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Federal Reserve Bank of Chicago
Measuring Productivity Growth in
Asia: Do Market Imperfections
Matter?
John Fernald and Brent Neiman
WP 2003-15
Preliminary
Comments Welcome
Measuring Productivity Growth in Asia: Do Market Imperfections Matter?
John Fernald
Federal Reserve Bank of Chicago
Brent Neiman
Harvard University
October 7, 2003
Abstract: Recent research reports contradictory estimates of productivity growth for the newly
industrialized economies (NIEs) of Asia. In particular, estimates using real factor prices find
relatively rapid TFP growth; estimates using quantities of inputs and output find relatively low TFP
growth. The difference is particularly notable for Singapore, where the difference is about 2-1/4
percentage-points per year. We show that about 2/3 of that difference reflects differences in
estimated capital payments. We argue that these differences reflect economically interesting
imperfections in output and capital markets, including sizeable economic profits in Singapore and
government-directed credit. We derive a measure of technology growth, corrected for the
imperfections that we quantify.
Please address correspondence to John Fernald at fernald@frbchi.org. We thank Jonathan
Anderson, Susanto Basu, Jeff Campbell, Chang-Tai Hsieh, Boyan Jovanovic, Alwyn Young, and
seminar participants at the Federal Reserve Board and Federal Reserve Bank of Chicago for helpful
discussions or comments. The views are our own and do not necessarily reflect those of anyone else
affiliated with the Federal Reserve System.
1
I. Introduction
In empirical assessments of economic growth, the experience of Asia’s newly industrialized
economies (NIEs) looms large. Singapore, Hong Kong, Korea, and Taiwan grew at rates of 8 or 9 percent
for decades, thereby pulling themselves in rankings of economies from the among the poorest to
(particularly in the case of Singapore and Hong Kong) among the richest.
Controversy surrounds the sources of growth in the NIEs. Did total factor productivity (TFP) growth
(presumably capturing, to a large extent, the process of technology transfer) play an important role? Or did
these economies grow almost exclusively through factor accumulation?
In a series of extraordinarily influential and widely cited papers, Young (1992, 1994, 1995)
overturned the notion that TFP growth played an important role. He undertook careful ‘primal’ (quantitybased) growth accounting and established the new conventional wisdom that the NIEs grew almost
exclusively through factor accumulation with only a modest contribution from TFP.1 This new
conventional wisdom, however, has not gone unchallenged. In particular, Hsieh (2002) reexamines the
issue from the point of view of dual (price-based) growth accounting. With internally consistent data, the
primal and the dual measures of TFP are necessarily equal. But with independent data on quantities and
factor prices, the two measures can and, in the case of these economies, do differ. Hsieh finds that in the
NIEs, TFP grew reasonably quickly.
This controversy has generated considerable heat and smoke. For Singapore, in particular, Hsieh
attributes the sizeable differences to errors in the national accounts data used by Young. Young (1998), in
turn, responding to an early version of Hsieh’s paper, cites a long list of what he sees as errors in Hsieh’s
implementation of the dual.
In this paper, we seek to shed further light on Asia’s growth experience. We reinterpret the
primal/dual results as complementary rather than competing. In particular, two “facts” lie at the heart of
the controversy over Asian productivity growth. First, primal TFP growth—particularly in Singapore—
1
The influence extends well beyond the academic literature. For example, in an investment research letter, Anderson
(2003) says, “Ten years ago, one of the most famous economics series in Asian history—as set of papers that
generated a storm of controversy and are credited in part with fomenting the Asian crisis—was published by Alwyn
Young…”
2
was abysmal. Indeed, the rapid increases in capital–output ratios in the national accounts imply rapid
declines in returns to capital. But second, reasonable cost-of-capital measures show little decline.
We show that heterogeneity in the cost-of-capital—consistent with Asian governments’ efforts to
direct growth and resources—as well as large economic profits, can reconcile the differences. We provide
a range of evidence that in Singapore, where the difference is most pronounced, these aspects do indeed
play an important role in reconciling the two results.
In our benchmark case, we assume that the national accounts and Young’s quantity-based growth
accounting were done completely correctly. We also assume that Hsieh’s factor-price based growth
accounting is completely correct except for observing factor payments for only a part of the economy—for
example, he misses heterogeneity in the cost-of-capital coming from unobservable preferential tax rates
and subsidies. The primal-dual difference then reflects economically interesting imperfections in output,
labor, and capital markets including heterogeneity in the user cost of capital and sizeable economic profits.
At the same time, these distortions imply that standard TFP growth does not measure technology.
Under these assumptions, we conclude that Young was, in part, too optimistic: He overstates
technological progress in the favored sector of Singapore’s economy. We estimate that in the favored
sector, output grew nearly 10 percent per year for two decades, with negative TFP growth. However, this
does not mean that Singapore had no worthwhile investments. In particular, under our interpretation, the
relatively unfavored sector had slower output growth, about 6 percent per year, despite rapid TFP growth
of around 2-1/2 percent per year.
Our interpretation of the divergent primal-dual results seems more plausible than the alternatives—
that the National Accounts grossly overstate investment or that major computational errors render Hsieh’s
calculations irrelevant. Young (1998) thoroughly rebuts concerns about the national accounts (at least
relative to concerns about the reliability of factor-price measures).2 But dismissing Hsieh’s dual results as
2
Moreover, given the national accounts identity, reducing real investment growth means adjusting real output and
income growth downwards, or adjusting other expenditure growth upwards. How the mismeasurement shows up
matters. For example, suppose nominal GDP (in principle, equaling factor payments and value added) is measured
accurately but real GDP is overestimated by a growing amount. Then dual TFP, measured by growth in real factor
prices (deflated by the GDP deflator) are biased upwards. This case would undo Hsieh’s results, even if investment
were overestimated. Given Young’s defense of the national accounts, though, we do not make this argument. Barro
(1999) also discusses possible interpretations of the primal-dual discrepancy for the national accounts.
3
error-laden throws out the important information they contain. Young argues effectively that Hsieh’s
measurements for the cost of capital are unlikely to capture the entire economy and ignore key tax benefits.
We agree. In our interpretation, these measurement difficulties are indeed central—but the pattern of
mismeasurement is economically interesting. The market distortions (such as market power, favorable
access to capital, and tax preferences)—which, in many cases, grew over time—favored parts of the
economy but not others. We interpret Hsieh as coming close to measuring technology growth in the nonfavored sector (it’s not exact, though, since factor-shares need to be adjusted). In sum, our explanation is
largely consistent with Young’s, except that we view the dual growth accounting results as informative
about a large chunk of the economy.
Section II shows how the primal and dual could yield different results with market distortions.
Section III discusses anecdotal evidence for Singapore (where the gap is largest) suggesting the plausibility
that these distortions played an important role. Section IV calibrates our identities with results from
Young and Hsieh, seeking to quantify the importance of these distortions for the dual-primal discrepancy.
Our results indicate that profits in Singapore play a substantial role and contribute approximately half of
the total gap. Section V takes these results—which largely involve manipulating identities—and interprets
them in terms of technology in the overall economy, the favored sector, and the unfavored sector. Section
VI discusses why these effects are more important in Singapore than elsewhere. We then conclude.
II. Primal and Dual Measures of Productivity
This section defines our terms (primal and dual TFP) and shows that these measures ought to be
similar, if not identical. But in practice, they are substantially different. We present a simple
decomposition to clarify the role of labor versus capital in explaining the differences—since both play a
role. Finally, we show conditions under which the two measures might differ, for economically interesting
reasons, in an economy with substantial distortions.
A.
Identities
In the national accounts, real output Y equals real factor payments to capital and labor:
Y = RK + WL .
(1)
4
R is the real rate of payments to capital, K is capital input, W is the real wage, and L is labor input. R and
W are deflated by the GDP deflator. Implied payments to capital RK include any economic profits.
For any variable J, define $j as the percent change dJ/J . Define sL to be the share of labor in output.
The share of payments to capital, taken as a residual, is then (1-sL). Totally differentiating (1):
yˆ = sL lˆ + (1 − sL )kˆ + [ sL wˆ + (1 − sL )rˆ ]
(2)
TFP, aka the Solow residual, is defined as output growth in excess of share-weighted input growth:
TFPPrimal ≡ yˆ − sLlˆ + (1 − sL )kˆ . (Later, we assess whether TFP, so defined, measures technology.)
Rearranging equation (2), one finds that this primal measure of TFP necessarily equals a “dual” (i.e., price)
measure that is a weighted average of the growth in real factor prices.:
TFPPrimal ≡ yˆ − sLlˆ + (1 − sL )kˆ = [ sL wˆ + (1 − sL )rˆ ] ≡ TFPDual
(3)
The second equality shows that in data satisfying the accounting identity (1), the primal and the dual
approaches necessarily give the same result. However, there are independent data on factor prices. Hence,
if one is skeptical of the national accounts—as Hsieh is—dual TFP provides an alternative.
Implementing the dual requires estimating a Hall-Jorgenson (1963) cost of capital, C. 3 As we discuss
below, different investors may have different costs of capital. (For example, government capital may have
a different shadow value than private capital, or some borrowers may have preferred access to bank loans.)
In principle, we need an appropriate weighted average of these factor costs.
Given practical difficulties, the “dual” cost of capital—which we call CDual —may differ from the
national accounts’ rate of payments to capital, R. In principle, wage data are easier to observe.
Nevertheless, in practice Young and Hsieh use slightly different data sources and methods, so their
measures of wages as well as capital-costs differ. Then the dual Solow residual becomes:
TFPDual ≡ sL wˆ Dual + (1 − sL ) cˆDual
3
One common cost-of-capital specification (see, for example, Hall 1990) is C = ( ρ + δ ) T , where
ρ is the required real rate of return, δ is the
is the corporate tax rate, d is depreciation allowances, and itc is the investment tax credit.
