Munich Personal RePEc Archive

Labor productivity, capital accumulation,
and aggregate efficiency across countries:
Some stylized facts
Mendez-Guerra, Carlos
Kyushu University

7 November 2017

Online at https://mpra.ub.uni-muenchen.de/82461/
MPRA Paper No. 82461, posted 08 Nov 2017 00:16 UTC

Labor Productivity, Capital Accumulation,
and Aggregate Efficiency across Countries:
Some Stylized Facts
Carlos A. Mendez-Guerra∗
Kyushu University
November 6th, 2017
Abstract
This paper studies the cross-section dynamics of the proximate determinants of labor productivity: physical capital, human capital, and aggregate efficiency. Using a panel data set for 74 countries covering the 19502010 period, it first documents that labor productivity of the median country has been mostly stagnant, while cross-country differences have drastically increased. An evaluation of proximate sources points to a similar
pattern of stagnation and increasing dispersion in both physical capitaland aggregate efficiency. Human capital is the only variable where medianprogress and inequality reduction can be observed. Next, the paper shows
how standard regression methods consistently overestimate the fraction of
the variation in labor productivity that is explained by physical capital. The
source of this upward bias appears is the unaccounted covariance between
capital accumulation and aggregate efficiency. Taking this covariance into
account, most of the variation in labor productivity turns out to be explained by differences in aggregate efficiency. Finally, the paper concludes
arguing that allocative inefficiencies at the sectoral level, such as those predicted by dual-economy type models, are important for understanding thelarge and increasing differences in aggregate efficiency across countries.
Keywords: labor productivity, capital accumulation, aggregate efficiency,
stylized facts
JEL classification: E01, O40, O47∗

Contact Email: carlosmendez777@gmail.com

2

CARLOS A. MENDEZ-GUERRA

1. Introduction
Arguably, most research studies in the growth and development literature analyze cross-country differences in labor productivity according to the following
chain of causation (Hsieh and Klenow, 2010):
Figure 1: Cross-Country Differences in Labor Productivity: A Chain of Causality

Geography, Climate,
Luck

Aggregate
Efficiency

Human
CapitalPhysicalCapitalInstitutions, Culture

Aggregate
Efficiency

Human
CapitalPhysicalCapital

Policies, Rule ofLaw, Corruption

Aggregate
Efficiency

Human
CapitalPhysicalCapitalCross-Country
Differences in Labor
Productivity

Source: Adapted from Hsieh and Klenow (2010)

Factors that affect labor productivity are typically classified into two groups.
The first includes the most proximate sources such as physical capital, humancapital, and aggregate efficiency. The second includes more fundamental or
deeper determinants such as geography, culture, and institutions and policies.
In the context of Figure 1, this paper analyzes the proximate sources of laborproductivity. First, it quantifies the differences both over time and across countries of each proximate source. Next, the paper revisits the debate about therelative importance of capital accumulation versus aggregate efficiency. On the
one hand, the work of Mankiw, Romer, and Weil (1992) uses regression methods
to conclude that capital accumulation differences explain most of the variationof labor productivity across countries. On the other, the work of Klenow andRodriguez-Clare (1997) uses calibration methods to highlight the prevalenceof aggregate efficiency over capital accumulation. On this debate, this paperemphasizes that the source of disagreements relies on strong conceptual andLABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

3

methodological assumptions of both lines of research. On the one hand, capital
fundamentalists rely on the independence between capital accumulation andaggregate efficiency to consistently estimate an unbiased OLS regression. On
the other hand, efficiency proponents rely on competitiveness of factor markets to calibrate key parameters.
After clarifying the relative importance of capital accumulation and aggregate efficiency, this paper discusses a structural change channel through whichsome of the deeper determinants described in Figure 1might affect the proximate sources of labor productivity. This channel has to do with the degreeof allocative efficiency across productive sectors within an economy. In particular, it argues that the degree of misallocation resources across sectors canpotentially have a large negative effect on aggregate efficiency. This observation is consistent with the dual-economy structures that are typically foundin developing countries (Lewis 1954,1979). Empirically, the work of Vollrath(2009) shows that degree of resource misallocation between agricultural andnon-agricultural sectors can account for up 80 percent of the cross-country
variation in aggregate efficiency. Finally, the paper provides further evidence on
the dynamics of misallocation. Using the recent sector-level data from McMillan and Rodrik (2011, 2014), this paper presents the case of Chile as an illustrative example in which workers secularly move from relatively high-productivity
sectors to low-productivity sectors.
The rest of the paper is organized as follows. Section 2 describes the evolution of the cross-country disparities in labor productivity, capital accumulation,
and aggregate efficiency. Section 3 evaluates the relative importance of capital
accumulation and aggregate efficiency. Section 4 presents an structuralist pointof view about the sources of aggregate efficiency. Finally, Section 5 offers someconcluding remarks and open questions for further research.

