تقاضای نیروی کار پویا سن خاص و سرمایه گذاری سرمایه انسانی

To study the optimal age-specific labor demand and human capital investment at the firm level we extend the standard dynamic labor demand model by introducing ‘age’ as a second dynamic variable and distinguish between two types of workers: ‘low skilled’ and ‘high skilled’. Applying an age-structured optimal control model we derive qualitative features of the optimal age-specific hiring and training effort. For the case of a linear revenue and production function we prove that firms do not anticipate changes in adjustment costs in their optimal decisions. This result no longer holds if a nonlinear revenue or production function is considered.

The balance among the age groups in the labor force is expected to change markedly over the next decades. In the majority of industrialized countries we will have a shift of the age distribution of the labor force to older ages. The changes in the age distribution of the workforce and their implications for labor market outcomes such as wages and unemployment have been extensively studied at the macro-level (e.g., Bloom et al., 1987, Korenman and Neumark, 2000 and Welch, 1979). Imperfect substitutability of workers at different ages together with increasing demand for educated workers and technological progress are key factors explaining the relation between demographic change and labor market outcomes. To understand the process of employment changes that result from shifts in the age structure of the workforce, it is important to move to the firm level. The question is then how firms will react in their hiring and firing strategy to the expected change of the labor supply that is caused by demographic change. Adjustments of the workforce will entail costs and it is the shape of these costs that determines the dynamics of employment changes (hiring and firing strategy) at the firm level. Hiring costs essentially account for recruitment (advertising, searching, screening) and initial training costs, while firing costs essentially consist in severance payments, administrative constraints and possible reorganization costs. A growing literature exists that empirically tests the shape of the adjustment costs (distinguishing between fixed and variable costs, symmetric and asymmetric costs, cf. Hamermesh, 1989 and Hamermesh and Pfann, 1996) that underlie observed employment changes.1 Adjustment costs also reflect differences in regulatory frameworks in the labor market. Various studies have shown that hiring costs exceed separation costs in America while the opposite holds for most European countries. As argued in Kraft (1997), high labor regulations in the EU countries put pressure on firing costs, while hiring costs are higher in the US due to investment into initial firm-specific skills.2 So far the dependence of adjustment costs on age has been neglected. Yet evidence from the management literature indicates that older and younger workers do exhibit different attributes. For a short summary of this literature, see Guest and Shacklock (2005) and Skirbekk (2005). For example, employers report that younger workers tend to have better physical strength and endurance, vision, hearing, cognitive processing, intellectual capital and adaptability. While older workers are perceived as having better people management skills, judgment that depends on experience, reliability/dependability, loyalty and attendance. These differences suggest differences by age for the initial training costs that are part of the hiring costs. Moreover firing costs increase with age, tenure and wage. Further arguments for the dependence of adjustment costs on age can be found in the search-matching models in labor economics (cf. Pissarides, 2002). A key assumption is that firms cannot hire employees instantaneously, but must search (through a costly and time-consuming process) in the pool of unemployed workers. The probability that a vacancy is matched with an unemployed worker will then depend on the tightness of the labor market as represented by the ratio of vacancies to unemployed. Obviously, the lower this ratio the more likely a match will occur and this may be related to lower adjustment costs of hiring workers.3 Since unemployment rates are known to be age dependent (generally decreasing with age), a change in the demographic composition of the workforce will have a direct effect on the overall unemployment rate and hence the probability of a job match (assuming no change in vacancies). Moreover, as recently illustrated in Hetze and Ochsen (2005), young and old workers may be characterized by different rates of job separation and productivity, thereby indirectly affecting the equilibrium unemployment rate.4 As indicated in Hetze and Ochsen (2005), the altered age composition may either increase or decrease the equilibrium unemployment rate depending on specific parameter values of the model. Hence, the consequences of an aging of the labor supply on age-specific adjustment costs are not clear a priori. We therefore allow for a general form of age-specific adjustment costs and present analytical results on how the age structure of the optimal labor demand depends on quite general parametric variations in the adjustment cost function. That the employment structure at the firm level indeed follows a rather peculiar age shape is supported by empirical data. In Fig. 1a we plot the mean age structure of employees for selected industries in the mining and manufacturing sector in Sweden for 1996.5 The structure of employees shows a clear hump-shaped age pattern. The aging of the employee structure becomes clear if we consider the evolution of the mean age over time (Fig. 1b). As we will show in this paper, by including age structure into a standard dynamic labor demand model we are able to model the empirically observed age structure of employees at the firm level and its evolution over time. Full-size image (85 K) Fig. 1. Age structure of employees in selected industries of Swedish mining and manufacturing sector. Figure options So far, we have only considered the heterogeneity of the workforce by age. The skill level constitutes a further important heterogeneity and numerous studies have investigated the labor market outcomes (in particular