1

Global Development Horizons: Capital for the Future – Technical Annexes

Annex 1.1. Alternative definitions of capital and investment

The focus of this report is on gross capital formation, which is traditionally defined as real investment

activity by economists. This definition includes purchases of physical structures, plants, machinery, and

equipment, together with inventory accumulation, but gross of depreciation. In certain cases—where it is

more appropriate to examine longer-run phenomena—the definition of investment is refined to gross

fixed capital formation, which excludes inventories. Importantly, the definition of capital formation

excludes capital outlays accruing to financial assets, and purchases and sales of land (although land

improvement is included).

However, alternative notions of investment exist. The allocation of financial resources toward

interest-bearing assets is often defined as financial investment, and this literature has a long intellectual

history in economics (especially financial economics). The vast majority of the profession regards the

identification of investment opportunities in financial markets to be beyond the purview of economists;

indeed, a large literature explicitly argues that it is impossible to systematically identify and exploit

investment opportunities so that one obtains excess returns from financial markets, after accounting for

differences in risk (Malkiel 2007).

Another form of investment that is pertinent to economic performance is human capital

investment, or the accumulation of education and training, and maintenance of health, by workers in an

economy (Becker 1993). One major conceptual difference between human capital and physical capital

(insofar as it pertains to economic performance) is that the stock of human capital is commonly modeled

to be operative via its accretive effect on the supply of labor (see, for example, Bils and Klenow 2000),

rather than independently as a factor of production. Estimates of human capital (Barro and Lee 2010)

typically use some measure of educational attainment as a proxy for human capital.

Finally, recent critiques of traditional national income accounting argue that it is important to

include a measure of natural capital in the production process. Natural capital investment is perhaps best

viewed as limits on the depreciation of natural resources such as land, minerals, forests, and energy. This

is best understood in the context of the Hartwick rule, which defines the optimal amount of investment in

physical capital that would be required to exactly offset declines in stocks on nonrenewable natural

capital (Hartwick 1977). Estimates of national wealth that include natural capital can differ dramatically

from those that exclude it (World Bank 2006, 2011), and accounting for natural capital can significantly

alter the computation of traditional measures related to the stock of overall physical capital, such as its

marginal product (Caselli and Feyrer 2007).

2

Annex 1.2. Incremental capital-output ratios for selected developing countries

The discussion of capital usage efficiency in Table 1.2 of the text focused on the use of marginal product

of capital. Computations using an alternative metric, the incremental capital-output ratio (ICOR), yield

very similar results, and are reported in Table 1.A.1. Additional care should be exercised in interpreting

cross-country, cross-sectoral comparison of ICORs, however, since country and sectoral capital intensities

may legitimately differ even in the absence of inefficiencies. Nevertheless, excessively large divergences

in ICORs—both within a given country across sectors, and relative to other countries within the same

sector—suggest possible inefficiencies.

Table 1.A.1: Incremental capital-output ratios, economywide and sectoral, selected developing

countries, 1991–2007

Brazil China Indonesia India Mexico Russia Turkey

Economywide 0.8 2.8 1.7 2.4 2.0 1.0 1.5

Agriculture 1.6 0.3 1.8 0.7 2.1 0.7 0.5

Manufacturing 5.9 7.3 2.2 0.8 0.8

Services 0.1 3.4 2.5 1.4

Source: World Bank staff calculations, from UNIDO Industrial Statistics, FAOStat, and World Development Indicators.

Notes: ICORs are computed as averages of annual data over the full period, from the formula It-1/(Yt – Yt-1), where It and Yt are

gross fixed capital formation and GDP corresponding to each sector (or economywide) in year t. Sectoral GDPs are computed

from sectoral value-added shares of total GDP. In most cases, annual data for manufacturing and services are not available for the

full period, and reported ICORs are computed from available data. Observations greater or less than two standard deviations from

the respective means were omitted. The computation excludes years between and 1998–1999 (financial crisis) for Brazil, years

prior to 1996 (transition) and between 1999–2000 (financial crisis) for Russia, 1997–1998 (financial crisis) for Indonesia, 1994

(financial crisis) for Mexico, and 1999–2000 (financial crisis) for Turkey.

3

Annex 1.3. Simulating the effect of uncertainty shocks on investment

The data set for the VAR was based on separate time series for gross fixed capital formation as a share of

GDP and conditional volatility, covering the developing and high-income country aggregates over the

period 1970–2010. The volatility series was constructed in two stages: first, the conditional variance was

obtained from a GARCH (1,1) specification of inflation; real exchange rate; and agricultural, metals, and

energy commodity price indexes. Inflation for each country group is constructed as the current GDP-

weighted geometric average of all within-group countries’ inflation rates, rebalanced every five years.

The real exchange rate is constructed in a similar fashion. Agricultural, metals, and energy commodity

price indexes were obtained from the World Bank’s Development Prospects Group. In the second stage, a

contribution-weighted average of all principal components with eigenvectors greater than unity was

generated from the five GARCH (1,1) conditional variances.

A VAR in levels was then estimated for each aggregate investment-volatility pair, with two lags,

as suggested by the Akaike Information Criterion. Cointegration tests fail to reject the null of no

cointegration, which obviates the need for an error correction model. Impulse response functions (IRFs)

of an investment rate shock on uncertainty are obtained using Cholesky one standard deviation

innovations with +/– 2 standard errors and allowing a projection 25 years into the future (Figure 1.A.1).

Although not of direct interest to the applications in the report, the IRFs for the response of uncertainty to

investment rate shocks is presented here for completeness.

Figure 1.A.1: Response of uncertainty to an investment rate shock, high income (left) and

developing (right) economies

Source: World Bank staff calculations.

Notes: The investment rate shock is a one standard-deviation shock to the investment rate, measured as the fixed investment

share of output. Uncertainty is defined as the contribution-weighted principal components of GARCH (1,1) conditional variances

of inflation; real exchange rate; and agricultural, metals, and energy commodity price indexes. The figures show impulse

response functions for a one standard deviation innovation (solid blue) with +/– 2 standard error bands (dashed red), for 25

periods (years) into the future, generated from a level vectorautoregressive (VAR) specification with two AIC-selected lags.

-.012

-.008

-.004

.000

.004

.008

.012

2 4 6 8 10 12 14 16 18 20 22 24

Response of INVSH_NOM_HIC to INVSH_NOM_HIC

-.012

-.008

-.004

.000

.004

.008

.012

2 4 6 8 10 12 14 16 18 20 22 24

Response of INVSH_NOM_HIC to PCA_HIC

-.4

-.2

.0

.2

.4

.6

2 4 6 8 10 12 14 16 18 20 22 24

Response of PCA_HIC to INVSH_NOM_HIC

-.4

-.2

.0

.2

.4

.6

2 4 6 8 10 12 14 16 18 20 22 24

Response of PCA_HIC to PCA_HIC

Response to Cholesky One S.D. Innovations ± 2 S.E.

-.4

-.2

.0

.2

.4

.6

.8

2 4 6 8 10 12 14 16 18 20 22 24

Response of PCA_DEV to PCA_DEV

-.4

-.2

.0

.2

.4

.6

.8

2 4 6 8 10 12 14 16 18 20 22 24

Response of PCA_DEV to INVSH_NOM_DEV

-.012

-.008

-.004

.000

.004

.008

.012

.016

2 4 6 8 10 12 14 16 18 20 22 24

Response of INVSH_NOM_DEV to PCA_DEV

-.012

-.008

-.004

.000

.004

.008

.012

.016

2 4 6 8 10 12 14 16 18 20 22 24

Response of INVSH_NOM_DEV to INVSH_NOM_DEV

Response to Cholesky One S.D. Innovations ± 2 S.E.

Uncertainty

Years

Uncertainty

Years

4

Annex 1.4. Estimating infrastructure investment requirements

Separate estimates were calculated for each of the four major infrastructural subsectors outlined in the

text: power, transportation, telecommunications, and water and sanitation. For all subsectors, investment

needs are estimated based on projections of demand, which, with the exception of transportation, take into

account population growth (and, in the case of power infrastructure, economic growth). Importantly, the

estimates for needs reported here are gross of maintenance, and so may be lower than estimates that

include infrastructure maintenance costs. All population and economic growth data were obtained from

the gradual convergence scenario of the report, with population data in turn from the UN Population

Statistics. All monetary units are expressed in 2010 U.S. dollars. The methodology used to produce

infrastructure investment estimates for individual subsectors follows.

Power: Generation, transmission, and distribution estimates are based on electricity consumption

patterns in low- and middle-income countries as presented by the U.S. Energy Information

Administration (EIA). Beginning with estimates of country-by-country electricity consumption per capita

for 2009, electricity consumption per capita through 2030 for each country was projected using eigi,

where ei is elasticity per capita of electricity consumption to per capita income for country i, and gi is per

capita growth rate. The total increase in electricity consumption ΔC (in kWh) was determined using the

formula

C = ΔPCPC

t + PtΔCPC

+ (ΔP ΔCPC

), (1.1)

where CPC

t is electricity consumption per capita at year t, and Pt is population at year t, and Δ indicates a

change between two years. The additional generation capacity required to meet the increase in

consumption requirements through 2030 was calculated using a plant capacity factor of 70 percent.

Finally, the investment required to finance the increase in installed generation capacity was determined

using a figure of $2.26 million per MW of installed capacity and associated transmission and distribution

costs. The investment required through 2030 was then calculated as

INVP = ΔG I

GC, (1.2)

where ΔG is the additional generation capacity required to meet increase in consumption of electricity

(equal to ΔC/(8,760 0.70)), and IGC

is investment per kW of installed capacity and associated

transmission and distribution costs, assumed to be $2,258.

Telecommunications: Teledensity (defined as lines per 100 persons) was computed for fixed and

mobile lines separately, with 2009 values obtained from World Development Indicators. Projections of

fixed line teledensity data through 2030 were calculated using an 8.2 percent annual increase for low-

income countries and a 9.1 percent annual increase for middle-income countries, assuming an investment

requirement of $475 per line to obtain total investment in fixed line telephony, which was calculated as

INVFT

= (TF30/100 P30 – TF10/100 P10) IFL

, (1.3)

where TFt is the fixed line teledensity at year t, and IPL

is investment per fixed line of $475.

5

Mobile line teledensity data are projected through 2030 using a schedule of decreasing annual percent

changes, starting at 17.8 percent for low-income countries and 14.9 percent for middle-income countries.

