Assignment on empirical problem

Question

Assignment:

Empirical Problem

As a part of your job in a research institution, you are asked to work with a group of other colleagues on a model of household labor/leisure choice. You optimally decide to split the problem among the members of the group: other colleagues solve the mathematical problem, while you are in charge of the empirical part.

They tell you that, after carefully analyzing the problem, they reached two different solutions under two different behavioral assumptions. Under the first behavioral assumption, the members of the household play a Stackelberg game to decide how much is their optimal choice of leisure. Under this assumption, the preferences for leisure of an individual i on household consisting of individuals i and j is:

λi = [w_iL_i] / [w_iT + w_jT + V]

if individual i is the one that chooses first and individual j chooses depending on what individual i decided.

Under the second behavioral assumption, the members of the household behave independently and they reach a Nash Equilibrium. In this case, the preferences for leisure for an individual i on household consisting of individuals i and j is:

λi = [wiLi ] / [w_iT + w_j (T − L_j ) + V]

In both cases, L_i and L_j are the optimal choices of leisure of individuals i and j respectively, w_i and w_j are the wage rates of individuals i and j, V is the non-labor income of the household and T is the total discretionary time of the individual (112 hours a week).

Your work now is to estimate the preferences for leisure of the husband in a panel of households selected from the 2005 wave of the Panel Study of Income. Dynamics (PSID).

1. Estimate the preferences for leisure of all the individuals in the sample under the two different behavioral assumptions.

NOTE: Write any additional assumptions that you make.

2. Plot a histogram of the estimated λ_i’s under the two behavioral assumptions.

3. After observing these graphs, can you tell which behavioral assumption is correct?

4. If someone asks you which of these two assumptions make husbands happier, what would be your answer? Why?

Data Variables

The dataset house hours.txt consists of a sample of households in the PSID in which both spouses are between the ages of 30-49 and both work. It contains five variables:

• Weekly hours of work of husband

• Hourly wage of husband

• Weekly hours of work of wife

• Hourly wage of wife

• Weekly non labor income of the household

Attachment:- tamplate.zip