4

CARLOS A. MENDEZ-GUERRA

2. Labor Productivity its Proximate Sources
Figure 2 shows two key features of the dynamics of labor productivity acrosscountries. First, contrary to the convergence predictions of the Neoclassicalgrowth model,1 relative labor productivity of the medium country was almost
stagnant during the 1950-2010 period.2 For instance, in 1950, output per workerof the median country relative to that in the United States was 22 percent. After61 years, it decreased to 20 percent.3 Second, the standard deviation increased
from 23 to 32 during this period. That is, productivity differences across countries increased by a factor of 1.4 during this period. What explains this lack ofconvergence and increasing disparities in labor productivity?
Standard growth theory provides the beginning of an answer by organizing
our thoughts around an aggregate production function. For instance, Hall andJones (1999) and Caselli (2005, 2014) suggest the following functional form:
Yi = Ai Kiα (hi Li )1−α for all α ∈ (0, 1),(1)where Yi is the total real GDP in country i , Ai represents aggregate efficiency4 ,Ki is the total physical capital stock, hi is the human capital per worker, Li is thetotal labor force, and α is the elasticity of GDP with respect to physical capital.
Dividing Equation 1 by the labor force Li , and rearranging terms, we can obtain1

See Solow (1956) for details.
Providing some empirical support about the convergence predictions of the Neoclassicalmodel, Barro (1992) finds conditional convergence across countries after controlling for otherfactors such as fertility, education, population growth, government expenditures, investment
rates, among others. Durlauf, Johnson and Temple (2005), however, criticize this finding arguing that the typical convergence regressions implemented in the literature suffer from model
uncertainty, parameter heterogeneity, endogeneity issues, and lack of robustness.
3
If in this computation the mean is used, average productivity increased from 33 percent to35 percent. As a measure of centrality, however, the median is typically preferred to the mean
when a sample contains extremely large or small values.
4
The literature typically refers to Ai as total factor productivity (TFP). To avoid confusion
with other productivity terms in this paper I use the term aggregate efficiency instead to totalfactor productivity.
2

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

5

Figure 2: Cross-Country Differences in Labor Productivity Over Time

Relative Output per Worker(USA=100)
80

60

40

20

0
1950

1960

1970

1980

1990

2000

2010

Year

Source: Author’s calculations using data from Fernandez-Arias (2014)

an expression for the average productivity of labor:
Yi
= Ai
Li



Ki
Li

α

h1−α
.
i

(2)

Equation 2 shows that the (proximate) forces driving the behavior of labor productivity can be organized into three variables: aggregate efficiency, physicalcapital per worker, and human capital per worker. Alternatively, they can also
be categorized into two factors: aggregate efficiency and capital accumulation,
where the concept of capital in this case includes both physical and humancapita. In any of these classifications the interpretation is equivalent: laborproductivity in country i will be high if its workers accumulate productive resources (e.g., physical capital and human capital) and/or if those resources areused more efficiently.
Ideally, one would like to use Equation 2 for answering comparative analysis

6

CARLOS A. MENDEZ-GUERRA

questions such as: how much does labor productivity increase in response to anincrease in aggregate efficiency? One problem, however, is that capital accumulation responds endogenously to changes in aggregate efficiency (Klenow andRodriguez-Clare, 1997). Conceptually, this endogeneity arises because physicalcapital is defined in units of final output. As a result, any increase in aggregate
efficiency would affect labor productivity both directly and indirectly throughcapital accumulation. Hsieh and Klenow (2010) argue that keeping physicalcapital constant when there is an increase in efficiency requires a decrease in
the investment rate. However, it is not obvious why the investment rate should
decrease to improvements in efficiency. Thus, to deal with the endogeneity issue in a more natural way, Klenow and Rodriguez-Clare (1997) rearrange Equation2 and suggest the following (steady-state) production function:1
Yi= Ai1−α
Li



Ki
Yi

α
 1−α

hi .

(3)

Equation 2 is consistent with the steady state equilibrium of the neoclassicalgrowth model, where the capital-output ratio, KY , is exogenous to changes inaggregate efficiency, A. More intuitively, Equation 3 controls for the indirect1
effects of improvements in efficiency by raising its elasticity from one to 1−α.

