ï»¿ WPS6335
Policy Research Working Paper 6335
Structural Change and Cross-Country
Growth Empirics
Markus Eberhardt
Francis Teal
The World Bank
Development Economics Vice Presidency
Partnerships, Capacity Building Unit
January 2013
Policy Research Working Paper 6335
Abstract
One of the most striking features of economic growth functions for agriculture and manufacturing in a panel
is the process of structural change whereby the share of 40 developing and developed countries for the period
of agriculture in GDP decreases as countries develop. from 1963 to 1992. It empirically models dimensions
The cross-country growth literature typically estimates of heterogeneity across countries, allowing for different
an aggregate homogeneous production function or choices of technology within both sectors. The paper
convergence regression model that abstracts from this argues that heterogeneity is important within sectors
process of structural change. This paper investigates across countries implying that an analysis of aggregate
the extent to which assumptions about aggregation data will not produce useful measures of the nature of
and homogeneity matter for inferences regarding the the technology or productivity. It shows that many of the
nature of technology differences across countries. Using puzzling elements in aggregate cross-country empirics
a unique World Bank dataset, it estimates production can be explained by inappropriate aggregation across
heterogeneous sectors.
This paper is a product of the Partnerships, Capacity Building Unit, Development Economics Vice Presidency. It is part
of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy
discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org.
The authors may be contacted at markus.eberhardt@nottingham.ac.uk and francis.teal@economics.ox.ac.uk.
The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the
names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those
of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and
its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent.
Produced by the Research Support Team
Structural Change and Cross-Country Growth Empirics
Markus Eberhardt and Francis Teal*
JEL codes: O47, O11, C23
Keywords: dual economy model; cross-country production function; technology heterogeneity;
aggregation; common factor model; panel time series econometrics
Sector Board: Economic Policy (EPOL)
* Markus Eberhardt (markus.eberhardt@nottingham.ac.uk, corresponding author) is a lecturer in
economics at the University of Nottingham and a research associate at the Centre for the Study
of African Economies (CSAE), Department of Economics, University of Oxford. Francis Teal
(francis.teal@economics.ox.ac.uk) is a university reader in economics at the University of
Oxford, deputy director of CSAE, and a research fellow at the Institute for the Study of Labor
(IZA), Bonn. This research was supported by the UK Economic and Social Research Council
[grant numbers PTA-031-2004-00345 and PTA-026-27-2048 to M.E.] and the Bill and Melinda
Gates Foundation [to M.E.]. The authors thank Anindya Banerjee, Alberto Behar, Steve Bond,
Josep Carrion-i-Silvestre, Areendam Chanda, Hashem Pesaran, MÃ¥ns SÃ¶derbom, Ron Smith,
Dietz Vollrath, three anonymous referees, and seminar/session attendants at Oxford, Manchester,
and Birmingham as well as the CSAE Annual Conference 2009, the 13th Applied Economics
Meeting, the 16th International Panel Data Conference, and the 7th Annual Meeting of the Irish
Society of New Economists for useful comments and suggestions. The usual disclaimers apply.
The early literature on developing countries distinguished between the processes of economic
development and economic growth. Economic development was considered a process of
structural transformation by which, in Arthur Lewisâ€™ frequently cited phrase, an economy that
was â€œpreviously saving and investing 4 or 5 percent of its national income or less, converts itself
into an economy where voluntary savings is running at about 12 to 15 percent of national
incomeâ€? (Lewis 1954: 155). An acceleration in the investment rate was only one part of this
process of structural transformation; of equal importance was the process by which an economy
moves from dependence on subsistence agriculture to one in which a modern industrial sector
absorbs an increasing proportion of the labor force (e.g., Jorgensen 1961; Ranis and Fei 1961;
Robinson 1971). In contrast to these models of â€œdevelopment for backward economiesâ€?
(Jorgensen 1961: 309), where duality between the modern and traditional sectors was a key
feature of the model, was the analysis of economic growth in developed economies. 1 Here, the
processes of factor accumulation and technical progress occur in an economy that is already
developed, in the sense that it has a modern industrial sector and agriculture has ceased to be a
major part of the economy (e.g. Solow 1956; Swan 1956).
Since the early 1990s, the literature on economic development and economic growth has
yielded a wide array of models with increasing interaction between theory and empirics (Durlauf
and Quah, 1999; Easterly, 2002; Durlauf, Johnson, and Temple, 2005). The applied literature
continues to be dominated by an empirical version of the aggregate Solow-Swan model (Temple
2005), with much of the debate focusing on the roles of factor accumulation versus technical
progress (Young 1995; Klenow and Rodriguez-Clare 1997a, b; Easterly and Levine 2001; Baier,
Dwyer, and Tamura 2006). Although some new theoretical and empirical work has used a dual
economy approach (e.g., Vollrath 2009a, b; Lin, 2011; McMillan and Rodrik 2011; Page 2012),
2
this model is largely absent from textbooks on economic growth and has not been the central
focus for most empirical analyses (Temple 2005). A primary reason for this focus has been the
availability of data. The Penn World Table (PWT) dataset (most recently, Heston, Summers, and
Aten 2011) and the Barro-Lee data on human capital (most recently, Barro and Lee 2010) have
supplied macrodata that facilitate the estimation of the aggregate human capital-augmented
Solow-Swan model. However, a team at the World Bank has developed comparable sectoral data
for agriculture and manufacturing (Crego, Larson, Butzer, and Mundlak 1998) that allow for a
closer matching between a dual economy framework and the data, which we seek to exploit in
this paper.
We estimate production functions for the manufacturing and agriculture sectors and
contrast the results with those from â€˜stylizedâ€™ aggregate production functions where we construct
all variables by adding up the sectoral values in each country. In addition, we follow the standard
approach in the literature using data from the PWT to estimate aggregate functions. Our findings
indicate that technological differences across countries and sectors are important and that
aggregate specifications are likely to produce misleading inferences regarding total factor
productivity (TFP).
The remainder of the paper is organized as follows: section I provides motivations for
technology heterogeneity across sectors and countries. In section II, we introduce an empirical
specification for our dual economy framework, discuss the data, and briefly review the empirical
methods and estimators employed. Section III reports and discusses empirical findings at the
sector level. Section IV presents empirical findings from stylized and PWT aggregate data as
well as evidence for technology heterogeneity. Summary remarks and conclusions are provided
in section V.
3
<>TECHNOLOGY HETEROGENEITY
In the following sections, we sketch our theoretical arguments for technology heterogeneity
across sectors of production and across countries, building on the dual economy and new growth
literature.
<**>Technology Heterogeneity across Sectors
From a technical point of view, an aggregate production function only offers an appropriate
construct in a cross-country empirical framework if the economies under investigation do not
display large differences in sectoral structure (Temple 2005) because a single production
function framework assumes common production technology across all firms facing the same
factor prices. Consider two distinct sectors, assuming marginal labor product equalization and
capital homogeneity across sectors, and Cobb-Douglas-type production technology. Then, if
technology parameters differ between sectors, aggregated production technology cannot be of the
(standard) Cobb-Douglas form (Stoker 1993; Temple and WÃ¶ÃŸmann 2006). Thus, finding
different technology parameters across sectoral production functions is potentially a serious
challenge to treating production in the form of an aggregated function.
An alternative motivation for focusing on sector-level rather than aggregate growth
across countries is the following: it is common practice in applied work to exclude oil-producing
countries from any aggregate growth analysis because â€œthe bulk of recorded GDP for these
countries represents the extraction of existing resources, not value addedâ€? (Mankiw, Romer, and
Weil 1992: 413). The underlying argument is that sectoral â€˜distortions,â€™ such as resource wealth,
justify the exclusion of these observations. Therefore, it could be argued that given the large
share of agriculture in GDP for countries such as Malawi (25 to 50 percent over the period
between 1970 and 2000), India (25 to 46 percent), or Malaysia (8 to 30 percent), these countries
4
should be excluded from any aggregate growth analysis because a significant share of their
aggregate GDP is derived from a single resource, namely, land. 2 A sector-level analysis
mitigates this problem because manufacturing and agriculture are clearly more homogeneous
sectors than any aggregate construct.
<****>Technology Heterogeneity across Countries
A theoretical justification for heterogeneous technology parameters across countries can be
found in the â€˜new growthâ€™ literature. This strand of the literature on theories of economic growth
argues that production functions differ across countries and seeks to determine the sources of this
heterogeneity (Durlauf, Kourtellos, and Minkin 2001). As Brock and Durlauf (2001: 8/9) remark,
â€œâ€¦ the assumption of parameter homogeneity seems particularly inappropriate when one is
studying complex heterogeneous objects such as countries.â€? Azariadis and Drazenâ€™s (1990)
model can be considered the â€˜grandfatherâ€™ for many of the theoretical attempts to allow countries
to possess technologies that differ from one another or over time. Other theoretical studies lead
to interpretations of multiple equilibria as factor parameter heterogeneity in the production
function (e.g., Murphy, Shleifer, and Vishny 1989; Durlauf 1993; Banerjee and Newman 1993).
The â€˜appropriate technologyâ€™ literature provides a further challenge to the assumption of a
common technology, arguing that different technologies are appropriate for different factor
endowments (see Basu and Weil 1998): global R&D leaders develop productivity-enhancing
technologies that are suitable for their own capital-labor ratios and that cannot be used
effectively by poorer countries; therefore, the latter do not develop. Empirical evidence that
lends support to this hypothesis can be found in Clark (2007) and Jerzmanowski (2007). A
simpler justification for heterogeneous production functions is offered by Durlauf, Kourtellos,
and Minkin (2001: 929), who suggest that the Solow model was never intended to be valid in a
5
homogeneous specification for all countries but that it might be a good way to investigate each
country, that is, if we allow for parameter differences across countries.
Formal insights for empirical modeling can be gained from the microproduction
framework introduced in Mundlak (1988) and applied to macrodata for agriculture in Mundlak,
Larson, and Butzer (1999) and Mundlak, Butzer, and Larson (2012). In these studies, the
technology of production available to individual firms is a collection of possible techniques, each
with its own production function, with optimal output over implemented techniques defined as
(1) Y * â‰¡ F ( X * , s) = Ï• (s)
where X* and Y* represent (optimal) inputs and output aggregated over implemented techniques,
and s is a vector of state variables determining both optimal input choice X*and implemented
technique F(â‹…). 3 In each period, 4 firms face the economic problem of choosing inputs and the
appropriate production technique. This joint determination of inputs and technique makes it
difficult to identify parameter coefficients in an empirical equivalent of equation (1) unless
additional structure is imposed on the problem. Adopting a number of simplifying assumptions,
Mundlak, Butzer, and Larson (2012) provide the following approximation for their empirical
model of output and inputs (i.e., production/supply and factor demand functions), explicitly
including the exogenous state variables s
(2) yit = xit Î² ( s ) + sit Î³ + m0it + u0it
(3) x jit = sitÎ³ + m0it + Îµ jit
where subscript j refers to the specific observed input to production x, and y is observed output; 5
m0it represents a firm-specific productivity shock at time t that is observed by the firm, thus
influencing its input choice but is unknown to the econometrician. A large body of
microeconometric literature (for a recent survey, see Eberhardt and Helmers 2010) has attempted
6
to address the resulting â€˜transmission biasâ€™ first highlighted by Marschak and Andrews (1944).
Mundlak, Butzer, and Larson (2012) simplify this productivity shock by requiring that it be
decomposable into firm- and time-specific effects, m0it = m0i + m0t (similarly for the input
equations). This setup further highlights two â€˜technology shiftersâ€™: first, the state variables affect
output directly and indirectly through the selection of inputs, acting as input/output shifters;
second, the state variables directly influence the technology parameters Î². The state variables act
as technology shifters in the sense that, conditional on s, (i) different countries might have
different Î² coefficients, and/or (ii) at different points in time, the same country might have
different Î² coefficients. The presence of the state variables in the equations for y and x prevents
the straightforward application of instrumental variables. 6
Following some simplifying assumptions regarding aggregation (see Mundlak, 1988), the
above framework is extended to apply at the country level. Empirical testing in the case of the
cross-country production function for agriculture is conducted with the following set of state
variables: proxies for human capital, level of development, institutions, peak agricultural yield,
and a number of indicators for prices and price variability. 7 Using the simplifying assumption
Î²(s) = Î², where Î² is referred to as a â€˜sample-dependent constant,â€™ the model is estimated using
ordinary least squares (OLS) following a within-country-time transformation of the variables
(i.e., applying the two-way fixed effects estimator). The authors refer to the results from this
regression as â€˜core technology.â€™ 8 Further empirical analysis in this paper and in a related study
by one of the coauthors (Butzer, 2011) investigates parameter constancy over time and parameter
heterogeneity across countries by splitting the data into two periods and two country groups. Our
own empirical approach discussed below builds on the theoretical model by Mundlak (1988) but
7
allows for more flexibility in the empirical implementation than Mundlak, Butzer, and Larson
(2012).
<****>AN EMPIRICAL MODEL OF A DUAL ECONOMY
In the following section, we first present a general, empirical specification for our sector-specific
analysis of agriculture and manufacturing that shows how recent developments in the
econometric modeling of production functions link to the framework proposed by Mundlak.
Next, we review a number of empirical estimators, focusing on those arising from the recent
panel time series literature, before we briefly discuss the data.
<****>Empirical Specification
Our empirical framework adopts a â€˜common factorâ€™ representation for a standard log-linearized
Cobb-Douglas production function model. Each sector/level of aggregation is modeled
separately. For ease of notation, we do not identify this multiplicity in our general model. Let
(4) yit = Î² iâ€²xit + uit uit = Î± i + Î»iâ€² ft + Îµ it
(5) â€² g mt + Ï†1mi f1mt + ï?‹ + Ï†nmi f nmt + vmit
xmit = Ï€ mi + Î´ mi
(6) ft = Ï„ + Ï? â€²ft âˆ’1 + Ï‰t and gt = Âµ + Îº â€²gt âˆ’1 + Ï…t
for i = 1,â€¦, N countries, t = 1,â€¦, T time periods, and m = 1,â€¦, k inputs. 9 Equation (4)
represents the production function, with y as sectoral or aggregated value-added and x as a set of
inputs: labor, physical capital stock, and a measure for natural capital stock (arable and
permanent crop land) in the agriculture specification (all variables are transformed to log values).
We consider additional inputs (human capital, livestock, and fertilizer) as robustness checks for
our general findings (see supplemental appendix S4, available at http:/wber.oxfordjournals.org/).
The output elasticities associated with each input (Î²i) are allowed to differ across countries. 10
8
For unobserved TFP, we employ the combination of a country-specific TFP level (Î±i) and
a set of common factors (ft) with country-specific factor loadings (Î»i). TFP is therefore, in the
spirit of a â€˜measure of our ignoranceâ€™ (Abramowitz 1956), driven by latent processes that are
either difficult to measure or that are truly unobservable. Equation (6) provides some structure
for these unobserved common processes that are modeled as simple AR(1) processes with drift
terms. We do not exclude the possibility of unit root processes (Ï? = 1, Îº = 1) leading to
nonstationary observables and unobservables. Note that the potential for spurious regression
results arises in this setup if the empirical equation is misspecified.
Equation (5) details the evolution of the set of inputs, that is, the input demand functions.
Crucially, some of the same processes determining the evolution of inputs are assumed to drive
TFP in the production function equation. 11 Economically, this assumption implies that the
processes that make up TFP (e.g., knowledge, innovation, absorptive capacity) affect choices of
inputs, including the accumulation of capital stock, the evolution of the labor force, and (in the
agriculture equation) the area of land under cultivation, while at the same time affecting the
production of output directly. Thus, technical progress affects both production and the choice of
productive inputs. Econometrically, this setup leads to endogeneity whereby the regressors are
correlated with the unobservables, making it difficult to identify Î²i separately from Î»i and Ï†i
(Kapetanios, Pesaran, and Yamagata 2011). The nature of macroeconomic variables in a
globalized world, where economies are strongly connected to each other and latent forces drive
all of the outcomes, provides a conceptual justification for the pervasive character of unobserved
common factors. The presence of these latent factors makes it difficult to argue for the validity of
traditional approaches to causal interpretation of cross-country empirical analyses. Instrumental
variable estimation in cross-section growth regressions or Arellano and Bond-type (1991) lag-
9
instrumentation within pooled panel models become invalid in the face of common factors
and/or heterogeneous equilibrium relationships (Pesaran and Smith, 1995; Lee, Pesaran, and
Smith, 1997).
This framework can be viewed as an empirical version of theoretical Mundlak model,
developed above. Equations (4) and (5) capture the jointness property that is made explicit in
their empirical model by the inclusion of a set of â€˜state variables,â€™ which affect inputs and output
in an identical fashion: Î³ in equations (2) and (3). Conversely, our framework allows underlying
unobserved factors to affect inputs and output differentially via the country-specific factor
loadings Î»i. 12 These factors are conceptually similar to the state variables in the Mundlak model;
they represent any variable or process that might affect both factor choice and TFP. The
empirical implementation of our model differs from that of Mundlak. We allow the data to
identify the different choices for the Î² coefficients. The evolution of the factors is fairly general,
including nonstationarity, and the setup provides for global shocks (strong factors) as well as
local spillovers (weak factors). The productivity shock term m0it is accounted for by a fixed
effect Î±i (m0i) and the common factor structure (m0t = Î»ft).13 Finally, we allow for technology
heterogeneity Î²i across countries and analyze whether parameter constancy holds over time (Î²it=
Î²i). The parameter constancy tests will provide further insights into the â€˜core technologyâ€™ by
highlighting whether technology parameters are likely to be functions of unobservable processes
(in our case, ft, in the Mundlak, Butzer, and Larson [2012] notation, s). Our empirical
implementation is focused on recent panel time series estimators that address nonstationarity,
parameter heterogeneity, and cross-section dependence. The following section introduces these
methods in more detail.
