The Return On Private Capital Across Countries:
Rising And Diverging

Robert S. Chirinko*,a,b
Debdulal Mallickc
June 2023

For Presentation At Keio University,
July 7, 2023
Not For Wide Circulation* Corresponding AuthoraDepartment of Finance, 2333 University Hall, University of Illinois at Chicago,
601 South Morgan (MC 168), Chicago, Illinois 60607-7121, USA, PH: (1) 312 355 1262,
EM: Chirinko@uic.edubcCESifo, Munich, Germany

Department of Economics, Deakin University, Burwood, VIC 3125, Australia,
PH: (61) 4 2994 6110, EM: dmallic@deakin.edu.au).

The Return On Private Capital Across Countries:
Rising And Diverging
Table of Contents
Abstract
Highlights
1.

Introduction

2.

Measuring The Return On Private Capital (ROK P)

3.

Movements In The ROKP’s
3.1 The Rising And Diverging ROKP’s: Baseline Results
3.2 Robustness
3.3 Decomposing Movements In The ROKP’s

4.

Explaining Movements In The ROKP’s
4.1 Deriving The User Cost Of Capital
4.2 Relating The User Cost Of Capital To ROKP

5.

Summary And Conclusions

6.

Addendum 1: Estimating Steady-State Values

7.

Addendum 2: The Optimal Reallocation Of Private Capital

References
Appendices:
A: Glossary, Variable Definitions, And Sources
B: Underlying Data For The Baseline ROKP’s In Figure 1
C: List of 88 Countries
D: Formula For Decomposing Movements In The ROKP’s--continued--

The Return On Private Capital Across Countries:
Rising And Diverging
Table of Contents(continued)
Tables:1: Descriptive Statistics
2: Return On Private Capital (ROKP), 1970-2014
3: Decomposing Movements In The Return On Private Capital (ROK P)
Average (1987-1990) To Average (1991-2014)
4: Explaining Movements In The Return On Private Capital (ROK P)
Average (1987-1990) To Average (1991-2014)
Figures:
1: Return On Private Capital (ROKP), 1970-2014
2: Relative Price Of Output (PY/PKP) And Output Price (PY) And
Capital Price (PKP) Deflators, 1970-2014

The Return On Private Capital Across Countries:
Rising And Diverging
Abstract
Across 88 countries for 1970-2014, the return on private capital (ROK P) has exhibited twophases, approximately constant from 1970-1990, but then rising dramatically from 1991-2014.
This latter increase occurs for both Rich/Developed and Poor/Developing countries, though at an
uneven pace; the Lucas Paradox seems to have become more pronounced in recent years.
Despite falling real interest rates lowering ROKP’s, 60% [163%] of the secular rise in ROKP,POOR[ROKP,RICH] is explained by rising equity risk, depreciation, and markups and by the capital loss
from expected decreases in the relative price of new capital. Policy implications are discussed.

JEL Codes:
F21 (International Capital Movements), E22 (Capital), O10 (Economic Development)
Keywords:
International Capital Allocations, Return On Private Capital

The Return On Private Capital Across Countries:
Rising And Diverging
Highlights

The return on private capital (ROKP) has exhibited two phases between 1970-2014
Across 88 countries, ROKP has been approximately constant from 1970-1990
But, from 1991-2014, ROKP has risen dramatically, especially for Poor countries
The Lucas Paradox seems to have become more pronounced in recent years
A good part of ROKP increases can be explained by the user cost of private capital

The Return On Private Capital Across Countries:
Rising and Diverging…the central concept in capital theory should be the rate of return on investment…
almost any important planning question we wish to ask about the saving-investment
process has an unambiguous if perhaps approximate answer in terms of rates of return…
Solow, 1964, p. 16…the welfare effects of debt depend not only on how low the average safe rate is, butalso on how high the average marginal product is.
Blanchard, 2019, p. 1200

1. Introduction
The return on an investment in private capital is central to many ongoing academic and policy
discussions. The Secular Stagnation hypothesis advanced by Summers (2015, 2020) links apersistent decline in investment demand to a persistent decline in the return on capital. The
extent to which capital is misallocated globally and hence the scope for foreign aid and otherpolicies to improve welfare depends on the return on capital (Caselli and Feyer, 2007). Along abalanced growth path, the “Golden Rule” (Phelps, 1961) and dynamic efficiency (Diamond,
1965; Abel, Mankiw, Summers, and Zeckhauser, 1989) depend on the return on capital. The
ominous prediction by Piketty (2014) of a secular increase in wealth inequality is based on the
return on capital exceeding the growth rate of income. Understanding capital formation isimportant for understanding the divergence in per capita income across countries (Mankiw,
Romer, and Weil, 1992). The implications for fiscal and debt policies are highly dependent on
the return on capital. Reis (2022) argues that the sustainable level of government borrowing
increases with the return on capital relative to the return on a public bond. Blanchard (2019)emphasizes the link between the cost of public debt and the profitability of alternative uses ofresources in capital formation. He finds that this return is low, and hence the cost of public debt

2

is low as well. As indicated by the above two quotations, the centrality of the return on capital
has endured for decades.
This paper examines the return on capital across countries. Based on data for 1970 to2014, we find that return on private capital (ROKP) has exhibited two phases, being more or lessconstant from 1970 to 1990, but then rising dramatically for the remaining part of the sample.
This latter increase occurs for both Rich/Developed and Poor/Developing countries, though at
different rates. Thus, the gap has widened in recent years; that is, the Lucas Paradox -- why the
return on capital remains relatively high in Poor countries – seemingly has grown even more
perplexing.1 The secular rise in the price of output relative to the price of new capital is one ofthe primary reasons for the rising and diverging ROKP’s. A rising ROKP may seem puzzling inlight of the well-known dramatic fall in real interest rates. However, ROK P and the real rate are
separated by several wedges -- risk, depreciation, capital losses, markups, and taxes. To
understand the quantitative importance of these wedges, we evaluate the sources of rising anddiverging ROKP’s in a calibration exercise with the user cost of capital. Despite a falling realinterest rate, 60% [163%] of the overall secular rise in ROKP’s for Poor [Rich] countries can be
explained by rising equity risk premia, depreciation, and markups and by the capital loss fromexpected increases in the relative price of new capital. Policy implications are discussed in the
concluding section.

1

The Lucas Paradox (Lucas, 1990) is properly evaluated in terms of steady-state values of the ROKP’s. In thepresence of costly capital adjustment and gradual transition paths, the steady-state ROK P’s depend on the “spot”
ROKP’s studied in this paper, a model of capital adjustment, and adjustment parameters.

3

2. Measuring The Return On Private Capital (ROKP)
We take the perspective of investors allocating private capital and compute the return they would
enjoy. Relating ROKP to observables follows from two identities (Poterba, 1998, eqns. 2 and 3),
(1)











ROKP  CISP * Y / KP * PY / PKP  MPKP * PY / PKP ,where CISP is the private capital income share and (Y/KP) is the output/private capital ratio.
Their product equals the marginal product of capital (ROK P; this result follows from anapplication of Euler’s Theorem; cf. (3) below). The latter component (PY/PK P) is the inverted
relative price of capital. This relative price, which we refer to as the relative price of output, isunity in a one-good model and, in this case, the ROKP equals the ROKP. However, asemphasized by Caselli and Feyrer (2007), this relative price is required in a two-good model inwhich the prices of capital and output may diverge. This divergence proves very important in
the empirical work to follow.
Several challenges exist in estimating the ROKP. While data are readily available for the
price indices for capital and output, estimating ROKP is made difficult by competing claims on
capital income. This problem becomes clearer when analyzing a production function. Output ineach country is determined by a constant returns to scale production function (F[.]) depending onlabor (L) augmented by productivity increases (A), and three types of capital -- private (K P),
natural (KN), and government (KG),(2)

Y  F AL,KP ,KN ,KG  ,where, for notational simplicity, country (i) and time indices (t) have been omitted.
The contributions of labor and private capital to GDP are well known, and their value
added corresponds to increases in corporate profits or proprietors’ income. Government capital4is the accumulated and depreciated value of tangible government investments in equipment,
structures, and intellectual property. Value added that flows from government capital adds to
GDP in three different ways. Government capital can be operated within a government
enterprise (which results in an increase in the government enterprise surplus) or within a private
enterprise (which results in an increase in corporate profits or proprietors’ income; thisrelationship was relevant, for example, in the United States before and during World War II(Gordon, 1969)). Additionally, government capital can be part of general government
operations, and its implicit contribution to value added is the difference between the expenses abusiness does not need to incur as a result of the services associated with government capital(e.g., security) less the taxes needed to finance the capital acquisition. The net amountcorresponds to an increase in corporate profits or proprietors’ income in the GDP accounts.
Natural capital is the capitalized value of rents from non-reproduced assets -- oil, naturalgas, coal (hard and soft), minerals, and forests. (Unimproved land is excluded from the natural
capital stock.) These rents increase GDP irrespective of ownership. The impact on GDP ofgovernment ownership is the same as for government capital discussed in the above paragraph.
Private ownership results in an increase in corporate profits or proprietors’ income in the GDP
accounts.
Returning to the production function, we apply Euler’s Theorem of Homogeneous
Functions to (2), we obtain,(3)

Y  A F L  F P K P  F N K N  F G KG
L

K

K

K

If labor is paid a wage equal to its marginal product ( w  A FL ), (3) can be rewritten to equate
the capital income share for private, natural, and government capital (CIS P+N+G) to marginal

5

products ( F h  MPK h , h  P, N,G ) for three types of capital weighted by their capital/output
K

ratios,
(4)

P
N
G
 wL
P NG
P K
N K
G K
Y  w L  1 
 MPK
 MPK
 MPK
.
 Y  CIS
Y 
Y
Y
Y


We assume that the flow of private capital is the operative margin along which capital isallocated internationally. Equation (4) highlights the fundamental problem in measuring ROK P
given the competing claims on CISP+N+G. 2
This problem is addressed by stating the weighted marginal products for natural andgovernment capital in terms of observables. Following Monge-Naranjo, Sánchez, andSantaeulàlia-Llopis (2019, MSS), we measure the income flow attributable to natural capital(CISN).3 The MSS approach allows us to directly address an important aspect of the fundamental
measurement problem, replacing (ROKN KN / Y) in equation (4) with data for CISN.
The impact of government capital is accounted for in a similar manner. Data publishedby the IMF provides separate estimates for KP and KG. This distinction is important because theratio of government to private capital (RKG,P) is large, and government capital formation has
absorbed substantial resources in some developing countries (Gourinchas and Jeanne, 2013). 4
Dividing our sample into Poor and Rich groups of countries, we confirm that the average value

2

An important advantage of this formulation of ROK’s is that it properly accounts for differences in productivity(A) across countries. In (4), the effects of A are incorporated into the labor share, and hence the capital share. Thisrobustness is important in forming international comparisons because of the cross-country differences in A
documented by Gourinchas and Jeanne (2006).
3

Caselli and Feyrer (2007) initially proposed a similar adjustment for natural capital. However, their correction(using natural capital stocks) was limited by data availability at the time they wrote. The MSS approach using flows
is to be preferred. We use flow data from the World Bank because of its longer time span.
4This adjustment separating government and private capital parallels the adjustment by Caselli and Feyrer (2007)
separating natural from produced (government plus private) capital (cf. fn. 3).

6

for RKG,P is 1.28 and 0.56, respectively. Further dividing our sample into earlier (1970-1990)
and later (1991-2014) periods, we find that, stated in terms of percentage changes, RK G,P falls
modestly for Rich countries (13%) but sharply for Poor countries (53%). While these capitalstock data are an important element in solving the fundamental measurement problem (4),comprehensive data for one component, ROKG, is unavailable. Returning to the Euler
representation in (4), we assume that the marginal product of government capital is proportional
to that for private capital for Poor and Rich countries separately ( MPK G,g  g MPK P,g ,g  Poor, Rich) . With these adjustments for natural and government capital and rearrangementsof (1) and (4), we obtain the following equation,









ROK P  CISP  N  G - CIS N * Y / K P * PY / PK P * 1 + φ * RK G,P

(5)

 .
-1

In computing international ROKP’s, it is important to recognize that the extent of
economic activity outside the market will vary systematically across countries, and hence will
not be captured by officially reported output. This “shadow economy” adjustment adds to ourmeasure of ROKP legal, market-based production of goods and services that are deliberately
concealed from public authorities. The share of economic activity in the shadow economy (SE,measured as a percentage of reported GDP) is twice as large for Poor countries than Rich
countries, and this ratio is approximately constant over the two sub-periods (see Table 1). The
ROKP’s are modified by multiplying the output by one plus the share of shadow economic
activity, 5









(6) ROK P  CISP  N  G - CIS N * Y / K P * PY / PK P * 1   * RK G,P5 * (1 + SE) .
1

We do not adjust the capital stock for shadow economy activity because assets are more difficult to conceal thanincome. We are thus assuming that businesses per se are not hidden, just their value added.

