Testing Okun’s Law for Turkey (1923-2019)

Abstract

This study tests Okun’s law for Turkey using annual data gathered for almost a century (1923–2019). In contrast to the rest of the literature focusing on a linear relationship between unemployment and output levels, we argue for a cointegrating nonlinear autoregressive distributed lag (NARDL) model. We find clear evidence of an asymmetric cointegrating relationship between unemployment and output as well as asymmetric short-run impacts. Interestingly, these relationships are positive. Asymmetric cumulative dynamic multipliers confirm the results, which can be explained by the structural features of the Turkish unemployment such as the high female and youth unemployment rates, a large agricultural sector, high firing costs, and the high level of informal employment as well as hysteresis. Therefore, effective labour market reforms should consider asymmetries in the long-run unemployment and output relationship as well as asymmetries in their short-run impacts in order to handle jobless recoveries in Turkey.

Keywords:

• Unemployment-output trade-off
• asymmetric cointegrating relationships
• NARDL ECM-based estimation and tests
• asymmetric dynamic multipliers
• Turkey

JEL Classification:

• C22
• E32
• J64

1. Introduction

Turkey has been suffering from high unemployment rates during the last decades, and its current unemployment rate is around 14%. Işığıçok (2011) and Apaydın (2018) argue that unemployment in Turkey is structural due to a large youth labour force; low labour force participation, especially by women; a low level of education and qualifications; a high agricultural employment rate; employment and skill mismatches; high internal migration and urbanisation; and high firing costs. A close examination of the link between output and unemployment will help explain the mechanisms underlying Turkish unemployment and will make suggestions for structural reforms. Conventional economic wisdom is that strong growth will cause unemployment to fall, whereas low or negative growth rates will increase unemployment, as both variables are affected by the business cycle. However, research on the relationship between output and unemployment has delivered disappointing results, suggesting a nonlinear relationship, which is consistent with the theory of hysteresis (Schorderet 2001).

Okun (1962) first formally introduced the unemployment–output relationship with Okun’s law. This law is particularly important for monetary policy transmission, through which inflation-targeting monetary policy is assumed to operate according to the link between unemployment and output. Okun’s law consists of two equations: The first equation relates the deviation of the unemployment rate from its natural rate to a fraction of the output gap. The second law relates unemployment and output in first differences. Okun’s estimates show that in the United States (US), an output growth of 3% above its potential level is required to reduce the unemployment rate by one percentage point, assuming that the equilibrium level of unemployment is about 4%. However, Okun’s law was unable to explain the unemployment dynamics in subsequent decades because cyclical upturns and downturns might not have simple, symmetric effects on unemployment. In addition, it was difficult to connect these two variables in levels.¹ Lang and de Peretti (2009) explain that employers do not necessarily hire the same number of workers after a positive shock as they fire after a negative shock. Schorderet (2001) argues that the findings of the two series take unrelated paths or independently move away from each other are the results of an exclusive focus on linear models. In fact, this relationship could be nonlinear, which is compatible with the hysteresis hypothesis. Shin, Yu and Greenwood-Nimmo (2014) discuss how linear models may not be rich enough to facilitate strong inferences or to yield reliable forecasts. More importantly, the assumption of linear adjustment can be restrictive in general for economically interesting situations, particularly where transaction costs are high, and policy interventions are observed in-sample (Hamermesh and Pfann 1996). For instance, in an early study, Neftci (1984) reveals that the output–unemployment relationship for the US exhibits clear asymmetry. Altissimo and Violante (2001) and Crespo-Cuaresma (2003) confirm evidence of nonlinearity between output and unemployment, showing significantly larger asymmetry in recessions than in expansions. The latter are more persistent in the expansionary regime. Sögner and Stiassny (2002) and Perman and Tavera (2005) examine the fitness and stability of Okun’s law, finding no evidence of the symmetric pattern in the unemployment–output relationship.² In addition, the direction of asymmetry may differ between the short-run and the long-run. Thus, a positive shock may have a larger (absolute) impact in the short-run, whereas a negative shock can have a larger (absolute) impact in the long-run.

The failure to find a relationship between output and unemployment has led researchers to depart from the economic theories explaining unemployment with a natural or equilibrium rate around which the actual levels are seen as temporary deviations (Friedman 1968). Instead, they have turned to the hysteresis theory, which argues that cyclical shocks can affect the structural part of unemployment, and past unemployment rates matter for current unemployment (Phelps 1972). In addition, the hysteresis hypothesis indicates an asymmetric response of unemployment to economic booms and busts; that is, unemployment drops sharply during the economic downturns but slowly decreases during recoveries (Courtney 1991; Palley 1993).³ Blanchard and Summers (1986) were able to explain the persistence of high unemployment in Europe during the eighties in a model of insiders–outsiders wage-setting with dynamic dependence. Similarly, long-term unemployment prolongs the chances of finding a job in the models of human capital depreciation, and hysteresis is strong when there are not enough substitution possibilities between labour and capital within the theory of capital shortage (Hargreaves Heap 1980; Bean 1989). Nebot et al. (2019) provide three theoretical explanations for asymmetric Okun’s law: the institutional rigidity, the labour hoarding, and the risk aversion hypotheses.

Elmeskov and MacFarlan (1993) and Mitchell (1993) draw an attention to unit root processes of unemployment rate. Peel and Speight (1995) test the hysteresis hypothesis with threshold autoregressive models, and Brännäs and Ohlsson (1999) utilise asymmetric ARMA formulations as nonlinear representations. Schorderet (2001, 2003) studies the bivariate asymmetric cointegrating relationship between unemployment and output, where output is divided into partial sum processes of positive and negative changes. The results of this nonlinear specification reveal a hysteric relationship between unemployment and output in which the impact of recessions on unemployment is larger in absolute terms than that of recoveries. Elsewhere, Granger and Yoon (2002) call the cointegrating relationship, which includes the positive and negative components of the underlying variables, ‘hidden cointegration’. They show that the output–unemployment relationship, which is nonlinear, can also explain the ambiguous cointegration test results in linear models.

