Wages in and voluntary quits from an establishment internal labour market

This paper analyses wage rates in and quit rates from two production departments in an establishment based structured internal labour market in which labour allocation between grades and the wage rate of these grades are managerially determined. First, it is assumed that management makes effective use of the ‘private’ information about individual employees collected through time, proxied by tenure, to allocate them to the most appropriate tasks. However, in an OLS regression the elasticity of the wage rate with respect to tenure, although statistically significant, is not economically important. Further, it is assumed that this labour allocation process together with the wage structure will facilitate labour retention. However, in a probit model analysing the quit probability, the probability of quitting increases with the wage rate. Both results are compatible with an internal labour market labour allocation process and wage structure that is not competitive with wage rates prevailing in the external labour market.     

C.E.S. production functions in the light of the Cambridge critique

The Cambridge debate of the 1960s showed conclusively that the aggregation of capital, so as to obtain a surrogate production function according to Samuelson, is not possible in general, with critical implications also for other variants of neoclassical theory. The framework for the demonstration is that of linear activity analysis.There is an individual wage curve in function of the rate of profit for each technique. If these individual wage curves were straight lines, their envelope would define a wage curve resulting from all techniques, from which a surrogate production function could be derived, but all wage curves are straight only, if there is only one industry. And if wage curves are not straight, phenomena such as reswitching show that essential neoclassical hypotheses need not hold. A recent empirical investigation by Han and Schefold has found one empirical example for reswitching and several for reverse capital deepening.A rigorous derivation of surrogate production functions thus is ruled out also on empirical grounds, but the paradoxes seem not to be as frequent as the critics once thought, so that the question arises whether approximate surrogate production functions could be derived, with individual wage curves which would be sufficiently linear to construct approximate surrogate production functions, indicating a relationship between the intensity of capital and output per head which would be sufficiently precise to work with.The paper is part of a wider investigation, in which conditions for the existence of quasi-linear wage curves and the possibility of the construction of approximate surrogate production functions are given. The emphasis here is on the special hypotheses needed to obtain C.E.S. production functions.     

Knightian uncertainty and poverty trap in a model of economic growth

This paper explores how Knightian uncertainty affects dynamic properties in an economic growth model. The decision-making theory employed in the analysis is the theory of expected utility under a non-additive probability measure, i.e., the Choquet expected utility model of preference. We apply this decision-making theory to an overlapping generations model where producers face “uncertainty” in their technologies. When the producer is averse to uncertainty, the firm's profit function may not be differentiable. Therefore, the firm's decision to invest and hire labor becomes rigid for a certain measurable range of real interest rates. In dynamic equilibrium, the existence of firm-level rigidity causes discontinuity in the wage function; this makes multiple equilibria the more likely outcomes under the log utility and Cobb–Douglas production functions. In this paper, we show that even if aversion to uncertainty is small, the “poverty trap” can arise for a wide range of parameter values.     

Dual interpersonal comparisons of utility and the welfare economics of income distribution

Interpersonal comparisons can be of utility levels and/or of utility differences. Comparisons of levels can be used to define equity in distributing income. Comparisons of differences can be used to construct an additive Bergson social welfare function over income distributions. When both utility levels and utility differences are compared, one can require the constructed additive Bergson social welfare function to indicate a preference for more equitable income distributions. This restricts the form of both the individual utility functions and the optimal distribution of income. The form of these restrictions depends on whether the levels and differences of the same utility functions are being compared.     

Choice and individual welfare

We propose an abstract method of systematically assigning a “rational” ranking to non-rationalizable choice data. Our main idea is that any method of ascribing welfare to an individual as a function of choice is subjective, and depends on the economist undertaking the analysis. We provide a simple example of the type of exercise we propose. Namely, we define an individual welfare functional as a mapping from stochastic choice functions into weak orders. A stochastic choice function (or choice distribution) gives the empirical frequency of choices for any possible opportunity set (framing factors may also be incorporated into the model). We require that for any two alternatives x and y, if our individual welfare functional recommends x over y given two distinct choice distributions, then it also recommends x over y for any mixture of the two choice distributions. Together with some mild technical requirements, such an individual welfare functional must weight every opportunity set and assign a utility to each alternative x which is the sum across all opportunity sets of the weighted probability of x being chosen from the set. It therefore requires us to have a “prior view” about how important or representative a choice of x at a given situation is.     