7

Data needed to compute (6) for 88 countries are available from a variety of sources. The
CISP+N+G, PY, and PKP series are from the Penn World Tables (PWT) created by Summers andHeston (1991), revised several times (Feenstra, Inklaar, and Timmer, 2015), and currently
updated (version PWT9) and further developed by the Groningen Growth and Development
Centre (2019). Subsequently, the IMF has used these data as a starting point and added somerefinements and extensions. We use data from the IMF for KP, KG, and Y. The CISN data arefrom the World Bank; the  parameters from Lowe, Papageorgiou, and Perez-Sebastian (2012);
shadow economy data from Schneider, Buehn, and Montenegro (2010). Further information
about the data used in this study is presented in Appendix A, which contains a glossary anddetails concerning variable definitions and sources.
Table 1 contains descriptive statistics for the five objects defining the ROK P in (6), as
well as the price indices for output and private capital considered separately.

8

3. Movements In The ROKP’s
This section documents the rise and divergence in ROK P’s. The key results can be easily
understood in terms of the time-series plots in Figure 1 (Appendix B contains the underlying
time series for the baseline). Results are presented for 1970 to 2014 and are divided in two
dimensions: 1) by sub-periods, 1970-1990 and 1991-2014 because of a clear break in the timeseries in 1990 and 2) by income per capita, sorting countries into Poor and Rich groups and then,for the former, Upper Middle, Lower Middle, and Low income groups. The Poor/Rich divide is
between Malaysia (the highest income Poor country) and Uruguay (the lowest income Rich
country). (Appendix C contains a list of the countries and groups.) For a given group, thecountry ROKP’s are aggregated with capital weights defined as averages for the full sample.
3.1. The Rising And Diverging ROKP’s: Baseline Results
Figure 1.A shows that ROKP, aggregated over all 88 countries, exhibits two phases. From 1970
to 1990, the ROKP is approximately constant. However, starting in 1991, the ROK P moves
steadily upward. As shown in the baseline results reported in Table 2.A, the average ROK P’s forthese two sub-periods is 0.13 and 0.19, respectively.
This aggregate figure hides an important result. While the rising pattern is shared by both
Poor and Rich countries, it occurs at different rates. Figure 1.B shows that the ROK P,Poor isalways greater than ROKP,Rich and that, since 1990, the two series have diverged. Gaps between
Poor and Rich countries, stated in terms of percentage differentials, are 48% and 78% in theearlier and later periods, respectively.
Figure 1.C and Table 2.A document that the pattern of rising ROK P’s that diverge fromthe Rich countries also holds for the three sub-groups of Poor countries.

9

Table 2 offers a second perspective on the rising ROKP. Column 4 contains thepercentage change in the average ROKP for 1991-2014 (column 2) relative to a starting point,
defined as the four-year average for 1987-1990 (column 3). Poor countries grew 72.2%,
substantially greater than the comparable growth of Rich countries of 15.5%.
3.2. Robustness
Before proceeding further, it is useful to explore the robustness of results in four dimensions.
First, intangible capital is a productive factor growing in importance in recent years. National
income accountants have recognized these developments, and the data we use capture several
types of intangible capital -- R&D, mineral exploration, computer software and databases, andentertainment, literary and artistic originals. Nonetheless, there are other forms of intangible
capital -- designs, financial innovations, and economic competencies such as advertising, market
research, training, and organization capital -- excluded from our measure of capital.
Excluded intangible capital (EIK) is unlikely to affect our results for two reasons.
Capital stock data presented by Corrado, Haskel, Jona-Lasinio, and Iommi (CHJI, 2016, Table 3,
for 14 EU countries, the United States, and four formerly Communist countries for 2000-2013)
show that the ratio of EIK to the reported capital stock is 6.9% and 9.8% for poorer and richer
countries, respectively.6 If we assume that no other ROKP components are affected byintroducing EIK and make the extreme assumption that the EIK ratio in the later period (19912014) is three times greater than its value in the initial interval (1987-1990), then the aggregate
ROKP would rise by 27.2% in the latter period (relative to 1987-1990), rather than the 33.9%
increase reported in Table 2.A. Moreover, in the later period, the gap between Poor and Rich

6

The richer countries in the CHJI dataset are the 14 EU+USA countries with Greece and Portugal removed andplaced in the poorer group. If Ireland is excluded because of its peculiar tax system that attracts intangible capital,
the EU+USA ratio falls to 9.3.

10

countries would widen slightly from 1.78 to 1.82. Our rising and diverging ROK P results appear
robust to EIK.
Second, for computing ROKP, two of the adjustments – government capital and the
shadow economy -- are clearly necessary for assessing the intertemporal and cross-sectional
returns to private capital. However, they rely on data lacking the pedigree and longevity of thenational income data measuring other ROKP components. These two adjustments are removed
from (6) by setting RKG,P=0=SE, and these restricted ROKP’s are reported in Figure 1.D and
Table 2.B. The patterns of rising ROKP’s remain. The gap is attenuated because of a decrease in
ROKP,POOR and an increase in ROKP,RICH in both earlier and later periods. Nonetheless, the
ROKP’s continue to diverge after 1990.
Third, the classification of countries into Poor and Rich groups is based on the four-way
World Bank country classification (by income) – high, upper middle, lower middle, and low.
Our baseline results define the Poor and Rich groups as follows: Poor = {upper middle, lower
middle, low}; Rich = {high}. To examine the sensitivity of our results to this classification, wemove the upper middle countries from the Poor to the Rich group. This alternative classification
raises the averages for both groups in both periods, and it has a modest impact on reducing the
Poor/Rich ratios from 1.48 to 1.36 in the earlier period and 1.78 to 1.62 in the later period.
Fourth, in evaluating the international allocation of capital, it is essential to aggregate the
ROKP’s with capital weights, but the results could be influenced by some large countries. We
consider the impact of skewed weights in two ways. First, we re-compute (6) with equal
weights. The results in Figure 1.E and Table 2.C show that equal weighting has little effectrelative to our baseline ROKP results. ROKP,RICH is higher in both periods, more so in the later
period. These results attenuate but do not eliminate the widening gap between Poor and Rich

11

countries. Second, we re-compute (6) after removing the following large countries: Rich (USA,Japan, Germany), Poor (Brazil, China, India, Indonesia), Upper Middle (Brazil, China), Lower
Middle (India, Indonesia), Low (Tanzania). As shown in Figure 1.F and Table 2.D, the results
again are largely robust. While ROKP,POOR and ROKP,RICH are both higher in the later period, thegap is unaffected.
3.3. Decomposing Movements In The ROK P’s
We return on our preferred measure of ROKP defined in (6) and explore which ROKP
components are responsible for the rise in the later period. Equation (6) is composed of fivemultiplicative components (indexed by j). For a given component, its contribution to the overall
ROKP growth rate (  j ) is computed as its growth rate -- holding the other four components
fixed at their starting values – relative to the growth rate in ROK P (see Appendix D, especiallyequation (D7), for details),
88

(7a)

j 

 i Gij88i 1

 i  G1i  Gi2  G3i  G i4  G5i 



i 1

Gj
5

.

j=1,5

Gj
j1

88

(7b)

G j   i G ij .

j=1,5

i 1

Country growth rates ( G ij ) are capital-weighted ( i ) across the 88 countries to form group
growth rates ( G j ). When we evaluate sub-groups (e.g., Poor, Rich), some of the i 's are set to
0 and the positive i 's renormalized to sum to 1.0. The starting and ending values are theaverage values for 1987-1990 and 1991-2014, respectively.

12The  j ’s are reported in Table 2.A for the five components and six groups of countries.
We begin with all 88 countries considered together (aggregate) in column 1. The rise in PY/PK P(shown in Figure 2.A) is the dominant influence, explaining 52% of the growth in ROK P.
Increases in the capital income share have received significant attention in both the popular andacademic literatures (e.g., Karabarbounis and Neiman (2014), Piketty (2014)), and it is
responsible for 24% of the rise in aggregate ROKP. The decline in the share of governmentcapital, through the RKG,P variable and the 1   * RK G,P term appearing in (6), is the third
1

important component affecting ROKP, resulting in an increase of 19%. The share of economic
activity in the shadow economy and capital shallowing (as measured by Y/K P) have only modest
effects on the ROKP growth rate.
However, these aggregate results hide important differences between Poor and Rich
countries. While the rise in the capital income share is important in both groups, it plays a muchlarger role in Rich countries (40%) than in Poor countries (16%) (as shown in Table 2.A,
columns 2 and 3). The slowdown in private capital formation in Rich countries (Crouzet andEberly, 2018; Gutiérrez and Philippon, 2017), and the resulting capital shallowing has
contributed to a 29% rise in ROKP in Rich countries; Y/KP has had almost no effect (-2%) in
Poor countries. The fall in government capital has a much larger impact in Poor countries (24%)
than Rich countries (8%). (These results highlight the importance of adjusting for government
capital in evaluating the return on private capital.) Lastly, the relative price of output, thePY/PKP variable translating $1 of capital investment into the value of output, plays a much more
important role in Poor countries (63%) than Rich countries (25%), as shown in Figure 2.B.
These differential movements casts new light on the role of relative prices in international
capital allocation (Easterly, 1993; Jones, 1994), and they supplement the well-known results of13

Hsieh and Klenow (HK, 2007). HK documented that 1) the PY/PK P ratio was lower in poorer
countries, 2) this differential was due to relatively lower output prices in Poor countries, and 3)
capital goods prices were approximately the same in both groups of countries.
The HK results were based on actual prices for 1980, 1985 and 1996. Since our study isbased on price indices, we cannot evaluate levels, only changes over time. Our data indicate that
there have been two major developments starting in 1990 that refine the HK results. First, while
PY has increased in both Poor and Rich countries since 1990 (cf. Figure 2.C), the percentage
increase has been somewhat greater for Poor countries (cf. Figure 2.D). Second, capital goods
prices have moved in opposite directions, falling slightly in Poor countries, but rising in Rich
countries (cf. Figures 2.E and 2.F). Both movements -- %ΔPY POOR > %ΔPYRICH and%ΔPKP,POOR < %ΔPKP,RICH – attenuate the HK results and provide a new perspective on the roleof relative prices. In recent years, a $1 investment in a Poor country allows investors to buy
more capital and the return on that purchase is higher. Both channels contribute to a relatively
higher ROKP,POOR.
Our results documenting a rising and diverging ROKP’s leads to a fundamental puzzle –why has this marked increase in ROKP’s not led to a substantial flow of capital that would lower
returns in both Poor and Rich countries and that would narrow the gap between the two? Does
the rising and diverging ROKP’s reflect a systematic misallocation of capital or an equilibrium
response to cost factors? To examine the cost channel, we perform a calibration exercise withthe user cost of capital in the next section.

