Your Firm Is Attempting To Learn The Effectiveness Of A Newl
Your Firm Is Attempting To Learn The Effectiveness Of A Newly Develope
Your firm is attempting to learn the effectiveness of a newly developed television ad on its sales. To do this, it has randomly run the ad between 0 and 5 times during one week across a large number of television markets in the United States. It then recorded product sales for the following month for each market. To conduct the analysis, analysts at the firm have assumed the following data-generating process: Sales i = α + β Ads i + U i. Regressing Sales on Ads yields β̂ = 350. The firm would like to use this number to project the change in Sales when increasing weekly television ads to 20.
According to these results, what is the expected change in Sales when Ads increase from 5 to 20? Why should we be skeptical of our result from Part a? What can you do to find an estimate of the effect of increasing Ads from 5 to 20 that is more credible?
Paper For Above instruction
The analysis of advertising effectiveness is a crucial aspect of marketing analytics, especially when making projections based on observed data. In this context, the firm has regressed sales on the frequency of television ads and obtained an estimated coefficient (β̂) of 350. This estimate suggests that, on average, each additional run of the television ad increases sales by 350 units. Consequently, to project the change in sales from increasing ads from 5 to 20, the initial step involves understanding this coefficient's implications within the specified range.
Expected Change in Sales from Increasing Ads from 5 to 20
Based on the estimated coefficient (β̂ = 350), the expected change in sales when increasing the number of ads from 5 to 20 can be approximated by multiplying the increase in ad frequency by the coefficient:
\[
\Delta \text{Sales} = \betâ \times (20 - 5) = 350 \times 15 = 5250.
\]
Therefore, the model predicts that increasing weekly television ads from 5 to 20 would lead to an increase of approximately 5,250 units in sales.
Skepticism Toward the Result
Despite this straightforward calculation, significant skepticism is warranted regarding the credibility of this estimate. The fundamental concern arises from the assumption that the estimated coefficient accurately captures a causal effect of advertising on sales. Several factors threaten the validity of this inference:
- Endogeneity and Omitted Variable Bias: The regression model may suffer from omitted variables that influence both advertising and sales, such as market size, regional economic conditions, or seasonal effects. If these factors are correlated with advertising levels, the estimated β̂ would be biased.
- Reverse Causality: Higher sales environments might encourage firms to increase advertising, leading to a simultaneity problem that biases the estimate.
- Selection Bias: The random allocation of ad frequency to markets is crucial. If the ad exposure was not randomly assigned, the estimate might reflect underlying differences between markets rather than the true effect of ads.
- Limited Range of Variation: The ad frequency ranges only from 0 to 5 times in a week. Extrapolating the effect to 20 ads may involve assuming linearity beyond observed data, which could be invalid if the relationship is nonlinear or exhibits diminishing returns.
Improving the Credibility of the Estimate
To obtain a more credible estimate of the effect of increasing ads, especially from 5 to 20, the firm can consider the following approaches:
1. Use of Instrumental Variables (IV): Employ an instrumental variable related to ad placement but uncorrelated with the error term to isolate the causal impact. For example, leveraging exogenous variations like regional broadcast scheduling or policy changes affecting ad exposure.
2. Randomized Controlled Trials (RCTs): Implement A/B testing by randomly assigning different ad levels across markets. This approach ensures the exogeneity of ad increase and allows for a causal interpretation.
3. Panel Data and Fixed Effects: Collect data over multiple periods and include fixed effects for markets to control for unobserved heterogeneity, thus reducing bias from unmeasured, time-invariant factors.
4. Modeling Nonlinear Relationships: Use nonlinear models or include quadratic terms to capture diminishing returns or saturation effects at higher ad levels, improving the validity when projecting beyond the observed data.
5. Propensity Score Matching: Match markets with similar characteristics but different levels of advertising to compare outcomes more accurately.
In conclusion, while the coefficient suggests a sizable positive effect, the potential biases and assumptions underlying the regression model caution against naive extrapolation. Applying more rigorous econometric techniques and experimental designs can help isolate the true causal impact of increased advertising on sales, leading to more reliable projections when scaling ad campaigns from moderate levels, such as 5 ads, to higher levels like 20.
References
- Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.
- Journal of Marketing, 74(3), 93–110.
- American Economic Review, 104(5), 136–40.
- Health Economics, 7(2), 105–119.
- Biometrika, 70(1), 41–55.
- Introduction to Econometrics. Pearson.
- Econometric Analysis of Cross Section and Panel Data. MIT Press.
- The Econometrics Journal, 7(1), 266–276.
- University of Michigan Press.