T = (1 − τd − itc) (1 − τ ) measures various tax adjustments.
depreciation rate,
τ
(4)
5
Not surprisingly, the primal measure differs from the dual if either wage growth or capital-payment
growth differs between them. This relationship is:
TFPDual − TFPPrimal = sL ( wˆ Dual − wˆ ) + (1 − sL )( cˆDual − rˆ ) .
(5)
Table 2 provides this decomposition for the NIEs, using data from Young (1995, 1998) and Hsieh
(2002). Hsieh provides several estimates of the cost of capital for each country. These measures generally
tell the same story, so Table 2 averages them. Table 3 takes a closer look at Singapore, where results are
most different, for each cost-of-capital estimate. Young does not explicitly report factor prices, but we
back them out from his data on factor shares and quantity growth. (For example, sL = wL Y , implying
that w$ = s$L + y$ − l$ ).4 Lines 1 to 3 show the individual items that appear on the right hand side of
equation (5), while Line 4a and 4b show the primal and dual measures of TFP growth. Lines 5 and 6,
respectively, show the contribution of wages and capital payments to the primal-dual difference.
This decomposition clarifies whether the discrepancies arise primarily from the labor/wage data or
the capital/rental data. Tables 1 and 2 show that the primal and dual differ substantially only in Singapore
and Taiwan. In both cases, wages play an important role; indeed, wages account for the bulk of the
difference in Taiwan. Hsieh (2002) has little discussion of the role of wages. Young (1998, Section V)
expresses concerns with Hsieh’s wage data but does not quantify their importance. Table 2 (line 5) makes
clear that for Singapore and Taiwan, the wage differences are, in fact, quantitatively important. However,
we view the wage discrepancies as a pure measurement issue.
In the rest of the paper, we focus on economic or conceptual issues raised by capital’s contribution on
Line 6. In Singapore, especially, capital payments account for most (1.6 percentage points) of the primaldual gap. Hsieh suggests that the national accounts data overstate the cost-of-capital decline. In response,
Young (1998) asserts that Hsieh’s methods for estimating the cost-of-capital ĉDual are flawed.5 We now
present an alternative interpretation.
4
Young (1998, p.13) discusses this differentiation. Note that with multiple types of labor (e.g., with different
educational levels), labor input is a composition-corrected index. The corresponding growth in wages is the difference
between the growth rate of nominal payments to labor and the growth rate of composition-corrected labor input.
5
For example, Young (1998, page 13) argues that Hsieh conflates the real rental rate (i.e., the cost of capital, which
includes the real interest rate, depreciation, and tax adjustments) and “real capital returns” (i.e. the real interest rate).
Hsieh (2002), however, addresses some of Young’s major concerns.
6
B. Role of directed credit/capital market imperfections/profits:
Suppose the national accounts and hence r$ are measured appropriately on the primal side. Also
suppose that a researcher does a careful job constructing the cost-of-capital measure ĉDual from available
data. r$ and ĉDual may nevertheless differ from one another, for at least two economically interesting
reasons. First, different borrowers may face different costs of capital—perhaps reflecting government
intervention such as directed credit—which may grow at different rates. Second, even if the cost of capital
does not change, the rate of pure economic profits—which are included in r$ —may change.
Suppose the economy has one type of capital and two firms, with different costs of capital, CU and CF
(ultimately, though for now without loss of generality, representing “unfavored” and “favored” sectors). 6
Payments to capital RK (calculated as a residual from (1)) include “required” payments—which depend on
the costs of capital—and any economic profits. The economy’s implied rate of payments to capital R is
total “payments” to capital divided by the capital stock. If the aggregate capital stock is K = KU + K F
and total economic profits are Π = Π1 + Π 2 , then:
R≡
CU KU + CF K F + ΠU + Π F KU
=
KU + K F
K
KF
CU + K
Π
CF + K .
(6)
The implicit rate of payments to capital in (6) has two parts. The first is a capital-share-weighted
average of the two costs of capital CU and CF. Hence, the capital-payment rate R can change if the firms’
costs of capital change, or if the weights change. The second is the ratio of true economic profits to the
capital stock. If profits fall relative to capital, then R can fall even if the costs of capital are unchanged.
In practice, it is difficult both to measure costs of capital for all firms and to measure pure economic
profits—especially in countries where the government creates heterogeneous costs of capital through
privately negotiated, or firm-specific, tax treatment or other financing advantages. Suppose we measure
dual TFP growth using just the first firm’s cost-of-capital estimate, so CDual=CU. From equation (6), this
6
The extension to multiple types of capital is straightforward. Each type of capital has a different depreciation rate
and, possibly, different tax treatment. The overall growth in the cost of capital is a weighted average of the different
cost-of-capital growth rates. Perfect capital markets would imply that different borrowers have the same cost of capital
for a given type of capital. This extension is not central to our main points.
7
measure may differ from the aggregate accounting measure R for three reasons: (i) CU differs from CF; (ii)
the weights of capital K i K in the two industries change; (iii) the profits-capital ratio changes.
Clearly, these three reasons may also cause the relative growth rate of aggregate capital payments r$ to
differ from the observed (unfavored) cost of capital cˆU . From equation (5), these relative growth rates,
along with those of payments to labor, determine the relationship between the primal and dual measures of
productivity. To see this relationship, take the total differential of equation (6) and divide through by RK.
Substituting into equation (5) and ignoring the wage term, one obtains a relatively intuitive equation:
TFPDual − TFPPr imal = (1 − sL )(cˆU − rˆ)
= sK (cˆU − cˆ) + sΠ cˆU + kˆ − πˆ
(7)
where the profit share is sΠ = Π Y , the average cost of capital is C = ( CU KU + CF K F ) K , and the
‘true’ capital share in costs is sK ≡ CK Y = 1 − sL − sΠ .
The two terms in Equation (7) capture important factors for understanding why the dual might exceed
the primal. The first term reflects the “representativeness” of cˆU : does its observed growth rate differ from
the unobserved overall average? The second term reflects economic profits, since the national accounting
measure R includes them. Note that we can rewrite the profits term as:
(
)
(
sΠ cˆU + kˆ − πˆ = sΠ cˆU + (kˆ − yˆ ) − (πˆ − yˆ )
)
(8)
Suppose there are true economic profits, so sΠ is non-zero. For unchanged cˆU , the profits term is
likely to be positive if the profit rate falls over time, if the capital-output ratio rises, or both.
With free factor mobility and competitive output markets, these terms disappear: rates of return are
equalized, and there are no profits. Indeed, Fernald and Ramnath (2003) find that in the U.S., the primal
and the dual give quite similar results. But the vast literature on the Asian crisis makes clear that Asian
economies did not have competitive factor and output markets. Hsieh uses a range of real interest rates to
construct the cost of capital. But these measures are unlikely to capture much of the capital-costheterogeneity, since many of the differences are not easily observed. For example, governments
intentionally directed credit to particular firms through access to low interest government loans or through
pressure on banks to lend to favored firms. Even a cursory reading of Young (1992, 1995, 1998) makes
8
clear that tax rates and investment incentives often varied across firms in ways that are difficult to control
for in any systematic way. Direct government investment was often very high, with an unobservable level
and growth rate of the shadow value of that capital.
Do capital and product market interventions/distortions necessarily lead the dual to exceed the
primal? Clearly no. In steady state, for example, the terms in equation (7) should equal zero. If the profit
rate and capital-output ratio are constant, then the profits term is zero. And even if the level of CU and CF
differ, their steady state growth rates will be the same (in most models, equaling zero), so the capital-costheterogeneity term is also zero.
During the transition to steady state, the two terms may, but need not, be positive. For example,
state-preferred firms may have market power but not earn profits, so the second term would disappear.
And even if CU and CF differ, their rates of change may be similar. In part, this will depend on the
institutional structure of the economy and the way in which preferences were extended. In particular, these
terms appear substantial in Singapore but not in Korea, even though Korea also intervened heavily in
markets. To better understand the reasons, we now discuss the Singaporean case in greater detail. We
return to Korea and the other NIEs in Section VI.
III. Singapore: Large Profits and Favoritism
Anecdotal evidence strongly suggests that economic profits were large and the cost of capital
heterogeneous in Singapore. Singapore’s transition from a poor country in the 1960s to a rich, modern
economy involved considerable direct and indirect government participation in the economy as well as vast
inflows of FDI. Firms in “preferred” or “favored” sectors appeared to earn large (though diminishing)
profits, reflecting market power and favorable factor prices for so-called government linked corporations
(GLCs), statutory boards (SBs), and the multinationals that directly invested in Singapore. Indeed,
favoritism appears to have increased over time, suggesting that the (unobserved) preferred cost of capital
fell more rapidly than that of the (observed) unpreferred sector. These profit and cost-of-capital effects,
capturing the two terms in equation 7, plausibly account for the primal-dual gap.
9
A. Large Profit Share
GLCs, companies at least 20-percent government-owned, contributed as much as 25 percent of
Singapore’s GDP by the late 1980’s.7 The closely-related SBs have mandates such as regulating industries
and infrastructure, providing education and other public services, and managing state utility assets.
Examples of SBs include the Telecom board, the Port of Singapore Authority, and the Housing and
Development Board. As U.S. Embassy (2001) notes, “some analysts assert that the presence of top civil
servants as directors on the boards of GLCs and statutory boards … constitutes an unfair advantage.”
