9.2 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(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.

9.2.1 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)) 
    )

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