14

4. Explaining Movements In The ROKP’s
This section utilizes the Jorgensonian user cost of capital to understand the fundamental factors
driving the rise in the ROKP. The first sub-section formally derives the relation between the
ROKP, the marginal product of private capital (ROKP), and the user cost of private capital(UCCP). The second sub-section calibrates the user cost and examines to what extent it explains
the rise in the ROKP’s.
4.1. Deriving the User Cost Of Capital
We assume that a representative firm chooses private capital and labor inputs to maximize its
value at time 0 ( V(0) ), the discounted value of its net-of-tax profits over an infinite horizon
stated in continuous time,s  ((s)(s))ds(8)

V(0)   e 00

PY(t)Y(t)  PL(t)L(t)  PKP (t)IP (t) * (1  (t)) dt ,where (t) is the real discount rate,  (t) is the equity risk premium, PY(t) is the output price,Y(t) is output, PL(t) is the price of labor, L(t) is labor input, PK P (t) is the price of new private

capital, IP (t) is investment in new private capital, and (t) is the tax rate. (To preserve
notational simplicity, we model only the private capital good; extension to a multi-capital modelis straightforward.)
In choosing labor and private capital ( K P (t) ) inputs that maximize (8), the firm faces
three constraints,
 Technology: Y(t)  F  L(t), K P (t)  , where output is determined by a neoclassical
production function ( F . ) that depends on labor and private capital inputs;

15



P
P
P P
 Capital accumulation: K (t)  I (t)   K (t) , where the capital stock is increasedby new investment and decreased by depreciation/obsolescence that occurs at ageometric rate ( P).
 Market power: PY(t)  G  Y(t), X(t)  , where G . is decreasing in Y(t) withconstant inverse price elasticity at a point in time (  (1 /  (t)),  (t)  1 ) and X(t) is aset of exogenous factors.
Substituting the three constraints into (8), we obtain,
s

(9)

P
P
   ((s)  (s)) ds  G  F  L(t), K (t)  , X(t)  F  L(t),K (t)       * (1  (t)) dt ,
  PL(t) L(t)  PK P (t)(K P(t)   P K P (t)) 

V(0)   e 00

The Euler equation for the optimal choice of private capital in (9) is as follows,

(10a)

(10b)
(10c)





P
P
 PK P (t)  (t)   (t)     (t)MPK (t)  * (t) ,* PY(t) (1  (t))


P





P (t)   dPKP (t) / PKP (t)  dPY(t) / PY(t) ,(t) 

(t) 1,
(t)  1

where (t) is the markup of price over marginal cost and  P (t) is the capital loss when theprivate capital goods price does not rise as fast (or falls) as the rise in the output price. The
 P (t) term is often overlooked in studies using the user cost of capital. However, consider asituation where the price of a capital good (or any asset) is expected to fall next period. That
expected loss is a cost that needs to be considered when purchasing the capital good today. This
loss may be attenuated (or even reversed) by the expected fall in the price of output. If the fall(or rise) in the capital goods and output prices are equal (which can occur by happenstance or ina one-good model), then  P  0 . As will be documented in Table 4,  P (t) can be particularly

16

important when analyzing the intertemporal behavior of the ROK P across countries, especiallyfor Poor countries given the significant declines in their capital goods prices.
The ROKP(t) is the MPKP(t) adjusted for differences between the prices of private capital
investment and output,          UCCP ,PY
ROK  MPKPPK
(1  )
P

(11)

P

P

P

where time subscripts have been omitted for notational convenience. We assume that the U.S.
market represents the alternative investment opportunity for international investors and measure and  accordingly. The user cost of private capital is defined by the last equality in (11).
Note that using this last equality to define the UCC P creates some tension with traditionalterminology.7 These six variables – , ,  P ,  P , , (1  ) 1 – are factors driving ROKP and theirroles in raising ROKP’s will be quantified in the next sub-section.
4.2 Relating The User Cost Of Capital To ROK P
Equation (11) highlights that the real interest rate is only one of many factors determining the
ROKP. The real interest rate and ROKP are separated by several wedges -- risk, depreciation,
capital losses, markups, and taxes, and a proper assessment of ROKP must be based on UCCP.
Data sources for the six factors are discussed in Appendix A, Section II. We use (11) to quantify
the extent to which the factors explain the growth rate in ROK P between 1987-1990 and 19912014. The procedure is similar to that used in the Section 3.3 decomposition with the exception
that, since the first four factors enter additively, their impact is quantified by including an
additional weight ( ih ) evaluated at the starting values,

7

The Jorgensonian user cost of capital (Jorgenson, 1963) is usually defined inclusive of the relative price of capital.
In our calculations, the inverse of that variable has been multiplied by ROK P to define ROKP in (11).

17

88



(12a)

h



 i ih G ih
i 1

G

ROK P



ih G h
G

ROK P

P

88

GROK  i GiROK

(12c)

i 1

P

h=1,…,6

ih  1 h  ,(1  )1

ih  h / (    P  P ), h  , , P , P ,

(12b)

,

88

Gih  i Gih .

h=1,…,6i 1where the six factors are indexed by h. All country growth rates ( G ih ) are capital-weighted ( i )
across the 88 countries. For a given factor h, its contribution to the growth in ROK P is given byh in (12a).
Results based on (12) are presented in Table 4 for six groups of countries. We begin withall 88 countries considered together (aggregate). The well-documented fall in the real rate leads
to a fall in ROKP of 45%. This decline is counterbalanced by the rise in the equity risk premium,contributing a 44% boost in ROKP,AGG.8 On balance, changes in the cost of funds (    ), as
well as changes in the corporate tax rate, have not affected movements in the ROK P,AGG.
By contrast, the remaining three factors each contributed to a roughly comparable rise in
ROKP. The largest impact was the rise in markups lifting ROKP,AGG by 39%.9 The risingdepreciation rate contributed 27% and the capital loss, due to the falling relative price of capital,
contributed 26%. Taken together, these six factors account for nearly all of the rise in ROK P,AGG(94%).

8

In the accounting exercise by Caballero, Farhi, and Gourinchas (2017a),  is a dominant driver of the seculartrends in the return to capital and three other macroeconomic stylized facts.
9

The importance of markups in analyzing the return to capital has been noted in several studies: Farhi and Gourio(2018), Eggertsson, Mehrotra, and Robbins (2019), and Barkai (2020). By contrast, Karabarbounis and Neiman(2018) conclude that markups do not play a significant role.

18

As an aside, we note that UCCP is a combination of additive and multiplicative
components. The latter introduce second-order and third-order terms to the Table 4
computations (cf. Appendix D, (D4) to (D7)). These terms are presented at the bottom of Panel
B and explain a further 7% and 0%, respectively, of increases in ROK P. If included in thecalculations by being distributed across the six factors proportionally, the contribution of eachfactor would be raised by 7.4%, and the movement in the UCC P factors would then explain
slightly more than 100% (101.3%) of the movement in the ROK P,AGG. Since we do not have aclear procedure for allocating these interactions to the individual factors and their impact ismodest, they will be ignored in the remaining calculations.
Returning to the six first-order terms, we find that the results change markedly when we
divide the sample into Poor and Rich countries. While the movements in  and  continue toapproximately cancel and (1  )

1

has a very modest effect,  P ,  P , and  have differential

impacts.10 For Poor countries, the sharply falling relative price of capital creates a capital loss
that contributes to 35% of the rise in UCC P, and hence ROKP,Poor. By contrast, for Rich
countries, the capital loss has little impact (7%). However, increases in the depreciation rate
(due to greater investment in equipment and intangible capital) and markups (due to greater firm
concentration and market power) explain 62% and 94%, respectively, of the rise in ROK P,Rich.
A further difference is that, taken together, the six user cost factors imply that ROK P has
risen in the latter period either too much or too little. For Poor countries, the movement in theuser cost accounts for 60% of the rise in ROKP. This result suggests that there is some factor(s)not included in our user cost definition that should increase UCC P,Poor so that, in equilibrium, it

10

Since the percentage change in ROKP to be explained is much greater for Poor countries (cf. row A), thecontribution of a factor common to both Poor and Rich countries (e.g., the real interest rate) will be much less for
Poor countries relative to Rich countries.

19

would approximately equal ROKP,Poor. The opposite result applies to Rich countries, where thesix user cost factors account for a 163% rise in ROKP, and thus there is some additional factor(s)that should decrease UCCP,Rich to the estimated ROKP,Rich. These omitted factors would be
represented by additional terms (  ' s ) to the financial cost (        ) only in the latter
period. Based on the results in Table 4, POOR   0.041 and RICH   0.015 .11
One candidate omitted factor is a “reach for safety.” As noted by Caballero, Farhi, andGourinchas (2017b, p. 43), the supply of safe assets issued by credible governments became
scarce relative to demands due to “central banks’ international reserve accumulation, regulatorychanges, and demographic factors.” Much of this demand emanated from emerging market
countries. In response, firms in Rich countries had an incentive to become safer by building a
sturdier capital structure. These changes are consistent with the data presented by Chen,
Karabarbounis, and Neiman (2017, Table 4) -- 1) a substantial increase in the surplus of saving
over capital formation in the corporate sector 12 and 2) a use of this surplus to increase cash
holdings by 32 cents and reduce debt by 40 cents per $1 of surplus. As a result, investing in Rich
countries would be perceived as relatively safer in more recent years. This channel would bereflected in negative [positive]  's for UCCP,Rich [UCCP,Poor], a flow of funds to Rich [fromPoor] countries, and downward [upward] pressure on ROK P,RICH [ROKP,POOR].
It is beyond is beyond the scope of this paper to rigorously evaluate the “reach for safety”
channel, but two pieces of evidence cast doubts about its plausibility. For Poor countries, theincrease in the default risk premium in the latter period of 410 basis points seems implausibly

11
12

These calculated θ’s are similar in spirit to the capital wedges computed by Gourinchas and Jeanne (2013).

For the earlier and later periods, corporate saving rose from 9.8 to 12.2 percent of world GDP. Household andgovernment saving fell: 12.3 to 8.6 and 1.4 to 0.7, respectively. The earlier period is for 1980 to 1990, and the latter
period for 1991 to 2013 due to available data.

20

large. For Rich countries, the required fall of 150 basis points is more plausible. But data for theUnited States indicates that default risk premia have changed little in the latter period. The risk
premium for Baa bonds has fallen only 20 basis points. The Aaa bond risk premium change is in
the opposite direction and equals a modest +20 basis points.13
Demographic changes may be an alternative candidate factor that has differential effects
on Rich and Poor countries. Population aging is a global phenomenon particularly evident inRich countries (Sudo and Takizuka, forthcoming). The increased dependency ratio lowers theeffective labor force that, in turn, puts downward pressure on ROK P,RICH. Goodhart and Pradham(2020) advance a novel theory that increased globalization had a substantial impact on increasing
the effective labor force by integrating workers from Poor countries into the global economy.
The mobilized labor force puts upward pressure on ROK P,POOR. Introducing the differential
effects of aging and integration and their dynamics on the effective labor force explicitly into ourmodel may well prove to be useful in understanding the evolution of the ROK P’s.
In sum, our analysis of user costs provides a good although partial accounting of the
movements in the return to capital in Poor and Rich countries. Fuller explanations for theevolutions of the ROKP’s over time and across countries remain for future research.

13

The risk premia is the yield on Aaa [Baa] corporate bonds less the yield on 20-year constant maturity Treasury
bonds. The data are from FRED; the corporate bond data are supplemented with information from Council of
Economic Advisers (1999, Table B-73) for 1970-1985.

21

5. Summary And Conclusions
This paper has examined the secular evolution of the return to private capital (ROK P) across 88
countries for 1970-2014. We document that ROK P has exhibited two phases, being
approximately constant from 1970-1990, but then rising dramatically for 1991-2014 (cf. Figure
1.A and Table 2.A). There is important heterogeneity in this increase (cf. Figure 1.B). While the
1991-2014 rise occurs for both Rich/Developed and Poor/Developing countries, the increases areat an uneven pace, 72% for Poor countries and 15% for Rich countries. These differences are
driven by movements in capital income shares, capital shallowing, government capital, and theprice of output relative to the price of investment (cf. Table 3). The Lucas Paradox seems tohave become more pronounced in recent years.
Apart from these results, the paper introduced two refinements in the computation of
ROKP – explicit adjustments for government capital and shadow economic activity. Both varysystematically across Poor and Rich countries and proved important in the quantitative
comparisons of these different groups of countries (cf. Figures 1.B and 1.D and Table 2.B),though did not alter the qualitative results of rising and diverging ROK P’s.
A good part of the increases in ROKP are an optimal response to movements in the user
cost of private capital. Despite a falling real interest rate lowering ROK P, 60% of the secular risein ROKP,POOR is explained by rising equity risk, depreciation, and markups and by the capital
loss from expected decreases in the relative price of new private capital (cf. Table 4). The same
factors explain 163% of the rise for Rich countries.
Our rising and diverging results are relevant to several policy issues.
Secular Stagnation. As emphasized by Summers (2015, 2020), a combination of a downward
shift in the supply of capital schedule due to the “saving glut” (Bernanke, 2005) affecting Rich

22

countries combined with an insufficient upward shift in the demand for capital results in anegative full-employment real interest rate. However, the increase in ROK P,RICH in the latter
period that is more than fully explained by an increase in the user cost of capital raises questions
about weak capital demand and the relevance of the secular stagnation perspective.
Wealth Inequality. As emphasized by Piketty (2014), the ROKP (relative to income growth) is
crucial for continuing and expanding wealth inequality. 14 Thus our results highlighting rising
ROKP’s suggest that wealth inequality will continue and possibly accelerate.
Public Debt. As emphasized by Blanchard (2019), the ROKP is the opportunity cost of public
debt. The rising ROKP’s documented in this paper suggest that the cost associated withgovernment debt has been growing in recent years.
Misallocated Capital. As emphasized by Caselli and Feyer (2007), proper measurement of the
ROKP’s is paramount and, in their work, leads to the conclusion of equality between the returns
to capital in Poor and Rich countries. 15 This equality suggests that the global capital stock isallocated efficiently. Based on new data for a longer sample, our results of a divergence between
ROKP,POOR and ROKP,RICH suggests misallocation. Before proposing corrective policies, it isimportant to know whether this divergence represents an optimal response to heretofore hidden,
country-specific factors entering the user cost, micro level misallocations and TFP (Hsieh andKlenow, 2009, 2010), or frictions such as home bias (French and Poterba, 1991; Coeurdacier andRey, 2013), political bias (Kempf, Luo, Schäfer, and Tsoutsoura, 2022), or home currency bias
(Maggiori, Neiman, and Schreger, 2020) that impede international capital flows. Moreover, the14

Piketty’s model depends crucially on an elasticity of substitution between capital and labor exceeding 1.0. Ourreading of the evidence does not support this view and suggests a value of 0.5 is more appropriate (Chirinko, 2008;
Chirinko and Mallick, 2017).
15

As a matter of notation, Caselli and Feyer’s marginal products of capital are equivalent to our ROKP’s. See
equation (11) for the definitions used in the current paper.

