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 Quantlet: select Description: select calculates semiparametric estimates of the intercept and slope coefficients in the "outcome" or "level" equation of a self-selection model. It is the second step of the two-step estimator of these models. It combines the procedures in the quantlets powell (slope estimator) and andrews (intercept).

 Usage: {a,b} = select(x,y,id,h) Input: x n x M regressor matrix. WARNING: x may not contain a vector of ones ! id n x 1 vector containing the estimated index of the first-step selection equation. y n x 1 matrix containing n observ. of the dependent variable h 2 x 1 vector of bandwidth. the first element of h is the bandwidth used for estimating the intercept coefficient while the second element of h is the bandwidth used for estimating the slope coefficients. Output: a scalar estimated intercept coefficient b M x 1 vector of estimated slope coefficients

Example:
```library("metrics")
randomize(66666)
n       = 200                           ; sample size
ss1     = #(1,0.9)~#(0.9,1)             ; covariance matrix of error terms
g       = #(1)                          ; true coefficient of decision equation
b       = #(-9, 1)                      ; true intercept and slope of outcome equation
u       = gennorm(n, #(0,0), ss1)       ; generate realizations of joint distribution of error terms
ss2     = #(1,0.4)~#(0.4,1)             ; covariance matrix of regressors
xz      = gennorm(n, #(0,0), ss2)       ; generate realizations of joint distribution of regressors
z       = xz[,2]                        ; regressor of decision equation
q       =(z*g+u[,1].>=0)               ; generate binary dependent variable of decision equation
hd      = 0.1*(max(z) - min(z))         ; bandwidth for dwade procedure
id      = z*d                           ; estimated first-step index
h       =(quantile(id, 0.7))|(0.2*(max(id) - min(id))) ;  bandwidth for select procedure
x       = matrix(n)~xz[,1]              ; regressors for outcome equation
y       = x*b+u[,2]                     ; dependent variable for outcome equation
zz      = paf(y~x~id, q)                ; impose censored sampling
y       = zz[,1]
x       = zz[,3:(cols(zz)-1)]
id      = zz[,cols(zz)]
{a,b}   = select(x,y,id,h)
d~a~b   ; first-step estimate ~  intercept estimate ~ slope estimate

```
Result:
```two-step estimates of a semiparametric
sample selection model according to Ahn and Powel (1993) and
Andrews and Schafgans (1994)
```

Author: A. Werwartz, 20000920
(C) MD*TECH Method and Data Technologies, 05.02.2006