Price index weights (prid_weight, prim_weight, prix_weight)

Table of contents

Overview

These parameters define the weights used to construct aggregate price indices in the G-Cubed model. They determine how individual sectoral prices are aggregated into economy-wide price measures for domestic output, imports, and exports.

Parameters

prid_weight

SYM Declaration:

parameter prid_weight(goods,regions)    'weights in PRID'

Definition: Weights used to construct the aggregate domestic output price index (PRID). Each weight represents the share of a sector’s output in total domestic production.

Calibration: Calculated as domestic production for each sector divided by total domestic production:

def set_weight_parameters(self):
    """
    prid_weight - Domestic production for each sector in a region
    as a fraction of total domestic production across all sectors
    for that region.
    """
    oup = self.calibration_database.get_data(r"^OUP\(", self.calibration_year)
    oup_matrix = oup.to_numpy().reshape(
        (self.sym_data.sectors_count, self.sym_data.regions_count)
    )
    oup_by_region = np.sum(oup_matrix, axis=0)
    prid_weight = pd.DataFrame(oup_matrix / oup_by_region)

Usage in Model: Used to construct the weighted domestic output price index:

PRID = sum(goods, prid_weight*PRD)

Where PRD is the price of domestic output for each good.

prim_weight

SYM Declaration:

parameter prim_weight(goods_o,regions)    'weights in PRIM'

Definition: Weights used to construct the aggregate import price index (PRIM). Each weight represents the share of imports of a particular good in total imports.

Calibration: Calculated as imports by good type divided by total imports at the destination:

"""
prim_weight - DF imports by good type divided by
the value of imports in total at the destination.
"""
imq_matrix = imq.to_numpy().reshape(
    (self.sym_data.non_electricity_generation_goods_count, self.sym_data.regions_count)
)
imqt = self.calibration_database.get_data(r"^IMQT\(", self.calibration_year)
prim_weight = pd.DataFrame(imq_matrix / imqt)

Usage in Model: Used to construct the weighted import price index:

PRIM = sum(goods_o, prim_weight*PMQ)

Where PMQ is the landed, duty-paid price of imports for each good.

Also used in the import quantity aggregation:

IMQT = sum(goods_o, exp(PMQ)*IMQ) / exp(PRIM)

prix_weight

SYM Declaration:

parameter prix_weight(goods_o,regions)    'weights in PRIX'

Definition: Weights used to construct the aggregate export price index (PRIX). Each weight represents the share of exports of a particular good in total exports.

Calibration: Calculated as exports by sector as a fraction of region total exports:

"""
prix_weight - Exports by non-electricity generating sector as a fraction 
of region total exports where exports are measured as a percentage of 
real GDP for the region.
"""
exq = self.calibration_database.get_data(r"^EXQ\(", self.calibration_year)
exports_region_totals = np.sum(exq, axis=0)
prix_weight = pd.DataFrame(exq / exports_region_totals)

Usage in Model: Used to construct the weighted export price index:

PRIX = sum(goods_o, prix_weight*PRX)

Where PRX is the export price for each good.

Also used in the export quantity aggregation:

EXQT = sum(goods_o, exp(PRX)*EXQ) / exp(PRIX)

Economic Interpretation

Price Index Construction

The price indices are weighted averages of sectoral prices:

\[P^{agg} = \sum_i w_i \cdot P_i\]

Where:

  • $P^{agg}$ is the aggregate price index (PRID, PRIM, or PRIX)
  • $w_i$ are the weights (prid_weight, prim_weight, or prix_weight)
  • $P_i$ are the individual sectoral prices

Weight Properties

All weight parameters satisfy: \(\sum_i w_i = 1 \quad \text{for each region}\)

This ensures that the aggregate price indices are proper weighted averages.

Calibration Year Dependency

All weights are calibrated from the calibration year data and remain fixed during simulations. This means:

  • The composition of domestic output is based on base year shares
  • Import and export compositions reflect base year trade patterns
  • Changes in economic structure are not reflected in the weights
Variable Description Weight Parameter
PRID Weighted price of domestic output prid_weight
PRIM Weighted price of imports prim_weight
PRIX Weighted price of exports prix_weight
PRD Price of domestic output by good -
PMQ Landed, duty-paid import price -
PRX Export price by good -

References