
Testing Asymmetric Cointegration between Real Wage, Labour Productivity and Job Opportunity in South Africa

Thomas Habanabakize^{1}
Abstract: Labour productivity and real wage are two dynamic economic indicators that, among many others, influence employment changes. Their effects on employment or job opportunities can either be positive or negative. This study investigates the asymmetric cointegration between real wage, labour productivity and job opportunity in South Africa between 1994 and 2018. The used methodology includes the application of a nonlinear autoregressive distributed lag (NARDL) model, ECM and the dynamic multipliers. The obtained results from the bound testing suggested the existence of a long run relationship among the underlined variables. The estimated NARDL model revealed that real wage and labour productivity asymmetrically influence job opportunity dynamism. While positive component of productivity dominates over negative components; negative component of real wage dominates the positive component leading. Thus, labour productivity growth creates job opportunities whilst increase in real wage leads to a decline in the job opportunity. The study, therefore, recommends improvement in both labour productivity capacity through skills enhancement and real wage management through currency strengthening.
Keywords: asymmetry; employment; nonlinear; productivity; real wage; South Africa
JEL Classification: J01
1. Introduction
Over the last two decades, working opportunities (employment) has been and remains a concern in South Africa. Between 1995 and 2001 more than 1.6 million jobs were created within south African; however, owing to the growing labour force, in 2002 the number of unemployed people was over seven million (Bhorat, 2003). Unemployment situation worsened in 2008 where the country lost approximately five percent of its total employment due to the financial crisis (Klein, 2012). In 2019, the South African unemployment rate reached the rate of 29.9 percent (South African Reserve Bank (SARB) 2020) and the total number of unemployed people extended ten million (Stats SA, 2020).
Besides the effect of the 2008 financial crisis on job opportunities, unemployment growth is caused by sluggish economic growth and labour market fluctuations associated with imbalances between labour productivity and rapid increase in real wages (Klein, 2012; Wittenberg, 2014). A number of studies was conducted to assess the effect of productivity and real wages on employment in South Africa
(Morton & Blair, 2020; Habanabakize et al., 2019; Klein, 2012; Wakeford, 2004). Nonetheless, none of these studies considered asymmetric relationship among these economic indicators, they only were interested in assessing a linear (symmetric) association between of productivity, real wages and employment. This study aims to analyse the asymmetric effects of both real wages and labour productivity growth on job opportunity in South African.
The study is divided into five sections: the first section provides the introductory background, the second section briefly discusses the theoretical and empirical relationship among the underlined variables, the third section provides the study methodology, the four section deal with analysis findings and discussion; while the last section provides a concise conclusion and policy recommendations. Throughout the study, two concepts namely job opportunity and employment are used interchangeably.
2. Literature Review
2.1. Real Wages, Labour Productivity and Employment Theoretical Nexus
Wages and labour productivity are considered as the main driver of job opportunities in the labour markets (Elżbieta & Danuta, 2015; Landmann, 2004). The relationship between economic indicators is anchored within two main economic theories namely Keynesian and Neoclassical theory. The neoclassical theory argues that due to marketclearing, the economy operates always at full employment and productivity is determined by the state of technology within the economy (Landmann, 2004). The main drawback of this theory is the ignorance of technological and monetary fluctuations within the business cycle. Thus, the neoclassical theory was contested by Keynesian theory. The letter asserts that employment and productivity behaviours are mainly determined by adjustments in aggregate demand for both labour and output (Landmann, 2004). In Keynesian theory, wages can only have a significant short term impact on job opportunities, while the productivity impacts on long term employment levels.
Though contradictory in some ways, these two theories are still relevant to explain the realworld economic behaviours as each holds its own strengths and weaknesses (Arestis & Bittes, 2018; Onyimadu, 2015). These theories discuss the interrelationships that may exist between labour productivity, job opportunities and wage shocks. In case the labour supply curve is not perfectly elastic, high productivity leads to both job opportunity and high wages (Pettinger, 2017).
