final_06may6 - Assume that the utility for brand j for...

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1 ARE213 Econometrics Spring 2006 UC Berkeley Department of Agricultural and Resource Economics Final Assignment Due: Thursday May 18th, 2006 You will be asked to analyze data for yogurt purchases using a conditional logit model. Use the data in the ascii Fle yogurt 06may6.mat posted on the course website. The data set contains three variables, Y, X and Z. All matrices have length N = 189, equal to the number of purchases. Y is a discrete outcome, taking values from 1 through 4, referring to the choice. Z is a matrix of household characteristics, a constant, income and household size. X is a matrix of choice characteristics. There are two characteristics, price and an indicator for promotions. The eight columns of X are ordered by choice with the Frst column referring to the price for choice 1, the second to the promotion for choice 1, the third to the price for choice 2, etcetera.
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Unformatted text preview: Assume that the utility for brand j for household i is equal to U ij = Z i β j + X ± ij γ + ε ij , where the ε ij have an extreme value distribution. Individuals choose the brand with the highest utility: Y i = j if U ij = max M k =1 U ik . 1. Specify the log likelihood function. 2. Calculate the value of the log likelihood function at β j = (0 , , 0) and γ = (0 . 1 , . 2). 3. Estimate the parameters of the model by maximum likelihood. 4. Estimate the standard errors using second derivatives. 5. Test whether the coefficients on price and promotion are both equal to zero using the likelihood ratio test. 6. Predict the market share for Danon after Danon Fxes its price at 70 cts in all markets (Danon is the brand with the highest market share). Final Assignment, ARE213 Spring ’06 2 7. Calculate the standard error of this prediction....
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This note was uploaded on 08/01/2008 for the course ARE 213 taught by Professor Imbens during the Spring '06 term at University of California, Berkeley.

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final_06may6 - Assume that the utility for brand j for...

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