Main effect vs. interaction in multi-way fixed effects

Nae Khar

Join Date: Dec 2018
Posts: 56

Main effect vs. interaction in multi-way fixed effects

21 Feb 2024, 09:36

Hello All,

I am estimating a multi-way fixed effects model.

I want to examine how macro level factors such as infrastructure, regulation quality and labor force, impact innovation differently across multiple regions.

For example, if I have a model where the main effect is infrastructure investment and the interaction is - infrastructure investment x OECD region- what does it mean if only the interaction is significant versus if both main effect and interaction are significant?

Should we look at the significance of the the interaction only or both the main effect and interaction?

Does it create a better model if the main effect is dropped when an interaction is added?

Example with main effects and interaction:

Code:

reghdfe Innovation ICT_AnnualInvestment KnowledgeCapitalFem LaborForceParticipFem RegulatoryQualityEstimate DomesticCredit DomesticMarketScale FDINetOutflow_prcntGDP i.OECD_nonOECD#(c.ICT_AnnualInvestment), absorb (ccode year) cluster (ccode)

Code:

HDFE Linear regression                            Number of obs   =        374
Absorbing 2 HDFE groups                           F(   8,     81) =       2.05
Statistics robust to heteroskedasticity           Prob > F        =     0.0509
                                                  R-squared       =     0.9691
                                                  Adj R-squared   =     0.9589
                                                  Within R-sq.    =     0.0632
Number of clusters (ccode)   =         82         Root MSE        =     4.4788

                                                        (Std. err. adjusted for 82 clusters in ccode)
-----------------------------------------------------------------------------------------------------
                                    |               Robust
                         Innovation | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
------------------------------------+----------------------------------------------------------------
               ICT_AnnualInvestment |  -1.12e-09   4.26e-10    -2.64   0.010    -1.97e-09   -2.76e-10
                KnowledgeCapitalFem |   .0392724   .0197721     1.99   0.050     -.000068    .0786128
              LaborForceParticipFem |   .2695543   .2103904     1.28   0.204    -.1490566    .6881651
          RegulatoryQualityEstimate |    4.50043   5.835112     0.77   0.443    -7.109613    16.11047
                     DomesticCredit |   .0798555   .0662213     1.21   0.231    -.0519041     .211615
                DomesticMarketScale |   3.55e-13   2.40e-12     0.15   0.883    -4.41e-12    5.12e-12
             FDINetOutflow_prcntGDP |  -.0041192   .0041898    -0.98   0.328    -.0124555    .0042171
                                    |
OECD_nonOECD#c.ICT_AnnualInvestment |
                           NonOECD  |   1.19e-09   5.65e-10     2.11   0.038     6.62e-11    2.31e-09
                                    |
                              _cons |   13.19419   15.29075     0.86   0.391     -17.2296    43.61797
-----------------------------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
       ccode |        82          82           0    *|
        year |         5           1           4     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

Example only with the interaction:

Code:

reghdfe Innovation KnowledgeCapitalFem LaborForceParticipFem RegulatoryQualityEstimate DomesticCredit DomesticMarketScale FDINetOutflow_prcntGDP i.OECD_nonOECD#(c.ICT_AnnualInvestment), absorb (ccode year) cluster (ccode)

Code:

HDFE Linear regression                            Number of obs   =        374
Absorbing 2 HDFE groups                           F(   8,     81) =       2.05
Statistics robust to heteroskedasticity           Prob > F        =     0.0509
                                                  R-squared       =     0.9691
                                                  Adj R-squared   =     0.9589
                                                  Within R-sq.    =     0.0632
Number of clusters (ccode)   =         82         Root MSE        =     4.4788

