Consumption behavior parameters (fore_c, mpc)

Table of contents

Overview

These parameters govern household consumption behavior in the G-Cubed model. The model distinguishes between two types of consumers:

  1. Forward-looking consumers: Follow the permanent income hypothesis and base consumption on lifetime wealth
  2. Liquidity-constrained consumers: Base consumption on current income using a marginal propensity to consume

The split between these two types of behavior is controlled by fore_c, while mpc determines how strongly liquidity-constrained consumers respond to current income.

Parameters

fore_c

SYM Declaration:

parameter fore_c(regions)    'shr of C driven by foresight'

Definition: The share of aggregate consumption that is driven by forward-looking (foresighted) behavior. This represents the fraction of consumers who optimize their consumption based on lifetime wealth rather than current income.

Calibration: Default value: 0.3 (30% of consumption is forward-looking)

# Share of consumers that are forward looking in their consumption decisions
FORE_C: float = 0.3

Usage in Model: Used in the consumption equation:

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

Where:

  • First term: Forward-looking consumption based on wealth (WELT)
  • Second term: Liquidity-constrained consumption based on income (INCM)
  • SHKC: Consumption shock

mpc

SYM Declaration:

parameter mpc(regions)    'marginal propensity to consume'

Definition: The marginal propensity to consume out of current income for liquidity-constrained (non-forward-looking) households. This parameter determines how much of each additional dollar of income is spent on consumption.

Calibration: Calibrated from model configuration. The value is set in the model configuration file and represents the fraction of current income that liquidity-constrained households consume.

def set_mpc_parameters(self):
    """
    mpc - Marginal Propensity to Consume for households that are unable 
    to conform to the lifetime income hypothesis.
    """
    mpc: pd.DataFrame = pd.DataFrame(
        self.configuration.marginal_propensity_to_consume,
        index=["mpc"],
        columns=self.sym_data.regions_members,
    )
    self.insert_parameter("mpc", mpc)

Usage in Model: Used in the consumption equation (see above). The term (1-fore_c)*mpc*INCM represents consumption by liquidity-constrained households.

Economic Interpretation

Forward-Looking vs. Liquidity-Constrained Behavior

The consumption equation can be written as:

\[C = \underbrace{\text{fore\_c} \cdot (r + \text{risk}) \cdot W}_{\text{Forward-looking}} + \underbrace{(1-\text{fore\_c}) \cdot \text{mpc} \cdot Y}_{\text{Liquidity-constrained}}\]

Where:

  • $C$ is consumption
  • $W$ is wealth
  • $Y$ is current income
  • $r$ is the time preference rate

Policy Implications

  • Higher fore_c:
    • Consumption responds more to changes in wealth and interest rates
    • Monetary policy has stronger effects through wealth channels
    • Consumption is smoother over time
  • Lower fore_c (more liquidity-constrained):
    • Consumption responds more to current income changes
    • Fiscal policy (tax cuts, transfers) has larger immediate effects
    • Consumption is more volatile
  • Higher mpc:
    • Stronger consumption response to income changes for constrained households
    • Larger fiscal multipliers
    • Greater sensitivity to business cycle fluctuations

References