1
, ;
冱
ln
exp exp
L v v
w X
g t v
v
Z v
v Z
v v
6 1
si s
s si
i s
i s
s s
ki k
k k
si s
s s
1 2
1 2
1 2
2 2
5 1
1 1
2 1
2 1
1 1
2 1
2
= -
- -
-
+ +
+ +
v z b
c d
d
c d
d c
d d
v
= k
J L
K K
N P
O O
Removing the conditioning on v
1
and v
2
makes the specialty selection and wage com- ponents of the likelihood function contribution of doctors from specialty s no longer
separable:
12
, ,
, ,
L p p L v
a v
a p
p L v a
v a
p p
L v a
v a
p p
L v a
v a
7 1
1 1
1
si si
si si
si 1
2 1
11 2
12 1
2 1
21 2
12 1
2 1
11 2
22 1
2 1
21 2
22
i
= =
= +
- =
= +
- =
= +
- -
= =
i
e e
e e
R T
S S
S V
X W
W W
Let A
s
be the set of doctors who pick specialty s. Then the likelihood function is:
1
L L
8
si i
5
s
=
= fA
s
IV. Data
My main data source is the 1991 Survey of Young Physicians YPS, conducted by the Robert Wood Johnson Foundation in conjunction with the American
Medical Association AMA. The data set is representative of the 1991 population of physicians under the age of 45 years with two to nine years of practice experience.
Half the sample comes from a similar survey conducted in 1987, while half is drawn randomly from the AMA physician masterfile. The survey enjoyed a nearly 70 per-
cent response rate—5,884 doctors with MD degrees.
13
From this initial sample of 5,884, I remove all doctors who do not report income, hours of work, or any of the
other variables included in the model, leaving a final sample of 4,148 doctors.
14
Yearly income consists of all pre-tax monetary returns from medical practice, including pension benefits. I construct log hourly wages using the following formula,
each element of which is available for everyone in the estimation sample:
15
12. I use sample weights because of the sampling scheme used to collect the data set. The weights, θ
i
, incor- porate information not available in the other covariates X and Z. If the sample weights were not included,
maximum likelihood estimation would yield biased parameter estimates even if the likelihood function were conditioned on the correct covariates. Pfeffermann 1996 formalizes this argument. He argues that includ-
ing the weights yields consistent parameter estimates if the model is specified correctly and guards against some forms of model misspecification.
13. Cantor, Baker, and Hughes 1993 provide a more complete discussion of the construction of the data set, the sampling scheme, and the calculation of the sample weights.
14. It might concern some readers that so many doctors are excluded from the initial sample. In calculations not reported here, I compared what is observed about these excluded doctors with those in the included sam-
ple. The two samples are quite similar with respect to personal characteristics, though a slightly higher pro- portion of doctors in the excluded sample choose FP, IM, and Radiology and a slightly lower proportion
choose surgery and the IM subspecialties. Physicians in the estimation sample have about 7,000 higher med- ical school debt than those in the excluded sample. A detailed table is available upon request from the author.
15. I convert all monetary variables to 1990 real dollars by applying the Consumer Price Index. Because income in the 1991 YPS is denominated in 1990 dollars, all monetary variables are in the same real units.
Bhattacharya 121
The Journal of Human Resources 122
Table 1 Descriptive Statistics for the Various Specialties
Internal Internal medicine
medicine Family Practice
Pediatrics Surgery
subspecialties Radiology
Standard Standard Standard Standard Standard Variables
Mean Deviation
Mean Deviation
Mean Deviation
Mean Deviation
Mean Deviation
Personal Information Board-certified
0.88 0.33
0.83 0.37
0.78 0.42
0.93 0.27
0.81 0.38
Age 36.2
3.01 36.3
2.93 37.3
2.90 37.5
2.70 37.2
2.80 Male
0.75 0.44
0.62 0.48
0.81 0.39
0.84 0.38
0.75 0.41
USMG 0.91
0.30 0.81
0.39 0.89
0.31 0.80
0.41 0.86
0.33 White
0.92 0.27
0.86 0.35
0.89 0.32
0.87 0.34
0.90 0.29
Black 0.035
0.19 0.038
0.19 0.035
0.19 0.022
0.15 0.020
0.13 MD awarded at age
28.6 2.33
28.7 2.18
28.3 2.04
28.3 1.86
28.8 2.04
Years of residency 2.81
0.60 3.00
0.10 4.56
0.74 4.67
0.48 3.6
0.50 training
Father’s years of 14.0
3.28 14.4
2.96 14.3
2.94 14.4
2.92 14.3
2.95 education
Mother’s years of 13.4
3.18 13.6
2.88 13.7
2.72 13.7
2.84 13.5
2.68 education
Bhattacharya
123 Practice and financial information
Experience in practice 5.7
2.3 5.5
2.25 5.5
2.27 5.5
2.37 5.8
2.18 years
Debt at graduation 31.6
30.2 25.5
26.8 26.1
31.2 20.0
26.0 24.3
24.4 from medical school
thousands of Income in 1990
89.7 43.3
97.6 61.6
198 117
129 82.1
137 76.3
thousands of Hours in 1990
2670 910
2600 883
2990 871
3020 905
2420 665
Wage per hour 38.8
64.3 41.7
41.5 71.1
46.6 44.4
28.1 63.0
84.8 Logwage
3.49 0.50
3.56 0.54
4.09 0.63
3.62 0.61
3.95 0.54
Average yearly wage growth rates between 1985 and 1995 for the 1985 cohort of physicians 36 years in 1985
4.04 2.88
5.28 4.74
3.66 36–45 years in 1985
3.46 3.15
2.56 4.30
3.34 46–56 years in 1985
0.68 1.45
1.05 −0.97
−0.051
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
