Logit and probit regressions

You are to estimate a logit regression of the form: $\ln \left(\frac{p}{1-p}\right)={\beta }_0+{\displaystyle \sum _i{\beta }_i{x}_i}+\epsilon ,$ where p is the probability that a patient received advice about his level of consumption of alcohol and x _i are the explanatory variables.

Provide the following information:

1. Make a table of the means of all of the variables.
2. Offer an economic justification for the inclusion of each explanatory variable you use in your regression (including a prediction of its expected sign).
3. Make a table reporting the results of the estimation of (1) an OLS linear estimation, (2) a probit estimation, and (3) a logit estimation. Also include a column with the ratio of each of the logit parameters to the probit parameter. Do not use the abbreviated name of the explanatory variables in the table.
4. Present a table of results of a logit model with all of the variables and with whatever other models you feel are suggested by your empirical results. Discuss the results of the estimation and what the estimation tells you about how physicians decide whether to give advice on alcohol consumption to their male patients.

Data Set 1: The data for this project are in the MS Excel file FLABOR . These data are observations on married females drawn from the 1987 wave of Michigan Panel Study of Income Dynamics (PSID). The data set has observations for 3,382 individuals.

Data Set 2: These data are from Portugal. The data set is a sample from Portuguese Employment Survey, from the interview year 1991, and has been provided by the Portuguese National Institute of Statistics (INE). The data are in the Excel file Martins. This file is organized into seven columns, corresponding to seven variables, with 2,339 observations.

Answer the following questions:

1. What factors other than wage levels determine the number of hours that a wife will spend in the work force? Remember to use economic theory in answering this question.
2. Clearly, one of the major factors in determining if a wife will enter the labor force is the wage level she can earn. The US data set does not include the wife’s wage level. Is there any other variable in the data set that economic theory suggests will be a good proxy for wage levels?
3. The variable Age is a proxy for the work (or life) experience of a woman. We would expect that its effect on the probability that a woman will enter the labor force will be non-linear—that is, its marginal impact will be positive and decreasing. This reasoning suggests that you should use Age and Age ² as explanatory variables. Can the same reasoning be used with the variable Education? What are your expectations about the signs of the parameters of these two explanatory variables? The same reasoning can be used about the number of years of education.
4. Estimate and report in a table the following two logit regressions: (1) US women enter the labor force at all and (2) US women enter the labor force for at least 1,000 hours if they enter the labor force,. In each of these cases, compare your results to a linear model.
5. The Portuguese data set has a different problem. We have reported the wage rate of women who are working, but no wage level for women who are not working. We will get around this problem by first using the data for women who actually work to estimate the relationship between wage rates and the age and education of the women. We will then use this relationship to predict the wage rate for both women who do work and women who do not work. We will then use this predicted wage rate data series as an independent variable in a logit model explaining the probability that a married woman will enter the labor force. When completing the logit regression be sure that you separate all of the children in a family into those 3 and under and those between 4 and 18. Also, include the years of education in this regression to see if a Portuguese married woman’s taste for participation in the labor force increases or decreases with the level of her education.
6. Is it reasonable to compare your results for the two countries?

References

Amemiya, T. (1981). Quantitative Response Models: A Survey. Journal of Economic Literature 19 : 1483-1536.

Cramer, J. S. (2003). Logit Models from Economics and Other Fields (Cambridge: Cambridge University Press).

Cameron, A. Colin and Pravin K. Trivedi (2005). Microeconometrics: Methods and Applications (Cambridge: Cambridge University Press).

Ladd, G. W. (1966). Linear Probability Functions and Discriminant Functions. Econometrica 34 : 873-888.

Maddala, G. S. (1983). Limited-Dependent and Qualitative Variables in Economics (Cambridge: Cambridge University Press).

McFadden, D. (1974). Conditional Logit Analysis of Qualitative Choice Behavior. In P. Zarembka (ed.) Frontiers in Econometrics (New York: Academic Press): 105-142.

Wald, A. (1943). Test of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is Large. Transactions of the American Mathematical Society 54 : 426-482.