Growth Trends in the Developing World: Country Forecasts and Determinants

The authors present real per capita GDP growth forecasts for all developing countries for the period 2005-14. For 55 of these countries, representing major world regions and accounting for close to 80 percent of the developing world's GDP, they forecast the growth effects of the main forces underpinning growth, assuming that these evolve following past trends. The authors find that for the average developing country the largest growth dividend comes from continued improvement in public infrastructure, followed by the growth contributions of rising secondary school enrollment, trade openness, and financial deepening. The joint contribution of these four growth determinants to average, annual per capita GDP growth in the next decade is estimated to be 1 percentage point. Failure to keep improving public infrastructure alone could reduce this growth dividend by 50 percent. The forecasted growth contributions differ by country qualitatively and quantitatively.


Introduction
The paper forecasts growth trends in the developing world, and for a large sample of countries, identifies the main forces likely to underpin growth in the period 2005-14. The paper presents real per capita GDP growth forecasts for all developing countries for the next ten year period. For 55 of these countries, 1 representing all major world regions except Europe and Central Asia and accounting for close to 80% of the developing world's GDP, the paper presents real per capita GDP growth forecasts that reflect the growth effects of various growth determinants assuming that these evolve following past trends.
The forecasting exercise contributes to the literature a collection of econometrically derived country forecasts of real per capita GDP growth for the next decade and all developing countries in the world. Such forecasts are often an input into various types of economic sector work -from debt sustainability analysis to scenario building for macroeconomic and policy modeling exercises, and we could not find a set of growth forecasts of this kind in the literature. The IMF's World Economic Outlook, the World Bank's Unified Surveys and CAS documents publish country growth forecasts for only the next 3 to 5 years, while the World Bank's Global Economic Prospects report presents growth forecasts at the regional, not the country level.
Our analysis, based on a cross country regression framework, suggests that for the average developing country the growth effects of continued improvements in public infrastructure will be larger than those of improved secondary school enrollment, trade openness, and financial deepening. The joint contribution of increases in these growth factors to average, annual real per capita GDP growth in the developing world in the next decade is 1 We focused on the group of fifty five developing countries, which jointly with twenty three developed countries, is a part of the panel data used by Loayza et al. (2005) to estimate the cross-country growth model employed in this study. The rest of the developing countries were not part of the panel data because of missing data on real per capita GDP growth. The bulk of the excluded countries are transition economies, countries that did not exist during the sample period, and very small developing economies. estimated to be 1 percentage point. Half of this increase is due to the anticipated improvements in public infrastructure.
The forecasts presented in this paper should not be interpreted as predictions but as estimates of economic growth possibilities given a set of assumptions that may not reflect accurately economic conditions in some developing countries and/or may change in the future. The modeling framework can be used as a simulation tool to assess, based on historical averages, how much growth in a country may be affected by changes in the growth indicators included in the model. However, it is important to keep in mind that the tool uses proxies for growth determinants, and changes in these should not be interpreted literally. For instance, although the model uses main phone lines as a proxy for public infrastructure, investment in main phone lines alone will not lead to growth. The value of this type of exercise is in the discipline it generates in obtaining the forecasts and the possibilities it presents for scenario analysis.
We acknowledge that the quality of the growth forecasts depends on the correct specification of the econometric model, the accuracy and future stability of the estimated regression coefficients, and the quality of the forecasts of all explanatory variables. Hence, we have outlined carefully all the assumptions made to produce the growth forecasts and have tested extensively the sensitivity of these forecasts to the model specification and the time horizon of the estimation procedure. Given all this the forecasts presented in this paper should be used together with other pertinent country specific information, such as rigorous analysis of the growth prospects of individual industries and country specific circumstances, to form consensus growth forecasts.
We would like to emphasize that the forecasting model is not a tool that can guide country policy design. Since the cross-country framework used in this paper does not capture policy interactions, does not allow us to sequence policy reforms, identify binding constraints to growth, discuss policy effectiveness, or identify policies that underpin changes in the growth determinants we restrict our discussion to the growth effects of changes in the indicators representing the growth determinants. A discussion of what policies lead to these changes is beyond the scope of this paper.
Section 2 presents stylized facts about growth and output volatility in the developing world. Section 3 presents the forecasting methodology and the data. Section 4 discusses the forecasts, the performance of the forecasting model, the growth effects of changes in growth determinants, and sensitivity tests. Section 5 offers caveats and concludes this paper.

