction Regional income inequality within a country has been receiving more attention lately (Kennedy et al., 2017). The persistence of regional income inequality and poverty in the US prompted researchers to identify the proximate causes for such a situation (Chetty et al., 2016). The researchers argue that where one is born plays an important role in one's economic success. Even in 2016, the median household in the South earns about 83.6% of the income of a median household in the Northwest (Sommeiller et al., 2016; Semega et al., 2017). It is therefore important to explore why poor regions in the US remain poor even when there is no overt barrier to labor mobility. The literature on regional income convergence may shed some light on this crucial issue. Using aggregated state-level data, researchers have examined regional income convergence and found the presence of unconditional convergence, consistent with the predictions of neoclassical growth models, in the pre-2000 data (Barro et al., 1991; Barro and Sala-i-Martin, 1992; Evans and Karras, 1996; Young et al., 2008; Higgins et al., 2006). Many recent studies, however, have found no evidence or scant evidence of the catching up of income across the US states in recent data (Berry and Glaeser, 2005; Heckelman, 2013; Ganong and Shoag, 2017). Caselli and

Coleman (2001) argue that a crucial factor in income convergence across the US during the pre-2000 period is the falling cost of education that enabled unskilled workers from the agriculture sector to acquire skills and move to non-agricultural sectors. In addition, Freemana and Yerger (2001) attribute this convergence to technological spillovers and trade. In a recent paper, Molloy et al. (2011) find a sharp decline in interstate migration in the US which began around 1980. Compton and Pollak (2009) show that most Americans now live within 25 miles of their mother's home. Berry and Glaeser (2005) show that skilled new entrepreneurs demand more skilled labor, but a rising cost of education turns out to be a crucial barrier for unskilled workers to acquire required skillsets. Rising education costs coupled with a higher cost of living in cities may result in significantly reduced intra-country migration. These studies on economic convergence across US states focused mostly on aggregate variables like per capita state GDP. One can argue, however, that technological spillover, increased competition, and lower inter-state migration may affect different sectors of a state's economy in various ways. For example, international trade and increased use of automation in production affect manufacturing sector employment more than that of the service sector (Blum, 2008). Moreover, these effects are not the same qualitatively and quantitatively for all subsectors of the

* Corresponding author. E-mail addresses: [email protected] (B. Kinfemichael), [email protected] (A.K.M.M. Morshed).

https://doi.org/10.1016/j.econmod.2018.08.008 Received 9 August 2017; Received in revised form 8 August 2018; Accepted 9 August 2018 Available online xxxx 0264-9993/© 2018 Elsevier B.V. All rights reserved.

Please cite this article in press as: Kinfemichael, B., Morshed, A.K.M.M., Convergence of labor productivity across the US states, Economic Modelling (2018), https://doi.org/10.1016/j.econmod.2018.08.008

B. Kinfemichael, A.K.M.M. Morshed

Economic Modelling xxx (2018) 1–11

manufacturing and service sectors.1 These variations of impact on different subsectors result in economic hardships in some areas, while in others people may receive benefits from positive effects of the same shock due to their different output mix. Since we observe differential impacts on different subsectors of manufacturing and service sectors in response to exogenous shocks (like technology shocks), a subsector-level study will likely yield valuable information about income dynamics. This paper is an attempt to fill that gap by investigating labor productivity convergence profiles in US states using a highly disaggregated dataset. We believe that understanding which subsectors are converging, as well as which are not, will provide valuable input in macroeconomic policy-making focused on growth and inequality. Researchers have been encouraging more subsector-level or industry-level studies as aggregation creates “aggregation bias” (in the context of price convergence, see Imbs et al., 2005). Although a number of cross-country studies on labor productivity convergence are conducted using a disaggregated dataset (for manufacturing, see Rodrik, 2013), to the best of our knowledge no regional convergence study is found in which disaggregated subsector level data are used. Using disaggregated data for the 48 contiguous states2 of the US, we find that the catching-up process of labor productivity has progressively declined for most of the sectors in recent years. Following Bureau of Economic Analysis (BEA) suggestions, we examine the convergence profile for two separate periods: 1987–1997 and 1998–2015.3 While examining each subsector separately, we obtain mixed results. The catching-up process has stopped for some subsectors, such as lumber and wood products, furniture and related products, and paper products manufacturing. On the other hand, a new catching-up process is detected for other subsectors, such as printing and publishing, chemical products, primary metal, fabricated metal, accommodations, and amusement, gambling, and recreation services. Our regional analysis suggests a weakening of the convergence process for the majority of subsectors in most regions during 1998–2015, excluding regions like the Rocky Mountains and the Far West, in which we find new signs of convergence. Our study is related to a small literature on the regional convergence of income (Chanda and Panda, 2016; Hamit-Haggar, 2013; Brown and Macdonald, 2015; and Otsuka and Goto, 2016). While most of the studies

