A Comparison of the Beveridge Curve Dynamics in Italy and U.S.A. Carlo Di Giorgioa,b and Massimo Gianninia* a
Tor Vergata University of Rome, bCeMASM, Luiss University of Rome
Abstract
In this paper we investigate the Beveridge curve dynamics in USA and Italy by means of a cointegrated structural VAR model. A simple economic model is introduced to motivate the identifying assumptions of the empirical analysis. A stable long-run relationship is found for both countries. In order to study the dynamic behaviour of the model, and to decompose unemployment and vacancy fluctuations, we identify three common stochastic trends. The empirical results suggest that there are some sources of hysteresis in unemployment in both countries. Transitory shocks are also identified to account for the short run dynamics of the model. The approach allows us to detach the long run from the short run dynamics, in order to provide information on the cyclical and structural Beveridge curve. J.E.L. classification: C32, E24, J63 Keywords: Beveridge curve, common trends, SVECM, hysteresis.
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Correspondence authors: Carlo Di Giorgio, Massimo Giannini, Università di Roma Tor Vergata, Via Orazio Raimondo, 18, 00173, Roma, Italy, Tel. +39672592405. E-mail address:
[email protected] ;
[email protected]. The authors thank Anders Warne for his helpful comments and suggestions on an early draft. We are also grateful to Michele Cuppone, Anna Mocavini and Achille Paliotta for kindly providing us with Italian vacancy data survey of Isfol-CSA. The usual disclaimer applies. Any remaining errors are ours.
1
Introduction The Beveridge curve, that identifies the negative relationship between unemployment rate and job vacancies, is still often used to identify the state of the labour market. Although the Beveridge curve is not a structural economic relationship, in sense that workers and firms do not consciously decide to make unemployment negatively related to vacancies 1, in this paper, through some methodological and empirical steps, we try to explain the underlying behaviours of the workers and firms, in accumulating skills, setting wages, and the involved policy makers actions, that indirectly result in the patterns of the Beveridge curves of various countries. In order to study the dynamic behaviour of the Beveridge curve in two countries we identify a common trends model that allows us to decompose unemployment and vacancy fluctuations stemming from three permanent shocks, namely a technology shock, and a labour supply shock for both countries, an aggregate activity, and a reallocation shock, for U.S. and Italy, respectively. Our aim is to isolate shocks and structural changes from the Beveridge curve, in order to assess its long run dynamics and adjustment. To achieve the goal, in a first stage we present a simple labour market model and its solution, in way to investigate upon the model cointegration properties and to assess the structural stability of the equilibrium relationship. The estimated model allows - in particular for U.S.- to identify two regimes in the sample, representing low and high efficiency phases of the labour market. Out of equilibrium, dynamics has been investigated by the common stochastic trends approach; this allows us to study the economic model in its long and short run dynamics. This work is close in spirit to Blanchard and Diamond, 1989 (henceforth BD); in that paper the authors try to isolate short run dynamics from the steady state in order to assess whether the US Beveridge curve undertakes regular movements in the u (unemployment), v (vacancy) space, even though, unlike them, we use a discrete time model of the labour market. Theoretical microfoundation of the short run dynamics in the Beverdige curve is investigated in Giannini, 2006, by means of the Dynamic Monte Carlo Markov Chain approach. The first two sections of the paper describe the data and present a small model of the labour market that will be used to motivate the identifying restrictions in the following empirical analysis. Section 3 contains the cointegration properties of the model for the United States. Sections 4 exposes a brief review of the econometric common stochastic trends analysis, while in section 5 we identify and estimate a common trends model and use it to study the dynamics of U.S. Beveridge curve. Section 6 describes the empirical results for Italy. Section 7 concludes and tries to describe a final comparison of the results of the analysis in the two countries.
1
Bleakley and Fuhrer (1997).
