OECD global long‑run economic scenarios

Annex B. Recent changes to the structure and coverage of the OECD Long-Term Model

B1. Introduction

1. This Annex describes the changes that have been made to the modelling of potential output in the OECD Long-Term Model (LTM) and the extension of the geographical coverage to include those countries currently missing from the framework, representing about 17% of current global GDP. Covering the (near) totality of global output makes long-run scenarios more comprehensive and widens the range of scenarios that can be explored using the model, including the incorporation of the impact of climate damages on output described in Annex C. These changes are interrelated. As the carbon cycle is inherently global, incorporating it into the LTM requires a global projection of GHG emissions and therefore a global output projection. In turn, the broader coverage of the model to incorporate a greater number of emerging and developing economies has prompted a reassessment of some key underlying relationships within the LTM, in particular the speed and extent of productivity convergence. Finally, given the slow dynamics of the carbon cycle and the fact that choices regarding the energy transition will have implications for many decades, the horizon of the model is extended from 2060 to 2100. This extension also facilitates the use of LTM results as inputs into other models with horizons beyond 2060.

2. The Annex is structured as follows: section B2 details the countries being added to the model and recaps the production function at the core of the LTM. Sections B3 to B5 then take up the components of the production function one by one, explaining in turn the methods used to construct historical estimates and then projections. Finally, section B6 presents illustrative results for convergence in living standards for all countries/regions in the LTM. All the results presented in this Annex are based on the BAU1 scenarios presented in the main part of the paper but abstract from the new climate damage channel presented in Annex C.

B2. Expanded geographical coverage and potential output framework

B2.1. New countries

3. Up until now, the LTM was made up of 49 individual countries: the 38 OECD member countries, eight non-OECD G20 countries (Argentina, Brazil, China, India, Indonesia, Russia, Saudi Arabia and South Africa) and three other accession or partner countries (Bulgaria, Croatia and Romania). Together, these account for just over 82% of global GDP at Purchasing Power Parity (PPP) exchange rates. The extension described in this Annex adds coverage for a further 145 countries, together accounting for almost all of the rest of global GDP.1 Because of missing individual-country data in some of the sources (notably for energy), 55 of the new 145 countries are aggregated into three regions at an intermediate stage within the LTM, thus leaving 139 countries modelled individually in the final stage and 55 as part of the three regions (Table A B.1).

Table A B.1. Countries in the OECD Long-Term Model

Note: Colours indicate in which regional aggregate countries/regions are included (legend at bottom). These aggregates follow World Bank definitions to the extent possible. The regions ‘Other Latin America’, ‘Other Africa’ and ‘Other Asia’ are allocated to the most related aggregate, even though some of their constituent countries would belong to a different one according to World Bank definitions.

4. The newly added countries and regions account for less than a fifth of global GDP currently but are essential to having a comprehensive perspective on the evolution of the global economy. Collectively, they include around three billion in population, including some of the world’s most populous countries, such as Pakistan (about 240 million) and Nigeria (about 220 million). Moreover, population growth is substantially higher in these countries (around 1.8% per year) than in the 49 countries that previously made up the LTM (around 0.4% per year). While population growth is projected to decline in both blocks, the growth discrepancy is projected to persist, and by 2070, most of the world’s population is projected to be in the newly added economies (Figure A B.1). It is natural to expect the collective economic weight of this new block to increase over time, purely on demographic grounds, and even more if some degree of economic convergence occurs. The newly added countries include some of the world’s poorest, where damages from climate change are expected to be most severe.

Figure A B.1. Most of the world’s population will eventually be in the newly added countries

Total population, billion

Source: Population projections are from the OECD Economics Department on the basis of demographic assumptions from the United Nations Population Division’s World Population Prospects, 2024 revision, medium scenario (see section B3.2).

5. For consistency with the rest of the model, and to make as much use as possible of the available country-level data, modelling for the new countries is done primarily at the country level. However, the simplified approach for those new countries necessarily omits many factors relevant to these countries’ futures, especially as the new additions cover a wide spectrum of economies, from oil-rich ones to extremely poor ones. The uncertainty surrounding projections for these new countries is thus particularly high and, consequently, results are often be presented in aggregate form (for regions). Some country-level results are nevertheless presented in this Annex to illustrate the approach.

B2.2. General framework for potential output

6. As is the case for the existing 49 countries in the LTM, future trend output growth for the new countries is assumed to be a function of trend growth in inputs (labour and capital) and the efficiency with which those inputs are combined (labour efficiency). The production function for potential output (${GDPVTR}_{i,t}$) is the same as in Box 1 in the main part of the paper but re-arranged so that the capital stock measure is expressed as a ratio to output (${kratio}_{i, t}$):

${GDPVTR}_{i,t}={EFFLABS}_{i,t}\bullet {ETPT}_{i,t}\bullet {{kratio}_{i, t}}^{ \frac{1-\alpha }{\alpha }}$

[B1]

with subscripts $i$ and $t$ (annual frequency) indexing country and time throughout the Annex. Using mnemonics as they appear in OECD Economic Outlook databases where possible, ${EFFLABS}_{i,t}$ is trend labour efficiency, ${ETPT}_{i,t}$ is trend employment and $\alpha$ is the labour income share, assumed to be 0.67 in all countries. The reason for expressing the capital stock as a ratio to output is that the approach chosen to estimate the historical capital stock for the new set of countries, detailed below in section B5, yields a ratio to output.

7. The assumption of a fixed labour share, common to all countries, is the same as that used in potential output estimation for the OECD Economic Outlook (EO) and is analytically convenient but has limitations. First, the labour income share has generally been falling across advanced economies (Schwellnus et al., 2018[18]). Second, although poor data quality can cloud the picture, the recorded labour share tends to be lower in low-income than in high-income countries. This is partly because a large portion of the workforce in low-income countries is engaged in informal or subsistence activities, which often do not generate substantial wages. The simplifying assumption of a common and stable labour income share in the LTM could be revisited in future work.

B2.3. Data sources

8. Historical data on real GDP, employment, investment and PPP exchange rates for the 145 new countries are from the World Bank’s World Development Indicators (WDI) database, which is complemented in a few instances with the latest IMF World Economic Outlook (WEO) database. The WDI/WEO databases are preferred as sources of historical data for the set of new countries because they are updated often, allowing for the timeliest starting point when the LTM is updated. Historical population estimates are from the United Nations Population Division’s World Population Prospects (UNWPP) and projections are explained below.

9. For the aggregate trend employment equation estimated below, however, the latest version of the Penn World Tables (v10.01) is used as the data source, because it has longer historical coverage than WDI/WEO databases. Having time series going as far back as possible is important when estimating the impact of slow-moving demographic variables such as the age structure of the workforce. The Penn World Tables collect concepts equivalent to those mentioned above, mostly from official national accounts.

B3. Trend employment

B3.1. Historical estimates of trend employment

10. Depending on the country and data availability, total employment (${ET}_{i,t}$) is either obtained directly or constructed using other labour market data. It can be expressed as the product of an aggregate employment rate (${ER1574}_{i,t}$) and the working-age population (${POP\_1574}_{i,t}$) whereby the working-age population is defined as those 15 to 74 or, equivalently, as the product of the labour force (${LF}_{i,t}$) and one minus the unemployment rate (${UNR}_{i,t}$).

