**by L Pan · 2017 · Cited by 8 — where in our case per capita energy consumption or its catch-up rate of individual fixed effects and/or an individual specific time-trend, and second, the test /wp-content/uploads/2016/07/AGIFinancingAfricanInfrastructure_FinalWebv2.pdf **

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monash.edu/ business – economics ABN 12 377 614 012 CRICOS Provider No. 00008C Department of Economics ISSN number 1441 – 5429 Discussion number 16 /17 Stochastic convergence in per capita energy consumption and its catch – up rate: Evidence from 26 African countries Lei Pan * & Svetlana Maslyuk – Escobedo Abstract Using annual data from 1971 to 2014 , we examine stochastic conditional convergence in per capita energy consumption and its catch – up rate for 26 low income, lower middle income and upper middle income African countries . To do so, we use a battery of conventional panel unit root tests, panel tests that allow for cross – sectional dependence and structural breaks as well as the recently developed univariate RALS – LM unit root test with structural brea ks. Although for most countries we find evidence in support of stochastic conditional convergence, we find divergence for four countries including DR Congo, Senegal, Egypt and Botswana. The per capita energy consumption in Africa is growing faster than tha t of other countries, driven by improved infrastructure and inward investment from China. Over time, as regional energy consumption disparity narrows, we find African countries will catch up to China. This catching up effect will l energy demand in the future. Keywords: energy consumption, catch – up rate, stochastic convergence , unit roots, cross – sectional dependence, structural breaks JEL Classification : C12, O40, O43 * Corresponding author. Department of Economics Monash University 900 Dandenong Road, Caulfield East, Vic, 3145, Australia Email: lei.pan@monash.edu School of Education and Arts Australian Catholic University 34 Brunswick St, Fitzroy, Vic, 3065, Australia Email: Svetlana.Maslyuk@acu.edu.au T he authors are grateful to Jinyue Yan and Mita Bhattacharya for their helpful comments and suggestions on the earlier versions of this paper. Lei would like to thank Prof. Vinod Mishra for sharing the codes of Pesaran (2004) cross – sectional dependence test and Pesaran (2007) CIPS unit root tests used in this study. All errors are our own. © 201 7 Lei Pan & Svetlana Maslyuk – Escobedo All rights reserved. No part of this paper may be reproduced in any form, or stored in a retrieval system, without the prior written permission of the author.

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2 1. I n troduction Over the past 60 years, the African continent enjoyed poor income growth together with high and persistent population growth (Khan, 2014, p. 354). Lack of economic performance can be attributed to the colonial past, poor governance and corruption, insuffic ient investment in human capital (in particular, education and health), civil wars and regional conflicts. Many African economies recognised the need for a change and, due to prudential macroeconomic policies and favourable external factors between 2000 an d the Global Financial Crisis (hereafter GFC) , African countries were growing on average at 5% or more per year ( African Development Bank (ADR), 2009 ). Since many African economies rely heavily on agriculture , limited manufacturing and extractive industries (Anoruo, 2014), they would require industrialisation which is impossible without an increase in energy consumption. Do energy consumption per capita levels among African nations converge towards a common level? Do energy consumpt ion levels in low income and middle income African countries catch – up rate with those in China, an economy that grew from an agrarian state with limited manufacturing in the 1960s to a rapidly growing middle income economy? What are the important events (i .e. structural breaks) that affected the energy consumption path of African economies? This paper strives to answer these questions for 26 countries from the African continent (mainly North Africa and South Africa) from 1971 to 2014 using advanced recent panel and univariate tests for stochastic conditional convergence. There are several types of convergence in the literature including absolute, club and conditional convergence 1 . In this paper, we focus on stochastic convergence , which is consistent with the conditional convergence hypothesis (Strazicich et al., 2004). Stochastic conditional convergence allows understanding the impact of shocks on the trajectory of e to the group average is stationary, this is interpreted as the sign of convergence towards the group average (Fallahi, 2017), which implies that the impact of various shocks to energy consumption would be temporary in nature. Otherwise, the impact of sho cks to energy consumption would have permanent effects . In addition to stochastic convergence, we