Capacity Utilisation and Unemployment in Selected West Africa Countries

The purpose of this research paper is to examine the proposition that capacity utilisation is an important factor in the determination of unemployment and wages. Underlying this proposition is the notion that capacity utilisation helps to determine the future path of the economy and is a significant factor in the response of the economy to different supply and demand shocks. We derived capacity utilisation and unemployment relationships, which were estimated and tested using data covering from 1997 to 2016 for three West Africa countries. The results suggest that long-term unemployment and capacity utilisation have a significant impact on unemployment. The policy implications of our findings are that in view of the strong effect of capacity utilisation on unemployment, programmes that enhance efficiency in production and investment enhancing policies may allow unemployed to regain access to the labour market.


Introduction
During the period under investigation, from 1997 to 2016, West Africa countries experienced big shocks, which affected their labour and product markets. The dramatic rise in unemployment from 2008 to 2010 in Nigeria and Niger and from 2010 to 2012 in Senegal was attributed by a large extent to adverse demand shocks. However, after the reversal of the shocks, unemployment persisted which economists explained by resorting to notions of inflexibility in the labour markets. Although there appears to be some consensus that changes in labour market institutions and legislation may affect structural unemployment (see, for example, Barrell [1] for the UK), the origins of high and persistent unemploy-  in West Africa region are much debated. This is particularly so, since institutions and legislation were well in place before the high unemployment era.
The rise in unemployment during the 1990s, for example, was not associated with any marked increase in labour market "inflexibility".
More recently, attention has been diverted from labour market "flexibility" to the potential impact of changes in interest rates and capital shortage on the unemployment rate that is consistent with non-accelerating inflation (NAIRU), and wages (Allen and Nixon [2], Arestis and Biefang-Frisancho Mariscal [3], Bean [4], Rowthorn [5] [6], Sawyer [7]). Much of the debate on the relationship between capital shortage and unemployment seems to be concerned with the degree of substitutability between labour and capital (Bean [4], Jerger [8], Rowthorn [6]). In response to the fluctuations in oil prices, contractionary monetary and fiscal policies were introduced which squeezed profits and investment, so that capital stock fell below a level adequate for high levels of employment. Real wages were too high for changed productivity conditions and excessive substitution of capital for labour with a prevalence of capital intensive investment was introduced. As a result, labour requirement for any given level of output was reduced. As a consequence of the pace and quality of capital accumulation, the level of employment corresponding to full utilisation of capital stock was lower than that would correspond with full employment (however that may be measured). Gordon [9] finds that countries that experienced the largest slowdown in capital accumulation per labour hour faced the highest unemployment rates. He concluded that the European countries did not have sufficient capital in the 1980s to equip all employees who would have had a job if unemployment rates remained the same as in the 1970s. Bean [4] predicted a similar result. Capacity utilisation adjustment is an important mechanism ensuring adjustment to the macroeconomic equilibrium. Low capacity utilisation is a concern for fiscal and monetary authorities that are willing to engage in simulation aiming particularly at the level of unemployment. The argument of this study is that low capacity utilisation leads to higher unemployment which in turn creates even greater slake in the economy. The main research question which remains unanswered in the literature, is how the labour market reacts to capacity utilisation changes.
The aim of this paper is to examine the proposition that capacity utilisation is a determinant of the rate of unemployment and the level of real wages in a range of West Africa countries. The following three West Africa countries were selected on the basis of purely data availability and consistency: Nigeria, Niger and Senegal. We argue that adverse demand shocks affect investment. When shocks reverse, unemployment may not fall to previous levels, due to the fact that recovery of employment takes longer than the recovery of output. One of the reasons could be that firms do not want to make a commitment to hiring new workers until there is a certain level of certainty about the strength and sustainability of the recovery.
The layout of the paper is the following: Section 1 highlights the literature on

