Labour market fluctuations: An RBC model for emerging countries

Coskun, Sevgi Article Labour market fluctuations: An RBC model for emerging countries Central Bank Review (CBR) Provided in Cooperation with: Central Bank of The Republic of Turkey, Ankara Suggested Citation: Coskun, Sevgi (2019) : Labour market fluctuations: An RBC model for emerging countries, Central Bank Review (CBR), ISSN 1303-0701, Elsevier, Amsterdam, Vol. 19, Iss. 4, pp. 141-153, https://doi.org/10.1016/j.cbrev.2019.11.002 This Version is available at: https://hdl.handle.net/10419/217339 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/ Labour market fluctuations: An RBC model for emerging countries * Sevgi Cos¸ kun Faculty of Economics and Administrative Sciences, Ardahan University, Turkey article info Article history: Received 9 August 2019 Received in revised form 25 October 2019 Accepted 17 November 2019 Available online 4 December 2019 JEL classification: E31 E32 E52 F41 O50 Keywords: Labour market Emerging market economies Real business cycle model Labour wedge abstract In this paper, we examine the labour market properties of business cycle fluctuations for a group of 15 emerging market economies (EMEs) and the US using annual data from 1970 to 2013. We find that on average, the hours worked and employment volatility (relative to output volatility) are lower, while the volatility of productivity and wages are 2e3 times higher in EMEs compared to the US. We then assess the performance of a standard RBC model and an augmented RBC model with capacity utilization, investment adjustment cost and indivisible labour with temporary and permanent productivity shocks to explain labour market facts observed in the data. We find that these models fail to explain labour market fluctuations in the business cycles of these countries, but the model with investment adjustment cost improves the performance of relative volatility of wages and hours, as well as the cyclicality of hours, compared to the standard RBC model. Lastly, we investigate the cyclical properties of the labour wedge and find that the total labour wedge (relative to output volatility) is more volatile over the business cycle in emerging economies (1.72) compared to the US (0.95). Further, fluctuations in the total labour wedge reflect the ones in the household component rather than the firm component of the wedge in EMEs and the US. ©2019 Central Bank of The Republic of Turkey. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). 1. Introduction In developed markets, the quantitative analysis of business cycle fluctuations has long been of interest to researchers since the work of Kydland and Prescott (1982). 1 It has been found that hours worked fluctuate more than productivity, as this is almost as volatile as output. Labour productivity and employment are more volatile than real wages. Such analysis is also an old issue for emerging market economies (EMEs), but it has only recently been revived within equilibrium business cycle models. It is well known in the relevant literature, where the frictionless real business cycle (RBC) model has received considerable attention as being incapable of replicating the second moments of labour market dynamics; however, it tends to perform well in explaining a good portion of aggregate fluctuations such as output, consumption and investment. 2 Most analyses have focused on developed countries, predominantly on the US, while other markets in the economy have remained unexplored. The aim of the paper is, first, to present the key labor market dynamics of business cycle fluctuations using annual data in EMEs and then to assess the performance of a standard RBC model and an augmented RBC model with capacity utilization, investment adjustment cost and indivisible labor with temporary and permanent productivity shocks to explain those facts. We lastly investigate the fluctuations of total labor wedge (the discrepancy between a representative household’s marginal rate of substitution between consumption and leisure and the marginal product of labour) by decomposing it into the household component of labor wedge and the firm component of labor wedge to explore which of these two component are mostly responsible for business cycle fluctuations of the total labor wedge in EMEs. * I am grateful to Miguel Leon Ledesma, Peter J. N. Sinclair, Mathan Satchi and audiences at the MMF Conference (Bath), EcoMod Conference (Lisbon), ICMAIF Conference (Crete) as well as seminar participations at Kent and two anonymous referees at the CBR for valuable comments and suggestions. E-mail address: [email protected]. Peer review under responsibility of the Central Bank of the Republic of Turkey. 1 See also Backus and Kehoe (1991),Stock and Watson (1999) and Ohanian and Raffo (2012). 2 These have then led to a whole branch of the literature addressing these problems by introducing matching frictions. See Christiano and Eichenbaum (1992), Hansen and Wright (1992),Fairise and Langot (1994) and Fiorito and Kollintzas (1994). These studies present some basic stylised facts of labour dynamics (such as productivity and hours worked) and find that the standard RBC model cannot account for these facts in the US and G7 countries. Contents lists available at ScienceDirect Central Bank Review journal homepage: http://www.journals.elsevier.com/central-bank-review/ https://doi.org/10.1016/j.cbrev.2019.11.002 1303-0701/©2019 Central Bank of The Republic of Turkey. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http:// creativecommons.org/licenses/by-nc-nd/4.0/). Central Bank Review 19 (2019) 141e153 The interest in this topic has been spurred on for several reasons. First, aggregate fluctuations in EMEs are different from those in developed countries. 3 For example, in emerging economies, output is twice as volatile as it is in developed countries, and, wages are highly volatile and pro-cyclical. Moreover, the variability of employment in emerging countries is about half the variability of output. 4 Second, EMEs have different labor market institutions and their market behaviour is substantially different compared to developed countries. For example; flexibility in contracts, employment protection, firing and hiring costs, and the unions in these countries are quite different from those in developed countries. Furthermore, EMEs have less wage rigidity, larger informal sectors and less social protection, unemployment benefits. 