A reassessment of total factor productivity convergence: Evidence from cross-country analysis

Economic Modelling xxx (xxxx) xxx

Contents lists available at ScienceDirect

Economic Modelling journal homepage: www.journals.elsevier.com/economic-modelling

A reassessment of total factor productivity convergence: Evidence from cross-country analysis Badri Narayan Rath a, *, Vaseem Akram a a

Department of Liberal Arts, Indian Institute of Technology, Hyderabad, India

A R T I C L E I N F O

A B S T R A C T

JEL classification: O47 C22 C23

This study revisits total factor productivity (TFP) convergence by employing the latest Lagrange multiplier and residual augmented least squares Lagrange multiplier unit root tests and Phillips and Sul panel club convergence technique. The study uses annual data for 44 developing and 29 developed countries covering the time-period 1970–2014. Our findings from these unit root tests support evidence of TFP convergence. Region-based results (Africa, Asia, and Latin America and the Caribbean) also confirm TFP convergence. Further, results derived from the Phillips and Sul test support evidence of TFP convergence, although the speed of convergence varies by region. The highest speed is noted in the Asia region, whereas, the lowest of speed productivity convergence is observed in the Africa region.

Keywords: TFP Convergence LM and RALS-LM unit root tests Phillips and sul panel club convergence

1. Introduction A plethora of studies examines per capita output or total factor productivity (TFP) convergence (see, e.g., Baumol, 1986; Baumol and Wolff, 1988; De Long, 1988; Bernard and Charles, 1996; Apergis and Christou, 2016; Maryam and Jehan, 2018). These studies explore the “convergence hypothesis” of productivity for various countries by employing distinct datasets and differing methodologies to capture convergence. Although many studies examine this issue, considerable discussion and debate on the meaning of the central notion of “convergence” persists (Jones, 1997). Three broad ideas of convergence are well documented in the literature: (i) beta convergence, which refers to convergence of per capita income or output growth between low-income countries/regions and developed countries (for output dispersion, this is considered a necessary but not sufficient condition); (ii) sigma convergence, which emphasizes mainly cross-country variance of income or output growth over time (Quah, 1996); and (iii) unit root, which is a concept around the integrated property of the series. In this framework, one can examine the common deterministic and/or stochastic trend (Bernard and Durlauf, 1995; Lee et al., 1997). The main motivation behind this paper is to reassess TFP convergence. This research issue is important for understanding the distribution of TFP across countries. According to the neoclassical model, a steady state distribution of per capita output or productivity is possible if all

countries are growing at the same rate. But in reality, not all countries can follow the same steady state of equal growth. To overcome this problem, we can relax this assumption such that countries do not necessarily require the same level of productivity; rather, relative productivity needs to be similar along a transition path to the steady state (Barro and Sala-i-Martin, 1992, 1997; Evans and Karras, 1996; Jones, 1997). Further, this study investigates TFP convergence because of considerable improvement in TFP, particularly in the case of developing countries; this stems from a significant increase in trade openness, research and development (R&D), and foreign direct investment (FDI) over the past couple of decades (Maryam and Jehan, 2018). Thus, we focus mainly on the third notion of convergence described above, as opposed to standard neoclassical beta and sigma convergence, which assume an initial steady state for all countries. By employing the third notion of convergence, we examine mainly whether a group of countries clustering themselves by forming a club follow the same transition path to reach the steady state. In other words, instead of having a single steady state equilibrium path, the countries form different clusters and share a common stochastic trend within the group. In the process of examining convergence, we investigate whether the TFP of each developing country in our sample converges to the average TFP of the Organisation for Economic Co-operation and Development (OECD) countries. Further, we not only check whether developing countries converge to OECD TFP, but also investigate the issue of TFP convergence by selecting different geographic regions of the world. TFP varies across regions, thus, a

* Corresponding author. IIT Hyderabad, Kandi, Sangareddy, Telangana, 502285. E-mail address: [email protected] (B.N. Rath). https://doi.org/10.1016/j.econmod.2019.08.002 Received 9 April 2019; Received in revised form 1 August 2019; Accepted 1 August 2019 Available online xxxx 0264-9993/© 2019 Elsevier B.V. All rights reserved.

Please cite this article as: Rath, B.N., Akram, V., A reassessment of total factor productivity convergence: Evidence from cross-country analysis, Economic Modelling, https://doi.org/10.1016/j.econmod.2019.08.002

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

Table 1 Summary statistics. Country

Obs.

Mean

S.D.

Min.

Max.

Country

Obs.

Mean

S.D.

Min.

Max.

Bahrain Barbados Bolivia Brazil Burkina Cameroon Chile China Hong Kong Colombia Costa Rica CotedIvoire Ecuador Egypt Honduras India Indonesia Iran Iraq Jamaica Jordan Venezuela Avg. OECD

45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45

1.46 1.25 1.08 1.03 0.84 1.22 0.98 0.70 0.81 0.99 0.99 1.17 1.09 1.10 1.09 0.78 0.99 1.31 0.79 1.09 1.19 1.17 0.93

0.57 0.24 0.14 0.08 0.09 0.24 0.07 0.16 0.12 0.04 0.09 0.19 0.12 0.06 0.11 0.12 0.08 0.64 0.23 0.13 0.29 0.23 0.06

1.00 0.95 0.94 0.94 0.72 0.97 0.84 0.51 0.58 0.92 0.89 0.99 0.93 0.94 0.90 0.63 0.83 0.84 0.22 0.94 0.84 0.84 0.83

2.75 1.61 1.38 1.26 1.01 1.77 1.12 1.04 1.00 1.05 1.19 1.59 1.32 1.19 1.29 1.05 1.10 2.85 1.24 1.46 1.74 1.76 1.04

Kenya Kuwait Malaysia Mauritania Morocco Mozambique Niger Nigeria Panama Paraguay Peru Philippines Qatar Saudi Arabia Senegal Singapore South Africa Sri Lanka Sudan Thailand Tunisia Uruguay Avg. Developing

45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45 45

1.01 1.43 0.96 1.22 1.12 0.77 1.05 0.89 0.95 1.10 1.14 0.98 1.23 1.34 1.01 0.92 1.07 0.70 1.15 0.93 0.93 0.84 1.04

0.06 0.78 0.05 0.22 0.08 0.14 0.15 0.20 0.05 0.21 0.27 0.14 0.23 0.39 0.04 0.05 0.08 0.15 0.11 0.06 0.06 0.09 0.17

0.92 0.45 0.85 0.93 1.00 0.57 0.88 0.65 0.87 0.80 0.83 0.82 0.88 0.93 0.93 0.82 0.94 0.52 0.93 0.83 0.76 0.67 0.82

1.15 3.59 1.05 1.83 1.30 1.02 1.43 1.34 1.03 1.50 1.62 1.25 1.67 2.21 1.08 1.04 1.23 1.11 1.47 1.04 1.05 1.06 1.43

Notes. This table illustrates key summary statistics such as mean, standard deviation, and minimum and maximum TFP. The results show that average TFP of OECD countries is 0.93%, whereas it is 1.04% for developing countries. Similarly, comparing the standard deviation figures between average developed and developing countries reveals that variation in productivity growth is slightly higher than variation in productivity among developed countries. Obs. ¼ observations. S.D. ¼ standard deviation. Max. ¼ maximum. Min. ¼ minimum. Avg. ¼ average. Source: Authors’ own calculation.

