Time-varying fixed effects

[Chris White]

Dear all,

I am currently working on my master's thesis where I estimate a FE model which looks the following:

y_it = a_0 + a_i + x_it*beta1+ crisis*(d_0 + d_i + x_it*beta2) + epsilon_it,

where "crisis" is a dummy that has value one with the beginning of recent financial crisis in Europe. "a_i" and "d_i" are country-specific fixed effects and "x_it" explanatory variables. The model allows to investigate changing coefficients "beta1" to "beta1 + beta2" and "a_i" to "a_i + d_i" when the crisis occurs.

Currently I am struggeling with an argumentation whether to include country-specific fixed effects in the crisis interaction or not. This is done in a reference paper. However, results seem to be more economically meaningful when not including the "d_i"-dummies.

The economic argumentation would be - as I understand - that there are time-constant unobservables for each country that only change with the beginning of the crisis.
But are there other econometric argumentations to include these "d_i"? Is it somehow necessary because I use FE estimation? Or is there no econometric cause - only the economic theory described at the beginning of this paragraph? And would you agree on this argumentation or not?

I would very much appreciate some thoughts on this problem.
Thanks in advance!

Chris

[Carlo Lazzaro]

Chris:
whether that makes sense or not, also depend on the literature of your research field.
At a very first glance, the definition of time-varying fixed effects (-fe-) seems a bit weird.
As far as the -fe- machinery is concerned, your chances of getting helpful replies are conditional on posting what you typed and what Stata gave you back (as per FAQ). Thanks.

[Chris White]

Carlo: Thanks for your answer. I tried to simplify things but probably left out a bit too much. So here is what I did:

xtset country_id month_date
xtscc spread debt_cut debt_gdp_inp gdp_growth_inp ca_gdp_inp_diff bb_gdp_inp_diff vix_diff reg_spread c_debt_gdp_inp c_gdp_growth_inp c_ca_gdp_inp_diff c_bb_gdp_inp_diff c_vix_diff c_reg_spread b_debt_gdp_inp b_gdp_growth_inp b_ca_gdp_inp_diff b_bb_gdp_inp_diff b_vix_diff b_reg_spread crisis_const crisis_fe_1-crisis_fe_10 bailout_fe_1-bailout_fe_10, fe

where actually three time periods are sperated: Base period, crisis period, period after bailout. Variables beginning with "c_" are interactions with a dummy that is one during the crisis and 0 before and after. Those beginning with "b_" are interactions with a dummy that is one in after the Greek bailout. As done in the reference paper (http://www.diw.de/sixcms/detail.php?...01.c.458586.de) there are additional dummies for each of my 10 countries which turn one during "crisis" (crisis_fe_1-crisis_fe_10) or after "bailout" (bailout_fe_1-bailout_fe_10).

Now I tried the same model without crisis_fe_1-crisis_fe_10 and bailout_fe_1-bailout_fe_10

xtscc spread debt_cut debt_gdp_inp gdp_growth_inp ca_gdp_inp_diff bb_gdp_inp_diff vix_diff reg_spread c_debt_gdp_inp c_gdp_growth_inp c_ca_gdp_inp_diff c_bb_gdp_inp_diff c_vix_diff c_reg_spread b_debt_gdp_inp b_gdp_growth_inp b_ca_gdp_inp_diff b_bb_gdp_inp_diff b_vix_diff b_reg_spread crisis_const bailout_const, fe

which changed results considerably:

  Variable | First model   Second model  
-------------+--------------------------------
    debt_cut | -454.60651**     188.59683     
debt_gdp_inp |  .31332394***    4.2408348***  
gdp_growt~np | -.71873371**    -5.9179986***  
ca_g~np_diff |  .44093771      -.89014163     
bb_gdp_inp.. | -.04412465      -.45136812     
    vix_diff |  .00724692       .21574753     
  reg_spread |  .99578513***    .97141013***  
c_debt_gdp~p |  16.948769***    3.2142874***  
c_gdp_grow~p | -22.919073***   -18.459225***  
c_ca_gdp_i~f |  4.0689151       10.992675     
c_bb_gdp_i~f | -.62845011       2.3222966     
  c_vix_diff | -1.1397012       .55001938     
c_reg_spread | -.77377099***   -.25720694***  
b_debt_gdp~p | -32.108306***    3.2744592***  
b_gdp_grow~p | -65.637201***   -123.64531***  
b_ca_gdp_i~f | -2.2512266       52.774464     
b_bb_gdp_i~f | -1.9137455      -8.3867437     
  b_vix_diff |  2.9846339      -14.596178     
b_reg_spread | -1.5196194***   -.81553489***  
crisis_const |          0      -293.25226***  
 crisis_fe_1 | -1528.6332***                  
 crisis_fe_2 | -1153.7811***                  
 crisis_fe_3 |  -1779.677***                  
 crisis_fe_4 |  -732.1259***                  
 crisis_fe_5 | -1216.1677***                  
 crisis_fe_6 | -1732.0976***                  
 crisis_fe_7 | -869.42925***                  
 crisis_fe_8 | -1168.1955***                  
 crisis_fe_9 | -618.15045***                  
crisis_fe_10 |   -890.754***                  
bailout_fe_1 |  3917.3676***                  
bailout_fe_2 |  2940.6312***                  
bailout_fe_3 |   6508.014***                  
bailout_fe_4 |  3312.1409***                  
bailout_fe_5 |  3394.6581***                  
bailout_fe_6 |  4540.1618***                  
bailout_fe_7 |  2493.0841***                  
bailout_fe_8 |  4836.3072***                  
bailout_fe_9 |   2022.627***                  
bailout_f~10 |   4607.859***                  
bailout_co~t |                 -279.75538     
       _cons | -18.671977***   -255.23716***  
-------------+--------------------------------
           N |       1545            1545     
----------------------------------------------

Most importantly, debt seemed to have a negative effect on spreads after the bailout in the first model which is very contradictive to intuition. In the second model this effect turned to the - more meaningful - opposite.

I would appreciate help with two things:
1) Which model would you prefer for econometric reasons?
2) What could be the reason that results differ so much?

As far as I see the literature on my research field tends to use the second model version without those country-time-dummies.

Best,

Chris

[Carlo Lazzaro]

Chris:
I would go with the second model, quoting the previous research experiences that follows the same approach.
It's difficult to say (for me, at least) at first glance why those results differ that much.

[Chris White]

Carlo: Thank you for your opinion!

I was now wondering whether there is an econometric rational which argues against using these country_crisis dummies? My idea isthat the FE-model needs variation of the variables over time and that the estimation of these dummies is only based on the point in time where they switch from 0 to 1 which would be a quite small empirical basis. Would that argumentation hold or is it nonsense? (Sorry for maybe asking stupid questions. Its my first time doing econometric research.)

Best regards, Christoph

[Carlo Lazzaro]

Chris:
this sounds more as practical than a theorethical problem. The fixed effect machinery works as you described.
The second model is more parsimonious (i.e. clearer to get vs the first one): that's why I would prefer it.
You can take a look at what happens when country_crisis dummies (please, see -fvvarlist- if you're intended to follow that road) are added as predictors in yuou second model, but I would not take for granted that they could turn out meaningful (in either statistical or practical sense).