examine per capita regional income, Chanda and Panda (2016) examine multi-factor productivity convergence in the goods sector and service sector using a dual growth accounting approach based on factor prices proposed by Hsieh (2002). Unlike Chanda and Panda (2016), however, we consider the disaggregated subsectors within the agriculture, mining, construction, manufacturing, and service sectors using the Standard Industrial Classification (SIC) for the years 1987–1997 and the North American Industrial Classification System (NAICS) for the years 1998-2015.4 The remainder of this paper is organized as follows: Section 2 presents literature review; Section 3 discusses the data and data sources; Section 4 explains the methodology used in the study; Section 5 presents results; Section 6 presents robustness check results; and Section 7 concludes. 2. Literature review Empirical studies on income convergence with data prior to 2000 yield unconditional convergence among the US states (Barro et al., 1991; Barro and Sala-i-Martin, 1992; Young et al., 2008; Higgins et al., 2006). Barro et al. (1991) and Barro and Sala-i-Martin (1992) use gross state product and personal income for US states for the period 1840–1988, while Young et al. (2008) and Higgins et al. (2006) use county-level income data from the US covering the period from 1970 to 1998. These studies find signs of convergence suggesting that poor states are growing at a faster rate than rich states. Recent studies find that starting in the late 1990s, the rate of convergence for US states appears to have declined (Berry and Glaeser, 2005; Heckelman, 2013; Ganong and Shoag, 2017). A number of contributing factors have been identified. Berry and Glaeser (2005) argue that the difference in human capital (in terms of the skilled and unskilled population) accounts for the fall of convergence in the US. US metropolitan areas with high income and higher initial education levels are attracting a more skilled population than cities with lower initial educational levels. Moreover, skilled entrepreneurs who establish new firms demand skilled labor. As a result, the share of the adult population with college degrees has grown more in cities with higher initial schooling levels. On the other hand, Ganong and Shoag (2017) show that, unlike the period prior to 1980, migration of labor from low-income states to high-income states declined significantly during 1990–2010. In addition, they contend that the higher and rising housing prices may have contributed to a lower migration of people from a low-income state to a high-income state, and as a result, they observe income convergence to be very weak or nonexistent. Although a few attempts have been made to include sectoral income or productivity convergence with state-level data (for example, Chanda and Panda, 2016), no such study with more disaggregated state-level data has been conducted. A study of this kind is, however, warranted. By comparing the results from both aggregated and disaggregated data, we can appraise the issue of “aggregation bias”, which stands for the stark differences between the dynamic properties of aggregated variables and the dynamic properties of components individually. This paper is an attempt to fill this void.

1 In a cross-country study, Sondermann (2014) finds different convergence profiles for service and manufacturing sectors in Euro areas. Bernard and Jones (1996) and Madsen and Timol (2011) also find different convergence profiles in the manufacturing and service sectors using data from OECD. 2 We also have data for Alaska, Hawaii, and Washington D.C. Contrary to the 48 contiguous states, however, these locations are significantly different in terms of economic activity. Alaska relies on natural resources, Hawaii on tourism, and D.C. on government services. Data from these three are, therefore, excluded, as is done in Ganong and Shoag (2017). Even so, in order to verify the robustness of our results, convergence coefficients were estimated using all available data. The results (not reported here) turn out to be qualitatively similar. 3 The BEA issued the following cautionary note about data compilation: There is a discontinuity in the GDP-by-state time series at 1997, where the data change from SIC industry definitions to NAICS industry definitions. This discontinuity results from many sources. The NAICS-based statistics of GDP by state are consistent with U.S. gross domestic product (GDP) while the SIC-based statistics of GDP by state are consistent with U.S. gross domestic income (GDI). With the comprehensive revision of June 2014, the NAICS-based statistics of GDP by state incorporated significant improvements to more accurately portray the state economies. Two such improvements were recognizing research and development expenditures as capital and the capitalization of entertainment, literary, and other artistic originals. These improvements have not been incorporated in the SIC-based statistics. In addition, there are differences in source data and different estimation methodologies. This data discontinuity may affect both the levels and the growth rates of GDP by state. Users of GDP by state are strongly cautioned against appending the two data series in an attempt to construct a single time series for 1963 to 2016 (https://www.bea.gov/regional/docs/ product/).

4 Some studies examine convergence on a sectoral level using cross-country data. These studies rely mainly on data from OECD countries. For example, Bernard and Jones (1996) find that the service sector exhibits convergence in 14 OECD countries. They, however, do not find any evidence of convergence in manufacturing sectors in OECD countries. Madsen and Timol (2011) find both absolute and conditional convergence in manufacturing for 19 OECD countries. Sondermann (2014) finds no convergence in real labor productivity in most subsectors within both the service and manufacturing sectors in Euro areas for the period 1970–2007. Fung (2005) finds statistically significant conditional convergence and weak absolute convergence in labor productivity in both US and non-US firms.

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3. Data and data sources

Table 1 US Sectoral labor productivity (in natural logarithm) (1987–1997).

Labor productivity is measured as the value added per worker. We have collected data for both value added and employment in each sector from the Bureau of Economic Analysis (BEA) of the US Department of Commerce. The value added data is from the states' annual real GDP broken down by sectors. Employment data is collected from “The Total Full-Time and Part-Time Employment by Industry” (U.S. Bureau of Economic Analysis, 2017a, 2017b). The BEA uses two methods to classify industries. For the period from 1987 to 1997, the industry classification is based on the Standard Industrial Classification (SIC). For the remaining period (1998–2015) the classification is based on the North American Industry Classification System (NAICS). We use real value added to control for inflation, based on chained dollars, with 1997 as a base year for 1987–1997, and 2009 for 1998–2015. The BEA advised against combining the two data sets to form a single time series dataset as the source and estimation methodologies of the two data series differ (BEA, 2014). Both SIC and NAICS industry classifications have a two-digit level of industry aggregation.5 As the economies of Alaska, the District of Columbia (D.C.), and Hawaii are significantly different from the other 48 contiguous states, our analysis maintains focus on the data from these 48 states.

