Labor productivity growth (labgrow)

Table of contents

Overview

The labgrow parameter represents the growth rate of effective labor (labor productivity) in each region. This is a fundamental parameter that determines the long-run growth rate of the economy and affects capital accumulation, wealth dynamics, and asset holdings.

Parameter

labgrow

SYM Declaration:

parameter labgrow(regions)    'growth of effective labor'

Definition: The steady-state growth rate of effective labor (labor augmenting technical progress) for each region. This parameter captures both population growth and labor-augmenting technological change.

Calibration: Set from the model configuration file, representing the effective labor productivity growth rate in steady state:

def set_labgrow_parameters(self):
    """
    labgrow - labor productivity growth rate for each region.
    """
    labgrow: pd.DataFrame = pd.DataFrame(
        self.configuration.effective_labor_productivity_growth_rate_in_steady_state,
        index=["labgrow"],
        columns=self.sym_data.regions_members,
    )
    self.insert_parameter("labgrow", labgrow)

Usage in Model:

  1. Capital Accumulation: 
    lead(CAP)  = JNV  + (1-delta-labgrow)*CAP
lead(CAPY) = JNVY + (1-delta-labgrow)*CAPY
lead(CAPZ) = JNVZ + (1-delta-labgrow)*CAPZ
  2. Human Wealth Evolution: 
    lead(WELH) = (1 + RISW + RISH + INTR - labgrow)*WELH
        - TRAN + TAXH + TAXL
        - (exp(WAGE)*(IITL+CNPL) + exp(WAGG)*GOVL + sum(sec_std,exp(WAG)*LAB)) / exp(PRID)
  3. International Asset Accumulation: 
    lead(ASSE) = ASSE*(1-labgrow(owner))
        + (ashr*ABUY + aeye*(CURR(owner)-ABUY)) / exp(REXN(currency))

Economic Interpretation

Balanced Growth Path

The labgrow parameter ensures that the model has a balanced growth path where:

  • All real quantities grow at the rate labgrow
  • All prices and ratios are constant in the steady state
  • The model is normalized so that variables are expressed in efficiency units

Capital Accumulation

In the capital accumulation equation:

\[K_{t+1} = J_t + (1 - \delta - g) K_t\]

Where:

  • $K$ is capital stock
  • $J$ is net investment
  • $\delta$ is depreciation rate
  • $g$ is labgrow

The term $(1-\delta-g)$ represents the effective depreciation rate when variables are measured in efficiency units. This ensures that capital-to-effective-labor ratios are stable in steady state.

Wealth Dynamics

In the human wealth equation, labgrow affects the discount rate for future labor income. Higher labor productivity growth implies:

  • Future labor income is discounted more heavily (relative to efficiency units)
  • Lower present value of human wealth in efficiency terms

International Assets

For international asset accumulation, labgrow ensures that asset holdings are properly scaled to the growing economy:

\[A_{t+1} = A_t (1-g) + \text{new purchases}\]

Typical Values

Labor productivity growth rates typically range from:

  • Developed economies: 1-2% per year
  • Emerging economies: 2-5% per year (catching up)
  • Frontier economies: Higher rates with convergence dynamics
Parameter Description
delta Depreciation rate
timepref Time preference rate
TECHNOLOGY_ADVANCEMENT_RATE Technology advancement rate (1.4% default)
TECHNOLOGY_CATCHUP_RATE Technology catchup rate (2.0% default)

References