Productivity differentials along the development process: A “MESO” approach

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PRODUCTIVITY DIFFERENTIALS ALONG THE DEVELOPMENT PROCESS: A “MESO” APPROACH Massimo Tamberi PII: DOI: Reference:

S0954-349X(18)30126-7 https://doi.org/10.1016/j.strueco.2020.01.006 STRECO 897

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Structural Change and Economic Dynamics

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20 April 2018 4 November 2019 15 January 2020

Please cite this article as: Massimo Tamberi , PRODUCTIVITY DIFFERENTIALS ALONG THE DEVELOPMENT PROCESS: A “MESO” APPROACH, Structural Change and Economic Dynamics (2020), doi: https://doi.org/10.1016/j.strueco.2020.01.006

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Highlights    

The main hypothesis is that productivity differentials across firms/sectors should be higher in developing countries Panel estimations test the relationship between per capita income and some measures of sectoral productivity diversification in manufacturing Several alternative forms of the dependent variable, and control variables, are considered Results suggest a negative and robust relationship between productivity differentials and per capita income

PRODUCTIVITY DIFFERENTIALS ALONG THE DEVELOPMENT PROCESS: A “MESO” APPROACH Massimo Tamberi

Abstract “Firms are different”, and everyone knows it by direct experience. From the point of view of productivity differentials, we know that their intensity depends on the interaction of forces acting in the opposite direction, some increasing and others limiting productivity differentials. It is possible to imagine that those forces act with different intensity in developed and developing countries: the catching up process, coupled with a weaker firm selection process, could reinforce productivity differentials in the economic system of less advanced economies. Empirical indications suggest that productivity differential among firms/sectors is effectively higher in poorer countries. This paper is a step to deep this question in more general terms: it proposes and empirically tests a “development” perspective to analyze productivity differentials, and this seems a substantial novelty. Results, with a few limits, support the hypothesis that inter-industry productivity differentials are negatively associated with the level of development.

KEYWORDS: productivity differentials, economic development JEL codes: L16, O33

Corresponding author: Address: Department of Economics and Social Sciences, Marche Polytechnic University, piazza Martelli 8, 60121 Ancona, Italy e-mail: [email protected]

1 Introduction This work concerns productivity differentials across firms/sectors and I will present and test the idea that productivity dispersion should be higher in less advanced countries. From a logic and methodological point of view, the present analysis is parallel to a recent literature on product, instead than productivity, dispersion (a useful summary in Mau, 2016): we ask if it is possible to identify a process of sectoral productivity diversification along the development path. A recent study by McMillan et al. (2014) discusses the inverse linkage between productivity dispersion among sectors and the level of development. They show evidence of this (table 1, p. 13, and fig. 2, p. 15). In the previous literature this subject was not systematically and/or explicitly dealt, even if there are partial exceptions. My work closely relates to the initial part the McMillan et al. paper, even if my analysis is limited to manufacturing sectors. The reason for investigating this subject has to do with more than one aspect: - productivity differentials can influence functional and personal income distribution - it could be an element inducing structural change, changing the overall efficiency of the economy - indirectly, it is a way of highlighting possible effects of international integration on the economy. From a practical point of view, comparable data at firm level for a large amount of countries and long periods are not easily available; for this reason the empirical section of the paper will be focused on sector productivity dispersion. Since the purpose is to relate productivity dispersion to the level of development, also this latter could be defined in several ways, and, moreover, it can be conceived as a collection of several aspects (technological and social capability, governance quality, poverty, etc.). It would be difficult to exploit, theoretically and empirically, all the dimensions of this complex concept, and I will use, as it is commonly done, per capita income as a general proxy of the phenomenon, also considering this paper as a first step in a substantially new field of analysis. The dataset, as it will be discussed, is substantially unbalanced; for that reason, initially I run pooled OLS; in a second step, after reorganization of the data, I run panel estimations with individual specific effects; several control variables are introduced; many robustness trials have been carried out, including changes in the index defining the dependent variable, and in the number of sectors and years involved.

Results seem to clearly support the hypothesis that productivity dispersion is higher in less advanced countries. The paper is organized as follows. First, starting from the existing literature, I present evidence of productivity differentials among firms/sectors, and shortly summarize the role of some factors which can be considered as a general explanation of the presence and persistence of them. Then, these factors are discussed in the light of the features of less advanced economies (developing, catching up or still quasi-stagnant), features probably acting in the direction of increasing productivity dispersion of less rich economies, relatively to more advanced ones. Finally, after a description of the dataset and of the variables included in the empirical test, I will run some estimations whose results are converging toward a confirmation of the hypothesis.