side in their mean TFP than the United States’ TFP. Therefore, it is vital to check the convergence against a set of advanced economies. Third, we disaggregate 44 developing countries into subgroups based on regions, such as Asia, Africa, and Latin America and the Caribbean and further investigate the issue of productivity convergence. In so doing, we claim that the TFP of developing countries varies across regions. Therefore, from the policy perspective, it is imperative to see how each region’s TFP growth converges with the average productivity of OECD countries. Fourth, we not only examine the catch-up hypothesis, but we also explore the speed of convergence (or transition path) by applying the Phillips and Sul (2007, hereafter, PS) approach, which, to best of our knowledge, has not been investigated thus far. The PS approach is superior to the neoclassical approach in many instances. First, it captures the heterogeneity in groups of countries and accounts for the non-linear “time-varying” factor in the model. Second, it has higher power to sense asymptotic co-movement in the presence of unit root. Finally, PS constructs a new algorithm to identify clusters of convergence for groups. Therefore, findings from this test will provide new insight to the income convergence literature by removing the disparities between the subgroups of countries. Fifth, we use both T€ ornqvist and welfare indices for measurement of TFP computed by Feenstra et al. (2015) to examine TFP convergence. Though Penn World 9.0 releases this productivity data, to the best of our knowledge, no existing study uses this data to test convergence. Thus, we use this welfare-based productivity as part of our robustness checks. This paper proceeds as follows. Section 2 reviews the literature pertaining to productivity convergence. Section 3 describes the methodology and data sources. Section 4 presents the empirical results. Finally, Section 5 sets forth our conclusions.

reassessment of productivity convergence remains vital for developing countries to assess their use of inputs and adoption of technology to boost productivity. If poor countries share a common trend or follow the same transition path along with developed countries, then this process will make efficient use of technology in developing countries, thereby increasing the pace of improvement in standards of living. By keeping this objective in mind, the present study makes five essential contributions: First, the recent study by Maryam and Jehan (2018) examines the factors of TFP convergence in developing countries, focusing on the role of trade openness and FDI. However, this study employs the traditional notion of so-called sigma and beta convergence, which has several drawbacks. Rather, our study focuses on stochastic conditional convergence using the latest Lagrange multiplier (LM) and residual augmented least squares Lagrange multiplier (RALS-LM)1 unit root test proposed by Lee et al. (2012) and Meng et al. (2014). These unit root tests yield robust evidence of the “catch-up” hypothesis including endogenous breaks. Further, Maryam and Jehan (2018) consider 91 developing countries and check whether these countries as a group converge to the USA, which they treat as the frontier country. But we argue that all developing countries may not have the same growth path, hence, our study yields more insight by checking whether each developing country shares a common stochastic trend with developed countries. Second, our study differs from Maryam and Jehan (2018) by considering an average of TFP of OECD countries as a frontier, where these authors consider only the USA as a benchmark. The data collected from the Penn World Tables show that such countries as Australia, Austria, Belgium, Canada, Denmark, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal, Korea, Spain, Sweden, Switzerland, Turkey, and the United Kingdom are on the higher

2. Literature review This section reviews empirical studies on convergence related to labor productivity and TFP based on firms, sectors, regional level and across countries. There is a wide range of literature that examines productivity convergence by focusing on the firm level (see, e.g., Surjaningsih and Permono, 2014; Bournakis and Mallick, 2018; Burda and Severgnini, 2018; Kijek et al., 2019; among others). Burda and Severgnini (2018)

1

The advantages of these unit root tests are well explained in Mishra and Smyth (2017). In brief, these unit root tests avoid the nuisance parameters, and they account for non-normal error information unaccounted for in the earlier tests. The existence of non-normal errors in the series is likely to result in loss of power. 2

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

work is based on labor and TFP convergence for states of Germany at the sector level. Their findings show that various factors affect the process of productivity convergence in Germany. Their results based on a panel unit root test show evidence for the catch-up hypothesis. The Bournakis and Mallick (2018) analysis is based on 7400 manufacturing firms’ TFP convergence in the UK over the period 2004–2011. These authors find evidence of TFP growth convergence. Kijek et al. (2019) investigate TFP convergence by emphasizing the agriculture sector for 25 European Union (EU) member states for the period 2004–2016; the results support TFP convergence for the majority of EU member states. There are several seminal works on TFP convergence based on

Table 2 Decadal TFP. Variable

1970–79

1980–89

1990–99

2000–09

2010–14

Avg. Developing Avg. OECD

1.22 0.86

1.03 0.89

0.96 0.95

0.98 1.01

1.00 0.99

Notes: Avg. ¼ average. OECD ¼ Organisation for Economic Co-operation and Development. This table presents decadal TFP of both developed and developing countries. The figures indicate that TFP of developing countries is higher than the average for OECD countries in most periods, except 2000-09. Average TFP rate for developing countries is highest for 1970-79, whereas, for OECD countries, TFP is highest for 2000–2009. Source: Authors’ own calculation.

Panel A. TFP of developing and developed countries. Panel A presents TFP of 44 developing countries against average developed countries’ TFP, indicated by the red line, whereas black lines indicate developing countries. Source: Authors’ own calculation based on TFP data.

Panel B. Coefficient of variation of TFP for a group of countries. The graph in Panel B shows the coefficient of variation of TFP over the period for a group of both developed and developing countries. Note the sigma convergence between developing and OECD countries as the variation declines over the period. Source: Authors’ own calculation based on TFP data.

3

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

aggregate country-level data (see, e.g., Miller and Upadhyay, 2002; Madsen, 2007; Maryam and Jehan, 2018; Rath, 2019). We begin with the influential paper by Miller and Upadhyay (2002), who investigate TFP convergence and gross domestic product convergence via parsimonious specification of the aggregate production function. These authors employ the neoclassical notion of beta and sigma convergence and find both absolute and conditional convergence across a set of countries. Madsen (2007) finds that knowledge spillover is a crucial factor for TFP convergence in OECD countries over the period 1870–2004. Maryam and Jehan (2018) examine TFP convergence for 91 developing countries and observe that FDI plays a significant role in achieving conditional convergence. Rath (2019) examines TFP convergence in ASEAN countries using the LM, RALS-LM and PS panel convergence technique for the period 1968–2014. This author’s findings suggest evidence of TFP convergence in the ASEAN-5 countries. From the above literature, we note that there is a wide range of research emphasizing both TFP as well as labor productivity convergence starting from the firm level, states/regions within a country, or by examining multiple countries, particularly the OECD countries. The findings based on these empirical studies are not only mixed in nature but also strongly driven by the approaches used and the data periods employed. We note only two studies that investigate TFP convergence using a sample of developing countries, Miller and Upadhyay (2002) and Maryam and Jehan (2018). However, both studies are based on the assumption of a single steady state equilibrium path, which seems unrealistic.