Stylized facts about growth and volatility in the developing world
The average, annual per capita GDP growth rate for the world as a whole has been declining since the 1960s (Table 1B) reflecting to a large extent the declining GDP trend in the developed countries and their influence on the world.
There are some notable differences across developing countries and regions. East Asia grew at the highest growth rate in the last four decades (column 2, Table 1A). With the exception of the 1970s, South Asia grew at the second highest growth rate in the developing world (Table 1B). Other developing regions, including Latin America and the Caribbean, Sub-Saharan Africa, and Middle East and North Africa, have shown much less success in sustaining high growth rates. These three regions had their best growth rates in the 1960s and 1970s, suffered a large decline in the 1980s, and except for Sub-Saharan Africa recovered somewhat in the 1990s.
There are some interesting differences across countries within regions and a number of success stories. In Africa, Botswana is the only country that grew at an average, yearly real per capita GDP growth rate above 1.5% for the past four decades (Table 1A). Uninterrupted civilian leadership, good macroeconomic and fiscal policies, progressive social policies as evidenced by the steep rise in secondary school enrollment (Figure 1), as well as a steady rise in investment (Figure 1) resulted in an average annual per capita GDP growth rate of 6.3% in the past four decades. In the last decade there was a sharp drop in the output growth partly due to the impact of extremely high HIV/AIDS infection rate (highest in the world), but also due to leveling off in diamond mining production. The rest of the countries in Sub-Saharan Africa grew in the sixties, but most of them slumped into low or negative growth rates in the seventies, eighties and the nineties due to a combination of poor policies, social conflict and negative external shocks.
In East Asia, there are more success stories driven by the booming economies of Japan, the Republic of Korea, Hong Kong (China), Taiwan (China) and Singapore. China leads the group of developing countries in the region whose per capita incomes grew on average above 3% per year over the past 4 decades. After a range of market-oriented reforms were implemented in the late 1970s, trade openness increased (Figure 2), growth accelerated and in the 1980s and 1990s public infrastructure and the economy grew at rates unseen anywhere else in the world ( Figure 2, Table 1A).
In the Middle East and North Africa, two economies grew at rates above 3% per year over the past 40 years -Egypt and Tunisia. Egypt's emphasis on education ( Figure 3) and its "open" door policies, boosted by sizable increases in foreign direct investment, foreign assistance and workers' remittances, launched the country on a path of high growth in the 1970s. As the impact of these policies faded the government implemented structural and stabilization policies at the end of the 1980s (Figure 3) that led to sustained growth during much of the 1990s. Tunisia's good growth record was a result of sound macroeconomic and public debt management policies, diversified economic base, gradual lessening of government control over economic affairs, steady pace of structural reforms in the 1980s and 1990s, good social policies and political stability.
In South Asia, two economies grew at per capita growth rates above 3 percent in the last two decades -India and Sri Lanka. India benefited from its liberalization efforts, and in the 90s capitalized on its large number of well-educated people to become a leading exporter of services. However, its relatively low ratio of total secondary school enrollment (Figure 3) suggests that the potential gains from future investment in human capital in India could be sizable. Sri Lanka embarked on the path of market-oriented policies and export-oriented trade in the late seventies. Since then economic growth has been healthy due to good macroeconomic management, and steady progress in trade liberalization, privatization, and financial sector reforms.
In Latin America, 15 out of 17 countries on the continent experienced negative growth rates in the 1980s. Chile and Columbia were the exceptions. Chile benefited from initiating reforms earlier than other countries in the region, while Columbia had the best record of macroeconomic stability and external credit worthiness in the region. Most of the continental countries recovered in the 1990s as they conducted strong market-oriented reforms and accomplished economic and political stability.
The Caribbean countries showed less uniform pattern of economic growth. The Dominican Republic, Trinidad and Tobago, Guyana, and Suriname had a similar experience to the continental countries -a sharp drop in economic activity in the 1980s and a recovery in the 1990s. The Bahamas, Barbados, Belize and the small island countries followed a decreasing growth pattern over the past 40 or 30 years. Political instability and economic mismanagement doomed Haiti to three decades of negative per capita growth. Jamaica failed to sustain the increase in growth in the 1980s due to crime, frequent banking crises, and rising debt burden.
The developed countries experienced the least output volatility, followed by the countries in South Asia (Table 2B). In both regions output volatility has been declining since the 1970s -the decade of oil shocks. Although at larger levels of volatility than developed and South Asian countries, a similar declining trend characterizes Africa and the Middle East (Table 2A). After declining over the 1970s and the 1980s, volatility in East Asia increased and surpassed the levels observed in the 1960s. However, while in the 1960s China generated most of the volatility in the region, in the 1990s the responsible parties were the other economies in the region. In Latin America and the Caribbean volatility increased in the poor decade of the 1980s and declined in the decade of recovery (the 1990s). These patterns are similar across countries in the region (Table 2B).

