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Assignment3 - take account of the censoring 4 Write a...

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Problem set, Econ 513 1 Problem Set 3 Due: Wednesday November 2 Use again the data in the ascii file DURATION.DAT. We will consider the exponential model, using only one of the covariates, namely years of education, denoted by x . ONLY USE THE FIRST 50 OBSERVATIONS. We use the hazard h ( y | x ) = exp( β 0 + β 1 · x ) . 1. Report descriptive statistics for this data set. What is the fraction of durations that are censored? 2. Compute the MLE of β 0 if β 1 = 0. Do this with and without accounting for censored observations. Note that the MLE have closed form solutions in this case. 3. Show that the log likelihood function at β 0 = β 1
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Unformatted text preview: take account of the censoring. 4. Write a program for the first and second derivatives of the log likelihood. Check the program by comparing analytical and numerical derivatives. 5. Maximize the log likelihood function using the Newton-Raphson algorithm with ana-lytic derivatives. Use zeros as starting values. Also use the MLE for β obtained above and β 1 = 0. 6. Compute the standard errors of the MLE. 7. Use another algorithm, e.g. DFP, to compute the MLE using the same starting values as above. Compare the results....
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