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研究論文
ARTICLE

Labor Productivity, Capital Accumulation,
and Aggregate Efficiency Across Countries:
New Evidence for an Old Debate
Carlos MENDEZ

50-4
名古屋大学大学院国際開発研究科

GRADUATE SCHOOL OF INTERNATIONAL DEVELOPMENTNAGOYA UNIVERSITY

Forum of International Development Studies. 50-4 (Mar. 2020)
doi: 10.18999/forids.50.4

Labor Productivity, Capital Accumulation, and Aggregate
Efficiency Across Countries: New Evidence for an Old Debate

Carlos MENDEZ*

Abstract
This article studies the proximate sources of labor productivity differences across countries.
Using a panel dataset for 74 countries covering the 1960-2010 period, it first documents that,
relative to the US, labor productivity of the median country has been mostly stagnant, whilecross-country disparities have drastically increased. Next, through the lens of a production
function framework, it evaluates the proximate sources of labor productivity: physical capital,
human capital, and aggregate efficiency. Results show stagnation and increasing disparities inphysical capital, growth and decreasing disparities in human capital, and decline and increasing
disparities in aggregate efficiency. By including the commonly unaccounted covariance between
capital and aggregate efficiency into the analysis, disparities in aggregate efficiency explain
most of the disparities in labor productivity across countries.
Keywords: Productivity, Capital Accumulation, Efficiency, Stylized Facts

1. Introduction
As summarized by Hsieh and Klenow (2010), most recent research studies in the growth anddevelopment literature analyze income and labor productivity differences across countries in way thatis consistent with the schematic relations depicted in Figure 1. Factors that affect labor productivity
are commonly classified into two layers. The first one includes proximate production sources such as
capital accumulation (both physical and human) and aggregate efficiency. Going one step further, thesecond layer includes more fundamental or deeper determinants such as geography, culture,
institutions and policies.
————————————————————————————————————————* Associate Professor at the Graduate School of International Development, Nagoya University.

1Forum of International Development Studies. 50-4 (Mar. 2020)

Figure 1 Sources of Labor Productivity and Income Differences Across Countries

Note: In their original diagram, Hsieh and Klenow (2010) use the term “total factor productivity (TFP)” instead of aggregate
efficiency. Both terms are conceptually equivalent. Also, their original diagram only points to per-capita income differences
rather than labor productivity differences.
Source: Adapted from Hsieh and Klenow (2010).

In the context of Figure 1, the present article analyzes the proximate sources of labor productivity.
First, it quantitatively describes the cross-country dynamics of each proximate source. Next, thearticle revisits the debate about the relative contribution of capital accumulation versus aggregate
efficiency. On the one hand, Mankiw et al. (1992) apply regression methods to conclude that capital
accumulation differences explain most of the variation of labor productivity across countries. On theother hand, Klenow and Rodriguez-Clare (1997) apply calibration methods to conclude that aggregate
efficiency explains most of this variation. On this debate, this article emphasizes that the source ofdisagreement is on the methodological assumptions of both lines of research. On the one hand, capital
proponents rely on the independence between capital accumulation and aggregate efficiency toconsistently estimate an unbiased OLS regression. On the other hand, efficiency proponents rely oncompetitiveness of factor markets to calibrate their model parameters.
It has been documented that, relative to the US, labor productivity of the median country of theworld has been mostly stagnant, at least since the 1960s. Also, labor productivity differences acrosscountries have drastically increased in the postwar period (Duarte and Restuccia 2006; MendezGuerra 2015; Parente and Prescott 1993). To shed some light on these global development problems,
the main objective of the present article is to understand the sources of labor productivity by analyzing
the novel productivity database of Fernandez-Arias (2014). The methodological approach foranalyzing the data follows the production function framework of Hall and Jones (1999) and it is also2Forum of International Development Studies. 50-4 (Mar. 2020)

