Changes in intercept term/constant from model to model

[Prathvajeeth Rajmohan]

hi there I am investigating the effect of FX derivative usage on lntobinsq (with control variables added) I

have 3 regressions: 2 pooled ols models (1 with industriy dummies) and one fixed effects regression:

pooled:

regress lntobinsq lnassets Derivatives10 bookleverage_w1 roa_w1  rnd_rev_w1 cash_to_totalassets_w1 div_yield_w1 year2016 if inlist(year,2015,2016), robust

Linear regression                               Number of obs     =        586
                                                F(8, 577)         =      64.62
                                                Prob > F          =     0.0000
                                                R-squared         =     0.6569
                                                Root MSE          =      .3282

----------------------------------------------------------------------------------------
                       |               Robust
             lntobinsq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
              lnassets |  -.0280999   .0091509    -3.07   0.002     -.046073   -.0101268
       Derivatives10 |   .0522034   .0310484     1.68   0.093    -.0087782     .113185
       bookleverage_w1 |   .1777102   .0570362     3.12   0.002     .0656864    .2897341
                roa_w1 |   .0831313   .0058784    14.14   0.000     .0715857     .094677
            rnd_rev_w1 |   .0157784   .0034542     4.57   0.000     .0089941    .0225627
cash_to_totalassets_w1 |   .2948839   .1538507     1.92   0.056    -.0072918    .5970596
          div_yield_w1 |  -.0586209   .0094744    -6.19   0.000    -.0772295   -.0400124
              year2016 |  -.0057626   .0266702    -0.22   0.829     -.058145    .0466198
                 _cons |    .267082   .0835158     3.20   0.001       .10305    .4311141
----------------------------------------------------------------------------------------

pooled #2 (ind2*) where we have industry dummies (ind2*) included but not shown here:

.  regress lntobinsq lnassets FXDerivatives10 bookleverage_w1 roa_w1  rnd_rev_w1 cash_to_totalassets_w1 div_yield_w1 year2016 ind2* if inlist(year,2015,2016), robust
note: ind240 omitted because of collinearity
note: ind247 omitted because of collinearity
note: ind249 omitted because of collinearity

Linear regression                               Number of obs     =        586
                                                F(55, 529)        =          .
                                                Prob > F          =          .
                                                R-squared         =     0.7518
                                                Root MSE          =     .29155

----------------------------------------------------------------------------------------
                       |               Robust
             lntobinsq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
              lnassets |  -.0150159   .0102229    -1.47   0.142    -.0350984    .0050665
       Derivatives10 |   .0020754   .0304516     0.07   0.946    -.0577454    .0618962
       bookleverage_w1 |   .0411962   .0605595     0.68   0.497    -.0777704    .1601628
                roa_w1 |   .0743793   .0069553    10.69   0.000     .0607158    .0880428
            rnd_rev_w1 |   .0079455   .0030852     2.58   0.010     .0018847    .0140062
cash_to_totalassets_w1 |   .2033755    .179466     1.13   0.258    -.1491781    .5559291
          div_yield_w1 |   -.051623    .008881    -5.81   0.000    -.0690694   -.0341765
              year2016 |  -.0131488   .0236852    -0.56   0.579    -.0596774    .0333798
                   _cons |   .5296384   .0540485     9.80   0.000     .4234624    .6358144

Fixed effects model

.  xtreg lntobinsq lnassets FXDerivatives10 bookleverage_w1 roa_w1  rnd_rev_w1 cash_to_totalassets_w1 div_yield_w1 year2016 if inlist(year,2015,2016), fe robust

Fixed-effects (within) regression               Number of obs     =        586
Group variable: firmid                          Number of groups  =        306

R-sq:                                           Obs per group:
     within  = 0.3443                                         min =          1
     between = 0.1362                                         avg =        1.9
     overall = 0.1489                                         max =          2

                                                F(8,305)          =      12.98
corr(u_i, Xb)  = -0.7578                        Prob > F          =     0.0000