5 Because of these differences between EMEs and developed countries, their reaction to changes in the macroeconomic fluctuations will be different and this makes these countries a good benchmark to compare the models of business cycle fluctuations. That’swhy we are interested in labor market fluctuations of business cycles to know whether RBC models fit the features of these economies given that the institutions are different. Finally, the stylised facts of the labour market in EMEs are not as well known as those in developed countries, and there is no consensus on these economies. Agenor et al. (2000) and Male (2010) have pointed out that the results depend on which countries are included in the analysis, as Rand and Tarp (2002) have shown that the stylised facts of business cycles across emerging countries are more diverse than those of the developed countries. It is important to ensure that the stylised facts are as accurate as possible since they are a crucial basis for the construction of a model. We first systematically document some stylised facts of the labour market properties of the business cycle in EMEs for the period 1970e2013. Then we compare the results with available features of the business cycles in 15 emerging countries with the US. For this analysis, we use sufficient annual data (the sample lengths are long enough to measure business cycles) to provide an accurate picture of labour market properties of business cycle fluctuations. 6 The data we collected shows that the average volatility of wages and productivity relative to output volatility in emerging countries is about 2e3 times higher than that of the US. Moreover, fluctuations of the extensive margin (0.55) are mostly responsible for fluctuations in the total hours worked (0.64) in these economies, rather than fluctuations in the intensive margin (0.26). Another important finding of this study is that the correlations among employment, hours worked per employed and total hours worked with output in the US are much higher than in EMEs, whereas there are no significant differences in the cyclicality of real wages and productivity between emerging economies and the US. These results reveal that the labour markets in EMEs adjust more through prices, while the quantities are subdued. Motivated by these stylised facts, we then investigate whether a set of variants of the RBC model, with no nominal rigidities, can reproduce the labour market features observed in the data from emerging countries. We first look at the performance of the most standard frictionless RBC model as a benchmark model, driven solely by permanent and temporary productivity shocks, as in Aguiar and Gopinath (2007). In the data, we observe that the behaviour of labour market variables in emerging economies differ from each other. On average we find that a frictionless RBC model with temporary and permanent shocks does a good job of matching the relative volatility of hours worked in emerging countries; however, it fails to capture for the rest of the relevant moments in our analysis. In order to further improve the fit, we introduce an RBC model augmented with capacity utilization, as in Greenwood et al. (1988), investment adjustment costs, as in Christiano et al. (2005) and indivisible labour, as in Hansen (1985). 7 Burnside and Eichenbaum (1994) find that allowing for capacity utilization in RBC model magnifies and propagates the effects of the shocks over the business cycle. Our results show that this amplification allows an RBC model with this mechanism to generate hours volatility very similar to the data with much smaller shocks, whereas it decreases significantly the ability of the model to produce the relative volatility of wages and productivity for these economies, compared to the standard RBC model. In addition, we find that the RBC model with investment adjustment costs performs better than the simple RBC model for the relative volatility of wages and hours, and for the correlation between hours and output. This mechanism into the RBC model prevents investment quickly responding to change in economic conditions as it mitigates the effect of shocks on capital stock. Hence, hours worked fluctuate less than wages and productivity. Lastly, the model with indivisible labour improves the ability of the model to explain the cyclicality of productivity for EMEs as well as it increases the relative volatility of hours because individuals are assigned to jobs randomly so there is a large labour supply elasticity. We conclude overall that most of our RBC models fail to explain labour market fluctuations in the business cycles of emerging countries, but that the model with investment adjustment cost improves the performance of the model in regard to the relative volatility of wages and hours, as well as the cyclicality of hours, compared to the standard RBC model for these countries. There has been ongoing research to capture the stylised facts of business cycles in EMEs since Agenor et al. (2000) and reconcile these results in the real business cycle model Aguiar and Gopinath (2007),Garcia-Cicco et al. (2010),Neumeyer and Perri (2005), Chang and Fern andez (2010). These studies have presented various characteristics of business cycles in EMEs focusing on mostly consumption, output, productivity, investment, interest rate, net export and trade balance to output ratio. However, these papers have largely remained silent to explore labor market dynamics over business cycles in EMEs. Aguiar and Gopinath (2007) find that RBC model driven by permanent productivity shock does a good job at explaining business cycles features in EMEs. Garcia-Cicco et al. (2010) show that RBC model driven by permanent and temporary shocks does a poor job in explaining business cycle in terms of trade balance and consumption. Neumeyer and Perri (2005) focus on the cyclical movement of interest rate and introduce the model with interest rate shocks or financial shocks. They find that the model can explain the facts well. Chang and Fern andez (2010) build an encompassing model that unify stochastic trends with interest rate shocks and financial frictions influenced by Aguiar and Gopinath (2007),Neumeyer and Perri (2005). There are very limited studies focusing on the labor market variables. Li (2011) presents the cyclical wage movements in emerging countries and find that the volatility of wages relative to output in developing countries is 3 The seminal paperAgenor et al. (2000)- present the main stylised facts of macroeconomic fluctuations (output, interest rate, wages, etc.) for a group of 12 emerging countries. 