†
‡
Preliminary and Incomplete - Do Not Cite
Abstract
This study analyzes the effect of foreign direct investment (FDI) on economic activity through a spatially augmented Solow growth model that takes technological interdependence into account.
The technological interdependence manifests itself through spatial externalities that allow technology level of a country to depend on technology levels of its neighbors. The modified growth model yields regression specifications that are insightful to study the impact of FDI on economic growth. The correlations across sections–often cited in the empirical growth literature– is properly accounted for. Estimations are carried out with the tools from spatial econometrics. Our findings indicate that FDI inflows have a significant positive effect on the growth rate of host countries.
JEL-Classification: F3, F4, C1, C5, O1
Keywords: FDI, Economic Growth, Spatial Dependence, Panel Econometrics, Spatio-temporal
Diffusion, Technological Interdependence
∗
We would like to thank Wim Vijverberg and Francesc Ortega for their instructive comments on this study.
Remaining errors are our own.
†
Economics Department, Queens College, The City University of New York, New York, email:
STaspinar@qc.cuny.edu.
‡
Ph.D. Program in Economics, The Graduate School and University Center, The City University of New York,
New York, email: ODogan@gc.cuny.edu.
1

Foreign direct investment (FDI) by the multinational firms is assumed to create technological externalities, i.e., knowledge spillovers, in host countries and thus promotes economic growth (Alfaro
et al., 2010, 2004; Borensztein, Gregorio, and Lee, 1998; Markusen and Venables, 1999; Romer,
1993). However, measuring the growth impact of FDI in cross-country studies has proven to be
a challenging task. The identification of a separate impact of FDI from a pool of other factors that significantly affect economic growth is not straightforward. Also, it may be the case that FDI is attracted to large, dynamic, less risky and growing countries, which yields a reverse causality problem. This paper focuses instead on a less well-known problem, that is, how to take into account the technological interdependence among countries in gauging the effect of FDI on economic growth.
We argue that the effect of FDI should be analyzed through an economic growth model that allows technological interdependence among countries.
In this study, we estimate the effect of FDI inflows on host countries’ economic growth through a spatially augmented Solow growth model that allows for spatial externalities in the form of technological spillovers. Our approach extends the current literature in two ways: (i) we explicitly account for the interactions among countries in cross-country regression specifications through the technological interdependence, (ii) we simultaneously account for correlations over space and time by employing a spatial dynamic panel data (SDPD) model and estimate it via a recently developed bias corrected quasi maximum likelihood (QML) estimator. Below, we mention some of the previous findings and suggest an alternative way to properly study the relationship between
FDI and economic growth.
The literature on the growth impact of FDI inflows is replete with empirical findings where the hypothesis that FDI inflows have a positive independent contribution to economic growth is rejected by the sample data. To overcome this problem, mainly three approaches have been suggested in the literature: (i) regression specifications embedding a local conditions hypothesis, (ii) estimation results based on better estimators with more reliable data sets, and (iii) regression specifications allowing for possible nonlinear relationships between the dependent variable and the exogenous variables.
The local conditions (or absorptive capacities) hypothesis states that a host country’s capacity to take advantage of FDI spillovers is constrained by its absorptive capacities such as human capital, macroeconomic management, infrastructure and financial development. Therefore, researchers often try to use specifications allowing for the interaction between FDI and the dimension of ab-
sorptive capacity. For example, Borensztein, Gregorio, and Lee (1998) consider human capital as
the dimension of absorptive capacity and set up an endogenous growth model in which technological progress takes place through a process of capital deepening (i.e., creation of new capital good
varieties as formulated in Romer (1990), Grossman and Helpman (1991) and Barro and Sala-i-
Martin (1995)). The authors conclude that the contribution of FDI to economic growth can only
be realized by its interaction with the level of human capital in the host country.
The human capital dimension is also considered in Xu (2000), who investigates the technology
diffusion of US multinational enterprises (MNE) in 40 countries from 1966 to 1994, and concludes that a country needs to reach a minimum human capital threshold level to benefit from the technology transfer of US MNEs.
In contrast, an earlier study by Blomstrom, Lipsey, and Zejan
(1994) documents that human capital is not a critical variable, and FDI has a positive growth
effect only when the host country is sufficiently rich. Balasubramanyam, Salisu, and Sapsford
(1996, 1999) stress the export channel as the dimension of absorptive capacity and conjecture that
export-oriented policies (e.g., outward oriented trade policy) enhance the positive impact of FDI on economic growth. They find that the beneficial effect of FDI on economic growth is stronger in
2

the countries that implement export-oriented policies than that of the countries adopting import
substitution policies. Alfaro et al. (2010, 2004, 2003) consider the financial market of a host country
as the dimension of absorptive capacity and formalize a mechanism through which the financial sector affects the contribution of FDI to economic development. Financial institutions finance set-up costs for new firms which then reap the spillovers from FDI. The authors show that the financial inefficiencies reduce the marginal return from foreign capital and that the positive impact of FDI on output growth can only be realized in the presence of a well-developed financial sector.
Regardless of the dimension of absorptive capacities, the aforementioned studies provide some evidence for the claim that a positive FDI effect on growth is realized only when a particular dimension of the local conditions exists in a host country. In other words, FDI does not invoke an independent positive effect on the economic growth of host countries. Our methodology, on the other hand, does not require such local capacity restrictions. We show that a proper handling of cross-country correlations via a modified technology process in production function is sufficient to observe an independent positive effect of FDI.
Another strand of literature considers measurement error in FDI as the potential source of
inconclusive findings, and suggests the use of more reliable data set.
1
In general, measurement error in both the dependent variable and exogenous variables is a central problem for cross-country growth empirics, since the suggested estimators generally produce biased estimates in the presence of
measurement error (Hauk and Wacziarg, 2009). Carkovic and Levine (2005) gather a more reliable
data set from the World Bank database and estimate their specification with the generalized method
of moments (GMM) estimator for panel data models designed by Arellano and Bover (1995) and
Blundell and Bond (1998). They find that FDI inflows do not exert an independent impact on
economic growth. The authors also test for the absorptive capacities hypothesis. Their findings do not suggest any strong evidence towards any of the aforementioned dimensions, but they do invalidate the view that FDI in financially developed countries invokes an exogenous impact on growth.
Recently, the literature has also considered the issue of functional misspecification for the crosscountry regression specifications. The effect of FDI on economic growth may be nonlinear, because
FDI in different sectors might entail different productivity levels among countries. For example,
Kottaridi and Stengos (2010) use a semi-parametric partially linear regression specification together
with a benchmark cross-country regression specification. The authors reach inconclusive results regarding the linear specification for the FDI impact depending on the samples and the estimators employed. They test for the validity of the linear parametric specification for FDI and human capital and reject the linear specification. Therefore, they estimate a semi-parametric partially linear regression specification and find that the slope estimates for the non-parametric components
are positive and statistically significant. Blonigen and Wang (2005) question the assumption of
the homogeneity of slope coefficients in cross-country growth regressions, and claim that pooling of less developed and developed countries may not be appropriate, since the productivity effect of
FDI may differ across countries. They show that the FDI effect in regressions that are based on pooling is small and often insignificant. FDI combined with a sufficient level of human capital has a significant positive effect on growth in less developed countries.
This study provides a different perspective from the aforementioned studies to analyze the impact of FDI on economic growth.
We think that an important reason for the inconclusive empirical findings in the literature is the use of cross-country growth regression specifications that are derived from the Solow growth model.Within the framework of the Solow growth model, the
1
Note that the definition of FDI and the measurement of FDI data have changed over time. For the historical
evolution of FDI data and related concepts, see Lipsey (2003).
3

world becomes a collection of noninteracting closed economies. Hence utilizing the usual crosscountry growth specifications imposes the implicit assumption that each country is an isolated island. However, in reality countries interact in various ways. Hence, the regression specifications derived from this model cannot provide an adequate inference. We suggest regression specifications based on a spatially augmented Solow growth model to measure the effect of FDI on economic growth.
Recently, Ertur and Koch (2007) and Lee and Yu (2012) have considered models that allow
interaction among countries through a specification that addresses the international technological interdependence. They explicitly specify technological interdependence among countries and incorporate it into the standard textbook growth model. The degree of technological interdependence is subject to exogenous frictions which are determined by the geographic and economic proximities among countries. This modified growth model is referred as the spatially augmented Solow growth
model (Ertur and Koch, 2007). We modify the total factor productivity specification of this model
in such a way that the technology level in a host country also depends on the FDI intensity in that country. This modification is relevant, since there is extensive empirical evidence in the literature showing that FDI provides a channel for the diffusion of technology to host countries (Keller,
2010). The theoretical equations for the steady state equilibrium and convergence dynamics of the
resulting model provide empirical regression specifications that involve spatial lags of the dependent variable and exogenous variables. Through these new regression specifications, the effect of FDI on economic growth can be properly studied.
We test the effect of FDI inflows on economic growth through these new specifications by utilizing a panel data set constructed for 85 countries over the period 1980-2010. Our findings indicate that FDI inflows have a significant positive direct effect on the growth rate of host countries: a simultaneous one percentage point increase in FDI inflows to total output ratio in all countries initially increases a host country’s output per-worker by approximately 0 .
24 percent and rises gradually over time to 1 .
76 percent. However, our results also indicate that the indirect effects of
FDI inflows are not statistically significant.
2
Our results show that the spatial effects, i.e., spatial lag terms, that are omitted in non-spatial regression models are statistically significant. Hence, we conclude that the earlier insignificant findings regarding to role of FDI in the economic growth process are due to model mis-specifications in the form of omitted spatial effects.
The rest of this paper is organized in the following way. Section 2 provides details of the spatially
augmented Solow growth model. The theoretical motivation and important model implications are
elaborated. Section 3 presents the description of the data. Section 4 reviews the estimation methods
for the spatial dynamic panel data model. Section 5 describes the interpretation of parameters in
the spatial dynamic panel data model. Section 6 presents the empirical results. Section 7 includes
sensitivity analysis of our core results. Section 8 closes with concluding remarks.
In light of the mixed findings presented in the introduction, we raise two important questions: (i) how does the above reviewed empirical literature relate to theoretical models? and (ii) how are the assumptions behind the theoretical models incorporated in the empirical studies? In the empirical
FDI literature, the textbook Solow model often motivates the suggested regression specifications.
The transition from this growth model to econometric models produces what is known as the canonical cross-country growth regression models, which are empirical analogues of the theoretical convergence dynamic equation of the Solow growth model. In its modern form, the cross-country
2
The direct and indirect effects are defined in Section 5.
4

regression model is
Y it
= β
0
+ β
1
Y i,t − 1
+ X
0 it
β
2
+ c i
+ α t
+ u it
, (2.1) where Y it is the log of output per-worker in country i at time t , c i and α t are respectively country and time fixed effects, and X it is a vector of control variables capturing cross-country differences with matching parameter vector of β
2
. Various cross-section versions of (2.1) have been considered to
investigate convergence dynamics to a steady state and the impact of control variables on economic
growth (Barro, 1991; Barro and Martin, 1992; Mankiw, Romer, and Weil, 1992). Recently, the
panel data and time series versions of (2.1) are also considered to shed light on the time series
nature of growth process (Durlauf, Johnson, and Temple, 2005). In this regard, the dynamic panel
data specification in (2.1) is suggested, among others, by Knight, Loayza, and Villanueva (1993),
Islam (1995) and Acemoglu (2008).
3
To investigate the impact of FDI on economic growth, cross-section and panel data versions of
(2.1) are employed by adding FDI inflows as a control variable to the regression model, i.e., the vec-
tor X it includes the FDI with the other standard control variables. The parameter estimate of FDI provides the empirical evidence for the impact of foreign investment. The cross-country regression model is the empirical analogue of the theoretical convergence equation of the Solow growth model
which treats each country as an isolated island. Therefore, the regression specification in (2.1) may not capture the fact that countries interact.
4
Recently, the literature has considered growth models that allow technological interdependence among countries through spatial externalities so that knowledge accumulated in one country depends on the levels of knowledge in neighboring countries.
Empirical studies on the diffusion of technology indicate that geographic distance between countries
determines the effectiveness of the technological externalities. For example, Keller (2002) shows
that the productivity effects from R&D spendings of G-5 countries in other OECD countries decline with geographic distance, which suggests that the diffusion of technology is localized. Along the
same lines, Bottazzi and Peri (2003) show that technology spillovers are very localized and exist
only within a distance of 300 km for the European regions.
Next, we discuss the spatially augmented Solow growth model where human capital, physical capital and FDI externalities are allowed in the production of technology. The resulting steadystate and convergence dynamic equations will be the regression specifications through which the impact of FDI is analyzed.
The Solow model with human capital can be considered as a non-stochastic dynamic general equilibrium model, where a unique final good is produced and consumed. Consider a world with n countries, each of which has a continuous time economy populated by a representative household and a representative firm. By assumption households in the Solow model do not optimize their consumption and saving; rather, they save a constant fraction of their disposable income for investment in physical and human capital. The production side of each economy is modeled by a representative firm that produces the final good according to the Cobb-Douglas production function: Y i
( t ) = f ( A i
( t ) , K i
( t ) , H i
( t ) , L i
( t )) = A i
( t ) K i
( t )
α
H i
( t )
β
L i
( t )
1 − α − β
, where Y i
( t ) is the total amount of production of final good in country i at time t , K i
( t ) is physical capital stock, L i
( t ) is total employment, H i
( t ) is human capital, and A i
( t ) is the stock of technology. The production
3 A huge part of empirical growth literature is about the convergence hypothesis, i.e., the claim that the effect of the
initial conditions on the economic growth will eventually disappear. In the context of (2.1), the convergence is termed
as unconditional/conditional β -convergence. The unconditional β − convergence holds if ( β
1
− 1) < 0 in the model without any control variables and fixed effects. When control variables and fixed effects are present, ( β
1
− 1) < 0 implies conditional β −
convergence (Durlauf, Johnson, and Temple, 2005).
4
For the bias properties of various estimators suggested for (2.1), see Hauk and Wacziarg (2009) and Islam (2001).
5

