Question

10. You have a data set that contains information about individuals gender, the number of children they have, their family income, and whether they are in the labor force You estimate the following linear probability model: Plaborforcel po+B1 children +B2 female +B3 (children x semale)+u a.) In terms of the model's parameters, what is the marginal effect of having an additional child on a woman's probability of being in the labor force? What is the marginal effect of having an additional child on a man's probability of being in the labor force? b.) Based on the graph below, what signs do you expect for the parameters ßo. B1. B2 and B3? Be specific about your reasoning for each parameter Plaborforce 1) Male Female Children c.) Suppose that the government implements a program that provides free childcare to families with income below $20,000 a year (and no assistance to families with higher income) i. Propose an estimation technique to estimate the effect of this program on labor participation. Write down the regression equation you would use for the technique (ignore gender and the number of children for this part). ii State the assumption you need to make in order for this technique to successfully recover the causal effect of the program on labor participation. Finally.give an example of a test you might perform to test this assumption?

Answer 1

P(laborforce = 1) = $\beta_0$ +
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children + $\beta_2$ female + $\beta_3$ (children x female) + u

Ans a)  Marginal effect of having an additional child on a woman's probability of being in the labor force is
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+ $\beta_3$ (since the no. of children term increases by
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and the interaction term increase by $\beta_3$ if female=1 for females).

Marginal effect of having an additional child on a man's probability of being in the labor force is only since the interaction term doesn't contribute (since female=0 when studying men's probability).

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b)   $\beta_0$ is the intercept of the model which is positive as shown in the graph.
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is the rate of change in labor participation per unit increase in children, or the slope of the line, which is positive for males and negative for females. Sign for $\beta_2$ may be positive or negative (not clear from the graph). The interaction term coefficient $\beta_3$ is negative for females (since having more children reduces the probability of participation, while it is positive for males.

c)  

i) The model can be of the following form:

P(Laborforce=1) = $\beta_0$ + * LowIncome + u (where LowIncome = 1 if income is below $20000, and 0 otherwise)

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The estimation can be done by using a simple random sample of population with income below $ 20000 and counting the number of people, irrespective of gender, participating in labor force)

ii) The assumption is that gender and childcare do not make a difference in the relationship between LowIncome indicator and labor participation.

iii) We can perform an unpaired t-test to compare the mean labor force participation before and after the program.