Aggregation and the Estimation of Quality Change: Application to U.S. Import Prices

We characterize the contribution of changes in quality, price, and variety entry/exit to the aggregate price index for smooth, invertible demand systems, generalizing the standard results derived in the CES case. The results require the knowledge of heterogeneous cross-product elasticities of substitution. To apply them in practice, we also show how to identify rich demand systems using data only on prices and market shares, without the need for external cost-shock instruments or strong assumptions on the covariance between supply and demand shocks. Using this approach, we compute the U.S. import price index based on the Kimball demand system. We find that quality change on average lowered the inflation in import prices by around 0.007 log points annually (1989–2016). To further validate our approach, we show that it estimates price elasticities and quality changes similar to those found by the standard mixed logit (BLP) demand in data on the U.S. auto market.