function is characterized by constant returns to scale, and the parameters α and β are, respectively, physical and human capital output elasticities. It is assumed that α > 0, β > 0, and α + β < 1 so that there are decreasing marginal returns to all inputs. Technology is a non-excludable non-rival good and its diffusion among countries is subject to frictions that are determined by the geographic proximities among countries. More specifically, the stock of knowledge is modeled as
A i
( t ) = Ω( t ) k i
( t )
φ
1 h i
( t )
φ
2 e
φ
3
F i
( t ) n
Y
A j
( t )
γw ij , j = i
(2.2) where Ω( t ) = Ω(0) e
µt represents the common stock of knowledge that is available to all countries.
This portion of technology is exogenous with the growth rate µ . FDI intensity in country i at time t is denoted by F i
( t ) and is assumed to be exogenous. The degrees of externalities stemming from these variables are respectively represented by the parameters φ
1
∈ [0 , 1), φ
2
∈ [0 , 1) and
φ
3
∈ [0 ,
1). The last term in (2.2) is the weighted technology stock in other countries. The weight
w ij is exogenous, and determined by a measure of geographic or economic distance between country i and j . It is assumed that 0 ≤ w ij
≤ 1, w ij
= 0 if i = j and P n j =1 w ij parameter γ ∈ [0 , 1) reflects the degree of technological interdependence.
= 1 for i = 1 , . . . , n . The
For our main results, we use geographical proximities among countries to specify weights in
(2.2). The element
w ij is specified as the inverse of the exponential distance between countries i and j . The distance d ij between any two countries
between country capitals.
5
i and
Based on this measure, we set j is measured by the great-circle distance w ij
=
(
0
P n exp( − d ij j =1 exp( −
) d ij
) if i = j if i = j.
(2.3)
This kind of specification is useful for two main reasons: (i) empirical studies on the diffusion of technology indicate that geographic distance between countries determines the effectiveness of
technological externalities (Bottazzi and Peri, 2003; Keller, 2002), and (ii) according to the gravity
literature, distance is a significant determinant of international trade, which in turn determines
the extend of technological spillovers between countries (Grossman and Helpman, 1991, p.169).
Therefore, proximity based on geographic distance also reflects economic distance based on bilateral
trade (Klenow and Rodriguez-Clare, 2005; Moreno and Trehan, 1997). In particular, Klenow and
Rodriguez-Clare (2005, p. 842) suggest that trade and FDI related spillovers would be captured by
the bilateral distance between countries.
Our technology specification in (2.2) differs from the one stated in Ertur and Koch (2007) and
Lee and Yu (2012). It depends not only on both types of capital but also on the FDI intensity, which is partly motivated from Knight, Loayza, and Villanueva (1993, Eq.(3) pg. 516) in light of the findings in Keller (2010). This modification is relevant since FDI plays a role of a conduit for the transfer of knowledge based assets to host countries. Keller (2010) stresses the significance of
FDI channel for technology spillovers. For example, technology can diffuse to a domestic economy from a parent firm and its affiliates through local workers. The tasks that are not imported from the parent firm are completed by its affiliates in host countries through local production. The local workers are hired and trained for these tasks. When these workers change jobs within the industry, knowledge diffuses (i.e., FDI spillovers through worker turnover). Furthermore, spillovers from affiliates can also occur through their business operations in host countries. One of the most salient
5 d ij
= R
0
× arccos cos | longitude i
− longitude j
| cos( latitude i
) cos( latitude j
) + sin( latitude i
) sin( latitude j
) , where R
0 is the Earth’s radius.
6

feature of multinational affiliates is that their production is more knowledge and capital intensive
relative to the production of domestic firms (Alfaro and Chen, 2014). Many multinational affiliates
engage in business relations with local firms through either outsourcing certain intermediate inputs or selling new quality-upgraded inputs to domestic final goods producers. In either case, technology transfers can occur.
We assume that all goods and factor markets are competitive. Households own labor and both types of capital endowment. Labor is supplied inelastically so that all labor endowment is supplied regardless of its price, and the labor market clears at each instant in time. Let n i rate of labor so that at time t , L i
( t ) = L i
(0) e n i t be the growth
. The market clearing conditions for both types of capital require the demand from firms to be equal to the supply of both types by household.
The dynamics of the economy are determined by the laws of motion for physical and human capitals:
K i
( t ) = s ik
Y i
( t ) − δ k
K i
( t ) , H i
( t ) = s ih
Y i
( t ) − δ h
H i
( t ) , (2.4) where s ik and s ih are the exogenous rate of investment in physical and human capitals.
depreciation rates are given by δ k and δ h
The
, respectively, and are assumed to be the same in all
countries. From (2.4), the evolutions of physical and human capital per-worker are
˙ i
( t ) = s ik
( t ) y i
( t ) − ( n i
+ δ k
) k i
( t ) ,
˙ i
( t ) = s ih
( t ) y i
( t ) − ( n i
+ δ h
) k i
( t ) .
(2.5)
Let W n be an n × n
reduced form of (2.2) is
spatial connectivity matrix of weights with an ( i, j )th entry of w ij
. The
A i
( t ) = Ω( t )
1
1 − γ k i
( t )
φ
1 h i
( t )
φ
2 e
F i
( t ) φ
3 n
Y h k j
( t )
φ
1
P
∞ r =1
γ r w r ij h j
( t )
φ
2
P
∞ r =1
γ r w r ij e
F j
( t ) φ
3
P
∞ r =1
γ r w r ij i
, j =1
(2.6) where w r ij denotes ( i, j )th element of
per-worker and using (2.6) yield
W r n
.
6
Writing the production function in terms of output y i
( t ) = Ω( t )
1
1 − γ k i
( t ) u ii h i
( t ) v ii e
F i
( t ) $ ii n
Y h k j
( t ) u ij h j
( t ) v ij e
F j
( t ) $ ij i
, j = i
(2.7) where y i
( t ) = Y i
( t ) /L i
( t ), u ii
β + φ
2
(1 + P
∞ r =1
γ r w r ii
), v ij
=
= α + φ
1
(1 + P
∞ r =1
γ r w r ii
), u ij
φ
2
1 + P
∞ r =1
γ r w r ij
, $ ii
= φ
3
= φ
(1 +
1
1 + P
∞ r =1
γ r w r ij
, v ii
P
∞ r =1
γ r w r ii
), and $ ij
=
=
φ
3
1 + P
∞ r =1
γ r w r ij
. There are two important implications of (2.7): (i) there exists parame-
ter heterogeneity in the production function, and (ii) output per-worker of country i depends on
both types of capital and the FDI intensity in neighboring countries.
7
The production function given in (2.7) can be used to evaluate the social elasticity of output per-
worker with respect to both types of capital and FDI. When there is an increase in these variables in country i , the social return of this increase will be ( u ii
+ v ii
+ $ ii
). On the other hand, if there is a simultaneous increase in physical capital, human capital and FDI in all countries, then country
6
For details, see the web-appendix.
7
If there are no externalities, i.e., φ
1
in Mankiw, Romer, and Weil (1992).
= φ
2
= φ
3
= 0, then the production function reduces to the usual form given
7

i receives a social return of u ii
+ v ii
+ $ ii
+ P n j = i u ij
+ P n j = i v ij
+ P n j = i
$ ij
. Local convergence requires a decreasing social return which implies the condition of α + β +( φ
1
+ φ
2
+ φ
3
) / (1 − γ ) < 1.
The production function in (2.7) is characterized with decreasing returns to physical and human
capital, which ensures a steady state equilibrium for the level of output per-worker. The transition dynamics of the economy to the steady state can be studied by exploring the evolutions of physical
and human capital. As a system of differential equations, (2.5) can be log-linearized around the
steady-state levels from which the transition dynamics of output per-worker can be recovered.
The speed of transition to the steady-state equilibrium is measured by a convergence rate that is assumed to be the same for all countries. Under this assumption, there are two empirical equations that can be derived as the analogues of the theoretical equation of the transition dynamics of the model: (i) a growth-initial level specification that implies a cross sectional regression model over the period consisting of the time between the initial point ( t
1
( t
2
= 0) and an arbitrary point in time
= T
) (Ertur and Koch, 2007; Mankiw, Romer, and Weil, 1992), and (ii) a dynamic panel data
specification that divides the whole period T
into several shorter time spans (Islam, 1995; Knight,
Loayza, and Villanueva, 1993; Lee and Yu, 2012).
In this study, we consider the dynamic panel data specification, where the whole period T is divided into equal time-spans of τ
.
8
The resulting regression specification including FDI as a covariate is ln y it
= γ
0 ln y i,t − 1
+ β
10 ln s ik
+ η
10 n
X w ij ln s jk
+ β
20 ln
+ η
20 n
X w ij s ih ln
+ β
30 ln ( n i
+ δ k s jh
+ η
30 n
X w ij
+ g ) + β
40
F i ln ( n j
+ δ k
+ g ) j = i j = i j = i
+ η
40 n
X w ij
F j j = i
+ λ
0 n
X j = i w ij ln y jt
+ ρ
0 n
X w ij j = i ln y j,t − 1
+ c ni
+ α t
+ u it for i = 1 , . . . , n and t = 1 , . . . , T,
(2.8) where γ
0
, β
0
= ( β
10
, β
20
, β
30
, β
40
)
0
, η
0
= ( η
10
, η
20
, η
30
, η
40
)
0
, λ
0 and ρ
0 are parameters; and c ni and α t
are fixed effects. Stacking cross sectional units for each period, (2.8) can be written more
compactly as
Y nt
= λ
0
W n
Y nt
+ γ
0
Y n,t − 1
+ ρ
0
W n
Y n,t − 1
+ X nt
β
0
+ W n
X nt
η
0
+ c n 0
+ α t 0 l n
+ u nt
(2.9) for t = 1 , . . . , T
.
9
The spatial weight matrix W n is an n × n matrix of known constants describing geographic or economic proximities among countries. Its diagonal elements are set to zero by construction, i.e., the distance of a country to itself is zero. The convergence rate λ is determined from the relation γ
0
= e
− τ λ . The other parameter constraints implied by the theoretical convergence
equation are relaxed so that the regression model in (2.9) can be compatible with a more general
setting. The dependent variable Y nt stacks the log of output per-worker of all countries at time t into an n × 1 vector. On the right hand side, there are spatial lags of current and time lag of Y nt
, denoted respectively by W n
Y nt and W n
Y n,t − 1
. The exogenous variables at time t are represented by n × 4 matrix X nt
0
( β
10
, β
20
, β
30
, β
40
)
= (ln s k
, ln s h
. The matrix W n
, ln (
X nt n +
= ( g
W
+ n
δ ) , ln s k
F ) with a matching parameter vector
, W n ln s h
, W n ln ( n + g + δ the spatial lags of exogenous variables at time t , and η
0
= ( η
10
, η
20
, η
30
, η
40
)
0
) , W n
β
0
=
F ) contains is the matching
8 For advantages of the dynamic panel data specification over the cross-sectional regression model, see Knight,
Loayza, and Villanueva (1993), Islam (1995), Caselli, Esquivel, and Lefort (1996), and Acemoglu (2008).
9 For details, see the web-appendix.
8