An inverse relationship exists between job opportunity and real wages. Increasing real wages implies rising labour cost for a firm and the latter may decide to substitute labour with capital to increase its marginal productivity (Wakeford, 2004). On the other hand, it is not always that high labour productivity results in high real wage. It is possible to experience productivity growth with a constant real wage. This is because the equation of wageproductivity includes other economic factors such as labour cost adjustment and price legalities (Klein, 2012). Additionally, labour market regulations and employment protection are also factors that may cause the absence longrun relationship between labour productivity, real wage and workers bargaining power (Karabarbounis & Neiman, 2014).
Besides the Keynesian and new classical economic theory, the standard economic theory represented by Hammermesh (1993) and supported by Borjas (2010) suggests a strong relationship between wages, productivity and job opportunity. Labour productivity includes both positive and negative impact on job opportunity. Productivity growth leads to jobless in both short and medium run to create more jobs in the long run (Gallegati et al., 2016; Partridge et al., 2019). Additionally, the effect of productivity on employment differs among industries as it creates job opportunities in those with elastic demand and destroys jobs in those industries with inelastic demand (Blien & Ludewig, 2014).
2.2. Review of Empirical Studies
Many studies were conducted to assess the effect of labour productivity and real wages on employment or job opportunities. A brief summary of some of those studies and their findings is provided in Table 1.
Table 1. Effect of Labour Productivity and Real Wages Fluctuation on Job Opportunities
Author &Date 
Country 
Sample period 
Methods 
Findings/study conclusion 
Habanabakize et al. (2019) 
South Africa 
1995  2019 
ARDL 
A negative relationship exists between real wage and employment. 
Bjuggren (2018) 
Sweden 
1997  2003 
Panel OLS 
Productivity has no significant effect on employment. 
Falk & Hagsten, 2018 
EU countries 
2002  2010 
System GMM 
A positive relationship between productivity and job opportunity 
Graetz & Michaels, 2018 
7 of developed countries 
1993  2007 
OLS & SLS 
A positive relationship exists between labour productivity and real wages. 
Autor& Salomons (2017) 
OECD countries 
19702007 
Panel OLS 
Productivity growth increases have an asymmetric effect on employment levels 
Adudu & Ojonye (2015) 
Nigeria 
1990  2009 
Granger causality 
High job opportunity induces wage reduction and vice versa. 
Bakker (2015) 
OECD countries 
2007  2014 
OLS 
An asymmetric relationship exists between real wage and employment. 
Amassoma & Nwosa (2013) 
Nigeria 
1986  2010 
ECM 
Insignificant relationship between unemployment and productivity. 
Junankar (2013) 
developed and developing countries 
1950  1989 1990  2010 
GMM estimation 
Tradeoff and inverse relationship exist between productivity and employment. 
Alani (2012) 
Uganda 
1972 2008 
OLS 
An inverse relationship between labour productivity and employment. 
Klein (2012) 
South Africa 
2008  2011 
Panel OLS 
A positive relationship between employment and labour productivity 
Seputiene (2011) 
EU countries 
2000  2010 
OLS 
Asymmetric relationship exists between real wage and employment 
Yusof (2008) 
Malaysia 
1992  2005 
VECM 
A positive relationship exists between employment growth and labour productivity; while an inverse relationship exists between employment and real wages. 
3. Data Description and Research Methodology
3.1. Source and Definition of Data
The study employs quarterly time series data with a sample size spanning the period from 2002 to 2019. The used data is sourced from the South African Reserve Bank website. The analysed variables are job opportunity as a proxy of total employment (dependent variable), real wages and labour productivity (explanatory variables).
3.2. Methodology
The aforementioned variables are expected to have both linear and nonlinear relationship. The linear relationship (longrun and shortrun) among variables can be expressed as follow:
_{ } = _{ } + _{ } + _{ } + _{ } (1)
Where _{ } denotes natural log of job opportunity, _{ } is the natural log of labour productivity and _{ } is the natural log of real wages, _{ } is the constant term, _{ } are the model coefficients, _{ } is the error correction term and t denotes the period. Equation 2 is obtained by transforming the equation 1 into the generic ARDL estimation form:
_{ } = _{ } + _{ } + _{ } + _{ } + _{ } +_{ }+_{ } + _{ } (2)
Where _{ } denotes a differentiated variable, _{ } is the white noise, _{ } to _{ } denote longrun coefficients, _{ } to _{ } are shortrun coefficients and (t1) denotes a lagged period.
