Calculating Welfare Costs of Inflation in a Search Model with Preference Heterogeneity: A Calibration Exercise

Using U.S. cross-sectional data, this paper calculates the welfare cost of a 10% inflation for different individuals and finds that the difference in cost between the poorest 10%, measured by their expenditure share on cash goods, and the richest 10% is in the order of 176%. That is, a poor person is on average willing to forgive 176% more of their total consumption in order to have inflation reduced from 10% to 0. In absolute terms this represents a cost of 2.687% of consumption for the poorest and 0.974% for the richest. I accomplish this by introducing preference heterogeneity in a monetary search model first developed by Lagos and Wright (2005), and calibrate the model to match the expenditure share on cash goods and total expenditures for each individual type using data from the Consumer Expenditure Survey (CEX) for the second quarter of 1996. I also show that this welfare difference increases to 210% (10.522% for the poorest 10% and 3.401% for the richest 10%) whenever frictions in the use of money are imposed (holdup problem). The ability to explicitly model these frictions is the advantage of using this model. Hence, inflation in this framework, as other studies have shown, acts as a regressive consumption tax; and this regressiveness is augmented with the holdup problem.