Many SBs and GLCs appeared to earn huge profits by capitalizing on entry barriers. Some barriers,
e.g., in telecom, reflected traditional “natural monopoly” considerations. Others, though, reflected
government entry restrictions. For example, the Port of Singapore Authority (PSA) controls a valuable
public asset with no competition. The Economist (2001) reports that the port had profit margins as high as
40 percent. Even with a large customer, Maersk, “begging PSA for years for permission to run its own
terminal in Singapore … The Singaporeans, determined to keep control, rebuffed Maersk.” Similarly,
Seaward (1985) reports that a GLC, the National Iron and Steel Mills (NISM), controlled 90 percent of the
steel market. He notes, “It is no secret that NISM benefited from strong government protection in the early
1960s … which essentially gave the company a monopoly over the market.” Singapore Airlines, in an
industry where the government controls access to airport gates, had decades of accounting profitability and
high relative return on equity to shareholders (presumably indicating economic profits). EuroMoney
(1984) estimates that the (accounting) profits of GLCs and SBs alone equaled about one-third of GDP.8
Over time, profits seem to have declined. Recently, some notable GLCs and SBs, including
Singapore Airlines, have encountered serious problems and have not been profitable. But over the decades
studied by Hsieh and Young (primarily the 70’s and 80’s), stories abound of high profits by these firms.
Singapore’s active enticement of FDI also led to large profits. From 1972 to 1990, FDI amounted to
an average of almost ¼ of gross fixed capital formation (IFS). Singapore negotiated a wide range of
incentives (not available to domestic firms) to entice such extraordinary inflows. Negotiated terms are not
7
Most of the GDP contribution comes from GLCs more than half government-owned. Late 1980s share is from IMF
(1995). Since the 1980s, some SBs have been privatized and are now GLCs. Department of Statistics (2001) argues,
however, that by the mid-90s, the GLC share of GDP was only a bit over 10 percent.
10
public, so it is hard to quantify the exact measures used. But even if foreign companies faced competition
in export markets, the measures likely reduced production costs and allowed for economic profits. As an
article entitled “A juicier carrot for foreign investors ” (Senkuttuvan, 1975) notes: “Shrewd industrialists
who invest when times are not so good can receive enormous incentives from the Singapore Government.”
Incentives ranged from tax and depreciation benefits to training grants to beneficial export treatment.9
Further, anecdotal evidence suggests that beneficial tax treatment, such as tax holidays for
technology upgrades granted by the Economic Development Board, resulted in multinationals adjusting
internal transfer pricing to realize high profits in low-tax Singapore.10 In sum, given these statistical
differentials and anecdotal evidence, it seems logical and consistent to posit that foreign companies, like
the government’s “favored” domestic firms, received “special” treatment leading to large economic profits.
B. Heterogeneous Cost of Capital
SBs, GLCs, and multinationals also help explain the dual-primal gap because their cost of capital
grew at different rates from the rest of the economy. They received “special treatment” including
artificially high credit worthiness (reflecting the assumption that the government would bail out bad
performers)11, tax relief, political connections, or direct government financing. Further, these benefits
seemed to grow over time, so the favored cost of capital fell faster than the non-favored one.
According to Burton (1995), GLCs generally “enjoy a competitive advantage in terms of financing.
Their costs of capital are usually lower than for companies in the private sector ….” U.S. Embassy (2001)
argues that this seems to be “because they enjoy an implicit Government guarantee of repayment. In the
early years of economic development, GLCs were given preferential rates by DBS Bank, itself a GLC.”
Other benefits took the form of tax relief. For example, the Economic Expansion Initiatives Act reduced
taxes from 40% to 4% on certain export-intensive industries. “Pioneer” firms, designated by the
8
We obtained this citation from Young (1992).
Singapore, A Case Study in Rapid Development, IMF Occasional paper, February, 1995.
10
For multinationals, financing presumably occurs at a world rate. As such, the “preferential” treatment would be
through tax or other benefits as opposed to access to capital. Regardless, these benefits would drive the
multinational’s cost of capital below its level elsewhere.
11
This holds particularly true for GLCs, like the utility Pan-Electric. Far Eastern Economic Review (1995), in an
article titled, “A politic helping hand: Creditors offer Singapore’s debt-plagued Pan-Electric a long lifeline” states that
“Bankers and brokers regard Pan-Electric as too important a company to be allowed to go under.”
9
11
government, received major tax relief and in 1991 accounted for nearly 2/3 of manufacturing value added
and 4/5 of value added in chemicals, electronics, and instruments (IMF 1995).
These sectors had very heavy GLC and foreign involvement, so this program acted to reduce the cost
of capital for a favored subset of the economy. Indeed, as discussed in Young (1998), the tax breaks to
these companies increased over time. Hsieh (2002) notes, in response, that the overall average effective tax
rate increased. Together, these observations suggest that even while the effective tax rate for favored firms
was falling, the rate for unfavored firms rose—thus accounting for rising overall tax collection with a
widening gap in the cost of capital.
Foreign companies were also well suited to take advantage of Singapore’s official, formal tax breaks.
Young [1992] describes such tax incentives as neutral in principal, but biased toward foreign investment in
practice. Bowring (1995) claims that “Government critics do not find it difficult to show that the tax …
systems have not only directed cash flow to officially decreed ends, but have in effect also discriminated in
favour of state and foreign enterprises.” Preferential treatment extended beyond tax breaks. Young [1992]
cites claims of academics and popular writers that “the Singaporean government … subsidize[s] the return
to foreign capital (beyond the tax incentives) by, for example, providing preferential loans, leasing land
and buildings at reduced cost, shouldering labor-training costs, and assuming large equity positions.”
In addition to some of the more subtle subsidization methods above, many of these government
linked and foreign organizations were financed by direct government loans. As described in more depth by
Young [1992], the government was able to sustain such outflows by borrowing from the Central Provident
Fund (CPF), a public saving fund akin to Social Security in the U.S. The government required increasing
contributions to the CPF though did not offer reasonable returns directly to the workers. 12 Indeed, other
than for medical costs and housing investments, it was quite difficult to access the fund at all! The
government relied heavily on the fund, though, and as Young [1992] describes, some 95% of the fund was
invested in government shares. In essence, the CPF served as a very large tax on private savings to
subsidize the cost of capital of certain firms – namely SBs, GLCs, and multinationals. This increasing
12
As detailed by Young, the [employee/employer match] contribution increased from 5%/5% to 15%/15% to
25%/25% over the time period studied. IMF(1995, p45) documents the below-market returns to CPF investments.
12
subsidization, regardless of its form, resulted in an increasing wedge between the “favored” and
“unfavored” costs of capital.
IV. Measuring the Effects of Economic Distortions
Singapore was not alone in intervening heavily in markets.13 We now assess the empirical
importance of this intervention for the primal-dual difference, in terms of equation (7). Combining
capital’s contribution to the dual-primal gap (from Table 3) with an estimate of the profits term, we back
out the contribution of the cost-of-capital-heterogeneity term.
A. Accounting for the Dual-Primal Gap
We begin by calibrating the role of profits. Section III argued qualitatively that in Singapore,
government policy led to market power, low average factor prices, and large profits. Suppose market
power is the only imperfection, with no heterogeneity in capital costs. The right-hand side of equation (7)
then reduces to sΠ [ sˆK − sˆΠ ] . This expression equals zero if profits are zero or if the “true” capital share,
sˆK , grows at the same rate as the profit share, ŝΠ . Given a relatively constant labor share, however, this
condition becomes sˆK = sˆΠ = sˆL = 0 . Hsieh (2002, p.505) thinks it unlikely that profits drive much wedge
between the primal and dual. But his argument requires that either the level or the growth rate of the profit
share be small. We argue below that both conditions are violated in Singapore, although not elsewhere.
How large are profits? Singapore’s strikingly low labor share—about ½—matches qualitative stories
of large pure profits. Labor’s share is often low in developing countries because self-employment income
(e.g., from farming) is allocated to capital not labor. This story does not explain Singapore: The
agricultural sector is tiny and, besides, Young (1995) carefully allocated proprietors’ income.14
13
This was widely noted even before the Asian crisis. See, for example, the World Bank (1993); Leipziger and
Thomas (1994), and the discussions of Singapore in Young (1992, 1995, and 1998).
14
Gollin (2002) reports that after correctly allocating proprietors’ income, labor shares are almost always in the range
of 0.65 to 0.8. He cites Young (1995) as exemplifying the “best approach” to estimating factor shares (Gollin, p.
467). If anything, though, Young overstates labor’s share, implying that we may understate profits. First, Young
(2000) suggests that he overcompensated for proprietors’ income, since it appears that national accountants already
attribute some proprietors’ income to labor, in contravention of the U.N. System of National Accounts. Second,
Young (1995, footnote 8) also implies that, if anything, he has overstated labor’s share, since he explicitly ignores a
labor share series from Singapore Statistics that has an even lower labor share than the input-output series he used.
13
Labor’s share could also be abnormally low because of the country’s mix of industries. For example,
Sarel (1997) reports that in financial services, labor’s share (averaged across countries for which industry
data are available) is about 0.4. We estimate “true” factor shares in cost (as opposed to output or revenue)
by combining Sarel’s data on industry capital-cost shares with data on the industry mix of output.15 Given
these estimated cost shares, we can back out the implied profit share, sΠ . In particular, if capital’s share
in total cost is α and labor’s share is (1 − α ) , then the profit rate sΠ equals ( (1 − sL ) − α ) (1 − α ) .
Table 4 shows our estimates of cost shares and the profit rate for the NIEs. Line 1 shows Young’s
estimated ‘residual’ capital share, (1-sL); Line 2 shows the estimate using Sarel’s approach, α . Line 3 is
the implied capital share in revenues and line 4 is the estimated profit share. Singapore is the only country
with substantial profits. Labor’s share is about ½ but our estimated capital cost share is only a bit above
1/3 (line 2). When we decompose (1 − sL ) = sK + sΠ , capital’s output share sK equals about ¼ (line 3)
and the profit share sΠ is also about ¼ (line 4). (Note that with a profit share of 1/4, costs (i.e., sK+ sL)
account for 3/4 of output. Labor payments are then 2/3 of cost, and capital payments are 1/3 of cost.)
Although the anecdotal evidence supports the notion of large profits, pure economic profits
amounting to ¼ of GDP clearly raises questions. We used two alternative back-of-the-envelope estimates
to confirm its magnitude. First, we follow Hall (1990) and Rotemberg and Woodford (1995), who provide
careful, indirect arguments that U.S. pure profits are small. In particular, we use evidence on the capitaloutput ratio to back out the implied rate of return to capital consistent Singapore’s measured output shares.