2 Factors fostering and limiting productivity differentials and their linkage with the level of development 2.1 Insights from two different literatures The subject of the present paper is the evolution of productivity differentials in the process of economic development. Three elements are present: productivity differentials, the process of growth, the interconnections between the two. There are not many papers clearly and systematically focused on the subject of my work. Nevertheless, we may find indications in two different strands of literature, one micro and one macro, different in many aspects, but providing some common and useful insights. As regards productivity differentials, it is well known that, following a period more conditioned by the concept of the “representative firm” (Nelson, 1991), in the recent past the share of investigation based on micro-data at firm and/or plant level has grown spectacularly. One outcome of this stream of analysis has pointed out that firms are effectively different; in particular, several scholars have documented "virtually without exception, enormous and persistent measured productivity differences across producers, even within narrowly defined industries" (Syverson 2011, p. 326); those differences have been analyzed in several papers (Bartelsman, Haltiwanger, and Scarpetta, 2004 and 2013; Ito K., Lechevalier S., 2010 )1.

1

A relevant share of this literature also focused on trade, after some seminal papers (Melitz, 2003; Helpman, Melitz, Yeaple, 2003).

Generally speaking, and strongly synthesizing, the tendency toward a differentiation of productivities is a consequence of a “differential impact of technological innovations on the several production sectors” (Kuznets, 1973, p.250), i.e. new goods and new processes are introduced somewhere in the market and they are more efficient than old ones. This introduce in an economy a mechanism inducing dispersion of productivities: high productivity in new firms/sectors, low productivity in old ones. This tendency can be partly offset by two factors: first, the fact that technological advancements tend to spread also to firms/sectors initially not touched by it, through several channels that we can summarize in the word "imitation"; second, and perhaps more important, an efficient process of firm selection should eliminate less productive units, so reducing the more or less drastic differences across firms/sectors. The selection process, if interpreted in a broad sense, implies a mobilization of factors of production toward more efficient units of the economy, both intra and inter sectors. Large productivity differentials are interpreted as a consequence of the existence of frictions limiting the process of selection (exit of less efficient units), “preventing less efficient producers from fully replicating industry leaders’ best practice” (Syverson, 2011, p. 350), finally limiting the mobilization of factors (from some sectors to others). In general, some drivers for the time evolution of productivity dispersion have been suggested: rates of technology adoption, internationalization, rate of competition, institutions (for a summary, see ITO, 2009; Syverson, 2011). Some overlapping points have been analyzed in a more macro perspective, in a literature with a long tradition, both empirical and theoretical, about “structural change” with “dualism” (for a theoretical reference, see Matsuyama, 2008; the empirical view is well presented in Kuznets, 1973; a recent survey in Krueger, 2008). The expression “structural change” should be interpreted as a broad and multifaceted phenomenon, involving many deep and interconnected changes in the economy, including aspects of the social and institutional structure. Nevertheless, most of the economic scientific literature identifies “structural change” in a more limited meaning: the change of sectoral structure of the production, in many cases with reference to a highly aggregated version of the economy, only distinguishing between two (agriculture, industry) or three sectors (services added).

This is a departure from the one-sector models (as in growth literature); logically, it is a first step for the explanation of “dualism”, a dual organization of the economy of less developed countries, i.e. characterized by the contemporaneous presence of sectors that are “traditional” (low productivity) and “modern” (high productivity) (the seminal work is Lewis, 1954). There are specific assumptions about market structure, both on the demand-side (Engel effect) and on the supply-side (Baumol effect), and some kind of frictions slowing the intersectoral reallocation of factors. The supply-side element is parallel to the analysis carried out at micro level, and above sketched: in both perspectives, micro and macro, is the differentiated technological advancement of firms that leads to productivity dispersion; moreover, in both approaches, the persistence of this dispersion over time is a consequence of the existence of some kind of friction that weakens, delays, prevents its disappearance. One aspect of the structural change literature is the idea that factors of production will move from less to more efficient sectors; nevertheless, recent analysis has showed that this process is not “guaranteed”: it is possible to get also perverse processes, as documented for some countries or geographical areas by McMillan et al (2014), in their analysis covering a time span of 15 years. We may interpret this result considering that many factors influence sectoral allocation of factors, among which institutional ones, and there are not automatic mechanisms in factor reallocation. The process of economic growth is based also on a progressive spread of technology and human capital to all sectors of the economy; this should reduce, in the long run, productivity differentials. Nevertheless, a recent literature has highlighted a process of sectoral product diversification along the development path, both in trade and in employment/value added (Imbs and Wacziarg, 2003; De Benedictis et al., 2009; Cadot et al., 2011; Parteka and Tamberi, 2013; Mau, 2016): the technological progress and the growth of human capital imply that new products/sectors are continuously introduced in the market. Since different sectors have different technologies, this process of product diversification should increase the level of productivity dispersion in the economy. Summarizing, the process of growth and development introduces elements influencing productivity differentials in opposite directions, some increasing and some others decreasing productivity differentials. In the end, if one of the other prevails it is a matter of empirical verification.

