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An Econometric Model of International Growth Dynamics for Long-Horizon Forecasting
Abstract
We develop a Bayesian latent factor model of the joint long-run evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in century-long samples, and a sparse correlation pattern (“convergence clubs”) between countries. The joint Bayesian structure allows us to compute a joint predictive distribution for the output paths of these countries over the next 100 years. This predictive distribution can be used for simulations requiring projections into the deep future, such as estimating the costs of climate change. The model's pooling of information across countries results in tighter prediction intervals than are achieved using univariate information sets. Still, even using more than a century of data on many countries, the 100-year growth paths exhibit very wide uncertainty.
... Projections of 21st-century global and regional GDP per capita span a wide range, and long-term economic forecasting has consequently been identified as a key priority by the Intergovernmental Panel on Climate Change (IPCC) 18 and the US National Academies of Sciences, Engineering and Medicine (NASEM) 19 . Previous statistical forecasts [20][21][22][23] , expert surveys 20,23 , and socioeconomic scenarios 15 have identified, as plausible, ranges of 21st-century growth rates leading to ranges of 2100 world GDP per capita spanning an order of magnitude ( Fig. 1b; Supplementary Information, Supplementary Fig. 1), and even wider ranges for today's developing regions. Scenarios and expert outlooks having relatively slow growth are characterized by relatively low trade and international cooperation, less convergence between poor and rich regions, and less innovation; and vice versa (e.g., ref. 15 ). ...
... Scenarios and expert outlooks having relatively slow growth are characterized by relatively low trade and international cooperation, less convergence between poor and rich regions, and less innovation; and vice versa (e.g., ref. 15 ). Damages from climate change, and other possible large-scale disruptions such as future pandemics, are not directly included in most scenarios and forecasts 15,[20][21][22] . ...
... In Fig. 3 and Supplementary Fig. 2, we evaluate the SSP scenarios 6,15 in light of these historical dynamics. The SSPs span a similar range of economic futures as expert projections 20,23 and statistical forecasts [20][21][22] (Fig. 1). We compare SSP projections to: (i) historical dynamics shown in Fig. 1a, (ii) projections to 2100 from both DEMs (see Methods and Fig. 3), and (iii) the "base" projection from the IFs model 28,29 (IFs version 7.81). ...
Future economic growth will affect societal well-being and the environment, but is uncertain. We describe a multidecadal pattern of gross domestic product (GDP) per capita growth rising, then declining, as regions become richer. An empirically fitted differential-equation model and an integrated assessment model—International Futures—accounting for this pattern both predict 21st-century economic outlooks with slow growth and income convergence compared to the Shared Socioeconomic Pathways, similar to SSP4 (“Inequality”). For World Bank income groups, the differential-equation model could have produced, from 1980, consistent projections of 2100 GDP per capita, and more accurate predictions of 2010s growth rates than the International Monetary Fund’s short-term forecasts. Both forecasts were positively biased for the low-income group. SSP4 might therefore represent a best-case—not worst-case—scenario for 21st-century economic growth and income convergence. International Futures projects high poverty and population growth, and moderate energy demands and carbon dioxide emissions, within the Shared Socioeconomic Pathway range.
... Our UN region-specific demographic data comprise country-and age-specific projections of births, deaths, net migration, and population. 8 Our baseline assumed labor-productivity (output per worker) catch-up growth-rate assumptions are based on special univariate simulations provided by the authors of Müller et al. (2019). This paper studies productivity growth in 131 countries with data ranging from 1900 to 2017. ...
... Univariate references predicting a country's future productivity growth based only on its own growth history. Our sensitivity analysis considers a) Müller et al. (2019)'s multivariate projections in which one region's labor productivity growth rate is co-determined with those of other regions with similar growth experiences and b) continuation of the region-specific productivity growth rates observed, on average, over the period 1997 to 2017. Table 2 shows 2017 (our base year) levels and shares of global GDP and GNI (gross national income) based on IMF PPP data. ...
... These results are, however, highly sensitive to our assumed region-specific rate of productivity catch up. Relative to the recent recent record, the econometrically sophisticated study of Müller et al. (2019) predicts an almost complete end to Chinese, Indian, Russian, Eastern European, and former Soviet Union catch-up labor productivity growth. Other regions experience moderate to major And dramatically altering the course of a country's demographics require immediate, massive changes in fertility, mortality, or net immigration rates -changes that may be entirely implausible. ...
... Each individual component in GIVE is based on recent peer-reviewed research on socioeconomic projections, climate modelling, climate impact assessments and economic discounting. We implement GIVE with a set of internally consistent, probabilistic projections of population 9 , per capita economic growth 3,10 , and CO 2 , CH 4 and N 2 O emissions 3 generated using a combination of statistical modelling and expert elicitation, collectively referred to as the Resources for the Future Socioeconomic Projections 3 (RFF-SPs). Many existing IAMs use outdated climate models and have been shown to produce temperature dynamics inconsistent with more sophisticated Earth system models 1,11 . ...
... We further incorporated feedback and improvements suggested by a panel of nine leading demographic experts convened to review preliminary results. Our trajectories of country-level GDP per capita from 2018 to 2300 come from a multifactor Bayesian dynamic model, in which each country's GDP per capita is based on a global frontier of developed economies and country-specific deviations from that frontier 10 . We reweight the probabilities of the Bayesian model trajectories using results from the RFF Economic Growth Survey, a formal expert elicitation focused on quantifying uncertainty in long-run economic growth 3 . ...
... Refs. 3,9,10,15,16,18,19,74 . ...
