The Journal of Human Resources 124
ln log
wage yearly income
9 =
number weeks of practice hours of practice per week e
o Table 1 presents descriptive statistics for the estimation sample broken down by
specialty grouping.
16
This table confirms some well-known facts about the medical profession. Specialists’ yearly income is significantly higher than generalists’; for
example, surgeons earn an average of 221 percent more than FP doctors. Also, a higher proportion of surgeons and IM Subspecialists are male, compared to doctors in
FP or IM. Surgeons and IM Subspecialists work longer hours than do doctors in other specialties.
Because the YPS is limited to young physicians and does not contain some other important information, I require some other data sources. The AMA’s 1986,
1996 Socioeconomic Characteristics of Medical Practice SCMP report the average yearly income of all practicing doctors by specialty, as well as the annual
probability of a malpractice suit in each specialty in 1985.
17
Various yearly ver- sions of the American Association of Medical College’s AAMC, 1980–90
Directory of Graduate Medical Education provide information on the training years required to obtain board certification in each specialty. Information about
nominal resident wages for the years 1977–89 comes from the AAMC website http:www.aamc.org.
18
I use this information to calculate physician wages during residency.
V. Identification
In this section, I introduce and justify my identification strategy. I consider in turn the unique determinants of specialty selection and of market
wage setting. In a formal sense, such an argument is unnecessary since the model is identified simply by the nonlinearity of the error distributions. However, such
an identification scheme would be unappealing. Ideally, to identify the selection equations, there should be some variable that determines wages but does not
determine specialty selection. Similarly, to identify the wage equations, there should be some variable that exogenously sends some candidates into one
16. The contrast category for white and black throughout the paper is “other races.” This category includes mostly Asians. Hispanics are included in the white category. USMG refers to graduates of U.S. medical
schools. The contrast category consists of all graduates of foreign medical schools, whether or not they were U.S. citizens at the time of medical school.
17. Because these figures are typically reported for a more disaggregated set of specialties than is used here, I average over them, weighting by the number of doctors in each specialty, to obtain these figures
at the proper level of aggregation. The main difficulty with this procedure is that the SCMP does not dis- tinguish general internal medicine doctors from specialized internal medicine doctors. Thus, the
weighted average from the Internal Medicine and Pediatrics categories in the SCMP is assigned to this IM category, while the Internal Medicine category in the SCMP is assigned to my IM Subspecialties cat-
egory. 18. This source reports yearly income for residents, but not hours of work. I assume that residents work
3,000 hours per year. My qualitative results are not sensitive to varying this number of hours by 500 hours in either direction. My quantitative results do not change much either.
specialty over the others, but has little to do with the wage setting process within the specialty.
19
A variable that determines wages observed at time t but that does not determine specialty selection is easy to find: the survey sampling year works perfectly since it
could not have been foreseen when specialty was chosen. More formally, since spe- cialty selection is made at the end of medical school before any wages streams are
realized, in principle the observed determinants of selection, Z
si
, cannot include {
} w
sit
or any other variables not known at t = 0. On the other hand, Z
si
should include projected specialty specific wage streams, { [
]} E w
sit si
X
e
, where
si
X is the
information that doctor i has about each specialty s upon graduation. But, the com- plete set of information observed by each doctor includes only Z
si
and
si
h , so {
, }
Z
si si
si
= h
X . Including information about projected wage streams in the specialty
selection equations is tantamount to including functions of Z
si
. Because t—the date at which doctors’ wages were sampled—cannot belong in Z
si
, it is a theoretically defensible instrument.
Finding an instrument that identifies the wage equation is harder; an easy tem- poral argument, such as the one in the previous paragraph, is not possible. My
candidate variable is medical school debt at the time of graduation. This is strongly correlated with specialty choice, as my results demonstrate. Conversely,
it is at least intuitively appealing to argue that initial assets should have little to do with the unobserved determinants of equilibrium wage later in life. Medical
school debt, which for many doctors is determined by the ability of their parents to pay medical school tuition, seems like it should be unrelated, or only tangen-
tially related, to the skill of the doctors years after their residency training, and thus with wage.
