Do women receive compensating wages for earnings uncertainty?

• Author: McGoldrick, Kimmarie

1. Introduction

   The area of earnings uncertainty has received considerable attention in the literature. Many different measures of income uncertainty have been presented. For example, when individuals choose an occupation they face earnings uncertainty until they obtain a particular job. This uncertainty arises from the variability in earnings within an occupation. Once individuals find a job they face additional uncertainty in that jobs differ in their future earnings stability. Earnings uncertainty thus arises from the unknown wage pattern over time.

   The impact of uncertainty is well documented, including its impact on wages [3; 4; 6; 7; 8]; investment in human capital [9; 12]; and occupational choice [10; 11]. The purpose of this study is to examine gender differences in compensating wages associated with income risk.(1)

   The contribution of this paper to the literature on income uncertainty is the extension of the analysis to gender differences. Key to analyzing such gender differences arc the definitions and estimation procedure of systematic and unsystematic earnings. Earnings uncertainty for women is expected to be affected more by systematic, supply-side characteristics such as age, education, and migration differences for which compensating differentials are not expected. Thus, women may not receive significant compensating differentials with respect to measures of total variation when controlling for skewness in earnings.(2) Earnings uncertainty for men is expected to be influenced more by unsystematic, demand-side factors for which one would anticipate compensating differentials.

   Results indicate that both men and women receive a positive wage differential for variation in unsystematic earnings when controlling for skewness. Men and women receive negative compensating differentials for positively skewed unsystematic earnings, as expected. Women receive significantly greater compensating wages for unsystematic variations in earnings than men, but are willing to give up less for the possibility of receiving higher earnings (as indicated by positive unsystematic skewness).

   The next section presents the theoretical framework, reviews what has been done to date, and discusses the contribution of this paper. This is followed by a section describing the data. Section IV includes empirical results and discussions. A comparison of the findings of this paper to those in earnings uncertainty literature is provided in the concluding section.

2. Theoretical Development

   This section provides theoretical support for the risk premium hypothesis and results of this paper. The model is partially based on the work of Bellante and Link [1]. A worker is assumed to maximize utility:

   U = U (W, R, S, X) (1)

   where W represents the worker's wages over time, R is the measure of uncertainty, S is the measure of skewness, and X represents a vector of non-wage job characteristics. The typical assumptions of [U.sub.W] [greater than] 0, [U.sub.WW] [less than] 0, [U.sub.R] [less than] 0, and [U.sub.RR] [less than] 0 are made. Additionally, it is assumed that [U.sub.S] [greater than] 0. Thus workers are assumed to be risk averse and, ceteris paribus, will prefer entering occupations which have less uncertainty about occupational earnings and that are characterized by small probabilities for receiving higher earnings.

   Wages are assumed to be determined in the form of the following earnings function:

   Ln [W.sub.i] = a + b [multiplied by] [R.sub.i] + c [multiplied by] [S.sub.i] + [Delta] [multiplied by] [X.sub.i] + [[Epsilon].sub.i] (2)

   where Ln [W.sub.i] is the log of real wages for individual i. By maximizing (1) subject to (2), we obtain the following relationship.

   L = U (W, R, S, X) - [Lambda](W - a - b [multiplied by] R - c [multiplied by] S - [Delta] [multiplied by] X) (3)

   First order conditions of the Lagrangian are:

   [Delta]L/[Delta]W = [U.sub.W] - [Lambda] = 0 (4)

   [Delta]L/[Delta]R = [U.sub.R] + b [multiplied by] [Lambda] = 0 (5)

   [Delta]L/[Delta]S = [U.sub.s] + c [multiplied by] [Lambda] = 0 (6)

   [Delta]L/[Delta]X = [U.sub.x] + [Delta] [multiplied by] [Lambda] = 0 (7)

   [Delta]L/[Delta][Lambda] = W - a - b [multiplied by] R - [Delta] [multiplied by] X = 0. (8)

   These can be easily solved to find the following relationship:

   [U.sub.W] = -[U.sub.R]/b = -[U.sub.S]/c = -[U.sub.X]/[Delta] = [Lambda] (9)

   Of primary interest are the relationships of risk and skewness with wages. By solving (5) and (6) we find:

   b = -[U.sub.R]/[U.sub.w] [greater than] 0 (10)

   and

   c = -[U.sub.S]/[U.sub.W] [less than] 0. (11)

   Thus workers who face greater uncertainty will require higher wages to enter riskier occupations and will be willing to receive lower earnings for the opportunity of receiving higher incomes.

   Beginning with Friedman and Kuznets [5], many authors have found a distinctive relationship between average income levels and income variability. Occupations can be classified by the level of risk as measured by the variation observed in their income distribution. Assuming risk aversion, the individuals in question will have little incentive to enter a risky occupation. If risky occupations would offer the same wage as riskless occupations, they would face a shortage of workers. Consequently, one can expect to observe compensating wages for occupational earnings risk.

   The literature on earnings uncertainty is fairly small, thus a review of some of these articles is appropriate. King [7] tested whether riskier occupations offered employees higher expected average income. Risk was measured as the standard deviation of earnings within an occupation. Males, age 35-54, that had completed four years of college and were currently employed in professional occupations were examined. Compensating differentials for income variability were found to exist.

   Johnson [6] used a similar approach to estimate the tradeoff between risk and average earnings across all occupations for a sample of male workers. He further stratified the sample into groups by race, age, and education levels. Risk was measured as the standard deviation of earnings within an occupation for each cohort of workers. Again, compensating wages were found for all groups.

   Feinberg [3] considered the instability of earnings over time using six years of panel data for both men and women. Risk was measured as the standard deviation of the residuals from a regression over time for each individual. Results indicated that average earnings over the time period increased with risk. Gender differences indicated that women earned significantly lower compensating wages for income uncertainty. While Feinberg noted this difference, he suggested that future empirical work focusing on "how other compensating differentials vary across classes of jobs and workers" would be useful [3, 163].

   In an attempt to combine the risk affects at a point in time and across time, Leigh [8] used a slightly different approach. Data consisted of white and blue collar male workers who were in the same industry over a three year period. A measure of risk was calculated that incorporated individual wage growth and industry wage variation components. Compensating wages were found to exist for white collar workers but not for blue collar workers.

   Despite this literature, questions concerning earnings uncertainty remain unanswered. Gender differences in compensating differentials for income uncertainty have not been adequately considered. For example, King [7], Johnson [6] and Leigh [8] restrict their...