DE ECONOMIST 151, NO. 3, 2003
UNEMPLOYMENT DYNAMICS, AND PROPAGATION OF AGGREGATE AND REALLOCATION SHOCKS IN THE NETHERLANDS**** BY KEES VAN MONTFORT*, FRANK A.G. DEN BUTTER** AND GERBEN T.J. WEITENBERG***
Summary
This paper models the propagation at the macro level of four types of shocks using the SVAR approach. Time series data for the Netherlands on job creation, job destruction, the number of vacancies and labour supply are used to identify aggregate demand and supply shocks, and reallocation demand and supply shocks as different sources of unemployment dynamics. Each of these four types of shocks appears to have at least some influence on unemployment both in the short and long run. The long run influence of the aggregate labour supply shock is estimated to be very limited. It indicates that additional labour supply is almost fully absorbed by labour demand in the long run. Key words: aggregate and reallocation shocks, labour market flows, SVAR model
1 INTRODUCTION
Traditional models of the real business cycle theory make a distinction between two types of shocks, namely aggregate demand and aggregate supply 共or technology兲 shocks 共Kydland and Prescott 共1982兲, Long and Plosser 共1993兲兲. The aggregate demand shocks are assumed to have a temporary influence on economic activity, whereas aggregate supply shocks are identified as permanent shocks. In this way both types of shocks represent the classical dichotomy between cyclical and structural developments in the economy. Following the seminal work of Blanchard and Quah 共1989兲 a number of empirical studies have investigated the sources and propagation of these aggregate demand and aggregate supply shocks using the methodology of structural vector autoregressive models 共SVAR models兲. * Corresponding author: Free University, Applied Labour Economics Research Team 共ALERT兲, Department of Econometrics, Amsterdam, the Netherlands; phone: 0031-20-4446028, fax: 0031-204446020, e-mail:
[email protected]. ** Scientific Council for Government Policy, Tinbergen Institute, and Free University, Applied Labour Economics Research Team 共ALERT兲, Department of Economics, De Boelelaan 1105, 1081 HV Amsterdam, the Netherlands. *** Free University, Department of Econometrics, Amsterdam, the Netherlands. **** The authors want to thank two anonymous referees for their useful comments. De Economist 151, 253–270, 2003. © 2003 Kluwer Academic Publishers. Printed in the Netherlands.
254
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
However, new developments in equilibrium search theory 共Pissarides 共1988, 1990兲, Mortensen 共1986兲兲 and in the flow approach to the labour market 共see e.g. Blanchard and Diamond 共1992兲兲 show that for the analysis of the sources and propagation of shocks, and how these shocks affect the labour market, and more in particular unemployment, it does not suffice to consider aggregate shocks only. Reallocation shocks appear to play an important role as well 共see also Davis and Haltiwanger 共1999兲 with distinguish two types of shocks, i.e. aggregate and reallocation shocks兲. For labour market policy, and more in particular labour market policy directed at combating unemployment, it is important to know which types of shocks hit the economy, and how these shocks propagate in the economy. Although, as our empirical analysis illustrates, the various types of shocks are difficult to disentangle, it is meaningful for policy purposes to know about their relative sizes and incidence. This research question becomes even more important now that within the EU it is mainly labour market policy which can be used by national governments in reaction to autonomous shocks. From that policy perspective this paper identifies and estimates a SVAR model for unemployment dynamics in the Netherlands. Four types of shocks are distinguished, namely aggregate demand and aggregate labour supply shocks, and reallocation shocks both at the demand and the supply side of the labour market 共see Balakrishnan and Michelacci 共1997兲 for an analysis in the same vein兲. The structural VAR 共SVAR兲 methodology pioneered, among others, by Bernanke 共1986兲 and Blanchard and Quah 共1989兲 seems well suited to the research problem. In fact, if a structural VAR is estimated, the impulse response function represents how shocks propagate in the economic system, while the variance decompositions weight the contribution of each shock in the forecasting errors of the relevant variables. For the exercise to be meaningful, however, the shocks must have robust economic interpretation that is the call for a theoretical framework. To identify the shocks we develop a structural VAR model with orthogonal shocks and additional identification restrictions, and not an unstructured VAR model. Following Balakrishnan and Michelacci 共1997兲, in a somewhat elective way we want our results to conform to insights and restrictions obtained from theoretical models of the flow approach to the labour market. Therefore we use a set of time series of data on worker and job flows for the Netherlands, which is newly constructed on the basis of administrative micro data sources 共Broersma et al. 共2000兲, Kock 共2002兲兲. These data allow us to identify the four different types of shocks at the macro level. The remainder of the paper is organised as follows. Section 2 discusses the background of the four types of shocks and their different influence on job creation and job destruction. This determines the majority of the identification restrictions and the theoretical framework for the labelling of the shocks. Section 3 summarises the construction method of the time series data. In section 4 and 5
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
255
we specify the four-variate SVAR model and discuss the identification procedure and the estimation results. Section 6 concludes. 2 THEORETICAL FRAMEWORK FOR THE IDENTIFICATION RESTRICTIONS AND THE LABELLING OF THE SHOCKS