The social cost of carbon dioxide (SC-CO2) measures the monetized value of the damages to society caused by an incremental metric tonne of CO2 emissions and is a key metric informing climate policy. Used by governments and other decision-makers in benefit-cost analysis for over a decade, SC-CO2 estimates draw on climate science, economics, demography, and other disciplines. However, a 2017 report by the US National Academies of Sciences, Engineering, and Medicine1 (NASEM) highlighted that current SC-CO2 estimates no longer reflect the latest research. The report provided a series of recommendations for improving the scientific basis, transparency, and uncertainty characterization of SC-CO2 estimates. Here we show that improved probabilistic socioeconomic projections, climate models, damage functions, and discounting methods that collectively reflect theoretically consistent valuation of risk, substantially increase estimates of the SC-CO2. Our preferred mean SC-CO2 estimate is 44-413/t-CO2: 5-95% range, 2020 US dollars) at a near-term risk-free discount rate of 2 percent, a value 3.6-times higher than the US government’s current value of $51/t-CO2. Our estimates incorporate updated scientific understanding throughout all components of SC-CO2 estimation in the new open-source GIVE model, in a manner fully responsive to the near-term NASEM recommendations. Our higher SC-CO2 values, compared to estimates currently used in policy evaluation, substantially increase the estimated benefits of greenhouse gas mitigation and thereby increase the expected net benefits of more stringent climate policies.
... 9. The method used by Müller, Stock, and Watson (2020) extends the approach provided in Müller and Watson (2016), which was suitable only for global estimates of economic growth, to generate internally consistent growth projections at the country level. models over long time scales. ...
... METHODS The probabilistic projections of economic growth often used in analyses by governments and the private sector have not incorporated the time scale of centuries, as is needed to support SCC estimates and other economic analyses of climate change. Müller, Stock, and Watson (2020) took a significant step forward by providing probabilistic econometric projections over long periods. Their methodology involves a multifactor Bayesian dynamic model in which each country's GDP per capita is based on a global frontier of developed economies (countries in the OECD) and country-specific deviations from that frontier. ...
... As in the UN (2004) projections, these very extreme outcomes are likely due in part to the perfect correlation between countries implied by the deterministic scenarios and the aggregation of such results. fully below; for more information about the model, see Müller, Stock, and Watson (2020). ...
... Projections of 21st-century global and regional GDP per capita span a wide range, and long-term economic forecasting has consequently been identified as a key priority by the Intergovernmental Panel on Climate Change (IPCC) 18 and the U.S. National Academies of Sciences, Engineering and Medicine (NASEM) 19 . Previous statistical forecasts [20][21][22] , expert surveys 20 , and socioeconomic scenarios 14 have identified, as plausible, ranges of 21st-century growth rates leading to ranges of 2100 world GDP per capita spanning an order of magnitude ( Fig. 1b; Supplementary Information, SI, Fig. S1), and even wider ranges for today's developing regions. Scenarios and expert outlooks having relatively slow growth are characterized by relatively low trade and international cooperation, less convergence between poor and rich regions, and less innovation; and vice versa (e.g., ref. 14 ). ...
... Scenarios and expert outlooks having relatively slow growth are characterized by relatively low trade and international cooperation, less convergence between poor and rich regions, and less innovation; and vice versa (e.g., ref. 14 ). Damages from climate change, and other possible large-scale disruptions such as future pandemics, are not directly included in most scenarios and forecasts 14,[20][21][22] . ...
... 38, 39 ) and predictions that could have been made by the DEMs in 1980, 1990, 2000, and 2010 (see Methods), at the scale of World Bank income groups 33 .InFig. 3 and SI Fig. S2, we evaluate the SSP scenarios5,14 in light of these historical dynamics. The SSPs span a similar range of economic futures as expert projections 20 and statistical forecasts[20][21][22] (Fig. 1). We compare SSP projections to: (i) historical dynamics shown inFig. ...
Future economic growth will affect societal well-being and the environment, but is uncertain. We describe a multidecadal pattern of GDP per capita growth rising, then declining, as regions become richer. A fitted differential-equation model (DEM) and an integrated assessment model (International Futures, IFs) accounting for this pattern both predict 21st-century economic outlooks with slow growth and income convergence compared to the widely used Shared Socioeconomic Pathways (SSPs)—similar to SSP4 (‘Inequality’). For World Bank income groups, the DEM could have produced, from 1980, consistent projections of 2100 GDP per capita, and more accurate predictions of 2010s growth rates than the International Monetary Fund (IMF)’s short-term forecasts. DEM and IMF forecasts were positively biased for the low-income group. SSP4 might therefore represent a best-case—not worst-case—scenario for 21st-century growth and income convergence. IFs projects high poverty and population growth, and moderate energy demands and CO2 emissions, within the SSP range.
... Galor (1996) argues that club convergence is consistent not only with the neoclassical paradigm in general but also with constant returns to scale and diminishing marginal productivity in particular. Müller et al. (2022) find evidence of convergence clubs. ...
... Although (1) is the dominant representation, it is not the only one. Phillips and Sul (2009) treat the time series representation differently, with a fixed initial income, a time varying technology A it = A i0 exp(g it t) where it is a time varying speed of convergence: Müller et al. (2022) use low frequency projections combined with a linear factor structure. It is designed for long term forecasting and they discuss the relation between their model and the ones common in the literature. ...
The literature on convergence in per-capita income across countries has not converged on a common concept of convergence. It may be within a country towards its own steady state or between countries. Between country convergence may be absolute convergence to the same steady state; conditional convergence to country specific steady states, functions of observed variables; or club convergence to different steady states. It may be measured by beta convergence; sigma convergence; or the presence of a common trend. This paper surveys the econometric issues involved in estimating the rate of convergence; testing for convergence; and specifying the unobserved steady state. The survey suggests that rather than there being different ways to measure a single concept, convergence, the different measures are measuring different things.
... Note that gt = (1/t) t τ =1 Gτ . 11 In addition, Weitzman models the immediate resolution of uncertainty, which is not consistent with the way that stochasticity evolves under the consumption growth process of Müller, Stock & Watson (2022) that is employed by Newell, Pizer & Prest (2022 ...
... This requires three key inputs. The single-period growth process, G τ = ln(c τ /c τ −1 ), is estimated in a way that is consistent with the stochastic process in Müller, Stock & Watson (2022). The longterm process for r ce t is then set in a way that is consistent with the declining term structure of Bauer & Rudebusch (2023), which is estimated based on econometric models of historic Treasury bond yields. ...
... Population-weighting (rather than area-weighting) is more likely to capture the effects of climate onto socio-economic activity (see Tol, 2017). To project climate impacts to the end of the century, we construct a dataset of country-level changes in temperatures based on CMIP5 climate models (Taylor et al., 2012) and use long-term country-level forecasts of GDP per capita for our baseline (Müller et al., 2019). In the appendix, we also consider the impact of precipitation (see Figure C.10). ...