Table 3 Zero/one/two breaks LM and RALS-LM unit root test of TFP. Country

Bahrain Barbados Bolivia Brazil Burkina Faso Cameroon Chile China Hong Kong SAR Colombia Costa Rica C^ ote d’Ivoire Ecuador Egypt Honduras India Indonesia Iran Iraq Jamaica Jordan Kenya Kuwait Malaysia Mauritania Morocco Mozambique Niger Nigeria Panama Paraguay Peru Philippines Qatar Saudi Arabia Senegal Singapore South Africa Sri Lanka Sudan Thailand Tunisia Uruguay Venezuela Regions Africa Asia Latin America and the Caribbean All Developing

3. Methodology and data sources In the convergence literature, the empirical findings are inconclusive mainly due to the use of different approaches toward convergence. Apergis and Christou (2016) argue that the presence of sigma convergence is not necessary and that there is no catch-up evidence; rather, it is a transitional dynamic that can reject the null hypothesis of sigma convergence. Similarly, Quah (1996) has criticized beta convergence. This author argues that if each country eventually becomes as wealthy as all other countries, then the dissimilarity of the series must vanish in the long run. The other limitation in the notion of convergence developed by the neoclassical growth model is that it focuses only on a single steady state. To overcome this problem, the present paper uses the notion of stochastic conditional convergence and panel club convergence proposed by PS. The stochastic conditional convergence of relative TFP can be computed via the following equation:
 TFPit yit ¼ ln Aveg:TFPt

(1)

b k

RALS-LM

τLM

τRALSLM

b ρ2

b B1 T

b B2 T

6.869*** 5.470*** 5.497*** 7.723*** 6.148*** 4.288* 4.894** 5.888*** 6.703*** 8.006*** 4.484** 4.251* 4.302* 4.794*** 6.489*** 5.593*** 6.410*** 4.732** 6.192*** 5.632** 4.141* 1.818 3.558 4.841** 5.055** 6.036*** 3.998 4.882** 5.581*** 6.068*** 5.755*** 4.152* 6.896*** 6.170*** 5.518*** 5.868*** 7.172*** 4.8402** 5.104** 7.035*** 3.677 5.148** 3.013 5.415***

7.806*** 6.405*** 5.545*** 7.854*** 5.709*** 4.543*** 4.640** 4.924*** 6.268*** 7.850*** 4.965*** 4.223** 3.092* 4.288*** 6.390*** 9.145*** 6.033*** 5.431*** 7.031*** 6.285*** 3.180 2.623 4.250*** 5.864*** 4.802*** 7.855*** 4.871*** 4.918*** 5.577*** 6.880*** 5.162*** 4.172** 7.471*** 5.916*** 8.282*** 6.005*** 7.574*** 4.858** 6.335*** 7.298*** 3.572 4.990*** 2.660 7.666***

0.60 0.70 0.94 0.83 0.97 0.70 0.89 0.96 0.74 0.88 0.73 0.77 0.84 0.75 0.88 0.41 0.99 0.79 0.76 0.64 0.82 0.60 0.79 0.52 0.82 0.66 0.60 0.93 0.88 0.70 0.78 0.74 0.82 0.98 0.33 0.83 0.87 0.94 0.70 0.77 0.98 0.97 0.89 0.55

1983 1987 1980 1979 1981 1983 1980 1989 1985 1988 1979 1981 1981 1988 1989 1982 1996 1987 1989 1987 1982 1990 1988 1983 1987 1980 1994 1982 1984 1979 1981 1986 1983 1979 1986 1980 1996 1983 1988 1985 1995 1979 1980 1988

1996 2004 2000 1993 1996 1993 1983 2000 1996 1997 1985 2006 1987 … 2000 2001 1999 1995 1992 1994 1999 2002 1991 2000 1994 1994 1999 1985 2000 2003 2003 1991 2002 1995 1992 1991 2002 1998 2003 1995 1998 1988 1984 2001

8 7 7 7 0 8 7 5 8 8 1 3 1 2 5 6 3 6 4 6 7 7 7 8 0 2 2 3 8 1 2 1 5 6 8 7 5 1 5 6 3 1 5 7

5.761*** 5.222*** 5.640***

5.652*** 5.309*** 5.729***

0.92 0.83 0.90

1981 1979 1980

1999 1990 1999

3 6 6

4.778**

3.726*

0.76

1979

1991

5

Notes: The sample period is 1970–2014, as in our analysis. b k stands for optimum b B1 and T b B2 stand for break period 1 and 2, b B indicates the break periods. T lag. T

where yit represents relative TFP for country i and time t; Aveg:TFPt indicates the average TFP of 29 OECD countries; and TFPit is the TFP of i-th developing country over time t.

respectively. τLM and τRALSLM denote test statistics for LM and RALS-LM tests. LM and RALS-LM are invariant to the breaks periods. ***, **, and * show 1%, 5%, 2

and 10% significance levels. b ρ reflects the relative ratio of the variances of the two error terms. Asymptotic critical values for LM and RALS-LM are given in Meng et al. (2014). The same CVs can be used irrespective of number of breaks in the series, since RALS-LM test statistics are not based on break location coefficients. The LM and RAS-LM test statistics are significant for most countries and regions with two breaks. This implies that we reject the null of a unit root. Thus, our results confirm that the developing countries are converging to developed countries in productivity growth, subject to the presence of two breaks in the data series. Similarly, the results show that developing countries as a whole and the other three regions (Africa, Asia, and Latin America and the Caribbean) are also converging to the developed countries, subject to the presence of two breaks in the data series.

3.1. Two-step LM and three-step RALS-LM unit root approach The LM and RALS-LM unit root tests are applied to attain our goal of convergence. These tests capture structural breaks, which are endogenously determined (Lee et al., 2012; Meng et al., 2014; Mishra and Smyth, 2017). Moreover, Meng et al. (2014) and Mishra and Smyth (2017) hold that Eq. (1) is free from cross-sectional shocks. We make use of Eq. (1) to test convergence. There will be evidence in favor of stochastic conditional convergence if relative TFP is stationary. The RAS-LM can be written as per the Meng et al. (2014) notation. yt ¼ ψ t þ ξt þ xt ; where xt ¼ βxt1 þ et

bB T

LM

(2)

Eq. (1) removes country shocks that influence all individual countries in a group. This infers, for the mean, that any positive shock in yt among countries would enlarge the mean by an equal proportion. The null 4

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

Panel C. Plot of actual and adjusted series with breaks. From this panel, we observe that the break date(s) coincide with actual series (black lines). Source: Authors’ own calculation based on TFP data.

 ’ b t ¼ be 2t  m2 ; be 3t  m3  3m2 ebt w

hypothesis of the unit is assumed β ¼ 1, against the alternative hypothesis of β < 1, where ψ and ξ show the deterministic of intercept and trend. The more general form of Eq. (2) is re-written in the following form: yt ¼ Z ’t δ

þ xt ;

xt ¼ βxt1 þ et

The concluding regression of RALS-LM test is as follows: Δyt ¼ δ’ Zt þ φ~yt1 þ

(3)

p X

ft1 þ et gi Δy

(4)

To compute the speed of convergence (or transition path), we employ the PS test. This test includes the non-linear, time-varying factor, which also identifies the convergence by clustering algorithms. The PS model has common and as well as individual-specific components. Let us assume the series is yit (in our case relative TFP), country i and time t. The model based on the single factor is written as follows:

autocorrelation, the lagged-difference of yt is included in Eq. (4), that is, f tj . According to Meng et al. (2014), the LM test statistic is symbolized Δy by ~τLM , and the null hypothesis of this test statistic is φ ¼ 0. Next, the higher moments non-normal errors are taken into account to tackle the issue of nonlinearity functional form (Meng et al., 2014). This

yit ¼ δi μt þ uit

’

and Ft ¼ ðΔZ ’t ; f ’t Þ . By following the two moment conditions:

(6)

where et stands for error of LM from Eq. (4), whereas K ¼ Eðet Þ and hðet Þ are a non-linear function of et : Further, Meng et al. (2014) extend their approach by following Im and Schmidt (2008). Meng et al. (2014) T T T P P 2 3 ’ b b Þ; D b Þ; and mj ¼ T 1 P b¼1 describe hðbe t ; be t Þ ; K ¼ T1 h ðe h’ ðe t t T t¼1

t¼1

(9)

where δi captures the idiosyncratic distance that occurred by a common factor μt and systematic part of yit . uit stands for the error term. To study the progression of a single yit with the common factor, the average of δi and uit is taken. In Eq. (9), we include the systematic idiosyncratic that develops over the years by a time-varying factor loading coefficient δit . A random component is included in Eq. (9) to absorb δit that denotes the convergence activity with respect to the common factor μt over the time-span. The time-varying model is given as follows:

’

can be done by introducing ξt ¼ ðΔ~ y t1 ; Δ~ y t2 ; …; Δ~ y tp Þ’ , ft ¼ ð~ y t1 ; ξ’t Þ

E½ðhðet Þ  KÞ  Ft  ¼ 0

(8)

3.2. PS convergence approach

e t ¼ 2, …, T, e δ exhibits the vector coefficients in where y~t ¼ yt  ψ~  Zt δ; Eq. (4), whereas ψ~ is an estimated restricted maximum likelihood. In δ, this indicates the first observed model. To control for view of y1  Z1e

(5)

ft1 þ w b ’t γ þ ut gi Δy

Using the least squares estimation, one can obtain the test statistic of RALS-LM and the t-statistic allied with the null hypothesis (ϕ ¼ 0) for τRLM . The moment condition is related to the asymptotic distribution of τRLM .2 The optimal lags and significant break dummies of RALS-LM are determined through a Max-F test. The trimming value is set at 10% to ensure the observations before and after the breaks. These tests can be applied when there are 0, 1, or 2 breaks in the series.

j¼1

E½et  Ft  ¼ 0

p X j¼1

Z ’t represents deterministic terms, including structural break points. For the intercept, trend and N structural breaks, Z ’t is symbolized as [1, t, D1t, … … DNt]; Djt ¼ 1 for t  TBj þ 1, j ¼ 1, … …,N and 0 otherwise. TBj is the location of the ith structural break, where DNt are dummy variables denoting the positions of the ith level breaks. We compute LM test statistics through Eq. (4). Δyt ¼ δ’ Zt þ φ~yt1 þ

(7)

2 The asymptotic critical values for the LM and RALS-LM are given in Meng et al. (2014). The same critical values can be used irrespective of the number of breaks in the series, since RALS-LM test statistics are not based on the break location coefficients.

t¼1

be jt and augment Eq. (4) as follows: 5

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

yit ¼ δit μt

(10)

0.33 as per the PS3 suggestions, which is appropriate for T  50.

yit ¼ Git þ Bit

(11)

3.3. Data We make use of TFP data, which covers the period 1970–2014 for 44 developing countries. Sample selection is based solely on data availability. This study considers two types of TFP data collected from Penn World Table 9.0 constructed by Feenstra et al. (2015). The first type of TFP data is based on the T€ ornqvist quantity index, which can be written as follows:

where yit is classified into two parts: Git (systematic component), and Bit (transitory components). Eq. (11) is divided and multiplied by μt , and illustrated as: yit ¼

  Git þ Bit

μt

μt ¼ δit μt ;

8i; t

(12)

where μt signifies a club steady state. δit is an idiosyncratic expression that accounts for time- and country-related effects. Also, δit is a share of the common factor ðμt Þ of each individual country. Moreover, δit indicates the transition paths. Since convergence is a dynamic procedure, δit suggests the transition paths. The convergence can be tested by investigating temporal relative evolution of δit . Another important point raised by PS is that their test does not consider any parametric form for μt , rather PS simply factors it out and concentrates on δit . Eq. (12) cannot be directly feasible if the observations are less than the unknown in the panel model. Thus, they impose the same structure on δit and μt and assume a semiparametric form for δit . PS mentions that the test of long-term convergence is possible whenever unobservable heterogeneity is dissipated (when Git → Gt ). To remove μt , they rescale Eq. (12) by dividing the panel average: y hit ¼ 1 PN N

i¼1 yit

δit ¼ 1 PN N

i¼1 δit

TFPNA jt;t1

(13)

Clubs

Full developing counties

(14)

lows ii d, (0, 1) country i. The L(t) function is steadily rising and dispersing at LðTÞ → ∞ as t → ∞. The convergence null hypothesis for the whole sample for a country under a particular form is γ it : H0 : δi ¼ δ; 8 i with a  0, and the alternative convergence hypothesis is H1 : δi 6¼ δ;8 i with a  0 or a < 0. As per PS, the null is convergence, and this can be tested from Eq. (15).   H1  2logLðtÞ ¼ bc þ b blog t þ b ut Ht

Full Club 1

(15) Club 2

where t ¼ ½rT; ½rT þ 1; ……; T and r > 0; the country variance ratio is denoted HH1t ; LðtÞ ¼ logðt þ1Þ is incorporated in Eq. (15); and

Full Full

N P

b are the least squares estimated ðhit  1Þ2 and b b ¼ 2b α, α   parameter. The null hypothesis, log HH1t diverges while a  0. In this Ht ¼ N1

 QT vj; vk; wj; wk;

(16)

Table 4 Speed of convergence TFP and WTFP.

The above assumption is needed for club convergence in semiparametric form for the time-varying coefficients ðδit Þ, where σi σ it ¼ LðtÞt α ; σ i > 0; t  1 and where ξit is dimly based on time t, and it fol-

log

RGDPNA jt1

,

where RGDPNA is real GDP computed using national account data. QT indicates T€ ornqvist quantity index, which is based on the factor endowments. This index is estimated through observed factor prices and shares, where v and w denote the inputs labor and capital as a share of income, respectively. The second TFP index is based on the welfare-relevant measure, given as follows:

where hit expresses the transition path to the average of the country group and hit differs between countries in the short run, but convergence is attained in the long run if hit → 1 for all countries i, when time t → ∞. Convergence is achieved in the long run when country variance is equal to zero, that is, hit → 0. δit ¼ δi þ σ it ξit

¼

RGDPNA jt

i¼1

TFP

WTFP

Regions

b-Coefficient [log t-Stat]

b-Coefficient [log t-Stat]

Bahrain, Barbados, Bolivia, Brazil, Burkina Faso, Cameroon, China, Chile, Hong Kong, Colombia, Costa Rica, C^ ote d’Ivoire, Ecuador, Egypt, Honduras, India, Indonesia, Iraq, Iran, Jamaica, Jordan, Kenya, Kuwait, Malaysia, Mauritania, Morocco, Mozambique, Niger, Nigeria, Panama, Paraguay, Peru, Philippines, Qatar, Saudi, Arabia, Senegal, Singapore, South Africa, Sri Lanka, Sudan, Thailand, Tunisia, Uruguay, Venezuela Africa Burkina Faso, Cameroon, C^ ote d’Ivoire, Egypt, Kenya, Morocco, Mozambique, Niger, Nigeria, Senegal, South Africa, Tunisia Mauritania, Sudan

0.12**[1.92]

2.82**[1.64]

5.68 [-4.75] 1.16** [-0.59]

0.55**[0.41]

1.71** [-0.65] 1.55** [1.03] 1.29** [1.21]

…

Asia Latin America and the Caribbean

Regions Developing countries Asia Latin America and the Caribbean Africa

case, convergence can be investigated via one sided t-test of the inequality, a  0 using b. The t  statisticeð0; 1Þ and it obtains from b b.