                                         (Std. Err. adjusted for 306 clusters in firmid)
----------------------------------------------------------------------------------------
                       |               Robust
             lntobinsq |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
              lnassets |  -.4679803   .0687184    -6.81   0.000    -.6032024   -.3327582
       Derivatives10 |   .0544599   .0836445     0.65   0.515    -.1101334    .2190531
       bookleverage_w1 |   .2358255   .1360899     1.73   0.084    -.0319684    .5036195
                roa_w1 |   .0136564   .0069675     1.96   0.051    -.0000541    .0273669
            rnd_rev_w1 |  -.0147865   .0134586    -1.10   0.273      -.04127     .011697
cash_to_totalassets_w1 |  -.1290604   .3411373    -0.38   0.705    -.8003409    .5422201
          div_yield_w1 |  -.0390374   .0083692    -4.66   0.000    -.0555062   -.0225687
              year2016 |   .0248787   .0141368     1.76   0.079    -.0029393    .0526967
                 _cons |    3.83923   .4928974     7.79   0.000      2.86932     4.80914
-----------------------+----------------------------------------------------------------
               sigma_u |   .7890989
               sigma_e |  .12121952
                   rho |  .97694566   (fraction of variance due to u_i)
----------------------------------------------------------------------------------------

My question is: is there any cause for concern that the constant term jumps from 0.2-0.5 in the ols regression to 3.8 in the Fixed effects model?

- or is this completely normal/should'nt be stressed about?

Thanks

[Clyde Schechter]

It's completely normal. Two things: when you change a model by adding or removing any variable or fixed effect, everything can change, and can change radically. So there is never any reason to expect any two different models to produce the same or similar results for any particular thing. The second point is that the constant term in a regression model is seldom of any interest, unless you are using the model specifically for prediction. Most people, I think don't even look at the constant term in the output and wouldn't have even noticed this.

And a third thing: the constant term in a fixed effects model is nothing but an artifact of the way the model is parameterized. Think of it this way: if instead of using the -xtreg, fe- apparatus, you emulated a fixed-effects regression by including i.firmid indicator (dummy) variables. There is an exact colinear relationship among the firm indicators and the constant term, so something would have to be dropped. Depending on which firm indicator you dropped, you would get a different value for the constant term. So in a fixed effects regression, a change in the constant term means even less than it would in an OLS model.

[Prathvajeeth Rajmohan]

IThe second point is that the constant term in a regression model is seldom of any interest, unless you are using the model specifically for prediction. Most people, I think don't even look at the constant term in the output and wouldn't have even noticed this.

.

Hi clyde again thanks so so much, really can't describe how helpful you have been in all these threads.

- what do you mean by "unless you are using the model specifically for prediction" if you don't mind me asking?

-So I presume the magnitude changes of all the explanatory variables from model to the next is completely normal aswell, ie the Derivatives10 (which the variable of focus) changing from .0522034 in ols to .0020754 in the ols with industry dummies , its not out of the ordinary right?

there's no reason to expect this variable or any of the other explanatory variables to stay the same ie terms of sign significance and magnitude (most importantly) from model to model right?

Thanks so so much, eagerly waiting for you reply.

[Clyde Schechter]

there's no reason to expect this variable or any of the other explanatory variables to stay the same ie terms of sign significance and magnitude (most importantly) from model to model right?

That's correct.

what do you mean by "unless you are using the model specifically for prediction"

In most setting, people build these regression models to estimate the size of the effects of various predictors on an outcome, or to test hypotheses about the effects of predictors. In this situation, the constant term is just a nuisance parameter: it carries no information about the effects of any of the variables. I think that people, without perhaps even being consciously aware of it, tend to not even bother looking at the _cons row of the output.

But sometimes we build a regression model because we want to use it prospectively to predict the outcome in new entities based on the values of their predictors. In that case, the model's predicted values are calculated from all of the coefficients, including the constant term. So in this situation, the value of the constant term is as important as any of the coefficients for the purpose at hand.