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I have a question regarding time fixed effects and their definition in empricial Papers.

Authors often talk about (1) estimating an OLS Regression and employing time and country fixed effects. What I don't understand that sometimes these same Authors in the same Paper do another regression and say they implement a (2) fixed effects model and include year fixed effects.

Can someone please explain to me what the difference between both specifications are? Is (1) just a linear regression using OLS and employing time dummy variables (by using the lm function in R), to exert the changes caught by the year. So in this case do they call the time dummy variables "fixed effects" or are they using a fixed effect model you would code in R using the plm package?

Here is an example to clarify what i mean: See Hibbeln (2020) Simple is Simply not Enough – Features versus Labels of Complex Financial Securities*: https://deliverypdf.ssrn.com/delivery.php?ID=668089000120105019080011005080098106020020059065037078000115088006104097006096109071022118037001014005040068007075003124112077052021093009085106072094127106109067069026001016083102112105027067085026119088074066127095086014078029071080118011106003021118&EXT=pdf&INDEX=TRUE

P. 14-15: we run the following pooled OLS regression (...) and other macroeconomic factors, we implement trading day fixed effects. Additionally, we control for unobservable differences in originator characteristics using originator fixed effects. With these fixed effects, we also control for country fixed effects.

P. 18: As we are interested in the within-tranche effect of receiving the STS labels, we implement a fixed effects model on tranche-level (Equation 2). By including tranche fixed effects λi, we control for all time-constant tranche-specific characteristics in general and for the security design features in particular.

If an author is talking about a linear regression (OLS) and then using fixed effects like mentioned above is he doing a fixed effects model or an OLS Regression with time dummies, but he's just calling those time dummies "fixed effects"?

Other authors use the term OLS Regression and time dummies, while some say OLS Regression and fixed effects, that's what makes it difficult for me to understand what is done.

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    $\begingroup$ Please do not simply delete and repost a closed question. Instead, please follow our guidance to edit and improve the closed post. Any edit will automatically put it up for a vote on reopening, and if enough voters agree that the post now is acceptable, it will be reopened. $\endgroup$ Commented Nov 7, 2023 at 15:46
  • $\begingroup$ I'm not sure why you are trying to make a distinction between fixed effects and categorical dummy variables, usually 'fixed' means 'not random', i.e. they are 'interesting in themselves' (specifically marginal estimates or predictions at specific values of those effects). See also here and here for more explanation on fixed vs. random. $\endgroup$
    – PBulls
    Commented Nov 7, 2023 at 19:54
  • $\begingroup$ @PBulls I'm examining the effect of complex asset backed securities deals on the demanded Credit-Spread by Investors. For my thesis I've collected a few Papers that have a similiar research question to mine. That's why i want to unterstand the distinction the authors seem to make, so i can just understand what the author is doing with the regression so i can apply it on my regression to see if i get similiar results. Due to the questions shared above i've problems identifying if a linear regression is used with time Dummy variables or a Fixed- Effect Model $\endgroup$ Commented Nov 7, 2023 at 21:18
  • $\begingroup$ @StephanKolassa sorry about that, i thought the question got deleted $\endgroup$ Commented Nov 7, 2023 at 21:18

1 Answer 1

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This is an economics-flavored answer, which is appropriate given your research question. Other fields have their own jargon that is fairly different.

There are typically two ways to estimate fixed effects:

  1. add dummies to the regression
  2. wipe them out with transformation like demeaning or first-differencing.

You can also do both. For example, with large N and small T panels (aka short panels), people will frequently wipe out the entity effects with the demeaning transformation but still include time dummies. Your setting sounds more like a long panel (relatively small N, large T), where you may have to take a more time-series approach.

