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The Beta-Delta-DELTA Sweet Spot

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Listed:
  • David Laibson
  • Peter Maxted

Abstract

When solving discrete-time consumption models with present-biased time preferences, backwards induction generates equilibria that are non-robust in the sense that policy functions are often sensitive to parameter choices, including the modeler's choice of the time-step. The current paper identifies a range of "sweet-spot" time-steps that (i) contains the psychologically relevant present bias horizons, and, (ii) generates numerically indistinguishable (i.e., robust) policy functions. This sweet spot includes both a computationally feasible range of discrete-time cases and the limiting continuous-time case (Harris and Laibson, 2013). Accordingly, researchers modeling present bias in buffer stock models can choose either discrete-time cases calibrated to be in the sweet spot or the analytically tractable continuous-time case; these approaches yield essentially identical policy functions.

Suggested Citation

  • David Laibson & Peter Maxted, 2023. "The Beta-Delta-DELTA Sweet Spot," NBER Working Papers 30822, National Bureau of Economic Research, Inc.
    • Handle: RePEc:nbr:nberwo:30822
    Note: AG EFG ME PE
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    JEL classification:

    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • D9 - Microeconomics - - Micro-Based Behavioral Economics
    • D99 - Microeconomics - - Micro-Based Behavioral Economics - - - Other
    • E03 - Macroeconomics and Monetary Economics - - General - - - Behavioral Macroeconomics
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth
    • E7 - Macroeconomics and Monetary Economics - - Macro-Based Behavioral Economics
    • G51 - Financial Economics - - Household Finance - - - Household Savings, Borrowing, Debt, and Wealth

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