Methodology
Our model of choice is the cross-country growth framework which follows the vast empirical literature spawned by the neoclassical growth model. According to the neoclassical model 2 income converges to its steady state as follows: where y is real per capita income, y* is the steady state per capita income, and ) )( 1 ( is a function of the following exogenous parameters -the capital share α , the rate of population growth n, the rate of growth in technology g, and the rate of capital depreciation δ. Equation (1), which holds for any type of production function, is derived by taking the first order Taylor expansion of the right-hand side of the capital accumulation equation around the steady state and the production function y=f(k), where k is capital K per efficiency unit of labor AL (k=K/AL).
2 Solow (1956) introduced its most basic version, in which the saving rate is exogenous. This assumption can be relaxed if we add explicit household behavior as in an overlapping generations model a la Paul Samuelson and Peter Diamond or in a Ramsey type model with a single, infinitely lived representative consumer. Although the two models can differ substantially, the two approaches yield similar results to the Solow model. In particular, in both models the economy reaches a steady state with a constant saving rate and this steady state has the same characteristics as the steady states in the Solow model. Therefore, for the purpose of studying economic growth, the household behavior is not essential. Despite its shortcomings 3 and empirical inadequacies, 4 the neoclassical model is useful for explaining cross country variations in economic growth. The model fits the evidence that a country's initial level of per capita income is not correlated with its subsequent growth rate, i.e. poor countries do not tend to grow fast relative to developed countries. The model does not predict convergence to the same steady state, but predicts that different countries reach different steady-state levels determined by different growth determinants and external factors, and countries have different rates of growth, depending on each country's initial deviation from its own steady state ( Figure 4).
In the last couple of decades, the availability of international data made it possible to conduct cross-country empirical research on economic growth (Barro 1991(Barro , 1999King and Levine 1993;Loayza et al. 2005). The typical empirical cross-country regressions follow directly from Solow's equation (1). They have on their left-hand side each country's average growth rate over a long period, while on the right-hand side is a set of variables expected to determine the growth rate: The growth rate is diminishing in the initial level of per capita output y given y* and rising in the steady state level of per capita output y* for given y ( Figure 4).
The growth equation (2) can also be written in log form as: 3 The model does not explain the existence of growth without assuming exogenous advances in technology and that different countries use the same production function at a given point in time. Neither of these shortcomings is serious. It is obvious that income per capita grows as knowledge expands. Endogenous growth models address the first shortcoming explicitly. The basic endogenous growth model (the AK model) can be viewed as a limiting case of the neoclassical growth model in which the steady state is independent of saving. While endogenous growth models help explain the existence of worldwide technological progress and offer a more realistic explanation of the process of innovation, there have been few attempts to evaluate these models empirically and use them to explain international differences in growth rates. The second shortcoming is also not serious since one can consider different countries to be at different points along the same production possibilities frontier. 4 The neoclassical model predicts the rate of convergence, income and rate of return differentials observed in the world only for large values of the capital share. Possible explanations for a large capital share (e.g. two-thirds) include externalities to capital and redefinition of capital income to include not only return to physical capital, but also human capital.
where X is the set of variables determining steady state growth y*, ε is the error term, and subscripts i and t refer to country and time period, respectively. The set of steady state determinants in X typically includes indexes or proxies that represent outcomes of effective structural policies and institutions, stabilization policies, and external conditions. These include indexes reflecting the state of education, financial markets, trade, public sector and governance, macroeconomic conditions, and external factors.
Education has both a direct and indirect positive effect on growth. The direct effect counteracts the diminishing returns on other factors of production and affects long-run growth positively (Lucas, 1988). The indirect effect stems from the fact that human capital is a complement to physical capital, sets the pace for technological innovations, and facilitates technological absorptions (Borensztein et al., 1998;Olofsdotter, 1998).
Well functioning markets also promote growth. Developed financial markets promote growth since they facilitate risk diversification, investment and saving, and reduce the incidence of inefficient investment. Openness to trade promotes long-run growth since it leads to increased specialization thereby boosting productivity, expands potential markets allowing local firms to take advantage of economies of scale; facilitates diffusion of technological innovations and base-case managerial practices; and lessens anticompetitive practices and rent-seeking.
The actions of the government affect growth in a number of ways. Inefficient government policies including high taxes, ineffective public programs and large bureaucracy can distort markets, and interfere negatively in the economy by assuming roles most suited for the private sector. Governments' failure to invest in public infrastructure affects negatively long run growth as it lowers productivity and deters investment. Governance encompasses several aspects of institutional quality including respect for civil and political rights, bureaucratic efficiency, enforcement of contractual agreements, and the prevalence of law and order (Mauro 1995;Knack and Keefer 1995;Barro, 1996;Kaufmann, Kraay and Zoido-Lobaton, 1999). Recent empirical research supports the importance of institutional quality (Easterly and Levine 2003;IMF, World Economic Outlook 2003).
Macroeconomic stability is important for growth. By reducing uncertainty, a stable macroeconomic environment encourages firms to invest, and allows agents to concentrate on productive activities rather than on managing risk. Macroeconomic conditions are represented in cross-country regression models by including indexes measuring price stability, output volatility, real exchange rate overvaluation, the risk of a balance of payment crisis, and systemic banking crises. 5 Finally, external conditions influence the domestic economy. Terms of trade shocks capture changes in the international demand for countries' exports and the cost of production and consumption inputs. Period-specific changes affecting countries globally summarize prevalent global conditions at a given period of time and reflect worldwide recessions and booms, changes in the allocation and cost of international capital flows, and technological innovations.
We chose the empirical cross-country growth framework from a vast range of forecasting tools. 6 Our choice was motivated by the following reasons. While for some developed countries extrapolations of historical data using log-linear trends can produce surprisingly accurate predictions of current GDP levels (Fatás 2000), 7 Kraay and Monokroussos (1999) find that it is difficult to choose the "best" model for forecasting real 5 Systemic banking crisis can result from overly contractionary monetary policies and overly expansionary fiscal policies. They may also be a product of an inadequate regulatory framework for financial transactions, which leads to over-lending and unsustainable consumption booms. 6 We do so despite the belief that empirical growth regressions have been misused through flexible specifications that can lead to any desired result. 7 For instance, a linear trend model estimated using data from 1880 to 1929 can help predict the GDP level in the U.S. in 2000 with a forecast error of less than 5% (Jones, 1995).
per capita GDP for a particular country or group of countries. Their comparison of the univariate time series model for real per capita GDP and a cross-country growth regression model for a sample of developed and developing countries reveals that neither one clearly dominates as a forecasting tool.
The time series techniques of separating the business cycle from the long-run trend 8 will not allow us to decompose the growth effects of various growth determinants precluding scenario analysis or exercises aimed at assessing for instance the impact of a terms-of-trade shock on growth. Moreover, lack of sufficiently long time series for the transition and newly formed countries precludes the use of this technique for many developing economies.
The IMF production function methodology, which represents the middle ground between a full-scale structural model to determine potential output, and the mechanistic time series models, allows for an explicit growth accounting in terms of the capital, labor and total factor productivity contributions (De Masi 1997), but it too is not appropriate for forecasting developing countries' growth. The data requirements are significant and some variables such as capital stock are difficult to measure and update. Since total factor productivity is not directly observable, estimating its trend poses many of the same challenges and uncertainties as estimating potential output. The existence of large informal labor markets in developing countries implies that the potential input of labor cannot be determined by the behavior of unemployment relative to its natural rate.
For transition economies, the short period of time which has elapsed since the transition process began, combined with the lack of reliable data prior to the beginning of the transition process, preclude using the IMF's standard production function approach, the de-trending techniques to estimate potential output growth, or vector autoregressions. 9 The IMF has chosen to construct long term growth scenarios for the transition countries based on the long term growth experiences in other parts of the world. 10 A major shortcoming of this approach is the need to estimate the rate of total factor productivity growth, which typically varies substantially over time and across countries. 11 Although we could choose from the myriad of cross-country growth regression models in the literature, we adopted the growth framework and forecasting methodology in Loayza et al. (2005). The main reason for our choice is the fact that we had access to their panel dataset.  Kraay and Monokroussos (1999) suggest that vector autoregressions in a small set of key macroeconomic variables, estimated country by country, may be a way to improve over the forecast performance of both univariate time series and cross-country growth regression models. The advantage of this approach over the univariate time series models is that it draws on a larger information set. Another advantage is that it relaxes the restrictive assumption of cross-country regression models that the parameters of the model are equal across countries. 10 where s=5 and T s it s it y y − − − ln ln is the output gap. They also add a time specific effect t μ , and a country-specific effect i η . Controlling for the initial output gap allows them to improve the regression fit and avoid overestimating the speed of transitional convergence. The output gap in the regression is given by the difference between (the log of) potential (trend) and actual GDP per capita around the start of the period. The trend output is obtained using the Baxter-King filter for each country in the sample (Baxter and King, 1999).
The inclusion of the initial output gap in the growth regression model is contentious because with the steady state shifting over time there is no stable long-run trend that can be identified using the filter. We therefore forecast real per capita GDP growth using a pure cross section version of the regression model (4). The model includes all variables representing convergence factors and structural policies mentioned earlier, and only one variable in the category of stabilization policy (inflation). These are the most pertinent to growth over a long time span and the most commonly found in the empirical growth literature. and 23 developed economies), we quantify the growth effects of individual growth 14 We can do this because the growth model is estimated using averages of the underlying growth determinants in the five year prior to the last year of the current period. Kraay and Monokroussos (1999) use this approach determinants in X by forecasting their future values using univariate forecasting models and assuming that they evolve following past trends. For the 20 countries in Latin America and Caribbean we cite results from Loayza et al. (2005). Next we discuss the panel data, the estimation methodology, and the forecasting models. Growth per capita (dlny) is the log difference of real GDP per capita, represented in 1995 PPP-adjusted US dollars and constructed using Summers and Heston (1991) and World Bank (2002). For the calculation of a period's growth rate, the base corresponds to the final year of the previous period. Initial per capita GDP (lny) is the initial value of the ratio of total GDP to total population 15 and is computed using data in Summers and Heston (1991) and the World Bank (2002). Initial output gap (lny-lny T ) is the difference between the log of actual per capita GDP and the log of potential (trend) per capita GDP at the start of the period. The trend per capita GDP is identified using the Baxter-King filter.

