Data on the individual characteristics and practice locations of physicians who, at any one time, practiced in California were obtained from the American Medical Association (AMA) Masterfile for the years 1997–2003. The AMA Masterfile is the best available data source at this time, but its primary limitation is that updating physician addresses is often done with a lag averaging 2 years (Kletke 2004
Because physician movement is measured with a lag, this means that in our departure models, the dependent variable is measured with error. If this measurement error has a mean different from 0 due to the average 2-year lag, but is otherwise random across physicians, then there will be no bias to the estimated coefficients (with the exception of the constant term that is biased due to the mean measurement error not being 0—this bias is unimportant here), but the standard errors will be larger (Wooldridge 2006
). The assumption of measurement error being random with a mean different from 0 is reasonable given the available evidence.
This data limitation also suggests that there is some error in the measure of minority physician representation in our departure models. In this case, the parameter bias resulting from such error depends on the ratio of the variance of the true measure of representation and the variance of representation when it is measured with error (Wooldridge 2006
). If this ratio is close to 1, then any bias to the parameter will be small. In the current case measurement error will be very small since in our data only 6.9 percent of physicians relocate (or leave practice) on average over the entire period examined.3
Note that the true percentage of physicians who migrate (or leave practice) in any given year may be somewhat greater or less than the long-run 6.9 percent figure depending on the specific configuration of lags in any given year, with the long-run measured migration percentage becoming more accurate the longer the period is that is being examined. This suggests that reporting lags regarding physician location will result in an average error rate of much less than 6.9 percent (because only some observations will be in error). This further suggests that the parameters of the physician representation measures may be slightly biased toward 0 as well as there being some relatively small but unpredictable effects on the parameter estimates of the other covariates to the degree that they are correlated with the measure of representation (Nugent, White, and Basham 2000
; Wooldridge 2006
This data limitation also implies that there is also some small measurement error in the destination models. There are two concerns about measurement error in these models. The first is that some physicians did not move at the time that the data states: there may be a mismatch between the timing of the dependent variable and with some of the time-varying independent variables, which is equivalent to a small amount of measurement error in each of these independent variables to the extent that they change over time. Because most of these variables change very little over time, this measurement error is likely to be quite small.
The second concern is with regard to the physician representation variables in the destination model. In these variables there is, on average, <6.9 percent measurement error and we use interval measures that will mask much of this already very small error. Thus, in each of the two concerns above with respect to measurement error in the destination model, any resulting biases to the estimated parameters are likely to be small and thus of little consequence depending on the correlation of the independent variables with each other (Stefanski and Carroll 1985
; DeVaro and Lacker 1995
An additional issue is the geographical level at which to measure minority physician representation. There will necessarily be more variation in minority physician representation across geographical units as the geographical unit used becomes smaller. We must determine whether to measure minority physician representation only in the area where a patient lives or also to include the area where they work. The first approach assumes that patients do not access medical care outside of the area where they live. If patients access a significant amount of medical care outside of this area, and the levels of minority physician representation differ between areas, then measuring minority physician representation only in the area where patients live may result in an inaccurate measure.
The second approach assumes that patients may access medical care across larger areas, such that the heterogeneity in minority physician representation between smaller areas is unimportant. In other words, the second approach assumes that patients may access medical care around their home, around their place of employment, and anywhere in between. In this situation, the average level of minority physician representation across this larger area may be a more accurate measure. Someone living in an area where there are few physicians who are racially/ethnically concordant to them will often be able to access such physicians who are nearby but outside of the area around their home.
The fundamental issue in deciding which geographical measure to use is how convenient it is to access the medical resources that exist between patients' regular travel destinations. The level of convenience depends on the most common mode of transportation used in an area. If this is public transportation, then the convenience factor is low and assuming that most patients will access medical resources anywhere between their home and workplace is inappropriate. However, if private vehicles are the most common mode, then the convenience factor is high and the assumption that most patients will access medical resources anywhere between their home and workplace is warranted.
In a “car culture” such as California the convenience factor is high. In 2002, 92 percent of housing units had one or more vehicles available, 96 percent of employed individuals commuted to work (mean time: 27 minutes) with only 5.2 percent using public transportation (other than taxicabs) (U.S. Census Bureau 2002a
;). Thus, in California the average level of physician representation as measured across a larger area that likely includes most patients' home and workplace appears to be more meaningful.
The 53,606 physicians included in this analysis represent active patient-care physicians with known race/ethnicity (approximately 70 percent) and valid zip codes. We include physicians who are white, black, Hispanic, and Asian/PI.
We also model the departure and destination choices for 9,806 recently graduated California residents. These models exclude the variable measuring the number of years residing in one's current location. and report descriptive statistics.
Descriptive Statistics for Individuals
Descriptive Statistics for California Counties*