20
The YPS data provide some justification for this identification strategy. Table 2 shows results from regressions analyzing the effect of medical school debt on a vari-
ety of medical practice style variables and an important lifestyle variable at the time of the 1991 YPS, t years after medical school graduation. The practice style variables
are yearly hours of work, proportion of patients seen with Medicare, and indicator variables for whether the doctor has ever faced a malpractice claim, whether the doc-
tor is salaried, and whether the doctor is an employee of an HMO. The lifestyle vari- able is an indicator of whether the doctor in the sample is married to another doctor.
Each column represents a separate set of regressions limited to physicians in the indi- cated specialty. Each cell reports the marginal effect of a 1,000 increase in medical
Bhattacharya 125
19. Heckman and Honore 1990 discuss conditions under which Roy-type selection models, such as this one, are nonparametrically identified when there is an instrument.
20. One may argue that the level of tuition paid for medical school is correlated with the skill of the physician within a specialty later in life, and thus with the realized wage in each specialty. The single
factor explaining most of the variation in medical school tuitions is whether the school is publicly or privately run—there are large subsidies to students attending public medical schools. Private and pub-
lic medical school students do not differ on observable measures of ability. Using 2001 medical school level data from the AAMC, I compare the average Medical College Admissions Test MCAT and
undergraduate GPA at private and public medical schools, weighted by enrollment. The differences between these measures of average student quality between public and private schools are small: mean
MCAT scores are 14th of a standard deviation point higher at private schools, while mean GPA is identical to two decimal places.
school debt on the row’s dependent variable. In the case of binary outcomes, for which I ran probit regressions, each cell reports marginal probability effects at the
mean.
21
The striking result is how little medical school debt predicts any of these practice and lifestyle outcomes. The HMO employee, salaried employee, and spouse is a doc-
tor regressions have nothing but statistically insignificant and nearly zero estimates of the effect of debt. The debt coefficients in the yearly work hours regression for fam-
ily practice doctors, internal medicine doctors, and for internal medicine specialists are statistically significant, but economically small—a 1,000 increase in debt raises
hours by 2.7, 2.9, and 6.4 hours annually. The effect sizes of increasing debt by 1,000 range from 0.04 percent for surgeons to 0.2 percent for internal medicine
specialists of total yearly hours. There are only two other statistically significant The Journal of Human Resources
126
21. The other variables in the regression are age, age
2
, male, dad’s years of education, mom’s years of edu- cation, USMG, race dummies, and a dummy for board certification. These regression results are available
upon request.
Table 2
a
Effect of 1,000 Increase in Medical School Debt on Practice Style
Specialties Internal
Dependent Type of
Family Medicine
Medical Variable
Regression Practice
Pediatrics Surgery
Subspecialties Radiology
Yearly work OLS
2.7 2.9
1.3 6.4
1.6 hours
1.1 1.0
0.83 1.5
1.1 Proportion of
Linear 0.00022
0.00097 −0.00024
0.00041 0.000040
patients seen Probability
0.00031 0.00026
0.00024 0.00043
0.00031 with Model
Medicare Ever had a
Probit 0.00069
0.000047 −0.0012
0.00051 0.00045
malpractice 0.00054 0.00052
0.00041 0.00073
0.00051 claim filed?
HMO employee? Probit
0.000059 −0.00015
−0.00017 −0.00022
−0.00034 0.00015
0.00013 0.00015
0.00026 0.00029
Salaried Probit 0.00046
−0.00056 0.00040
−0.00021 −0.00015
physician? 0.00061
0.00055 0.00047
0.00089 0.00059
Spouse is a Probit
−0.000081 −0.00038
0.00078 0.00056
−0.00032 doctor?
b
0.00062 0.00048
0.00043 0.00068
0.00056 0.01p0.05
p0.01 a. Each row in the table reports the marginal effect of a 1,000 increase in medical school debt on the row’s
dependent variable. In the case of the probit regressions, each row reports marginal probability effects at the mean. Each column represents a separate regression limited to physicians in the indicated specialty. The
other variables in the regression are age, age
2
, male, dad’s years of education, mom’s years of education, USMG, race dummies, and a dummy for board certification. The regression coefficients for these other vari-
ables are available upon request. b. The sample in this probit regression is limited to married doctors N = 3,460.
coefficients for debt: in the proportion of patients seen with Medicare regression for IMPeds doctors, and in the malpractice claim regression for surgeons. Both are
precisely measured zeroes.
22
VI. Cohort Wage Growth Restrictions