From 1985 through 1990, the ratio of tangible capital to GDP averaged 2.89; the investment-output
ratio was 0.38 (both ratios were relatively stable over the sample period). 16 Over the 1970-90 period,
investment growth averaged 8.5 percent per year. Thus, the implied average rate of depreciation was about
5 percent (since, with a single type of capital, I K = g + δ ), equal to the U.S. rate reported by Rotemberg
15
We obtained one-digit GDP-by-industry data from CEIC Asia Database (downloaded Feb. 1999). Sarel estimates
industry capital and labor shares from a large sample of (primarily developed) countries. We assume constant factor
shares within an industry. (Jones (2003) argues that factor shares are not constant; but as long as deviations from strict
Cobb-Douglas are small relative to mean differences across industries, this won’t matter much.)
16
We used constant S$1985 figures on investment, capital stocks, and GDP. Numbers would probably be similar
with disaggregated nominal values, which would better allow for variation in the relative investment prices.
14
and Woodford. Taking payments to capital (including profits) as an implicit capital-payment rate r plus
the depreciation rate implies that: (r + δ ) ( K Y ) = sK + sΠ = 0.484 .
The implicit r equals about 13 percent—substantially in excess of the corresponding U.S. rate of 6
percent. Rotemberg and Woodford argue that 6 percent approximately equals the U.S. required return to
capital, including an equity premium; hence, their estimate implies pure profits are small. If, because of
capital mobility, Singapore’s required rate of return was similar to the U.S. rate, then the ‘excess’ return of
7 percent represents profits. Multiplying that 7 percent excess return by the capital-output ratio again
suggests a rate of profit in Singapore that was plausibly around 20 percent.
As a second alternative estimate, we took Hsieh’s estimates of the cost of capital C literally, while
assuming the national accounts measure investment properly. In particular, we estimate required payments
to capital by multiplying Hsieh’s cost-of-capital estimates by the estimated value of capital stock.17 This
method assumes that all of the dual-primal gap comes from the profit term of equation (7). The implied
profit shares, though variable, are frequently in the 15-20% range and generally show a downward trend.18
Although such large pure profits are clearly unusual, studies for other countries do sometimes suggest
that product market distortions (e.g., entry restrictions) lead to substantial economic rents. For example,
Blanchard and Giavazzi (2002) discuss the sharp decline in labor’s share in income in many European
economies between the early 1980s and the mid-1990s. Consider Italy, where labor’s share fell from about
78 percent to only about 60 percent (their Figure 5). They attribute this decline to a reduction in labor’s
ability to capture the rents arising from product market restrictions. For such a large shift in rents to occur,
the rents themselves must be large—e.g., in the case of Italy, on the order of 15 to 20 percent of GDP.
17
We assume that there is only one cost of capital C. We downloaded Hsieh’s data for C (from
http://www.wws.princeton.edu/~chsieh/data.html) and backed out the profit rate as sΠ = (1 − sL ) − C ⋅ (Y
K).
Hsieh argues that the national accounts overstate investment and, hence, implies that the capital-output ratio is
overstated. A lower capital-output ratio would imply even larger profits. Alternatively, if there are no profits and
Singapore overstates investment, then either: (i) Hsieh’s cost-of-capital estimates are too low (so growth rates are
suspect); or (ii) the true capital-output ratio is actually much higher than implied by the national accounts.
18
This method, which assumes that profits explain the entire gap, produces a lower average profit share than that
shown in Table 4, where we considered an additional contribution from heterogeneous costs of capital. This results
because the high-calculated level was accompanied by lower profit-share growth whereas the lower level was coupled
with higher profit-share growth. Both profit level and growth rate are important in the third term of equation (7).
15
What happened to Singapore’s profit share over time? We estimated this time series using the GDPby-industry data. Consistent with government subsidies for capital-intensive industries, we estimate that
the “true” capital share in revenue, sK (estimated with Sarel’s industry shares) grew over time. A rising
true capital-cost share combined with a relatively constant labor share implies that the profit share fell over
time. A large level and negative growth rate of the profit share yields a large magnitude contribution of the
second term of equation (7), i.e., a significant contribution of profits to the dual-primal gap.
Table 5 uses this calibration to decompose Singapore’s dual-primal gap into the role of profits and
cost-of-capital heterogeneity. Across Hsieh’s three methods, capital on average contributes about 2/3 of
the total gap; and profits on average contribute 2/3 of capital’s portion. Heterogeneous capital costs
contribute about 1/3 of capital’s portion. Hence, both wedges appear significant in driving a wedge
between the primal and the dual, with profits being the single most important factor.19
B. How did Hsieh miss the “favored” cost of capital and profits?
Is it sensible to presume that dual TFP estimates incorporate the cost of capital only for the
“unfavored” subset of the economy? To assess this, we now discuss the three rate-of-return measures
Hsieh uses to estimate the cost of capital in Singapore: the earnings-to-price ratio (E/P); an average lending
rate; and the published return on equity (ROE).
First, consider the earnings-price ratio. Using a standard (Brealey and Myers) formula, a company’s
share price Pi is Pi = Ei r i + PVGOi —the value of a perpetuity yielding Ei, plus the present value of
growth opportunies. Rearranging implies that Ei P i = ri − ( ri ⋅ PVGOi Pi ) . With perfect capital
mobility, this interest rate is the expected (or required) return for the global representative investor, equal
to a discount rate, ρ , plus a firm-specific risk premium θ i .
19
We have referred to the second term as the contribution of profits, as if it were distinct from heterogeneous costs of
capital. However, the second term depends in part on the “representativeness” of the observed cˆU . An alternative
representation of equation (7) is
TFPDual − TFPPr imal = sK (cˆU − cˆ) + sΠ cˆ + kˆ − πˆ + sΠ (cˆU − cˆ) . The first two
terms capture heterogeneity and profits, respectively, while the third term captures a combination of the two.
However, zero profits would leave only the first term in our existing equation (7) and zero heterogeneity would leave
only the second term, so we use this form to measure the impact of the two effects.
16
Singapore’s stock market does not comprise a representative set of companies, and it is unlikely to
capture expected returns for ‘favored’ companies (namely, GLCs, SBs and foreign firms). In particular,
few GLCs were listed prior to the government’s 1985 privatization strategy, and multinationals generally
list elsewhere. This wouldn’t matter if capital were freely mobile (so required returns are set by the global
representative investor) and if unlisted companies had risk premia and growth opportunities that were
similar to those of listed companies. But GLCs, SBs, and multinationals tend to be lower-risk firms, with
lower implicit or explicit θ i – either because the government backed them (GLCs and SBs) with favorable
access to funds and/or implicit insurance; or because they were substantially larger and likely more
diversified (multinationals). 20 As such, the E/P ratio is likely to be a better measure of expected returns in
the ‘unfavored’ sector than the favored sector. 21 Finally, the earnings-price ratio would also exclude any
tax/subsidy components of the cost-of-capital formula—which clearly favor certain firms over others.
Second, Hsieh’s average bank lending rate also more likely represents the required returns for the
“unfavored” sector than for the “favored” sector. As Young (1998) describes in detail, the banks were
heavily regulated in a “cartel arrangement” through at least 1985, with lending rates above competitive
levels.22 But GLCs, SBs, and multinationals generally had alternative, likely cheaper sources of funding.
These sources, for example, included loans from the Central Providence Fund, international lending
(especially for MNCs, who didn’t need to rely on local cartel lenders), and very low-interest loans
available to exporters (see the discussion in Young 1998). In addition, the lending rate will, again, miss
any favorable tax/subsidy treatment.
20
This classification is more subtly suggested in a 1999 report funded by the National University of Singapore
(“Singapore’s Global Reach: An Executive Report,” by Henry Wai-Chung Yeung) that determined that many surveyed
private sector firms found Singapore’s business and commercial laws to be biased in favor of bigger corporations, both
GLCs and foreign multinationals.
21
Hsieh (2002) dismisses the idea that a declining overall risk premium could explain the primal-dual divergence.
More specifically, he argues that in developing countries, private and public risk premia are highly correlated; he then
shows that Singapore’s public risk premium is low. For all the reasons described in Section III, though, the premise of
a close correlation between the public and private premia in Singapore is flawed. Moreover, our argument here relies
on the heterogeneity of risk premia across firms.
22
Though the Singaporean Yearbook of Statistics indicates the end of interest rate regulation in 1975, Young explains
in detail why in practice, this did not occur until the mid-80’s.
17
Of course, the average rate may still not be a perfect measure of the opportunity cost of funds to the
less-favored sector, given the heavily regulated financial sector. But it appears more representative of the
cost of capital for less favored than for favored firms, for all the reasons discussed.
Finally, Hsieh uses a ROE calculation from the Singapore Registry of Companies and Businesses. In
principle, these figures cover most, if not all, firms and should incorporate economic profits. Given our
arguments in Section II, it should therefore give results similar to primal estimates. But closer examination
of the ROE figures, and the return-on-asset figures underlying it—suggest that these figures may not be
reliable.23 The ratio of assets to output averages over 13 for 1980-1990—an extremely high number, far
larger than the capital-output ratio of under 3 in the national accounts (a figure that Hsieh implies is
overstated). A large share of these assets (and equity) are in the financial sector, and represent financial
claims rather than tangible, non-financial assets. But even in the non-financial sector alone, the assetoutput ratio still averages 4.5, well in excess of national accounts estimates. In terms of growth rates, the
overall and non-financial asset-output ratios grow at 4.7 percent and 3 percent, respectively, from 19801990, in line with the rate of capital-output growth in the national accounts.