... Projected Damage Curve: Using our above estimates, we derive an overall damage curve relating the level of warming in 2100 to levels of GDP per capita. We project the non-linear climate impact estimates from (4.1) and (4.2) to the end of the century by combining gridded temperature projections from individual CMIP5 model ensemble runs and econometric long-term GDP per capita growth forecasts on a country level from Müller et al. (2019) as baselines (see Schwarz & Pretis 2020 for additional details on the methodology linking econometric estimates to overall damage curves). Accounting for both climate and estimation uncertainty, all our estimates indicate substantial reductions in GDP per capita levels for high levels of warming when compared to our baseline of no additional warming (see Figure 4.6 and Table 4.2). ...
... We consider the projections described in , obtained from Bayesian hierarchical models and expert elicitations. Müller et al. (2022) and Raftery and ševčíková (2023) present detailed descriptions of the GDP per capita and population models, respectively. To obtain these projections, we utilize the dataset . ...
Risk assessments of complex systems are often supported by quantitative models. The sophistication of these models and the presence of various uncertainties call for systematic robustness and sensitivity analyses. The multivariate nature of their response challenges the use of traditional approaches. We propose a structured methodology to perform uncertainty quantification and global sensitivity analysis for risk assessment models with multivariate outputs. At the core of the approach are novel sensitivity measures based on the theory of optimal transport. We apply the approach to the uncertainty quantification and global sensitivity analysis of emissions pathways estimated via an eminent open‐source climate–economy model (RICE50+). The model has many correlated inputs and multivariate outputs. We use up‐to‐date input distributions and long‐term projections of key demographic and socioeconomic drivers. The sensitivity of the model is explored under alternative policy architectures: a cost‐benefit analysis with and without international cooperation and a cost‐effective analysis consistent with the Paris Agreement objective of keeping temperature increase below 2°C. In the cost‐benefit scenarios, the key drivers of uncertainty are the emission intensity of the economy and the emission reduction costs. In the Paris Agreement scenario, the main driver is the sensitivity of the climate system, followed by the projected carbon intensity. We present insights at the multivariate model output level and discuss how the importance of inputs changes across regions and over time.
... When Gillingham et al. (2018) faced the same issue in their study, they conducted an expert elicitation . Later, for the Rennert et al. (2021) scenarios mentioned in Section 4.1, Müller et al. (2022) produced the most rigorous econometric study to date, estimating a long-run growth process. However, when RFF first proposed the need for a stochastic forecast spanning over a century, one of the authors humorously compared the task to reading tea leaves. ...
... To assess the long-term impact of M&A activity on forecasting energy prices and volatility, we conduct an in-depth analysis over an extended timeframe. Prior research has highlighted the variability in forecasting accuracy across different periods and time horizons (Quaedvlieg, 2021;Müller et al., 2022), noting a rapid decay in volatility predictive accuracy as the horizon increases (Christoffersen and Diebold, 2000). It is imperative to investigate the persistency of M&A deals in forecasting energy prices and volatility over longer time horizons. ...
... More mainstream treatments of the prediction problem in the economic literature normally are in stark contrast to EC's approach by involving a much larger number of factors. In a recent paper, Muller et al. [9] introduce a Bayesian factor model of GDPpc growth with a very long time horizon (up to 100 years), motivated by the need for long-run planning in issues like policy evaluation and climate change. The model leverages more than 800 parameters and builds a hierarchical structure of factors by dividing the countries into correlated nested clusters [10]. ...
... We extend Acemoglu and Molina's bias argument on the convergence parameter in the absence of fixed effects. Their argument has some credence when Müller et al. (2022) use a longer data span, finding that the country-specific intercepts are persistent. But we show that imposing all countries must converge at the same rate or not also biases convergence towards zero. ...
Recent literature revisits cross-country convergence patterns over the last six decades. Whilst the debate has been about unconditional or conditional convergence, we question whether convergence rates differ across countries. Using the same dataset as in the recent studies of Kremer et al. (NBER Macroecon Annu 36:337–412, 2022) and Acemoglu and Molina (NBER Macroecon Annu 36:425–442, 2022) (GDP per capita for 108 countries over 58 years, 1960–2017), we systematically search models where the degree of heterogeneity varies from the mean group, pooled mean group, fixed effects and pooled estimators of convergence. The Bayesian Information Criterion selects the heterogeneous model whether we use the U.S., a common factor or country-specific trends as the steady state. We estimate a multi-country technological catch-up statistical model using the U.S. as the technological frontier. We show empirically that a failure to allow for heterogeneous rates of convergence creates a bias in the convergence coefficient towards zero. The long-run elasticity to the U.S.—another convergence parameter of interest—associates positively (0.79) with the country’s average growth. Countries that learn from the technological frontier also grow faster.
... The adoption of Bayesian methodologies in simulating long-run growth rates is often preferred to classical statistics, mostly on the basis of superior performance in long-run forecasting (Geweke, 2001). 3 For this reason, several models forecasting national or regional growth in the very long run adopt a Bayesian structure (see, e.g., Müller et al., 2022, for a recent example and a review). ...
During the past decade, world economic development was coupled with disruptive challenges. Among them, digitalisation and new forms of globalisation represent a potential threat for economic growth opportunities and for the future of labour markets. Digital transition calls for the assessment of the impact of robotisation and digitalisation on skill composition, employment levels, productivity and growth dynamics. In turn, the largest wave of globalisation after that taking place before the First World War caused, first, the emergence of global value chains and, more recently, their disintegration with partial mechanisms of reshoring, with consequences for growth and employment opportunities. All these challenges call for comprehensive approaches to their modelling. This paper presents the main advances introduced in the fifth generation of the MAcroeconomic, Sectoral, Social, Territorial (MASST5) model, which carved a relevant niche in the empirical literature on macro-econometric regional growth, and has now been strengthened to model future digitalisation transitions, as well as the national and regional breakdown of the way global value chains will reorganise. A longer time series, especially in the regional submodel, also allows one to take the major changes taking place in Europe following the 2007–08 financial crisis, and the 2020 COVID-induced contraction into account.