23

structural break that occurred in 1990 hints that, in countries with weak financial systems andsubstantial domestic financial frictions, financial liberalizations may have amplified
misallocations (Gertler and Rogoff, 1990; Gourinchas and Jeanne, 2013) and hence led to the
sharp upward movement in ROKP,POOR. Further research is needed to determine the roles playedby these and other factors in the international allocation of capital.

==========================The paper includes two additional sections, “Addendum 1: Estimating Steady-State
Values” and “Addendum 2: The Optimal Reallocation Of Private Capital.” They represent
material relevant to the analysis of ROK but that has not yet been incorporated into the paper.
They are discussed briefly here.
“Addendum 1: Estimating Steady-State Values” highlights a bias in the above
computations. We have assumed so far that the steady-state ROK can be estimated as an averageof ROK’s over a sample period. This Addendum presents two cases where a wide-discrepancy
can exist. The possibility of a quantitatively important bias is documented by the hypothetical
relationships between observed ROK data and the unobserved steady-state in Figures Addendum
1.A and 1.B. The data are generated by a deterministic partial adjustment model; see table notes
for details. Figure Addendum 1.A is based on the assumptions that the initial conditions andultimate steady-states are identical for poor and rich countries but that the transition speed to thesteady-state is relatively slower for poor countries (  poor  0.10   rich  0.25 ). Using average
spot ROK’s as a measure of steady-state capital allocation leads to a bias that can be misleading.
In this case, the Poor/Rich ratio computed from average spot ROK’s is 1.33. The bias disappears
as T gets very large but, even over a 20-year interval, the bias can be substantial.
The analysis in Figure Addendum 1.B reveals a similar bias, though in this case thedifferentiating factor between poor and rich countries is the initial conditions. For countries
approaching the steady-state from above by accumulating more capital, the bias is positive.
Even with equal transition speeds, estimates of the steady-state based on spot ROK averages

24overstate the true value. Again, the Poor/Rich ratio computed from average spot ROK’s is 1.33,
thus suggesting an LP when none exists.
Addendum 1 shows how a partial equilibrium model can generate unbiased estimates ofthe state-state. The procedure maps the “spot” ROK’s discussed in this paper into steady-statevalues using estimated parameter values (equation A.1.6). Future work will estimate the steadystate ROK’s using this procedure, replacing the current procedure of using sample averages.
“Addendum 2: The Optimal Reallocation Of Private Capital” takes a global
perspective and quantifies the additional output that would be forthcoming if the existing capitalstock was allocated optimally across all countries. As is well known, the capital allocation thatmaximizes global output equates the ROK’s across all countries to a single ROK, ROK** . This
global optimum ROK is calculated according to an iterative scheme; details are provided inAppendix Addendum 2.A. For the full sample period (1970-2014), global output would increaseby 1.2% if allocated optimally and if the elasticity of substitution is 0.5 (Table Addendum 2.1,
panel A). This figure represents a transfer of capital from the relatively low ROK Rich countries
to the Poor countries, and is a weighted sum of the output increase in Poor countries of 4.9% andthe output decrease in Rich countries of 1.1%.
As shown in Table Addendum 2.1, panel B, if the allocation is constrained so that Rich
countries as a whole do not suffer any output loss, the output increase for Poor countries falls
from 4.9% to 3.2%.
The results are sensitive to the value of the substitution elasticity. If it is raised to the
Cobb-Douglas value of 1.0, all of the above results double. See Table Addendum 2.1 for details.
Future work will incorporate these results into a separate section.

25

Addendum 1: Estimating Steady-State Values
I. Bias Due To Transition Dynamics
While the above results are interesting, these spot ROK’s may not be fully informative.
In evaluating capital allocations, we are interested in the steady-state ROK and how quickly an
economy is moving towards this direct measure of capital allocation/misallocation. Even if thesteady-states for poor and rich countries are equal, dynamics of the capital accumulation processfrom initial conditions toward steady-states distort the mapping of spot ROK’s into the steadystate ROK’s. As we shall discuss in the next section, transition speeds depend on, inter alia, thecosts of misallocation, adjustment, and finance. Different transition speeds, as well as different
initial conditions, are consistent with average spot ROK’s showing an LP even if the steadystates are in fact equal.
The possibility of a quantitatively important bias is documented by the hypothetical
relationships between observed ROK data and the unobserved steady-state in Figures Addendum
1.A and 1.B. The data are generated by a deterministic partial adjustment model; see table notes
for details. Figure Addendum 1.A is based on the assumptions that the initial conditions andultimate steady-states are identical for poor and rich countries but that the transition speed to thesteady-state is relatively slower for poor countries (  poor  0.10   rich  0.25 ). Using average
spot ROK’s as a measure of steady-state capital allocation leads to a bias that can be misleading.
In this case, the Poor/Rich ratio computed from average spot ROK’s is 1.33. The bias disappears
as T gets very large but, even over a 20-year interval, the bias can be substantial.
The analysis in Figure Addendum 1.B reveals a similar bias, though in this case thedifferentiating factor between poor and rich countries is the initial conditions. For countries
approaching the steady-state from above by accumulating more capital, the bias is positive.
Even with equal transition speeds, estimates of the steady-state based on spot ROK averages
overstate the true value. Again, the Poor/Rich ratio computed from average spot ROK’s is 1.33,
thus suggesting an LP when none exists.
The important point to be drawn from the above analyses is that an averaging procedureof spot ROK’s does not give due allowance to transition dynamics. To support more accurateinferences about capital allocations, steady-states, and transitions thereto we need to rely on theformal model developed in the next section.

26

II. A New Framework
A. Derivation Of The Estimating Equation
Our estimating equation is derived from an explicit optimization problem. It is considered “semi-structural” because the choice variables are not the policy variables per se. Rather,
the means by which policymakers influence the ROK is left in the background, and we assume
that policymakers directly choose ROK’s. While a more structural model could be easily
constructed, it is not easy to estimate. The semi-structural approach pursued here allows us toderive explicitly a linear estimating equation that will prove useful in pursuing our objective ofgenerating an unbiased estimate of the steady-state ROK that accounts for transition dynamics.
We rely on a partial adjustment model developed in the literature in several places,
staring with Eisner and Strotz (1959) and Lucas (1967). Our formulation closely follows thederivation in Kennan (1979), though the policymaker’s problem is defined in disaggregate terms
over a set of industries within a country.
Policymakers choose ROK’s to minimize costs. Costs arise from misallocation andadjustment for country i for each of its j industries. Misallocation costs occur because thecurrent ROK deviates from ROK*. These deviations are squared and then multiplied by acoefficient,  M , that translates squared deviations into pecuniary costs. The second cost arises
from the adjustment of the ROK’s (and the underlying capital stocks). These costs represent lost
output from disruptions to the existing production process as the ROK is altered and capital
allocated. These installation and “teething” costs are a standard element in modeling input
demands (see the surveys by Chirinko (1993), Caballero (1999), and Bond and van Reenen(2007)). Adjustment costs are modeled as the change in the ROK, squared, and then multiplied
by a coefficient,  A , that translates squared changes into pecuniary costs.
Misallocation and adjustment costs are embedded in the following dynamic cost
minimization problem for the jth industry in country i, discounted over time t by a constantdiscount factor (R), and summed across industries,(A.1.1)

Li, j ROKi, j,t  t 1

MIN

 R t  M  ROKi, j,t  ROK*i, j   ( A / 2)  ROKi, j,t  ROKi, j,t 1  wti, j,t
2

2



27

where R  (1  r) 1  1 (0  r  1) and wt i, j,t is a fixed weight representing the relative
importance of industry j in country i at time t. Optimal choices of the ROK lead to the wellknown partial adjustment model. Differentiating equation (A.1.1) with respect to ROKi, j,t andrearranging, we obtain the following equation,









(A.1.2a) ROK i, j,t wt i, j,t   g ROK*i, j  ROK i, j,t 1 wt i, j,t  i, j   g ROK i, j,t 1 wt i, j,t

i, j  g ROK*i, j(A.1.2b)where  g is the stable root solving the second-order difference equation generated by the firstorder conditions and determines the speed of adjustment to the steady-state. Summing across the
J industries and defining the aggregates as weighted averages of the industry components, we
obtain the following equation for the aggregate ROK’s for a given country,
ROK i,t  i   g ROK i,t 1 .

(A.1.3)The econometric estimates are based on a panel of all countries, and equation (A.1.3) is
supplemented with time fixed effects ( t ) and a stochastic error term ( i,t ),ROKi,t  i  g ROKi,t 1  t  i,t ,(A.1.4)gwhere the adjustment speed parameter (  ) varies by poor and rich groups of countries. As iscommon in the literature starting with at least Sims (1974), the model variables are specified aslogs. Thus, percentage changes in the ROK are proportional to the percentage difference
between the steady-state and current ROK’s.
gB. Adjustment Speed (  )The adjustment speed parameter is a complicated function of the primitives in the
optimization problem –  M ,  A , and R,(A.1.5) g

 (1  R   M /  A )  (1  R   M /  A ) 2  4R 


M A


   ,  , R[r]  1  
.


2R



Differentiation of equation (A.1.5) with respect to each of the arguments and some tedious
manipulations yield some interesting insights:

28

g


  M  0 implies that the higher the cost of misallocation, the faster countries will
converge to the long-run desired value because, ceteris paribus, they wish to eliminate
losses as quickly as possible.
g  A  0 implies the obvious result that, with larger adjustment costs, the approach to thesteady-state is slower.
  gr  0 implies the higher the interest rate (or the lower the discount factor), the slower
adjustment. Higher r could reflect finance constraints. With higher interest rates, thediscounted costs of misallocation are lower, so they are eliminated more slowly by
optimizing countries. In a sense, this result is the mirror image of that for  M above.
C. Country-Specific Steady-State ROK ( ROK i* )An appealing property of the partial adjustment specification is that it readily yields anestimate of the country-specific steady-state ROK in terms of estimated parameters. The steadystate is defined by ROK i,t  ROK i,t 1 , i,t  0 , and t  0 t . The latter assumption
effectively treats the t 's as incidental parameters that we remove from i by subtracting themean of the time fixed effects (  ). With these restrictions, logarithmic versions of equations(A.1.4) and (A.1.2b) imply that the steady-state marginal product of capital is as follows,(A.1.6)  [ g ]   
ROK*i  EXP  i g
,




where  is the average of the time fixed effects and the dependence of i [g ] on  g (throughthe second term on the right-side of equation (A.1.6)) is indicated explicitly. 16
D. Correcting For The Nickell Bias
In panel models with country-specific effects and a “small” number of observations in thetime dimension, the coefficient on the lagged dependent variable is biased. The conventional
analysis of this bias is conducted in terms of an AR(1) model in which the positive coefficient on

16

In the two-way fixed effects model, one time fixed effect (  t ) is dropped to avoid singularity

during estimation. The  term is included in (A.1.6) so that the computation ROK*i is invariant
to which time fixed effect is dropped.

29

the lagged dependent variable is biased downward. In our first-difference model, this effect willg

result in an upwardly biased estimate of  . One solution to this problem is to transform themodel appropriately and then find suitable instruments. We do not follow this approach becauseof the general difficulty of finding suitable instruments, a challenge that is even more daunting in
our panel of 88 countries for 45 years. Instead, we exploit the simple structure of our model that
excludes additional endogenous regressors and correct the bias directly with the formuladeveloped by Nickell (1981) in his seminal article (see the Table 4 note for details). Correcting
for the Nickell bias has a very small impact on our estimates of the steady-state ROK because

 g has a similar effect on both the numerator and denominator of ROK*i in equation (A.1.6).
--continued--30

Figure Addendum 1.A: Hypothetical Bias In Estimating
Steady-State ROK’s
Different Speeds Of Adjustment
35.00
30.00
25.00

Avg. Poor ≈ 1.33
Avg. Rich

20.00

Poor
Rich

15.00

SS-Poor=SS-Rich

Area Under
Curves Used
For Average
Spot ROK Calculations

10.00
5.00
0.00
1

5

10

15

20

Notes: Hypothetical data are generated by the following partial adjustment model,

ROK t  g (ROK*  ROK t 1) , where  poor  0.10,  rich  0.25,
ROK g0  30.0, ROK*g  10.0, g  {poor, rich} .