10
<****>Empirical Implementation
Our empirical setup incorporates a large degree of flexibility concerning the impact of
observable and unobservable inputs on output. Empirical implementation will necessarily lead to
different degrees of restrictions on this flexibility, which will then be formally tested: the
emphasis is on a comparison of different empirical estimators allowing for or restricting the
heterogeneity in the observables and unobservables outlined above. The two-by-two matrix in
table 1 indicates the assumptions that are implicit in the various estimators implemented below. 14
For the estimators marked with stars, we confine the results to the supplemental appendix to save
space. 15
TABLE 1. Estimators and Assumptions about the Data Generating Process
Impact of Unobservables:
COMMON IDIOSYNCRATIC
Production Technology: COMMON POLS, 2FE, CCEP,
GMM*, PMG* CPMG*
IDIOSYNCRATIC MG, FDMG CMG
The panel time series econometric approach is given particular attention in this study for
a number of reasons (for a detailed discussion, see Eberhardt and Teal, 2011a). First, we know
that many macrovariables are potentially nonstationary (Nelson and Plosser, 1982; Granger,
1997; Pedroni, 2007), a property that cannot be rejected for the variables in our data (see
supplemental appendix S1). When variables are nonstationary, standard regression output must
be treated with extreme caution because results are potentially spurious. Provided variables (and
11
unobserved processes) are cointegrated; however, we can establish long-run equilibrium
relationships in the data. The practical indication of cointegration is when regressions yield
stationary residuals, whereas nonstationary residuals indicate a potentially spurious regression.
Panel time series estimators can address this concern over spurious regression, and below, we
investigate the residuals of each empirical model using panel unit root tests. Second, panel time
series methods allow for parameter heterogeneity across countries, which, as discussed above, is
a central interest in our analysis. Third, panel time series methods can address the problems
arising from cross-section correlation. Whether this is the result of common economic shocks or
local spillover effects, cross-section correlation can potentially induce serious bias in the
estimates because the impact assigned to an observed covariate in reality confounds its impact
with that of the unobserved processes. Although the panel time series approach does not allow us
to quantify their impact, common shocks and local spillovers can be accommodated in the
empirical analysis to obtain unbiased technology coefficients for the observable inputs. Below,
we will employ diagnostic tests to analyze each modelâ€™s residuals for the presence or absence of
cross-section dependence.
We introduce the Common Correlated Effects (CCE) estimators developed in Pesaran
(2006) and extended to nonstationary variables in Kapetanios, Pesaran, and Yamagata (2011) in
some more detail because relatively few applied studies employ these estimators (e.g., Holly,
Pesaran, and Yamagata, 2010; Moscone and Tosetti, 2010; Cavalcanti, Mohaddes, and Mehdi,
2011; Eberhardt, Helmers, and Strauss, forthcoming). 16
The CCE estimators augment the regression equation with cross-section averages of the
dependent ( yt ) and independent variables ( xt ) to account for the presence of unobserved
12
common factors with heterogeneous impact. For the Mean Group version (CMG), the individual
country regression is specified as
k
(7) yit = ai + biâ€²xit + c0i yt + âˆ‘ cmi xmt + eit
m =1
Ë† are averaged across countries similar to the practice
In a second step, the parameter estimates bi
in the Pesaran and Smith (1995) Mean Group (MG) estimator. 17 The pooled version (CCEP) is
specified as
yit = ai + bâ€² xit + âˆ‘ c0i ( yt D j ) + âˆ‘âˆ‘ cmi (xmt D j ) + eit
N k N
(8)
j =1 m =1 j =1
where Dj represents country dummies. 18 The CMG is thus a simple extension to the Pesaran and
Smith (1995) MG estimator based on country-specific OLS regressions, whereas the CCEP is a
standard fixed effects estimator augmented with additional regression terms.
To obtain insight into the mechanics of this approach, consider the cross-section average
of our model in equation (4). As the cross-section dimension N increases, given Îµ t = 0 , we
obtain
(9) yt = Î± + Î² â€² xt + Î» â€² f t â‡” f t = Î» âˆ’1 ( yt âˆ’ Î± âˆ’ Î² â€² xt )
This simple derivation provides a powerful insight: working with the cross-sectional means of y
and x can account for the impact of unobserved common factors (TFP) in the production
process. 19 Given the assumed heterogeneity in the impact of unobserved factors across countries
(Î»i), the estimator is implemented in the manner detailed above, which allows for each country i
to have different parameter estimates for yt and the xt and, thus, implicitly for ft. Simulation
studies (Pesaran, 2006, Coakley, Fuertes, and Smith, 2006; Kapetanios, Pesaran, and Yamagata,
2011; Pesaran and Tosetti, 2011) have shown that this approach works well even when the cross-
13
section dimension N is small, when variables are nonstationary, cointegrated, or not integrated,
in the presence of local spillovers and global/local business cycles and when the relationship is
subject to structural breaks. 20 In the present study, we implement two versions of the CCE
estimators in the sector-level regressions: estimators in a standard form as described above and
estimators in a variant form that includes the cross-section averages of the input and output
variables from both sectors. This variant specification allows for cross-section dependence across
sectors, albeit at the cost of a reduction in degrees of freedom. It is conceivable that the evolution
of the agricultural sector in developing countries influences that of the wider economy in general
and the manufacturing sector in particular, such that this extension is sensible in the dual
economy context.
This completes our discussion of the empirical implementation within each sector/level
of aggregation. We highlight the direct link between the issues that these estimators seek to
address and the problem of identifying the technology parameters of interest raised in the
previous section. Heterogeneity in the impact of observables and unobservables across countries
can be directly interpreted as differences in the production technology and a differential TFP
evolution across countries. The above discussion suggests that, from an economic theory
standpoint, there are reasons to prefer a more flexible empirical approach. Empirically, however,
we do not impose this more flexible approach on our data. We compare models with differing
degrees of parameter heterogeneity and use established econometric diagnostics (tests for
residual stationarity and cross-section independence) to identify the models that are rejected and
those that are supported by the data.
14
<****>Data
Descriptive statistics and a more detailed discussion of the data can be found in the appendix.
We conduct our empirical analysis with four datasets:
(i) for the agricultural sector, building on the sectoral investment series collected by Crego,
Larson, Butzer, and Mundlak (1998) and output from the WDI (World Bank, 2008) as
well as sectoral labor and land data from FAO (2007);
(ii) for the manufacturing sector, building on the sectoral investment series collected by
Crego, Larson, Butzer, and Mundlak (1998), output data from the WDI, and labor data
from UNIDO (2004);
(iii) for a stylized aggregate economy made up of the aggregated data for the agriculture and
manufacturing sectors; 21
(iv) for the aggregate economy, building on data provided by the PWT (we use version 6.2,
Heston, Summers, and Aten 2006).
The capital stocks in the agriculture, manufacturing, and PWT samples are constructed
from investment series following the perpetual inventory method (see Klenow and Rodriguez-
Clare, 1997b). For the aggregated sample, we simply added up the sectoral capital stocks. A
comparison across sectors and with the stylized aggregate sector is possible because of the
efforts by Crego, Larson, Butzer, and Mundlak (1998) in providing sectoral investment data for
agriculture and manufacturing. All monetary values in the sectoral and stylized aggregated
datasets are transformed into US dollar values for the year 1990 (in the capital stock case, this
transformation is applied to the investment data), following Martin and Mitra (2002). In light of
concerns that the stylized aggregate economy data might not offer a sound representation of true
15
aggregate economy data, we have adopted the PWT data, which measure monetary values in
international dollars (purchasing power parity adjusted), as a benchmark for comparison. Despite
a number of vocal critics (e.g., Johnson, Larson, Papageorgiou, and Subramanian, 2009), the
PWT data are undoubtedly the most popular macrodataset for cross-country empirical analysis. 22
Our sample is an unbalanced panel 23 for 1963 to 1992, consisting of 40 developing and
developed countries with a total of 918 observations (average T=23). Our aim is to compare
estimates across the four datasets, which requires us to match the same sample, thus reducing the
number of observations to the smallest common denominator. Only eight countries in our sample
are in Africa, whereas approximately half are present-day â€˜industrialized economies.â€™ However,
these numbers are deceiving if one recalls that structural change and development in many of
these industrialized economies has primarily been achieved during our period of study. For
example, prior to 1964, GDP per capita was higher in Ghana than in South Korea. In 1970, the
share of agricultural value-added in GDP for Finland, Ireland, Portugal, and South Korea
amounted to 13 percent, 16 percent, 31 percent, and 26 percent, respectively, whereas the 1992
figures were 5 percent, 8 percent, 7 percent, and 8 percent. This is strong evidence of economies
undergoing structural change. A detailed description of our sample is available in table A1 and
descriptive statistics for each sample are provided in table A2.
<****>EMPIRICAL RESULTS
Panel unit root and cross-section dependence tests for our data are available in the supplemental
appendix (S1, S2) of the paper. We adopt the Pesaran (2007) CIPS panel unit root test to analyze
the time series properties of each variable series. The results provide strong indication that
16
variables in log levels for the agriculture and manufacturing data as well as the two aggregate
economy representations are nonstationary.
A number of formal and informal tests were conducted to investigate cross-section
correlation in the data. The results (see supplemental appendix S2) show very high average
absolute correlation coefficients for the data in log levels and in the data represented as growth
rates. Formal tests for cross-section dependence (Pesaran, 2004; Moscone and Tosetti, 2009)
reject cross-section independence in virtually all variable series tested.
Below, we discuss the empirical results from sectoral production function regressions for
agriculture and manufacturing, first assuming technology parameter homogeneity and then
allowing for differential technology across countries. For all regression models, we report
residual diagnostic tests, including the Pesaran (2007) panel unit root test (we summarize results
using I(0) for stationary residuals, I(1) for nonstationary residuals, and I(1)/I(0) for ambiguous
results), and the Pesaran (2004) cross-section dependence (CD) test (H0: cross-section
independence), which we use to build our judgment for a preferred empirical model. Residual
nonstationarity invalidates the inferential tools (for example, t-statistics) employed (Kao, 1999)
and indicates that regression results are potentially spurious. In the same way that serial
dependence indicates dynamic misspecification, residual cross-section dependence violates the
assumption that the error terms are independent and identically distributed (iid). This suggests
that the specific model tested fails to adequately address the correlation of inputs, output, and
unobservables across different countries, induced by, for example, common shocks or local
spillover effects. 24
Note that our empirical regressions express all variables in per-worker terms (in logs).
The inclusion of the log labor variable therefore indicates the deviation from constant returns to
17
Ë† +Î²
scale (i.e., Î² L
Ë† +Î²
K
Ë† âˆ’ 1 ): a positive (negative) significant coefficient on log labor indicates
N
increasing (decreasing) returns; an insignificant coefficient indicates constant returns. The
coefficient on labor in the regression is thus not the output elasticity with respect to labor, which
we also report in a lower panel of each table (â€˜Implied Î²
Ë† â€™) 25 along with the returns to scale
L
(â€˜Implied RSâ€™). This setup allows for an easy imposition of constant returns (CRS) by dropping
the log labor variable from the model. In each table, Panel (A) shows results with no restrictions
on returns to scale, whereas Panel (B) imposes CRS.
<****>Pooled Models
Table 2 presents the empirical results for agriculture and manufacturing. Beginning with
agriculture, the empirical estimates for models [1] and [2] neglecting cross-section dependence
are quite similar, with the capital coefficient of about .63 and statistically significant decreasing
returns to scale. The land coefficient is insignificant in all pooled specifications, except in the
2FE model, where it carries a negative sign. Diagnostic tests indicate that the residuals in these
models are cross-sectionally dependent and that the standard POLS and 2FE models yield
nonstationary residuals and, thus, might represent spurious regressions. The two CCEP models
yield stationary and cross-sectionally independent residuals, capital coefficients of approximately
.5 and insignificant land coefficients. There is no substantial change in these results when CRS
(Panel (B)) is imposed, with the exception of the 2FE estimates, where the land variable
(previously negative and significant) is now insignificant and the capital coefficient has become
further inflated. Land is still insignificant, but in models [3] and [4] it now has a plausible
coefficient estimate.
18
TABLE 2. Pooled Regression Models for Agriculture and Manufacturing
PANEL (A) UNRESTRICTED RETURNS TO SCALE
Agriculture Manufacturing
[1] [2] [3] [4] [5] [6] [7] [8]
POLS 2FE CCEP CCEPb POLS 2FE CCEP CCEPb
log labor âˆ’0.060 âˆ’0.199 âˆ’0.266 âˆ’0.142 0.043 0.081 0.082 0.002
Î²L + Î²K (+ Î²N) âˆ’ [7.20]** [9.60]** [2.13]* [0.55] [3.53]** [4.35]** [1.53] [0.03]
1
log capital pw 0.618 0.661 0.480 0.531 0.897 0.845 0.472 0.469
Î²K [73.80]** [43.62]** [9.87]** [5.92]** [55.38]** [32.69]** [7.62]** [5.34]**
log land pw 0.011 âˆ’0.160 âˆ’0.165 0.052
Î²N [1.02] [4.93]** [0.98] [0.20]
implied RS â€ DRS DRS DRS CRS IRS IRS CRS CRS
implied Î²L â€¡ 0.322 0.300 0.254 0.469 0.147 0.236 0.528 0.532
Ãª integrated â—Š I(1) I(1) I(0) I(0) I(1) I(1) I(0) I(0)
CD test p-value # 0.00 0.00 0.45 0.38 0.19 0.34 0.00 0.93
R-squared 0.94 0.86 1.00 1.00 0.84 0.67 1.00 1.00
RMSE 0.446 0.127 0.095 0.086 0.439 0.128 0.090 0.066
PANEL (B) CONSTANT RETURNS TO SCALE IMPOSED
Agriculture Manufacturing
[1] [2] [3] [4] [5] [6] [7] [8]
POLS 2FE CCEP CCEPb POLS 2FE CCEP CCEPb
log capital pw 0.644 0.725 0.496 0.526 0.919 0.860 0.490 0.500
Î²K [85.46]** [48.87]** [11.22]** [6.70]** [70.80]** [34.01]** [13.55]** [8.38]**
log land pw 0.008 âˆ’0.007 0.092 0.126
Î²N [0.66] [0.20] [1.24] [1.02]
implied Î²L â€¡ 0.356 0.275 0.504 0.474 0.081 0.140 0.510 0.500
Ãª integrated â—Š I(1) I(0)/I(1) I(0) I(0) I(1) I(1) I(0) I(0)
CD test p-value # 0.00 0.00 0.87 0.52 0.02 0.00 0.00 0.00
R-squared 0.94 0.85 1.00 1.00 0.84 0.66 1.00 1.00
RMSE 0.457 0.132 0.098 0.089 0.444 0.129 0.094 0.074
Source: Authorsâ€™ analysis based on data sources discussed in the text.
Note: N = 40 countries, 918 observations, average T = 23. Dependent variable: value-added per worker (in logs). All
variables are suitably transformed in the 2FE equation. Estimators: POLS, pooled OLS; 2FE, Two-way Fixed
Effects; CCEP, Common Correlated Effects, Pooled version (see below). We omit reporting the estimates on the
intercept term. Absolute t-statistics reported in brackets are constructed using White heteroskedasticity-robust
standard errors. For CCEP in [3], [4], [7], and [8], we report results on the basis of bootstrapped standard errors (100
replications). Time dummies are included explicitly in [1] and [5] or implicitly in [2] and [6]. Augmentation with
cross-section averages in [3], [4], [7], and [8] (estimates not reported).
b The model includes cross-section averages for both the agricultural and manufacturing sector variables. â€ Returns
to scale are based on the significance of the log labor estimate. â€¡ Based on returns to scale and significant parameter
estimatesâ€”see the main text. â—Š Order of integration of regression residuals is determined using Pesaran (2007) CIPS
19
(full results available on request), H0: nonstationary residuals. # Pesaran (2004) CD-test, H0: cross-sectionally
independent residuals. RMSE: root mean squared error.
* significant at the 5 percent level, ** significant at the 1 percent level
In the manufacturing data, the models ignoring cross-section dependence in [5] and [6]
yield increasing returns to scale and capital coefficients in excess of .85. Residuals again display
nonstationarity; however, the CD tests now imply that they are cross-sectionally independent.
Surprisingly, the standard CCEP model in [7], with a capital coefficient of approximately .5 (as
in agriculture data), does not pass the cross-section correlation test. However, further accounting
for correlations across sectors in [8] yields favorable diagnostics and a similar capital coefficient.
Following the imposition of CRS, all models reject cross-section independence, whereas
parameter estimates are more or less identical to those in the unrestricted models. Based on these
pooled regression results, the diagnostic tests (stationary and cross-section independent
residuals) favor the CRS CCEP results in [3] and [4] for the agriculture data, whereas in the
manufacturing data the unrestricted CCEP model in [8], which accounts for cross-sectoral
impact, emerges as the preferred specification. Results for the other empirical models cannot be
readily interpreted in the standard manner because of the presence of nonstationary and/or
correlated residuals. 26
In sum, relying on diagnostic testing, the alternative CCEP estimator emerges as the
preferred estimator for both the agriculture and manufacturing samples. For agriculture, the
imposition of CRS seems valid, whereas for manufacturing, the data reject this restriction.