3.71**[2.03] 2.28**[1.26]

Speed of convergence 0.06 1.41 0.78 1.86 0.65 1.14 1.44 0.28

Notes: The critical value of t-statistics is 1.67 at the 5% level. The calculated tstatistics values are presented in parentheses. **shows significance level at 5%. TFP and WTFP stand for total factor productivity based on the T€ ornqvist quantity and welfare-based index, respectively; b stands for coefficients; and log t-Stat indicates the log t-statistics. Log t-Stat values are given in square brackets. This table presents the speed of TFP convergence using both TFP measures. The results indicate productivity convergence for a full sample of developing countries as well as for sub-samples based on region. The results also demonstrate that the speed of productivity convergence of the Asia region is faster than for Africa and Latin America and the Caribbean.

This model also takes care of heteroscedasticity and is autocorrelation consistent. One cannot accept the null of convergence if the t-statistic value is less than the critical value 1.65. We consider r value equal to

3 Detailed explanation of the formation of clubs, which is based on the four steps, can be found in the original PS article. PS argue that their approach overestimates clubs. Thus, they suggest repeating the log(t) test for merging the clubs.

6

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

Panel D. Plot of club 1 and club 2 for Africa. We plot the average TFP series of club 1 and club 2 to visualize the transition paths. Note that both clubs follow a distinctive pattern. These results show evidence of club convergence for Africa. Both clubs lie below the average of all developing countries as a panel. Source: Authors’ own calculation based on PS results.

WTFPNA jt;t1

¼

CDANA jt CDANA jt1

,

 QT vj; vk; wj; wk;

tests to examine TFP convergence for each of 44 developing countries compared to average TFP of OECD countries. The results are summarized in Table 3. The LM test statistic ðτLM Þ is labeled in the second column of Table 3, whereas the fourth column presents the results for the RALS-LM statistic (τRALSLM ). These tests assume the null of unit root. The results presented in Table 3 show that the statistics of these unit tests are significant for all the countries except Kenya, which implies that we do reject the null of unit root. In other words, we find convergence, which shows that developing countries catch up in productivity growth to developed countries subject to the presence of two breaks in the data series. Most of the identified breaks are close to events that occurred across the developing and developed countries, such as oil and energy crises (1973, 1979), recession (1980), Asian financial crisis (1997), and the Global Financial Crisis (2007-08). The majority of crises hit the developing countries badly because of the adverse impact on important determinants of productivity growth such as FDI, fluctuations in the cost of labor, slower pace of technological progress, lower capital investment, and slowdowns in international trade (see, for instance, Oulton, 2017). Convergence in developing countries is primarily due to the following factors. First, improvements in knowledge and technological transfer through FDI can increase TFP in developing countries (Barro and Sala-i-Martin, 1997). Second, increased trade openness is a key factor that enhances productivity growth through high competition resulting in expansion of firm productivity. A higher degree of openness also leads to improved terms of trade, which eventually reduces domestic deviations from purchasing power party. Overall, the TFP convergence hypothesis holds for developing counties. This study also looks at the convergence hypothesis at the regional level. We consider Africa, Asia, Latin America and the Caribbean, and all developing countries together, by comparing average TFP against advanced-country average TFP. Our results again reveal evidence of convergence, which implies that Africa, Asia, Latin America and the Caribbean, and all developing countries, converge to developed countries. In all regions, the LM and RAS-LM test statistics are significant with two breaks. These findings suggest that poorer economies tend to grow faster using innovation and imitation of techniques with better absorption capacity, which speeds up the convergence process. Considering Meng et al. (2014) and Mishra and Smyth (2017), to better understand our findings, we overlay the level and trend breaks

(17)

The above index is based on relative domestic absorption rather than on real GDP.4 4. Results and discussion Before we formally check for evidence of productivity convergence, this section discusses the summary statistics of TFP of the selected sample countries. The mean values of TFP shown in Table 1 indicate that the TFP of Bahrain, Barbados, Cameroon, C^ ote d’Ivoire, Iran, Jordan, Kuwait, Mauritania, Qatar, and Saudi Arabia are relatively higher than the other developing countries in our sample. Further, we compare the advanced countries’ TFP with those of developing countries. Note that the average TFP rates of developing countries are much faster than the developed countries. These findings initially suggest the catch-up hypothesis based on neoclassical theory. Next, to understand TFP dynamics, we divide our observations at the decadal level. The results depicted in Table 2 show high TFP for developing countries as compared to developed countries, except for the period 2000–09. This hollow growth in developing countries during the 2000–09 period may be attributable to the Global Financial Crisis, which severely affected most the developing countries. Further, in visualizing the TFP of developing and advanced economies, we plot the TFP series in Panel A. In all graphs, the thick red line shows the trend of TFP for advanced countries, whereas the black lines represent developing countries. From Panel A,5 we note that all the developing countries are following the developed countries. These graphical findings corroborate the summary statistics results. Next, we compute the coefficient of variation (CV) of average TFP for developing and advanced countries over the sample period. The CV of these countries is illustrated in Panel B. We see from Panel B that the gap between the CV of developing and developed countries decreases over the years, which again suggests the catch-up hypothesis in these countries. We next apply both LM and RALS-LM two structural breaks unit root

4

For detailed methodology, please refer to Feenstra et al. (2015). It is difficult to view all the series in one map. Thus, we have fragmented the 44 countries into 4 maps to gain a clear picture against the average of OECD countries. 5

7

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

Table 5 Club convergence of a full set of countries for TFP. Clubs

Countries

b-Coefficient [log tStat]

Full samples Club 1

All countries

3.47 [-3.01]

Austria, Bahrain, Barbados, Belgium, Bolivia, Brazil, Cameroon, Canada, Chile, China, Colombia, Costa Rica, C^ ote d’Ivoire, Denmark, Ecuador, Egypt, Greece, Honduras, Hungary, Indonesia, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Kuwait, Malaysia, Mauritania, Morocco, the Netherlands, New Zealand, Niger, Norway, Panama, Paraguay, Peru, Philippines, Portugal, Qatar, Senegal, Singapore, South Africa, Spain, Sudan, Switzerland, Thailand, Tunisia, Turkey, Venezuela India, Iraq, Nigeria, Uruguay Sweden, United States Burkina Faso, Poland Iceland, Ireland, Mexico Finland, France, Saudi Arabia Hong Kong, Iran, Mozambique, Republic of Korea Australia, Germany, Luxembourg, Sri Lanka, United Kingdom

1.44** [0.78]

Club 2 Club 3 Club 4 Club 5 Club 6 Club 7 Group Merge Club 1 þ 2 Club 2 þ 3 Club 3 þ 4 Club 4 þ 5 Club 5 þ 6 Club 7 þ 2 Group Final club Club 1