Lee (2000) and Virén (2001) investigate Okun’s law by applying partial sum decompositions to the analysis of dynamic asymmetry. However, they employ the two-step Engle–Granger (EG) technique to model short-run asymmetry, which is less efficient than single-step error correction model (ECM) estimation. In general, the papers modelling long- and short-run asymmetries in unemployment and output relationship jointly are scarce. Shin et al. (2014) show that the EG test cannot reject the null of no cointegration in the static asymmetric case, suggesting an appropriate dynamic specification. They also point out the power-dominance of the ECM-based tests, which include valuable information about the correlation between the regressors and the underlying disturbances compared with the EG residual-based approach.

In this article, an alternative approach to testing Okun’s law is suggested while considering several problematic issues, highlighted above. There are several notable contributions of this approach. First, the paper adopts a nonlinear dynamic framework to model asymmetries, both in the long-run relationship and in the patterns of dynamic adjustment. Research on the relationship between unemployment and output in Turkey has delivered inconclusive results depending on the time period, data frequency, and methods used (Yılmaz 2005; Kızılgöl 2006; Saraç and Atabey 2008; Aydıner-Avşar and Onaran 2010; Barışık, Çevik and Çevik (2010); Ceylan and Şahin 2010; Takım 2010; Tarı and Abasız (2010); Tunah 2010; Muratoğlu 2011; Tiryaki and Özkan 2011; Altuntepe and Güner 2013; Şentürk and Akbaş 2014; Altunöz 2015; Göçer (2015); Arı 2016; Bayrak and Tatlı 2016; Saraç and Yıldırım 2016; Mucuk, Edirneligil and Gerçeker 2017; Yüksel and Adalı 2017; Arabacı and Yüksel-Arabacı 2018; Bağcı and Börü 2018; Öztürk and Sezen (2018); Pata, Yurtkuran and Kalca 2018; Apaydın and Taşdoğan 2019; Dayıoğlu and Aydın 2020). Second, the long-run time series data spanning from 1923 until 2019 for Turkey are utilised to investigate asymmetric relationships between unemployment and output. The existence of a long-run relationship between unemployment and output would imply that unemployment and output dynamics are governed by a common factor whose presence rules out persistent deviations in unemployment and output in the long-run. This is the only study that investigates the Turkish unemployment-output relationship for such a long period. Therefore, the ‘long-run’ relationships established in other studies rely on a smaller number of more recent cyclical episodes, which may reflect modern economic realities. Third, Turkey - like many other economies - have undergone substantial economic changes which are potentially difficult to control for. This is the typical long data and structural change problem in time-series econometrics. Indeed, there are several important structural breaks that occur in the dataset, which covers almost a century. The structural breaks, shifts and outliers are accommodated by means of impulse dummies. However, rapid shifts could also be a result of non-linear reactions, so those are considered as well. Fourth, a bounds-testing procedure for the existence of a stable long-run relationship, valid irrespective of whether the underlying regressors are I(0), I(1), or mutually cointegrated is employed for testing the existence of a long-run relationship (Pesaran and Shin 1998; Pesaran, Shin and Smith 2001). This procedure is based on an unrestricted error-correction model that allows joint estimation of both long- and short-run effects. Fifth, asymmetric cumulative dynamic multipliers are calculated to trace the asymmetric adjustment patterns succeeding positive and negative shocks to the explanatory variable. Finally, policy recommendations are provided.

The results of the bounds-testing procedure show evidence of both long- and short-run asymmetries in unemployment and output relationship. The dynamic multipliers confirm these findings. These results validate the benefits of the use of an unrestricted error-correction model, permitting joint estimation of long- and short-run effects, as well as asymmetric relationships.

The outline of the paper is as follows. The next section presents the asymmetric cointegrating regression model. Section 3 describes the data. Section 4 is devoted to empirical evidence, and Section 5 concludes.

2. Model

Shin et al. (2014) generalise the concept of a nonlinear relationship, and Schorderet (2001) defines the following asymmetric long-run regression of the unemployment–output trade-off: (1) $$u_t={\beta }^{+}{y}_t^{+}+{\beta }^{-}{y}_t^{-}+e_t$$(1) where $u_t$ is the unemployment rate; $y_t$ is output (real GDP); and $\beta =\left({\beta }^{+},{\beta }^{-}\right)$ is a cointegrating vector or a vector of long-run parameters to be estimated. In Equation (1)(1) $$u_t={\beta }^{+}{y}_t^{+}+{\beta }^{-}{y}_t^{-}+e_t$$(1) , the long-run relation between the unemployment rate and output increase (${\beta }^{+}$), and the output reduction (${\beta }^{-}$) is expected to be negative. In addition, it is assumed that unemployment rate reacts differently according to the sign of output under the hysteresis hypothesis. That is, the coefficient on economic expansion is expected to be smaller in absolute value than its counterpart $\left|{\beta }^{+}\right|<\left|{\beta }^{-}\right|.$ (2) $$\Delta y_t=v_t$$(2)

$y_t$ is decomposed as $y_t=y_0+y_t^{+}+y_t^{-}$ where $y_t^{+}$ and $y_t^{-}$ are partial sums of positive and negative changes in $y_t:$ (3) $$y_t^{+}=\sum _{j=1}^t\Delta y_j^{+}=\sum _{j=1}^t\mathrm{\text{max}}\hspace{0.17em}\left(\Delta y_j,0\right)$$(3) (4) $$y_t^{-}=\sum _{j=1}^t\Delta y_j^{-}=\sum _{j=1}^t\mathrm{\text{min}}\hspace{0.17em}\left(\Delta y_j,0\right)$$(4)

The disturbances $u_t$ and $v_t$ in (1) and (2) follow iid processes with zero means and finite variances (${\sigma }_u^2$ and ${\sigma }_v^2$), and they are independently distributed.