Following Fay and Yepes (2003), an investment requirement of $689 per line was used to obtain total

investment in mobile phones, calculated as

INVMT

= (TM30/100 P30 – TM10/100 P10) IML

, (1.4)

where TMt is the mobile line teledensity at year t, and IML

is investment per mobile line of $689.1

Transportation: The total road network (in kilometers) for each country was sourced from World

Development Indicators. Countries were classified by income category, with projections for annual

increases in paved road length of 1.33 percent for low-income countries and 2.11 percent for middle-

income countries (Fay and Yepes 2003). An investment amount of $487,168 per kilometer of two-lane

paved road was applied to this figure to determine the total investment requirements for road

infrastructure, calculated as

INVT = ΔRN IPR

KM, (1.5)

where ΔRN is the change in road network between the two periods, and IPRKM

is the investment per

kilometer of two-lane paved road of $487,168. The starting point for the projections was each country’s

most recent figure, but only if it was reported between 2004 and 2008 (the latest available year). Since

data are either unavailable or for a year prior to 2004 for about two-fifths of developing countries, there is

systematic underestimation of transportation needs.

Water: The data for percent of population with access to improved water source in 2008 was

obtained from World Development Indicators. Using projected populations for 2030, population access

was assumed to attain full coverage by that year. The number of persons in each household was assumed

to be six in low-income countries, five in lower-middle-income countries, and four in upper-middle-

income countries. The annual increase in the number of connected households was computed using

constant percentage changes in the share of population with access until each country reaches 100 percent

access by 2030. An investment amount of $475 per connected household was used to determine the

investment requirements for potable water infrastructure, using the formula

INVW

= (PPA30/100 P30 – PPA10/100 P10) (1/HM) IPC

, (1.6)

where PPA is the percent of population with access to improved water sources at time t, HM is the

average size of households, and IPC

is the investment per household connected to improved water source

of $475. An analogous formula was used for wastewater treatment investment calculations, with IWT

set at

$832. Unit cost assumptions for all sectors are summarized in Table 1.A.2.

1 Note that the methodology employed here differs somewhat from Fay and Yepes (2003), who in both cases calculate total

investment in telecommunications as INV = ΔTM/100 P30 IPL.

6

Table 1.A.2: Unit costs assumptions for infrastructure subsectors

Sector Cost (US$) Measurement unit

Electricity 2,258 Per kW of generating capacity, including associated network cost

Fixed mainlines 475 Per line

Mobile lines 689 Per subscriber

Roads 487,168 Per km of two lane paved road

Potable water 475 Per connected household

Sanitation 832 Per connected household

Source: Fay and Yepes (2003), and World Bank staff estimates.

Notes: Cost estimates by Fay and Yepes (2003), provided in 2003 U.S. dollars, are rebased to 2010 using the U.S. inflation rate.

7

Annex 1.5. Structural determinants of investment financing and national saving

This annex documents the econometric analysis underlying the structural determinants of investment

financing and national saving, discussed in chapters 1 and 2, respectively.2 The estimates also serve as

inputs to calibrating the CGE model (discussed in Annex 1.6). The dataset for investment financing is an

unbalanced country-level panel covering up to 105 economies over the period 1985–2009, while the

saving regressions use an unbalanced country-level panel, covering 56 economies over the period 1970–

2011.

The dependent variable for investment financing is the gross fixed capital formation rate;

analogous regressions with gross capital formation (which includes inventory accumulation3) or the

investment level yielded qualitatively similar results. The primary dependent variable for national saving

is the domestic saving share of income (although for two robustness checks, the private saving share of

income or the public saving share of income is used); analogous regressions with gross saving as a share

of gross national income, which accounts for the effect of net factor payments, yielded qualitatively

similar results. The independent variables are sourced variously from the World Bank’s World

Development Indicators (per capita income, growth, trade openness, dependency ratio) and Financial

Development and Structure database (financial development, financial structure), the International

Monetary Fund’s International Financial Statistics (real interest rate) and World Economic Outlook

(private and government saving), Chinn and Ito (2006) (capital openness), International Country Risk

Guide (institutional quality, investor protection, democratic development), and Bloom et al (2007) (social

security systems).

The primary econometric specification for investment financing is an estimate of the investment

rate in country i at time t, (I/Y)it, given by

,''~

,01 ititititritgitYI

itYI urY

ZΓXβ (1.7)

where Y is the output growth rate, r~ is the yield relative to the global average, X is a vector of structural

determinants, Z0 is a vector of covariates that correspond to other determinants of investment, and u is an

error term that comprises fixed country and time effects, of the form uit = i + t + it, where N (0, 2)

is an i.i.d. disturbance term. This specification for investment financing is inspired by a Jorgensen (1963)-

type flexible accelerator (neoclassical) model, where the investment rate is a function of output growth

and the cost of capital.4 Partial adjustment is captured by further including lagged investment.

2 Additional details on the structural determinants of investment—including a description of data sources, estimation

methodology, and additional robustness checks—are reported in an accompanying background paper to this report (Lim 2013).

3 Inventories may be excessively influenced by business cycle effects, which justify their exclusion.

4 A very simple theoretical specification of the neoclassical model is one where the optimal capital stock at time t, Kt*, is a

function of production, Yt, and the cost of capital, rt, so that Kt* = Yt /rt

, where and are the output and substitution

elasticities of capital. To obtain investment, substitute the optimal capital stock with the equation of motion of capital Kt+1 = (1 –

)Kt + It, keeping in mind that in the steady state, the growth rate of capital is the growth rate of output, so that Kt+1 = (1 + gt) Kt.

This yields It/Yt = (gt + )/rt. Taking logarithms on both sides yields the recognizable empirical specification where the

investment rate is a function of (depreciation-adjusted) growth and the cost of capital. This implicitly imposes a parameter

8

The primary econometric specification for saving is an estimate of the saving rate in country i at

time t, (S/Y)it, given by

,''

~,11 ititititditgitY

SitY

S vdy

ZΠYθ (1.8)

where y is the per capita income growth rate, d~

is the aged dependency ratio, Y is a vector of structural

determinants, Z1 is a vector of covariates that correspond to other determinants of saving, and v is the

error term. This specification for national saving is akin to the empirical aggregate saving function of

Brumberg (1956), which is essentially a life-cycle model that includes (lagged) saving, growth of per

capita income, and capital gains (represented by the real interest rate). Overall wealth, a mainstay of

precautionary saving models (Carroll 1997), is proxied by per capita income (substituting this with a

measure of per capita national wealth does not substantially modify the results, and comes at the cost of a

significant reduction in sample size).

The estimation methodology relies on fixed effects estimates for annual data, presented in Table

1.A.3 (for investment financing) and Table 1.A.5 (for saving) (Hausman [1978] tests reject a random

effects approach), and system GMM for 5-year averages, presented in Table 1.A.4 (for investment

financing) and Table 1.A.6 (for saving). The estimates using the former methodology relies on within

variation, but the use of annual data allows one to capture the possibility of cyclical variations, to the

extent that such cyclical variations may be important.5 In contrast, the estimates using the latter

methodology allow cross-sectional variation to potentially influence coefficient estimates (which explains

in part the differences in the magnitude of the point estimates), while also smoothing out the business

cycle effects and hence better reflect longer-run influences. System GMM also offers some (weak)

control of potential endogeneity, using internal instruments.6

For investment financing, the minimal benchmark specification (I1) estimates equation (1.7)

without X and Z0.7,8

Specification (I2) adds economic controls. To allow open-economy effects, two

restriction (of one) for the coefficient on growth. In the empirical specifications, this elasticity is allowed to deviate from unity.

The accompanying technical paper considers a specification that imposes this restriction, with little impact on the qualitative

results.

5 While the inclusion of a lagged dependent variable in the fixed effects specification may introduce the possibility of (Nickell)

bias, estimates with bias-corrected coefficients (Bruno 2005) results in only small variations in the point estimates.

6 In the GMM specifications, growth and the interest rate differential are treated as endogenous entered into the (orthogonalized)

internal instrument matrix with two lags and deeper, while the lagged investment rate, trade openness, and financial openness

were treated as predetermined and entered with one or more lags. Financial development, institutional quality, investor

protection, and democratic structure are instrumented with their lagged values. The internal instrument set is also collapsed to

limit instrument proliferation.

7 The identification issue from simultaneity is relieved, in part, by recognizing that while interest rates affect both investment

demand and investment financing supply, only supply is responsive to the differential (investment demand responds directly to

the interest rate). There are nevertheless a number of additional econometric issues with including the relative interest rate in the

specification. First, the relevant interest rate differential is the relative rental rate between countries; but since relative rental rates

are not observed, and only imperfectly calculated from relative marginal products, it has to be proxied (by the interest rate

arbitrage differential, computed as d = r/er*, where e is the change in the exchange rate and r* is the global risk-free interest

rate as proxied by the U.S. interest rate). Second, observed real interest rates, especially for developing countries, may be

distorted by financial repression or capture country risk or uncertainty. The sensitivity of varying this estimate for the CGE

exercises described in Annex 1.6 is explored in an accompanying background paper (Bussolo, Lim, and Maliszewska 2013).

9

medium-term determinants (Calderón, Chong, and Loayza 2002; Chinn and Prasad 2003) of external

accounts are included: trade openness (the sum of imports and exports to GDP) and restrictions on capital

account openness (the Chinn-Ito index). Specifications (I3)–(I7) incrementally add structural variables of

interest: (I3) includes a measure of financial market development, measured as the private credit to GDP

ratio; (I5) adds institutional quality, measured as the simple average of indices of corruption and rule of

law; (I6) adds investor protection (measured as the investment risk profile); and (I7) adds political

structure (measured as voice and accountability). Specification (I4) includes only the two structural

variables typically found to be significant—financial development and institutional quality—and no

additional economic controls (this specification matches, exactly, the investment financing equation used

in the CGE model, as described in detail in Annex 1.6). The inclusion of additional variables, such as the

lagged capital stock or a financial crisis dummy, does not substantively change the results, nor does the

use of alternative measures of the two key structural variables (as documented in Bussolo, Lim, and

Maliszewska 2013). Specifications (J1)–(J7) are analogous to (I1)–(I7), but for the 5-year average sample

estimated via system GMM.