... For the socioeconomic and emissions scenarios, we implemented the Resources for the Future Socioeconomic Projections (RFF-SPs) within the coupled models (Extended Data Fig. 1). The RFF-SPs provide a set of internally consistent, probabilistic socioeconomic projections for economy, population and GHG emissions [24][25][26][27] . Compared with the well-known Intergovernmental Panel on Climate Change's Shared Socioeconomic Pathways (IPCC SSPs), the RFF-SPs are more suitable for conducting uncertainty assessments of the social cost of greenhouse gases. ...
The social cost of greenhouse gases (SC-GHGs), indicating marginal damage from GHG emissions, is a valuable and informative metric for policymaking. However, existing social cost estimates for methane (SC-CH4) and nitrous oxide (SC-N2O) have not kept pace with the latest scientific findings in damage functions, climate models and socioeconomic projections. We applied a multimodel assessment framework, incorporating recent advances that are neglected by past studies to re-estimate SC-CH4 and SC-N2O. Models of gross domestic product (GDP) level effects reveal US49,600 per t-N2O for SC-N2O for the emissions year 2020, indicating a 2-fold increase over previous estimates. Models incorporating GDP growth effects over time present a further 15–25-fold increase in estimates, dominating the uncertainty in social cost estimates. Although substantial uncertainty remains, our findings suggest greater benefits from CH4 and N2O mitigation policies compared with those of previous studies.
... Here that would have some disadvantages, including the loss of observations at the start and end of the sample, and the use of ultimately arbitrary conventions when translating break tests into period classifications. 14 The long-horizon forecasts of Müller et al. (2022) also use the mean OECD growth rate to proxy the growth of the frontier in-sample. 15 ...
... For a T × n panel x of n variables observed over T time periods, the quantile factor model is of the form x = f (τ ) λ ′ (τ ) + u (τ ) , where f (τ ) is the T × r matrix of factors, r ≪ n, λ (τ ) is an n × r loadings matrix, and τ ∈ (0, 1) denotes the quantile level. CDG propose an iterative procedure that can be viewed as a generalization of principal component analysis (PCA) to the case of a check function loss (while PCA minimizes a 1 For example, the factor model has become the ground for characterizing international business cycle comovements (Kose et al., 2003;Müller et al., 2022); for modeling mixed frequency macro data (Mariano and Murasawa, 2003); and for structural VAR analysis (Bernanke et al., 2005), among numerous other applications. ...
This paper extends quantile factor analysis to a probabilistic variant that incorporates regularization and computationally efficient variational approximations. By means of synthetic and real data experiments it is established that the proposed estimator can achieve, in many cases, better accuracy than a recently proposed loss-based estimator. We contribute to the literature on measuring uncertainty by extracting new indexes of low, medium and high economic policy uncertainty, using the probabilistic quantile factor methodology. Medium and high indexes have clear contractionary effects, while the low index is benign for the economy, showing that not all manifestations of uncertainty are the same.
... 9 9 The derivations of these paths, and the conditions that must hold for global balanced growth in that environment, open up applications beyond nominal rigidities, for example with respect to the study of long-run global change. See Müller, Stock, and Watson (2020) for a statistical analysis of the joint long-run evolution of GDP per capita for 113 countries over 118 years from 1900 to 2017. From a structural modeling standpoint, the assumption that varieties z are drawn from a Fréchet distribution in much of the trade literature is not innocuous. ...
... The national population is not assumed to grow very much, except for the two African countries. Therefore, the SSP2 scenario is very optimistic about economic growth in Africa (for an alternative view, see Müller et al., 2019), although the per capita effect is curbed by the contemporary increase in the population. ...
Most projections of long-term economic development, such as the shared socioeconomic pathway (SSP) scenarios in climate change research, do not quantify future effects on income distribution and poverty. To reduce this knowledge gap, we present some numerical simulations based on a recursive-dynamic general equilibrium model with household details, focusing on relative and absolute poverty in six developing countries: Albania, Bolivia, Ethiopia, Malawi, Nicaragua, and Vietnam. The results under the SSP2 reference scenario suggest that the exogenously projected gross domestic product (GDP) and population growth, combined with long-term structural change, produce lower absolute but higher relative poverty. An alternative scenario of stronger trade integration further amplifies the impact on income inequality. Indeed, more international trade tends to increase capital income, which mainly benefits rich households, but generally decreases agricultural earnings, which are important for rural poor households.
The determinants of an economy's growth path for income per head may vary over time. In this paper, we apply unobserved components analysis to an otherwise standard panel model of economic growth dynamics so that an economy's long‐run relative income per head can change at any point of time. We apply this model to data for US states for 1929–2021 and the world economy for 1970–2019. In both datasets an economy's initial relative income per head is a good predictor of its long‐run relative income per head. Relatively poor economies on average remain relatively poor.
This review of recent advances in biosphere research aims to provide information on selected issues related to changes in biodiversity, ecosystem functioning, social and economic interactions with ecosystems, and the impacts of climate change on the biosphere. We highlight advances on nine themes that have been recently published in peer-reviewed journals that are gaining importance in the scientific community and have the potential to guide future actions as well as inspire future research questions. Our focus is on the interactions between climate, biosphere and society, and on strategies to sustain, restore or promote ecosystems and their services. While mitigating climate change is expected to reduce many risks and associated costs, rapid emission reductions are also crucial to secure various co-benefits of ecosystems, such as coastal protection or stabilization of regional hydrological cycles. In this context, conservation measures implemented in cooperation with local actors are key to efficient resource allocation. At the same time, holistic action frameworks at the global level are required to guide and support such efforts.
The present study examines the assumptions, modeling structure, and results of DICE-2023, the revised Dynamic Integrated Model of Climate and the Economy (DICE), updated to 2023. The revision contains major changes in the treatment of risk, the carbon and climate modules, the treatment of nonindustrial greenhouse gases, discount rates, as well as updates on all the major components. Noteworthy changes are a significant reduction in the target for the optimal (cost-beneficial) temperature path, a lower cost of reaching the 2 °C target, an analysis of the impact of the Paris Accord, and a major increase in the estimated social cost of carbon.
