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Estimate the Just-Pope mean production function with selectivity correction

Source: R/estimate_mean_function.R
estimate_mean_function.Rd

Step 2 of Koundouri & Nauges (2005). Fits one of three functional forms for the mean function `f(x)` plus extra shifters and the Inverse Mills Ratio.

Usage

estimate_mean_function(
  data,
  output_var,
  input_vars,
  shifter_vars,
  imr_var = "imr",
  form = c("linear_quadratic", "quadratic", "cobb_douglas"),
  mean_scale = TRUE
)

Arguments

data

Data frame of the selected subsample (`D_l == 1`) containing all variables listed below.

output_var

Character. Name of the output / yield variable.

input_vars

Character vector. Variable inputs.

shifter_vars

Character vector. Extra production shifters that enter the mean function linearly (in all three forms).

imr_var

Character. Name of the Mill's ratio column (default "imr").

form

Functional form: `"linear_quadratic"` (default), `"quadratic"`, or `"cobb_douglas"`. See *Details*.

mean_scale

Logical. If `TRUE` (default), mean-scale all variables before estimation, as in Table A1 of the paper. Ignored under `form = "cobb_douglas"`, where log-scaling makes the transformation meaningless.

Value

A list with the fitted `lm` object, a coefficient table with HC1-robust standard errors, the residuals, fitted values, adjusted \(R^2\), the formula used, the (possibly scaled) data frame, and the functional form.

Details

  • `"linear_quadratic"` (default): linear, quadratic, and pairwise interaction terms in inputs. This is the form used in Koundouri & Nauges (2005). Compatible with additive interaction between the mean and variance functions, the key Just-Pope requirement.

  • `"quadratic"`: linear and quadratic terms in inputs, no pairwise interactions. A more parsimonious version, useful when the sample is small.

  • `"cobb_douglas"`: log-log specification, \(\log y = \beta_0 + \sum_j \beta_j \log x_j + \text{shifters} + \sigma M + w\). Requires strictly positive output and inputs. Shankar & Nelson (1999) showed that the Cobb-Douglas mean + Cobb-Douglas variance specification is robust to input endogeneity in the JP framework.

Coefficients are obtained by OLS; with the regressors serving as their own instruments, GMM point estimates coincide with OLS, and the paper's heteroskedasticity-robust GMM standard errors are reproduced via HC1 sandwich variances.

If the Mill's ratio column is constant (e.g. all zero for the "without selectivity" comparison), the term is dropped from the formula before fitting.

Examples

farms <- simulate_kiti_data(seed = 1)
sel   <- estimate_selection(farms, "vegetables",
                            c("rainfall","irrigated","dist_town",
                              "dist_coast","experience"))
farms$imr <- sel$imr
veg <- farms[farms$vegetables == 1, ]
mf  <- estimate_mean_function(
  data = veg, output_var = "revenue",
  input_vars   = c("fertilizers","pesticides","labor","water"),
  shifter_vars = c("machinery","rainfall","irrigated",
                   "dist_town","dist_coast","experience"))
head(mf$coefficients)
#>                  Coefficient   Std.Error t.Statistic      p.Value
#> (Intercept)      0.430540546 0.075148661   5.7291845 2.113282e-07
#> fertilizers      0.026561214 0.018828474   1.4106939 1.625822e-01
#> pesticides       0.073992857 0.011917726   6.2086389 2.939031e-08
#> labor            0.036699580 0.009318418   3.9383918 1.857306e-04
#> water            0.136547397 0.016804271   8.1257556 8.172466e-12
#> I(fertilizers^2) 0.001663074 0.002801760   0.5935821 5.546265e-01