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I am running a FE regression of firm characteristics on the dependant variable effective tax rates. I tried both plm package and fixest package. I understand the differences in the standard errors (and I correct them with coeftest for the plm regression, not shown here), however I do not understand the difference in adjusted R-squared between fixest and plm. Coefficients are the same in both models, so adjusted R-squared should be the same, right?

> fe <- feols(GETR ~ SIZE + LEV + CAPINT + INVINT + ROA + LLEV + CF + EK| id + year,data = panel52,cluster = ~ id+year)
> summary(fe)
OLS estimation, Dep. Var.: GETR
Observations: 19,240 
Fixed-effects: id: 1,924,  year: 10
Standard-errors: Clustered (id & year) 
        Estimate Std. Error   t value  Pr(>|t|)    
SIZE    0.031979   0.010624  3.010150 0.0147123 *  
LEV    -0.021880   0.033039 -0.662243 0.5244090    
CAPINT  0.098979   0.027374  3.615754 0.0056088 ** 
INVINT  0.045080   0.039294  1.147250 0.2808605    
ROA     0.222094   0.089892  2.470664 0.0355315 *  
LLEV    0.015973   0.025740  0.620558 0.5502796    
CF     -0.237174   0.098485 -2.408230 0.0393631 *  
EK      0.027064   0.063651  0.425196 0.6806793    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
RMSE: 0.160357     Adj. R2: 0.212174
                 Within R2: 0.004764
> summary(fe52)
Twoways effects Within Model

Call:
plm(formula = GETR ~ SIZE + LEV + CAPINT + INVINT + ROA + LLEV + 
    CF + EK, data = panel52, na.action = na.exclude, effect = "twoways", 
    model = "within")

Balanced Panel: n = 1924, T = 10, N = 19240

Residuals:
      Min.    1st Qu.     Median    3rd Qu.       Max. 
-0.7032714 -0.0635238 -0.0079128  0.0376269  0.9293129 

Coefficients:
         Estimate Std. Error t-value  Pr(>|t|)    
SIZE    0.0319790  0.0065342  4.8941 9.967e-07 ***
LEV    -0.0218800  0.0356996 -0.6129    0.5400    
CAPINT  0.0989786  0.0222388  4.4507 8.612e-06 ***
INVINT  0.0450804  0.0366761  1.2292    0.2190    
ROA     0.2220941  0.0389295  5.7050 1.182e-08 ***
LLEV    0.0159730  0.0180534  0.8848    0.3763    
CF     -0.2371736  0.0425711 -5.5712 2.567e-08 ***
EK      0.0270641  0.0380943  0.7104    0.4774    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Total Sum of Squares:    497.11
Residual Sum of Squares: 494.74
R-Squared:      0.004764
Adj. R-Squared: -0.10685
F-statistic: 10.3509 on 8 and 17299 DF, p-value: 1.4467e-14```
Helix123
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Alex
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  • If you check the `?fixest::r2` help page you'll see it offers several aternatives. For example, should the fixed effects count as "explaining variance", or not? This may help you understand which statistic is being offered. – dash2 Dec 18 '21 at 20:04
  • Sorry, if I don't understand what you mean. I think I understand the adjusted R2 in fixest. The plm only seems to display the within R2. Can I change this to the similar R2 as in fixest? – Alex Dec 18 '21 at 20:33
  • I dunno, but maybe the plm package documentation will tell you. Try `?plm::r.squared`. – dash2 Dec 19 '21 at 12:25

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