As people get richer, and ecosystem services scarcer, policy-relevant estimates of ecosystem value must rise
Economic growth in the 19th and 20th centuries, following the Industrial Revolutions, was much faster than in preceding centuries. This unprecedented global growth coincided with the global proliferation of democracy, with some evidence for bidirectional causation. Macroeconomic forecasts have predicted slower economic growth in the 21st century--perhaps substantially slower--for structural reasons such as aging populations, slowdowns in innovation, and debt. Long-run effects of COVID-19 and climate change could further slow growth. Moreover, some sustainability scientists assert that slower growth, stagnation, or even de-growth is an environmental imperative. Whether slow growth is inevitable or planned, we argue that democracies should prepare for additional fiscal and social stress--some of which is already apparent. Focusing on developed democracies, we propose that preparations should include efforts to: (i) reduce inequality; (ii) socially integrate diverse populations and build shared identities; (iii) increase economic opportunity for youth; (iv) improve return on investment in taxation and public spending; (v) strengthen formal democratic institutions; and (vi) invest in improving non-economic drivers of subjective well-being. Many aspects of our analysis likely also apply to other types of societies besides developed democracies.
We examine the record of crosscountry growth over the past 50 years and ask if developing countries have made progress on closing income gap between their per capita incomes and those in the advanced economies. We conclude that, as a group, they have not and then survey the literature on absolute convergence with particular emphasis on that from the last decade or so. That literature supports our conclusion of a lack of progress in closing the income gap between countries. We close with a brief examination of the recent literature on cross-individual distribution of income which finds that, despite the lack of progress on cross country convergence, global inequality has tended to fall since 2000. (JEL E01, E13, O11, O47, F41, F62)
Here are the first two paragraphs of the Executive Summary.
The social cost of carbon (SC-CO2) is an economic metric intended
to provide a comprehensive estimate of the net damages—that is,
the monetized value of the net impacts, both negative and positive—
from the global climate change that results from a small (1 metric
ton) increase in carbon dioxide (CO2) emissions. Under Executive Orders
regarding regulatory impact analysis and as required by a court ruling,
the U.S. government has since 2008 used estimates of the SC-CO2 in federal
rulemakings to value the costs and benefits associated with changes
in CO2 emissions. In 2010, the Interagency Working Group on the Social
Cost of Greenhouse Gases (IWG) developed a methodology for estimating
the SC-CO2 across a range of assumptions about future socioeconomic and
physical earth systems.
The IWG asked the National Academies of Sciences, Engineering,
and Medicine to examine potential approaches, along with their relative
merits and challenges, for a comprehensive update to the current methodology.
The task was to ensure that the SC-CO2 estimates reflect the best
available science, focusing on issues related to the choice of models and
damage functions, climate science modeling assumptions, socioeconomic
and emissions scenarios, presentation of uncertainty, and discounting.
The US government recently developed a range of values representing the monetized global damages associated with an incremental increase in carbon dioxide (CO[subscript 2]) emissions, commonly referred to as the social cost of carbon (SCC). These values are currently used in benefit–cost analyses to assess potential federal regulations. For 2010, the central value of the SCC is 5, 65 per ton of CO[subscript 2] (2007 dollars). This article summarizes the methodology and interagency process used to develop these SCC values, offers our own commentary on how the SCC can be used to inform regulatory decisions, and identifies priorities for further research. (JEL: Q54, Q51, and Q58)
[eng] Transportation costs and monopoly location in presence of regional disparities. . This article aims at analysing the impact of the level of transportation costs on the location choice of a monopolist. We consider two asymmetric regions. The heterogeneity of space lies in both regional incomes and population sizes: the first region is endowed with wide income spreads allocated among few consumers whereas the second one is highly populated however not as wealthy. Among the results, we show that a low transportation costs induces the firm to exploit size effects through locating in the most populated region. Moreover, a small transport cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. [fre] Cet article d�veloppe une statique comparative de l'impact de diff�rents sc�narios d'investissement (projet d'infrastructure conduisant � une baisse mod�r�e ou � une forte baisse du co�t de transport inter-r�gional) sur le choix de localisation d'une entreprise en situation de monopole, au sein d'un espace int�gr� compos� de deux r�gions aux populations et revenus h�t�rog�nes. La premi�re r�gion, faiblement peupl�e, pr�sente de fortes disparit�s de revenus, tandis que la seconde, plus homog�ne en termes de revenu, repr�sente un march� potentiel plus �tendu. On montre que l'h�t�rog�n�it� des revenus constitue la force dominante du mod�le lorsque le sc�nario d'investissement privil�gi� par les politiques publiques conduit � des gains substantiels du point de vue du co�t de transport entre les deux r�gions. L'effet de richesse, lorsqu'il est associ� � une forte disparit� des revenus, n'incite pas l'entreprise � exploiter son pouvoir de march� au d�triment de la r�gion l
This paper studies cross-country patterns of economic growth from the viewpoint of income distribution dynamics. Such a perspective raises new empirical and theoretical issues in growth analysis: the profound empirical regularity is an "emerging twin peaks" in the cross-sectional distribution, not simple patterns of convergence or divergence. The theoretical problems raised concern interaction patterns among subgroups of economies, not only problems of a single economy's accumulating factor inputs and technology for growth. Copyright 1997 by Kluwer Academic Publishers
Convergence concerns poor economies catching up with rich ones. At issue is what happens to the cross sectional distribution of economies, not whether a single economy tends towards its own steady state. It is the latter, however, that has preoccupied the traditional approach to convergence analysis. This paper describes a body of research that overcomes this shortcoming in the traditional approach. The new findings--on persistence and stratification, on the formation of convergence clubs, and on the distribution polarizing into twin peaks of rich and poor--suggest the relevance of a class of theoretical ideas different from the production-function accounting traditionally favored. Copyright 1996 by Royal Economic Society.
Traditional empirical strategies for studying convergence - more generally, the dynamics and determinants of economic growth, can be misleading if important, underlying permanent or growth components are stochastically time-varying. This paper documents the degree to which this instability characterises the data, and then offers an alternative empirical framework. This alternative, directly modelling the dynamics of the evolving cross-section distributions, applied to cross-country income data yields some interesting insights: economies across the world seem to be converging to a distribution where many remain wealthy, and many remain poor. Those economies able to make the transition from low to high income levels are primarily small and sparsely populated; middle-income ones, by contrast, are a vanishing class.