analyse catch – up rate or the rate with which African nations can be potentially converging the level of a rapidly developing country (China). This allows for an understanding of how a relatively higher income. Studying stochastic conditional convergence in energy consumption is important for several reason s. First , because per capita energy consumption in addition to GDP per capita is one of the most commonly used measures of welfare (see for example Mohammadi and Ram, 2012; Meng et al. , 2013) , studying stochastic conditional convergence will allow an under standing of the impact of shocks to energy consumption. Since the current structure of African economies makes them very vulnerable to external and internal shocks, this has important implications from economic and environmental policy standpoints for each country in the sample. Second , in addition to being a vital input in the production of goods and services , energy consumption is the major contributor to human development. Currently, many African 1 Galor (1996) defined 3 types of hypotheses on convergence. They are the absolute convergenc e hypothesis, where in our case per capita energy consumption or its catch – up rate of countries (or regions) converge to one another in the long – run, regardless of their initial conditions; the club convergence hypothesis, where per capita energy consumpti on or the catch – up rate are the same in their structural characteristics and in the long – run converge to one another, given their similar initial conditions; the conditional convergence hypothesis, where per capita energy consumption or its catch – up rate a re the same in their structural characteristics and in the long – run converge to one another, regardless of their initial conditions.

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3 countries, especially in Sub – Saharan Africa, experience en ergy poverty that serves as an additional obstacle to economic development. Third , when formulating realistic targets for regional growth and greenhouse gas emissions, both domestic and global policy makers need to understand the path of convergence betwee n less and more developed countries. Given the energy availability constraints (e.g. predominant use of non – renewable fossil fuels such as coal and petroleum ( Anoruo, 2014 ) and limited involvement of renewables into the energy mix in Africa), poor access t o essential energy services and infrastructure, uncertain geopolitical situations, convergence in energy consumption (and potentially economic growth) and catching up with other developing nations, such as China and potentially developed nations, could be even more difficult for African countries. Studying convergence is not new and was investigated mostly for developed countries and some emerging nations (see Table 1 below). Recent trends in the literature include analysing large panels of data containi ng both developing and developed countries ( Fallahi, 2017) as well as analysis of states within the same country (Mohammadi and Ram, 2017; Payne et al., 2017, Herreiras et al. 2017 ) or specific sectors of individual countries (Lean et al., 2016; Mishra and Smyth, 2017). The consensus among such studies is convergence in energy consumption per capita (see for example Meng et al., 2013; Payne et al., 2017). However, convergence levels of the developed and developing countries are not directly comparable and d epend on the choice of the reference time frame with different initial conditions, prior history as well as the previous economic successes ( Sy, 2016, p. 4 – 5). The fact that literature has largely ignored the issue of energy consumption for African nations represents a significant gap because Africa represents an important case from the economic development perspective . Despite the efforts of regional integrati on, there is significant variation in per capita energy consumption among countries, access to essential energy infrastructure as well as the cost of energy. According to Oyuke et al. (2016 ), two major problems that affect these nations are the rolling bla ckouts (North Africa) and complete lack of essential electricity infrastructure (Sub – Saharan Africa). At the same time, the African continent has vast energy endowments (both renewable and non – renewable energy) which are not evenly distributed among countr ies (International Energy Agency (IEA), 2014). Together with the lack of essential infrastructure to generate and consume energy this crea t es significant energy poverty for some countries , especially the ones in Sub – Saharan Africa. For example, in Sub – Saha ran Africa , as a whole, of the 915 million people only 290 million (or 25.13%) have access to electricity (IEA, 2014, p. 13) . Because 80% of those 600 million people without access to electricity live in rural areas, which are either financially or logisti cally problematic for the grid expansion, there is a stunning difference between rural and urban electrification rates (14.3% vs 59% , respectively) . This is different from North Africa where more than 90% of the population ha s access to electricity ( Oyuke et al. , 2016 ) but which suffers from blackouts and irregularities in supply ( Oyuke et al. , 2016). In addition to these issues of poor reliability and access to energy, the World Bank (2017) lists the high cost of energy as an additional key factor that aff today. For instance, in Sub – Saharan Africa the average electricity tariff is US$0.14 while in other developing countries energy tariffs range from US$0.04 to US$0.08 2 . 