Empirical evidence of higher productivity differentials in less developed economies can be introduced through an anecdotal example about the Mexican economy: as the Economist reports (2015) "economic productivity in Nuevo León, a heavily industrialized state close to the American border, is at South Korean levels. In the south of Mexico it is close to that of Honduras". In the same direction, McMillan et al. (2014) clearly suggest the existence of a systematic and negative relationship between productivity dispersion among sectors and the level of development of an economy: “developing economies are characterized by large productivity gaps between different parts of the economy” in “broad sectors of the economy”, but “significant differentials within modern, manufacturing activities” also exist 2 (p. 11). This idea was also presented in an older study, appeared in end of the seventies (Fuà, 1978, 1980), which showed a limited but meaningful empirical evidence for six lagged European countries. The literature based on micro data is less systematic on this perspective; nevertheless some interesting insights derive from several contributions. Ito et al. (2008), analysing three countries, find that while, as expected, the level of TFP is higher in Japan than in South Korea and China, TFP dispersion across firms (also within industries) is lower in Japan than in the other two countries. Syverson (2011, p. 237), comparing his results with those of Hsieh and Klenow (2009), highlights that while in USA “the plant at the 90th percentile of the productivity distribution makes almost twice as much output with the same measured inputs as the 10th percentile plant” we find “larger productivity differences in China and India, with average 90–10 TFP ratios over 5:1”. More limited evidence can be found in other papers, sometimes with indirect indications (Faggio and al., 2007; Ito and Chevalier, 2008 and 2010; Kalantsis, Kambayashi, and Chevalier, 2012; Del Gatto et al., 2008; Restuccia, Jang, Zhu, 2008). 2.2 Push and pull factors act differently in countries at different level of development The point of my paper is that both push and pull factors may have different strength in economies at different level of development, and this is the main hypothesis of the paper: forces enhancing firm differences in term of productivity act stronger in developing/catching-

2

This research product of McMillan et al. is closely related to my paper, and I will discuss later similarities and differences.

up economies (and this include also factor intensities), while mechanisms reducing firm differences, particularly the selection process, could be weaker in those same economies. The first consideration has to do with the potential process of economic convergence led by technological catch-up, considering that the world technological frontier is far from the average level of less developed countries; this constitutes a potential for very large gains in productivity that can be realistically exploited, in the short and medium term, only by a limited share of firms, and we can imagine that this process fosters the productivity differences between the already modernized/modernizing and the still traditional firms, both across and within sectors: catch-up “relative to the global frontier has been a highly localized process in which only a few establishments have achieved near best-practice performance. Most of the other plants stayed in business while operating far from the technological frontier.” (Van Dijk and Szirmai, 2011, relatively to the Indonesian case). This should be specific of the “developing” (in broad terms) countries of today, since the nowadays developed countries had, when still undeveloped, no or only limited catching-up possibilities, given their position near the frontier (and, moreover, the world economic environment was less globalized). Second, it is possible to imagine that the selection process is much weaker in less advanced countries, where the “vast majority of firms are simply stagnant in that they neither exit nor expand” (Akcigit, Alp, Peters, 2014, p. 2). While several forces can be potentially responsible for this misallocation of resources (Hiseh and Kleanow, 2011; Akcigit, Alp, Peters, cit.), a general approach has been clearly proposed by Acemoglu et al. (2006); the authors distinguish between different “stages” (broadly speaking) of development: the first phases of development are characterized by an “investment based strategy, relying on long-term relationships between entrepreneurs (or managers) and firms (or financiers) in order to maximize investment” and, in this phase, the “selection is less important, insiders are protected, and savings are channeled through existing firms in an attempt to achieve rapid investment growth and technology adoption” (p. 39); on the contrary, “selection become more important as an economy approaches the world technology frontier”, i.e. in later “stages” of development. Moreover, we may guess that this lack, or weakness, of selection can be also a consequence of the large presence of informality or quasi-informality, a feature correlated with the level of development; in low and medium income economies a large informal, not modern sector exists, characterized by a very low level of productivity and largely disconnected from the

formal economy (La Porta and Shleifer, 2014). This disconnection also implies a weaker selection process. Even if along the process of “modern economic growth” the informal sector shrinks, its reduction takes a very long time. In the following the idea that productivity differentials are inversely related to the level of development will be tested. Because of lack of data, I cannot investigate the specific channels through which this happens; as a consequence, the analysis will be limited to test the presence of a possible inverse linkage between productivity differentials (across manufacturing sectors) and a measure of the level of development. In the light of the previous discussion, per capita income, i.e. the measure of the level of development, is meaningful as it is related to the possibilities of catch-up and to the weaker process of firm selection. I present an empirical analysis that is not macro, but nevertheless cannot be defined micro: it is in the between, since I use a sectoral disaggregation with several tents of sectors. For this reason, in the title, you have seen the expression “a meso approach”. As said, a similar point has been provided by McMillan et al (2014), even if their paper is more focused on another point, and the evidence of the larger productivity differentials in developing economies3 is presented as a starting point for the following analysis, but not fully investigated in itself. My paper is, instead, focused exactly in describing and measuring this fact, through several econometric strategies. Moreover, they work at the at a more macro level, with 9 sectors covering the whole economy (from agriculture to government services), while I focus on intersectoral differentials within manufacturing, working with several tents of sectors. I also cover a longer period (1980-2010 instead of their 1990-2005), that can be interesting and useful since the subject is inherently structural and, as a consequence, its evolution linked to the long run. Finally, I have a significantly wider set of countries.

3 Data and methodologies 3.1 Data I will test the hypothesis above sketched using a sufficiently detailed number of manufacturing sectors and measuring productivity through the average labor productivity.

