Time preference (timepref)

Table of contents

Overview

The timepref parameter represents the rate of time preference (or discount rate) for households in each region. This fundamental parameter determines how households value future consumption relative to current consumption and plays a central role in the consumption-saving decision.

Parameter

timepref

SYM Declaration:

parameter timepref(regions)    'time preference rate'

Definition: The pure rate of time preference for households. This parameter represents the rate at which households discount future utility relative to current utility, independent of any changes in consumption levels.

Calibration: Set from the model configuration file:

def set_timepref_parameters(self):
    """
    timepref - time preference rate for each region.
    """
    timepref: pd.DataFrame = pd.DataFrame(
        self.configuration.rate_of_time_preference,
        index=["timepref"],
        columns=self.sym_data.regions_members,
    )
    self.insert_parameter("timepref", timepref)

Usage in Model: Used in the consumption equation for forward-looking consumers:

CONP = fore_c*(timepref+RISW)*WELT*exp(PRID-PRCT)
     + (1-fore_c)*mpc*INCM*exp(PRID-PRCT)
     + SHKC

Where:

  • fore_c: Share of consumption driven by forward-looking behavior
  • timepref: Time preference rate
  • RISW: Risk premium on wealth
  • WELT: Total wealth
  • PRID: Domestic price index
  • PRCT: Consumption price index

Economic Interpretation

Euler Equation

The consumption equation is derived from the household’s intertemporal optimization problem. For forward-looking consumers, optimal consumption satisfies:

\[C = (\rho + \text{risk}) \cdot W\]

Where:

  • $C$ is consumption
  • $\rho$ is timepref (time preference rate)
  • $\text{risk}$ is the risk premium (RISW)
  • $W$ is total wealth (WELT)

Relationship to Interest Rates

In steady state, the time preference rate is related to the real interest rate:

\[r = \rho + g\]

Where:

  • $r$ is the real interest rate
  • $\rho$ is the time preference rate
  • $g$ is the growth rate of consumption (related to labgrow)

Savings Behavior

Higher timepref values imply:

  • Households are more impatient
  • Higher propensity to consume out of wealth
  • Lower savings rates
  • Higher equilibrium real interest rates

Lower timepref values imply:

  • Households are more patient
  • Lower propensity to consume out of wealth
  • Higher savings rates
  • Lower equilibrium real interest rates

Typical Values

Time preference rates are typically in the range of 1-5% per year:

  • Patient households: 1-2% per year
  • Moderate impatience: 2-3% per year
  • Impatient households: 3-5% per year

Policy Implications

Fiscal Policy

The time preference rate affects:

  • Government debt sustainability: Higher timepref means households discount future tax burdens more heavily
  • Ricardian equivalence: Lower timepref strengthens the Ricardian offset to fiscal policy

Monetary Policy

The time preference rate affects:

  • Interest rate transmission: The gap between market rates and timepref drives savings/consumption decisions
  • Intertemporal substitution: How households respond to changes in real interest rates

Climate/Long-term Policy

The time preference rate is crucial for:

  • Discounting future damages: How much weight to give to long-term climate impacts
  • Infrastructure investment: Valuation of long-lived capital projects
Parameter Description
fore_c Share of consumption driven by foresight
mpc Marginal propensity to consume
labgrow Growth rate of effective labor
RISW Risk premium on wealth (variable)

References