complemented with some basic regression models. For a sample of 74 countries over the 1960-2010
period, results suggest a similar pattern of stagnation and increasing dispersion in physical capital, an
improvement and decreasing dispersion in human capital, and a deterioration and increasing
dispersion in aggregate efficiency.
The article also shows how standard regression methods tend to overestimate the fraction of thevariation in labor productivity that is explained by physical capital. The source of this upward bias is
the unaccounted covariance between capital and aggregate efficiency. Taking this covariance into
account, most of the variation in labor productivity turns out to be explained by aggregate efficiency.
After this introduction, Section 2 describes the methods and data. Section 3 presents an evaluationof the three proximate sources of labor productivity. Section 3 discusses what factors could be driving
the dynamics of aggregate efficiency. Section 4 offers some concluding remarks

2. Methods and Data
2.1. A Production Function Approach
Based on the standard neoclassical growth model, Hall and Jones (1999) apply the following
production function approach to evaluate the relative contribution of proximate sources of laborproductivity:
𝑌𝑌𝑖𝑖 = 𝐴𝐴𝑖𝑖 𝐾𝐾𝑖𝑖𝛼𝛼 (ℎ𝑖𝑖 𝐿𝐿𝑖𝑖 )1−𝛼𝛼 for all 𝛼𝛼 ∈ (0,1).

(1)

In Equation 1, 𝑌𝑌𝑖𝑖 is total real GDP in country 𝑖𝑖, 𝐴𝐴𝑖𝑖 is an aggregate efficiency index, 𝐾𝐾𝑖𝑖 is the total

physical capital stock, ℎ𝑖𝑖 is human capital of the average worker, 𝐿𝐿𝑖𝑖 is the labor force, and 𝛼𝛼 isthe elasticity of GDP with respect to physical capital.1 Dividing Equation 1 by the labor force 𝐿𝐿𝑖𝑖 , andrearranging terms, we can obtain an expression for the average productivity of labor:
𝑌𝑌𝑖𝑖
𝐾𝐾𝑖𝑖 𝛼𝛼 1−𝛼𝛼
= 𝐴𝐴𝑖𝑖 � � ℎ𝑖𝑖 .
𝐿𝐿𝑖𝑖
𝐿𝐿𝑖𝑖

(2)

Equation 2 shows that the forces driving the behavior of labor productivity can be organized into
three variables: aggregate efficiency, capital-labor ratio, and human capital per worker. Similar to theinterpretation of Equation1, labor productivity in country 𝑖𝑖 would be higher if its workers
accumulate more productive resources (e.g., physical capital and human capital) and/or if thoseresources are used more efficiently.
Ideally, one would like to use Equation 2 for answering questions such as: How much does laborproductivity increase in response to an increase in aggregate efficiency? One problem, however, isthat capital accumulation responds endogenously to changes in aggregate efficiency (Klenow and3

Forum of International Development Studies. 50-4 (Mar. 2020)

Rodriguez-Clare 1997). Conceptually, this endogeneity arises because physical capital is defined inunits of final output (that is, GDP). As a result, any increase in aggregate efficiency would affectlabor productivity both directly and indirectly through capital accumulation. To address thisendogeneity issue, Klenow and Rodriguez-Clare (1997) rearrange Equation 2 and suggest thefollowing steady-state production function:
𝛼𝛼

1
𝑌𝑌𝑖𝑖
𝐾𝐾𝑖𝑖 1−𝛼𝛼� �= 𝐴𝐴1−𝛼𝛼
ℎ𝑖𝑖 .
𝑖𝑖
𝐿𝐿𝑖𝑖
𝑌𝑌𝑖𝑖

(3)

Equation 3 is in line with the equilibrium of the standard Solow growth model. In steady-state, thecapital-output ratio, 𝐾𝐾/𝑌𝑌 , is exogenous to changes in aggregate efficiency, 𝐴𝐴. More intuitively,
perhaps, Equation 3 is more useful to control for the indirect effects of efficiency by raising its
1elasticity from one to 1−𝛼𝛼.

