## 9.2 Fixed Effects Model

• We can use the plm package to replicate the following investment equation as considered by Grunfeld (Grunfeld, 1958).

$\begin{equation} I_{it}=\alpha+\beta_{1}F_{it}+\beta_{2}C_{it}+\varepsilon_{it} \tag{9.1} \end{equation}$

The model in equation-1 is a one-way panel regression model which attempts to quantify the dependence of real gross investment ($$I_{it}$$) on the real value of the company ($$F_{it}$$) and real value of its capital stock ($$C_{it}$$).

• studied 10 large manufacturing firms from the United States over 20 years (1935-954). A fixed effect estimation can be obtained with the following code
# using plm with 'within' estimator for fixed effects
fe1 = plm(inv ~ value + capital, data = pdata1, model = "within")
# the output can be summarised with summary
summary(fe1)
Oneway (individual) effect Within Model

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

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

Residuals:
Min.    1st Qu.     Median    3rd Qu.       Max.
-184.00857  -17.64316    0.56337   19.19222  250.70974

Coefficients:
Estimate Std. Error t-value  Pr(>|t|)
value   0.110124   0.011857  9.2879 < 2.2e-16 ***
capital 0.310065   0.017355 17.8666 < 2.2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Total Sum of Squares:    2244400
Residual Sum of Squares: 523480
R-Squared:      0.76676
F-statistic: 309.014 on 2 and 188 DF, p-value: < 2.22e-16
• The summary output for the fitted model object gives details about the fitted object.

• The individual fixed effects can be obtained using the function , a summary method is also available as shown next

# individual fixed effects
fixef(fe1)
        1         2         3         4         5         6         7         8
-70.2967  101.9058 -235.5718  -27.8093 -114.6168  -23.1613  -66.5535  -57.5457
9        10
-87.2223   -6.5678 
# summary
summary(fixef(fe1))
    Estimate Std. Error t-value  Pr(>|t|)
1   -70.2967    49.7080 -1.4142   0.15896
2   101.9058    24.9383  4.0863 6.485e-05 ***
3  -235.5718    24.4316 -9.6421 < 2.2e-16 ***
4   -27.8093    14.0778 -1.9754   0.04969 *
5  -114.6168    14.1654 -8.0913 7.141e-14 ***
6   -23.1613    12.6687 -1.8282   0.06910 .
7   -66.5535    12.8430 -5.1821 5.629e-07 ***
8   -57.5457    13.9931 -4.1124 5.848e-05 ***
9   -87.2223    12.8919 -6.7657 1.635e-10 ***
10   -6.5678    11.8269 -0.5553   0.57933
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

### References

Grunfeld, Yehuda. 1958. “The Determinants of Corporate Investment: A Study of a Number of Large Corporations in the United States.” PhD thesis, Department of Photoduplication, University of Chicago Library.