[Clyde Schechter]

By the way what is your take on the first model (1) in the image that I have attached?
...
My real doubt is the interpretation of model (1) where only crisis dummy is involved without interaction term. How to interpret that crisis dummy? what does it exactly show?

Assuming that you created the PostGFC variable correctly, so that it is 1 during the crisis period and 0 before the crisis period, it represents a crude (i.e. unadjusted) estimate of the expected outcome difference in INCRS between the crisis period and the pre-crisis period. If your goal is simply to predict levels of INCRS in the two periods, this could be an adequate model. If, however, you are trying to understand underlying relationships and infer causality, a simple model like this is unlikely to be of much use.

is it that the interpretation of the variables involved in interaction term is two way, on one side it can be interpreted as you said the average impact of PostGFC on dependent variable conditional on X being zero, on the other side coefficient on X represents the average change in dependent variable during the non crisis period.

Yes. That's correct.

at least in my case it seems Counterintuitive given the the average value of INCRS (dependent variable) is already found significantly lower than Pre-GFC period from univariate analysis.

Two things. First you don't even describe, let alone show, your univariate analysis, I can't say anything about why the results differ from the results of your model (1) above. For that matter, since you didn't provide the code underlying model (1) and you provide only the coefficient table, not the output that precedes it, I cant tell if model (1) is a fixed-effects model or a random effects-model. So I do not have nearly enough information here to respond to this question.

[Minhaj uddin]

Thank you so much Sir for your help!

[Minhaj uddin]

Sorry to bother you again.

Two things. First you don't even describe, let alone show, your univariate analysis, I can't say anything about why the results differ from the results of your model (1) above. For that matter, since you didn't provide the code underlying model (1) and you provide only the coefficient table, not the output that precedes it, I cant tell if model (1) is a fixed-effects model or a random effects-model. So I do not have nearly enough information here to respond to this question.

My dataset comprises of 23 years (2000 to 2023). Where PreGFC(2000-2007) and Post GFC (2008-2017)

T-Test result

. . ttest INCRS2 , by( PeriodPre )

Two-sample t test with equal variances
------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. err.   Std. dev.   [95% conf. interval]
---------+--------------------------------------------------------------------
Post GFC |     715    .7270573     .005861    .1567206    .7155505    .7385642
  PreGFC |     599    .8059866    .0055794    .1365518    .7950291    .8169442
---------+--------------------------------------------------------------------
Combined |   1,314    .7630381    .0042195    .1529549    .7547603    .7713158
---------+--------------------------------------------------------------------
    diff |           -.0789293    .0081905               -.0949972   -.0628614
------------------------------------------------------------------------------
    diff = mean(Post GFC) - mean(PreGFC)                          t =  -9.6367
H0: diff = 0                                     Degrees of freedom =     1312

    Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
 Pr(T < t) = 0.0000         Pr(|T| > |t|) = 0.0000          Pr(T > t) = 1.0000

Tobit regression

 xttobit INCRS c.LerTA ROA ZROA CAR Liquidity2 LLPTL LnTA BSD GDP  Inflation SMD
>  PostGFC, ll(0) ul(1), if Year >= 2000 & Year <= 2017

result

Random-effects tobit regression                     Number of obs     =  1,314
                                                           Uncensored =  1,159
Limits: Lower = 0                                       Left-censored =      0
        Upper = 1                                      Right-censored =    155

Group variable: Id                                  Number of groups  =     97
Random effects u_i ~ Gaussian                       Obs per group:
                                                                  min =      1
                                                                  avg =   13.5
                                                                  max =     18

Integration method: mvaghermite                     Integration pts.  =     12

                                                    Wald chi2(12)     = 322.50
Log likelihood = 622.94966                          Prob > chi2       = 0.0000

------------------------------------------------------------------------------
       INCRS | Coefficient  Std. err.      z    P>|z|     [95% conf. interval]
-------------+----------------------------------------------------------------
       LerTA |   .2529081   .0577455     4.38   0.000      .139729    .3660872
         ROA |   .0018053   .0048957     0.37   0.712    -.0077901    .0114006
        ZROA |  -.0003107   .0004996    -0.62   0.534    -.0012899    .0006684
         CAR |   .0010183   .0007149     1.42   0.154     -.000383    .0024195
  Liquidity2 |    .224931   .0449305     5.01   0.000     .1368688    .3129931
       LLPTL |  -.7458961   .1964408    -3.80   0.000    -1.130913   -.3608791
        LnTA |   .0167606   .0057552     2.91   0.004     .0054806    .0280406
         BSD |  -.0088806   .0013769    -6.45   0.000    -.0115792   -.0061819
         GDP |  -2.42e-06   .0019548    -0.00   0.999    -.0038337    .0038289
   Inflation |  -.0038793   .0019441    -2.00   0.046    -.0076896    -.000069
         SMD |   .0008163   .0001883     4.33   0.000     .0004472    .0011854
     PostGFC |   .0544165   .0213271     2.55   0.011     .0126162    .0962168
       _cons |   .7410358   .0618454    11.98   0.000     .6198211    .8622506
-------------+----------------------------------------------------------------
    /sigma_u |   .1178614   .0102485    11.50   0.000     .0977747    .1379481
    /sigma_e |   .1141379   .0025068    45.53   0.000     .1092246    .1190511
-------------+----------------------------------------------------------------
         rho |   .5160457   .0449227                       .428322    .6029964
------------------------------------------------------------------------------
LR test of sigma_u=0: chibar2(01) = 481.50             Prob >= chibar2 = 0.000