3

The term "developing economies" should be understood, in this context, in very general terms, as a synthetic term to identify non-advanced countries. Obviously, the set of "developing" economies is now significantly more differentiated than a few decades ago.

Both a richer, more detailed sector/product specification and TFP measures would be preferable, but the lack of these data, at the international cross-country level and in time, prevents from a more complete step. It is not unusual, in this context, to find works based on average labor productivity, as in Rodrik (2013) and McMillan et al. (2014). Passing to the data used in the paper, the two main variables, dependent and explanatory, are, respectively, a transformation of average labor productivity and per capita income. While I will discuss later the specific form used in the empirical analysis for these two variables, in the following the reader can find the description of all data and sources: - Data on labor productivity of industrial sectors, on which my dependent variable is built, are derived from UNIDO INDSTAT 2 (2 digit) and INDSTAT 4 (3 and 4 digit), where both value added and employment are available. UNIDO is the only source of industrial data covering many countries and many sectors, but they are far from perfect. One problem derives from the fact that the coverage is incomplete, at least in two different senses: first, in earlier years there are many missing data; second, and above all, data come from national industrial surveys, whose coverage differs across countries; in some case very small firms are not included, especially for several developing countries. These problems are especially severe for INDSTAT 4 (data at 3 and 4 digits). For this reason, I concentrated on INDSTAT 2 (2 digits), and I use INDSTAT 4 only for robustness purposes. - In order to analyze the diversification-development linkage, the explanatory variable is the level of development: for this purpose, I have used per capita income, PPP adjusted (that will be call YPC), from PWT 8.1. Other data, for the “control” variables, come from different sources, and they are listed below: - a couple of variables measure two different aspects of openness, both potentially relevant because of the presence of processes of international catching-up: total trade, i.e. the sum of export plus import, and the inflow of foreign direct investment, both as % of GDP, respectively named TRADE and FDI (both from World Bank - World Development indicators, WB WDI). - since there is evidence of some outliers (see figure 1, below), mainly identifiable in oil producer countries, I also added a variable measuring the RENTS (% of GDP) deriving from oil and natural gas (WB WDI). Data of this variable are estimations, taking into account prices and costs of natural resources, presented in World Bank (2011).

- also POP (the size of the population, from WB WDI) can potentially have an impact on the level of diversification. Since it has been demonstrated that larger countries produce a richer mix of products (Parteka and Tamberi, 2013), we may believe that this product diversification could influence also productivity differentiation. As discussed above, the presence of more sectors could mean higher productivity differentials (direct effect); on the other hand, a richer sector structure can be also the consequence of the spread, in the economy, of technology, organizational methods, human capital, etc., and this may have the opposite effect, i.e. a reduction of productivity differentials (indirect effect). - the impact of technological innovation is measured by the volume of national patents to residents (WB WDI). In the estimations I use the per capita measure PATPC, that is the patent volume divided by employment (this last from UNIDO INDSTAT). Patent data are collected by WB and originally come from World Intellectual Property Organization (WIPO), WIPO Patent Report: Statistics on Worldwide Patent Activity. - the incidence of the shadow economy is SHADOW, downloaded from KNOEMA (reporting the data of Schneider et al., 2010). The SHADOW variable is the results of a complex econometric strategy taking into account multiple causes and indicators of the phenomenon, as can be seen in the just cited paper of Schneider. - finally, I also introduce “regional” dummies4 that are defined with a mix of economic and geographical criteria. Initially, I set a first group, named OECD, and socio-economic in spirit, identifying developed OECD rich countries (i.e. this group includes the “traditional” OECD economies). Then, I split the remaining countries according to the regional aggregation of the WDI-WB: the resulting groups are East Asia and Pacific, South Asia, Middle East and North Africa, Sub-Saharan Africa, Latin America and Caribbean, East Europe and Central Asia. In principle data on institutions should also be used in the analysis: the serious lack of them has prevented from their utilization. The UNIDO data presents many missing: I needed to treat the dataset before running regressions. First, they potentially cover the 1962-2010 period. In reality, data before 1980 are much more sparse and for this reason I concentrate on the time span 1980-2010, even if I will present some analysis also for a more limited period, from 1990, where more countries are included. 4

The term “regional” is partly inappropriate, because OECD countries are not a geographical aggregation.

Second, while 23 sectors are available in principle at two digits level, there are actually country/year pairs for which there are missing data for some or many (even all) sectors. The distribution of data, for country/year pairs, have two tails; in particular, a first peak is present for country/year pairs for which no data, for any sector (as an example, we have no data, for any sector, for Argentina in 1980); a second peak is present in the distribution for country/year pairs with at least 18 sectors (out of the 23 potentially available). After a proper aggregation, we can see that data are distributed as showed in table 1. table 1 - missing sectoral data % of year/country pairs zero (not missing) sectors

