The following information/data refers to Questions 7-10:

You were hired as a consultant by SeeEverything, a store chain, which sells binoculars. You obtain the data “binoculars_midterm.csv” (as shared on CANVAS: Download_Section_DataSets_Exams).

The file contains the following variables:

Sales: Sales volume data

Prices: Price of binoculars

Year: Calendar year

Country: Country of branch

Order_type: Sales channel the binoculars were sold through

Cost_plastic: costs of plastic (per kg)

Cost_sugar: costs of sugar (per 10 kg)

Cost_sand: costs of sand (per kg)

Note: We assume a constant price elasticity.

If we rely on naive OLS but still want to control for as many [observable] confounders as possible, what is the price elasticity of demand?

Question

The following information/data refers to Questions 7-10:

You were hired as a consultant by SeeEverything, a store chain, which sells binoculars. You obtain the data “binoculars_midterm.csv” (as shared on CANVAS:  Download_Section_DataSets_Exams).

The file contains the following variables:

Sales: Sales volume data

Prices: Price of binoculars

Year: Calendar year

Country: Country of branch

Order_type: Sales channel the binoculars were sold through

Cost_plastic: costs of plastic (per kg)

Cost_sugar: costs of sugar (per 10 kg)

Cost_sand: costs of sand (per kg)

Note: We assume a constant price elasticity.

If we rely on naive OLS but still want to control for as many [observable] confounders as possible, what is the price elasticity of demand?

BlackTom AI · Accepted Answer

First, I will restate what we’re given and what we’re being asked to do, then I’ll walk through how to approach estimating price elasticity of demand using a naive OLS framework with observable controls.

Restated scenario and goal:
- Data: binoculars_midterm.csv with variables Sales, Prices, Year, Country, Order_type, Cost_plastic, Cost_sugar, Cost_sand.
- Goal: If we rely on naive OLS while controlling for as many observable confounders as possible, what is the price elasticity of demand?
- Note in the prompt: The provided answer field contains a single value -0.457, but there are no answer choices listed for us to evaluate.

Key concept: price elasticity of demand via regression
- Price elasticity of demand (in a basic sense) measures the percentage change in quantity demanded (or Sales, in this case) in response to a 1% change in price.
- In a regression framework, if you log-transform both the dependent variable (Sales) and the price variable (Prices), the coefficient on log(Prices) is the own-price elasticity (assuming a log-log model). Specifically, if you estimate: log(Sales) = beta0 + beta1 * log(Prices) + controls + error, then beta1 is the elasticity (percentage change in Sales for a 1% change in Price).
- If you instead keep Sales in levels and Prices in logs, or keep both in levels, the interpretation changes and elasticity is not directly the coefficient on Prices. For elasticity, the standard approach is a log-log specification.

What to include as controls to approximate “as many observable confounders as possible”
- Time trends and fixed effects:
  - Year fixed effects or a flexible time trend to capture secular demand shifts, seasonality, or macroeconomic conditions that vary over time.
- Geography/fixed effects:
  - Country indicators to account for country-specific demand preferences, income levels, competing products, or market conditions.
- Channel/operational controls:
  - Order_type (sales channel) dummy variables to capture differential demand elasticities across channels (e.g., online vs in-store).
- Cost controls that plausibly affect demand and/or pricing:
  - Cost_plastic, Cost_sugar, Cost_sand arrays capture input costs that could influence pricing or demand through cost pass-through or product quality, though the exact channels should be theoretically justified.
- If you include these controls in a log-log model, you would interpret the coefficient on log(Prices) as the price elasticity conditional on those observables.

Why the answer -0.457 might be reported in this context
- If the regression specification used is a log-log model: log(Sales) = alpha + beta * log(Prices) + gamma' * X + error, and after estimating with the available controls X, the estimated beta could plausibly be around -0.457 for a consumer goods product like binoculars, depending on data, sample, and controls.
- The exact value depends on data sample, the time period, how sales are measured (e.g., volume), and which controls are included. It also depends on the treatment of zero sales (log of zero is undefined) and how missing data are handled. If you indeed ran such a regression and obtained beta ≈ -0.457, that would reflect the estimated elasticity given your model specification.

Why other plausible specifications or mis-specifications could lead to different conclusions
- If you do not log-transform Sales and Prices, the coefficient on Prices does not equal elasticity; interpreting elasticity would require additional transformations or a different estimation approach.
- If Prices is endogenous (e.g., pricing responds to unobserved demand shocks or to lagged sales), OLS may yield biased elasticity estimates. In a naive OLS framework, you typically assume exogeneity of Prices conditional on the controls.
- Omitting important confounders (e.g., income, marketing spend, promotions, seasonality) or mis-specifying fixed effects can bias the elasticity estimate away from the true value.
- If the price data vary little within groups or over time, the estimated elasticity could be unstable or imprecise due to weak variation in the independent variable.

Data handling considerations for this dataset
- Transformations: decide whether to work in logs for both Sales and Prices to obtain elasticity directly, ensuring there are no zero or negative values (add a small constant if necessary and theoretically justified).
- Controls: ensure that Cost_plastic, Cost_sugar, Cost_sand are included in a way that makes sense: if they proxy for input costs affecting product pricing or demand conditions, keep them in the model; if they are not relevant, consider excluding them to avoid multicollinearity or overfitting.
- Fixed effects: depending on the data structure, consider adding Year fixed effects or a year trend, and Country fixed effects, to isolate the variation in Prices that is exogenous to demand.
- Robustness: report robustness checks (alternative specifications, different subsets, or instrumental variable approaches if endogeneity is a concern) to see how elasticities vary.

Important note about the task as given
- The provided input shows an answer of -0.457 but lists no answer options. Since the instruction requires analyzing all answer options and explaining why each is correct or incorrect, the absence of options means we cannot evaluate multiple-choice alternatives. In practice, you would compare the estimated elasticity from the log-log OLS specification to the options provided and discuss why each option is or isn’t supported by the data and the model.

Summary guidance for answering in an exam or assignment
- Use a log-log regression specification to directly estimate elasticity:
  log(Sales) ~ log(Prices) + Year + Country dummies + Order_type dummies + cost controls + error
- The coefficient on log(Prices) is the price elasticity of demand conditional on the included observables.
- Interpret with caveats about endogeneity, omitted variables, and data limitations, and provide robustness checks if possible.
- If you must report a single elasticity value like -0.457, ensure you specify the exact model specification that produced it (transformation, sample, controls), so the value is interpretable and reproducible.

BUSA90544_2025_OCT Marketing Analytics Mid-term Exam 2025

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