Figure Addendum 1.B: Hypothetical Bias In Estimating
Steady-State ROK’s
Different Initial Conditions
45.00
40.00
35.00

Avg. Poor = 1.33
Avg. Rich

30.00
25.00

Poor
Rich

20.00
15.00

SS-Poor=SS-Rich

Area Under
Curves Used
For Average
Spot ROK Calculations

10.00
5.00
0.00
1

5

10

15

20

Notes: Hypothetical data are generated by the following partial adjustment model,

ROK t  g (ROK*  ROK t 1) , where  poor   rich  0.25,
ROK 0poor  40.0, ROK 0rich  20.0, ROK*g  10.0, g  {poor, rich} .

31Addendum 2: The Optimal Reallocation Of Private CapitalThis section takes a global perspective and quantifies the additional output that would beforthcoming if the existing capital stock was allocated optimally across all countries. As is wellknown, the capital allocation that maximizes global output equates the ROK’s across all
countries to a single ROK, ROK** . This global optimum ROK is calculated according to an
iterative scheme; details are provided in Appendix Addendum 2.A. We begin by assuming an
arbitrary initial value for ROK** . This initial estimate determines for the first iteration thepercentage changes in the ROK’s (from the country-specific steady-state ROK’s, the ROK*i ’s)that equate ROK’s across all countries. In turn, this percentage change determines the private
capital stocks with a discrete version of equation (19) normalized to K iP . We then compute thedeviation between the sum of these estimated K iP and the fixed amount of global private capitaland use this deviation to compute a new estimate of the global optimum ROK. The process isrepeated until the deviation is close to zero. Given the negative and monotonic relation between
ROK’s and capital stocks, the process is guaranteed to converge to a unique solution. Thechange in global output due to this globally optimal allocation of private capital is computedwith an output-weighted average of a discrete version of equation (18) with dK iP / K iP defined byequation (19).
The percentage changes in global output are presented in Table Addendum 2.1, row 1,
columns 1 to 3 and range from 1.0% to 1.5%. 17 Our estimate of the change in output increases
with the elasticity of substitution; with an overly large elasticity of 1.5, the increase in global
output is 4.4%. The 1.2% increase is our preferred estimate and represents an increase in output
of $1,047 billion (2019 first quarter U.S. dollars) (see Appendix Addendum 2.B for details about
the dollar figure computations reported in this paragraph). By way of comparison, the fiscal
stimulus programs enacted by the United States (ARRA) and China in response to the global
financial crisis amounted to $774 and $677 billion (2019 first quarter U.S. dollars).
17

CF (2007, Table VI) and MSS (2019, Table 6, average of QROK) estimate capital reallocation benefits of 0.1%
and 3.0%. Since these estimates are based on a Cobb-Douglas production function, they are most comparable tothose in our Table 7 with   1 of 2.4%. Our estimate is much larger than that of CF because they found nearequalization of ROK’s for poor and rich countries and hence little scope for beneficial reallocation. Note that theestimates are not strictly comparable because of differences in spot ROK’s for produced capital (CF and MSS) vs.
steady-state ROK’s for private capital (this study), as well as differences in samples.

32

The remaining entries in panel A separate the change in global output between poor andrich countries. The ROK*Rich 0.144 , which is very close to ROK**  0.156 . This resulti
indicates that the rich countries as a group are fairly close to the globally optimal capital
allocation. By contrast, the ROK*Poor 0.235 is very far from ROK** , and the scope fori
improvement lies in reallocating capital from rich to poor countries. For   0.5 for the fullsample, output in poor countries increases by 4.9%, while it decreases by -1.1% in rich countries.
These figures are consistent with the modest gain in global output discussed above because adisproportionate amount of world capital and world output is concentrated in the rich countries.
The above results may be somewhat unrealistic since it involves the rich countries
suffering a loss in output and the rich countries control the international economic organizations
that might lead the effort at such a redistribution. A second scenario imposes an additional
constraint that the rich countries do not suffer any loss in output due to an ex-post transfer of
output from the poor countries under the new ROK** (i.e., a “compensating variation,” aconcept used frequently in public economic analyzes). In this case, the results in columns 1 to 3
are identical in panels A and B, and the percentage increase in output for poor countries drops
from 4.9% to 3.2%. Insofar as incremental income has very high utility in poor countries, thischange may have meaningful welfare consequences.
Lastly, we examine the impact of the shadow economy and government capitaladjustments on reallocations by repeating the analysis in panel A with steady-state ROK that
does not incorporate the government capital and shadow economy adjustments replacing an
ROK that does include these adjustments. As shown in panel C, the estimated benefits of
optimally reallocating capital are now approximately one-third lower than the values reported inpanel A for steady-state ROK with the two adjustments. These lower values are due to the
Poor/Rich ratio based on the unadjusted ROK’s being smaller than the Poor/Rich ratio based on
the adjusted ROK’s and hence the scope for beneficial reallocations being smaller. The shadow
economy and government capital adjustments introduced in Section II matter for quantitativeevaluations.

33

Table Addendum 2.1: Reallocation Of Private Capital
Equalizing ROK’s Subject To A Capital Constraint
Percentage Changes In Output
Adjusting ROK’s

1970 1970 1991
2014 1990 2014
(1)
(2)
(3)
------- Global -------

A. Maximize Global Output

  0 .5
  1.0
  1.5
B. Maximize Global Output
With No Loss to Rich  0 .5
  1.0
  1.5

1.2
2.4
3.7

1.2
2.4
3.7

1.0
2.1
3.1

1.0
2.1
3.1

1970-2014
(4)
Poor

(5)
Rich

1970-1990
(6)
Poor

(7)
Rich

1991-2014
(8)
Poor

(9)
Rich

( ROK**  0.156 )
1.5
4.9
-1.1
2.9
9.9
-2.2
4.4
14.8
-3.4

( ROK**  0.124 )
4.2
-0.4
8.5
-0.9
12.7
-1.3

( ROK**  0.187 )
5.7
-1.6
11.4
-3.1
17.1
-4.7

( ROK**  0.156 )( ROK**  0.124 )( ROK**  0.187 )

1.5
2.9
4.4

3.2
6.3
9.5

0.0
0.0
0.0

3.3
6.6
9.9

0.0
0.0
0.0

3.5
7.1
10.6

0.0
0.0
0.0

C. Maximize Global Output (ROK3) (no govern( ROK**  0.163 ) ( ROK**  0.127 ) ( ROK**  0.200 )ment capital or shadow economy adjustments)  0 .5
0.8
0.6 1.0
2.6
-0.3
1.0
0.4
3.4
-0.6
  1.0
1.6
1.1 2.1
5.1
-0.5
2.0
0.7
6.7
-1.3
  1.5
2.5
1.7 3.1
7.7
-0.8
2.9
1.1
10.1
-1.9
Notes: See Section VIII for a discussion of these results. ROK** is chosen as follows: Panel A, to maximize global output by
equating ROK’s across all countries subject to a capital constraint; Panel B, in a manner similar to that in Panel A with the additional
constraint that output levels in rich countries as a group do not change by a transfer of output from poor to rich countries; Panel C, in amanner similar to that in Panel A with ROK3 used in place of ROK6. The ROK**’s vary across the three intervals and between Panels
A, B, and C and are presented in columns (4)/(5), (6)/(7), and (8)/(9). The percentage changes in output reported in this table arebased on the percentage changes in ROK** relative to country-specific steady-state ROK’s ( ROK*i ’s).

34

Appendix Addendum 2.1.A: Iterative Scheme For Computing The
Global Reallocation Of Private Capital And
The Increase In Global Output
This global optimum ROK is calculated according to the following four-step iterative

1** , where thescheme. First, we begin by assuming an arbitrary initial value for ROK** , ROK
subscript 1 indicates the first iteration. Second, this initial estimate determines for the first
iteration the percentage changes in the ROK’s (from the country-specific steady-state ROK’s, theROK *i 's ) that equate ROK’s across all countries,(D-1)

i,1 

1**  ROK*
ROK
i
ROK*i

 dROK i / ROK i .

Third, a discrete version of equation (19) determines the private capital stock associated with
i,1 ,

(D-2)





P
K i,1
 1     i,1  / 1  CIS iP

 K iP .

Fourth, we compute the extent to which the sum of the country capital stocks in the first iteration( K1P ) deviates from the fixed amount of global private capital ( K P ),(D-3a)(D-3b)

 2  K1P  K P / K P ,P
K1P   K i,1,i(D-3c)PK P   K i.0,
i(D-3d)

2  1  2 ,where Ki.0 is the initial value of country i’s private capital stock.
We begin the second iteration by using this deviation to compute a new estimate of the
global optimum ROK,
(D-4)

 **
 **
ROK
2   2 ROK1 , **return to step 1, and insert ROK
2 into equation (D-1). The process continues until  N is
sufficiently close to 0.

35

Convergence is assured. Consider, for example, the situation where the total amount of

 n in the nth iteration exceeds the fixed, global, private
private capital consistent with ROK
**

P
 **
capital stock. In this case,  n 1 is positive,  n 1 is greater than one, ROKn 1 rises, and K n 1P
 **falls. Since the negative relation between ROK
n 1 and K n 1 is monotonic, the process isguaranteed to converge to a unique solution, KiP**, i  1,88 .
The change in output from this globally optimal allocation of private capital is computedwith a discrete version of equation (18), weighted by country-specific output shares,

(E-5)

**

dY
Y

  Yi**  Yi 

 i

 Yi
i


dK iP**  Yi.
   C ISiPK iP   Yi
i 
i

36

Appendix Addendum 2.1.B: Computing The Gains From
Capital Reallocations
In Terms Of 2019 (First Quarter) U.S. Dollars
This appendix provides details about the computations of the gains from reallocating capitalfrom rich to poor countries discussed in Addendum 2. All dollar figures are in billions of U.S.
dollars in 2019.1 (the first quarter of 2019). The Renminbi figure is in billions.
1. Increase in world GDP.
$1,047 = 0.012 [Table 7, panel A, column 1] * $87,270 [IMF-WEO]$873 = 0.010 [Table 7, panel A, column 2] * $87,270 [IMF-WEO]$1,309 = 0.015 [Table 7, panel A, column 3] * $87,270 [IMF-WEO]
2. United States’ stimulus program, The American Recovery and Reinvestment Act(ARRA). Outlays occurred over several years. We assume all outlays were made in 2009.
$774 = $663 [CBO] * 1.168 [1 + percentage change in the GDP price deflator from 2009 to
2019.1, FRED-PGDP].
3. China’s stimulus program, We assume all outlays are made in 2008.
$677 = 4,000 Renminbi [CGPY] / 6.9477 [Renimbi/Dollar exchange rate in 2008, FRED-ER] *1.176 [1 + the percentage change in the GDP price deflator from 2008 to 2019.1, FRED-GDP].

LEGEND
CBO: Congressional Budget Office, “Estimated Impact of the American Recovery andReinvestment Act on Employment and Economic Output in 2014,” (February 2015), Table 1.
CGPY: Cong, William Lin, Gao, Haoyu, Ponticelli, Jacopo, and Yang, Xiaoguang, “Credit
Allocation under Economic Stimulus: Evidence from China,” Chicago Booth (November 2018),
p. 1.
FRED-ER: Federal Reserve Economic Data, “China / U.S. Foreign Exchange
Rate (DEXCHUS),” https://fred.stlouisfed.org/series/DEXCHUS#0 .
FRED-PGDP: Federal Reserve Economic Data, “GDP Implicit Price Deflator in UnitedStates (USAGDPDEFAISMEI),” https://fred.stlouisfed.org/series/USAGDPDEFAISMEI .
IMF-WEO: International Monetary Fund, “IMF DataMapper,”https://www.imf.org/external/datamapper/NGDPD@WEO/WEOWORLD .