We propose to use the attractiveness of pooling relatively short time series that display similar dynamics, but without restricting to pooling all into one group. We suggest estimating the appropriate grouping of time series simultaneously along with the group-specific model parameters. We cast estimation into the Bayesian framework and use Markov chain Monte Carlo simulation methods. We discuss model identification and base model selection on marginal likelihoods. A simulation study documents the efficiency gains in estimation and forecasting that are realized when appropriately grouping the time series of a panel. Two economic applications illustrate the usefulness of the method in analysing also extensions to Markov switching within clusters and heterogeneity within clusters, respectively.
Many questions in economics involve long-run or “trend” variation and covariation in time series. Yet, time series of typical lengths contain only limited information about this long-run variation. This paper suggests that long-run sample information can be isolated using a small number of low-frequency trigonometric weighted averages, which in turn can be used to conduct inference about long-run variability and covariability. Because the low-frequency weighted averages have large sample normal distributions, large sample valid inference can often be conducted using familiar small sample normal inference procedures. Moreover, the general approach is applicable for a wide range of persistent stochastic processes that go beyond the familiar I (0) and I (1) models.
INTRODUCTION
This paper discusses inference about trends in economic time series. By “trend” we mean the low-frequency variability evident in a time series after forming moving averages such as low-pass (cf. Baxter and King, 1999) or Hodrick and Prescott (1997) filters. To measure this low-frequency variability we rely on projections of the series onto a small number of trigonometric functions (e.g., discrete Fourier, sine, or cosine transforms). The fact that a small number of projection coefficients capture low-frequency variability reflects the scarcity of low-frequency information in the data, leading to what is effectively a “small-sample” econometric problem. As we show, it is still relatively straightforward to conduct statistical inference using the small sample of low-frequency data summaries.Moreover, these low-frequency methods are appropriate for both weakly and highly persistent processes. Before getting into the details, it is useful to fix ideas by looking at some data.
Figure 1 plots the value of per-capita GDP growth rates (panel A) and price inflation (panel B) for the United States using quarterly data from 1947 through 2014, and where both are expressed in percentage points at an annual rate. The plots show the raw series and two “trends.” The first trend was constructed using a band-pass moving average filter designed to pass cyclical components with periods longer than T/6 ≈ 11 years, and the second is the full-sample projection of the series onto a constant and twelve cosine functions with periods 2T/j for j = 1, …, 12, also designed to capture variability for periods longer than 11 years.
World GDP per capita is forecast to grow at 2.6 percent annually over the next 100 years. Convergence of less developed countries toward output levels of the world frontier accounts for much of the forecast. Projecting recent growth in China and India accounts for much of the forecast convergence. The forecast differs from the earlier literature because the facts of convergence have changed in recent decades. A Markov‐switching model is estimated for each country, allowing each country to switch on‐or‐off a path of convergence to the world output frontier. Bayesian estimates of the historical process and posterior forecasts are offered.
We develop inference methods about long-run comovement of two time series. The parameters of interest are defined in terms of population second moments of low-frequency transformations (“low-pass” filtered versions) of the data. We numerically determine confidence sets that control coverage over a wide range of potential bivariate persistence patterns, which include arbitrary linear combinations of I(0), I(1), near unit roots, and fractionally integrated processes. In an application to U.S. economic data, we quantify the long-run covariability of a variety of series, such as those giving rise to balanced growth, nominal exchange rates and relative nominal prices, the unemployment rate and inflation, money growth and inflation, earnings and stock prices, etc.
The recently published Intergovernmental Panel on Climate Change (IPCC) projections to 2100 give likely ranges of global temperature increase in four scenarios for population, economic growth and carbon use. However, these projections are not based on a fully statistical approach. Here we use a country-specific version of Kaya's identity to develop a statistically based probabilistic forecast of CO 2 emissions and temperature change to 2100. Using data for 1960-2010, including the UN's probabilistic population projections for all countries, we develop a joint Bayesian hierarchical model for Gross Domestic Product (GDP) per capita and carbon intensity. We find that the 90% interval for cumulative CO 2 emissions includes the IPCC's two middle scenarios but not the extreme ones. The likely range of global temperature increase is 2.0-4.9 °C, with median 3.2 °C and a 5% (1%) chance that it will be less than 2 °C (1.5 °C). Population growth is not a major contributing factor. Our model is not a business as usual' scenario, but rather is based on data which already show the effect of emission mitigation policies. Achieving the goal of less than 1.5 °C warming will require carbon intensity to decline much faster than in the recent past.
Why are people in the richest countries of the world so much richer today than 100 years ago? And why are some countries so much richer than others? Questions such as these define the field of economic growth. This paper documents the facts that underlie these questions. How much richer are we today than 100 years ago, and how large are the income gaps between countries? The purpose of the paper is to provide an encyclopedia of the fundamental facts of economic growth upon which our theories are built, gathering them together in one place and updating them with the latest available data.
We describe the theory and practice of real GDP comparisons across countries and over time. Version 8 of the Penn World Table expands on previous versions in three respects. First, in addition to comparisons of living standards using components of real GDP on the expenditure side, we provide a measure of productive capacity, called real GDP on the output side. Second, growth rates are benchmarked to multiple years of cross-country price data so they are less sensitive to new benchmark data. Third, data on capital stocks and productivity are (re) introduced. Applications including the Balassa-Samuelson effect and development accounting are discussed.
Long-run forecasts of economic variables play an important role in policy, planning, and portfolio decisions. We consider
forecasts of the long-horizon average of a scalar variable, typically the growth rate of an economic variable. The main contribution
is the construction of prediction sets with asymptotic coverage over a wide range of data generating processes, allowing for
stochastically trending mean growth, slow mean reversion and other types of long-run dependencies. We illustrate the method
by computing prediction sets for 10 to 75 year average growth rates of U.S. real per-capita GDP and consumption, productivity,
price level, stock prices and population.