Most identifying restrictions in our SVAR model relate to the effects that the four types of shocks we distinguish have on the processes of job creation and job destruction according to three different theoretical models of the flow approach to the labour market. These are 共i兲 the search equilibrium approach with non-cooperative wage bargaining by Mortensen and Pissarides 共1994, 1995兲, 共ii兲 the appropriability cost approach of Caballero and Hammour 共1996兲 and 共iii兲 the timing of job reallocation as explained by Davis and Haltiwanger 共1990兲; see also Gautier 共1997, chapter 4兲. All three models explain, in their own way, the observation that job destruction is more counter cyclical than job creation is pro-cyclical. It implies that the net effect is counter-cyclical so that most job reallocation occurs in bad times with negative demand shocks. The main mechanism in these models is that opportunity costs are lowest during recessions. In our discussion of the various types of shocks we start with the demand side. In principle all shocks that hit a firm from the demand side can be regarded as firm-specific. Yet usually firm-specific shocks are associated with shocks that are uncorrelated with respect to firms and, therefore, hit each firm in a different way. Due to changes in tastes and technology some firms are hit by a positive shock and are successful in expanding their production, whereas other firms are hit by an adverse shock and are bound to downsizing, or even go bankrupt. Hence, on the aggregate a compilation of such firm-specific shocks leads to a reallocation of production amongst the firms. Therefore at a macro level these shocks take the form as reallocation shocks. An example of such a shock is the introduction of an environmental tax, which gives fiscal advantages to firms with a clean production technology over firms with polluting production technology. A positive reallocation shock will increase the cross-sectional variance of the profitability of jobs. This leads to the creation of additional jobs in sectors and firms where the shock has a positive effect, while in firms, which are negatively hit by the shock job, destruction will occur. It implies that the reallocation shock will enhance both job destruction and job creation. We will utilise this property of a reallocation shock as identifying restriction in our model. On the other hand, the situation may occur that all firm-specific shocks are completely correlated. In that case the shocks hit all firms in the same direction. At the macro level we then have an aggregate demand shock. A positive aggregate demand shock will result in higher profitability of jobs and therefore in an increase of job creation, as in the three theoretical models referred to above. Due to the enhanced economic activity jobs also remain productive over a longer time period so that job destruction decreases. Inversely, a negative aggregate demand
256
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
shock will enhance job destruction and induce a decrease in job creation. So these opposite influences of an aggregate demand shock on job creation and destruction constitute our identifying restrictions of such a shock in the model. These two types of demand shocks relate to economic activity and hence to labour demand. At the supply side of the labour market we also distinguish two types of shocks. Comparable to the aggregate demand shock is an aggregate supply shock. This shock relates to an autonomous increase or decrease in labour supply. Such a shock can be caused by an increase in the working age population 共potential labour supply兲 and/or by an autonomous or policy induced change in the labour participation rate. An identification criterion which is often used for this type of labour supply shock is the assumption that it has no influence on the unemployment rate in the long run 共see Balakrishnan and Michelacci 共1997兲 and Layard et al. 共1991兲兲. In this paper we will be less restrictive in our identification of a labour supply shock. We note that a positive labour supply shock may enhance job creation as, due to the additional labour supply, the opening of a vacancy for a new job becomes less costly. Inversely, a negative labour supply shock will induce a decrease in job creation. This short-run effect on job creation may, however, vanish in the long run because changes in wages will bring the economy back to its original equilibrium. Moreover, both the short-run and the long-run effects of an aggregate labour supply shock on job destruction are ambiguous. The fourth type of shock we distinguish can be labelled a labour productivity shock. Here, in case of a positive productivity shock, the labour force becomes, given its size, more productive. In this case we can think of the implementation of labour-saving technology. The cause of such a positive shock may also be an increase in the level of education of the work force. When this labour productivity shock does not coincide with an aggregate demand shock it implies that the change in productivity is not matched by an equal change in labour demand. In that case an increase in productivity will lead to a decrease in employment and vice versa. Therefore, in our model we take as identifying restrictions for a labour productivity shock that a positive shock leads to a decrease in job creation and an increase in job destruction, whereas a negative productivity shock is associated with an increase in job creation and a decrease in job destruction. This TABLE 1 – LONG-RUN EFFECTS OF A POSITIVE SHOCK ON JOB CREATION AND DESTRUCTION, CETERIS PARIBUS 共E ⫽ EMPLOYMENT兲
Type of shock
⌬
Aggregate demand shock Reallocation shock Labour supply shock Labour productivity shock
↑ ↑ ? ↓
JC E
⌬ ↓ ↑ ? ↑
JD E
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
257
