Working Paper: NBER ID: w30037
Authors: Emmanuel Farhi; Alan Olivi; Iván Werning
Abstract: We provide a price theory for incomplete markets that extends the traditional Walrasian analysis. We derive formulas expressing the consumption response to current and future changes in interest rates and income. Our analysis provides a natural decomposition of these responses into substitution and income effects with structural interpretation, emphasizing statistics such as the marginal propensity to save and local measures of prudence in utility. We handle general uncertainty in a compact and intuitive manner by adjusting probability distributions: a risk-adjusted probability, commonly used in finance, and a novel prudence-adjusted probability, specifically useful for incomplete markets. Our formulas reveal various cross-restrictions implied by the theory on consumer behavior. Numerical explorations show that the new statistics we identify matter significantly to understand aggregate demand in incomplete markets, beyond the impact of heterogeneous marginal propensities to consume or binding borrowing constraints.
Keywords: No keywords provided
JEL Codes: D1; D52
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| change in interest rates (E43) | current consumption (E20) |
| change in income (E25) | current consumption (E20) |
| change in income (E25) | income effects (H31) |
| change in interest rates (E43) | income and substitution effects (H31) |
| marginal propensity to save (E21) | responsiveness to future interest rate changes (E43) |
| binding of borrowing constraints (D10) | marginal propensity to save (E21) |
| risk-adjusted probability (C46) | consumption responses (D12) |
| prudence-adjusted probability (D81) | consumption responses (D12) |
| marginal value of wealth * net present value of income change (E21) | consumption response to future income changes (E21) |
| precautionary effect (D18) | dampens income effect of future interest rate cuts (E43) |