Data
The regression includes the following steady state growth determinants in X' (equation 4): education, financial depth, trade openness, government burden, public infrastructure, and governance.
Education is measured as the ratio of total secondary enrollment to the population of the age group that officially corresponds to that level of education. This "flow" variableused as proxy for human capital in Barro (1991), Mankiw, Romer andWeil (1992), and Easterly (2001) -captures more closely current education policies and human capital investment than "stock" measures related with the educational attainment of the adult population or life expectancy. The World Bank (2002) is the source for the data on total secondary school enrollment and population of the age group corresponding officially to that level of education. Financial depth is computed as the ratio to GDP of the stock of claims on the private sector by deposit money banks and other financial institutions from Beck, Demirguc-Kunt and Levine (2000). This measure of financial depth is significantly correlated with other proxies such as the traditional measure of financial depth (M2/GDP). Indicators of other aspects of financial markets, such as the size and activity of the stock markets, can also be used as proxies for financial depth. However, data availability and the fact that incentives to perform efficiently are clearer and stronger for private agents make this measure the preferred proxy for the size and activity of financial markets in recent empirical studies (Levine, Loayza and Beck, 2000).
Trade openness is the residual of a regression of the log of the trade (exports and imports) to GDP ratio on the logs of area and population, and dummies for oil exporting and landlocked countries. The variables in the regression are constructed from data in the World Bank (2002). This structure-adjusted trade openness measure ensures that one would not be attributing to trade policy outcomes resulting from structural country characteristics. 16 Government burden is measured with the ratio of government consumption to GDP (World Bank, 2002). The rationale for this choice is that current government consumption is devoted mainly to covering the bureaucracy's wage bill. One might argue that not all of government consumption is wasteful as expenditures on health, education and law and order promote growth. Loayza et al., however, did not adjust for these growth promoting expenditures because they could not find consistent data on these expenditures for a large sample of countries in their panel. 17 Public infrastructure is measured with the number of telephone mainlines per capita in a country (Canning, 1998). Alternative proxies of public infrastructure are energy generation capacity and transport facilities. Loayza et al. (2005) found these to be highly correlated with each other and concluded that results would be quantitatively similar for any of them.

