Aggregate Matching in Spain: Time Series Analysis Using Cointegration Techniques

I analyze the matching process in the Spanish labor market from 1994-2005. I use monthly registered unemployment data and refer solely to public employment intermediation. This period reflects an upward movement along a downward sloping Beveridge curve; therefore, major changes in the process efficiency should not be observed. I narrow the considerations to a job queuing model, which is the most relevant description of the labor market matching process in Spain, according to the literature. I apply various quantitative methods to address the problem of non-stationary data. The Engle- Granger estimates emphasize the crucial role of the demand in generating the outflows from unemployment to employment. The ECT coefficient confirms that the model efficiently approaches the new equilibrium. These findings confirm that job seekers find themselves on the disadvantaged side of the market and compete for scarce job offers, which, in turn, are ascribed randomly to the workers. The diagnostic tests of the VAR models question the relevance of a multivariate space analysis because the outflow from unemployment to employment appears to be the sole endogenous variable.

Spain joined the European Economic Community in 1986 and implemented a series of reforms with the objective of increasing the elasticity of the market, encouraging companies to create better quality jobs and hiring workers on permanent contracts (e.g., reforms implemented in 1984, 1994, 1997 and 2001). Among the outcomes of these changes, one can list the duality of the labor market; this originates from the extensive use of temporary contracts (approximately 25% in 2010) and the high volatility of (un)employment. Petrongolo and Pissarides (2008) prove that both unemployment inflow and outflow contribute to high unemployment volatility.
One can find a few literature surveys that concern the matching function estimates for the Spanish labor market, for example: (Alujas Ruiz, 2002;Álvarez de Toledo, Núñez and Usabiaga, 2004;Núñez, 2006;Núñez & Usabiaga, 2007). The main qualitative conclusions arise from using registered data. Antolín (1994) proposes a method to recalculate the vacancy data for the entire economy (but for a stock-based model). The analyses imply that vacancies are the driving force of the outflow from unemployment to employment creation. Moreover, the findings indicate that the job queuing model, which assumes random matching between unemployment stock and vacancy inflow, most properly describes the public employment intermediation in Spain. This paper is organized as follows. In section 2, I present data. Section 3 includes a univariate space analysis using Engle-Granger and Engle-Yoo techniques. I refer to the job queuing model to present matching between the stock of the job seekers and the inflow of new vacancies. I extend the dimension of the analysis in section 4, in which I apply the Johansen approach. In section 5, I interpret the results and compile concluding remarks in section 6.

Data characteristics
I base quantitative analysis on the registered unemployment and vacancy data from public employment offices (Servicio Público de Empleo Estatal). These time series possess certain valuable features. Companies are obliged to register each job offer (as a vacancy or as a covered job post). The outflow from unemployment to employment can be directly assigned to public employment intermediation, which refers to the job offers registered at public employment offices. Once we compare this time series with the total hires, we can assess the fraction of the total job creation that arises from public employment offices intermediation.

A single equation model
The empirical research of the matching function focuses on determining the values of the outflow from unemployment to employment elasticities with respect to the job seekers and vacancies. This focus allows the identification of the matching process character and the indication of the impact of the other variables on the trade process efficiency, e.g., means of the active labor market policy. Shapiro and Stiglitz (1984) where: M t -outflow from unemployment to employment during month t ; U t 1 -unemployment stock at the end of month t 1 , or J t 1 -total job seekers stock at the end of month t 1; and v t -vacancy inflow during month t .
I estimate the job queuing matching function using the OLS estimator. The results suffer from high autocorrelation, which is addressed by using the AR(1)   Table 4). I analyze the lag structure, the inverse roots of the characteristic AR polynomial and the residuals.
The stability condition is satisfied for both models.
The model with the unemployment stock requires 4 lags; the model with total job seekers stock requires 2 lags. The LM autocorrelation tests imply no serial correlation (at the 1% significance level for the unemployment stock model and at the 5% significance level for the other model). The Doornik-Hansen skewness test indicates multivariate normal distribution of the residuals.
Next, I perform a cointegration test and a Granger block exogeneity test (compare Table 5

Discussion
I have encountered two papers that refer to non-stationary data in analyzing labor market matching in Spain. Bell (1997) performs comparative analysis of the matching process in three European countries, including Spain. She adopts a general dynamic error correction regression specification with differences and lagged levels of the dependent and explanatory variables. Gałecka-Burdziak (2013) uses two-step Engle-Granger and three-step Engle-Yoo procedures. In both papers, the unemployment negatively influences the matching process, whereas the impact of vacancies is positive.
The diagnostic tests of the VAR models question the analysis of a public intermediation matching process in the Spanish labor market. It appears that the outflows from unemployment are explained by the number of agents present in the labor market; however, the inverse relation does not hold.
Thus, the single equation model estimates appear to provide consistent results. However, one must remember that the Engle-Granger procedure provides one cointegrating vector. If there are more such vectors, the outcome may constitute a linear combination of the basis vectors (Welfe 2009). The quantitative results show that demand appears to be the driving force in the job creation process that occurs through public employment intermediation, which is in accordance with previous analyses. ECT estimates express the high efficiency of the market. For a comparison, we can recall the Berman (1997) and Gałecka-Burdziak (2013) analyses. Berman (1997)  Supply's role is much smaller; therefore, the workers exert a higher congestion effect on each other. Job seekers compete for job offers. The relevance of the job queuing model confirms that job seekers are randomly ascribed to new job offers. There arises the need to Aggregate matching in Spain. Time series analysis using cointegration techniques increase the number of job offers available to match to improve the public employment intermediation matching process.