4 For details, see also Boz et al. (2009),Li (2011), and Altug et al. (2011). 5 See Freeman (2007),Freeman (2009) and Campos and Nugent (2012). 6 Typically, the standard business cycle analysis uses quarterly data, but we use annual data, since hours worked data is available only with annual frequency from emerging economies. 7 There has been a substantial amount of research that the standard RBC model has been criticized due to its inability to explain some key aggregates variables. See Mendoza (1991),Burnside and Eichenbaum (1994),Cogley and Nason (1995), and Boileau and Normandin (1999). These studies have found that allowing for real frictions improved the ability of the model to account for some features of the data. S. Cos¸kun / Central Bank Review 19 (2019) 141e153142 almost twice as high as those in developed economies. She also finds that real wages are positively correlated with output. Our results are roughly in line with her results. Also, she builds a small open economy model with productivity shock and countercyclical interest rate, then figure out that the model can explain the high volatility of wage. These studies ignore changes in the hours worked while changes in wages have been examined in the real business cycle model for a small set of EMEs. In this paper, we focus on labor market dynamics including wages and hours worked as well as output and productivity with a larger set of EMEs. In a frictionless RBC model setting, the marginal rate of substitution (MRS) and the marginal product of labour (MPL) should be equal, but in reality, the observation that these diverge when calibrated to the data, has led to a growing body of literature investigating the so-called labour wedge. 8 In this study we are also interested in the labour wedge in EMEs and the USA because, firstly, it has relevance in explaining the business cycle, secondly, it provides information about labour market frictions during business cycles, thirdly, it has helped researchers to build a successful model of business cycle. We use the methodology proposed by Karabarbounis (2014), who studied the fluctuations in the labour wedge by decomposing this wedge in two: a gap between the MPL and real wage (firm’s component) and a gap between the MRS and real wage (household’s component). This methodology helps us to see which components are most responsible for the fluctuations in total labour wedge in these economies. We find that most of the fluctuations in the total wedge come from the household, rather than the firm, component of the labour wedge in both EMEs and the USA. It means that researchers need to focus more on frictions coming from the household side of the model in order to better understand the labour market fluctuations of business cycles in these countries. We also find that the total labour wedge (relative to output volatility) is more volatile in emerging countries (1.72) than in the US (0.95). Note that higher labour wedge would then represent a higher degree of labour market distortions. In particular, the relative volatility of the household component (2.09) and the firm component (1.24) of the labour wedge in the selected emerging countries is 2e3 times higher than the same components in the US. Last, the wedge in the US moves counter-cyclically to output; however, for EMEs, we obtain heterogeneous results. The heterogeneous cyclicality of the labour wedge shows that labour and product market distortions that affect the labour wedge are different among EMEs. In this study, our aim is to show how far the various RBC models with permanent and transitory productivity shocks can take us in explaining the labor market fluctuations of business cycles in EMEs, rather than to show a model that incorporates all extensions of the RBC can produce all labor market facts. We believe that we contribute to the limited literature making a more complete description of behaviour of the labor market variables in a large set of group of EMEs covering the sample period 1970e2013. Studies are mostly focusing on developed countries, small set of developing economies or particularly in one country. Also, compared to the existing literature, our paper includes more comprehensive labor market variables, not just wages, it also includes hours worked as well as output and productivity. In addition, we build different types of RBC models with real frictions driven by temporary and permanent shock to match the labor market facts of business cycle in EMEs countries rather than just giving only one model results. Overall, the results in this paper provide a useful guide for researchers about labour market properties of business cycle fluctuations in EMEs and where to introduce frictions to make the business cycle models more consistent with the data for these economies. The remainder of this paper is organized as follows. In section 2, we present the data. Section 3lays out our models and discusses the values of parameters. Section 4evaluates the performance of the models. Section 5presents the labour wedge. Finally, section 6 provides concluding remarks. 2. The data This section intends to provide a set of empirical facts to characterize the properties of the business cycles in emerging countries. We chose countries based on the availability of data; it is difficult to find quality data for certain variables and especially for data on hours worked and wages and there are a lot of missing observations. Hence, we had to reduce the time period for some countries and some variables. Still, we have sufficient annual data to provide an accurate picture of business cycles. However, for some countries, the results show that there is a nature of measurement error in the data as some of our results are not significant. The data on GDP (total GDP, in millions of 1990 US dollars), hours worked, employment, and population (the population aged 15e64) are compiled from the Conference Board Total Economy Database (TED). 