Earnings Functions in Applied Economic Research Report

Introduction

Earning functions are an important econometric tool utilized in applied economic research, especially where it concerns the labor market by study of which a management firm assesses rates of return and employee remuneration procedures for standard company fair treatment policies (Heckman & Learner, 2007). Historical trends talk volumes about huge disparities between wage income for different levels of employees in an organization; male and female, White and Black, etc.

Thanks to positive action taken in recent decades, many of these trends have now shifted and there is increased potential for employees cutting across gender/race, etc. to be awarded similar compensation packages as other employees. These trends have to be observed, studied, and referenced for making decisive conclusions about wage scale differences for all variables concerned.

This paper consists of a research study that tries to get into the root of this topic (disparities on wage scale). A sample of 540 individuals cutting across age, sex, and race have been selected from US Longitudinal Survey conducted by investment firm Dougherty & Company LLC (official website). This data is further subjected to a rigorous analysis for assessing the true values of earning functions when any of the variables (group) is changed according to methods of simultaneous equations using non-parametric regression variables (using 1, 2, or 3 regressors).

The equations EQ0,1,2,3…n obtained formulated under selective conditions (using PcGive) software will be subjected to further testing and analysis using standard methods mentioned in the paper. To gain a theoretical perspective, it’s worth understanding the requirements in the following literature review.

Literature Review and Methodology

According to standard literature evidence, earning functions are expressed as a single-dependent variable in non-parametric simultaneous equations as given below (Dougherty, 2007; Gleicher & Stevens, 19991; Pagan & Ullah, 1999)

E(t) = (constant)β0 + β1(Variable 1) + β2 (Variable 2) + β3 (Variable 3) +…(1)

The constants have to be determined by multiple regression analysis with multiple heteroskedasticity (Heckerman & Learner, 2007; Dougherty, 2007). Heteroskedasticity occurs when the variance of the standard regression relationship (R2) is inconstant and indicates bias in the variable relationships (Heckerman & Learner, 2007; Dougherty, 2007). The objective of this paper is to represent the bias from standard data in use.

Regression analysis is a smart tool that gives the degree and extent of correlation between some variables in analyzing simultaneous equations as shown in (i). In the case of cross-sectional modeling (which uses comparisons between any two-column variables for the given objective equations at hand), the bias is used to support evidence for the preponderance of one defining a variable at the expense of another (Heckerman & Learner, 2007; Dougherty, 2007). This research study will look into a variety of such close relationships and offer commentary on what constitutes an ideal relation.

The variables were chosen for this model-estimation: age, sex, marital status, height, weight, educational attainment, number of siblings, etc. highlight the correlation/impact these parameters have on earning values which offer support for their inclusiveness in the given non-parametric equation (Dougherty, 2008). In this paper, we have used multiple regression model analysis with heteroskedasticity to account for testing and validation of field variables as surveyed by Dougherty & Company LLC.

These variables are collected by this investment firm to act as consultancy advice for numerous companies which rely on them for advice on handling a range of issues including labor market utilization (Dougherty, 2008). The equations consist of various tests and functions which highlight the correlation between variables.

A little about the methods and practices used in this sample study. The formulation, testing, and validation results used here have been conducted on two different platforms: Microsoft Excel and PcGive which is a proper econometrics tool to evaluate complex cross-sectional data analysis. A total of 1,2 or 3 regressors (explanatory variables) has been suggested for given equation comparisons. The multiple linear regression tool uses the least-squares method to fit a line according to the range of chosen observations. The “weights” used in each independent variable correspond to the coefficients to variables (Variable 1), (Variable 2), (Variable 3), etc. used in equation (1).

The fitness of the regression model is determined by the closeness of R2 to 1. In case the line does not fit, an explanation for heteroskedasticity is given which corresponds to the influence of random noise factors on the validity of findings. Regression plots are designed to understand the precise values/estimates of given regression equations. Plots of actual and scattered values are performed to measure the closeness of fit (Heckerman & Learner, 2007, Gleicher & Stevens, 1991).

Findings and Results

As has been discussed earlier, regression analysis in this study is dependent on the impact produced by different variables such as age, sex, educational attainment, experience, etc. on the earning function E(t) for the given sample of data values. Categories in any variable are given signs of 1 or 0 to give answers to their existence in the given sample. For example, if we have to compare earnings for given Black people in a sample of Master’s degree holders, the non-existence of Black people in the Master’s degree sample gives it a value of 0. The variables used for comparison are as per the given table:

Fig 1. Distribution of data for given sample from Dougherty (Source: Dougherty, 2008).

Next step is to develop some preliminary differences between different categories of the same variables. For the purpose of evaluation, the author has aimed to achieve further racial breakdown for four set of values in earning functions: age, sex, race and educational attainment as shown in table below:

Fig.2: Educational attainment distribution for different racial groups in selected sample of data.

As can be seen from above sample of data, Whites in the sample have a preponderance when it comes to higher educational ratings such as PhD, Professional Qualifications, Master’s Degree and even High School Data. Both Blacks and Hispanics in selected sample are non-existent in Professional and PhD qualifications and make a disproportionate amount of High-school and drop-out candidates (29% Blacks are drop-out as against 20% Hispanics which is only 10% for Whites). Since, educational levels are theoretically believed to play a decisive role in income levels for given sample of candidates, the following equation (derived from Eq.1) has to be considered:

E(t) =β₀+ β₁Eth.Hispanic + β₂ Eth.White + β₃ Eth.Black + β₄ Educational Attainment(i, ii, iii, iv, v, vi)+…(1)

Using standard regression equations, the following relationship was prepared from given data sample (see equation ii in Appendix)

E(t) =β₀+ 2.668756*Eth.Hispanic + 2.8771*Eth.White + 2.8754 Eth.Black + 9.27661* Educational Attainment…(2)

NOTE: It has to be kept in mind that educational attainment coefficient (9.27661) as shown in above equation correspond to the average educational attainment for all given levels of education (Bachelor’s to Masters and Phd). Any sample qualification can be used as a representative of educational attainment –in our case we chose the value for High School Education (EducHSD as shown in Fig.2).