Given cross-country data on total production, labor force, physical and human capital, previous studies have used regression or calibration methods toempirically implement either equation 2 or 3. In fact, Caselli (2005) and Hsieh
and Klenow (2010) survey the literature that uses calibration methods. In thesesurveys, physical capital typically explains around 20 percent, human capital
explains 10 to 30 percent, and aggregate efficiency explains 50 to 70 percent of
the cross-country differences in labor productivity5 . Although most economies
would tend to agree with these findings, there are important caveats and lim5

Originally, Caselli (2005) and Hsieh and Klenow (2010) report cross-country differences in
output per capita (i.e., differences in income). However, it is well-know that differences in output per capita imply differences in output per worker when the employment-to-population
ratio does not systematically vary with output per capita.

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

7

itations. It is also important to analyze why a calibration approach would still
be preferred to a regression-based approach (See section 3.). Before going into
methodological concerns, however, I first discuss the general patterns about
the evolution of the cross-country differences in capital accumulation and aggregate efficiency in the post-World War II period

2.1. Differences in Physical CapitalLong data series on physical capital are not readily available from the national
income accounts of most countries. The standard procedure in the literature
is to build such series by adding investment inflows within an accumulation
framework that includes depreciation outflows. For instance, the Penn World
Tables V.8 database and the database of Fernandez-Arias (2014), which are themain datasources for this section, uses the perpetual inventory method to construct the physical capital series for 167 countries between 1950 and 2011. This
inventory method requires only two parameters: the depreciation rate and theinitial capital stock. Although the first is typically set to six or ten percent, thelatter is not readily available. Thus, there exist a variety of methods for computing the initial capital stock. For instance, Jones (1997) and Hall and Jones(1999) use the capital stock in steady state. As described in Caselli (2005), independently of the chosen method, initial capital depreciates over time and given
a six percent depreciation rate, the effect of the initial capital would almost disappear after the first 30 years.
Figure 3 shows the two features that characterize the evolution of crosscountry differences in physical capital per worker. First, similar to labor productivity, relative physical capital per worker of the medium country was almost
stagnant during the 1950-2010 period. For instance, in 1950, physical capitalper worker relative to that in the United States was 20 percent. After 61 years,
it only increased to 23 percent. Second, cross-country differences in physicalcapital are even larger than those in labor productivity. For instance, standard

8

CARLOS A. MENDEZ-GUERRA

Figure 3: Cross-Country Differences in Physical Capital Over Time
Capital-Labor ratio(USA=100)
80
70
60
50
40
30
20
10
0
1950

1960

1970

1980

1990

2000

2010

Year

Source: Author’s calculations using data from Fernandez-Arias (2014)deviation increased by a factor of 1.6. over the sample period6 .
Figure 4 illustrates the strong correlation between labor productivity andphysical capital. Moreover, this correlation appears to become stronger overtime. To further clarify the sources of these results, consider a simplified logarithmic version of Equation 2:
log



Yi
Li



= β + α log



Ki
Li



+ εi .

(4)

In this simplified model, cross-country differences in human capital and aggregate efficiency at a point in time would be included in the error term εi .
Moreover, under the strong assumption that these two factors are independent
to physical capital, the elasticity of output per worker with respect to physicalcapital, α , could be estimated using a standard OLS regression.
6

Specifically, the standard deviation increased from 24 to 39.

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

9Given the estimates of Equation 4 and the previously described assumption,
results from Figure 4 would suggest that most of the cross-country variationin labor productivity is explained by physical capital (the R-squared is close
to one). For instance, in 2010 differences in aggregate efficiency and humancapital would only explain four percent of the differences in labor productivity. Although the correlation between labor productivity and physical capitalis indeed strong, the reported values for both the capital elasticity and the Rsquared statistic are at odds with those suggested by national accounts (Gollin,
2002). As it will be discussed in Section 3., one can reduce the explanatory
power of physical capital by adding measures of human capital, controlling for
fixed effects, and changing the estimation framework. Yet, before such discussion, let us evaluate how large the differences in human capital are across countries.
Figure 4: Labor Productivity versus Physical CapitalLog (Output per Worker)
5

To be covered in white

4

3

2

R2 in 2010 = 96%
R2 in 1990 = 91%
R2 in 1970 = 89%

1

Elasticity in 2010 = [0.84-0.92]
Elasticity in 1990 = [0.72-0.83]
Elasticity in 1970 = [0.66-0.78]

0
-2

0

2

4

6

Log (Capital-Labor ratio)

Source: Author’s calculations using data from Fernandez-Arias (2014)

