** 4 Empirical Strategy**

**5.3 Persistent effects of residency characteristics**

This section examines the long-term impact (FJEs) of eight residency characteristics: salary, rurality of location, proportion of specialists, number of specialists in internal medicine, surgery, diagnostic medicine and psychiatry, and hospital size (number of doctors). We instrument for residency char- acteristics using the strategies detailed in Section4.2and show that FJEs on income, specialization and location decisions of doctors can persist for up to ten years.

**5.3.1 First stage**

Summary statistics (mean, median, variance) of hospital characteristics in Ci sets qualify as in-
strumental variables for residency characteristics actually chosen by i. We use the refinements
described in Section4.2 to increase their first stage explanatory power. Motivated by the prefer-
ence patterns documented above, we sort individuals into four demographic groups: foreigners,
rural-born Norwegians, urban female Norwegians and urban male Norwegians. Each resident i’s
choices are assigned probability weights based on the choices of other residents belonging to the
same demographic group in the same lottery. We then use these probability weights in two ways.
One, we restrict attention to the top seven choices when calculating summary statistics.26 _{Second,}

25_{The negative coefficients on hospital salary are not economically intuitive, but may be driven by the fact that we do}
not observe hours worked. Also seeAgarwal(2015) for another instance in the literature.

we create weighted summary statistics, which prioritize hospitals that are most likely to be chosen by i.

Our first set of instruments consists of the expected values of residency characteristics, as well
as the standard deviation of average hospital salary and number of doctors.27 _{Figure}_{3}_{illustrates}

how relevance increases when we constrain attention to higher ranks to construct instruments:
for each refinement, we plot first stage Kleibergen-Paap Wald rk statistics for the highest rank
summary statistics are constrained to.28 _{Instrument relevance is highest for weighted summary}

statistics based on the top seven hospitals of each resident’s choice set. Appendix FigureA.5dis- plays weak instrument tests for alternative summary statistics like quartiles as instruments, which deliver weaker first stages than the one outlined above. Therefore, we use expected values and standard deviations as instruments in the analysis that follows.

**5.3.2 Second stage: effects on long-run outcomes**

In this section, we instrument for residency characteristics and show that they continue to influence doctors’ careers for over ten years after the completion of their residencies.

We focus on three aspects of doctors’ careers: earnings, the decision to specialize and location.
2 _{tests are used to test whether FJEs of eight residency characteristics are collectively different}
from zero. Figure4 displays these tests for each year following the lottery. We find that FJEs on
each of these outcomes continue to be significantly different from zero for over ten years after the
residency period.29 _{The pattern documented in the middle panel is especially interesting. Most}

doctors become specialists 8-12 years after their residencies, and the peaked pattern of 2 tests
suggests that FJEs significantly affect the decision to specialize in fields that take less time, or
that FJEs are more significant for the decision to specialize sooner (than average) in one’s career.
FigureA.6repeats this exercise separately for the four demographic groups described above: FJEs
continue to impact earnings and the decision to specialize well beyond ten years after residency
27_{This enables us to run weak instrument tests, which require the number of instruments to exceed the number of}
endogenous variables (henceforth, EV) by at least two. The critical value for maximal 10 per cent bias with 1 EV and 3
instruments is 9.08, 2 EV and 4 instruments is 7.56, 3 EV and 5 instruments is 6.61. Stock & Yogo(2005) do not report
critical values for more than 3 EV - we assume that the declining trend from the above 3 numbers means that 6.61 is an
upper bound for the critical value in the 4 EV 6 instrument case.

28_{Actual first stage statistics will vary, because both stages are jointly estimated in a 2SLS regression.}

29_{Tables}_{A.4}_{-}_{A.6}_{display the year-by-year effects of each hospital characteristic on post-residency hospital salary,}
specialization and location.

completion across demographic categories.

To shed light on how residencies affect long-term earnings, we separately examine the FJEs of each residency characteristic. TableA.4 displays these characteristic-specific FJEs on hospital salary for up to fifteen years after the completion of doctors’ residencies. Residency salary low- ers long-term earnings, which is consistent with our estimates of negative doctor preferences for earnings during the residency period. On the other hand, residencies that are located in rural areas and those in which doctors are exposed to a high proportion of specialists appear to con- sistently increase long-term earnings, which is most consistent with our preference estimates for rural Norwegians. Last, the number of doctors a resident is exposed to exerts a negative influ- ence on earnings for the first few years following the residency, and then begins to exert a positive influence.

Table A.5 displays these characteristic-specific FJEs on the decision to specialize. Residency salary and rurality lower the probability that a doctor will specialize in most years following her residency. This is consistent with most medical graduates valuing residency earnings negatively. The proportion of specialists that a doctor is exposed to during her residency, however, exerts a uniformly positive influence on the decision to specialize in the long term. Consistent with the pattern of 2tests above, the coefficients are largest in magnitude 8-12 years after doctors enter the labor market.

Finally, we examine the pattern of characteristic-specific FJEs on doctor location in the long term. TableA.6shows that residencies with high salary and more specialists reduce the expected rurality of location in the long term. On the other hand, residencies in rural areas exert a positive influence on how rural doctors’ locations are throughout their careers.