program drop _all
use "http://spears.okstate.edu/~ladkins/class/stata/tbrate.dta", clear
/* Prepare the data */
gen New_t = q(1950q1) + obsn  - 1
format New_t %tq 
tsset New_t
/*
gen pi_1 = pi[_n-1]
gen y_1 = y[_n-1]
gen r_1 = r[_n-1]

gen D_pi=pi-pi_1
gen D_y=y-y_1
gen D_r=r-r_1

gen D_r1=r[_n-1]-r[_n-2]   
gen D_r2=r[_n-2]-r[_n-3]
 
*/ 
/*  drop if year == 1950 & qtr < 4 */
/*  regress D_r D_pi D_y D_r1 D_r2 */

regress D.r D.pi D.y L.D.r L2.D.r
predict yhat, xb
predict ehat, residual
scatter yhat ehat obsn

regress ehat yhat
regress yhat ehat

regress D.r D.y L.D.r L2.D.r
predict ehat2, residual
regress D.pi D.y L.D.r L2.D.r
predict ehat3, residual

regress ehat2 ehat3, nocons