The stationary linear combination of the partial sum components is defined by Schorderet (2001): (5) $$z_t={\beta }_o^{+}{u}_t^{+}+{\beta }_o^{-}{u}_t^{-}+{\beta }_1^{+}{y}_t^{+}+{\beta }_1^{-}{y}_t^{-}$$(5) $u_t$ and $y_t$ are ‘asymmetrically cointegrated’ only if $z_t$ is stationary. The standard linear (symmetric) cointegration, which is a special case of (5), can only be obtained if ${\beta }_o^{+}={\beta }_o^{-}$ and ${\beta }_1^{+}={\beta }_1^{-}.$

However, the presence of weak endogeneity of the regressors and/or serially correlated errors will significantly affect both the asymptotic and the small sample properties of the estimators in Equation (1)(1) $$u_t={\beta }^{+}{y}_t^{+}+{\beta }^{-}{y}_t^{-}+e_t$$(1) . The OLS estimators in Equation (1)(1) $$u_t={\beta }^{+}{y}_t^{+}+{\beta }^{-}{y}_t^{-}+e_t$$(1) may remain super-consistent, but the asymptotic distribution will be non-Gaussian, and the resulting OLS estimators of the cointegrating parameter will be poorly determined in finite samples. Both the serial correlation and the endogeneity of the regressors are needed to be removed for hypothesis testing.

The solution to these twin problems in a dynamic regression model is provided by Pesaran and Shin (1998) and Pesaran et al. (2001). They develop a flexible, dynamic, parametric framework in which relationships combine long- and short-run asymmetries. Equation (1)(1) $$u_t={\beta }^{+}{y}_t^{+}+{\beta }^{-}{y}_t^{-}+e_t$$(1) can be re-written in an ARDL setting, as shown by Pesaran and Shin (1998), Pesaran et al. (2001) and Shin et al. (2014). For this purpose, we first introduce the nonlinear ARDL (p, q) model: (6) $$u_t=\sum _{j=1}^p{\mathrm{\varnothing }}_j{u}_{t-j}+\sum _{j=0}^q({\theta }_j^{+}{y}_{t-j}^{+}+{\theta }_j^{-}{y}_{t-j}^{-})+{\epsilon }_t$$(6) $y_t$ (output) is defined as $y_t=y_0+y_t^{+}+y_t^{-},$ ${\varnothing }_j$ is the autoregressive parameter, ${\theta }_j^{+}$ and ${\theta }_j^{-}$ are the asymmetric distributed-lag parameters, and ${\epsilon }_t$ is an iid process with zero mean and constant variance, ${\sigma }_{\epsilon }^2.$

Equation (6)(6) $$u_t=\sum _{j=1}^p{\mathrm{\varnothing }}_j{u}_{t-j}+\sum _{j=0}^q({\theta }_j^{+}{y}_{t-j}^{+}+{\theta }_j^{-}{y}_{t-j}^{-})+{\epsilon }_t$$(6) can be re-written in the error correction form as shown by Pesaran et al. (2001): (7) $$\begin{array}{c}\Delta u_t=\rho u_{t-1}+{\theta }^{+}{y}_{t-1}^{+}+{\theta }^{-}{y}_{t-1}^{-}+\sum _{j=1}^{p-1}{\gamma }_j{\Delta u}_{t-j}+\sum _{j=0}^{q-1}({\phi }_j^{+}\Delta y_{t-j}^{+}+{\phi }_j^{-}\Delta y_{t-j}^{-})+{\epsilon }_t=\rho \\ {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\phi }_j^{+}\Delta y_{t-j}^{+}+{\phi }_j^{-}\Delta y_{t-j}^{-})+{\epsilon }_t\\ \mathrm{\text{where}}\mathrm{ }\rho =\sum _{j=1}^p{\mathrm{\varnothing }}_j-1;{\gamma }_j=-\sum _{i=j+1}^p{\mathrm{\varnothing }}_j\text{for}j=1,\dots ,p-1;{\theta }^{+}=\sum _{j=0}^q{\theta }_j^{+};{\theta }^{-}=\sum _{j=0}^q{\theta }_j^{-};\\ {\phi }_0^{+}={\theta }_0^{+};{\phi }_j^{+}=\sum _{i=j+1}^q{\theta }_j^{+}\text{for}j=1,\dots ,q-1;{\phi }_0^{-}={\theta }_0^{-};{\phi }_j^{-}=\sum _{i=j+1}^q{\theta }_j^{-}\text{for}j=1,\dots ,q-1;\end{array}\mathrm{ }$$(7) $\rho ,$ ${\theta }^{+}$ and ${\theta }^{-}$ are the long-run coefficients, ${\phi }^{+}$ and ${\phi }^{-}$ are the short-run coefficients, ${\mathit{\text{nect}}}_t=u_t-{\beta }^{+}{y}_t^{+}-{\beta }^{-}{y}_t^{-}$ is the nonlinear error correction term, p and q are lag orders, and ${\beta }^{+}=-\frac{{\theta }^{+}}{\rho }$ and ${\beta }^{-}=-\frac{{\theta }^{-}}{\rho }$ are the long-run impacts of output (real GDP) increase and output (real GDP) reduction on the unemployment rate, respectively. That is, the latter factors are the associated asymmetric long-run parameters. Equation (7)(7) $$\begin{array}{c}\Delta u_t=\rho u_{t-1}+{\theta }^{+}{y}_{t-1}^{+}+{\theta }^{-}{y}_{t-1}^{-}+\sum _{j=1}^{p-1}{\gamma }_j{\Delta u}_{t-j}+\sum _{j=0}^{q-1}({\phi }_j^{+}\Delta y_{t-j}^{+}+{\phi }_j^{-}\Delta y_{t-j}^{-})+{\epsilon }_t=\rho \\ {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\phi }_j^{+}\Delta y_{t-j}^{+}+{\phi }_j^{-}\Delta y_{t-j}^{-})+{\epsilon }_t\\ \mathrm{\text{where}}\mathrm{ }\rho =\sum _{j=1}^p{\mathrm{\varnothing }}_j-1;{\gamma }_j=-\sum _{i=j+1}^p{\mathrm{\varnothing }}_j\text{for}j=1,\dots ,p-1;{\theta }^{+}=\sum _{j=0}^q{\theta }_j^{+};{\theta }^{-}=\sum _{j=0}^q{\theta }_j^{-};\\ {\phi }_0^{+}={\theta }_0^{+};{\phi }_j^{+}=\sum _{i=j+1}^q{\theta }_j^{+}\text{for}j=1,\dots ,q-1;{\phi }_0^{-}={\theta }_0^{-};{\phi }_j^{-}=\sum _{i=j+1}^q{\theta }_j^{-}\text{for}j=1,\dots ,q-1;\end{array}\mathrm{ }$$(7) is referred as the NARDL model in Shin et al. (2014).