${ET}_{i,t}={POP\_1574}_{i,t}\bullet \frac{{ER1574}_{i,t}}{100}={LF}_{i,t}\bullet \left(1-\frac{{UNR}_{i,t}}{100}\right)$

[B2]

Trend employment (${ETPT}_{i,t}$) is obtained by HP-filtering ${ET}_{i,t}$. Then, a historical trend employment rate (${ERS1574}_{i,t}$) is computed as:

${ERS1574}_{i,t}=\frac{{ETPT}_{i,t}}{{POPS\_1574}_{i,t}}\bullet 100$

[B3]

where ${POPS\_1574}_{i,t}$ is the trend working-age population, obtained by HP-filtering historical population estimates and projections together.

B3.2. Projections of trend employment

11. For most of the original LTM countries, trend employment rate projections are obtained by aggregating up from a detailed cohort-based model (Cavalleri and Guillemette, 2017[3]). When possible, this approach is replicated for the new 90 individual countries, on the basis of age and sex specific historical employment rate estimates from the International Labour Organisation. The cohort model relies on estimating entry and exit rates into employment along the employment lifecycle of different cohorts. As employment is a cyclical variable, a cyclical adjustment is applied to the raw historical age/sex-specific employment rates before entry and exit rates are estimated. When possible, this cyclical adjustment is based on the aggregate employment gap estimated for the country in question in the latest OECD Economic Outlook (EO). This applies to most of the original 49 countries in Table A B.1. Many of the new countries are not covered individually in the EO, however. For them, the cyclical adjustment is based on the aggregate employment gap for the G20 advanced region. While imperfect, this procedure should at least capture global shocks such as the Global Financial Crisis and the COVID-19 pandemic. The sensitivity parameters used for the cyclical adjustment are the system estimates obtained by pooling all countries for which individual employment gap estimates exist (see section 2.3.2 of Cavalleri and Guillemette (2017[3])).

12. For 13 of the new countries, as well as many of the individual countries within the three regions, the historical employment rate series disaggregated by age and sex necessary to apply the cohort approach are lacking or incomplete (Table A B.2). In these cases, a simplified approach is used that relates the aggregate trend employment rate (${ERS1574}_{i,t}$) to the age structure of the population and life expectancy (${LEX}_{i,t}$) based on estimated coefficients from the following system of equations:

${ERS1574}_{i,t}={\alpha }_i+{\gamma }_i\bullet t+{\beta }_1\bullet \frac{{POP\_1524}_{i,t}}{{POP\_1574}_{i,t}}+{\beta }_2\bullet \frac{{POP\_5564}_{i,t}}{{POP\_1574}_{i,t}}+{\beta }_3\bullet \frac{{POP\_6574}_{i,t}}{{POP\_1574}_{i,t}}$ $+ {\beta }_4\bullet {LEX}_{i,t}+ {\beta }_5\bullet \frac{{PO{P}_{6574}}_{i,t}}{{PO{P}_{1574}}_{i,t}}\bullet {LEX}_{i,t}+{\epsilon }_{i,t} for i=1,\dots ,N.$

[B4]

The system has $N=182$ equations in total, one per country included in the dataset for estimation.

Table A B.2. Individual countries with no cohort model for which the simplified approach is used

13. The specification is based on the observation that the age structure of the population affects the aggregate employment rate, given that different age groups have different labour force participation rates (and possibly unemployment rates as well). An interaction term between the share of people aged 65 to 74 in the working-age population and life expectancy is included, because if higher life expectancy tends to lengthen working lives (in addition to health effects on all age groups), the effect presumably comes primarily through that age band. Historical aggregate employment data are from the Penn World Tables while population and life expectancy series are from UNWPP. Given the parsimoniousness of the specification, country-specific constants (${\alpha }_i$) and time trends (${\gamma }_i\bullet t$) are included to help reduce omitted-variable bias.2 The coefficients of interest (${\beta }_1$ to ${\beta }_5$) are restricted to be the same across countries. The system of equations is estimated with weighted least squares, accounting for cross-equation heteroskedasticity, using data from 1960 to 2019, for a total of 8 906 observations.

14. The estimated coefficients conform to priors and indicate that each 1 pp increase in the share of youth (15-24) in the working-age population (at the expense of the omitted 25-to-54 age group) depresses the aggregate trend participation rate by 0.2 pp (p < 0.01), each 1 pp increase in the share of mid- to late-career people (55-64) increases it by 0.5 pp (p < 0.01), and each 1 pp increase in the share of older people (65-74) in the working-age population depresses it by 1.8 pp (p < 0.01). At the mean share of 65-74 in the working-age population of about 8% in 2019, a one-year increase in life expectancy raises the trend employment rate by a little less than 0.3 pp (p < 0.01).

15. For the projection of trend employment rates, only the demographic-related estimated coefficients (${\widehat{\beta }}_1$ to ${\widehat{\beta }}_5$) are used in an equation for the annual change in the aggregate employment rate, so omitting the estimated constants and time trends. Projected changes in trend employment rates are thus a function of evolving age mixes and life expectancies. Because it does not differentiate gender, this aggregate approach, unlike the cohort approach, is unable to account for any historical catch-up between female and male employment rates that could be expected to continue in the future. Nevertheless, taking a representative low-income African country among the new ones being added to the model as illustration, the trend employment rate is projected to increase modestly and very gradually over the projection period (Figure A B.2). While the share of people aged 65 to 74 tends to rise with ageing populations, pulling down the aggregate employment rate, this effect is more than compensated by the others and in particular by the falling share of 15- to 24-year-olds.

Figure A B.2. The projected evolution of the trend employment rate in a representative low-income African country, from 2025

% pts of working-age population (15-74)

16. Based on the cohort approach for the majority of countries and the simplified approach for the 13 countries shown in Table A B.2 as well as most individual countries within the three regions, the global aggregate employment rate is projected to rise by 5 percentage points through 2100 (Figure A B.3). Regions with faster female employment growth recently as well as more favourable demographics, such as South Asia, show greater progress than this global aggregate, and vice-versa. Aggregate employment rates in South Asia and Middle East and North Africa remain substantially lower than in other regions, reflecting social and cultural norms that are implicitly assumed to persist in the projection framework. The implications for growth and living standards of gradual convergence of employment rates toward those of other regions is an issue that could be explored in future scenarios.

Figure A B.3. Projected trend employment rates

% of population aged 15 to 74

Note: Regional groupings are based on World Bank definitions.

17. The projection for trend employment in persons (${ETPT}_{i,t}$) is obtained by combining the projected trend employment rate with trend working-age population projections:

${ETPT}_{i,t}={POPS\_1574}_{i,t}\bullet \frac{{ERS1574}_{i,t}}{100}$

[B5]

Population projections are done by sex and 5-year age groups using an in-house demographic projection model but relying on fertility/mortality/migration assumptions from UNWPP, 2024 revision, medium scenario. The reason for using an in-house model rather than official projections from UNWPP is to keep the ability to tweak assumptions and generate alternative scenarios. However, projections used normally in the LTM match the UN’s medium scenario almost exactly as the same assumptions are used.