Across preferred specifications, the mean capital coefficients for agriculture and manufacturing
are quite similar, approximately .5. Our shift to heterogeneous technology models, discussed in
the next section, will allow us to determine whether these results are representative of the
underlying technology. Although the CCEP imposes common technology coefficients, theory
20
and simulations (Pesaran, 2006) have shown that if technology differs results reflect the mean
coefficient across countries. However, outliers might exert undue influence on this mean.
Therefore, our heterogeneous parameter models account for this possibility and report outlier-
robust average coefficients. 27
<****>Averaged Country Regressions
Table 3 presents the robust means for each regressor across N country regressions for the
unrestricted (Panel (A)) and CRS models (Panel (B)), respectively. The t-statistics reported for
each average estimate test whether the average parameter is statistically different from zero,
following Pesaran and Smith (1995). In addition, we report the share of countries for which the
country results rejected CRS as well as the share of countries for which linear country trends are
statistically significant (at the 10 percent level).
21
TABLE 3. Heterogeneous Parameter Models for Agriculture and Manufacturing (Robust Means)
PANEL (A) UNRESTRICTED RETURNS TO SCALE
Agriculture Manufacturing
[1] [2] [3] [4] [5] [6] [7] [8]
MG FDMG CMG CMGb MG FDMG CMG CMGb
log labor âˆ’1.935 âˆ’0.474 âˆ’0.682 âˆ’0.068 âˆ’0.132 âˆ’0.127 0.069 0.003
Î²L + Î²K (+ Î²N) âˆ’ 1 [2.43]* [0.53] [1.05] [0.08] [0.92] [1.15] [0.78] [0.03]
log capital pw âˆ’0.084 0.133 0.496 0.360 0.195 0.179 0.525 0.284
Î²K [0.42] [0.58] [2.25]* [1.37] [1.32] [1.12] [6.46]** [3.35]**
log land pw âˆ’0.430 âˆ’0.269 âˆ’0.445 âˆ’0.129
Î²N [1.46] [0.96] [1.44] [0.50]
country trend/drift 0.015 0.010 0.015 0.018
[1.55] [1.06] [2.70]** [3.31]**
implied RS â€ DRS CRS CRS CRS CRS CRS CRS CRS
implied Î²L â€¡ n/a n/a 0.504 n/a n/a n/a 0.475 0.717
reject CRS (10%) 0.38 0.20 0.23 0.23 0.50 0.13 0.38 0.25
sign. trends/drifts
(10%) 0.40 0.18 0.40 0.20
Ãª integrated â—Š I(0) I(0) I(0) I(0) I(0) I(0) I(0) I(0)
CD test p-value # 0.00 0.00 0.49 0.75 0.00 0.00 0.02 0.18
RMSE 0.081 0.094 0.069 0.059 0.080 0.077 0.068 0.047
Observations 918 872 918 918 918 872 918 918
PANEL (B) CONSTANT RETURNS TO SCALE IMPOSED
Agriculture Manufacturing
[1] [2] [3] [4] [5] [6] [7] [8]
MG FDMG CMG CMGb MG FDMG CMG CMGb
log capital pw âˆ’0.050 0.300 0.538 0.620 0.291 0.346 0.509 0.413
Î²K [0.29] [2.22]* [4.55]** [2.98]** [2.60]** [3.64]** [6.19]** [6.37]**
log land pw 0.260 0.031 0.082 0.073
Î²N [1.03] [0.20] [0.47] [0.38]
country trend/drift 0.016 0.014 0.012 0.013
[2.71]** [3.09]** [2.72]** [3.61]**
implied Î²L â€¡ n/a 0.700 0.462 0.380 0.709 0.654 0.491 0.588
sign. trends/drifts
(10%) 0.45 0.13 0.55 0.23
Ãª integrated â—Š I(0) I(0) I(0) I(0) I(0) I(0) I(0) I(0)
CD test p-value # 0.00 0.00 0.93 0.73 0.00 0.00 0.00 0.00
RMSE 0.087 0.096 0.076 0.068 0.088 0.078 0.080 0.059
Observations 918 872 918 918 918 872 918 918
Source: Authorsâ€™ analysis based on data sources discussed in the text.
Note: N = 40 countries, average T = 23 (21.8 for FDMG). Dependent variable: value-added per worker (in logs). All
variables are suitably transformed in the FD equations. Estimators: MG, Mean Group; FDMG, MG with variables in
22
first difference; CMG, Common Correlated Effects, Mean Group version. We report outlier-robust means; estimates
on intercept terms are omitted. Absolute t-statistics are in brackets following Pesaran and Smith (1995). Estimates
on cross-section averages in [3], [4], [7], and [8] are not reported.
b The model includes cross-section averages for both the agricultural and manufacturing sector variables. â€ Returns
to scale are based on the significance of the log labor estimate. â€¡ Based on returns to scale and significant parameter
estimatesâ€”see the main text. â€˜reject CRSâ€™ and â€˜sign. trends/driftsâ€™ report the share of countries where CRS is
rejected and where country trends/drifts are statistically significant (in both cases, applying a 10 percent level of
significance). â—Š Order of integration of regression residuals, determined using Pesaran (2007) CIPS (full results
available on request), H0: nonstationary residuals. # Pesaran (2004) CD-test, H0: cross-sectionally independent
residuals. RMSE: root mean squared error.
* significant at the 5 percent level, ** significant at the 1 percent level
Beginning with the unrestricted models in Panel (A), we observe that MG and FDMG
estimates for the agriculture and manufacturing equations are very imprecise. Furthermore, in the
agriculture model, MG yields decreasing returns to scale that are nonsensical in magnitude.
Simulations for nonstationary and cross-sectionally dependent data (Coakley, Fuertes and Smith,
2006; Bond and Eberhardt, 2009) show that MG estimates are severely affected by their failure
to account for cross-section dependence, and this is the likely cause of these results. Standard
CMG in agriculture and manufacturing yield similar capital coefficients of approximately .5,
whereas the alternative CMG results provide somewhat lower estimates, approximately .3 (these
models allow for agriculture sectors to influence manufacturing sectors and vice-versa).
Diagnostics are sound in the case of the two CMG results in agriculture, but only for the
alternative CMG estimator in manufacturing (cross-sectionally dependent residuals in model
[7]). Panel (B) shows how the imposition of constant returns affects the results: MG and FDMG
in both sectors are generally more sensible, but the diagnostic tests suggest cross-section
correlation in the residuals that might indicate serious misspecification. The two CMG estimates
for agriculture are now more similar. Land coefficients are still insignificant, but positive.
Manufacturing results for the standard CMG remain virtually unchanged from the unrestricted
23
model; however, diagnostic tests still indicate cross-sectionally dependent residuals. The same
caveat applies to the alternative CMG for manufacturing.
In sum, the diagnostic tests support the use of the CRS versions of the CMG estimators
for agricultural data and the unrestricted returns to scale version of the â€˜alternativeâ€™ CMG
estimator for the manufacturing data. These preferred models suggest that average technology
differs across sectors, with a manufacturing capital coefficient of approximately .3 and an
agriculture capital coefficient of approximately .5. 28
The results for the land coefficient, where our preferred estimates indicate a positive,
albeit statistically insignificant, average coefficient, warrant additional comment. Given the
relative persistence of the area under cultivation, the short time series dimension of the data
might be responsible for this outcome. Any form of land quality adjustment would require time-
varying information on land quality, which is not available at an annual rate over a long time
horizon. 29 Time-invariant adjustments are accounted for by the country-specific intercepts.
Because of the aim of our study, we do not put too much emphasis on providing the best
estimate for the â€˜trueâ€™ sectoral technology coefficients. Instead, we highlight the discrepancy
between these sectoral results and the results obtained when analyzing aggregate economy data.
<****>AGGREGATION VERSUS HETEROGENEITY
In this section, we provide practical evidence that the use of an aggregate production function
will lead to severely biased technology estimates. We then provide some insights into the nature
of technology heterogeneity across sectors and countries.
24
<****>Aggregation Bias: Empirical Evidence
To investigate the impact of aggregation across heterogeneous sectors with technology
furthermore differing across countries, we create a stylized â€˜aggregated economyâ€™ from our data
on agriculture and manufacturing. To avoid the suggestion that our results might be critically
distorted by this overly simplistic design, we compare them with those obtained from a matched
sample of aggregate economy data from the PWT. Pre-estimation testing reveals that both
datasets utilized in this section consist of nonstationary series that are cross-sectionally
correlated; the results are provided in the supplemental appendix (S1, S2). 30
We begin our discussion with the results for the pooled models in table 4. Across all
specifications, the estimated capital coefficients in the stylized aggregated data far exceed those
derived from the respective agriculture and manufacturing samples in table 2. Furthermore, the
patterns across estimators are replicated one-to-one in the PWT data, which also yield
excessively high capital coefficients across all models. All models suffer from cross-sectional
dependence in the residuals. There are also indications that the residuals in the CCEP model for
the aggregated data are nonstationary (those in the two other specifications in levels are always
nonstationary). We also investigate the impact of human capital (via a proxy variable, average
years of schooling attained in the population over 15 years of age) in these aggregate economy
data models, but as the results in the supplemental appendix (S4) reveal, the basic bias remains.
25
TABLE 4. Pooled Regression Models for Aggregated and PWT Data
PANEL (A) UNRESTRICTED RETURNS TO SCALE
Aggregated data Penn World Table data
[1] [2] [3] [4] [5] [6]
POLS 2FE CCEP POLS 2FE CCEP
log labor 0.010 âˆ’0.082 âˆ’0.054 0.035 âˆ’0.131 âˆ’0.097
Î²L + Î²K (+ Î²N) âˆ’ [1.32] [3.75]** [0.78] [7.57]** [4.57]** [0.76]
1
log capital pw 0.828 0.798 0.657 0.742 0.704 0.631
Î²K [107.55]** [66.20]** [19.43]** [113.76]** [51.43]** [13.71]**
implied RS â€ CRS DRS CRS IRS DRS CRS
implied Î²L â€¡ 0.172 0.120 0.343 0.293 0.165 0.369
Ãª integrated â—Š I(1) I(1) I(0)/I(1) I(1) I(1) I(0)
CD test p-value # 0.40 0.00 0.04 0.10 0.00 0.00
R-squared 0.96 0.89 1.00 0.96 0.82 1.00
RMSE 0.358 0.109 0.078 0.195 0.095 0.061
observations 918 918 918 912 912 912
PANEL (B) CONSTANT RETURNS TO SCALE IMPOSED
Aggregated data Penn World Table data
[1] [2] [3] [4] [5] [6]
POLS 2FE CCEP POLS 2FE CCEP
log capital pw 0.825 0.824 0.666 0.730 0.745 0.651
Î²K [120.48]** [73.01]** [20.85]** [130.30]** [63.41]** [19.33]**
implied Î²L â€¡ 0.175 0.176 0.334 0.270 0.255 0.349
Ãª integrated â—Š I(1) I(1) I(0)/I(1) I(1) I(1) I(0)
CD test p-value # 0.31 0.30 0.06 0.00 0.00 0.00
R-squared 0.96 0.88 1.00 0.96 0.82 1.00
RMSE 0.358 0.109 0.086 0.202 0.097 0.069
observations 918 918 918 912 912 912
Source: Authorsâ€™ analysis based on data sources discussed in the text.
Note: See table 2 for definitions and further details on diagnostic testing.
* significant at the 5 percent level, ** significant at the 1 percent level
26
TABLE 5. Heterogeneous Parameter Models for Aggregated and PWT Data (Robust Means)
PANEL (A) UNRESTRICTED RETURNS TO SCALE
Aggregated data Penn World Table data
[1] [2] [3] [4] [5] [6]
MG FDMG CMG MG FDMG CMG
log labor âˆ’0.154 âˆ’0.079 0.117 âˆ’1.152 âˆ’1.681 âˆ’0.389
Î²L + Î²K (+ Î²N) âˆ’ 1 [0.36] [0.25] [0.62] [1.23] [2.28]* [1.03]
log capital pw 0.220 0.297 0.609 0.655 1.004 0.753
Î²K [1.17] [1.66] [6.11]** [4.22]** [5.38]** [5.26]**
country trend/drift 0.025 0.020 0.010 âˆ’0.010
[2.73]** [2.42]* [0.90] [1.88]
implied RS â€ CRS CRS CRS CRS DRS CRS
implied Î²L â€¡ n/a n/a 0.391 0.345 n/a 0.247
reject CRS (10%) 0.60 0.23 0.38 0.68 0.33 0.53
sign. trends/drifts
(10%) 0.55 0.33 0.43 0.18
Ãª integrated â—Š I(0) I(0) I(0) I(0) I(0) I(0)
CD test p-value # 0.00 0.00 0.00 0.00 0.00 0.16
RMSE 0.081 0.094 0.051 0.080 0.077 0.041
observations 918 872 918 918 872 918
PANEL (B) CONSTANT RETURNS TO SCALE IMPOSED
Aggregated data Penn World Table data
[1] [2] [3] [5] [6] [7]
MG FDMG CMG MG FDMG CMG
log capital pw 0.293 0.202 0.725 0.619 0.923 0.811
Î²K [1.92] [1.90] [10.95]** [6.36]** [6.01]** [12.09]**
country trend/drift 0.014 0.002 âˆ’0.007
[2.93]** [0.50] [1.97]*
implied Î²L â€¡ n/a n/a 0.275 0.381 0.077 0.189
sign. trends/drifts
(10%) 0.48 0.28 0.48 0.25
Ãª integrated â—Š I(0) I(0) I(0) I(0) I(0) I(0)
CD test p-value # 0.00 0.00 0.05 0.00 0.00 0.00
RMSE 0.074 0.064 0.067 0.061 0.044 0.059
observations 918 872 918 912 866 912
Source: Authorsâ€™ analysis based on data sources discussed in the text.
Note: See table 3 for definitions and further details on diagnostic testing.
* significant at the 5 percent level, ** significant at the 1 percent level
27
In the results from averaged country regressions in table 5, the MG and FDMG models
indicate differences between the aggregated and PWT data. The capital coefficients in the MG
model are estimated very imprecisely but seem to center at approximately .3, whereas in the
FDMG model, they are considerably higher, approximately .7 to .9. The results for the
conceptually superior CMG, however, are very consistent between the two samples and across
unrestricted and CRS models, with capital coefficients of approximately .7. Residual testing
suggests that all specifications yield stationary residuals. Cross-section correlation tests reject
independence in all but the PWT data unrestricted CMG residual series.
For ease of comparison, table 6 provides an overview of the preferred empirical results at
the sectoral and aggregate data level, assuming common technology (top panel) or technology
differences across countries (bottom panel). 31 Thus, across a large number of empirical
specifications, we have found a systematic difference between the results for the sectoral data, on
the one hand, and the results for the stylized aggregated and aggregate economy data, on the
other hand. Theoretical work by Hsiao, Shen, and Fujiki (2005) provides insight into potential
causes of this phenomenon. These authors find that if variable series are nonstationary and
cointegrated at the â€˜micro unitâ€™ level (in their empirical illustration, in Japanese prefectures),
then aggregation will only yield stable macrorelations if all technology parameters are the same
across units or if the weights used to construct the aggregate economy series from the micro units
stay the same over time. In terms of our empirical question, time-invariant weights would imply
the absence of any structural change in the economy over time, which clearly is not given here.
28
TABLE 6. Comparison of Preferred Models
PANEL (A) HOMOGENEOUS TECHNOLOGY
Sectoral Data Aggregate Data
Agri Manu Stylized PWT
[1] [2] [3] [4]
CCEPb CCEPb CCEP CCEP
log labor 0.002 âˆ’0.097
Î²L + Î²K (+ Î²N) âˆ’ 1 [0.03] [0.76]
log capital pw 0.526 0.469 0.666 0.631
Î²K [6.70]** [5.34]** [20.85]** [13.71]**
log land pw 0.126
Î²N [1.02]
implied Î²L â€¡ 0.474 0.532 0.334 0.369
Ãª integrated â—Š I(0) I(0) I(0)/I(1) I(0)
CD test p-value # 0.52 0.93 0.06 0.00
RMSE 0.089 0.066 0.086 0.061
observations 918 918 918 912
PANEL (B) HETEROGENEOUS TECHNOLOGY
Sectoral Data Aggregate Data
Agri Manu Stylized PWT
[1] [2] [3] [4]
CMGb CMGb CMG CMG
log labor 0.003 âˆ’0.389
Î²L + Î²K (+ Î²N) âˆ’ 1 [0.03] [1.03]
log capital pw 0.620 0.284 0.725 0.753
Î²K [2.98]** [3.35]** [10.95]** [5.26]**
log land pw 0.073
Î²N [0.38]
implied Î²L â€¡ 0.380 0.717 0.275 0.247
reject CRS (10%) 0.25 0.53
Ãª integrated â—Š I(0) I(0) I(0) I(0)
CD test p-value # 0.73 0.18 0.05 0.16
RMSE 0.068 0.047 0.067 0.041
observations 918 918 918 912
Source: Authorsâ€™ analysis based on data sources discussed in the text.
Note: See tables 2 and 3 for definitions and further details on diagnostic testing. In the
agricultural regressions where the CCEP and CCEPb both had sound diagnostics (and very
similar coefficient estimates), we report results for the CCEPb because it allows for greater
flexibility.
