## 9.3 Random Effects Model

• A random effect model can be estimated by setting the argument to .

• There are five different methods available for estimation of the variance component () which can be selected using the argument.

• The following output is obtained using the default Swamy-Arora () random method.

# random effect model
re1 = plm(inv ~ value + capital, data = pdata1, model = "random")
# summary
summary(re1)
Oneway (individual) effect Random Effect Model
(Swamy-Arora's transformation)

Call:
plm(formula = inv ~ value + capital, data = pdata1, model = "random")

Balanced Panel: n = 10, T = 20, N = 200

Effects:
var std.dev share
idiosyncratic 2784.46   52.77 0.282
individual    7089.80   84.20 0.718
theta: 0.8612

Residuals:
Min.   1st Qu.    Median   3rd Qu.      Max.
-177.6063  -19.7350    4.6851   19.5105  252.8743

Coefficients:
Estimate Std. Error z-value Pr(>|z|)
(Intercept) -57.834415  28.898935 -2.0013  0.04536 *
value         0.109781   0.010493 10.4627  < 2e-16 ***
capital       0.308113   0.017180 17.9339  < 2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    2381400
Residual Sum of Squares: 548900
R-Squared:      0.7695
Adj. R-Squared: 0.76716
Chisq: 657.674 on 2 DF, p-value: < 2.22e-16

### References

Baltagi, Badi. 2005. Econometric Analysis of Panel Data. 3rd ed. John Wiley & Sons.
Swamy, PAVB, and Swarnjit S Arora. 1972. “The Exact Finite Sample Properties of the Estimators of Coefficients in the Error Components Regression Models.” Econometrica: Journal of the Econometric Society, 261–75.