B4. Trend labour efficiency

B4.1. Historical estimates of trend labour efficiency

18. Labour efficiency is not directly observable. Historical estimates for the new countries are therefore calculated as a residual, by plugging estimates of ${GDPV}_{i,t}$, ${ET}_{i,t}$ and ${kratio}_{i, t}$ in [B1] (in place of their trend counterparts) and solving for ${EFFLAB}_{i,t}$. Then, trend labour efficiency (${EFFLABS}_{i,t}$) is obtained by HP-filtering ${EFFLAB}_{i,t}$.

B4.2. Projections of trend labour efficiency

19. Previously, trend labour efficiency was projected in the LTM using a conditional convergence framework (Guillemette et al., 2017[19]). The idea of conditional convergence is that individual countries are each converging to their own equilibrium labour efficiency level. The equilibrium is unique to each country because it is a function of several growth determinants. The speed of convergence to those equilibria varied across countries and was a function of two structural indicators: one for governance and one for trade openness. This introduced another element of conditional convergence in the framework.

20. Keeping exactly the same approach for the new set of countries is not feasible, as there are too many data gaps in the previous set of growth determinants (for instance the Product Market Regulation indicator, which affected the equilibrium level, is lacking for the large majority of the new countries). Moreover, in practice, the conditional convergence framework was not very successful at explaining cross-country differences in contemporaneous trend labour efficiency growth, consistent with the finding in other studies that no simple theory does a good job of explaining cross-country growth patterns over different time periods and country groupings (Johnson and Papageorgiou, 2020[20]). This reality is difficult to reconcile with the need for a simple, parsimonious approach to projecting trend labour efficiency in the LTM. The chosen approach, set out below, is primarily based on the idea of absolute convergence, meaning that all countries are converging to the same frontier level of labour efficiency, but retains a conditional element in allowing convergence speeds to vary across countries according to three framework conditions based on lessons from the growth literature. This ‘mixed convergence’ approach is consistent with a variety of growth outcomes and does not necessarily imply full convergence in per capita GDP in the long run.3

21. The simplified approach described previously for trend employment rates and the approach described below for estimating capital stocks apply only to the new countries being added to the model. In contrast, the revised framework for trend labour efficiency projections applies to all countries in the LTM, replacing the approach described in Guillemette et al. (2017[19]) for the original 49 countries.

B4.2.1. Three framework conditions

22. The first framework condition is a broad indicator of the quality of governance, namely the World Bank’s rule of law indicator (${RULELAW}_{i,t}$), as used in previous versions of the LTM. The economic history of the past two centuries, and much recent work on the economics of institutions, has established a strong theoretical and empirical case that the quality of governance and institutions matters a great deal for growth (Hall and Jones, 1999[21]; Acemoglu, Johnson and Robinson, 2005[22]). A legal environment that allows entrepreneurs to protect their intellectual and physical property and appropriate a significant fraction of the revenues generated by their innovations should encourage innovative investments and productivity growth.

23. The rule of law indicator is published by the World Bank as part of the Worldwide Governance Indicators (WGI), a research dataset summarizing views on the quality of governance (Kaufmann, Kraay and Mastruzzi, 2010[23]). More specifically, rule of law captures perceptions of the extent to which agents have confidence in and abide by the rules of society, and in particular the quality of contract enforcement, property rights, the police, and the courts, as well as the likelihood of crime and violence. The data are gathered from a number of survey institutes, think tanks, non-governmental organizations, international organizations and private sector firms. The variable is normalised so it has a mean of zero and a standard deviation of one (Figure A B.4, Panel A and Table A B.3).

24. The second framework condition is an indicator of the degree of economic globalisation, namely the economic globalisation index (${KOFECGI}_{i,t}$) of the KOF Swiss Economic Institute. Trade and investment are well-documented channels for technology transfers and spillovers between countries, so more open economies are expected to catch up more quickly to the technology frontier. More open economies also tend to grow faster as stronger external competition and a higher threat of entry tends to encourage innovation by incumbent firms. Much empirical work has demonstrated that trade openness has a positive impact on economic growth (Irwin, 2019[24]; Égert and Gal, 2017[25]), and this also seems true of the broad economic globalisation index chosen here (Dreher, 2006[26]; Potrafke, 2015[27]).

Figure A B.4. Frequency distributions for selected framework conditions

Number of countries

Note: Statistics are given for 2022 (rule of law), 2021 (economic globalisation) and 2023 (macro stability).

Source: World Bank’s World Governance Indicators, OECD Economic Outlook and KOF Swiss Institute’s KOF Globalisation Index databases.

Table A B.3. Summary of structural indicators affecting the speed of convergence

	Rule of law	Economic globalisation	Macro stability
Number of countries covered	205	193	142
Time series coverage (longest available)	1996, 1998, 2000 and 2002 to 2023	1970 to 2022	1990 to 2023
Range (worst to best)	-2.29 to 1.96	28.2 to 93.8	0 to 9.8
Average	0.0	58.0	8.4
Standard deviation	1.0	16.1	1.9
Five best performers	Finland, Denmark, Singapore, Luxembourg, Norway	Singapore, Belgium, Netherlands, Ireland, United Arab Emirates	Canada, Australia, Malta, Vietnam, Bolivia
Five worst performers	Somalia, Venezuela, Syria, South Sudan, Yemen	Venezuela, Nepal, Chad, Ethiopia, Somalia	Argentina, Lebanon, Sudan, Zimbabwe, Türkiye
Impact of a one-standard deviation increase on speed of convergence	+0.3 percentage points	+0.3 percentage points	+0.09 percentage points
More information	https://www.worldbank.org/en/publication/worldwide-governance-indicators	https://kof.ethz.ch/en/forecasts-and-indicators/indicators/kof-globalisation-index.html

Note: Statistics are given for 2022 (rule of law), 2021 (economic globalisation) and 2023 (macro stability).

Source: World Bank’s World Governance Indicators, OECD Economic Outlook and KOF Swiss Institute’s KOF Globalisation Index databases.

25. The economic globalisation index is a sub-index of the composite globalisation index produced by the KOF Swiss Economic Institute (Gygli et al., 2019[28]). The economic dimension of the index is itself made up of four sub-indices and a total of 15 indicators, providing a more comprehensive measure of economic globalisation than the openness measure used previously in the LTM (trade as a percentage of GDP adjusted for population size), trade being just one sub-component of the new index (Table A B.4).

• De facto trade globalisation refers to the exchange of goods and services over long distances. The variable trade partner diversity favours countries whose export and import structure is globally oriented as compared to countries that primarily trade regionally.

• De jure trade globalisation relates to policies that facilitate and promote trade flows between countries.

• De facto financial globalisation is measured by stocks of foreign assets and liabilities instead of flows to mitigate the problem of volatility and measurement errors in the flow variables.

• De jure financial globalisation measures the openness of a country to international financial flows and investments.

