The Sargent model can then be easily adapted to solve

The Sargent (1978) model can then be easily adapted to solve our proposed problem. Our problem requires that the representative firm decides on hiring competing human capitals with different sets of schooling years. A simplified version of the model requires that the representative firm makes a choice between hiring any two human capitals that are different in qualification or years of schooling.where y is the output; ψ1 and ψ2 are parameters; H human capital qualified with higher schooling years; H less qualified human capital (lower schooling years);); f0, f1 represents their average productivity parameters; a and a are exogenous stochastic processes that might affect the average productivity aleatory. The overtime changes in a and a obeys a stochastic process with E(a)=0 and E(H)=0. Thus, the human capitals hiring costs obeys the following quadratic function.where d and e represent direct hiring costs of each human capital. The market wages are as follows: and , being p<1, hence the wage of less qualified human capital is assumed to be lower compared to the more qualified one. Given Eqs. (1)–(7), the present value of the profit can be written as follows:where 00, p<1 are the productivity and cost parameters. The solutions to the Euler equation (8) that obeys the transversality conditions are given by the following functions: The variables and represents the optimum long run level of employment of each human capital. They are the level to which the equation systems are expected to converge over the long run. Sargent (1978) assumed their representation as follows: The above solutions implies that (1/λ2)=bλ1 and that λ1 is a direct function of d. As the cost of human capital d increases it Biotin-HPDP also increases the adjustment parameter λ1. Similarly (1/μ2)=bμ1 and μ1 increases with the value of e. Even though we do not observe d and e, their level can be obtained indirectly through the estimates of λ1 and μ1. By estimating them we learn about the adjustment cost of the labor market. Sargent\'s empirical estimates of Eqs. (9)–(12) required additional assumptions about the behavior of the aleatory shocks and wages. The optimum level of human capital was set to be a function of the level of the lagged human capital and real wages: and , where γ(L) was the lag operator. The log functions of the Eqs. (9)–(11) took the following forms: The author provided several empirical estimates; however the most important results showed that λ1 was between 0.94 and 0.96, and μ1 was between 0.74 and 0.76. The author reached the conclusion that the extra hours’ hiring costs were lower than hiring new labor for the firm. The wage variance decomposition also showed the adjustment cost was responsible for 49% of the new hired human capital. The same wage variance decomposition of the adjustment cost related to the cost of extra working time explained only 16.0% of the new hirings. Moreover, long run payments of extra time may explain 29.0% of the new hired human capital. In simple words, as the firm starts hiring extra working time, the chances that it will create a new position increases from 16.0% to 29.0%.
Conclusion The theoretical model based on Sargent (1978) enabled us to learn about the labor market\'s adjustment cost role. According to our estimates the adjustment cost of human capital with degree of superior education (12 years or more of schooling) present the lowest cost compared to the others. In second place comes human capital with fundamental education level (1–8 years of schooling). The highest adjustment cost belongs to human capital with intermediate education level (9–11 years of schooling).
Introduction Mechanism design and implementation theory made possible an approach such that virtually all allocation forms could be understood through formal mathematical models. Auction theory, for example, is undisputedly considered as a successful case in designing new market institutions. The applications of auction theory surpassed its basic purposes, which are the understanding of allocation rules and price formation, as examples like first- and second-price all-pay auctions, double auctions and score auctions indicate.