Andrew M. Jones 60112.5.4 Applications of quantile regression and other
semiparametric methods
Quantile regression is of particular value when there is interest in the full condi-
tional distribution of an outcome rather than just the conditional expectation of
the variable. The method provides one way to allow for heterogeneity in treat-
ment effects over the range of the conditional distribution. It is a semiparametric
approach that avoids distributional assumptions about the error term. It also
has the attractive property of invariance to monotone transformations ofyand
therefore avoids the retransformation problem.
Kan and Tsai (2004) apply quantile regression to the conditional distribution of
BMI using data from the Cardiovascular Disease Risk Factors Two-Township Study
(CVDFACTS) for Taiwan. Quantile regression is well suited to an analysis of obesity
as interest focuses on the upper tail of the distribution of BMI rather than the area
around the mean. Other studies have tended to create an indicator variable for
obesity using the published clinical thresholds, but the quantile approach makes
better use of the available variation in BMI in the upper tail of the distribution.
Lee and Jones (2006) use the same dataset for Taiwan dentistry as Lee and
Jones (2004) to provide evidence on heterogeneity in dentists’ activity. The hetero-
geneity is of particular importance because dentists’ responses are likely to differ
widely from high- to low-activity dentists. Quantile regressions provide a useful
method to investigate the differential responses of dentists to various observable
variables. It is shown that time trends for dentists at higher quantiles have greater
fluctuations than those at lower quantiles. The clinic–hospital gap in activity at
higher quantiles is greater than at low quantiles. Clinic dentists at higher quantiles
have much higher numbers of visits and numbers of treatments than those at lower
quantiles, but they provide less intensity of care. Dentists in deprived areas have
higher activity than those in non-deprived areas, but only when they are located
at higher quantiles.
Winkelmann (2006) applies quantile regression to count data on doctor visits
in the GSOEP. This allows an evaluation of the impact of the 1997 reform of co-
payments for medicines on the full conditional distribution and not just the mean.
The quantiles of a count are integer valued and cannot be represented by a continu-
ous function of the covariates, such as exp(x′β), so Winkelmann (2006) adopts the
method proposed by Machado and Santos Silva (2005). This transforms the data
by “jittering”: adding a uniform random variable to the counts and then applying
quantile regression to the resulting continuous variable. The results show a greater
impact of the reform on the lower quantiles, which is consistent with the earlier
evidence from a hurdle model in Winkelmann (2004) that showed a larger effect
in the first part of the model.
Applications of other semiparametric regression methods are relatively sparse
in the health economics literature. Askildsenet al.(2003) use Kyriazidou’s (1997)
semiparametric estimator for a panel data sample selection model in order to esti-
mate nurses’ labor supply in Norway. This allows for individual effects in the
selection equation and the hours equation that may be correlated with each other