For national saving, the minimal benchmark specification (S1) estimates equation (1.8) without

without Y and only per capita income in Z1. Specification (S2) adds economic controls, as well as

demographics (measured as the aged dependency ratio).9 Specifications (S3) and (S4) incrementally

introduce structural variables: financial market development (the ratio of private credit to GDP); and (S4)

social protection, measured as the replacement rate (of pre-retirement earnings met by post-retirement

pension payouts) in a pay-as-you-go social security system.10

Specification (S5) is a parsimonious

specification with only two structural variables, financial development and social protection (and

matches, exactly, the saving equation used in the CGE model, as described in detail in Annex 1.6). As

robustness checks, two final specifications are considered: (S6) private saving as the dependent variable

(with government saving included as an additional covariate); (S7) government saving as the dependent

variable (with private saving included as a control).11

Specifications (T1)–(T7) are analogous to (S1)–

(S7), but for the 5-year average sample estimated via system GMM.

The results suggest that investment both investment and saving have relatively strong persistence

(significant and positive coefficients).

8 Despite its parsimony, there is still the possibility that there remains collinearity in this baseline specification. Besides weak

control of endogeneity afforded by system GMM estimates, the sensitivity of this baseline is also explored in several additional

ways: a specification that drops the real interest rate; and specifications that include the capital stock, both as a lagged

independent variable and as a denominator for investment (so that I/Kt-1 is the dependent variable). There are few changes to the

qualitative results reported here as a result of these alternatives, and the results are reported in Bussolo, Lim, and Maliszewska

(2013).

9 In contrast to some of the existing literature (e.g. Loayza, Schmitt-Hebbel, and Servén 2000), the youth dependency ratio is

statistically insignificant across most of the specifications, possibly due to multicollinearity issues (it is highly correlated to the

aged dependency ratio).

10 Robustness checks, where additional variables such as the lagged national wealth or a dummy capturing universal coverage of

the social security system are added as controls, do not make a major difference to the results.

11 Due to sample size limitations, these final two specifications are not estimated with the five year-averaged data.

10

For investment financing, there is also a positive and significant effect from growth (faster

growing economies tend to invest more12

). Due to the econometric and measurement issues raised in

footnote 7, the coefficient from the yield differential is insignificant in all specifications. To the extent

that trade openness matters (one specification, I2), its effect is marginal but positive (economies more

open to trade flows tend to have higher investment rates). To the extent that financial openness is

significant (one specification, J7), its effect is negative and significant (economies with more restrictions

on capital tend to have lower investment rates).13

Among the structural variables, financial development

and institutional quality tend to have significant and positive coefficients, as may be expected a priori. A

10 percent increase in financial development (institutional quality) results in a 0.1–0.5 (0.1–0.3) percent

increase in the investment rate. In level terms, this 10 percent increase is equivalent to an increase in

investment of as much as 3.4 (2.5) percent (as reported in Bussolo, Lim, and Maliszewska 2013).

Interestingly, the coefficient on investor protection is typically insignificant. While

counterintuitive at first, a careful perusal of the underlying data is illuminative: many economies with

strong investor protection scores tend to be relatively less developed. The result can thus be rationalized

in two ways. First, it could be the case that, when investor protection clauses are in conflict with the

broader sense of the rule of law, investors may regard de jure laws as a negative signal and reduce their

investment activity (hence a negative coefficient). Second, laws concerning investor protection tend to

matter more for cross-border investment, so if domestic investors—with superior informational

advantages—increase their investment activity to compensate, this offsets losses from foreign investment

(hence an insignificant coefficient).

As is the case in investment financing, growth exerts a positive and significant effect on saving

(economies with faster increases in per capita income tend to save more), and there is an economically

small (but statistically significant) impact of per capita income levels. Financial development enters with

a negative coefficient, suggesting that agents in economies with more mature financial systems tend save

less, possibly because they can easily access loans from the banking system when necessary. Consistent

with other studies of cross-country saving (Loayza, Schmidt-Hebbel, and Luis Servén 2000), the aged

dependency ratio is negative and significant, and the greater the level of social protection available, the

less individuals save (which verifies the finding in Bloom et al 2007). Interestingly, this result does not

retain its statistical significance when only private saving is considered, although including the dummy

for universal coverage yields a coefficient that is positive and approaching statistical significance (p =

0.11), a finding consistent with Bloom et al (2007).

12 For the specification to be totally consistent with theory, growth rates should be adjusted for depreciation. However, since

depreciation is typically (assumed) constant across countries, this adjustment amounts to the addition of a constant to all growth

rates, and regressions with such adjusted growth rates leave the results virtually unchanged. The unadjusted growth rate is used

here to ease interpretation.

13 Although potentially counterintuitive, this can be the case if foreign direct investment (FDI) flows not only substitute but

displace domestic investment more than one-for-one, which could occur if FDI were more productive than domestic investment.

11

Table 1.A.3: Fixed effects regressions for fixed investment rate, unbalanced annual panel, 1985–

2009

I1 I2 I3 I4 I5 I6 I7

Lagged investment rate 0.832

(0.02)***

0.826

(0.03)***

0.816

(0.03)***

0.815

(0.02)***

0.814

(0.02)***

0.814

(0.02)***

0.816

(0.02)***

Output growth 0.142

(0.02)***

0.137

(0.04)***

0.143

(0.04)***

0.147

(0.04)***

0.141

(0.04)***

0.140

(0.04)***

0.140

(0.04)***

Yield differential 0.000

(0.00)

0.000

(0.00)

0.000

(0.00)

0.000

(0.00)

0.000

(0.00)

0.000

(0.12) 0.000

(0.00)

Trade openness

0.016

(0.01)*

0.013

(0.01)

0.014

(0.01)

0.013

(0.01)

0.014

(0.01)

Financial openness

0.002

(0.00)

0.001

(0.00)

0.001

(0.00)

0.001

(0.00)

0.001

(0.00)

Financial development

0.011

(0.01)**

0.015

(0.01)***

0.011

(0.01)*

0.010

(0.01)*

0.010

(0.01)*

Institutional quality

0.005

(0.00)*

0.005

(0.00)

0.006

(0.00)*

0.007

(0.00)*

Investor protection

0.001

(0.00)

0.002

(0.00)

Democratic structure

-0.005

(0.00)

Adj, R2 0.724 0.726 0.727 0.727 0.728 0.728 0.728

R2 (within) 0.725 0.727 0.728 0.728 0.729 0.729 0.729

Sample 1,582 1,582 1,582 1,582 1,582 1,582 1,582

Countries 106 106 106 106 106 106 106

Notes: All variables were transformed to logarithms. The investment rate differential is the arbitrage differential (d = r/er*,

where e is the change in the exchange rate and r* is the global risk-free interest rate as proxied by the U.S. interest rate).

Standard errors robust to heteroskedasticity and autocorrelation are reported in parentheses. * indicates significance at the 10

percent level, ** indicates significance at the 5 percent level, and *** indicates significance at the 1 percent level. A constant term

was included, but is not reported.

12

Table 1.A.4: System GMM regressions for fixed investment rate, unbalanced 5-year average panel,

1985–2009

J1 J2 J3 J4 J5 J6 J7

Lagged investment rate 0.296

(0.16)*

0.270

(0.21)

0.345

(0.19)*

0.293

(0.17)*

0.386

(0.17)**

0.326

(0.17)*

0.249

(0.18)

Output growth 0.180

(0.05)***

0.176

(0.06)***

0.256

(0.04)***

0.257

(0.04)***

0.271

(0.04)***

0.258

(0.04)***

0.242

(0.04)***

Yield differential 0.001

(0.00)

0.001

(0.00)

0.002

(0.00) 0.003

(0.00)

0.001

(0.00)

0.000

(0.00)

0.000

(0.00)

Trade openness

0.015

(0.02)

-0.015

(0.04)

0.002

(0.03)

0.006

(0.03) 0.005

(0.04)

Financial openness

-0.005

(0.01)

-0.019

(0.01) -0.013

(0.01)

-0.017

(0.01)

-0.035

(0.01)**

Financial development

0.044

(0.01)***

0.017

(0.01)

0.026

(0.01)**

0.032

(0.01)**

0.040

(0.02)**

Institutional quality

0.029

(0.02)*

0.019

(0.01)**

0.013

(0.01) 0.012

(0.01)

Investor protection

0.003

(0.01)

0.016

(0.02)

Democratic structure

0.249

(0.18)

Wald 2

Hansen J

AR(2) z

13.2***

16.8

0.40

43.5***

18.1

0.62

89.1***

11.8

0.17

50.9***

10.5

0.00

97.2***

16.5

0.20

95.2***

21.4*

0.05

89.1***

22.7

-0.01

Instruments

16 18 20 18 22 23 33

Sample

323 323 323 323 323 323 323

Countries 105 105 105 105 105 105 105

Notes: All variables were transformed to logarithms. The investment rate differential is the arbitrage differential (d = r/er*,

where e is the change in the exchange rate and r* is the global risk-free interest rate as proxied by the U.S. interest rate).

Standard errors robust to heteroskedasticity and autocorrelation are reported in parentheses. * indicates significance at the 10

percent level, ** indicates significance at the 5 percent level, and *** indicates significance at the 1 percent level. A constant term

was included, but not reported.

13

Table 1.A.5: Fixed effects regressions for domestic saving rate, unbalanced annual panel, 1970–

2002

S1 S2 S3 S4 S5 S6 S7

Lagged saving rate 0.715

(0.03)***

0.678

(0.04)***

0.670

(0.04)***

0.669

(0.04)***

0.745

(0.03)***

Lagged private saving rate

0.399

(0.06)***

Government saving

-0.573

(0.06)***

Lagged government saving

0.494

(0.06) ***

Private saving

–0.338

(0.07) ***

Per capita GDP 0.006

(0.00)**

0.012

(0.00)**

0.015

(0.01)***

0.015

(0.01)***

0.020

(0.01)***

0.015

(0.01)**

Per capita GDP growth 0.064

(0.01)***

0.062

(0.01)***

0.059

(0.01)***

0.058

(0.01)***

0.059

(0.01)***

0.031

(0.02)*

0.064

(0.02)***

Real interest rate -0.021

(0.01)**

-0.016

(0.01)*

-0.009

(0.01)

-0.015

(0.01)*

-0.025

(0.01)***

-0.020

(0.01)**

Aged dependency ratio

-0.111

(0.01)***

-0.106

(0.04)***

-0.109

(0.04)***

-0.024

(0.03)

-0.165

(0.05)***

-0.097

(0.05)*

Trade openness

0.012

(0.01)

0.013

(0.01)

0.013

(0.01)

0.024

(0.01)**

0.026

(0.01)***

Capital openness

-0.003

(0.00)

-0.003

(0.00)

-0.003

((0.00)*

0.001

(0.00)

-0.000

(0.00)

Financial development

-0.009

(0.01)*

-0.010

(0.01)*

-0.001

(0.00)

-0.006

(0.01)

-0.006

(0.01)

Social protection

replacement

-0.005

(0.00)*

-0.002

(0.00)

-0.005

(0.01)

Social protection

universality

0.011

(0.01)

Adj. R2

0.623 0.631 0.634 0.635 0.614 0.582 0.661

R2 (within) 0.624 0.633 0.637 0.638 0.615 0.587 0.665

Sample 1,102 1,102 1,102 1,102 1,102 900 949

Countries 56 56 56 56 56 54 56

Notes: All variables were transformed to logarithms. Estimates for the final two specifications were for 1981–2002.