9 The data on wages, which are total compensation of employees, and consumption (household consumption expenditure data at constant (2005) prices in national currency, included non-profit institutions serving households) are collected from the United Nation Statistics Division, which publishes data on national accounts. The real wages data are calculated by deflating the total compensation of employees by the consumer price index. We collected the data for 15 emerging economies (Brazil, Bulgaria, Chile, Colombia, Costa Rica, the Czech Republic, Estonia, Hungary, Jamaica, Mexico, Peru, Slovenia, South Korea, Thailand, and Turkey) and for the US for the period 1970e2013. We have used annual data instead of quarterly data since hours worked data is available only with annual frequency from emerging countries and all of the variables are converted to per capita terms. We construct the variables as follows. Employment per working age population (e) is defined as the ratio of the level of employment (E) in the economy to the total working age population (P) of the country; real GDP per capita (y) is constructed using real GDP (Y) and the total working age population (P). Then real wages per hour (w) is constructed using the total real wages (W) over total hours worked (H) in the dataset. Labour productivity (p) is the ratio of real GDP (Y) to total hours worked (H) and, lastly, consumption per capita (c) is constructed by dividing household consumption expenditure (C) over total working age population (P). We used two measures of hours worked as in Ohanian and Raffo (2012). First, we constructed hours worked per employed person (he), using total hours worked (H) and employment (E). Second, we constructed hours worked per working age population (hw), using total hours worked and working age population. Hours worked per working age population (hw) can be split into two parts as the intensive margin (hours worked per employed person) and the extensive margin (employed people divided by working age population). The reason for this split is to investigate whether most of the fluctuations in total hours worked come from the extensive margin or from the intensive margin in EMEs. 8 See Chari et al. (2007),Shimer (2009) and Ohanian and Raffo (2012). 9 The GGDC Total Economy Database is the main source of estimates of hours worked per worker that are comparable across countries. These series are adjusted to reflect most sources of cross-country variation in hours worked, including the contracted length of the work week, statutory holidays, paid vacations, sick days and days lost due to strikes, and they are consistent with output. S. Cos¸kun / Central Bank Review 19 (2019) 141e153 143 To explain business cycle movements, any given data series is expressed in logs and de-trended using a Hodrick-Prescott (HP) filter (Hodrick and Prescott (1981)) with the standard smoothing parameter at 100 for annual data. For each variable j,Table 1 reports the standard deviation relative to the standard deviation of output s j = s y . Table 2 documents the autocorrelation of output autocorðyÞand the correlation with output corrðj;yÞfor the business cycle frequencies of each emerging country and the US. We present the extensive margin, the intensive margin and hours worked per working age population,as well as productivity and wages to get familiar with the particularities of the business cycle in these economies. Note that we use hours worked per working age population (hw) when we compare the data and model moments in section 4, since we cannot separate employment from hours due to the fact that the whole population is employed in our models, except the model with indivisible labour. Here, on average, are the second order moments of the labour market variables for these economies for the period of 1970e2013: - The relative volatility of wages is about two times as volatile as the relative volatility of productivity for emerging countries. In terms of quantity, the intensive margin is clearly the least volatile of all. - The relative volatility of wages (1.58) and productivity (0.81) are almost 2e3 times higher in EMEs than in the US, at 0.77 and 0.42, respectively. Notice that the relative volatility of hours worked (0.89) is higher than that of real wages (0.77) and productivity (0.42) in the US. - In terms of quantity, the differences between the relative volatilities in emerging countries and the US are not large. The average value of the relative standard deviation of the extensive margin is 0.73 versus 0.27 for the intensive margin in the US, and 0.55 versus 0.26 in emerging economies, respectively. This finding reveals that the extensive margin contributes more to the variability of the total hours in these countries. 10 - The co-movement of the labour market variables with output, on average, are all positively correlated for these countries, although at different levels of intensity. Pro-cyclical behaviour corresponds most strongly with productivity (0.71) in EMEs, while total hours worked (0.90) and employment (0.88) correspond most strongly in the US. Compared to the US, the results show that extensive margin, total hours worked and real wages correlate less with output while productivity correlate more with output in emerging countries. - The correlation of intensive margin (0.61) with output in the USA is about three and half times higher than in the emerging countries (0.18). Lastly, output is somewhat more persistent in the EMEs, with an autocorrelation of 0.63, compared to the USA, at 0.55. We now turn our attention to the country-level analysis. It is obvious that the properties of labour market fluctuations in many emerging countries differ from each other despite the similar picture emerges among some economies. - Bulgaria (0.89) shows the highest relative volatility of extensive margin among EMEs while Peru (0.24) is the least volatile. Furthermore, the relative volatility of extensive margin in Brazil, Columbia, Hungary, Jamaica and Slovenia are about as volatile as USA (0.73). - Brazil, Costa Rica, Thailand and Turkey have the highest volatile productivity among all countries but they do not deviate very much from the average (0.81). - The relative volatility of wages in Brazil (3.10), Peru (2.32), Mexico (2.30) and Turkey (2.68) are much higher than the average volatility of wages in emerging countries (1.58) while Slovenia shows the lowest wages volatility, at 0.51. - The co-movement of the labour market variables with output for these economies are positively correlated. However, Costa Rica, Mexico and Turkey are the only countries in our sample where the correlation of intensive margin with output is negative at 0.21, 0.23 and 0.14, respectively. - Lastly, the correlation of wages and productivity is strongest with output in Peru at 0.78 and 0.97, respectively while Estonia shows the lowest correlation of productivity with output (0.36). Table 1 The standard deviations relative to standard deviations with output in emerging countries and the USA. Countries s ðeÞ s ðyÞ s ðheÞ s ðyÞ s ðhwÞ s ðyÞ s ðpÞ s ðyÞ s ðwÞ s ðyÞ Brazil 0.76 0.04 0.76 1.07 3.10 Bulgaria 0.89 0.21 0.92 0.90 1.29 Chile 0.45 0.10 0.45 0.84 1.73 Colombia 0.77 0.43 0.91 0.71 1.24 Costa Rica 0.39 0.48 0.62 0.96 1.17 Czech Republic 0.36 0.33 0.51 0.83 0.94 Estonia 0.39 0.27 0.78 0.36 0.91 Hungary 0.75 0.39 0.86 0.73 1.28 Jamaica 0.74 0.38 1.01 0.63 1.19 Mexico 0.35 0.18 0.39 0.83 2.30 Peru 0.24 0.01 0.24 0.91 2.32 Slovenia 0.76 0.37 0.62 0.65 0.51 South Korea 0.59 0.37 0.67 0.71 1.76 Thailand 0.42 0.22 0.50 0.96 1.31 Turkey 0.51 0.21 0.50 1.09 2.68 Average 0.55 0.26 0.64 0.81 1.58 Median 0.51 0.37 0.62 0.83 1.29 USA 0.73 0.27 0.89 0.42 0.77 Note: This table presents the relative standard deviation of the extensive margin (e), intensive margin (he),total hours worked (hw),productivity (p), and wages (w) with the output (y) for the period 1970e2013. The series are logged first and then filtered using the Hodrick-Prescott filter with a smoothing parameter of 100. Table 2 Autocorrelation and correlation with output in emerging countries and the USA. Countries r ðyÞ r ðe;yÞ r ðhe;yÞ r ðhw;yÞ r ðp;yÞ r ðw;yÞ Brazil 0.57 0.27 0.14 0.28 0.73 0.68 Bulgaria 0.65 0.64 0.32 0.41 0.55 0.061 Chile 0.61 0.55 0.01 0.54 0.89 0.67 Colombia 0.71 0.68 0.32 0.73 0.47 0.11 Costa Rica 0.62 0.65 0.21 0.36 0.75 0.46 Czech Republic 0.58 0.38 0.04 0.43 0.70 0.27 Estonia 0.73 0.66 0.83 0.92 0.65 0.30 Hungary 0.73 0.63 0.34 0.72 0.54 0.07 Jamaica 0.68 0.55 0.32 0.75 0.17 0.12 Mexico 0.58 0.76 0.23 0.59 0.93 0.63 Peru 0.60 0.45 0.47 0.47 0.97 0.78 Slovenia 0.74 0.57 0.37 0.71 0.79 0.08 South Korea 0.47 0.75 0.06 0.70 0.74 0.54 Thailand 0.76 0.25 0.23 0.30 0.90 0.81 Turkey 0.48 0.12 0.14 0.059 0.89 0.41 Average 0.63 0.52 0.18 0.56 0.71 0.39 Median 0.62 0.57 0.23 0.59 0.74 0.41 USA 0.55 0.88 0.61 0.90 0.47 0.54 Note: This table presents the autocorrelation of output (y), correlation of the extensive margin (e),intensive margin (he),total hours worked (hw),productivity (p), and wages (w) with the output (y) for the period 1970e2013. The series are logged first and then filtered using the Hodrick-Prescott filter with a smoothing parameter of 100. 10 It would have been worth analysing wages in the informal and formal sectors as well as employment in private and public sector. However, we could not ascertain which sector is most accountable for the variability of these variables in our sample countries, since we are not able to obtain data for these sectors. S. Cos¸kun / Central Bank Review 19 (2019) 141e153144 The results confirm the fact that business cycles in emerging countries do not follow the same patterns as in US albeit some similar patterns emerge in country-level analysis. The striking aspect of these results is that the labour markets in EMEs adjust more through prices while quantities are subdued. In the emerging market business cycle literature, Neumeyer and Perri (2005),Boz et al. (2009) and Li (2011) document statistics on labour market variables using semi-annualized, quarterly and both annual and quarterly data, respectively. They find that the quantity variables are less variable and less correlated with output in EMEs compared to the US. Moreover, they find that the volatility of wages relative to output in EMEs is almost twice as high as that in the developed economies, and real wages are positively correlated with output. Our findings on these variables are roughly in line with those studies. 3. The model The benchmark model we present here, motivated by the findings in the previous section, is a canonical RBC model designed to assess fluctuations in the hours worked, wages, productivity and output of business cycles in EMEs including transitory TFP shock and a permanent labour-augmenting productivity shock as in Aguiar and Gopinath (2007). These shocks have been widely studied in the literature 11 which find that the business cycles in emerging countries are mainly driven by shocks to trend growth rather than transitory fluctuations around a stable trend. They interpret the shocks to the trend growth as dramatic changes in institutions and policy in emerging countries. Then we look at several variants of the standard RBC model in the literature. The model consists of households and firms. The households consume, invest in capital and provide labour and capital for the firms. The firms rent labour and capital from the households. 12 3.1. The standard Real Business Cycle (RBC) model 3.1.1. The households problem The model economy is populated by a continuum of identical consumers. The preferences of households are defined by consumption, C t , and hours worked, H t , and are described by the utility function: E0X ∞ t¼0 b tuðCt;HtÞ;(1) where preferences are non-separable: UðCt;HtÞ¼C j tð1HtÞ1 j 1 s 1 s :(2) E(.) denotes the expectation operator, conditional on information available at time t, b is the discount factor between zero and one. As a baseline we use a non-separable utility function which implies that the preferences are non-separable in terms of consumption and hours. U(.) represents a period utility function. The parameter s is the inverse of the inter-temporal elasticity of substitution for consumption. j determines the inverse of the Frisch elasticity of labour supply. This utility function eliminates the wealth effect on leisure; hence, the labour supply depends on wages. We have further simulated the model with the separable utility function. In contrast to the non-separable utility function, this implies an effect of wealth on leisure. Household maximizes