To handle the possibility of non-zero contemporaneous correlation between output (real GDP) and the residuals in (7), the following reduced-form, data-generating process for $\Delta y_t$ is considered: (8) $${\Delta y}_t=\sum _{j=1}^{q-1}{\delta }_j{\Delta y}_{t-j}+v_t$$(8) where $v_t\sim \mathit{\text{iid}}\mathrm{ }(0,{\sigma }_v^2).$

The conditional presentation of ${\epsilon }_t$ on $v_t$ is given by the following: (9) $${\epsilon }_t=\omega v_t+{\tau }_t=\omega \left({\Delta y}_t-\sum _{j=1}^{q-1}{\pi }_j{\Delta y}_{t-1}\right)+{\tau }_t$$(9)

${\tau }_t$ is uncorrelated with $v_t$ by construction.

The following conditional nonlinear error correction model (ECM) (the NARDL-based ECM) is derived by substituting (9) into (7) and rearranging it: (10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) where ${\pi }_0^{+}={\theta }_0^{+}+\omega ;{\pi }_0^{-}={\theta }_0^{-}+\omega ;{\pi }_j^{+}={\theta }_0^{+}-\omega {\pi }_j;{\pi }_j^{-}={\theta }_0^{-}-\omega {\pi }_j\text{for}j=1;\dots ;q-1.{\sum }_{j=0}^{q-1}{\pi }_j^{+}$ measures the short-run influences of output increases on the changes in unemployment rate, whereas ${\sum }_{i=0}^{q-1}{\pi }_j^{-}$ gives the short-run influences of output reduction on the changes in unemployment rate. In this nonlinear ARDL model setting, the asymmetric long-run relationship, as well as the asymmetric short-run influences on unemployment rate, are captured. In addition, the weak endogeneity of any nonstationary explanatory variables is assured, and no residual serial correlation is achieved with the choice of an appropriate lag structure.

Reliable estimation of Equation (10)(10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) can be obtained by standard OLS, since the model is linear in all of the parameters, including ${\theta }^{+},$ ${\theta }^{-},$ ${\pi }^{+},\mathrm{\text{and}} {\pi }^{-}.$ The null hypotheses of a symmetric long-run relationship (${\beta }^{+}={\beta }^{-}$) and symmetric short-run coefficients (${\sum }_{j=0}^{q-1}{\pi }_j^{+}={\sum }_{i=0}^{q-1}{\pi }_j^{-}$) can be tested with Wald statistics following an asymptotic ${\mathrm{\chi }}^2$ distribution. This is possible because, in Equation 10(10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) , the OLS estimators of the long-run parameters (${\widehat{\beta }}^{+}=-\frac{{\widehat{\theta }}^{+}}{\widehat{\rho }}$ and ${\widehat{\beta }}^{-}=-\frac{{\widehat{\theta }}^{-}}{\widehat{\rho }}$) are T-consistent and have a mixture normal distribution, and the OLS estimators of all the short-run dynamic parameters are $\sqrt{T}$-consistent and follow an asymptotic normal distribution.

The existence of an asymmetric (cointegrating) long-run relationship based on the NARDL ECM in Equation (10)(10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) is tested by t- and F-tests, following the work of Pesaran et al. (2001) and Shin et al. (2014). The t-statistic ($t_{\mathit{\text{BDM}}}$) tests whether $\rho =0$ implies that there is no long-run relationship between the levels of $u_t,$ $y_t^{+}$ and $y_t^{-}.$ Similarly, an F-test ($F_{\mathit{\text{PSS}}}$) of the joint null ($\rho ={\theta }^{+}={\theta }^{-}=0$) tests for a long-run relationship – no asymmetric cointegration. If the null hypothesis is rejected based on the bounds testing procedure (Pesaran et al. 2001), then there exists a long-run relationship. Furthermore, the NARDL model is valid, irrespective of the integration orders of the regressors. Pesaran et al. (2001) propose two extreme cases, one in which the level regressors, $y_t^{+}$ and $y_t^{-},$ in Equation (10)(10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) are all I(1) and another in which they are all I(0). Pesaran et al. (2001) tabulate the critical value bounds for both the $t_{\mathit{\text{BDM}}}$ and $F_{\mathit{\text{PSS}}}$ statistics.

The transition between the initial equilibrium, short-run disequilibrium after a shock, and the new long-run equilibrium can be analysed by using dynamic multipliers (Shin et al. 2014). Both the asymmetric short-run adjustment and the asymmetric long-run reaction – as well as observing the responsiveness of the labour market reforms to cyclical output – can be shown in this way. In addition, the asymmetric cumulative dynamic multiplier effects of a 1% change in $y_t^{+}$ and $y_t^{-},$ respectively, are shown as follows: $$m_h^{+}=\sum _{j=0}^h\frac{\partial u_{t+j}}{\partial y_{t-1}^{+}}=\sum _{j=0}^h{\mu }_j^{+}$$ $$m_h^{-}=\sum _{j=0}^h\frac{\partial u_{t+j}}{\partial y_{t-1}^{-}}=\sum _{j=0}^h{\mu }_j^{-}$$

h = 0, 1, 2 …

Note that $h\to \infty ,$ $m_h^{+}\to {\beta }^{+}$ and $m_h^{-}\to {\beta }^{-}$ where ${\beta }^{+}$ and ${\beta }^{-}$ are the asymmetric long-run coefficients.

3. Data

The sample covers annual data on the Turkish unemployment rate and real GDP over the period from 1923 to 2019. Data for unemployment rate for the period from 1923 until 1987 are from Kafkas (2014, p. 70) and for the period since 1988 are obtained from the Turkish Statistical Institute (TurkStat). The real GDP series for the period from 1923 to 2019 are gathered from the TurkStat.