Heteroskedasticity and autocorrelation robust standard errors reported in parentheses. * indicates significance at 10

percent level, ** indicates significance at the 5 percent level, and *** indicates significance at the 1 percent level. A

constant term was included, but not reported.

14

Table 1.A.6: System GMM regressions for domestic saving rate, unbalanced 5-year average panel,

1987–2011

T1 T2 T3 T4 T5

Lagged saving rate 0.794

(0.11)***

0.495

(0.17)***

0.541

(0.23)***

0.756

(0.16)***

0.610

(0.23)***

Per capita GDP -0.002

(0.00)

0.007

(0.01)

0.014

(0.01)*

0.012

(0.01)*

Per capita GDP growth 0.091

(0.02)***

0.059

(0.02)***

0.050

(0.02)**

0.029

(0.04)

-0.002

(0.08)

Real interest rate -0.005

(0.05)

-0.012

(0.06)

-0.015

(0.04) -0.016

(0.06)

Trade openness

0.047

(0.02)**

-0.037

(0.02)**

0.00

(0.03)

Capital openness

0.001

(0.00)

0.000

(0.00) 0.001

(0.01)

Financial development

-0.031

(0.02) -0.029

(0.01)**

0.003

(0.02)

Aged dependency ratio

-0.194

(0.10)*

0.091

(0.06)

Social protection

-0.008

(0.01)

-0.055

(0.02) **

Wald X2

Hansen J

AR (2) z

Instruments

Sample

Countries

398.9***

18.9

-2.32**

23

183

56

360.2***

31.9

-2.16**

35

183

56

454.4***

31.7

-1.90*

41

183

56

433.7***

18.6

-1.79*

31

183

56

94.6***

2.8

-1.26

12

183

56

Notes: All variables were transformed to logarithms. Heteroskedasticity and autocorrelation robust standard errors

reported in parentheses. * indicates significance at 10 percent level, ** indicates significance at the 5 percent level, and ***

indicates significance at the 1 percent level. A constant term and period dummies were included, but not reported.

15

Annex 1.6. Details of modeling investment and saving in the gradual and rapid convergence scenarios

This report adopts a modified version of the World Bank’s LINKAGE model, which endogenizes

investment demand, investment financing, and saving, with the current account as a residual.14

Investment demand in the model derives from capital demand in the production process. Capital

(K) accumulates across j sectors in economy i according to investment across sectors (I):

,1

1, itittiIKK

(1.9)

where is the depreciation rate, and Kit = j Kj,it aggregates the capital across all sectors j for country i,

which is supplemented in each period by the aggregate flow of investment Iit = j Ij,it. The demand for

capital obtains from a CES production function, which responds to the sector-specific rental rate (R):

,

,

,

,,

itj

ititj

ij

d

itjR

YK

(1.10)

where is the share of the sector’s value-added in economy-wide output Y, α is the contribution of capital

to value-added in the sector, and the (constant) elasticity of substitution between capital and labor. In

this manner, equation (1.9) determines the allocation of investment across sectors within a given country.

There is no public investment in the model.

The allocation of investment across countries follows an investment financing equation, which

motivates the specification of equation (1.7) of Annex 1.5. The investment share of output (I/Y) is a

function of its first lag, the growth of output, the yield in a country relative to global yields ( r~ ), financial

sector development (FD), and institutional quality (IN). More formally, investment financing is given by

,~

1 titftrtgtYI

tYI INFDrY

(1.11)

where a dot above a variable indicates its growth rate, and a tilde indicates that the variable is measured

relative to the world average. It is important to recognize that the variables on the right-hand side of

(1.11) are endogenously determined alongside equations within the LINKAGE model, and only the

assumed paths of productivity and labor force growth are truly exogenous.

The saving share of income (S/Y) is a function of the first lag of the same series, the growth of per

capita income ( y ), financial sector development (FD), the old-age dependency ratio (DEP), and social

security coverage (SS). More formally, the saving function is:

,1 tstdtftgtY

S

tYS SSDEPFDy

(1.12)

Investment-saving relations are closed with an accounting identity that equates the difference

between a country’s domestic saving and investment with the current account, and an accounting identity

14 Additional details regarding the modeling procedure, along with a host of robustness checks, are reported in an accompanying

background paper to this report (Bussolo, Lim, and Maliszewska 2013).

16

that ensures that saving equal investment at the global level. This, along with all other equations and

assumptions in the baseline model, are described in further detail in van der Mensbrugghe (2011).

All endogenous variables, including saving, investment, GDP, GDP growth, and the structural

variables, are determined entirely within the CGE model. To obtain these CGE estimates, however, (1.11)

and (1.12) must first be calibrated for the persistence parameters and , the behavioral parameter

vectors and , and the structural parameter vectors and .15

The coefficient estimates for the exact and

full specifications (presented in bold) obtained in the econometric regressions reported in Table 1.A.4–

Table 1.A.6 of Annex 1.5 are used to establish upper and lower bounds for these parameters.

In the scenarios, the upper bound (in terms of magnitude) is used to parameterize the

corresponding equation in the CGE model, with the exception of the persistence parameter, where the

lower bound is used (other non-estimated parameters, such as the elasticity of substitution between

factors, are calibrated according to standard assumptions). This calibration choice is designed to limit the

impact of the (analytically uninteresting) lagged term, while maximizing the potential impact of the

remaining variables of interest (the accompanying background paper considers the sensitivity of the

results to a number of calibration assumptions). The initial calibrations for the various parameters are

reported in Table 1.A.7 for the investment financing and saving equations.

Table 1.A.7: Calibration of parameters of the investment financing and saving functions

Parameter Symbol Coefficient

Persistence of investment 0.25

Investment elasticity to output growth g 0.26

Response of investment to yield differential r 1.26†

Response of investment to financial development f 0.04

Response of investment to institutional quality i 0.03

Persistence of saving rate 0.61

Saving elasticity to per capita income growth g 0.06

Response of saving rate to financial development f –0.03

Response of saving rate to aged dependency d –0.19

Response of saving rate to social security coverage s –0.06

Notes: † Despite its theoretical importance, statistical issues (discussed in footnote 7) surrounding estimating the yield elasticity

of investment (r) means that it is not possible to accurately establish a coefficient for this term. Consequently, this parameter is

calibrated to the coefficient on real interest rate levels (rather than differentials). Robustness checks that consider the sensitivity

of the results to this assumption are reported in Bussolo, Lim, and Maliszewska (2013).

Additional assumptions required for all the scenarios are the exogenous paths for productivity

growth and the evolution of demographics. For productivity in agriculture, the average annual growth rate

of productivity is assumed to be unity for high-income countries, and twice that for developing ones.

Productivity in manufacturing is assumed to be two percentage points higher than that in services. Finally,

15 This choice reflects a compromise between the FE estimates obtained from the annual data, which is a closer specification to

the equations of the CGE model, and the system GMM estimates obtained from the 5-year average data, which are potentially

more stable and reflective of longer-run effects.

17

services productivity is calibrated so that it matches actual per capita GDP growth for 2007 (the

benchmark year), and to match growth in potential per capita GDP growth from 2014 onward (with a

linear transition path between the two years). To better match available data and short-term forecasts,

values for output, investment, and saving for 2011–13 are replaced with estimates from the World Bank’s

Global Economic Prospects database, and spliced onto their respective model-determined paths. For

demographics, the old-age dependency ratios for both scenarios are constructed using UN population

projections, for the medium variance case.

In the gradual convergence scenario, the productivity growth assumptions detailed above,

together with the other determinants of production, result in an endogenously-determined growth rate that

averages 5.0 (1.0) percent over the 2010–30 period for the developing (high-income) world. The paths for

the structural variables (financial sector development, institutional quality, and social protection) are

obtained by first estimating the (bivariate) historical relationship between any given structural variable (S)

and per capita income:

,

ttyS

(1.13)

with separate coefficient estimates performed for high income and developing countries (so that = [h

d]). The estimated pooled least squares estimates for the coefficients of equation (1.13) are reported in

Table 1.A.8 below (the equation is estimated in logarithmic form). This relationship between the two is

then incorporated into the model with the additional equation above, so that the structural variable is

allowed to co-evolve endogenously with the per capita income path of the model.16

Table 1.A.8: Coefficient estimates for structural variables

Variable Developing High income

Financial development 0.09 0.18

Institutional quality 0.03 0.27

Social protection 0.15 0.00

Notes: Coefficient estimates are obtained from a pooled OLS bivariate regression of the respective structural variable on per

capita income, measured in logarithms, for each income group.

In the rapid convergence scenario, the productivity path is assumed to be 50 percent higher than

in the gradual convergence scenario for developing countries. The resulting growth rate averages 5.9 (0.9)

percent over the 2010–30 period for the developing (high-income) world. The structural variables are

assumed to converge toward the 2030 U.S. level, closing a quarter of the initial gap by 2030 (this is

implemented by overriding the structural equation above with an exogenous target S, and allowing to

evolve endogenously). Since countries begin at different starting points relative to the U.S., however, the

16 Whether the evolution of structural variables ultimately favors convergence between developing and high-income countries

depends on the interaction between growth in per capita incomes (which is generally slower in high-income countries relative to

developing ones) and the size of this coefficient.

18

growth rate of the specific variable will differ by the country, with countries initially further away from

U.S. levels catching up faster than countries closer to U.S. levels.

19

Annex 1.7. Rebasing estimates in the gradual and rapid convergence scenarios

It has long been recognized that macroeconomic series collected using different accounting systems and

from different sources may not reconcile, as required by theory. For example, current account balances

computed from the national income accounts and the balance of payments, even when calculated

correctly, do not match perfectly, and when aggregated across all countries, the balance of payments do

not sum to zero (the data indicate that the world runs a small deficit).

When reporting estimates from a model, this inconsistency between data and theory is further

compounded by the fact that models are generally unable to perfectly match empirical reality. In the

context of CGE models (used by this report for the projections), there are well-known issues especially

with matching price levels (although relative price estimates, along with estimates of quantities, are

generally more consistent with the data) (see, for example, the papers in Dixon and Jorgenson 2012); an

issue that is potentially compounded as a series extends further into the future. Moreover, the model-data

mismatch is introduced from the first year after initialization (2008), in spite of actual data for the 2008–

10 period already being available.