Here's an example in Stata of (1) and (2) done with demeaning, but without covariates:

. webuse pig, clear
(Longitudinal analysis of pig weights)

. xtset id week

Panel variable: id (strongly balanced)
 Time variable: week, 1 to 9
         Delta: 1 unit

. xtreg weight i.week, fe vce(cluster id)

Fixed-effects (within) regression               Number of obs     =        432
Group variable: id                              Number of groups  =         48

R-squared:                                      Obs per group:
     Within  = 0.9857                                         min =          9
     Between = 0.0000                                         avg =        9.0
     Overall = 0.9311                                         max =          9

                                                F(8,47)           =     755.48
corr(u_i, Xb) = 0.0000                          Prob > F          =     0.0000

                                    (Std. err. adjusted for 48 clusters in id)
------------------------------------------------------------------------------
             |               Robust
      weight | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        week |
          2  |   6.760417   .1639224    41.24   0.000     6.430647    7.090186
          3  |   13.84375   .3134776    44.16   0.000     13.21311    14.47439
          4  |     19.375   .3375316    57.40   0.000     18.69597    20.05403
          5  |   25.13542   .4579635    54.89   0.000     24.21411    26.05672
          6  |   31.42708   .4699493    66.87   0.000     30.48167     32.3725
          7  |    37.4375   .5593798    66.93   0.000     36.31217    38.56283
          8  |   44.28125   .6311341    70.16   0.000     43.01157    45.55093
          9  |   50.19792   .7815318    64.23   0.000     48.62568    51.77016
             |
       _cons |   25.02083    .374458    66.82   0.000     24.26752    25.77415
-------------+----------------------------------------------------------------
     sigma_u |  3.9534984
     sigma_e |  2.0729165
         rho |  .78436522   (fraction of variance due to u_i)
------------------------------------------------------------------------------

. regress weight i.week i.id, vce(cluster id)

Linear regression                               Number of obs     =        432
                                                F(7, 47)          =          .
                                                Prob > F          =          .
                                                R-squared         =     0.9865
                                                Root MSE          =     2.0729