Thus, although total assets are not the same as tangible capital, it is nevertheless the case that the
ROE and ROA data are inconsistent with Hsieh’s implicit or explicit claims that the national accounts
overstate the level and rate of growth of the capital-output ratio. In sum, accountants and statisticians who
calculate (and then aggregate) the book values of individual companies have a different focus than do
growth accountants. In our view, these figures are significantly less reliable as a measure of the
opportunity cost of funds than the E/P ratio or the average lending rate, both of which correspond primarily
to the unfavored sector.
The above indicates that Hsieh did not capture the heterogeneous costs of capital in two of his three
calculations (and casts doubt on what exactly the third measure captures). Our argument also assumes that
23
Asset data taken from the Department of Statistics report, “Efficiency of Singapore Companies: A Study of the
Returns to Assets Ratios,” June 1992. This is the same report cited by Hsieh as the source of the ROE data, even
though ROA data (not ROE data) is actually found in the report. Numbers consistent with Hsieh’s ROE calculations
are found in “Foreign Equity Investment in Singapore, 1992,” also by the Department of Statistics in March 1995.
18
Hsieh’s measures exclude profits.24 The lending rate would clearly exclude profits. The numerator of ROA
should incorporate profits, but as just discussed, we have serious questions about the reliability of the
denominator. Finally, if exchange-listed companies earned large pure profits, those would show up in
earnings, but would also be capitalized into the price in the denominator. In equilibrium, returns embodied
in the earnings-price ratio are those expected by the investor. If profits are expected to be temporary (so
prospects for the growth in earnings are low), then profits could cause the E/P ratio to be high.
Nevertheless, in our view, most profits in Singapore were earned by GLCs, SBs, and multinationals –
typically not listed on the Singaporean market.
V. Primal vs. Dual revisited: Productivity and Technology
We have argued that, in practice, the primal and the dual differ because of output and factor-market
distortions and, hence, the gap reflects important aspects of the economic environment. Even more
important, these distortions imply that TFP growth does not equal technology growth. But with a few
assumptions, the primal and dual estimates together yield insight into technology growth in the favored and
unfavored sectors.
A. Productivity and technology
In Singapore, economic profits were large. With market power, of course, the Solow residual does
not measure technology (see, for example, Hall 1988, 1990). Hall suggested that with market power but
constant returns to scale, a cost-based TFP residual measures technology. The standard and cost-based
residuals differ by a single term, reflecting the different weighting of capital and labor:
yˆ − (1 − sL )kˆ + sL lˆ = yˆ − (1 − sLCost )kˆi + sLCost lˆi + sLCost − sL (lˆ − kˆ)
As in Hall (1988, 1990), we have defined the share of required payments to each factor in total costs by
sJCost
, i = s j , t ( sK , t + sL , t ), J = K , L .
24
Young [1998, p33] dismisses the role of profits in reconciling the results because he concludes that Hsieh’s
measures of the cost of capital would include profits.
19
How does the aggregate cost-based residual relate to technology? Hall’s argument applied to a single
firm. But suppose there are two sectors, each of which has constant returns, takes factor prices as given,25
but potentially produces with market power. We define aggregate technology growth as a share-weighted
average of technology growth, tˆ = ωU tˆU + ω F tˆF , where ωi is the sector’s nominal share in aggregate
output, PY
i i
( PU YU + PF YF ) ≡ PY
i i
PY .
As shown in the appendix, the aggregate Solow residual equals:
yˆ − sL lˆ + (1 − sL )kˆ = tˆ + sLCost − sL (lˆ − kˆ) + [ ΣΠ + Σ K ] ,
(9)
where ΣΠ and Σ K reflect reallocations of inputs across uses:
ωω
ΣΠ = F U ( sΠ ,F − sΠ ,U ) ( xˆF − xˆU )
(1 − sΠ )
K ω s C
Σ K = U F K,F 1 − U (kˆF − kˆU )
K 1 − sΠ CF
ΣΠ reflects reallocations of inputs across sectors where they have different profit rates. The term is
positive (i.e., TFP grows more quickly than technology) if high-profit sectors grow more quickly than lowprofit sectors. This term arises because aggregate output reflects relative market prices (i.e., relative
valuations) rather than relative costs of production.
Σ K , which reflects reallocations of capital across sectors with different costs of capital, is positive if
capital grows more quickly in sectors with a higher cost of capital. With cost minimization, capital’s
marginal product is proportional to the cost of capital. If capital shifts to where its marginal product is
higher, then output rises. At least for a while, directed credit likely leads this term to be negative, since
favored sectors have both a lower cost of capital and (during transition to a new steady state) grow faster.
25
Blanchard and Giavazzi (2002) discuss alternative labor market assumptions, e.g., efficient bargaining. Their paper
suggests the question of why, given the rents, workers didn’t bargain for a larger share of them. We view the process
of Singapore’s wage negotiations as, essentially, giving all of the bargaining power to employers.
20
In Singapore’s case, these reallocation terms appear to largely offset: The high-profit sector was the
same as the low cost-of-capital sector, and grew more quickly.26 We therefore ignore these terms in
Singapore. (In Korea, profits were small but resources were pushed towards the favored sector, so the
capital-reallocation term is likely negative—suggesting that tˆ exceeds measured TFP growth.)
We now use equation (9) to calibrate aggregate technology in Singapore. Measured TFP growth
differs from technology growth because, with profits, TFP underweights labor relative to capital. Labor’s
share in cost averages about 2/3 (0.67) using the Sarel approach; but labor’s share in revenue averages
about ½ (0.51). Hence, sLCost − sL is about 1/6. Young (1998, Table II) reports that from 1970 to 1990,
lˆ averaged 6.2 percent and k̂ averaged 11.0 percent. Thus, the entire non-technological term is
sLCost − sL (lˆ − kˆ) is (0.15)(4.8 percent)=0.77 percent.
Thus, we find that Young understates overall technological progress by about 3/4 percentage point
per year from 1970 to 1990. He reports TFP growth of –0.5 percent per year, so true technology growth
averaged about +0.3 percent (-0.5+0.77) per year.27 Nevertheless, the qualitative conclusion from this
exercise is that, as Young suggests, technology growth in Singapore was singularly unimpressive.
B.
Sectoral differences in technology growth
We can now use Hsieh’s dual estimate to estimate sectoral technology growth in the unfavored
sector, which we take to be everything except manufacturing, finance, utilities, and transport.
We assume that there are no profits in this sector (this is easily generalized), that all unfavored firms
pay the same wages and cost of capital, and have the same distribution of capital/worker types as the
aggregate economy. (These assumptions ensure that within-sector reallocation terms are zero and that the
sector’s input composition equals the aggregate.) Cost shares and revenue shares are then equal, so
standard TFP growth (calculated either from the primal or the dual) correctly measures technology growth
(see appendix). The key difference from Hsieh’s calculations are (i) he used Young’s aggregate labor
26
ωU =0.4, sΠ ,U = 0 , sΠ , F = 0.3 , CU=20 percent, CF=10 percent, K1/K =1/3, xˆU = 4.5
xˆF = 10 , kˆU = 5.5 , and kˆF = 13.7 . ΣΠ = +0.5 percent and Σ K = -0.5 percent. We experimented with a
For example, we set
percent,
range of other values, but if the favored sector has both higher profits and faster growth, the sum is generally small.
21
shares, and (ii) we need to measure real factor prices in terms of sectoral, not aggregate, deflators. Since
Hsieh deflates wages and the cost of capital by the GDP deflator, we have to add the difference between
the aggregate and unfavored sector deflators, ( pˆ − pˆU ) . Sectoral technology growth equals:
Cost
ˆ
ˆ
ˆ ˆ
tˆU = sLCost
,U w + (1 − s L ,U )cU + ( p − pU ) .
(8)
The relative price term (measured with Tornquist price indices calculated from one-digit data) averages
only -0.11 percent per year.
Using Sarel’s estimated industry cost shares for the five unfavored industries, labor’s share averages
0.81 (the unfavored sectors tend to be labor intensive). Using Hsieh’s (average) estimates of wage and
cost-of-capital growth shown in from Table 2, technology growth in the unfavored sector averaged about
2.5 percent per year. This figure is a good bit higher than his reported estimate of 1.8 percent because the
cost-share weight on labor (whose factor price grew faster) is much larger than labor’s aggregate share in
revenue. Given a value for ω P , we can now back out technology growth in the favored sector:
tˆF = ( tˆ − (1 − ω F )tˆU ) ω F .
For our categories of ‘favored’ industries, the share ω F averaged 0.6 from 1970-90. Hence, tˆ equal
to 0.25 percent per year and tˆU equal to 2.2 percent per year implies that tˆF equals –1.0 percent per year.28
Hence, we find that Hsieh’s dual TFP underestimates technology growth in Singapore’s unfavored
sector; Young’s primal TFP overestimates technology growth in the favored sector. The favored sector
had output growth of 9.9 percent per year with negative technology growth. The less favored sector grew
at 6.3 percent per year, with technology growth of 2.2 percent per year.
What of other Asian economies? Given small pure profits we do not adjust for differences between
labor’s cost and revenue shares. However, in Korea and, to a lesser extent Taiwan, directed credit appears
to have shifted resources to where they had a lower marginal product – thereby reducing measured TFP
27
Young (1995, p.648) discusses the possibility of monopoly profits, noting that ‘the reader can make an easy
correction for this factor’. This is in essence what we have done here.
28
Young’s estimates implied lower wage growth than Hsieh’s. The same calculations, but using Young’s implicit wage
growth from Table 2, would imply
tˆU equal to 1.2 percent per year, whereas tˆF equals –0.3 percent.
22
relative to technology growth (by a magnitude that, by some back-of-the-envelope calibrations, is probably
under ½ percent). Such adjustments do not substantively change one’s assessment of these economies.29
VI. If Singapore, why not Korea?
We have argued that large, variable profits and different growth rates for different capital costs – both
resulting largely from governments’ subsidizing and protecting certain sectors – created the large primaldual TFP gap in Singapore. But why isn’t there a gap in Korea? State intervention in Korea has garnered
as much or more attention as Singapore, Inc. Indeed, the development strategy of both countries involved
large government intervention. Why should the primal and dual match better for Korea than Singapore?