There are no universally agreed-on solutions to these issues, and so any resolution ultimately

reflects a certain degree of independent judgment. The approach adopted in this report seeks to exploit the

best data available at the time of publication, while also seeking to be consistent with the data commonly

understood and utilized by the policymaking community. Consequently, the report rebases all

macroeconomic series reported in the figures and tables involving scenario projections so that they are

consistent with observed data in 2010 U.S. dollars, and retains this base year through the projections.

The mechanics of the rebasing are as follows. The main macroeconomic variables presented in

the report (GDP, GNI, investment, saving, current account balance) are constructed using a combination

of World Bank’s World Development Indicators (WDI, for historical data), Global Economic Prospects

(GEP, for short-term forecast data), and the LINKAGE CGE model’s long-term projections. Converting

these inputs into single constant-dollar series is a necessary first step in order to have consistent data

series.

In the case of GDP, investment, private consumption, and government expenditure, 2010 is used

as the base year, where the 2010 observation is the respective value from in current dollars. Values for the

years 2000–09 and 2011–14 are calculated by splicing the corresponding constant-dollar series, also from

GEP. For all years after 2014, GDP and investment observations are calculated to grow at the rates

projected by the LINKAGE CGE model, with the specific path dictated by the scenario (gradual or rapid

convergence).

For the case of variables for which constant-dollar series are not available, and/or potentially

inconsistent with the national income accounts series (the current account balance, net income from

abroad, and net current transfers from abroad), a different approach is required, and this is discussed in

detail in Annex 3.1. These rebased series are applied to all figures and tables involving scenario

projections at the macro level.

20

Annex 2.1. Theory and estimation of savings from cohort data17

The basic life cycle model of saving assumes no uncertainty and postulates that consumption follows an

age-profile determined by (age) preferences and real interest rates and that the level of the profile depends

on lifetime resources. Life time resources for individual i, Wi, are the sum of inherited resources and the

discounted present value of the flow of future earnings:

(2.1)

where L is the length of life, r is the constant interest rate, a is age and yi,a are the earnings of individual i

at age a. Consumption at age a will be a proportion of life cycle resources that depends only on age

preferences and the constant real interest rate (which can then be eliminated):

. (2.2)

Assuming, as in the original Modigliani’s paper, that earnings have an age profile that is

independent of the growth rate of the economy (i.e. that with growth acceleration what is modified is the

distance between the income profiles of different cohorts, but not the age profile). Given the Modigliani

specification, labor income (earnings) can be written as proportional to lifetime resources:

. (2.3)

The shape of gi is set by the age profile of earnings and is scaled so that equation (2.3) holds.

Inheritance can be rewritten as proportional to lifetime resources as:

. (2.4)

Then the lifetime budget constraint, requiring the present value of consumption to be equal to that of

earnings and assets (inheritance), can be written as:

= 0, (2.5)

which is independent from the scale factor Wi provided that is independent of Wi. Assets evolve over

the lifecycle in order to allow equations (2.2) and (2.3) to hold simultaneously; for individual i assets

evolve from age a-1 to a as follows:

(2.6)

which can also be rewritten as the accumulation of assets from age 0 to age a as:

(2.7)

Total income is the sum of asset income, rAi,a, and labor income (earnings) and this can be written as:

17 From Deaton and Paxson (2000).

21

, (2.8)

where the scale factor is given by equations (2.7), (2.4) and (2.3) as:

. (2.9)

Saving, si,a , is the difference between total income and consumption. Note that the difference

between the logs of total income and logs of total consumption represents (approximately) the saving rate,

as:

. (2.10)

The saving rate depends on, age, the interest rate and on idiosyncratic variation in tastes, but not

on lifetime resources, nor on the growth of lifetime resources.

Using repeated cross sections of household surveys, it is possible to track the average

consumption and the average income of cohorts (defined as groups of individuals with the same year of

birth). Denoting year of birth as b, and taking the average of the logs of equation (2) for all individuals

born in b, gives:

. (2.11)

where the bar denotes the average. Equation (11) can be estimated by regression of the average of the

logarithm of consumption for those born in b and observed in b + a on a set of age and cohort dummies:

(2.12)

where is a stacked vector of log consumption levels with elements corresponding to each cohort in

each year, Da is a matrix of age dummies, and Db is a matrix of cohort (i.e. year of birth) dummies. The

coefficients and are the age and cohort effects in consumption, and uc is the sampling (or

equivalently measurement) error that comes from the fact that is a sample estimate of the average

log consumption of all individuals born at b and observed at a + b.

Corresponding to equation (12), there is an equation representing regression for income:

, (2.13)

where and are the age and cohort effects in income. Subtracting (12) from (13) yields:

(2.14)

22

Annex 2.2: Projections of age related public expenditures

For each 5-year age cohort in each country, the National Transfer Accounts (NTA) data on public

transfers were converted into expenditures per person at that age, relative to GDP per working-age person

(defined as ages 20-64). This ratio was calculated for Sweden and the United States in addition to the six

developing countries shown in the widget. For each of the six countries, three alternative paths of this

ratio from 2010 through 2050 were constructed:

1) One in which it remains constant;

2) One in which it changes at a constant rate to reach Sweden’s base-year (2003) level by 2050;

and

3) One in which it changes at a constant rate to reach the US base-year (2003) level by 2050.

For each set of the three projected ratios above, this value was then multiplied by the UN's

projection of the population of the cohort, and divided by the projection of the working-age population.

The resulting measure of total expenditures on each cohort, relative to GDP, was summed across cohorts

to estimate total transfers as a percent of GDP, annually. In the case of pensions, total transfers may differ

from total expenditures depending on the design of a country's pension system(s); reliable 2010 estimates

of total public pension expenditures are available from the IMF (IMF 2011), so the projections are

rescaled so that 2010 levels match the IMF estimates. Country coverage was limited to those developing

countries for which IMF estimates as well as NTA data are available.

There are some caveats to bear in mind. First, health care and education transfers are not

calibrated to an observed 2010 value, so the projections in the table use as a base year the latest available

NTA data for each country, which ranges from 1996 to 2004. Secondly, pension reforms since each

country's base year are accounted for only to the extent to which they are reflected in the 2010 estimates

to which the projections are calibrated. Changes in the shape of the age distribution of benefits due to

reforms which took place, or are due to take place, after the year of the latest-available NTA data are

unaccounted for, as are reforms affecting generosity or coverage that had not been implemented as of

2010.

The years for which the countries in Table 2.4 have NTA data are as follows:

1) Brazil: 1996

2) Chile: 1997

3) China: 2002

4) Costa Rica: 2004

5) India: 2004

6) Mexico: 2004

For more information on the NTA project, see http://www.ntaccounts.org and Lee and Mason (2011).

23

Annex 2.3: Projections of public pension expenditures

The set of projections in Table 2.5 of the text seeks to approximate the path of expenditures for a

larger set of countries than are covered by the NTA project. The set of countries is selected according to

availability of 2010 data on public pension expenditure estimates from IMF (2011). The projections rely

on a particular feature of the age distribution of public pension systems: payments into the system come

almost entirely from one cohort (those in their working years), and payments from the system go almost

entirely to another cohort (those in their retirement age) 18

. Thus, the identity in Box 2.7 simplifies to:

where total public pension expenditures as a fraction of GDP, E/Y, depends on the ratio of average

expenditures per person of retirement age E/C (where the retirement-age cohort, C, is defined in this

application as 50+), to output per working-age person, Y/W (where the working-age population, W, is

defined here as 20-64)19

, and the ratio of the populations of the two cohorts (i.e., the dependency ratio).

Under the assumptions that generosity and coverage remain constant, and, implicitly, that the

labor participation rate and labor compensation portion of output remain constant, percent change in E/Y

equals the percent change in C/W. This result forms the basis of the projections in Table 2.5. Public

pension expenditures are projected by applying projected growth rates of the ratio of 50+ year-olds to 20-

64 year-olds (calculated from UN projections by 5-year cohort) to 2010 public pension expenditures

(estimates from the IMF), as a fraction of GDP.

The cut-off ages for defining the working age cohort and retirement age cohort used for the

projections were selected by the following procedure: For the developing countries with NTA-based

projections given in Table 2.4, projections were made by the same methodology as those in Table 2.5, but

using a range of alternative cut-off ages by 5-year increments for defining the retirement-age and

working-age cohorts (allowing them to overlap), and each projection was compared to the NTA-based

projection for the same country. The cut-off ages that matched the two sets of projections the most closely

across countries were selected as the preferred ones for defining the working-age and retirement-age

cohorts.

18 The same method could be used to project education expenditures, but the magnitude of the impact of demographic change on

public finances via education expenditures is typically modest under the assumption used in this set of projections (that average

education transfers to people of each age are constant relative to GDP per working-age person), as illustrated in Table 1. It cannot

be applied to health care expenditures with any precision, since people at all ages receive some share of health care transfers.

19 There is no reason why the working-age and retirement-age cohorts should not overlap, and the NTA data show that for the 50-

64 year-old cohort in developing countries, per-capita gross transfers into public pensions and per-capita gross transfers from

public pensions both tend to be fairly high.

24

Annex 2.4: Projections of population by region and age structure

Table 2.A.1: Population by region and age, 2010 levels and future evolution

Regions Age

groups

2010 Cumulative Change, %

Population

millions % 2030-2010 2050-2010

0–14 190.9 16.5 5 8 High-income economies 15–64 875.3 75.7 10 20 65+ 90.7 7.8 50 55

0–14 431.6 21.7 -16 -26 East Asia and Pacific 15–64 1,465.9 73.6 12 15 65+ 93.3 4.7 107 153

0–14 78.2 19.0 -4 -11 Eastern Europe and Central 15–64 308.9 74.8 2 2 Asia 65+ 25.6 6.2 56 86

0–14 162.9 27.5 -10 -21 Latin America and Caribbean 15–64 405.1 68.4 28 46 65+ 24.1 4.1 108 207

0–14 102.7 30.8 7 7 Middle East and North Africa 15–64 220.6 66.2 41 72 65+ 10.0 3.0 131 364

0–14 513.4 31.3 -2 -13 South Asia 15–64 1,074.7 65.5 37 62 65+ 53.7 3.3 102 251

0–14 362.2 42.3 40 73 Sub-Saharan Africa 15–64 475.4 55.5 71 167 65+ 19.5 2.3 78 273

0–14 1,842.0 26.4 3 3 World 15–64 4,825.9 69.1 25 46 65+ 316.8 4.5 85 154

All ages 6,984.7 100.0 22 40 Source: World Bank staff calculations from World Development Indicators and UN projections.