wage dispersion) for different skill groups (Katz and Autor, 1999).6 Since a large portion of human capital accumulation in the form of training and on-the-job learning takes place inside firms (see Becker, 1964 and Mincer, 1974), it is important to understand the dynamics of skill composition at the firm level.7 The theory of optimal life cycle human capital investment (through education and training) predicts that human capital accumulation will concentrate at the beginning of life (see Weiss, 1986 for a review of the theoretical literature). According to this theory, human capital in an economy characterized by population aging will be of an ‘older vintage’. Also from a firm level point of view, human capital investment/upgrading is less common for the older workforce due to lower learning capabilities and less time till retirement.8 It is therefore of interest how firms will react in terms of their age-specific human capital investment under conditions of labor force aging as implicitly represented by the age dependency of the adjustment costs.9 In summary, our paper is intended to raise and to address the following questions: under which conditions will it be optimal for firms to hire more older workers? How will the optimal age structure of the labor force look like? Will firms increase their investment into firm-specific human capital in accordance with the optimal age structure of hiring/firing? Are changes in age-specific costs of hiring/firing also anticipated in the optimal decisions at the firm level? While the importance of age and skill heterogeneity has been recognized in recent empirical studies on the labor market effects of demographic changes, our aim is to provide a formal economic model that can explain the optimal age and skill heterogeneity that is chosen at the firm level. We investigate the problem of optimal employment and training policy at the firm level allowing for heterogeneity of workers with respect to their age and firm-specific human capital and considering the changing age structure of the labor supply as represented by the adjustment costs of labor. The theoretical framework we choose is a classical dynamic labor demand model ( Nickell, 1986). To capture the heterogeneity of workers by age and human capital: (i) We introduce ‘age’ as a second dynamic variable and distinguish two types of workers: unskilled versus skilled workers. (ii) We introduce age-specific adjustment costs of hiring/firing and human capital investment and age-specific wage schedules (the specific form of the adjustment costs of hiring/firing we postulate may represent the tightness of the labor market for specific age groups of the labor force10). (iii) We go beyond comparative statics and investigate the optimal dynamic path of hiring/firing and training intensities if adjustment costs vary over time. While the age structure has been introduced into the neoclassical theory of optimal investment in several recent contributions (e.g., Barucci and Gozzi, 2001 and Feichtinger et al., 2005a), we are only aware of one paper (cf. Christiaans, 2003) that augmented the classical theory of labor demand by modelling the age structure of the workers. As outlined in Christiaans (2003) there are clear differences between the theory of capital and the theory of labor demand. These include the facts that: (a) a firm accumulates the capital stock that it buys in the capital goods market, while the firm rents labor services at current wage rates; (b) political decisions may influence the span of working life time and (c) a large part of labor adjustment does not arise for technical reasons but because of legal regulations. We argue that adjustment costs will also reflect the tightness of the labor market as caused by demographic shifts in the anticipated labor supply. In addition to the optimal age-specific hiring/firing at the firm level (as in Christiaans, 2003), we also allow for an optimal investment in age-specific human capital. To solve the continuous-time dynamic optimization model we apply the maximum principle for systems with distributed parameters developed in Feichtinger et al. (2003). The structure of the paper is as follows. In the next section we present the theoretical framework of our study. Optimality conditions and the optimal steady state are presented in 4 and 3. We show that the optimal steady state is reached in one generation if the firm's revenue function is linear. Section 5 is devoted to the case of a linear revenue and a linear production function. First we obtain certain relations between the optimal level of hiring/firing (and the human capital investment) for different adjustment cost functions of hiring/firing. Then we present a general proposition for the sensitivity of the optimal mean age of hiring with respect to parametric changes of the adjustment cost function. We apply this proposition to establish some qualitative consequences for the optimal mean age of hiring, of changes in the magnitude, the slope or the shape of the adjustment cost function with respect to age. We conclude this section with a key property of the optimal policies in the case of a linear production and linear revenue function: the non-anticipation property. Changes of the adjustment costs are not incorporated into the firms’ optimal decisions prior to the point in time when these changes occur. The validity of our analytical results and in particular the non-anticipation property are illustrated (through numerical simulations) in the final subsection of Section 5. In Section 6 we extend our framework to allow for nonlinear production and revenue functions. We show numerically that most of our analytical results also hold in this more general case (though analytical results are not provided in this case). However, in contrast to the case of linear production and revenue functions, the firm anticipates a change in adjustment costs and reacts in advance to the change by adjusting its optimal hiring/firing and human capital investment policy. The final section concludes the paper. The benchmark data specifications are given in Appendix A. Some more technical proofs are collected in Appendix B. Appendix C presents an approach for identifying from scarce data the quit rates of workers used in the model.

