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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.
- Spring '06