vector of parameters. The terms respectively, where l n is the n × c n 0 and α t 0 l n can be considered as country and time fixed effects,
1 vector of ones. The disturbance term u nt
= ( u
1 t
, . . . , u nt
)
0 is n × 1 vector, where u it is assumed to be simply i.i.d with mean zero and variance σ
2
0 for all i and t .
The regression equation in (2.9) is based on a spatially augmented growth model with the
assumption that there exists technological interdependence among countries. This assumption turns the model into an interdependent system such that the steady state determinants of a country become relevant for the steady state level of output per-worker in other countries. The spatial
econometrics literature refers to the model in (2.9) as the spatial dynamic panel data model (SDPD).
This model can be estimated with tools from spatial econometrics.
The data on FDI inflows, outflows and stocks are taken from the UNCTAD Statistics database. FDI statistics are recorded in the sub-account of Direct Investment in Financial Account in Balance of
Payments using a directional basis. The Direct Investment account consists of three components: (i)
Equity capital, (ii) Reinvested earnings and (iii) Other capital. All transactions in these components are recorded on a debit and credit basis. Net decreases in assets or net increases in liabilities are recorded as credits, while net increases in assets or net decreases in liabilities are recorded as debits.
Negative values indicate reverse investment or dis-investment. The UNCTAD Statistics database provides annual data on inward and outward foreign direct investment flows for the period 1970-
2011. FDI stock estimates are recorded in the International Investment Positions statement, which shows the stock of external financial assets and liabilities for a given time period. The UNCTAD statistics database provides annual data on inward and outward foreign direct investment stocks for the period 1980-2011. FDI stock is the total sum of the value of the shares and reserves (including retained profits) that are attributable to the parent enterprises. The stock also includes the net indebtedness of affiliates to the parent enterprises.
Figure 1 shows how the pattern of inward FDI flows and stocks have evolved over the last 30 years. Figure 1(a) shows total world inward FDI flows from 1980 to 2010. There is a significant
increase in the flows throughout the 1990s: from mid-to late 1990s, inward FDI flows quintupled.
During the period from the early 2000s to the 2007 financial crisis, a similar upward trend has
occurred. As Figure 1(a) shows the inward FDI flows is very uneven with two peaks and two
troughs. The burst of the financial bubble (dot-com bubble) in 2000 induced a huge decline in worldwide inward FDI flows. Likewise, the recent financial crisis of 2007 also has induced large contractions in worldwide inward flows. The same worldwide pattern of inward FDI flows can also
be seen in Figure 1(b) which shows the distribution of FDI inflows across developing, developed and
transition countries: developed countries are the biggest recipients of inward FDI. However, the level of FDI inflows is also much more volatile for developed countries. Throughout the whole period, there exists a relatively steady expansion in the inflows for developing and transition countries.
According to UNCTAD (2012), developing and transition economies witnessed a rise of 12 percent
in 2011 relative to 2010, and the inflows reached a record level of $777 billion in 2011. Developed countries saw a 21 percent increase in 2011. The source of the increase has been greenfield projects in developing and transition economies, and in case of developed countries the source has been largely cross-border mergers and acquisitions.
The evolution of the magnitude of the worldwide inward FDI stock is presented in Figure 1(c)-
1(d). The recent financial crisis is the major event that induces a significant decline in inward FDI
stock. The total inward FDI stock in 2011 rose by 3 percent compared with 2010 and reached $20.4
trillion level (UNCTAD, 2012). Figure 1(d) shows that this rise occurs in all three major groups of
9

1980 1990
Total World Inward FDI
YEAR
2000 2010
Sample Countries Inward FDI
(a) Total World Inward FDI Flows
1980 1990
YEAR
Developing Countries
Developed Countries
2000
Transition Countries
2010
(b) Distribution of Inward FDI Flows
1980 1990
Total World FDI Stock
YEAR
2000 2010
Sample Countries FDI Stock
1980 1990
YEAR
Developing Countries
Developed Countries
2000
Transition Countries
2010
(c) Total World Inward FDI Stock (d) Distribution of Inward FDI Stock
Figure 1: FDI Inflows and Stocks economies: developed, developing and transition economies.
In our empirical study, we consider FDI inflows data expressed as a ratio of domestic GDP for a sample of 85 countries over the period 1980-2010. Most of the studies in the literature use FDI
inflows data, since FDI as a form of investment is a flow variable (Alfaro et al., 2004; Borensztein,
Gregorio, and Lee, 1998; Carkovic and Levine, 2005; Kottaridi and Stengos, 2010). The sample
country list is provided in Appendix A. Finally, time series graphs given in Figure 1(a) and 1(c)
suggest that the effect of missing countries from our sample should be immaterial, since our sample captures the big portion of FDI inflows.
The data for the real output per worker, physical investment and population variables are taken from the latest version of Penn World Tables (PWT version 7.1), which contain data for
10

main macroeconomic variables for a large number of countries over the period 1950-2010. For the physical investment share, the share of gross investment in GDP is used. The population growth is the growth rate of working-age population (ages 15 to 64). Following Ertur and Koch
(2007) and Caselli (2005), we calculate the number of workers for a country
i at time t by
( RGDP CH it
× P OP it
) /RGDP W it
, where RGDP CH it is real GDP per-capita computed by the chain method, P OP it is the total population, and RGDP W it is real GDP per worker computed by chain method. We use the secondary school enrollment rate to proxy human capital. The series is
taken from Barro and Lee (2001).
The detailed definitions and descriptive statistics of all variables are provided in Appendix A.
Table 8 in Appendix A shows that the between variations of all variables are quite close to overall
(pooled) variations except for the population growth and FDI inflows variables. The statistics in the table suggest that the cross-sectional variation dominates our data which is the case for date
sets used in cross-country growth studies (Hauk and Wacziarg, 2009).
The spatial weight matrix in the spatially augmented Solow growth model specifies technological interdependence among countries. The regression model recovered from the model shows that the weight matrix determines the ways in which spillovers across countries occur. A single weight matrix may not be appropriate for different kinds of spillovers. As a result, different specifications
have been considered in the literature (Conley and Ligon, 2002; Ertur and Koch, 2011, 2007;
Kelejian, Murrell, and Shepotylo, 2013; Moreno and Trehan, 1997). Our core results are based on
the distance based spatial weight matrix defined in the previous section. This weight matrix is dense in the sense that each country is related to all other countries in the sample. To test the robustness of our core estimates, we also employ several other measures of distance described in
Section 7.
The regression model in (2.9) with dependence in both time and space dimensions is classified as
the spatial dynamic panel data (SDPD) model to better link the terminology to the dynamic panel
data models (Lee and Yu, 2010b). In this section, we present the estimation approach for the model in (2.9). The recent surveys in Anselin, Gallo, and Jayet (2008) and Lee and Yu (2010b) on spatial
panel data models provide in-depth reviews for many issues surrounding model specification and
0 estimation. Let ζ
0
= β
0
0
, η
0
0 and
X nt
= ( X nt
, W n
X nt
). Then, the SDPD model in (2.9) can be
written as
Y nt
= λ
0
W n
Y nt
+ γ
0
Y n,t − 1
+ ρ
0
W n
Y n,t − 1
+
X nt
ζ
0
+ c n 0
+ α t 0 l n
+ u nt
(4.1) for n × 1 cross-section units for t = 1 , 2 , . . . , T . The reduced form of this model is given by
Y nt
= S
− 1 n
( γ
0
I n
+ ρ
0
W n
) Y n,t − 1
+ S
− 1 n
X nt
ζ
0
+ S
− 1 n c n 0
+ α t 0
= A n
Y n,t − 1
+ S
− 1 n
X nt
ζ
0
+ S
− 1 n c n 0
+ α t 0
S
− 1 n l n
+ S
− 1 n u nt
,
S
− 1 n l n
+ S
− 1 n u nt
(4.2) where S n
= ( I n
− λ
0
W n
) and A n
= S
− 1 n
( γ
0
I n
+ ρ
0
W n
). Depending on the eigenvalues of A n
, Lee
and Yu (2011, 2010b) show that the process for
Y nt can be decomposed into a sum of a possibly stable part, a possibly unstable part, and a time effect part. The stability of each part depends on the size of the fraction
γ
0
+ ρ
0
1 − λ
0 relative to 1. Thus, depending on the value of the fraction
γ
0
+ ρ
0
1 − λ
0
,
Lee and Yu (2011, 2010b) specify the following three cases for the process of
Y nt
: (i) a stable case if
γ
0
+ ρ
0
1 − λ
0
< 1, (ii) a spatial cointegration case if
γ
0
+ ρ
0
1 − λ
0
= 1 and γ
0
= 1, and (iii) an explosive case
11

if
γ
0
+
1 − λ
ρ
0
0
> 1. In each case the data generating process for the SDPD model is different, which implies that the asymptotic properties of the QMLE will be different for each case.
To simplify the notation, let with Y nT
=
1
T
P
T t =1
Y nt and Y
∼
Y nt nT , − 1
=
=
Y
1
T nt
−
P
T
Y t =1 nT and
∼
Y n,t − 1
= Y n,t − 1
− Y nT , − 1 for t = 1 , 2 , . . . , T
Y n,t − 1
. Furthermore, let θ = γ, ρ, ζ
0
, λ, σ
2
0 and
0
ϑ = θ
0
, c
0 n
, α
0
T
, where c n
= ( c n 1
, . . . , c nn
)
0 and α
T
= ( α
1
, . . . , α
T
)
0 are vectors of fixed effects.
At the true parameter values, these vectors are denoted by θ
0
= γ
0
, ρ
0
, ζ
0
0
, λ
0
, σ
2
0
0
θ
0
0
, c
0 n 0
, α
0
T 0
. Let Z nt
= ( Y n,t − 1
, W n
Y n,t − 1
,
X nt
). Assume that W n
0 and is row-normalized, i.e., W
ϑ n l
0 n
=
= l n
. The estimation approach is based on the elimination of time fixed effects by transforming the model with J n
= I n
− 1 n l n l
0 n
. For a row-normalized W n
, the relation J n
W n
= J n
W n
I n
=
J n
W n
J n
+
1 n l n l
0 n
= J n
W n
J n
holds. Thus, premultiplying (4.1) with
J n yields the following transformed model:
J n
Y nt
= λ
0
J n
W n
J n
Y nt
+ γ
0
J n
Y n,t − 1
+ ρ
0
J n
W n
J n
Y n,t − 1
+ J n X nt
ζ
0
+ J n c n 0
+ J n u nt
.
(4.3)
The time fixed effects are eliminated. However, the transformation introduces linear dependence among the elements of J n u nt since the variance of J n u nt is σ 2
0
J n
. Let F n,n − 1
, √ n l n be a n × n orthonormal matrix, where F n,n − 1 is a n × ( n − 1) sub-matrix containing orthonormal eigenvectors of J n
corresponding to the eigenvalue of 1.
10
The column √ n
0 l n corresponds to the eigenvalue of 0.
Premultiplication of the transformed model in (4.3) with
F n,n − 1 eliminates the linear dependence
among the transformed disturbance terms. Lee and Yu (2010a) show that the log-likelihood function
0 for the model obtained from the transformation with F n,n − 1 is ln L n,T
( θ, c n
) = −
( n − 1) T
2
−
2
1
σ 2 ln 2 π −
( n −
2
1) T
T
X u
0 nt
( θ, c n
) J n u nt
( θ, c n
) , t =1 ln σ
2
− T ln(1 − λ ) + T ln | I n
− λW n
| (4.4) where u nt
( θ, c n
) = ( I n
− λW n
) Y nt
− γY n,t − 1
− ρW n
Y n,t − 1
−
X nt
ζ − c n
. From the first order condition with respect to c n
, the QMLE of the individual fixed effects can be obtained. Then, the individual
fixed effects can be concentrated out from the log-likelihood function in (4.4), and the resulting
concentrated log-likelihood is ln L n,T
( θ ) = −
( n − 1) T
2
−
2
1
σ 2 t =1 ln 2 π −
( n −
2
1)
T
X ∼
0 u nt
( θ ) J n
∼ u nt
( θ ) ,
T ln σ
2
− T ln(1 − λ ) + T ln | I n
− λW n
| (4.5) where
∼ u nt
( θ ) = ( I n
− λW n
)
∼
Y nt
− γ
∼
Y n,t − 1
− ρW n
∼
Y n,t − 1
−
∼
X nt
ζ .
The asymptotic properties of the QMLE obtained from the maximization of the concentrated
log-likelihood in (4.5), i.e., ˆ
the behavior of
ˆ nT is nT
T nT
= argmax
θ ∈ Θ ln L n,T
( θ ), depends on the behavior of n relative to
. Lee and Yu (2010a) show that when
T is large relative to n such that
-consistent with an asymptotic normal distribution centered around θ
0 n
T
. When
→ n
0, is
10 Note that J n is symmetric and idempotent. Its eigenvalues are 1 and 0. The algebraic multiplicity of 1 is n − 1.
12