Conceptually, aggregate efficiency is a measure that quantifies the way in which an economy uses

its productive resources. Efficiency gains arise due to improvements in both technological knowledge
and reallocation of resources to better uses. Empirically, however, aggregate efficiency is measured
as a residual variable. It captures everything else that affects labor productivity that is not alreadymeasured in the capital inputs. According to this definition, most studies compute aggregate
efficiency for a country at a point of time as the following ratio:
𝐴𝐴 =

𝑌𝑌
𝐿𝐿

𝐾𝐾 𝛼𝛼
� 𝐿𝐿 � ℎ1−𝛼𝛼.

(4)To compute this ratio, one needs data about a key parameter: the output elasticity with respect tocapital, 𝛼𝛼 . Given the results of Figure 4, this parameter tends to be overestimated when using

regression methods. Alternatively, one could obtain such information from other sources. For instance,
it is well known that in a competitive market with a production function that exhibits constant returns
to scale, this parameter can be computed as the GDP share that accrues to physical capital. Based on
this criteria, Gollin (2002) collects data from developed and developing countries to constructmeasures of the capital income share. He finds that the average capital share is about 0.33.
2.2. Data: Labor Productivity and Sample Coverage
To empirically evaluate the previously described production framework across countries and overtime, one needs to construct a balanced panel dataset. Largely based on the data from the Penn World
Table 8.0, Fernandez-Arias (2014) constructs an unbalanced panel dataset that contains different

measures of productivity and capital inputs for a large sample of both developing and developed4Forum of International Development Studies. 50-4 (Mar. 2020)

countries over the 1950-2011 period. By exploiting this dataset, in the present article I construct abalanced panel dataset that covers 74 countries over the 1960-2010 period (See Appendix A for a
detailed list of countries and some descriptive statistics). Furthermore, to facilitate the scale ofcomparison across variables, countries, and time, I re-scaled all variables relative to their level in the
United States. In other words, for all variables and all years, the performance of the United States will
be used as a benchmark. This is a common practice in the literature (see Caselli 2005) and it helps us
identify to what extent the median country of the world is converging to the technological frontier.
Note that in the following results, the median country is not fixed to a certain country over time. As
some countries move forward and others backward within the cross-country distribution, the country
that occupies the center of distribution is likely to change in a year-by-year basis.
Figure 2 Labor Productivity: Median Country and Dispersion Across Countries

Source: IADB Productivity Database. See Fernandez-Arias (2014) for details.

To measure labor productivity, this paper starts by dividing PPP-adjusted real GDP by the numberof workers in the labor force.2 Next, to remove short-run fluctuations, the statistical filter of Hodrick
and Prescott (1997) is applied with a smoothing parameter of 100. Based on this approach, Figure 2
summarizes the two key features of labor productivity across countries. First, relative to the US, laborproductivity of the median country was mostly stagnant over the 1960-2010 period.3 For example,
labor productivity of the median country was 19 percent in 1960. After 51 years, it only increased to
22 percent. Moreover, this 3 percent difference is not statistically different from zero. Second, thedispersion of labor productivity across countries (measured by the interquartile range) largely

5Forum of International Development Studies. 50-4 (Mar. 2020)

increased. For instance, in 1960, the difference between the 75th percentile and the 25th percentile ofthe cross-country distribution was 29 percentage points. After 51 years, this dispersion increased to58 percentage points. This difference means that labor productivity disparities across countries almost
doubled over the 1960-2010 period. What explains this lack of convergence and increasing disparities
in labor productivity? Section 3 aims to provide an answer to this question based on the proximate
sources of labor productivity: physical capital, human capital, and aggregate efficiency. Before
moving to the results, however, let us briefly describe how these variables were constructed andmeasured.4