Industry

Year

Mean

Standard Deviation

minimum

maximum

Construction

1987 1997 1987 1997 1987 1997 1987 1997 1987 1997 1987 1997 1987 1997 1987 1997 1987 1997

10.537 10.622 11.558 11.682 10.841 11.141 10.841 11.312 9.988 10.206 10.405 10.402 11.213 11.396 10.827 11.229 10.776 10.999

0.202 0.192 0.190 0.242 0.254 0.220 0.793 0.630 0.120 0.129 0.159 0.180 0.178 0.141 0.123 0.133 0.556 0.564

10.191 10.207 11.183 11.234 10.189 10.795 9.062 9.525 9.732 9.858 10.119 10.083 10.974 11.194 10.573 10.997 9.062 9.525

11.039 11.103 12.073 12.248 11.641 12.093 13.847 13.399 10.217 10.463 10.876 10.929 12.163 11.899 11.144 11.679 13.847 13.399

Finance, insurance, and real estate Manufacturing Mining Retail trade Services Transportation and public utilities Wholesale trade Total

Table 2 US Sectoral labor productivity (1998–2015).

4. Empirical specification

Industry

Year

Mean

Standard Deviation

Minimum

Maximum

The empirical model in the convergence literature generally follows the neoclassical growth model, where studies estimate the relationship between the growth rate of GDP (or labor productivity) and its initial value per capita real GDP (Sala-i-Martin, 1996a, 1996b; Barro and Sala-i-Martin, 2004). We accordingly estimate the following equation to examine the presence or absence of convergence in labor productivity,

Accommodation and food services Administrative and waste management services Arts, entertainment, and recreation Educational services

1998 2015 1998 2015

10.370 10.335 10.325 10.646

0.236 0.191 0.181 0.170

10.036 10.090 9.873 10.246

10.983 10.935 10.742 11.014

1998 2015 1998 2015 1998 2015 1998 2015 1998 2015

10.466 10.362 10.563 10.291 11.149 11.447 10.848 10.918 11.768 11.741

0.347 0.305 0.230 0.285 0.355 0.331 0.098 0.087 0.244 0.257

9.852 9.799 10.044 9.770 10.534 10.907 10.630 10.764 11.402 11.305

11.606 11.056 11.106 10.916 12.377 12.584 11.055 11.144 12.360 12.634

1998 2015

11.167 11.234

0.233 0.230

10.674 10.865

11.959 12.011

1998 2015 1998 2015 1998 2015 1998 2015 1998 2015 1998 2015 1998 2015 1998 2015 1998 2015 1998 2015 1998 2015

12.439 12.363 11.230 10.975 11.402 12.143 11.220 11.751 12.069 11.761 10.551 10.771 11.141 11.135 12.849 12.951 11.552 11.819 11.237 11.329 10.370 10.335

0.210 0.210 0.188 0.206 0.276 0.314 0.287 0.256 0.541 0.687 0.132 0.123 0.198 0.281 0.218 0.298 0.136 0.143 0.748 0.791 0.236 0.191

11.995 11.987 10.784 10.397 10.958 11.577 10.452 11.240 10.790 10.457 10.263 10.501 10.811 10.495 12.365 12.510 11.314 11.461 9.852 9.770 10.036 10.090

13.198 12.801 11.639 11.379 12.434 13.009 12.007 12.447 13.749 13.299 10.831 11.179 11.838 12.185 13.479 14.324 11.943 12.226 13.749 14.324 10.983 10.935


gij ¼ αj þ β ln pij þ εij

(1)

Finance and insurance Health care and social assistance Management of companies and enterprises Professional,, scientific, and technical services Real estate and rental and leasing Construction

where gij is the real growth rate of labor productivity in sector i in state j; αj combines both a constant and a j state-specific shock (Mankiw et al., 1992); p represents the initial level of labor productivity, and εij is the error term for sector i and state j. A statistically significant negative β coefficient would suggest conditional convergence. If we exclude the state fixed effect, a statistically significant negative β coefficient would indicate unconditional convergence. Our main estimation methodology relies on a cross-sectional analysis method that considers one data point of growth in labor productivity and initial labor productivity. We apply this method to estimate equation one for the two sets of time series data (1987–1997 and 1998–2015). For example, for 1987–1997 data, the dependent variable is the compound annual growth rate of productivity from 1987 to 1997, and the independent variable is labor productivity in 1987. As we have one data point for growth and initial productivity, we use a cross-sectional regression. We similarly estimate a cross-sectional regression for the 1998–2015 data.

Information Manufacturing Mining Other services, except government Retail trade Transportation and warehousing Utilities

5. Results 5.1. Summary statistics of state labor productivity

Wholesale trade

Tables 1 and 2 show summary statistics for labor productivity across sectors and states between the periods 1987–1997 and 1998–2015. Table 1 shows that, between 1987 and 1997, labor productivity increased for all sectors of the US economy. At the same time, there exist significant variations in labor productivity across states and sectors. The most

Total

productive sector was the finance, insurance, and real estate sector and the least productive sector was the retail trade sector in both 1987 and 1997. The mining sector exhibited the highest variation in productivity across states in both 1987 and 1997. We also observe a rise in the dispersion of labor productivity for four sectors (finance, insurance, and

5 Although discouraged by the BEA, and while still following suggestions from the US Census, we compiled single time series and we discuss results in Appendix 1.