2 refer to the website of the World Bank: http://web.worldbank.org/WBSITE/EXTERNAL/COUNTRIES/AFRICAEXT/0,,contentMDK:219355 94~page PK:146736~piPK:146830~theSitePK:258644,00.html

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4 This paper makes the following contribution to the litera ture. First, this paper focuses on Sub – Saharan and North Africa; the former is a region with extreme energy poverty and the latter is a region with large scale access to unreliable electricity resources. Focusing solely on Africa allows us to obtain more r obust results as compared to previous panel studies which investigated both developed and developing countries together. Understanding African energy consumption dynamics is crucial as energy consumption is closely linked with environment, poverty and econ omic growth on the continent. Since there is a close relationship between energy consumption and economic growth (see for example: Yuan et al, 2008; Ozturk et al, 2010; Tsani, 2017; Belke et al, 2011), we split the sample into low income, lower middle inco me and upper middle income levels based on the income levels classification proposed by the World Bank 3 . S econd, due to the convergence findings in the majority of the existing studies for high income and other developing non – African nations, the implications for potential divergence in energy consumption largely have been ignored in the literature. In fact, several studies have found divergence in income levels in Africa ( Djennas and Ferouani, 2014; Ra njbar, et al., 2014 ) which could be potentially linked to divergence in energy consumption . Given substantial heterogeneities between countries in the sample, including significant spread in access to energy resources, disparities in energy infrastructure, historical conditions (some of the nations have colonial background), government issues including wide – spread c orrupt ion, civil wars, and terms of trade shocks, we should expect to find divergence in energy consumption for some African countries. Divergen ce in energy consumption indicates that an adverse supply shock to these economies will have a permanent macroeconomic effect, such as lower productivity, lower output and high unemployment that may further exacerbate poverty. The present study fills this gap by providing policy implications for divergence in energy consumption which are ignored in the previous studies. Third, we investigate stochastic convergence among per capita energy consumption by adopting the Pesaran (2007) cross – sectionally augmen ted IPS (CIPS) panel unit root tests as well as the Carrion – i – Silvestre et al. (2005) panel KPSS unit root tests that allow multiple (up to five) structural breaks which are endogenously determined in the data. This enables us to reject a false unit root n ull hypothesis unambiguously . The advantage of CIPS is that it controls for cross – sectional dependence of the errors. It is particularly appropriate to use African data as it is reasonable to expect that economic, political and cultural inter – relationships can lead to cross – country correlations that will affect our results. Carrion – i – Silvestre et al. (2005) panel KPSS test has the following advantages: first, it includes individual fixed effects and/or an individual specific time – trend , and second , the test allows for multiple structural breaks that may potentially appear at different unknown dates in addition to varying numbers of breaks for each individual panel member. It should also be noted that convergence results given by the conventional pa nel unit root tests without structural breaks might not be reliable. To check the robustness of our results we use the recently developed Residual Augmented Least Squares – Lagrange multiplier (RALS – LM) unit root test by Meng et al. (2014). As compared to ot her tests, RALS – LM tests allow for trend 3 World Bank categorizes all countries into four groups based on their income levels. For the current 2018 fiscal year, low – income economies are those with a GNI per capita, calculated using the World B ank Atlas method , of $1,005 or less in 2016; lower middle – income economies are those countries with a GNI per capita between $1,006 and $3,955; upper middle – income economies are those with a GNI per capita between $3,956 and $12,235; high – income economies are those with a GNI per capita of $12,236 or more.