                                                        (Std. err. adjusted for 82 clusters in ccode)
-----------------------------------------------------------------------------------------------------
                                    |               Robust
                         Innovation | Coefficient  std. err.      t    P>|t|     [95% conf. interval]
------------------------------------+----------------------------------------------------------------
                KnowledgeCapitalFem |   .0392724   .0197721     1.99   0.050     -.000068    .0786128
              LaborForceParticipFem |   .2695543   .2103904     1.28   0.204    -.1490566    .6881651
          RegulatoryQualityEstimate |    4.50043   5.835112     0.77   0.443    -7.109613    16.11047
                     DomesticCredit |   .0798555   .0662213     1.21   0.231    -.0519041     .211615
                DomesticMarketScale |   3.55e-13   2.40e-12     0.15   0.883    -4.41e-12    5.12e-12
             FDINetOutflow_prcntGDP |  -.0041192   .0041898    -0.98   0.328    -.0124555    .0042171
                                    |
OECD_nonOECD#c.ICT_AnnualInvestment |
                              OECD  |  -1.12e-09   4.26e-10    -2.64   0.010    -1.97e-09   -2.76e-10
                           NonOECD  |   6.68e-11   1.73e-10     0.39   0.700    -2.77e-10    4.11e-10
                                    |
                              _cons |   13.19419   15.29075     0.86   0.391     -17.2296    43.61797
-----------------------------------------------------------------------------------------------------

Absorbed degrees of freedom:
-----------------------------------------------------+
 Absorbed FE | Categories  - Redundant  = Num. Coefs |
-------------+---------------------------------------|
       ccode |        82          82           0    *|
        year |         5           1           4     |
-----------------------------------------------------+
* = FE nested within cluster; treated as redundant for DoF computation

Tags: None

George Ford

Join Date: Aug 2014

Posts: 3036
#2

21 Feb 2024, 16:48

The second model does not include ICT_AnnualInvestment, so not helpful.

In the first model, the IC_AnnualInvestment coefficient measures the effect for OECD (assuming OECD_nonOECD means not OECD). The interaction is the difference of the effect of ICTInv for NonOECD countries, so the effect for that group is the sum of the coefficients.

You have a NonOECD variable, so it's not exactly clear to me what OECD_nonOECD is.
1 like
Comment
Nae Khar

Join Date: Dec 2018

Posts: 56
#3

23 Feb 2024, 09:30

Many thanks for your help.

OECD_nonOECD is a dummy that has two levels (1-OECD and 2-non-OECD).
Comment
George Ford

Join Date: Aug 2014

Posts: 3036
#4

23 Feb 2024, 09:50

I'd just use the NonOECD dummy for consistency, and it will permit you to use margins.

reg y ICT_AnnualInvestment c.NonOECD#c.ICT_AnnualInvestment or reg y i.NonOECD#c.ICT_AnnualInvestment

I prefer the former since it provides a direct test of equality.

The latter will given you the coefficients for OECD and NonOECD directly, but then you'll have to test the equality.
1 like
Comment

Nae Khar

Join Date: Dec 2018
Posts: 56

28 Feb 2024, 05:45

Many thanks!

Do you suggest to use margins after plain reg with one explanatory variable? Or reghdfe with all the x variables in the original model?

Former command

Code:

. reg Innovation ICT_AnnualInvestinTelecomServ c.NonOECD#c.ICT_AnnualInvestinTelecomServ




      Source |       SS           df       MS      Number of obs   =       575

-------------+----------------------------------   F(2, 572)       =    115.42

       Model |  97193.0159         2  48596.5079   Prob > F        =    0.0000

    Residual |  240834.063       572  421.038572   R-squared       =    0.2875

-------------+----------------------------------   Adj R-squared   =    0.2850

       Total |  338027.079       574   588.89735   Root MSE        =    20.519




-------------------------------------------------------------------------------------------------

                     Innovation | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

--------------------------------+----------------------------------------------------------------

  ICT_AnnualInvestinTelecomServ |   2.280483   .1640094    13.90   0.000     1.958349    2.602617

                                |

                      c.NonOECD#|

c.ICT_AnnualInvestinTelecomServ |  -1.203503   .0804845   -14.95   0.000    -1.361585   -1.045422

                                |

                          _cons |   27.30575   1.316073    20.75   0.000     24.72083    29.89068

-------------------------------------------------------------------------------------------------




. 

margins, at (ICT_AnnualInvestinTelecomServ =(0(25)300) NonOECD==(1 2))




. marginsplot

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Former command all variables

Code:

. reg Innovation ICT_AnnualInvestinTelecomServ  KnowledgeCapitalFem LaborForceParticipFem RegulatoryQuali

> tyEstimate DomesticCredit DomesticMarketScale FDINetOutflow_prcntGDP c.NonOECD#c.ICT_AnnualInvestinTele