asymptotically proportional to
T
T such that n
T
→ asymptotic distribution is not centered around θ n
→ ∞ , the QMLE has convergence rate of T
0 k ∈
R
, ˆ nT has convergence rate of
. Finally, when n is large relative to
√ nT but its
T such that with a degenerate distribution. Thus, when T is relatively smaller than n the QMLE ˆ nT
has asymptotic bias. Lee and Yu (2010a) suggest a bias
reduction procedure for ˆ nT
.
The above outlined transformation approach requires a row normalized weight matrix. Lee and
Yu (2010a) also consider a direct approach, where the estimation is based on the maximization
of the log-likelihood function of the untransformed model, which yields an asymptotic bias of the order O max { 1 n
, }
. Without any transformation, the log-likelihood of the model in (4.1) is given
by
1
T ln L n,T
( ϑ ) = − nT
2 ln 2 π − nT
2 ln σ
2
+ T ln | I n
− λW n
| −
1
2 σ 2
T
X u
0 nt
( ϑ ) u nt
( ϑ ) , t =1
(4.6) where u nt
( ϑ ) = ( I n
− λW n
) Y nt
− γY n,t − 1
− ρW n
Y n,t − 1
−
X nt
ζ − c n
− α t l n fixed effects can be obtained from first order conditions with respect to c n
. The QML estimates of and α
T
. This operation yields the following results:
ˆ t
( θ, c n
) =
1 n l
0 n
( I
1
J n
ˆ n
( θ ) = J n
T
T
X t =1 n
−
( I
λW n n
) Y nt
− λW n
− γY
) Y nt n,t −
− γY
1
− ρW n,t − 1 n
Y n,t
− ρW n
− 1
−
X
Y n,t − 1 nt
−
ζ − c n
X nt
ζ .
,
Then, concentrating out c n and α
T
from (4.6) yields
(4.7)
(4.8) ln L n,T
( θ ) = − nT
2 ln 2 π − nT
2 ln σ
2
+ T ln | I n
− λW n
| −
1
2 σ 2
T
X u
0 nt
( θ ) J n u nt
( θ ) , t =1
(4.9) where
θ nT u nt
( θ ) =
= argmax
θ
1
T
P
T t =1
( I n
− λW n
) Y nt
− γY n,t − 1
− ρW n
Y n,t − 1
−
X ln L n,T
( θ ) has the asymptotic bias of order O max { nt
1 n
,
ζ
1
T
. The QMLE defined by
}
. Lee and Yu (2010a)
suggest an analytical bias reduction procedure to correct the bias.
Both transformation and direct approaches outlined so far are based on the assumption that the data generating process is a stable one, i.e., λ
0
+ γ
0
+ ρ
0
<
1. Lee and Yu (2011) suggest a
unified transformation approach that can be used to estimate all three cases, namely, stable, spatial cointegrated and explosive cases. The unified approach is based on the spatial difference operator
( I n
− W n
) through which time effects and unstable or explosive components are eliminated. Pre-
multiplying (4.1) with (
I n
− W n
) yields
( I n
− W n
) Y nt
= λ
0
W n
( I n
− W n
) Y nt
+ γ
0
( I n
− W n
) Y n,t − 1
+ ρ
0
W n
( I n
− W n
) Y n,t − 1
+ ( I n
− W n
)
X nt
ζ
0
+ ( I n
− W n
) c n 0
+ ( I n
− W n
) u nt
,
(4.10) where we use ( I n
− W n
) α t l n
= 0 since W n where Σ n
= ( I n
− W n
) ( I n
− W n
)
0 l n
= l n
. The variance of the term ( I with a column rank of n
?
. Here, n
?
n
− W n
) u nt is σ
2
0
Σ n is the number of degrees of
,
freedom for the transformed equation in (4.10). Since the rank of Σ
n is the number of non-zero eigenvalues, we have n
?
= n − m n
, where m n is the number of unit eigenvalues of W n
.
Let F n and H n be the orthonormal matrix of eigenvectors of Σ n such that Σ n
F n
= F n
Λ n and
Σ n
H n
= 0, where Λ n is the diagonal n
?
× n
?
matrix of nonzero eigenvalues of Σ n
. Here, F n is
13

an n × n
?
matrix of orthonormal eigenvectors corresponding to the eigenvalue matrix Λ n corresponds to zero eigenvalues of Σ n
. Lee and Yu (2011) use
F n and Λ n and H n to further transform the model in order to remove multicollinearity of ( I n
− W n
) u nt
. Pre-multiplying the above equation with Λ
− 1 / 2 n
0
F n yields
Y
?
nt
= λ
0
W
?
n
Y
?
nt
+ γ
0
Y
?
n,t − 1
+ ρ
0
W
?
n
Y
∗ n,t − 1
+
X
?
nt
ζ
0
+ c
?
n 0
+ u
?
nt
, (4.11) where
σ
2
0
I n
?
Y
?
nt
= Λ
− 1 / 2 n
0
F n
( I n
− W n
) Y nt
, W
?
n
= Λ
− 1 / 2 n
0
F n
W n
F n
Λ
1 / 2 n
. Then, the log-likelihood function can be written as and the other starred variables are
defined in the same way. The number of observations in (4.11) is
n
?
and the variance of u
?
nt is now ln L n,T
( θ, c
?
n
) = − n
?
T
2 ln 2 π − n
?
T
2 ln σ
2
+ T ln | S
?
n
( λ ) | −
1
2 σ 2
T
X u
?
0 nt
( θ, c
?
n
) u
?
nt
( θ, c
?
n
) , (4.12) t =1 where S
?
n
= ( I n
− λ
0
W
?
n
) and u
?
nt
( θ, c
?
n
) = S
?
n
( λ ) Y
?
nt
− Z
?
nt
δ − c
?
n with Z
?
n
= ( Y
?
nt
, W
?
nt
Y
?
n,t − 1
,
X
?
nt
).
Lee and Yu (2011) show that the log-likelihood function in (4.12) can be written in terms of
the original variables (i.e., the variables without star). The resulting concentrated log-likelihood function is given by ln L n,T
( θ ) = − n
?
T
2
−
2
1
σ 2 ln 2 π −
2
T
X ∼
0 u nt
( θ )( I n t =1 n
?
T ln σ
2
+ ( n − n
?
) T ln(1 − λ ) + T ln | S n
− W n
)Σ
+ n
( I n
− W n
)
∼ u nt
( θ )
( λ ) | (4.13) where
∼ u nt
( θ ) = S n
( λ )
∼
Y nt
−
∼
Z nt
δ and Σ
+ n
= F n
Λ
− 1 n
0
F n
. The QMLE ˆ nT is the extremum estimator
derived from the maximization of the log-likelihood function in (4.13). The asymptotic argument
in Lee and Yu (2011) is based on the assumption that
n
?
is a non-decreasing function of T and
T
tends to infinity. Under this assumption, Lee and Yu (2011) establish the consistency of ˆ
nT
.
Similar to Lee and Yu (2010a), ˆ
nT has an asymptotic bias of O ( proportional to T , and n
?
is large relative to suggest a bias reduction procedure.
T (i.e., n
?
T
→ ∞
1
T
) when n
?
is asymptotically
). Therefore, Lee and Yu (2011)
To summarize, when T is relatively smaller than n or n
?
, the QMLEs based on transformations
suggested in Lee and Yu (2010a, 2011) have an asymptotic bias of order
O (
1
T this, analytical bias reduction procedures are suggested. The bias corrected estimators are
√ nT consistent and their asymptotic distributions are properly centered around the true parameter value, when
T n 1 / 3
→ ∞ . That is, if T grows faster than n
1 / 3
, then the bias corrected estimators is
√ nT -consistent and asymptotically centered normal, when
T n
3
→ 0 and
T n
3
→
0.
11
The SDPD model in (2.9) includes the spatial lag of the control variables to allow for an
exogenous interaction among countries. Therefore, our SDPD model can be considered as a panel data version of the spatial Durbin model (for short the Durbin model). When the true model does not involve the spatial lags of explanatory variables (i.e., η
0
= 0), the Durbin model reduces to the
11 For brevity, the bias correction formulas and asymptotic covariances of estimators are not provided. See Lee
and Yu (2010a, 2011). In Monte Carlo studies, Lee and Yu (2010a, 2011) indicate that the bias corrected estimators
have desirable finite sample properties even for small T . We also provide some Monte Carlo results based on a more realistic data generating process in Section 5 to evaluate the performance of the bias correction procedures for our application.
14

spatial autoregressive (SAR) model. In terms of estimation, the discussion in Section 4.1 is still valid and we can use the same estimators. Moreover, the Durbin model simplifies to a spatial error
(SE) model when the nonlinear constraints, known as the common factor constraints, hold. The specification for the SE model is Y nt where | γ
0
| < 1, and v
Substitution of u nt
= S nt
− 1 n is n × 1 vector of innovation terms with mean zero and variance σ
2
0 v nt
= γ
0
Y n,t − 1
+ X nt into the SE model yields
β
0
Y nt
+ c n 0
= λ
0
+
W
α n t 0
Y l n nt
+
+ γ u
0 nt
Y
, u nt n,t − 1
= λ
0
− γ
0
λ
W
0 n
W u n nt
Y
+ v nt n,t − 1
I n
+
,
.
X nt
β
0
− W n
X nt
λ
0
β
0
+ S n c n 0
+ S n
α t 0 l n
+ v nt
, where S n c n 0 and S n
α t 0 l n can be considered as the new transformed fixed effects. This reduced form of the SE model imposes the common factor constraints of ρ
0
= − γ
0
λ
0 and η
0
= − λ
0
β
0 on the Durbin model. Therefore, the SE model can be estimated from the estimation approach outlined so far by imposing the common factor constraints on the log-likelihood function. Both null hypotheses H
0
: θ
0
= 0, and H
0
: ρ
0
= − γ
0
λ
0
, and
η
0
= − λ
0
β
0 can be tested by the Wald test. In subsequent sections, we denote the Wald test for the first null by Wald-test (SAR), and for the second null by Wald-test (SE).
The marginal effects accounting for the exogenous variables require a different analysis due to spatial and time dependence structure of the model. A change in an explanatory variable for a country not only affects the associated dependent variable of that country but also affects the dependent
variable of other countries (Elhorst, 2010; LeSage and Pace, 2009). For our regression model, the
reduced form is
Y nt
= S
− 1 n
( γ
0
I n
+ ρ
0
W n
) Y n,t − 1
+ S
− 1 n
X nt
β
0
+ S
− 1 n
W n
X nt
η
0
+ S
− 1 n c n 0
+ α t 0
S
− 1 n l n
+ S
− 1 n u nt
.
(5.1)
Denote the k th exogenous variable in X nt by x kt
= ( x
1 kt
, x
2 kt
, . . . , x nkt
)
0
. Then, the partial derivative of the dependent variable with respect to the k th explanatory variable yields the following matrix of marginal effects:
∂Y nt
∂x
0 kt
=





