Univariate Diff-in-Diff test of medians

[Niel Smith]

I have a panel data set. The observations are conditionally sorted on two dimensions. I sorted observations into quartiles by variable A, and then conditionally sorted the observations into quartiles by variable B within the variable A quartiles, yielding 16 groups.

I calculated the mean and median of my Y variable for each group. Then I calculated the difference in means and medians between firms in the highest and lowest variable A quartiles (for each Variable B quartile). Now I want to test whether the differences in means and medians that I just calculated are significantly different in the highest and lowest variable B quartiles.

So essentially it is a univariate diff-in-diff test. I was able to do this for the means, but I can't figure out how to do it for the medians. Does anyone know?

[Carlo Lazzaro]

Niel:
welcome to the list.
A feasibe option for difference in medians is reported in the following toy-example:

. use "http://www.stata-press.com/data/r14/nlswork.dta", clear
(National Longitudinal Survey.  Young Women 14-26 years of age in 1968)

. ranksum age if idcode<=2, by(idcode)

Two-sample Wilcoxon rank-sum (Mann-Whitney) test

      idcode |      obs    rank sum    expected
-------------+---------------------------------
           1 |       12       142.5         150
           2 |       12       157.5         150
-------------+---------------------------------
    combined |       24         300         300

unadjusted variance      300.00
adjustment for ties       -1.43
                     ----------
adjusted variance        298.57

Ho: age(idcode==1) = age(idcode==2)
             z =  -0.434
    Prob > |z| =   0.6643

. return list

scalars:
                r(N_2) =  12
                r(N_1) =  12
              r(Var_a) =  298.5652173913043
                  r(z) =  -.434051896082475
            r(sum_exp) =  150
            r(sum_obs) =  142.5
             r(group1) =  1

. bootstrap r(z), reps(10000):ranksum age if idcode<=2, by(idcode) nodots
(running ranksum on estimation sample)
option nodots not allowed
an error occurred when bootstrap executed ranksum
r(198);

. bootstrap r(z), reps(10000)nodots:ranksum age if idcode<=2, by(idcode)

Warning:  Because ranksum is not an estimation command or does not set e(sample), bootstrap has no way to
          determine which observations are used in calculating the statistics and so assumes that all
          observations are used.  This means that no observations will be excluded from the resampling because
          of missing values or other reasons.

          If the assumption is not true, press Break, save the data, and drop the observations that are to be
          excluded.  Be sure that the dataset in memory contains only the relevant data.

Bootstrap results                               Number of obs     =         24
                                                Replications      =     10,000

      command:  ranksum age, by(idcode)
        _bs_1:  r(z)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |  -.4340519   .9981592    -0.43   0.664    -2.390408    1.522304
------------------------------------------------------------------------------

. estat bootstrap, all

Bootstrap results                               Number of obs     =         24
                                                Replications      =      10000

      command:  ranksum age, by(idcode)
        _bs_1:  r(z)

------------------------------------------------------------------------------
             |    Observed               Bootstrap
             |       Coef.       Bias    Std. Err.  [95% Conf. Interval]
-------------+----------------------------------------------------------------
       _bs_1 |   -.4340519   .0069415   .99815921   -2.390408   1.522304   (N)
             |                                      -2.343773    1.55339   (P)
             |                                      -2.320017   1.582628  (BC)
------------------------------------------------------------------------------
(N)    normal confidence interval
(P)    percentile confidence interval
(BC)   bias-corrected confidence interval

.