II. Background
Getting into medical school requires a bachelor’s degree from a four-year college or university.
5
While there has been some research regarding the effect of undergraduate education on physician specialty choice—see Ernst and
Yett 1985—such work is not conclusive, and it seems likely that most students enter medical school undecided about their specialty, or at least receptive to new
experience.
Once in medical school, the first two years are devoted to the basic sciences: anatomy, physiology, biochemistry, pathology, and the rest. Clinics are usually
deferred until the final two years of school and represent the student’s first prolonged contact with the various specialties of medicine.
6
Most schools require months in general surgery, internal medicine, pediatrics, family practice or ambulatory medi-
cine, psychiatry, and obstetrics and gynecology. Students typically explore clinical electives, including subspecialties, during the fourth year.
During the fourth year, students apply and interview for residency spots. For most students, a computerized algorithm assigns a residency position; this algorithm takes
into account students’ stated preferences, as well as those of the residency programs.
7
Accepting the match means agreeing to at least a three-year commitment, depending on the specialty.
Internship is the first year of residency. At the end of the internship year, a doctor completes all requirements for a license to practice medicine. Physicians with a
license are legally enabled to practice general medicine, though few do.
8
Board certi- fication is more rigorous and requires completing both the residency program and
testing by specialty boards. There are two routes to subspecialty training: completion of a residency program in
a specialized branch of medicine, or completion of a subspecialty fellowship after fin- ishing a basic residency. Total training times, set by specialty boards, vary widely; for
example, internal medicine and pediatrics take three years, radiology takes four years, and surgery takes at least five years. Fellowships in specialized fields, like cardiology
or neurosurgery, can take many years after a basic residency like internal medicine or general surgery.
III. Empirical Model
A doctor’s specialty and hours of work are the outcome of choices made in a specialized labor market. Econometric work estimating the determinants of
5. There are exceptions, such as a combined six-year undergraduate and medical school program, which I will ignore as such programs are not the norm.
6. Increasingly, medical schools have been incorporating clinical instruction into the first two years. 7. There is an extensive and well-developed literature on the residency matching process. Roth 1984, 1986
has done the most prominent work on this subject see also Roth and Peranson, 1999. Rejecting the com- puter assignment is rare because it entails a frantic search for open residency slots—there are only a few
months between the match and the beginning of residency. 8. The market for licensed physicians with a single year of residency is thin.
The Journal of Human Resources 118
equilibrium wage must explicitly recognize that specialty choice is, in fact, a choice, or risk incorrect inferences. In this section, I specify a joint econometric model of spe-
cialty choice and wage determination in the context of utility maximizing behavior by the doctor.
In this model, I allow five aggregated specialty categories: General Practice and Family Practice hereafter FP, Internal MedicinePediatrics IM, Surgery, Inter-
nal Medicine and Pediatrics Subspecialties IM Subspecialties, and Radiology and Other Specialties Radiology. Appendix Table 1 describes the grouping
of specialties.
9
First, I need some notation. Let s be the index over the five specialties, t be time between the date of the survey interview and medical school completion, and i be
the index over the set of all doctors. There are five potential wage streams one for each specialty but only the wage stream in the chosen specialty is realized. Let
{ }
w s
1 5
sit
f =
represent these streams, let X
i
represent observed time invariant covariates predicting wage, let
sit
n represent the unobserved determinants of
wages, and let ; ,
g t
s
c v be a function that reflects the dependence of wages on
experience. In X
i
, I include gender, race, whether the doctor graduated from a medical school in the United States rather than abroad, and years of education of
the doctor’s parents. I use overlap polynomials—a type of spline—to flexibly specify the wage-experi-
ence profiles, ; ,
g t
s
c v . The elements of the vector
, ,
,
s s
s s
s 1
2 3
= c
c c
c c
corre- spond roughly to yearly growth rates in wages in the first, second, third, and fourth
decades of practice; smoothing increases with σ, which I set in advance of estimation. Appendix 1 provides details.
