How to justify the use of country fixed effects?

[Silvia Haertl]

Dear Statalist,

I am currently doing a fixed-effects panel regression and try to study the effects of private credit booms before the occurence of a financial crisis on the economic recovery after the crisis.

I have a panel-dataset covering 17 developed economies (Japan, US, Germany , ...). The dataset holds macroeconomic aggregates like gdp, interest rates, public debt, ... for the 17 countries for the years 1870 - 2016.
For me, it makes sense to include country fixed effects. But how could I justify the use of fixed effects reasonably?

I used the following command:

foreach v in `irvars5' {
    forvalues i =1/5 {
    
    //LHS-VARIABLES are lrgdp lriy lcpi rprv rpub
    //RHS-VARIABLES are constant of normal recessions (pk_norm), constant of
    //                financial recessions (pk_fin), beta*(excess_private) for
    //                normal or financial crises,
    //                history of l-lags (`rhs8a'), country fixed effects (d1-d17)
    
    qui reg `v'`i' pk_norm pk_fin excess_prv `rhs8a' d1-d17  ///
        if (pk_fin==1|pk_norm==1) , noconstant vce(cluster iso)
       }
     }

pk_fin corresponds to a financial crisis
pk_norm corresponds to a non-financial crisis
d1-d17 would be my country fixed effects

Is there any possible stata-command to show in numbers, that country fixed effects are reasonable?

Thank you very much in advance

[Carlo Lazzaro]

Silvia:
usually, this kind of justifications are based on previous literature.

[Silvia Haertl]

My work consists on the Paper of Jordà, Schularick and Taylor (2016) - Sovereigns vs. Banks: Credit Crisis and Consequences which is available under
https://academic.oup.com/jeea/articl...4/1/45/2319810

In their empirical part, they used contry fixed effects, but didn´t justify why or for what reason. I would like to do this, but I don´t know how

[Carlo Lazzaro]

Silvia:
I would simply quote in my paper the previous research experience you mention.

[Maarten Buis]

Notice that these fixed effects control for characteristics of countries that remain constant over time. How many characteristics do you think remain constant over the period 1870 - 2017? Your justification should include some thoughts on that.

[Phil Bromiley]

If you xtset your data and use xtreg, fe, it will provide a test whether the country effects are zero. It is also likely that you'll want clustered standard errors. However, this doesn't answer the substantive issues raised by Maarten and Carlo.

[Silvia Haertl]

Thank you a lot for your really good hints!

Phil:
I tried your approach also, because I wanted to see whether the country fixed effects are all zero.
Unfortunately, something is wrong with my model.

I used the follwing command for estimating my model:

//define the RHS 8 variables (see Jordá et. al. (2016) p. 64)
//including the lags
local rhs8a ///
dlrgdp   drprv  dlcpi  dlriy  drpub  stir  ltrate  cay ///
ldlrgdp ldrprv ldlcpi ldlriy ldrpub lstir lltrate lcay

//define the LHS 5 variables
local irvars5 lrgdp lriy lcpi rprv rpub

********country dummies***********

forvalues n=1/17 {
    gen d`n' = .
    replace d`n' = 1 if ccode == `n'
    replace d`n' = 0 if ccode != `n'
    }
//generates d1, d2, d3, d4, .... , d17

sort ccode year
xtset ccode year, yearly

foreach v in `irvars5' {
    forvalues i =1/5 {
xtreg `v'`i' pk_norm pk_fin excess_prv `rhs8a' d1-d17 ///
        if core==1 & (pk_fin==1|pk_norm==1) ,fe vce(cluster iso)
}
}

That means, I applied a loop, where I have 5 variables on the Left hand side (these are my endogenous variables) and pk_norm (if there is a "non-financial" crisis), pk_fin (financial crisis), excess_prv (growth of private credit before a crisis), the rhs8a-variables as explanatory variables. And d1-d17 are the country fixed effects.

Unfortunately, my regression output looks as following (for log-real-GDP in the first year):

Fixed-effects (within) regression               Number of obs      =       186
Group variable: ccode                           Number of groups   =        17

R-sq:  within  = 0.1951                         Obs per group: min =         5
       between = 0.0958                                        avg =      10.9
       overall = 0.1851                                        max =        20

                                                F(16,16)           =         .
corr(u_i, Xb)  = -0.0835                        Prob > F           =         .

