2. Suppose you are intorested in studying the impact of advertisement on sales in the ice cream market. Suppose there are N brands of ice eream in the market. You condict a survey and collect datin an average daily number of lee cream sold Qi (in thousands of units) and advertisement spending Adi (in millions of lira) by each firm i in a given year. Note: When needed in this exercise, use t0.90=1.96 (a) You estimnte the following equation: Qi=1+2Adi+ei Suppose your OLS estimates for are ^=[520,19.8] and the estimated standard erron of the estimator are SE(^)=[98,5.4]. i. Is the coefficient 2 statistically significant? Based on the results above, construct, a 95% confidence interval for 2. ii. Under what condition can you claim that the estimate you found above is a causal estimate of the impact of advertisement on ice cream sales? Is this condition likely to be true in this setup? If you were to summarize your findings about the relationship between advertisement and sales in a sentence, what would you say given the estimates found above? iii. It is likely that advertisement spending is non-random. Can you think of potential self-selection mechanisms into different levels of advertisement spending (i.e. why would certain firms choose to spend more than others on advertisement and how would that be correlated with quantity of sales)? What would the ideal experiment to estimate the causal effect look like? Is it feasible in practice? iv. Someone claims that the equation above is missing an important variable. This variable is the unit price per brand of ice cream (Pi). Do you think this variable is important in this setting? Do you think omitting this variable will bias the estimate of 2 ? Explain. 1 (b) You collect data on average price of ice cream unit for each firm Pi (in thousands of Lira), and you estimate the following equation: Q1=1+2Adi+3Pi+i The new OLS estimates are ^[483,15.3,2.1] and the estimnted standard errors of the estimator are SE(^)=[80,4.8,0.98]. i. When you show the results to your coworkers they are a little bit surprised. They ask you to provide an explanation for two things: (1) What does it mean when the estimate of 2 decreases when you include the price in the regression? (2) Why is the coefficient 3 positive? Doesn't that violate the law of demand 1 ? ii. Explain why the introduction of the price variable in the regression affected the estimated standard errors as well as the coefficient estimates. (c) You finally consider estimating this equation Qi=1+2Adi+3Pi+4Premium+Xi+ei where Premium, is a dummy variable that indicates if brand i is a premium brand of ice cream, and X is a vector of brand characteristics used as control variables. i. Explain what a dummy variable is. How do you think the introduction of the premium dummy variable will impact the estimate of 2 and 3 ? ii. Enumerate a set of controls that could be part of the X vector. Do you think that controlling for these variables will allow you to estimate the causal effect of advertisement on sales