12.2 Panel

make.pbalanced(x, balance.type = "fill") is useful to make a panel balanced by filling missing time periods with NA values. This is useful when you include individual specific time trends in the model.

plm::plm() is the horse force for panel data estimation.

plm::plm(formula, data, effect = c("individual", "time", "twoways", "nested"), model = c("within", "random", "ht", "between", "pooling", "fd"), index = NULL )

  • index the index attribute that describes individual and time dimensions; has to be the exact order, i.e. entity first, can’t reverse;

    It can be:

    • a vector of two character strings which contains the names of the individual and of the time

      indexes;

    • a character string which is the name of the individual index variable. In this case, the time index is created automatically and a new variable called “time” is added, assuming consecutive and ascending time periods in the order of the original data;

    • an integer, the number of individuals. In this case, the data need to be a balanced panel and be organized as a stacked time series (successive blocks of individuals, each block being a time series for the respective individual) assuming consecutive and ascending time periods in the order of the original data. Two new variables are added: “id” and “time” which contain the individual and the time indexes.

12.2.1 Two-way fixed effects

With effect = "twoways", the model includes both firm FE and year FE. The year fixed effects absorb all variation that is common across firms within a year — which is exactly what these macro variables capture. They are perfectly collinear with the year dummies, so plm silently drops them.

In a two-way FE panel, you cannot separately identify time-invariant cross-sectional variables (absorbed by firm FE) or cross-sectionally invariant time-series variables (absorbed by year FE).

Q: Do I have to convert the data to a panel data frame with pdata.frame() before using plm()?
A: Not necessarily. You have two options:

  1. Convert to pdata.frame() and estimate with plm().
  2. Use plm() directly on a regular data frame, specifying the index argument to indicate the panel structure.
# Option 1: Convert to pdata.frame
library(plm)
data("Grunfeld", package = "plm")
grunfeld_pdata <- pdata.frame(Grunfeld, index = c("firm", "year"))
model_fe <- plm(inv ~ value + capital, data = grunfeld_pdata, effect = "twoways", model = "within")

# Option 2: Use plm directly on regular data frame
model_fe_direct <- plm(inv ~ value + capital, data = Grunfeld, effect = "twoways", model = "within", index = c("firm", "year"))

Note that ggplot2 accepts regular data frames only. If you want to plot the data with ggplot2, it is suggested to save a panel data frame version of the data (grunfeld_pdata) for estimation and use the original data frame (grunfeld) for plotting.

Robust standard errors for panel data models can be computed with the vcovHC() function from the sandwich package.

# clustered by firm
coeftest(model_fe, vcov = vcovHC(model_fe, type = "HC1", cluster = "group"))
# clustered by year
coeftest(model_fe, vcov = vcovHC(model_fe, type = "HC1", cluster = "time"))

Firm- vs. Year-level clustering

Firm-level clustering (cluster = "group") Year-level clustering (cluster = "time")
Correlation structure Allows within-firm correlation of errors across years Allows within-year correlation of errors across firms
What it accounts for Firm-specific shocks that persist over time Common shocks affecting all firms in the same year
When to use Default choice for panel data with many firms and multiple observations per firm Appropriate when aggregate macro shocks dominate (e.g., COVID, financial crisis, policy changes)
Example Firm culture, management quality, industry-specific trends affecting the same firm over time All firms affected by the same Fed rate change, recession, or regulatory change in a given year

12.2.1.1 fixest package

It is a better alternative to plm for panel data estimation.

ref:

12.2.2 Dynamic Panel

data("EmplUK", package = "plm")
form <- log(emp) ~ log(wage) + log(capital) + log(output)
# Arellano and Bond (1991), table 4, col. b 
empl_ab <- pgmm(
    dynformula(form, list(2, 1, 0, 1)),
    data = EmplUK, index = c("firm", "year"),
    effect = "twoways", model = "twosteps",
    gmm.inst = ~ log(emp), lag.gmm = list(c(2, 99)) 
    )

\[ \boldsymbol \Gamma_n = \begin {pmatrix} \gamma_0 & \gamma_1 & \gamma_2 & \cdots & \gamma_{n - 1} \\ \gamma_1 & \gamma_0 & \gamma_1 & \cdots & \gamma_{n - 2} \\ \gamma_2 & \gamma_1 & \gamma_0 & \cdots & \gamma_{n - 3} \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ \gamma_{n - 1} & \gamma_{n - 2} & \gamma_{n - 3} & \cdots & \gamma_0 \end {pmatrix} \]