10

CARLOS A. MENDEZ-GUERRA

2.2. Differences in Human Capital
The availability of comprehensive cross-country data on human capital seems
be improving every decade. In the early 1990s, growth regressions typicallyproxied human capital using measures of school enrollment (Barro and Sala-iMartin, 1992; Mankiw et al., 1992). In the late 1990s and early 2000s, growth anddevelopment decompositions (Klenow and Rodriguez-Clare, 1997; Hall and Jones,
1999) typically used measures of years of schooling (from Barro and Lee, 2013)
and the Mincerian return associated to the average years of schooling (fromPsacharopoulos and Patrinos, 2004). More recently, some decomposition studies started to use measures of the quality of schooling and returns to each yearof work experience (See Kaarsen, 2014; Lagakos et al., 2012 for details).
Figure 5: Cross-Country Differences in Human Capital Over Time
Human Capital per Worker(USA=100)
80

70

60

50

40
1950

1960

1970

1980

1990

2000

2010

Year

Source: Author’s calculations using data from Fernandez-Arias (2014)

Using the human capital production function suggested by Hall and Jones(1999), Figure 5 shows the two features that characterize the evolution of crosscountry differences in human capital per worker. First, contrasting the pat-

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

11

terns of both labor productivity and physical capital, relative human capital per
worker of the medium country notably increased during the 1950-2010 period.
After two initial decades of stagnation, human capital accumulation started a
rapid increase. For instance, in 1950, human capital per worker relative to thatin the United States was 54 percent; by 2010 it reached to 74 percent. Second,cross-country differences in human capital slightly decreased over this period.
For instance, in 1950 the standard deviation was 18 percent; by 2010 it was 16
percent.
Figure 6 shows that human capital is also highly correlated with labor productivity, though not as much as physical capital. As in Equation 4, an OLS
regression would suggested that more than 60 percent of the cross-country differences in labor productivity are explained by differences in human capitalalone. Again, here the credibility of this explanatory power relies on the strong
assumption that human capital is independent of physical capital and aggregate efficiency.

2.3. Differences in Aggregate Efficiency
Conceptually, aggregate efficiency is a measure that quantifies the efficiency
with which an economy uses its productive resources. Efficiency gains arise due
to improvements in either technical knowledge or reallocation of resources tobetter uses (or both). Empirically, aggregate efficiency is a residual measure. It
captures everything else that affects output that is not already measured in theother inputs (e.g., physical and human capital). According to this definition,
most studies compute aggregate efficiency for a country at a point of time as
the following ratio7 :output=Ait ≡inputs
7

Yit
Lit

.
K α 1−αhL(5)See Van Beveren (2012 ) for a practical survey on how to compute aggregate efficiency. Also,
see Isaksson (2006, 2007) for an overview of the determinants of aggregate efficiency. Finally,see Felipe, (1999, 2007) for a critical review of the residual approach to aggregate efficiency
measurement.

12

CARLOS A. MENDEZ-GUERRA

Figure 6: Labor Productivity versus Human CapitalLog (Output per Worker)
5

To be covered in white

4

3

2

R2 in 2010 = 72%
R2 in 1990 = 72%
R2 in 1970 = 60%

1

Elasticity in 2010 = [3.74-5.01]
Elasticity in 1990 = [3.09-4.17]
Elasticity in 1970 = [2.19-3.22]

0
3.5

4

4.5

5

Log (Human Capital per worker)

Source: Author’s calculations using data from Fernandez-Arias (2014)

The only missing information to compute this ratio is the output elasticity
with respect to capital, α. Given the results of Figure 4, this parameter tends tobe overestimated when using regression methods. An alternative would be to
extract such information from other sources. For instance, it is well known that
under perfect competition and constant returns to scale, the output elasticity
with respect to capital is defined as the share of national income that accrues tophysical capital. That is
α=

rK
,
Y

(6)

where r is the price of physical capital. Gollin (2002) collects data from difference sources across countries to construct measures of the capital income
share. After adjusting for the income of self-employed workers, he finds no relationship between the capital share and the level of income per capita (andlabor productivity) across countries (See Figure 7). Moreover, the average capital share is about 13, which is consistent with the long-run evidence of capitalLABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

13

Figure 7: Physical Capital Share versus Labor Productivity

Physical Capital Share
.6
ECU
PRY

.5

kshare

VEN

SGP
MEX

PER

HKG

URY
CHL

PHL
JAM

.4

Average= 0.33

NOR

ZAFTUN
JOR

COL

BOL

KOR

MYS

NZL

.3
ZMB

PRT

CRI PAN

ESP
JPN

NLD
CAN
AUS
DEU
ISR
AUT
DNK FIN
FRA

GBR
LKA

EGY

BEL

IRL

USA

SWE
GRC

.2
0

ITA

20

40

60

80

100

Output per Worker(USA=100)