25

Annex 3.1: Computing country yields to suppliers of capital

As discussed in Annex 1.7 and Annex 3.2, the reconciliation of data from distinct sources necessitates the

rebasing of the yield series. The reporting of country yields to suppliers of capital presents an additional

problem: there is no single, observed series with which yields may be obtained. Consequently, the

reported yields adopt a multi-step process, involving first the calculation of initial yields in a base year,

followed by the application of the rebasing technique to this base year.

The first step requires the computation of the marginal product of capital for each country, which

is calculated as the value added that is attributed to capital in a country’s national income accounts,

divided by an estimate of the country’s reproducible capital stock (which in turn is calculated, as in

chapter 1, using a perpetual inventory method). The value-added share of capital used is computed from

national income accounts evaluated at national prices, and both accounts for labor due to self-employment

(Gollin 2002), and explicitly excludes income flows from land and natural resources. Compared to the

method applied by Caselli and Feyrer (2007), the approach employed here adjusts for capital value-added

only for land and natural resource inputs, rather than the entire stock of natural wealth. Although the

method used here may underestimate the contribution of land and natural resources, it errs on the side of

caution in favor of attributing more of measured factor payments to measured factor inputs. The

corrections applied nevertheless reduce the difference between returns in developing and advanced

countries relative to methods that ignore these factors (for example, when the capital income share is

estimated as one minus the labor income share).

Next, the yield is inferred from the marginal product of capital. In the LINKAGE model, the first

order condition equilibrating the capital market is , where the value of the

marginal product of capital (MPK) multiplied by the output price ( ) equals the cost of capital to the

investor—that is, the rental rate, given by the yield to the supplier of capital (r) plus the depreciation rate

( , multiplied by the price of the capital good ( . The initial value of r is calibrated by estimating

MPK for the initial year (2007), and then solving the equation for r.

Finally, the rate of growth of the yield obtained from the LINKAGE model for each respective

scenario is applied to the initial computed 2007 series, in order to obtain country yield paths. In contrast

to the other macroeconomic series—which were rebased to 2010—yields were rebased to 2007 because

this is the latest year for which the value-added data are available.

In 2007, this measure results in developing countries having an average yield of 13.9 percent,

compared to 7.6 percent in advanced countries (averages are calculated by weighting countries within

each income group by their capital stocks). By way of comparison, combining the value added by land

and natural resources in the national income accounts with the value added by capital raises the measure

to 16.0 percent for developing countries, and only to 7.8 percent for advanced countries.

26

Annex 3.2: Modeling of net capital flows in the gradual and rapid convergence scenarios

As described in detail in Annex 1.7, the main macroeconomic variables presented in the report are

constructed using a rebasing technique. A different approach was necessary, however, for variables for

which constant-dollar series were not available, and/or potentially inconsistent with the national income

accounts series: current account balance, net income from abroad, and net current transfers from abroad.

For these series, the 2010 observation of the rebased series is again set to equal the 2010 current-dollar

value.20

For the years 2000–09 and, in the case of the current account balance, also for 2011–14, current-

dollar ratios were applied to an already rebased GDP series. For example, for 2009:

.

This approach was possible due to the fact that differences between the deflators of GDP and of various

balance-of-payments series were not substantial.

The final variable of interest, national saving (Sn), is then obtained from the other, already

rebased, series by applying, for the years before 2015, the identity:

Sn GDP + NFI + TR – G – C, (3.1)

where NFI, TR, G, and C are net foreign income, net transfers, government expenditure, and private

consumption expenditure, respectively (note that the sum of GDP and NFI yields gross national income

GNI). Thereafter, just as in the case of output and investment, the saving series is computed based on the

growth rates projected by the LINKAGE CGE model, according to the two possible scenarios.

Finally, the current account balance projection after 2014 was calculated as the difference

between saving and investment, plus a correction factor. Applying the national account identity:

GDP C + I + G + X – M, (3.2)

where I, X, and M are investment, exports, and imports, respectively, and applying (3.1):

Sn – I = GDP + NFI + TR – G – C – I, (3.3)

therefore, in theory:

Sn – I = X – M + NFI + TR = CAB. (3.4)

However, given the discrepancies observed between data reported by the systems of national

accounts and the balance of payments, this equality rarely holds in practice. A correction factor () is thus

calculated as follows:

CAB = Sn – I + ( * GDP). (3.5)

Solving for in 2014, this constant, together with the rebased saving, investment, and output

series, is used to calculate current account balance for the years 2015–30.

20 Net income from abroad and net current transfers from abroad data were sourced from the WDI database.

27

It is worth examining briefly here why the magnitudes of countries’ corresponding current

account balances in the scenarios are in the same order of magnitude as historical balances, even though

there are no explicit frictions to capital flows in the model. This is in large part because the investment

financing equation (equation 1.11 in Annex 1.6), reproduced here,

,~1 titftrtgtY

I

tYI INFDrY

(1.11)

plays an important role in how capital flows are generated by the LINKAGE CGE model. This set-up

means that while capital flows respond to cross-country differences in returns, it does so only to a limited

extent, since a combination of the lagged investment term and cross-country differences in growth and

structural factors prevents the kinds of huge one-time capital flows that would eliminate return

differentials in a truly frictionless world. Consequently, the reallocation of capital stocks in the model in

response to return differentials is gradual, and there are no large surges in cross-country balance of

payments.

28

Annex 3.3: Determinants of gross capital flows

Since the mid-1990s, global gross capital flows have tended to grow much faster than net flows

and economic output. Initially, this was an advanced country phenomenon, but since the early to mid-

2000s a number of developing countries have followed a similar pattern. While a fairly large body of

literature has looked at the determinants of net capital flows, gross flows remain understudied in

comparison. However, there is a strong link between gross flows and the literature on home bias in

international portfolios. It has been a longstanding stylized fact that international portfolio diversification

has occurred much less than implied by models of risk sharing, unless they incorporate frictions such as

asymmetric information or other sources of transaction costs.21

A reduction in these frictions would imply

a large increase in gross flows into and out of a given country, as domestic agents diversify by sending

capital abroad and foreign agents diversify by sending capital in. Advanced countries seem to have been

following this pattern at least until the onset of the global financial crisis, as their financial markets

integrated and gross flows expanded rapidly.

More recently, developing countries have seen a dramatic expansion in inflows and outflows as

well, suggesting a reduction in the frictions that give rise to home bias similar to that seen in advanced

economies. These changes might include, for example, the relaxation of exchange rate and other capital

controls; standardization of accounting conventions; and, broadly, the regional and global integration of

financial markets. In addition, the risk-adjusted return to investment has likely been rising relative to that

in advanced economies, attracting foreign investors, due to robust economic growth, human capital

accumulation, a growing working-age population, reduced policy uncertainty and expropriation risk, and

broad improvements in governance.

Only a handful of literature has looked at gross inflows and outflows explicitly. Fernandez-Arias

(1996) tests a portfolio allocation model against inflow data, distinguishing between ―push‖ factors,

proxied by US bond yields, and ―pull‖ factors, proxied by the secondary market price of a country’s debt

and a measure of its investment climate. Both are found to be important, but especially external returns.

Mody, Taylor, and Kim (2001) extend this line of research with a larger set of country-specific and global

factors, including measures of financial market development and U.S. growth. Lane and Milesi-Ferretti

(2001, 2007) document the global expansion of gross flows, and also a transition in the composition of

emerging markets’ international balance sheets to a large FDI and portfolio equity component of

liabilities, and heavy reserve accumulation on the asset side. Devereux (2007) examines this large two-

way flow with a focus on East Asia, showing that over time it is getting closer to an efficient pattern of

international risk sharing implied by a country portfolio model. Speller, Thwaites, and Wright (2011)

project gross inflows and outflows based solely on scenarios of growth convergence and demographic

change. Broner et al. (2012) document that gross flows are very large and volatile compared to net flows,

and pay special attention to changes in gross inflows and outflows during crises and the heterogeneity in

21 Lucas (1990) compares international diversification to that predicted by a portfolio model, and reviews a range of possible

sources of home bias. Kraay et al. (2006) incorporate sovereign risk in such a model to reconcile the predictions of the model to

the data.

29

the behavior of domestic and foreign agents, building a case that asymmetric information and sovereign

risk are important factors in explaining changes in flows in response to shocks.

The notion that asymmetric information is an important friction on capital flows is supported by

research on the relationship between capital flows and geographic distance. A strong portfolio

diversification motive for capital flows might imply a positive relationship between the distance between

countries and bilateral capital flows, since the correlation of business cycles tends to decrease with

distance. However, Portes, Rey, and Oh (2001) and Portes and Rey (2005) find the opposite, that bilateral

flows decrease with distance, with information asymmetries being the likely explanation. More broadly,

they find that market size and transactions technologies are important. More direct proxies for

informational frictions than distance also come in significant, for example telephone call volume, degree

of overlap of trading hours, multinational bank branches, and an index of insider trading. These results

suggest a strong link between the expansion of gross flows and financial market integration in

overcoming informational problems.22

Economic theory indeed suggests that market size and integration can raise asset returns, and thus

stimulate gross capital inflows. For example, Martin and Rey (2004) build a theoretical model with

transaction costs in which financial assets are imperfect substitutes and the number of assets is

endogenous, which gives rise to a link between market size and integration, and asset returns.23

Thus, a

country’s levels of financial market development and integration may have multiple roles to play in

attracting capital inflows. Innovation and structural change in financial markets can reduce informational

frictions and other types of transaction costs; and growth in the scale of financial markets, and an increase

in the share of firms and households with access to credit and financial services, can increase the effective

market size, offering international investors higher returns and greater opportunities for diversification.

The large literature on net capital flows is also pertinent, notwithstanding that not all of the

factors that drive net capital flows are relevant to gross flows, and the mechanisms by which a given

variable impacts gross and net flows can differ in important ways. One strand of research has focused on

the relationship between demographics and capital flows. Relatively young populations should experience

greater investment demand due to a growing labor force, and thus attract capital inflows, whereas

countries with older workforces should save more, and accumulate foreign assets in the face of slower

expected growth (Higgins 1998; Lane and Milesi-Ferreti 2002). This highlights that the impact of

demographic change not only on net capital flows, but also on gross inflows and outflows, depends on the

degree of openness, since saving and investment can only diverge to the extent that capital is able to flow

into and out of the country.