is in line with the theoretical predictions of the three models referred to above. Table 1 summarises our discussion of the effects of the four types of shocks on job destruction 共JD兲 and job creation 共JC兲 by showing the long-run effects of positive shocks. These relations in Table 1 shall be used to identify and label the four unobserved shocks by the SVAR model. For a complete identification we have to make some additional assumptions in section 4. 3 THE DATA
Since we distinguish four types of shocks we need four times series in order to enable identification of these shocks. In this paper we use annual time series for job creation 共JC兲, job destruction 共JD兲, labour supply 共LS兲, and the number of vacancies 共V兲. These time series are on a macro level for the Netherlands in the period 1970-1997. They are constructed by data from administrative sources that register the social security transactions of Dutch citizens 共see the Chronicle of Social Insurance 共1998兲兲. Additional assumptions are used to construct the time series, which are not directly available from the primary data source or which follow from definition equations. These additional assumptions do not interfere with the identification restrictions of our model. Kock 共2002兲 contains a detailed description of the time-series data we used whereas Broersma et al. 共2000兲 summarises the construction method for one pivotal year. The discussion of the previous section illustrates that data on job destruction 共JD兲 and job creation 共JC兲 are essential for identification in our model. The net result of job creation and job destruction gives the change in the total number of jobs 共⌬J ⫽ JC ⫺ JD兲. In accordance with the definition of jobs in the data set the total number of jobs is equal to employment plus the total number of vacancies 共J ⫽ E ⫹ V兲. Now it is essential for the identification of our model to confront these flows and stocks of jobs with flows and stocks of workers. Data on stocks of workers are obtained in a straightforward way: labour supply is equal to employment plus unemployment 共LS ⫽ E ⫹ U兲. For the calculation of job creation and job destruction in connection with worker flows we have used the primary data source which is based on administrative registrations. A major feature of the construction of the data set is that the links between worker flows and job flows are exploited as much as possible. Appendix A summarises how job creation and job destruction are compiled in this data set. 4 THE MODEL
4.1 SVAR Specification First we give a technical introduction to the SVAR model, which we use in order to disentangle and estimate the sources and propagation of the four types of
258
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
shocks mentioned before. We begin with defining the following two vectors of length 4: Y t and t. Vector Y t consists of 4 input variables and vector t represents the shocks to which the model is submitted. The vector Y t will be chosen as follows:
冤冥 JC t Et
JD t
Yt ⫽
Et
共4.1兲
⌬ LS t LS t
⌬ Vt LS t
Using unity root tests we have specified the components of Y t in such a way that they are stationary time series. More specifically, we have chosen ⌬ LS t / LS t and ⌬V t / LS t as components of Y t , because the tests indicate that they are stationary while LS t and V t / LS t are not stationary. Assume Y t is a vector of linearly regular covariant-stationary stochastic processes with mean zero. Then, with the use of Wold’s decomposition theorem, each element of Y t can be represented as a process driven only by a white noise process 共see e.g. Whiteman 共1983兲兲. So, we have the innovative process of Y t , which is denoted as follows: ∞
Yt ⫽
兺 C L ⫽ C共L兲 j
j⫽0
j
t
t
,
共4.2兲
where the coefficients C j are 共M ⫻ M兲 matrices, C 0 is the identity matrix and t is a vector of white noise processes with Var 关 t 兴 ⫽ ⍀. The lag operator L is defined as follows Lx t ⫽ x t ⫺ 1 . L共Lx t兲 is denoted as L 2 x t ⫽ x t ⫺ 2. Thus, L p x t ⫽ x t ⫺ p . By convention L 0 x t ⫽ x t . C共L兲 is a polynomial of infinite order. Assume further that Y t and t , can be represented by a Moving Average 共MA兲 process: ∞
Yt ⫽
兺 B L ⫽ B共L兲 j
j⫽0
j
t
t
,
共4.3兲
Thus, B共L兲 is a polynomial matrix of infinite order. The matrix coefficients B j are the impulse response characteristics that determine the effect of the shocks on the system. The polynomial B共L兲 determines the effect of the disturbances on the Y t .
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
259
Furthermore it is assumed that the structural disturbances are uncorrelated white noise processes. This last assumption may not seem very realistic at first sight. It is clear to see that many shocks have both an aggregated and a reallocation component, as was the case with the oil price shock in the seventies. However, this assumption of orthogonality is needed for the identification of the problem discussed in this paper, using the SVAR approach. We note that den Butter and Koopman 共2001兲, using the structural time series modelling as an alternative approach, allow for correlation in a bivariate model for aggregate supply and demand shocks. However, we assume that the reallocation component only depends on the size of the shock and not on the direction and moreover we assume that fundamental shocks consist of a random mix of positive and negative aggregated shocks during a long period of time. In that case there is almost no correlation between the aggregated and the reallocation shocks. After normalisation it follows that Var 关 t兴 is equal to the identity matrix I. Equations 共4.2兲 and 共4.3兲 are equal. The distinctions between 共4.2兲 and 共4.3兲 are the restrictions of C 0 and var 共兲 , which have to be equal to the identity matrix. With these two equations it follows that the vector of innovations and the vector of disturbances are related like t ⫽ B 0 t . Furthermore B共L兲 can be computed with B j ⫽ C j B 0 , j ⬎ 0 . Hence, to solve the system of equations it is sufficient to find B 0. This can be done in the following way:
⍀ ⫽ var 共 t 兲 ⫽ var 共B 0 t 兲 ⫽ B 0 var 共 t 兲 B 0⬘ ⫽ B 0 B 0⬘ .
