We use three quasi-natural experiments in Mexico and one in Panama to estimate the effects of having the option to pay with cash on Uber rides. The ability to pay in cash affects the demand for rides, which is reflected in large changes in the total number of trips, fares, miles, and number of users after Uber introduced cash payments, particularly in lower-income city blocks. On the other hand, the effects on prices, estimated times of arrival, and competitor pricing are negligible, consistent with the supply of trips being very elastic. Although cash payments naturally increase the fraction of users that pay exclusively with cash, more than half of the users have access to both cards and cash, and alternate between payment methods. We find evidence consistent with cash and card payments being imperfectly substitutable at both the intensive and extensive margins, which magnifies the effect of policies that restrict the availability of payment methods.

We propose an analytical method to analyze the propagation of an aggregate shock in a broad class of sticky‐price models. The method is based on the eigenvalue‐eigenfunction representation of the dynamics of the cross‐sectional distribution of firms' desired adjustments. A key novelty is that we can approximate the whole profile of the impulse response for any moment of interest in response to an aggregate shock (any displacement of the invariant distribution). We present several applications for an economy with low inflation and idiosyncratic shocks. We show that the shape of the impulse response of the canonical menu cost model is fully encoded by a single parameter, just like the Calvo model, although the shapes are very different. A model with a quadratic hazard function, arguably a good fit to the micro data on price setting, yields an impulse response that is close to the canonical menu cost model.

We give a full analytic characterization of a large class of sticky-price models where the firm’s price-setting behavior is described by a generalized hazard function. Such a function allows for a vast variety of empirical hazards to be fitted. This setup is microfounded by random adjustment costs, as in Caballero and Engel (1999), or by information frictions, as in Woodford (2009). We establish two main results. First, we show how to identify all the primitives of the model, including the distribution of the fundamental adjustment costs and the implied generalized hazard function, using the distribution of price changes. Second, we derive a sufficient statistic for the aggregate effect of a monetary shock: given an arbitrary generalized hazard function, the cumulative impulse response of output to a once-and-for-all monetary shock is proportional to the ratio of the kurtosis of the steady-state distribution of price changes over the frequency of price adjustment. We prove that Calvo’s model yields the upper bound and Golosov and Lucas’s model the lower bound on this measure in the class of random menu cost models.