* significant at the 5 percent level, ** significant at the 1 percent level
29
<****>Technology Heterogeneity
Our empirical analysis has been based on the theoretical model first developed in Mundlak
(1988). As the empirical implementations in Mundlak, Larson, and Butzer (1999) and Mundlak,
Butzer, and Larson (2012), we have had to make simplifying assumptions to take this model to
the data. By assuming parameter constancy over time, we have had to impose the same
restriction on the parameter coefficients in the time series dimension as these studies. Our
empirical model has however allowed for more flexibility in the cross-section dimension, where
we have allowed for parameter heterogeneity across countries within each of the sectors. In the
following, we critically review these modeling choices. First, we discuss our insights into
technology heterogeneity across countries, and then, we provide evidence for parameter
constancy.
From the empirical results in table 2, all pooled specifications, except for the CCEP
estimators, yield residual series that are nonstationary. Therefore, we cannot rule out that the
estimated coefficients are spurious. In addition the unrestricted POLS and 2FE models for
agriculture as well as all POLS and 2FE models where the constant return to scale restriction has
been imposed (a restriction rejected by the data) result in cross-sectionally dependent residual
series. In contrast, the preferred heterogeneous parameter models for agriculture and
manufacturing in table 6 do not suffer from nonstationary or cross-sectionally correlated
residuals (or both). In conclusion, it appears that the data for both sectors reject the crucial
assumptions underlying a pooled regression model (well-behaved residuals) and cannot reject
those underlying a heterogeneous one. We interpret this evidence for misspecification in the
pooled models as an indication of heterogeneous production technology within each sector of
production. 32
30
Given this finding for heterogeneity, one would naturally want to investigate the patterns
of parameter heterogeneity across countries. With the specific data at our disposal (unbalanced
panel, average T = 23), a closer analysis of whether we can identify discernible patterns must be
interpreted with caution, and we view our results below as merely indicative. Previous empirical
analysis averaging individual country regressions has frequently observed that although country
estimates are widely dispersed and, at times, economically implausible, averages represent very
plausible estimates (Boyd and Smith 2002; Baltagi et al. 2003). Pedroni (2007: 440) calls for
caution when interpreting the estimates for any individual country because the â€œlong-run signals
contained in [limited] years of data may be relatively weak,â€? whereas the cross-section averages
will amplify the signal patterns sufficiently. Abstracting from the presence of common factors,
Boyd and Smith (2002) discuss this issue somewhat more formally. Arguing for omitted variable
bias in the country regression, assume a simple data generating process
(10) yit = Î² i xit + wit + uit
where w represents all variables omitted from the empirical model. Here, w is assumed to be
correlated with the included regressor x in a particular country i and over a particular period of
time T, indicated by the parameter subscript iT:
(11) wit = biT xit + vit
In a single country regression of y on x, we obtain
(12) Î•Î²( )
Ë† = Î² +b
i i iT
If the wit are structural, operating in all time periods and countries, this would cause a
systematic bias in the cross-country average estimate Î²
Ë† MG . 33 If they are not structural but are
only correlated in a particular subsample, they will lead to bias in these countriesâ€™ estimates of Î²i.
31
However, averaging estimates across countries in this case yields E(biT) = 0, such that the biases
cancel out in the average estimate Î²
Ë† MG . The same principle applies to the CMG estimators in the
presence of unobserved common factors.
We perform a basic analysis to obtain insight into the patterns of technology
heterogeneity across countries. We begin by plotting the country-specific capital coefficients
from the preferred agriculture and manufacturing models in table 6 against country mean
aggregate income per capita (from PWT, in logs). Figure 1 presents individual country estimates
and linear regression lines together with 90 percent confidence intervals for the two sectors. 34
Although the capital coefficients in agriculture appear to rise with income and those in
manufacturing appear to fall, the confidence intervals indicate that neither relationship is
statistically precise, and (full-sample) robust regressions of the two equations yield statistically
insignificant slope coefficients. 35
Figure 2 is somewhat less ambitious than the previous analysis. This figure provides
density and distribution plots to highlight the differential distribution of capital coefficients in the
agriculture and manufacturing equations. In the density plots on the left, manufacturing
coefficients (dashed line) are distributed over a much narrower range than the agriculture
coefficients. In other work on the cross-country production function in agriculture (Eberhardt
and Teal 2011b), we have argued that this heterogeneity 36 might be due in part to the difference
in output structure (wheat vs. rice vs. livestock) and the commercialization of agriculture
(subsistence vs. industrialized farming), both of which are functions of the level of development
and productive specialization across countries. Manufacturing production, in comparison,
represents a more homogeneous undertaking, such that the heterogeneity might be less
pronounced. As the cumulative distribution plots on the right of figure 2 indicate, the robust
32
means that we report in our regression results do not distort the underlying relative relationship,
namely, that most agriculture coefficients are further to the right and thus larger than those for
manufacturing.
The graphs in figures 3 and 4 address the question of slope parameter constancy over
time by estimating each model with an increasing number of observations and plotting the
resulting estimates. 37 We plot the estimates for the CCEP (in figure 3) and CMG (figure 4)
capital coefficient Î²
Ë† from the preferred agriculture, manufacturing and aggregated data models,
K
corresponding to the models presented in columns [1] to [3] of table 6, Panels (A) and (B) for
pooled and heterogeneous parameter models, respectively. In each plot, the number of
observations increases as we move to the right. In the left plots, all regressions include data from
1963 to 1979. These graphs show the parameter estimates when we add one year of data at a
time, at the end of the sample period, until we reach 1992. In the right plots, all regressions
include data from 1976 to 1992. These graphs show the parameter estimates when we add one
year at a time, at the beginning of the sample period, until we reach 1963. In each case, we begin
(on the left of the plot) with a reduced sample, where Timin=11 and Timax =18, corresponding to
n=473 (623 for the right plot) observations from N=34 (38) countries. The solid grey line
indicates the results for the aggregated data, and solid and dashed black lines indicate results for
agriculture and manufacturing, respectively. In the CCEP plots in the second row of figure 3, we
indicate the 90 percent confidence intervals for the agriculture (grey area) and manufacturing
(area between the dashed lines) estimates. The estimates for the aggregated data are omitted to
improve legibility. In the CMG plots in figure 4, squares indicate that coefficients are statistically
insignificant at the 10 percent level.
33
We use these graphs to provide insight into two specific questions: (i) From an
econometric point of view, are the Î²
Ë† coefficients on average constant over time? (ii) Following
K
the suggestion in Mundlak, Butzer, and Larson (2012), if the Î² K parameters are functions of
common factors (â€œstate variables,â€? in their terminology), implying that any estimated coefficient
is a constant associated with the specific sample under analysis Î²( )
Ë† ( s ) , we would expect results
K
to vary over time given different samples. Do our recursive plots provide evidence for sample
dependence in the estimated Î² K coefficients? The answers to (i) and (ii) are clearly dependent on
each other because these questions seek the same information but are motivated from
econometric and economic theory, respectively.
In the pooled specification where the preferred CCEP models yield relatively similar
capital coefficients of approximately .5 in the full samples, the recursive regressions in figure 3
suggest that the agriculture (manufacturing) capital coefficient decreases (increases) over time as
we increase our sample. Because the same pattern results whether we add years at the beginning
or the end of the sample, it seems that this result is driven by small sample bias: as more
observations become available in each country, the results become more precise. The associated
confidence intervals included in the plots in the second row of the figure support this hypothesis.
Coefficient estimates in the extreme left of each plot (the reduced sample) are contained within
the 90 percent confidence interval of the coefficient estimates at the extreme right of each plot
(the full sample). Turning to the heterogeneous parameter model estimates in figure 4, the robust
mean coefficients marked with a square are statistically insignificant. If we eliminate these
estimates from the graphs, we find remarkably stable recursive estimates for both the
manufacturing and agriculture capital coefficients. Thus, the answer to question (i) on parameter
constancy is a tentative â€˜yes.â€™ The answer to question (ii) on sample dependence is a tentative
34
â€˜no.â€™ The former answer suggests that the assumption Î²it = Î²i is valid, and the latter answer
implies that we find no evidence for a systematic relationship between technology coefficients
and unobserved time-varying factors (or state variables).
<****>CONCLUDING REMARKS
In this paper, we employed unique panel data for agriculture and manufacturing sectors to
estimate sector-level and aggregate production functions. Our empirical analysis emphasized
contributions from the recent panel time series econometrics literature and, in particular,
emphasized the importance of parameter heterogeneity across countries as well as sectors. In
addition, we took the nonstationarity of observable and unobservable factor inputs into account
and addressed concerns over cross-sectional dependence commonly found in macropanel data.
We draw the following conclusions from our attempts to highlight the importance of
structural makeup and change for the empirical analysis of cross-country growth and
development. First, duality matters. The empirical analysis of growth and development across
countries benefits significantly from the consideration of the modern and traditional sectors that
make up a developing economy. Comparing our analysis of agriculture and manufacturing with
that of a stylized aggregated economy suggests that the latter analysis yields severely distorted
empirical results with serious implications for estimates of TFP derived from aggregate analysis.
An analysis of PWT data in parallel with the aggregated data suggests that this finding is not an
artifact of our stylized empirical setup. Growth accounting exercises at the aggregate economy
level thus provide misleading results in that any technology differences across sectors within
countries are assumed away, and the constructed TFP series might reflect this misspecification
rather than true technological progress.
35
Second, focusing on technology and TFP within each sector, we find that the data
rejected empirical specifications that impose common technology, common TFP evolution, and
the independence of shocks across countries. Thus, the assumption of common technology in the
existing work on the dual economy model using growth accounting methods is not in line with
the data. If these restrictions were correct, we should be able to find pooled technology models
that satisfy the most basic assumptions of stationary and cross-sectionally independent residuals.
In practice, however, we find results that are much more in line with the notion of differential
technology across countries, for which we have provided support from economic theory.
Third, the presence of unobserved common factors, both as latent processes driving all
observables and as a conceptual framework for TFP, has been shown to have a substantial impact
on empirical results. Much of the cross-country empirical literature ignores the presence of
global economic shocks with heterogeneous impact and spillovers across country borders. With
the experience of the recent global financial crisis, it is now more evident than ever that
economic performance in a globalized world is highly interconnected and that domestic markets
cannot â€˜de-coupleâ€™ from the global financial and goods markets. In econometric terms, latent
forces drive all of the observable and unobservable variables and processes that we attempt to
model. An important implication is that commonly applied instruments in cross-country growth
regressions are invalid, a sentiment that is echoed in recent work by Bazzi and Clemens (2009).
We argue that panel time series methods allow us to develop a new type of cross-country empiric
that is more informative and more flexible in the problems that it can address than its critics have
allowed.
Fourth, we are aware of the serious data limitations for sectoral data from developing
economies, particularly regarding the high data requirements of panel time series methods. The
36
Crego, Larson, Butzer, and Mundlak (1998) dataset allowed us to directly compare sectoral
analysis between manufacturing and agriculture. However, for alternative research questions, the
use of data from one sector or the other might be sufficient. There are at least two existing data
sources, FAO data for agriculture and UNIDO data for manufacturing, which are ideally suited
to inform this type of analysis at the sector level for a large number of countries and over a
substantial period of time.
Cross-country panel data play a crucial role in policy analysis for development. The
present work represents a first step toward establishing an empirical version of a dual economy
model to inform this literature. From the perspective of dual economy theory, we have only
analyzed one aspect of the canon, technology heterogeneity between traditional and modern
sectors of production. In future work, we will implement empirical tests to investigate the
suggested sources of growth arising from this literature, including marginal factor product
differences and heterogeneous TFP levels for growth across sectors.
37
FIGURES AND NOTES TO FIGURES
FIGURE 1. Investigating Technology Heterogeneity and Income
Note: These graphs investigate the issue of slope heterogeneity across countries. We plot the
CMG country estimates for the capital coefficient Î²K from the preferred heterogeneous
agriculture and manufacturing models, corresponding to the models presented in columns [1] and
[2] of table 6, Panel (B). The shaded areas represent the 90 percent confidence intervals of a
linear regression of the respective capital coefficients on mean income per capita, where means
are computed from aggregate PWT data over the entire 1963 to 1992 time horizon. Robust
regression of these relationships yields the following (statistically insignificant) slope parameters
(standard errors in square brackets): .108 [.217] and âˆ’.079 [.087] for agriculture and
manufacturing, respectively. For both plots, we exclude outliers on the basis of weights
computed from these robust regressions. Any coefficient with a weight less than .5 is excluded
from the graph (for agriculture, five countries; for manufacturing, one country).
Source: Authorsâ€™ analysis based on data sources discussed in the text.
FIGURE 2. Investigating Technology Heterogeneity across Sectors
38
Note: These graphs investigate the issue of slope heterogeneity across sectors. In the density
plots on the left, we estimate separate Epanechnikov kernels (using common bandwidth .34) for
the agriculture (solid line) and manufacturing (dashed line) capital coefficients from table 6,
Panel (B); the right plots chart the cumulative distribution functions of the respective sector
coefficients. For both sets of plots, we follow the same strategy as in figure 1 to exclude extreme
outliers.
Source: Authorsâ€™ analysis based on data sources discussed in the text.
FIGURE 3. Investigating Technology Constancyâ€”Recursive Estimates (i)
Note: These graphs investigate the issue of slope parameter constancy over time by estimating
each model with an increasing number of observations and plotting the resulting estimates. We
plot the robust estimates for the CCEP capital coefficients from the preferred agriculture,
manufacturing, and aggregated data models, corresponding to the results presented in columns
[1] to [3] of table 6, Panel (A).
In each plot, the number of observations increases as we move to the right. In the left plots, all
regressions include data from 1963 to 1979. The graphs then show the parameter estimates when
we add one year of data at a time, at the end of the sample period, until we reach 1992. In the
right plots, all regressions include data from 1976 to 1992. The graphs show the parameter
39
estimates when we add one year at a time, at the beginning of the sample period, until we reach
1963. In each case, we begin (on the left of the plot) with a reduced sample where Timin = 11 and
Timax = 18, corresponding to n = 473 (623 for the right plot) from N = 34 (38) countries.
In each plot, the grey solid line represents aggregated data; black solid line, agriculture data; and
black dashed line, manufacturing data. In the plots in the second row we indicate the 90 percent
confidence intervals for the agriculture (grey area) and manufacturing (area between the dashed
lines) estimates. Here, the estimates for the aggregated data are omitted to improve the legibility.
Source: Authorsâ€™ analysis based on data sources discussed in the text.
FIGURE 4. Investigating Technology Constancyâ€”Recursive Estimates (ii)
Note: These graphs investigate the issue of slope parameter constancy over time by estimating
each model with an increasing number of observations and plotting the resulting estimates. We
plot the robust estimates for the CMG capital coefficients from the preferred agriculture,
manufacturing and aggregated data models, corresponding to the results presented in columns [1]
to [3] of table 6, Panel (B). See figure 3 for further details on how these plots are constructed.
Squares indicate coefficients that are statistically insignificant at the 10 percent level.
40
<>APPENDIX
<****>Data construction and descriptive statistics
We use a total of four datasets in our empirical analysis, consisting of data for agriculture
and manufacturing (Crego, Larson, Butzer, and Mundlak 1998; UNIDO 2004; FAO 2007), an
â€˜aggregated datasetâ€™ in which the labor, output, and capital stock values for the two sectors are
summed, and a PWT (6.2) dataset (Heston, Summers, and Aten 2006) for comparative purposes.
The first three datasets differ significantly in their construction from the last, primarily in the
choice of exchange rates and deflation: the first three datasets use international exchange rates
for the year 1990, whereas the PWT dataset uses international dollars (purchasing power parity
adjusted) with the year 2000 as the comparative base. The first three datasets thus emphasize
traded goods, whereas the PWT is generally perceived to better account for nontradables and
service. Provided that all monetary values incorporated in the variables for each regression are
comparable (across countries and over time) and given that the comparison of sectoral and
aggregated data with the PWT is intended for illustration purposes, we have no concerns about
presenting results from these two conceptually different datasets.
In all cases, the results presented are for matched observations across datasets, so that the
four datasets are identical in terms of country and time period coverage. We prefer this design
for direct comparison even though more observations are available for individual data sources,
which could improve the robustness of empirical estimates. We provide details on the sample
makeup in table A1. The next two subsections describe the data construction. Descriptive
statistics for all variables in the empirical analysis are presented in table A2.
41
TABLE A1. Descriptive Statistics: Sample Makeup for all Datasets
# ISO COUNTRY OBS # ISO COUNTRY OBS
1 AUS Australia 20 22 KEN Kenya 29
2 AUT Austria 22 23 KOR South Korea 29
3 BEL Belgium-Luxembourg 22 24 LKA Sri Lanka 17
4 CAN Canada 30 25 MDG Madagascar 20
5 CHL Chile 20 26 MLT Malta 23
6 COL Colombia 26 27 MUS Mauritius 16
7 CYP Cyprus 18 28 MWI Malawi 23
8 DNK Denmark 26 29 NLD Netherlands 23
9 EGY Egypt 24 30 NOR Norway 22
10 FIN Finland 28 31 NZL New Zealand 19
11 FRA France 23 32 PAK Pakistan 24
12 GBR United Kingdom 22 33 PHL Philippines 24
13 GRC Greece 28 34 PRT Portugal 20
14 GTM Guatemala 19 35 SWE Sweden 23
15 IDN Indonesia 22 36 TUN Tunisia 17
16 IND India 29 37 USA United States 23
17 IRL Ireland 23 38 VEN Venezuela 19
18 IRN Iran 25 39 ZAF South Africa 26
19 ISL Iceland 20 40 ZWE Zimbabwe 25
20 ITA Italy 21
21 JPN Japan 28 Total 918
Source: Authorsâ€™ analysis based on data sources discussed in the text.