共4.4兲
In short, the procedure is as follows. Ê First we estimate a matrix containing an autoregressive representation of Y t . After inversion we get equation 共4.2兲, with vector t and matrices C共L兲 and ⍀. Ê Then B 0 is computed with 共4.4兲. This makes it possible to compute B j ⫽ C j B 0 共for j ⬎ 0兲 . The shocks in the short run can be calculated by the relation t ⫽ 共B 0兲 ⫺ 1 t , while the shocks in the long run can be obtained by choosing the lag operator equal to 1, and calculate t ⫽ 共B共1兲兲 ⫺ 1 Y t . 4.2 Identification of B 0 by Additional Restrictions Until now the system is not yet identified. Given ⍀, equation 共4.4兲 imposes ten restrictions on sixteen elements of B 0 :
B0 ⫽
冤
1 b 21 1
b 12 2 b 13 3 b 14 4
2
b 31 1 b 32 2
b 23 3 b 23 4
3
b 41 1 b 42 3 b 43 3
b 34 4
4
冥
.
共4.5兲
260
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
Identification requires both an order condition and a rank condition 共see Giannini 共1992兲兲. In order to fulfil the order condition six more restrictions on the elements of B 0 are needed. The literature gives several possible additional restrictions 共see Blanchard and Quah 共1989兲, Mortensen and Pissarides 共1994兲, Davis and Haltiwanger 共1999兲, and Balakrishnan and Michelacci 共1997兲 for an extensive overview兲. The choice for the additional restrictions depends on the definition and interpretation of the observed vector Y t and the shocks t . We can use weak restrictions that constrain the admissible range of the contemporaneous responses to the shocks. However, these inequality restrictions do not fully identify the SVAR model. We can achieve greater precision by imposing neutrality restrictions similar to the long-run sort emphasized by Shapiro and Watson 共1992兲, Blanchard and Quah 共1989兲, and Davis and Haltiwanger 共1999兲. We will assume that the long-term effects of each of the four shocks on the changes in unemployment are equal to zero. These assumptions are also needed to get a realistic model. Nevertheless, long-term effects of any of the shocks on the absolute values in unemployment are allowed to be unequal to zero. To implement these restrictions we use the relations between unemployment on one hand and the separate shocks on the other hand, which are derived in Appendix B. The appendix shows that for each shock, where the size of the impulse is unity, the change in unemployment will be a linear function of the cells of the matrix B 0 . As a consequence, the restrictions result to four linear equations, with the cells of B 0 as the unknown variables. The remaining two restrictions cannot, like the restrictions discussed in section 2, be derived from 共existing兲 theoretical models and will be chosen as follows. Assume that changes in labour supply are independent of the short-term effects of the shocks that influence the demand side of the labour market. The result is that the short-term effects of the aggregated and reallocation shocks on the change in the labour supply is zero. This means b 31 and b 32 must be equal to zero. One could, of course, argue whether this is a realistic assumption. For example, increasing labour demand as a result of positive expectations on future demand may enhance labour participation of people who first were not looking for a job in the labour market. This encouragement effect can, on the other hand, be compensated by a decrease in participation because the higher wages, which are the result of the labour demand shock, lead to some substitution between work and leisure. Empirical research for the Netherlands does at least show that wage elasticities of 共male兲 labour supply are rather low. However, we note that our assumption of independence is rather limited: the condition is that the two demand shocks do not influence the labour supply in the period that the shocks occur. Hence, no restrictions are imposed to the effects these shocks might have in future periods 共i.e. after one or more years兲. Thus, b 31 共k兲 and b 32 共k兲k ⬎ 0, are unrestricted. The above mentioned sixteen restrictions generate 10 quadratic and six linear equations. We can remove all the unknown model parameters and constants to
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
261
the left-hand side of these equations. The rank condition for identification of the model requires that the matrix of first-order derivatives of the left hand side of the sixteen equations toward the sixteen unknown elements of the matrix B 0 has to be regular. However, this condition characterises local identification. It may be that even if a model satisfies both the rank and the order condition, there are two non-contiguous estimates of B 0 for which the likelihood has the same value for the realisation of the data 共see Hamilton 共1994兲兲. For instance, if a matrix 共B 0兲 * satisfies the above rank and order conditions, this matrix multiplied by ⫺ 1 also satisfies these restrictions. To capture this problem we additionally assume the short-term relation between job destruction and the aggregate demand shock has to be negative, i.e. b 21 has to be smaller than zero. The matrix B 0 can be identified by the discussed SVAR model and the additional restrictions. As a consequence four shocks are determined uniquely. Furthermore for each shock we can empirically determine the signs of the long run effects on job creation and job destruction. Using these empirical relations and using the corresponding theoretical relations from section 2 共see Table 1兲 and the last three theoretical restrictions for B 0 of this section, we can label the four shocks as an aggregate demand shock, a reallocation shock, a labour supply shock and a labour productivity shock. 5 ESTIMATIONS AND RESULTS