3

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manufacturing still record negative and highly significant convergence coefficients. The convergence coefficient for manufacturing dropped to β ¼ -0.034 while retail trade and finance and insurance sectors yield signs of convergence. When we combine all sectors, we obtain evidence of convergence, albeit weaker. With industry fixed effect, the convergence coefficient in the latter period in absolute terms becomes larger than it was in the earlier period (β ¼ -0.013 vs β ¼ -0.034). Fig. 1 consists of two component-plus-residual plots which illustrate the presence of convergence in labor productivity during the 1987–1997 period and the weakening of signs of convergence during the 1998–2015 period. Each dot in Fig. 1 stands for labor productivity of a particular subsector. A downward sloping line indicates signs of convergences while a horizontal line indicates that there is no systematic tendency for state-level labor productivity to grow for a state with a low-level of initial labor productivity. In a recent study, Rodrik (2013) has shown, by using disaggregated subsector level data for 118 countries, that the manufacturing sector yields unconditional convergence in labor productivity, while aggregated labor productivity shows no such tendency. To examine whether the same pattern holds for state-level data within a country, we estimated convergence coefficients for all 48 subsectors for the period 1987–1997 and found a negative and significant convergence coefficient for 24 subsectors. For the 1998–2015 period, 24 subsectors out of 39 realigned subsectors yield a negative and significant coefficient, while four subsectors yield signs of divergence (that is, a positive and significant β coefficient). Results of subsector level convergence regressions are reported in Tables 4–6. Regression results for the disaggregated manufacturing sector are reported in Table 4. The results for the 1987–1997 period are reported in the first three columns, while the results for the 1998–2015 period are presented in the next three columns. As the BEA changed subsector

real estate, retail trade, services, and wholesale trade). The remaining sectors experienced a fall in the dispersion of productivity between the two time periods. This indicates signs of weakening convergence even in the 1987–1997 period. The most productive sector in terms of labor productivity, in both 1998 and 2015, was transport and warehousing, while the least productive was administrative and waste management services in 1998 and educational services in 2015 (Table 2). In recent data (the 1998–2015 period), with 18 industry classifications, we find eight sectors that exhibited a fall in mean labor productivity. For nine subsectors within this group, the standard deviation becomes larger. This indicates strong confirmation of a drop in the rate of convergence in the US economy in recent years (Berry and Glaeser, 2005; Heckelman, 2013; Ganong and Shoag, 2017). 5.2. Main results Regression results concerning the convergence of sectoral labor productivity for the 48 contiguous US states for 1987–1997 and 1998–2015 are reported in Table 3. This reveals that for the period 1987–1997 there are signs of unconditional convergence for most of the aggregated sectors, excepting retail trade and finance, insurance, and real estate. For manufacturing the convergence coefficient is the largest (in absolute terms) with β ¼ -0.091, which is highly significant, followed by transport and mining. When we combine all sectors, we still obtain a smaller but statistically significant convergence coefficient (β ¼ -0.007). As expected, with industry fixed effect, the convergence coefficient in absolute terms becomes larger (β ¼ -0.034). These results support the findings of convergence in the studies conducted with the pre-2000 data for the US states (Barro et al., 1991; Barro and Sala-i-Martin, 1992; Higgins et al., 2006; Young et al., 2008). For the 1998–2015 period, construction and Table 3 Convergence of labor productivity in contiguous 48 U.S. States. Dependent Variable: Growth Rate All Sectors Without Industry Fixed Effect A. Time Span 1987–1997 Log of Initial Labor 0.007*** Productivity (0.002) No of States 48 No. of Observations 384 B. Time Span 1998–2015 Log of Initial Labor 0.002*** Productivity (0.001) No of States 48 No. of Observations 812

Construction

Mining

Manufacturing

Transport

Wholesale Trade

Retail Trade

Finance and Insurance

0.034*** (0.007) 48 384

0.021*** (0.009) 48 48

0.036*** (0.008) 48 48

0.091*** (0.035) 48 48

0.039*** (0.011) 48 48

0.016* (0.010) 48 48

0.004 (0.006) 48 48

0.016 (0.010) 48 48

0.013*** (0.002) 48 812

0.015* (0.008) 48 48

0.008 (0.008) 45 45

0.034*** (0.010) 48 48

0.004 (0.010) 48 48

0.016 (0.009) 48 48

0.015** (0.006) 48 48

0.015*** (0.004) 48 48

With Industry Fixed Effect

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01.

Fig. 1. Unconditional Convergence during 1987–1997 period while lacking convergence during 1998–2015 in US states. 4

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Table 4 Convergence of Labor Productivity for Different Disaggregated Manufacturing Sectors in the Contiguous 48 US states' economy (1987–1997 and 1998–2015). Dependent Variable: Growth Rate Sector

Food and Kindred Products Tobacco Products Textile Mill Products Apparel and Other Textile Products Lumber and Wood Products Furniture and Fixtures Paper and Allied Products Printing and Publishing Chemicals and Allied Products Petroleum and Coal Products Rubber and Miscellaneous Plastic

Leather and Leather Products Stone, Clay and Glass Products Primary Metal Industries Fabricated Metal Products Industrial Machinery and Equipment

Time Span 1987–1997

Sector

Log Initial Labor Productivity

No. of Observation

0.017* (0.009) 0.013 (0.012) 0.020 (0.032) 0.032 (0.021) 0.038*** (0.009) 0.018* (0.010) 0.034*** (0.006) 0.012 (0.009) 0.012 (0.009) 0.051*** (0.013) 0.088*** (0.020)

48

0.010 (0.012) 0.026* (0.014) 0.024 (0.016) 0.008 (0.013) 0.010 (0.012)

Other Transportation Equipment Instruments and Related Products Miscellaneous Manufacturing