> comServ




      Source |       SS           df       MS      Number of obs   =       364

-------------+----------------------------------   F(8, 355)       =     46.58

       Model |   90933.509         8  11366.6886   Prob > F        =    0.0000

    Residual |  86631.7253       355  244.033029   R-squared       =    0.5121

-------------+----------------------------------   Adj R-squared   =    0.5011

       Total |  177565.234       363  489.160425   Root MSE        =    15.622




-------------------------------------------------------------------------------------------------

                     Innovation | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

--------------------------------+----------------------------------------------------------------

  ICT_AnnualInvestinTelecomServ |   .9409816   .2082645     4.52   0.000     .5313944    1.350569

            KnowledgeCapitalFem |   .2201895   .0361564     6.09   0.000     .1490818    .2912971

          LaborForceParticipFem |  -.0173902   .0645444    -0.27   0.788    -.1443277    .1095474

      RegulatoryQualityEstimate |    7.29829    1.55817     4.68   0.000     4.233885     10.3627

                 DomesticCredit |   .0317696   .0166748     1.91   0.058    -.0010242    .0645634

            DomesticMarketScale |   3.52e-12   6.38e-13     5.52   0.000     2.27e-12    4.77e-12

         FDINetOutflow_prcntGDP |   -.019732   .0374924    -0.53   0.599    -.0934672    .0540033

                                |

                      c.NonOECD#|

c.ICT_AnnualInvestinTelecomServ |  -.5260217   .1042799    -5.04   0.000    -.7311056   -.3209377

                                |

                          _cons |   24.28462    4.26382     5.70   0.000      15.8991    32.67014

-------------------------------------------------------------------------------------------------




. margins, at (ICT_AnnualInvestinTelecomServ =(0(25)300) NonOECD==(1 2))




. marginsplot

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Comment

George Ford

Join Date: Aug 2014
Posts: 3036

29 Feb 2024, 14:52

you need NonOECD as a variable too. both lines should be positively sloped.

here's a mickey mouse model to show the difference.

Code:

clear all

sysuse auto, clear

reg mpg headroom foreign c.foreign#c.headroom
margins, at(headroom = (1.5(.5)5)) over(foreign)
marginsplot

reg mpg headroom c.foreign#c.headroom
margins, at(headroom = (1.5(.5)5)) over(foreign)
marginsplot

Comment

Nae Khar

Join Date: Dec 2018
Posts: 56

01 Mar 2024, 03:48

Thanks for pointing this out.

Code:

. reg Innovation KnowledgeCapitalFem NonOECD c.NonOECD#c.KnowledgeCapitalFem

      Source |       SS           df       MS      Number of obs   =       550
-------------+----------------------------------   F(3, 546)       =    117.97
       Model |  112998.497         3  37666.1658   Prob &gt; F        =    0.0000
    Residual |  174323.934       546  319.274604   R-squared       =    0.3933
-------------+----------------------------------   Adj R-squared   =    0.3899
       Total |  287322.431       549  523.355977   Root MSE        =    17.868

-------------------------------------------------------------------------------------------------
                     Innovation | Coefficient  Std. err.      t    P&gt;|t|     [95% conf. interval]
--------------------------------+----------------------------------------------------------------
            KnowledgeCapitalFem |  -.3798399   .1439433    -2.64   0.009    -.6625902   -.0970895
                        NonOECD |  -36.78169   2.931203   -12.55   0.000    -42.53951   -31.02388
                                |
c.NonOECD#c.KnowledgeCapitalFem |   .3287951   .0786167     4.18   0.000     .1743668    .4832234
                                |
                          _cons |   93.49115   5.521899    16.93   0.000     82.64438    104.3379
-------------------------------------------------------------------------------------------------

. margins, at (KnowledgeCapitalFem=(0(5)71.2) NonOECD==(1 2))

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Code:

. reg Innovation KnowledgeCapitalFem ICT_AnnualInvestment LaborForceParticipFem RegulatoryQualityEstimate Do
> mesticCredit DomesticMarketScale FDINetOutflow_prcntGDP NonOECD c.NonOECD#c.KnowledgeCapitalFem