  A number of treatments are applied to the raw series, including imputation of missing data, normalisation and aggregation using weights, see Gygli et al. (2019[28]) for the details. Notably, individual variable weights within each of the four subcomponents in Table A B.4 are computed on a 10-year rolling window using principal components analysis, helping to account for structural changes in the relevance of individual components for globalisation over time. The overall economic globalisation index is essentially a weighted average of percentile ranks in the four sub-categories, each receiving equal weight. In the latest available year, it varies between 28 and 94 (Figure A B.4, Panel B and Table A B.3).

Table A B.4. Composition of the KOF Swiss Economic Institute economic globalisation index

	Variable name	Variable definition
De facto trade globalisation	Trade in goods	Exports and imports of goods (% of GDP)
	Trade in services	Exports and imports of services (% of GDP)
	Trade partner diversity	Average of the Herfindahl-Hirschman market concentration index for exports and imports of goods (inverted)
De jure trade globalisation	Trade regulations	Average of two subcomponents: Prevalence of non-tariff trade barriers and compliance costs of importing and exporting
	Trade taxes	Income from taxes on international trade as percentage of revenue (inverted)
	Tariffs	Unweighted mean of tariff rates
	Trade agreements	Number of bilateral and multilateral free trade agreements
De facto financial globalisation	Foreign direct investment	Sum of stocks of assets and liabilities of foreign direct investments (% of GDP)
	Portfolio investment	Sum of stocks of assets and liabilities of international equity portfolio investments (% of GDP)
	International debt	Sum of inward and outward stocks of international portfolio debt securities and international bank loans and deposits (% of GDP)
	International reserves	Includes foreign exchange (excluding gold), SDR holdings and reserve position in the IMF (% of GDP)
	International income payments	Sum of capital and labour income to foreign nationals and from abroad (% of GDP)
De jure financial globalisation	Investment restrictions	Prevalence of foreign ownership and regulations to international capital flows
	Capital account openness	Chinn-Ito index of capital account openness
	International investment agreements	Number of Bilateral Investment Agreements (BITs) and Treaties with Investment Provisions (TIPs)

Source: Gygli, S. et al. (2019), “The KOF Globalisation Index – Revisited”, Review of International Organizations, Vol. 14/3, pp. 543-574. See Table A.1 in the supplementary materials of this reference for the detailed data sources.

26. The third framework condition is an index of macroeconomic stability (${MACROSTABILITY}_{i,t}$). The quality of macroeconomic management helps to set the foundations for investment and growth. This can include fiscal and various other policy areas, but the growth literature has often found low and stable inflation to be particularly important (Bruno and Easterly, 1998[29]; Hartmann and Roestel, 2013[30]), as reflected in the mandates of most central banks. In addition to the benefits of a low positive average inflation rate, it is also helpful if inflation is as stable as possible, as predictability helps households and firms to make intertemporal trade-offs with a greater degree of certainty. The index thus gives equal weights to both features of the inflation process. It is the same one used in Guillemette et al. (2017[19]) and is based on the following formula:

$\frac{V_{max}-min\{<!--\; -->\left|{\pi }_{i,t}-2\right|, V_{max}\}}{V_{max}}\bullet 10$

[B6]

where ${\pi }_{i,t}$ is a five-year moving average of the annual headline inflation rate based on the consumer price index, sourced from the OECD Economic Outlook and the World Bank’s World Development Indicators (WDI) databases, and $V_{max}$ is set at 48. This formula produces a rating between zero and 10. Countries with exactly 2% inflation over the previous five years earn a rating of 10. As the smoothed inflation rate moves toward 50%, the rating moves toward zero. A zero rating is assigned to all countries with an inflation rate of 50% or more. Inflation below 2% is penalised symmetrically. A similar formula is applied to the stability of inflation, except that the absolute-value term in the numerator becomes a five-year moving average of the standard deviation of inflation and $V_{max}$ is set to 25. A perfect 10 results when there is no variation in the rate of inflation over the five-year period. The rating declines toward zero as the standard deviation of inflation approaches 25%. The overall macroeconomic stability index is then computed as an equally weighted average of the two sub-indices and varies between 0 and 10, with most countries scoring between 8.0 and 9.5 (Figure A B.4, Panel C and Table A B.3).

27. Other factors are, of course, important in the growth process, but one important constraint for estimation is to have broad country and time coverage. In addition, different framework conditions tend to be highly correlated, so adding more does not necessarily improve explanatory power very much. The three selected ones should be interpreted broadly with the understanding that they are proxying a wider set of correlated growth determinants.

B4.2.2. Estimated model for trend labour efficiency convergence

28. Formally, the following mixed convergence model is specified for trend labour efficiency expressed in USD at fixed 2021 prices and PPPs (${EFFLABS\_D}_{i,t}$):

$∆\log \left({EFFLABS\_D}_{i,t}\right)=\phi +{\delta }_{i,t}\bullet \log \left({EFFLABS\_D}_{i,t-1} / {EFFLABS\_D\_EQ}_{i,t-1}\right)+{\mu }_{i,t}$ ${\delta }_{i,t}={\gamma }_0+{\gamma }_1\bullet {RULELAW}_{i,t}+{\gamma }_2\bullet {KOFECGI}_{i,t}+{\gamma }_3\bullet {MACROSTABILITY}_{i,t}$ ${\mu }_{i,t}=\rho \bullet {\mu }_{i,t-1}+{\epsilon }_{i,t}$

[B7]

where ${\epsilon }_{i,t}$ is an error term and other variables are explained below. The model is estimated using panel least squares on an unbalanced dataset covering the 139 individual countries in the LTM over the 1996 to 2023 period, for a total of 3 426 observations (Table A B.5). Missing values for the framework condition variables are filled by linear interpolation when both preceding and succeeding values are available (this fills in ${RULELAW}_{i,t}$ values for 1997, 1999 and 2001 when the index was not produced), or the variables are kept at their last historical values when missing at the end of the estimation period (this keeps ${KOFECGI}_{i,t}$ at its 2022 estimate in 2023).

Table A B.5. Estimated equation for mixed convergence in trend labour efficiency

	∆log⁡(EFFLABS_Di,t)
Constant (φ^)	-0.00678*
Speed of convergence at mean framework conditions (γ^0)	-0.0125***
Effect of RULELAWi,t on speed of convergence (γ^1)	-0.00329***
Effect of KOFECGIi,t on speed of convergence (γ^2)	-0.000181***
Effect of MACROSTABILITYi,t on speed of convergence (γ^3)	-0.000495***
Decay rate of momentum factor (ρ^)	0.871***
Estimation period	1996-2023
Adjusted R2	0.943
# of countries	139
# of observations	3 426

Note: Asterisks (*, **, ***) indicate the statistical significance level (10%, 5%, 1%) of the estimated coefficients based on (White) standard errors robust to arbitrary heteroskedasticity and within-country serial correlation (cross-sectional clustering). The three variables impacting the speed of convergence are de-meaned for estimation.