0.088*** (0.023) 0.029** (0.014) 0.025 (0.017) 0.054*** (0.006) 0.033** (0.012)

No. of Observation

0.006 (0.006) 0.013 (0.009) 0.012 (0.011) 0.020*** (0.004) 0.016** (0.007) 0.023** (0.011) 0.041*** (0.006) 0.036*** (0.007)

46

0.043** (0.020) 0.011* (0.006) 0.010 (0.007) 0.039*** (0.012) 0.034*** (0.010) 0.023* (0.012) 0.012 (0.012)

42

14 35 47 44

Wood Products Manufacturing

45

Furniture and Related Products

47

Paper Products Manufacturing

48

Printing and Related Activities

48

Chemical Products Manufacturing

41

Petroleum and Coal Products

47

Plastic and Rubber Product Manufacturing Non Metallic Mineral Products

46 27 48 48 42 48 48

37

45

Primary Metal Manufacturing

48

Fabricated Metal Products

48

Machinery Manufacturing Computer and Electronic Product

Electronic and Other Electric Equipment Motor Vehicles and Equipment

Time Span 1998–2015 Log Initial Labor Productivity

48

Electrical Equipment and Appliance

46

Motor Vehicle, Body, Trailer, and Parts Other Transportation Equipment

47

48 48 48 43 21 27

46 48

Miscellaneous Manufacturing

0.003 (0.005)

48

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01.

metal manufacturing—yield a new sign of convergence in the recent period. Subsector-level regression results for mining and transport and public utilities are provided in Table 5. It is evident from these results that none of the subsectors in mining for the 1987–1997 period yields any sign of convergence, while in the 1998–2015 period mining (except oil and gas) and support activities for mining yield signs of convergence. For transportation and public utilities, five out of nine subsectors show signs of convergence for the earlier period, while four out of seven subsectors yield similar results in the latter period. Rail transportation, warehousing and storage, and pipeline transportation produce highly significant positive coefficients (indicating divergence) in the latter period. For both periods, subsector-level results for the service sector are reported in Table 6. We find that eight out of 18 subsectors of the service sector show signs of convergence of labor productivity in the earlier period, while eight out of 13 subsectors yield signs of convergence in the latter period. A high convergence rate of insurance carriers' labor

definitions for the two periods, we provide results for the similarly named subsectors in both periods in the same row in this table. For example, results for lumber and wood products (subsector with SIC code 24) and woods product manufacturing (subsector with 1997 NAICS code 321) are reported in the same row. Although the coverage for subsectors is potentially different under different industrial classification schemes, we believe that the results of the same named subsectors would allow an imperfect but important comparison in the context of subsector level convergence in labor productivity for the two different time periods. For the 1987–1997 period, we obtain ample signs of convergence for 11 out of 21 sub-sectors of manufacturing, while for the 1998–2015 period, an indication of convergence is obtained for 10 out of 16 subsectors. For four subsectors—lumber and wood products, furniture and fixtures, paper and allied products, and miscellaneous manufacturing—the sign of convergence observed in the earlier period is not present in the latter period. However, four other subsectors—printing and publishing, chemical products, primary metal manufacturing, and fabricated

5

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Table 5 Convergence of Labor Productivity for Different Disaggregated Mining and Transport Sectors in the Contiguous 48 US states' economy (1987–1997 and 1998–2015). Dependent Variable: Growth Rate Sector

Mining Metal Mining Coal Mining Oil and Gas Extraction

Time Span 1987–1997

Time Span 1998–2015

Log Initial Labor Productivity

No. of Observation

0.019 (0.017) 0.008 (0.015) 0.000 (0.010)

23

Log Initial Labor Productivity

No. of Observation

0.026 (0.029) 0.022* (0.012)

29

Support Activities for Mining

0.054*** (0.016)

26

Rail Transportation

0.044*** (0.016)

29

Truck Transportation

0.043*** (0.007) 0.020** (0.008) 0.042** (0.015) 0.011* (0.006) 0.023*** (0.003) 0.054* (0.029)

48

15 30

Oil and Gas Extraction Mining Except Oil and Gas

Nonmetallic Minerals, except Fuel

Transportation and Public Utilities Railroad Transportation Local and Interurban passenger Transport Trucking and Warehousing

0.015 (0.013)

0.028 (0.021) 0.026* (0.015) 0.035*** (0.009)

41

41 48 48

Warehousing and Storage Water Transportation Transportation by Air

Pipelines, except Natural Gas Transportation Services Communications Electric, Gas and Sanitary Services

0.031*** (0.010) 0.009 (0.012)

0.011* (0.006) 0.008 (0.015) 0.026 (0.021) 0.050*** (0.012)

44

34

Water Transportation

47

Air Transportation

34

Transit and Ground Passenger Transportation Pipeline Transportation

45 26 46 48 35

46 48 47

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01.

