Labor Markets That Emphasized Heterogeneity in Wage Policies - Essay Example

There is a long history in labor economics and industrial relations of studying wages in specific labor markets. This interest s back to early micro studies of labor markets that emphasized heterogeneity in wage policies across employers. Some more recent work has also studied the issue of within- versus between-employer wage differentials in the United States. The role played by employers in determining wage structures, however, has received less attention in recent years. Aggregate Assume there are N workers indexed by i = 1, ..., N, and M firms indexed by j = 1, ..., M, in a given industry. The standard utility maximization and profit maximization problems yield individual labor supply functions hi (w) and labor demand functions Ej (w) for labor, which are functions of the wage w. To get the industry labor supply and labor demand functions these must be added. Industry Labor Supply = H (w) = h1 (w) + h2 (w) + ... + hN (w) Industry Labor Demand = E (w) = E1 (w) + E2 (w) + ... + EM (w) Graphically this amounts to adding up the individual labor supply and labor demand curves horizontally. In the case with identical workers and identical firms H (w) = N hi (w) and E (w) = M Ej (w). Minimum wages are intended to benefit low-paid workers. In practice a job is described by a set of characteristics, so in addition to the wage rate features such as the hours of work and the effort level required are relevant. If the impact of the minimum wage is to create an excess supply of workers, employers may benefit by degrading the non-wage aspects of the employment package. More effort, longer hours, fewer perks and a less agreeable working environment can all be imposed without a firm losing its workers. As indicated above, in response to the minimum wage employers raise hours of work to such an extent that the benefit of a higher wage is more than offset. Consequently, both the workers remaining in employment and those who become unemployed are made worse-off by the minimum wage. It also results in a loss of profit for the firm and introduces aggregate inefficiency. In this situation, there is nothing to commend a minimum wage policy. Under a fairly weak condition, a monopsonist responds to a minimum wage by reducing hours, which is a double bonus for those with jobs. Unlike the standard analysis of monopsony, which shows that a minimum wage, if set below the marginal revenue product of labor, is efficiency enhancing, it turns out that when hours are a choice variable there may be a loss of efficiency. A minimum wage on its own can no longer replicate the perfectly competitive outcome, but when combined with a limit on hours of work, a first-best outcome can be achieved. Prior discussions of minimum wages and the contrast between competition and monopsony have focused on whether the minimum wage will raise or lower employment - with it taken as granted that those remaining in employment always benefit. When hours are variable, a job is described by its two characteristics: the wage rate and hours of employment. It is not surprising that a competitive firm forced to pay a minimum wage has to adjust the non-wage element of the employment package in a manner deleterious to the interests of the workers. Proposition 1 gives a result much stronger than this: the increase in hours more than offsets the benefit of the minimum wage. In the competitive environment the imposition of a minimum wage is always harmful to the workers. Moreover, this is even true for those who remain in employment and receive the increased wage. This is a simple consequence of the firm being able to adjust an inefficient variable (hours of work) to clear the market at the new wage. The standard monopsony result is that the introduction of a minimum wage that is below the marginal revenue product of labour (MRPL) must be beneficial to those employed and also have the effect of increasing employment. The latter effect arises because the marginal labour cost curve facing the firm is replaced by the fixed minimum wage at points below the minimum wage. This effectively removes the firm's monopsony power so it responds by increasing employment. Minimum Wage Suppose the government sets a minimum wage w. In the competitive model, only two things can happen. (1) If w w* then the minimum wage has no effect (it does not bind) and employment stays at E* or (2) If w > w*, in which case the minimum wage will bind and employment will be at a lower level, namely E = E ( w ), as firms will cut down on labor inputs. This second case usually results in a loss of producer surplus, a gain in worker surplus (if w is not set "too far" above w*), and a loss in total surplus known as deadweight loss (DWL). Although the minimum wage will result in the loss of employment, if properly set it may be socially optimal if a dollar redistributed to workers is worth more than a dollar redistributed to firms. Example 1: Setting w = $4, 000 will have no effect. Setting w = $6, 000 will cause employment to fall to E (6,000) = 4,000. Workers' surplus will rise to WS = 16,000,000 while producers surplus will fall to 8,000,000 and a small deadweight loss triangle will be created DWL = 1,000, 000. Surveys suggest that considerably more workers would like to reduce their working hours at the current wage than wish to increase them. It is shown that this can be explained by both fixed costs of employment and by monopsony. The effect of a minimum wage is investigated in both these frameworks. With a competitive labor market and fixed costs, firms respond to a minimum wage by raising hours of work to such an extent that even the employed are worse off. Under monopsony, the minimum wage instead leads to shorter hours of work so together with the increased wage there is a double benefit to workers. Even so, aggregate welfare may be reduced by the minimum wage and, to achieve a first-best outcome, it must be combined with a restriction on maximum hours of work. Although the minimum wage benefits the workers, it does reduce the profits of the firm and leads to an inefficient equilibrium. The effect