35 meaningful proxy for the search effectiveness index c, its function in an equation like (5) needs to be briefly discussed. Recall that c takes on values between 0 and 1, the lower this value the less efficient becomes the stock of unemployed in the matching process. Note that in equation (5) the lower c, the more is subtracted from In U. The value of c in turn is a function of the duration structure of unemployment: the larger the proportions of longer duration categories in the unemployment pool the smaller is the value of c. Essentially one can think of the search effectiveness index c as an index which tracks the duration composition of the stock of unemployment over time.<sup>32</sup> A very simple way to track this composition over time is to split the pool of unemployed into short-term and long-term unemployed, i.e. unemployed with an uninterrupted duration of less and more than twelve months respectively. This can be done with the Polish data. The regression then becomes (for the precise derivation of this type of equation, see Boeri, 1994): In H =So + _S,_ In V + _62_ In _UsT + 63_ In _ULT + S4 TR±+ 65_ (In UsT-In ULT)<sup>2</sup> + 6 (6)

# where UST and ULT are the short-term and long-term stocks of unemployment.

Table 11 shows estimates of an augmented matching function using equation (6) for males and females jointly, covering six quarters form January 1993 to June 1994 and using pooled cross section time series data of the 49 voivodships. This regression has an exploratory character. Further work is required before safe conclusions can be drawn from this type of empirical evidence. Employing the Scarpetta-Huber taxonomy of Polish regions (cf. Gora and Lehmann, 1995) dummies are included to control for region-specific fixed effects<sup>33</sup> as well as time dummies to control for the time varying macroeconomic environment that is common to all voivodships. The coefficients on the dummies are not shown; however, while the region-specific fixed effects were not significant the time dummies were highly 32The search effectiveness index c is constructed in the following way. Assume that there are D duration categories in the stock of registered unemployed. Let fd be the outflow rate of duration category d (d=1,....,D) in a certain steady state where, as observed in most OECD countries, +1 > +2 > - > 4D for all d (d=1,....,D), i.e. the shorter the duration category the larger the steady state outflow rate from unemployment. Also, let at the beginning of time interval t wd.t = Ud / Ut for all d (d=1,...,D) where Ud.t is the stock of unemployment duration d and Ut is the total stock of unemployment. Then Ct = Ed Wdt fd so that the search effectiveness index c, can be indeed thought of an index which tracks the duration composition of the stock of unemployed over time. 33There are six types of Polish regions enumerated by Scarpetta and Huber: agricultural, developed; agricultural, others; heavily industrialized, developed; heavily industrialized, others; diversified, developed and diversified, others. By having dummies for the regional type rather than for each voivodship one reduces endogeneity problems which can arise from the fact that some voivodships respond to high unemployment (low hirings) by increasing the stocks of ALMP participants.