Rodrik (2013) shows that aggregated data may produce no sign of convergence while disaggregated data may, in fact, yield signs of convergence. In the context of real exchange rates and the law of one price, results with aggregated price indices show a slow rate of convergence, while disaggregated commodity-level prices yield faster convergence (Imbs et al., 2005), a phenomenon termed “aggregation bias.” Since we have collected data for both disaggregated and aggregated sectors, we are able to shed light on this issue in the context of labor productivity convergence. It is interesting to note that for the time span 1987–1997, manufacturing yields a faster convergence rate (β ¼ - 0.091, reported in Table 3), but if we look at the subsector level, we find 11 out of 21 subsectors yielding negative and significant β coefficients, indicating convergence. Even a few subsectors such as tobacco products, chemical and allied products, and fabricated metal product yield positive but insignificant β coefficients (shown in Table 4). For the time span of 1998–2015, the manufacturing sector as a whole still yields a highly significant but smaller convergence coefficient (β ¼ - 0.034, reported in Table 3). At the subsector level, however, 10 out of 16 subsectors yield negative and significant β coefficients. For aggregate mining, we observe signs of convergence in labor productivity in the earlier period when mining is taken as an aggregate variable (β ¼ - 0.036, reported in Table 3), but the disaggregated subsectors yield no sign of convergence (shown in Table 5). For the

productivity in the earlier period did not continue in the latter period. For three other comparable subsectors, however, such as accommodation, amusement, gambling and recreation, and social assistance, new signs of convergence are apparent in the latter period. All of these results suggest that convergence processes in labor productivities vary in different sectors and subsectors. While for some manufacturing subsectors we observe no signs of convergence in recent periods, there is evidence of convergence in some subsectors of the service sector. The nature of economic activity seems relevant in the context of convergence in labor productivity. 5.3. Convergence: aggregated vs disaggregated data6 The differences in convergence patterns observed in data with different levels of aggregation have lately received deserved attention.

6 We have also carried out convergence estimates for aggregate per capita GDP to contrast with the sectoral results. The result for 1987–1997 shows a statistical significant beta coefficient of 0.022, but we could not find evidence of beta convergence for the post-1997 data (results are not reported here). We also find, in general, no sign of a reduction of dispersion of labor productivity over time (sigma convergence) during both periods (results are not reported here).

6

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Table 6 Convergence of Labor Productivity for Different Disaggregated Service Sectors in the Contiguous 48 US states' economy (1987–1997 and 1998–2015). Dependent Variable: Growth Rate Sector

Time Span 1987–1997 Log Initial Labor Productivity

Security and Commodity Brokers Insurance Carriers Insurance Agents, Brokers, and Service

Real Estate Holding and Other Investment Offices Hotels and Other Lodging Places Personal Services

Business Services Auto Repair, Services and Parking

Miscellaneous Repair Services Motion Pictures Amusement and Recreation Services Health Services

Legal Services Educational Services Social Services Membership Organizations Private Households

0.004 (0.016) 0.250*** (0.053) 0.002 (0.008)

0.007 (0.007) 0.002 (0.017) 0.009 (0.008) 0.025** (0.010)

0.003 (0.009) 0.017*** (0.006)

0.045*** (0.009) 0.027** (0.012) 0.010 (0.013) 0.024*** (0.006)

0.001 (0.008) 0.010 (0.008) 0.003 (0.008) 0.009* (0.005) 0.014** (0.006)

Time Span 1998–2015 No. of Observation

Log Initial Labor Productivity

No. of Observation

Publishing including Software

0.018*** (0.005)

48

Insurance Carriers

0.002 (0.006)

48

Administrative and Support Services

0.022*** (0.006) 0.005 (0.004) 0.011 (0.027) 0.029*** (0.005)

48

48 48 48

48

Real Estate

47

Funds, Trusts, and Other Financial Vehicles Accommodation

48

48 27 48

48 Food Services and Drinking Places

0.018** (0.003)

48

Waste Management and Remediation Services

0.029*** (0.005)

48

48

Motion Pictures and Sound Recording

48

48

Amusement, Gambling, and Recreation

0.013 (0.011) 0.029*** (0.006)

48 48

48

48

48 Ambulatory Health Care Services

0.022*** (0.007)

48

48

Educational Services

48

48

Social Assistance

0.011*** (0.003) 0.020*** (0.004)

48

48

48 46

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01.

5.4. Regional variation of convergence estimates

1998–2015 period, however, aggregated data yields no sign of convergence, while two out of three disaggregated subsectors in mining yield signs of convergence. Labor productivity in the aggregated transport and public utilities yields signs of convergence for the 1987–1997 period (β ¼ - 0.039, reported in Table 3) while for the disaggregated data, five out of nine subsectors yield signs of convergence (Table 5). In the latter period, the aggregated transport sector yields no sign of convergence, but four out of seven subsectors do yield signs of convergence, while the remaining three subsectors yield positive and significant β coefficients, suggesting a divergence in labor productivity for these subsectors. Most of the disaggregated service subsectors yield signs of convergence, while educational services show signs of divergence. These results suggest that by aggregating data we face “aggregation bias”, but the direction of bias depends on the nature of the industry or production processes.

It is important to note that the dominant economic activities are different in different parts of the US. This is evident if we inspect the Beige Book of the Board of Governors of the Federal Reserve Bank (FRB, 2017). For example, while the Boston and New York Feds would put an emphasis on economic activities related to finance and high tech manufacturing, the Kansas City Fed would put more of an emphasis on agriculture, and the Dallas Fed would put more emphasis on oil and gas production, all due to the differences in the geographic concentration of industries. In this context, there have been efforts to understand the regional variations in the effects of monetary policy and economic shocks (Carlino and DeFina, 1998, 1999; Crone, 2007). A secular decline in steel industries affected Rust Belt states like Ohio and Pennsylvania more than any other states in the country (Kahn, 1999). Similarly, weather shocks or policy changes in agriculture would affect the Plains states and the Midwest, while New England states would be affected only marginally. 7

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Economic Modelling xxx (2018) 1–11

disaggregation (1987 SIC code) for 1987–1997 data, and 3-digit level disaggregation (1997 NAICS code) for 1998–2015 data, we observe signs of convergence for most of the regions, contrary to results obtained from aggregated data. It is evident from the results reported in Table 8 that we now observe convergence in all regions for the 1987–1997 period, and seven out of eight regions for the 1998–2015 period. The size and significance level of convergence coefficients are lower in the latter period for most of the regions, excepting the Rocky Mountains. When including only disaggregated manufacturing subsectors in our regression, we obtain large convergence coefficients for all regions in the earlier period. In the latter period, we obtain convergence coefficients for all regions, with the Southeast region yielding a larger convergence coefficient. Thus, in the manufacturing sector observed by Rodrik (2013) in disaggregated cross-country data, the presence of unconditional convergence in labor productivity is here validated with disaggregated regional data. For New England, we find that labor productivity convergence in manufacturing is faster in both periods.