2.3. Measuring Physical Capital, Human Capital, and Aggregate Efficiency
To measure physical capital per worker, total physical capital stock is divided by the labor force,and then its long-run trend is estimated.5 It is important to note that to construct this variable,
Fernandez-Arias (2014) uses investment data from the Penn World Tables 8 and a fixed depreciation
rate of 7 percent. With this information, he applies the perpetual inventory method to accumulate
investment flows and recover the physical capital stock.6
To measure human capital per worker, Fernandez-Arias (2014) follows the standard approach in
the economic growth literature and constructs a human capital index.7 It is important to note, however,that this index is mostly a proxy for the quantity of human capital (years of schooling) as opposed toa quality measure (learning scores). Although some recent studies, such as Kaarsen (2014) and
Lagakos et al. (2012), have started to include some measures of the quality of schooling and the rates
of returns to work experience, country and time coverage remains limited, particularly for developing
countries before the 1990s.
To measure aggregate efficiency, Equation 4 is applied. Given the estimates of labor productivity,
physical and human capital, it is possible to compute a measure of aggregate efficiency that depends
on one key parameter: the the output elasticity with respect to physical capital (that is, α in Equation
1).

Klenow and Rodriguez-Clare (1997) argue that since this elasticity parameter is typicallyoverestimated when using standard regression methods, one could try to calibrate its value in a waythat is consistent with the national income accounts of a country. Based on this approach, Gollin(2002) collects data from a representative sample of countries and constructs a measure for thisparameter. He finds that on average the capital income share (α) is about 0.33. Thus, given this value,
and all the explanatory variables of Equation 4, aggregate efficiency is also measured for 74 countries
over the 1960-2010 period.

6

Forum of International Development Studies. 50-4 (Mar. 2020)

3. Results: The Proximate Sources of Labor Productivity
3.1. Physical Capital: Differences Across Countries and Over Time
Figure 3 shows the two features that characterize the evolution physical capital across countries.
First, similar to labor productivity, physical capital per worker of the median country shows recurrent
periods of stagnation (lack of catch up with the frontier) and very little progress overall. In 1960,
physical capital per worker relative to that in the United States was 15 percent. After 51 years, it only
increased to 23 percent. Second, cross-country disparities in physical capital drastically increased
over time and this increasing dispersion is noticeable larger in the upper tail of the cross-country
distribution. For instance, in 1960, the interquartile range was 26 percentage points. After 51 years,
this dispersion increased to 70 percentage points. This growth over time means that disparities inphysical capital per worker across countries almost tripled over the 1960-2010 period.
In some previous studies, the similarity between the patterns of labor productivity and physicalcapital is summarized by a (log-log) linear regression. Figure 4 presents this summary approach andfurther indicates that the relationship between labor productivity and physical capital has become
stronger over time. Note that as time passes from 1970 to 2010, both the R-squared statistic and theconfidence interval of the slope coefficient are approaching to 100 percent and 1, respectively.
Figure 3 Physical Capital: Median Country and Dispersion Across Countries

Source: IADB Productivity Database. See Fernandez-Arias (2014) for details.

7Forum of International Development Studies. 50-4 (Mar. 2020)

Figure 4 Labor Productivity and Physical Capital

Note: The figure shows three simple regression lines for the years 1970, 1990 and 2010, respectively. The goodnessof fit of each regression is summarized by coefficient of determination (R-squared). A 95-percent confidence
interval for the slope coefficient of each regression is presented in brackets.
Source: IADB Productivity Database. See Fernandez-Arias (2014) for details

However, the values of these two indicators need to be interpreted with caution and conditional toa strong assumption. First, let us consider a simplified logarithmic version of Equation 2:
𝑌𝑌𝑖𝑖
𝐾𝐾𝑖𝑖
𝑙𝑙𝑙𝑙𝑙𝑙 � � = 𝛽𝛽 + 𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 � � + 𝜀𝜀𝑖𝑖 .
𝐿𝐿𝑖𝑖
𝐿𝐿𝑖𝑖

(5)

By construction, in this model (and in the results of Figure 4), both human capital and aggregate
efficiency would be included in the error term 𝜀𝜀𝑖𝑖 . From an econometric perspective, however, only

under the strong assumption that these two variables are independent to physical capital, the value ofthe slope coefficient 𝛼𝛼 (and the R-squared) would be consistently estimated using a standard OLS

regression. Only if we were willing to accept this brave assumption, we could be confident that mostof the cross-country differences in labor productivity are explained by differences physical capital,
and the role of human capital and aggregate efficiency would be minimal. For instance, given thehigh R-squared of 96 percent in 2010, the combined effect of human capital and aggregate efficiency
would only explain 4 percent of the labor productivity differences across countries.