While analysing a time series data, it is important to determine the integration order for variables of interest. The knowledge of variables integration order assists in evading spurious regression (Gujarati & Porter, 2009). Variables can either be integrated of order zero (at level) and are noted as I(0), integrated of order one (after being differentiated once) and are noted as I(1) or integrated of order one (after being differentiated twice) and are noted as I(2). This study employed both Augmented DickeyFuller (ADF) suggested by Dickey and Fuller (1979) and KPSS suggested by Kwiatkowski et al. (1992) tests to ascertain variables integration order.
When variables order of integration is known, the next step is to perform a cointegration analysis. Various tests can assist in testing for cointegration among variables. These tests include Engle and Granger (1987) and JohansenJuselius (1990) cointegration tests. However, both models are associated with some deficiencies and limitations. For instance, these tests cannot be applied to a mixture of I(0) and I(1) of variables. To overcome this inability, Pesaran et al. (2001) suggest the use of the Autoregressive Distributed Lag (ARDL) model. This approach is applicable when variables are either I(0), I(1) or a mixture of the two. This model was selected for the current study. To estimate the bestfitted model exhibited in equation 3, each variable was considered as the dependent variable and expressed as follows:
_{ } = _{ } + _{ } _{ } + _{ } + _{ } (3)
Where _{ } to _{ } denote constant terms, _{ } to _{ } represent longrun coefficients for both long and shortrun relationships. The longrun relationship is tested under the following hypothesis:
_{ } : no longrun relationship [_{ }= 0)]
_{ } :longrun relationship exists [_{ }≠ 0)]
_{ } : no shortrun relationship [_{ }= 0)]
_{ } : short relationship exists [_{ }≠ 0)]
The decision and conclusion of the abovelisted hypothesis are made based on a comparison between the Fstatistics from the bound test for cointegration and the Pesaran et al. (2001) critical values. Subsequently, one of the following three conclusions is made.
If the Fstatistics is > upper bound critical value: variables cointegrate
If the Fstatistics is < lower bound of critical value: variables do not cointegration
If the Fstatistics is > lower bound and yet < upper bound of critical value: no conclusion
Once cointegration is established, the subsequent step is to estimate long and shortrun coefficients. Using ARDL (m, q, p), the model equilibrium is expressed as follows:
_{ } = _{ } + _{ } + _{ } + _{ } (4)
_{ } = _{ } + _{ } + _{ } + _{ } + _{ } (5)
Using Schwarz information criteria (SIC), two lags were selected as the optimum lag length for the model. Shortrun elasticities were also derived from the following error correction model:
_{ } = _{ } + _{ } + _{ } + _{ } +_{ } + _{ } (6)
The _{ } is expressed as:
_{ } = _{ } − _{ } − _{ } − _{ } − _{ } (7)
To examine a directional causal relationship among variables, the subsequent vector error correction (VECM) is considered during the analysis.
_{ } = _{ } + _{ } _{ }+ _{ } _{ } + _{ } (8)
Since the core objective of the study is to examine the existence of an asymmetric relationship between job opportunity (employment), real wages and labour productivity, the nonlinear ARDL) suggested by Shin et al. (2014) is applied on variables. Thus, considering both positive and negative alterations of independent variables, the new denotation was expressed as follows: real wages (RW^{+}, RW^{−}); labour productivity (LP^{+}, LP^{−}). Decomposition of each variable is represented as:
_{ } (9)
_{ } (10)
Applying nonlinear features on Equation 2, the nonlinear ARDL is expressed in Equation 11:
_{ } = _{ } + _{ } + _{ } + _{ } + _{ } + _{ } + _{ } + _{ } + _{ } + _{ } + _{ } + _{ } (11)
The relationship expressed in equation 11, follows the model proposed by Shin et al. (2014), and it is evaluated using the Pesaran et al. (2001) critical values.
4. Results and Discussion
4.1. Graphical Representation of Explanatory Components
The NARDL model is based on the assertion that a specific economic of financial variable possesses different impact during the positive and negative shocks. Therefore, the NARDL approach divides productivity and real wages into positive and negative components. Figure 1 and Figure 2 exhibit positive and negative components of both productivity and real wages. Looking at figure 1, between the third quarter of 2002 and the third quarter of 2003 productivity had a symmetric (linear) positive effect on employment. Then it had a slightly negative effect between the fourth quarter of 2003 and the fourth quarter of 2007. From 2007 up to 2019, the negative effect of productivity was gradually increasing.
Considering the effect of the negative component of real wages on employment was zero between 2002 and 2006. From 2007 to 2019, the negative component of real wages experiences an ongoing movement of stable – down – stable – down up to 2019. On the other hand, between 2002 and 2019.