37

38

Acknowledgements
We would like to acknowledge the helpful comments offered by Olivier Blanchard, Tim Cawley,
Steve Fazzari, Johannes Forkman, Fumio Hayashi, Loukas Karabarbounis, Mark Ludwick,
Robert Kornfeld, Dave Merriman, Paul Pieper, Greg Prunchak, Toshitaka Sekine, and Nao Sudo,and seminar participants at the Einaudi Institute of Economics and Finance. Particular thanks is
owed to Daisuke Ikeda for his careful reading of the entire manuscript. We thank Fernando
Duarte, Jan De Loecker & Jan Eeckhout, and Brent Neiman for kindly providing their data on
the equity premium, global markups, and saving, respectively. Chirinko initiated this research
while serving as a Visiting Scholar at the Institute of Monetary and Economic Studies/Bank ofJapan. He is gratefully for their financial support and for a most pleasant environment in whichto conduct this research. All errors, omissions, and conclusions remain the sole responsibility of
the authors and do not necessarily reflect the views of the organizations with which they areassociated or who have supported this work.

39

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43

Appendix A: Glossary, Variable Definitions, And Sources
Section I discusses data needed to construct the return on private capital analyzed in Sections 2
and 3 of the text. Section II discusses data needed to construct the components of the user costof capital and other variables analyzed in Section 4 of the text.

I. Data For The Return On Private Capital Analyzed In Sections 2 and 3
Notes:
1. Roman letters define variables. Greek letters define econometric parameters andcalibrated parameters or variables.
2. International prices are purchasing power parity prices. “A country’s PPP gives thenumber of local currency units (e.g. euro’s) that are needed to buy a bundle of products
worth one dollar in the US. Dividing the PPP by the nominal exchange rate (also in local
currency units per dollar) then gives the “price level” of that country relative to the US.
A price level of 0.5, for example, indicates that local prices converted to US dollars with
the nominal exchange rate are ½ as high on average as in the United States, as might be
the case for a developing country” (PWT-USER, p. 2, fn. 2).
3. Some of the text below is taken directly from government documents that are in the
public domain.
Roman Letters
N
Capital income share for natural capital. Source: WB-WDI
CISi,t(NY.GDP.TOTL.TR.ZS). Capital income for natural capital is the sum of rents
from oil, natural gas, coal (hard and soft), minerals, and forests. For many
countries, especially the developing countries, the rent share data are not available
for the entire 1970-2014 period. However, data are usually missing at the tails.
The missing data for beginning periods are replaced by the value for the earliest
available period, and the missing data for end periods are replaced by the value
for the most recently available period.
These rents increase GDP irrespective of ownership. The impact on GDP ofgovernment ownership is the same as for government capital discussed in theGentry for K i,t. Private ownership results in an increase in the corporate profits or
proprietors’ income categories in the GDP accounts.
Natural capital is the capitalized value of these rents. (Unimproved land is
excluded from the natural capital stock.)

44

PG
CISi,tCapital income share for private and government (public) capital (also referred toas produced capital) based on an adjustment using flow data. Transformation:PG  NN.
CISi,t CISi,tPG  N
CISi,tCapital income share for private, government, and natural capital.
Transformation: (1  LISi,t) .

EIK

Excluded intangible capital. Source: CHJI
Intangible capital not included in our measures of capital -- designs, financial
innovations, and economic competencies such as advertising, market research,training, and organization capital. Included in our capital data are several types ofintangible capital -- R&D, mineral exploration, computer software and databases,
and entertainment, literary and artistic originals. The richer countries in the CHJI
dataset are the 14 EU+USA countries with Greece and Portugal removed andplaced in the poorer group.

F[.]

Neoclassical production function.

g

Subscript indexing a group of countries. Two groupings are employed in thisstudy based on the four-way World Bank country classification (by income)defined by WB-CLG: high, upper middle, lower middle, low. For the 2018 fiscal
year, high / upper middle / lower middle / low economies are defined as having
Gross National Income (formerly Gross National Product) per capita falling in thefollowing intervals: greater than $12,236 / $12,235 to $3,956 / $3,955 to $1,006 /less than $1,005. These figures are calculated with 2016 data using the method in
WB-ATLAS. See Appendix C for the countries included in each of the groupings.
The first grouping defines the rich group as the high income countries and thepoor group as the sum of the upper middle, lower middle, and low income
countries.
The second grouping defines the rich group as the sum of the high income andupper middle countries and the poor group as the sum of the lower middle andlow income countries.

i

Subscript indexing a country. See Appendix C for a list of the countries,
organized by groups. See the entry above for “g” for further information about
the groups.

45

G
K i,t

Government (public) capital stock, billions of constant 2011 international dollars.
Source: IMF (kgov_rppp). Government capital is the accumulated anddepreciated value of tangible government investments in equipment, structures,and intellectual property. Value added that flows from government capital adds
to GDP in three different ways. Government capital can be operated within agovernment enterprise (which results in an increase in the government enterprisesurplus) or within a private enterprise (which results in an increase in corporate
profits or proprietors’ income; this relationship (Gordon, 1969) was relevant, forexample, in the United States before and during World War II). Additionally,
government capital can be part of general government operations, and its implicit
contribution to value added is the difference between the expenses a business does
not need to incur as a result of the services associated with government capital(e.g., security) less the taxes needed to finance the capital acquisition. The net
amount corresponds to an increase in corporate profits or proprietors’ income in
the GDP accounts.

N
K i,t

Natural capital stock. Rather than computing this stock, this paper utilizes therents from non-reproduced assets -- oil, natural gas, coal (hard and soft), minerals,
and forests. (Unimproved land is excluded from the natural capital stock.)
Natural capital is the capitalized value of these rents, which increase GDP
irrespective of ownership. The impact on GDP of government ownership is theGsame as for government capital discussed in the entry for K i,t. Private ownershipresults in an increase in corporate profits or proprietors’ income in the GDP
accounts.

P
K i,t

Private capital stock, billions of constant 2011 international dollars.
Source: IMF (kpriv_rppp).

P G
Ki,t

Private plus government (public) capital stock, billions of constant 2011
international dollars. Also referred to as the produced capital stock.
P
G
Transformation: K i,t.
 K i,tLi,tLabor input.

LISi,tLabor income share, ratio of labor compensation to GDP all in current national
prices. Source: PWT-9 (labsh).

P
PK i,tPrice index for private capital, 2011 base year. Transformation: equal to Pi,Kt

PG

.

46

PG
PK i,tPrice index for private plus government capital, 2011 base year. Source:
PWT-9 (pl_k). This variable is measured as the price index for new capital goods(i.e., investment).

PYi,tPrice index for output, 2011 base year. Source: PWT-9 (pl_gdpo).

p
ROK i,t

The return on private capital. Transformation: See equation 6 reproduced here:

 CISP  N  G - CISN  *  Y / K P  *  PY / PK P  * 1   * RK G,P  * (1  SE) .
1

G ,P
RK i,tRatio of capital stocks, government relative to private.
G
P
Transformation: K i,t.
/ K i,tSE i,tShare of economic activity in the shadow economy, measured as a percentage ofreported GDP. Source: SBM (Table 2, pp. 454-456). Definition: “The shadow
economy includes all market-based legal production of goods and services thatare deliberately concealed from public authorities for any of the following
reasons: (1) to avoid payment of income, value added or other taxes, (2) to avoid
payment of social security contributions, (3) to avoid having to meet certain legal
labor market standards, such as minimum wages, maximum working hours, safety
standards, etc., and (4) to avoid complying with certain administrative procedures,such as completing statistical questionnaires or other administrative forms” (p.
444). Data for 1970-1998 have been extrapolated by the 1999 value. Data for2008-2014 have been extrapolated by the 2007 value.

t

Subscript indexing calendar time. t = {1970, 2014}.

Yi,t

Output, gross domestic product, billions of constant 2011 international dollars.
Source: IMF (GDP_rppp).

Greek Letterg

Ratio of government ROK’s to private ROK’s for group g. Source: Computedfrom LLP (2012, Table 1). Data are available only as a cross-section. For agiven country, we compute the ratio of the marginal product of government
capital to the marginal product of private capital. These country-specific ratios
are then sorted into poor and rich groups, and averaged: POOR  1.2 andRICH  1.9 . These estimates reflect two economic forces. The general
phenomenon of the underprovision of government goods is consistent with bothratios being greater than one. The greater proportions of government to private

47

G,P
capital in poor countries relative to rich countries (cf. RKi,tin Table 1, panel 4)

POOR

is consistent with  RICH .

LegendCHJI: Corrado, Carol, Haskel, Jonathan, Jona-Lasinio, Cecilia, and Iommi, Massimiliano,“Intangible investment in the EU and US before and since the Great Recession and its
contribution to productivity growth,” EIB 2016/8 (European Investment Bank) (August 2016).
GORDON: Gordon, Robert J., "$45 Billion of U.S. Private Investment Has Been Mislaid,"
American Economic Review 59 (June 1969), 221-238.
IMF: International Monetary Fund, The IMF and Public Investment Management.
http://www.imf.org/external/np/fad/publicinvestment/data/data122216.xlsx
LLP: Lowe, Matt, Papageorgiou, Chris, and Perez-Sebastian, Fidel, “The Public and Private
ROK,” International Monetary Fund (July 2012).
PWT-9: Groningen Growth and Development Centre. Penn World Table, Version 9.
www.ggdc.net/pwt .
PWT-USER: Feenstra, Robert C., Inklaar, Robert, and Timmer, Marcel, “PWT 8.0 – a user
guide.” https://irs.princeton.edu/sites/irs/files/event/uploads/PWT%2080%20%20a%20user%20guide.pdf .
SBM: Schneider, Friedrich , Buehn, Andreas, and Montenegro, Claudio E.,”New Estimates for
the Shadow Economies all over the World,” International Economic Journal 24/4 (December2010), 443-461. DOI: 10.1080/10168737.2010.525974.
WB-ATLAS: World Bank, The World Bank Atlas method – detailed methodology.
https://datahelpdesk.worldbank.org/knowledgebase/articles/378832-what-is-the-world-bankatlas-method .
WB-CLG: World Bank, Country and Lending Groups, Data. https://datahelpdesk.worldbank.org/knowledgebase/articles/906519-world-bank-country-and-lending-groups .
WB-WDI: World Bank, World Development Indicators.
https://databank.worldbank.org/data/source/world-development-indicators .

48

II. Data For The Components Of The User Cost Of Capital
And Other Variables Analyzed in Section 4P
i,t

Depreciation rate for private capital. Source: IMF-FAD. The depreciation rates are only
available for high, middle, and low income countries as a group, and they are available
only for 1960 (Low = 0.0425, Middle = 0.0628, High = 0.0751) and 2015 (Low = 0.0425,
Middle = 0.0628, High = 0.0751). Values between each pair of years are linearlyinterpolated.

t

P
i,t

The equity risk premium for the United States (we assume that the U.S. market represents
the alternative investment opportunity for international investors). Source: DR. The
data are the first principal component from monthly estimates of the equity risk premiumfrom 20 models.
Capital loss on private capital. Transformation: the percentage change in PK P/PY
multiplied by minus one. Unusual volatility in the data led us to truncate the earlier
period from 1986-1990 to 1987-1990 and to replace Mozambique (with an unreasonable
increase in the 1987-1990 value of -17.3) with the average for all Low countries.

i,tMarkup of price over marginal cost. Source: DE. Markups are only available forcontinents.

t

Risk-free real discount rate for the United States (we assume that the U.S. market
represents the alternative investment opportunity for international investors).
Transformation: the 7-Year Constant Maturity Rate For U.S. Treasury Bonds (FRED,
DGS7) less the expected inflation rate seven years into the future. Expected inflation isequated to actual inflation. Inflation is measured by the Consumer Price Index for All
Urban Consumers: All Items in U.S. City Average (FRED, CPIAUCSL). Owing to theunprecedented variation due to the pandemic, expected inflation in 2014 is measured only
over six future years.

 i,tCorporate tax rate: Transformation: ITAX / (GOS – DEPC). Source: UN -- ITAX:
current taxes on income, wealth, etc.; GOS: gross operating surplus; DEPC:
consumption of fixed capital.
The following countries appear in the UN dataset but have been removed because of an
inadequate amount of data: Rich: Bahrain and Kuwait; Upper Middle: Botswana, Costa
Rica, Dominican Republic, Ecuador; Lower Middle: India; Low, Guinea.
Relative to the 88 countries in our study, the UN data are incomplete in both the time andcross-country dimensions. A balanced panel has been constructed as follows. For agiven country, missing values are set equal to the “nearest neighbor,” that is, the i,t in

49

the year closest to the missing value year. The procedure results in a balanced panel of
29 countries.
There are 32 Rich countries in our study. For 21 Rich countries, there is sufficient data tocompute  i,t . For the remaining 11 Rich countries, the i,t 's equal the unweighted
average of the 21 i,t 's . There are 56 Poor countries in our study. There is sufficient
data to compute the i,t 's for 8 countries. The i,t 's for all 56 Poor countries equal theunweighted average of the 8 i,t 's . Thus, all Poor countries have the same i,t 's .
Legend
DE: De Loecker, Jan and Eeckhout, Jan, “Global Market Power,” NBER Working Paper No.
24768 (June 2018). Figure 5; underlying data kindly provided by the authors.
DR: Duarte, Fernando and Rosa, Carlo, “The Equity Risk Premium: A Review of Models,”
FRBNY Economic Policy Review 21/2 (December 2015), 39-57. Chart 1; underlying data kindly
provided by the authors.
FRED: Federal Reserve Economic Data. Published by the Federal Reserve Bank of St. Louis.
https://fred.stlouisfed.org/
IMF-FAD: International Monetary Fund, FAD Investment And Capital Stock Database 2019:
Manual & FAQ - Estimating Public, Private, And PPP Capital Stocks (no date), p. 4.
https://www.imf.org/external/np/fad/publicinvestment/data/info080219.pdf .
UN: United Nations National Accounts, Table 4.3, Non-financial Corporations.
https://unstats.un.org/unsd/nationalaccount/madt.asp .