29. The underlying conceptual framework and assumptions are as follows:

• Constant term. In the estimated equation, the constant ($\widehat{\phi }$) is not statistically significant at the conventional 5% level. In the projection equation, the constant is used as the trend growth rate in global technical progress (in log points) that is assumed to accrue to all countries annually, independently of the other effects. It is set to 0.01, close to the geometric mean trend labour efficiency growth rate of advanced G20 economies over the past 30 years.4 It also happens to be close to the mean dependent variable for the estimation sample of 0.009.

• Absolute convergence term. Trend labour efficiency is assumed to be converging, or ‘catching up’, to a frontier level (${EFFLABS\_D\_EQ}_{i,t}$), taken to be the US level, or a country’s own if it is higher than that of the United States, in which case the convergence term is zero by construction. This applies, for most of the sample, to countries with a high share of oil production in GDP, such as Kuwait, Qatar, Brunei, United Arab Emirates and Saudia Arabia.5 Projections of trend labour efficiency growth for these countries are thus only a function of the 1% constant and the momentum factor explained below based on the autoregressive error term in [B7].

• Conditional speed of convergence. The speed at which convergence in trend labour efficiency takes place, ${\delta }_{i,t}$, varies in both country and time dimensions, as it is assumed to be a function of the three framework conditions described previously. As the variables measuring the framework conditions are de-meaned for the purposes of estimation, ${\widehat{\gamma }}_0$ measures the speed of convergence when all three variables are at their sample means. It is estimated at 1.3% annually, somewhat below the 2% ‘iron-law’ speed of convergence put forward by Barro (2015[31]), no doubt because of the relatively recent sample period used and the fact that convergence speeds have slowed over time. As expected, better governance than average increases the speed of convergence. Likewise for greater economic globalisation and better macroeconomic stability. A one-standard deviation (measured in the cross-section) improvement in governance / globalisation / macro stability raises the speed of convergence by 0.3 / 0.3 / 0.1 percentage points, respectively. Based on 2023 values for the explanatory variables (the end of the estimation sample), convergence speeds range from close to zero for those economies with poor framework conditions (e.g. Zimbabwe) to 2.6% for those with the best ones (e.g. Singapore). Overall, the convergence speeds of the new countries added into the LTM are lower than those for the existing economies (Figure A B.5).

Figure A B.5. Frequency distribution of implied convergence speeds in 2023 (${\widehat{\mathit{\delta }}}_{\mathit{i},2023}$)

Number of countries in LTM

Note: As per the specification in [B7], a negative value implies convergence toward the frontier, whereas a positive value implies divergence.

• Momentum factor. The residual for the convergence equation (${\mu }_{i,t}$) is modelled as an AR(1) process (and referred to as “momentum” hereafter). The idea is that any residual source of trend labour efficiency growth that is explained neither by the constant nor the catch-up term (i.e. the product of the absolute convergence term and the conditional speed) decays over time.6 The estimated decay rate ($\widehat{\rho }$) implies a half-life of about six years. This decay rate ensures a smooth transition from estimated trend labour efficiency growth rates at the jump-off point to longer-run projections. Given the parsimoniousness of the specification [B7], the momentum factor reflects many country-specific growth determinants beyond those affecting the speed of convergence. Nevertheless, the estimates imply that this growth impetus eventually tapers off, the implicit suggestion being that the growth determinants for which it proxies are persistent, but not permanent.

B4.2.3. Implications for trend labour efficiency projections

30. In a business-as-usual scenario (such as BAU1 or BAU2 in the main paper), the variables measuring framework conditions are assumed to remain fixed at their last historical values, implying that speeds of convergence are constant over the projection period.7 Equilibrium trend labour efficiency (${EFFLABS\_D\_EQ}_{i,t}$) is assumed to grow at the rate of global technical progress (which is set at 1% per annum), plus the momentum factor of the frontier country.8 In the very long run, trend labour efficiency would grow at this rate in all countries, but this very long run lies beyond 2100. Countries fall in four broad categories:

• In some cases, the global 1% assumption, together with the absolute convergence term, matches a country’s estimated trend labour efficiency growth at the jump-off point well, in which case the momentum factor is close to zero (Figure A B.6, Panel A).

• A second possible case is when the global rate of technical progress and the convergence term together under predict trend growth at the jump-off point, in which case momentum is positive (Figure A B.6, Panel B). To the extent the momentum factor reflects permanent or very slow-moving structural conditions that are largely uncorrelated with the selected framework conditions (i.e. omitted variables in the projection framework), this could result in a pessimistic projection.

• A third possible case is when relatively high trend labour efficiency growth would be predicted on the basis of the convergence term, but the estimate at the jump-off point is much lower, resulting in negative momentum (Figure A B.6, Panel C). In this case, trend growth is projected to strengthen gradually, and in some cases strongly, as momentum dissipates. To the extent the momentum factor reflects permanent or very slow-moving structural conditions that are largely uncorrelated with the selected framework conditions (i.e. omitted variables in the projection framework), this could result in an optimistic projection.

• A final possible case is a country with both very low or negative trend labour efficiency growth and poor structural conditions. In this case divergence can continue in the medium run and, even after negative momentum has fully dissipated, no or little convergence occurs without improvements in framework conditions (Figure A B.6, Panel D).

Figure A B.6. Some stylised examples of trend labour efficiency growth patterns

Trend labour efficiency growth, %

31. On its own, this new projection approach implies that all countries would eventually end up at the same level of labour efficiency (the projected US level), except those that start off above the US level (see above) or those with very poor framework conditions and a near-zero speed of convergence. This was not the case with the previous projection approach. However, given a low average convergence speed, this full convergence in levels in the revised approach is only true in a very long run that is, for most countries, well beyond the 2100 horizon of the LTM. So, while the new framework is substantially different from the previous one conceptually, short and medium-run projections are not necessarily so different in practice, especially given the persistence of the momentum factor in [B7].

B4.2.4. Other elements of the projection framework for trend labour efficiency

32. Moreover, other elements of the full projection framework for trend labour efficiency imply that equilibrium levels can differ between countries even in the (conceptual) very long run:

• The model retains the previously estimated impacts of structural policy indicators on equilibrium trend labour efficiency levels for the original set of 49 countries in the LTM, allowing scenarios with structural policy reforms in these countries to be undertaken. For instance, it remains possible to simulate the impact of an improvement in product market regulation, or the other variables used in the Guillemette et al. (2017[19]) framework.9 This makes it possible to have scenarios in which labour efficiency in some countries could overtake the United States, as should be possible in a very long run projection.