 ∂Y
1 t
∂x
1 kt
∂Y
2 t
∂x
1 kt
.
..
∂Y nt
∂x
1 kt
∂Y
1 t
∂x
2 kt
∂Y
2 t
∂x
2 kt
.
..
∂Y nt
∂x
2 kt
· · ·
· · ·
. ..
· · ·
∂Y
1 t
∂x nkt
∂Y
2 t
∂x nkt
.
..
∂Y nt
∂x nkt






= I n
− λ
0
W n
− 1
β k 0
I n
+ η k 0
W n
, (5.2) where β k 0 and η k 0 are respectively the k th component of vectors β
0 and η
0
. Evidently, a change in k th explanatory variable in a country affects not only the per capita real income in that country
but also the per capita real income in its neighbors. Since each diagonal element in (5.2) represents
a direct effect and is generally not equal to other diagonal elements, the interpretation is not as
straightforward as the interpretation in a non-spatial model. LeSage and Pace (2009) suggest taking
the average of the diagonal elements as a scalar measure of direct effects. Similarly, since every non-diagonal element represents an indirect effect, a scalar measure of indirect effects is defined as
the average sum of the row sums (or the sum of the column sums) of the non-diagonal elements.
12
Then, a scalar measure of total effects is given by the average sum of direct and indirect effects, which reflects the average overall impact of a change in the k th exogenous variable occurring
12 The sum of the row sums for the non-diagonal elements are equal to the sum of the column sums for the non-
diagonal elements for the matrix in (5.2). The average row sums of the non-diagonal elements is defined as the sum
of all non-diagonal elements divided by the number of countries n .
15

simultaneously in all n countries.
( I n
The direct and indirect effects can be analyzed through the Neumann series representation of
− λ
0
W n
)
− 1
= P
∞ q =0
λ q
0
W q n
= I n
+ λ
0
W n
+ λ
2
0
W
2 n
+ · · · . In this representation, the first term I n represents the own-region impacts with no spillovers since the non-diagonal elements are zero. The diagonal elements in the second term λ
0
W n are zero, hence this term reflects solely the first-order indirect effects. All other terms in the infinite series representation represents second and higher order direct and indirect effects.
Note that (5.2) represents the contemporaneous effects. One can also analyze the diffusion
effects over time following the methodology suggested in Debarsy, Ertur, and LeSage (2012). Due
to the presence of time lag variable in the model, a change in x kt at time t also produces future responses in the dependent variable. These future responses are called diffusion effects. In order
0 to formulate diffusion effects, we again stack the model over t . Let Y
0 n
0
= Y n 0
0
, Y n 1
0
, . . . , Y nT be the n ( T + 1) × 1 vector of the dependent variable, where Y n 0
K n
= − ( γ
0
I n is the initial period vector. Define
+ ρ
0
W n
). Let
P n be the nT × n ( T + 1) space-time filter given by
P n
=
 K n
S n
0 n × n
. . .
0 n × n





0 n × n
K n
S n
. . .
0 n × n
.
..
· · ·
. ..
. ..
..
.




.
0 n × n
. . .
0 n × n
K n
S n
(5.3)
Then, the model can be written as
P n
Y
0 n
= X n
β
0
+ ( I
T
⊗ W n
) X n
η
0
+ ( l
T
⊗ c n 0
) + ( α
0
⊗ l n
) + u n
, (5.4)
0
= u
0 n 1
, . . . , u
0 nT
0 where X n
0
= X n 1
0
, . . . , X nT
, α
0
= ( α
10
, . . . , α
T 0
)
0
, and u n
. Debarsy, Ertur,
and LeSage (2012) write (5.4) conditional on the initial value of the dependent variable, and assume
that the first period value of dependent variable Y n 1 is governed only by the spatial dependence.
Under this assumption, the space-time filter is given by
Q n
=




 S n
0 n × n
0 n × n
. . .
0 n × n

K n
S n
0 n × n
. . .
0 n × n
.
..
. ..
. ..
· · ·
..
.




.
0 n × n
. . .
0 n × n
K n
S n
(5.5)
Then, (5.4) can be written as
Y n
=
K
X
Q
− 1 n k =1
( I nT
β k 0
+ η k 0
( I
T
⊗ W n
) x k
+
Q
− 1 n
( l
T
⊗ c n 0
) + ( α
0
⊗ l n
) + u n
, (5.6) where x k is the nT × 1 k th column of X n
. The inverse of
Q n is a lower triangular block diagonal
16

matrix given by
Q
− 1 n

=






S
− 1 n
D
1
D
2
.
..
D
T − 1
0
S
D n × n
− 1 n
D
1
.
..
T − 2
0 n × n
. . .
0 n × n

0 n × n
. . .
0 n × n 

S
− 1 n
. . .
. ..
. ..
0 n × n
.
..




,
· · · D
1
S
− 1 n
(5.7) where D p
= ( − 1) p S
− 1 n
K n p
S
− 1 n for p = 0 , . . . , T − 1. The diffusion effects over time can be
determined from (5.6) and (5.7). When there is a permanent change in the
k th variable starting at time t , i.e., ∂x k
= 0 , . . . , 0 , x kt are respectively given by S
− 1 n
[ β k 0
+ ∆ , x k,t +1
I n
+ η k 0
W
+ ∆ , . . . , x n
] and D
1 kT
+ ∆
+ S
− 1 n
, the impact at time
[ β k 0
I n
+ η k 0
W n t and at t + 1
]. Notice that the impact at time t
is the same as the one stated in (5.2). In general, the
M -period ahead impact of this change is given by P
M p =0
D p
β k 0
I n
+ η k 0
W n
. When there is a temporary change at time t in the k -th variable, i.e., ∂x k
= 0 , . . . , 0 , x kt
+ ∆ , 0 , . . . , 0 , the M -period ahead impact is simply given by D
M
β k 0
I n
+ η k 0
W n
.
The direct and indirect summary statistics suggested in LeSage and Pace (2009) can also be
formulated for the diffusion effects. For the statistical inference, the dispersions of direct, indirect and total effects are needed. Since the scalar measures of these effects are complicated functions of
the parameters of the spatial model as shown in (5.2), LeSage and Pace (2009) suggest a simulation
method through which the estimated dispersions can be recovered by using the covariance matrix of parameters of the model. Let Ω n be the variance-covariance matrix of the parameter vector and
ε n be a random vector that has multivariate standard normal distribution. Denote the parameter vector of a spatial model with θ
0
. The simulation technique depends on the recursive relation:
θ of r
= L n
ε r n
θ
0
+ ˆ
, and ε r n nT for r = 1 , 2 , . . . , R , where R θ nT is a consistent estimate is the random vector drawn from the multivariate standard normal distribution. Here,
L n is the lower-triangular matrix recovered from the Cholesky decomposition of b n
, where Ω n is a consistent estimate of Ω n
. A total number of R draws of the parameter vector θ r can be recovered, through which a simulated sample of the direct and indirect effects can be obtained. Then, the mean and the dispersion of direct and indirect effects can be calculated from the simulated samples for the purpose of statistical inference.
In this section, estimation results for the empirical analogue of the convergence equation of the spatially augmented growth model is presented. The purpose of this empirical investigation is to
estimate the effect of FDI on economic growth through the regression model in (2.9).
In general, the transition from a single cross section data model to a panel data model is
made possible by dividing the total period into several shorter time spans. We recover (2.9) by
dividing the whole period T into equal time-spans of τ . There are different suggestions about
the appropriate length of time spans in the growth literature (Hauk and Wacziarg, 2009; Islam,
1995; Mankiw, Romer, and Weil, 1992). Short time-spans are generally considered inappropriate
for studying growth convergence in a panel data framework, because unobservable factors may loom large and the disturbance terms over short time-spans are more likely to be influenced by business cycle fluctuations. We choose three-year time intervals, i.e., τ = 3, so that we have ten data points over the period 1980-2010. We construct exogenous variables by taking averages over non-overlapping time-spans.
17

First, we consider the estimation results for the non-spatial regression model recovered from the augmented Solow growth model under the assumption that there is no technological interdependence among countries, which corresponds to γ
= 0 in (2.2). Moreover, the non-spatial panel data
model given (2.1) is nested in our SDPD model in (2.9). That is, the SDPD model simplifies to
a non-spatial panel data model when λ
0
= ρ = 0 and η
0
= 0. The purpose of estimating the non-spatial model is to verify that our panel data generates estimates that are consistent with the
results reported in the empirical FDI literature. The estimation results are reported in Table 1.
We estimate the model in (2.1) using within (FE), between (BE), pooled OLS (OLS), Arellano
and Bond (1991) (AB) and Blundell and Bond (1998) (BB) estimators. In the case of AB and
BB estimators, assumptions about the correlation between the pertinent explanatory variables
0 x it
= ln s k
, ln s h
, ln( n + .
05) , F and the components of the disturbance term c i
+ α t
+ u it determine the moment functions for the estimation. In our application, we consider two cases: (i) we assume that x it is predetermined in the sense that E x
0 it u is
= 0 for s < t , and zero otherwise; (ii) x it is endogenous in the sense that x it with u i,t +1
and subsequent shocks.
13
is correlated with u it and earlier shocks, but uncorrelated
The BE and OLS estimators are inconsistent, since the time lag of the dependent variable is correlated with the error components of the model that are omitted in these models. This correlation is expected to be positive so that the coefficient estimates on ln Y t − 1 is biased upward in the case of BE and OLS estimators. This problem is known as the heterogeneity bias or omitted
variable bias (Hauk and Wacziarg, 2009). The FE estimator removes the heterogeneity bias via the
within transformation, which wipes out the country and time fixed effects. However, the within transformation induces a substantial correlation between the transformed lagged dependent variable and the transformed disturbances, resulting an asymptotic bias of order O
1
T
. The mechanism of the within transformation indicates that the correlation between the transformed time lagged dependent variable and the transformed disturbance term is negative, implying a downward bias on the estimates of the lagged dependent variable.
Based on these observations, Bond (2002) and Roodman (2009a) state that a reasonable estimate
for the lagged dependent variable should be in the interval determined by the OLS and FE estimates.
In Table 1, both AB and BB estimators report estimates in this interval. The AR(2) test results
reported for the AB and BB estimators show that the null hypothesis of uncorrelated disturbance terms is rejected at 5 percent significance level in all columns. Hence, there is significant statistical evidence for second-order serial correlation in differences (first-order serial correlation in levels).
On the other hand, the AR(3) test results shows that there is no third-order serial correlation in differences (second-order serial correlation in levels). Therefore, in the estimation of columns (4) through (7), we restrict the instrument set to lags 3 and longer of the dependent variable. The
Hansen J test results indicate that the null hypothesis that the moment functions are valid cannot be rejected. A large number of instruments can generally impose substantial finite sample bias on the parameter and standard error estimates, and reduce the power of the specification tests such as
Hansen and Sargan tests of over-identification (Roodman, 2009b). Furthermore, the Hansen J test
results indicate that there is no evidence for the relatively bigger set of moment function used in
13
Caselli, Esquivel, and Lefort (1996) formulate moment functions under case (i). The moment functions involving
x it are in the following forms: For difference equation, case (i) E x
0 i,s − 1
∆ u it
= 0 for t = 3 , . . . , T and 1 ≤ s ≤ t − 1 and case (ii) E x
0 i,s − 1
∆ u it
(2001).
= 0 for t = 3 , . . . , T ; and 2 ≤ s ≤ t − 1. For the level equation, case (i) E ∆ x
0 it u it for t = 2 , . . . , T ; and case (ii) E ∆ x
0 i,t − 1 u it
= 0 for t = 3 , . . . , T
= 0
. For details, see Blundell, Bond, and Windmeijer
18