38.5%

1-17 (not missing) sectors

21.7%

18-23 (not missing) sectors

39,8%

In order to maximize the available information, but taking into account that we need a consistent number of sectors in order to compute an index of dispersion, I decided to keep only those countries/years pairs for which data for at least 18 sectors were present, i.e. around 40% of the original data. If we do not consider country/year pairs with zero data, clearly completely useless, my choice catches about 65% of the pairs 5. Differently from the otherwise parallel analysis of export differentiation, concentration indexes are not useful here. As a measure of inter-sectoral labor productivity dispersion I opted for the CV, or coefficient of variation (in the estimations cv_labprod6); this is similar to the already cited work of McMillan et al. (2014). Since countries have very different average level of productivities both in space (when different countries are compared) and potentially also in time (considering the long period covered by the analysis), the CV seems more suitable than a simple standard deviation because this latter is sensible to absolute differences, while the CV is instead sensible only to change in relative values. The dataset, as stressed also in other sections, is highly unbalanced. I have done choices in order to limit this problem (choice of years, number of sectors, countries), nevertheless the problem remains and is unavoidable. The choice of the CV is also a partial and indirect 5 6

Detailed distribution of data in Appendix A.2 Figures of cv_labprod utilized in the text are multiplied by 100.

answer to it: first, the standard deviation is an average measure, since its denominator is the number of sectors; second, the denominator of the CV is the mean, a measure that can change if there are, in some years and/or countries, missing sectors whose value is far from the average value. In the robustness analysis I present results got with other dispersion indexes. The number of countries included and of the number of the cross-section observations varies according to the set of variables used in the regressions. Data are highly dispersed, as evidenced is the following figure, which shows the distribution of country/year pairs in terms of cv_labprod and ypc. fig 1 - CV of sector labor productivity and logarithm of per capita income 1980- 2010

Dispersion is very high, but the correlation is negative, as highlighted by the OLS line. There are some outliers: in particular, the about twenty dots with the highest ypc values and relatively high value of the CV (a small cloud and some others); they are relative to small countries, and all but one oil producers. They are listed in table 2.

table 2 - countries and number of observations for ypc>50 (thous.) country

Number of observations

Kwait

6

Qatar

9

Norway

5

Singapore

1

sum

21

As anticipated, I include a specific variable (RENTS) for taking into account this aspect; a special behavior of oil producers has been also highlighted in the literature on product differentiation (Mau, 2016). Finally, before passing to the model, the following table 3 shows the descriptive statistics for all variables of the dataset used for the estimations table 3 - descriptive statitistics cv_labprod

ypc

fdi

trade

pop

density

rents

Mean

117.0

15.1

3.2

72.7

76.3

2.8

4.7

Max

441.6

126.5

173.4

439.7

1317.9

212.7

68.4

Min

20.6

0.4

-10.0

6.3

0.4

0.0

0.0

sd

72.3

13.6

7.1

55.5

12.2

12.2

10.3

3.2 Methods My basic model will be cv_labprod = +f(ypc)+ ; and it will be implemented in at least two ways: 1 - introducing some control variables, i.e. cv_labprod = +f(ypc)+X+ , where X is a set of explanatory variables different from ypc 2 - introducing space and time controls (panel estimations)

I tested several alternative forms of the relationship between cv_labprod and ypc, and I will

present four of them, all of them implying a nonlinear relationship between the two variables7: - Two of them consider the absolute level of ypc: a lin-log form, cv_labprod=f(ln(ypc)) and a quadratic form, where cv_labprod=f (ypc, ypc_sq). These two forms assume that any country will follow, other things being equal, the same path. - Two further forms take into consideration the ratio ypcgap= max(ypc)/ypc, where max(ypc) is the highest per capita income of the period (among all countries). This is because it is possible to conceive that the level of productivity dispersion depends not so much on the absolute level of per capita income, but, rather, on the distance from the "frontier", i.e. from the gap in terms of development. In particular, in a first form simply is cv_labprod=f(ypcgap), the second variant is cv_labprod=f(ln(ypcgap)); the difference between the two is the following: in the first, when the numerator and the denominator have the same value (developed economy) the ratio is equal the unity, implying that a given degree of productivity dispersion persists also for rich economies (if the estimated parameter is positive). In the second form, when ypcgap is equal to 1 its log will be 0, meaning that we should expect no productivity dispersion across sectors at high development levels. The presentation of these different forms can be considered as a first step in robustness tests. Concluding this section, it is to be stressed that in the case of ypc, the expectations are of a negative coefficient in the case of the lin-log estimation; a negative coefficient for the linear term, and a positive one for the quadratic term in the case of the second order polynomial. In the case of ypcgap, I expect a positive coefficient (higher gap, higher productivity dispersion). We will see that results do not permit to discriminate between the various forms8.

4 Results As somehow anticipated, all forms will be tested in the following along these lines: - pooled OLS regressions, both with and without control variables - panel regressions 7

The linear correlation of cv_labprod with ypc is negative (and near 0.2), but I a nonlinear relationship is expected, because of at least two reasons: first, because the dependent variable cannot assume negative values; second, because it is probable that a positive, even if limited, amount of "inequality" persists also at high level of income. 8

Other forms have been tested: as an example an equation in which all variables are in levels, and another one in which all variables are in logs. Results do not change qualitatively.

