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How can economists peer into the future without a crystal ball?

How can economists peer into the future without a crystal ball?

The main objective of the Global Development Horizons – Capital for the Future is identifying emerging trends of investment and saving. This is achieved not in terms of a set of forecasts, but rather by asking a series of “what if” questions and building scenarios. For example, the report addresses the question of what are the consequences for global saving if aging will hasten and will continue to exert negative pressure. Or, what will happen to the demand for capital if productivity catch-up accelerates in developing countries. 

A simple approach would just rely on correlations, and by extrapolating the trends of key determinants, such as aging and productivity growth, infer their impact on saving and investment. Thus, in the example above, this simple approach would suggest that saving will decline. However, aging does not happen in isolation and other factors counterbalance its negative impact. Likewise, faster rates of productivity growth will—for a given population growth rate—translate into faster economic growth and higher per capita incomes; higher incomes in turn will affect the pace of financial development and institutional improvement. These serve to reinforce the positive impact that faster economic growth alone has on attracting investment financing.

To account for the direct and indirect effects of multiple factors affecting the emerging trends of investment and saving – and the fact that income, saving and investment affect each other – a more complex, structural model is needed. This is the best next thing to a crystal ball. In the report then a global computable general equilibrium (CGE) dynamic model is used to build scenarios and to generate an internally consistent quantitative assessment of these emerging trends. This global model provides the unifying analytical approach applied across all the questions addressed in Capital for the Future. In addition, other analytical tools—such as panel data econometrics—are used (i) to estimate key parameters for the global CGE model, and (ii) to complement the results obtained from it.

Given the focus of the methodological approach on capturing the impact of certain key determinants of interest, the potential effects of some other long-term trends and persistent economic shocks are omitted from the analysis. For example, crises—whether commodity-based, financial, or environmental in nature—may engender increased uncertainty that result in longer-term effects on investment. Other elements— such as, changes in habits arising from shifts in cultural factors behind saving behavior, or changes in the global pattern of migration and remittances—also remain  not modeled.

It should also be noted that there are numerous potential outcomes of future changes in productivity, ensuing growth patterns, and accompanying policy changes. While there is broad agreement on demographic projections, there is no consensus on the exogenous values governing productivity changes, or on the correct parameterization of saving functions or functions of demand and supply of capital goods. Thus, even with sophisticated models, growth, investment, and saving rates for any specific country or region are subject to a large margin of error. With this in mind, the main advantage of a model-based scenario analysis is that it provides an opportunity to explore the interaction among broad trends, rather than providing exact forecasts.

The crystal ball: a global dynamic general equilibrium framework

The global CGE model—which is a modified version of the World Bank’s Linkage model, a dynamic model—comprises 17 country-regions, 7 sectors (encompassing agriculture, manufacturing, and services), and 3 factors of production (capital, and skilled and unskilled labor). The version of the model used here relies on the most recent Global Trade Analysis Project (GTAP) dataset, whose base year is 2007. Scenarios are developed by solving for a new equilibrium in each subsequent year through 2030.

At its core, Linkage is a neo-classical model with aggregate growth, saving and investment endogenously determined and predicated on assumptions regarding key exogenous determinants such as productivity changes, demographic shifts, financial market development, and institutional improvement. Unlike more simple growth models, however, Linkage has considerably more structure. First, it is multi-sectoral. This allows for more complex productivity dynamics including differentiating productivity growth between agriculture, manufacturing, and services and picking up the changing structure of demand (and therefore output) as growth in incomes leads to a relative shift into manufactures and services. Second, it is linked multi-regionally allowing for the influence of openness—via trade and finance—on domestic variables such as output and wages. Third, Linkage includes a set of equations for capturing saving and investment behavior.

A full description of the LINKAGE model is available in van der Mensbrugghe (2011), and here a brief description of the equations governing the dynamics of investment and saving is presented together with the main assumptions concerning the projected paths of exogenous determinants.