      Source |       SS           df       MS      Number of obs   =       378
-------------+----------------------------------   F(9, 368)       =     39.41
       Model |  90975.9278         9  10108.4364   Prob > F        =    0.0000
    Residual |  94397.5102       368  256.514973   R-squared       =    0.4908
-------------+----------------------------------   Adj R-squared   =    0.4783
       Total |  185373.438       377  491.706732   Root MSE        =    16.016

-------------------------------------------------------------------------------------------------
                     Innovation | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
--------------------------------+----------------------------------------------------------------
            KnowledgeCapitalFem |  -.2113847   .1547938    -1.37   0.173     -.515776    .0930067
           ICT_AnnualInvestment |   2.45e-10   5.36e-10     0.46   0.648    -8.09e-10    1.30e-09
          LaborForceParticipFem |   .0406452   .0648221     0.63   0.531     -.086823    .1681134
      RegulatoryQualityEstimate |   5.042419   1.711027     2.95   0.003     1.677803    8.407035
                 DomesticCredit |   .0285328   .0173172     1.65   0.100    -.0055203    .0625858
            DomesticMarketScale |   3.00e-12   1.20e-12     2.50   0.013     6.44e-13    5.36e-12
         FDINetOutflow_prcntGDP |  -.0248731   .0383744    -0.65   0.517    -.1003338    .0505875
                        NonOECD |  -21.27443   4.340024    -4.90   0.000    -29.80878   -12.74007
                                |
c.NonOECD#c.KnowledgeCapitalFem |   .2565829   .0870368     2.95   0.003     .0854311    .4277346
                                |
                          _cons |   58.78922   9.282453     6.33   0.000     40.53591    77.04252
-------------------------------------------------------------------------------------------------

. margins, at (KnowledgeCapitalFem=(0(5)71.2) NonOECD==(1 2))

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It seems the differences between OECD and NonOECD disappear as KnowledgeCapFem increases in the second model.

I noticed in one journal the common marginsplot included in these types of studies looks different. It has the mean and SD.

Any commands in Stata to generate this type of marginsplot?

Click image for larger version

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ID: 1745153

Comment

George Ford

Join Date: Aug 2014

Posts: 3036
#8

01 Mar 2024, 08:30

NonOECD needs to be 0/1 not 1/2. For many things it doesn't matter (it doesn't affect marginsplot), but here it is affecting the coefficient on Knowledge... which is confusing.

Y = aX + bD + cXD
dY/dX = a + c*D

With D = 1/2, the c coefficient is correct, but the a coefficient is too large by c. Margins sorts it all out, but you're going to confuse readers with the coefficients (unless you make it explicit NonOECD is 1,2, which most readers would conclude is odd).

Dummies are 0/1. There could be other problems with 1/2, such as multiplication where you want the 0 to apply or taking means. The mean of NonOECD is not the share of NonOECD sample members (it is 1 + the mean).

Code:

sysuse auto, clear reg mpg headroom foreign c.foreign#c.headroom margins, at(headroom = (1.5(.5)5)) over(foreign) marginsplot reg mpg headroom c.foreign#c.headroom margins, at(headroom = (1.5(.5)5)) over(foreign) marginsplot g for = foreign + 1 reg mpg headroom for c.for#c.headroom margins, at(headroom = (1.5(.5)5)) over(for) marginsplot summ foreign for
Comment

Nae Khar

Join Date: Dec 2018
Posts: 56

02 Mar 2024, 04:31

Code:


. gen NonOECD_redone = 0




. replace NonOECD_redone = 1 if NonOECD_name=="NonOECD"

(936 real changes made)




. tab NonOECD_redone




NonOECD_red |

        one |      Freq.     Percent        Cum.

------------+-----------------------------------

          0 |        228       19.59       19.59

          1 |        936       80.41      100.00

------------+-----------------------------------

      Total |      1,164      100.00




. tab NonOECD




OECD_nonOEC |

          D |      Freq.     Percent        Cum.

------------+-----------------------------------

       OECD |        228       19.59       19.59

    NonOECD |        936       80.41      100.00

------------+-----------------------------------

      Total |      1,164      100.00




. tab NonOECD_name




OECD_nonOEC |

     D_Name |      Freq.     Percent        Cum.

