Labour market institutions are one of the most influential factors in macroeconomic dynamics. As pointed out in Ghoshray, Ordóñez, and Sala (2016), high and persistent unemployment problem in the European countries has been recognised. For a persistent high unemployment rate in the European countries, labour market reforms have been undertaken to eliminate the labour market rigidities since 1970s. Faccini (2013) and Giannelli, Jaenichen, and Villosio (2012) point out that the important features of the reforms are the reduction in adjustment costs and the introduction of fixed-term contracts (FTC). Alonso-Borrego, Fernández-Villaverde, and Galdón-Sánchez (2005) and Jiménez-Rodríguez and Russo (2012) indicate that the employment fluctuations have become more volatile after the reforms. Moreover, De Serres and Murtin (2013) and OECD (2012) show that the increase in the share of FTC amplifies the employment fluctuations.
In the dynamic labour demand literature, adjustment cost models are widely used. Hamermesh and Pfann (1996) thoroughly explain the property of the adjustment cost models. In these models, indefinite-term contracts (ITC) are assumed. Matsue (2018) creates two types of dynamic labour demand models: One is a model with FTC and the other is a model with ITC. It shows that the FTC and ITC models are different in terms of property of employment dynamics. In the ITC model, an expected productivity shock does not cause the oscillatory behaviour of total employment and new hiring, while it causes the oscillatory behaviour in the FTC model.
Layard, Nickell, and Jackman (2005) discuss the importance of trade unions in the European labour market. Union membership ratio and union coverage ratio are proxy variables for influence of trade union on wage setting or union power. The union membership ratio has been declining in European countries recently, whereas the union coverage ratio is still high, as shown in OECD (2015). Booth (2014) argues, using French data, that the union coverage ratio is a better measure of union influence than the union membership ratio.
A relationship between union influence and unemployment rates has been investigated extensively in the research of business cycles. Faccini and Bondibene (2012) analyses a relationship between some labour market institutions and cyclical behaviour of unemployment rates for some OECD countries. It indicates that increase in the union coverage ratio amplifies cyclical fluctuations of unemployment rates.
This paper presents a FTC model and analyzes the effects of FTC and union influence on employment dynamics. It explains some empirical evidences in the labour market. In addition to the analysis in Matsue (2018), this paper enables us to analyse the effects of supply side of labour on employment fluctuations. First, we present the model with FTC and analyzes the dynamics of the model. Similar to the dynamic labour demand model, numerical examples show that an expected productivity shock causes oscillatory behaviour of total employment and new hiring in the model with FTC. Zipperer and Skott (2011) exhibit cyclical employment trend with short-run cycles in French and Spanish economies, which is consistent with simulation results in this paper.
Second, this study analyzes the relationship between union influence and employment dynamics. The numerical examples show that the stronger union influence on wages leads to larger employment fluctuations. The strong union influence puts an upward pressure on wage rates. Then, firms need to adjust employment significantly when the productivity shock takes place. This is consistent with the results of Faccini and Bondibene (2012).
Third, this study examines the relationship between elasticity of wage with respect to employment rate and employment dynamics. The numerical examples show that the higher elasticity of wage with respect to the employment rate leads to smaller employment fluctuations. The firms do not need to adjust employment largely because wage varies significantly when the elasticity of wage with respect to the employment rate is high.
The rest of this paper is organised as follows: Section 2 sets up the model, Section 3 discusses the property of the model with simulation analysis, Section 4 investigates the influence of the labour supply side on employment fluctuations, and Section 5 concludes the paper.
Let us set up the model with FTC. Firms plan their production during the finite time period
Then,
Similar to Blanchard (1997), suppose that the aggregate supply function is as follows:
Eq. (7) is rewritten as follows:
Suppose that agents save and invest a fixed fraction
It is assumed that equation for capital dynamics with depreciation rate
From Eq. (10) and (11) and the production function, the capital dynamics is as follows:
The equilibrium is determined by Eq. (2), (7), and (12); the initial conditions; and the terminal conditions. Now, consider the steady state
Eq. (13) indicates that the new hiring is as much as the labour who leaves a job in the steady state. From Eq. (11), we find that the investment is equal to the depreciation at the steady state. In addition, the investment is determined as a fixed fraction
If we substitute
Now, we analyse the effects of expected productivity shocks on employment by running some simulations. We set the parameter values as given in Table 1. The parameters
Parameters in Section 3.
