The QUANTSELECT Procedure

This example shows how you can use the QUANTREG procedure to further analyze the final selected models from the QUANTSELECT procedure, and how you can find the set of observations for a specified range of conditional quantile levels. The data under investigation contain economic growth rate records for countries during two time periods: 1965–1975 and 1975–1985. This data set comes from a study by Barro and Lee (1994) and is also analyzed in the section Quantile Regression for Econometric Growth Data of Chapter 83: The QUANTREG Procedure.

The data set contains 161 observations and 16 variables. The variables, which are listed in Table 84.17, include the national GDP growth rates (GDPR), 14 covariates, and a name variable (Country) that identifies the countries in one of the two periods.

The goal is to compare the effect of the covariates on GDPR at different quantile levels. The following statements perform effect selection at three quantile levels (): 0.1, 0.5, and 0.9.

data growth;
   length Country$ 22;
   input Country GDPR lgdp2 mse2 fse2 fhe2 mhe2 lexp2 lintr2 gedy2
         Iy2 gcony2 lblakp2 pol2 ttrad2 @@;
   if(index(country,'75')) then period='65-75'; 
   if(index(country,'85')) then period='75-85'; 
   datalines; 
Algeria75              .0415 7.330 .1320 .0670 .0050 .0220 3.880 .1138 .0382
                       .1898 .0601 .3823 .0833 .1001
Algeria85              .0244 7.745 .2760 .0740 .0070 .0370 3.978 -.107 .0437
                       .3057 .0850 .9386 .0000 .0657
Argentina75            .0187 8.220 .7850 .6200 .0740 .1660 4.181 .4060 .0221
                       .1505 .0596 .1924 .3575 -.011
Argentina85            -.014 8.407 .9360 .9020 .1320 .2030 4.211 .1914 .0243

   ... more lines ...   

                       .0654 .1224 .9393 .7022 -.007
Zambia75               .0120 6.989 .3760 .1190 .0130 .0420 3.757 .4388 .0339
                       .3688 .2513 .3945 .0000 -.032
Zambia85               -.046 7.109 .4200 .2740 .0110 .0270 3.854 .8812 .0477
                       .1632 .2637 .6467 .0000 -.033
Zimbabwe75             .0320 6.860 .1450 .0170 .0080 .0450 3.833 .7156 .0337
                       .2276 .0246 .1997 .0000 -.040
Zimbabwe85             -.011 7.180 .2200 .0650 .0060 .0400 3.944 .9296 .0520
                       .1559 .0518 .7862 .7161 -.024
;

proc quantselect data=growth;
   class period;
   model GDPR = period lgdp2 mse2 fse2 fhe2 mhe2 lexp2
               lintr2 gedy2 Iy2 gcony2 lblakp2 pol2 ttrad2
               / quantile=0.1 0.5 0.9 selection=backward(choose=sbc sh=5);
run;

The SELECTION=BACKWARD option specifies the BACKWARD method as the effect selection method, and the CHOOSE=SBC option specifies the Schwarz Bayesian information criterion for choosing the final selected effects. The estimates for the final selected effects are shown in Output 84.2.1 for , Output 84.2.2 for , and Output 84.2.3 for .

Comparing the three quantile models, you can see that the final selected models for and have the same set of selected effects, but the final selected model for excludes the effects for time period and political instability. In other words, if a country’s annual change in per capita GDP represents the 90% quantile conditional on the explanatory effects, then its GDP growth rate seems consistent for both the 1965–1975 and 1975–1985 periods and resistant to political instability. In addition, if a country’s GDP growth rate represents the 50% or less quantile conditional on the explanatory effects, then the country’s 1975–1985 GDP growth rate seems lower than its 1965–1975 GDP growth rate, and the effect for political instability has a negative impact on its GDP growth rate.

To further investigate the impact of time period and political instability on GDP growth rate, you can use the QUANTREG procedure to test the final selected effects. In the previous statements, PROC QUANTSELECT creates a macro variable for the final selected model at each of the three quantile levels. For the current example, the macro variable _QRSINDT1 contains the final model at ; _QRSINDT2 contains the final model at ; and _QRSINDT3 contains the final model at . The following statements show how to use _QRSINDT2 to specify the model for the QUANTREG procedure at :

proc quantreg data=growth;
   class period;
   model GDPR =  &_qrsindt2 / quantile=0.5;
   Time_Period: test  period;
   Political_Instability: test  pol2;
run;

Output 84.2.4 shows more information for the final selected model at . Output 84.2.5 and Output 84.2.6 show the test results for the effects of time period and political instability on GDP growth rate. You can see that both time period and political instability are significant for the model.

As mentioned earlier, _QRSINDT1 and _QRSINDT2 are identical, and _QRSINDT3 excludes two effects from _QRSINDT2: time period and political instability. The following statements retest time period and political instability for the final selected model at :

proc quantreg data=growth;
   class period;
   model GDPR =  &_qrsindt2 / quantile=0.9;
   Time_Period:           test period;
   Political_Instability: test pol2;
   Period_and_Political:  test period pol2;
run;

Output 84.2.7, Output 84.2.8, and Output 84.2.9 show the test results for the effects of time period and political instability on GDP growth rate at . You can see that time period, political instability, and their combination are all insignificant for the model.

Another interesting question for quantile regression is to find the observations for a certain range of conditional quantile levels. For example, you might want to know which countries are winners in terms of conditional GDP growth rate at the level. The following statements compute the quantile predictions and then search, sort, and print the list of winner countries:

proc quantselect data=growth;
   class period;
   model GDPR = period lgdp2 mse2 fse2 fhe2 mhe2 lexp2
               lintr2 gedy2 Iy2 gcony2 lblakp2 pol2 ttrad2
               / quantile=0.9 selection=backward(choose=sbc sh=5);
   output out=growth90Out p=Pred;
run;

data growth90;
   set growth90Out;
   drop lgdp2  mse2  fse2  fhe2  mhe2 lexp2   lintr2 gedy2   Iy2
        gcony2 lblakp2  ttrad2;
   where  GDPR-Pred >= -1E-4;
   GdpDiff = GDPR-Pred;
run;

proc sort data=growth90;
   by GdpDiff;
run;
proc print data=growth90;
run;

Output 84.2.10 lists the countries whose conditional GDP growth rates are equal to or higher than their quantile predictions.