Lifetime Skill Premiums Counterfactual Lifetime Skill Premiums

1 , 冱 exp exp specialty d v a v a Z a a Z a a P 18 , , , , , , k m r r r k r m d d d k d m 1 1 2 2 5 1 2 1 2 2 2 1 2 1 2 2 2 = = = = + + + + a d d a d d = r a k It is difficult to compare the counterfactual wage paths across specialties because they vary across a large number of dimensions—one dimension for each year in practice. Let r be the discount rate and H a fixed supply of hours. The usual convention in empirical human capital applications, which this paper follows, is to consider the net present value of income in the alternate specialties— NPV d s —as a summary index of the desirability of each occupation: 32 , , 冱 冱 NPV d r t d H H r t d 19 1 1 s T t s T t s = + = + ~ ~ = = t t

B. Lifetime Skill Premiums

A lifetime skill premium is defined as the percent difference between what doctors from some specialty, say d , would earn if moved to another specialty, say s, and the earnings of doctors who actually picked specialty s with the earnings of doctors in specialty s as the base: Lifetime skill premium d NPV s NPV d NPV s 20 s s s s = - To calculate lifetime skill premiums, I first plot the difference between the projected wages of doctors from each of the alternate specialties, , , t d s ~ and the projected wage of the doctors who chose the specialty under consideration, , t s s ~ , at each point in time between graduation from medical school and retirement. The plots show what wages the average physician from each specialty would earn in each of the alter- native specialties, from graduation to retirement. Figure 1 shows a representative plot for the five alternative wage paths of surgeons in the two-factor model. There are five such plots, one for each of the specialties. 33 Table 4 shows the mean lifetime skill premiums calculated from the projected wage paths. Since the discount rate, r, is not observed, Table 4 reports the lifetime skill premium assuming r 5 = percent. 34 These tables should be read going across rows. Start with the lifetime skill premium of FP doctors—the first row of Table 4. Going across the row, the table reports that FPs would enjoy a statistically and economically significant 1.4 percent lifetime skill premium over IM doctors. 35 In other words, they would earn more in net present value terms as IM doctors than doctors that actually chose IM earn. Continuing across the row, FP doctors would earn a positive skill pre- mium in surgery relative to practicing surgeons 2.7 percent. This should not be sur- The Journal of Human Resources 134 32. By holding hours of work fixed, NPV s d ignores any labor-leisure tradeoffs. The specialty with the largest income stream may not be the most desirable one if it requires many more hours of work than the other specialties. 33. These graphs are available from the author upon request. 34. The qualitative results are not sensitive to a range of different values of r. 35. Significance tests are reported for the H : NPV s d = NPV s s in each cell of Table 4. Standard errors are constructed using the sample distribution of predicted NPV.. values. Bhattacharya 135 Table 4 a Lifetime Skill Premiums Relative to Doctors Who Chose the Specialty Skill Premium Relative to Physicians in Specialty Internal Internal Physicians in Family Medicine Medicine Specialty Practice Pediatrics Surgery Subspecialties Radiology Family practice — 1.43 † 2.74 † −9.54 −0.42 Internal medicinepediatrics 2.18 — −6.30 −11.38 −3.84 Surgery 0.05 0.07 — −3.10 0.08 Internal medicine 0.63 0.08 −0.92 — −0.96 subspecialties Radiology 1.59 1.83 1.51 −4.78 — a. The table should be read going across rows. For example, in the no-selection model, family practice doc- tors would earn 0.45 percent more as internal medicine doctors than actual internal medicine doctors earn. † 0.05p0.1 0.01p0.05 p0.01 Figure 1 Projected Difference between Wages of Doctors from Each Specialty in Surgery and Surgeon Wages -20.0 -15.0 -10.0 -5.0 0.0 5.0 10.0 5 10 15 20 25 30 35 40 45 Difference in Wages Family Practice IMPediatrics IM Specialties Radiology and Other Specialties Years since Graduation prising since many Family Practice doctors who are included in the FP category receive some training in surgical techniques, and thus may have unobserved attributes that are similar to Surgeons. IM doctors enjoy a 2.2 percent skill premium over FP doctors, but have large neg- ative skill premiums in all the specialized branches. There is a curiosity here: IM doc- tors would earn a positive skill premium in FP over FP doctors, and conversely FP doctors would earn a positive skill premium in IM over IM doctors. Since years of required specialty training are the same in the two specialties, from these results it may seem odd that FP doctors did not instead choose to be IM doctors, and vice versa. Such curiosities can arise in Roy-type models such as this one if the covariance between the unobserved determinants of returns in two specialties exceeds the vari- ance of unobserved returns in one of those specialties see Heckman and Honoré, 1990. In that case, the average specialty-specific skills of doctors within that spe- cialty may be less than the population average level of that specialty-specific skill. In contrast to received wisdom, surgeons earn nearly zero lifetime skill premiums in all the other specialties except in IM Subspecialties, where surgeons earn a . 3 1 - per- cent skill premium. Conversely, it is also not true that the lifetime skill premiums of other nonsurgical doctors in surgery are negative. The only doctors who earn statisti- cally and economically significant negative skill premiums in surgery are IM doctors. Though it is not true that surgeons would earn more in any other specialty than the doctors who actually picked that specialty and vice versa, there is one group of doc- tors who come close to meeting this standard. IM Subspecialists would do no worse in any alternate specialty than the average doctor in that specialty. Conversely, doc- tors from all other specialties suffer a large negative lifetime skill premium in the IM Subspecialties that is, NPV s IM Subspecialties NPV IM Subspecialties IM Subspecialties s 6 IM Subspecialties. Radiologists would also fare well in any spe- cialty except IM Subspecialties relative to the doctors who chose the specialty, and no doctors would earn significantly more in radiology than radiologists.

IX. Explaining High Specialist Incomes