Source: Data on the capital share is from Bernanke and Gurkaynak(2002), table 10 and note 18. Data on output per worker are author’s
calculation using data from Fernandez-Arias (2014).

share series of the United States and other advanced economies.
Using a physical capital share value of 13, Figure 8 shows the two key featuresthat characterize the evolution of aggregate efficiency across countries. First,
relative aggregate efficiency of the medium country actually decreased during
the 1950-2010 period. For instance, in 1950, aggregate efficiency relative to thatin the United States was 62 percent; by 2010 it decreased to 48 percent. Second,
aggregate efficiency differences across countries increased by a factor of 1.2.
That is, the standard deviation increased from 24 percent to 29 percent during
this period.
Figure 9 shows that aggregate efficiency is strongly correlated with laborproductivity. Moreover, the R-squared of a simple linear regression would suggest that in 2010 differences in aggregate efficiency explained 96 percent of thecross-country differences in labor productivity. Given these findings, one would

14

CARLOS A. MENDEZ-GUERRA

Figure 8: Cross-Country Differences in Aggregate Efficiency Over Time
Aggregate Efﬁciency(USA=100)
100
90
80
70
60
50
40
30
20
1950

1960

1970

1980

1990

2000

2010

Year

Source: Author’s calculations using data from Fernandez-Arias (2014)

not only conclude that differences in aggregate efficiency could be as importantas physical capital, but also that these two measures are highly correlated. In
fact, for the year 2010 the pairwise correlation between them was 0.93.

3.

Capital Accumulation or Aggregate Efficiency?

The main criticism to the regression approach is that both the elasticity of output with respect to capital (α) and the R-squared tend to be upwardly biased.
The source of this overestimation is the uncontrolled correlation between capital accumulation and the residual term, which by the definition of Equation 1
represents aggregate efficiency. Additional regression analyses, summarized inTable 1, suggest that the implausible values for α (and the R-squared) persist after controlling for human capital, country fixed effects, and constant returns toscale. As a result, if the correlation between capital and the residual is so strong,LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

15

Figure 9: Labor Productivity versus Aggregate Efficiency

Log (Output per Worker)
5

To be covered in white

4

3

2

R2 in 2010 = 96%
R2 in 1990 = 90%
R2 in 1970 = 83%

1

Elasticity in 2010 = [1.73-1.90]
Elasticity in 1990 = [1.73-2.02]
Elasticity in 1970 = [1.67-2.07]

0
2

3

4

5

Log (Aggregate Efﬁciency)

Source: Author’s calculations using data from Fernandez-Arias (2014)

how can we identify the variation of labor productivity that is due to capitaldifferences alone? Consistent with the calibration methodology suggested by
Klenow and Rodriguez-Clare (1997), Vollrath (2014) describes a simple solution
for controlling the previously described correlation.
Let us rewrite the simple econometric model described in Equation 4 as:
log yi = β + α log ki + εi ,(7)where labor productivity y and the capital-labor ratio k are expressed as lowercase letters just to simplify notation. Then, define the variation of the dependent variable that is explained by the model as:
R2 =V ar (β + α log ki ).
V ar (log yi )(8)

Next, utilize the statistical properties of the variance and covariance operators

16

CARLOS A. MENDEZ-GUERRA

Table 1: Different Estimations of Output Elasticities: 1950-2010 Period

Dependent Variable: Labor Productivity
Model (1)Model (2)Model (3)Model (4)

0.74

0.74

0.59

0.55

(0.01)(0.06)(0.05)(0.01)

0.26

0.26

-0.78

0.45

(0.03)(0.06)(0.14)(0.01)

Fixed Effects

NO

NO

YES

YES

Constraint (β1 + β2 = 1)

NO

YES

NO

YES

R2

0.90

na

0.84

na

Observations

4284

4284

4284

4284

Physical Capital

Human Capital

Note: Numbers in parentheses indicate robust standard errors. All variables are
significant at 1 percent. All regressions include a constant term that is not reported in the table.

and the definition of the OLS estimator to show that
V ar (log ki )V ar (log yi )Cov (log ki , log yi ) V ar (log ki )= αV ar (log ki )V ar (log yi ){z}|

R2 = α2

α

=

=
=
=

Cov (αlog ki , log yi )V ar (log yi )Cov (αlog ki , β + α log ki + εi )V ar (log yi )Cov (αlog ki , β) Cov (αlog ki , α log ki ) Cov (αlog ki , ε)++V ar (log yi )V ar (log yi )V ar (log yi )V ar (αlog ki ) Cov (αlog ki , ε)0++V ar (log yi )V ar (log yi )(9)Equation 9 shows that we can compute the unbiased R-squared by letting