This suggests that what has been happening to different regions of the US regarding labor productivity convergence or divergence deserves adequate attention. We estimate the convergence coefficients for labor productivity by sectors and subsectors in each region; the results are reported in Tables 7–9. The regional classification is based on the US Bureau of Economic Analysis (BEA) classification that divides the US into 8 regions. Regional convergence coefficients for aggregated data for both periods are reported in Table 7. For each region in the period 1987–1997, we include sectors with 1987 SIC codes A-I, while for 1998–2015, we include the 1997 NAICS two-digit level of aggregated sectors. For the earlier period, we observe the presence of convergence in labor productivity for the Mideast, the Great Lakes, and the Southeast, with signs of divergence in the New England regions. For the latter period, we observe signs of convergence in the Southeast, the Rocky Mountains, and the Far West regions. Having used more disaggregated labor productivity data, 2-digit level

Table 7 Regional variations in unconditional convergence in labor productivity with aggregated data. Dependent Variable: Growth Rate Variable Time Span 1987–1997 Log of Initial Labor Productivity Number of States Number of Observations Time Span 1998–2015 Log of Initial Labor Productivity Number of States Number of Observations

New England

Mideast

Great Lakes

Plains

Southeast

Southwest

Rocky Mountain

Far West

0.008* (0.003) 6 48

0.021** (0.005) 5 40

0.014* (0.003) 5 40

0.008 (0.004) 7 56

0.010** (0.004) 12 96

0.007 (0.011) 4 32

0.004 (0.004) 5 40

0.009 (0.006) 4 32

0.001 (0.001) 6 100

0.000 (0.001) 5 84

0.002 (0.002) 5 85

0.000 (0.003) 7 119

0.003** (0.001) 12 204

0.002 (0.001) 4 68

0.004* (0.002) 5 84

0.004** (0.001) 4 68

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01. Table 8 Regional variations in unconditional convergence in labor productivity with disaggregated data. Dependent Variable: Growth Rate Variable Time Span 1987–1997 Log of Initial Labor Productivity Number of States Number of Observations Time Span 1998–2015 Log of Initial Labor Productivity Number of States Number of Observations

New England

Mideast

Great Lakes

Plains

Southeast

Southwest

Rocky Mountain

Far West

0.013*** (0.003) 6 276

0.014** (0.005) 5 227

0.009** (0.002) 5 243

0.010** (0.003) 7 327

0.011*** (0.002) 12 586

0.011*** (0.001) 4 198

0.008** (0.002) 5 242

0.010*** (0.001) 4 189

0.014 (0.024) 6 202

0.010*** (0.001) 5 180

0.007** (0.002) 5 192

0.008** (0.003) 7 244

0.003* (0.001) 12 204

0.007* (0.002) 4 150

0.012*** (0.002) 5 173

0.010*** (0.001) 4 146

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01. Table 9 Regional variations in unconditional convergence in labor productivity in subsectors of manufacturing. Dependent Variable: Growth Rate Variable Time Span 1987–1997 Log of Initial Labor Productivity Number of States Number of Observations Time Span 1998–2015 Log of Initial Labor Productivity Number of States Number of Observations

New England

Mideast

Great Lakes

Plains

Southeast

Southwest

Rocky Mountain

Far West

0.059*** (0.009) 6 120

0.047** (0.012) 5 92

0.049*** (0.004) 5 97

0.036** (0.005) 7 128

0.026*** (0.003) 12 241

0.042* (0.015) 4 75

0.031** (0.007) 5 95

0.043*** (0.004) 4 77

0.035*** (0.005) 6 81

0.030*** (0.002) 5 73

0.022** (0.004) 5 80

0.027*** (0.003) 7 95

0.032*** (0.004) 12 182

0.014* (0.004) 4 60

0.026* (0.005) 5 64

0.031** (0.010) 4 57

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01. 8

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Table 10 Robustness test. Dependent Variable: Growth Rate (1)

(2)

(3)

(1)

(2)

(3)

(1)

(2)

(3)

Baseline

Pooled OLS

GMM

Baseline

Pooled OLS

GMM

Baseline

Pooled OLS

GMM

0.004 (0.009) 47 366

0.120*** (0.010) 46 271

All Sectors Log Initial Productivity Number of States Number of observations

0.002*** (0.001) 48 812

Construction 0.004*** (0.001) 48 6491

0.096*** (0.001) 48 4836

Manufacturing Log Initial Productivity Number of States Number of observations

0.034*** (0.010) 48 48

0.015* (0.008) 48 48

Mining 0.037*** (0.009) 48 381

0.078*** (0.006) 48 281

Retail Trade 0.053*** (0.011) 48 383

0.105*** (0.004) 48 285

0.015** (0.006) 48 48

0.008 (0.008) 45 45

Finance and Insurance 0.037*** (0.006) 48 384

0.085*** (0.003) 48 288

0.015*** (0.005) 48 48

0.018*** (0.005) 48 384

0.096*** (0.004) 48 288

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01.