In sequel, we will denote unemployment rate in levels as u and the logarithmic transformation of real GDP as y. Furthermore, the growth rates of unemployment and the growth rates of the logarithm of real GDP are denoted as $\Delta u$ and $\Delta y,$ respectively. Both the unemployment rate and the logarithm of real GDP (in levels) and the corresponding growth rates are displayed in Figures 1 and 2. Clearly, during the early periods until the second half of the 1970s, the unemployment rate and real GDP in levels move in opposite directions, and from the mid-1970s until the mid-1990s, they move in the same direction. Both series tend to increase: The increase in the unemployment rate began in 1939, followed a sharp decrease in 1950, but has had an increasing trend since 1950. Similarly, the real GDP experienced a dip in 1945, but since 1945, it has displayed a strong tendency to increase. In addition, similar dynamics are observed in growth rates of time series; spikes in growth rates included those in 1924, 1946, 2001, 2009, 2010, and 2019, reflected in a stepwise shift in the levels of the two series.⁴

Figure 1. Unemployment rate and real GDP (in Logs).

Figure 2. First difference of unemployment rate and first difference of real GDP (in logs).

Overall, visual inspection suggests that unemployment rate and the logarithm of the real GDP tend to move together, suggesting that they react similarly to common shocks. However, this informal conclusion will be verified by application of NARDL model. Modelling methodology in this paper follows Castle and Hendry (2010; 2014) and Hendry (2015) that all forms of non-stationarity are modelled, including stochastic trends, measurement changes, non-linearities, location shifts and outliers.

4. Estimations

Empirical implementation of the nonlinear ARDL approach consists of the following steps: First, it remains necessary to conduct unit root tests so that there are not any I(2) variables, even though the ARDL approach to cointegration is applicable irrespective of whether the variables are I(0) or I(1). This is because the presence of an I(2) variable invalidates the computed F-statistics for testing cointegration. ADF, PP, KPSS and Zivot–Andrews unit root tests are used to establish the variables’ orders of integration. Second, Equation (10)(10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) is estimated and reduced to the final specification of the NARDL model by adopting the general-to-specific procedure suggested by Katrakilidis and Trachanas (2012) and Shin et al. (2014). Third, the presence of cointegration among the variables is examined using the bounds-testing approach of Pesaran et al. (2001) and Shin et al. (2011). This is the F-test of the null hypothesis, $(\rho ={\theta }^{+}$ = ${\theta }^{-}$ = 0). Fourth, with the presence of cointegration, an examination is conducted long- and short-run asymmetries in the relations between unemployment rate and output, and inferences are drawn. Finally, the asymmetric cumulative dynamic multiplier effects are also calculated and shown.

We perform three unit root tests, namely augmented Dickey–Fuller (ADF), Phillips–Perron (PP) and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests, as reported in Table 1, to test for the null hypothesis of non-stationarity and stationarity. The process of the combined use of unit root (ADF and PP) and stationarity (KPSS) tests is referred to as confirmatory data analysis (Burke 1994). Unemployment rate and the real GDP (in logs) tend to be non-stationary in levels according to at least one of the tests. However, the results depend on whether a constant and a trend are included in the unit root tests. In addition, unemployment rate and the real GDP (in logs) reject the null for a unit root in first differences for all three tests, again depending on whether a constant and a trend are included in the tests.

Table 1. Unit root tests.

	With constant	With constant and trend	Without constant and without trend	With constant	With constant and trend	Without constant and without trend
	U			Y
Augmented Dickey–Fuller test (ADF)
Level	−0.3748	−3.4661**	0.3401	−0.6418	−3.4911**	6.5211
First difference	−7.3209***	−7.5110***	−7.3153***	−11.1875***	−11.1258***	−4.4072***
Phillips–Perron test (PP)
Level	−0.5892	−4.1285**	0.2778	−0.6572	−3.5573**	7.2912***
First difference	−6.9517***	−7.2159***	−6.9519***	−11.1814***	−11.1187***	−8.3850***
Kwiatkowski–Phillips–Schmidt–Shin test (KPSS)
Level	1.0608***	0.1782**	–	1.2999***	0.0782	–
First difference	0.4376*	0.1082	–	0.0579	0.0463	–

*** and **indicates a 1% and 5% level of significance, respectively

Table 2 presents the results of the Zivot–Andrews structural break unit root test. This analysis shows that unemployment rate and real GDP (in logs) have non-stationarity in levels in the presence of the structural breaks in 1948 and 1967 (unemployment rate) and 1941, 1946 and 1951 (real GDP [in logs]).

Table 2. Zivot-Andrews unit root test.

	Level
	Constant		Trend		Constant and Trend
Variables	t statistic	Year of break	t statistic	Year of break	t statistic	Year of break
U	−4.114	1967	−4.055	1948	−4.726	1967
Y	−4.432	1941	−3.863	1946	−4.660	1951
	First difference
	Constant		Trend		Constant and Trend
	t statistic	Year of break	t statistic	Year of break	t statistic	Year of break
U	−7.339***	1979	−6.483***	1941	−7.204***	1942
Y	−11.657***	1946	−11.315***	1942	−13.521***	1946

*** and **indicates a 1% and 5% level of significance, respectively

Table 3 presents descriptive statistics and the correlation matrix. Unemployment rate mirrors a normal distribution with a negative kurtosis (platykurtic). Real GDP has a long-right tail (positive skewness) and a positive kurtosis (leptokurtic). Jarque-Bera statistics also confirm the results, indicating a problem of outliers in the series. The correlation matrix shows real GDP has a significant positive and robust correlation with unemployment rate.

Table 3. Descriptive statistics and correlation matrix.