2005
). Cyclical volatility, which reflects the lack of output stability, is computed as the standard deviation of the output gap for the period. Real exchange rate overvaluation -a measure for external imbalances and the risk of balance-of-payments crises -is given by the 17 Loayza et al. note that the presence of initial GDP per capita and the governance indicator in regression model (4) help to control for the fact that not all government consumption can be regarded as an obstacle to growth. 18 See Fischer (1993), Easterly, Loayza, and Montiel (1997), Barro (2001), Bekaert, Harvey and Lundblad (2001). real effective exchange rate, adjusted so that the average for 1976-85 equals Dollar's (1992) index of overvaluation 19 (Source: Easterly 2001). The number of years in which a country underwent a systemic banking crisis as a fraction of the number of years in the corresponding period is computed based on data from Caprio and Klingebiel (1999) and Kaminsky and Reinhart (1998).
The terms of trade shock in the matrix of growth determinants X' in model (4)

The forecasting model
The forecasting model used in this study is derived by differencing model (4): where s=10 since we work with 10 year periods, matrix G contains the initial output gap, matrix X, and the time specific shift; and ) , ' , ( 20 In general, the forecasting model (5) can be used to forecasts growth for any number of periods of length s, where s could be any positive integer number. However, using this model to produce growth forecasts for the next 1 to 3 years is not recommended since many of the factors affecting the short term outlook are not included in the model.  Table 1 and the fourth column, Appendix Table 2). The GMM systems estimator, developed by Arellano and 19 The Dollar's index of overvaluation gives an idea to what extent the real exchange rate is distorted away from its free-trade level by the trade regime. 20 As a result of the differencing the country specific term is eliminated from forecasting model (5). 21 The 5-year panel dataset contains 78 countries -fifty five of them developing -and for each of them, a minimum of 3 and a maximum of 8 non-overlapping 5-year observations (the sample is unbalanced). A minimum of 3 observations per country is required to implement the instrumental -variable methodology for the GMM estimators. The total number of observations equals 350. Bover (1995) and Blundell and Bond (1997), combines in a system regression model (4) in differences and levels. The regression in differences requires differencing model (4) and using instruments to deal with the likely endogeneity of the independent variables, and the fact that in the differenced model the error term is correlated with one of the explanatory variablesthe lagged dependent variable. The instruments consist of previous observations of the explanatory and lagged-dependent variables. The GMM estimator assumes that the error term in model (4) is not serially correlated and the explanatory variables are weakly exogenous.
The instruments for the regression in levels are the lagged differences of the corresponding variables. These are appropriate instruments assuming there is no correlation between the differences of the independent variables in model (4) Table 1), and the OLS estimator for the pure-cross section model 24 (Appendix Table 2). Each of these alternative techniques has its shortcomings. The 'pooled' OLS estimator ignores the presence of country-specific effects and treats all variables as exogenous, while the 'within' OLS estimator ignores the joint endogeneity of the explanatory variables. The GMM levels estimator uses instruments to control for joint endogeneity but ignores country specific effects. 22 The consistency of the GMM estimators depends on whether lagged values of the dependent variables are valid instruments in the regression. Loayza et al. conducted a Sargent test of over-identifying restrictions, which tests the overall validity of the instruments by analyzing the sample analog of the moment conditions used in the estimation process, and tested the null hypothesis for serial correlation of the error term in model (4). The Sargan and serial correlation tests could not reject the null hypothesis of correct specification of the main model. 23 The sample based on 10-year averages consists of an unbalanced panel of 65 countries and 175 observations. 24 The sample based on 30-year averages consists of one observation for 70 countries. A country is excluded from the pure cross section sample if there is no complete information for at least 30 years during the period 1966-99.
All estimated coefficients, except governance, are robust to changes in the estimation method (Appendix Table 1). The statistical significance and estimated size of most coefficients are similar across methods. The coefficient on governance changes its sign, but it is not statistically significant. Governance is not statistically significant despite the fact that the governance index has the second largest positive correlation with the growth rate of GDP per capita. This result is robust to changes in the governance index -for instance replacing it with its components, which include indicators on bureaucratic efficiency, corruption, law and order, and accountability or with Gastil's index on civil rights. The result is similar to that of Dollar and Kraay (2003), and contrasts that in Easterly and Levine (2002).
The signs of the estimated coefficients are robust to changes in the time horizon (30- year averages vs. 5-year averages, see Appendix Table 2). 25 However, there are differences in the size and significance of some coefficients. Financial depth and trade openness are not statistically significant in the case of pure cross-section OLS. A possible explanation for the lack of significance is the omission of banking crisis and terms of trade shocks, which control for some negative aspects of financial depth (credit booms) and trade openness (external vulnerability).
Given these differences and the fact that we would like to forecast real per capita GDP using a pure cross-section regression, which resembles most closely the models in the empirical literature and excludes the initial output gap from the set of independent variables, we produce growth forecasts using the pure-cross section version of growth forecasting model (5). In this case, matrix G does not include the initial output gap and stabilization policies other than inflation. Coefficients ( φ αˆ , ) were estimated by Loayza et al. (2005) using the OLS estimator (see second column, Appendix Table 2). We compare the forecasts from the pure cross-section model estimated with the OLS estimator with those from the dynamic panel estimated with the GMM estimator below (see Table 5).

