In this problem set we will decompose a nave comparison of averages into a treatment effect and selection bias. Suppose a wine seller has 1000

In this problem set we will decompose a naïve comparison of averages into a treatment effect and  selection bias. Suppose a wine seller has 1000 different wines on offer and decides to advertise half  of them. We are asked to assess the effect of advertising on wine sales, and are given last month's 

sales figures.

Assume average sales for advertised wines were $600, whereas non-advertised wines were $800. 

Assume also that the selection bias in y0 is $300 and the selection bias in y1 is -$400. Complete

the table below and explain your answers. (Note: Half of wines are advertised).

Not Advertised Advertised Total

Sales with advertising $600

Sales without advertising $800

Difference

Consider the regression model Yi = 0 +1Di +Ui and suppose an analyst has sales figures for 100 randomly selected wines, some of which were advertised and some which were not. When the analyst runs the regression, what sign do you expect  1 to have? Explain why correlation is not indicative of causation in this example by comparing the expected value of  1 with the ATE, ATT and ATU of advertising. Suppose that the profit margin is 25% of sales. If the cost of advertising a bottle of wine is $40 per month, should the wine merchant also advertise the 500 wines that have not yet been advertised  in the coming month?

 If the wine merchant only knew the ATE before advertising the wines, would they pay to have  all wines advertised in the coming month?