Note: ISO indicates the three-letter ISO code for each country; OBS reports the number of
observations (levels regression).
42
TABLE A2. Descriptive Statistics
Agriculture Manufacturing
PANEL (A) VARIABLES IN UNTRANSFORMED LEVELS TERMS
variable mean median st. dev. min. max. variable mean median st. dev. min. max.
Output 1.8E+10 6.0E+09 3.0E+10 3.5E+07 2.2E+11 Output 7.6E+10 8.8E+09 2.1E+11 7.2E+06 1.4E+12
Labor 9.6E+06 1.3E+06 3.5E+07 3.0E+03 2.3E+08 Labor 1.7E+06 4.8E+05 3.4E+06 9.6E+03 2.0E+07
Capital 6.5E+10 1.1E+10 1.5E+11 2.9E+07 8.6E+11 Capital 1.3E+11 2.0E+10 3.0E+11 1.4E+07 1.8E+12
Land 1.8E+07 3.5E+06 4.1E+07 6.0E+03 1.9E+08
in logarithms
Output 22.39 22.51 1.73 17.38 26.13 Output 22.84 22.89 2.29 15.79 27.99
Labor 14.00 14.04 2.02 8.01 19.27 Labor 13.10 13.08 1.65 9.17 16.79
Capital 22.96 23.07 2.28 17.18 27.48 Capital 23.64 23.74 2.27 16.46 28.22
Land 15.11 15.07 1.99 8.70 19.07
in growth rates (percent)
Output 1.7 1.9 10.4 âˆ’41.5 53.9 Output 4.4 3.9 10.1 âˆ’40.9 84.2
Labor âˆ’0.6 âˆ’0.0 3.0 âˆ’28.8 13.4 Labor 1.9 1.1 6.8 âˆ’38.8 78.1
Capital 1.9 1.2 3.6 âˆ’5.1 31.4 Capital 4.8 3.6 5.0 âˆ’5.1 53.0
Land 0.1 0.0 2.2 âˆ’23.1 13.6
PANEL (B) VARIABLES IN PER WORKER TERMS
variable mean median st. dev. min. max. variable mean median st. dev. min. max.
Output 12,724 6,644 13,161 44.18 57,891 Output 27,093 20,475 22,111 753 101,934
Capital 52,367 9,925 63,576 13.10 222,397 Capital 63,533 43,577 64,557 1,475 449,763
Land 9.66 3.00 20.34 0.29 110
in logarithms
Output 8.39 8.80 1.83 3.79 10.97 Output 9.74 9.93 1.09 6.62 11.53
Capital 8.96 9.20 2.71 2.57 12.31 Capital 10.54 10.68 1.09 7.30 13.02
Land 1.11 1.10 1.41 âˆ’1.24 4.70
in growth rates (percent)
Output 2.3 2.5 10.5 âˆ’43.7 56.0 Output 2.5 2.5 9.0 âˆ’67.0 73.0
Capital 2.5 2.0 4.2 âˆ’7.8 31.1 Capital 2.9 2.9 6.6 âˆ’71.7 42.4
Land 0.7 0.5 3.4 âˆ’18.4 28.8
(continued)
43
TABLE A2. Descriptive Statistics (continued)
Aggregated Data Penn World Table Data
PANEL (A) VARIABLES IN UNTRANSFORMED LEVELS TERMS
variable mean median st. dev. min. max. variable mean median st. dev. min. max.
Output 9.3E+10 1.7E+10 2.3E+11 1.1E+08 1.6E+12 Output 4.3E+11 1.3E+11 1.0E+12 1.3E+09 8.0E+12
Labor 1.1E+07 2.4E+06 3.6E+07 2.2E+04 2.4E+08 Labor 5.1E+07 1.3E+07 1.2E+08 2.1E+05 8.5E+08
Capital 2.0E+11 2.9E+10 4.3E+11 1.0E+08 2.3E+12 Capital 1.2E+12 3.3E+11 2.9E+12 3.3E+09 2.3E+13
in logarithms
Output 23.50 23.58 2.01 18.55 28.07 Output 25.44 25.58 1.71 21.02 29.71
Labor 14.66 14.67 1.74 10.01 19.30 Labor 16.49 16.41 1.63 12.27 20.57
Capital 24.10 24.08 2.21 18.44 28.44 Capital 26.38 26.52 1.80 21.92 30.75
in growth rates (percent)
Output 3.1 3.1 7.4 âˆ’33.9 42.1 Output 4.0 4.0 5.0 âˆ’37.1 26.6
Labor 0.2 0.4 2.6 âˆ’11.4 19.3 Labor 1.5 1.4 1.1 âˆ’1.9 4.8
Capital 3.6 2.7 3.6 âˆ’5.0 25.1 Capital 4.6 4.2 2.9 âˆ’1.3 16.4
PANEL (B) VARIABLES IN PER-WORKER TERMS
variable mean median st. dev. min. max. variable mean median st. dev. min. max.
Output 19,493 11,197 19,212 72 76,031 Output 11,445 10,630 8,193 594 31,074
Capital 49,634 23,140 55,541 53 236,312 Capital 37,059 32,981 31,765 661 136,891
in logarithms
Output 8.84 9.32 1.85 4.28 11.24 Output 8.95 9.27 1.02 6.39 10.34
Capital 9.44 10.05 2.20 3.96 12.37 Capital 9.87 10.40 1.37 6.49 11.83
in growth rates (percent)
Output 3.0 3.3 7.0 âˆ’31.0 44.5 Output 2.5 2.6 5.0 âˆ’41.2 23.2
Capital 3.4 3.2 3.8 âˆ’18.4 22.2 Capital 3.1 2.8 2.9 âˆ’4.2 14.3
Source: Authorsâ€™ analysis based on data sources discussed in the text.
Note: We report the descriptive statistics for value-added (in US dollars for the year
1990 or purchasing power parity-adjusted international dollars for the year 2000), labor
(headcount), capital stock (the same monetary values as VA in each respective dataset),
and land (in hectares) for the regression sample (levels sample: n = 918; N =
40)<****>Sectoral and aggregated data
Investment Data. Data for agricultural and manufacturing investment (AgSEInv,
MfgSEInv) in constant year 1990 local currency units (LCU), the US$-LCU exchange
rate (Ex_Rate, see comment below), and sector-specific deflators (AgDef, TotDef) were
taken from Crego, Larson, Butzer, and Mundlak (1998). 38 Note that these authors also
44
provide capital stock data, which they produced through their own calculations from the
investment data. Following Martin and Mitra (2002), we believe that the use of a single
year exchange rate is preferable to the use of annual rates in the construction of real
output (see next paragraph) and capital stock (see below).
Output data. For manufacturing, we use data on aggregate GDP in current LCU
and the share of GDP in manufacturing from the World Bank WDI (World Bank, 2008).
For agriculture, we use agricultural value-added in current LCU from the same source.
The two sectoral value-added series are then deflated using the Crego, Larson, Butzer,
and Mundlak (1998) sectoral deflator for agriculture and the total economy deflator for
manufacturing before we use the 1990 US$-LCU exchange rates to make them
comparable across countries.
The currencies used in the Crego, Larson, Butzer, and Mundlak (1998) data differ
from those applied in the WDI data for a number of European countries because of the
adoption of the Euro. Therefore, we must use alternative 1990 US$-LCU exchange rates
for these economies. 39
Labor data. For agriculture, we adopt the variable â€˜economically active
population in agricultureâ€™ from the FAOâ€™s (2007) PopSTAT. Manufacturing labor is
taken from UNIDOâ€™s (2004) INDSTAT.
Additional data. The land variable is taken from ResourceSTAT and represents
â€˜arable and permanent crop landâ€™ (measured in hectares) (FAO 2007). For the robustness
checks (results available on request), the livestock variable is constructed from the data
for the following animals in the â€˜live animalsâ€™ section of ProdSTAT: asses (donkeys),
buffalos, camels, cattle, chickens, ducks, horses, mules, pigs, sheep, goats, and turkeys.
45
Following convention, we use the formula below to convert the numbers for individual
animal species into the livestock variable:
livestock = 1.1 camels + buffalos + horses + mules + 0.8 cattle + 0.8 asses
+ 0.2 pigs + 0.1 (sheep + goats) + 0.01 (chickens + ducks + turkeys).
The fertilizer variable is taken from the â€˜fertilizers archiveâ€™ of ResourceSTAT and
represents â€˜agricultural fertilizer consumed in metric tons,â€™ which includes â€˜crudeâ€™ and
â€˜manufacturedâ€™ fertilizers. For human capital, we employ years of schooling attained in
the population by those aged 25 years and above, from Barro and Lee (2001),
interpolated to create an annual series.
Capital stock. We construct capital stock in agriculture and manufacturing by
applying the perpetual inventory method described in detail in Klenow and Rodriguez-
Clare (1997b), using the investment data from Crego, Larson, Butzer, and Mundlak
(1998), which are transformed into US dollars by applying the 1990 US$-LCU exchange
rate. For the construction of a sectoral base year capital stock in each country i, we
employ average sector value-added growth rates gij (using the deflated sectoral value-
added data), the average sectoral investment to value-added ratio (I/Y)ij and an assumed
depreciation rate of 5 percent to construct
(K/Y)0ij = (I/Y)ij / (gij +0.05)
for sector j (agriculture, manufacturing). This ratio is then multiplied by the sectoral
value-added data for the base year to yield K0j. Note that the method deviates from that
discussed in Klenow and Rodriguez-Clare (1997b) because they use per capita GDP in
46
their computations and therefore need to account for population growth in the
construction of the base year capital stock.
Aggregated data. We combine the agriculture and manufacturing data to produce
a stylized â€˜aggregate economy.â€™ For labor, we simply sum the headcount; for the
monetary representations of output and capital stock, the same treatment is applied.
Crego, Larson, Butzer, and Mundlak (1998) developed the first large panel dataset that
provides data on investment in agriculture for a long span of time, and their work affords
us this ability to sum variables for the two sectors.
<****>Penn World Table Data
As a means of comparison, we also provide production function estimates using
data from PWT version 6.2. We adopt real per capita GDP in international dollars
Laspeyeres (rgdpl) as measure for output and construct capital stock using investment
data (derived from the investment share in real GDP, ki, and the output variable, rgdpl) in
the perpetual inventory method described above, again adopting 5 percent depreciation
(at this point, we must use the data on population from PWT, pop, to compute the
average annual population growth rate).
47
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NOTES
1
We refer to â€˜dual economy modelsâ€™ as representing economies with two stylized sectors of
production (agriculture and manufacturing). â€˜Technologyâ€™ and â€˜technology parametersâ€™ refer to
the coefficients on capital and labor in the production function model (elasticities with respect to
capital and labor), not Total Factor Productivity (TFP) or its growth rate (technical/technological
progress).
2
The quoted shares are from the WDI database (World Bank 2008). For comparison, the
maximum share of oil revenue in GDP, computed as the difference between â€˜industry share in
GDPâ€™ and â€˜manufacturing share in GDPâ€™ from the same database, yields the following ranges for
some of the countries mentioned by Mankiw, Romer, and Weil (1992): Iran (12 to 51 percent),
Kuwait (15 to 81 percent), Gabon (28 to 60 percent), and Saudi Arabia (29 to 67 percent).
3
Crucially, all changes in X* are instigated by the state variables, and with the exception of error,
it is deemed â€˜meaninglessâ€™ to think of any other factors driving inputs (Mundlak, Larson, and
Butzer, 1999).
4
For simplicity, the exposition in Mundlak, Butzer, and Larson (2012) is limited to a static
model.
5
u0it and Îµjit are white noise.
6
Mundlak, Butzer, and Larson (2012) refer to the presence of state variables in both equations as
technology â€˜heterogeneity.â€™ Our use of the term differs from theirs because we refer to Î²i â‰ Î² as
technology heterogeneity.
59
7
The between-country regressions further include time-invariant proxies for countriesâ€™ physical
environment.
8
Between-time and between-country estimates are also provided, but the 2FE results are the
focus of attention.
9
Further, fâ‹…mt is a subset of ft, and the error terms Îµit, vmit, Ï‰t and Ï…t are white noise.
10
Heterogeneity over time will be addressed in section IV.
11
Others, namely, gt, are specific to the input evolution.
12
A detailed review of the important contribution of factor models to empirical
macroeconometrics is beyond the scope of this study. See Stock and Watson (2002), Bai and Ng
(2008), and Onatski (2009) for details.
13
The shock can never be truly idiosyncratic; m0it differs for each country i at each point in time
t. We consider this assumption reasonable given the interconnectedness of economies.
14
Abbreviations: POLS, Pooled OLS; 2FE, 2-way Fixed Effects; GMM, Arellano and Bond
(1991) Difference GMM and Blundell and Bond (1998) System GMM; MG, Pesaran and Smith
(1995) Mean Group estimator (with linear country trends); FDMG, dto with variables in first
difference and country drifts; PMG, Pesaran, Shin, and Smith (1999) Pooled Mean Group
estimator; CPMG, dto augmented with cross-section averages following Binder and Offermanns
(2007); CCEP/CMG, Pesaran (2006) Common Correlated Effects estimators. Note that our
POLS model is augmented with T-1 year dummies.
60
15
GMM, PMG, and CPMG estimation was based on an error correction model specification; see
Pesaran, Shin, and Smith (1999) for details. Further discussion of the empirical setup and results
is available on request.
16
We abstain from discussing the standard panel estimators here in great detail and refer to the
articles by Coakley, Fuertes, and Smith (2006), Bond and Eberhardt (2009), and Bond (2002) for
more information. We also investigate the Pooled Mean Group (PMG) estimator by Pesaran,
Shin, and Smith (1999) as well as a simple extension to the PMG in which we include cross-
section averages of the dependent and independent variables (CPMG), as suggested in Binder
and Offermanns (2007).
17
Although yt and eit are not independent, their correlation goes to zero as N becomes larger.
18
Thus, in the MG version, we have N individual country regressions with 2k + 2 RHS variables,
and in the pooled version, there is a single regression equation with k + N (k + 2) RHS variables.
19
Most conservatively, the CCE estimators require Î» â‰ 0 : the impact of each factor is, on
average, non-zero (Coakley, Fuertes, and Smith 2006). Alternative scenarios (see Pesaran 2006;
Kapetanios, Pesaran, and Yamagata 2011) allow for this assumption to be dropped in certain
situations, but for the sake of generality, we maintain it here.
20
An alternative approach to empirically implementing equation (4) is to estimate factors, factor
loadings, and slope coefficients jointly, as in the estimators developed in Bai and Kao (2006) and
Bai, Kao, and Ng (2009). Computational complexity aside, two recent theoretical contributions
support the Pesaran (2006) approach adopted in this study. Theoretical work by Westerlund and
Urbain (2011: 17f) compares the two approaches and concludes that â€œone is unlikely to do better
61
than when using the relatively simple CA [cross-sectional average augmentation] approach.â€?
Similarly, a study by Bailey, Kapetanios, and Pesaran (2012: 25) concludes that the methods
used to determine the number of strong factors on which the approach by Bai and co-authors
relies are â€œinvalid and will select the wrong number of factors, even asymptotically.â€?
21
We sum the values for value-added, capital stock (both in per worker terms), and labor and
then take logarithms.
22
We are, of course, aware that the difference in deflation between our sectoral and stylized
aggregated data, on the one hand, and PWT, on the other hand, makes them conceptually very
different measures of growth and development. The aggregated data emphasize tradable goods
production, whereas the PWT data equally emphasize tradable and non-tradable goods and
services. However, we believe that these differences are comparatively unimportant for the
purposes of estimation and inference in comparison to the distortions introduced by neglecting
the sectoral makeup and technology heterogeneity of economies at different stages of economic
development.
23
We do not account for missing observations in any way. The preferred empirical specifications
presented below are based on heterogeneous parameter models, in which (arguably) the lack of
balance (25 percent of observations in the balanced panel are missing) is less relevant than in the
homogeneous models because of the averaging of estimates.
24
If the correlation is caused by the same factors as those present in the inputs, the situation is
altogether more serious than mere lack of efficiency, namely, that Î² might be unidentified.
Residual diagnostics and their importance for empirical modeling are discussed in more detail in
Eberhardt and Teal (2011a) and Banerjee, Eberhardt, and Reade (2010).
62
25
This computation is based on statistically significant parameters only:
Ë† =1âˆ’ Î²
Î² L
Ë† +Î²
K [ (
Ë† , where Î²
Ë† +Î²
N RS )]Ë† is the log labor coefficient discussed above. If any of
RS
Ë† ,Î²
Î² K
Ë† or Î²
N
Ë† is insignificant, it is omitted from this calculation; if all parameters are
RS
insignificant, we report â€˜not applicableâ€™ (n/a).
26
The implication is that these empirical results are potentially spurious. We conduct a number
of robustness checks adding further covariates in the agriculture equations (livestock per worker,
fertilizer per worker) in the pooled regression framework. Results (available on request) do not
change from those presented above. We also conduct robustness checks to include human capital
in the estimation equation of both sectors. The results are presented in supplemental appendix S4
(see also discussion below).
27
We use robust regression to produce a robust estimate of the mean; see Hamilton (1992) and
Eberhardt (2012) for details.