• Mitigation of carbon emissions is assumed to impact potential output via the trend labour efficiency channel. As explained in Guillemette and Château (2023[1]), the projection for trend labour efficiency growth in scenarios other than the business-as-usual ones ($s=0$) is given by:

$∆\mathrm{l}\mathrm{o}\mathrm{g}\left({EFFLABS\_D}_{i,t,s}\right)=∆\mathrm{l}\mathrm{o}\mathrm{g}\left({EFFLABS\_D}_{i,t,s=0}\right)+m_{i,t}\bullet ∆log\left(\frac{{CO2\_NET}_{i,t,s}}{{CO2\_NET}_{i,t,s=0}}\right)$

[B8]

where ${CO2\_NET}_{i,t,s}$ measures net carbon emissions from energy use and $m_{i,t}$ measures the elasticity of output to carbon mitigation. These elasticities are country specific and estimated from a range of scenarios produced with the ENV-Linkages model (Château, Dellink and Lanzi, 2014[2]). Scenarios that involve a more rapid pace of carbon mitigation than the business-as-usual ones have lower trend labour efficiency growth. Given the Cobb-Douglas functional form of the production function and the assumption of a 0.67 labour income share, this means that two-thirds of the output costs of CO₂ mitigation come through lower trend labour efficiency, with the remainder coming through lower capital accumulation as the LTM targets a fixed capital-to-output ratio over the long run (see below). Combining the direct impact on trend labour efficiency and the indirect impact on capital accumulation, the total long-run impact on potential output of a 1% reduction in net CO₂ emissions relative to business-as-usual works out to $m_{i,t}$.

• In all scenarios, projected climate damages also impact potential output via the trend labour efficiency channel, with differentiated impacts between countries. Climate damages are not part of the estimation framework in [B7] but are added in an additional step (see Annex C).

33. Abstracting from these three channels to illustrate the new convergence approach in [B7], a few regional trends can be discerned (Figure A B.7):

• In the East Asia and Pacific region, trend labour efficiency growth continues to slow but remains well above the 1% frontier assumption.

• In North America, trend labour efficiency growth is just above 1% at the start of the projection period and it declines very slowly toward this rate given that the United States is used as the frontier and accounts for most of the region. Trend labour efficiency growth is also broadly stable in the South Asia region for many decades, before declining slowly toward the end of the projection period.

• In all other regions, and at the global level, trend labour efficiency growth strengthens initially before converging toward 1% from above. The initial acceleration is due to many large economies in these regions having negative momentum components at the start of the projection period which fade within a few years.

Figure A B.7. Projected trend labour efficiency growth rates

Per cent

Note: Regional groupings are based on World Bank definitions and aggregates use country-level trend employment as weights. Projections in this chart do not account for climate damages.

34. The projected substantial improvement in trend labour efficiency growth in several regions could be seen as optimistic, particularly if recent weak productivity growth performance in these regions is associated with very persistent structural factors. At the same time, some of the recent weakness could be associated with temporary factors, such as pandemic-related supply-chain disruptions or global energy price increases, which would be expected to dissipate over time and possibly more quickly than projected.

35. Moreover, even where the projected upturn in trend labour efficiency appears impressive in growth terms, it is typically not so impressive when looking at implied convergence in level terms. Sub-Saharan Africa is a case in point. Projected trend labour efficiency growth remains below the global average until the mid-2040s. In a pure absolute convergence framework, this region would be expected to show much faster progress given its very low relative starting point. In the mixed convergence framework used here, it is held back throughout the projection period by a relatively low convergence speed associated with poor framework conditions and a negative momentum factor in the early party of the projection. Even with its projected upturn, trend labour efficiency in Sub-Saharan Africa would remain below 20% of the US level in 2100 (Figure A B.8). Other regions show a greater degree of convergence, but all except Europe and Central Asia still remain more than one-third below the frontier level by 2100.

Figure A B.8. Projected trend labour efficiency levels relative to the United States

USA = 100

Note: Regional groupings are based on World Bank definitions and aggregates use country-level trend employment as weights. Underlying trend labour efficiency series are expressed in USD at fixed purchasing power parity exchange rates for comparison. Projections in this chart do not account for climate damages.

B5. Capital stock

B5.1. Historical estimates

36. For the existing 49 countries in the LTM, historical capital stock estimates are computed using a Perpetual Inventory Method (PIM) on the basis of historical investment series, as described in section 5 of Chalaux and Guillemette (2019[32]). One methodological change since this paper was published is that the capital stock now includes dwellings and is based on cumulating total gross fixed capital formation (GFCF) as opposed to GFCF excluding housing. The tricky part of the PIM is setting the size of the capital stock for an initial period, typically when the investment series begin, after which the regular stock-flow equation can be applied. For the existing LTM countries, the initial point is set by using 10-year averages for investment rates and GDP growth. The assumption implicit in this approach is that capital stock growth is equal to GDP growth at the initial point, which is true if the capital-to-output ratio is in steady state. Even if this is not the case, any error in the initial stock estimate dissipates over time and has only a small impact on contemporaneous capital stock estimates, provided the initial point is far enough in the past.

37. This steady-state assumption is defensible for advanced economies with relatively rich data, but much less so for developing ones. As Warner (2024[33]) demonstrates, the conventional PIM based purely on investment data yields implausible capital-to-output ratios for many lower-income economies. ‘Errors’ at the starting point can be so large as to still influence capital stock estimates decades later. In addition, with labour efficiency being calculated as a residual, implausible capital stock estimates imply dubious labour efficiency estimates. Instead, Warner (2024[33]) observes that electricity usage, for which accurate data are available for a wide range of countries, can proxy for the size of the capital stock (Figure A B.9). Initial capital stocks can be set on the assumption that the empirical relationship between capital stock and GDP is the same as that for the capital proxy (electricity usage) and GDP, together with one data point for the capital-to-output ratio for a country where that figure is believed to be accurate. This assumption appears more reasonable for low-income countries than the alternative of assuming that capital-to-output ratios are in steady state at the point where investment series become available, and is applied here for the 145 new countries in the LTM (some of which are subsequently combined into regions).

Figure A B.9. Relationship between estimated capital stock per capita and electricity demand in advanced economies in 2019

Source: OECD Economic Outlook No. 115 database and Ember via Our World in Data.

38. The approach proceeds in the following steps:

• First, a cross-sectional relationship is estimated between log electricity usage per capita – which serves as proxy for the size of the capital stock – and log real GDP per capita measured at purchasing power parity (PPP) exchange rates. Warner (2024[33]) reports an elasticity of 1.12 based on data for 126 countries in the year 2000. Replicating this approach but with data for 186 countries gives a somewhat higher elasticity of 1.32 in the year 2005 (p < 0.01). This estimated coefficient is very stable over time (the estimated elasticity is virtually identical if the analysis is repeated with data for the year 2015 instead). The higher elasticity than Warner (2024[33]) is almost certainly down to differences in the electricity data.10

• Second, a reference country is selected where the capital-to-output ratio is thought to be well measured. The United States is chosen here, with estimates taken from the latest OECD Economic Outlook database. The capital-to-output ratio series of the reference country is converted into a capital stock per capita series by multiplying it by GDP per capita.

• Third, for each individual country, the initial year is set to when the fixed investment series begins for that country (t=0).11 The initial capital stock per capita (${KP}_{i,0}$) is then based on the estimate for the United States for that year (${KP}_{USA,0}$) plus the difference predicted by the estimated relationship described previously between electricity usage and real GDP per capita at the initial point (${GDPVD\_CAP}_{i,0}$):

$\log \left({KP}_{i,0}\right)=\log \left({KP}_{USA,0}\right)+1.32\bullet \mathrm{l}\mathrm{o}\mathrm{g}({GDPVD\_CAP}_{i,0} /{ GDPVD\_CAP}_{USA,0})$

[B9]

where 1.32 is the elasticity estimated previously. This initial capital stock per person estimate is converted into a capital-to-output ratio by dividing it by GDP per capita at the initial point.