columns (4) and (5) are worse. Hence, there is no significant evidence for the potential endogeneity of x it
.
The convergence rate λ ranges from 0 .
18 percent to 6 .
9 percent, where the AB estimator as-
signs relatively larger value as expected. For example, Caselli, Esquivel, and Lefort (1996) report
approximately 10 percent for the convergence rate using the AB estimator. However, Blundell and
Bond (1998) and Bond (2002) show that the AB estimator induces significant finite sample bias on
coefficient estimates when the autoregressive process is persistent and the relative variance of fixed effects is larger. In that case, the lagged levels of variables provide weak instruments for the first
differences of variables. The Monte Carlo studies in Blundell and Bond (1998) for an autoregressive
panel model without explanatory variables show that when the true value of the time lag term of the dependent variable is around 0 .
8, the AB estimator suffers from severe weak instrument problems and imposes huge downward bias in the direction of the FE estimator. For a more general data generating process that includes an explanatory variable, Blundell, Bond, and Windmeijer
(2001) obtain similar results. For our application, estimation results in Table 1 and in subsequent
spatial models indicate that the coefficient estimates of ln Y t − 1 is more likely to be bigger than 0 .
8, implying poor performance for the AB estimator. In addition, the extensive Monte Carlo study in
Hauk and Wacziarg (2009) shows that the AB estimator overestimates the convergence rate and
underestimates the impact of the pertinent explanatory variables in the presence of measurement error.
The BB estimator is designed to improve the properties of the AB estimator by exploiting the information in the lagged differences of variables as additional instruments for the level variables.
The coefficient estimates of ln Y t − 1 reported by the BB estimator are 0 .
9822 and 0 .
9874 in columns
(5) and (7), which imply convergence rates of 0 .
6 and 0 .
4 percent, respectively.
In terms of statistical inference, estimators provide different sets of inference regarding to the role of variables in the growth process. The t -statistics reported for the BB estimator indicate important efficiency gains due to extra moment functions formed from the first differences for the level equation. Estimates of the human capital variable (the secondary school enrollment rate) are mostly insignificant except for column (5) at the 10 percent level, suggesting that the lag differences of this variable as instruments are more informative. Overall, the AB and BB estimators give more reasonable values for the human capital coefficient. For other variables, the estimation results
replicate the findings of empirical growth literature.
14
In columns (6) and (7), pertinent explanatory variables are assumed to be endogenous rather than predetermined. Moving from column (5) to column (7), the human capital variable becomes insignificant. Theoretically inconsistent estimators
in columns (1) and (3) report a statistically significant coefficient for the FDI variable.
15
In all other columns, the FDI variable is positive and insignificant, which is consistent with the findings in the
literature (Blonigen and Wang, 2005; Borensztein, Gregorio, and Lee, 1998; Carkovic and Levine,
2005; Kottaridi and Stengos, 2010).
16
In the next section, we show that the omitted variables due to technological interdependence in the non-spatial model are strongly significant, implying model misspecifications. Once the omitted variables are incorporated through the spatial lag terms, a significant positive impact for FDI is
14
This can be seen by just comparing our results in Table 1 with the results reported in Table 13 of Hauk and
Wacziarg (2009).
15 For all specifications in this section, we also considered including the square of the FDI variable to allow for the potential nonlinear effect of FDI in the growth process. We did not find any evidence for the nonlinear specification of FDI.
16
We also employed the collapse technique to reduce the set of instruments as described in Roodman (2009b,
2009a). This method collapses the set of moment functions to a smaller set to investigate the effect of instruments
proliferation for the BB estimator.
19

Table 1: Non-spatial Model Estimations ln ln ln ln(
λ
Y s s n t − 1 k h
FDI
+
Nobs.
Ninst.
inst.)
.
Half-life
05) constant
(convergence)
AR(2) test
AR(3) test
Hansen J (all
(1)
(FE)
0.8130
∗∗∗
(0.0172)
0.0948
∗∗∗
(0.0139)
0.0098
(0.0120)
-0.0813
∗∗∗
(0.0182)
0.2095
∗∗
(0.1008)
–
0.0690
(0.0071)
10.0456
765
–
–
–
–
∗∗∗
(2)
(BE)
0.9945
∗∗∗
(0.0071)
0.0597
∗∗∗
(0.0134)
(3)
(OLS)
0.9832
∗∗∗
(0.0042)
0.0715
∗∗∗
(0.0083)
(4)
(AB
0.8396
(0.0408)
0.0822
i
)
∗∗∗
∗∗
(5)
(BB i
)
0.9822
∗∗∗
(0.0100)
0.0866
∗∗∗
(6)
(AB
0.8265
(0.0448)
0.0917
ii
)
∗∗∗
∗∗∗
(7)
(BB
0.9874
0.0826
ii
)
∗∗∗
(0.0092)
∗∗∗
-0.0077
(0.0109)
-0.1515
∗∗∗
0.0095
(0.0065)
-0.1146
∗∗∗
(0.0278) (0.0154) (0.0254) (0.0192)
0.0296
(0.0164)
0.0302
∗
(0.0131)
0.0296
(0.0161)
0.0273
(0.0171)
(0.0357)
0.1007
(0.0161)
0.2632
∗∗
(0.0828)
-0.0192
(0.0450)
0.4093
-0.0635
(0.0422)
0.1900
-0.0190
(0.0502)
0.2714
-0.0343
(0.0475)
0.1752
(0.1888)
-0.2285
∗
(0.1042)
0.0018
(0.0572)
0.0056
∗∗∗
(0.2127) (0.1710) (0.1931) (0.1737)
–
0.0583
∗∗∗
0.1896
(0.1366)
0.0060
∗
–
0.0635
∗∗∗
0.2103
(0.1385)
0.0042
0.0018
(0.0024) (0.0014) (0.0162) (0.0034) (0.0181) (0.0031)
385.0818
123.7763
11.8893
115.5245
10.9157
165.0350
765 765 680 765 680 765
–
–
–
–
177
-2.5195
[0.0118]
217
-2.3487
[0.0188]
145
-2.3645
[0.0181]
181
-2.3425
[0.0192]
–
–
–
–
1.1619
[0.2453]
82.3878
[1.0000]
0.6372
[0.5240]
80.7946
[1.0000]
1.0301
[0.3030]
80.8546
[0.9999]
0.8366
[0.4028]
80.5975
[1.0000]
Note:
All regressions include time fixed effects except columns (2) and (3). Test for AR(2) stands for the Arellano-
Bond test for the first difference of residuals. Finally, AB stands for the Arellano and Bond (1991) estimator,
and BB for the Blundell and Bond (1998) estimator. The AB and BB estimators are robust two-step GMM
estimators with the Windmeijer (2005) correction. The subscripts i and ii denote aforementioned cases on the
endogeneity of x it
.
∗∗∗ if p < 0 .
01 ,
∗∗ if 0 .
01 ≤ p < 0 .
05, and
∗ if 0 .
05 ≤ p < 0 .
10.
observed.
Before we discuss the estimation results, we evaluate the performance of the estimators described
in Section 4 through a Monte Carlo design described in Appendix B. The aim of the Monte Carlo
study is to evaluate the bias properties of the estimators suggested in Lee and Yu (2010a, 2011)
through simulated data with moments resembling to those of our sample data.
17
We consider two
17 We would like to thank Jihai Yu for sharing his estimation routines with us.
20

data generating processes. In Model 1, the data, disturbance terms, and fixed effects are generated from i.i.d. Normal(0 , 1). In Model 2, the sample moments of our panel data are used to generate exogenous variables and fixed effects. For both models, we use the estimated parameter values
reported in the first column of Table 2.
18
The simulation results for the bias corrected QMLE are presented in Table 9 of Appendix B.
The simulation results show that the bias corrected estimator imposes almost no bias. Although trivial, the amount of bias on on γ
0 and ρ
0 in Model (2) is relatively larger compared to Model 1, which in turn suggests that the performance of estimators should be considered in realistic data generating processes. For the case where ( n, T ) = (85 , 10), the amount of bias for these parameters decreases substantially in both models. For all other parameters, the bias corrected direct approach
QMLE imposes trivial bias.
The estimates of γ
0 is used in the calculation of the implied convergence rate. Therefore, more reliable results can be obtained when T is larger in convergence studies based on these estimators.
Therefore, it is sensible to allow for 3 year time intervals to end up with 10 periods. Our main concern is about the estimates of λ
0
, γ
0
, ρ
0 and β
40
, which determine the estimates of the diffusion effects for FDI inflows. As the bias corrected estimators impose trivial biases on these parameters in all cases, the concern that can be raised about the accuracy of our estimates regarding the role of FDI inflows in the economic growth process is unfounded.
Now, we turn to estimation results. Tables 2 reports the estimation results for the SDPD model. For models in Table 2, the estimation method is the bias corrected QMLE based on the
transformation approach.
19
Consistency of the bias corrected QML estimation used for the Durbin
and SAR models in Table 2 depends on the true data generating processes, characterized by the
sum ( λ
0
+ γ
0
+ ρ
0
) relative to 1. For all models in Table 2, the estimated value of (
λ
0
+ γ
0
+ ρ
0
) is around 0 .
9. When the value of ( λ
0
+ γ
0
+ ρ
0
) is less than 1, the data generating process of the
SDPD model is a stable one. In that case, the estimation results reported in Table 2 are valid.
The Wald test (Cointegration) statistic in column (2) indicates that the data generating processes for the Durbin model with only country fixed effects may not be stable, as the p -value for the null hypothesis of ( λ
0
+ γ
0
+ ρ
0
) = 1 is 0 .
2977. For other models in columns (1), (3) and (4), the null
hypothesis can be rejected at 10 percent significance level. Lee and Yu (2011) provide simulation
results for the power of this test. For a nominal size of 5 percent, the simulation results indicate that this test has a lower power when the value of ( λ
0
+ γ
0
+ ρ
0
) is around 0 .
9. Hence, the test may not be reliable when it comes to reject the false null hypothesis of ( λ
0
+ γ
0
+ ρ
0
) = 1. To
confirm the robustness of our result in Tables 2, we estimate the model with the unified approach
in Section 7. The estimates based on the unified approach are almost identical to the ones presented
in Tables 2, which confirms the validity of our results.
The other test statistics provided in Table 2 can be used to select the model that best describes
the sample data. To find out whether time period fixed effects are significant, we perform an F-test.
The test statistic is 3 .
4345 ( p -value = 0 .
0002) for the Durbin model in column (3) and 5 .
0950 ( p value=0 .
0000) for the SAR model in column (4), which suggests that time fixed effects are jointly significant and should be included. Turning our focus on the Wald test statistics in column (3), the SAR and SE models are rejected in favor of the Durbin model at conventional significance levels. Furthermore, the spatial lags of explanatory variables in columns (1) and (3) are generally insignificant. The spatial lag of human capital is significant at 1 percent level. Two spatial lag terms, W × ln Y nt and W × ln Y n,t − 1
, are strongly significant in all columns. Hence, neither the
SAR nor the SE model should be adopted as they would suffer from the omitted variable bias. We
18
For details of the design, see Appendix B. We use the QMLE based on the transformation approach described in
Section 4.
19
The direct approach yields similar results, which are available upon request. For details, see Section 4.
21

Table 2: Bias Corrected QML Estimation Results ln ln ln ln(
W
W
W
W
W
W
λ
Y s s n
FDI k h
×
×
×
×
×
× n,t − 1
+ ln ln ln ln
.
ln(
FDI
(convergence)
Half-life
05)
Y
Y s s n nt n,t k h
+
−
.
Wald-test (Cointegration)
Wald-test (SAR)
Wald-test (SE)
F-test (time)
1
05) log-likelihood
Country Dummy
Time Dummy
(1)
0.9319
∗∗∗
(0.0180)
0.0821
∗∗∗
(0.0137)
-0.0091
(0.0119)
-0.0819
∗∗∗
(0.0168)
0.2015
∗∗
(0.1005)
0.3792
∗∗∗
(0.0503)
-0.3720
∗∗∗
(0.0546)
-0.0442
(0.0294)
0.0606
∗∗∗
(0.0218)
0.0159
(0.0526)
0.0606
(0.2158)
0.0235
∗∗∗
(0.0064)
29.4799
5.6666
[0.0173]
11.3746
[0.0227]
8.8120
[0.1168]
–
1261.2237
Yes
No
0.0211
(0.0064)
32.7918
1.0845
[0.2977]
Yes
No
(2)
0.9386
(0.0180)
0.0815
∗∗∗
(0.0129)
0.0072
(0.0098)
-0.0853
∗∗∗
(0.0169)
0.2686
(0.0935)
0.3881
(0.0480)
-0.3496
(0.0554)
–
–
–
–
–
–
–
∗∗∗
∗∗∗
∗∗∗
∗∗∗
∗∗∗
1251.6385
(3)
0.9341
∗∗∗
(0.0180)
0.0829
∗∗∗
(0.0138)
-0.0072
(0.0120)
-0.0869
∗∗∗
(0.0169)
0.2204
∗∗
(0.1016)
0.3347
∗∗∗
(0.0557)
-0.3166
∗∗∗
(0.0602)
-0.0222
(0.0335)
0.0864
∗∗∗
(0.0311)
-0.0329
(0.0557)
0.2611
(0.2689)
0.0227
∗∗∗
(0.0064)
30.4965
2.9275
[0.0871]
10.0074
[0.0403]
11.7442
[0.0385]
3.4345
[0.0002]
1254.4863
Yes
Yes
(4)
0.9346
∗∗∗
(0.0179)
0.0866
∗∗∗
(0.0132)
-0.0002
(0.0116)
-0.0892
∗∗∗
(0.0169)
0.2247
∗∗
(0.1008)
0.3561
∗∗∗
(0.0535)
-0.3389
∗∗∗
(0.0583)
–
–
–
–
0.0226
(0.0064)
30.7381
3.1833
[0.0744]
–
–
∗∗∗
5.0950
[0.0000]
1249.5474
Yes
Yes
Note:
Standard errors are in parentheses and p -values are in brackets.
0 .
01 ≤ p < 0 .
05, and
∗ if 0 .
05 ≤ p < 0 .
∗∗∗ if p < 0 .
01 ,
∗∗ if
10. Wald-test (Cointegration), Wald-test (SAR), Waldtest (SE) denote, respectively, the Wald test for the null hypotheses
H
0
: η
0
= 0, and H
0
: ρ
0
= − γ
0
λ
0
, and η
0
= − λ
0
β
0
.
H
0
: λ
0
+ γ
0
+ ρ
0
= 1, conclude that the Durbin model is the appropriate model to explain the sample data, confirming the theoretical prediction. Note also that the Durbin model is the correct specification from the economic theory standpoint as it corresponds to the theoretical convergence equation of the spatially augmented Solow growth model.
22