28
We further implement alternative specifications for both sectors that include the level and
squared human capital terms (average years of schooling in the adult population) as additional
covariates (see supplemental appendix S4). In the agriculture data, augmentation with human
capital does not lead to statistically significant results (not reported). Manufacturing results for
the MG and FDMG mirror those in the unaugmented models presented above. For the standard
CMG models, we find capital coefficients somewhat below those in the unaugmented models but
within each otherâ€™s 95 percent confidence intervals (we do not estimate the â€˜alternative CMG
estimatorâ€™ with human capital because we encounter a dimensionality problem due to the large
number of covariates). Average education coefficients are significant and indicate high returns to
63
education in manufacturing: 11 percent and 12 percent in the unrestricted and CRS models,
respectively.
29
It can be argued that the CCE approach accounts for the induced bias for systematic distortion
of the land variable. In Eberhardt, Helmers, and Strauss (forthcoming), we suggest that similar
â€˜mismeasurementâ€™ of research and development investments leading to â€˜expensingâ€™ and â€˜double-
countingâ€™ bias can be addressed in a common factor approach to the Griliches knowledge
production function.
30
The supplemental appendix (S3) also contains details of an extensive simulation exercise in
which we formulate a number of production technologies for agriculture and manufacturing,
reflecting our insights into the effects of parameter heterogeneity, variable nonstationarity, and
cross-section dependence and analyze stylized aggregate data constructed from these two sectors.
This exercise suggests that, more than any other feature, the introduction of common factors
(even different ones across sectors) creates the largest problems in the aggregate empirical
results.
31
As a further robustness check, we ran regressions where, rather than aggregating the data, we
forced manufacturing and agriculture production to follow the same technology using cross-
equation restrictions. Results (available on request) did not differ qualitatively from the
aggregated results presented above. Additionally, we estimated dynamic pooled models,
introducing the PMG and CPMG estimators (for the results, see supplemental appendix S4). All
of these results confirm the patterns across the sectoral and aggregated data described above.
32
The importance of correctly specified technology heterogeneity in the presence of
nonstationary processes is discussed in detail in Eberhardt and Teal (2011a: 139f).
64
33
This is akin to ignoring common factors when these drive both y and x; see Eberhardt and Teal
(2011a: 137f).
34
We exclude the most extreme outliers from this plot using the following rule: we run a robust
regression of the capital coefficients on mean income pc (in logs), reported in the note to figure
1, further computing the weights assigned to each observation by the algorithm. Countries with
weights below 0.5 are then excluded (five countries in the agriculture and one country in the
manufacturing sample).
35
We also replaced the mean income variable in this analysis with a number of proxies for
institutions and â€˜social capital,â€™ provided and investigated by Hall and Jones (1999). The patterns
and significance levels for the correlations between sectoral capital coefficients and these
alternative variables were very similar to those for the income correlations presented above.
36
Note that whether this refers to true technology heterogeneity or simply greater bias in the
country regression for agriculture cannot be determined in this context.
37
Following the example in our main results, we use robust means for the heterogeneous
parameter models.
38
Data are available at http://go.worldbank.org/FS3FXW7461. All data discussed in this
appendix are linked at http://sites.google.com/site/medevecon/devecondata. Stata code for
empirical estimators and tests is available from SSC: pescadf, xtmg, xtcd. See also Eberhardt
(2012) on xtmg.
39
In detail, we apply exchange rates of 1.210246384 for AUT, 1.207133927 for BEL,
1.55504706 for FIN, 1.204635181 for FRA, 2.149653527 for GRC, 1.302645017 for IRL,
65
1.616114954 for ITA, 1.210203555 for NLD, and 1.406350856 for PRT. See table A1 for
country codes.
66
SUPPLEMENTAL APPENDIX
Structural Change and Cross-Country Growth Empirics
World Bank Economic Review
by
Markus Eberhardt1 and Francis Teal
Contents
S1 Time-series properties of the data 2
S2 Cross-section dependence in the data 3
S3 Monte Carlo Simulations 4
S3.1 Data Generating Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
S3.2 Overview of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
S3.3 Detailed results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
S4 Additional tables and ï¬?gures 8
References 13
List of Tables
1 Second generation panel unit root tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Cross-section correlation analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4 Pooled regression models (HC-augmented) . . . . . . . . . . . . . . . . . . . . . . . . . 8
5 Heterogeneous Manufacturing models (HC-augmented) . . . . . . . . . . . . . . . . . 9
6 Aggregate & PWT data: Pooled models (HC-augmented) . . . . . . . . . . . . . . . . 10
7 Aggregate & PWT data: Heterogeneous models with HC . . . . . . . . . . . . . . . . . 11
8 Alternative dynamic panel estimators . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
List of Figures
1 Box plots â€” Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1 Corresponding author: School of Economics, University of Nottingham, Room C6, Sir Clive Granger
Building, University Park, Nottingham NG7 2RD, UK. Email: markus.eberhardt@nottingham.ac.uk, Website:
http://sites.google.com/site/medevecon
1
S1 Time-series properties of the data
Table 1: Second generation panel unit root tests
Panel (A): Agriculture data
Variables in levels Variables in growth rates
log VA pw log Labour log Cap pw VA pw Labour Cap pw
lags Ztbar p Ztbar p Ztbar p lags Ztbar p Ztbar p Ztbar p
0 -0.93 0.18 7.88 1.00 7.14 1.00 0 -16.11 0.00 1.01 0.84 -1.63 0.05
1 -1.25 0.11 5.94 1.00 3.03 1.00 1 -10.88 0.00 2.66 1.00 -1.10 0.14
2 2.23 0.99 7.65 1.00 4.78 1.00 2 -5.82 0.00 5.94 1.00 3.49 1.00
3 4.18 1.00 9.18 1.00 4.80 1.00 3 -2.09 0.02 6.64 1.00 4.48 1.00
Land pw Land pw
lags Ztbar p lags Ztbar p
0 9.15 1.00 0 -10.40 0.00
1 6.34 1.00 1 -3.05 0.00
2 5.48 1.00 2 -0.17 0.43
3 3.42 1.00 3 2.65 1.00
Panel (B): manufacturing data
Variables in levels Variables in growth rates
log VA pw log Labour log Cap pw VA pw Labour Cap pw
lags Ztbar p Ztbar p Ztbar p lags Ztbar p Ztbar p Ztbar p
0 0.57 0.72 2.05 0.98 1.61 0.95 0 -18.64 0.00 -11.52 0.00 -9.27 0.00
1 1.69 0.95 1.12 0.87 0.28 0.61 1 -9.58 0.00 -7.76 0.00 -5.71 0.00
2 1.68 0.95 3.52 1.00 1.62 0.95 2 -4.61 0.00 -4.36 0.00 -2.94 0.00
3 3.00 1.00 3.08 1.00 2.75 1.00 3 -1.50 0.07 -0.81 0.21 0.23 0.59
Panel (C): Aggregated data
Variables in levels Variables in growth rates
log VA pw log Labour log Cap pw VA pw Labour Cap pw
lags Ztbar p Ztbar p Ztbar p lags Ztbar p Ztbar p Ztbar p
0 2.29 0.99 5.90 1.00 6.41 1.00 0 -15.30 0.00 -5.25 0.00 -4.01 0.00
1 2.28 0.99 3.84 1.00 3.00 1.00 1 -9.45 0.00 -2.38 0.01 -1.78 0.04
2 4.43 1.00 4.76 1.00 3.51 1.00 2 -3.90 0.00 -0.52 0.30 0.49 0.69
3 4.89 1.00 4.75 1.00 3.77 1.00 3 -1.24 0.11 1.87 0.97 2.89 1.00
Panel (D): Penn World Table data
Variables in levels Variables in growth rates
log VA pw log Labour log Cap pw VA pw Labour Cap pw
lags Ztbar p Ztbar p Ztbar p lags Ztbar p Ztbar p Ztbar p
0 5.05 1.00 -2.57 0.01 2.27 0.99 0 -14.49 0.00 0.46 0.68 -4.73 0.00
1 5.81 1.00 5.78 1.00 5.26 1.00 1 -7.32 0.00 -2.91 0.00 -3.19 0.00
2 6.10 1.00 6.93 1.00 6.26 1.00 2 -4.99 0.00 1.06 0.86 -2.48 0.01
3 7.62 1.00 6.26 1.00 6.74 1.00 3 -1.78 0.04 1.52 0.94 -1.20 0.12
Notes: We report test statistics and p-values for the Pesaran (2007) CIPS panel unit root test of the variables in our
four datasets. In all cases we use N = 40, n = 918 for the levels data. â€˜Lagsâ€™ refers to the augmentation with lagged
dependent variables (Augmented Dickey-Fuller test).
2
S2 Cross-section dependence in the data
Table 2: Cross-section correlation analysis
Variables in levels Variables in FD
Agriculture Â¯
Ï? Â¯|
|Ï? CD ( p) Â¯
Ï? |Ï?
Â¯| CD ( p)
log VA pw 0.33 0.51 42.42 0.00 0.05 0.23 6.32 0.00
log Labour 0.00 0.80 0.94 0.35 0.07 0.56 8.55 0.00
log Capital pw 0.41 0.71 51.52 0.00 0.08 0.41 8.86 0.00
log Land pw 0.02 0.67 3.57 0.00 0.02 0.29 2.91 0.00
Manufacturing Â¯
Ï? Â¯|
|Ï? CD ( p) Â¯
Ï? |Ï?
Â¯| CD ( p)
log VA pw 0.39 0.59 49.87 0.00 0.05 0.22 6.19 0.00
log Labour 0.15 0.62 18.98 0.00 0.14 0.26 17.31 0.00
log Capital pw 0.59 0.76 74.15 0.00 0.07 0.22 8.01 0.00
Aggregated Â¯
Ï? |Ï?Â¯| CD ( p) Â¯
Ï? |Ï?Â¯| CD ( p)
log VA pw 0.55 0.67 69.67 0.00 0.08 0.23 10.18 0.00
log Labour 0.04 0.71 5.50 0.00 0.07 0.32 7.93 0.00
log Capital pw 0.76 0.85 94.70 0.00 0.07 0.29 7.78 0.00
PWT Â¯
Ï? |Ï?Â¯| CD ( p) Â¯
Ï? |Ï?Â¯| CD ( p)
log VA pw 0.58 0.72 72.20 0.00 0.14 0.24 17.08 0.00
log Labour 0.94 0.94 114.37 0.00 0.05 0.39 6.21 0.00
log Capital pw 0.70 0.88 87.01 0.00 0.26 0.37 31.57 0.00
Notes: We report the average correlation coefï¬?cient across the N ( N âˆ’ 1) variable series Ï? Â¯ , as well as the average
Â¯ |. CD is the formal cross-section correlation tests introduced by Pesaran (2004).
absolute correlation coefï¬?cient |Ï?
Under the H0 of cross-section independence its statistics is asymptotically standard normal. We use our regression
sample N = 40, n = 918 for the levels data. The same sample is used for the ï¬?rst difference data (n = 884) with the
exception of the PWT analysis: here we are forced to drop the series for CYP to be able to compute correlation
coefï¬?cients.
3
S3 Monte Carlo Simulations
S3.1 Data Generating Process
We run M = 1, 000 replications of the following DGP for N = 50 cross-section elements and T = 30
time periods. Our basic setup for the DGP closely follows that of Kapetanios, Pesaran, and Yamagata
(2011), albeit with a single rather than two regressors. For notational simplicity we do not identify
the different sectors (agriculture and manufacturing) in the following, but all processes and variables
are created independently across sectors, unless otherwise indicated.
y y
yit = Î² i xit + uit uit = Î±i + Î»i1 f 1t + Î»i2 f 2t + Îµ it (1)
xit = ai1 + ai2 dt + Î»ix1 f 1t + Î»ix3 f 3t + vit (2)
for i = 1, . . . , N unless indicated below and t = 1, . . . , T .
The common deterministic trend term (dt ) and individual-speciï¬?c errors for the x-equation are
zero-mean independent AR(1) processes deï¬?ned as
dt = 0.5dtâˆ’1 + Ï…dt Ï…dt âˆ¼ N (0, 0.75) t = âˆ’48, . . . , 1, . . . , T dâˆ’49 = 0
vit = Ï?vi vi,tâˆ’1 + Ï…it Ï…it âˆ¼ N (0, (1 âˆ’ Ï?2
vi )) t = âˆ’48, . . . , 1, . . . , T vi,âˆ’49 = 0
where Ï?vi âˆ¼ U [0.05, 0.95]. The common factors are nonstationary processes
f jt = Âµ j + f j,tâˆ’1 + Ï… f t j = 1, 2, 3 Ï… f t âˆ¼ N (0, 1) t = âˆ’49, . . . , 1, . . . , T (3)
Âµa m
j = {0.01, 0.008, 0.005}, Âµ j = {0.015, 0.012, 0.01} f j,âˆ’50 = 0
where we deviate from the Kapetanios et al. (2011) setup by including drift terms. Unless indicated
the sets of common factors differ between sectors.
Innovations to y are generated as a mix of heterogeneous AR(1) and MA(1) errors
Îµ it = Ï?iÎµ Îµ i,tâˆ’1 + Ïƒi 1 âˆ’ Ï?2 i Îµ Ï‰it i = 1, . . . , N1 t = âˆ’48, . . . , 0, . . . , T
Ïƒi
Îµ it = (Ï‰it + Î¸iÎµ Ï‰i,tâˆ’1 ) i = N1 + 1, . . . , N t = âˆ’48, . . . , 0, . . . , T
1 + Î¸i2Îµ
where N1 is the nearest integer to N /2 and Ï‰it âˆ¼ N (0, 1), Ïƒi2 âˆ¼ U [0.5, 1.5], Ï?iÎµ âˆ¼ U [0.05, 0.95], and
Î¸iÎµ âˆ¼ U [0, 1]. Ï?vi , Ï?iÎµ , Î¸iÎµ and Ïƒi do not change across replications. Initial values are set to zero and
the ï¬?rst 50 observations are discarded for all of the above.
Regarding parameter values, Î±i âˆ¼ N (2, 1) and ai1 , ai2 âˆ¼ iid N (0.5, 0.5) do not change across replica-
tions. To begin with TFP levels Î±i are speciï¬?ed to be the same across sectors. The slope coefï¬?cient
Î² can vary across countries and across sectors (see below). In case of cross-country heterogeneity
we have Î² i = Î² + Î·i with Î·i âˆ¼ N (0, 0.04). If the mean of the slope coefï¬?cient Î² is the same across
sectors we specify Î² = 0.5, otherwise Î² a = 0.5 and Î²m = 0.3 for agriculture and manufacturing
respectively.
For the factor loadings may be heterogeneous and are distributed
Î»ix1 âˆ¼ N (0.5, 0.5) and Î»ix3 âˆ¼ N (0.5, 0.5) (4)
y y
Î»i1 âˆ¼ N (1, 0.2) and Î»i2 âˆ¼ N (1, 0.2) (5)
4
The above represents our basis DGP for the simulations carried out. We investigate the following
ten models (the focus is on those marked with stars):
(1) Cross-country homogeneity ( Î²) and no factors. We set all Î»i to zero such that x and y are
stationary and cross-sectionally independent; technology is the same across countries and
sectors.
(2) As Model (1) but now we have heterogeneous Î² across countries.
(3) As Model (2) but with substantially larger heterogeneity in TFP levels across countries.
(4) As Model (2) but with TFP levels in manufacturing are now 1.5 times those in agriculture.
We keep this feature for the remainder of setups.
(5) This sees the introduction of common factors ( f 2t and f 3t ) albeit with homogeneous factor
loadings across countries. Both factors and loadings are independent across sectors. The
absence of f 1t means there is no endogeneity problem.
(6) As Model (5) but now we have factor loading heterogeneity across countries.
(7) As Model (6) but with factor-overlap between x and y equations: f 1t is contained in both of
these, inducing endogeneity in a sectoral regression.
(8) As Model (7) but slope coefï¬?cients now differ across countries and sectors â€” for the latter
we specify Î²m a
i = 1 âˆ’ Î²i .
(9) As Model (8) except we now have independent slope coefï¬?cients across sectors with means
Î²m = 0.3 and Î² a = 0.5.
(10) As Model (9) but we now have the same factor f 1t contained in y and x-equations of both
sectors, although with differential (and independent) factor loadings.
Models (1) to (4) analyse a homogeneous parameter world without common factors, where aggrega-
tion should lead to no problems for estimation. Models (5) to (7) show what happens when factors
are introduced. Models (8) and (9) introduce parameter heterogeneity across sectors and Model (10)
adds factor-overlap between sectors (on top of overlap across variables within sector).
5
S3.2 Overview of results
Figure 1: Box plots â€” Simulation results
Notes: We present box plots for the M = 1, 000 estimates using various estimators under 4 DGP setups. In all cases
the true coefï¬?cient is subtracted from the estimates, such that the plots are centred around zero.
The estimators are as follows: â€˜CMG Agriâ€™ and â€˜CMG Manuâ€™ â€” Pesaran (2006) CMG regressions on the sector-level
m with Î² j the mean sectoral slope
data; Weighted â€” this is not an estimator but the weighted average Î² a sia + Î²m si
coefï¬?cient and s j the sectoral share of total output; the remaining four estimators use the aggregated data: OLS â€”
pooled OLS with T âˆ’ 1 year dummies; 2FE â€” OLS with country and time dummies; FD â€” OLS with variables in ï¬?rst
differences (incl. time dummies); CMG â€” Pesaran (2006) CMG. We omit the results for the Pesaran and Smith (1995)
MG estimator as these are very imprecise and would counter the readability of the graphs. The MC setups are
described in detail in Section S3.1 of the Appendix.
