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  Measurement Error and Misspecification in Demand-Based Diversion Ratios Author Names(s)
                  Patrick Sun

        
                  **Date Issued:**
        August 3, 2022

        
          Body
                  **OEA Working Paper 53**

**Abstract:** When analyzing a horizontal merger it is often important to determine the extent to which the products of the merging firms are close substitutes. A commonly-used measure to assess the closeness of substitution is the diversion ratio: the fraction of demand leaving a product due to a price increase that goes to a specific rival product. One method of estimating diversion ratios is to first estimate a demand system and then calculate the implied diversion ratios. When estimating a demand system, two issues arise. First, using incorrect data values leads to measurement error. Second, using an incorrect model of demand leads to specification error. Through simulated datasets and using a known demand system, I examine how these errors can bias the diversion ratio estimates and a related, preliminary estimate of competitive harm, the Gross Upward Pricing Pressure Index (GUPPI). I find that even moderate measurement error results in biases comparable to the biases in share-based estimates of diversion that underestimate diversion between similar products. Further, I find that model specification error can result in substantial bias in the diversion and GUPPI estimates resulting in either overestimates or underestimates, depending on the specific nature of the specification error. My results suggest that: (1) measurement error is a serious concern when using demographic data to proxy for differences in price-sensitivity if that data do not very accurately represent the sample demographics; (2) practitioners should prefer flexible random coefficient models to avoid specification error; (3) practitioners should consider using observed markups for GUPPIs instead of estimating them; and (4) practitioners should more carefully consider the use of demand-based diversion ratios relative to alternatives.

**OEA Working Paper 53**
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