Excess supply equilibria

This paper addresses a fundamental problem in economic theory: How can there be equilibria of the economic system where some commodity is in excess supply, yet that commodity's relative price shows no tendency to fall? Of course, the principal example of such a phenomenon is an economy experiencing a prolonged period of involuntary unemployment of the labor force during which there is no significant change in the real wage.In the following pages, I shall describe a two-commodity, general equilibrium model that has a continuum of unemployment equilibria, one for any given unemployment rate. The important feature of this model is that workers establish their wage rates in an attempt to maximize expected utility. The information upon which these wage setting decisions are based is provided by actual labor market transactions.Despite the voluntary nature of the wage setting decision, I shall argue that each equilibrium of this economy exhibits involuntary unemployment in the Keynesian sense. For there will always be another equilibrium with a lower real wage, a higher level of employment, and at which (at least when workers are risk neutral) each worker achieves a higher level of expected utility.     

ECONOMIC MODELLING OF SUICIDE UNDER INCOME UNCERTAINTY: FOR BETTER UNDERSTANDING OF MIDDLE‐AGED SUICIDE*

This paper formalises an individual's decision about suicide within a framework of lifetime utility maximisation models. This is in line with the literature on economic modelling of suicide. The novelty of the paper is to take into account income uncertainty. Income uncertainty reduces a risk‐averse individual's expected utility, making them more likely to commit suicide. On the other hand, income uncertainty creates a value to postponing suicide even when their income gets sufficiently low. This is because income uncertainty means that if things go well, they will get higher income in the future. Thus, income uncertainty has two opposite effects on suicidal behaviour. The main objective of this paper is to construct an economic model of suicide for investigating net impacts of income uncertainty on suicidal behaviour. For this purpose, it is assumed that the wage evolves according to a stochastic process. Then, the threshold wage, below which an individual commits suicide, is derived as a function of the parameters of the stochastic process assumed for the wage evolution. Impacts of changes in these parameters on the threshold wage are calculated. With the result, the paper shows how income uncertainty affects suicidal behaviour.     

Towards a More Complete Efficiency Wage Theory

The efficiency wage is an important topic in the theory of employment. In a traditional efficiency wage model, only the representative firm is optimizing against an assumed S‐shaped effort supply function. This S‐shaped supply curve is critical for the model and the absence of a derivation of the curve in the literature means that it is an incomplete theory. In the present paper, we extend the model by specifying a worker's representative utility function so that the corresponding argmax function will be the S‐shaped effort supply curve. This will make the worker's decision process endogenous and will produce a more complete model. The importance of this extension is clear. The characterization of the utility function will make explicit the necessary conditions and crucial assumptions of the traditional model. More importantly, the extension will allow researchers to introduce employment compensation factors into the worker's utility function for analysis. This has important bearings on future development in employment theory. For example, a worker's satisfaction from shirking (net of dismissal risks), or his or her willingness to search for jobs (net of search cost), can now be included in his or her utility function to form an optimal work or search strategy. Incorporating the worker's optimization behaviour into the model will also enable researchers to study policy directed not just towards firms but also towards the worker's decision process. Furthermore, this approach provides a framework for researchers to generate comparative statics. These comparative statics can lead to interesting topics for econometric models or to further research within this field.     

Expected work experience and the gender wage gap: A new human capital measure

Work experience is a key variable in earnings function estimates and wage gap decompositions. Because data on actual work experience are rare, studies commonly use proxies, such as potential experience. But potential experience is identical for all individuals of the same age and level of education, so it ignores labor market intermittency because of childbirth and child rearing—a critical omission when analyzing gender differences in earnings. This paper constructs a better proxy: expected work experience, which is the sum of the annual probabilities that an individual worked in the past. This measure can be generated using commonly available data on labor force participation rates by age and gender to gauge the probability of past work. Applying the measure to labor force survey data from the Philippines shows that conventional proxies underestimate the contribution of gender differences in work experience in explaining the gender wage gap.     

