## Distributed Lags and Dynamic Models

6.1 a. Using the Linear Arithmetic lag given in Eq. (6.2), a 6 year lag

on income gives a regression of consumption on a constant and

6

Zt = J2 (7 — i) Xt_i where Xt denotes income. In this case,

i=0

Zt = 7Xt C 6Xt_i + .. + Xt_6,

The Stata regression output is given below:

. gen ^6=7*ly+6*l. ly+5*l2.ly+4*l3.ly+3*l4.ly+2*l5.ly+l6.ly (6 missing values generated)

. reg lc z_6

Source |
SS |
df |
MS |
Number of obs F(1,41) Prob > F R-squared Adj R-squared Root MSE |
= 43 = 3543.62 = 0.0000 = 0.9886 = 0.9883 = .03037 |
||

Model Residual |
3.26755259 .037805823 |
1 41 |
3.26755259 .000922093 |
||||

Total |
3.30535842 |
42 |
.07869901 |
||||

lc |
Coef. |
Std. Err. |
t |
P>|t| |
[95% Conf. Interval] |
||

z_6 .cons |
.0373029 .0006266 -.4950913 .1721567 |
59.53 -2.88 |
0.000 0.006 |
.0360374 -... |