We have estimated the above specification of the SVAR with 1970 – 1997 as sample period. First, the autoregressive representation of the SVAR model is estimated. For JC t /E t , JD t /E t , ⌬LS t /LS t and ⌬V t /LS t autoregressive equations are estimated separately. The model is also tested on autocorrelation, autoregressive conditional heteroskedasticity, normal distributed error terms, heteroskedasticity and the specification of the model 共i.e. the lag length兲. It turns out that all of the tests give satisfactory results and do not indicate misspecification. For instance, the r-squares values for the four separate autoregression equations are equal to 0.82, 0.81, 0.79 and 0.77 respectively. Furthermore, the order and rank conditions for identification of the model are fulfilled. From Table 1 follow the theoretical long-run effects of a positive shock on job creation and destruction, ceteris paribus. We compare the signs of these theoretical relations with the signs of the empirical results. This comparison leads to the labelling of the four latent shocks. However, in terms of signs a negative aggregate demand shock will have an impact that is similar to that of a positive labour productivity shock. Additionally, we use the theoretical assumptions about the matrix B 0 to distinguish, among others things, the 共negative兲 aggregate demand shock and a 共positive兲 labour productivity shock 共i.e. B 0共3,1兲 ⬅ 0 and B 0共3,2兲 ⬅ 0兲. The estimation results enable us to label the four 共unobserved兲 shocks. Moreover, they yield the sizes of the four types of shocks and their propagation in the
262
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
short run and in the long run to job creation, job destruction, the change in labour supply, and the number of vacancies. From an economic perspective, it is interesting to consider the actual sizes of the long run shocks, which are equal to 共B共1兲兲 ⫺ 1 Y t . This is illustrated in Figure 1. It appears that the shocks are about equal size, that the largest negative shocks occur around 1972, and that the largest positive shocks occur in 1987. More specifically, reallocation shocks, aggregate demand and labour supply shocks appear to be large and positive in the second half of the 1980s. This may relate to the turn to a supply-oriented policy with wage restraint and a reform of budgetary policy after the Wassenaar Agreement in 1982, and could be a reaction to the recession in the beginning of the 1980s. It is interesting to note that the reallocation shock is seen to lead the aggregate demand and supply shocks during this period. All four types of shocks appear to become less sizeable in the 1990s as compared to the previous decades. The next step is to determine the influence of each of the four disturbances on unemployment. To this end we use the following relation between unemployment and our time series from the SVAR model that holds approximately 共see Appendix B兲:
⌬ Ut LS t
⫽
冉
JD t Et
⫺
JC t Et
冊冉
⭈ 1⫺
Ut LS t
冊
⫹
⌬ LS t LS t
⫹
⌬Vt LS t
.
共5.1兲
Ut
is taken to be 0.06 because the unemployment rate in the reference LS t period was on average about 6%.
Here
Figure 1 – Time profiles of each of the four types of shocks in the reference period 1972–1997, where the matrix of long-run effects, B 共1兲, is used for the calculation of the shock
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
263
Replacing the terms of the right hand side in equation 共5.1兲 by corresponding cells of B 0 , we get the short-run effects of the separate shocks on changes in unemployment. For instance, for the short-run effect of the first shock 共i.e. the aggregate demand shock兲 we substitute B 0共1,1兲, B 0共2,1兲, B 0共3,1兲, and B 0共4,1兲 in JC t /E t , JD t /E t , ⌬LS t /LS t and ⌬V t /LS t respectively. Using cells of the matrix B共1兲, instead of cells of the matrix B 0, we get the long-run effects on unemployment growth. In fact, the change of the unemployment rate in 共5.1兲 is simply a linear combination of the four variables in the system with weights ␣ ⫽ 共 ⫺ 0.94; 0.94; 1; 1兲. Therefore, the short- and long-run effects of the shocks on the change in the unemployment rate are ␣ • B 0 and ␣ • B共1兲, respectively. In the identification of the model we assumed the long run effects of the shocks on changes in unemployment to be equal to zero. Nevertheless, the long-run effects of the shocks on the absolute values of unemployment can differ from zero and can be estimated by counting the effects on changes in unemployment for year 1 up to year 15. The short-run and long run effects of the shocks on the absolute values of unemployment are given in Table 2. The variances and corresponding t-values are calculated by the delta-method 共see Hamilton 共1994兲兲. TABLE 2 – SHORT AND LONG RUN EFFECTS OF THE FOUR TYPES OF SHOCKS ON UNEMPLOYMENT, WHERE THE SIZE OF THE IMPULSES IS UNITY 共* INDICATES THAT CORRESPONDING T-VALUE IS SIGNIFICANT AT THE 0.05 LEVEL兲
Aggregate demand shock Reallocation shock Labour supply shock Labour productivity shock
Short run
Long run
⫺ 0.488* ⫺ 0.140* 0.092 0.320*
⫺ 0.119* ⫺ 0.011 ⫺ 0.001 0.198*
From Table 2 it follows, for instance, that an increase of 1 person in the aggregate demand shock reduces the unemployment by 0.119 person in the long run. It is noticeable that in all cases the short run effects are, in absolute value, larger than the long run effects. Furthermore, the aggregate demand shock and the labour productivity shock seem to have a rather substantial effect on unemployment dynamics even in the long run. Yet, mainly for empirical reasons we did not impose the restriction that the long run effects on the level of unemployment of the four types of shocks be equal to zero. Therefore it is interesting to note that not only the labour productivity shock seems to have a rather substantial effect on unemployment dynamics in the long run, but also the aggregate demand shock. The latter is in contradiction with the traditional neo-classical dichotomy where demand shocks have temporary effects only and supply shocks 共at the goods market兲 have permanent effects. Yet this result is in line with the empirical finding of den Butter and Koopman 共2001兲, and with the theoretical literature