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

17

Cov (αlog ki , ε) = 0 and selecting a value for α. Using the results of Figure 7,
most calibration studies set α = 13. Given this setting, in the year 2010 differences in physical capital accumulation explain only 14 percent of the differences in labor productivity across countries. One can also apply the same procedure for computing the contribution of aggregate efficiency8 . For the same
year, differences in aggregate efficiency explain 44 percent of the differences inlabor productivity across countries. This finding is consistent with previous literature (Baier et al., 2006; Caselli, 2005; Hall and Jones, 1999; Hsieh and Klenow,
2010 ) in the sense that aggregate efficiency is the main driving force behind thelabor productivity.

4. What Explains Aggregate Efficiency? A
Structuralist View
Classical development economics models, such as Lewis (1954), focus on thecoexistence of fundamentally different structures of production within an economy.9 In its simplest representation, Lewis’ dual economy model conceptualizes the process of economic development as the movement of workers fromlow productivity sectors (e.g., agriculture) to relatively high productivity sectors (e.g., manufacturing). However, it is possible that some factors of production face mobility barriers across sectors. In this case, the economy would suffer from efficiency losses, as factors of production are not reallocated to theirmost efficient use.10 Another possibility is that workers (and firms) may have
incentives to move to even lower productivity sectors. For instance, if laborand product markets are highly regulated, so that operational costs are higher
8

Note that in this case Cov (log Ai , ε) = 0
See Ross (2000, 2013) for a recent textbook treatment on how to integrate the insights fromclassical development economics into modern growth theory.
10
See Banerjee and Duflo (2005), Hsieh and Klenow (2009), and Restuccia and Rogerson(2008, 2013) as examples of recent seminal contributions dealing with the relationship between
resource misallocation and aggregate efficiency.
9

18

CARLOS A. MENDEZ-GUERRA

in the formal sector, many firms (and the workers they hire) would have additional incentives to move to the informal sector, where the regulation burden(and its associated cost) is minimized. The main lesson of this type of models isthat structural productivity differences across sectors have aggregate efficiency
implications.11 In particular, resource misallocation across sectors reduces aggregate efficiency, and ultimately labor productivity.

4.1. Dual-Economy and Misallocation Effects
Figure 10 illustrates how structural productivity differences and resource misallocation reduces total output. In this example, an economy maximizes its efficiency when the marginal productivity of labor is equal across sectors (M P L1 =M P L2 ). At Point D, the economy allocates L∗1 workers to sector one and L∗2workers to sector two. The efficiency maximizing level of output is represented
by Y ∗ . If there exist market failures or government distortions (or both), wedges
between the marginal products ( M P L1 6= M P L2 ) will be generated. At point W,
the economy allocates more workers to sector one LM
1 and less workers to sector two LM
2 . Given the wedges between marginal products (M P L1 < M P L2 ),the efficiency loss in the economy is represented by the DWL triangle and the
new level of output is Y M < Y ∗.
Given the theoretical insights of Figure 10, one would like to have a quantitative measure of the productivity wedges across sectors and their effect on aggregate efficiency. Vollrath (2009) is a seminal contribution in this line of research.
He first constructs agricultural and non-agriculture production functions forsample of countries in 1985. Then, he calibrates the parameters of each production structure to have measures of wedges in marginal productivities between
agriculture and non-agriculture. As expected, marginal productivity differences
tend be larger in developing countries. Figure 11 not only illustrates the original
finding of Vollrath (2009), but it also shows that such inter-sectorial productivity
11

See Temple (2005) for a premier treatment on how to integrate dual-economy models into
growth theory.

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

19

Figure 10: The Deadweight Loss of Resource Misallocation
Units ofoutputMarginal productof labor
in sector 1

Marginal productof labor
in sector 2

Output lost due tomisallocation

D

Y*

L

DWL

W

YM

Labor allocatedto sector 1

L*1

LM 1

L*2

LM 2

Labor allocatedto sector 2

Source: Adapted from Weil (2013)

gaps are highly correlated with differences in aggregate labor productivity.
Following the logic of Figure 10, the next step is to compute the DWL triangle
for sample of 42 developed and developing countries. Vollrath (2009) first hypothetically equalizes the the marginal products between agriculture and nonagriculture for each country. This equalization pins down the optimal allocation of resources across sectors. Then, using this optimal allocation, he recomputes the aggregate production for each country. He finds that resource misallocation between agriculture and non-agriculture explains up to 80 percent of
the variation in aggregate efficiency and between 30 percent to 40 percent of thevariation in labor productivity. Based on the data of these calculations, Figure
12 shows that countries with the lowest aggregate labor productivity are thosewith the largest efficiency losses due to misallocation.

