Catchup growth model

Table of contents

G-Cubed models typically include projections of growth for labor-augmenting technical progress as part of the baseline projections. The growth rates are based on the Barro (1991) catchup growth model. Three sources of information are combined to generate projections of growth rates for each sector in each region:

  • the common frontier growth rate in model configuration plus sector-specific deviations, which together determine annual frontier progress;
  • the technology gaps for each sector in each regions, the percentage behind that technology frontier at the start of the projections; and
  • the catchup rates for each sector in each regions, expressed as projections from the first to the last projection year.

This data is made available in the three CSV files described below and it is combined to produce labor-augumenting technical change projections for each sector in each region. Those sectors that are further behind the technology frontier experience faster growth rates as do those sectors with faster catchup rates.

The labour-augmenting technical change projections are stored in the model’s data folder in labor_augmenting_technical_change.csv. Model-data preparation normally regenerates this file. Explicit preservation settings retain a maintained file only when its growth values remain consistent with the source assumptions. Changing the growth setting requires dependent inputs and saved solutions to be refreshed; follow the baseline regeneration sequence.

Technology advancement rates

From build 200 onwards, the technology frontier progress file, technology_advancement_rates.csv, stores percentage-point deviations from calibration.effective_labor_productivity_growth_rate_in_steady_state for each sector and projection year. If configuration specifies 1.4, a zero cell means 1.4 per cent annual log frontier growth; 0.6 means 2.0 per cent and -0.4 means 1.0 per cent. G-Cubed adds the configured rate before applying the catchup recurrence. Default generation writes zeros:

sector 2023 … 2150
a01 0.0 … 0.0
a02 0.0 … 0.0

The final 50 configured projection years must contain exact zero deviations in every sector. See the data-file contract for validation and the calibration guide for the joint migration of older absolute-rate inputs and decimal-valued YAML. Build 199 and earlier used absolute percentage rates in this CSV: a 1.4 per cent frontier path used 1.4, whereas build 200 uses 0.0 with configured growth of 1.4. Schema version remains 1; the updated runtime does not infer the old convention from an older build number.

Zero frontier deviations leave catchup active while productivity gaps remain. They therefore do not guarantee that a region’s productivity, or its GDP, grows at exactly the configured frontier rate during these years. Demographic growth and autonomous energy efficiency are separate assumptions too.

The existing timing is retained: the frontier rate labelled t+1 contributes to labour-augmenting growth labelled t. The final transition repeats the last frontier rate. Keep this convention when calibrating a varying path or fitting catchup rates to growth targets.

Technology gaps from the frontier

The CSV file containing the information about the technology gaps in each region for each sector, expressed as a percentage is technology_gaps.csv. Thus, a value of 50 means the region has a sector that is 50% as efficient as is possible in the first projection year. The data is stored with sector rows and region columns. The row labels are the SYM sector codes. The column labels are the SYM region codes.

For example, for the 2R model:

sector USA ROW
a01 90 100
a02 100 90

Note that the maximum value is 100 and the minimum value must be positive.

It is not mandatory, but it is typical that at least one region is on the technology frontier, with a sector value of 100.

Technology catchup-rates

The CSV file containing the information about the catchup rates for technology in each sector, through all projection years is technology_catchup_rates.csv. Values are expressed as a percentage so a value of 2.0 means that the technology gap will close by 2% in the associated year. The data is stored with region in the first column and sector in the second column. The columns are the projection years in YYYY format out to the last projection year.

For example, for the 2R model:

region sector 2018 … 2150
USA a01 2 … 2
USA a02 2 … 2
ROW a01 2 … 2
ROW a02 2 … 2

Note that the maximum value is 100 and the minimum value must be great than -100.

References

Barro, R. J. (1991) Economic Growth in a Cross Section of Countries. The Quarterly Journal of Economics, 106(2), 407–443.