                                   (Std. Err. adjusted for 17 clusters in iso)
------------------------------------------------------------------------------
             |               Robust
      lrgdp1 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     pk_norm |          0  (omitted)
      pk_fin |  -1.406748   .5936671    -2.37   0.031    -2.665266   -.1482306
  excess_prv |  -.0399314   .0746259    -0.54   0.600    -.1981313    .1182685
      dlrgdp |   -.075714   .0768012    -0.99   0.339    -.2385254    .0870973
       drprv |  -.0245351   .0295432    -0.83   0.418     -.087164    .0380938
       dlcpi |  -.1284554   .0372229    -3.45   0.003    -.2073645   -.0495463
       dlriy |  -.0268816   .0170058    -1.58   0.134    -.0629324    .0091691
       drpub |   .0005939   .0126089     0.05   0.963    -.0261358    .0273235
        stir |  -.0004711   .0013967    -0.34   0.740    -.0034319    .0024897
      ltrate |    .001843   .0013438     1.37   0.189    -.0010058    .0046918
         cay |  -.0624676   .0429448    -1.45   0.165    -.1535065    .0285712
     ldlrgdp |   .0297857    .123515     0.24   0.813    -.2320545    .2916259
      ldrprv |   .0700217   .0286394     2.44   0.026      .009309    .1307345
      ldlcpi |   .1536188   .0618848     2.48   0.025     .0224288    .2848089
      ldlriy |   -.001134   .0141155    -0.08   0.937    -.0310576    .0287897
      ldrpub |  -.0167395   .0171655    -0.98   0.344    -.0531288    .0196498
       lstir |  -.0021731   .0018505    -1.17   0.257    -.0060959    .0017497
     lltrate |   .0008915   .0018335     0.49   0.633    -.0029954    .0047784
        lcay |   .0243396   .0855943     0.28   0.780    -.1571122    .2057914
          d1 |          0  (omitted)
          d2 |          0  (omitted)
          d3 |          0  (omitted)
          d4 |          0  (omitted)
          d5 |          0  (omitted)
          d6 |          0  (omitted)
          d7 |          0  (omitted)
          d8 |          0  (omitted)
          d9 |          0  (omitted)
         d10 |          0  (omitted)
         d11 |          0  (omitted)
         d12 |          0  (omitted)
         d13 |          0  (omitted)
         d14 |          0  (omitted)
         d15 |          0  (omitted)
         d16 |          0  (omitted)
         d17 |          0  (omitted)
       _cons |  -1.755646   .4543258    -3.86   0.001    -2.718774   -.7925182
-------------+----------------------------------------------------------------
     sigma_u |   .7875395
     sigma_e |  2.1614709
         rho |  .11719538   (fraction of variance due to u_i)
------------------------------------------------------------------------------

So there are two questions:

I think, I just simply leave d1-d17 out of my regression?

And,

 F(16,16)

shows that there is obviously something wrong with my model. What does F(16,16) exactly mean? And why are the standard errors reported as dots? Where is my error?

I really can´t find it by myself, maybe someone can help

[Carlo Lazzaro]

Silvia:
- leave d1-d17 out of your regression;
- see -help j_robustsingular- for missing F test and related stuff.

[Silvia Haertl]

Thank you for your help, Carlo!
I left out d1-d17. The reason why there where no standard errors reported was the "vce(cluster iso)"option. Thanks for your hints!

allow me one follow up question:
i found the command "testparm", which is a joint test to see if the dummies for all years are zero
Is this command suitable only for time-fixed effects? Or can it also be applied to country-fixed effects?

Could I type for example:

testparm i.countrycode

?

[Carlo Lazzaro]

Silvia:
you can run

testparm i.countrycode

, too.

[Silvia Haertl]

Thank you very much Carlo!

[Justus Franz-Christoph Meyer]

Related to the point Maarten mentioned. I agree that its very difficult to find true fixed factors over time. But in case this has not been mentioned yet: What about factors such as geography or the climate. For most of your countries, the borders have rarely changed, for example. You could surely come up with a story why these factors shape particular financial institutions which in turn affect the developments in credit markets, or what do you think? Another reason could be culture if you capture or "deep determinants" these are not observable and arguably very slowly changing. You might capture these with country fixed effects.

For the presentation of your results, I suggest you show both including and excluding country-FE as common to show that results "survive". I apologize if this point is obvious. Same might be the case for time-fixed-effects.

Best J

[Silvia Haertl]

No that's a really good point Justus. Thank you!

I included the empirical results without country fixed-effects also in my work to show how the results are exluding CFE.