Starting with the latter, the key exogenous determinants are productivity and demographics. Productivity change is derived from a combination of estimates, and is also subjectively fine-tuned. Agricultural productivity is assumed to be factor neutral and exogenous and is set to estimates from empirical studies (e.g., Martin and Mitra, 1999). Productivity in manufacturing and services is labor-augmenting (Harrod-neutral technical change); it is skill-neutral but sector-biased, with productivity growth higher in manufacturing than in services. This gives rise to a long-term rate of TFP growth in the range of 0.1-0.2 percent for the high-income countries in the gradual convergence scenario, which lies toward the low end of the Bosworth and Collins (2003) estimates, but are consistent with the trends in the early and mid-2000s. The range for developing countries is somewhat wider—between 0.7 and 3.5 until 2015 and constant thereafter. There is significant variation in TFP growth across developing countries, ranging from above 3.5 percent in China (in line with Bosworth and Collins (2008) estimates) to around 1.5 percent in Sub-Saharan Africa.

The growth in the labor force is derived from the UN age specific population projections assuming no changes in participation rates. According to these population projections, the demographic transition is asynchronous across countries in several respects: the timing of its start, the speed with which the transition unfolds, and the relative sizes of bulge cohorts. In the current version of the model there is no differentiation between the growth of skilled and unskilled workers.

The other crucial dynamics of the model deals with the accumulation of physical capital. This results from the interaction of global saving supply, domestic investment demand, and international capital allocation (see figure), as follows:

  • In each country, saving behavior, in accordance to a standard life-cycle approach, depends on demography and per capita income growth; additional determinants include financial development, and social protection systems.
  • Investment demand is obtained from capital demand which, in turn, is derived from sector-specific production functions in a setting of perfectly competitive profit-maximizing firms. Investment demand thus relates positively to output and negatively to rental rates. 
  • The global pool of saving is allocated across countries following a function representing the global financing of investment. This responds to relative rental rates, but also to country-specific economic growth, and structural factors such as financial development and the quality of institutions. The global financing of investment also captures home bias by including a lagged term.

For each country, net capital flows make up the difference between the level of financing and domestic saving. Thus the model allows for global capital mobility, but only imperfectly since the financing of investment responds to rental rate differentials with a finite elasticity and depends on other factors as well. In this setup, net capital flows between countries remain within limits that are reasonable given their historical range; and there is no guarantee that rental rates will equalize across countries. For example, a country benefitting from productivity catch up will experience stronger capital demand and rental rates will be bid up. This will attract capital flows to the country, mitigating the upward pressure on rental rates, but not eliminating it fully.

Summing up, in the Linkage model saving, investment, output and income, as well as relative factor and good prices are simultaneously determined. However, for any specific country or region, income growth rates, investment and saving rates, as well as net capital flows generated by the model are subject to a margin of error. This is because the resulting trends in these variables depend on:

  • Assumptions on the path of exogenous variables; specifically on productivity, demography, financial sector development, quality of institutions;
  • Parameterization of the equations; and, more explicitly, the elasticity of the saving and investment rates with respect to aged dependency (only for saving), income growth, financial sector development, and quality of institutions.

Some of the key assumptions concerning point (i) have already been described above. By considering two scenarios Capital for the Future takes into account uncertainty in the future trends. In the fast convergence scenario, productivity is exogenously raised by a factor of 50 percent for all developing countries, and the rate of growth of structural variables is boosted so that they reduce by a quarter the distance between their current levels and that of the United States in 2030 (assumed to be the frontier). With regard to point (ii), a key assumption made is that the coefficients for the economic and structural variables in the saving and investment financing equations are indeed stable.