Parameter in production function | 0.64 | |
Discount factor | 0.985 | |
Elasticity of wage with respect to employment rate | 1.0 | |
Depreciation rate | 0.0125 | |
Wage at zero unemployment | 0.35 | |
Adjustment cost | 0.0 or 0.1 | |
Turnover rate | 0.5 | |
Saving rate | 0.30 | |
Labour force | 110.0 |
Figures 1 and 2 show the simulation results. These figures show the deviation of new hiring or total employment when the negative shock takes place from their steady state values. If the negative shock takes place at period 5, the firm decreases new hiring at periods 4 and 5 (
Employment fluctuations with
Employment fluctuations with τ = 0.1 : (a) New hiring and (b) Total employment.
To understand the role of FTC, the FTC model should be compared with a model without FTC. It is assumed that employees leave their job by a fixed fraction 0< σ < 1 of total employment. The employment dynamics is as follows:
Similar to the FTC model, consider the employment rate. From Eq. (6) and (18), we obtain the following equation:
If we transform Eq. (20), then the employment rate is obtained as follows:
Unemployment rate is obtained by substituting Eq. (21) in Eq. (9). The household behaviour is the same with the FTC model. Hence, the equilibrium is determined by Eq. (12), (17), and (20). At the steady state, Eq. (12), (17), and (20) are as follows:
Equation (22) shows that the new hiring is as much as the labour who leaves a job in the steady state. From Eq. (22)–(24), we obtain the steady state values
Then, by substituting
The simulation results are shown in Figure 3. The figure shows the deviation of new hiring or total employment when the negative shock takes place from their steady state values. The assumptions about the shock are similar to the case with the FTC model. To compare with the FTC model, at the steady state, half of the total employment leaves the job at the end of the period (
Employment fluctuations without fixed-term contracts: (a) New hiring and (b) Total employment.
In this section, we run some simulations to analyse the effects of labour supply side on employment dynamics, i.e., a relationship between union influence on wage
We analyse a relationship between union influence on wage
Parameters in Section 4.1.
Parameter in production function | 0.64 | |
Discount factor | 0.985 | |
Elasticity of wage with respect to employment rate | 1.0 | |
Depreciation rate | 0.0125 | |
Wage at zero unemployment | 0.35, 1.0, 1.5, or 2.0 | |
Adjustment cost | 0.1 | |
Saving rate | 0.30 | |
Labour force | 110.0 |
Figure 4 shows the simulation results of the model. The figure shows the deviation of total employment when the negative shock takes place from the steady state value. Figure 3 shows that the stronger union influence leads to larger employment fluctuations. The deviation of total employment when the negative shock takes place from the steady state value at period 5 is as follows: −0.261674% if
Union influence and employment fluctuations: (a)
In this model, we assume
We analyse a relationship between elasticity of wage with respect to the employment rate
Parameters in Section 4.2.
Parameter in production function | 0.64 | |
Discount factor | 0.985 | |
Elasticity of wage with respect to employment rate | 1.0, 2.0, 3.0, or 4.0 | |
Depreciation rate | 0.0125 | |
Wage at zero unemployment | 0.35 | |
Adjustment cost | 0.1 | |
Saving rate | 0.30 | |
Labour force | 110.0 |
Elasticity of wage with respect to employment rate and employment fluctuations: (a)
It shows that the increase in
Unemployment and employment dynamics have been studied in many theoretical and empirical analyses. The labour market institutions are one of the most influential factors in macroeconomic dynamics. This study analyzes the impact of labour market institutions on employment fluctuations using a model with FTC. Numerical examples show that the total employment and new hiring behave cyclically if an expected shock takes place. Moreover, the reduction in adjustment cost amplifies the fluctuations in the model.
The union influence in the labour market is important because the union coverage ratio is still at a high level. This study also analyzes the relationship between the union influence and employment dynamics. The numerical examples show that the stronger union influences on wage lead to larger employment fluctuations. The strong union influence puts upward pressure on the wage rate. Then, the firm needs to adjust its employment significantly when the productivity shock takes place, which is consistent with the results of Faccini and Bondibene (2012).
Further, this study analyzes additional influence of the labour supply side on employment fluctuations. The numerical examples show that the higher elasticity of wage with respect to the employment rate leads to smaller employment fluctuations. The firm does not need to adjust its employment largely because the wage varies significantly when the elasticity of wage with respect to the employment rate is high.
Nevertheless, the model in this study is restricted to a simple case in which the term of contracts is only two periods. Hence, it is necessary to analyse a more general case. Moreover, the models could be extended to consider the endogenous labour supply and intertemporal optimisation of consumption. Further investigation of these issues remains to be undertaken.