I discussed the role of the two basic forces which determine productivity differentials: technological progress and firm selection. I also suggested that the presence of shadow economy can influence the intensity of the second. Given the very limited amount of data available for estimations in which patpc and shadow are explicitly considered, results are presented and briefly discussed only in appendix A.3. In any case results are in line with the expectations. The first step presented below, with a pooled OLS, derives from the consideration of a characteristic of the panel: it is highly unbalanced. It should be noted that my dataset has potentially 31 years, but, in reality, there are countries with only one or very few observations, and others for which the whole time series is available. It is natural to think that we can have problems in identifying individual effects in this situation. I reach the highest number of observations when control variables are omitted (1548 obs, for about 100 countries), and this deserves as a benchmark for the reduced sample (1465 obs.) containing several control variables 9. Results of the pooled OLS are showed in table 4, in two panels, the first without and the second with several control variables. These results clearly support the idea that that the sector productivity dispersion decreases with the level of development: ypc is always significant, both in the estimation with and without the control variables and the signs of the coefficient are as expected. I do not attach much importance on the non-monotonicity suggested by the quadratic form, and I will show in the following (panel estimations) that the turning point happens for very high values of ypc. As indicated previously, regional dummies, as defined in the data section, are included.

9

The complete list of countries in appendix A.1.

table 4 - PRODUCTIVITY DIFFERENTIALS AND INCOME Pooled OLS 1980-2010 (robust standard errors, t stat in parenthesis) panel 1: without control variables ln_ypc

Cv_labprod -22.088 (11.01)***

Cv_labprod

ypc

Cv_labprod

-3.636 (15.36)*** 0.039 (12.32)***

Ypc_sq ypcgap

1.532 (5.38)***

ln_ypcgap F R2_A N

Cv_labprod

121.25 0.09 1548 *p>0.1

117.89 0.13 1548 **p>0.05

28.98 0.04 1548

24.430 (13.16)*** 173.25 0.11 1548

***p>0.01

panel 2: with control variables (“regional” dummies included)

trade fdi pop rents ln_ypc

Cv_labprod -0.042 (1.29) 0.127 (1.00) -0.031 (4.07)*** 1.835 (9.42)*** -14.204 (4.72)***

Cv_labprod -0.023 (0.69) 0.173 (1.35) -0.029 (3.89)*** 1.650 (7.71)***

ypc

Cv_labprod -0.096 (2.98)*** 0.006 (0.05) -0.035 (4.57)*** 1.674 (8.85)***

-2.381 (6.47)*** 0.023 (6.76)***

Ypc_sq ypcgap

1.158 (3.67)***

ln_ypcgap F R2_A N

Cv_labprod -0.030 (0.95) -0.270 (1.49) -0.039 (5.18)*** 1.791 (9.55)***

47.00 0.28 1465 *p>0.1

50.31 0.29 1465 **p>0.05

47.65 0.29 1465 ***p>0.01

23.132 (8.35)*** 51.37 0.31 1465

As for the controls, variables related to internationalization, fdi and trade, appear not significant, while pop and rents seem significantly impact on productivity differentials, the first negatively, while the second positively (as expected). In the following, we will see that only rents maintains its significance. It is to be stressed the unchanged role of ypc, in its various forms. As said, because of the strong unbalance of the dataset, I used pooled OLS estimations (also with regional dummies), that exploit both the within and the between dimension of the panel, but they are biased and inconsistent. A natural step forward is to introduce individual effects. To get meaningful results I dropped the observations for countries with less than 5 observations, in order to get a less unbalanced panel; obviously I also get a slightly reduced dataset. Even after this step, I have some explanatory variables that are only weakly variant in time, while, instead, there is a sensible "across-country" variability; the first variable with such a feature is ypc itself, as a consequence of the limited length of the average period (i.e. really available data) and the high number and variety of countries; the others is rents, and this depends mainly on the nature itself of that variable. One can conclude that, in this situation, a FE model doesn’t seem completely appropriate, since it would catch most of the variability of interest. As a consequence, a RE model seem "a priori" more suitable, but I also run Hausman tests and results of these tests are easily summarized: the FE model is preferred only when we use the quadratic form, while in the other cases the RE model passes, both with and without control variables. Everything considered, I present in table 5 the RE model results

table 5 - PRODUCTIVITY DIFFERENTIALS AND INCOME panel RE estimations 1980-2010 (time dummies included; robust standard errors; t stat in parenthesis) trade fdi pop rents ln_ypc

Cv_labprod -0.149 (0.69) 0.040 (0.50) 0.045 (1.77)* 1.719 (5.62)*** -24.163 (5.19)***

Cv_labprod -0.070 (0.33) 0.044 (0.55) 0.026 (1.00) 1.712 (5.56)***

ypc

Cv_labprod -0.120 (0.55) 0.020 (0.25) 0.043 (1.61) 1.540 (5.01)***

-2.677 (7.56)*** 0.025 (5.77)***

Ypc_sq ypcgap

1.953 (4.90)***

ln_ypcgap N

Cv_labprod -0.149 (0.69) 0.040 (0.50) 0.045 (1.77)* 1.719 (5.62)***

1434 *p>0.1

1434 **p>0.05

1434

24.163 (5.19)*** 1434

***p>0.01

It is immediate to verify that control variables turn to be not or not robustly significant, except rents, but what is relevant is that results for ypc are always confirmed, both in terms of parameters size and of the level of significance. If we consider the quadratic, it is worth saying that turning point of the curve, in terms of ypc level, is well beyond the maximum value of ypc itself included in the dataset; as a consequence, the relevant part of the curve is the one with a negative slope. Notwithstanding the previous analysis, we can consider that in this case, since the statistical units are represented by countries, it is a "textbook" indication that the FE model should be employed10. For this reason, and considering also the Hausman test in the case of the quadratic form, I believe that it can be interesting to present also the results of this model, and this is done in the following table 6.

