Determining the earnings function to best explain wage gaps is at the heart of labor economics. Earnings functions are the most widely used empirical equations in the economics of labor and of education. The Mincer model comes as the most used and talked about earnings function.
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Jacob Mincer (1958) was the first to develop an earnings function that explained earnings with potential experience as the standard regressor in his paper Schooling, Experience and Earnings. Jacob Mincer influenced altogether how labor economists specify earnings relationships. The Mincer model not only best explains the Human Capital Theory in one equation but also applies the Hedonic Wage Function by revealing productive attributes like schooling and work experience (Heckman, et al, 2003).
Jacob Mincer (1974) later popularized the justification for interpreting the coefficient on schooling as a rate of return originating from a model by Becker and Chiswick (1966). As a basis for economic studies for returns to education in developing countries, the returns to schooling quality derived from the Mincer earnings specification become widely used for measuring the impact of work experience on male-female wage gaps and other wage gaps.
Since the 1960’s, the Mincer model remains the most estimated in earnings determination in different time periods and countries as it uses a formal model of investment in human capital as basis. The Mincer model provides a parsimonious specification that fits the data remarkably well in most contexts (Lemieux, 2006). Recent studies in growth economics also use the Mincer model to analyze the relationship between growth and average schooling levels across countries.
The Mincer model identifies effectively both skill prices and rates of return to investment only in certainty and stationarity of the economic environment which is not always the case in reality. Special conditions in estimating the wage function with an assumption of stationarity were approximately valid in the 1960 Census data used by Mincer (1974) (Heckman, et al, 2003).
Mincer (1958, 1974) provided two theoretical motivations for his specification, one based on a compensating differentials principle and a second based on an accounting identity model of human capital formation. The two models are economically distinct, but both lead to very similar empirical specifications of the wage equation.
The assumptions in the first Mincer Model in 1958 are: (1) individuals have identical abilities and opportunities; (2) the conditions are perfectly certain; (3) credit markets are perfect, and (4) different positions require different amounts of training (Heckman & Lochner, 1998). The principle of compensating differences explains why individuals with different educational attainment receive different amounts of earnings over their lifetimes.
Mincer, in 1958, stated that the framework of the model included some interesting features:
The coefficient on years of schooling (T) in a Mincer regression is equal to the interest rate, r,
People with higher educational attainment receive higher earnings or wages
The difference between earnings levels of people with different years of schooling is increasing in the interest rate and age of retirement, and
The ratio of earnings for persons with education levels differing by a fixed number of years is roughly constant across schooling levels.
In his later paper in 1974, the model developed by Mincer is driven by a different set of assumptions from his earlier model. The second model by Mincer builds on an accounting identity developed by Becker in 1964 and Becker and Chiswick in 1966. Mincer’s approach focuses on the life-cycle dynamics of earnings and on the relationship between observed earnings, potential earnings, and human capital investment, both in terms of formal schooling and on-the-job investment” (Heckman & Lochner, 1998). This Mincer earnings specification has been widely used over the last five decades and continues to be applied in recent work.
The Mincer earnings specification captures many important empirical regularities, such as concavity of log earnings age and experience profiles, steeper profiles for persons with more years of education, and a U-shaped interpersonal variance of earnings over the life-cycle. Under the simplifying assumptions used by Mincer and others, the coefficient on schooling in a log earnings regression should equal the internal rate of return to schooling. However, many of these assumptions are no longer appropriate. Log earnings do not increase linearly with schooling, and experience profiles for log earnings are not parallel across schooling types in recent decades.
Heckman, Lochner & Todd (2000) revealed that the feature that made the Mincer model popular, its simplicity is actually its weakness. Non linear relationships between wages and its respective components will bias wage profiles even if the linear model can explain Mincer’s assumption of conditional mean of wages.
Data from later decades are inconsistent with inferences about trends in rates of return to high school and college obtained from the more general model, and differ substantially from inferences drawn from estimates based on a Mincer earnings regression. In the recent period of rapid technological change, widely used cross-sectional applications of the Mincer model produce considerably biased estimates of cohort returns to schooling (Heckman, et al, 2003).
Linear approximation may only be accurate in a stable environment where the growth in relative demand is matched by a corresponding growth in relative supply. Studies suggest that the post-1980 period has been unstable wherein relative supply did not increase enough to match the growth in relative demand. This has apparently led to both an increase in the returns to education (Katz & Murphy, 1992) and in the convexity of the schooling wage relationship (Mincer, 1997). Even when the static framework of Mincer is maintained, accounting for uncertainty substantially affects rate of return estimates (Lemieux, 2006).
Mincer in 1974 correctly concluded that it was not essential to control for cohort effects in an earnings regression. Coincidentally, a stable labor market environment prevailed in data used by Mincer. In a less stable environment, major shifts in the relative supply of different age-education groups can induce significant changes in the structure of wages. These changes have to be taken into account when estimating a standard Mincer equation. This can be achieved either by adding cohort effects to a standard Mincer equation, or by explicitly modelling the relative supply and demand for different groups of workers (Lemieux, 2006).
Changes in relative supply and demand for various labor categories can also explain other recent “failures” of the simplest version of the Mincer equation. Experience profiles are no longer parallel in recent data because of systematic cohort effects that are related to a slowdown in the rate of growth of educational attainment for workers born after 1950 (Lemieux, 2006).
