Cost Function of Electricity Producers (1955, Nerlove Data)

Cost function data for 145 (+14) US electricity producers in 1955.

Usage

data("Electricity1955")

Format

A data frame containing 159 observations on 8 variables.

cost: total cost.
output: total output.
labor: wage rate.
laborshare: cost share for labor.
capital: capital price index.
capitalshare: cost share for capital.
fuel: fuel price.
fuelshare: cost share for fuel.

Details

The data contains several extra observations that are aggregates of commonly owned firms. Only the first 145 observations should be used for analysis.

Source

Online complements to Greene (2003). Table F14.2.

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

References

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

Nerlove, M. (1963) “Returns to Scale in Electricity Supply.” In C. Christ (ed.), Measurement in Economics: Studies in Mathematical Economics and Econometrics in Memory of Yehuda Grunfeld. Stanford University Press, 1963.

Examples

data("Electricity1955")
Electricity <- Electricity1955[1:145,]

## Greene (2003)
## Example 7.3
## Cobb-Douglas cost function
fm_all <- lm(log(cost/fuel) ~ log(output) + log(labor/fuel) + log(capital/fuel),
  data = Electricity)
summary(fm_all)
#> 
#> Call:
#> lm(formula = log(cost/fuel) ~ log(output) + log(labor/fuel) + 
#>     log(capital/fuel), data = Electricity)
#> 
#> Residuals:
#>      Min       1Q   Median       3Q      Max 
#> -1.01212 -0.21789 -0.00753  0.16046  1.81898 
#> 
#> Coefficients:
#>                    Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)       -4.685776   0.885294  -5.293 4.51e-07 ***
#> log(output)        0.720667   0.017435  41.335  < 2e-16 ***
#> log(labor/fuel)    0.593972   0.204632   2.903   0.0043 ** 
#> log(capital/fuel) -0.008471   0.190842  -0.044   0.9647    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.3917 on 141 degrees of freedom
#> Multiple R-squared:  0.9316,	Adjusted R-squared:  0.9301 
#> F-statistic: 640.1 on 3 and 141 DF,  p-value: < 2.2e-16
#> 

## hypothesis of constant returns to scale
linearHypothesis(fm_all, "log(output) = 1")
#> 
#> Linear hypothesis test:
#> log(output) = 1
#> 
#> Model 1: restricted model
#> Model 2: log(cost/fuel) ~ log(output) + log(labor/fuel) + log(capital/fuel)
#> 
#>   Res.Df    RSS Df Sum of Sq      F    Pr(>F)    
#> 1    142 61.027                                  
#> 2    141 21.637  1     39.39 256.69 < 2.2e-16 ***
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

## Table 7.4
## log quadratic cost function
fm_all2 <- lm(log(cost/fuel) ~ log(output) + I(log(output)^2) + log(labor/fuel) + log(capital/fuel),
  data = Electricity)
summary(fm_all2)
#> 
#> Call:
#> lm(formula = log(cost/fuel) ~ log(output) + I(log(output)^2) + 
#>     log(labor/fuel) + log(capital/fuel), data = Electricity)
#> 
#> Residuals:
#>     Min      1Q  Median      3Q     Max 
#> -1.3825 -0.1373  0.0080  0.1277  1.1354 
#> 
#> Coefficients:
#>                    Estimate Std. Error t value Pr(>|t|)    
#> (Intercept)       -3.764003   0.702060  -5.361 3.32e-07 ***
#> log(output)        0.152648   0.061862   2.468  0.01481 *  
#> I(log(output)^2)   0.050504   0.005364   9.415  < 2e-16 ***
#> log(labor/fuel)    0.480699   0.161142   2.983  0.00337 ** 
#> log(capital/fuel)  0.073897   0.150119   0.492  0.62331    
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Residual standard error: 0.3076 on 140 degrees of freedom
#> Multiple R-squared:  0.9581,	Adjusted R-squared:  0.9569 
#> F-statistic: 800.7 on 4 and 140 DF,  p-value: < 2.2e-16
#> 

## More examples can be found in:
## help("Greene2003")