Labor market equilibrium

For a more complete picture of how safety policy affects labor market outcomes, including worker well-being, a researcher needs to examine the structural equations that underlie the popular regression equation summarized by (1.1). The canonical structural econometric model of the labor market where a sorting of workers into jobs yields a set of wage and safety levels for each job and worker, known as hedonic labor market equilibrium, has the three stochastic equations... 

Because employers differ in their abilities to reduce injury risk and workers differ in their attitudes regarding such risk, no single probability of a work-related injury is optimal for all parties. Here we describe the process generating labor market equilibrium when workers have differing views about risk and firms have differing capacities to produce safe work environments. 

LABOR MARKET EQUILIBRIUM WITH WORK-RELATED HEALTH HAZARDS... 

A MATHEMATICAL DESCRIPTION OF HEDONIC LABOR MARKET EQUILIBRIUM... 

We have discussed the crucial details involved in research that numerically simulates hedonic labor market equilibrium and disturbances to that equilibrium. When workplace safety levels are continuous hedonic labor market equilibrium can be described by the simultaneous solution to three first-order differential equations with associated boundary... 

From Rosen (1974), we know labor market equilibrium occurs within a given risk interval when... 

We described the output market with a unitary elastic demand function. We initially set the price of output at 1. Later, when we investigated the labor market effects of public policies geared toward improving industrial safety we allowed the price of ouqiut to adjust. Hence, changes in labor costs have direct effects and indirect effects on hedonic labor market equilibrium through their impact on product price. 

A numerical solution of hedonic labor market equilibrium requires specific functional forms to represent workers preferences, firms outputs, and the distribution functions of risk aversion and efficiency of safety measures. Appendix 4A fully describes the numerical model. Table 4-1 provides a summary listing of the model s structural equations and initial parameter values. In choosing starting values for the parameters underlying the model we reproduced labor market equilibrium just prior to the enactment of OSHA. 

Hedonic labor market equilibrium can have a massing of workers and firms only at the zero incremental risk level. As seen in Figure 4.2, 41 percent of the workforce chooses employment in firms that are no more dangerous than everyday life. In our baseline hedonic labor market equilibrium 55 percent of workers choose what could be labeled low-risk jobs (0 < ti < 0.001), 19 percent choose what we will call moderate-risk jobs (0 < n 0.002), and 26 percent choose high-risk jobs (71 > 0.002). 

To investigate the impact of workers compensation insurance we used a method identical to that described for investigating the impact of OSHA enforcement activities. Specifically, we first numerically simulated hedonic labor market equilibrium at four rates of income replacement (0.5, 0.8, 1.0, and 1.5) assuming no experience rating of WC premiums and no safety and health standards and then calculated changes caused by increasing WC benefits from the usual 0.50 rate of income replacement. To examine the interaction between OSHA and WC we varied the average fine for safety and health violations from 0... 

Finally, our numerical simulation used a fixed number of workers and firms. Because labor is measured in terms of dollars of net return to the firm payroll expenditures also equal total labor input. To reproduce labor market equilibrium prior to OSHA we varied the number of workers in the model until total payroll equaled the actual payroll in the manufacturing sector of the United States in 1972. The relevant number of establishments in our model includes both producing firms and potential entrants. To create the pre-OSHA situation we increased the number of firms observed in the U.S. manufacturing sector during 1972 to reflect an assumption of a 10 percent pool of potential entrants. Thus, the number of firms producing in our initial simulation, which is labor market equilibrium prior to the introduction of OSHA and any revisions in WC, equals the number of manufacturing firms actually in existence in 1972. 

As in the models developed in Chapters 3 and 4 the hedonic labor market equilibrium satisfies the equation... 

L(-) is the density function of workers with respect to their risk aversion parameter (a), where a takes on values between some maximum and minimum with equal probabilities N -) is the demand for labor by an individual firm, which solves the firms three necessary conditions for maximum profit and F(p) is the density function of firms with respect to their efficiency of safety production, where 0left-hand side in the hedonic labor market equilibrium equation, (5.5), is the number of workers supplying labor to employers at each risk (ti) level, and appearing on the right-hand side of (5.5) is the quantity of labor demanded. ... 

The differentials in the equation for hedonic labor market equilibrium, daldn and d ildn, describe how firms and workers match at the various degrees of exposure to work-related health hazards. There are three first-order conditions for the firm s maximum profit. We totally differentiated the three necessary conditions for maximum profit in (5.2)-(5.4) with respect to p and n to solve for the equilibrium pairings of firms and workplace safety levels, d x dn. Next, we re-arranged equation (5.5), the necessary condition for labor market equilibrium, to solve for da/dn, how workers sort against levels of injury risk. The differential equations of interest have the general expressions... 

Worker heterogeneity appears via interpersonal (stochastic) differences in the risk aversion parameter (a), which also determines whether a worker files an exaggerated WC claim. The condition for labor market equilibrium in (5.5) also has as an outcome that each firm, which is imiquely represented by a value of safety efficiency (p), hires a homogenous work force (as captured by a common value for a). The result of the matching mechanism in our simulation model is that at some levels of safety (p) all workers with nonimpairing injuries apply for WC benefits (fli = l) and all PPD workers apply for PTD benefits ( 2=1)-... 

In solving numerically for hedonic labor market equilibrium in (5.5) we respecified the differential equations (5.6)-(5.8) into three difference equations that locate a, p, and w at 13 pre-chosen probabilities of injury. We then jointly solved the nonlinear difference equations representing (5.5)-(5.8) via Newton s method, which is a gradient or hill climbing procedure. Chapter 3 has more details of the numerical simulation method we used. 

A Mathematical Description of Hedonic Labor Market Equilibrium... 

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