Descriptive statistics
	Unemployment Rate	Real GDP
Mean	6.20	4.10E + 08
Median	6.60	2.18E + 08
Maximum	13.70	1.76E + 09
Minimum	1.50	19702983
Std. Dev.	3.06	4.56E + 08
Skewness	0.22	1.42
Kurtosis	1.90	4.16
Jarque-Bera	5.65	38.02
Probability	0.06	0.00
Sum	3.97E + 10	601.15
Sum Sq. Dev.	2.00E + 19	898.83
Observations	97	97
Correlation (Probability)
	Unemployment Rate	Real GDP	Change in Unemployment Rate	Change in Real GDP
Unemployment Rate	1.00
Real GDP	0.86(0.00)	1.00
Change in Unemployment Rate	0.24(0.02)	0.23(0.02)	1.00
Change in Real GDP	−0.06(0.58)	−0.02(0.81)	−0.23(0.02)	1.00

Table 4 presents the results of the NARDL model, Equation (10)(10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) without the restricted error correction term. In the cointegration tests, both the bound $t_{\mathit{\text{BDM}}}$ and $F_{\mathit{\text{PSS}}}$ statistics reject the null of no cointegration between unemployment rate and the logarithm of real GDP. The computed t-statistics value (-3.762) and the computed F-statistics value (5.134) surpass the tabulated upper bound value at a 5% significance level. Table 5 presents the asymmetric bound $F_{\mathit{\text{PSS}}}$ statistics values.

Table 4. Dynamic asymmetric estimation of the unemployment-output relationship (dependent variable: $\Delta y_t$).

Variable	Coefficient	Std. Error	t-Statistic
$u_{t-1}$	−0.185	0.049	−3.762
$y_{t-1}^{+}$	0.563	0.171	3.291
$y_{t-1}^{-}$	1.214	0.578	2.102
${\Delta u}_{t-1}$	0.443	0.082	5.396
$\Delta y_{t-2}^{+}$	1.946	1.125	1.731
Dummy1967	1.012	0.527	1.918
Dumm2001	2.051	0.548	3.744
Dummy2009	2.673	0.528	5.059
Dummy2010	−2.561	0.596	−4.299
Dummy2019	2.610	0.530	4.922
Constant	0.173	0.230	0.752
$L_{y^{+}}$	3.046	0.451	6.753
$L_{y^{-}}$	6.568	2.367	2.775
$R^2$	0.628
${\overline{R}}^2$	0.583
F-statistic	13.853[0.000]
${\mathrm{\chi }}_{\mathit{\text{SC}}}^2$	0.699[0.705]
${\mathrm{\chi }}_{\mathit{\text{FF}}}^2$	1.045[0.307]
${\mathrm{\chi }}_{\mathit{\text{NOR}}}^2$	9.694[0.008]
${\mathrm{\chi }}_{\mathit{\text{HET}}}^2$	7.306[0.696]
$t_{\mathit{\text{BDM}}}$	−0.185[0.049]
$F_{\mathit{\text{PSS}}}$	5.134[0.003]
$W_{\mathit{\text{LR}}}$	3.149[0.076]
$W_{\mathit{\text{SR}}}$	–
Observations	93

Note: $L_{y^{+}}$ and $L_{y^{-}}$ denote the long-run coefficients associated with positive and negative changes of output, respectively. ${\mathrm{\chi }}_{\mathit{\text{SC}}}^2,$ ${\mathrm{\chi }}_{\mathit{\text{FF}}}^2,$ ${\mathrm{\chi }}_{\mathit{\text{NOR}}}^2,$ and ${\mathrm{\chi }}_{\mathit{\text{HET}}}^2$ are LM tests for serial correlation, functional form (Ramsey’s RESET test), normality, and heteroscedasticity, respectively. Figures in square parentheses are the associated p-values.

Table 5. Bounds test results in nonlinear specification.

F-Bounds Test		Null Hypothesis: No levels relationship
Test Statistic	Value	Significance	I(0)	I(1)
		Asymptotic: n = 1000
F-statistic	5.134	10%	4.04	4.78
k = 1		5%	4.94	5.73
		2.5%	5.77	6.68
		1%	6.84	7.84
F-statistic	5.134	10%	3.17	4.14
k = 2		5%	3.79	4.85
		2.5%	4.41	5.52
		1%	5.15	6.36
Actual Sample Size	95	Finite Sample: n = 80
k = 1		10%	4.14	4.90
		5%	5.06	5.93
		1%	7.10	8.26
k = 2		10%	3.26	4.25
		5%	3.94	5.04
		1%	5.41	6.78
t-Bounds Test		Null Hypothesis: No levels relationship
Test Statistic	Value	Significance	I(0)	I(1)
t-statistic	−3.762	10%	−2.57	−2.91
k = 1		5%	−2.86	−3.22
		2.5%	−3.13	−3.50
		1%	−3.43	−3.82
t-statistic	−3.762	10%	−2.57	−3.21
k = 2		5%	−2.86	−3.53
		2.5%	−3.13	−3.80
		1%	−3.43	−4.10

Note: Asymptotic values are based on calculations in Pesaran et al. (2001) and finite sample values are based on calculations in Narayan (2005).

Table 4 also demonstrates the long- and short-run impacts of positive and negative shocks in real GDP (in logs) on unemployment rate. The effects of the positive and negative shocks in real GDP are positive, with values of 0.563 and 1.214, respectively, which are quite far apart, suggesting asymmetry. The estimated long-run coefficients of $y_t^{+}$ and $y_t^{-}$ are $L_{y^{+}}={\widehat{\beta }}^{+}=-\frac{{\widehat{\theta }}^{+}}{\widehat{\rho }}$ = 3.046 and $L_{y^{-}}={\widehat{\beta }}^{-}=-\frac{{\widehat{\theta }}^{-}}{\widehat{\rho }}$ = 6.568, respectively. These indicate that an economic upturn of 32.83% increases unemployment rate by 1% in Turkey, whereas an economic downturn of 15.23% decreases unemployment rate by 1%. This pro-cyclical output and unemployment relationship does not necessarily indicate that Okun’s law does not hold. For example, a labour market miracle describes the positive relationship between unemployment and output in Germany during the Great Recession of 2008-2009. Low layoffs in the recession were the results of low hiring in the previous expansion because of the pessimistic expectations (Burda and Hunt 2011; Rinne & Zimmerman 2012). Similarly, Ben-Salha and Mrabet (2019) report jobless economic growth for youth population in North African countries. Elroukh, Nikolsko-Rzhevskyy and Panovska (2020) find strong evidence of jobless recoveries in the US, Canada, Japan, and Italy. Gordon (2010) discusses jobless recoveries that followed recessions in 1990–91, 2001, and 2007–09. The initial stages of the recovery were boosted by a productivity growth and a continuing decline in employment due to the ICT revolution as well as to the labour cost reductions. In addition, jobless recovery which generates asymmetry in Okun’s law is consistent with the risk aversion hypothesis and suggests that the effects of labour rigidities are curbed by risk aversion of firms (Nebot et al. 2019; OECD 2020). Barışık, Çevik and Çevik (2010), Tarı and Abasız (2010) and Arabacı and Yüksel-Arabacı (2018) also point out the jobless growth in Turkey with empirical evidence.