8Forum of International Development Studies. 50-4 (Mar. 2020)

Figure 5 Human Capital: Median Country and Dispersion Across Countries

Source: IADB Productivity Database. See Fernandez-Arias (2014) for details.

3.2. Human Capital: Differences Across Countries and Over Time
Figure 5 shows the two main features that characterize the evolution of human capital: growth ofthe median country and decreasing cross-country disparities.

In contrast to the labor productivity

and physical capital patterns, relative human capital of the median country increased during the 19602010 period. For example, human capital per worker was 56 percent in 1960; by 2010, it reached to74 percent. Also, in contrast to the labor productivity and physical capital patterns, cross-country
disparities in human capital slightly decreased over this period. For instance, in 1960, the interquartile
range was 25 percentage points. After 51 years, this dispersion decreased to 21 percentage points.
The upward trend in human capital can be explained by two factors: (1) the worldwide
accumulation of years of schooling; and (2) the upper boundary of 16 years of education in thebenchmark country (the US). If we could use cognitive test scores to construct a better human capitaltrend for all the countries in the sample over the 1960-2010 period, then it is reasonable to expect lessencouraging results. This is a limitation of the present study and it should be handled in future research,when more systematic data becomes available.

9Forum of International Development Studies. 50-4 (Mar. 2020)

Figure 6 Labor Productivity and Human Capital

Note: The figure shows three simple regression lines for the years 1970, 1990 and 2010, respectively. The goodness of
fit of each regression is summarized by coefficient of determination (R2). A 95-percent confidence interval for theslope coefficient of each regression is presented in brackets.
Source: IADB Productivity Database. See Fernandez-Arias (2014) for details.

Figure 6 shows that human capital is also highly correlated with labor productivity, though not asmuch as physical capital. Similar to Equation 5, an OLS regression would suggest that, in the 2010,human capital explained 72 percent of the labor productivity differences across countries. Again, thecredibility of this high explanatory power largely depends on the independence among human capital,
physical capital, and aggregate efficiency.

3.3. Aggregate Efficiency: Differences Across Countries and Over Time
Using a physical capital share value (α) of 0.33 and the previously described data on laborproductivity and capital inputs, Figure 7 shows the two key features that characterize aggregate:
decline of the median country and increasing cross-country disparities. Over the 1960-2010 period,
and relative to the United States, aggregate efficiency of the median country decreased from 53
percent to 47 percent. Cross-country disparities, on the other hand, increased. In 1960, theinterquartile range was 40 percentage points. After 51 years, this dispersion increased to 51
percentage points. Moreover, this increasing dispersion is occurring in both tails of the cross-country
distribution.
10

Forum of International Development Studies. 50-4 (Mar. 2020)

Figure 7 Aggregate Efficiency: Media Country and Dispersion Across Countries

Source: IADB Productivity Database. See Fernandez-Arias (2014) for details.

Figure 8 Labor Productivity and Aggregate Efficiency

Note: The figure shows three simple regression lines for the years 1970, 1990 and 2010, respectively. The goodnessof fit of each regression is summarized by coefficient of determination (R2). A 95-percent confidence interval
for the slope coefficient of each regression is presented in brackets.
Source: IADB Productivity Database. See Fernandez-Arias (2014) for details.