Club 2 Club 3 Group

0.23** [0.18] 0.27** [0.19] 0.97**[-0.99] 0.06** [0.03] 3.88** [2.11] 1.24** [2.33] 4.87 [-7.45] 0.950**[0.45] 2.08 [-4.69] 3.39 [-4.86] 2.35 [-2.73] 0.97** [-0.42] 0.94 [-4.92] 4.32 [-4.50]

Austria, Bahrain, Barbados, Belgium, Bolivia, Brazil, Burkina Faso, Cameroon, Canada, Chile, China, Colombia, Costa Rica, C^ ote d’Ivoire, Denmark, Ecuador, Egypt, Greece, Honduras, Hungary, Iceland, India, Indonesia, Iraq, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Kuwait, Malaysia, Mauritania, Mexico, Morocco, the Netherlands, New Zealand, Niger, Nigeria, Norway, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Senegal, Singapore, South Africa, Spain, Sudan, Sweden, Switzerland, Thailand, Tunisia, Turkey, United States, Uruguay, Venezuela Finland, France, Saudi Arabia Hong Kong Iran, Mozambique, Korea Australia, Germany, Luxembourg, Sri Lanka, United Kingdom

1.91** [-1.39]

3.88** [2.11] 1.25** [2.33] 4.87 [-7.45]

Notes: The critical value is 1.65 at the 5% level significance level. **Indicates the 5% level of significance. b stands for coefficients, and log t-Stat indicates the log tstatistics. Log t-Stat values are given in square brackets. This table presents club convergence using the TFP series. The results indicate the absence of productivity convergence for the full sample. The clustering algorithm is applied as suggested by PS to identify the clubs. Seven clubs are identified along with one group. A group indicates that there is no convergence. The results demonstrate three final clubs. Club 1 consists of a majority of countries, unlike clubs 2 and 3.

Panel E. Relative transition paths of TFP and WTFP. The graph shows that each club follows a distinctive transition path. These results show evidence of club convergence. Source: Authors’ own calculation based on PS results.

identified in Table 3 and then plot the TFP for each country6 and region. The linear trends are estimated with the help of ordinary least squares regression to connect the break points. From Panel C, we observe that the break date(s) for Africa, Asia, group of developing countries, and Latin

America and the Caribbean coincide with the actual series (black lines). The LM and RALS-LM tests do not reveal the countries’ transition path (or speed of convergence). To do so, we apply the PS approach, which forms the clubs through clustering algorithms. The PS results are reported in Table 4. We find that the speed of convergence of developing

6 To conserve space, we do not report the graphs of each of the 44 developing countries, but they are available upon request.

8

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

countries is 0.067 to catch up to the average TFP of OECD countries. Similarly, in the case of regions, we find that Asian countries’ TFP are catching up to OECD countries with a higher speed (that is, 0.78) as compared to other regions. The moderate speed of convergence is found for Latin America and the Caribbean. Most interestingly, the PS results suggest that the Africa region has two clubs (it follows two transition paths), which implies that the African countries are very heterogeneous with regard to their productivity growth. Burkina Faso, Cameroon, C^ ote d’Ivoire, Egypt, Kenya, Morocco, Mozambique, Niger, Nigeria, Senegal, South Africa, and Tunisia lie in club 1, which means that these countries have the same speed of convergence, whereas Mauritania and Sudan both are in club 2, the lowest speed of convergence observed in the Africa region. To visualize the relative transition paths, we plot club 1 and club 2 in Panel D. Note that both clubs have distinctive patterns. Club 2 runs distinctively above club 1 until 2010.8 After 2010, it is observed below club 1. Finally, we consider the full sample, a total of 73 countries (44 developing and 29 developed countries). The PS technique finds evidence of club convergence of TFP. The PS results presented in Table 5 show that the log(t) value (that is, 3.47) is lower than the critical value (1.65), which implies that we reject the null of convergence for the full sample. Moreover, this finding suggests using the clustering algorithms to find evidence of club convergence. Our results show that there are seven distinct club convergences and only one group that is not converging. PS suggest that their approach overestimate the clubs and recommend repeating the log(t) test to merge the clubs into larger clubs. The results yield evidence in favor of merging clubs, specifically that club 1 is merging into club 2 and club 5 into club 6. We end up with the final three clubs. Club 1 consists of a majority of countries, whereas there are few countries in clubs 2 and 3. These findings infer that most developing countries are converging toward the developed countries. To visualize these clubs, we plot the relative transition path using Eq. (13) (see Panel E). In club convergence, the relative transition paths of the individual members of each club should follow the different path unlike full sample convergence (that is, based on the neoclassical notion of beta and sigma convergence). The distinct pattern of TFP series for each club is notable. Club 1 is almost equal to unity because it consists of the majority of countries. Clubs 2 and 3 share a very different trend (see Panel E). These findings support the evidence for three distinct clubs.

Table 6 Zero/one/two breaks LM and RALS-LM unit root test of WTFP. Country

Bahrain Barbados Bolivia Brazil Burkina Faso Cameroon Chile China Hong Kong SAR Colombia Costa Rica C^ ote d’Ivoire Ecuador Egypt Honduras India Indonesia Iran Iraq Jamaica Jordan Kenya Kuwait Malaysia Mauritania Morocco Mozambique Niger Nigeria Panama Paraguay Peru Philippines Qatar Saudi Arabia Senegal Singapore South Africa Sri Lanka Sudan Thailand Tunisia Uruguay Venezuela Regions Africa Asia Latin America and the Caribbean All Developing

4.1. Robustness checking This study further uses an alternative measure of TFP that is based on the welfare measure (WTFP), which is linked with relative domestic absorption. To verify our results, we again employ both LM and RALS-LM unit root tests and the club convergence approach developed by PS. The results derived from these unit root tests indicate that the statistics τLM and τRALSLM are significant for all countries and regions except Kenya, which implies that we may reject the null of unit root. In other words, we find that the relative WTFP series is stationary in each country and region except Kenya, which conforms with the catch-up hypothesis. The results obtained from LM and RALS-LM tests are almost consistent with pervious results. In fact, the results of WTFP are more significant than TFP based on the T€ ornqvist quantity index. The results are given in Table 6. Now, we plot the actual WTFP series with respect to the trend breaks identified in Table 6 for each country and region. We estimate linear trends using the ordinary least squares regression to connect the break points. From Panel F, we observe that the break date(s) for Africa, Asia, developing, and Latin America and the Caribbean coincide with actual series (black lines).

bB T

b k

LM

RALS-LM

τLM

τRALSLM

b ρ2

b B1 T

b B2 T

6.420*** 4.608*** 5.014** 5.172** 5.022** 5.430** 4.661** 5.807*** 6.230*** 4.278** 3.659* 5.227*** 6.470*** 6.070*** 5.945*** 7.181*** 6.077*** 5.862*** 4.628** 6.569*** 5.697** 2.931 8.200*** 5.604** 5.433*** 6.352*** 6.865*** 4.481** 5.446*** 6.516*** 7.406*** 4.877** 3.560* 5.592*** 7.609*** 4.056* 7.547*** 5.719*** 4.499** 3.755 4.872** 5.807*** 7.746*** 5.545***

6.486*** 5.402*** 5.192*** 6.054*** 5.540*** 5.578*** 5.866*** 5.566*** 7.514*** 4.355** 3.372* 4.161** 7.512*** 5.865*** 5.916*** 6.863*** 5.164*** 6.413*** 4.105* 8.222*** 6.918*** 2.400 8.231*** 5.258*** 5.171*** 7.574*** 5.896*** 6.196*** 4.721** 6.348*** 6.323*** 5.370*** 2.966* 5.602*** 7.433*** 4.570*** 6.846*** 7.880*** 4.207*** 4.400*** 4.401*** 6.404*** 9.334*** 6.658***