The positive relation between unemployment and output can also be explained by ‘discouraged worker’ and ‘added worker’ effects (Murphy and Topel 1997; Rodríguez-Gutiérrez 2003; Gustavsson and Österholm 2006; Österholm 2010; Emerson 2011; Lee and Parasnis 2014; Kesselring and Bremmer 2015; Mankart and Oikonomou 2016; Evans 2018). Labour force participation rate may vary, especially in Turkey, because of movement of individuals in and out of the labour market in response to institutional and legislative changes such as the establishment of the early retirement scheme in the early 1990s and its abolition in the first half of 2000 in Turkey and/or business cycles. ‘Discouraged worker’ and ‘added worker’ effects describe the changes in labour force participation rate during the business cycles. For example, during business troughs in Turkey, decreased unemployment rate might reflect the withdrawal from the labour force into informal employment due to the discouraged worker effect, especially for women and youth population. During the booms, increased unemployment rate might reflect the increased labour force participation due to the increased in job applications, especially for recent graduates and women. These seem plausible explanations given the high unemployment rate among women and youth population, and high informal employment in Turkey. The current unemployment rate is 13.7% (in 2019): 12.4% for men and 16.5% for women. Similarly, labour force participation rate is 53% (in 2019), and this rate is 72% for men and 34.4% for women. The youth unemployment rate (ages 15 and 24) is 25.4% (in 2019): 22.5% for men and 30.6% for women (TurkStat 2019). In addition, while unregistered employment rate is 35% (in 2019), this rate is 31% for men and 42% for women. 81% of unregistered female employment in agricultural sector is in the form of ‘unpaid family worker’ (in 2019). However, this is 23% for men. The recent OECD estimates find that the share of informal activities in the total added value is about 27% in Turkey (OECD 2018) which is close to undeclared work that is 35% of all employment in Turkey (TurkStat 2019). Discouraged and added workers can move in and out of the formal and informal labour markets during the business cycles in Turkey.

Additionally, data on precarious (non-standard) work provide additional information. The temporary employment rate (% of dependent employment) which is 11.6% (in 2019) in Turkey is close to the OECD average of 11.8%. The temporary employment rates for men (12%) and for women (11%) are almost the same (OECD 2021). The temporary employment rate for youth population is 23.7% and it is the same for both men and women (in 2019). The part-time employment rate (total) (% of total employment) is 9.5% (in 2019), however, this rate is 6.4% (% of total male employment) for men and 16.2% (% of total female employment) for women. The part-time employment rate for youth population is 14.5% (in 2019): 11.9% for men and 19.6% for women (TurkStat 2019). Flexible temporary and part-time contracts can help explain the responsiveness of unemployment to changes in output, since these contracts require smaller adjustment costs of employment to output shocks for firms to terminate and optimize (Dixon, Lim and van Ours 2017). However, majority of people in Turkey – both men and women, and youth – have full-time and permanent contracts. This inflexible Turkish labour market suggests and is consistent with the findings in this study that the relationship between unemployment and output might be asymmetric and positively related.

Moreover, positive asymmetric relationship between unemployment and output can also be explained by the shock-absorber capacity of the Turkish agricultural sector. 87% of agricultural employment is unregistered or unrecorded or undeclared in Turkey (in 2019): this figure is 80% for men and 96% for women. Interestingly, 65% of unregistered ‘male’ agricultural employees work for their own account and 81% of unregistered ‘female’ agricultural employees are unpaid family workers. Similarly, the youth unemployment rate which is 29% is higher in the non-agricultural sector than in the agricultural sector (22%). The male (female) youth unemployment rates in the non-agricultural sector and in the agricultural sector are 25% and 20% (36% and 26%), respectively (TurkStat 2019). Thus, it is also easier for young people and women to be employed in the agricultural sector in Turkey. When there is a negative shock to output especially in industrial and service sectors when the economy slows down, employees can move to the unregistered agricultural sector. By reducing the labour force participation, they actually increase employment rate and reduce unemployment rate during the recessions. World Bank (2010) and Hanusch (2012) also point out that Okun’s Law is reversed for agricultural jobs, especially for developing economies, and the impact of a negative output shock on unemployment is smoothed out by the agriculture sector. Similarly, during the booms, Turkish workers appear in the labour force participation, however, they are more likely to accept the unregistered regular and casual jobs due to high firing costs in Turkey. 58% of regular and casual jobs in non-agricultural sectors are unregistered or undeclared. This figure is 56% (61%) for men (women) (TurkStat 2019).

In addition, given the persistence in differences between male, female and youth labour force participation, unemployment, unregistered employment, and the type of employment; the gender and age dimensions of Turkish unemployment can provide insights into explaining a positive asymmetric relationship between unemployment and output, since the unemployment dynamics over the business cycle might not be gender and age neutral. Clark and Summers (1981), Blank (1989), Azmat, Güell and Manning (2006), Queneau and Sen (2008, 2009, 2010), Hotchkiss and Robertson (2012), Hoynes, Miller and Shaller (2012), Peiró, Belaire-Franch and Gonzalo (2012), Hutengs and Stadmann (2013), Zanin (2014), Belaire-Franch and Peiró 2015, Marconi, Beblavý and Maselli (2016), Razzu and Singleton (2016), Bredemeier, Juessen and Winkler (2017), Dunsch (2017), Blázquez-Fernández, Cantarero-Prieto and Pascual-Sáez (2018), Ben-Salha and Mrabet (2019), Butkus and Seputiene (2019) and Bod’a and Považanová (2021) show theoretically and empirically that unemployment responds differently to business fluctuations by gender and age cohorts that can be the driving force for the asymmetric relationship. Indeed, Zanin (2014) and Bod’a and Považanová (2021) report that the output-unemployment relationship is asymmetric by gender in Turkey.