A Theoretical Model of Unemployment Determination
In this part we put forward a model that aims to explain the determination of wages and unemployment. Specific to this model is the effect of capacity utilisation on unemployment.
Unlike some studies that postulate that the long-run impact of capital accumulation on the rate of unemployment occurs through the impact of the former on firms' mark-ups, we postulate a different framework in which unemployment is determined by capacity utilisation in the economy.
where, we denote by ( ) i t f y the derivative of the production function with respect to i t y . It is simply the slope of the production function at i t y or the marginal product of i t y . Thus Equation (2) is saying that at optimum we must have: Assuming that the economy consists of a number, n , of identical firms, using an equal amount of capital and labour with the same level of technology, then at optimum with, f , mark-up, we must have: where l t mp is the marginal product of labour and t f is a mark-up set by firms in the economy.
Computing the optimal choice at i t y for Cobb-Douglas production function, the economy's output is equal to: where L , is employment, K is the amount of capital, 0 γ is constant and t λ is the rate of technological change.
Differentiating Equation (5) with respect to capital we can obtain the marginal product of capital as: In order to minimise capital and labour costs, a typical firm will have: Combining Equations (6)-(8), the marginal product of labour is: Assuming that the level of economic activity, captured by the level of unemployment, is influenced by the cyclicality of mark-ups, t m , and aggregate capacity utilisation, t z , which can be represented by the following equation: where ι , captured the level of uncertainty in the economy. If 0 t z , then the increase in capacity utilisation will raise the NAIRU and vice-versa.
Taking the logarithms of Equation (10), we get: Also taking the logarithms in Equation (4) Both Equation ( (13) and (14)) can be used to solve for the equilibrium rate of unemployment, where unemployment is a declining function of capacity utilisation. The effect of changes in capacity utilisation on unemployment can be explained as follow. If capacity utilisation is reduced or taxes or import costs rise, conflict over income distribution rises. Taking as an example the fall in oil prices in the early 1980s, which led to a fall in demand and then a reduction in capacity utilisation. Firms respond by reducing investment, which led to a lower (than otherwise) capital stock, which increases the NAIRU. In order to bring inflation down, governments introduced monetary and fiscal policies that reduce the supply-demand imbalance caused by the fall in capacity utilisation in response to fall in overall investment. As a result, unemployment rose. When oil prices return to their previous level, inflationary pressure and unemployment fall. However, due to a lower capital stock, the previous level of employment cannot be attained.

Estimable Equations
We proceed to formulate the equations to be estimated, by assuming that ex- pectations are formed as in Nickell [10], that is: We also assume that Equations ( (13) and (14)) describe a log-linear relationship. After some basic algebraic transformations, we may derive Equation (16): 1where lower case letters denote the logarithm of a variable.

Empirical Investigation
The first part of the empirical section discusses the data utilised for the three countries concerned. This is followed by the estimation of cointegrating relationships corresponding to Equations ( (14) and (15)). We apply the standard Johansen [11] maximum likelihood estimation procedure to estimate the num- , where Tx 2 is the tax rate paid by employers, Tx 1 is the tax rate on employee earnings, p c is consumer price deflator and p y is GDP price deflator; capacity utilisation (k) measures the proportion of potential economic output that is actually realised; (u) is the unemployment rate, computed as total unemployment divided by total labour force.
Empirical results All variables were tested for the level of integration, applying the standard Augmented Dickey-Fuller (ADF) unit root tests with the result that all variables have unit roots. 1 In a preliminary analysis we estimated and tested an unre- 1 The results of these tests can be obtained from the authors on request. We started with a maximal lag length of five for all countries. The optimal empirical lag length can be found in Table 2 of Appendix. In cases where the results of the information criteria were contradictory, we decided on the longer lag length provided by the Akaike information criterion to avoid misspecification, particularly serial correlation Stock [12] as reported in  Table 2. The cointegrating VAR was estimated with unrestricted intercepts and restricted trends. The deterministic trends were included because the data are trended and omitting them would have caused mis-specified models. The null hypothesis of the cointegration tests is that there is no cointegrating vector and the alternative is that there is at most one cointegrating vector. Table   3 shows that the non-cointegration hypothesis is rejected at the 5% level of significance in all three countries, also that there are at least two cointegrating vectors in each of all three countries. The two cointegrating vectors are reported in the sub-section that follows immediately below.