22 A growing body of literature supports the idea that informational asymmetries are important in explaining international capital

flows; also see, for example, Kang and Stulz (1997), Ahearne, Griever and Warnock (2004), and Leuz, Lins and Warnock (2009).

23 Another formal model of how greater integration of financial markets can drive an expansion of capital flows is developed by

Evans and Hnatkovska (2005); the model implies a relationship between integration and changes in the composition and

volatility of capital flows as well.

30

The econometric model of the determinants of gross capital inflows (as a share of GDP)

presented here, on which the long-run projections of capital flows presented in chapter 3 are based,

includes variables meant to capture frictions that limit risk diversification (measures of financial market

development and openness). The working age share of the population is included as another key variable

of interest, and in one specification the working age share of the population is interacted with capital

account openness. Other key country-specific variables included in the econometric model are economic

growth, and an education measure. It is intuitive that growth matters for expected returns to investment,

and it is commonly included in empirical models of the determinants of capital flows or international

positions (for example, Devereux 2007). Similarly, improvements in educational attainment of the work

force can be expected to raise the marginal product of capital and returns to investment (Lucas 1990).

The model uses panel data covering developing and advanced countries over the period 1980–

2010. In addition to the country level factors listed above, it includes a set of global factors. All factors

are explicitly specified in the model:

(3.6)

The dependent variable, , is the volume of gross capital inflows (FDI, portfolio flows, and bank

lending) as a share of GDP of country at time . The categories of independent variables are constructed

as follows:

denotes a vector of demographic variables representing country i at time t, including:

Share of working-age population (ages 20–64), to directly capture the impact of the age

structure of a country’s population on capital inflows;

Tertiary school enrollment (% gross), as a proxy for quality of the labor force, which has

been suggested in the literature to be an important determinant of productivity.

denotes a vector of economic variables representing country i at time t, including:

Real GDP growth (%), which affects investors’ expectations of medium to long-run rates

of returns to investment in the country;

International trade (% of GDP), measured as the sum of exports and imports as a

percentage of GDP, and included in some specifications because it is one measure of a

country’s integration with the rest of the world.

denotes a vector of structural variables that facilitate capital flows or influence the

efficiency of capital allocation in country i at time t, including:

Domestic credit extended to private sector (% of GDP), a measure of the level of

domestic financial sector development;

Chinn-Ito index score, a measure of de jure capital account openness (Chinn and Ito

2006);

31

ICRG, averaged indices of political risk from domestic corruption and lack of law and

order (the higher the measure, the lower the risk).

denotes a vector of global factors at time t, including:

G7 GDP-weighted average growth rate, a measure of the global business cycle;

U.S. federal funds rate, a measure of the cost of capital;

Difference between 10-year U.S. Treasury bond and 3-month U.S. Treasury bill yields, a

proxy of the market perception of risk in advanced economies.

A set of country group dummy control variables is included in the model, as follows:

Euro, which equals one, for all years, for countries in the euro area as of January 2013;

LIC, LMC, and UMC, which equal one if a country is low income, lower middle income,

or upper middle income, respectively, based on current World Bank country income level

classifications, and zero otherwise.

Data used in the regressions is drawn from the World Bank’s World Development Indicators and

Global Economic Monitor databases, the UN Department of Economic and Social Affairs Population

Division, the IMF Balance of Payments Statistics database, Chinn and Ito (2006), and the U.S. Federal

Reserve. For each country, capital inflows are measured as the sum of the flows under financial account

liabilities in the balance of payments.24

The econometric work underlying our forecast of capital flows finds that greater capital inflows

are associated with faster growth, financial development, the level of a country’s de jure capital account

openness, a greater working-age share of the population, greater tertiary school enrollment, lower

perceived risk in advanced economies, and easy U.S. monetary conditions.

Table 3.A.1 reports selected results of ordinary least squares (OLS) estimates of the model with

independent variables expressed in levels, allowing for year fixed effects and country fixed effects

(indicated over a random effects specification by a Hausman (1978) test), with errors corrected for serial

autocorrelation and heteroskedasticity across countries. Specification 1 uses annual data, and

specifications 2 through 4 measure all variables in five-year moving averages to smooth short term

fluctuations in gross inflows. This is especially important for small developing countries, in which a

single large deal can generate a spike in inflows in the particular year in which it occurred. Since our key

variables of interest are thought to be medium to long run factors, smoothing the data seems appropriate.

It is well recognized (see, for example, Reinhart 1999) that capital inflows to a country are likely

to depend on domestic economic activities and domestic growth, and at the same time, that economic

performance and financial development may be affected by capital inflows. To partially address this

24 For certain countries, data are not available for the whole sample period. Countries with missing data are in general closed

economies or small economies that do not use a standard balance-of-payments statistical system. This missing data problem is

minor.

32

endogeneity problem, in the annual specification all country-level variables are lagged one year. In the

smoothed specifications, three-year lags are used, so that the 5-year periods over which the left hand side

variable and lagged right hand side variables are measured overlap for only two out of five years.

Perhaps not surprisingly, higher real GDP growth is unequivocally positively associated with

capital inflows as a percentage of GDP, ceteris paribus, with a significant coefficient across all

specifications of the model. Trade as a percentage of GDP, however, is not statistically significant in any

specification, nor is the measure of political risk; in the interest of increasing coverage of the sample,

trade and political risk are dropped from the final specification selected for constructing the projections.

Level of domestic financial development, represented by domestic credit to the private sector as a

percentage of GDP, is positively associated with capital inflows and statistically significant in most

specifications. Capital account openness is, in most cases, associated with greater capital inflows as well.

There is some stability across specifications in the sign and magnitude of the correlation between

age structure of a country and the level of gross capital inflows as a share of GDP, and in the

specifications with greater country coverage the coefficient is significant at the 10% level. For each

percentage-point increase in the proportion of a country’s 20–64-year-old population during the years

1980–2010, the amount of foreign capital inflows the country received during a given year increased by

three-quarters of a percent of GDP, ceteris paribus. This result is in line with the idea that a growing labor

force and low dependency ratio attract capital. Tertiary school enrollment (investing in the effectiveness

of the future working population) is also positively correlated with capital inflows, with high statistical

significance.

Global factors also appear to be associated with variations in gross flows to some extent. A

greater yield spread, indicating market perceptions of default risk, has the expected negative sign and is

statistically significant, but the magnitude of the coefficient shows some instability across specifications.

The U.S. federal funds rate, typically considered a leading indicator of the U.S. business cycle, has a

positive and statistically significant coefficient in the specification used for the projections, but the sign

changes when the political risk measure is included; one possibility is that it is correlated highly enough

with some global shocks controlled for by year fixed effects that the coefficient is overly sensitive to

changes in the sample. The global business cycle, represented by the variable G7 GDP-weighted average

growth rate, is not found to be statistically significant at conventional levels in most specifications.

As mentioned above, it has been suggested in the literature that demographics may have an

interactive effect with openness. Intuitively, the sensitivity of gross capital inflows to any of the variables

of interest might be reduced by capital account restrictions. A set of specifications of the model allow the

capital account openness measure to interact with each of the other four country-level variables of

interest: growth, credit, working-age share of the population, and school enrollment. Results of this

second set of estimations are shown in Table 3.A.2.

When openness is interacted with the working-age share of the population, the interaction term

has a positive and statistically significant coefficient, which can be interpreted to mean that demography

33

has a greater influence on capital inflows when a country is more open to capital flows, or that openness

has a greater influence on capital flows when a country has a ―demographic dividend‖ to exploit. Both

ways of reading the result are intuitively plausible. The result suggests that policymakers considering

relaxing capital account restrictions may wish to consider that the effects of openness and demographics

can be interdependent. However, controlling for this interaction term, the coefficient on openness itself

turns negative and significant; this does not lend itself to an intuitive story and may indicate nonlinearity

in one or both of these variables, or a nonlinear interactive effect, the possibility of which merits further

investigation.

Parts of this annex are reproduced, and some additional details are provided, in a background

paper for the report: Adams-Kane and Jia (2013).

34

Annex 3.4: Projections of gross capital flows

Gross capital inflows, as a percentage of GDP, are projected country by country based on the

model selected in the econometric analysis (Table 3.A.1, specification 4), which retains only the variables

which are significant, or which do not limit the sample size; thus, the trade and political risk variables are

dropped. Projected paths of the determinants are built for the 158 countries that are in the sample of the

parsimonious specification. The country-level projections are then grouped into the 17 country groups

corresponding to those used in the LINKAGE CGE model. The gross capital inflow projections are

projected to 2030, based, alternately, on the gradual and rapid convergence scenarios presented in

chapters 1 and 2 (summarized in annex 1.6). Projections of country groups’ aggregate gross capital

inflows and determinant variables are real GDP weighted averages.

The gradual and rapid convergence scenarios used to project gross capital flows each consider

three possible paths of globalization for each developing country: its historical trend, its income group’s

average historical trend, and a convergence path in which, by 2030, an upper middle income country

converges to the average of high-income countries in 2010, a lower middle income countries converges to

that of upper-middle-income countries, and a low income country converges to that of lower middle

income countries. In the gradual convergence scenario, each developing country is assumed to follow the

minimum of those three possibilities for that particular country, while in the rapid convergence scenario

each one follows the maximum of the three (Figure 3.A.1). Each high income country is expected to

continue integrating as well, following the maximum of its historical trend or that of the group in the

gradual convergence scenario, and converging to 5 (a hypothesized maximum of the index) in the rapid

convergence scenario.25

Figure 3.A.1: Assumed convergence path of globalization

Gradual convergence scenario Rapid convergence scenario

Source: World Bank staff estimates based on the Chinn-Ito index (Chinn and Ito 2006).

Note: Income group aggregates are simple unweighted averages.

25 Strictly speaking, this relatively aggressive assumption for high income countries is an unrealistic path for the Chinn-Ito index

since it is a de jure measure of openness and advanced countries already tend to already have fairly open capital accounts, but it

is intended to capture a spillover effect from the rapid integration of developing countries, and rapid increase in their volumes of

gross capital outflows, to the de facto level of integration of advanced economies’ financial markets, since such a spillover is not

explicitly accounted for in the model.

-2

-1

0

1

2

3

4

5 Low income countries

Lower middle income countries

Upper middle income countries

High income countries

-2

-1

0

1

2

3

4

5

35

Demographic forces will also be a fundamental in driving international capital flows in the future.

