linear Regression with treatment and control variables

[Shahrzad Tarrahi]

Dear all,

I am interested to study the impact of monetary policy changes on the stock market return over the last 20 years.

the list of my variables for linear regression in an event study model is:

date	event date	DAX index	Conventional surprise pre-crisis	Expected change crisis	Expected change pre-crisis	Conventional surprise crisis	MSCI world index	crisis
1990/01/01	1	100						0
...	0	101						0
2020/12/30	0	102						1

1- "return of the DAX index" as my dependent variable;
2- "event dates or policy announcement dates" as the treatment variable which takes 1 when the event occurs in total 272 events;
3- "MSCI world index" and "crisis dummy" as The vector of control variables;
4- "Conventional surprise pre-crisis", "Expected change pre-crisis", Conventional surprise crisis", "Expected change crisis" as my independent variables.

my model:

return of the DAX index = constant + Conventional surprise pre-crisis + Expected change pre-crisis + Conventional surprise crisis + Expected change crisis + The vector of control variables+ residual

I was recommended to use "bacondecomp module" which shows a Bacon decomposition of difference-in-differences estimation with variation in treatment timing. The two-way fixed effects DD model is a weighted average of all possible two-group/two-period DD estimators. The command generates a scatterplot of 2x2 difference-in-difference estimates and their associated weights. The data must be xtset and the variable list must include an outcome as the first item, and a treatment that can only turn from zero to one during the time period examined as its second item.https://ideas.repec.org/c/boc/bocode/s458676.html

my question is that how can I use xtset data structure? because I don't have a factor variable that has different categories within the variable (like company1, comapy2, campany3, ...). my data is a time series for all of my variables and my dependent variable is just the return of the DAX index value (times series).

can someone please help me with this question?

thank you so much,
Shahrzad

[Justin Niakamal]

I've not heard of the Bacon decomposition, but from what you describe you might want to check out the community-contributed command eventdd (available from SSC). I would take a look at the authors' paper (linked below). Hope this helps.

Here's a silly illustration

clear all

set seed  `=$S_DATE'
set obs 50

gen id = _n
expand 10

bys id: gen year = 1990 + _n

gen y = runiform()
gen x = rbeta(10, 50)

// assign random treatment
gen randsort = runiform()

bys id (randsort): gen treat = (id <= 20 & _n == 1)
drop randsort
bys id (year): replace treat = 1 if treat[_n-1] == 1


replace y = cond(treat == 1, y * rnormal(4,.5), -y*rnormal(-1,1))
egen minyr = min(year) if treat == 1, by(id)
egen min = min(minyr), by(id)

gen t_to_treat = year - min

xtset id year
eventdd y x i.year, fe  timevar(t_to_treat)

Fixed-effects (within) regression               Number of obs      =       500
Group variable: id                              Number of groups   =        50

R-sq:  within  = 0.2500                         Obs per group: min =        10
       between = 0.6648                                        avg =      10.0
       overall = 0.3305                                        max =        10

                                                F(28,422)          =      5.02
corr(u_i, Xb)  = -0.2582                        Prob > F           =    0.0000

------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |  -.2564275   .8144306    -0.31   0.753    -1.857273    1.344418
             |
        year |
       1992  |   .0248702   .1630892     0.15   0.879    -.2956982    .3454386
       1993  |   .1477839   .1636536     0.90   0.367     -.173894    .4694617
       1994  |   .0473551   .1656703     0.29   0.775    -.2782866    .3729968
       1995  |   .2069887   .1666498     1.24   0.215    -.1205783    .5345557
       1996  |   .0506037   .1694123     0.30   0.765    -.2823934    .3836008
       1997  |   .0653017   .1716657     0.38   0.704    -.2721246     .402728
       1998  |  -.0371115   .1747161    -0.21   0.832    -.3805337    .3063107
       1999  |   .0939524   .1785348     0.53   0.599    -.2569758    .4448806
       2000  |  -.0622933   .1828802    -0.34   0.734    -.4217627    .2971762
             |
        lag9 |     .56447   .4433836     1.27   0.204    -.3070454    1.435985
        lag8 |   .4451548   .3822415     1.16   0.245    -.3061796    1.196489
        lag7 |  -.2394218   .3442743    -0.70   0.487    -.9161278    .4372842
        lag6 |   .1707841   .3291596     0.52   0.604    -.4762125    .8177807
        lag5 |  -.1010052   .2958485    -0.34   0.733    -.6825254    .4805149
        lag4 |  -.2808844   .2872971    -0.98   0.329    -.8455961    .2838272
        lag3 |  -.1426302   .2724303    -0.52   0.601    -.6781196    .3928591
        lag2 |  -.1027444   .2624225    -0.39   0.696    -.6185626    .4130737
       lead0 |   1.230649   .2552361     4.82   0.000     .7289569    1.732342
       lead1 |   1.186767    .277603     4.28   0.000     .6411105    1.732424
       lead2 |   1.293186   .2947188     4.39   0.000     .7138859    1.872485
       lead3 |   1.974063   .3131578     6.30   0.000      1.35852    2.589607
       lead4 |   2.047017   .3293661     6.22   0.000     1.399614    2.694419
       lead5 |   1.544327   .3767436     4.10   0.000     .8037997    2.284855
       lead6 |   1.432389   .4037212     3.55   0.000     .6388342    2.225944
       lead7 |   2.304363   .4783542     4.82   0.000     1.364109    3.244617
       lead8 |   1.342242   .6418521     2.09   0.037     .0806167    2.603867
       lead9 |    1.33457   .8797769     1.52   0.130    -.3947211     3.06386
       _cons |   .5014116   .1922258     2.61   0.009     .1235722     .879251
-------------+----------------------------------------------------------------
     sigma_u |  .26451997
     sigma_e |  .78345647
         rho |  .10233019   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(49, 422) = 1.02                     Prob > F = 0.4380

Clarke, Damian and Schythe, Kathya, Implementing the Panel Event Study. IZA Discussion Paper No. 13524, Available at SSRN: https://ssrn.com/abstract=3660271

http://ftp.iza.org/dp13524.pdf

[Shahrzad Tarrahi]

Hi @Justin Blasongame,

I have checked your recommended command eventdd, my problem is that this command also is designed for panel data, and my data structure is time series. I have only DAX index and not different companies. so I don't know how can I use
xtset id year command. any idea how can I solve this issue? many thanks!

[Justin Niakamal]

Hi Shahrzad,

If you have time-series data, then you can use regress. From the paper linked above;

This command [eventdd] can flexibly interact with both in-built Stata commands such as regress and xtreg, as well as the user-written regression command reghdfe"

And from the help file

ols Requests that the event study model should be estimated with Stata's regress command. This is the default.

Hope this helps.