Changes in the age distribution and skill distribution of the workforce and its implications for labor market outcomes (such as wages and employment patterns) have been extensively studied in the empirical labor market literature. Age and skill heterogeneity has, however, been neglected in the classical labor demand models at the firm level that aim to build the micro-foundations for observed employment patterns and skill compositions at the aggregate level. The aim of our paper is to extend the theoretical framework and introduce age structure into a classical model of dynamic labor demand and to allow for human capital upgrading at the firm level. To capture the heterogeneity of workers by age and human capital we introduce ‘age’ as a second dynamic variable and distinguish between two types of workers: unskilled versus skilled workers. While the age structure has been introduced into the neoclassical theory of optimal investment in several recent contributions, the introduction of age into the classic dynamic labor demand model constitutes a novel approach. As empirical data show (cf. Fig. 1), the employment structure follows a clear hump-shaped age pattern at the firm level and the age pattern itself is rather dynamic indicating an aging of the labor force. Within the framework of our proposed model we show that these stylized facts may be the result of an optimal age-specific labor demand at the firm level. We establish a number of qualitative features of the optimal age-specific hiring and training policies and the mean age of hiring as it will depend on the age structure of the adjustment costs. We motivate a change in the adjustment costs of labor by changes in the demographic structure of the labor supply. For the case of linear revenue and production functions, the optimal policy is not influenced by changes in the adjustment cost functions prior to the point in time when the changes have been introduced. We term this fact the non-anticipation property (similar to a finding in the capital investment literature, cf. Feichtinger et al., 2005b). Our results are not only valid for the stationary case but hold for the transient behavior as well. We also show that optimal investment in human capital remains unaffected by changes in the adjustment costs as long as we postulate that human capital investment does not require fixed costs. Under further assumptions (e.g., the surplus between age-specific productivity and wages decreases over age) we can prove that firms always hire more younger than older workers, a phenomenon clearly supported by empirical data and the theoretical literature. Once we allow for nonlinear revenue and production functions the non-anticipation property breaks down. Firms then adjust their optimal labor demand well in advance of the time when adjustment costs are going to change. Many of the results obtained are quite intuitive: e.g., an increase in adjustment costs at every age leads to a temporary increase in hiring, lowering the mean age of hiring and increasing the human capital investment already several years before the change takes place. Once the change in adjustment costs of labor has taken place, firms will react as predicted by our analytical results in the case of the linear production and revenue function. While our results are promising, further analysis requires various extensions. Our production function only includes labor as input, an obvious extension of our framework is to allow for physical capital in addition to human capital. So far we assume that low-skilled workers (and high-skilled workers, resp.) of different ages are perfectly substitutable. An extension of the model could also allow for different elasticities of substitution between workers of different ages within and between skill groups. The most interesting ultimate aim may be a double vintage structure (of capital and labor). Within such a framework one could allow for the fact that workers of different ages are often associated with capital of different vintage. A further extension of the model could assume a more general adjustment cost function, allowing for asymmetry and fixed costs. Obviously, empirical estimations on adjustment costs that are age specific are missing and should be a further topic of research. Another promising extension of our framework could be the introduction of job duration as a further dimension of heterogeneity of labor, in addition to age. Our model constitutes only a partial equilibrium analysis and an extension to a general equilibrium model would constitute an important next step. Obviously, such an approach would require to merge the firm-level labor demand model with the macro-level economic framework that includes endogenous wage setting. Notwithstanding these extensions, our framework should be regarded as a first important attempt to introduce age structure into models of dynamic labor demand. It is to be hoped that the vintage of labor demand will gain a similar role in economic theory as the promising and growing literature of vintage capital investment.