11Forum of International Development Studies. 50-4 (Mar. 2020)

Besides the increase in the cross-country dispersion, the most noteworthy tendency suggested by
Figure 7 is that since the early 1970s, the level aggregate efficiency shows a systematic decreasing
trend. This result implies a potential explanation for the stagnation of labor productivity (Figure 2).
Given the stagnation of physical capital (Figure 3), it seems plausible that the decreasing trend inaggregate efficiency (Figure 7) may off-set the positive effects associated with the increasing trend
in human capital (Figure 5). Note that the take-off time of these two trends is similar, both started in
the early 1970s. Thus, when combining these three tendencies (stagnant physical capital, increasing
human capital, and decreasing aggregate efficiency), it is plausible to expect little progress in laborproductivity.
Figure 8 shows that aggregate efficiency is also strongly correlated with labor productivity.
Moreover, for the year 2010, the R-squared of a simple linear regression would suggest that 96 percentof labor productivity differences are explained by aggregate efficiency alone. Given these findings,
one would not only conclude that differences in aggregate efficiency could be as important as physicalcapital, but also that these two measures are highly correlated. In fact, for the year 2010 the pairwise
correlation between them was 0.93.

4. Discussion
4.1. How to Disentangle the Effect of Physical Capital from Aggregate Efficiency?
Some regression studies, such as the seminal work of Mankiw et. al (1992), argue that physicalcapital is the main driver of labor productivity. However, the main criticism to the regression
approach is that both the estimated physical capital share (𝛼𝛼) and the R-squared tend to be upwardly
biased (Gollin 2002; Klenow and Rodriguez-Clare 1997). For Gollin (2002) shows that plausible
values for 𝛼𝛼 tend to be around 0.33. The results of Table 1 suggest that implausible large values forthe share of physical capital (𝛼𝛼) are persistent, even after controlling for human capital, country fixed
effects, and constant returns to scale.
As suggested by standard econometric theory, the source of this overestimation is the uncontrolledcorrelation between physical capital and aggregate efficiency. Thus, if the correlation between capitaland aggregate efficiency is so strong, how can we disentangle the variation of labor productivity thatis due to capital differences alone? In line with the methodology suggested by Klenow and RodriguezClare (1997), the work of Vollrath (2014) suggests the following method to identify the variation oflabor productivity that is due to capital differences alone.

12Forum of International Development Studies. 50-4 (Mar. 2020)

Table 1 Different Estimations of Output Elasticities: 1950-2010 Period
Model (1)Model (2)Model (3)

0.74

0.74

0.51

(0.009)***(0.007)***(0.01)***

0.25

0.26

0.49

(0.037)***(0.007)***(0.01)***

Fixed Effects

NO

NO

YES

CRS Constraint

NO

YES

YES

R-squared

0.90

NA

NA

Observations

3,774

3,774

3,774

Physical Capital (𝛼𝛼)Human Capital (1 − 𝛼𝛼)Note: The numbers in parenthesis indicate robust standard errors. All variables are significant
at 1 percent. All regressions include a constant term that is not reported in the table. CRS
stands for constant returns to scale. NA stands for Not Available in constrained regression
framework.
Source: IADB Productivity Database. See Fernandez-Arias (2014) for details.

First, let us rewrite the simple econometric model described in Equation 5 as:𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 = 𝛽𝛽 + 𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 + 𝜀𝜀𝑖𝑖 ,(6)where labor productivity 𝑦𝑦 and the capital-labor ratio 𝑘𝑘 are expressed as lower-case letters tosimplify notation. Next, define the variation of the dependent variable that is explained by the modelas:
𝑅𝑅 2 =𝑉𝑉𝑉𝑉𝑉𝑉(𝛽𝛽 + 𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 ).
𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )(7)Then, utilize the statistical properties of the variance and covariance operators and the definition of
the OLS estimator to show that𝑅𝑅 2 = 𝛼𝛼 2
𝑅𝑅 2 = 𝛼𝛼𝑅𝑅 2 =𝑅𝑅 2 =𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )𝐶𝐶𝐶𝐶𝐶𝐶(𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 ) 𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )�������������𝛼𝛼

𝐶𝐶𝐶𝐶𝐶𝐶(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑜𝑜𝑜𝑜 𝑦𝑦𝑖𝑖 )𝐶𝐶𝐶𝐶𝐶𝐶(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝛽𝛽 + 𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 + 𝜀𝜀𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )13Forum of International Development Studies. 50-4 (Mar. 2020)