Figure 1. Negative and Positive Components of Productivity


Figure 2. Negative and Positive Components of Real Wages
4.2. Test for Stationarity and Unit Root
Using both ADF and PP unit root tests, the result in Table 2 shows that job opportunity, labour productivity has a unit root at levels and become stationary at first difference. However, the stationarity test (KPSS) indicates that both job opportunity and real wages are stationary at levels while labour productivity becomes stationary at first difference. Since, the stationarity results infer that variables are a mixture of I(0) and I(1), and that the stationarity results are considered to produce more accurate results (Jafari et al., 2012), the ARDL model was selected based on KPSS results.
Table 2. Stationarity and Unit Root Results
Variable 
Levels 
1^{st} Difference 


ADF 
PP 
KPSS 
ADF 
PP 
KPSS 

LD (Y) 
intercept 
0.854 
0.857 
1.062 
0.000* 
0.000* 
0.093* 
Intercept & trend 
0.475 
0.706 
0.136* 
0.002* 
0.000* 
0.087* 

LRW 
intercept 
1.000 
1.000 
1.184 
0.064 
0.000* 
1.206 
Intercept & trend 
0.905 
0.928 
0.309 
0.000* 
0.000* 
0.109* 

LLP 
intercept 
0.402 
0.305 
1.194 
0.000 
0.000 
0.418* 
Intercept & trend 
0.976 
0.987 
0.284 
0.000 
0.000 
0.098* 
Note: * the series has no unit root (is stationary) at 5% significant level
4.4. Asymmetric Bound Test for Cointegration
Bound test testing for cointegration was used to assess the presence of a joint longrun relationship among variables. The results in Table 3 confirm the rejection of null hypothesis suggesting the absence of cointegration among variables. The decision was made based on that fact that the computed Fstatistics of 8.743383 greater than all the upper bound critical values.
Table 3. Asymmetric ARDL Bounds Test and Critical Bounds Value.
Test Statistic 
Value 

Fstatistic 
8.743383 

Critical Value Bounds 

Significance 
I (0) Bound 
I(1) Bound 
10% 
2.2 
3.09 
5% 
2.56 
3.49 
1% 
3.29 
4.37 
Having established the presence of cointegration among variables, it is now possible to estimate the asymmetric effect of both labour productivity and real wages on job opportunity. Following the results in Table 3, the longrun coefficients suggest that the positive effect of both productivity and real wages are 4.96 percent and 0.72 percent respectively; while the negative effects are 1.5 percent for productivity and 5.96 for real wages. These results imply that positive shocks in productivity level increase the quantity of job opportunity whilst negative changes in productivity level has a small effect on the job opportunity. On the other side, an increase in real wages leads to a reduction in job opportunity while a decline of real wages stimulates employers to demand more labour. These results support economic theories suggesting a positive relationship between productivity and job opportunity, and an inverse relationship between real wage growth and job opportunity (Gans et al., 2011). Besides the relationship proposed by those theories, some empirical findings also pointed out that productivity growth results in a rise in job opportunity whilst high real wage inversely relates to job opportunity (Apergis, 2008; Das et al., 2017; Klein, 2012). In regards to shortrun shocks, positive fluctuations of productivity result in a positive response to job opportunity while the negative changes in productivity are not statistically significant to impact on job opportunity behaviour. Similarly, both positive and negative components of real wages have no significant effects on job opportunities. This result of no significant effect of wage on employment is supported by the findings of Bocean (2015). The estimated coefficient of the error correction model (ECM) was 0.105633. As presented in Table 4, the value of the ECM is negative and statistically significant with 99 confidence level. This implies that approximately 11 percent of the model shortrun shocks are adjusted each quarter and converge to longrun the equilibrium.
Table 4. Asymmetric ARDL Coefficients and the ECM Results
Variable 
Longrun Coefficient 
Std. Error 
tStatistic 
Prob. 

