Real interest rate in panel regression

[Adam Klaas]

Hello everyone,

I have a question regarding the real interest rate which I want to include in my regression this is the data regarding the real interest rate:

* Example generated by -dataex-. For more info, type help dataex
clear
input float real_interest
     3.005
  .8583333
      1.59
     1.995
     2.795
 1.6741667
  2.680833
  2.686667
 1.7266667
  2.486667
 1.6916667
  .6891667
-.56583333
 -.5391667
      .455
 .09083333
    -.0075
    -.8775
-1.1233333
     -2.67
-1.6766667
     3.005
  .8583333
      1.59
     1.995
     2.795
 1.6741667
  2.680833
  2.686667
 1.7266667
  2.486667
 1.6916667
  .6891667
-.56583333
 -.5391667
      .455
 .09083333
    -.0075
    -.8775
-1.1233333
     -2.67
-1.6766667
     3.005
  .8583333
      1.59
     1.995
     2.795
 1.6741667
  2.680833
  2.686667
 1.7266667
  2.486667
 1.6916667
  .6891667
-.56583333
 -.5391667
      .455
 .09083333
    -.0075
    -.8775
-1.1233333
     -2.67
-1.6766667
     3.005
  .8583333
      1.59
     1.995
     2.795
 1.6741667
  2.680833
  2.686667
 1.7266667
  2.486667
 1.6916667
  .6891667
-.56583333
 -.5391667
      .455
 .09083333
    -.0075
    -.8775
-1.1233333
     -2.67
-1.6766667
     3.005
  .8583333
      1.59
     1.995
     2.795
 1.6741667
  2.680833
  2.686667
 1.7266667
  2.486667
 1.6916667
  .6891667
-.56583333
 -.5391667
      .455
 .09083333
end

Since I have a panel data of counties from 2000-2020, i was wondering what the best way is to include it in my regression? Because I thought it would make the regression problematic due to the negative rates that occurs in some years? I have included the real interest rate for each city for each year thats corresponding with the real interest rate in that year. The real interest rate is a national interest rate.
This is the regression result:

. xtreg log_realHP CPI_percentage Unemployment_rate real_interest logReal_income logenv i.low_dev i.Year,fe cluster(GM_code
> )
note: 2018.Year omitted because of collinearity
note: 2019.Year omitted because of collinearity

Fixed-effects (within) regression               Number of obs     =      2,532
Group variable: GM_code                         Number of groups  =        282

R-sq:                                           Obs per group:
     within  = 0.8890                                         min =          8
     between = 0.0001                                         avg =        9.0
     overall = 0.0520                                         max =          9

                                                F(12,281)         =    1004.22
corr(u_i, Xb)  = -0.2382                        Prob > F          =     0.0000

                                   (Std. Err. adjusted for 282 clusters in GM_code)
-----------------------------------------------------------------------------------
                  |               Robust
       log_realHP |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
   CPI_percentage |   .1478894   .0028882    51.21   0.000     .1422042    .1535746
Unemployment_rate |   .0319034   .0084486     3.78   0.000     .0152729     .048534
    real_interest |   .0555505   .0021625    25.69   0.000     .0512938    .0598073
   logReal_income |   .2497551   .1047908     2.38   0.018     .0434805    .4560297
           logenv |   .0001096   .0000378     2.90   0.004     .0000351    .0001841
        1.low_dev |    .010826   .0026449     4.09   0.000     .0056197    .0160324
                  |
             Year |
            2012  |  -.0178078   .0061264    -2.91   0.004    -.0298673   -.0057483
            2013  |  -.0895682   .0101582    -8.82   0.000     -.109564   -.0695724
            2014  |  -.0106152   .0067906    -1.56   0.119    -.0239821    .0027516
            2015  |   .0325508    .007373     4.41   0.000     .0180374    .0470641
            2016  |   .0814227   .0050252    16.20   0.000     .0715308    .0913146
            2017  |  -.0059734   .0028849    -2.07   0.039    -.0116522   -.0002947
            2018  |          0  (omitted)
            2019  |          0  (omitted)
                  |
            _cons |   9.073849   1.075941     8.43   0.000     6.955921    11.19178
------------------+----------------------------------------------------------------
          sigma_u |  .24154703
          sigma_e |  .02904954
              rho |  .98574266   (fraction of variance due to u_i)
-----------------------------------------------------------------------------------

In a paper I have used to do something similar as what they did in their study their coefficient for real interest rate is -0.03

[Carlo Lazzaro]

Adam:
if I'm correct, according to one of the many macoeconomic equations reported in my very old edition of

https://www.mheducation.com/highered/product/macroeconomics-dornbusch-fischer/M9781259290633.html:

real interest rate=(nominal interest rate-inflation rate)

Therefore, every time the inflation rate>nominal interest rate, the real interest rate<0.
Hence, your data are consistent with the macroeconomic theory: so, what's the issue?
As an aside, I would be careful in interpreting your coefficients, as you logged some of them only (along with the regressand).

ETA: the aforementioned equation is known as (Irving) Fisher's equation (https://en.wikipedia.org/wiki/Fisher_equation), whereas the macroeconomics textbook was coauthored by Stanley Fisher (https://en.wikipedia.org/wiki/Stanley_Fischer). The possible confusion between the two outstanding scholars was exploited by professors to reject students during Macroeconomics II final term.

[Adam Klaas]

Adam:
if I'm correct, according to one of the many macoeconomic equations reported in my very old edition of

https://www.mheducation.com/highered/product/macroeconomics-dornbusch-fischer/M9781259290633.html:

real interest rate=(nominal interest rate-inflation rate)

Therefore, every time the inflation rate>nominal interest rate, the real interest rate<0.
Hence, your data are consistent with the macroeconomic theory: so, what's the issue?
As an aside, I would be careful in interpreting your coefficients, as you logged some of them only (along with the regressand).

I thought it would wouldnt make sense to transform unemployment rate which is in percentages into log, but if you say its better to transform also those into log I will do that.
I have to add that the interest rate is cross sectional and ive used VLOOKUP in excel to give each city each year the corresponding interest rate, im not sure if thats the way to do it?

[Carlo Lazzaro]

Adam:
1) I did not mean to log any variable, but just to be careful in interpreting the coefficients. Do what is usual in your research field;
2) -bysort- is probably what you're looking for.