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5 breaks under the null hypothesis and utilize information on non – normal error terms making them superior to non – linear tests which tend to perform poorly when faced with non – normal errors ( Meng et al. , 2014 ). Fourth, in addition to investigating stochastic convergence, we estimate the catch – up rate between per capita energy consumption in African countries with per capita energy consumption in China. China was chosen for this analysis for two reasons: First, it represents a development path from an agrarian economy with limited manufacturing and significant extractive resources (the situation that many of the poorest African countries are in currently) to a post – industrial society in a relatively short period of time. Second, over the past decades, China has become the leading financier of global infrastructure, particularly in the African continent. A report from the Brookings Institution 4 showed that between 2009 and 2012, China was the single largest infrast ructure financier in 11 African nations. China doubled its effort in Africa in December 2015, pledging an additional $60 billion in aid. Furthermore, the recently developed Asian Infrastructure Investment Bank (AIIB) is an extraordinary initiative to finan ce infrastructure projects in the developing world. The remainder of the paper is organized as follows. Section 2 presents a brief review of related studies. In Section 3, we discuss the data. Section 4 is devoted to the framework used for catch – up rate. Section 5 presents the empirical methodology used in this study. Section 6 reports findings, section 7 interprets the break dates. Section 8 provides discussion of results and policy implications, and Section 9 concludes the paper. 2. Literature Review The work on examining stationarity and integration properties of energy variables is pioneered by Narayan and Smyth (2007). Since then, the literature has flourished with testing a unit root in energy consumption as the preliminary analysis to identif ying long – run relati onship and causality patterns between energy, economic growth and other variables of interest. Based on the methodologies used, the existing studies on conditional stochastic convergence in per capita energy consumption can be classi fied into four broad sets. The first one consists of studies applying univariate unit root tests such as conventional Augmented Dickey Fuller (ADF) and Phillips Perron (PP) unit root tests. For instance, applying the ADF unit root test to annual energy con sumption data from 1979 to 2010 for 182 countries, Narayan and Smyth (2007) found energy consumption was convergent for 31 percent of their sample. Nonetheless, the classical univariate unit root tests have several limitations which make them not sufficien tly reliable. First, the ADF test is likely to provide a biased result in the presence of structural breaks. Second, the ADF and PP test series are linear, hence, they have low power to reject the unit root null if the data process is non – linear. For these reasons, the literature on stochastic conditional convergence has moved to unit root tests with structural breaks (second set), panel unit root tests (third set) and non – linear unit root tests (fourth set). 4 Refer : Gutman, J., Sy, A. & Chattopadhyay, S. (2015). Financial African I nfrastructure : Can the world deliver? available at: https://www.brookings.edu/wp – content/uploads/2016/07/AGIFinancingAfrica nInfrastructure_FinalWebv2.pdf

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6 The second stream of conditional convergence literature (such as Lee and Strazicich , 2003; Narayan and Popp, 2010) employed univariate unit root tests with structural breaks to address non – rejection of unit root null hypothesis due to failure to consider structural breaks in the data. Most studies f ound energy consumption is stationary around a broken trend (see for example: Apergis and Payne, 2010; Narayan et al., 2010). Moreover, Mishra and Smyth (2014) when testing convergence in energy consumption per capita in the ASEAN – 5 between 1971 and 2011 f ound mixed evidence of convergence with univariate tests with breaks. While earlier studies utilised country – level data at low frequency, more recent studies concentrate on examining the convergence issue at the sector or organization level (Lean et al., 2 016; Mishra and Smyth, 2017). For example, using annual energy consumption per capita data at the sector level in Australia over the period 1973 – 74 to 2013 – 14, Mishra and Smyth (2017) found evidence of convergence in energy consumption in six of seven indu stry sectors in Australia. The third set of studies applied non – linear stationarity tests to avoid the drawbacks of the ADF and PP tests discussed earlier. As shown by Hasanov and Telatar (2011) and Alper and Hakan (2011), energy variables can be potent ially non – linear in mean. For example , Öztürk and Aslan (2015) studied stationary properties of per capita electricity consumption by employing a non – countries from 1960 to 2005. They found non – linear behaviour in electricity consumption for 70% of the OECD countries. Moreover, for electricity consumption was found to be a non – stationary process for 12 countries. While earlier studies focused on individual countries, studies utilisin g panel data (either large panels of countries or state – level) with or without structural breaks have emerged to overcome shortcomings of conventional univariate unit root tests. Studies that employed panel unit root tests without breaks provide mixed stat ionarity results (see for example: Agnolucci and Venn, 2011; Shahbaz et al., 2016) , while studies that applied panel unit root tests with breaks are unanimous in support ing stochastic convergence in energy consumption , which implies that the impact of shoc ks on energy consumption is likely to be temporary (see for example: Mishra and Smyth, 2014; Acaravci and Erdogan, 2016). A summary of recent li terature is presented in Table 1 to conserve space. In relation to Africa, despite Anorou and DiPietro (2014) a nd Fallahi (2017), there was very limited work on per capita energy consumption convergence among countries from the African continent , and to the best of our knowledge no literature had previously examined the catch – up rate between energy consumption of A frican countries and China . Using conventional panel unit root tests for 22 African countries, Anorou and DiPietro (2014) found that per capita energy consumption series have converged as a group, meaning that shocks to energy consumption were temporary an d mean reverting. However, once they introduced Sequential Panel Selection Zimbabwe, Morocco and Togo) energy consumption paths appeared to be diverging from the group a verage. The SPSMS was criticized by Costantini and L upi (2014) using Monte Carlo simulations and based on generating the individual test statistics and the p – values to be combined into panel stationarity tests, they examined the reliability of SPSMS under both the unit root null and the selected local alternatives. Their analysis showed that SPSMS does not perform better than the traditional time series unit r oot tests. Other studies such as Fallahi (2017) consider African energy consumption convergence but only as a part of the larger

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8 ) (1) where stands for the average energy consumption per capita for eac h specific economy in the sample. The main purpose of transforming the data is to ensure cross – sectional independence by removing common shocks that can influence all countries in the sample. Specifically, any negative shocks to the energy consumption acro ss all countries will reduce the average energy consumption amount by the same proportion , hence the relative energy consumption remains constant and the structural breaks identified in the transformed series will be country specific. 4 . Catch – up rate fra mework The theoretical foundation of the catch – up hypothesis can be traced to the neoclassical Solow – Swan model. Following Solow (1956) and Barro and Sala – i – Martin (1991), real per capita incomes are inversely related to the initial income levels corresp onding to the early stages of development. This implies poorer countries tend to grow faster than the richer countries and can potentially over time catch – up with the income levels of richer nations. Since energy use is an important factor in growing incom e, the hypothesis of the catch – up rate in energy consumption (consistent with the neoclassical growth models) would imply that African nations that have low per capita energy consumption levels should grow their energy consumption faster (i.e. catch – up) th an China, which is not yet a developed country but until recently has been growing rapidly. Since the market reforms started in 1978, China has transformed from a centrally planned to a market – based economy. Its annual GDP growth has averaged nearly 10 per cent, which is the fastest sustained economic expansion by a major economy in history, and has helped more than 800 million people out of poverty 6 . China had undergone rapid industrialization also. China is now the second largest economy in the world and is increasingly playing a significant role in global economic development. Post GFC China has been the largest contributor to world economic growth. Yet, China remains a developing country and market reforms are incomplete. The rapid economic growth also b rought many challenges to China which include: rapid urbanization, environmental sustainability, high income inequality, and so on. Hence, China needs significant policy adjustments to achieve sustainable