264
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
they refer to, that an aggregate cyclical demand shock may have permanent side effects. A similar explanation can be given to the small long-run effect, as compared to the short-run effect, found for the reallocation shock. On the other hand, the long-run effect of an aggregate labour supply shock on unemployment is very small in the long run. This outcome concords with the results of e.g. Broersma et al. 共2000兲 that in the long run enhanced labour supply will be 共almost兲 fully absorbed by labour demand in a new labour market equilibrium. Here it is somewhat surprising that also the short-run effect of a labour supply shock is rather small as compared to the short-run effects of the other shocks. It suggests that there are only small adjustment lags in the absorption of labour supply at the labour market. It may also indicate that in reality labour supply shocks and productivity shocks are not independent, and that our model has difficulties in separating them. Nevertheless, we also ran a SVAR model with only three shocks, i.e. aggregate demand, reallocation, and labour supply, and a very simple identification procedure for the shocks with only three additional identification restrictions 共see Weitenberg 共1998兲兲. The results of this simpler three-variate model give us some confidence, because the short and the long-run effects of the aggregate demand shock and the reallocation shock on unemployment have the same signs as in the four-variate model. Furthermore, the short and long-run effect on unemployment of the labour supply shock are also not significant on a 0.05 level. Additionally, we can determine the relative effect of each shock to the fluctuations of JC t /E t , JD t /E t , ⌬LS t /LS t , ⌬V t /LS t or ⌬U t /LS t by calculating the variance decomposition of the prediction errors. These prediction errors, which are defined as the differences between the observations 共at time t兲 and the predicted values 共at time t兲, can be caused by one or more of the four shocks. For a time span of 1, 5 and 10 years respectively the relative contributions of the different shocks on the fluctuations are given in Table 3. In Table 3 the labels AGGR, REALL, SUPPLY, and PROD indicate the aggregate demand shock, the reallocation shock, the labour supply shock, and the labour productivity shock, respectively. The variance decomposition of ⌬U t /LS t is the weighted mean of the other four variance decompositions. The results of Table 3 show that productivity shocks are the most important determinants of the variance of job creation. This is a plausible result from the perspective that newly created jobs will be most productive and that, for that reason, job creation is high during periods of positive productivity shocks and low during periods of negative, relative to average, productivity. Moreover, the influence of reallocation and labour supply shocks on job creation seems to be substantial, whereas the influence of aggregate demand shocks is small. On the other hand, job destruction appears to be driven mainly by aggregate demand shocks. Here the influence of changes in productivity is small. It is obvious that the major part of the variance of labour supply is linked to labour supply shocks,
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
265
TABLE 3 – THE VARIANCE DECOMPOSITION 共VD兲 FOR THE PREDICTION ERRORS OF JC T /E T , JD T /E T , ⌬LS T /LS T , ⌬V T /LS T AND ⌬U T /LS T
Horizon
K year
1
5
10
VD of JC t /E t
AGGR REALL SUPPLY PROD
5,56 25,76 26,12 42,80
4,48 24,92 22,97 47,63
6,21 21,99 27,14 44,66
VD of JD t /E t
AGGR REALL SUPPLY PROD
63,54 10,23 21,66 4,57
61,23 13,98 10,70 14,09
60,31 12,55 19,88 7,26
VD of ⌬LS t /LS t
AGGR REALL SUPPLY PROD
12,21 10,54 64,48 12,77
11,77 13,67 61,29 13,27
14,65 11,00 59,98 14,37
VD of ⌬V t /LS t
AGGR REALL SUPPLY PROD
21,55 44,42 13,87 20,16
9,43 53,47 14,38 22,72
11,24 47,41 12,24 29,11
VD of ⌬U t /LS t
AGGR REALL SUPPLY PROD
41,74 10,93 8,61 38,72
39,45 13,13 9,69 37,73
40,98 10,57 10,90 37,55
but the other three types of shocks appear to contribute to the variance of labour supply as well. It is also no surprise that changes in vacancies coincide with reallocation shocks, but the substantial contribution of aggregate demand 共in the short run兲 and productivity to the variation in the number of vacancies is remarkable. Finally, we see that aggregate demand shocks and productivity shocks yield the largest contributions to changes in unemployment. The first type of shocks relates to cyclical unemployment, and the second type of shocks to structural unemployment. It is noticeable that the influence of reallocation shocks on unemployment appears to be rather small, but part of frictional unemployment may be attributed to productivity shocks in our empirical analysis. 6 CONCLUSIONS
Combined worker and job flow data allow us to consider the sizes and propagation of reallocation shocks at the labour market in addition to the usual aggregate demand and supply shocks of real business cycle models. This paper uses flow
266
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