50Appendix B: Underlying Data for The Baseline ROKP’s In Figure 1
Year
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004

Aggregate
0.142
0.141
0.140
0.143
0.135
0.131
0.131
0.134
0.137
0.127
0.125
0.127
0.127
0.125
0.129
0.131
0.139
0.136
0.140
0.141
0.141
0.147
0.146
0.151
0.160
0.166
0.170
0.177
0.174
0.169
0.167
0.166
0.168
0.174
0.182

Rich
0.118
0.117
0.116
0.116
0.109
0.106
0.109
0.112
0.117
0.115
0.109
0.113
0.112
0.114
0.119
0.121
0.126
0.127
0.132
0.135
0.134
0.134
0.132
0.136
0.143
0.149
0.150
0.149
0.146
0.144
0.141
0.138
0.138
0.141
0.148

Poor
0.200
0.202
0.201
0.212
0.200
0.190
0.186
0.187
0.187
0.156
0.165
0.164
0.164
0.152
0.154
0.156
0.169
0.158
0.160
0.156
0.157
0.179
0.179
0.188
0.202
0.209
0.220
0.245
0.242
0.232
0.233
0.237
0.244
0.255
0.266

Upper
Middle
0.190
0.196
0.201
0.218
0.208
0.196
0.190
0.185
0.180
0.158
0.164
0.157
0.153
0.145
0.154
0.161
0.173
0.161
0.160
0.155
0.158
0.185
0.185
0.200
0.213
0.214
0.224
0.239
0.241
0.238
0.236
0.234
0.234
0.243
0.256

--continued--

Lower
Middle
0.220
0.216
0.200
0.201
0.187
0.179
0.180
0.191
0.203
0.152
0.168
0.180
0.188
0.166
0.153
0.148
0.163
0.151
0.159
0.157
0.154
0.166
0.168
0.167
0.181
0.200
0.211
0.257
0.244
0.221
0.228
0.244
0.263
0.279
0.284

Low
0.174
0.166
0.188
0.166
0.163
0.159
0.158
0.146
0.150
0.155
0.157
0.149
0.137
0.149
0.138
0.112
0.135
0.146
0.138
0.156
0.160
0.202
0.186
0.182
0.189
0.174
0.197
0.209
0.210
0.255
0.204
0.225
0.234
0.241
0.259

51

Appendix B: Underlying Data for The Baseline ROKP’s In Figure 1(continued)
Year
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014

Aggregate
0.190
0.202
0.212
0.205
0.207
0.217
0.222
0.227
0.239
0.245

Rich
0.155
0.163
0.169
0.165
0.159
0.167
0.170
0.173
0.176
0.179

Poor
0.277
0.300
0.317
0.304
0.327
0.340
0.350
0.360
0.394
0.407

Upper
Middle
0.262
0.281
0.298
0.290
0.309
0.325
0.335
0.345
0.369
0.373

Lower
Middle
0.307
0.336
0.354
0.333
0.362
0.368
0.377
0.388
0.443
0.471

Low
0.275
0.292
0.305
0.310
0.340
0.356
0.380
0.392
0.416
0.407

52

Appendix C: List Of 88 Countries

CountryCountry Code
(1)

Australia
Austria
BahamasBahrainBelgium
CanadaChile
China, Hong Kong SAR
CyprusFinlandFranceGermany
Iceland
IrelandIsraelItaly
Japan
KuwaitLuxembourg
Malta
Netherlands
New Zealand
NorwayOman
Republic of Korea
Singapore
SwedenSwitzerland
Trinidad and Tobago
United Kingdom
United States
Uruguay

Income Group(4 Categories;
World Bank)

Rich/Poor(2 Categories)

(3)

(4)

(2)

A. 32 Rich Countries
32 High Income Countries
AUS
High
AUT
High
BHS
High
BHR
High
BEL
High
CAN
High
CHL
High
HKG
High
CYP
High
FIN
High
FRA
High
DEU
High
ISL
High
IRL
High
ISR
High
ITA
High
JPN
High
KWT
High
LUX
High
MLT
High
NLD
High
NZL
High
NOR
High
OMN
High
KOR
High
SGP
High
SWE
High
CHE
High
TTO
High
GBR
High
USA
High
URY
High
-- continued –

Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich
Rich

53

CountryCountry Code(1)

Income Group(4 Categories;
World Bank)

Rich/Poor(2 Categories)

(3)

(4)

(2)

B.1. 56 Poor Countries
23 Upper Middle Income Countries
Argentina
Botswana
BrazilChina
Colombia
Costa Rica
Dominican Republic
EcuadorFiji
Gabon
Iran (Islamic Republic of)Lebanon
Malaysia
Mauritius
MexicoNamibia
PanamaParaguay
Peru
South Africa
SurinameThailandVenezuela

ARG
BWA
BRA
CHN
COL
CRI
DOM
ECU
FJI
GAB
IRN
LBN
MYS
MUS
MEX
NAM
PAN
PRY
PER
ZAF
SUR
THA
VEN

Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle
Upper Middle-- continued --

Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor

54

CountryCountry Code(1)

Income Group(4 Categories;
World Bank)

Rich/Poor(2 Categories)

(3)

(4)

(2)

B.2. 56 Poor Countries
22 Lower Middle Income Countries
Bolivia
Cameroon
Côte d'Ivoire
Egypt
GuatemalaHonduras
India
Indonesia
JordanKenya
Lao People's DR
Lesotho
Mauritania
Mongolia
MoroccoNicaragua
Nigeria
Philippines
Sri Lanka
Sudan (Former)
Swaziland
Tunisia

BOL
CMR
CIV
EGY
GTM
HND
IND
IDN
JOR
KEN
LAO
LSO
MRT
MNG
MAR
NIC
NGA
PHL
LKA
SDN
SWZ
TUN

Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle
Lower Middle-- continued --

Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor

55

CountryCountry Code(1)

Income Group(4 Categories;
World Bank)

Rich/Poor(2 Categories)

(3)

(4)

(2)

B.3. 56 Poor Countries
11 Low Income Countries
Benin
Burkina Faso
Central African Republic
Chad
GuineaMozambique
Niger
RwandaSenegalSierra Leone
U.R. Tanzania: Mainland

BEN
BFA
CAF
TCD
GIN
MOZ
NER
RWA
SEN
SLE
TZA

Low
Low
Low
Low
Low
Low
Low
Low
Low
Low
Low

Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor
Poor

Notes: Countries are excluded in the sample of 88 countries used in this paper if they(i) have produced capital stock (KP+G), labor income share (LIS), or output (Y) data missing
during any part of the 1970-2014 sample period; (ii) are ex-communist countries; or (iii) havenegative values for ROKP during any part of the sample period. Zimbabwe is excluded becauseof its extremely high values for ROKP. The Rich/Poor groups are defined in terms of the fourincome groups taken from the World Bank classification: Rich ={High}, Poor = {Upper Middle,
Lower Middle, Low}.

56

Appendix D: Formula For Decomposing Movements In the ROK P’s
This appendix provides details on the decomposition of ROK P discussed in Section 3.3 andP
Table 3. For a given country, ROKi,tis determined by five multiplicative components detailedin (6):
P
2
3
4
ROK i,t X1i,t * X i,t* X i,t* X i,t* X 5i,t ,(D1)

t=1970, 2014

where



2
P
Xi,t
  Yi,t / Ki,t
,P
X3i,t   PYi,t / PKi,t,
4G,P -1Xi,t 1  i *RKi,t,P  N GN
X1i,t  CISi,t- CISi,t,

X5i,t  (1+SEi,t ).
For a given group of countries defined by income (Aggregate, Rich, Poor, Upper Middle, Lower
P
Middle, Low), the ROK i,t's are aggregated with a fixed set of capital weights ( i ),ROKPt 

(D2)

88



i 1

P
i ROKi,t88

i  X1i,t * Xi,t2 * Xi,t3 * Xi,t4 * Xi,t5 i 1

t=1970, 2014
When we evaluate sub-groups, some of the i 's are set to 0 and the positive i 's renormalized
to sum to 1.0.
We are interested in quantifying how much of the growth rate in ROK P from 1990 to2014 is explained by each of the five components. The ROK P for 1990 can be written as follows
and redefined in terms of gross growth rates,

57

ROKP2014 

(D3a)

(D3b)

(D3c)

2
3
4
5
* Xi,2014* Xi,2014* Xi,2014,
i  X1i,2014 * Xi,2014
i 1

2
3
 X1i,2014

Xi,2014
Xi,2014
1
2
3

X
*
X
*
X
*
i,1990i,1990i,1990 
2
3
88  X1

Xi,1990
Xi,1990i,1990,
ROK P2014   i 
45
Xi,2014 4
Xi,2014 5i 1
Xi,1990 * 5
Xi,1990 4 Xi,1990

X
i,1990

ROKP2014 P(D3d) ROK2014 



88

j

2
2
3
3
 (1  G1)*X1
ii,1990 *(1  Gi )*Xi,1990 *(1  Gi )*Xi,1990 *

,

 i
4
4
5
5

i 1  (1  Gi )*Xi,1990 *(1  Gi )*Xi,1990

88

88

P
,
i  (1  G1i )*(1 Gi2 )*(1  G3i )*(1  Gi4 )*(1  G5i ) *ROK1990
i 1where 1  G i is the gross growth rate in component j between 1990 and 2014,jj/ Xi,1990
1  Gij    Xi,2014
.

(D3e)

j=1,5

Multiplying-out the five gross growth rates on the right-side of (D3d), we obtain thefollowing equation,
88





P
P
ROK P2014  ROK1990
  i G1i  G i2  G i3  G i4  G 5i ROK1990
i 1
88

(D4a)

P
  i Zi ROK1990
,
i 1

(D4b)

ROKP2014
P
ROK1990

88

88

i 1

i 1





 1  i Zi  i G1i  Gi2  G3i  Gi4  G5i ,where Zi represents the set of second-order, third-order, fourth-order, and fifth-order interaction
terms from multiplying-out the five gross growth rates on the right-side of (D3d).
There are two equivalent ways to treat this term and to make (D4b) empirically88

operational. The   i Z i term can be moved to the right-side of (D4b) and allocated to the fivei 1components in proportion to the size of the component’s first-order terms,

58

(D5a)

5 
88
 88
j

Z



Z
 i i    i i   i Gij ,
i 1
j1
i 1
 i 1(D5b)

88
5  88 j   i G ij /    i Gij  ,i 1
j1 i 1885

j  1.

(D5c)

j1

This allocation can be implemented by multiplying all terms in (D4b) by a proportionality
constant so that they sum to

ROK P2014
P
ROK1990

 1.

Alternatively, the adjusted growth rate of ROKP (the left-side of (D4b)) can be defined asfollows,
(D6)

G

ROK P



ROK P2014
P
ROK199088

 1   i Zi ,i 1

and measured by the five terms on the right-side of (D4b). The percentage contribution of any of
the five components to the change in ROKP from 1990 to 2014,  j , is given by the following
equation, the ratio of the weighted-average growth rates (for the countries in a group) for the
given component to the growth rate of ROKP for that group,88 i Gij, j  i 1
P
G ROK

(D7a)

j=1,5

88

(D7b)

j 

 i Giji 188

 i  G1i  Gi2  Gi3  Gi4  Gi5 
i 1

(D7c)

j

Gj

  5

G
j1

,
j

j=1,5

,

j=1,5

59

(D7d)

Gij 

88

i Gij ,

j=1,5

i1

5

(D7e)

 j  1 .
j1

The  j ’s are reported in Table 3 for the five components and six groups.

