Testfinal2005 - office(iv What is the density(pdf of the...

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Economics 513, Test Final, Fall 2005 Problem 1 In a study of unemployment durations an exponential model is used to analyze the data. To be specific, the rate at which the unemployed leave unemployment is specified as e x 0 β with x a vector of explanatory variables. (ii) What is the density (pdf) of a complete unemployment spell t ? (ii) What is the distribution function (cdf) of a complete unemployment spell t ? (iii) Let one of the explanatory variables be education in years. What is the average effect of a one year increase in education on the logarithm of the average duration of an unemployment spell? You have a random sample of observed explanatory variables x 1 , . . . , x n . Instead of observing a random sample of complete unemployment spells, you have a random sample of unemployment spells from the records of the un- employment benefits office. Because there is a waiting period of 1 month for unemployment benefits, only unemployed who stay unemployed for more than 1 month receive benefits and enter the records of the unemployment benefits
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Unformatted text preview: office. (iv) What is the density (pdf) of the unemployment spells in the records of the unemployment benefits office? (v) Give the log-likelihood function L ( β ) if we follow the unemployed until they leave unemployment? (vi) How would this log-likelihood function change if we follow the unemployed for at most 6 months? Problem 2 For a sample of size n of households we observe whether the household has an internet connection or not, and a vector of explanatory variables x . (i) What is the dependent variable y ? (ii) If you specify and estimate a linear regression model for y , can you use the usual formula for the standard errors? (iii) Specify a logit model for y . (iv) Give the log-likelihood of the logit model for this sample. (v) If we distinguish between high-speed and dial-up internet connections, specify a multinomial logit model for the choice between the three alter-natives. (vi) Do you think that IIA holds in this case? Why (not)? 1...
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