Group Differences in Equilibrium Wage Setting

VII. Wage and Selection Equation Estimates

This section discusses the parameter estimates from the joint model of specialty choice and wage setting. The top half of Table 3 shows the wage equation results, while the bottom half shows the selection equation results. 26 I organize my discussion of this table around three themes: race and gender differences in equilib- rium wage setting in medicine, other differences in wage setting, and tests of the empirical model’s validity.

A. Group Differences in Equilibrium Wage Setting

In this section, I examine racial and gender differences in wage setting within the spe- cialties of medicine. These differences are of particular interest because of the possi- bility that some groups—blacks and females in particular—face discrimination in physician labor markets. Some like Baker, 1996 have argued that observed differ- ences across groups in the incomes of physicians are explained by differences in spe- cialty choices. It is clearly beyond the scope of this paper to answer whether there is discrimination against these groups in medicine, but it is entirely within its scope to document whether group-specific wage differences persist within specialties in an empirical setting aimed at accounting for unobserved skill differences. Furthermore, documenting group wage differences is closely related to the main project of this paper—a decomposition of the returns to specialization into a competitive and non- competitive part—since invidious discrimination thrives best in an anti-competitive environment. I first compare the wages of black physicians with white and other race physicians. Consider the evidence from Table 3 on the generalist branches of medicine: black FP doctors earn 9 percent more than white FP doctors, while black IM doctors earn the same as white IM doctors. Other race FP doctors earn 21 percent more than white FP doctors, while other race IM doctors earn 10 percent more than white IM doctors. White, black and other race medical school graduates respond to these wage premi- ums in their specialty choices in ways one might expect—doctors of other races are 13 percent more likely than white doctors to enter FP and 116 percent more likely than white doctors to enter IM, while black doctors are more likely than whites to enter FP and IM. Bhattacharya 129 model. Because of the presence of these conditional logit variables, one of the constants other than in the Radiology branch in the logit part of likelihood function must be set to zero. For the estimation, I set all the constants in the specialty selection part of the model to zero. Finally, it is not possible to estimate all the factor-loading terms, since for a given doctor, I never observe the covariance between selection probabili- ties. I arbitrarily set , k Radiology d 2 for k = 1,2 the factor-loading terms in the Radiology specialty selection equation equal to 0.1 to identify the model. 26. The wage equation coefficient estimates are directly interpretable except for the overlap polynomial coefficients as percentage shifts in the wage-experience profiles, in response to a change in the covariates, holding fixed all other observables and controlling for selection into the specialty based on unobservables. On the other hand, because the specialty selection parameters do not lend themselves to such ready inter- pretation, I discuss them here in terms of the effect that changing each covariate has on the mean specialty selection probabilities, holding all else equal. The pattern in the more specialized branches of medicine is not as clean. Black sur- geons earn 13 percent less than white surgeons, while other race surgeons earn 3 per- cent more than white surgeons. Nevertheless, holding all else fixed, black doctors are more likely to enter surgery than whites and doctors of other races are a little less likely to enter surgery than whites. Black IM subspecialists earn 10 percent more than white IM subspecialists, while other race IM subspecialists earn 6 percent more than white IM subspecialists. Despite this wage premium, black and white doctors are equally likely to enter the IM subspecialties. Other race doctors respond in the The Journal of Human Resources 130 Table 3 Wage and Selection Equation Estimates Specialties Internal Family Medicine Medical Parameters Practice Pediatrics Surgery Subspecialties Radiology Wage equation estimates Constant −3.54 −3.35 −3.49 −2.99 −3.56 USMG −0.058 −0.064 0.20 −0.00085 0.0072 Male −0.079 0.090 0.13 0.082 0.076 White −0.21 −0.098 −0.027 −0.057 0.057 Black −0.12 −0.095 −0.16 0.041 0.25 Dad’s education 0.0086 0.0086 −0.016 −0.0092 0.011 Mom’s education 0.00045 −0.016 0.0044 −0.00094 −0.012 g 0.10 0.12 0.19 0.15 0.15 g 1 † −0.015 −0.059 −0.083 −0.096 −0.092 g 2 † 0.093 0.11 0.14 0.18 0.15 g 3 † 0.014 0.0098 0.0044 −0.020 −0.0083 δ 1 1s −0.35 0.51 −0.56 −0.24 −0.60 δ 1 2s 0.057 0.043 −0.0034 0.000024 0.0036 σ 2 0.60 0.63 0.67 0.64 0.59 Selection equation estimates Age MD awarded −0.010 −0.0091 −0.13 −0.15 — USMG −1.3 −1.96 0.40 −1.99 — Male −4.15 −4.76 0.79 −3.25 — White −0.12 −0.77 0.022 −0.82 — Black 0.040 −0.46 0.74 −0.69 — Debt at graduation 0.015 0.010 0.0018 −0.0040 — δ 2 1s 3.36 4.43 0.16 6.42 — δ 2 2s −7.73 −10.4 1.24 −13.4 — Common parameters in specialty selection equation Discrete factor 1 v 1 Discrete factor 2 v 2 Years of training 0.0023 p 1 0.96 p 2 0.58 Probability of a 1,1 † −0.21 a 1,2 † −1.27 malpractice claim 1.51 a 2,1 † 4.90 a 2,2 † 0.79 0.01p0.05 p0.01 † These parameters are identified with restrictions described in the text. expected way to their wage premium—they are 127 percent more likely than white doctors to enter the IM subspecialties. Finally, black radiologists earn 19 per- cent more than white radiologists, while other race radiologists earn 6 percent less than white radiologists. Again despite this wage premium, blacks are less likely to enter radiology than whites and in accord with the wage premium, other race doctors are a little less likely than white doctors to enter radiology. There are at least two competing explanations for the evidence on racial differences in wages across the specialties: group differences in practice style within specialties, or racial discrimination in the physician labor market. Disentangling these explana- tions is difficult without further evidence, but given the fact that black doctors on aver- age earn higher wages than doctors of all other races including whites in IM Subspecialties and Radiology, and doctors of other races earn more than whites in four of the five specialty categories, racial discrimination seems unlikely, at least without further auxiliary and possibly ad hoc assumptions. I turn next to gender differences: male doctors earn between 8 percent and 13 per- cent more than female doctors in all of the specialty branches, save FP, where female doctors earn 8 percent more. 27 Female medical graduates react to these earnings dif- ferences by picking surgery and radiology as specialties at lower rates than men and FP at higher rates. However, women are more likely than men to pick IM and IM sub- specialties. If discrimination against female physicians is the cause of the wage dif- ferences in these specialties, such a finding that women preferentially enter these specialties would be odd. In IM and IM subspecialties, discrimination again seems an unlikely explanation for observed wage differences, though such a conclusion remains open in Surgery and Radiology.

B. Other Determinants of Equilibrium Wage Setting