Philipp Hochmuth

Declining Hours Worked Among Entrepreneurs

Job Market Paper (PDF)

In this paper, I show that over the past 35 years, hours worked by entrepreneurs have fallen substantially: by five hours per week more than for workers. This decline accounts for the bulk of the fall in total hours worked and is present in all available subgroups (gender, age, education, number of children, occupation, and industry). It is robust to adjusting for compositional effects and occurs without noticeable changes in the relative hourly income of entrepreneurs. The decline originates from the top of the hours distribution: the share of entrepreneurs working more than 45 hours has dropped significantly. I interpret these facts using a Roy model of occupational choice, augmented with an intensive labor supply margin. The model allows the marginal return of working an additional hour to depend on the level of hours. I estimate the model at two points in time and find that a fall in the relative marginal return at higher hours worked is key for explaining the drop in hours and the drop in the share of entrepreneurs. I show that changes in the market structure of the goods or services that entrepreneurs sell can account for this.

A Nonhomothethic Price Index and Cost-of-Living Inequality

(joint with Markus Pettersson and Christoffer J. Weissert) Working Paper (PDF) Online Appendix (PDF)

We derive a price index based on nonhomothetic preferences and use it to document cost-of-living inequality in the United States. Our framework generalizes all known superlative price indices and admits heterogeneous indices across the distribution of household consumption expenditures which aggregate consistently into welfare-relevant group indices. When necessities and luxuries are separable in the expenditure function, this generalization avoids the need to estimate a complete demand system. Using CEX-CPI data for the period 1995–2020, we find no differences in average inflation rates across the expenditure distribution, but 2.5 times higher inflation volatility for the bottom decile compared to the top decile, stemming from a larger exposure to food, gasoline, and utilities. These results contrast with the inequality found by the typical approach of constructing separate homothetic price indices for different consumer groups, and our analysis suggests that the difference follows from an income-effect bias in the homothetic group-specific indices.

A Distributional PCE Price Index From Aggregate Data

(joint with Markus Pettersson and Christoffer J. Weissert) Working Paper (PDF)

This paper proposes a method to measure individual and aggregate changes in the cost of living when consumer behavior is nonhomothetic and microdata on consumption expenditures are not available. Aggregate prices and expenditure shares together with a single cross-sectional distribution of expenditures are sufficient to create a distribution of nonhomothetic cost-of-living indices with this approach. The cost-of-living indices derive from PIGL preferences, generalize the Törnqvist price index, and only contain one unknown parameter. Because PIGL preferences aggregate consistently, this parameter can be identified from aggregate data. Using US Personal Consumption Expenditure (PCE) data, we apply the method to obtain a nonhomothetic PCE price index covering 71 product groups for the period 1959 to 2023. This index reveals a 0.39 percentage point gap in average annual inflation rates between the poorest and richest ten percent since 1959 and a 1.9 percentage point gap throughout 2022, thus suggesting that poorer households are hit harder both in the long run and in the recent inflation surge.

Welfare Implications of an Energy Price Shock

(joint with Per Krusell and Kurt Mitman)