10

This also depends on the fact that "countries" are considered a closed sample; it can be noted that, since I have only a little less than 100 countries, a limited form of randomness of the sample is present.

table 6 - PRODUCTIVITY DIFFERENTIALS AND INCOME panel FE estimations 1980-2010 (time dummies included; robust standard errors; t stat in parenthesis)

trade fdi pop rents ln_ypc

Cv_labprod -0.076 (0.35) 0.110 (1.02) 0.206 (4.20)*** 1.747 (3.96)*** -20.185 (2.48)**

Cv_labprod 0.014 (0.07) 0.153 (1.43) 0.113 (2.28)*** 1.778 (4.16)***

ypc

Cv_labprod -0.073 (0.34) 0.107 (1.00) 0.172 (3.51)*** 1.516 (3.53)***

-3.869 (5.92)*** 0.024 (5.59)***

Ypc_sq ypcgap

1.555 (2.93)***

ln_ypcgap N

Cv_labprod -0.076 (0.35) 0.110 (1.02) 0.206 (4.20)*** 1.747 (3.96)***

1434 *p>0.1

1434 **p>0.05

1434

20.185 (2.48)** 1434

***p>0.01

The main and strong result is that it is evident that all previous results relative to ypc are confirmed. Secondarily, also rents maintains its role, while for pop we see that it turns out as significant, but the sign of the parameter is changed with respect to the pooled OLS estimations, and we can conclude that this is a sign of weakness for result related to this specific variable. Moreover, as discussed previously, the effect of pop was not clear a priori, and the lack of stability of the parameter (negative, positive; significant, not significant) can be interpreted as a confirmation of its multiple role. In the end, there are clear signs that the negative relationship between productivity differentials and per capita income is reasonable and possibly robust to several changes in the regression strategy.

5 Robustness As robustness checks I have further considered the following steps:

1) First, I make some changes at the set of control variables: - results are completely confirmed, in the RE and FE estimations completely omitting control variables; - using different combinations of the control variables, rarely happens that some forms of ypc can turn out as not significant, but the coefficient signs always remain unchanged. The quadratic form is always significant 2) Besides the CV presented in the text, I also used other indexes of dispersion: the interquartile range of logs of sector productivities, the kurtosis, the range (max – min) relative to the mean (i.e. a relative measure of the range). In all cases there are no relevant changes. 3) Then, I reduced the number of not missing sectors considered; in practice, I decided to keep in the analysis those country/year pairs for which data for at least 16 sectors were present, instead of 18 as in the previous analysis. The choice is based on data represented in figure A1 (appendix): pairs with 16 and 17 not missing sectors are still a sensible share of the total. In this way I can increase the number of observations, passing from about 1500 to about 1700. Again, results remain unchanged. 4) I also changed the time span: I selected the 1990-2010 period instead than 1980-2010, and through this procedure I can include an higher number of countries. Again I got similar results 5) Finally, I passed to 3 and 4 digits disaggregation levels. In the first case the available number of sectors passes from 24 to 60, and in the second to 127; time availability is 19852010 at 3 digits level, and 1990-2010 at 4. A problem with these levels of disaggregation is that the number of missing greatly increase. At 3 digits, I have about 27% country-year pairs with no data; if I consider only pairs with at least one sector, in order to have at least 50% of the distribution of this sub-sample I should consider pairs with 45 sectors or more; in order to have at least 75% I need to include pairs with at least 37 non missing data. Following this last configuration, I have about 770 observations, practically one half of the 2 digits case. In pooled OLS and in RE estimations, both with and without controls, the results for ypc are exactly the same, in the sense that parameters' sign and significance do not change (this is generally true also for control variables); instead, with fixed effects, parameters completely

lose their significance in all the equations, even if they maintain the same signs (but not in the quadratic form). Similar considerations for the 4 digits case (where the sample is further reduced to about 580 observations, roughly more than one third than the 2 digits case). We should consider that, since the dataset is strongly reduced at 3 and 4 digits, this could not be without consequences, especially in FE estimations, when we introduce many country dummies; in any case results can be interpreted as a general confirmation of those found with the larger sample at 2 digits level, notwithstanding some (minor) weaknesses.