20

CARLOS A. MENDEZ-GUERRA

Figure 11: Dual-Economy Evidence: Large Productivity Gaps across Sectors
Economy-wide Labor Productivity(USA=100)
United States
100
CanadaAustralia

80

FranceNetherlands
United Kingdom Denmark
SwedenFinland60

Italy

NorwayAustriaJapan

New Zealand

GreeceVenezuela

40

TurkeyUruguay

Portugal
Costa Rica

Colombia
Chile
South Korea
Tunisia
Dominican Rep.

20

Argentina
Sri Lanka
Syria

GuatemalaIranPhilippines
Indonesia

Peru
Egypt

Pakistan

Honduras

India

0
1

2

3

4

5

Marginal Product of Labor (non-agriculture)
Marginal Product of Labor (agriculture)

Source: Author’s calculations using data from Vollrath (2009)

4.2. Dynamic Dual-Economy Effects and Structural Change
Figures11 and 12 document the static aggregate efficiency effects of the dual
economy structure. The original insight of Lewis, however, focuses on the dynamics of reallocation, that is workers moving from traditional-low-productivity
sectors to modern-high-productivity sectors over time. McMillan and Rodrik(2011, 2013) aim to extend the research on the dynamics of the dual economy
by constructing a panel dataset that covers a sample of developing and developed countries for the period 1950-2005. The caveat of this dataset, however,is that it measures average labor productivity instead of marginal labor productivity. Note that the conceptual framework illustrated in Figure 10 depends on
the wedges between marginal products, which are not necessarily equal to average products. In spite of this limitation, one can still try to infer differences inmarginal products from differences in average products. Let us consider boththe average and marginal products of labor in a standard Cobb-Douglass pro-

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

21

Figure 12: How Large are the Dual Economy Effects?
Economy-wide Labor Productivity(USA=100)

United States

100

CanadaAustralia

80

Italy
FranceNorwayNetherlands

60

United Kingdom
Denmark
Austria
SwedenFinlandJapanNew Zealand
GreeceVenezuela

40

Dominican Rep.

20

TurkeyPortugal
Costa Rica
Chile
South Korea Colombia

Uruguay

Tunisia
Iran

Argentina

Guatemala

Peru

Sri
LankaHonduras
Philippines
PakistanIndonesia
Egypt

Syria

India

0
0

10

20

30

40

Deadweight Loss due to Misallocation

Source: Author’s calculations using data from Vollrath (2009)

duction function:
Y = AK 1−β Lβ

(10)

Y
L

(11)

Y
∂Y
=β .
∂L
L

(12)

Average Product of Labor ≡Marginal Product of Labor ≡If the parameter β is relatively constant across sectors and over time, then differences in average products will translate into differences in marginal products. Whether this is a valid assumption is a topic for further research. For the
purpose of exploration, and keeping in mind this key assumption, Figure 13
describes the dynamics of the dual economy for a sample country: Chile.
The striking feature of Chile (and Latin America in general) is that the structural change patterns described in Lewis (1954) appear to be working–in re-

22

CARLOS A. MENDEZ-GUERRA

verse (McMillan and Rodrik, 2011). Over time, workers keep gravitating from
relatively low-productivity sectors (e.g., agriculture and manufacturing) to evenlower-productivity sectors (e.g., wholesale and retail trade, and other services)12 .
More generally, McMillan and Rodrik (2013) document the structural change
patterns for sample of developing countries in Latin America, Asia, and Africa.
They conclude that after the year 2000, favorable labor reallocation increased
productivity growth both in Asia and Africa, whereas labor misallocation decreased the growth potential of Latin America.

5. Concluding Remarks
A central topic in the study of global development has to do with the huge differences in labor productivity across countries. The literature on this topic is
typically classified into two lines of research. One that studies a set of proximate sources: physical capital, human capital, and aggregate efficiency. And
the other that studies a set of deeper factors: geography, culture, and institutions.
From an empirical point of view, that key motivating fact is that, during the
1950-2010 period, labor productivity of the median country has been mostly
stagnant, while the cross-country differences have drastically increased. An
evaluation of the cross-section dynamics of the proximate sources of labor productivity reveals the following patterns:• Physical capital accumulation in the median country also appears largely
stagnant, with an increasing dispersion in the upper tail over time.
• Aggregate efficiency in the median country decreased over time, with anincreasing dispersion in both upper and lower tails.
12

Note that average productivity has been increasing both in the mining sector and in thefinance and business sector. However, the employment share in these sectors is relatively small
compared to other parts of the economy.