It is important to remember that market imperfections need not cause a dual-primal divergence. As
noted earlier, consider the steady state of a two-sector neoclassical growth model with market power and
favorable access to credit. In steady state, the profit share, capital-output ratio, and costs-of-capital are
constant; thus the primal-dual gap disappears. What about during the transition?
First, monopoly power, reflecting in part government entry barriers, led to high profits in Singapore.
But high profits are obviously not an inevitable consequence of government intervention—Singapore
seems the exception to world experience, not the rule. For Korea, we calculated in Table 2 that the profit
share was small (6.5 percent). Leipziger’s (1988) and Kihwan and Leipziger’s (1997) firm-level studies
also suggest relatively small profits. Kihwan and Leipziger suggest this lack of profitability may result
from Korea’s Confusion heritage, which emphasize freedom to hire workers but less freedom to fire them.
“Korean businessmen,” they argue, “often care more about business expansion than profits.”
Second, the mere existence of heterogeneous costs of capital need not necessitate differing growth
rates for the costs of capital, as occurred in Singapore. Though Korea’s transition also had heterogeneous
costs of capital for favored and unfavored sectors, these different costs seemed to grow at similar rates.
Hsieh notes the different levels of capital cost in Korea when he uses the curb loan rate (the market rate)
versus the discount rate (the “preferred” rate). However, these two rates both declined at very similar
29
Lee (1996) finds that TFP growth was lower in government-favored Korean industries than in non-favored ones.
Such effects are already incorporated into aggregate TFP.
23
paces. A transition with these characteristics would not produce a gap between the primal and dual.30
Finally, why was the favored cost-of-capital observed in Korea but not in Singapore? It is helpful to
think through the mechanisms by which heterogeneity was introduced. In Singapore, we argued that it is
difficult to include “unobservable” benefits to a favored sector. Differential tax rates, which affect the
cost-of-capital across firms, are difficult to account for. By contrast, Korea seemed to rely much more on
preferential access to capital (such as directed credit to state-owned enterprises and Chaebols), and the
different interest rates are more easily observed.
In addition, the idiosyncratic, one-time benefits offered to large multinationals to entice FDI are
particularly difficult to account for. FDI played a huge role in Singapore’s development but had negligible
impact on Korea in the 1970’s and 1980’s. Leipziger (1988) confirms that Korea “failed to encourage FDI
in their early development years … it took Korea until 1984 to become an active recipient of original FDI.”
Indeed, IFS statistics confirm that while FDI amounted to nearly half of investment (15% of GDP) in
Singapore by 1990, FDI amounted to only 1% of investment (a negligible share of GDP) in Korea by 1990.
In sum, though the broad development strategies were similar in Korea and Singapore, the lack of
profits and the similar measured growth rates in favored and unfavored costs of capital in Korea resulted in
consistent dual and primal TFP estimates.
VII. Conclusions
We show how product and output market distortions can, in principle and in practice, reconcile
apparently divergent quantity- and price-based measures of TFP in Asia. We thus view these divergent
results as complementary, providing insight into the economic environment. In particular, heterogeneity in
the cost-of-capital (reflecting intentional programs of many Asian governments to direct resources to
particular firms and/or sectors) and pure economic profits can explain much of the difference.
Perhaps our most striking empirical claim is that in Singapore, economic profits averaged nearly 1/4
of GDP. Such sizeable profits—especially when earned by state-favored firms—are clearly an anomaly in
30
Korea’s official bank rates, though lower than the curb loan rate, still relied on some market mechanism. Rhee
(1997) discusses the dual structure of Korea’s financial market.
24
world experience. But these large profits not only explain Singapore’s extremely low labor share, they are
also consistent with a wide range of indirect anecdotal evidence (e.g., on entry barriers) in Singapore.
With substantial distortions, TFP growth does not, of course, measure technology. Drawing on
recent macroeconomic literature on aggregating TFP under imperfect competition, we conclude that for
Singapore, Young was, in part, too optimistic: He overstates technological progress in the favored sector
of Singapore’s economy. Our best estimate is that in the favored sector, output grew nearly 10 percent per
year for two decades, with negative TFP growth. However, this does not mean that Singapore had no
worthwhile investments. In particular, under our interpretation, the relatively unfavored sector had slower
output growth, about 6 percent per year, despite rapid TFP growth of around 2-1/2 percent per year.
Taking a step back, it is striking that despite substantial economic distortions in several of the NIEs,
they nevertheless managed to achieve very rapid growth. In the case of Singapore, GDP per capita in the
Penn World Tables rose from a level 1/5 (19 percent) of the U.S. level in 1960 to a level comparable to (or
even slightly above) the U.S. level by the late 1990s. How did they achieve such stunning results, with
such a distorted economy? First, it appears that they have, as Young and Krugman argued, been successful
in marshalling substantial investment and capital accumulation. In 1998, Singapore was 2nd in GDP per
capita in the PWT, but was 24th per capita in consumption (including government consumption) per capita;
in terms of expenditures, about 57 percent of GDP was invested either at home or abroad.31 With an
apparently low social discount rate—in part reflecting intentional government policy to promote saving—
standard neoclassical growth theory would predict fast growth, albeit with a declining marginal product.
Endogenous growth models such as Ventura (1997) could help explain how Singapore was able to
maintain rapid growth with massive structural change. Second, some of the distortions in Singapore’s
economy could have offset each other. For example, a standard problem with monopolies is that they
underproduce relative to the social optimum; Singapore could have partially offset that distortion via
subsidies. Finally, large swaths of Singapore’s economy—ironically enough, the relatively unfavored
sector—maintained rapid TFP growth for decades.
31
Figures from http://www.bized.ac.uk/dataserv/penndata/penn.htm (downloaded July 27, 2003).
25
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27
Table 1
Asian Growth Estimates
(percent per year)
Total Factor Productivity
Output Growth
(1970-1990)
Young (1995, 1998)
Hsieh (2002)
Singapore
7.8
-0.5
1.8
Taiwan
8.8
2.2
3.7
Korea
9.5
1.7
1.9
Hong Kong
7.5
2.3
2.3
Unweighted
Average
8.4
1.4
2.4
Note: Here we give the arithmetic averages of Hsieh’s and Young’s results for each line above
from the calculations for each of the time periods used by Hsieh. Young’s numbers were adjusted
(using a weighted average of growth rates over subperiods) to cover the identical time period as each
of Hsieh’s measures. Hsieh (2002) offers three or four different measures of TFP, each based on
different measures of the real return and over slightly different time periods. The periods are all
highly similar and approximately cover 1970 -- 1990. Young (1998) was used for Singapore and
Young (1995) was used for Taiwan, Hong Kong, and Korea. For Hong Kong growth, Young’s data
for 1971-1991 was used. For Taiwan, data exclude agriculture and include Young’s adjustment of
public sector output. Numbers may not add up due to rounding.
28
Table 2
Decomposing the Sources of Difference in Primal and Dual Estimates
(Except where indicated, all entries are percent per year)
(1a)
Wage growth
(1b)
(2a)
(2b)
Capital
payment
Growth
Singapore
1.8
Taiwan
4.0
Korea
4.2
Hsieh w$ Dual
3.2
5.4
4.4
4.1
Young r$
-2.9
-3.4
-4.3
0.1
Hsieh c$Dual
0.3
-1.2
-4.1
-0.5
Young w$
Hong Kong
3.6
(3)
Labor’s share sL
(Sample average)
51.6
74.4
70.3
62.4
(4a)
Primal TFP growth
-0.5
2.2
1.7
2.3
(4b)
Dual TFP growth
1.8
3.7
1.9
2.3
(5)
Labor contribution to
difference: s L ( w$ Dual − w$ )
0.7
1.0
0.1
0.3
(6)
Capital contribution to
difference: sK ( c$Dual − r$ )
Difference
(Dual-Primal)
1.6
0.6
0.1
-0.3
2.3
1.6
0.1
0.1
(7)
Notes: Here we give the arithmetic averages of Hsieh’s and Young’s results for each line above from
the calculations for each of the time periods used by Hsieh. Young’s numbers were adjusted (using a
weighted average of growth rates over subperiods) to cover the identical time period as each of Hsieh’s
measures (e.g., for a measurement of the 1975-1990 rate, we would take 5/15 of the 1970-1980 rate and
add it to 10/15 of the 1980-1990 rate). The periods are all highly similar and approximately cover 1970 –
1990. When original growth rate calculations are needed (i.e. growth of average labor share), the best
approximation to end points are used (i.e. for 1975-1990 growth rates, the calculation might use the 10year growth from the average during the 1970-1980 period to that during 1980-1990). For Taiwan, data
exclude agriculture and include Young’s adjustment of public sector output. For Singapore, Young’s
primal data is taken from updated figures in Young (1998), other data are derived from Young (1995,
Tables V, VII, and IX), using: w$ = s$L + y$ − l$ and r$ = s$K + y$ − k$ . Young’s tables include data on y$ , l$ ,
k$ , s L , and sK . Numbers may not add up due to rounding.