6
S3.3 Detailed results
Table 3: Simulation results
Model 1 Model 2
mean median steâ€¢ ste mean median steâ€¢ ste
CMG Agri 0.4999 0.4990 0.0318 0.0324 CMG Agri 0.5007 0.4996 0.0425 0.0424
CMG Manu 0.4999 0.4990 0.0318 0.0324 CMG Manu 0.5007 0.4996 0.0425 0.0424
Weighted 0.5000 0.5000 0.0000 Weighted 0.5007 0.4998 0.0289
POLS 0.5054 0.5064 0.0462 0.0298 POLS 0.5058 0.5065 0.0572 0.0304
2FE 0.5002 0.5005 0.0248 0.0226 2FE 0.5014 0.5007 0.0392 0.0232
FD 0.5000 0.5007 0.0295 0.0257 FD 0.5014 0.5014 0.0441 0.0262
CCEP 0.4996 0.4997 0.0292 0.0271 CCEP 0.5008 0.5001 0.0424 0.0276
MG 0.4993 0.4987 0.0276 0.0283 MG 0.5001 0.4993 0.0389 0.0399
CMG 0.4999 0.4990 0.0318 0.0324 CMG 0.5007 0.4996 0.0425 0.0424
Model 3 Model 4
mean median steâ€¢ ste mean median steâ€¢ ste
CMG Agri 0.4999 0.4990 0.0318 0.0324 CMG Agri 0.4999 0.4990 0.0318 0.0324
CMG Manu 0.4999 0.4990 0.0318 0.0324 CMG Manu 0.4999 0.4990 0.0318 0.0324
Weighted 0.5000 0.5000 0.0000 Weighted 0.5000 0.5000 0.0000
POLS 0.5310 0.5280 0.1968 0.1128 POLS 0.5119 0.5112 0.0593 0.0365
2FE 0.5002 0.5005 0.0248 0.0226 2FE 0.5002 0.5005 0.0248 0.0226
FD 0.5000 0.5007 0.0295 0.0257 FD 0.5000 0.5007 0.0295 0.0257
CCEP 0.4996 0.4997 0.0292 0.0271 CCEP 0.4996 0.4997 0.0292 0.0271
MG 0.4993 0.4987 0.0276 0.0283 MG 0.4993 0.4987 0.0276 0.0283
CMG 0.4999 0.4990 0.0318 0.0324 CMG 0.4999 0.4990 0.0318 0.0324
Model 5 Model 6
mean median steâ€¢ ste mean median steâ€¢ ste
CMG Agri 0.4993 0.4987 0.0299 0.0298 CMG Agri 0.5005 0.5002 0.0238 0.0233
CMG Manu 0.5000 0.5014 0.0311 0.0321 CMG Manu 0.4994 0.5004 0.0253 0.0246
Weighted 0.5000 0.5000 0.0000 Weighted 0.5000 0.5000 0.0000
POLS 0.4936 0.4936 0.0753 0.0432 POLS 0.4558 0.4669 0.1059 0.0197
2FE 0.4563 0.4571 0.0331 0.0266 2FE 0.4382 0.4450 0.0588 0.0176
FD 0.4427 0.4416 0.0418 0.0268 FD 0.4181 0.4224 0.0517 0.0219
CCEP 0.4516 0.4502 0.0327 0.0278 CCEP 0.4231 0.4326 0.0522 0.0186
MG 0.4663 0.4687 0.3257 0.0369 MG 0.4305 0.4333 0.1816 0.0496
CMG 0.4498 0.4497 0.0362 0.0379 CMG 0.4161 0.4226 0.0516 0.0342
Model 7 Model 8
mean median steâ€¢ ste mean median steâ€¢ ste
CMG Agri 0.5000 0.4998 0.0448 0.0436 CMG Agri 0.5009 0.5020 0.0528 0.0520
CMG Manu 0.4979 0.4972 0.0454 0.0445 CMG Manu 0.4986 0.4978 0.0550 0.0528
Weighted 0.5000 0.5000 0.0000 Weighted 0.5007 0.4998 0.0289
POLS 0.4405 0.4469 0.1212 0.0236 POLS 0.4459 0.4452 0.1299 0.0248
2FE 0.4143 0.4161 0.0700 0.0210 2FE 0.4217 0.4234 0.0807 0.0220
FD 0.4027 0.4011 0.0541 0.0238 FD 0.4106 0.4073 0.0635 0.0245
CCEP 0.3956 0.3987 0.0619 0.0227 CCEP 0.4040 0.4047 0.0702 0.0233
MG 0.6759 0.6585 0.2510 0.0782 MG 0.6826 0.6644 0.2532 0.0828
CMG 0.3897 0.3928 0.0584 0.0496 CMG 0.3985 0.3976 0.0650 0.0560
Model 9 Model 10
mean median steâ€¢ ste mean median steâ€¢ ste
CMG Agri 0.5009 0.5020 0.0528 0.0520 CMG Agri 0.5009 0.5020 0.0528 0.0520
CMG Manu 0.2961 0.2972 0.0543 0.0526 CMG Manu 0.2961 0.2972 0.0543 0.0526
Weighted 0.3924 0.3928 0.0391 Weighted 0.3939 0.3946 0.0391
POLS 0.3383 0.3388 0.1324 0.0246 POLS 0.3400 0.3415 0.1322 0.0246
2FE 0.3151 0.3127 0.0814 0.0217 2FE 0.3163 0.3144 0.0816 0.0217
FD 0.3074 0.3053 0.0625 0.0242 FD 0.3086 0.3071 0.0626 0.0242
CCEP 0.2963 0.2973 0.0666 0.0229 CCEP 0.2976 0.2986 0.0667 0.0229
MG 0.5793 0.5562 0.2558 0.0814 MG 0.5796 0.5561 0.2558 0.0815
CMG 0.2956 0.2962 0.0625 0.0543 CMG 0.2970 0.2976 0.0627 0.0544
Notes: See Section S3.1 in the Appendix for details on the estimators and the DGP in each of the experiments.
steâ€¢ marks the empirical standard error and ste the mean standard error from 1,000 replications. â€˜CMG Agriâ€™ and
â€˜CMG Manuâ€™ employ the sector-level data, â€˜Weightedâ€™ calculates the aggregate slope coefï¬?cient based on the size
(output) and slope of the respective sector, the remaining six estimators use the aggregated data.
7
S4 Additional tables and ï¬?gures
Table 4: Pooled regression models (HC-augmented)
Panel (A): Unrestricted returns to scale
Agriculture Manufacturing
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
POLS 2FE CCEP CCEP FD POLS 2FE CCEP CCEP FD
log labour -0.079 -0.151 -0.457 -0.557 -0.085 0.005 0.029 0.121 -0.048 0.162
[11.71]âˆ—âˆ— [4.35]âˆ—âˆ— [1.54] [1.46] [1.46] [0.62] [0.88] [1.91] [0.47] [4.62]âˆ—âˆ—
log capital pw 0.471 0.671 0.554 0.676 0.595 0.692 0.851 0.533 0.446 0.654
[61.84]âˆ—âˆ— [27.20]âˆ—âˆ— [4.51]âˆ—âˆ— [4.32]âˆ—âˆ— [12.60]âˆ—âˆ— [44.38]âˆ—âˆ— [22.14]âˆ—âˆ— [8.00]âˆ—âˆ— [4.52]âˆ—âˆ— [14.56]âˆ—âˆ—
log land pw 0.018 -0.020 -0.154 -0.174 0.111
[1.17] [0.48] [0.56] [0.50] [1.14]
Education 0.241 0.087 0.007 -0.068 0.101 0.226 -0.006 0.152 -0.017 0.095
[9.95]âˆ—âˆ— [3.12]âˆ—âˆ— [0.07] [0.40] [1.30] [11.91]âˆ—âˆ— [0.21] [2.04]âˆ— [0.16] [1.53]
EducationË†2 -0.010 -0.007 -0.003 0.005 -0.006 -0.009 0.002 -0.006 -0.004 -0.005
[4.73]âˆ—âˆ— [4.15]âˆ—âˆ— [0.49] [0.50] [1.23] [6.22]âˆ—âˆ— [1.39] [1.32] [0.66] [1.10]
Implied RSâ€ CRS CRS CRS CRS IRS CRS CRS CRS IRS
Implied Î² L â€¡ 0.529 0.329 0.446 0.324 0.321 0.308 0.149 0.467 0.508
Mean Education 5.82 5.82 5.82 5.82 5.94 5.82 5.82 5.82 5.82 5.94
Returns to Edu 13.3% 0.7% -2.9% -0.7% 3.0% 12.3% 1.9% 8.5% -6.6% 4.1%
[t-statistic] [15.71]âˆ—âˆ— [0.50] [0.68] [0.11] [0.78] [19.88]âˆ—âˆ— [1.30] [3.11]âˆ—âˆ— [1.56] [1.54]
Ë† integrated
e I(1) I(1) I(0) I(1)/I(0) I(0) I(1) I(1) I(0) I(0) I(0)
CD test p-value 0.11 0.09 0.14 0.21 0.00 0.87 0.18 0.58 0.84 0.00
R-squared 0.91 0.57 1.00 1.00 - 0.91 0.57 1.00 1.00 -
Observations 830 830 830 775 793 860 860 860 775 817
Panel (B): Constant returns to scale imposed
Agriculture Manufacturing
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
POLS 2FE CCEP CCEP FD POLS 2FE CCEP CCEP FD
log capital pw 0.502 0.720 0.592 0.709 0.611 0.695 0.839 0.472 0.463 0.558
[59.09]âˆ—âˆ— [33.18]âˆ—âˆ— [5.32]âˆ—âˆ— [5.08]âˆ—âˆ— [13.29]âˆ—âˆ— [49.18]âˆ—âˆ— [24.30]âˆ—âˆ— [8.87]âˆ—âˆ— [5.59]âˆ—âˆ— [13.85]âˆ—âˆ—
log land pw 0.014 0.078 0.144 0.122 0.124
[0.71] [2.23]âˆ— [0.99] [0.69] [1.27]
Education 0.278 0.069 -0.003 -0.031 0.107 0.226 0.014 0.234 0.036 0.220
[11.54]âˆ—âˆ— [2.48]âˆ— [0.03] [0.23] [1.38] [11.80]âˆ—âˆ— [0.71] [3.67]âˆ—âˆ— [0.38] [3.91]âˆ—âˆ—
EducationË†2 -0.012 -0.005 0.000 0.002 -0.006 -0.009 0.001 -0.010 -0.007 -0.010
[6.17]âˆ—âˆ— [3.19]âˆ—âˆ— [0.06] [0.28] [1.26] [6.11]âˆ—âˆ— [0.98] [2.55]âˆ— [1.22] [2.41]âˆ—
Implied Î² L â€¡ 0.498 0.202 0.408 0.291 0.389 0.305 0.162 0.528 0.537 0.443
Mean Education 5.82 5.82 5.82 5.82 5.94 5.82 5.82 5.82 5.82 5.94
Returns to Edu 13.9% 0.8% -0.7% -0.3% 3.4% 12.3% 2.7% 11.7% -4.3% 10.5%
[t-statistic]â™ [16.25]âˆ—âˆ— [0.52] [0.18] [0.07] [0.90] [20.20]âˆ—âˆ— [2.30]âˆ— [5.25]âˆ—âˆ— [1.18] [4.62]âˆ—âˆ—
Ë† integrated
e I(1) I(1) I(0) I(1)/I(0) I(0) I(1) I(1) I(0) I(1)/I(0) I(0)
CD test p-value 0.29 0.23 0.07 0.23 0.00 0.88 0.04 0.08 0.02 0.00
R-squared 0.91 0.57 1.00 1.00 - 0.91 0.57 1.00 1.00 -
Observations 830 830 830 775 793 860 860 860 775 817
Notes: We include our proxy for education in levels and as a squared term. Returns to Education are computed from
the sample mean (E Ë† E2 E
Ë† E + 2Î²
Â¯ ) as Î² Ë† E2 are the coefï¬?cients on the levels and squared education terms
Ë† E and Î²
Â¯ where Î²
respectively. â™ computed via the delta-method. For more details see Notes of Table 1 of the main text.
8
Table 5: Heterogeneous Manufacturing models (HC-augmented)
Panel (A): Unrestricted Panel (B): CRS imposed
[1] [2] [3] [4] [5] [6]
MG FDMG CMG MG FDMG CMG
log labour -0.305 -0.293 0.097
[1.20] [1.50] [0.62]
log capital pw 0.059 0.144 0.426 0.352 0.347 0.386
[0.22] [0.74] [3.73]âˆ—âˆ— [3.25]âˆ—âˆ— [3.66]âˆ—âˆ— [3.95]âˆ—âˆ—
Education -0.478 0.237 1.248 -0.228 0.085 0.668
[1.02] [0.81] [2.66]âˆ— [0.62] [0.29] [2.43]âˆ—
Education squared 0.050 0.011 -0.098 0.005 -0.019 -0.042
[1.38] [0.35] [2.67]âˆ— [0.13] [0.67] [1.95]
country trend/drift 0.016 0.020 0.008 0.013
[1.55] [2.44]âˆ— [1.16] [2.23]âˆ—
reject CRS (10%) 38% 8% 38%
Implied Î² L â€¡ n/a 0.857 0.574 0.648 0.653 0.614
Mean Education 5.82 5.91 5.82 5.87 5.94 5.87
Returns to Edu -6.3% -1.3% 10.9% -6.2% -2.1% 11.9%
[t-statistic] [1.01] [0.25] [1.89] [1.00] [0.47] [1.70]
sign. trends (10%) 15 9 17 7
Ë† integrated
e I(0) I(0) I(0) I(0) I(0) I(0)
CD-test ( p) 0.00 0.00 0.71 0.00 0.00 0.27
Obs (N) 775 (37) 732 (37) 775 (37) 775 (37) 732 (37) 775 (37)
Notes: All averaged coefï¬?cients presented are robust means across i. The returns to
education and associated t-statistics are based on a two-step procedure: ï¬?rst the
country-speciï¬?c mean education value (E Ë† i , E2 E
Ë† i, E + 2 Î²
Â¯ i ) is used to compute Î² Â¯ i to yield the
country-speciï¬?c returns to education. The reported value then represents the robust mean of
these N country estimates, s.t. the t-statistic should be interpreted in the same fashion as that
for the regressors, namely as a test whether the average parameter is statistically different
from zero, following Pesaran and Smith (1995). For other details see Notes for Tables 2 (main
text) and 4 (above).
9
Table 6: Aggregate & PWT data: Pooled models (HC-augmented)
Panel (A): Unrestricted returns
Aggregated data Penn World Table data
[1] [2] [3] [4] [5] [6] [7] [8]
POLS 2FE CCEP FD POLS 2FE CCEP FD
log labour -0.001 -0.058 0.566 0.083 0.040 -0.064 -0.193 -0.032
[0.14] [1.97]âˆ— [4.13]âˆ—âˆ— [2.50]âˆ— [8.99]âˆ—âˆ— [3.27]âˆ—âˆ— [1.49] [1.11]
log capital pw 0.662 0.782 0.677 0.766 0.725 0.680 0.601 0.676
[97.95]âˆ—âˆ— [31.50]âˆ—âˆ— [7.25]âˆ—âˆ— [25.24]âˆ—âˆ— [72.79]âˆ—âˆ— [24.79]âˆ—âˆ— [9.12]âˆ—âˆ— [18.96]âˆ—âˆ—
Education 0.243 -0.004 0.086 0.065 0.041 0.043 0.032 0.103
[16.97]âˆ—âˆ— [0.15] [1.24] [1.22] [3.42]âˆ—âˆ— [2.86]âˆ—âˆ— [0.80] [3.41]âˆ—âˆ—
Education squared -0.010 0.003 -0.007 -0.003 -0.001 -0.002 -0.002 -0.006
[8.05]âˆ—âˆ— [1.82] [1.57] [0.77] [1.77] [2.97]âˆ—âˆ— [0.83] [2.94]âˆ—âˆ—
Implied RSâ€ CRS DRS CRS CRS CRS DRS CRS CRS
Implied Î² L â€¡ 0.337 0.160 0.890 0.318 0.315 0.256 0.206 0.292
Mean Education 5.824 5.824 5.824 5.885 5.822 5.822 5.822 5.883
Returns to Edu 12.9% 2.5% 1.0% 3.4% 2.4% 1.9% 0.9% 3.3%
[t-statistic] [22.35]âˆ—âˆ— [1.68] [0.37] [1.40] [6.82]âˆ—âˆ— [2.02]âˆ— [0.56] [2.26]âˆ—
Ë† integrated
e I(1) I(1) I(0) I(0) I(1) I(1) I(0) I(1)/I(0)
CD test p-value 0.00 0.02 0.59 0.00 0.34 0.22 0.01 0.00
R-squared 0.98 0.87 1.00 - 0.97 0.78 1.00 -
Observations 775 775 775 732 769 769 769 726
Panel (B): Constant returns to scale imposed
Aggregated data Penn World Table data
[1] [2] [3] [4] [5] [6] [7] [8]
POLS 2FE CCEP FD POLS 2FE CCEP FD
log capital pw 0.662 0.798 0.485 0.744 0.694 0.706 0.611 0.691
[102.10]âˆ—âˆ— [35.45]âˆ—âˆ— [7.03]âˆ—âˆ— [25.48]âˆ—âˆ— [73.08]âˆ—âˆ— [27.73]âˆ—âˆ— [10.05]âˆ—âˆ— [21.13]âˆ—âˆ—
Education 0.243 -0.016 0.210 0.111 0.043 0.037 0.016 0.092
[16.98]âˆ—âˆ— [0.62] [3.00]âˆ—âˆ— [2.21]âˆ— [3.30]âˆ—âˆ— [2.44]âˆ— [0.48] [3.22]âˆ—âˆ—
Education squared -0.010 0.004 -0.013 -0.005 -0.001 -0.002 -0.002 -0.006
[8.17]âˆ—âˆ— [2.75]âˆ—âˆ— [2.92]âˆ—âˆ— [1.37] [0.97] [2.12]âˆ— [0.95] [2.79]âˆ—âˆ—
Constant 1.586 1.843
[21.62]âˆ—âˆ— [20.44]âˆ—âˆ—
Implied Î² L â€¡ 0.338 0.203 0.515 0.256 0.306 0.294 0.390 0.309
Mean Education 5.824 5.824 5.824 5.885 5.822 5.824 5.824 5.883
Returns to Edu 12.9% 2.6% 6.5% 5.8% 3.3% 2.0% -0.6% 2.7%
[t-statistic] [22.41]âˆ—âˆ— [1.68] [2.56]âˆ—âˆ— [2.56]âˆ—âˆ— [8.62]âˆ—âˆ— [1.99]âˆ— [0.42] [1.98]âˆ—
Ë† integrated
e I(1) I(1) I(0) I(0) I(1) I(1) I(0) I(0)
CD test p-value 0.00 0.00 0.65 0.00 0.25 0.57 0.02 0.00
R-squared 0.98 0.86 1.00 0.97 0.78 1.00
Observations 775 775 775 732 769 769 769 726
Notes: We include our proxy for education in levels and as a squared term. Returns to Education are computed from
the sample mean (E Ë† E2 E
Ë† E + 2Î²
Â¯ ) as Î² Ë† E2 are the coefï¬?cients on the levels and squared education terms
Ë† E and Î²
Â¯ where Î²
respectively. computed via the delta-method. For more details see Notes for Tables 3 (in the main text) and (for the
education variables) 4 above.