------------+-----------------------------------

    NonOECD |        936       80.41       80.41

       OECD |        228       19.59      100.00

------------+-----------------------------------

      Total |      1,164      100.00







. reg Innovation KnowledgeCapitalFem NonOECD_redone c.NonOECD_redone#c.KnowledgeCapitalFem




      Source |       SS           df       MS      Number of obs   =       550

-------------+----------------------------------   F(3, 546)       =    117.97

       Model |  112998.497         3  37666.1658   Prob > F        =    0.0000

    Residual |  174323.934       546  319.274604   R-squared       =    0.3933

-------------+----------------------------------   Adj R-squared   =    0.3899

       Total |  287322.431       549  523.355977   Root MSE        =    17.868




--------------------------------------------------------------------------------------------------------

                            Innovation | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

---------------------------------------+----------------------------------------------------------------

                   KnowledgeCapitalFem |  -.0510448   .0696158    -0.73   0.464    -.1877923    .0857028

                        NonOECD_redone |  -36.78169   2.931203   -12.55   0.000    -42.53951   -31.02388

                                       |

c.NonOECD_redone#c.KnowledgeCapitalFem |   .3287951   .0786167     4.18   0.000     .1743668    .4832234

                                       |

                                 _cons |   56.70945   2.701815    20.99   0.000     51.40223    62.01668

--------------------------------------------------------------------------------------------------------




. margins, at (KnowledgeCapitalFem=(0(5)71.2) NonOECD_redone==(0 1))

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Name: reg.png
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ID: 1745268

Code:

reg Innovation KnowledgeCapitalFem ICT_AnnualInvestment LaborForceParticipFem RegulatoryQualityEstimate DomesticCredit DomesticMarketScale 

> FDINetOutflow_prcntGDP NonOECD_redone c.NonOECD_redone#c.KnowledgeCapitalFem




      Source |       SS           df       MS      Number of obs   =       378

-------------+----------------------------------   F(9, 368)       =     39.41

       Model |  90975.9278         9  10108.4364   Prob > F        =    0.0000

    Residual |  94397.5102       368  256.514973   R-squared       =    0.4908

-------------+----------------------------------   Adj R-squared   =    0.4783

       Total |  185373.438       377  491.706732   Root MSE        =    16.016




--------------------------------------------------------------------------------------------------------

                            Innovation | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]

---------------------------------------+----------------------------------------------------------------

                   KnowledgeCapitalFem |   .0451982   .0732222     0.62   0.537    -.0987882    .1891846

                  ICT_AnnualInvestment |   2.45e-10   5.36e-10     0.46   0.648    -8.09e-10    1.30e-09

                 LaborForceParticipFem |   .0406452   .0648221     0.63   0.531     -.086823    .1681134

             RegulatoryQualityEstimate |   5.042419   1.711027     2.95   0.003     1.677803    8.407035

                        DomesticCredit |   .0285328   .0173172     1.65   0.100    -.0055203    .0625858

                   DomesticMarketScale |   3.00e-12   1.20e-12     2.50   0.013     6.44e-13    5.36e-12

                FDINetOutflow_prcntGDP |  -.0248731   .0383744    -0.65   0.517    -.1003338    .0505875

                        NonOECD_redone |  -21.27443   4.340024    -4.90   0.000    -29.80878   -12.74007

                                       |

c.NonOECD_redone#c.KnowledgeCapitalFem |   .2565829   .0870368     2.95   0.003     .0854311    .4277346

                                       |

                                 _cons |   37.51479   5.736712     6.54   0.000     26.23394    48.79564

--------------------------------------------------------------------------------------------------------

margins, at (KnowledgeCapitalFem=(0(5)71.2) NonOECD_redone==(0 1))

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ID: 1745269

Fixed the dummies. Any thoughts?

Comment

George Ford

Join Date: Aug 2014

Posts: 3036
#10

02 Mar 2024, 11:15

This looks better. marginsplot is consistent with the coefficients.
Comment
Nae Khar

Join Date: Dec 2018

Posts: 56
#11

02 Mar 2024, 13:37

Thank you for the invaluable advice.
Comment
George Ford

Join Date: Aug 2014

Posts: 3036
#12

02 Mar 2024, 18:25

You could make the graph legend better by replace NonOECD rather than creating a new variable:

replace NonOECD = NonOECD - 1
1 like
Comment

Nae Khar

Join Date: Dec 2018
Posts: 56

#13

03 Mar 2024, 13:16

It didn't quite work in transforming the variable to match the original variable.

