* SHAZAM code downloaded from UCLA Econ 143 (CAMERON) WebSite: 
* HTML file called e143sh21.htm, and should have 
*  been downloaded as omitvar.sha


* PROGRAM TO EXPLORE "OMITTED VARIABLES BIAS"

sample 1 100
dim core 2 2
dim b1 98 b2 98 b3 98
dim b1omit 98 b2omit 98
dim t1 98 t2 98 t3 98
dim t1omit 98 t2omit 98
dim corr_x_z 98

* set default values for characteristics of the data
* sige=standard deviation of the regression error term, e
* mux=central tendency of the x variable
* muz=central tendency of the z variable
* sigx=scale of the x variable
* sigz=scale of the z variable
*   b1true= "true" intercept in the model
*   b2true= "true" slope on the x-variable (always in model)
*   b3true= "true" slope on the z-variable (sometimes erroneously omitted)

sige:3
mux:3
muz:5
sigx:3
sigz:2

b1true:1
b2true:2
b3true:3

*===================== start of makedata procedure =====================
proc makedata

do #=2,98
sample 1 100

* draw some random normal regression errors with given standard deviation
genr error=nor([sige])

* let correlation between x and z vary almost between -1 and +1
gen1 corxz=(#-50)/50

* save each value of the correlation as it is being considered
* we will need it for the plots at the end
matrix corr_x_z(#)=corxz

* this next batch of commands "creates" data for the x and z
* explanatory variables such that they have the specified 
* degree of negative or positive correlation  (advanced econometrics)

matrix core(1,1)=1
matrix core(1,2)=corxz
matrix core(2,1)=corxz
matrix core(2,2)=1

print core

matrix ccf=chol(core)
matrix cf=ccf

genr ux=nor(1)
genr uz=nor(1)
matrix u=ux|uz
matrix e=u*cf'
matrix mex=e(0,1)
matrix mez=e(0,2)
genr ex=mex
genr ez=mez
genr x=0
genr z=0
genr x=[mux]+[sigx]*ex
genr z=[muz]+[sigz]*ez

* now we "create" some data on the dependent variable y that has a
* "known" relationship to the current x and z variables with their
* specified level of correlation.  

genr y=[b1true] + [b2true]*x + [b3true]*z + error

* once we have these data on y, x, and z, we can run regressions with
* and without the z variable on the right-hand-side.  Objective:  see
* what happens to the intercept and the slope on x when z is omitted,
* for different levels of correlation between z and the included
* variable x.

ols y x z / coef=bhat tratio=trat
* remember that SHAZAM lists the intercept coefficient last
matrix b1(#)=bhat:3
matrix b2(#)=bhat:1
matrix b3(#)=bhat:2
matrix t1(#)=trat:3
matrix t2(#)=trat:1
matrix t3(#)=trat:2
* remember that SHAZAM lists the intercept coefficient last
ols y x / coef=bomit tratio=tomit
matrix b1omit(#)=bomit:2
matrix b2omit(#)=bomit:1
matrix t1omit(#)=tomit:2
matrix t2omit(#)=tomit:1

endo

procend
*======================end of makedata procedure======================

* NOW RUN THE PROCEDURE (using default settings):
exec makedata

* For a given set of conditions, you have estimated regression parameters 
* for different degrees of correlation between the included and excluded 
* variables.  For these default conditions, try some plots.  b*hat is the
* parameter estimate under the correct model and b*omit is the (biased) 
* parameter when a relevant variable is omitted.

*
* YOU WILL NEED TO USE THE FOLLOWING SET OF COMMANDS:
* sample 2 98
* plot b2 b2omit corr_x_z / gnu 
* plot b1 b1omit corr_x_z / gnu 
*
* plot t2 t3 t2omit corr_x_z / gnu

* After this, you can change the default settings to see how the results
* for omitted variables bias differ as conditions vary.