LNPROD+ 
4.963 
2.879 
1.723 
0.090 

LNPROD^{─} 
1.518 
1.883 
0.806 
0.423 

LNWAGE+ 
0.720 
0.497 
1.447 
0.153 

LNWAGE^{─} 
5.960 
5.519 
1.079 
0.284 

C 
15.727 
0.087 
181.81 
0.000 

Variable 
Shortrun Coefficient 
Std. Error 
tStatistic 
Prob. 


D(LNPROD+) 
0.386 
0.185 
2.093 
0.040* 


D(LNPROD^{─}) 
0.082 
0.386 
0.211 
0.833 


D(LNWAGE+) 
0.125 
0.089 
1.404 
0.166 


D(LNWAGE^{─}) 
0.075 
0.484 
0.155 
0.877 


ECT(1) 
0.106 
0.017 
6.062 
0.000* 

Note: * depict significance at 5 percent.
To validate the NARDL results, diagnostic tests were conducted before drawing inferences of explanatory variables on the dependent variable. As indicated by the results in Table 4, the NARDL model has passed all performed tests. Thus, the model is stable and the obtained NARDL findings are accurate.
Table 5. NARDL Diagnostic Statistics
Tests 
PValue of X^{2} 
Conclusion based on Pvalue 
Ramsey Reset Test 
0.2679* 
Model is accurately specified 
LM 
0.9798* 
No Serial Correlation 
White 
0.8157* 
No Heteroscedasticity 
Note: * specifies a pvalue that is greater than 0.05
4.5. NARDL Dynamic Multipliers
To assess asymmetric adjustment within the existing longrun equilibrium post to new longrun equilibrium owing to negative and positive shocks, a graph of dynamic multiplier was plotted for NARDL as depicted by both figure 5 and 6. On these figures, the asymmetry curves depict the linear mixture of the dynamic multipliers due to negative and positive shocks in productivity and real wages. These positive and negative fluctuations provide evidence for the asymmetric alteration of employment to negative and positive changes in productivity and real wages at a given period. The overall outcome of dynamic multiplier graphs suggests that while a positive shock in productivity levels influences more job opportunity fluctuations compared to negative shocks; the negative shocks from real wages influence job opportunity level compared to positive shocks.
Figure 5. NARDL Dynamic Multiplier Graph for Labour Productivity
Figure 6. NARDL Dynamic Multiplier Graph for Real Wages
5. Conclusion and Recommendations
The study attempts to provide both theoretical and empirical frameworks that explain how changes in both productivity and real wages influence the South Africa job opportunity. The theoretical assumptions were that positive change in productivity would lead to a rise in job opportunity whilst a decline in productivity would cause a job opportunity to decline. On the other side, it was assumed that real wages have an inverse relationship with job opportunity levels. For empirical assessment, the performed NARDL and Wild tests confirmed the presence of an asymmetric longrun relationship among variables. Findings suggest that the positive effects of the labour productivity on job opportunity dominate over negative effects component. Contrarily to labour productivity components, negative effects of real wages on job opportunity was found to exceed positive effects. However, findings indicated that real wages have no significant effect shortrun on job opportunity. Only positive component of productivity was found to impact on short term job opportunities.
Given the gravity of unemployment on the South African economy and welfare, serious measures should be introduced. Firstly, the labour union should encourage its members to first consider their productivity level before fighting for wages increment. Secondly, the monetary authorities would have to put in place policies that protect the value of received wages (protect the currency against depreciation). Since labour productivity, leads job opportunity, it is substantial to provide adequate knowledge and skills to the labour force through the provision of solid education and training to cope with new technologies.
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1 NorthWest University, South Africa, Address: Potchefstroom; Mafikeng; Vanderbijlpark, South Africa, Corresponding author: 26767007@nwu.ac.za.
AUDOE, Vol. 17, No. 1, pp. 177191