Overall, the estimation results indicates that there exists evidence for conditional convergence as the coefficient of ln Y n,t − 1 is less than 1 in all columns. The estimated convergence rate, λ , falls in the range from 0 .
0211 to 0 .
0235. In the previous section, the BB estimator in Table 1 reports an
estimate of 0 .
0060. The extensive study in Hauk and Wacziarg (2009) shows that the convergence
rate in non-spatial dynamic panel data model is around 0 .
8 percent. Our larger results indicate that the omitted spatial lag terms in non-spatial models introduce an upward bias in the estimate of ln Y n,t − 1
so that relatively lower convergence rates are obtained in non-spatial models.
20
The
spatial lag variables in Table 2 are significant, implying model misspecification for the non-spatial
model of the previous section. The coefficient of W × ln Y n,t − 1 is negative and significant in all models, suggesting that the initial conditions in other countries are also relevant for the growth process of a country. The spatial lag of output per worker, W × ln Y nt
, has a positive significant coefficient in all regression models, suggesting the presence of the endogenous interaction among countries.
Before we turn to results for (the cumulative and contemporaneous) direct, indirect, and total diffusion effects, we must emphasize again that a change in an explanatory variable in a spatial model not only affects its associated dependent variable but also affects the dependent variable
of neighboring units. The parameter estimates in Table 2 do not represent the marginal effects.
The feedback effects that arise from the impacts passing through neighboring countries and back to countries themselves must also be taken into account. For the Durbin model, the source of feedback effects are spatial lags of the dependent and exogenous variables.
Tables 3 through 6 report direct, indirect, and total effects for the explanatory variables, cor-
responding to parameter estimates in column (3) in Table 2. These effects are calculated by the
method described in Section 5. These tables report the simulated mean and 95 and 99 percent
confidence intervals for each period in the horizon.
21
Cumulative effects show the accumulation of effects over time as a result of a permanent change in an explanatory variable in period t . We choose directly calculate the cumulative effects without resorting to a simulation using the param-
eter estimates in Table 2, as the period by period simulated effects already relay the statistical significance of these effects. The results in Table 2 shows that ˆ
n
+ ˆ n
+ ˆ n
< 1 for all columns.
Therefore, we expect to see that estimates of direct effects decrease over time.
The direct effect estimate of physical capital elasticity for period zero is 0 .
083 in Table 3, which
is similar to the parameter estimate of 0 .
0829 reported in Table 2. As expected, physical capital
elasticity of output per-worker is larger in the long-run. A simultaneous 1 percent permanent increase in physical capital share in all countries increases output per-worker by about 0 .
67 percent
for a country, which can be seen from the total effects reported in Table 3. Most of this effect is
accounted by the direct effects, suggesting that the policy makers in a country have incentives for designing policies for domestic physical capital investment.
Before we interpret the diffusion effects for human capital elasticity, note again that the estimates
of human capital variable are mostly insignificant in Table 2. This anomalous result for the human
capital variable is not new in the growth literature. For instance, Knight, Loayza, and Villanueva
(1993) and Islam (1995) also report insignificant negative estimated coefficients for the human
capital variable. There are three explanations in the literature. The first explanation points out the discrepancy between the theoretical variable H in the production function and the actual variable used in regression models. According to this line of argument, the variable based on schooling reflects only a fraction of human capital investment rate, and the differences in the quality of
20
We also changed time interval of a period from 3 to 5 years in constructing the panel data. This new panel has
6 data points per country. The convergence rates varies between 0 .
0247 and 0 .
0273. These results also suggest that the non-spatial models may overestimate the convergence rate.
21
Results are based on 1000 draws.
23

Table 3:
Space-time effect estimates of physical capital elasticity for column (3) in Table 2
Cumulative Lower 0.01
Lower 0.05
Mean Upper 0.95
Upper 0.99
6
7
8
9
2
3
4
5
5
6
7
8
1
2
3
4
Horizon
0
9
Total
Horizon
0
1
2
3
4
0
1
Direct
Horizon
7
8
5
6
9
Indirect
0.008031
0.015008
0.021039
0.026221
0.030641
0.034381
0.037512
0.040102
0.042209
0.043888
0.083186
0.160867
0.233406
0.301144
0.364400
0.423470
0.478632
0.530143
0.578247
0.623168
0.091217
0.175875
0.254445
0.327365
0.395041
0.457851
0.516144
0.570245
0.620456
0.667056
-0.104683
-0.098441
-0.093930
-0.087349
-0.082175
-0.079237
-0.075870
-0.070979
-0.066393
-0.061876
0.049523
0.046470
0.043620
0.041055
0.038788
0.036152
0.033874
0.031319
0.028822
0.026632
-0.030282
-0.028704
-0.027208
-0.025789
-0.024445
-0.021989
-0.019512
-0.017314
-0.015364
-0.013634
0.058147
0.055093
0.051500
0.048134
0.044622
0.041313
0.038078
0.035169
0.032477
0.029470
0.000824
0.000792
0.000761
0.000699
0.000615
0.000541
0.000476
0.000418
0.000368
0.000324
-0.082756
0.007377
-0.075249
0.006545
-0.069786
0.005894
-0.064739
0.005395
-0.060057
0.005023
-0.056856
0.004757
-0.054770
0.004582
-0.051545
0.004480
-0.050631
0.004440
-0.048599
0.004450
0.082633
0.077149
0.072065
0.067350
0.062975
0.058913
0.055141
0.051636
0.048377
0.045347
0.090010
0.083695
0.077960
0.072745
0.067998
0.063671
0.059723
0.056116
0.052817
0.049797
0.094535
0.089157
0.085467
0.084198
0.084538
0.082897
0.082572
0.082750
0.083512
0.083646
0.107265
0.099763
0.093123
0.087534
0.082051
0.078149
0.074545
0.071482
0.068171
0.064632
0.183886
0.177640
0.169159
0.161407
0.154757
0.150336
0.145183
0.142952
0.140163
0.138976
0.117373
0.114742
0.109243
0.105636
0.105033
0.104283
0.105695
0.107511
0.111506
0.110518
0.112913
0.104450
0.098129
0.092545
0.088466
0.084943
0.080632
0.076562
0.073345
0.070579
0.212287
0.197024
0.182200
0.176034
0.174513
0.171296
0.170739
0.167699
0.164000
0.161717
schooling are ignored in the construction of this variable. Related to the first explanation, Cohen
and Soto (2007) present a new data set for years of schooling from various sources by taking into
account the age structure of the population. The authors claim that the anomalous result for the human capital variable in cross-country regression studies is due to measurement error. They show
that their new data set may perform better than the Barro and Lee (2001) series in cross-country
growth regressions. Unfortunately, this new data set is available for 10-year intervals for the period
1960-2010. Therefore, we do not consider this data set in our regression.
24

Table 4:
Space-time effect estimates of human capital elasticity for column (3) in Table 2
Cumulative Lower 0.01
Lower 0.05
Mean Upper 0.95
Upper 0.99
6
7
8
9
2
3
4
5
5
6
7
8
1
2
3
4
Horizon
0
9
Total
Horizon
0
1
2
3
4
0
1
Direct
Horizon
7
8
5
6
9
Indirect
0.121605
0.234549
0.339452
0.436885
0.527382
0.611436
0.689507
0.762021
0.829373
0.891933
-0.002643
-0.005180
-0.007615
-0.009949
-0.012185
-0.014325
-0.016372
-0.018330
-0.020200
-0.021985
0.118962
0.229369
0.331837
0.426937
0.515197
0.597111
0.673134
0.743691
0.809174
0.869948
0.022868
0.021201
0.019810
0.017382
0.015939
0.015342
0.013685
0.012205
0.010885
0.009314
-0.029385
-0.028507
-0.027386
-0.026266
-0.025156
-0.024233
-0.023481
-0.022739
-0.022007
-0.021288
0.015812
0.014751
0.013314
0.012319
0.011892
0.010534
0.008926
0.007563
0.006758
0.006506
0.046689
0.043536
0.039817
0.036287
0.033054
0.029620
0.026541
0.023874
0.021539
0.019259
0.041343
0.038455
0.034763
0.031717
0.028161
0.024470
0.021515
0.018553
0.015798
0.013645
-0.024597
-0.002043
-0.022986
-0.001964
-0.021484
-0.001880
-0.020223
-0.001791
-0.019090
-0.001701
-0.018229
-0.001609
-0.017402
-0.001517
-0.016276
-0.001426
-0.015444
-0.001335
-0.014838
-0.001247
0.122861
0.114504
0.106898
0.099965
0.093638
0.087858
0.082571
0.077729
0.073291
0.069218
0.120817
0.112540
0.105018
0.098173
0.091937
0.086249
0.081053
0.076303
0.071956
0.067972
0.200190
0.191288
0.182028
0.177811
0.172070
0.168925
0.165743
0.163203
0.161673
0.160652
0.019046
0.017918
0.016632
0.015990
0.015070
0.014222
0.013478
0.012390
0.011908
0.011502
0.204215
0.194453
0.186091
0.180534
0.175405
0.171702
0.167841
0.165970
0.164079
0.163500
0.221816
0.220940
0.210996
0.201640
0.203783
0.205250
0.205062
0.203494
0.205536
0.210212
0.024967
0.023494
0.022275
0.021188
0.020024
0.018986
0.018072
0.018188
0.017418
0.017111
0.224401
0.213213
0.212638
0.207429
0.209874
0.212349
0.211439
0.211699
0.216850
0.222126
The second explanation for the anomalous result for the human capital variable points out the temporal negative correlation between variation in human capital and output per-worker, especially for developing countries. In other words, a measure such as the secondary school enrollment rate rises steadily in many developing countries, while output per-worker can still remain stable or even
fall (Islam, 1995; Knight, Loayza, and Villanueva, 1993). The third explanation brings up the
issue of specification of human capital in the production function. According to this argument, the conventional production functions do not allow an adequate role for the human capital to invoke its
25