Growth forecasts
We forecast real per capita GDP growth rates for all developing countries for the period 2005-14 assuming no changes in any of the explanatory variables in matrix G of forecasting model (5). Under this assumption transitional convergence is the only factor determining the change in real per capita growth from one period to the next (α=-0.0176). Table 3 displays the country forecasts, which are point estimates representing the most likely growth outcomes, jointly with their 60% confidence bands. 26 From a policy perspective these confidence intervals are more useful than the 90% confidence bands reported in Table 5 since the later are large as is the case for other forecasting models, and most policy analysts are not interested in low probability outcomes.
The confidence intervals are computed by rewriting equation (4) and assuming that matrix Z, which incorporates all right-hand side variables other than initial income, is a function of non-random variables, and ϕ , which includes the respective coefficients, is also non-random.
From equation (5) it follows that the variance of the forecast for the next period is: 26 In the case of the 60% confidence bands, we can infer that growth rates higher (lower) than the upper (lower) end of the confidence interval occur with 20% probability.
Using actual and predicted values for growth, we compute the residuals it εˆ and its variance 2 ) ( i it V σ ε = . 27 The 60% confidence interval around the forecasted growth rate is then given , while the formula for the 90% confidence interval is We compute two types of regional averages. The first one reflects weights which represent the share of per capita income in the simple average, regional per capita income. The second one uses weights which reflect economic size and are computed as the share of income in the average regional income. The two measures may differ substantially if the region is dominated by a large country such as China in the case of East Asia and Pacific (Table 3A and Table 4).
For the developing world as a whole we forecast average, annual real per capita growth of 2.2%. We arrive at this growth rate if we use weights which represent the share of per capita income in the simple average, regional per capita income. If we use weights which reflect the size of the economies and are computed as the share of income in the average regional income, the growth rate for the developing world as a whole is 3.5%. This forecast is almost identical to the one published in Global Economic Prospects (2004) 29 and shown in Table 4. Even though in two instances (Europe and Central Asia and Sub-Saharan Africa, Table 4) the GEP's regional forecasts are close to ours, in all the other cases they are higher than our estimates implying a growth forecast for the developing world higher than 3.4%.
The forecasts, obtained using the pure cross section version of the forecasting model, determining the change in real per capita growth (α=-0.024). The forecasts obtained with the pure cross section model are close to those obtained with the dynamic panel model. On average the forecasts differ by 0.12 percentage points, and in only 4 cases they differ by more than 0.5 percentage points. A comparison of the confidence intervals suggests that the dynamic panel model estimated with the GMM estimator provides a better regression fit than the pure cross section model estimated with the OLS estimator.

Evaluation of the forecasting model
Next we undertake a formal and systematic evaluation of the ex-post performance of forecasting model (5). For this purpose we conduct an out-of-sample and with-in sample forecasting exercises.

Out-of-sample forecasting
The dynamic panel dataset used in the estimation of forecasting model (5) includes data up to 2000, and we use the model to obtain forecasts for 2004. We then compare these forecasts with actual data. We do so using two simple statistics that capture respectively the bias and mean squared error of the forecasts -the cumulative forecast error statistic (CFE) and the Theil-U statistic (TU). Since in this case there is only one period the CFE statistic is given by the following expression: where 5 + it y is the forecast and 5 + it y is the actual outcome. The statistic is scaled by the actual outcomes in order to make it comparable across countries. Similarly, the Theil-U statistic, which measures the variability or precision of the forecasts, is defined as follows: 30 30 For comparison purposes we compute and report the TU statistics following Kraay and Monokroussos (1999). All other things equal, one would prefer forecasting methods with CFE and TU statistics near zero.
For each country, we calculate the CFE and TU statistics and present the results in years. This value is very close in absolute terms to the median CFE with forecasting model (5) (-0.007), after the first 5 years. Their median value of the TU statistic for the growth forecasting model is slightly under 0.0002 after the initial 5 years. With forecasting model (5) the median CFE is 0.0001. The average value of the CFE (-0.0084) is slightly larger than the median in absolute value (-0.0070). The average TU statistic is also higher than the median (0.0004) but still relatively small.
The statistics suggest that in the first five years the growth forecasting model performs on average no worse than the growth forecasting model in Kraay and Monokroussos (1999).
However, while their growth model tends to overestimate the actual growth rate, the growth forecasting model (5) tends to underestimate the growth rate. Since the cumulative median bias in the level of forecasted real per capita GDP after 5 years is 7% of per capita GDP, the 31 They report the medians and not the averages since for some countries one model or the other delivered "crazy" forecasts resulting in very large TU or CFE statistics (in absolute value).
downward bias in average annual growth forecasts over this period is around 1.4% per year.
The upward bias in Kraay and Monokroussos estimates is of similar order of magnitude.
The statistics for individual countries reveal for which countries the forecasting model performs better or worse than the absolute value of the average cumulative forecast error (0.0084), and the types of the bias. For half of the countries in Table 6 the bias is larger than the average in absolute value. However, half of the countries for which the bias is larger than the average are not part of the panel dataset used to estimate the growth forecasting model (5).
The bias is positive in only 38 of the 127 cases. For only 13 of these 38 countries the positive bias is larger than the absolute value of the average (0.0084). The country cases for which forecasting model (5) performs no worse than the average are marked in grey. These are countries for which the absolute value of the CFE is smaller or approximately equal to the absolute value of the average CFE in Table 6.