Using the same type of data and the same empirical conventions employed by Mincer and many other scholars, Heckman, Lochner and Todd (2003) tested the assumptions that justify interpreting the coefficient on years of schooling as a rate of return. They exposit the Mincer model, showing conditions under which the coefficient in a pricing equation (the Mincer. coefficient) is also a rate of return. These conditions are not supported in the data from the recent U.S. labor market.
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Education, as years of schooling in the Mincer model is linear in the wage function. Education as a linear function poses inaccuracy. In reality individuals are heterogeneous in their preferences and earning opportunities. Average log earnings may either be a convex or a concave function of years of schooling. Credentials or sheepskin effects also have a direct impact on earnings-the return to a year of schooling will be higher (Lemieux, 2006).
Heckman & Polacheck (1976) later recognized that logarithmic transformation of wage data is more suitable to the estimation. Murphy & Welch (1990) studied further the biases inherent in the earnings-experience profile and found that quartic function in years of experience captures fittingly the main features of the empirical experience-earnings profiles.
Analysis of the linearity of schooling has different interpretations which depend on the labor market situation of the time period. Card and Krueger (1992) conclude from their analysis that log earnings are an approximately linear function of years of schooling except for the lowest two percentiles (for a cohort) of the schooling distribution. Mincer (1997) and Olivier Deschênes (2001) show that since 1980, log earnings have become an increasingly convex function of years of schooling. There is not much of a systematic departure anymore from a linear or quadratic specification around 16 years of schooling (Lemieux, 2006).
Growing convexity of the schooling-wage relationship, as opposed to local non-linearities around years of schooling, is now the leading source of non-linearity in recent data. A sudden growth in relative demand without a matching increase in relative supply of schooling increases the marginal return to schooling for more educated workers relative to less educated workers under a market with heterogeneous workers in preferences and earnings capacity (Lemieux, 2006).
Since the Mincer equation does not perfectly fit data from all time periods, labor economists find more specifications of the Mincer model. Most specifications maintain three key variables in their regression equation (schooling, experience, experience2), but sometimes include additional variables. Determination of earnings and education’s causal effect on earnings for most data sets are captured by the basic Mincer equation for as long as econometric specification testing is done to get a good approximation of earnings (Lemieux, 2006).
Dougherty & Jimenez (1991) confirms once more that the appropriate regressand of the Mincer model is the logarithm of earnings. They found that the error term is normally distributed but it does not support the implicit assumptions that there is no interaction between the effects of education and work experience. So the specification leads to upwardly biased estimates of the returns to education. To avoid using inappropriate methods of estimating work experience while covering the bias, they emphasize the need to introduce the schooling-experience interaction in the parametric structure.
Finding the appropriate econometric approach in estimating and testing the model for a given data is difficult enough especially when the economic environment becomes more unpredictable. Lemieux (2003), Bjorklund & Kjellstrom (2002) investigated the parametric assumptions of the Mincerian Model using Swedish data from 1968 to 1991 following Heckman’s and Polacheck’s transformations and find these assumptions misleading. They also found that it can be misleading to infer the schooling coefficient as returns to investments in education.
Schady (2003) confirms once again the nonlinearities in the relationship between log wages and schooling by concluding that wage function of Filipino men exhibits non linearities in schooling in the presence of Sheepskin effects. He suggested that in the Philippines, the earnings function may significantly change over time; thus, a need for further research for exploring a more flexible methodology to estimate and test wage effects with the addition of age, cohort and year.
Many inferential techniques emerged to assess the functional validity of the Mincer wage function. Non Parametric Econometrics has become of interest as concerns for robustness and consistency of testing parametric estimators grew (Dacuycuy, 2010). One of which, Zheng (2000), concluded using CPS data that no parametric specification can ever survive when tested against nonparametric alternative.
Miles and Mora (2003) has also shown using Uruguayan and Spanish Data that parametric assumptions do not support Mincerian Wage Function even after considering several generalizations that have appeared in the literature.
Dacuycuy (2005,2006,2009) shows the increasing evidence that popular variants of Mincerian model are misspecified relative to the non parametric alternative. He shows that semi parametric structures appear to be more promising alternatives than parametric counterparts.
Li, Racine & Hsiao (2007) recognizes the difficulty to estimate and test discrete type of variables which are common in labor survey. They propose a nonparametric kernel-based model specification test that can be used when the regression model contains both discrete and continuous regressors. Using the wild boot strap, simulations of the Mincer model show that the proposed test has significant power advantages over conventional frequency based kernel tests.
Using Hayfield and Racine (2008) non parametric kernel based procedures and factual and counterfactual analysis, Dacuycuy (2010) that the empirical value of the non parametric wage function bested all of the parametric models in terms of the Predicted Mean Square Error (PMSE).
Departures from the simple Mincer model are primarily due to the failure of recent increases in the relative supply of educated labor to keep up with relative demand’s growth (Heckman, et al, 2003).
In conclusion, the basic Mincer human capital earnings model remains a parsimonious and accurate model in a stable environment where educational achievement grows smoothly across cohorts as long as the standard Mincer equation’s robustness is verified to the inclusion of a quadratic term in years of schooling and cohort effects (Lemieux, 2006).
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