the following lifetime utility function: UðCt;HtÞ¼C1 s t 1 s  c H1þ j t 1þ j :(3) where c specifies the preference weight of hours in utility. The Frisch elasticity for labour supply is simply 1 j . The reason we consider both these preferences is to determine whether or not our results are sensitive to differences in preferences used in the analysis. A household is assumed to own capital, K t , which accumulates according to the following law of motion: Ktþ1¼ð1 d ÞKtþIt;(4) where I t denotes investment, and d is the depreciation rate of capital. The households are subject to the following inter-temporal budget constraints: CtþIt¼WtHtþRtKt;(5) where W t denotes the household’s real wage rate, and R t represents the rental rate of capital. Consumers choose to maximize utility subject to capital accumulation and their budget constraints: CtþKtþ1¼WtHtþRtKtþð1 d ÞKt:(6) 3.1.2. The firms problem Firms have access to the following Cobb-Douglas production function, which uses capital K t and labour H t from households. Production technology takes the form Yt¼ez t K1 a tðHt G tÞ a ;(7) where Y t is output and a ε(0,1) is the labour share in output. The parameters z t and G t are stochastic productivity processes which are characterized by different stochastic properties. Specifically the temporary shock, z t , to total factor productivity is stationary and follows the ARð1Þprocess: zt¼ r zzt1þεz t;(8) with j r z j<1 as the persistence of the transitory productivity shock and ε z t representing an independent and identical distribution (iid) drawn from a normal distribution with a zero mean and standard deviation s z . The permanent labour-augmenting productivity shock, G t , is non-stationary and represents the cumulative product of “growth shocks”; it is given by G t¼gt G t1¼Yt s¼0gs; lnðgtÞ¼1 r glog m gþ r glnðgt1Þþεg t: where the parameter g t represents the rate of growth of the permanent technology shock.  r g <1 represents the persistence parameter of the process g t , and ε g t represents iid drawn from a normal distribution with a zero mean and standard deviation s g . m g represents the long run average growth rate of productivity. Notice that shocks to g t permanently affect labour productivity, G t . 3.1.3. Labour and capital demand If we assume that the factor market is characterized by perfect 11 See also Chang and Fern andez (2010) and Garcia-Cicco et al. (2010). 12 The equilibrium of the models is derived in Appendix. S. Cos¸kun / Central Bank Review 19 (2019) 141e153 145 competition then the real rental rate on capital R K t and real wage W t is given by RK t¼ez t ð1 a ÞKt Ht a Ga t; Wt¼ez t a Kt Ht1 a Ga t: (9) 3.1.4. Equilibrium conditions in stationary form Since the model exhibits balanced growth all of the nonstationary variables have to be de-trended. Hence, we normalize all of the variables except H t with trend shock G t to induce stationarity. The de-trended versions of the respective variables are defined as follows: b Ct≡Ct G t;b Yt≡Yt G t;bIt≡It G t;b Ktþ1≡Ktþ1 G t;c Wt≡Wt G t: We have the following equilibrium conditions which characterized this economy: Cobb-Douglas production function: b Yt¼ez t b K1 a t1H a tg1 t;(10) Labour demand: c Wt¼ a b Yt=Ht; Demand for capital: RK t¼ð1 a Þb Yt.b Kt1g1 t; Labour supply: ð1 j Þb Ct¼ j ð1HtÞc Wt; Euler for capital: b C j ð1 s Þ1 tð1HtÞð1 j Þð1 s Þ¼ b g j ð1 s Þ1 tþ1 b C j ð1 s Þ1 tþ1ð1Htþ1Þð1 j Þð1 s Þð1þRtþ1 d Þ; Law of motion for capital: b Kt¼ð1 d Þb Kt1g1 tþbIt; Aggregate resource constraints: b Ctþb Kt¼b Ytþð1 d Þb Kt1g1 t; b Yt¼b CtþbIt: 3.2. Extensions It is well known in the early moment matching exercises where the standard RBC model are incapable of replicating the second moments of labour market dynamics. 13 Hence, different extensions to and modifications of the RBC model have been proposed by many researchers. Following the literature we have built an augmented RBC model with capacity utilization, investment adjustment cost and indivisible labour with temporary and permanent productivity shocks to explain labour market facts observed in the data. The idea using these extensions is to show how far these models can take us in explaining labour market fluctuations of EMEs. 3.2.1. The RBC model with capacity utilization The basic idea of using capacity utilization is that it allows capital to vary in response to productivity shocks in business cycle fluctuations by intensifying the capital while the capital enters for a predetermined period in the model. Hence, this mechanism substantially improves the ability of the model to account for the features of the data. Greenwood et al. (1988) suggest that a variable capacity utilization rate may be important for understanding of business cycles since it provides a channel through which shocks via their impact on capacity utilization can affect labour productivity and hence equilibrium employment. Moreover, Burnside and Eichenbaum (1994) study the role of capacity utilization in propagating shocks over the business cycle. They find that it magnifies and propagates the impact of the shock since it provides an additional margin to adjust the level of output (see also Cogley and Nason (1995) and Boileau and Normandin (1999)). Motivated by the findings in the literature, we hence examine the extent to which capacity utilization helps the RBC model match the labour market facts in EMEs. In this model, the law of motion for capital becomes Ktþ1¼1 d X U tKtþIt;(11) X t represents the capacity utilization rate, and the parameter U determines the intensity of capacity utilization. The term d X U t shows the capital depreciation rate, which depends on capital utilization, where d is increasing and convex in X t and U >1. The production function depends on hours, the amount of capital and utilization as follows: Yt¼ez t ðKtXtÞ1 a ðHt G tÞ a ;(12) The term K t X t represents capital services which depend on the production of utilization and the amount of physical capital. To understand the role of capacity utilization in amplifying and propagating business cycles in this model, it is useful to derive a reduced-form aggregate production function evaluated at the optimal rate of capacity utilization. The first order condition with respect to capacity utilization X t is ð1 a ÞYt Xt¼ Ud X U 1 tKt:(13) Equation (13) shows that marginal output of an increase in the capacity utilization rate equals to the marginal change in capital depreciation rate due to the intensified usage of existing capital stock. 