This data consists of 10 large US manufacturing firms from 1935 to 1954.
Your Task: Analyze the many types of panel models.
This code was based on the paper: Croissant, Y., Milo, G.(2008). Panel Data Econometrics in R: The plm Package, Journal of Statistical Software, 27(2).
invest: Gross investment, defined as additions to plant and equipment plus maintenance and repairs in millions of dollars deflated by the implicit price deflator of producers’ durable equipment (base 1947);value: Market value of the firm, defined as the price of common shares at December 31 (base 1947);capital: Stock of plant and equipment, defined as the accumulated sum of net additions to plant and equipment deflated by the implicit price deflator for producers’ durable equipment (base 1947);firm: American manufacturing firms;year: Year of data;firmcod: Numeric code that identifies each firm.
library(readxl) #read excel files
library(skimr) #summary statistics
library(foreign) #panel data models
library(plm) # Lagrange multiplier test and panel modelsdata <- read_excel("Data/Grunfeld_data.xlsx")
df <- data.frame(data)| invest | value | capital | firm | year | firmcod |
|---|---|---|---|---|---|
| 317.6 | 3078.5 | 2.8 | General Motors | 1935 | 6 |
| 391.8 | 4661.7 | 52.6 | General Motors | 1936 | 6 |
| 410.6 | 5387.1 | 156.9 | General Motors | 1937 | 6 |
| 257.7 | 2792.2 | 209.2 | General Motors | 1938 | 6 |
| 330.8 | 4313.2 | 203.4 | General Motors | 1939 | 6 |
| 461.2 | 4643.9 | 207.2 | General Motors | 1940 | 6 |
| 512.0 | 4551.2 | 255.2 | General Motors | 1941 | 6 |
| 448.0 | 3244.1 | 303.7 | General Motors | 1942 | 6 |
| 499.6 | 4053.7 | 264.1 | General Motors | 1943 | 6 |
| 547.5 | 4379.3 | 201.6 | General Motors | 1944 | 6 |
df$firmcod = NULL #another way or removing a variablefirm is a categorical nominal variable, and should be treated as so in
the modelling process. And for this example year should also be
considered as a categorical ordinal variable, instead of a continuous
one.
df$firm = factor(df$firm)
df$year = factor(df$year, ordered = T)Take a look at the summary of your data. Do you see the differences regarding the categorical ones?
summary(df)## invest value capital firm
## Min. : 0.93 Min. : 30.28 Min. : 0.8 American Steel : 20
## 1st Qu.: 27.38 1st Qu.: 160.32 1st Qu.: 67.1 Atlantic Refining: 20
## Median : 52.37 Median : 404.65 Median : 180.1 Chrysler : 20
## Mean : 133.31 Mean : 988.58 Mean : 257.1 Diamond Match : 20
## 3rd Qu.: 99.78 3rd Qu.:1605.92 3rd Qu.: 344.5 General Electric : 20
## Max. :1486.70 Max. :6241.70 Max. :2226.3 General Motors : 20
## (Other) :100
## year
## 1935 : 11
## 1936 : 11
## 1937 : 11
## 1938 : 11
## 1939 : 11
## 1940 : 11
## (Other):154
First run an Ordinary least square model without the firm variable.
Compare the results from this model to the many panel data models.
mlr = lm(invest ~ value + capital, data = df)
summary(mlr)##
## Call:
## lm(formula = invest ~ value + capital, data = df)
##
## Residuals:
## Min 1Q Median 3Q Max
## -290.33 -25.76 11.06 29.74 377.94
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) -38.410054 8.413371 -4.565 8.35e-06 ***
## value 0.114534 0.005519 20.753 < 2e-16 ***
## capital 0.227514 0.024228 9.390 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 90.28 on 217 degrees of freedom
## Multiple R-squared: 0.8179, Adjusted R-squared: 0.8162
## F-statistic: 487.3 on 2 and 217 DF, p-value: < 2.2e-16
Panel data models use one way and two way component models to overcome heterogeneity, correlation in the disturbance terms, and heteroscedasticity.
- One way error component model: variable-intercept models across individuals or time;
- Two way error component model: variable-intercept models across individuals and time.
Modelling Specifications:
-
With fixed-effects: effects that are in the sample. Fixed-effects explore the causes of change within a person or entity (In this example the entity is the firms);
-
With random-effects: effect randomly drawn from a population. The random effects model is an appropriate specification if we are drawing n individuals randomly from a large population.