6 Conclusions Conclusions from the previous analysis can be proposed in few and simple lines: in short, it seems that there are some signs that productivity dispersion is higher in poor countries. If we accept this result, it can be more interesting, and more fruitful for research and policy purposes, to read the results of the present analysis jointly with those derived from the product/export diversification quoted in the first sections of the paper. We can outline a picture of this kind: poor countries are usually relatively homogeneous, i.e. scarcely diversified, from the point of view of the types of goods they produce (and/or export); on the contrary, they are highly diversified in terms of the productivity levels of the same products. The mirror image is obviously that rich countries have a very diversified economy, i.e. they produce a lot of different products, and, in the meanwhile, these different products are produced with a relatively similar efficiency (productivity). If these results will be confirmed in further analysis, they should be considered for their policy implications. I guess that at least two should be stressed: 1) Sensible productivity differentials usually led (or should led) to a reallocation of resources between sectors of the economy, in order to increase the overall efficiency of the economy. As McMillan at al. (cit) stress, this is not necessarily true: in many African countries reallocation has rather reduced the efficiency, since resources have been moved from more productive to less productive sectors. This perverse phenomenon can have different causes, among which institutional, and stresses the possibility that perverse incentives can be at work in given periods and societies, and the design of industrial policies should be addressed at removing them.

2) Another relevant point had to do with the potential impact of productivity differentials in terms of income distribution (both functional and personal). This is something that has been already evidenced in the literature relative to the “Kuznets’ curve” of income inequality, and dispersion of productivities can be a cause of dispersion of individual income. Moreover, the latter is a topic that is under consideration both in scientific literature and in the public debate. In addition, if we consider that, recently, some authors (Cingano F., 2014) suggested the possibility that high levels of inequality can negatively impact the rate of economic growth, this side of the question is further stressed, and policies that can reduce the potentially negative social effects of the process of structural change could also potentially benefit the process of economic growth (some considerations on OECD, 2016).

Aknowledgements Many thanks to Stefano Staffolani, Roberto Esposti and Alessandro Sterlacchini for their suggestions; thanks also to the discussant and the participants of the session at the SIE annual meeting 2016, Milano. Finally, I sincerely thank the two anonymous referees of this journal.

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APPENDIX

A.1 List of countries (country codes according to World Bank). The complete list is relative to the sample with 1548 observations (pooled estimations without control variables); in bold underlined, countries not present in the sample with 1465 observation (pooled estimations with control variables); in bold italic, further countries not present in the sample with 1433 observation (panel FE and RE) ARG, AUS, AUT, AZE, BEL, BGD, BGR, BIH, BOL, BRA, CAN, CHE, CHL, CHN, COL, CRI, CYP, CZE, DEU, DNK, DOM, ECU, EGY, ESP, EST, ETH, FIN, FRA, GAB, GBR, GEO, GHA, GRC, GTM, HKG, HND, HRV, HUN, IDN, IND, IRL, IRN, IRQ, ISR, ITA, JOR, JPN, KEN, KGZ, KHM, KOR, KWT, LBN, LKA, LTU, LVA, MAC, MAR, MEX, MKD, MLT, MNG, MYS, NLD, NOR, NPL, NZL, OMN, PAK, PER, PHL, POL, PRT, PRY, QAT, ROU, RUS, SAU, SGP, SLV, SVK, SVN, SWE, THA, TTO, TUN, TUR, TZA, URY, USA, VEN, VNM, YEM, ZAF

A.2 The distribution of year/country pairs, omitting those with no data at all, is represented in the following figure A.1 fig. A.1 frequencies of not missing sectors, (0 not missing pairs excluded)

A.3 The use patpc and shadow strongly reduces the number of cross-country observations, and the number of available years: complessively, I get a number of observations that is between 1/4 and 1/3 of the previous estimations. Variables relative to the patenting activity and to the incidence of the shadow economy are used alone (first column) but also, since they are only partial proxies of a more complex mechanism, together with per capita income. table A.1 – DIFFERENTIALS WITH PATENTS AND SHADOW ECONOMY Pooled OLS 1980-2010 (robust standard errors, t stat in parenthesis)

patpc shadow

697.138 (3.55)*** 2.260 (7.68)***

ln_ypc

Cv_labprod 1286.566.138 (7.32)*** 1.106 (3.61)*** -30.324 (6.84)***

ypc

Cv_labprod 1456.920 (9.01)*** 0.908 (2.87)***

Cv_labprod 980.026 (5.25)*** 1.777 (5.88)***

-5.711 (5.44)*** 0.083 (3.16)***

Ypc_sq ypcgap

2.102 (4.73)***

ln_ypcgap F R2_A N

Cv_labprod 1174.350 (7.06)*** 1.281 (4.22)***

31.77 0.13 440

35.83 0.21 440 *p>0.1

40.51 0.23 440 **p>0.05 ***p>0.01

23.76 0.18 440

26.509 (6.59)*** 34.03 0.21 440

Patpc has a positive influence on the dependent variable, as expected; also shadow always has the expected positive sign; both are highly significant. We may conclude that a stronger technological dynamic and a higher share of shadow activities seem to promote a higher diversification of the productivity level. Finally, we may note that ypc, in its various forms, confirms its role. Nevertheless, the previous results have to be considered only as an evocative picture, given the very reduced size of the dataset.