Problem Set 3

Problem Set 3 Predictive Analytics for Business Strategy Be sure to include all group member names on submitted assignment file and display a screenshot of any relevant output. Solutions should be added in bold to this file. *If you are asked to show something with multiple steps, make sure those are listed clearly and not in paragraph form. Be concise with your answers. Each student is expected to work through the entire set and then discuss with the group. Utilize software that tracks changes so it is possible to see where you started and how each person contributed. 1. Suppose you have monthly observational data on sales of a specific children’s toy in the ToySales worksheet of PS3.xlsx. a. Write down a naïve model. Sales = b0 + b1(Price) + U b. Use the steps from class to identify confounding factors in that naïve model. 1. The treatment is sales price. 2. The treated are stores with a high price. The untreated are stores with a low price. 3. Differences between the treated and untreated are: - customer wealth - Competition - Pricing strategy (cost plus, target margin, premium, penetration, etc.) - Time of the year/seasonality - Economic conditions. 4. Which differences directly impact sales: - Customer Wealth (those with a lot of wealth can afford more discretionary purchases such as toys) - Competition (will impact the market’s spending habits) - Pricing strategy (the way we strategize our pricing can have a direct impact on sales) - Seasonality (holidays impacts consumers spending habits) - Economic conditions (will impact the average consumer’s ability to make discretionary purchases)

c. Write down the best model you can (in terms of exogeneity), given the data available to you. Discuss which of the confounding factors in the previous step your model controls for (and how). Sales it = b0 + b1(Price) it + ∑ k = 2 k = 12 α k Month(k) it + ∑ j = 2 j = 20 ± j Store(j) it + U it The above model is a two-way fixed effects model which controls for confounding factors using two tools. The first tool is a fixed entity effect. Store numbers are unchanged across the period for all entities, which means that every factor that is unchanged over the period is perfectly multicollinear with store number. Therefore, by adding a control for each store number, we can control for all factors that are also unchanged over the period for all entities, such as customer wealth, competition, and store pricing strategy. The next tool is a fixed time effect. Month moves parallel over time for all entities, which means that all factors which move in parallel over time for all entities are perfectly multicollinear with month, just as before. This means that by including a dummy variable for each month in the dataset, we can control for each factor that moves in parallel over time for all entities, such as seasonality. d. Estimate the latter model and discuss your estimate and whether it is exogenous (and why).

- Advertising budget - Competition - If they have a promotion to advertise - Customer loyalty (if they have very loyal customers they likely don’t need to advertise as much) - Market strategy - Market share - Seasonality - Brand image/recognition. 4. Factors that directly impact Revenues (In U) - Competition (competition impacts the market’s purchasing habits) - Customer loyalty (loyal customers will purchase more of their brand of choice) - Market share (market share indicates how much of the sales in the market the company makes) - Seasonality (holidays impact consumer spending habits) - Brand image/recognition (brand image in a market also impacts a company’s sales) c. Write down the best model you can (in terms of exogeneity), given the data available to you. Discuss which of the confounding factors in the previous step your model controls for (and how). Revenues it = b0 + b1(AdCampaign) it + b2(PriceIndex) it + b3(AvgPrice) it + ∑ k = 2 k = 12 α k Quarter(k) it + ∑ j = 2 j = 15 ± j Brand(j) it + U it We have used a two-way fixed effects model which controls for all variables which are fixed for every entity the whole period such as competition, customer loyalty (customer preferences are generally long-term), and brand image (once it is established it will remain) by including a dummy variable for each brand, controlling for all things that are unchanged during the period because they are perfectly multicollinear with brand in the dataset. Similarly, our model controls for every factor that moves in parallel for all entities, such as seasonality, by including a dummy variable for each month which controls for those factors because they are perfectly multicollinear with quarter in this dataset.

d. Estimate the latter model and discuss your estimate and whether it is exogenous (and why). According to our estimate, holding quarter, brand, price index, and average price constant, a brand with an ad campaign tends to have higher revenues by $51,864. However, our estimate is not exogenous because we did not control for market share, which is a category 3 confounding factor we identified earlier. Since we know there are confounding factors, we know our estimate of the causal impact of an ad campaign on revenues is incorrect.