In: Statistics and Probability
A study investigated the impact of house price appreciation on household mobility. The underlying idea was that if a house were viewed as one part of the household's portfolio, then changes in the value of the house, relative to other portfolio items, should result in investment decisions altering the current portfolio. Using 5,162 observations, the logit equation was estimated as shown in the table, where the limited dependent variable is one if the household moved in 1978 and is zero if the household did not move:
Regression model |
Logit |
constant |
-3.323 (0.180) |
Male |
-0.567 (0.421) |
Black |
-0.954 (0.515) |
Married78 |
0.054 (0.412) |
marriage change |
0.764 (0.416) |
A7983 |
-0257 (0.921) |
PURN |
-4.545 (3.354) |
Pseudo-R2 |
0.016 |
where male, black, married78, and marriage change are binary variables. They indicate, respectively, if the entity was a male-headed household, a black household, was married, and whether a change in marital status occurred between 1977 and 1978. A7983 is the appreciation rate for each house from 1979 to 1983 minus the SMSA-wide rate of appreciation for the same time period, and PNRN is a predicted appreciation rate for the unit minus the national average rate.
(a) Interpret the results. Comment on the statistical significance of the coefficients. Do the slope coefficients lend themselves to easy interpretation?
(b) The mean values for the regressors are as shown in the accompanying table.
Variable |
Mean |
male |
0.82 |
black |
0.09 |
married78 |
0.78 |
marriage change |
0.03 |
A7983 |
0.003 |
PNRN |
0.007 |
Taking the coefficients at face value and using the sample means, calculate the probability of a household moving.
(c) Given this probability, what would be the effect of a decrease in the predicted appreciation rate of 20 percent, that is A7983 = –0.20?
a)
TS = b^ / se(b^)
sincen is very large, |TS| > 1.96 ,variable is significant
here onlt A7983 is significant
b)
log(p /(1-p)) = b0+ b1 *x1 + b2*x2+..
b0 + b1*x1+ ..
log(p/(1-p)) = -4.61158
p = 1/(1+ e^(4.61158))
= 0.0098
c)
slope = -257
it means when it is is reduced by 20% , log odds is increased 257*0.2
= 51.4