Investment calibration parameters (base_jk, forei_y, forei_z)

Table of contents

Overview

These parameters govern investment behavior calibration in the G-Cubed model. They determine the base investment-to-capital ratio and the share of investment driven by forward-looking behavior in the capital-producing sectors.

Parameters

base_jk

SYM Declaration:

parameter base_jk(sec_std,regions)    'base J/K'

Definition: The base investment-to-capital ratio (J/K) for each standard sector and region in the calibration year. This parameter captures the steady-state relationship between gross investment and the capital stock.

Calibration: Calculated from calibration year data as the ratio of investment (INV) to capital stock (CAP):

def set_investment_parameters(self):
    """
    base_jk parameter - base investment (J) divided by capital (K)
    for the calibration year for each region/standard industry combination
    """
    inv = self.calibration_database.get_data_for_variables_with_prefix(
        prefix="INV", years=[self.calibration_year]
    ).to_numpy()
    cap = self.calibration_database.get_data_for_variables_with_prefix(
        prefix="CAP", years=[self.calibration_year]
    ).to_numpy()
    base_jk = (inv / cap).reshape(
        (self.sym_data.standard_sectors_count, self.sym_data.regions_count)
    )

Usage in Model: Used in the investment equation to convert gross investment to net investment:

JNV = ( INV + (phi/2)*(base_jk^2)*CAP ) / (1+phi*base_jk)

This equation inverts the adjustment cost function to recover net investment from gross investment.

fore_i_y

SYM Declaration:

parameter fore_i_y(regions)    'shr of I driven by foresight in capital sector'

Definition: The share of investment in the raw capital sector (sector Y) that is driven by forward-looking (foresighted) behavior. This represents the fraction of investors who respond directly to Tobin’s Q (TOBY) rather than the smoothed version (TPAY).

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

# Share of investors that are forward looking in their capital formation decisions
FOREI: float = 0.3

Usage in Model: Used in the net investment equation for the raw capital sector:

JNVY = CAPY * ( fore_i_y*TOBY + (1-fore_i_y)*TPAY - 1 ) / phi_y

Where:

  • TOBY: Tobin’s Q for raw capital sector (forward-looking)
  • TPAY: Smoothed Tobin’s Q (backward-looking)
  • CAPY: Capital stock in raw capital sector
  • phi_y: Adjustment cost parameter

fore_i_z

SYM Declaration:

parameter fore_i_z(regions)    'shr of I driven by foresight in household capital'

Definition: The share of investment in the household capital sector (sector Z) that is driven by forward-looking behavior. Similar to fore_i_y but for household capital (e.g., housing, durable goods).

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

Usage in Model: Used in the net investment equation for household capital:

JNVZ = CAPZ * ( fore_i_z*TOBZ + (1-fore_i_z)*TPAZ - 1 ) / phi_z

For standard production sectors, there is also:

SYM Declaration:

parameter forei(sec_std,regions)    'shr of I driven by foresight std sector'

This parameter serves the same function as fore_i_y and fore_i_z but for standard production sectors (a01-aN).

Economic Interpretation

Forward-Looking vs. Backward-Looking Investment

The investment equations combine two types of behavior:

\[J = K \cdot \frac{[\text{fore\_i} \cdot Q + (1-\text{fore\_i}) \cdot Q^{adj}] - 1}{\phi}\]

Where:

  • Forward-looking investors respond to current Tobin’s Q
  • Backward-looking investors respond to smoothed Q (TPA variables)

Policy Implications

  • Higher fore_i_*:
    • Investment responds more quickly to policy changes
    • Greater sensitivity to interest rate changes
    • More volatile investment dynamics
  • Lower fore_i_*:
    • More gradual investment adjustment
    • Investment is smoother over time
    • Delayed response to policy shocks

Base Investment Ratio

The base_jk parameter ensures that:

  1. The model replicates observed investment-to-capital ratios in the base year
  2. The steady-state investment behavior is consistent with calibration data
  3. The adjustment cost function properly inverts to recover net investment

References