In an 80-country panel since the 1960s, the convergence rate for per capita GDP is around 1.7% per year. This “beta convergence” is conditional on an array of explanatory variables that hold constant countries’ long-run characteristics. The introduction of country fixed effects generates a much higher—and, I argue, misleading—convergence rate. In a much longer time frame—28 countries since 1870—estimation with country fixed effects is more appropriate, and the estimated convergence rate is around 2.4% per year. Combining the point estimates from the post-1960s and post-1870 panels suggests that the conditional convergence rate is between 1.7% and 2.4% per year, an interval that contains the “iron-law” rate of 2%. In the post-1960s panel, estimation without country fixed effects supports the modernization hypothesis, in the form of positive effects of per capita GDP and schooling on democracy and maintenance of law and order. The long-term panel with country fixed effects also supports modernization, in the sense of a positive effect of per capita GDP on the Polity indicator for democracy. A measure of dispersion—the standard deviation of the log of per capita GDP across 25 countries—is reasonably stable since 1870. This lack of “sigma convergence” is consistent with the presence of beta convergence. For 34 countries—including China and India—observed since 1896, the dispersion of per capita GDP declines since the late 1970s, especially when the country data are weighted by population. This sigma convergence reflects particularly the incorporation of China and India into the world market economy. For 29 countries since 1919, the levels and trends in cross-country dispersion are similar for consumption and GDP.
This paper discusses the history of the use of cross-country regressions in modern growth economics. These regressions continue to be the workhorse of empirical growth analysis even though their meaning continues to be controversial. I argue that the early interpretations of these regressions have proven to be inappropriate and led to substantial exaggeration of the evidentiary support for various new growth theories. On the other hand, I argue that these regressions have a valuable role to play in identifying the modern analog of stylized facts for growth behavior.
We provide an overview of recent empirical research on patterns of cross-country growth. The new empirical regularities considered differ from earlier ones, e.g., the well-known Kaldor stylized facts. The new research no longer makes production function accounting a central part of the analysis. Instead, attention shifts more directly to questions like, Why do some countries grow faster than others? It is this changed focus that, in our view, has motivated going beyond the neoclassical growth model.
This article considers inference about the variance of coefficients in time-varying parameter models with stationary regressors. The Gaussian maximum likelihood estimator (MLE) has a large point mass at 0. We thus develop asymptotically median unbiased estimators and asymptotically valid confidence intervals by inverting quantile functions of regression-based parameter stability test statistics, computed under the constant-parameter null. These estimators have good asymptotic relative efficiencies for small to moderate amounts of parameter variability. We apply these results to an unobserved components model of trend growth in postwar U.S. per capita gross domestic product. The MLE implies that there has been no change in the trend growth rate, whereas the upper range of the median-unbiased point estimates imply that the annual trend growth rate has fallen by 0.9% per annum since the 1950s.
This paper develops a framework for inferring common Markov-switching components in a panel data set with large cross-section and time-series dimensions. We apply the framework to studying similarities and differences across U.S. states in the timing of business cycles. We hypothesize that there exists a small number of cluster designations, with individual states in a given cluster sharing certain business cycle characteristics. We find that although oil-producing and agricultural states can sometimes experience a separate recession from the rest of the United States, for the most part, differences across states appear to be a matter of timing, with some states entering recession or recovering before others.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.
This paper provides a framework for understanding the cross-section and time series approaches which have been used to test the convergence hypothesis. First, we present two definitions of convergence which capture the implications of the neo-classical growth model for the relationship between current and future cross-country output differences. Second, we identify how the cross-section and time series approaches relate to these definitions. Cross-section tests are shown to be associated with a weaker notion of convergence than time series tests. Third, we show how these alternative approaches make different assumptions on whether the data are well characterized by a limiting distribution. As a result, the choice of an appropriate testing framework is shown to depend on both the specific null and alternative hypotheses under consideration as well as on the initial conditions characterizing the data being studied.
This paper uses multi-level factor models to characterize within- and between-block variations as well as idiosyncratic noise in large dynamic panels. Block-level shocks are distinguished from genuinely common shocks, and the estimated block-level factors are easy to interpret. The framework achieves dimension reduction and yet explicitly allows for heterogeneity between blocks. The model is estimated using a Markov chain Monte-Carlo algorithm that takes into account the hierarchical structure of the factors. We organize a panel of 447 series into blocks according to the timing of data releases and use a four-level model to study the dynamics of real activity at both the block and aggregate levels. While the effect of the economic downturn of 2007-09 is pervasive, growth cycles are synchronized only loosely across blocks. The state of the leading and the lagging sectors, as well as that of the overall economy, is monitored in a coherent framework.
A key economic issue is whether poor countries or regions tend to grow faster than rich ones: are there automatic forces that lead to convergence over time in the levels of per capita income and product? The authors use the neoclassical growth model as a framework to study convergence across the forty-eight contiguous U.S. states. They exploit data on personal income since 1840 and on gross state product since 1963. The U.S. states provide clear evidence of convergence, but the findings can be reconciled quantitatively with the neoclassical model only if diminishing returns to capital set in very slowly. Copyright 1992 by University of Chicago Press.
This paper investigates the remarkable extremes of growth experiences within countries and the changes that occur across growth transitions. We find two main results. First, virtually all but the very richest countries experience both growth miracles and failures over substantial periods. Second, growth accelerations and collapses are asymmetric phenomena. Collapses typically feature reduced investment amidst increasing price instability, whereas growth takeoffs are primarily associated with large expansions in international trade. The results show that even very poor countries regularly grow rapidly, but sustaining growth is difficult and may pose a very different set of challenges than starting it. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
This paper examines whether the Solow growth model is consistent with the international variation in the standard of living.
It shows that an augmented Solow model that includes accumulation of human as well as physical capital provides an excellent
description of the cross-country data. The paper also examines the implications of the Solow model for convergence in standards
of living, that is, for whether poor countries tend to grow faster than rich countries. The evidence indicates that, holding
population growth and capital accumulation constant, countries converge at about the rate the augmented Solow model predicts.