• Finally, the normal stock-flow equation for the evolution of the capital-to-output ratio (${kratio}_{i, t}$) is applied to fill in the rest of the historical period ($t>0$):

${kratio}_{i, t}=\frac{{ITVQ}_{i, t}}{100}+\frac{1-{RSCRP}_t/100}{1+∆\mathrm{l}\mathrm{o}\mathrm{g}\left({GDPV}_{i,t}\right)}\bullet {kratio}_{i, t-1}$

[B10]

where ${ITVQ}_{i, t}$ is gross fixed capital formation as a percentage of GDP, ${RSCRP}_t$ is the capital stock scrapping rate and ${GDPV}_{i, t}$ is real GDP. Given the lack of reliable and comparable data on scrapping rates across countries, as an initial assumption and pending further work, the scrapping rate is assumed to be the same for all countries. Based on a variety of historical sources, this common scrapping rate rises gradually from around 3.4% in 1990 to 4.7% in 2023, reflecting a rising share of information and communication technologies in the capital stock, which have shorter working lives than more traditional structures and equipment (Figure A B.10). A further gradual increase to 5% is assumed over the projection period.

Figure A B.10. Capital stock scrapping rate

Per cent

Source: OECD Economic Outlook No. 115 database for historical period.

B5.2. Projections

39. The capital-to-output ratio varies a lot across countries but is generally estimated to be between two and five. Low values of ${kratio}_{i,t}$ tend to be associated with low development, but some low-income countries also have high ratios. Despite the use of the electricity and GDP per capita proxy to get around the problem of initial estimates, there may remain measurement issues that make these estimates less than perfectly comparable across countries, with other differences explainable in terms of natural endowments, sectoral composition, climate, etc. Among advanced economies, ${kratio}_{i,t}$ estimates are somewhat more tightly distributed, with an average of 3.4. Ratios among advanced economies also tend to be more stable historically. Indeed, one of the stylized facts of growth is that, in the long run, progress in living standards is almost entirely driven by trend labour efficiency, implying no strong trends in the capital-to-output ratio, see for example Jones (2015[34]). This is not necessarily true of developing countries, however, for which ${kratio}_{i,t}$ can be trending over long periods.

40. Based on these observations, the modelling assumption is that ${kratio}_{i,t}$ converges to a long-run value of 3.4 in all countries. For many advanced economies, this target is close to the current ratio, implying little contribution to growth from capital accumulation over the long run, consistent with the historical record. For countries far from this objective, it implies ratios that rise or fall over time. An alternative approach would be to keep ${kratio}_{i,t}$ broadly stable over the projection period. However, this would conceptually imply that, even after full convergence in labour efficiency levels, important differences in GDP per capita could remain due to differences in capital intensity. It seems more plausible that country heterogeneity in ${kratio}_{i,t}$ at the jump-off point will shrink over time.

41. The first step in projecting ${kratio}_{i,t}$ is to project the uniform capital stock scrapping rate mentioned previously. It is assumed to converge gradually to 5%, but at a very slow speed, continuing the upward trend thought to be associated with the increasing weight of technology-related goods (Figure A B.10). The following relationship is used:

$∆{RSCRP}_t=0.8\bullet ∆{RSCRP}_{t-1}-0.01\bullet ({RSCRP}_{t-1}-5)$

[B11]

The first term ensures a smooth transition from recent dynamics in the historical period and the second term ensures long-run convergence to the target. The 5% target is arbitrary but not very consequential in the context of the LTM. Given the assumption that capital-to-output ratios converge toward a fixed value, assuming a higher scrapping rate would simply imply higher gross investment rates in the steady state, which are not connected to other outputs in the model.

42. The next step is to project an equilibrium value for gross fixed capital formation as a percentage of GDP (${ITVQ}_{i,t}$). Combining the Cobb-Douglas production function in [B1] with the standard stock-flow equation for the capital stock, it can be shown that in a steady state, the capital-to-output ratio remains stable at a given target value (${kratio}^{*}$) when ${ITVQ}_{i,t}$ is equal to a target value (${ITVQ}_{i,t}^{*}$):

${ITVQ}_{i,t}^{*}=100\bullet \left[\frac{{RSCRP}_t/100+∆\mathrm{l}\mathrm{o}\mathrm{g}({EFFLABS}_{i,t}\bullet {ETPT}_{i,t})}{1+∆\mathrm{l}\mathrm{o}\mathrm{g}({EFFLABS}_{i,t}\bullet {ETPT}_{i,t})}\right]\bullet {kratio}^{*}$

[B12]

Combined with the ${ETPT}_{i,t}$ and ${EFFLABS}_{i,t}$ projections described previously, the ${RSCRP}_t$ projection from [B11], and the assumption that the target capital-to-output ratio is 3.4 (see above), this equation yields the investment rate that is needed to keep the capital-to-output ratio at target. An increase in either trend labour efficiency growth, trend employment growth, or the scrapping rate would imply that the investment rate must rise to keep the ratio stable.

43. Finally, ${ITVQ}_{i,t}$ needs to be projected so that it gradually converges to the target value defined by [B12]. The following relationship is used:

$∆{ITVQ}_{i,t}={∆ITVQ}_{i,t}^{*}-0.05\bullet ({ITVQ}_{i,t-1}-{ITVQ}_{i,t-1}^{*})$

[B13]

where the coefficient 0.05 is the speed of convergence, set low by assumption to ensure a smooth evolution of projected investment rates at the starting point of the projections. The rule also ensures a smooth transition of ${kratio}_{i,t}$ to ${kratio}^{*}$ because, first, ${ITVQ}_{i,t}$ goes only gradually to ${ITVQ}_{i,t}^{*}$ and, once it is there, it takes additional time for ${kratio}_{i,t}$ to fully reach ${kratio}^{*}$. Further work could attempt to estimate the transition dynamics for both investment and the capital stock, although the use of unobservable equilibrium concepts and the measurement issues mentioned previously makes this challenging.

44. Based on the framework just described, capital-to-output ratios respond to two main influences over the projection period:

• In the short to medium run, the main influence is the investment rate at the starting point of the projections (${ITVQ}_{i,t}$). If it is higher than the rate that would be consistent with keeping the initial capital-to-output ratio stable given projections of trend employment and trend labour efficiency, then that ratio rises and contributes positively to potential output growth, and vice-versa.

• In the long run, the main influence is the assumed 3.4 target. In economies where initial capital-to-output ratios are higher than this target, they eventually decline, and vice-versa.

The two influences can produce short run dynamics that are different from the longer-run ones. For instance, the capital-to-output ratio can rise initially because of a relatively high investment rate, before subsequently moderating as the investment rate gradually declines toward the level consistent with the 3.4 capital-to-output ratio target.