𝑅𝑅 2 =

𝐶𝐶𝐶𝐶𝐶𝐶(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝛽𝛽) 𝐶𝐶𝐶𝐶𝐶𝐶(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 ) 𝐶𝐶𝐶𝐶𝐶𝐶(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝜀𝜀𝑖𝑖 )++𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )𝑅𝑅 2 = 0 +𝑉𝑉𝑉𝑉𝑉𝑉(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 ) 𝐶𝐶𝐶𝐶𝐶𝐶(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝜀𝜀𝑖𝑖 )+𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )𝑉𝑉𝑉𝑉𝑉𝑉(𝑙𝑙𝑙𝑙𝑙𝑙 𝑦𝑦𝑖𝑖 )(8)Equation 8 shows that we can compute an unbiased R-squared by letting 𝐶𝐶𝐶𝐶𝐶𝐶(𝛼𝛼 𝑙𝑙𝑙𝑙𝑙𝑙 𝑘𝑘𝑖𝑖 , 𝜀𝜀𝑖𝑖 ) = 0

and selecting a value for 𝛼𝛼. Following the work of Gollin (2002), most studies set 𝛼𝛼 = 0.33. Given

this setting, in the year 2010, cross-country differences in physical capital explained only 14 percentof the differences in labor productivity.

Applying the same procedure to disentangle the contribution of aggregate efficiency.8 In the year
2010, aggregate efficiency explained 44 percent of the labor productivity differences across countries.
This finding is consistent with previous literature (Baier et al. 2006; Caselli 2005; Hall and Jones
1999; among others) in the sense that aggregate efficiency is the main driving force behind the laborproductivity.

4.2. What Could Explain a Decreasing Trend in Aggregate Efficiency?
Classical development economics models, such as Lewis (1954), focus on the coexistence offundamentally different structures of production within an economy.9 In its simplest representation,
Lewis’ dual economy model defines economic development as the secular movement of workers
from low-productivity sectors (such as agriculture) to high-productivity sectors (such as
manufacturing). The main lesson of this type of models is that structural productivity differences
across sectors have aggregate efficiency implications.10 In particular, when labor is misallocatedacross sectors, aggregate efficiency is expected to be lower.
McMillan and Rodrik (2012) and McMillan et. al (2014) study the growth effects of labor
misallocation across sectors. Their most compelling finding suggests that the economies of Latin
America and Africa suffer from efficiency loses largely due to labor misallocation. Workers appear
to be moving from low-productivity sectors to even lower-productivity part of the economy. To
further illustrate this mechanism, Mendez-Guerra (2017) highlights the dynamics of labor
misallocation in the case of Chile. The striking feature of Chile (and Latin America in general) is thatthe structural change patterns described in Lewis (1954) appear to be working–in reverse. Over time,
workers keep gravitating from relatively low-productivity sectors (e.g., agriculture andmanufacturing) to even lower-productivity sectors. For instance, the employment share of agriculture
declined from 31 percent to 11 percent and its relative productivity increased from 28 percent to 65
percent over the entire 1950-2005 period. Most agricultural workers migrated to the cities and instead

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Forum of International Development Studies. 50-4 (Mar. 2020)of finding jobs in manufacturing industries, they appear to have found jobs in service relatedindustries. Paradoxically, the relative productivity of most service industries is even lower than thatof agriculture. For instance, in 2010, the relative productivity of whole-sale and retail trade was 59
percent while the productivity of agriculture was 65 percent. Thus, as shown by standard economic
theory, when workers reallocate to lower-productivity industries, the aggregate economy suffers anefficiency loss.

