Abstract
Analysts of air travel markets, which include antitrust authorities, are interested in understanding the extent to which the presence of intermediate stop(s) products influences the pricing of nonstop products. This paper uses a structural econometric model to investigate the potential pricing interdependence between these two product types in domestic air travel markets. Counterfactual experiments using the estimated model suggest that in many (but far from a majority) markets the current prices of nonstop products are at least 5% lower than they would otherwise be owing to the presence of intermediate-stop(s) products.
Acknowledgments
We thank the editor, Julian Wright, two anonymous referees, Philippe Belley, Leilei Shen, Dong Li, Tian Xia, Kate Ho, and Yang-Ming Chang for very helpful comments and suggestions. Any remaining errors are our own.
Appendix
Appendix A: A Linear Demand Example Illustrating the Multi-product Firm Effect
The following example is used to illustrate the multi-product firm effect assuming linear demand and constant marginal cost.
Assume an airline is a multi-product monopolist who offers differentiated products 1 and 2 in an origin-destination market, where product 1 is a nonstop product while product 2 is an intermediate-stop(s) product. The products’ linear demand equations are:
where 0<β<1. For simplicity, assume each product has the same constant marginal cost, c. The variable profit for the airline is:
The corresponding first-order conditions are:
Thus, the equilibrium prices for products 1 and 2 are:
Now suppose we counterfactually eliminate the intermediate-stop(s) product, which is product 2. In other words, the airline becomes a single-product monopolist who only offers nonstop product 1 in the market. The product’s linear demand equation is:
With the assumption of constant marginal cost, c, the variable profit is:
The corresponding first-order condition is:
Thus, the monopoly price is:
Comparing the price of product 1 before and after the counterfactual exercise, we can see that
Appendix B: Additional Tables
Single-equation Estimation of Nested Logit Demand Equations with and without Instruments.
| Variable | With Instruments | Without Instruments | ||
|---|---|---|---|---|
| Coefficient | Std. Dev. | Coefficient | Std. Dev. | |
| Price | −12.640* | (1.206) | 0.358* | (0.135) |
| Interstop | −1.539* | (0.052) | −1.059* | (0.032) |
| Inconvenience | −0.921* | (0.088) | −0.950* | (0.060) |
| HUB_Origin | 1.101* | (0.071) | 0.864* | (0.032) |
| Tour | 0.611* | (0.048) | −0.592* | (0.036) |
| Slot_control | −0.392* | (0.056) | 1.131* | (0.043) |
| σ | 0.039 | (0.025) | 0.428* | (0.008) |
| Constant | −6.564* | (0.220) | −8.434* | (0.115) |
| R2 | – | 0.4662 | ||
| N | 11,425 | 11,425 | ||
*Represents statistical significance at the 0.05 level. Standard errors are in parentheses. Ticketing carrier dummy variables are included in the demand model for estimation even though the associated coefficient estimates are not reported in the table.
Counterfactual Experiment 2A – An Experiment that Assumes the Counterfactual Elimination of Intermediate-stop(s) Products Causes Marginal Cost of Nonstop Products to Uniformly Increase by 2.5%.
Counterfactual Experiment 2B – An Experiment that Assumes the Counterfactual Elimination of Intermediate-stop(s) Products Causes Marginal Cost of Nonstop Products to Uniformly Decrease by 2.5%.
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