45. Generally, slowing employment growth – due to population ageing – and slowing trend labour efficiency growth – due to gradual convergence toward the 1% long-run assumption – imply that less gross investment is required to maintain a given capital-to-output ratio once the scrapping rate has stabilised. Thus, investment rates tend to fall over time (Figure A B.11). At the global level, the investment share of GDP is projected to decline by about 5 pp by 2100. By the mid-2040s, Sub-Saharan African is projected to have the highest investment rate across regions, a consequence of its initially low capital-to-output ratio, the projected rise in trend labour efficiency growth described in the previous section and relatively favourable demographics.

Figure A B.11. Projected gross fixed capital formation by region

% of GDP

Note: Regional groupings are based on World Bank definitions and aggregates use country-level GDP in USD at fixed purchasing power parity exchange rates as weights. Projections in this chart do not account for climate damages.

46. In the East Asia and Pacific, and South Asia, investment rates are at initially high levels, implying continued increases in capital-to-output ratios into the medium term, before gradually falling (Figure A B.12). For the East Asia and Pacific, this means that the capital-to-output ratio initially diverges from the 3.4 target, before converging toward it later on.

Figure A B.12. Projected capital-to-output ratios by region

Note: Regional groupings are based on World Bank definitions and aggregates use country-level GDP in USD at fixed purchasing power parity exchange rates as weights. Projections in this chart do not account for climate damages.

B6. Summary and illustrative results

B6.1. Summary of methodological changes

47. The previous sections set out the approach used to project potential output components for the 90 new individual countries and three regions being added to the LTM, and also introduced modelling changes for the original set of 49 countries. Table A B.6 summarises where this leaves the different sets of countries for each of the main components of potential output.

Table A B.6. Summary of methodological changes to potential output projections

Component of potential output	Set of countries	Methodology
Employment	Original 49	Unchanged. Based on cohort model with age/sex-specific employment rates of Cavalleri and Guillemette (2017[3])
	New 90 + 3	Most individual countries (77) based on cohort model as above. The remaining individual countries (13) and many countries within the three regions based on simplified aggregate employment rate equation of section B3.2
Labour efficiency	Original 49	Based on new 'mixed convergence' approach of section B4.2, but retaining the ability to simulate impact of shocks to various structural indicators on the basis of estimates in Guillemette et al. (2017[19])
	New 90 + 3	Based on new 'mixed convergence' approach of section B4.2
Capital stock	Original 49	Unchanged. PIM method of Chalaux and Guillemette (2019[32]) with initial capital stock estimate based on 10-year average investment rate
	New 90 + 3	PIM method of section B5.2 with initial capital stock estimate based on electricity demand

B6.2. Convergence in living standards abstracting from climate damages

48. A projection for convergence in living standards (relative to the US) can be obtained by combining the projections for trend labour efficiency, trend employment and the capital stock described in previous sections (Figure A B.13). This picture looks remarkably similar to that of convergence in labour efficiency levels, which is not surprising given that it is the single most important growth factor over the long run. There is a fair degree of convergence in living standards over the projection period in several regions but gaps with the United States still remain substantial by 2100, except in Europe and Central Asia which reaches more than 70% of the US living standards by that point.

Figure A B.13. Projected trend real GDP per capita relative to the United States by region

USA = 100

Note: Regional groupings are based on World Bank definitions and aggregates use country-level GDP in USD at fixed purchasing power parity exchange rates as weights. Projections in this chart do not account for climate damages.

49. Country-level potential output per capita projections to 2100 offer a more granular picture, showing limited convergence in living standards for today’s poorer countries, in contrast to richer countries where greater convergence occurs (Figure A B.14). This is largely a result of making convergence in trend labour efficiency a function of initial framework conditions and assuming that these remain where they are today. A few relatively poor countries show greater convergence than neighbouring ones in the figure, a result of their better scores on the convergence speed determinants (e.g. Cambodia).

50. Other aspects of the results worth mentioning include:

• Some countries show a decline, or little change, in relative living standards by 2050, but an increase by 2100 (e.g. Italy). This is typically due to a fairly large negative momentum component for trend labour efficiency at the jump-off point, which dominates the positive convergence component for some time.

• Some countries with living standards initially below those of the United States match or surpass it by 2100 (e.g. Estonia). This is typically due to labour efficiency levels having largely converged to the US level by then, even if not fully, combined with a higher labour utilisation rate than the United States.

• A few countries that start with higher living standards than the United States slowly fall back towards it (e.g. Luxembourg). This is typically due to the momentum component of trend labour efficiency being lower in these countries at the jump-off point than that of the US. It could also conceivably be due to a fall in the capital-to-output ratio relative to the US and, less probably, a fall in the trend employment rate relative to the US.

All of these illustrative results abstract from climate damages and carbon mitigation costs. Taking mitigation costs into account reduces the projected amount of convergence particularly strongly for oil producers (e.g. Qatar).

Figure A B.14. Real GDP per capita relative to the United States

USA = 100

Note: Real GDP per capita is expressed in USD at 2021 PPP exchange rates. Projections in this chart do not account for climate damages.

Notes

← 1.  Countries that remain missing from the LTM, because one or more of the required historical series is missing, include Cuba, Guyana, Venezuela and Yemen. This list is subject to evolve depending on data availability.

← 2.  Given substantial country heterogeneity in such a large and varied set of countries, the country-specific constants capture a lot of the variation in employment rates, reflecting factors such as social norms and religion that make female employment rates much lower in some countries than others.

← 3.  For one, absolute convergence in labour efficiency does not necessarily imply perfect convergence in GDP per capita as there could remain differences in capital intensity and/or labour utilisation even by the end of the projection period. Also, given relatively low convergence speeds, full convergence in labour efficiency levels would, for most countries, only occur well beyond the 2100 projection horizon.

← 4.  The period selected is arbitrary, but what is clear is that this rate has been trending down. For this reason, the LTM standard assumption was revised from 0.015 down to 0.01 some years ago. The reason for focusing on G20 advanced economies is that they are conceptually close to the ‘frontier’ concept, whereas trend labour efficiency growth in less developed countries would also include a convergence component in the framework used here.

← 5.  The alternative of dropping countries with very high oil production intensity makes little difference to estimation results.

← 6.  This approach draws on Daly and Gedminas (2022[63]), who assume (rather than estimate) a half-life of five years for the momentum factor.

← 7.  Since both the governance and globalisation indicators are normalised variables, the assumption that these remain constant amounts to assuming that the relative positions of countries remain fixed going forward.

← 8.  One reason for this is to avoid trend labour efficiency of the frontier country itself going above equilibrium at the start of the projection period if its momentum factor is positive.

← 9.  One exception is the previous indicator of openness, which was based on trade intensity (imports and exports as a % of GDP) adjusted for population size. This indicator affected both the equilibrium labour efficiency level and the speed of convergence. In the new framework, simulations must be based on the new economic globalisation indicator, affecting the speed of convergence only.

← 10.  The data used are from Ember (via Our World in Data) for electricity demand and the World Bank’s World Development Indicators (WDI) database for GDP per capita.

← 11.  This is normally 1994 (to avoid the early 1990s recessions in many countries) or later when the investment series does not go that far back.