60

Table 1: Descriptive Statistics
1970-2014

1970-1990

1991-2014

(1)

(2)

(3)

1. Capital Income Share For Produced Capital (CISP+G = CISP+N+G – CISN)
Poor
0.489 [0.487] {0.233}
0.473 [0.472] {0.260}
0.503 [0.500] {0.223}
Rich
0.450 [0.419] {0.254}
0.434 [0.391] {0.281}
0.465 [0.452] {0.241}
Poor / Rich
1.086 [1.161]
1.090 [1.207]
1.082 [1.105]
2. Output/Private Capital Ratio (Y / KP)
Poor
1.168 [0.840] {0.893}
Rich
0.750 [0.543] {0.993}
Poor / Rich
1.558 [1.547]

1.309 [0.795] {1.345}
0.790 [0.491] {1.403}
1.657 [1.618]

1.045 [0.871] {0.586}
0.715 [0.569] {0.689}
1.462 [1.530]

3. Relative Price Of Output To The Price Of Private Capital (PY / PKP)
Poor
0.799 [0.809] {0.208}
0.642 [0.657] {0.363}
0.937 [0.942] {0.170}
Rich
1.002 [0.990] {0.156}
0.910 [0.959] {0.207}
1.081 [1.042] {0.158}
Poor / Rich
0.798 [0.816]
0.705 [0.686]
0.866 [0.904]
4. Ratio Of Capital Stocks, Government Relative To Private (RK G,P)
Poor
1.278 [0.547] {3.000}
1.776 [0.498] {4.188}
0.842 [0.576] {1.060}
Rich
0.557 [0.353] {1.130}
0.599 [0.359] {1.256}
0.521 [0.342] {1.046}
Poor / Rich
2.292 [1.550]
2.964 [1.385]
1.615 [1.684]
5. Share Of Economic Activity In The Shadow Economy (SE)Poor
0.378 [0.380] {0.305}
0.383 [0.384] {0.304}
Rich
0.190 [0.172] {0.446}
0.193 [0.177] {0.445}
Poor / Rich
1.988 [2.203]
1.986 [2.167]

0.373 [0.370] {0.307}
0.187 [0.168] {0.447}
1.990 [2.200]

6. Price Of Output (PY)
Poor
Rich
Poor / Rich

0.334 [0.325] {0.283}
0.656 [0.669] {0.238}
0.509 [0.487]

0.264 [0.248] {0.444}
0.417 [0.431] {0.245}
0.632 [0.575]

0.395 [0.370] {0.267}
0.864 [0.877] {0.247}
0.457 [0.422]

0.526 [0.379] {0.836}
0.469 [0.465] {0.288}
1.120 [0.814]

0.449 [0.422] {0.307}
0.831 [0.857] {0.274}
0.540 [0.492]

7. Price Of Private Capital (PKP)
Poor
Rich
Poor / Rich

0.485 [0.431] {0.516}
0.662 [0.661] {0.254}
0.732 [0.652]

Notes: A glossary and details concerning variable definitions and sources can be found in
Appendix A. The figures are the mean [median] {coefficient of variation = standard deviation /absolute value of the mean}. For a given Xi,t , we first compute the time mean ( Xi ), and thencompute the mean, median, and standard deviation reported in Table 1 based on Xi .

61

Table 2: Return On Private Capital (ROKP), 1970-2014
Income Group 1970-1990

1991-2014

1987-1990% Change

(2)

(3)

(4)

A. Baseline ROKP
Aggregate
0.134
Poor
0.175
Rich
0.118
Poor/Rich
1.484

0.187
0.271
0.153
1.777

0.139
0.158
0.132
1.192

33.90
72.16
15.48

Upper Middle
Lower Middle
Low

0.264
0.285
0.268

0.159
0.156
0.150

66.27
83.58
79.09

B. Restricted ROKP (RKG,P = 0 = SE)
Aggregate
0.135
0.184
Poor
0.141
0.222
Rich
0.132
0.168
Poor/Rich
1.072
1.324

0.142
0.129
0.147
0.880

29.77
72.52
14.59

Upper Middle
Lower Middle
Low

0.215
0.237
0.193

0.128
0.131
0.108

67.72
81.47
79.20

C. Equal Weighted ROKP
Aggregate
0.168
Poor
0.184
Rich
0.139
Poor/Rich
1.327

0.255
0.288
0.197
1.461

0.164
0.172
0.148
1.162

55.66
66.93
32.75

Upper Middle
Lower Middle
Low

0.289
0.289
0.283

0.161
0.169
0.203

79.44
70.97
39.42

D. Trimmed ROKP With Large Countries Removed
Aggregate
0.136
0.210
0.144
Poor
0.175
0.312
0.162
Rich
0.122
0.172
0.137
Poor/Rich
1.435
1.818
1.185

45.89
92.33
25.36

(1)

0.174
0.177
0.153

0.139
0.148
0.110

0.164
0.187
0.220

Upper Middle
0.175
0.293
0.165
78.03
Lower Middle
0.174
0.370
0.155
138.33
Low
0.197
0.250
0.164
52.17
Notes: The entries in columns 1, 2, and 3 are rates of return, except for the “Poor/Rich” rows,
which are ratios of the two entries immediately above. See equation (6) and sections 3.1 and 3.2
for further details. Column 4 is the ratio of column 2 to column 3, less 1 times 100. Entries inPanels A, B, and D are capital weighted.

62

Table 3: Decomposing Movements In The Return On Private Capital (ROK P)
Average (1987-1990) To Average (1991-2014)
Aggregate

Poor

Rich

Upper
MiddleLower
Middle

Low

(1)

(2)

(3)

(4)

(5)

(6)

A. All Five
Components(%)[arithmetic]

100.0[0.046]100.0[0.114]100.0[0.018]100.0[0.106]100.0[0.131]100.0[0.109]CISP+N+G - CISN
Y/KP
RKG,P
PY / PKP

23.6
7.6
18.8
-1.5
51.5

16.2
-2.0
23.5
-1.1
63.4

39.8
28.7
8.4
-2.3
25.4

13.6
-1.4
29.1
-1.2
59.9

20.9
-3.5
14.5
-0.9
69.0

4.4
20.7
4.8
-1.2
71.3

B. Relative Price
Components
PY
PKP

99.1
0.9

63.3
36.7

155.8
-55.8

83.7
16.3

21.8
78.2

37.6
62.4

SE

Table 3 Notes: See Section 3.3 and Appendix D, equation (D7) for the formula decomposing
ROKP growth. All computations based on equation (6), which is composed of five multiplicative
components. For a given component, its contribution to the overall ROK P growth rate iscomputed as its growth rate -- holding the other four components fixed at their starting values –relative to the growth rate in ROKP. Entries are the percentage of the overall ROKP change
explained by a given ROKP component. Entries in brackets are the arithmetic change in ROK P.
The starting and ending values are the average values for 1987-1990 and 1991-2014,
respectively. Note that RKG,P enters inversely. All entries are capital weighted.
Table 4 Notes: See Section 4, equation (11) for the formula determining the calculations. The
entries are the percentage change of the factor between the earlier and later periods. The earlier[later] period is the average value for 1987-1990 [1991-2014]. Panel A entries are the movement
in ROKP. Panel B entries are the percentage of the ROKP movement explained by a given factor.
The UCCP entry is the summation of the entries for the six factors. The second-order and thirdorder terms are the interactions among the additive factors in the UCC formula (11). Panel C
entries are the values of the average value of the factors in [1987-1990] and {1991-2014}. The
penultimate entry is for UCCP constrained to equal the six factors, thus preserving the adding-up
property between UCCP and its six factors. The final entry does not impose this constraint. The
percentage changes are computed by country and then capital weighted to create the groupentries in Table 4.

63

Table 4: Explaining Movements In The Return On Private Capital (ROK P)
Average (1987-1990) To Average (1991-2014)
All

Poor

Rich

Upper
MiddleLower
Middle

Low

(1)

(2)

(3)

(4)

(5)

(6)

35.3

82.0

16.5

68.0

108.8

93.7

B. Contribution Of Factors (% Of Movement In ROK P)
Real Interest Rate (  )
-45.1
-21.6
-92.2
Equity Risk Premium (  )
43.5
20.8
89.1
26.6
8.9
62.0
Depreciation Rate (  P )

-25.2
24.4
10.5

-17.3
16.7
7.2

-15.7
15.1
0.0

A.

ROKP % Change

Capital Loss (  P )

25.8

35.2

6.9

31.5

40.8

-7.4

 +  +  P + P

50.9

43.4

65.8

41.1

47.4

-7.9

Markup (  )Corporate Taxes ((1-  )-1)
Summation (UCCP)

39.4
4.0
94.3

12.0
4.6
60.0

94.3
3.0
163.1

10.3
5.7
57.1

14.0
3.3
64.7

17.1
4.0
13.2

Second-Order Terms
Third-Order Terms

6.9
0.1

5.4
0.2

10.0
-0.1

2.1
0.1

9.5
0.3

-0.9
-0.0

C. Values Of The Factors, [Average (1987-1990)] and {Average (1991-2014)}
Real Interest Rate (  )[0.047][0.047] [0.047][0.047] [0.047]{0.023}{0.023} {0.023}{0.023} {0.023}
Equity Risk Premium (  ) [0.035][0.035] [0.035][0.035] [0.035]{0.059}{0.059} {0.059}{0.059} {0.059}
P[0.073][0.063][0.076][0.063] [0.063]
Depreciation Rate (  ){0.087}{0.073} {0.093}{0.074} {0.074}
P[0.007][0.004][0.008][0.009] [-0.006]
Capital Loss (  ){0.013}{0.033} {0.005}{0.028} {0.041}
PP[0.161][0.149][0.166][0.154] [0.139]
 +  +  +
{0.181}{0.188} {0.179}{0.183} {0.196}
Markup (  )[1.237][1.273] [1.222][1.362] [1.107]{1.401}{1.379} {1.410}{1.435} {1.273}-1
Corporate Taxes ((1-  ) )[1.237][1.163] [1.267][1.162] [1.165]{1.251}{1.206} {1.270}{1.206} {1.207}
User Cost Of Capital[0.246][0.217] [0.257][0.237] [0.180](UCCP) Constrained{0.317}{0.311} {0.320}{0.317} {0.302}
User Cost Of Capital[0.255][0.257] [0.254][0.292] [0.190](UCCP) Unconstrained{0.319}{0.313} {0.321}{0.318} {0.304}
Notes: See the bottom of Table 3.

[0.047]{0.023}[0.035]{0.059}[0.043]{0.043}[0.059]{0.032}[0.183]{0.156}[1.089]{1.264}[1.166]{1.210}[0.226]{0.239}[0.214]{0.248}64

Figure 1: Return On Private Capital (ROKP), 1970-2014
1.B: ROKP (Rich, Poor).1

ROK - P ( K - weighted )
.2
.3
.4

ROK - P ( K - weighted )
.2
.3
.4

.5

.5

1.A: ROKP (Aggregate)

.1

1970
1970

1980

1990
Year

2000

1980

2010

2000

Rich

Poor

2010

1.D: ROKP, Restricted (Rich, Poor).1.1

ROK - P ( K - weighted )
.2
.3
.4

Restricted ROK - P ( K - weighted )
.2
.3
.4

.5

.5

1.C: ROKP, (UM, LM, Low)

1990
Year

1970

1980

1990
Year
UM

2000
LM

2010

1970

1980

Low

2000

Rich

Poor

2010

1.F: ROKP, Trimmed Weights (Rich, Poor).1.1

ROK - P ( Equal weights )
.2
.3
.4

ROK - P ( Trimmed K - weighted )
.2
.3
.4

.5

.5

1.E: ROKP, Equal Weights (Rich, Poor)

1990
Year

1970

1980

1990
Year

2000

Rich

Poor

2010

1970

1980

1990
Year

2000

Rich

Poor

2010

65

Figure 2: Relative Price Of Output (PY/PKP) And
Output Price (PY) And Capital Price (PKP) Deflators, 1970-2014
2.B: PY/PKP (Rich, Poor)

.6

.9

.9

All : PY / PK

PY / PK

1.2

1.2

1.5

1.5

2.A: PY/PKP (Aggregate)

.6

1970
1970

1980

1990
Year

2000

1980

2010

1990
Year

2000

Rich

Poor

1990
Year

2000

2010

2.D: PYPoor/PYRich

0

.4

PY

PY : Poor / Rich
.7

.8

1.1

1.2

2C: PY (Rich, Poor)

1980

1990
Year

2000

Rich

Poor

2010

.3

1970

1970

2010

1970

1980

1990
Year

2000

Rich

Poor

2010

.3

0

.4

PK

PK : Poor / Rich
.7

.8

1.1

2.F: PKP,Poor/PKP,Rich

1.2

2.E: PKP (Rich, Poor)

1980

1970

1980

1990
Year

2000

2010