Explain the key assumptions of the random effects model and the kinds of transformations done in each model to handle the violations of assumptions and come up with efficient and consistent estimates.

Why is endogeneity an important identification condition for simultaneous equation models? (2 pts)

1. Why is the probit model referred to as latent variable model? (2 pts)
2. Consider the following extended Keynesian model of income determination:

Consumption function: Ct=1+2Yt-3Tt+1t
Investment Function: It=0+1Yt-1+2t
Taxation Function: Tt=0+1Yt+3t
Income Identity: Yt=C1+It+Gt
Where, C consumption expenditure, Y income, I investment, T taxes, G government expenditure and u’s are the disturbance terms. Based on the information provided above, answer the following questions:

1. Identify the endogenous and predetermined variables in the model. (2 pts)
2. By applying order and rank condition for identification, check the identification status of each of the equations in the system. (4 pts)

1. The following two equations represent a simple wage-price model:

Wt=0+1Pt+2Qt+1t
Pt=0+1Wt+1Qt+2t
Where Wt is the wage in time period t, P represents prices, and Q is productivity.
Find the reduced form equations for the model above and explain why are finding the reduced form equations important? (4 pts)

1. Answer the following questions based your understanding of panel data models:

1. Explain the assumptions of the individual effect variable in both fixed and random effects model. Provide one example of your own for each model to further elaborate the unobserved individual effects in your explanation. (4 pts)
2. Explain the key assumptions of the random effects model and the kinds of transformations done in each model to handle the violations of assumptions and come up with efficient and consistent estimates. (4 pts)

1. From a survey of 200 individuals, an ordered logit model is estimated to know the effects of education (abbreviated as ‘educ’ and measured in years of schooling) and sex (measured as dummy: 1 for female and 0 for male) on participation to paid labor, i.e., the dependent variable: Y=2 if full time employed, Y=1 if partime employed, and Y=0 if unemployed at all.

The student run the following command in stata and found the results as below:
ologit Y educ sex, or
Yi=5.23+1.5 educ+0.5sex
t= 1.34 4.05 2.34
LR chi2=31.681 (P value=0.00)
Where Yi is the predicted dependent variable.

1. Interpret the slope parameters in this estimated model. (2 pts)
2. What does the LR Chi2 measures in this model? (2 pts)
3. Comment on the statistical significance of the individual regressors and the estimated model. What is the relevance of the estimated model for policy implication? (4 pts)

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