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Solutions_HW5 - PAM 305 Introduction to Multivariate...

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PAM 305 - Introduction to Multivariate Analysis Fall 2006 Homework 5 Due date: November 17th In this homework you will use the data set MROZ.dta to analyze the labor force participation decision of married women in 1975. The relevant variables for the analysis are: inlf : Binary variable that takes the value 1 if the woman participated in the labor force, 0 otherwise. nwifeinc : Other sources of income, including husband’s earnings (in thousands of dollars). exper : Labor experience expersq : The square of experience educ : Education age kidslt 6: Number of children less than 6 years old kidsge 6: Number of children between 6 and 18 years old Question 1 Estimate by OLS the following linear probability model (LPM)(ignoring that the homoskedasticity assumption is violated) 1
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inlf = β o + β 1 nwifeinc + β 2 educ + β 3 exper + β 4 expersq + β 5 age + β 6 kidslt 6+ β 7 kidsge 6+ u and use the estimates obtained to answer the following questions: a. Which variables are significant at the 5% level? All except kidsge6, see the STATA log file. The variable kidsge6 is the only one with a value of the t-statistic smaller than 1.96, which is the critical value for a t test with 745 degrees of freedom with 2-sided signif- icance level of 0.05 (see the STATA log file on how to obtain this critical value from STATA. In the exam you will need your tables. b. Do the variables that are statistically significant have the effects we would expect based on economic theory or common sense? Explain. Yes they do. You just had to explain, based on your theory and common sense, why you would expect the effects you estimated. Here I am going to give you a longer answer that explicitly proposes an economic model to think about this issue and shows how the parameters you estimated relate to the proposed model. This is to show you how economic theory helps us to build a sensible model, which we can take to the data and estimate its parameters. A married female is assumed to value consumption and leisure. Her preferences are represented by the utility function u ( c, l ) = α o c + α 1 l + α 2 lc where α 1 is assumed to depend on kidsge6, kidslt6 and age. That is, α 1 ( kidsge 6 , kidslt 6 , age ) = α 1 o + α 11 kidsge 6 + α 12 kidslt 6 + α 13 age This takes into account that the marginal utility of leisure for a female is affected by the ages of her kids, and by her own age.
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