Monetary policy parameters (int_elast, mongdp)

Table of contents

Overview

These parameters govern money demand and the role of money in the wealth equation of the G-Cubed model. They determine how households respond to interest rate changes in their money holdings and how money balances contribute to total wealth.

Parameters

int_elast

SYM Declaration:

parameter int_elast(regions)    'interest elasticity of money demand'

Definition: The interest elasticity of money demand. This parameter determines how sensitive the demand for money is to changes in the nominal interest rate. A negative value indicates that higher interest rates reduce money demand (opportunity cost effect).

Calibration: Default value: -0.6

# Interest elasticity of money demand
INT_ELAST: float = -0.6

Usage in Model: Used in the money demand equation:

MONE = PRID + ln(OUTP) + int_elast*INTN + SHKM

Where:

  • MONE: Money demand (logged)
  • PRID: Price index (logged)
  • OUTP: Aggregate output
  • INTN: Nominal interest rate
  • SHKM: Money demand shock

mongdp

SYM Declaration:

parameter mongdp(regions)    'coefficient on MONE in WELT'

Definition: The coefficient on real money balances in the total wealth equation. This parameter determines how much money holdings contribute to household wealth.

Calibration: Default value: 0 (set in set_other_parameters())

The default implementation sets this to zero, meaning money balances do not directly contribute to measured wealth:

def set_other_parameters(self):
    """
    mongdp - The coefficient on money in the equation for total wealth. 
    Set to zero in the default implementation of the parameter calibration system.
    """

Usage in Model: Used in the total wealth equation:

WELT = BOND
     + ASSU/exp(REXN)
     + mongdp*exp(MONE)/exp(PRID)
     + WELH
     + LAMY*CAPY
     + LAMZ*CAPZ
     + sum(sec_std,STM)

Where:

  • WELT: Total wealth
  • BOND: Government bond holdings
  • ASSU: Foreign asset holdings
  • mongdp*exp(MONE)/exp(PRID): Real money balances weighted by mongdp
  • WELH: Human wealth
  • LAMY*CAPY, LAMZ*CAPZ: Shadow value of capital holdings
  • STM: Equity holdings

Economic Interpretation

Money Demand

The money demand equation follows a standard specification:

\[M = P \cdot Y \cdot i^{\eta}\]

In log form: \(\ln(M) = \ln(P) + \ln(Y) + \eta \cdot i\)

Where:

  • $M$ is nominal money demand
  • $P$ is the price level
  • $Y$ is real output
  • $i$ is the nominal interest rate
  • $\eta$ is int_elast (interest elasticity)

Interest Elasticity

With int_elast = -0.6:

  • A 1 percentage point increase in interest rates reduces money demand by approximately 0.6%
  • This reflects the opportunity cost of holding money vs. interest-bearing assets
  • The negative sign is consistent with standard monetary theory

Money in Wealth

When mongdp = 0 (default):

  • Real money balances do not contribute to measured wealth
  • This is a simplifying assumption that treats money as a medium of exchange only

When mongdp > 0:

  • Real money balances contribute to household wealth
  • Higher money holdings increase total wealth
  • This can affect consumption through wealth effects

Policy Implications

Interest Rate Policy

The int_elast parameter affects:

  • Monetary transmission: How interest rate changes affect money demand
  • Velocity of money: The relationship between money supply and nominal GDP
  • Inflation dynamics: Through the quantity theory of money channel

Quantitative Easing

The mongdp parameter matters for:

  • Wealth effects: Whether money creation affects wealth
  • Consumption response: Through the marginal propensity to consume out of wealth
  • Portfolio rebalancing: How households view money vs. other assets
Variable Description
MONE Money demand (logged)
INTN Nominal interest rate
PRID Price index (logged)
WELT Total wealth
OUTP Aggregate output

References

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