Equipment {AER} | R Documentation

## Transportation Equipment Manufacturing Data

### Description

Statewide data on transportation equipment manufacturing for 25 US states.

### Usage

    data("Equipment")

### Format

A data frame containing 25 observations on 4 variables.

valueadded

  Aggregate output, in millions of 1957 dollars.

capital

  Capital input, in millions of 1957 dollars.

labor

  Aggregate labor input, in millions of man hours.

firms

  Number of firms.

### Source

Journal of Applied Econometrics Data Archive.

http://qed.econ.queensu.ca/jae/1998-v13.2/zellner-ryu/

Online complements to Greene (2003), Table F9.2.

http://pages.stern.nyu.edu/~wgreene/Text/tables/tablelist5.htm

### References

Greene, W.H. (2003). Econometric Analysis, 5th edition. Upper Saddle River, NJ: Prentice Hall.

Zellner, A. and Revankar, N. (1969). Generalized Production Functions. Review of Economic Studies, 36, 241–250.

Zellner, A. and Ryu, H. (1998). Alternative Functional Forms for Production, Cost and Returns to Scale Functions. Journal of Applied Econometrics, 13, 101–127.

### See Also

`Greene2003`

### Examples

    ## Greene (2003), Example 17.5
    data("Equipment")

    ## Cobb-Douglas
    fm_cd <- lm(log(valueadded/firms) ~ log(capital/firms) + log(labor/firms), data = Equipment)

    ## generalized Cobb-Douglas with Zellner-Revankar trafo
    GCobbDouglas <- function(theta)
     lm(I(log(valueadded/firms) + theta * valueadded/firms) ~ log(capital/firms) + log(labor/firms),
         data = Equipment)

    ## yields classical Cobb-Douglas for theta = 0
    fm_cd0 <- GCobbDouglas(0)

    ## ML estimation of generalized model
    ## choose starting values from classical model
    par0 <- as.vector(c(coef(fm_cd0), 0, mean(residuals(fm_cd0)^2)))

    ## set up likelihood function
    nlogL <- function(par) {
      beta <- par[1:3]
      theta <- par[4]
      sigma2 <- par[5]

      Y <- with(Equipment, valueadded/firms)
      K <- with(Equipment, capital/firms)
      L <- with(Equipment, labor/firms)

      rhs <- beta[1] + beta[2] * log(K) + beta[3] * log(L)
      lhs <- log(Y) + theta * Y

      rval <- sum(log(1 + theta * Y) - log(Y) +
        dnorm(lhs, mean = rhs, sd = sqrt(sigma2), log = TRUE))
      return(-rval)
    }

    ## optimization
    opt <- optim(par0, nlogL, hessian = TRUE)

    ## Table 17.2
    opt$par
    sqrt(diag(solve(opt$hessian)))[1:4]
    -opt$value

    ## re-fit ML model
    fm_ml <- GCobbDouglas(opt$par[4])
    deviance(fm_ml)
    sqrt(diag(vcov(fm_ml)))

    ## fit NLS model
    rss <- function(theta) deviance(GCobbDouglas(theta))
    optim(0, rss)
    opt2 <- optimize(rss, c(-1, 1))
    fm_nls <- GCobbDouglas(opt2$minimum)
    -nlogL(c(coef(fm_nls), opt2$minimum, mean(residuals(fm_nls)^2)))

[Package AER version 1.2-6 Index]