15.3. In studying the purchase of durable goods Y(Y= 1 if purchased, Y= 0 if no purchase) as a function of several variables for a total of 762 house- holds, Janet A. Fisher* obtained the following LPM results:
| Explanatory variable | Coef?cient | Standard error |
| Constant | 0.1411 |
— |
| 1957 disposable income, X1 | 0.0251 | 0.0118 |
| (Disposable income = X1)2, X2 | -0.0004 | 0.0004 |
| Checking accounts, X3 | -0.0051 | 0.0108 |
| Savings accounts, X4 | 0.0013 | 0.0047 |
| U.S. Savings Bonds, X5 | -0.0079 | 0.0067 |
| Housing status: rent, X6 | -0.0469 | 0.0937 |
| Housing status: own, X7 | 0.0136 | 0.0712 |
| Monthly rent, X8 | -0.7540 | 1.0983 |
| Monthly mortgage payments, X9 | -0.9809 | 0.5162 |
| Personal noninstallment debt, X10 | -0.0367 | 0.0326 |
| Age, X11 | 0.0046 | 0.0084 |
| Age squared, X12 | -0.0001 | 0.0001 |
| Marital status, X13 (1 = married) | 0.1760 | 0.0501 |
| Number of children, X14 | 0.0398 | 0.0358 |
| (Number of children = X14)2, X15 | -0.0036 | 0.0072 |
| Purchase plans, X16 (1 = planned; 0 otherwise) | 0.1760 | 0.0384 |
R2 = 0.1336
Notes:All ?nancial variables are in thousands of dollars.
Housing status: Rent (1 if rents; 0 otherwise) Housing status: Own (1 if owns; 0 otherwise)
Source:Janet A. Fisher, “An Analysis of Consumer Good Expenditure,” The Review of Economics and Statistics,vol. 64, no. 1, Table 1, 1962, p. 67.
a. Comment generally on the ?t of the equation.
b. How would you interpret the coef?cient of -0.0051 attached to checking account variable? How would you rationalize the negative sign for this variable?
c. What is the rationale behind introducing the age-squared and number of children-squared variables? Why is the sign negative in both cases?
d. Assuming values of zero for all but the income variable, ?nd out the conditional probability of a household whose income is $20,000 pur- chasing a durable good.
e. Estimate the conditional probability of owning durable good(s), given:
X1 = $15,000, X3 = $3000, X4 = $5000, X6 = 0, X7 = 1, X8 = $500, X9 =
$300, X10 = 0, X11 = 35, X13 = 1, X14 = 2, X16 = 0.
