A dissertation
CHAPTER 5: Review of Price Endogeneity
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- 5.2. Background
- 5.2.1. Causes of Endogeneity
- 5.2.2. Endogeneity Bias
- 5.2.2.1. Evidence of Endogeneity Bias in Air Travel Demand Literature
- 5.2.2.2. Evidence of Endogeneity Bias in Other Travel Demand Literature
- 5.2.2.3. Evidence of Endogeneity Bias in Other Industry Demand Literature
CHAPTER 5: Review of Price Endogeneity5.1. AbstractPrice endogeneity occurs when correlation exists between price and the error term (or unobserved factors) in a model. In demand models, prices are generally considered to be endogenous because prices are strongly influenced by demand and demand is, in turn, strongly influenced by prices. Price endogeneity is well documented in economics literature and is known to cause problems when analyzing data, as endogeneity can lead to unrealistic and misleading model coefficient estimates. Although price endogeneity has been shown to be prevalent in many industries, few studies of air travel demand have explored endogenous airline prices. In this chapter, we explain the causes of endogeneity and review literature that has corrected for price endogeneity, focusing on empirical studies that have demonstrated endogeneity bias in coefficient estimates. Instrumental variable methods, which are used to correct for endogeneity, are discussed. Also, several different types of instruments are reviewed, and studies that have utilized each type of instrument are cited as examples. Finally, tests for endogenous regressors, valid instruments, and weak instruments are discussed, and corresponding Stata® codes are provided. 5.2. BackgroundAn explanatory variable is called endogenous when there is correlation between that variable and the error term (or unobserved factors) in a model. In Ordinary Least Squares (OLS) regression models, this correlation means that the conditional expectation of the error term on the explanatory variable will not be equal to zero, which violates a main assumption required to ensure estimator consistency (Greene, 2003). Similarly, in discrete choice models, this correlation will lead to inconsistent estimators. Thus, models that are estimated without correcting for endogeneity will lead to inconsistent parameter estimates where some level of unobserved bias will exist. In this chapter, we explain the causes of endogeneity and review some of the literature that has corrected for price endogeneity, focusing on empirical studies that have demonstrated endogeneity bias in coefficient estimates. Instrumental variable methods, which are used to correct for endogeneity, are discussed and different types of instruments are reviewed. Finally, tests for endogenous regressors, valid instruments, and weak instruments are discussed, and corresponding Stata® codes are provided. This chapter provides an overview of the main concerns related to endogeneity and provides a literature review of some of the most cited papers. Where appropriate, applications in travel demand are discussed. Readers are referred to books by Greene (2003) and Train (2009) and a dissertation by Guevara-Cue (2010) for excellent comprehensive reviews of endogeneity.
Omitted variables can also cause endogeneity when one or more relevant explanatory variables have been omitted from the model. Endogeneity occurs when the omitted variable (often unobserved attributes of the product) affects demand and is also correlated with price. Theoretically, airline demand models could suffer from omitted variable bias if there are unobserved attributes of flights that influence customer choice and are also correlated with price. For example, variables that are not often captured in discrete choice models are variables related to entertainment (such as free Wi-Fi on some flights or equipment types). If free Wi-Fi influences customer choice of a flight and is also correlated with the price of a flight, then Wi-Fi would be an example of an omitted variable that causes endogeneity. Endogeneity can also occur as a result of measurement error when an independent variable is not measured perfectly. This could occur in airline demand models if we do not know the actual price a customer paid for a ticket.
To understand the direction of the bias better, it is helpful to think through the problem. In supply and demand models, when demand for a product is high firms often increase prices, and customers are willing to pay the higher prices to have access to the inventory. As a result, traditional modeling techniques will underestimate the influence of price on demand. In fact, sometimes traditional modeling techniques may even estimate that price positively impacts demand, which is counterintuitive. 5.2.2.1. Evidence of Endogeneity Bias in Air Travel Demand LiteratureWithin the airline literature, few studies have corrected for price endogeneity in models of air travel demand. Hsiao (2008) estimates discrete choice models of aggregate quarterly air passenger demand using aggregate quarterly data from DB1B and T100. Hsiao finds that without correcting for endogeneity, fare coefficients are underestimated, VOT estimates are greatly overestimated, and price elasticities are counterintuitive. For example, in three uncorrected models, VOT is estimated to be between $614 and $726 per hour (between 39 and 46 times larger than the median wage rate of 2004)17. After correcting for endogeneity, VOT is estimated to be $16.7 and $21.3 per hour, which is much more reasonable. Additionally, Hsiao shows that in models which did not account for endogeneity, mean fare elasticity estimates of market demand were inelastic (between 0.154 and 0.365), whereas in models that corrected for endogeneity the mean fare elasticity estimates of market demand were elastic (between 1.052 and 2.662). In a more recent study, Granados, Gupta and Kauffman (2012) estimate log-linear regression models and estimate price elasticity of demand for air travel booked through online and offline channels. The authors use a dataset of airline bookings sold by travel agencies through global distribution systems (GDSs)18. In a model estimated on the whole dataset, price elasticity of demand is estimated to be inelastic ( 0.14) in an OLS regression model that did not correct for endogeneity. However, in a model that corrected for endogeneity, fare elasticity of demand is estimated to be approximately unit elastic ( 1.03). Berry and Jia (2009) estimate the impact of demand and supply changes on airline profitability using a random-coefficient discrete choice model of demand and aggregate quarterly data from DB1B. Gayle (2004) uses aggregate quarterly data from DB1B to investigate air passenger itinerary choice behavior. Both studies correct for price endogeneity but do not report the change in parameter estimates for uncorrected models.
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