economic growth which would require changes in its energy mix towards renewable energy. This would suggest that shifting from a middle income to a high income country can be far more difficult than transitioning from a low income to a middle income country. In this study, we use the Barro and Sala – i – Mart in (2004) approximation as a framework for calculating the energy consumption catch – up rate. The approximation is as follows: D ( log – log ) = ( log – log ) (2) where is per capita energy consumption, denotes the steady – state value of , D ( log – log ) refers to the growth rate of log – log and is a negative parameter. If log – log 0 current per capita energy consumption is less than its steady – state value, resulting in D ( log – log ) 0 since 0. 6 Refer to the World Bank website: http://www.worldbank.org/en/country/china/overview

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9 In this paper, is proxied by the per capita energy consumption in China. We define = log ( / ) where is the per capita energy consumption of country i in year t and represents the per capita energy consumption of China. Eq. (2) shows that should be stationary, and perhaps with a broken trend. Figures 2 and 3 show the evolution of the catch – up rate and the catch – up growth rate respectively. One can see that over time the difference between the energy consumption per capita in African countries has been reducing as compared to energy consumption in Chin a. That is, over the time, there is a tendency for African nations to catch – up with the energy consumption levels of China. Over the past few years, China has rapidly become the number one country in global energy demand. The US EIA reported that China sur passed the US at consumption 7 . Figure 3 shows that for low and upper middle inco me catch – up growth rates were very volatile over time. For some low income economies, the growth rates became bigger towards the end of the sample period. For the upper middle income countries, catch – up growth rates were relatively stable over time and les s volatile as compared to the low and lower middle income nations. However, the exception was Libya where growth rates have tanked post 2010, which is the reflection of the on – going war. [ Insert Figure 2 & Figure 3 Here] 5. Econometric Methodology In this paper, we use a wide range of recent conventional panel unit root tests as well as the panel unit root tests with structural breaks to investigate the stochastic convergence of per capita energy consumption and its catch – up rate. Panel unit root tests are considered to be more powerful than time series unit root tests because they combine information from both time series and cross – sectional dimensions. In this paper, we utilise two conventional panel tests without structural breaks (Levin et al. (2002) (LLC hereafter), Hadri (2000) panel LM tests root test) that will serve as a benchmark for panel analysis. Results of these tests are presented in the Appendix. If the cross – sectional dependence is found in the data, then the conventional panel unit root tests without structural breaks will have large size distortions (see Maddala and Wu, 1999; Banerjee et al., 2005). To examine whether the transformation has removed the cross – sectional dependence in our panel, following Pesaran (2004) we estimate in dividual ADF( p ) regressions for lag length ( p ) = 1, 2, 3 and 4 and calculate pair – wise cross – section correlation coefficients of the residuals from these regressions (namely ). If the cross – sectional dependence is found to be present in the data, we employ the Pesaran (2007) CIPS panel unit test. Another potential problem of the conventional panel unit root tests is that these tests do not consider potential structural breaks in the data, which can lead to erroneous results. According to Bacon and Mat tar (2005), African countries are particularly sensitive to shocks such as the oil crisis due to the low energy intensity in Africa, inefficient energy supply mix (despite significant potential for renewable energy resources including solar, wind and hydro ) and dependence on imported oil as the primary energy source for many countries. To avoid such a result in this paper, we use the Carrion – i – Silvestre 7 R efer the EIA website: https://www.eia.gov/beta/international/analysis.cfm?iso=CHN