5. Concluding Remarks
A central topic in the study of global development has to do with the huge differences in laborproductivity across countries. The literature on this topic is typically classified into two lines ofresearch. One that studies a set of proximate sources such as production inputs (physical and humancapital) and aggregate efficiency. And the other that studies a set of deeper factors such as geography,
culture, and institutions. In this context, this article evaluates the relative contribution of each of theproximate sources of labor productivity. The novel productivity database of Fernandez-Arias (2014)
suggests that, during the 1960-2010 period, labor productivity of the median country has been mostly
stagnant, while cross-country productivity differences have drastically increased. The cross-country
dynamics of the three proximate sources of labor productivity reveal the following patterns:• Physical capital accumulation of the median country also appears largely stagnant, with anincreasing dispersion particularly around the upper tail of the cross-country distribution.
• Human capital accumulation of the median country increased over time. Contrasting the behaviorof other proximate sources, this is the only variable in which the cross-country dispersion decreased
over time• Aggregate efficiency of the median country decreased over time, with an increasing dispersion inboth tails of the cross-country distribution.
From a methodological standpoint, regression methods typically overestimate the fraction of thevariation in labor productivity that is explained by physical capital. Such overestimation arises fromthe uncontrolled covariance between capital accumulation and aggregate efficiency. Calibration
methods attempt to control such covariance and highlight that most of the variation in laborproductivity is actually explained by aggregate efficiency. As a result, the central finding of thisarticle highlights the role of aggregate efficiency as the main driver of the observed differences inlabor productivity across countries. This result is consistent with the recent literature summarized by
Caselli (2005) and Hsieh and Klenow (2010).
Labor misallocation across sectors could potentially help us understand the observed differences

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Forum of International Development Studies. 50-4 (Mar. 2020)in aggregate efficiency across countries. There is an emerging quantitative literature on resource
misallocation that provides new insights on the intermediate channels between the deep andproximate sources of labor productivity (McMillan and Rodrik 2012; Restuccia and Rogerson 2008,2013; Vollrath 2009). In particular, this literature suggests that the observed deterioration in aggregate
efficiency could be driven by both market allocation failures and policy distortions. The case of Latin
American economies is commonly highlighted in this literature. In this region, economies appear tobe suffering from inefficient sectorial production. Most of their labor force is concentrated in theservice sector, where the average productivity level is even lower than that of agriculture.

Notes ———————————————————————————————
1 The literature typically refers to A_i as total factor productivity (TFP). To avoid confusion with other productivity
terms in this article I use the term aggregate efficiency instead to total factor productivity. Also, in this article, theterms GDP and “output” refer to the same variable or concept. In some sections the term “output” is used to signal
and emphasize a conceptual input-output relation. In other sections, however, the term GDP is instead used tosignal and emphasize the empirical measurement of output at the national level.
2 In the database of Fernandez-Arias (2014), real GDP is named Y and the employed labor force is named Lemp.
3 In this paper, the word “stagnation” does not mean that countries are not growing in absolute terms. It simply
means that countries are not keeping up with growth pace of the US.
4 A common limitation of cross-country studies is that they do not consider within-country variations and thevariations across individuals within the world income distribution. For instance, although relative stagnation is acharacteristic of the median country of the world, this characteristic does not necessarily apply to the median
individual or household of the world. By using household data, instead of aggregate data, Milanovic (2016) showsthat middle income individuals (who are mostly from India and China) are actually catching up.
5 In the database of Fernandez-Arias (2014), total physical capital stock is named K.
6 To apply the perpetual inventory method, an estimate of the initial capital-output ratio is needed. In the databaseof Fernandez-Arias (2014), this ratio is estimated based on the steady-state condition described in Hall and Jones(1999).
7 For a detailed exposition on the construction of the human capital index, see the paper of Hall and Jones (1999).
It is worth noticing that, in contrast to labor productivity and physical capital, a long-run trend is not computed forhuman capital. This is because the human capital series do not show noticeable cyclical changes over the short run.
For reference purposes, the human capital index is named h in the original database of Fernandez-Arias (2014).
8 That is, Cov(log A_i,ε)=09 See Ros (2000, 2013) for a review on how to integrate the insights from classical development economics intomodern growth theory. Also, for a more comprehensive presentation about the role of resource misallocation on
aggregate efficiency, see Section 4 of Mendez-Guerra (2017).

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

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Appendix A

Available online at http://bit.ly/appendix-a-forum2019

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