Family labour force participation: Multinomial logit estimates

Studies of labour force participation choices are mostly aimed at explaining determinants of participation for individuals. The objective of this study is the empirical estimation of the parameters of family participation decisions.

Family participation decisions can be analysed as a choice problem of a family between a finite number of distinct alternatives. The appropriate estimation procedure for a model involving choice among multiple discrete alternatives requires a statistical technique different from ordinary least squares. In this study I use the multinomial logit model. A logit model allows me to explain the probability that a particular participation alternative will be chosen by a family as a function of a set of independent variables.

It is found that economic variables such as wage rates and wealth, play a significant role in affecting the probabilities of choosing a particular labour force participation alternative. This study shows that an increase in the market wage for a family member not only increases the probability of labour force participation for that family member, but at the same time also reduces the probability of participation for his or her partner. Hence there is both a pure and a cross-substitution effect in participation. There is also an income effect. As wealth increases families will, in some sense, buy more leisure. Furthermore, they will allocate the extra leisure in a certain order: it is found in this study that the wife's probability of participation reduces sooner and faster than the husband's probability, as wealth increases.     

INFORMATION SHARING IN UNION–FIRM RELATIONSHIPS*

Large firms often negotiate wage rates with labor unions. When they do, an ex ante agreement to share information should make it more likely that they will reach an agreement and capture the gains from trade. However, if the firm refuses to share information, the union may shade down its wage demand to increase the probability of acceptance. This reduction in the wage can increase the joint surplus of the agents and increase social welfare. As a result, there are some circumstances in which bargaining with incomplete information can be better for the agents and society than bargaining with complete information.     

AN ANALYSIS OF THE DISTRIBUTION OF WAGES IN COPENHAGEN IN THE SECOND QUARTER OF 1951*

This article presents the results of a study of distributions of wage rates in approximately 250 trades, comprising 225,000 workers, in Copenhagen in the second quarter of 1951. It examines particularly the effects of heterogeneity within trades and aggregation upon the resulting distributions, both for individual trades and for all trades combined. Separate distributions are studied for men and women, for skilled and unskilled, and for three types of institutional wage payment systems.     

Unemployment Risk, Labour Force Participation and Savings

This paper analyses labour force participation and precautionary savings in the presence of risks of being fired or failing to secure a job offer when out of the labour market. We use a finite horizon framework with two employment states and a stage utility function which is CARA in consumption but non-separable in leisure. The results are that there is precautionary labour force participation: employment risk lowers the reservation wage; generally it also reduces consumption. However due to the non-separability assumption, precautionary savings, as usually defined, may not be positive. We characterize the reservation wage and contrast the results with those in which the stage utility is additive in leisure and consumption. We extend the analysis to study the effects of cyclical variation in employment risk, of stochastic future wage rates, and of adding a third employment state of search.     

Black–white wage differentials: duration and probability unemployment effects in a multiple of sample selection bias model

The extent to which probability and duration of unemployment affect the black–white wage differentials is examined in this paper. The paper simultaneously incorporates in the wage equation the multiple sample selection bias that occurs as a result of individuals’ propensity to be in the labor force, and the firm’s hiring decisions. The results reveal a substantial contribution of the duration of unemployment variable to the black–white wage differential, but a small portion of the differential is explained by the probability of unemployment. The results also indicate a sizeable difference between the contribution of the duration of unemployment variable to the male’s wage differentials (26%) and to the female’s (35%). The study finds that an individual’s labor force decision as well as a firm’s hiring decision are important in the wage determination process and that failure to account for the sample selectivity bias due to these two decisions will result in either underestimating or overestimating the wage differentials between black and white workers. At the macro level, the results seem to suggest that promotion of racial wage equality should be associated with policies that will minimize blacks’ incidence of unemployment and duration of unemployment spells.     