For 98 countries in the period 1960–1985, the growth rate of real per capita GDP is positively related to initial human capital
(proxied by 1960 school-enrollment rates) and negatively related to the initial (1960) level of real per capita GDP. Countries
with higher human capital also have lower fertility rates and higher ratios of physical investment to GDP. Growth is inversely
related to the share of government consumption in GDP, but insignificantly related to the share of public investment. Growth
rates are positively related to measures of political stability and inversely related to a proxy for market distortions.
The historical path of gross domestic product (GDP) per capita in the United States is, except for the interlude of the Great Depression, well characterized by reasonably stable exponential trend growth with modest cyclical deviations: graphically, it is a modestly sloping, slightly bumpy hill. However, almost nothing that is true of U.S. GDP per capita (or that of other countries of the Organisation for Economic Co-operation and Development) is true of the growth experience of developing countries. A single time trend does not adequately characterize the evolution of GDP per capita in most developing countries. Instability in growth rates over time for a single country is great, relative to both the average level of growth and the variance across countries. These shifts in growth rates lead to distinct patterns. While some countries have steady growth (hills and steep hills), others have rapid growth followed by stagnation (plateaus), rapid growth followed by decline (mountains) or even catastrophic falls (cliffs), continuous stagnation (plains), or steady decline (valleys). Volatility, however defined, is also much greater in developing than in industrial countries. These stylized facts about the instability and volatility of growth rates in developing countries imply that the exploding econometric growth literature that makes use of the panel nature of data is unlikely to be informative. In contrast, research into what initiates (or halts) episodes of growth has high potential.
Jiangsu and Zhejiang are of two of China's most prosperous and dynamic provinces. This paper first presents a factual account of two empirical phenomena: 1) FDI has played a more substantial role in the economic development of Jiangsu than in Zhejiang, and 2) ownership biases against domestic private firms in Jiangsu were more substantial than in Zhejiang. The paper hypothesizes that there is a connection between these two empirical phenomena. Specifically, ownership biases against domestic private firms increase preferences for FDI because FDI provides a measure of relative property rights security. Thus a biased domestic private firm has an incentive to move its assets and/or future growth opportunities to the foreign sector. The paper uses two private-sector surveys—one conducted in 1993 and the other in 2002—to provide an empirical test of this hypothesis. Our analysis shows, controlling for a variety of firm-level attributes and industry and regional characteristics, those private firms which perceive ownership biases to be more severe are more likely to form joint ventures with foreign firms.
This paper proposes and tests new definitions of convergence and common trends for per capita output. We define convergence for a group of countries to mean that each country has identical long-run trends, either stochastic, while common trends allow for proportionality of the stochastic elements. These definitions lead naturally to the use of cointegration techniques in testing. Using century-long time series for 15 OECD economies, we reject convergence but find substantial evidence for common trends. Smaller samples of European countries also reject convergence but are driven by a lower number of common stochastic trends. Copyright 1995 by John Wiley & Sons, Ltd.
Density forecasting is increasingly more important and commonplace, for example in financial risk management, yet little attention has been given to the evaluation of density forecasts. The authors develop a simple and operational framework for density forecast evaluation. They illustrate the framework with a detailed application to density forecasting of asset returns in environments with time-varying volatility. Finally, the authors discuss several extensions. Copyright 1998 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
This paper presents empirical evidence against the standard dichotomy in macroeconomics that separates growth from the volatility of economic fluctuations. In a sample of ninety-two countries as well as a sample of OECD countries, the authors find that countries with higher volatility have lower growth. The addition of standard control variables strengthens the negative relationship. The authors also find that government spending-induced volatility is negatively associated with growth even after controlling for both time- and country-fixed effects. Copyright 1995 by American Economic Association.
We develop a framework to assess how successfully standard time series models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric series. The properties of these weighted averages are then compared to the asymptotic implications of a number of common time series models. We apply the framework to twenty U.S. macroeconomic and financial time series using frequencies lower than the business cycle. Copyright 2008 The Econometric Society.
A lo largo de la historia econ�mica moderna, los salarios reales han sido un buen indicador del nivel de vida material de la clase trabajadora. Este documento presenta series de salarios reales para diferentes sectores y �pocas en Colombia. Apoy�ndonos en datos compilados por varios autores, nuestra principal conclusi�n es que a lo largo de los �ltimos 170 a�os, los salarios reales en Colombia han aumentado menos que el crecimiento de PIB per capita. Esto puede ser una causa parcial de la mala distribuci�n del ingreso en la actualidad en Colombia.
The post-World War I period has seen substantial changes in the world income distribution. As a result, the shape of the distribution has changed from something that looks like a normal distribution in 1960 to a bimodal 'twin peaks' distribution in 1988. Projecting these changes into the future suggests a number of interesting findings. First, it seems likely that the United States will lose its position as the country with the highest level of GDP per worker. Second, the future income distribution will involve far more 'rich' countries and far fewer 'poor' countries than currently observed. Copyright 1997 by American Economic Association.
The Next Generation of the Penn World Tables
- R C Feenstra
- R Inklarr
- M P Timmer
Feenstra, R.C., R. Inklarr, and M.P. Timmer (2015), "The Next Generation of the Penn World
Tables," American Economic Review, 105(10), pp. 3150-3182.
Some Macreconomics for the 21st Century
- Lucas
Lucas, R.E. (2000), "Some Macreconomics for the 21 st Century," Journal of Economic
Perspectives, 14(1), pp. 159-168.
A Contribution to the Empirics of Economic Growth
- N G Mankiw
- D Romer
- D N Weil
Mankiw, N.G., D. Romer and D.N. Weil (1992), "A Contribution to the Empirics of Economic
Growth," Quarterly Journal of Economics, 107(2), pp. 407-437.
Valuing Climate Changes: Updating Estimation of the Social Cost of Carbon Dioxide
- M L Cropper
- R G Newell
National Academy of Sciences, Committee on Assessing Approaches to Updating the Social Cost
of Carbon, Cropper M.L. and Newell, R.G. co-chairs (2017). Valuing Climate Changes:
Updating Estimation of the Social Cost of Carbon Dioxide. National Academies Press at
http://www.nap.edu/24651.
Growth Accelerations,
- Hausmann
Rebasing `Maddison': New Income Comparisons and the Shape of Long-Run Economic Development
- Bolt