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       log:  c:\Imbook\bwebpage\Section4\mma16p2mills.txt
  log type:  text
 opened on:   7 Nov 2006, 17:31:05

. 
. ********** OVERVIEW OF MMA16P2MILLS.DO **********
. 
. * STATA Program 
. * copyright C 2005 by A. Colin Cameron and Pravin K. Trivedi 
. * used for "Microeconometrics: Methods and Applications" 
. * by A. Colin Cameron and Pravin K. Trivedi (2005)
. * Cambridge University Press 
. 
. * Chapter 16.3.4 page 540
. * Presentation of Mills ratio
. * It provides A CORRECTED VERSION (see explanation below) of 
. *   (1) Figure 16.1 (ch16millsratio.wmf)  
. * This program requires no data
. 
. ********** SETUP ***********
. 
. set more off

. version 8

. set scheme s1mono   /* Used for graphs */

.   
. ********** GENERATE DATA AND FUNCTIONS
. 
. * Create density cdf Mills ratio for N[0,1] 
. set obs 100 
obs was 0, now 100

. gen c = 4*(50-_n)/100

. gen PHIc = norm(c)

. gen phic = normden(c)

. gen lamdac = phic/PHIc 

. 
. /* EXPLANATION - 
>    The book in equation (16.22) defines the inverse Mills ratio as
>       E[z | z > -c] = lamda(c) = phi(c)/PHI(c) given in equation (16.22)
>    Others instead define the Mills ratio as  
>       E[z | z > c] = lamda(c) = phi(c)/[1-PHI(c)]
>    By mistake this latter alternative was given as Figure 16.2.
>    The current correction instead uses phi(c)/PHI(c)
>    The text at the bottom of page 540 also needs to change.  */
. 
. * Descriptive statistics
. summarize

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
           c |       100        -.02     1.16046         -2       1.96
        PHIc |       100    .4952275     .338039   .0227501   .9750021
        phic |       100    .2386177    .1157086    .053991   .3989423
      lamdac |       100    .9516584     .711416   .0599393   2.373216

. 
. *********** FIGURE 16.2 page 540 ***********
. 
. * This graph shows Mills ratio and cdf and density
. graph twoway (scatter lamdac c, c(l) msize(vtiny) clstyle(p1) clwidth(medthic
> k)) /* 
>   */ (scatter PHIc c, c(l) msize(vtiny) clstyle(p3) clwidth(medthick)) /*
>   */ (scatter phic c, c(l) msize(vtiny) clstyle(p2) clwidth(medthick)), /*
>   */ scale (1.2) plotregion(style(none)) /*
>   */ title("Inverse Mills Ratio E[z|z>-c] as Cutoff Varies") /*
>   */ xtitle("c", size(medlarge)) xscale(titlegap(*5)) /* 
>   */ ytitle("Inverse Mills, pdf and cdf", size(medlarge)) yscale(titlegap(*5)
> ) /*
>   */ legend(pos(11) ring(0) col(1)) legend(size(small)) /*
>   */ legend( label(1 "Inverse Mills ratio") label(2 "N[0,1] Cdf") label(3 "N[
> 0,1] Density"))

. graph export ch16millsratio.wmf, replace
(file c:\Imbook\bwebpage\Section4\ch16millsratio.wmf written in Windows Metafil
> e format)

. 
. ********** CLOSE OUTPUT ***********
. log close
       log:  c:\Imbook\bwebpage\Section4\mma16p2mills.txt
  log type:  text
 closed on:   7 Nov 2006, 17:31:08
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