4. We are interested in estimating demand for beer. We observe data on prices and quantities of 8 different beer brands i at 1000 different stores s. To start, suppose the model for sales is | log Quantityis = bo + b log prices + b Quality: + Us We don't directly observe quality. Use the data set beer_sales. a. Estimate by OLS a model of log quantity on log price and nothing else). Interpret coefficient on log price. Is it statistically significant? Does its sign make sense? b. For the regression in (a), how would you classify quality? c. We don't observe quality, but we do observe brand. Would a set of brand dummy variables be a valid proxy for quality? Explain why or why not. d. Make eight scatter plots of log price against log quantity, one for each of the 8 brands. Include them in your write-up. Does the linearity assumption seem valid? e. Regress log quantity on log price and the 8 brand dummy variables. Interpret coefficient on log price. Is it statistically significant? Does its sign make sense? f. We also observe "high income", a dummy variable for stores whose customers have above-median income. Write down a causal model which lets the effect of price on quantity be different for high- and low-income stores. 8. Use OLS to estimate the determining function from part (f). Interpret all the price coefficients.