29
Table 3
Decomposing the Sources of Difference in Primal and Dual Estimates for Singapore
(Except where indicated, all entries are percent per year)
(1a)
Wage growth
(1b)
(2a)
Capital
payment
Growth
(2b)
Young w$
Hsieh’s source for calculation of real interest rate
Return on Equity
Average Lending Rate E-P ratio
(1971-1990)
(1968-1990)
(1973-1990)
1.6
2.5
1.4
Hsieh w$ Dual
3.2
2.7
3.6
Young r$
-3.1
-3.0
-2.7
Hsieh c$Dual
-0.2
1.6
-0.5
(3)
Labor’s share sL
(Sample average)
51.6
51.5
51.6
(4a)
Primal TFP growth
-0.7
-0.2
-0.6
(4b)
Dual TFP growth
1.5
2.2
1.6
(5)
Labor contribution to
difference: s L ( w$ Dual − w$ )
0.8
0.1
1.2
(6)
Capital contribution to
difference: sK ( c$Dual − r$ )
1.4
2.3
1.1
(7)
Difference
(Dual-Primal)
2.2
2.4
2.2
Notes: Young’s primal data is taken from updated figures in Young (1998), other data are derived
from Young (1995, Tables V, VII, and IX), using: w$ = s$L + y$ − l$ and r$ = s$K + y$ − k$ . Young’s tables
include data on y$ , l$ , k$ , s L , and sK by subperiod. Young’s numbers were adjusted (using a weighted
average of growth rates over subperiods) to cover the identical time period as each of Hsieh’s measures
(i.e. for a measurement of the 1975 -- 1990 rate, we would take 5/15 of the 1970-1980 rate and add it to
10/15 of the 1980-1990 rate). When original growth rate calculations are needed (i.e. growth of average
labor share), the best approximation to end points are used (i.e. for 1975-1990 growth rates, the calculation
might use the 10-year growth from the average during the 1970-1980 period to that during 1980-1990).
Numbers may not add up due to rounding.
30
Table 4
Estimation of Profit Share
(Except where indicated, all entries are percent per year )
Singapore
Taiwan
Korea
Hong Kong
Share of profits and capital
(1-sL)
48.4
25.6
29.7
37.6
(1)
Estimated “true” capital cost
share (using Sarel)
32.7
30.1
24.8
34.7
(2)
Estimated “true” capital
revenue share
25.0
32.0
23.2
33.3
(3)
Estimated profit share
23.4
-6.3
6.5
4.3
(4)
Notes: Line 2 is calculated as a weighted average of Sarel’s capital share estimates, with the weights
determined by the industry-share of GDP (1-digit SIC from the CEIC database). Line 4, the estimated
profit share of revenues, is calculated as
(1 − sL − α )
, where α is the capital share of cost shown in line
1−α
two. Finally, the capital share in revenues (line 3) is equal to Young’s capital share (line 1) minus the
estimated profit share (line 4). Numbers may not add up due to rounding.
31
Table 5
Contributions to the Difference in Primal and Dual Estimates for Singapore
(Except where indicated, all entries are percent per year)
Hsieh’s source for calculation of real interest rate
Return on Equity Average Lending Rate
E-P ratio
(1971-1990)
(1968-1990)
(1973-1990)
(1)
Young’s capital share
48.4
48.5
48.4
(2)
Estimated “true” capital cost
share (using Sarel)
32.7
32.4
32.8
(3)
Estimated “true” capital
revenue share
25.1
24.7
25.2
(4)
Estimated “true” capital
revenue share growth
1.1
1.1
1.0
(5)
Estimated profit share
23.3
23.8
23.2
(6)
Estimated profit share growth
-1.2
-1.4
-1.0
(7)
Contribution of Profits to
Difference (Dual-Primal)
0.9
1.3
0.8
0.4
0.8
0.3
2.2
2.4
2.2
(8)
(9)
Contribution of Heterogeneous
Costs of Capital to Difference
(Dual-Primal)
Total Difference
(Dual-Primal)
Notes: Lines 1 to 3 and line 5 follow exactly as described in the note to table 4. Given CEIC
industry shares are known and changing over time, the calculation of “true” capital cost share changes over
time. Hence, we present growth rates for the key statistics. When original growth rate calculations are
needed (i.e. growth of average labor share), the best approximation to end points are used (i.e. for 19751990 growth rates, the calculation might use the 10-year growth from the average during the 1970-1980
period to that during 1980-1990). Then, using these data and the disaggregation of the capital-payments
contribution to the dual-primal gap in equation (7), we calculate lines 7 and 8. Note that lines 7 and 8 do
not add up to line 9. Line 9 is the total gap, not just that from the capital side, and includes differences in
wages growth estimates. Numbers may not add up because of rounding.
32
Appendix: Technology with multiple types of firms
We assume that there are two sectors, each of which produces potentially with market power but with
constant returns to scale. Output elasticities are then correctly given by the share of required factor
payments in total costs, sJCost
,i , J = K , L (Hall 1988, 1990. Basu and Fernald 2001 survey the literature
that followed Hall. Modifying the derivations for increasing returns and intermediate inputs is
straightforward). We assume that firms are price-takers in factor markets. Differentiating, we find:
Cost ˆ
ˆ
ˆ ˆ ˆ i = 1, 2.
yˆi = sKCost
,i ki + sL ,i li + ti ≡ xi + ti ,
(A.1)
xˆi is cost-share-weighted growth of capital and labor income, and tˆi is the growth rate of technology. If
there are pure economic profits in either of these sectors, then the cost-share weights do not equal the
weights used in calculating standard TFP. Hence, TFP would not correctly measure technology. In
particular, if sL ,i is the share of payments to labor in revenue, then TFP growth equals:
Cost ˆ
ˆ
Cost
ˆ ˆ
yˆi − (1 − sL ,i )kˆi + sLi lˆi = yˆi − (1 − sLCost
,i )ki + s Li li + s L ,i − sL ,i (l − ki )
ˆ ˆ
= tˆi + sLCost
,i − s L ,i (li − ki )
(A.2)
If capital growth exceeds labor growth (as Young 1995 reports it did it in every one of the NIE’s), then
standard TFP growth—the left hand side—will understate technology growth in the sector.
What will the dual measure show for the sector? As derived in the main text, the dual necessarily
equals the primal in equation (A.2), as long as the data are consistent with the accounting identity (1).
Hence, if the primal doesn’t measure technology, then neither does the dual. We will assume in what
follows that all sectors pay the same wages. Hence:
ˆ ˆ
ˆ
ˆ
tˆi + sLCost
,i − s L ,i (li − ki ) = sLi w + (1 − sL ,i ) ri
Some minor rearrangement yields the following:
((
) (
Cost
ˆ
tˆi = sLiCost wˆ + (1 − sLCost
wˆ + lˆ − rˆi + kˆi
,i ) ri − ( sL ,i − s L ,i )
i
))
With a constant labor share, the final term is zero and the cost-based dual residual measures
technology—as long as payments to capital includes profits. With an estimated cost of capital, we have:
Cost
ˆ
ˆ ˆ
tˆi = sLiCost wˆ + (1 − sLCost
,i )ci + (1 − sL ,i ) ( ri − ci )
33
(
)
Noting that rˆ = cˆ + ( Π RK ) πˆ − kˆ − cˆ , the above equation becomes:
(
ˆ
ˆ ˆ ˆ
tˆi = sLiCost wˆ + (1 − sLCost
,i )ci + ( Π i ( Ri K i + WLi ) ) π i − ki − ci
)
Thus, the cost-based dual residual potentially differs from technology with pure economic profits.
We aggregate across sectors with a Divisa index, which approximates chain weighting. Aggregate
output growth, ŷ , equals:
yˆ = ω1 yˆ1 + ω 2 yˆ 2
(A.3)
ωi is the sector’s nominal share in aggregate output, PY
i i
( PY
1 1 + P2 Y2 ) ≡ PY
i i
PY . It will also be
useful to define ωiCost = ( Ci K i + WLi ) ( C1 K1 + C2 K 2 + WL1 + WL2 ) as the sector’s share in total cost.
( ωi and ω iC differ if the rate of pure profit differs substantially across sectors.) Using (A.1), we find:
{
}
{
}
yˆ = ω1 sKCost
kˆ + s Cost lˆ + tˆ + ω 2 sKCost
kˆ + s Cost lˆ + tˆ
,1 1 L ,1 1 1
,1 1 L ,1 1 1
= ω1tˆ1 + ω 2 tˆ2 + ω1 xˆ1 + ω 2 xˆ2
(A.4)
ˆ + s Cost lˆ + ω cos t s Cost kˆ + s Cost lˆ
= tˆ + (ω1 − ω1cos t ) xˆ1 + (ω 2 − ω 2cos t ) xˆ2 + ω1cos t sKCost
k
L ,2 2
2
,1 1 L ,1 1
K ,2 2
cos t Cost ˆ
cos t Cost ˆ
ˆ
ˆ
sK ,2 k2 + ω1cos t sLCost
sL ,2 l2
= tˆ + (ω 2 − ω 2cos t )( xˆ2 − xˆ1 ) + ω1cos t sKCost
,1 k1 + ω 2
,1 l1 + ω 2
We have defined tˆ = ω1tˆ1 + ω 2 tˆ2 . The second term on the last line uses the fact that ω1 = (1 − ω 2 ) .
