Quantifying the Benefits of New Products with Residual-Income Demand: A Comment on Petrin (2002)

Abstract

Petrin (2002) specifies automobile demand with logarithmic residual income, α_i log(y_i - p_j), while the author-distributed estimation and markup programs use its first-order price term, -α_g p_j/y_i. This Comment traces the two operators through choice probabilities, price derivatives, markups, and welfare. A finite economy gives different rankings, choice probabilities, and compensating variation under a common shock law. In a public reconstruction, the linear operator reproduces the reported mean income of minivan purchasers, 36.091 thousand dollars, with a value of 36.051. Replacing the operator by the printed affordable-set model and recontracting every product share gives 45.349; a matched seven-parameter profile gives 40.456. The demand-moment comparison changes direction relative to the CEX value. A Taylor bound measures the approximation error. Three implementations using a common utility, derivative, and support show which welfare calculations the available archive can reproduce.

Technical point

The printed logarithmic residual-income utility and the distributed first-order price term can generate different rankings, choice probabilities, derivatives, markups, and welfare calculations.

Scope