Post on 19-Jan-2020
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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.
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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
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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.
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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
$832. Unit cost assumptions for all sectors are summarized in Table 1.A.2.
1 Note that the methodology employed here differs somewhat from Fay and Yepes (2003), who in both cases calculate total
investment in telecommunications as INV = ΔTM/100 P30 IPL.
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Table 1.A.2: Unit costs assumptions for infrastructure subsectors
Sector Cost (US$) 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.
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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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