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In economic research, participating in a training program will have different impacts on different income groups. How do we measure this heterogeneity? (This is just a simple binary policy variable, and we will talk about multi-value policy effects later.) Of course, we will think of quantile regression, because traditional mean regression is a special case of quantile regression.
So if we participate in a training program is endogenous or self-selective, because high-income groups are sometimes more likely to participate in a training program, then this type of heckman-type self-selection problem appears. Of course, we will think of using instrumental variable quantile regression to find an instrumental variable for this endogenous policy dummy variable. You can use ivqreg
But there is a problem that our traditional quantile regression is actually conditional expectation regression, which means that we need to explain our coefficients based on the condition of the covariate in the model. Once we change the covariate, such as increase or decrease a covariate, then our interpretation of the coefficients of the regression equation needs to change. Although many people use conditional quantiles for regression in empirical studies, the explanation is still explained by the set of unconditional expectations.
Understand the truth of this slide:
Take a look at Table 3 below. The above is the policy effect estimated by conditional IVQR, while the following is the policy effect estimated by GQR. Is there a big difference?
Many friends in the circle have asked, if my policy variable is more than one, for example, the training program is a policy variable, then unemployment insurance is also a policy variable, and the two policy variables affect a person’s income at the same time, how should I go about it? How about evaluating the effects of these policies? Or my policy variable is not a binary dummy variable. It may be an ordered variable or simply a continuous variable. What should I do?
These problems need to be solved in causal inference or policy evaluation. The generalized quantile regression that will be introduced below is to propose a generalized solution to the above problems. It is an unconditional expectation regression, which means that no matter how much your covariate increases, what I get is still an unconditional policy treatment effect. It can also deal with situations where your policy variables are ordered or continuous, and it can also deal with situations where your policy variables are multiple. After all, this is a generalized quantile regression, and it can also handle panel quantile regression. Generalized quantile regression simply doesn't care about whether you treat covariates as policy variables or policy variables as covariates.
看看这个论文的解释：genqreg can be used to fit the generalized quantile regression estimator developed in Powell (2016). The generalized quantile estimator addresses a fundamental problem posed by traditional quantile estimators: inclusion of additional covariates alters the interpretation of the estimated coefficient on the treatment variable.
As detailed in Powell (2016), the generalized quantile estimator implemented by genqreg addresses this problem and produces unconditional quantile treatment effects even in the presence of additional control variables. A special case of generalized quantile regression is quantile regression with panel data (see Powell (2015)); quantile regression with panel data can also be estimated using genqreg.
Numerical optimization proceeds via a Nelder-Mead algorithm. As estimation and calculation of standard errors can sometimes pose numerical challenges, the user can estimate generalized quantile regressions using Markov Chain Monte Carlo methods or grid-search methods.
Let's execute this command to see what the result looks like.
**Install this command
ssc install genqreg //If this method does not work, then use this link: https://ideas.repec.org/c/boc/bocode/s458158.html
**get data
use "http://fmwww.bc.edu/repec/bocode/j/jtpa.dta"
keep if sex==1 // gender male
**Mainly depends on whether participating in the training program has caused different income effects for people in different areas
qreg earnings training hsorged black hispanic married wkless13 class_tr ojt_jsa ///
age2225 age2629 age3035 age3644 age4554 f2sms, q(85) vce(robust) //Regression of the 85th quantile
**Solved using MCMC optimization method
genqreg earnings training hsorged black hispanic married wkless13 class_tr ojt_jsa ///
age2225 age2629 age3035 age3644 age4554 f2sms, q(85) optimize(mcmc) noisy draws(10000) burn(3000) arate(.5)
**The instrument variable assignment is used here to deal with the endogenous problem of training. Note that all covariates are also placed in the instrument, which is the same as the principle of ivregress
genqreg earnings training hsorged black hispanic married wkless13 class_tr ///
ojt_jsa age2225 age2629 age3035 age3644 age4554 f2sms, q(85)instruments(assignmt hsorged black ///
hispanic married wkless13 class_tr ojt_jsa age2225 age2629 age3035 age3644 age4554 f2sms)
Compare the results of conditional quantile regression and generalized quantile regression: 
you can read the following paragraphs, and then understand where the generalization of "generalized quantile regression" is embodied.
We introduce a new flexible framework for estimation of unconditional quantile treatment effects and a corresponding generalized quantile regression estimator. The estimator provides consistent estimates of quantile treatment effects, even in the presence of covariates, for one of more treatment variables, which may be discrete or continuous. These properties distinguish the estimator from alternatives found in the literature. Conditional quantile estimators require altering the structural quantile function to include additional covariates.
The GQR estimator allows one to condition on a separate set of covariates without altering the quantile function. Conditional quantile models assume that the relationship between the treatment variables and the outcome varies based only on unobserved factors and,consequently, the interpretation of the parameters changes as some of these factors become observed (i.e., covariates are added to the quantile function). This paper’s model assumes
that the treatment effects vary based on a nonseparable term which is a function of both observed and unobserved factors. Similar to mean regression, adding covariates when using GQR does not drastically alter the interpretation of the estimates (beyond their effect on
the plausibility of the identification assumptions).
Typically, researchers include control variables for the purposes of identification and do not necessarily want the interpretation of the estimates to change. In fact, much empirical work interprets conditional QTEs as the impact of the treatment variables on the unconditional outcome distribution. GQR provides a straightforward method to estimate unconditional QTEs when the treatments or instruments are conditionally exogenous. QR and IVQR are special cases of the estimator introduced in this paper. Furthermore, distri-
bution regression can also be nested in the framework.
Simulation results illustrate the usefulness of the GQR estimator given simple data generating processes with properties that likely resonate with applied researchers. I also apply the estimator to study the effect of temporary and direct-hire job placement on labor earnings. Given that the quantile function includes two endogenous variables, existing methods estimating unconditional QTEs for a single binary treatment are not applicable (or potentially difficult to apply). The literature has estimated conditional QTEs for this application, but the unconditional QTEs suggest that these understate the positive effects
of direct-hire placements on the lower part of the earnings distribution.
Many economic models imply heterogeneous effects of policies, motivating analysis which permits the treatment effects to vary throughout the outcome distribution. GQR provides an appropriate method to estimate quantile treatment effects and counterfactual distributions under different policies and should be useful broadly to estimate such heterogeneity.
The panel data quantile regression qregpd mainly solves the problems caused by the additive fixed effect. I will not introduce it in detail here. The do files and corresponding materials are placed in the measurement community and can be extracted and used.