Question

Suppose we estimate the following linear probability model, where 428 of the 753 women in the sample reported being in the labor force (inlfinlf) at some point during 1975:

inlfˆ=0.586(0.154)−0.0033(0.0014) nwifeinc+0.033(0.007) educ+0.039(0.006) exper−0.00060(0.00018) exper2−0.016(0.002) age−0.262(0.034) kidslt6+0.013(0.013) kidsge6inlf^=0.586(0.154)−0.0033(0.0014) nwifeinc+0.033(0.007) educ+0.039(0.006) exper−0.00060(0.00018) exper2−0.016(0.002) age−0.262(0.034) kidslt6+0.013(0.013) kidsge6

n=753, R2=0.264n=753, R2=0.264

	nwifeincnwifeinc = husband’s earnings, in thousands of dollars
	educeduc = years of education
	experexper = past years of labor market experience
	kidslt6kidslt6 = number of children less than six years old
	kidsge6kidsge6 = number of children between 6 and 18 years of age

Suppose that now we define outlfoutlf to be "1" if the woman is out of the labor force, and "0" otherwise, and regress outlfoutlf on all of the independent variables in the previous equation. (Hint: inlf=1−outlfinlf=1−outlf.)

Complete the following table by calculating the new intercept and slope coefficients.

Variable	Coefficient
Intercept
nwifeincnwifeinc
educeduc
experexper
exper2exper2
ageage
kidslt6kidslt6
kidsge6kidsge6

What happens to the standard errors on the intercept and slope estimates? Check all that apply.

The standard errors do not change.

The t-statistics change sign.

The standard errors decrease.

The standard error of the intercept does not change.

The t-statistics do not change.

R-squared ______ .

Answer 1

2. Binary response models
2.1 Linear probability model
Binary dependent variables in a microeconometric analysis:
These qualitative variables have exactly two possible categories and thus take
two values, namely one and zero
Examples for microeconometric analyses with binary response models:
• Analysis of the factors that explain whether a person is employed or unem-
ployed
• Analysis of the factors that explain whether a person uses a specific means
of transportation or other means of transportation (as multinomial variable)
• Analysis of the factors that explain whether a person strongly agrees with a
statement (based on an ordinal scale) or not
• Analysis of the factors that explain whether a household owns a certain in-
surance or not
• Analysis of the factors that explain whether the profits of a firm are at least
as high as a specific amount or are lower than this amount
• Analysis of the factors that explain whether a firm has realized an innovation
in the last three years or noIf yi
is a binary dependent variable with yi = 1 or yi = 0, xi = (xi1,…, xik)
‘
is a vec-
tor of k explanatory variables (including a constant), and β = (β1
,…, βk
)‘ is the
corresponding k-dimensional parameter vector, a microeconometric model can
simply be specified as a multiple linear regression model (for i = 1,…, n):
Such a linear regression model with a binary dependent variable is called linear
probability model. With E(εi
|xi
) = 0 it follows:
Since yi
is a binary variable with yi = 1 or yi = 0, it is Bernoulli distributed with
parameter pi and the following probability function:
In the linear probability model it follows:
Interpretation of the slope parameters in the linear probability model:
• Due to the binary character of yi
, the slope parameters βh
(h = 2,…, k) can-
not be interpreted as the change in yi
for a one-unit increase of the expla-
natory variable xih as in common linear regression models
• Instead, βh
(h = 2,…, k) indicates the change in the probability pi
(xi
, β) that yi
takes the value one if xih increases by one unit (for a quantitative explanato-
ry variable), ceteris paribus