3.2.2. The RBC model with investment adjustment costs The reason why we are interested in investment adjustment costs is that the standard RBC model causes a high volatility of investment since firms adjust their capital stock to the optimal level instantaneously. However, the incorporation of investment adjustment costs into the RBC model prevents investment quickly responding to changes in economic conditions. Furthermore, recent studies consider investment adjustment cost as a key mechanism that significantly improves the quantitative performance of the models along a number of dimensions. Burnside et al. (2004) find that these costs may explain the effects of a fiscal shock on hours 13 For details, see Hansen and Wright (1992) and Christiano and Eichenbaum (1992). S. Cos¸kun / Central Bank Review 19 (2019) 141e153146 and wages. Moreover, Albonico et al. (2012) find that the RBC model with investment adjustment costs could resolve the productivityhours puzzle and generate negative co-movements between hours and productivity. We have the following properties as in Christiano et al. (2005) for the functional form of these costs. The law of motion for capital, with adjustment costs for investments, is given by Ktþ1¼ 14 2It It1 12!Itþð1 d ÞKt;(14) The term 4 2  I t I t1 1 2 with 4>0 captures the adjustment costs on investment I t . It implies that there is a cost associated with changing the level of investment, that this cost is zero at steady state and that this cost is increasing in the change in investment. The Lagrangian multiplier for the model with investment adjustment costs is q t ¼ q t l t .Wedefine Tobin’sq t as the shadow value of having an extra unit of capital, q t , and marginal utility of consumption, l t . If there are no adjustment costs, q t equal to 1, that is the Tobin’s marginal q t should be equal to the replacement cost of installed capital in units of the final good. We do not present all of the stationarized equations since some of them are the same as in the basic RBC model. We have the following equilibrium conditions that characterize this economy Euler for capital: bqt¼ b b l tþ1 b l t g1 tþ1ðð1 d Þqtþ1þRtþ1Þ;(15) Euler for investment: 1¼bqt 14 2b It bIt1 gt12 4b It bIt1 gt1b It bIt1 gt!þ b bqtþ1 b l tþ1 b l t g1 tþ14bItþ1 b It gtþ11;bItþ1 bIt gtþ12 ; (16) Law of motion for capital: b Kt¼ 14 2b It bIt1 gt12!b Itþð1 d Þb Kt1g1 t:(17) where q t is the shadow price of capital in terms of consumption. Equation (17) is the present discounted value of having an additional unit of capital, measured in terms of its future value and the rental rate. 3.2.3. The RBC model with indivisible labour Hansen (1985) emphasizes that fluctuations in hours worked in the real world come from the changes in both the extensive and intensive margins. His findings about the US, which revealed that most of the fluctuations in hours are mainly due to variations in the extensive margin (i.e., the employment rate), support the modelling of the RBC model with indivisible labour. In this study, the adoption of the indivisible model is very close to the EMEs experience. As reported in previous sections, fluctuations of the extensive margin are mostly responsible for fluctuations in the total hours worked in these economies rather than fluctuations in the intensive margin. In this model, utility is linear in h t , and the intertemporal elasticity of substitution is infinite for households. Thereby, labour supply varies to a greater extent inter-temporally in this economy. The utility function is given by Uðct;htÞ¼lnðctÞþAlnð1htÞ;(18) Adescribes the weight on leisure in the utility function. Households uniformly have the same probability of working as they are identical in terms of skills and productivity. Thus, Uðct;htÞ¼lnðctÞþA½ p tlnð1h0Þþð1 p tÞlnð1Þ; Uðct;htÞ¼lnðctÞþA p tlnð1h0Þ; where h t represents hours worked per capita. Indivisible labour is modelled by restricting the consumption possibilities set so that households work h 0 with a probability of p t and the rest work zero (i.e., there is an employment lottery). This is given by ht¼ p th0;(19) Preferences can be written as U¼lnðctÞþAlnð1h0Þ h0 ht;(20) B¼Alnð1h0Þ h0 ;(21) Brepresents the dis-utility parameter of composite labour. Therefore, we can write it within the period utility function as Uðct;htÞ¼lnðctÞBht:(22) 3.3. Parameterization Table 3 shows the list of parameters we parametrize in order for the model to match data. It is important to have a good understanding of rationale behind the selection of the particular parameter values in order to properly evaluate the fit of the model for EMEs. In this study, the parameter values are generally picked from the existing literature due to lack of quality data in estimating these values governing stochastic productivity processes, preferences, production and adjustment costs in these countries. Therefore, we have relied on highly conventional parameters widely used in the DSGE models of annual frequency for the US. More specifically, the model is calibrated to match annual frequency and these values are fit for emerging countries. The labour share a is calibrated to match the capital share data. We hence set a in production to 0.68, which is a standard value for the long run labour share income so that the value of capital share is set to 1=3 to match the average fraction of total income going to capital in EMEs. The discount factor b is calibrated to match the steady-state capital-output ratio in the capital Euler equation to that in data. The value of b used in literature ranges from 0.92 to 0.99 for annual frequency for emerging countries. We set this value to 0.95, in order to imply a steady-state real interest rate at about 5% per year, which is a value compatible with the observed interest rate face by emerging countries. 