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10 et al. (2005) panel KPSS unit root test with multiple structural breaks for the whole panel as well as in dividual countries. Furthermore, we adopt the recently developed univariate RALS – LM unit root test by Meng et al. (2014) as a robustness check . The test has improved power with non – normal errors and is robust to some forms of non – linearity (Meng et al., 20 13). By applying the RALS – LM unit root test, we are able to remove the dependency of the test statistic on nuisance parameters that many endogenous break unit root tests have. 5.1 Carrion – i – Silvestre et al. (2005) panel KPSS unit root test with multiple b reaks This test has a null hypothesis of stationarity which addresses the criticism by Bai and Ng (2004) that it is more natural to take stationarity than non – stationarity as the null hypothesis for most economic applications. The Carrion – i – Silvestre et al. ( 2005 ) panel KPSS test model specification is as follows : = + D + t + D + (3) where is the relative energy consumption per capita in country i at time t ; t T which stands for time period and i = 1,.., N represents number of panel members and is the error term. D and D are dummy variables defined as D = 1 for t > otherwise 0, and D = t – for t > otherwise 0. The term stands for the k th date of the break for the i th individual where k }, 1. Eq. (3) is the panel counterpart with structural breaks for the univariate framework. It allows for structural shifts in the trend of the individual series in the panel and permits each country in the panel to have a different number of breaks occurring at different dates in time. The (2000) panel unit root test, which is the average of the univariate Kwiatkowski et al. (1992) stationarity test. The test statistic is as follow s : LM( ) = ) (4) where = denotes the partial sum obtained from the OLS residuals of Eq. (4) , and is a consistent estimation for t he long run variance of residual w hich allows the heteroskedastic disturbance among cross – section al units. The test statistic for the null hypothesis of a stationary panel with multiple shifts unde r the cross – sectional independence assumption and t he distribution of the test statistic via bootstrap is as follow s : Z ( ) = N (0, 1) (5) where and are the averages of the individual means and variances of , respectively. According to Carrion – i – Silvestre (2005), estimation f or the number of structural breaks and their locations are based on the procedure developed by Bai and Perron (1998) that calculates total minimization of the sum of the squared residuals (SSR). The procedure and selection of

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11 the break dates are based on minimizing the sequence of individual SSR ( ) and is expressed as: ( ) = arg min SRR ) (6) In the present study, following Bai and Perron (2005), the number of breaks for each individual country is estimated using the modified Schwartz Information C riterion . Following the suggestions of Carrion – i – Silvestre (2005), we allowed five as the maximum number of breaks . Furthermore, we compute the finite sample critical values by Monte Carlo simulations with 2000 replications. Namely, we use bo otstrap techniques to approximate the empirical distribution of the panel dat a statistic to avoid cross – sectional independence assumption. 5 .2 RALS – LM unit root tests with structural breaks Before implementing the RALS – LM tests, we first identify whether breaks exist in the data , a nd if so, they should entail one or two breaks by applying the procedure developed by Perron and Yabu (2009) and Kejriwal and Perron (2010) . This makes our findings more reliable over the existing literature on convergenc e that employed stationarity test methodology that accounts for endogenous breaks in the trend function under the trend stationary alternative. If the series under consideration contains no breaks, this testing approach has lower power due to accounting fo r extraneous break dummies, hence leading researchers to suffer the model misspecification issue. The Perron and Yabu (2009) method is implemented first to test the null hypothesis of no breaks against the alternative hypothesis of one break. For those cou ntries where Perron and Yabu (2009) identified there is one break, the Kejriwal and Perron (2010) procedure is used to test the null of one break against the alternative of two breaks. This method helps us to verify the number of structural breaks for each country. Assume the following data generating process: = + t + , = + (7) The null hypothesis is = 1 against the alternative of < 1. The parameters and stand for the deterministic components of intercept and trend, respectively. The model can be written in a general form as follows: = + , = + (8) where is the deterministic terms including potential structural changes. For example, with an intercept, trend and R breaks, can be represented as [1, t , ], where = 1 for t + 1, j R and zero otherwise. The LM test statistic can be obtained by conducting the following regression: = + + + (9) where = - - , t T ; denotes the coefficient vectors of , is the restricted maximum likelihood estimate of , which equals - ; and refer to the first observation of and , respectively. The term represents the lagged differences
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