data for the Netherlands based on administrative sources for specification and estimation of a four-variate structural vector autoregressive 共SVAR兲model which distinguishes four types of shocks, namely aggregate supply and demand shocks, a reallocation shock at the demand side of the labour market, and a productivity shock at the supply side of the market. The specification of the model needs a number of identifying restrictions which we have derived as much as possible from economic argumentation, and which is partly based on different models from the flow approach to the labour market. It appears that each of these four types of shocks has at least some influence on unemployment both in the short and in the long run. The fact that the long-run influence of the aggregate labour supply shock on unemployment is estimated to be very limited concords with other empirical studies for the Dutch labour market, which indicate that additional labour supply is absorbed by labour demand with relatively small adjustment lags. We find longer adjustment periods for the other three shocks we distinguished, namely aggregate demand shocks, reallocation shocks, and productivity shocks. Aggregate demand and reallocation initially yield less unemployment, whereas enhanced productivity leads to an increase in unemployment. As an identifying restriction, our model assumes that in the long run changes in unemployment will be zero after full propagation of the shocks. So the model describes the transition from an old to a new unemployment equilibrium for the four types of shocks. Our modelling exercise shows that in reality the combination of the shocks we distinguished give rise to very complicated unemployment dynamics. Yet, from the point of view of policy analysis it is very essential to disentangle these various shocks. That is because these shocks constitute different sources of labour market dynamics where each type of shock may lead to a specific policy reaction, or represents a different kind of policy measure. For instance, our results show that a policy aimed at enhancing labour participation will obviously benefit from a policy-induced labour supply shock. The long-run, but even the short-run effects of such a shock on unemployment are small which suggests that additional labour supply is turned quickly into additional employment. Yet, the variance decomposition shows that, besides an autonomous labour supply shock, also aggregate demand shocks, reallocation shocks, and productivity shocks may influence labour supply and employment to a considerable extent, so that instruments which focus on these types of shocks are also relevant for participation policy. A scope for future research is even to consider other types of shocks as well. By way of example we mention ‘skill-biased’ demand shocks which are, according to Mortensen and Pissarides 共1999兲 and Marimon and Zilibotti 共1999兲, behind differences in unemployment dynamics between the United States and Europe, given differences in the social security system.
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
267
APPENDIX A – DEFINITION OF DATA ON JOB CREATION AND JOB DESTRUCTION JC ⫽ VI j ⫹ F eej ⫹ F uej ⫹ F nej JD ⫽ 共F eu ⫺ VI eu兲 ⫹ 共F en ⫺ VI en兲 ⫹ 共F eej ⫹ F eev ⫺ VI e兲 ⫹ VO n , where JC JD VI j F eej F uej F nej
⫽ ⫽ ⫽ ⫽ ⫽ ⫽
F eu VI eu F en VI en F eev VI e VO n
⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽
Job creation Job destruction New vacancies Employed that find a new job for which there was no vacancy Unemployed who find a new job for which there was no vacancy People not participating who find a new job for which there was no vacancy Employed who become unemployed 共fires and quits兲 New vacancies as a result of fires and quits Employed becoming non-participants New vacancies as a result of employed becoming non-participants Employed who find a new job that had a vacancy New vacancies as a result of employed that find a new job Autonomous scrapping of unfilled vacancies
APPENDIX B – DERIVATION OF AN EXPRESSION FOR THE LONG-RUN EFFECTS OF THE SEPARATE SHOCKS ON THE CHANGES IN UNEMPLOYMENT We already mentioned the relations: J t ⫽ E t ⫹ V t and LS t ⫽ E t ⫹ U t . Using these relations it follows: U t ⫽ LS t ⫺ E t ⫽ LS t ⫺ J t ⫹ V t . We now write up the first order difference of U t : U t ⫺ U t ⫺ 1 ⫽ LS t ⫺ LS t ⫺ 1 ⫺ J t ⫹ J t ⫺ 1 ⫹ V t ⫺ V t ⫺ 1 .
268
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
Now we normalise this expression with LS t : 关U t ⫺ U t ⫺ 1 兴 LS t
⫽
关LS t ⫺ LS t ⫺ 1 兴 LS t
⫹
关V t ⫺ V t ⫺ 1 兴 LS t
.
We then substitute J t ⫺ J t ⫺ 1 by JC t ⫺ JD t and we substitute 1 Et
冉
⭈ 1⫺
Ut LS t
冊
1 LS t
by
.
This leads us to equation 共5.1兲: 关U t ⫺ U t ⫺ 1兴 LS t
⫽
冉
JD t Et
⫹
⫺
JC t Et
冊冉
⭈ 1⫺
关V t ⫺ V t ⫺ 1兴 LS t
Ut LS t
冊
⫹
关LS t ⫺ LS t ⫺ 1兴 LS t
.
The above equation gives the relation between the change in unemployment on the one hand and job creation, job destruction, change of labour supply and change of vacancies on the other. The long-run effects of the shocks on job creation, job destruction, change of labour supply, and change of vacancies can be estimated by counting the effects over, for instance, 15 years. Therefore the matrix B共1兲 for the long run effects, where the size of the impulses is unity, can be used: 15
B共1兲 ⫽
兺B
j⫽0
15
j
⭈ 1⫽
兺C B
j⫽0
j
0
⭈1.
Replacing the terms of the right hand side in equation 共5.1兲 by corresponding cells of B共1兲 we get the long-run effects of the separate shocks on changes in unemployment. For instance, for the long-run effect of the first shock 共i.e. the aggregate demand shock兲 we substitute the elements B 1,1共1兲, B 2,1共1兲, B 3,1共1兲 , and B 4,1共1兲 of the matrix B共1兲 in JC t /E t , JD t /E t , ⌬LS t /LS t and ⌬V t /LS t , respectively. So, for each shock the change in unemployment will be a linear function of the cells of B 0 . To identify the matrix B 0 we assume that the long-run effects of the separate shocks on the change in unemployment are zero. These assumptions result to four linear equations, with the cells of B 0 as the unknown variables.