Fixed effect

xtreg INCRS c.LerTA ROA ZROA CAR Liquidity2 LLPTL LnTA BSD GDP  Inflation SMD P
> ostGFC, fe, if Year >= 2000 & Year <= 2017

result

Fixed-effects (within) regression               Number of obs     =      1,314
Group variable: Id                              Number of groups  =         97

R-squared:                                      Obs per group:
     Within  = 0.2184                                         min =          1
     Between = 0.0842                                         avg =       13.5
     Overall = 0.1280                                         max =         18

                                                F(12,1205)        =      28.06
corr(u_i, Xb) = -0.1191                         Prob > F          =     0.0000

------------------------------------------------------------------------------
       INCRS | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
       LerTA |   .1522858   .0527476     2.89   0.004     .0487985    .2557731
         ROA |   .0047561   .0043955     1.08   0.279    -.0038676    .0133798
        ZROA |   .0003586   .0006448     0.56   0.578    -.0009064    .0016237
         CAR |  -.0002333   .0007724    -0.30   0.763    -.0017486    .0012821
  Liquidity2 |   .2070648   .0399529     5.18   0.000     .1286799    .2854498
       LLPTL |  -.6864723   .1813459    -3.79   0.000    -1.042261   -.3306835
        LnTA |   .0208361   .0076716     2.72   0.007     .0057849    .0358874
         BSD |  -.0088198   .0013304    -6.63   0.000      -.01143   -.0062097
         GDP |   -.000699   .0017767    -0.39   0.694    -.0041848    .0027869
   Inflation |  -.0031791   .0018066    -1.76   0.079    -.0067236    .0003654
         SMD |   .0008217   .0001717     4.79   0.000     .0004849    .0011586
     PostGFC |   .0469299   .0192593     2.44   0.015     .0091444    .0847155
       _cons |   .7326681    .067125    10.91   0.000     .6009733    .8643628
-------------+----------------------------------------------------------------
     sigma_u |  .11422678
     sigma_e |   .1049394
         rho |      .5423   (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(96, 1205) = 10.13                   Prob > F = 0.0000

.

In both regression I have restricted the Year to 2017 so that non-crisis period only comprise the Pre GFC years, to make the result comparable with above t-test period. I have run both tobit and fixed effect based on literature.

Now how to justify the positive and significant PostGFC coefficient in both model, when the above t test shows significant decline in dependent variable PostGFC.

[Clyde Schechter]

OK. So the ttest was done in a way that it is comparable to a non-interaction regression: the order of the categories is the same, and the estimation sample appears to be the same.

So, first there is everything that was said in #12. Some, perhaps all, of the other variables in the regression are related both to INCRS and themselves differ between the pre- and post-crisis periods. They are confounders of the crisis:INCRS relationship. Including them in the model resolves the confounding (aka omitted variable bias) inherent in the crude estimate provided by the ttest. The only concern is whether some of them are variables that should be excluded because they are mediators or colliders of the crisis:INCRS relationship. Identifying such excludable variables requires knowing what they are and how they are related (specifically, what the causal directionality of the relationship is) to crisis and INCRS.

There is an additional issue here. The t-test ignores the fact that many of the observations in the estimation sample are repeated observations on the same Id. It cannot distinguish pre-post crisis differences that arise from changes within the same ID from differences that reflect the different firms that are represented in each year's data. (The data is clearly unbalanced, so some Id's may be sampled more frequently in one period than in the other, and more frequently than other Id's in the same period.) By contrast, -xtreg, fe- estimates purely within-ID changes. These can very well be different. In another context where it is clearer: there are many differences in attributes between married and unmarried people, but not all of those things change when one gets married. -xtreg, fe- captures only those changes associated with "getting married," not those that simply differ between those that "are or are not married." So the difference being estimated by the t-test is a different thing from what is being estimated by -xtreg, fe-. However, I would not attach too much importance to this difference in your particular situation. I say that because -xttobit- is a random effects estimator, so that the difference it is estimating is similar to the one being estimated by the t-test, yet it produced results very similar to those of -xtreg, fe-. So my conclusion is that in this case, the two estimands (what -xttobit- is estimating as the difference vs what -xtreg, fe- is estimating as the difference) are probably not all that different. (Unless the censoring of INCRS at 1 in -xttobit- accounts for this--but that seems unlikely.) Rather the major distinction between the t-test and -xtreg, fe- results is the reduction omitted variable bias (confounding) in -xtreg, fe-.

Again, it is possible that some of these additional variables should properly be excluded, but figuring out which ones, if any, requires substantive knowledge that I don't have and can't help you with. From the variable names, I cannot identify what the variables actually are--at best, I can guess at a few of them. But even if I knew what they are, I have no expertise in finance or economics and would not be able to diagram the causal relationships among them. So you will need to resolve this aspect yourself or in consultation with somebody who works in your field and understands these things.

In summary, I see no errors in your statistical analyses or coding. That the different analyses produce markedly different results is unsurprising and does not indicate anything done wrong. It is largely or entirely explained by omitted variable bias in the t-test analysis, a common phenomenon in observational studies (and occasionally present even in experimental studies). You should consult someone with expertise in your field to consider whether the selection of which variables to include in the regression models was appropriate from a substantive perspective.

[Minhaj uddin]

Thank you so much, sir! That is some help!

By the way, all variables were selected using the previous studies as a reference.

[Clyde Schechter]

By the way, all variables were selected using the previous studies as a reference.

Well, while that is encouraging, it is not unheard of that a study gets published that contains an important error, and then subsequent studies copy that error.