Question

You have estimated the effects of the age of children, women’s age in years, years of schooling, unemployment rate in the county of residence, and whether the woman lives in metropolitan area on the woman’s probability of being in labor force. In Table 2, column 1 shows the coefficients from the linear probability model, column 2 shows the coefficients from a probit model, and column 3 shows the coefficients from a logit model.

1. Interpret coefficients on variables: # kids < 6 years and # kids 6-18 from column 1.

2. Calculate probability of being in the labor force when woman has 1 child that is less than 6 years old using columns 1, 2 and 3, holding everything else constant.

3. Calculate probability of being in the labor force when woman has 2 children that are less than 6 years old using columns 1, 2 and 3, holding everything else constant.

4. Compute the differences in probabilities when number of children that are less than 6 years old increases from 1 to 2 for each model. Compare the differences in the probabilities between these 3 models.

5. Interpret Pseudo R^2 from column 2.

6. Table 2. Estimation results

   	(1)	(2)	(3)
   	=1 if in lab frce, 1975	=1 if in lab frce, 1975	=1 if in lab frce, 1975
   	Coeff./Std. err.	Coeff./Std. err.	Coeff./Std. err.
   # kids < 6 years	-0.307***	-1.467***	-0.883***
   	(0.036)	(0.195)	(0.112)
   # kids 6-18	-0.017	-0.089	-0.053
   	(0.014)	(0.067)	(0.040)
   woman's age in years	-0.013***	-0.061***	-0.037***
   	(0.003)	(0.013)	(0.008)
   years of schooling	0.044***	0.206***	0.124***
   	(0.008)	(0.038)	(0.023)
   unemployment rate in	-0.004	-0.018	-0.011
   county of residence	(0.006)	(0.026)	(0.016)
   =1 if live in metro area	-0.030	-0.129	-0.074
   	(0.037)	(0.171)	(0.104)
   Constant	0.727***	1.093	0.661
   	(0.165)	(0.781)	(0.473)
   R-squared/Pseudo R-2	0.1248	0.0980	0.0978
   N. of cases	753.0000	753.0000	753.0000

7. p < 0.05, ^**p < 0.01, ^***p < 0.001

Answer 1

a) For a unit increase in the number of children below 6 years of age, the probability of the women being in the labor force falls by .307.

For a unit increase in the number of children between 6-18 years of age, the probability of the women being in the labor force falls by .017.

b) Probability of being in the labor force when woman has 1 child that is less than 6 years; equation:

woman in labor force= b+ b1* #kid<6 years---- 1

For LPM; .727 + -.307*1

Probability = .42

For logit model: The logit model gives the dependent variable as log odds

log odds: .661+ -.883*1 = -.222

Odds= exp(-.222)= .8009

Now, Probability= odds/1+odds

= .8009/1.8009

= .447

For probit model

y: 1.093+ -1.467*1 = -.374

odds= .687

probability= .407

c) Probability of being in the labor force when woman has 2 children that are less than 6 years old

Using eq 1:

For LPM: .727 + -.307*2

Prob= .113

For logit:

log odds:

log odds: .661+ -.883*2 = -1.105

Odds= exp(-1.105)= .331

Now, Probability= odds/1+odds

= .331/1.331

= .2486

For probit model

y: 1.093+ -1.467*2 = -1.841

odds= .1586

probability= .1368

d) Difference  in probabilities when number of children that are less than 6 years old increases from 1 to 2

For LPM: difference: .307

For logit: difference: .1984

For probit: difference: .2684

The difference in probabilities of women being in labor force when the number of kids below 6 years increase from 1 to 2 years is highest in the Linear probability model followed by probit model and the lowest is for logit model.

e) If comparing two models, McFadden’s(pseudo r squared in probit model) would be higher for the model with the greater likelihood.

Since the Pseudo R-2 here is too small it is not considered to be a good fit for the model.