Exchange rate intervention parameter (alph_rex)

Table of contents

Overview

The alph_rex parameter controls the speed of adjustment of the actual real exchange rate toward the shadow (market-determined) real exchange rate in regions with capital controls. This parameter is central to modeling capital account interventions and managed exchange rate regimes.

Parameter

alph_rex

SYM Declaration:

parameter alph_rex(regions)    'weight on shadow real exchange rate in CA intervention'

Definition: The weight on the shadow real exchange rate in the current account (CA) intervention mechanism. This parameter determines how quickly the controlled real exchange rate (REXB) adjusts toward the market-determined real exchange rate (REXC) in regions with capital controls.

Calibration: Default value: 0.2

# Shadow exchange rate partial adjustment is at the rate determined by alph_rex 
# for regions with capital controls.
ALPH_REX: float = 0.2

Usage in Model:

For regions with capital controls (e.g., China), the real exchange rate follows a partial adjustment mechanism:

REXB = (1/(1+alph_rex))*REXL + (alph_rex/(1+alph_rex))*REXC

Where:

  • REXB: Controlled real exchange rate (affects economic decisions)
  • REXL: Lagged real exchange rate
  • REXC: Shadow/market-determined real exchange rate from interest parity

For regions without capital controls:

REXN = REXC

The actual exchange rate used in economic behavior is REXN, which equals REXB for capital-controlled regions and REXC for others.

Economic Interpretation

Capital Controls Mechanism

The partial adjustment equation can be rewritten as an Error Correction Model (ECM):

\[\text{REXB}_t = \frac{1}{1+\alpha} \text{REXL}_t + \frac{\alpha}{1+\alpha} \text{REXC}_t\]

This implies:

  • When alph_rex = 0: REXB = REXL (exchange rate is completely fixed)
  • When alph_rex → ∞: REXB = REXC (no capital controls, market-determined)
  • Default alph_rex = 0.2: Gradual adjustment toward market rate

Adjustment Speed

With the default value of 0.2:

  • Weight on lagged rate: $\frac{1}{1+0.2} = 0.833$ (83.3%)
  • Weight on market rate: $\frac{0.2}{1+0.2} = 0.167$ (16.7%)

This means approximately 16.7% of the gap between the controlled and market exchange rate is closed each period.

Policy Implications

Higher alph_rex values indicate:

  • Faster convergence to market-determined exchange rate
  • Weaker capital controls
  • Greater exchange rate flexibility

Lower alph_rex values indicate:

  • Stronger capital controls
  • More rigid exchange rate management
  • Greater deviation from interest parity conditions
Variable Description
REXN Actual real exchange rate used in economic behavior
REXC Shadow/market real exchange rate from interest parity
REXB Controlled real exchange rate (capital control regions)
REXL Lagged real exchange rate
EXCH Nominal exchange rate (US$ per unit of currency)

Model Configuration

The capital controls module (gggopt-with-capital-controls.sym) must be included for alph_rex to have effect. Without this module, REXN = REXC for all regions.

To enable capital controls for specific regions:

  1. Define the capcon set for regions with capital controls
  2. Include the capital controls optional module

References