6. Robustness check

The results suggest that there is a decline in the convergence process for the post-1997 data. The speed of convergence considerably differs across subsectors and regions. We find that the tendency to converge in labor productivity in mining, transport, and wholesale trade weakened in recent years. The speed of convergence for aggregate manufacturing labor productivity also slows in recent years. We observe, however, signs of convergence for many subsectors of manufacturing. We also notice ample signs of “aggregation bias”, but the direction of this bias depends on the nature of the production processes. As the service sector accounts for the lion's share of the US economy, the observed lack of convergence on the aggregate GDP may be attributed to the widening in productivity gaps in the major service sectors across US regions, along with weaker convergence in labor productivity in manufacturing. Our regional estimates reveal that labor productivity in the Great Lakes and Mideast regions are not converging, thus creating more inequality. Since the main purpose of this paper is to show that sector- and subsector-level disaggregation provides a clear picture of various catching-up patterns of labor productivity in US states as aggregated variables mask these crucial variations, no effort is made here to find the proximate factors behind these patterns, which we want to pursue in the future. Knowledge spillover from one state to another may provide a clue to this process. The sub-sectoral variations of skill premium in response to technological progress can be another determinant responsible for such a dynamic shift in labor productivity in recent periods, as suggested by Mallick and Sousa (2017). Knowledge spillover from one state to another may provide a clue to this process. In the international context, Bournakis et al. (2018) made an important contribution to exploring this issue. Also a closer look at factors such as the low mobility of labor, higher cost of education, and higher costs of living expenses in cities is warranted to fully appraise the sources behind this observed pattern of the sub-sectoral convergence of labor productivity.

Our main result is based on a cross-section analysis and thus we call this result the baseline. The recent data (1998–2015) allows us to carry out a panel data estimation technique. This is because we can find eight data points for growth in labor productivity (representing eight decadal growth rates) and initial productivity for each US state, with a maximum total of 384 data points for 48 US states and with a continuous dataset for decadal growth rate and initial productivity covering the years 2008–2015. As a result we conduct different panel data estimation techniques to test for the robustness of the cross-sectional regression results. To test for the robustness of the cross-sectional results, we conduct two panel data estimation techniques: pooled ordinary least square (OLS) and dynamic panel data estimation.7 The dynamic panel data estimation method follows Arellano and Bond (1991). The Arellano–Bond model derives a consistent generalized method of moments (GMM) estimator. Table 10 presents the panel data based robustness test results. The robustness test result shows that the panel data estimation results are similar to the cross-sectional method in terms of both statistical significance and sign for almost all sectors. The result further indicates that the panel data estimation methods yield larger coefficients (in absolute terms) compared to the OLS estimates. The size of the coefficient estimates under different panel estimation techniques does not show significant variation; therefore the robustness test confirms our baseline results. 7. Conclusions The US states have been a convenient testing ground for classical economic growth theories, as the states are very similar in terms of structural parameters such as saving rate, population growth rate, and level of technology. Studies found unconditional convergence in per capita state GDP prior to the 1980s, consistent with classical growth theories. Recent studies, however, do not find evidence for catching-up in per capita GDP among US states, suggesting sustained regional inequality. In this study, we have examined sectoral and sub-sectoral unconditional convergence in labor productivity in the US states for the period 1987–2015.

Acknowledgments We would like to thank Zsolt Becsi, Scott Gilbert, Kevin Sylwester, and Wanki Moon for helpful comments. The constructive suggestions of two referees and the editor, Sushanta Mallick, are also gratefully acknowledged.

7 We also carried out static panel data estimation techniques of fixed effects and random effects. The result is similar to the dynamic panel data estimation technique (GMM).

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Economic Modelling xxx (2018) 1–11

Appendix 1 Although the BEA discourages compiling a single time series, we still combine the two sets of time series data, pre- and post-1997, into a single time series data following suggestions from the United States Census Bureau.8 The NAICS has a total of twenty aggregate industry groups while SIC has only ten broad sectors.9 We are able to find a single time series data for the following seven broad sectors: mining; construction; manufacturing; transportation, communications and public utilities; wholesale trade; retail trade; and finance, insurance, and real estate. Appendix Table 1 shows the convergence test results. The dependent variable is the growth of labor productivity from 1987 to 2015, and the independent variable is output per worker in 1987. The estimation results based on a single time series data indicate that there is evidence of convergence for mining and construction sectors suggesting that states with low labor productivity in 1987 grew faster than states with high labor productivity. However, we do not find evidence of convergence for most of the service sectors and manufacturing, which imply that labor productivity in these sectors did not grow more rapidly in states with low initial labor productivity. Appendix Table 1 Convergence Test for a combined Dataset. (1)

(2)

(3)

(4)

(5)

(6)

(7)

Mining

Construction

Manufacturing

Transportation

Wholesale Trade

Retail Trade

Finance, Insurance, and Real Estate

base

0.016*** (0.004)

0.013*** (0.004)

0.002 (0.008)

0.016 (0.011)

0.008 (0.005)

0.009* (0.004)

0.005 (0.005)

Number of States Number of observations

46 46

48 48

48 48

48 48

48 48

48 48

48 48

Note: Standard errors are in the parenthesis. *p < 0.1, **p < 0.05, ***p < 0.01.

Appendix A. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.econmod.2018.08.008.

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