We now consider each of the non-technology terms in turn. First, we can rewrite the second term in
terms of profit reallocations as follows:
(ω 2 − ω 2cos t )( xˆ2 − xˆ1 ) = ω 2 (1 − ω 2cos t / ω 2 ) ( xˆ2 − xˆ1 )
(
)
(1 − (1 − s ) / (1 − s ) ) ( xˆ − xˆ )
= ω 2 1 − ( sK ,i + sL,i ) / ( sK + sL ) ( xˆ2 − xˆ1 )
= ω2
Π ,2
Π
2
1
ω2
=
( sΠ ,2 − sΠ ) ( xˆ2 − xˆ1 )
1
−
s
(
)
Π
Since sΠ = ( Π1 + Π 2 ) PY = ω1 sΠ ,1 + ω 2 sΠ ,2 , we can write this expression as:
ωω
(ω 2 − ω 2cos t )( xˆ2 − xˆ1 ) = 1 2 ( sΠ ,2 − sΠ ,1 ) ( xˆ2 − xˆ1 )
(1 − sΠ )
(A.5)
34
Second, we can write the next-to-last expressions in equation (A.4) in terms of aggregate capital
growth, plus reallocation effects.
cos t Cost ˆ
ˆ
ω1cos t sKCost
sK ,2 k2
,1 k1 + ω 2
C K + WL1
C1 K1
C K + WL2
C2 K 2
kˆ1 + 2 2
kˆ2
= 1 1
CK + WL C1 K1 + WL1
CK + WL C2 K 2 + WL2
=
C ( K1 + K 2 )
C1 K1
C ( K1 + K 2 ) C2 K 2
kˆ1 +
kˆ2
CK + WL C ( K1 + K 2 )
CK + WL C ( K1 + K 2 )
=
C ( K1 + K 2 )
K1
C ( K1 + K 2 )
K2
(C − C ) K1 ˆ (C2 − C ) K 2 ˆ
kˆ1 +
kˆ2 + 1
k1 +
k2
CK + WL ( K1 + K 2 )
CK + WL ( K1 + K 2 )
CK + WL
CK + WL
= sKCost kˆ +
(A.6)
(C1 − C ) K1 ˆ (C2 − C ) K 2 ˆ
k1 +
k2
CK + WL
CK + WL
Note that C ≡ C1 ( K1 ( K1 + K 2 ) ) + C2 ( K 2 ( K1 + K 2 ) ) . Hence,
(C1 − C ) = C1 − C1 ( K1 /( K1 + K 2 )) + C2 ( K 2 /( K1 + K 2 ))
= (C1 − C2 )( K 2 /( K1 + K 2 ))
Substituting this expression into (A.6), we find:
K1 K 2
ˆ + wcos t s Cost kˆ = s Cost kˆ +
ˆ ˆ
w1cos t sKCost
k
(C1 − C2 )(k1 − k2 )
,1
1
2
K
,2
2
K
(CK + WL )( K1 + K 2 )
(A.7)
Since we have assumed that labor is paid the same wage in both sectors, the corresponding
expression for labor is even simpler:
cos t Cost ˆ
ˆ
w1cos t sLCost
sL ,2 l2 = sLCost lˆ
,1 l1 + w2
(A.8)
We inserting (A.7) and (A.8) into (A.4) and rearrange. The aggregate cost-based residual equals:
yˆ − sLCost lˆ + sKCost kˆ = tˆ + Σ Π + Σ K
(A.9)
where ΣΠ and Σ K reflect reallocations of inputs across uses:
ω ω
ΣΠ = F U ( sΠ , F − sΠ ,U ) ( xˆF − xˆU )
(1 − sΠ )
K F KU
ˆ
ˆ
ΣK =
(CF − CU )(k F − kU )
(
CK
+
WL
)(
K
+
K
)
F
U
(A.10)
35
Hence, after a fair amount of tedious algebra, we have derived a relatively straightforward result: the
cost-based residual equals technology growth plus two reallocation terms. The first reallocation term
represents shifts of resources towards sectors where the profit rate is higher, i.e., where the share of the
sector in output exceeds the share in cost. Economically, this reflects the fact that output is measured
using relative market prices not relative costs of production. With differential profit rates, relative prices
need not equal relative costs of production (i.e., the marginal rate of substitution is not equal to the
marginal rate of transformation). Output is (quite appropriately) aggregated using prices, which are
equated to marginal rates of substitution, not using marginal rates of transformation.
The second reallocation term reflects the fact that if capital is shifted to where it has a higher cost-ofcapital, aggregate output and aggregate TFP rises, other things equal. With a higher cost-of-capital, firms’
cost-minimizing conditions for capital input use imply that the marginal product of capital is higher.
Reallocating resources to where their marginal products are higher raises aggregate output.
Note that we can rewrite this term in a way that is easier to calibrate:
K F KU
ˆ
ˆ
ΣK =
(CF − CU )(k F − kU )
(CK + WL )( K F + KU )
KU
CU
Y
PY
i i CF K F
=
1 −
CF
i i
K F + KU CK + WL Y PY
K
= U
K
ω F sK , F CU ˆ
ˆ
1 − s 1 − C (k F − kU )
F
Π
ˆ
ˆ
(k F − kU )
36
Appendix Table 3A
Decomposing the Sources of Difference in Primal and Dual Estimates for Taiwan
(Except where indicated, all entries are percent per year)
(1a)
Wage growth
(1b)
(2a)
Capital
payment
Growth
(2b)
Young w$
Hsieh’s source for calculation of real interest rate
Curb loan rate
One-year
Secured loan rate
deposit rate
(1966-1990)
(1966-1990)
(1966-1990)
4.0
4.0
4.0
Three-month
treasury bill rate
(1975-1990)
4.0
Hsieh w$ Dual
5.3
5.3
5.3
5.8
Young r$
-3.7
-3.7
-3.7
-2.4
Hsieh c$Dual
-0.4
-0.1
-2.0
-2.1
(3)
Labor’s share sL
(Sample average)
74.3
74.3
74.3
74.6
(4a)
Primal TFP growth
2.1
2.1
2.1
2.4
(4b)
Dual TFP growth
3.8
3.9
3.4
3.8
(5)
Labor contribution to
difference: s L ( w$ Dual − w$ )
0.9
0.9
0.9
1.3
(6)
Capital contribution to
difference: sK ( c$Dual − r$ )
0.9
0.9
0.4
0.1
(7)
Difference
(Dual-Primal)
1.8
1.8
1.3
1.4
Notes: Data exclude agriculture and include Young’s adjustment of public sector output. Young’s
primal data is taken from updated figures in Young (1998), other data are derived from Young (1995,
Tables V, VII, and IX), using: w$ = s$L + y$ − l$ and r$ = s$K + y$ − k$ . Young’s tables include data on y$ , l$ ,
k$ , s L , and sK by subperiod. Young’s numbers were adjusted (using a weighted average of growth rates
over subperiods) to cover the identical time period as each of Hsieh’s measures (i.e. for a measurement of
the 1975 -- 1990 rate, we would take 5/15 of the 1970-1980 rate and add it to 10/15 of the 1980-1990 rate).
When original growth rate calculations are needed (i.e. growth of average labor share), the best
approximation to end points are used (i.e. for 1975-1990 growth rates, the calculation might use the 10year growth from the average during the 1970-1980 period to that during 1980-1990). Numbers may not
add up due to rounding.
37
Appendix Table 3B
Decomposing the Sources of Difference in Primal and Dual Estimates for Korea
(Except where indicated, all entries are percent per year)
(1a)
Wage growth
(1b)
(2a)
Capital
payment
Growth
(2b)
Young w$
Hsieh’s source for calculation of real interest rate
Curb market
Deposit rate
Discount rate
Loan rate
(1966-1990)
(1966-1990)
(1966-1990)
4.2
4.2
4.2
Hsieh w$ Dual
4.4
4.4
4.4
Young r$
-4.3
-4.3
-4.3
Hsieh c$Dual
-4.0
-3.4
-4.9
(3)
Labor’s share sL
(Sample average)
70.3
70.3
70.3
(4a)
Primal TFP growth
1.7
1.7
1.7
(4b)
Dual TFP growth
1.9
2.1
1.6
(5)
Labor contribution to
difference: s L ( w$ Dual − w$ )
0.1
0.1
0.1
(6)
Capital contribution to
difference: sK ( c$Dual − r$ )
0.1
0.3
-0.2
(7)
Difference
(Dual-Primal)
0.2
0.3
-0.1
Notes: Young’s primal data is taken from updated figures in Young (1998), other data are derived
from Young (1995, Tables V, VII, and IX), using: w$ = s$L + y$ − l$ and r$ = s$K + y$ − k$ . Young’s tables
include data on y$ , l$ , k$ , s L , and sK by subperiod. Young’s numbers were adjusted (using a weighted
average of growth rates over subperiods) to cover the identical time period as each of Hsieh’s measures
(i.e. for a measurement of the 1975 -- 1990 rate, we would take 5/15 of the 1970-1980 rate and add it to
10/15 of the 1980-1990 rate). When original growth rate calculations are needed (i.e. growth of average
labor share), the best approximation to end points are used (i.e. for 1975-1990 growth rates, the calculation
might use the 10-year growth from the average during the 1970-1980 period to that during 1980-1990).
Numbers may not add up due to rounding.
38
Appendix Table 3C
Decomposing the Sources of Difference in Primal and Dual Estimates for Hong Kong
(Except where indicated, all entries are percent per year)
(1a)
Wage growth
(1b)
(2a)
Capital
payment
Growth
(2b)
Young w$
Hsieh’s source for calculation of real interest rate
Prime Lending
Call money rate
E-P ratio
Rate
(1966-1991)
(1966-1991)
(1973-1991)
3.7
3.7
3.4
Hsieh w$ Dual
4.1
4.1
4.1
Young r$
0.0
0.0
0.3
Hsieh c$Dual
-1.1
-1.5
1.0
(3)
Labor’s share sL
(Sample average)
62.8
62.8
61.6
(4a)
Primal TFP growth
2.3
2.3
2.2
(4b)
Dual TFP growth
2.1
2.0
2.9
(5)
Labor contribution to
difference: s L ( w$ Dual − w$ )
0.2
0.2
0.5
(6)
Capital contribution to
difference: sK ( c$Dual − r$ )
-0.4
-0.6
0.2
(7)
Difference
(Dual-Primal)
-0.2
-0.3
0.7
Notes: Young’s primal data is taken from updated figures in Young (1998), other data are derived
from Young (1995, Tables V, VII, and IX), using: w$ = s$L + y$ − l$ and r$ = s$K + y$ − k$ . Young’s tables
include data on y$ , l$ , k$ , s L , and sK by subperiod. Young’s numbers were adjusted (using a weighted
average of growth rates over subperiods) to cover the identical time period as each of Hsieh’s measures
(i.e. for a measurement of the 1975 -- 1990 rate, we would take 5/15 of the 1970-1980 rate and add it to
10/15 of the 1980-1990 rate). When original growth rate calculations are needed (i.e. growth of average
labor share), the best approximation to end points are used (i.e. for 1975-1990 growth rates, the calculation
might use the 10-year growth from the average during the 1970-1980 period to that during 1980-1990).
Numbers may not add up due to rounding.
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