/*
  Replicate the results in Wooldridge, Econometric Analysis of Cross
  Section and Panel Data, section 15.10, using pension-plan data from
  Papke (AER, 1998).

  The dependent variable, pctstck (percent stocks), codes the asset
  allocation responses of "mostly bonds", "mixed" and "mostly stocks"
  as {0, 50, 100}.

  The independent variable of interest is "choice", a dummy indicating
  whether individuals are able to choose their own asset allocations.
*/

open pension.gdt

# demographic characteristics of participant
list DEMOG = age educ female black married
# dummies coding for income level
list INCOME = finc25 finc35 finc50 finc75 finc100 finc101

# Papke's OLS approach
ols pctstck const choice DEMOG INCOME wealth89 prftshr
# save the OLS choice coefficient 
choice_ols = $coeff(choice)

# estimate ordered probit
probit pctstck choice DEMOG INCOME wealth89 prftshr

k = $ncoeff
matrix b = $coeff[1:k-2]
a1 = $coeff[k-1]
a2 = $coeff[k]

/* 
   Wooldridge illustrates the 'choice' effect in the ordered probit 
   by reference to a single, non-black male aged 60, with 13.5 years 
   of education, income in the range $50K - $75K and wealth of $200K, 
   participating in a plan with profit sharing.
*/
matrix X = {60, 13.5, 0, 0, 0, 0, 0, 0, 1, 0, 0, 200, 1}

# with 'choice' = 0
scalar Xb = (0 ~ X) * b
P0 = cdf(N, a1 - Xb)
P50 = cdf(N, a2 - Xb) - P0
P100 = 1 - cdf(N, a2 - Xb)
E0 = 50 * P50 + 100 * P100

# with 'choice' = 1
Xb = (1 ~ X) * b
P0 = cdf(N, a1 - Xb)
P50 = cdf(N, a2 - Xb) - P0
P100 = 1 - cdf(N, a2 - Xb)
E1 = 50 * P50 + 100 * P100

printf "\nWith choice, E(y) = %.2f, without E(y) = %.2f\n", E1, E0
printf "Estimated choice effect via ML = %.2f (OLS = %.2f)\n", E1 - E0,
  choice_ols