UNEMPLOYMENT DYNAMICS AND PROPAGATION OF SHOCKS
269
REFERENCES Balakrishnan, R. and C. Michelacci 共1997兲, ‘Unemployment Dynamics across OECD Countries,’ paper presented at EALE, 1997. Bernanke, B. 共1986兲, ‘Alternative Explanations of Money-Income Correlation,’ Carnegie-Rochester Conference Series on Public Policy, 25, pp. 49-100. Blanchard, O.J. and D. Quah, 共1989兲, ‘The Dynamic Effects of Aggregate Demand and Supply Disturbances,’ American Economic Review, 79, pp. 655-673. Blanchard, O.L. and P. Diamond 共1992兲, ‘The Flow Approach to Labor Markets,’ American Economic Review, Papers and Proceedings, 82, pp. 354-359. Broersma, L., F.A.G. den Butter, and U. Kock 共2000兲, ‘A National Accounting System of Worker Flows,’ Economics Letters, 67, pp. 331-336. Broersma, L. , J. Koeman, and C. Teulings 共2000兲, ‘Labour Supply, the Natural Rate and the Welfare State in The Netherlands; The Wrong Institutions at the Wrong Point in Time,’ Oxford Economic Papers, 52, pp. 96-118. Butter, F.A.G. den and S.J. Koopman 共2001兲, ‘Interaction Between Structural and Cyclical Shocks in Production and Employment,’ Weltwirtschaftliches Archiv, 137 共2兲, pp. 273-296. Caballero, R.J. and M.L. Hammour 共1996兲, ‘On the Timing and Efficiency of Creative Destruction,’ Quarterly Journal of Economics, 111, pp. 805-852. Chronicle of Social Insurance 共1996兲. Report of the Dutch College of Social Insurance, CTSV, Zoetermeer. Davis, S.J. and J. Haltiwanger 共1999兲, ‘On the Driving Forces behind Cyclical Movements in Unemployment and Job Reallocation.’ American Economic Review, 89 共5兲, pp. 1234-1258. Gautier, P.A. 共1997兲, The Flow Approach to the Labor Market, Tinbergen Institute Research Series 160, Amsterdam, Thesis Publishers. Giannini, C. 共1992兲, Topics in Structural VAR Econometrics, New York, Springer Verlag. Hamilton, J.D. 共1994兲, Time Series Analysis, Princeton, NJ, Princeton University Press. Kock, U. 共2002兲, Social Benefits and the Flow Approach to the Labor Market, Tinbergen Institute Research Series 261, Amsterdam, Thela Thesis. Kydland, F. and E. Prescott 共1982兲, ‘Time to Build and Aggregate Fluctuations,’ Econometrica, 50, pp. 259-293. Layard, R., S. Nickell, and R. Jackman 共1991兲, Unemployment; Macroeconomic Performance and the Labour Market, Oxford, Oxford University Press. Long, J.B. and C.I. Plosser 共1993兲, ‘Real Business Cycles,’ Journal of Political Economy, 91, pp. 39-69. Marimon, R. and F. Zilibotti 共1999兲, ‘Unemployment versus Mismatch of Talent: Reconsidering Unemployment Benefits,’ Economic Journal, 109, pp. 266-291. Mortensen, D.T. 共1986兲, ‘Job Search and Labor Market Analysis,’ in: O.C. Ashenfelter and R. Layard 共eds.兲, Handbook of Labor Economics, 2, Amsterdam, Noord-Holland. Mortensen, D.T. and C.A. Pissarides 共1994兲, ‘Job Creation and Job Destruction in the Theory of Unemployment,’ Review of Economic Studies, 61, pp. 397-415. Mortensen, D.T. and C.A. Pissarides 共1995兲, ‘Technological Progress, Job Creation and Job Destruction,’ CEPR Discussion Paper, 264. Mortensen, D.T. and C.A. Pissarides 共1999兲, ‘Unemployment Responses to Skill biased Technology Shocks: The Role of Labour Market Policy,’ The Economic Journal, 109, pp. 242-265.
270
K. VAN MONTFORT, F.A.G. DEN BUTTER, G.T.J. WEITENBERG
Pissarides, C.A. 共1988兲, ‘The Search Equilibrium Approach to Fluctuations in Unemployment,’ American Economic Review, Papers and Proceedings, 78, pp. 363- 368. Pissarides, C.A. 共1990兲, Equilibrium Unemployment Theory, Oxford, Basil Blackwell. Shapiro, M. and M. Watson 共1988兲, ‘Sources of Business Cycle Fluctuations,’ in: J. Blanchard and S. Fisher 共eds.兲, NBER Macroeconomics Annual 1988, Cambridge, MA, MIT Press, pp. 111-147. Weitenberg, G.T.J. 共1998兲, Dynamics on the Dutch Labor Market, Research report of the Free University Amsterdam, Department of Econometrics, Amsterdam. Whiteman, C. 共1983兲, Linear Rational Expectation Models: A User’s Guide, Minneapolis, Minnesota University of Minnesota Press.