Code:

. tab NonOECD

OECD_nonOEC |
          D |      Freq.     Percent        Cum.
------------+-----------------------------------
       OECD |        228       19.59       19.59
    NonOECD |        936       80.41      100.00
------------+-----------------------------------
      Total |      1,164      100.00



. replace NonOECD = NonOECD - 1
(1,164 real changes made)

. tab NonOECD

OECD_nonOEC |
          D |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        228       19.59       19.59
       OECD |        936       80.41      100.00
------------+-----------------------------------
      Total |      1,164      100.00

Comment

George Ford

Join Date: Aug 2014

Posts: 3036
#14

03 Mar 2024, 16:08

Worked, just need to reassign labels.
Comment

Nae Khar

Join Date: Dec 2018
Posts: 56

#15

04 Mar 2024, 02:55

I see it now.

Code:

. replace NonOECD = NonOECD - 1
(1,164 real changes made)

. tab NonOECD

OECD_nonOEC |
          D |      Freq.     Percent        Cum.
------------+-----------------------------------
          0 |        228       19.59       19.59
       OECD |        936       80.41      100.00
------------+-----------------------------------
      Total |      1,164      100.00

. label define NonOECD 0 "OECD" 1 "NonOECD"
. label values    NonOECD NonOECD

Code:

 label values NonOECD NonOECD

. tab NonOECD

OECD_nonOEC |
          D |      Freq.     Percent        Cum.
------------+-----------------------------------
       OECD |        228       19.59       19.59
    NonOECD |        936       80.41      100.00
------------+-----------------------------------
      Total |      1,164      100.00

. xtset ccode year

Panel variable: ccode (strongly balanced)
 Time variable: year, 2017 to 2022
         Delta: 1 unit

. reg Innovation KnowledgeCapitalFem ICT_AnnualInvestment LaborForceParticipFem RegulatoryQualityEstimate DomesticCre
> dit DomesticMarketScale FDINetOutflow_prcntGDP NonOECD_redone c.NonOECD_redone#c.KnowledgeCapitalFem

      Source |       SS           df       MS      Number of obs   =       378
-------------+----------------------------------   F(9, 368)       =     39.41
       Model |  90975.9278         9  10108.4364   Prob > F        =    0.0000
    Residual |  94397.5102       368  256.514973   R-squared       =    0.4908
-------------+----------------------------------   Adj R-squared   =    0.4783
       Total |  185373.438       377  491.706732   Root MSE        =    16.016

--------------------------------------------------------------------------------------------------------
                            Innovation | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
---------------------------------------+----------------------------------------------------------------
                   KnowledgeCapitalFem |   .0451982   .0732222     0.62   0.537    -.0987882    .1891846
                  ICT_AnnualInvestment |   2.45e-10   5.36e-10     0.46   0.648    -8.09e-10    1.30e-09
                 LaborForceParticipFem |   .0406452   .0648221     0.63   0.531     -.086823    .1681134
             RegulatoryQualityEstimate |   5.042419   1.711027     2.95   0.003     1.677803    8.407035
                        DomesticCredit |   .0285328   .0173172     1.65   0.100    -.0055203    .0625858
                   DomesticMarketScale |   3.00e-12   1.20e-12     2.50   0.013     6.44e-13    5.36e-12
                FDINetOutflow_prcntGDP |  -.0248731   .0383744    -0.65   0.517    -.1003338    .0505875
                        NonOECD_redone |  -21.27443   4.340024    -4.90   0.000    -29.80878   -12.74007
                                       |
c.NonOECD_redone#c.KnowledgeCapitalFem |   .2565829   .0870368     2.95   0.003     .0854311    .4277346
                                       |
                                 _cons |   37.51479   5.736712     6.54   0.000     26.23394    48.79564
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. margins, at (KnowledgeCapitalFem=(0(5)71.2) NonOECD ==(0 1))

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Do you think correlations between variables matter when running reghdfe or country year fixed effects?

I have one IV highly correlated with the DV.

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Main effect vs. interaction in multi-way fixed effects

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