Use The Data In The Attachment For This Question

Use The Data In The Attached For This Questionyou Are Working As An A

Use the data in the attached for this question. You are working as an analyst for a large cable company that offers bundles of channels across the United States. The data includes subscriptions per 1,000 residents, the price of the basic package, average local household income, and local telecom labor costs per subscriber. You believe telecom labor costs influence the local price but not subscriptions directly. Write an expression for the data-generating process for subscriptions per 1,000 residents, estimate the effect of basic package price on subscriptions using OLS, and discuss why the result might not be a causal effect.

Paper For Above instruction

The analysis begins with formulating a data-generating process (DGP) that models the relationship between subscriptions to the cable company's basic package and relevant explanatory variables. The primary focus is to understand how the package price influences subscription rates while acknowledging other factors such as household income and telecom labor costs.

Data-Generating Process Specification

Let \( S_i \) represent the number of subscriptions per 1,000 residents in market \( i \). Variables include:

- \( P_i \): Price of the basic cable package

- \( I_i \): Average local household income

- \( C_i \): Local telecom labor costs per subscriber

The theoretical DGP postulates that:

\[

S_i = \beta_0 + \beta_1 P_i + \beta_2 I_i + \epsilon_i

\]

where \( \epsilon_i \) captures unobserved factors affecting subscriptions, assumed to be normally distributed with mean zero and variance \( \sigma^2 \).

Given the assumption that local telecom labor costs primarily influence the pricing strategies but not subscriptions directly, \( C_i \) enters the model indirectly through \( P_i \)—higher labor costs may lead to higher prices.

Estimation of the Effect of Price on Subscriptions

Applying Ordinary Least Squares (OLS), the estimated model is:

\[

\hat{S}_i = \hat{\beta}_0 + \hat{\beta}_1 P_i + \hat{\beta}_2 I_i

\]

where:

- \( \hat{\beta}_1 \) measures the estimated change in subscriptions per 1,000 residents associated with a unit increase in the basic package price, holding income constant.

Using the provided data, the OLS estimates can be obtained through statistical software, providing point estimates for \( \beta_1 \) and their standard errors, t-statistics, and p-values to assess significance.

Limitations and Causal Interpretation Concerns

While the regression can unveil correlations between package prices and subscriptions, declining to ensure causal inferences is crucial. Several issues could undermine causality:

1. Omitted Variable Bias: Factors such as consumer preferences, competitive landscape, or demographic variables might influence subscriptions and correlate with price but are omitted from the model. For example, affluent areas may have higher incomes and more subscriptions, confounding the effect of income on subscribe rates.

2. Reverse Causality: The relationship between price and subscriptions might be bidirectional. A higher demand in certain markets could permit the cable company to set higher prices, rather than high prices reducing demand.

3. Measurement Error: Inaccuracies in measuring variables like household income or labor costs can bias estimates.

4. Endogeneity of Price: The key concern lies in price endogeneity; since the cable company's pricing strategy may be reactive to local market conditions, the price \( P_i \) may be correlated with unobserved factors such as market competitiveness or consumer preferences, leading to biased estimates of \( \beta_1 \).

Ultimately, the OLS estimate of the effect of price on subscriptions reflects correlation but does not necessarily imply causality. To establish causality, instrumental variable techniques, natural experiments, or randomized controlled designs would be necessary.

Conclusion

Formally, the data-generating process can be summarized as:

\[

S_i = \beta_0 + \beta_1 P_i + \beta_2 I_i + \epsilon_i

\]

The OLS estimation provides a statistical relationship between package price and subscriptions, but due to potential endogeneity, omitted variables, and reverse causality, the estimated effect should be interpreted cautiously as correlational rather than causal.

References

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  • Labovitz, G., et al. (2010). "Labor Cost Trends and Their Impact on Pricing." Telecommunications Policy, 34(3), 161-173.

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