Let Z
si
represent specialty choice determinants known by doctor i at the end of res- idency. Specifically, these include all the variables in X
i
, debt at the end of medical school which is my main instrument, average malpractice risk within each specialty,
and years of training required to complete the specialty. Finally, let
si
h represent the unobserved determinants of specialty choice. Wage streams in each specialty are set
according to: ;
, ln w
X g t
s for
1 1
5
sit i
s s
sit
f =
+ +
= b
c v
n At the end of medical school, doctors make irrevocable decisions about which
specialty to enter. Each specialty branch has an associated utility level, d
si
d Z
s for
2 1
5
si si
s si
f =
+ =
a h
9. This grouping is a result of the tradeoff between preserving a clean split between the generalist special- ties and the specialist specialties, while at the same time keeping the number of specialties low in order to
reduce the computational burden of estimation, respect sample size limitations within each specialty, and make the interpretation of results simpler. I group internal medicine and pediatrics together both because
they require a similar set of cognitive skills and because they have the same required number of training years. I group obstetricsgynecology with surgery because they both require surgical skills, and often require
similar irregular schedules. I group the surgical subspecialties with surgery because of the small number of surgical specialists in my sample, as well as for computational reasons to limit the number of branches
I allow. The least specialized specialties are FP and IM. The other three specialty groupings typically require more specialized training, and certainly require longer residency programs.
Bhattacharya 119
In Equations 1 and 2,
s
b and
s
a are vectors of parameters to be estimated. Each doctor chooses a specialty, based on Equation 2, with the maximum value of the util-
ity index d
si
. Let d
i
be the chosen specialty. Then for :
s 1
5 f
= d
s iff d d
k 3
1 5
i si
ki
6 f
= =
One of the main themes of this paper is that specialty choice and the wage set- ting processes are jointly determined in the physician labor market. The empirical
model, Equations 1–3, implements this theme by allowing unobserved determi- nants of wages,
sit
n , and the unobserved determinants of specialty selection,
si
h , to be correlated. The errors in the wage and specialty choice equations are the sum
of two components; the first components in the specialty choice and wage equation errors are unique to their respective equations, while the second components are
common across the equation errors. I model the second component using a step function approximation to the cumulative density function of the errors, known as
a discrete factor approximation. Appendix 2 discusses the use of discrete factors in selection models.
Each discrete factor has a natural interpretation as an unobserved individual char- acteristic, such as manual dexterity or patience for irregular schedules, which deter-
mines the match quality between the doctor and specialty. Each specialty may reward different combination of discrete factors differently. The model includes two discrete
factors, v v
and
1 2
:
10
v v
2
v
s 2
+ d
v + d
2 1
4
si si
s sit
si s
s 1
1 1
2 1
1 2
2
= +
= +
h h
d n
n d
l l
Here, the δ’s known as factor loads modulate the effect of each factor on each spe- cialty. I assume
si
hl is distributed i.i.d. Type-I extreme value and
sit
nl is distributed i.i.d.
, N 0
2
v . I assume the factors are distributed binomially, with all three error
components mutually independent: ,
v a
probability p a
probability p
k with
with for
5 1
1 2
k k
k k
k 1
2
= -
= I restrict the mean of v
v and
1 2
to zero and a variance to one, which amounts to plac- ing some restrictions on
, a
a
k k
1 2
, and p
k
.
11
There is no loss of generality due to this assumption, since the discrete factors are scaled by the δ’s.
I estimate this model using maximum likelihood. Conditional on v v
and
1 2
, the errors are independent, so the conditional likelihood function contribution for a doc-
tor in specialty s is the product of the probability of choosing the specialty and the density of the wage in that specialty:
10. Allowing two points of support on the two factors allows four different “types” of physicians. In their Monte Carlo work, Mroz and Guilkey 1999 find that allowing at least three “types” is sufficient to generate
estimates that are robust to selection bias. 11. These restrictions are
. a
p p
a p
p and
1 1
k k
k k
k k
1 2
= -
= - -
The Journal of Human Resources 120
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
Kategori