                                    (Std. err. adjusted for 48 clusters in id)
------------------------------------------------------------------------------
             |               Robust
      weight | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
        week |
          2  |   6.760417    .173866    38.88   0.000     6.410643     7.11019
          3  |   13.84375   .3324932    41.64   0.000     13.17486    14.51264
          4  |     19.375   .3580064    54.12   0.000     18.65478    20.09522
          5  |   25.13542   .4857437    51.75   0.000     24.15823    26.11261
          6  |   31.42708   .4984565    63.05   0.000     30.42432    32.42985
          7  |    37.4375   .5933118    63.10   0.000     36.24391    38.63109
          8  |   44.28125   .6694188    66.15   0.000     42.93455    45.62795
          9  |   50.19792   .8289396    60.56   0.000     48.53031    51.86553
             |
          id |
          2  |   2.666667   1.44e-13  1.9e+13   0.000     2.666667    2.666667
          3  |  -.2777778   1.44e-13 -1.9e+12   0.000    -.2777778   -.2777778
          4  |  -.1111111   1.44e-13 -7.7e+11   0.000    -.1111111   -.1111111
          5  |  -1.555556   1.44e-13 -1.1e+13   0.000    -1.555556   -1.555556
          6  |  -2.166667   1.44e-13 -1.5e+13   0.000    -2.166667   -2.166667
          7  |  -.7222222   1.44e-13 -5.0e+12   0.000    -.7222222   -.7222222
          8  |  -.2777778   1.44e-13 -1.9e+12   0.000    -.2777778   -.2777778
          9  |  -5.222222   1.44e-13 -3.6e+13   0.000    -5.222222   -5.222222
         10  |   2.944444   1.44e-13  2.1e+13   0.000     2.944444    2.944444
         11  |   2.277778   1.44e-13  1.6e+13   0.000     2.277778    2.277778
         12  |   .9444444   1.44e-13  6.6e+12   0.000     .9444444    .9444444
         13  |  -.6666667   1.44e-13 -4.6e+12   0.000    -.6666667   -.6666667
         14  |  -1.666667   1.44e-13 -1.2e+13   0.000    -1.666667   -1.666667
         15  |   4.333333   1.44e-13  3.0e+13   0.000     4.333333    4.333333
         16  |  -2.611111   1.44e-13 -1.8e+13   0.000    -2.611111   -2.611111
         17  |          9   1.44e-13  6.3e+13   0.000            9           9
         18  |  -1.777778   1.44e-13 -1.2e+13   0.000    -1.777778   -1.777778
         19  |   7.666667   1.44e-13  5.3e+13   0.000     7.666667    7.666667
         20  |   2.222222   1.44e-13  1.5e+13   0.000     2.222222    2.222222
         21  |   .3888889   1.44e-13  2.7e+12   0.000     .3888889    .3888889
         22  |   4.611111   1.44e-13  3.2e+13   0.000     4.611111    4.611111
         23  |   6.722222   1.44e-13  4.7e+13   0.000     6.722222    6.722222
         24  |          3   1.44e-13  2.1e+13   0.000            3           3
         25  |  -4.277778   1.44e-13 -3.0e+13   0.000    -4.277778   -4.277778
         26  |         -4   1.44e-13 -2.8e+13   0.000           -4          -4
         27  |  -3.111111   1.44e-13 -2.2e+13   0.000    -3.111111   -3.111111
         28  |  -.7222222   1.44e-13 -5.0e+12   0.000    -.7222222   -.7222222
         29  |   7.333333   1.44e-13  5.1e+13   0.000     7.333333    7.333333
         30  |  -5.666667   1.44e-13 -3.9e+13   0.000    -5.666667   -5.666667
         31  |   1.055556   1.44e-13  7.4e+12   0.000     1.055556    1.055556
         32  |   5.388889   1.44e-13  3.8e+13   0.000     5.388889    5.388889
         33  |   1.666667   1.44e-13  1.2e+13   0.000     1.666667    1.666667
         34  |   5.111111   1.44e-13  3.6e+13   0.000     5.111111    5.111111
         35  |   2.722222   1.44e-13  1.9e+13   0.000     2.722222    2.722222
         36  |   1.555556   1.44e-13  1.1e+13   0.000     1.555556    1.555556
         37  |   1.777778   1.44e-13  1.2e+13   0.000     1.777778    1.777778
         38  |   5.611111   1.44e-13  3.9e+13   0.000     5.611111    5.611111
         39  |   2.944444   1.44e-13  2.1e+13   0.000     2.944444    2.944444
         40  |   1.111111   1.44e-13  7.7e+12   0.000     1.111111    1.111111
         41  |  -3.722222   1.44e-13 -2.6e+13   0.000    -3.722222   -3.722222
         42  |   1.333333   1.44e-13  9.3e+12   0.000     1.333333    1.333333
         43  |   .2222222   1.44e-13  1.5e+12   0.000     .2222222    .2222222
         44  |   4.777778   1.44e-13  3.3e+13   0.000     4.777778    4.777778
         45  |   8.888889   1.44e-13  6.2e+13   0.000     8.888889    8.888889
         46  |   4.555556   1.44e-13  3.2e+13   0.000     4.555556    4.555556
         47  |   11.11111   1.44e-13  7.7e+13   0.000     11.11111    11.11111
         48  |   8.055556   1.44e-13  5.6e+13   0.000     8.055556    8.055556
             |
       _cons |   23.28241   .3971727    58.62   0.000      22.4834    24.08142
------------------------------------------------------------------------------
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  • $\begingroup$ Hello dimitriy, thx for your reply! I will consider your points. To my dataset: I've 500 Tranches (3-7 Tranches contain to a deal) over the last 10 years, where each Tranches of a deal is just collected once at the time the Deal is launched. From my understanding - because each tranche is just collected once and their data is not collected again at a different time period - my dataset is pooled cross sectional data. So I'd say that i have Large N (>500 Observations) and a large T (10 years). Would it still be able to use your approach? I also read that a FE-Model isn't possible with my dataset $\endgroup$ Commented Nov 8, 2023 at 8:39
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    $\begingroup$ This is not my field and I don't know your research question, so hard for me to say. That should be a separate question. There are some new techniques for doing high-dimensional fixed effects that you can use that are variants of (2). Just search for that phrase. $\endgroup$
    – dimitriy
    Commented Nov 8, 2023 at 15:28

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