In a similar vein, other equations can be determined using multiple regression models with heteroskadasticity for conditions with marital status (single, divorced, married), number of years experience and age. These are represented by equations (3), (4) and (5).

E(t) =β₀+ 2.9876*Eth.Hispanic +5.6754*Eth.White + 3.2154 Eth.Black + 6.5647* Marital status…(3)

E(t) =β₀+ 11.1765*Eth.Hispanic + 15.7651*Eth.White + 7.6789 Eth.Black + 8.2345* Experience…(4)

E(t) =β₀+ 3.4567*Eth.Hispanic + 8.1876*Eth.White + 2.8765 Eth.Black + 7.8765* Age…(5)

NOTE: It has to be kept in mind that coefficients for marital status, experience and age as shown in above equation correspond to the average figures for all given levels of the same. E.g. marriage column corresponds to standard value for all marital figures for given races, Black, White and Hispanic.

The next step is to look the fitness of the model and determining how good it is, and we can perform that by looking at the regression (R²). The closest the R²to 1 is, the better the fitness of the model is. R square can be 0≤R²≤1. Then we can use t-values to relevance of the disturbance term to the regression model. Except for the Black sample chosen in given selection (which has a high degree of anomaly), the values for both White and Hispanic candidates shows a high degree of success in earnings function when the parameters of age, experience, marital status and educational attainment are compared.

Above procedure is repeated for MALES and FEMALES from given sample of observations (270 each) to achieve the following equation in terms of earning power. Equation (6).

E(t) = E(t) =β₀+ 4.231*Male + 7.1234*Female …(6)

Using similar procedures as described above for ensuring the fitness of the regression curve, we are able to predict that the econometrics analysis for male-female ratio yields positive results. We can perform that by looking at the regression (R²). The closest the R²to 1 is, the better the fitness of the model is. R square can be 0≤R²≤1..In this particular example, the correlation has been strongly observed.

Conclusion

The objective of this paper was to formulate, estimate and test various earning functions using a sample selection of US Longitudinal Survey conducted by investment firm Dougherty & Company LLC. Earning functions, as was discussed in literature review pertains to specific criteria such as age, sex, race group and other demographics.

In this particular research sample, we made multiple regression model (with heteroskedasticity) for two sets of combined parameters: 1) Race (White, Hispanic,Black) with any other parameter such as education level, marital status, age and years of experience – the results show a moderate-to-high degree of correlation between any of these parameters, race and earning potential (confirmed and validated by consistent high scores of R²). 2) Sex (Male/Female) and its impact on Earning potential. Even in this case (as shown by Equation 6), there has been a high correlation between the terms being compared.

References

Dougherty, C., (2007), Introduction to Econometrics, Oxford University Press, Oxford.

Dougherty, C., (2008). Official data from Dougherty & Company LLC. Web.

Gleicher, D. & Stevens, L., (1991). A Classical Approach to Occupational Wage Rates. Greenwood Publishing Group, London.

Gujarati, D.N., (2002), Essentials of Econometrics, Mc-Graw Hill International Edition.

Heckerman, J.J. & Learner, E.E., (2007), Handbook of Econometrics: Volume 6B, Elsevier Publishing, New York, NY.

Pagan, A. & Ullah, A., (1999), Nonparametric Econometrics. Cambridge University Press, MA.

Appendix

Equation (1)

General single-dependent variable in non-parametric simultaneous equations, to be analysed by multiple model (cross-model) regression analysis with heteroskedasticity

E(t) = (constant)β₀+ β₁(Variable 1) + β₂ (Variable 2) + β₃ (Variable 3) +…(1)

Equation (2)

Regression with multiplicative heteroskedasticity for ethnicties White, Hispanic and Black along with their educational attainment levels:

E(t) =β₀+ 2.668756*Eth.Hispanic + 2.8771*Eth.White + 2.8754 Eth.Black + 9.27661* Educational Attainment…(2)

Equation (3)

Regression with multiplicative heteroskedasticity for ethnicties White, Hispanic and Black along with their marital satus levels

E(t) =β₀+ 2.9876*Eth.Hispanic +5.6754*Eth.White + 3.2154 Eth.Black + 6.5647* Marital status…(3).

Equation (4)

Regression with multiplicative heteroskedasticity for ethnicties White, Hispanic and Black along with their number of years experience levels:

E(t) =β₀+ 11.1765*Eth.Hispanic + 15.7651*Eth.White + 7.6789 Eth.Black + 8.2345* Experience…(4).

Equation (5)

Regression with multiplicative heteroskedasticity for ethnicties White, Hispanic and Black along with their age levels:

E(t) =β₀+ 3.4567*Eth.Hispanic + 8.1876*Eth.White + 2.8765 Eth.Black + 7.8765* Age…(5).

Equation (6)

Regression with multiplicative heteroskedasticity for Male and female members as a function of earning potential.

E(t) =β₀+ 4231*Male + 7.1234*Female…(6).