of even a low (but finite) minimum wage on net welfare is therefore ambiguous. One clear-cut case is when the reservation utility is the same for all workers - then any finite minimum wage must reduce aggregate welfare. In the general case, when monopsony is present, a policy package of a minimum wage and a restriction upon hours is necessary to achieve full efficiency. Also, if female labor supply tends to be more elastic than that of males, in a standard monopsony model, could it imply higher pay for females The Monopsony Model If it may be assumed that there is a single firm that has no control over the price of its product, but faces no competition in the labor market, allowing it to set wages w, making it a monopsonist (single buyer) in the labor market.1Assume further that the monopsonist is non-discriminating so that it only sets a single w for all workers and it has production function f (E). Note, that if the monopsonist has control over M, identical plants (with decreasing returns to scale in E) then it will divide total employment equally amongst all plants. The total production will then be given by f (E) = M fj (E/M), and the value of marginal product curve VMPE will be identical to the inverse industry supply curve in the perfectly competitive case of w D (E) (although technically no "labor demand" curve exists in the monopsony world). The monopsonist, being the only employer, does not take wages as given but understands that by hiring more labor it will affect the wage it has to pay. This relationship is given by the inverse supply curve w S (E). The change in the cost of employment (aka "wage bill") CE (E) = E w S (E) when E changes is given by the marginal cost of employment MCE = [dCE. (E)] / E = d / dE [E w S (E)] = w S (E) + E [dw S (E)] /dE The second term E [dw S (E)] /dE is generally positive as E is positive and is [dw S (E)] /dE is positive as presumably the labor supply curve is upward sloping. Therefore, the MCE curve will lie above the inverse labor supply curve given w S (E). Note that with competitive firms, the second term does not exist and MCE is a flat line at w. Example 2: As w S (E) = E then CE (E) = E2 and so MCE = 2E. Therefore, the slope of the MCE line is double the slope of the labor supply line. (Note this curve looks just the shifted labor supply curve above in the payroll tax case - this is just a numerical coincidence made for your convenience) Minimum Wage (Under Monopsony Model) Where the minimum wage is binding, i.e. where H (w) < H (w), then MCE = w and is constant. At H (w), MCE jumps vertically back up to the original MCE curve. Graphically we can show wM w w* then EM = H (w) while if w > w* then employment will be set where VMPE = w. Unlike in the perfectly competitive model, in the monopsony model, the minimum wage can actually increase employment, especially if w is set between wM and w*, and will increase worker surplus and decrease producer surplus, while the amount of deadweight loss will depend on how far w is from w*. Example 3: Taking the case where w = 4, 000 we get not only a higher wage for workers but also a higher level of employment of 4,000 (shown above). If w = 6,000 you would in fact get the same level of employment, 4,000, but with more of total surplus going to workers over producers. Total surplus would be maximized at w = 5, 000 = w*. The lower employment and wage caused by monopsony power has two distinct effects: First, it redistributes welfare away from workers and to their employer(s). Secondly, it reduces the aggregate enjoyed by both groups taken together, as the employers' net gain is smaller than the loss inflicted on workers. Equilibrium Equilibrium is achieved at the equilibrium wage w* where supply equals demand, i.e. H (w*) = E (w*) (i.e. Equilibrium Condition) This equation can be solved to yield w* and then equilibrium employment E* = E (w*). Note that this problem could also be solved using the inverse functions by solving for E* first as w S (E*) = w D (E*) and then finding w* = w D (E*). Example 4: Supply equals demand implies: H (w*) = E (w*) w* = 10,000 w* w* = 5,000 and E* = E (5, 000) = 5, 000. Individual amounts are h* = h (5, 000) = 1/2 and E*firm = E*firm (5, 000) = 250. During the 1990s, some empirical phenomena in the labour market were documented that appeared to contradict the standard competitive model. An often-cited example is Card and Krueger's (1994) case study of the impact of a minimum wage increase, where, contrary to competitive theory, they found that an increase in the minimum wage increased employment in fast food outlets in New Jersey, United States. Another interesting case is the research of Blanchflower and Oswald (1990), who, using American and British data, found evidence for an inverse relationship between the level of pay of individuals and the prevailing local unemployment rate, which they labeled the 'wage curve'. Subsequently, they and many others have reported additional evidence for this relationship.2 Determining the equilibrium effects of minimum wage changes on labor market outcomes is a challenging modeling and estimation problem; arriving at policy recommendations is a task even more daunting. Faced with the inherent difficulties of modeling equilibrium labor market events given the limited amount of data to which researchers have access, much recent research has been performed outside of an explicit behavioral framework, with researchers pursuing the more limited objective of carefully describing the observed effects of recent minimum wage changes using quasi-experimental methods as discussed by Card and Krueger (1995). In their 1997 book Myth and Measurement: The New Economics of the Minimum Wage, they argued the negative employment effects of minimum-wage laws to be minimal if not non-existent (at least for the United States). For example, they look at the 1992 increase in New Jersey's minimum wage, the 1988 rise in California's minimum wage, and the 1990-91 increases in the federal minimum wage. They assume that the demand for low-wage workers is inelastic. The importance of Card and Krueger's work does not necessarily lie in its empirical findings (which have been challenged by several studies more rigorous than Deere, Murphy and Weltch) but in its emphasis on the importance in recognizing that theoretical economics is not incompatible with positive employment effects from the minimum wage. If the Cobweb Model is a theoretical model of an adjustment process that on a price/quantity or supply/demand graph spirals toward equilibrium. Also critical to cobweb model is that the demand curve be always lower or flatter to the supply curve. The cobweb 'explodes' when demand shifts and an equilibrium wage is never reached, which means that there are greater chances of compromise on the minimum wage policy or a great lag of labour supply. A fully-elaborated, competitive equilibrium model of the effects of minimum wages presumably would require a system of labor demand functions for various observationally-differentiated classes of labor and capital in addition to a well-specified system of labor supply functions. Using individual level data on individuals at a point in time or from a short panel, the requisite information on the demand-side of the market would be missing, so that to estimate equilibrium model in this case requires one to make a number of stringent assumptions concerning the behavior of firms. If the price elasticity of demand is less than the price elasticity of supply, the fluctuations would increase in magnitude per cycle, so a plot of the equilibria in for each cycle would look like an outward spiral (divergent). This is referred to as an unstable cobweb model. Alternatively, if the price elasticity of demand is more than the mean price elasticity of supply, fluctuations decrease in magnitude per cycle, so a plot of the equilibria in for each cycle would look like an inward spiral (convergent). This is referred to as a stable cobweb model. Fluctuations may also remain of constant magnitude, so a plot of the equilibria would produce a simple quadrangle. Such a result would be given from a unit elastic price elasticity of both supply and demand. While the quasi-experimental results have raised a number of interesting challenges to orthodox theory, few cogent models have been advanced that are consistent with the results that have been found. Some of the explanations for these empirical findings (e.g., lack of significant employment losses, impacts on the wage distribution above the minimum) do not seem to be testable given our current data resources. In fact, it appears difficult to operationalize many of the explanations proposed even for the more modest purpose of empirical implementation. The costs associated with repeated and systematic mistakes in forecasting prices makes both models of expectation formation implausible as a model of rational behavior because the firm has an incentive to gather information on the market structure. In fact, a simple diagram depicting supply versus market clearing price for past periods suffices to obtain the required information. The cyclical fluctuations are ruled out in the Cobweb model on the basis of these considerations: Under rational expectations perceived and actual distribution of prices have to coincide, which is only possible in a steady state of the Cobweb model. One has to point out that strong assumptions underlie this reasoning. For instance, what convinces an agent to believe that the distribution of past prices have been used to determine the supply in every past period The decision-maker in the firm has to have access to a complete record of historically perceived distribution of prices in order to decide that matter. Observed data however can be interpreted in many different ways and thus may support or "rationalize" many different supply decisions. This note illustrated that permanent price fluctuations of the "cobweb type" can be reconciled with rational behavior when interpreting the model in the theory of rational beliefs, Kurz (1994)3. Flinn and Heckman (1982), Eckstein and Wolpin (1989)4 and the subsequent literature have adjusted theoretical models to account for empirical regularities in the data used to estimate their models. In fact, current theoretical developments are driven to a substantial extent by the need to explain regularities found in the empirical literature. In particular, many equilibrium search models with heterogeneity have been developed in response to the empirical studies that were unable to explain important findings with homogeneous models. The empirical work based on the structure of the simple search model is growing. The models provide the basis for the analysis of active labor market dynamics that aim at reducing unemployment and increasing participation. For example, Fougere, Pradel and Roger (1998)5 estimate the classical job search model with endogenous search efforts, focusing on the impact of a public employment service. It is widely believed that the labor supply elasticity at the extensive margins is large. The simple search model provides a useful analytical framework for a quantitative analysis of this elasticity. Such empirical survey tells the researchers how far this literature has reached so far! Works Cited 1. Blanchflower, David G. and Oswald, Andrew J., 1994. The wage curve, Cambridge MA: MIT Press. 2. Flinn, C.J. and J.J. Heckman (1982), New methods for analyzing structural models of labor force dynamics, Journal of Econometrics, 18, 115{168}. 3. Fougere, D., J. Pradel and M. Roger (1998), Public employment offices and the transition rate from unemployment to employment, Working paper, CREST-INSEE, Paris. 4. Janssens, S. and Konings, J. (1998). 'One more wage curve: the case of Belgium', Economics Letters, vol. 60, pp. 223-227. 5. Kurz, M. (1994) On the Structure and Diversity of Rational Beliefs. Economic Theory 4, 877-900. 6. Pannenberg, M. and Schwartze, J. (1998). 'Labor market slack and the wage curve', Economics Letters, vol. 58, pp. 351-354. 7. Papps, K.L. (2001). 'Investigating a wage curve for New Zealand', New Zealand Economic Papers, vol. 35, pp. 218-239. 8. Pekkarinen, T. (2001). 'The wage curve: Evidence from the Finnish metal industry panel data', Finnish Economic Papers, vol. 14, pp. 51-60. Read More