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?

What will be an ideal response?

Answer:
(a) Since the logit model is nonlinear, the slope coefficients cannot be easily interpreted. However, the signs of the coefficients indicate the direction of the relationship between the regressors and the binary dependent variable. Accordingly, being married or having experienced a marriage change increases the probability of moving. A male-headed household or a black household is less likely to move. If the predicted appreciation rate relative to the national average increased, then the household is less likely to move. The same holds for the actual appreciation rate from 1979 to 1983. None of the slope coefficients are statistically significant with the exception of the black household and marriage change coefficients. The two t-statistics are –1.85 and 1.84 respectively. These would be statistically significant at the 5% level of a one-sided hypothesis test.
(b) The probability is 0.021.
(c) The resulting probability would be 0.051, i.e., more than twice the value in the previous result.