Definition of full-time and part-time employment,and distributional assumptions: the implications for the estimated full-time and part-time wage equations

This paper demonstrates that rejecting the standard definition of full-time and part-time workers, the estimated number of hours that an individual is likely to work as a full-time worker is a function of the type of distribution one assumes about the error term in the wage equation. Adopting a switching regression model with unknown sample selection, we have found that the normality assumption generates higher hours for full-timers in comparison with the non-normal distributions. We also noted that regardless of the distribution assumed, the hours differ from one industry to another. The implication is that the standard definition of full-time and part-time worker may not be appropriate for all firms irrespective of the distribution assumed. The paper also shows the sensitivity of parameter estimates to the distributional assumptions about the error term in the wage equation. The results indicate that the normal distribution wage equation estimates are relatively larger than the Weibull and exponential distributions. This finding is particularly important because such differences in estimated coefficients may have a direct wage influence on the wage gap between full-time and part-time workers across distributions.     

Workfare in an efficiency wage model

The impacts of introducing work requirements for welfare recipients are studied in an efficiency wage model. If the workfare package is not mandatory, it will reduce employment, profits, and utility levels of employed and unemployed workers. In contrast, mandatory effort requirements will generally raise both employment and profits and reduce the tax rate. The impact on the net wage is ambiguous. Changes of utility levels of employed and unemployed workers have the same sign as the variation in the net wage. The possibility of a Pareto improvement may explain the widespread support for welfare to work experiments.      

AN APPROXIMATION FOR THE OPTIMAL LINEAR INCOME TAX RATE

This paper derives a convenient method of calculating an approximation to the optimal tax rate in a linear income tax structure. Individuals are assumed to have Cobb-Douglas preferences and the wage rate distribution is lognormal. First, the optimal tax rate is shown, for a general form of social welfare function, to be the smallest root of a quadratic equation involving a welfare-weighted average wage rate. Second, an approximation to this average is derived for an isoelastic social welfare function. This average depends on the degree of inequality aversion of the welfare function and the coefficient on consumption in individuals' utility functions. Calculations show that the method performs well in comparison with standard simulation methods of computing the optimal tax rate.     

Is it efficient to analyse efficiency rankings?

When production functions are estimated as frontier functions, the deviations from the frontier can be interpreted as individual inefficiency estimates. Unfortunately, it has recently been shown that efficiency differences across individuals are very often statistically insignificant. In this paper, we will analyse the consequences of the consideration of confidence statements for the reliability of efficiency rankings. The stochastic frontier and confidence intervals derived by Horrace and Schmidt are compared to the COLS approach and bootstrap confidence intervals. The membership function is proposed as a simple Monte-Carlo approximation for the probability for an individual to be the most efficient in the sample. First version received: May 1998/final version accepted: July 1999     

Knightian uncertainty and moral hazard

This paper presents a principal-agent model in which the agent has imprecise beliefs. We model this situation formally by assuming the agent?s preferences are incomplete as in Bewley (1986) [2]. In this setting, incentives must be robust to Knightian uncertainty. We study the implications of robustness for the form of the resulting optimal contracts. We give conditions under which there is a unique optimal contract, and show that it must have a simple flat payment plus bonus structure. That is, output levels are divided into two sets, and the optimal contract pays the same wage for all output levels in each set. We derive this result for the case in which the agent?s utility function is linear and then show it also holds if this utility function has some limited curvature.     

A utility-based analysis of the wage subsidy program

Because the poverty line is usually defined in terms of income, two families may be classified as having poverty-level incomes even though their hours of work and, therefore, their utilities may be very different. This paper compares a government income support program that defines the poverty line in terms of utility with several other support programs that define the poverty line in terms of income. Through the use of the wage solution of the indirect utility function, we find the amount of wage subsidy required to raise a subpoverty-line family to the poverty line as defined by the utility function. This subsidy is compared with wage subsidies based on directly observable quantities such as income.