Complementary analytical approaches: estimating parameters
The parameterization of the investment demand function draws on the large, and by now standard, empirical literature that estimates the parameters of the production function. This literature is, however, somewhat more circumspect with regard to parameter estimates of the saving and investment financing functions. Accordingly, this report performs estimates for the elasticities corresponding to the described determinants using econometric techniques designed to limit the impact of endogeneity in the regressors as well as measurement error (details are given in annex 1.5 in this website).

The signs of these estimated coefficients are consistent with underlying theory. For example, the coefficient on demography—measured by the aged dependency ratio—is negative and statistically significant, which implies that economies with older populations tend to save less. As another example, even after accounting for the possible endogeneity of economic growth, faster growth is positively related with both saving and investment financing.
The coefficients on the structural variables also accord with a body of empirical and theoretical work. For instance, financial development is positively associated with the investment rate (more sophisticated financial markets are able to lend more readily to firms for investment purposes) (Benhabib and Spiegel 2000), but negatively related to the saving rate (households with easier access to consumer credit need to save less for the purposes of consumption smoothing) (Loayza, Schmidt-Hebbel, and Servén 2000).

Complementary analytical approaches: enriching the CGE results
The CGE analysis requires a number of simplifying assumptions and cannot generate some of the results which are of interest to policy makers and development practitioners. For example, the population age structure of a country (or groups of countries) is approximated by a simple old-age dependency ratio; and, given the fact that the model works with a representative household, it cannot provide any insights on different saving behavior for different categories of households. Therefore, complementary analytical tools are used to address these issues.

In the case of savings, a complementary approach studies the future of saving by considering how demography and income growth will affect saving at the household level. Examining the issue from a microeconomic perspective provides a more realistic and nuanced view of the likely evolution of savings, although at the price of considering a limited set of countries due to data availability. While the household-level analysis confirms the broad conclusions of the CGE analysis, the micro-level data also expose the complexities of the interaction among aging, saving, and growth. The micro analytical approach is described in more technical detail in annex 2.1 in this website.

While the CGE model generated saving and investment scenarios have direct implications for net capital flows (essentially countries’ saving-investment differentials), a separate model is required to complement these findings with scenarios for countries’ gross volumes of capital inflows and outflows. The approach taken here is more straightforward, since it need only generate scenarios for one variable of interest, and can draw on some of the results from the CGE based analysis as inputs. An econometric model is specified to model gross inflows (outflows can be backed out from these and net flows), drawing on the literature to identify key determinants, and also controlling for any country-level effects that do not vary over time, and for global shocks across time. Two scenarios for gross flows are generated by fitting projected paths of the independent variables to the estimated equation, which correspond to the two CGE model generated scenarios (details are given in annexes 3.3 and 3.4 in this website).


Benhabib, Jess, and Mark M. Spiegel. 2000. “The Role of Financial Development in Growth and Investment.” Journal of Economic Growth 5(4): 341–60.

Bosworth, Barry P., and Susan M. Collins. 2003. “The Empirics of Growth: An Update.” Brookings Papers on Economic Activity 34 (2): 113–206.

———. 2008. “Accounting for Growth: Comparing China and India,” Journal of Economic Perspectives 22 (1): 45–66.

IMF International Financial Statistics database, International Monetary Fund, Washington, DC.

Loayza, Norman V., Klaus Schmidt-Hebbel, and Luis Servén. 2000. “What Drives Private Saving Across the World?” Review of Economics and Statistics 82 (2): 165–81.

Martin, Will, and Devashish Mitra. 1999. “Productivity Growth and Convergence in Agriculture and Manufacturing.” Policy Research Working Paper 2171, World Bank, Washington, DC.

Spence, A. Michael. 2011. The Next Convergence: The Future of Economic Growth in a Multispeed World. New York: Farrar, Straus, and Giroux.

Van der Mensbrugghe, Dominique. 2011. “Linkage Technical Reference Document, version 7.1.” World Bank, Washington, DC.

World Bank Global Economic Monitor database, World Bank, Washington, DC.

World Bank World Development Indicators database, World Bank, Washington, DC.


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