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

23

Figure 13: Dynamic Dual-Economy Effects: An Example from Chile(PSOR\PHQW
Share

Finance and Busines Services

Agriculture

3URGXFWLYLW\ (PSOR\PHQW
Sectoral/Total
Share

.35

.7

3URGXFWLYLW\
Sectoral/Total
4

.12

.12

.65

.31

.3

.6

.25

.5

.2

.4

.1

3.28

3
.08

.06
2

.15

.28

.11

.1
1945

1955

1965

1975

1985

1995

.04

.2

.02

2005

1.20

.02

1
1945

1955

1965

1975

1985

1995

2005

Wholesale and Retail Trade

Mining(PSOR\PHQW
Share

.3

3URGXFWLYLW\
Sectoral/Total

3URGXFWLYLW\ (PSOR\PHQW
Sectoral/Total
Share

.06

.25

1.2

7
6.62

.05

.05

.22

6

1

.2
.04

5

.03

4

.8

.15
3

.02

.01

.96

1945

2

.01

1.83

1955

(PSOR\PHQW
Share

1965

1975

1985

1995

Manufacturing

.25

.1

2005

.10

1945

.59

1955

1965

1975

1985

1995

.6

2005

&RPPXQLW\3HUVRQDODQG*RY6HUYLFHV

3URGXFWLYLW\ (PSOR\PHQW
Sectoral/Total
6KDUH
1.61

1.6

3URGXFWLYLW\
6HFWRUDO7RWDO

.35

1.6
1.48

1.4
1.4
.2

.3
.19

1.2
1.2
.26

.15

1

.25
1
.8
.22
.11

.1

.8

.78

1945

1955

1965

1975

1985

1995

2005

.61

.2
1945

1955

1965

1975

1985

1995

.6

2005

Source: Author’s calculations using data from McMillan and Rodrik(2011)• Human capital accumulation in the median country increased over time.
Contrasting the behavior of other proximate sources, this is the only vari-24

CARLOS A. MENDEZ-GUERRA

able in which the cross-country dispersion decreased over time.
From a methodological standpoint, regression methods typically overestimate
the fraction of the variation in labor productivity that is explained by physicalcapital. Such overestimation arises from the uncontrolled covariance between
capital accumulation and aggregate efficiency. Calibration methods attempt tocontrol such covariance and highlight that most of the variation in labor productivity is actually explained by aggregate efficiency.
Figure 14 presents an expanded version of the chain of causality suggested
by Hsieh and Klenow (2010)13 . The recent empirical literature on resource misallocation across sectors provides new insights on the intermediate channels
between the deep and proximate sources of labor productivity. A large fractionof the observed deterioration in aggregate efficiency is most likely to be driven
by allocation failures. For instance, the economies of Latin America appear tobe suffering from inefficient sectorial production, since most of their labor force
is concentrated in the service sector, which is the part of the economy where
average productivity is the lowest. Ultimately, resource misallocation is most
likely to be driven by policy failures, institutional weaknesses, and cultural barriers.
Over the next decades, research in economic growth and development is
expected generate new insights based on the potentially fruitful integration of
the recent quantitative dual-economy models and the standard productivity
accounting methods. In this context, some of the major questions for further
analysis may include the following14 : In what dimensions the production function of human capital differs across sectors? What kind of allocative inefficiencies have the largest effects? Are the misallocation effects across sectors larger
than those across firms? Under what conditions does a reduction in misallocation imply an unambiguous gain in welfare? Why is there a secular deteriorationin allocative efficiency in Latin America?
13
14

See Figure 1.
Some of these questions are from Hsieh and Klenow (2010).

LABOR PRODUCTIVITY, CAPITAL ACCUMULATION, AND AGGREGATE EFFICIENCY

25

Figure 14: Cross-Country Differences in Labor Productivity: An Extended Chainof Causality

Geography,
Climate,Luck

Aggregate
Efficiency

Human
CapitalPhysicalCapitalInstitutions,CultureAggregate
Efficiency

Human
CapitalPhysicalCapitalAggregate
Efficiency

Human
CapitalPhysicalCapital

Policies,
Rule of Law,
Corruption

Resource
Misallocation
acrossSectors

Cross-Country
Differences inLabor Productivity

Source: Adapted from Hsieh and Klenow (2010)

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