As discussed in chapter 2, the working age share of the population will increase in low income and lower

middle income countries on average, and fall in upper middle income countries but much more slowly

than in advanced countries (Figure 3.A.2). These paths are assumed to be the same in both the gradual

and rapid convergence scenarios. Differences in the timing and speed of demographic shifts between

developing and high income countries in the coming decades will affect long run growth and returns to

investment. A young, growing labor force should raise returns to capital and stimulate investment

demand, whereas countries with older workers approaching retirement should save more and accumulate

assets overseas in the face of slower expected growth (Higgins 1998; Lane and Milesi-Feretti 2002). This

implies that developing countries should attract more capital in the future.

The projected paths of the population aged 20–64, as a percentage of the total population, are

from the UN Department of Economic and Social Affairs Population Division, and are assumed to be the

same in both the gradual and rapid convergence scenarios (Figure 3.A.2).

Figure 3.A.2: Average share of working age population (ages 20-64), by income group

Source: World Bank staff calculation based on UN Population Division data.

Projections of domestic credit to the private sector in the two scenarios follow the assumptions

given in Annex 1.6. The paths of real GDP growth under the gradual convergence scenario and high

convergence scenario are determined endogenously in the LINKAGE model (also described in Annex 1.6).

Tertiary enrollment rates are assumed constant at their 2010 levels into the future. Global factors

are assumed constant into the future, except the G7 growth rates, which are constructed as a weighted

average drawn from the results of the LINKAGE model.

The high overall R-squared, relative to within-country R-squared, of the estimated model used for

the projections indicates that the country fixed effects explain a significant amount of the total variation in

capital flows. The estimated country fixed effects are included in the projections, held constant over time.

35

40

45

50

55

60

65

High income countries

Low income countries

Lower middle income countries

Upper middle income countries

Working age population/total population (%)

36

These should capture any factors which impact capital inflows that vary by country but not significantly

over time, for example natural resource endowments.26

In-sample prediction errors are estimated, country by country, by comparing the average gross

inflows predicted by the model for 2010-11 to the actual 2010-11 average, and multiplying the 2011

projection either by the ratio of the historical two-year average to the predicted two-year average, or by

two in cases when the ratio exceeds two.27

It is assumed that there will be the same projection error into

the future, so the projected paths through 2030 are shifted, additively, by the adjustment to the in-sample

2011 projections.

Volumes of global gross capital flows by country group (CGE groups and developing vs.

advanced) are calculated by multiplying the projected group gross capital inflows, as a percentage of

GDP, by projected nominal GDP of the country group, including the countries not in the sample,

assuming that the out of sample countries have the average rates of the country group. Nominal GDP

numbers are projected based on CGE projected real growth for country groups and assumed 3.5% average

annual U.S. dollar inflation rates.

Projections of gross capital outflows are derived from gross capital inflows and current account

balance, adjusted by reserve accumulation according to the identity

, (3.7)

where net capital outflows are measured as projected saving minus projected investment, i.e. the current

account, and reserve holdings of each country are assumed to remain a constant share of GDP (the 5 year

average of 2007–11) throughout the projection period. The identity is solved for gross nonreserve capital

outflows, and total gross capital outflows are given by the sum of gross nonreserve capital outflows and

reserve accumulation.28

Parts of this annex are reproduced, and some additional details are provided, in a background

paper for the report: Adams-Kane and Jia (2013).

26 Observable measures of natural resource endowments, such as proven reserves or rates of depletion, may vary significantly

over time and also may be more relevant for foreign investment than unobservable underlying endowments, but including these

explicitly in the model could introduce serious endogeneity problems since exploration and extraction may be significantly

impacted by foreign investment.

27 In the special case in which the historical 2010-11 average is positive but the predicted 2010-11 average is negative, the

absolute value of the ratio is used, this having the desired effect of splicing the projection to the historical series.

28 In this report, the separation of the projection into reserve and non-reserve outflows is only relevant for establishing lower- and

upper-bounds of South-South capital flows (Annex 3.5).

37

Table 3.A.1 Regression results of gross capital inflows as share of GDP

Notes: P-values are reported in parentheses. * indicates significance at 10 percent level; ** indicates significance at 5 percent

level; *** indicates significance at 1 percent level.

Model 1 Model 2 Model 3 Model 4

Annual

Smoothed

(5-yr moving

average)

Smoothed

(5-yr moving

average),

ICRG dropped

Model for

projection

(parsimonious,

5-yr MA)

GDP growth (annual %)(lagged) 0.567 0.944 0.675 0.687

(0.016)** (0.045)** (0.023)** (0.027)**

Domestic credit to private sector (% of GDP)(lagged) 0.200 0.065 0.079 0.080

(0.022)** (0.143) (0.070)* (0.068)*

Capital account openness (Chinn-Ito index)(lagged) 2.102 1.265 1.420 1.429

(0.015)** (0.143) (0.092)* (0.091)*

Population age 20-64, % of total (lagged) 1.086 0.912 0.768 0.769

(0.125) (0.113) (0.097)* (0.099)*

School enrollment, tertiary (% gross)(lagged) 0.111 0.215 0.166 0.168

(0.198) (0.002)*** (0.018)** (0.017)**

Total trade as % of GDP (lagged) 0.017 -0.092 0.007

(0.734) (0.263) (0.846)

Corruption, Law & Order (ICRG)(lagged) 0.067 0.987

(0.959) (0.558)

G7 GDP weighted average growth 0.224 4.355 1.160 1.163

(0.651) (0.018)** (0.288) (0.250)

10y-3m US interest rates -1.623 -12.392 -3.684 -3.633

(0.095)* (0.000)*** (0.056)* (0.051)*

Fed funds rate 2.327 -2.592 1.052 1.066

(0.035)** (0.001)*** (0.010)*** (0.010)***

Observations 1884 1867 2589 2616

Number of countries 125 125 156 158

within R-Sq 0.12 0.15 0.15 0.15

overall R-Sq 0.31 0.49 0.44 0.44

38

Table 3.A.2 Regression results of gross capital inflows as share of GDP with interaction terms

Model I1 Model I2 Model I3 Model I4

Growth

interacted with

openness

Credit

interacted with

openness

Smoothed

(5-yr moving

average),

ICRG dropped

Model for

projection

(parsimonious,

5-yr MA)

GDP growth (annual %)(lagged) 0.681 0.694 0.669 0.690

(0.038)** (0.027)** (0.029)** (0.027)**

Domestic credit to private sector (% of GDP)(lagged) 0.083 0.057 0.074 0.077

(0.058)* (0.290) (0.070)* (0.090)*

Capital account openness (Chinn-Ito index)(lagged) -0.046 0.690 -11.114 0.506

(0.969) (0.417) (0.039)** (0.677)

Population age 20-64, % of total (lagged) 0.635 0.849 0.845 0.923

(0.116) (0.090)* (0.075)* (0.121)

School enrollment, tertiary (% gross)(lagged) 0.159 0.152 0.063 0.087

(0.021)** (0.022)** (0.402) (0.398)

Capital account openness × Growth 0.421

(0.138)

Capital account openness × Domestic credit 0.017

(0.346)

Capital account openness × Population age 20-64 0.247

(0.026)**

Capital account openness × School enrollment 0.043

(0.433)

G7 GDP weighted average growth 0.798 1.200 0.987 1.183

(0.397) (0.238) (0.319) (0.242)

10y-3m US interest rates -3.813 -3.615 -3.654 -3.564

(0.045)** (0.054)* (0.051)* (0.054)*

Fed funds rate 1.001 1.098 1.028 1.088

(0.011)** (0.011)** (0.009)*** (0.011)**

Observations 2616 2616 2616 2616

Number of countries 158 158 158 158

within R-Sq 0.16 0.15 0.16 0.15

overall R-Sq 0.45 0.44 0.45 0.45

Robust p values in parentheses

* significant at 10%; ** significant at 5%; *** significant at 1%

Notes: P-values are reported in parentheses. * indicates significance at 10 percent level; ** indicates significance at 5 percent

level; *** indicates significance at 1 percent level.

39

Annex 3.5: Upper and lower bounds of South-South gross capital flows

Although no global dataset exists on bilateral gross capital flows at the country level, it is intuitively

plausible that in a world in which developing countries account for a greater share of both gross capital

inflows and outflows, the share of global gross flows that are between developing countries, ―South-

South‖ flows, will also be greater. Under the scenarios of gross capital flows presented in this report,

some straightforward arithmetic illustrates that the South-South share almost certainly must increase,

despite that the exact volumes of South-South flows cannot be estimated with any precision. Table 3A.3

shows lower and upper bounds of South-South gross flows in 2010, and under each scenario in 2030. The

only assumptions made are that all reserve accumulation consists of outflows to advanced countries, and

that reserve holdings of each country remain a constant share of GDP (the 5 year average of 2007–11)

throughout the projection period. The first of these assumptions helps keep the estimates of the range of

South-South conservative, since South-South flows would be still greater in a world in which some

reserves are denominated in developing country currencies.

Table 3.A.3 South-South gross capital flows will be much greater than today under both the

gradual and rapid convergence scenarios

South-South flows, lower bound

South-South flows, upper bound

2010

from:

2010

from: Advanced Developing sum

Advanced Developing sum

to: Advanced 51 26 77

to:

Advanced 63 14 77

Developing 23 0 23

Developing 11 12 23

sum 74 26 100

sum 74 26 100

2030 (gradual convergence) from:

2030 (gradual convergence) from:

Advanced Developing sum

Advanced Developing sum

to: Advanced 0 53 53

to:

Advanced 37 16 53

Developing 37 10 47

Developing 0 47 47

sum 37 63 100

sum 37 63 100

2030 (rapid convergence) from:

2030 (rapid convergence) from:

Advanced Developing sum

Advanced Developing sum

to: Advanced 0 40 40

to:

Advanced 30 10 40

Developing 38 22 60

Developing 8 52 60

sum 38 62 100

sum 38 62 100

It is noteworthy that even in the extreme case in which, in 2030, there are zero North-North flows

(advanced economies’ reserve accumulation rounds to zero percent of total outflows), which establishes

the lower bound for South-South flows, South-South flows would comprise 10 percent of global gross

flows even under the gradual convergence scenario. The upper bound of South-South flows in 2010 is 12

percent, corresponding to the special case in which there are zero South-North flows apart from reserve

accumulation. Given that the 2010 and 2030 ranges barely overlap, and that the extreme cases that

correspond to the minima and maxima are highly implausible, it is very unlikely that, under the two

scenarios considered, South-South gross capital flows do not increase between 2010 and 2030.

40

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