Cointegrating vector for real wages and unemployment
The two cointegrating vectors as discussed in the last sub-section, may not be    vectors is also a stationary vector, the estimates produced for any particular column in β are not necessarily unique. Therefore, it will be necessary to impose restrictions to obtain unique vectors lying within that space Harris [14]. Consequently, general joint restrictions on the cointegration vectors, β, and the speedof-adjustment parameters, α, according to the theoretical model were imposed and tested for significance Harris [14], Hendry Doornik and Hendry [15] A. M. Soliman DOI: 10.4236/tel.2017.76117 Theoretical Economics Letters Hunter [16], and Mosconi and Giannini [17] 3 . A χ 2 (n) test is used as shown below the α estimates in the sub-section "Cointegrating vector for real wages and unemployment". The likelihood ratio test accepts the joint restrictions for the three countries. 4 Table 4.
For Nigeria, tax and import costs are significant in the unemployment equation. Tax costs raise the NAIRU significantly. Long-term unemployment has a significant effect on raising both real wages and the NAIRU. These results suggest that the effect of higher long-term unemployment (relative to total unemployment) is to raise real wages, rather than the usually supposed mechanism of For Nigeria, the unemployment equation is particularly interesting in that there is a significant impact on unemployment in response to changes in capacity utilisation. Long-term unemployment also has a significant effect on both, real wages and the NAIRU. For Niger, there is significant impact on (the equilibrium level of) unemployment in response to changes in capacity utilisation.
We also find that there is a significant impact on real wages in response to changes in capacity utilisation. For both countries, the real wage and the unemployment equation, tax and import costs were insignificant. We obtain similar results for Senegal, however, long-term unemployment has a significant effect on both, real wages and the NAIRU. The cointegrating VAR included a proxy meant to capture unemployment benefits which, however, proved to be insignificant, and was consequently dropped. As for Nigeria and Senegal, tax and import costs were not found to have any effect on both real wages and unemployment equations. Note, for all three countries, long-term unemployment increases wages, a result, which confirms the insider-outsider theory. The long-term unemployed are effectively excluded from the labour force so that a rise in the pool of the long-term unemployed (relative to total unemployment) strengthens insiders' bargaining power and raises wages. Consequently, a relative rise in long-term unemployment allows insiders (those who are employed of only recently unemployed) to press for higher wages, regardless of the general increase in the unemployment rate.

Summary and Conclusions
We have presented an innovative aggregate unemployment model, which incorporates a number of ideas on unemployment and wage determination, and the model is concerned with explaining the long-run level of unemployment. In this model, the effect of demand on unemployment and wages is emphasised.
The mechanism works through changes in capacity utilisation, which themselves depend on economic activity and the stock of capital. We derived capacity utilisation and unemployment relationships, which were estimated and tested with comparable data sets for all three countries. For all the three countries the data sets provided two cointegrating vectors, which could be identified as unemployment and capacity utilisation relationships. The empirical results, based on quarterly time series data for three countries, can be summarised as follows.
The results show that in Senegal, long-term unemployment and capacity utilisation have a significant impact on NAIRU, while tax and import costs significantly raise unemployment in Nigeria. However, the results show that there is little evidence that in the long run, a tax cut reduces unemployment or real wages. For Niger, there is significant impact on (the equilibrium level of) unem- The policy implications of our findings are that in view of the strong effect of long-term unemployment on the NAIRU, programmes that enhance the skills of displaced workers may allow them to regain access to the labour market. Furthermore, the results suggest that capacity utilisation significantly affects unemployment. This is important since investment-enhancing policies can lead the way in reducing unemployment.