The Wald statistics ($W_{\mathit{\text{LR}}}$) tests whether the long-run coefficients are equal. The null hypothesis of a symmetric long-run relationship (${\beta }^{+}={\beta }^{-}$) rejects the null of symmetry. This indicates nonlinearity with an affirmed positive association between output and unemployment.

The Wald statistic ($W_{\mathit{\text{SR}}}$) that tests the short-run dynamic asymmetry could not be calculated since there is only one positive shock ($\Delta y_{t-2}^{+}$) in the short run. Moreover, the positive shock in the short-run have a smaller impact than the long-run shocks.

In addition, these results are consistent with the results of Phelps (1972), showing that cyclical shocks affect the structural part of unemployment, and past unemployment rates matter for current unemployment rates.

Several dummies are included in Equation 10(10) $${\Delta u}_t=\rho {\mathit{\text{nect}}}_{t-1}+\sum _{j=1}^{p-1}{\gamma }_j\Delta u_{t-j}+\sum _{j=0}^{q-1}({\pi }_j^{+}\Delta y_t^{+}+{\pi }_j^{-}\Delta y_t^{-})+{\tau }_t$$(10) in order to manage the outliers and breaks since, the outliers have been identified as those residuals exceeding regression standard errors by a factor 2 in the estimated regression. The dummy for the year 1967 reflects the results of the import-substitution industrialization strategy and a large drop in imports in 1967; the dummy for the year 2001 explains the 2001 Turkish banking and currency crisis; the dummy for the year 2009 stands for the 2008–2009 global financial crisis; the dummy for the year 2010 reflects the strong economic recovery following the financial crisis; and the dummy for the year 2019 records the highest unemployment rate in the Turkish economic history.

Dynamic multipliers in Fig. 3 show that the Turkish labour markets respond rapidly and strongly to cyclical downturn of outputs in the short-run, and mildly to upturns. However, full adjustment to the new equilibrium is takes a long time. Fig 4. confirms the model stability with the CUSUM test.

Figure 3. Output dynamic multipliers. The solid black line indicates the positive impact of output. Blackline in dots displays a negative effect of output. The strong dotted red line shows an asymmetry, while thin red lines represent critical bounds.

Figure 4. Cumulative sum of recursive residuals.

5. Conclusions

Understanding asymmetries in the unemployment–output relationship is crucial in implementing the optimal structural reforms, since structural reforms might produce different results when the long- and short-run unemployment–output relationships are nonlinear (Silvapulle et al. 2004; Belaire-Franch and Peiró 2015).

Therefore, this study has investigated the asymmetric unemployment-output trade-off in the Turkey using the NARDL approach. The NARDL estimates confirm that short- and long-run asymmetric relationships between unemployment and output exist in Turkey. The long-run impacts are larger than the short-run impact. The structural instabilities, breaks and outliers are handled with by means of impulse dummies. Dynamic multipliers demonstrate that the Turkish labour markets respond quickly to the cyclical output troughs in the short-run, but the full correction takes a long time.

The positive short- and long-run asymmetric relationships between unemployment rate and output are explained by jobless recovery, labour market rigidities, high firing costs, ‘discouraged worker’ and ‘added worker’ effects, a large informal employment, the shock-absorber capacity of the Turkish agricultural employment, and gender and age differences in labour market in Turkey.

The findings suggest new research on a relationship between labour force participation (men, women and youth population) and output as well as on informal employment of women and youth population during the business cycles in Turkey in order to manage high unemployment rate and informal employment during the economic booms. In addition, the asymmetry determinants can be identified by utilising a multivariate regression and including variables such as tax rate, minimum wage, labour cost, government deficit/surplus, industrial production, imports (% of GDP), and exports (% of GDP) as in Tang and Bertencourt (2017). Understanding labour force participation and informal employment by gender and age during the business cycles as well as the determinants of asymmetries might help conduct better and effective labour market reforms in Turkey.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

Conflict of interest

Both authors declare that they have no conflict of interest.

Notes

1 The results of linear models vary substantially across countries and over time, and are sensitive to model specification and inconclusive (Gordon 1984; Hamanda and Kurosaka 1984; Clark 1989; Prachowny 1993; Weber 1995; Moosa 1997, 1999, 2008; Attfield and Silverstone 1998; Freeman 2001; Christopoulos 2004; Gabrisch and Buscher 2006; Ahmed and Awadalbari 2014; Ball, Leigh and Loungani 2017).

2 See Wilson (1960) for the early discussion of unstable unemployment-output relationship and Lee (2000) for the importance of structural breaks in the 1970s.

3 For a nonlinear unemployment-output relationship, see Lee (2000), Harris and Silverstone (2001), Sögner and Stiassny (2002), Crespo-Cuaresma (2003), Vougas (2003), Silvapulle, Moosa and Silvapulle (2004), Huang and Chang (2005), Holmes and Silverstone (2006), Huang and Lin (2006), Marinkov and Geldenhuys (2007), Fouquau (2008), Beaton (2010), Zanin and Marra (2011), Jardin and Stephan (2012), Çevik, Dibooğlu and Barişik (2013), Chinn, Ferrara and Mignon (2014), Shin et al. (2014), Abbas and Russell (2015), Österholm (2016), Gouider, Nouira and Sboui (2018), Grant (2018), Christopoulos, McAdam and Tzavalis (2019), Nebot, Beyaert and García-Solanes (2019) and Bod’a and Považanová (2019, 2021).

4 The graphics, regression output, and residual diagnostic and tests were all calculated using EViews 11.