14 We set the inverse of the Frisch elasticity of the labour supply j of the utility function to 0.33 so that it matches the steady state labour input level in the labour first order condition to that in data which is commonly used in the RBC literature. The value of the depreciation rate d ranges from 0.03 to 0.12 per year for EMEs in the 14 However, Garcia-Cicco et al. (2010) set the parameter b to 0.92, which implies a relatively high average real interest rate of about 8.5 percent annually. They also explained that this value is empirically plausible for emerging market like Argentina. S. Cos¸kun / Central Bank Review 19 (2019) 141e153 147 literature. We have used a 7% annual depreciation rate to match the capital law of motion as it falls almost in the middle of that range. 15 Since we have a permanent shock in the model, we set the coefficient of relative risk aversion s to 1 in the case of the separable utility function in order to have a balanced growth path. However, we set the inverse of the inter-temporal elasticity of substitution to 2 which ranges from 1 to 2 in the case of the non-separable utility function in the standard business cycle literature. 16 We set the investment adjustment cost parameter, 4, to 4 following Albonico et al. (2012). 17 We used the five parameters to define the stochastic processes of the productivity shocks, g, r z , r g ,ε g ,ε z . The persistence value of the temporary shock, r z , is set to 0.6 and the persistence of the permanent shock, r g , is set to 0.01. 18 Then we set the long-run productivity growth, m g , to log (1.0066) as in Aguiar and Gopinath (2007), who calibrate this value based on the average growth factor of the Mexican economy in their data. The standard deviation of the temporary shock, ε z , and the permanent shock, ε g ,are normalized to 1%, which is compatible with the commonly used values in literature. In the next section, we first present the results based on our baseline parameter values in Table 4. Then we discuss the sensitivity of our results, in light of the different parameter values used in other studies. 4. Results The aim of this section is to show how the RBC models fit the features of the data for emerging countries and the US. The model we built generates data de-trended by the stochastic trend therefore, we have to obtain the level by adding back the permanent shock. We then log and de-trend this data as well using HP filter so that we can compare properly the data and the model moments. Note that Table 4 shows the marginal and average productivity of labour are proportional to each other; therefore, the moments of the model for productivity and wages are the same. The results for the standard RBC model are presented in column 3 and corresponds to the case in which we introduce only permanent and temporary productivity shocks. It can be seen that this model does a fairly good job of matching the relative volatility of hours, but it does not generate enough volatility of productivity and especially wages for these economies since the volatility of wages relative to output is much higher in the data than in the model. In addition, the model produces a positive and significant correlation for hours worked, wages and productivity with output, which are at odds with the data for EMEs. Moreover, this model replicates satisfactorily the correlation between hours and output for the US but it fails to capture the rest of the moments although the results are slightly better for this country compared to emerging economies. The standard RBC model fails to account for many features of the data as it does not embody quantitatively important propagation mechanism. Model 3 introduces the capacity utilization in propagating shocks over the business cycle to the standard RBC model. In this model, we assume that the production function depends on labour, the amount of capital available and its utilization so capacity utilization alters the equilibrium production function as it amplifies the shocks. If capacity utilization does not vary much, it may be possible to increase the impact of shocks on hours worked and hence decrease labour productivity and real wages. As intuition would suggest we see that this model increases the relative Table 3 Parameters values in models. Parameters Definition Value b The Discount factor 0.95 j The inverse of the Frisch elas. of labour supply 0.33 a The labour share of output 0.68 s The inter-temporal elasticity of subs. for consumption 2 d The depreciation rate of capital 0.07 m g The productivity’s mean growth rate log(1.0066) r z The persistence of transitory shocks 0.6 r g The persistence of growth shock 0.01 4The adjustment cost on investment 4 Table 4 Business cycle moments. Data USA Model1 Model2 Model3 Model4 Model5 Model6 Model7 s ðhÞ/ s ðyÞ0.64 0.89 0.54 0.51 0.65 0.60 0.63 0.63 0.72 s ðwÞ/ s ðyÞ1.58 0.77 0.60 0.64 0.45 0.50 1.02 1.03 0.51 s ðpÞ/ s ðyÞ0.81 0.42 0.60 0.64 0.45 0.50 1.02 1.03 0.51 r ðyÞ0.63 0.55 0.36 0.37 0.35 0.36 0.32 0.32 0.36 r ðy;hÞ0.56 0.90 0.86 0.83 0.94 0.94 0.57 0.56 0.87 r ðy;wÞ0.39 0.54 0.89 0.90 0.87 0.90 0.99 1.00 0.73 r ðy;pÞ0.71 0.47 0.89 0.90 0.87 0.90 0.99 1.00 0.73 Note: s represents relative volatility with the output and r represents the correlation with output. The terms h,y,w, and pstand for hours, output, wages and productivity, respectively. The first column of the table reports the results for the data moments on average for emerging countries and the second column presents the moments of US data for business cycle frequencies between 1970 and 2013. In the following columns, Model 1, Model 3 and Model 5 show the moments of our benchmark model, the model augmented capacity utilization and investment adjustment costs with the non-separable utility function, respectively. Model 2, Model 4 and Model 6 represent the results of these models associated with the separable utility function. Lastly, Model 7 shows the performance of the RBC model with indivisible labour. 15 Li (2011) have set the depreciation rate to 3% while Garcia-Cicco et al. (2010) have set this value to 12% for annual frequency. 16 As in Li (2011). She calculates the s based on data from Mexico. 17 They use the values between 0 and 20 for the investment adjustment cost. 18 The persistence of the permanent shock, r g is taken from Aguiar and Gopinath (2007). They set the persistence value of the temporary shock, r z as 0.95. The reason why we choose the lower value for r z is that we use annual data but they use quarterly data. The persistence of the temporary shocks with annual data should be lower than quarterly data. S. Cos¸kun / Central Bank Review 19 (2019) 141e153148