You can also try other types of model estimation:
| model | argument |
|---|---|
| Fixed effects | within |
| Random effects | random |
| Pooling model | pooling |
| First-diference model | fd |
| Between model | between |
See ?plm for more options, regarding the effects and instrumental
variable transformation types.
fixed = plm(
invest ~ value + capital,
data = df,
index = c("firm", "year"), #panel settings
model = "within" #fixed effects option
)
summary(fixed)## Oneway (individual) effect Within Model
##
## Call:
## plm(formula = invest ~ value + capital, data = df, model = "within",
## index = c("firm", "year"))
##
## Balanced Panel: n = 11, T = 20, N = 220
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -184.00792 -15.66024 0.27161 16.41421 250.75337
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## value 0.11013 0.01130 9.7461 < 2.2e-16 ***
## capital 0.31003 0.01654 18.7439 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2244500
## Residual Sum of Squares: 523720
## R-Squared: 0.76667
## Adj. R-Squared: 0.75314
## F-statistic: 340.079 on 2 and 207 DF, p-value: < 2.22e-16
random = plm(
invest ~ value + capital,
data = df,
index = c("firm", "year"),
model = "random" #random effects option
)
summary(random)## Oneway (individual) effect Random Effect Model
## (Swamy-Arora's transformation)
##
## Call:
## plm(formula = invest ~ value + capital, data = df, model = "random",
## index = c("firm", "year"))
##
## Balanced Panel: n = 11, T = 20, N = 220
##
## Effects:
## var std.dev share
## idiosyncratic 2530.04 50.30 0.29
## individual 6201.93 78.75 0.71
## theta: 0.8586
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -178.0540 -18.9286 4.2636 14.8933 253.3183
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) -53.9436014 25.6969760 -2.0992 0.0358 *
## value 0.1093053 0.0099138 11.0256 <2e-16 ***
## capital 0.3080360 0.0163873 18.7972 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2393800
## Residual Sum of Squares: 550610
## R-Squared: 0.76999
## Adj. R-Squared: 0.76787
## Chisq: 726.428 on 2 DF, p-value: < 2.22e-16
Use the Hausman test to evaluate when to use fixed or random effects
phtest(random, fixed)##
## Hausman Test
##
## data: invest ~ value + capital
## chisq = 3.9675, df = 2, p-value = 0.1376
## alternative hypothesis: one model is inconsistent
Note: The null hypothesis is that random effect model is more appropriate than the fixed effect model.
fixed_tw <-
plm(
invest ~ value + capital,
data = df,
effect = "twoways", #effects option
model = "within", #fixed
index = c("firm", "year") #panel settings
)
summary(fixed_tw)## Twoways effects Within Model
##
## Call:
## plm(formula = invest ~ value + capital, data = df, effect = "twoways",
## model = "within", index = c("firm", "year"))
##
## Balanced Panel: n = 11, T = 20, N = 220
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -163.4113 -17.6747 -1.8345 17.9490 217.1070
##
## Coefficients:
## Estimate Std. Error t-value Pr(>|t|)
## value 0.116681 0.012933 9.0219 < 2.2e-16 ***
## capital 0.351436 0.021049 16.6964 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 1672200
## Residual Sum of Squares: 459400
## R-Squared: 0.72527
## Adj. R-Squared: 0.67997
## F-statistic: 248.15 on 2 and 188 DF, p-value: < 2.22e-16
random_tw <-
plm(
invest ~ value + capital,
data = df,
effect = "twoways",
model = "random",
index = c("firm", "year"),
random.method = "amemiya"
)
summary(random_tw)## Twoways effects Random Effect Model
## (Amemiya's transformation)
##
## Call:
## plm(formula = invest ~ value + capital, data = df, effect = "twoways",
## model = "random", random.method = "amemiya", index = c("firm",
## "year"))
##
## Balanced Panel: n = 11, T = 20, N = 220
##
## Effects:
## var std.dev share
## idiosyncratic 2417.89 49.17 0.256
## individual 6859.38 82.82 0.726
## time 175.63 13.25 0.019
## theta: 0.8684 (id) 0.2544 (time) 0.2535 (total)
##
## Residuals:
## Min. 1st Qu. Median 3rd Qu. Max.
## -176.9380 -16.0966 3.9358 15.6184 237.6072
##
## Coefficients:
## Estimate Std. Error z-value Pr(>|z|)
## (Intercept) -58.498376 27.083483 -2.1599 0.03078 *
## value 0.110623 0.010299 10.7413 < 2e-16 ***
## capital 0.320686 0.017630 18.1897 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Total Sum of Squares: 2119700
## Residual Sum of Squares: 523110
## R-Squared: 0.75321
## Adj. R-Squared: 0.75094
## Chisq: 662.3 on 2 DF, p-value: < 2.22e-16
The Lagrange multiplier statistic, is used to test the null hypothesis
that there are no group effects in the Random Effects model.
Large values of the Lagrange Multiplier indicate that effects model is
more suitable than the classical model with no common effects.
plmtest(random_tw)##
## Lagrange Multiplier Test - (Honda) for balanced panels
##
## data: invest ~ value + capital
## normal = 29.576, p-value < 2.2e-16
## alternative hypothesis: significant effects
Note: Large values of H indicate that the fixed effects model is prefered over the random effects model. While, a large value of the LM statistic in the presence of a small H statistic indicate that the random effects model is more suitable.