With-in sample forecasting
One question of interest is whether the model forecasts well changes in growth between decades.
In order to answer this question we have compared actual and forecasted changes in growth rates between the 1980s and the 1990s for the 55 developing countries that are part of the panel data used in the estimation of the forecasting model. In 76 percent of the cases the model projects an increase (decrease) when growth accelerated (decelerated) ( Table 7). In 44 percent of the cases (marked in grey), the model's forecasted changes in growth are relatively close to the actual changes (less than a percentage point away from the actual change). In nearly half of these cases (marked with asterisks in Table 7), the model performs well both within and out-of sample.
The reasons why in some cases the forecasted changes are very different from the actual ones can be traced to developments not captured in the model. Falling into civil war the determinants in the model. Conversely, recovering from civil conflict or a natural disaster is bound to have a beneficial impact on growth. For example, Zaire (DRC), Republic of Congo, and Sierra Leone were torn by civil conflicts in the 90s. This effect -not captured in the model -explains why the forecasted growth changes between the two decades in these three countries are positive, while the actual changes are negative. The impact of financial crisis in a country has an effect that spreads to economies in the region and beyond. This effect, also not captured by the model, is a reason why the forecasts for China, Indonesia, and Thailand overestimate the growth change for these countries between the 90s and the 80s.
Another reason for the discrepancy between the forecasted and actual changes in the growth rates is that some countries may not be close to the "average" country in the sample.

Growth effects of public policies
For 55 of the countries in the panel used to estimate model (5), we present a set of real per capita GDP growth forecasts that reflect the growth effects of various factors underpinning long term growth assuming that these growth determinants evolve following past trends. 32 We forecasted the growth determinants in matrix Z of forecasting model (6) by building 280 univariate forecasting models -one model for each of the variables in matrix Z and each of the 35 countries. 33 We use univariate stochastic trend models with ARMA terms in the case of a unit root (I(1) or I(2)) and deterministic linear trend models with ARMA terms in the case of a stationary variable (I(0)) to forecast the growth determinants. 34 The forecasts of the 32 Although the panel estimation procedures employed take into account the endogeneity of the various growth determinants (right-hand-side variables), this endogeneity is ignored in this forecasting exercise where the growth determinants are described using simple univariate models. 33 We forecast only 8 of the 11 variables in matrix Z. For reasons discussed in this section of the paper we leave the other 3 variables unchanged. 34 The forecasting models are available upon request.
underlying growth determinants for the 20 countries in Latin America and the Caribbean come from Loayza et al. (2005).
We test each growth determinant for a unit root, I(1). The unit root tests include a trend implying that the test has unit root as the null hypothesis. This is consistent with the presumption that we 'accept' the null hypothesis of a unit root unless confronted with strong evidence to the contrary. To account for possible heteroskedasticity we compute White heteroskedasticity-consistent standard errors. In most cases the changes to the standard errors were insignificant.
Instead of considering that a variable has a quadratic trend or a unit root plus trend, we consider the more plausible specification that the variable is I(2). It is possible to test whether there is a significant trend in the presence of a unit root. However, such a model is rarely used since it is difficult to justify that the growth rate shrinks or grows in a linear fashion. Often, a naïve curve fitting exercise (ignoring unit roots) will find a quadratic trend term that is significant (and perhaps higher order terms). Although the higher-order trend terms allow you to fit the data better ex post, the model will often perform poorly in out of sample forecasting (Sims, 1999).
A few growth determinants were treated in a different way. We assume that the number of years in which a country underwent a systemic banking crisis remains the same over the next decade. We believe that this is the best we could do given that the occurrence of a banking crisis is difficult to predict even with sophisticated models. Loayza et al. (2005)  that did not have one in the 90s and the early 2000s, and for those that had crises they estimate a gradually decreasing probability of reoccurrence.
We assume that cyclical volatility in the next decade is the same as in the 90s. While we saw that in many countries cyclical volatility declined over the past 4 decades, this trend was not universal and in many countries cyclical volatility increased. Given the difficulties involved in predicting accurately changes in output volatility, we believe that it is best if we leave the cyclical volatility unchanged.
In Finally, as in Loayza et al. (2005) we assume that world growth conditions that determine the period shift will remain approximately the same in the next decade as in the 90s. While this is likely to be untrue, given that world growth conditions have differed notably between decades in the past, it allows us to focus on the contribution of structural and stabilization policies rather than on external conditions that are very difficult to forecast.
Once we obtain the univariate forecast of a growth determinant, we compute the rate of change in the growth determinant's average for the period and multiply it with the corresponding coefficient's estimate in model (5) (displayed in the forth column of Appendix   (5), and the forecasted per capita growth rates for the 55 countries. The results suggest that for the average developing country the largest growth dividend comes from continued improvements in public infrastructure, followed by the growth contributions of rising secondary school enrollment, trade openness, and financial deepening. The joint contribution of these four growth determinants to average, annual per capita GDP growth in the next decade is estimated to be 1 percentage point (Table 8B). Failure to keep on improving public infrastructure alone could reduce this growth dividend by 50%.
The large estimated contributions of public investment to the forecasted growth changes are due to the large forecasted changes in this growth determinant, not to the size of the estimated coefficient on this variable. The estimated coefficient on public investment is 60 percent smaller than the coefficient on secondary education, 30 percent smaller than the coefficient on trade openness and approximately equal to the coefficient on financial depth (Appendix Table 1).
A comparison of the implied growth rates of the growth determinants also suggests that the results are driven by the projected increases in the respective growth determinants.
For instance, the estimated contribution of infrastructure investment to per capita GDP growth of the average country in South Asia is close to 1 percentage point (Table 8B). Such an increase implies an annual, average growth in the investment measure -the number of main telephone lines per capita, of around 27 percent. This growth rate is 10 times the growth rate of secondary school enrollment in the region. The implied yearly growth rates of the investment indicator for the average country in the other regions in Table 8 are between 4 and 5 times the annual growth rates in secondary school enrollment in these regions.
developing country in East Asia and Latin America the growth effects of improving trade openness will be larger than those of financial sector deepening. The reverse is the case in South Asia, Sub-Saharan Africa, and the Middle East and North Africa. In these three regions efforts to reduce the government burden will be beneficial to growth. For example, preventing further increases in government consumption could add 0.2 percentage points per year to average real per capita GDP growth in South Asia and Latin America in the next decade.
At the country level, the results in Table 8  In India, failure to invest in infrastructure could cost real per capita growth 1.32 percentage points. This will bring down the average, annual real per capita GDP growth rate from 4.90 percent to 3.58 percent over the next decade -a growth rate that is unlikely to lead to a significant drop in the country's poverty rate. Efforts to prevent further increases in the size of the government sector could add a quarter of a percentage point to per capita real output growth.
Nigeria's growth prospects may be dimmed if following past trends the government increases its consumption. We estimate that the negative effect of such an increase on growth cancels out completely the positive effect of all other reform efforts (Table 8A). If Nigeria manages to prevent further increases in the share of government consumption in the country's 36 Failure to improve infrastructure in China is modeled by assuming that there is no improvement in public infrastructure. In this case, the average per capita real GDP growth rate would fall down by 0.89 percentage points from 8.76% to 7.91%. GDP its average, annual per capita real growth rate in the period 2005-2014 could increase to more than 2 percent, compared to the expected stagnation in real output per capita under the continuous trend scenario (Table 8A).
In Brazil the greatest growth dividend is expected to come from reducing the probability of banking crises, followed by improvements in macro management and cyclical output volatility. Mexico is another country where continued progress with stabilization policies makes a sizable contribution to growth. 37