2
1. The Data We use quarterly data for the United States and Italy extended to cover the period 1960:1-2007:4 for U.S., 1992:4-2006:4 for Italy: details are in the Appendix. The variables are: the log of the civilian labour force, the log of the productivity measured as real output per worker, the unemployment rate and vacancy rate, yt = [lt , yt − et , lt − et , vt ] 2. The variables for United States '
are graphed in Figure A1. The first and third panels show the strong trend in both labour force and productivity. The second and fourth panels graph the unemployment and vacancy rates with less marked trends. Looking at the chart of vacancy data, the remarkable downward trend characterizing data since early 1990s, it is likely due to recent increased alternative sources of job search, such as the Internet, that have reduced the importance of the traditional help-wanted advertisings. In a first step of the analysis we investigate upon the statistical properties of the series; if the series are non-stationary will be evaluated the presence of cointegration. ADF and KPSS unit root tests carried out on the levels of the single variables suggest that all the variables can be regarded as nonstationary for both countries. In empirical investigation on these type of data, Juselius (2006) suggests testing stationarity using the cointegrated VAR approach rather than the single equation unit root tests; however, results reported in Table A1 and A2, confirm our single variable unit root testing3. In Figure 1 is graphed US Beveridge curve for the full sample, it is worth noting inward shift of the curve from late 1980’s to early 2000s. This process can be described defining4 the job matching function ht = α ⋅ m(ut , vt ),
∂m ∂m > 0, >0 ∂u ∂v
where the rate of job matching or hiring, h, is expressed as a function of the unemployment rate, u, and the job vacancy rate, v, while α is a parameter that describes the efficiency of the matching process. It is usually assumed that the matching function is characterized by constant returns to scale and it is increasing in both arguments. These assumptions imply that the Beveridge curve is convex to the origin and downward sloping in u-v space . It represents a steady-state relationship in sense that the job matching rate h, i.e. the percentage of workers flowing out of unemployment into jobs, is equal to the flow into unemployment, at an exogenous constant rate of job separation, s. Outward or inward shifts of the curve over time, are due to a lower or higher levels of the Unemployment rate can be defined as ut ≈ lt − et , where lt and et are the natural logarithms of labor force and employment, respectively. 3 Unlike the usual univariate unit root tests that have nonstationarity as the null, this multivariate procedure has stationarity as the null hypothesis given the cointegration space. 4 Pissarides (2000). 2
3
efficiency of the job matching (measured by α ); these movements are induced by changes in the search intensity of firms and workers, changing demographics, barriers to occupational and geographical mobility, etc.
U.S. Beveridge curve 1960-2007 0.150 0.125
79 78
73 70
0.100 Vacancy
88 89 97
99
0.075
72
87 74
86 77
85 80 84 81 76
95
83
71
93
75
91
0.050
05
0.025
Beveridge curve 1960-1988
Beveridge curve 1989-2007
01
06
82
02 03
07
0.000 2
4
6
8
10
12
Unemployment
Figure 1. - US Beveridge curve.
In order to identify short and long run dynamics of the Beveridge curve, we perform firstly the cointegration analysis, applying Johansen’s procedure5, while in the second stage we use, if any, the cointegration properties of the VECM to derive and identify the common stochastic trends that drive the system. We study the characteristics of the system found in the first stage carrying out a common trends analysis in order to analyse the properties of the Beveridge curve. 2. A model of the labour market The model used in this paper consists of a production function, a labour supply relation, a Beveridge curve relation, and a labour market tightness equation:
(1)
= yt β et + θt
where yt is output, et is employment, and the parameter β measures returns to scale. θt is a stochastic technology trend and evolves according to
5
See Johansen (1996), Juselius (2006).
4
= θt θt −1 + ε y ,t with the pure technology shock ε y ,t .
( 2)
= lt δ yt +ψ t
According to equation (2) labour force is influenced by the output, since positive aggregate demand movements lead to a decrease in unemployment, as well as an increase in the labour force, 6 and a stochastic labour supply trend following the process:
ψ =t ψ t −1 + ε s ,t where ε s ,t is a pure labour supply shock. Equation (3) is a Beveridge curve relation, ut = −η vt + ωt
(3)
where ωt is an exogenous aggregate activity variable that evolves according to = ωt ωt −1 + ε c ,t with the pure activity shock ε c ,t . As observed by Petrongolo and Pissarides (2001), strong negative correlation, at least for US labour market, between unemployment and vacancies supports an aggregate demand interpretation of US employment fluctuations. vt − u=t γ ( yt − et ) + ε m ,t
( 4)
In equation (4) labour market tightness (v-u ratio) – that is a broad measure of the cycle - is influenced by the labour productivity: for a given separation rate s, an increase in labour productivity reduces the unemployment rate and raises vacancy rate, increasing the v-u ratio , so that unemployment and vacancy move in opposite direction. ε m ,t is a pure market tightness shock, and if equation (4) is a stationary relation, ε m ,t follows the process
ε m ,t = φ ε m,t −1 + ϕm,t ,
φ