0.90 0.71 0.85 0.67 0.74 0.81 0.65 0.92 0.64 0.64 0.81 0.87 0.68 0.98 0.80 0.99 0.93 0.81 0.99 0.67 0.64 0.95 0.92 0.82 0.88 0.60 0.95 0.53 0.95 0.99 0.97 0.74 0.59 0.84 0.85 0.81 0.79 0.62 0.74 0.74 0.88 0.52 0.66 0.72

1983 1985 1986 1979 1981 1983 1980 1983 1990 1997 2006 1985 1981 1979 1986 1981 1996 1981 1981 1985 1987 1993 1989 1996 1985 1982 1981 1986 1980 1986 1982 1986 2006 1998 1980 1987 1987 1982 1985 1980 1995 1981 1981 1987

1995 1995 2003 1988 1993 1994 1983 1997 1996 2000 … 2005 1998 1983 1991 1998 2000 1994 1993 1996 1997 2004 1992 1999 2001 1995 1996 2006 1999 1989 1998 2005 … 2007 1995 2000 2001 1999 2006 1990 1999 1994 1993 2004

6 3 6 2 5 8 7 5 7 6 1 6 3 3 7 8 1 3 8 7 5 7 7 1 4 4 0 7 8 0 7 1 7 8 6 4 8 1 5 3 0 3 7 1

5.377*** 6.928*** 5.700***

10.839*** 10.628*** 5.726****

0.23 0.42 0.92

1999 1982 1994

2006 1999 2003

7 8 7

5.104***

4.896***

0.68

1980

2000

5

Notes: The sample period is 1970–2014, as in our analysis. b k stands for optimum b B1 and T b B2 stand for break period one and b B indicates the break periods. T lag. T

two, respectively. τLM and τRALSLM denote the test statistics for LM and RALS-LM tests. LM and RALS-LM are invariant to the break periods. ***, **, and * show 2

1%, 5%, and 10% significance levels. b ρ reflects the relative ratio of the variances of two error terms. The asymptotic critical values (CVs) for LM and RALS-LM are given in Meng et al. (2014). The same CVs can be used irrespective of number of breaks in the series, since RALS-LM test statistics are not based on break location coefficients. The LM and RAS-LM test statistics are significant for most countries and regions with two breaks. This implies that we reject the null of a unit root. Thus, our results confirm that the developing countries are converging to developed countries in TFP subject to the presence of two breaks in the data series. Similarly, the results show that developing countries as a whole and the other three regions (Africa, Asia, and Latin America and the Caribbean) are also converging to the developed countries, subject to the presence of two breaks in the data series.

7 The speed of convergence is estimated through b ¼ 2α and where b is a scaled estimator. 8 We do not plot the transition paths for other regions, because there is no evidence of club convergence.

9

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

Panel F. Plot of actual and adjusted series with breaks. From Panel C, we observe that the break date(s) coincide with actual series (black lines). Source: Authors’ own calculation based on WTFP data.

Again, we apply the PS approach, which forms the clubs through clustering algorithms. The PS results are reported in Table 4. The speed of convergence for developing countries is 1.41. However, the speed of convergence differs little from TFP, which is based on the T€ ornqvist quantity index due to a different measure. We also note that the Asian countries are catching up to advanced countries with higher speed (that is, 1.86 as compared to other regions). The moderate speed of convergence is found for Latin America and the Caribbean region (that is, 1.14) and the lowest speed of productivity convergence is noted in the African region (that is, 0.28). Overall, our results are consistent irrespective of the productivity index used. Finally, we apply the PS approach for WTFP to validate our results obtained from TFP based on the T€ ornqvist quantity index for the full sample, which comprises a total of 73 countries (44 developing and 29 OECD countries). The PS results reported in Table 7 indicate that the critical value (1.65) is higher than the calculated log(t) value (that is, 1.88). Thus, the null of convergence is rejected in the case of the full sample. This infers using clustering algorithms to find evidence of club convergence. Similar to the TFP results, we again note that majority of countries are in club 1 (see Table 7). There are only two countries in club 2, China and Sri Lanka. We also find a group in which Iraq is the only country that does not converge. There is also no evidence of club merging in the case of WTFP. To summarize, our results are robust irrespective of the productivity measures used. Further, we plot the club 1 and club 2 relative transition paths of WTFP series in Panel E. Again, we observe a distinct transition pattern of WTFP series for each club. Club 1 is almost equal to unity because it comprises the majority of countries. Similarly, club 2 falls below club 1 and follows an increasing trend. These findings support evidence for two distinct clubs.

Table 7 Club convergence of a full set of countries for WTFP. Clubs

Countries

b-Coefficient [log t-Stat]

Full samples Club 1

All countries

2.25 [-1.88]

Australia, Austria, Bahrain, Barbados, Belgium, Bolivia, Brazil, Burkina Faso, Cameroon, Canada, Chile, Colombia, Costa Rica, C^ ote d’Ivoire, Denmark, Ecuador, Egypt, Finland, France, Germany, Greece, Honduras, Hong Kong Iran, Korea Hungary, Iceland, India, Indonesia, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Kuwait, Luxembourg, Malaysia, Mauritania, Mexico, Morocco, Mozambique, the Netherlands, New Zealand, Niger, Nigeria, Norway, Panama, Paraguay, Peru, Philippines, Poland, Portugal, Qatar, Senegal, Singapore, South Africa, Spain, Sudan, Sweden, Switzerland, Saudi Arabia, Thailand, Tunisia, Turkey, United States, Uruguay, Venezuela, United Kingdom China, Sri Lanka Iraq

2.32**[-1.49]

Club 2 Group Merge Club 1 þ 2 Group

2.23**[-1.487] … 2.232 [-1.670] 4.502 [-2.816]

Notes: The critical value is 1.65 at the 5% level of significance. **Indicates the 5% level of significance. b stands for coefficients, and log t-Stat indicates the log t-statistics. Log t-stat values are given in square brackets. This table presents club convergence using the TFP series. The results indicate the absence of productivity convergence for the full sample. The clustering algorithm is applied as suggested by PS to identify the clubs. The results demonstrate three clubs. Club 1 consists of the majority of countries, unlike club 2. The results show a group that is not converging. This group includes only one country, Iraq. There is no evidence showing smaller clubs merging into larger clubs. 10

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx

5. Conclusions

TFP, which can be attained through boosting R&D and openness (as knowledge spillover and technology diffusion), to become more competitive and to catch up to rich countries. Second, findings from the speed of convergence suggest that, though African countries are catching up to OECD countries, this region needs to improve its technological progress to further boost productivity growth. Third, the developing countries in the Asia region should maintain their development process through attracting more FDI inflows, which essentially encourages technological capability through transfer or import of technologies from developed countries, thereby enhancing TFP. Finally, findings from the PS test for the full sample (OECD and developing countries together) suggest that club-specific policy should be taken into account to achieve overall TFP convergence in the long run.