Sensitivity analysis
As mentioned earlier the estimated coefficients in Loayza et al. (2005) (Appendix Table 1) are robust to changes in the estimation method. The signs of the coefficients are also robust to changes in the time horizon: 30 year averages (pure cross section estimation) vs. 5 year averages (dynamic panel estimation). However, there are differences in the size and significance of some of the coefficients (Appendix Table 2). Given these differences and the fact that the pure cross-section regression resembles most closely the models in the empirical literature we test the sensitivity of the growth effects to changes in the time horizon. We estimate the growth effects of the forecasted changes in the underlying growth determinants using the estimated coefficients from the pure cross country regression (shown in the second column of Appendix Table 2) and compare them to the ones obtained using the estimated coefficients from the dynamic panel estimation (5-year averages) (shown in the fourth column of Appendix Table 2).
The main conclusions for the relative importance of the growth determinants at the regional level and for the developing world as a whole remain unchanged (compare Tables 6   and 9). Again we find that the largest growth dividend comes from continued improvement in  Table 2). At the regional level, the forecasted growth rates with the pure cross section model are less than half a percentage point away from those obtained with the dynamic panel estimation method. 38 There are some differences at the country level, but these are more than one percentage point for only 18 of the 55 countries, and are associated with a sign change in only 3 cases.

Concluding remarks
The paper presents real per capita GDP growth forecasts for all developing countries for the period 2005-2014. For 55 of these countries the paper forecasts the growth effects of the main forces underpinning growth assuming that these evolve following past trends. We find that for the average developing country the largest growth dividend comes from continued improvement in public infrastructure, followed by the growth contributions of rising secondary school enrollment, trade openness, and financial deepening. The joint contribution of these four policy indicators to average, annual per capita GDP growth in the next decade is estimated to be 1 percentage point. Failure to keep on improving public infrastructure alone could reduce this growth dividend by 50 percent. 38 East Asia and the Pacific region is an exception with the difference slightly more than half a percentage point (0.68).

Egypt
Tunisia India Sri Lanka Chile Colombia *Public education is proxied with the ratio of total secondary enrollment to the population of the age group that officially corresponds to that level of education. Public infrastructure is proxied with the number of telephone mainlines per capita.        Source: Authors' estimates produced with forecasting model (5). *The regional average is computed using weights which represent the share of per capita income in the average regional per capita income computed as a simple average and based on data for 2004. **The regional average is computed using weights which represent the share of income in the average regional income based on data for 2004.***Note that at the regional level the level of confidence depends on assumptions about the joint distribution of individual country outcomes.  (5). *The regional average is computed using weights which represent the share of per capita income in the average regional per capita income computed as a simple average and based on data for 2004. **The regional average is computed using weights which represent the share of income in the average regional income based on data for 2004.

3.40
Source: Author's estimates produced with forecasting model (5) and Global Economic Prospects 2004. *The regional average is computed using weights which represent the share of per capita income in the average regional per capita income computed as a simple average and based on data for 2004. **The regional average is computed using weights which represent the share of income in the average regional income based on data for 2004. ***Global Economic Prospects 2004, Table 1.5, pp.43.         (5) performed well out of sample (those cases are also shown in Table 6).  (5) and authors' forecasts of underlying determinants. *The regional averages are computed using weights which represent the share of per capita income in the average regional per capita income computed as a simple average and based on data for 2004.  Loayza et al. (2005). *The regional average is computed using weights which represent the share of per capita income in the average regional per capita income computed as a simple average and based on data for 2004.  Loayza et al. (2005) and authors' forecasts of underlying determinants. *The regional average is computed using weights which represent the share of per capita income in the average regional per capita income computed as a simple average and based on data for 2004.  Source: Loayza et al. (2005).