10
Table 7: Aggregate & PWT data: Heterogeneous models with HC
Panel (A): Unrestricted returns to scale
Aggregated data Penn World Table data
[1] [2] [3] [4] [5] [6]
MG FDMG CMG MG FDMG CMG
log labour -0.066 0.269 -0.428 -1.609 -2.478 -1.324
[0.16] [0.57] [1.22] [1.97] [3.76]âˆ—âˆ— [2.79]âˆ—âˆ—
log capital pw -0.070 -0.021 0.453 0.963 1.245 1.122
[0.26] [0.07] [2.47]âˆ— [4.44]âˆ—âˆ— [5.99]âˆ—âˆ— [5.52]âˆ—âˆ—
Education 0.601 0.637 0.489 0.123 0.004 -0.012
[1.29] [1.75] [0.98] [0.52] [0.02] [0.05]
Education squared -0.089 -0.065 -0.063 -0.002 0.004 -0.001
[1.76] [1.70] [1.48] [0.11] [0.25] [0.03]
country trend/drift 0.005 0.005 0.021 0.008
[0.33] [0.29] [2.25]âˆ— [0.77]
Implied RSâ€ CRS CRS CRS CRS DRS DRS
Implied Î² L â€¡ n/a n/a 0.547 n/a n/a n/a
reject CRS (10%) 38% 3% 19% 38% 18% 33%
sign. trends (10%) 44% 32% 44% 10%
Mean Education 5.72 5.84 5.72 5.72 5.84 5.72
Returns to edu -7.1% -3.2% -11.1% -4.5% 0.5% 1.3%
[t-statistic] [1.33] [0.65] [1.24] [1.33] [0.18] [0.43]
Ë† integrated
e I(0) I(0) I(0) I(0) I(0) I(0)
CD-test ( p) 7.23(.00) 7.88(.00) -0.50(.61) 7.59.00) 9.29.00) 0.98(.33)
Panel (B): CRS imposed
Aggregated data Penn World Table data
[1] [2] [3] [4] [5] [6]
MG FDMG CMG MG FDMG CMG
log capital pw 0.093 0.151 0.528 0.779 1.052 0.906
[0.49] [0.90] [4.90]âˆ—âˆ— [5.75]âˆ—âˆ— [6.43]âˆ—âˆ— [5.86]âˆ—âˆ—
Education 0.075 0.260 0.683 -0.215 -0.134 0.089
[0.18] [0.99] [1.73] [1.25] [0.84] [0.42]
Education squared -0.023 -0.023 -0.075 0.013 0.014 -0.023
[0.65] [0.89] [1.57] [0.82] [1.13] [1.16]
country trend/drift 0.017 0.015 -0.001 -0.010
[1.96] [1.33] [0.21] [2.08]âˆ—
Implied Î² L â€¡ n/a n/a 0.472 0.221 n/a 0.094
sign. trends (10%) 37% 32% 37% 34%
Mean Education 5.79 5.84 5.79 5.79 5.84 5.79
Returns to edu -9.3% -4.0% 3.2% -1.4% 0.3% -0.2%
[t-statistic] [1.34] [0.88] [0.50] [0.50] [0.16] [0.05]
Ë† integrated
e I(0) I(0) I(0) I(0) I(0) I(0)
CD-test ( p) 8.05(.00) 8.59(.00) 0.11(.92) 9.75(.00) 10.84(.00) 3.12(.00)
Notes: All averaged coefï¬?cients presented are robust means across i. The returns to education and associated
t-statistics are based on a two-step procedure: ï¬?rst the country-speciï¬?c mean education value (E Â¯ i ) is used to compute
Â¯
Î² i,E + 2 Î² i,E2 Ei to yield the country-speciï¬?c returns to education. The reported value then represents the robust mean
of these N country estimates, s.t. the t-statistic should be interpreted in the same fashion as that for the regressors,
namely as a test whether the average parameter is statistically different from zero, following Pesaran and Smith
(1995). For other details see Notes for Tables 2 (in the main text) and 5 above.
11
Table 8: Alternative dynamic panel estimators
Panel (A): Agriculture
Dynamic FE PMG CPMG DGMM SGMM
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
EC [ytâˆ’1 ] -0.293 -0.312 -0.300 -0.460 -0.459 -0.624 -0.466 -0.482 -0.503 -0.455 -1.087 -0.432
[11.80]âˆ—âˆ— [12.43]âˆ—âˆ— [11.91]âˆ—âˆ— [10.63]** [9.34]âˆ—âˆ— [14.29]âˆ—âˆ— [10.44]âˆ—âˆ— [10.06]âˆ—âˆ— [9.74]âˆ—âˆ— [9.34]âˆ—âˆ— [2.60]âˆ—âˆ— [5.38]âˆ—âˆ—
capital pw 0.672 0.684 0.582 0.652 0.714 0.036 0.132 0.501 0.464 0.530 1.135 0.776
[12.47]âˆ—âˆ— [12.69]âˆ—âˆ— [7.50]âˆ—âˆ— [20.16]âˆ—âˆ— [18.52]âˆ—âˆ— [0.57] [3.01]âˆ—âˆ— [10.78]âˆ—âˆ— [11.05]âˆ—âˆ— [10.83]âˆ—âˆ— [2.85]âˆ—âˆ— [12.59]âˆ—âˆ—
land pw 0.124 0.121 0.135 0.136 0.367 0.867 0.361 0.247 0.494 0.228 0.083 -0.247
[1.30] [1.29] [1.45] [2.90]âˆ—âˆ— [6.43]âˆ—âˆ— [8.27]âˆ—âˆ— [8.05]âˆ—âˆ— [5.03]âˆ—âˆ— [8.95]âˆ—âˆ— [4.73]âˆ—âˆ— [0.35] [1.17]
trend(s)â€ 0.001 0.008 0.012
[1.59] [3.36]âˆ—âˆ— [12.26]âˆ—âˆ—
Constant 0.667 0.679 0.896 1.072 0.644 4.273 3.084 1.545 1.402 1.298 0.714
[5.03]âˆ—âˆ— [4.75]âˆ—âˆ— [4.58]âˆ—âˆ— [10.48]âˆ—âˆ— [7.53]âˆ—âˆ— [13.11]âˆ—âˆ— [10.27]âˆ—âˆ— [10.38]âˆ—âˆ— [9.69]âˆ—âˆ— [9.94]âˆ—âˆ— [4.21]âˆ—âˆ—
lags [trends]â€¡ 1 2 1 [l-r] 1 2 1 [s-r] 1 [l-r] 1 2 1 i: 2-3 i: 2-3
impl. labour 0.328 0.316 0.418 0.212 -0.081 0.098 0.507 0.253 0.042 0.242 -0.135 0.224
obs 894 857 894 894 857 894 894 894 857 872 857 894
Panel (B): Manufacturing
Dynamic FE PMG CPMG DGMM SGMM
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
EC [ytâˆ’1 ] -0.196 -0.195 -0.195 -0.219 -0.181 -0.543 -0.214 -0.245 -0.194 -0.272 -2.196 -0.041
[9.40]âˆ—âˆ— [9.16]âˆ—âˆ— [9.31]âˆ—âˆ— [6.59]âˆ—âˆ— [5.97]âˆ—âˆ— [4.04]âˆ—âˆ— [4.13]âˆ—âˆ— [7.16]âˆ—âˆ— [6.45]âˆ—âˆ— [7.33]âˆ—âˆ— [0.72] [0.65]
capital pw 0.711 0.708 0.637 1.016 1.044 0.298 1.379 0.598 1.264 0.505 1.866 -1.515
[12.96]âˆ—âˆ— [12.34]âˆ—âˆ— [6.85]âˆ—âˆ— [29.64]âˆ—âˆ— [33.09]âˆ—âˆ— [5.34]âˆ—âˆ— [26.80]âˆ—âˆ— [11.58]âˆ—âˆ— [22.28]âˆ—âˆ— [9.47]âˆ—âˆ— [3.25]âˆ—âˆ— [0.40]
trend(s)â€ 0.001 0.001 -0.010
[1.00] [0.24] [6.77]âˆ—âˆ—
Constant 0.452 0.456 0.588 -0.212 -0.228 3.493 -0.977 0.225 -0.434 0.372 1.042
[3.87]âˆ—âˆ— [3.73]âˆ—âˆ— [3.29]âˆ—âˆ— [5.43]âˆ—âˆ— [4.95]âˆ—âˆ— [3.87]âˆ—âˆ— [4.18]âˆ—âˆ— [5.68]âˆ—âˆ— [5.77]âˆ—âˆ— [6.48]âˆ—âˆ— [1.80]
lags [trends]â€¡ 1 2 1 [l-r] 1 2 1 [s-r] 1 [l-r] 1 2 1 i: 2-3 i: 2-3
impl. labour 0.289 0.292 0.363 -0.016 -0.044 0.702 -0.379 0.402 -0.264 0.495 -0.866 2.515
obs 902 880 902 902 880 902 902 902 880 879 880 902
Panel (C): Aggregated data
Dynamic FE PMG CPMG DGMM SGMM
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
EC [ytâˆ’1 ] -0.172 -0.176 -0.173 -0.279 -0.277 -0.429 -0.284 -0.292 -0.294 -0.317 -0.380 -0.243
[8.59]âˆ—âˆ— [8.39]âˆ—âˆ— [8.59]âˆ—âˆ— [6.89]âˆ—âˆ— [7.25]âˆ—âˆ— [9.55]âˆ—âˆ— [6.72]âˆ—âˆ— [6.98]âˆ—âˆ— [7.38]âˆ—âˆ— [7.48]âˆ—âˆ— [0.71] [4.21]âˆ—âˆ—
capital pw 0.705 0.709 0.668 0.974 1.015 0.128 0.899 0.891 0.949 0.905 0.271 0.896
[15.25]âˆ—âˆ— [14.65]âˆ—âˆ— [8.17]âˆ—âˆ— [36.86]âˆ—âˆ— [37.38]âˆ—âˆ— [1.90] [21.11]âˆ—âˆ— [24.84]** [24.92]âˆ—âˆ— [27.54]âˆ—âˆ— [0.27] [22.80]âˆ—âˆ—
trend(s)â€ 0.000 0.011 0.004
[0.54] [6.07]âˆ—âˆ— [2.42]âˆ—
Constant 0.390 0.393 0.446 -0.100 -0.200 3.061 0.082 -0.062 -0.169 -0.145 0.120
[4.96]âˆ—âˆ— [4.62]âˆ—âˆ— [3.42]âˆ—âˆ— [3.73]âˆ—âˆ— [5.18]âˆ—âˆ— [9.30]âˆ—âˆ— [4.20]âˆ—âˆ— [2.53]âˆ— [4.97]âˆ—âˆ— [4.58]âˆ—âˆ— [1.44]
lags [trends]â€¡ 1 2 1 [l-r] 1 2 1 [s-r] 1 [l-r] 1 2 1 i: 2-3 i: 2-3
impl. labour 0.295 0.292 0.332 0.026 -0.015 0.872 0.102 0.109 0.051 0.095 0.729 0.104
obs 879 836 879 879 836 879 879 879 836 879 836 879
Panel (D): Penn World Table data
Dynamic FE PMG CPMG DGMM SGMM
[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
EC [ytâˆ’1 ] -0.098 -0.101 -0.107 -0.333 -0.138 -0.567 -0.392 -0.338 -0.081 -0.347 0.835 0.031
[5.82]âˆ—âˆ— [6.01]âˆ—âˆ— [6.22]âˆ—âˆ— [6.70]âˆ—âˆ— [4.37]âˆ—âˆ— [12.63]âˆ—âˆ— [7.88]âˆ—âˆ— [6.63]âˆ—âˆ— [2.56]âˆ— [8.24]âˆ—âˆ— [1.07] [0.49]
capital pw 0.538 0.553 0.356 0.923 0.916 0.698 0.652 0.903 -0.125 0.731 0.604 0.863
[8.14]âˆ—âˆ— [8.66]âˆ—âˆ— [3.44]âˆ—âˆ— [130.34]âˆ—âˆ— [71.72]âˆ—âˆ— [65.10]âˆ—âˆ— [67.96]âˆ—âˆ— [52.90]âˆ—âˆ— [1.81] [86.83]âˆ—âˆ— [0.60] [1.88]
trend(s)â€ 0.001 0.002 0.006
[2.44]âˆ— [2.57]âˆ— [19.84]âˆ—âˆ—
Constant 0.363 0.360 0.567 -0.122 -0.020 1.085 0.935 -0.071 0.456 0.504 0.010
[5.38]âˆ—âˆ— [5.29]âˆ—âˆ— [5.28]âˆ—âˆ— [4.44]âˆ—âˆ— [1.63] [13.05]âˆ—âˆ— [7.79]âˆ—âˆ— [3.47]âˆ—âˆ— [2.99]âˆ—âˆ— [8.29]âˆ—âˆ— [0.07]
lags [trends]â€¡ 1 2 1 [l-r] 1 2 1 [s-r] 1 [l-r] 1 2 1 i: 2-3 i: 2-3
impl. labour 0.462 0.447 0.645 0.077 0.084 0.302 0.349 0.097 1.125 0.270 0.396 0.137
obs 914 904 914 914 904 914 914 904 873 904 914
Notes: All results are based on an unrestricted error correction model speciï¬?cation (ECM), which is equivalent to a
ï¬?rst order autoregressive distributed-lag model, ARDL(1,1) (see Hendry, 1995, p.231f). We report the long-run
coefï¬?cients on capital per worker (and in the agriculture equations also land per worker). EC [ytâˆ’1 ] refers to the
Error-Correction term (speed of adjustment parameter) with the exception of Models [11] and [12], where we report
the coefï¬?cient on ytâˆ’1 â€” conceptually, these are the same, however in the latter we do not impose common factor
restrictions like in all of the former models. Note that in the PMG and CPMG models the ECM term is heterogeneous
across countries, while in the Dynamic FE and GMM models these are common across i. â€ In model [6] we include
heterogeneous trend terms, whereas in [7] a common trend is assumed (i.e. linear TFP is part of cointegrating vector). â€¡
â€˜lagsâ€™ indicates the lag-length of ï¬?rst differenced RHS variables included, with the exception of Models [11] and [12]:
here â€˜i:â€™ refers to the lags (levels in [11], levels and differences in [12] used as instruments. In the models in [8] and
[9] the cross-section averages are only included for the long-run variables, whereas in the model in [10] cross-section
averages for the ï¬?rst-differenced dependent and independent variables (short-run) are also included.
References
Hendry, D. (1995). Dynamic Econometrics. Oxford University Press.
Kapetanios, G., Pesaran, M. H., & Yamagata, T. (2011). Panels with Nonstationary Multifactor Error
Structures. Journal of Econometrics, 160(2), 326-348.
Pesaran, M. H. (2004). General diagnostic tests for cross section dependence in panels. (IZA Discussion
Paper No. 1240)
Pesaran, M. H. (2006). Estimation and inference in large heterogeneous panels with a multifactor
error structure. Econometrica, 74(4), 967-1012.
Pesaran, M. H. (2007). A simple panel unit root test in the presence of cross-section dependence.
Journal of Applied Econometrics, 22(2), 265-312.
Pesaran, M. H., & Smith, R. P. (1995). Estimating long-run relationships from dynamic heteroge-
neous panels. Journal of Econometrics, 68(1), 79-113.
13
**