Although a wide range of studies examines productivity convergence, this paper re-examines this issue by employing the LM and RALS-LM unit root test and PS panel club convergence approach. This study uses annual data from 44 developing and 29 OECD countries covering the period 1970–2014. Our findings can be summarized as follows. First, we find evidence of TFP convergence for developing countries. This means that each of the developing countries in our sample, except Kenya, shows a tendency to converge in TFP with the average TFP of OECD countries. Further, we note that the two break points are significant for 42 out of 44 developing countries. Second, apart from the individual countries, we also note evidence of TFP convergence for Africa, Asia, and the Latin America and Caribbean regions. Third, we test the speed of TFP convergence for Africa, Asia, Latin America and the Caribbean, and for all 44 developing countries as a group by employing the PS panel club convergence method. Our results show that the speed of convergence for overall developing countries as a group is 0.12. Further, our results reveal that the speed of productivity convergence in the case of Asia is higher compared to other regions. We also check the robustness of our results using an alternative measure of WTFP. The results remain similar to our initial results (that is, TFP based on T€ ornqvist quantity index). However, the speed of convergence differs slightly due to different measures. Our findings offer the following policy insights. First, a developing country like Kenya should be more concerned about improvement in

Acknowledgments The authors gratefully acknowledge the suggestions of the editor and anonymous referees on an earlier draft of this paper. The earlier draft of this paper was presented at the 7th Applied Financial Modelling Conference, Melbourne. The first author acknowledges the comments and suggestions of Prof. Yaobo Shi and other participants. The authors also acknowledges the help from Dr. Vindo Mishra and Dr. Kerui Du for sharing LM & RALS-LM unit root tests and Phillips and Sul club convergence estimation codes, respectively.The usual disclaimer applies.

Appendix B. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.econmod.2019.08.002. Appendix A

Classification of countries Developing countries

OECD countries

Africa region

Asia region

Latin America and the Caribbean regions

Bahrain, Barbados, Bolivia, Brazil, Burkina Faso, Cameroon, China, Chile, Hong Kong, Colombia, Costa Rica, C^ ote d’Ivoire, Ecuador, Egypt, Honduras, India, Indonesia, Iraq, Iran, Jamaica, Jordan, Kenya, Kuwait, Malaysia, Mauritania, Morocco, Mozambique, Niger, Nigeria, Panama, Paraguay, Peru, Philippines, Qatar, Saudi, Arabia, Senegal, Singapore, South Africa, Sri Lanka, Sudan, Thailand, Tunisia, Uruguay, Venezuela

Australia, Austria Belgium, Canada, Denmark, Finland France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Luxembourg, Mexico, the Netherlands, New Zealand, Norway, Poland, Portugal Korea, Spain, Sweden, Switzerland, Turkey, United Kingdom, United States

Cameroon, C^ ote d’Ivoire Egypt, Kenya, Mauritania, Morocco, Mozambique, Niger, Nigeria, Senegal, South Africa, Sudan, Tunisia

Bahrain, China, Hong Kong SAR, India Indonesia, Iraq, Iran, Jordan, Kuwait, Malaysia, Philippines, Qatar, Saudi Arabia, Singapore, Sri Lanka, Thailand

Barbados, Bolivia, Brazil, Chile, Colombia Costa, Rica, Ecuador, Honduras, Jamaica, Panama, Paraguay, Peru, Uruguay, Venezuela,

De Long, J.B., 1988. Productivity growth, convergence, and welfare: comment. Am. Econ. Rev. 78, 1138–1154. Evans, P., Karras, G., 1996. Convergence revisited. J. Monet. Econ. 37, 249–265. Feenstra, R.C., Robert, I., Marcel, P.T., 2015. The next generation of the Penn world table. Am. Econ. Rev. 105, 3150–3182. Im, K.S., Schmidt, P., 2008. More efficient estimation under non-normality when higher moments do not depend on the regressors, using residual augmented least squares. J. Econ. 144, 219–233. Jones, C.I., 1997. Convergence revisited. J. Econ. Growth 2, 131–153. Kijek, A., Kijek, T., Nowak, A., Skrzypek, A., 2019. Productivity and its convergence in agriculture in new and old European Union member states. Agric. Econ. 65, 01–09. Lee, J., Strazicich, M.C., Meng, M., 2012. Two-step LM unit root tests with trend breaks. J. Stat. Econom. Methods 1, 81–107. Lee, K., Pesaran, M.H., Smith, R., 1997. Growth and convergence in multi-country empirical stochastic Solow model. J. Appl. Econom. 12, 357–392. Madsen, J.B., 2007. Technology spillover through trade and TFP convergence: 135 years of evidence for the OECD countries. J. Int. Econ. 72, 464–480. Maryam, K., Jehan, Z., 2018. Total factor productivity convergence in developing countries: role of technology diffusion. S. Afr. J. Econ. 86, 125–267.

References Apergis, N., Christou, C., 2016. Energy productivity convergence: new evidence from club converging. Appl. Econ. Lett. 23, 142–145. Barro, R.J., Sala-i-Martin, Xavier, 1992. Convergence. J. Political Econ. 100, 223–251. Barro, R.J., Sala-i-Martin, Xavier, 1997. Technological diffusion, convergence, and growth. J. Econ. Growth 2, 1–26. Baumol, W.J., 1986. Productivity growth, convergence, and welfare: what the long run data show. Am. Econ. Rev. 76, 1072–1085. Baumol, W.J., Wolff, E.N., 1988. Productivity growth, convergence, and welfare: Reply. Am. Econ. Rev. 78, 1155–1159. Bernard, A.B., Charles, I.J., 1996. Productivity across industries and countries: time Series theory and evidence. Rev. Econ. Stat. 78, 135–146. Bernard, A., Durlauf, S., 1995. Interpreting tests of the convergence hypothesis. J. Econom. 71, 161–173. Bournakis, I., Mallick, S., 2018. TFP estimation at firm level: the fiscal aspect of productivity convergence in the UK. Econ. Modell. 70, 579–590. Burda, M.C., Severgnini, B., 2018. Total factor productivity convergence in German states since reunification: evidence and explanations. J. Comp. Econ. 46, 192–211.

11

B.N. Rath, V. Akram

Economic Modelling xxx (xxxx) xxx Phillips, P.C.B., Sul, D., 2007. Transition modeling and econometric convergence tests. Econometrica 75 (6), 1771–1855. Quah, D., 1996. Twin peaks: growth and convergence in models of distribution dynamics. Econ. J. 106, 1045–1055. Rath, B.N., 2019. Does total factor productivity converge among ASEAN countries? Bull. Monetary Econ. Bank. 21 (special issue), 477–494. Surjaningsih, N., Permono, B.P., 2014. The dynamics of total factor productivity of medium and large manufacturing in Indonesia. Bull. Monetary Econ. Bank. 16, 277–308.

Meng, M.K., Im, J., Lee, M., Tieslau, 2014. More powerful LM unit root tests with nonnormal errors. In: Sickles, R., Horrace, W. (Eds.), The Festschrift in Honor of Peter Schmidt, vols. 343–357. Springer Publishing Co, Berlin, Germany. Miller, S.,F., Upadhyay, M.,P., 2002. Total factor productivity and the convergence hypothesis. J. Macroecon. 24, 267–286. Mishra, V., Smyth, R., 2017. Conditional convergence in Australia’s energy consumption at sector level. Energy Econ. 62, 396–403. Oulton, N., 2017. Effects of financial crises on productivity, capital and employment. Rev. Income Wealth 63, S90–S112.

12