full impact in the production process. A complex specification with respect to human capital will open channels through which the full potential of human capital can be transmitted to the growth
process (Benhabib and Spiegel, 1994; Cohen and Soto, 2007; Kalaitzidakis et al., 2001; Kottaridi
and Stengos, 2010). Related to this third explanation, Delgado, Henderson, and Parmeter (2014)
use the schooling data from various leading educational attainment databases with non-parametric techniques that are robust to functional form mis-specifications, and report statistically insignificant results for the mean years of schooling.
The striking result for the human capital variable is that its spatial lag is quite significant as
can be seen from Tables 2. In fact, the calculated indirect effects are positive and significantly
different from zero in Table 4. This result is consistent with the results reported in the literature.
For example, Conley and Ligon (2002) provide empirical evidences for positive significant spillovers
by using primary and secondary school enrollment rates for human capital. Similar to results of
physical capital, the human capital elasticity estimate is larger in the long-run as shown in Table 4.
The last row of Table 4 shows that a simultaneous 1 percent permanent increase in human capital
variable in all countries increases output by about 0 .
86 percent for a country in the long-run. Most of this effect is accounted by the indirect effects, suggesting that the policy makers in a country have incentives for designing policies for supporting human capital investment in its neighbors.
The diffusion effects for the drag variable, i.e., ln( n + .
05) are reported in Table 5. The direct
effect estimate for the period zero is − 0 .
09 which is similar to the parameter estimate reported in
Table 5. In the long-run, cumulated direct and indirect effects have similar magnitudes. However,
the contemporaneous indirect effect estimates are not statistically significant. The total effects estimates are significant at 5 percent level but are not significant at 1 percent level. The estimated drag elasticity of growth is about − 1 .
3 in the long-run: a simultaneous 1 percent permanent increase in the drag term in all countries decreases output per-worker of a given country by about 1 .
3 percent in the long-run.
Now, we turn to the estimation results for FDI inflows. For all models in Table 2, the coefficient
of FDI has the expected sign and it is statistically significant. We also consider these specifications by including a squared FDI variable to capture possible nonlinear impact of FDI on growth. The coefficient of the squared FDI variable was insignificant in all models.
The estimation results
for the Durbin model in Table 2 indicate that the coefficient of the FDI variable is positive and
significant at 5 percent level, but its spatial lag is insignificant. Table 6 presents the space-time
effects corresponding to column (3) in Table 2, i.e., the Durbin model with time fixed effects. The
FDI semi-elasticity is higher in the long-run. The direct effect estimates are statistically significant at 1 percent level, whereas indirect and total effect estimates are not statistically significant at 5 percent level.
To better understand how the direct, indirect and total effect measures are calculated, we illustrate the surface plots of the estimated n × n matrix D p
β k 0
I n
+ η k 0
W n when p = 0 and p = 9
in Figure 2 for FDI. Recall that the (
i, j )th cell in this n × n matrix represents the marginal effect of a change in the explanatory variable k in country j on country i ‘s outcome in period p . Therefore, the diagonal and off-diagonal cells correspond respectively to direct and indirect effects from which
scalar measures are calculated by taking their averages. As seen in Figure 2, the estimates of direct
effects given in the diagonal of the surface plot are larger than the estimates of direct effects given in the off-diagonal elements of the surface plots.
The results in Table 6 show that the estimated direct effect (own semi-elasticity) is about 0
.
24 at period 0, in other words, on average a simultaneous 1 percentage point increase in FDI flows in all countries contemporaneously increases the output per-worker of a given country by about 0 .
24 percent. In the long-run, this effect accumulates to about 1 .
78, suggesting that the policy makers in a country have incentives for designing domestic policies for promoting FDI inflows. Relative to
26

6
7
8
9
2
3
4
5
5
6
7
8
1
2
3
4
Horizon
0
9
Total
Horizon
0
1
2
3
4
0
1
Direct
Horizon
7
8
5
6
9
Indirect
Table 5:
Space-time effect estimates of drag elasticity for column (3) in Table 2
Cumulative Lower 0.01
Lower 0.05
Mean Upper 0.95
Upper 0.99
-0.089789
-0.172652
-0.249116
-0.319671
-0.384768
-0.444826
-0.500231
-0.551339
-0.598479
-0.641956
-0.090317
-0.174610
-0.253281
-0.326705
-0.395233
-0.459191
-0.518885
-0.574599
-0.626599
-0.675132
-0.180107
-0.347262
-0.502397
-0.646376
-0.780001
-0.904018
-1.019116
-1.125938
-1.225078
-1.317088
-0.295029
-0.274466
-0.272625
-0.261893
-0.246376
-0.241387
-0.242223
-0.237087
-0.240212
-0.245544
-0.130433
-0.122489
-0.115196
-0.109523
-0.103646
-0.099466
-0.096503
-0.092324
-0.088401
-0.085824
-0.402999
-0.371472
-0.364301
-0.346707
-0.327506
-0.318807
-0.326536
-0.329721
-0.332937
-0.335887
-0.124198
-0.090439
-0.059826
-0.115540
-0.084399
-0.056327
-0.107928
-0.078807
-0.052000
-0.100593
-0.073629
-0.048304
-0.095629
-0.068829
-0.045121
-0.090463
-0.064378
-0.041805
-0.085846
-0.060249
-0.038567
-0.080831
-0.056416
-0.035532
-0.077683
-0.052856
-0.032695
-0.074283
-0.049548
-0.030019
-0.253742
-0.092183
-0.231058
-0.084654
-0.215462
-0.077964
-0.201996
-0.072012
-0.193172
-0.066711
-0.187045
-0.061984
-0.181584
-0.057763
-0.180777
-0.053990
-0.171586
-0.050612
-0.168224
-0.047586
-0.355785
-0.182622
-0.030135
-0.326445
-0.169053
-0.028345
-0.305217
-0.156771
-0.026119
-0.285809
-0.145641
-0.023366
-0.268619
-0.135540
-0.020758
-0.256855
-0.126362
-0.018528
-0.247807
-0.118013
-0.016728
-0.241323
-0.110406
-0.014964
-0.231268
-0.103469
-0.013873
-0.228860
-0.097134
-0.012706
0.053355
0.050293
0.046709
0.043756
0.041640
0.039573
0.038800
0.036924
0.034653
0.033291
0.115353
0.107369
0.103837
0.100421
0.097118
0.093924
0.090835
0.087847
0.084958
0.082163
-0.051381
-0.048822
-0.046091
-0.042752
-0.039657
-0.036789
-0.033452
-0.030439
-0.027373
-0.024624
0.042711
0.041345
0.040023
0.038744
0.037505
0.036306
0.035145
0.034021
0.032934
0.031881
the direct effect values, the estimated indirect and total effect values are larger in magnitude in the long-run: 3 .
51 and 5 .
29 respectively. However, the contemporaneous indirect and contemporaneous total effect estimates are not significant at 5 percent level. Hence, a policy suggestion at a broader perspective (i.e., as a union) encouraging FDI inflows is available at higher significance levels.
Finally, we compare the direct and total effects of FDI inflows reported in Table 6 with the
estimated coefficients of FDI inflows reported in the empirical FDI literature. The non-spatial dynamic panel data models are estimated to investigate the effect of FDI on economic growth in
27

0.3
0.25
0.2
0.15
0.1
0.05
ZM
US
TR TG
SY
LK
SG
RW PE
PA
NE
NL MA
MR
MW
JO
IT ID
HN
GH
SV
DO CR
CO
CA
BR BJ
AT
ATBJ
BRCA
DOSV
COCR
ID IT
GHHN
MRMA
JOMW
PAPE
NLNE
SGLK
SYTG
ZM
TRUS
(a) Marginal effects when p = 0
0.3
0.25
0.2
0.15
0.1
0.05
ZM
US
TR
TG SY
LK
SG
RW PE
PA
NE
NL
MA MR
MW
JO
IT
ID HN
GH
SV
DO CR
CO
CA
BR
BJ AT ATBJ
BRCA
DOSV
COCR
ID IT
GHHN
MRMA
JOMW
PAPE
NLNE
SGLK
SYTG
ZM
TRUS
(b) Marginal effects when p = 9
Figure 2: Diffusion effects of FDI for column (3) in Table 2 when
p = 0 and p = 9.
28

Table 6:
Space-time effect estimates of FDI semi-elasticity for column (3) in Table 2
Cumulative Lower 0.01
Lower 0.05
Mean Upper 0.95
Upper 0.99
6
7
8
9
2
3
4
5
5
6
7
8
1
2
3
4
Horizon
0
9
Total
Horizon
0
1
2
3
4
0
1
Direct
Horizon
7
8
5
6
9
Indirect
0.484919
0.933866
1.349500
1.734284
2.090500
2.420262
2.725528
3.008110
3.269689
3.511820
0.238803
0.461536
0.669281
0.863049
1.043780
1.212353
1.369586
1.516245
1.653040
1.780637
0.723723
1.395402
2.018781
2.597332
3.134280
3.632615
4.095114
4.524355
4.922729
5.292456
-0.409884
-0.379318
-0.362849
-0.339190
-0.305745
-0.275659
-0.248587
-0.226680
-0.209851
-0.194271
-0.013385
-0.012512
-0.011697
-0.012520
-0.015101
-0.017230
-0.016080
-0.014867
-0.013743
-0.012702
-0.216882
-0.200703
-0.185731
-0.171875
-0.159054
-0.147188
-0.136208
-0.126047
-0.114148
-0.107943
0.044587
0.041088
0.037867
0.034902
0.032172
0.029452
0.024927
0.021003
0.019771
0.018774
-0.199104
0.489813
-0.184405
0.455700
-0.174813
0.425025
-0.170226
0.397408
-0.161806
0.372516
-0.150733
0.350056
-0.140557
0.329769
-0.131688
0.311427
-0.131137
0.294830
-0.123866
0.279801
-0.025501
0.736030
-0.022665
0.685331
-0.020130
0.639329
-0.017879
0.597540
-0.015879
0.559538
-0.014103
0.524941
-0.012998
0.493415
-0.012034
0.464658
-0.011142
0.438405
-0.010114
0.414419
0.246217
0.229631
0.214303
0.200132
0.187021
0.174886
0.163646
0.153231
0.143575
0.134618
1.224198
1.134635
1.078254
1.028385
1.022157
0.985116
0.975765
0.966517
0.956588
0.934286
0.438194
0.405887
0.385201
0.358208
0.336416
0.319489
0.301494
0.289637
0.276737
0.262205
1.511791
1.415918
1.325862
1.286456
1.267552
1.216827
1.178563
1.155181
1.161231
1.124389
1.510466
1.352655
1.337194
1.333139
1.288451
1.293811
1.369108
1.375182
1.380612
1.385448
0.484167
0.447490
0.414923
0.392319
0.373134
0.354512
0.337874
0.328120
0.315340
0.306132
1.748771
1.703586
1.660404
1.581172
1.534758
1.596569
1.601686
1.591845
1.588388
1.584939
the literature. The estimation results based on the system GMM method in Carkovic and Levine
(2005) and Kottaridi and Stengos (2010) mainly yield negative insignificant or positive insignificant
coefficients for FDI inflows, which we replicated mostly in Table 1. Our positive and significant
direct effect estimates of FDI inflows in Table 6 contrast with these results and highlight the effect
of omitted spatial effects in non-spatial models.
In the next section, we provide some modifications to our core model specification to subject
the estimates of Table 2 to many robustness checks.
29

In this section, we provide some modifications to our core specification to test the robustness of the
estimation results presented in Section 6.2. In the first robustness check, we estimate the Durbin
specification using the unified transformation approach described in Section 4, as this approach can
eliminate the possible unstable and/or explosive components in the data generating processes. The other robustness checks relate to how the weight matrix is defined and the time interval chosen to generate number of periods for the panel data.
We collect all results from these exercises in Table 7. In this table, the corresponding columns
for these robustness exercises are denoted with sub- and super-scripts for W . We change the specification of the weight matrix in three ways. We first calculate the weights based on distance by taking the inverse of the squared distance , i.e., w ij
= 1 /d
2 ij
, where d ij is the great-circle distance between i and j . The weight matrix with the superscript d denotes this modification. Second, we change our dense distance based spatial weight matrix with a sparse weight matrix: a distance based binary matrix such that spatial lag terms now reflect the average of pertinent variables in the nearest 10 countries for a particular country. More formally, if N i is the set of 10 nearest countries to country i , we set w ij
= 0 .
1 if j ∈ N i and 0 otherwise. We choose 10 nearest countries by comparing log-likelihood function values of different models with weight matrices based on different number of nearest countries. Our results show that when the number of nearest countries is between 9 and
13, the model log-likelihood values are relatively larger. The weight matrix constructed in this way
has the superscript 10 in Table 7.
Third, we consider the level of bilateral trade as a measure of proximity. Since this weight matrix is likely to be endogenous, we use 10 year lags for the trade volume. Here, we again employ two specifications to obtain the weights: (i) trade volume level, and (ii) exponent of the scaled trade volume. We denote the corresponding matrices with the superscripts tv and etv , respectively,
in Table 7.
Finally, we change the time interval of a period from 3 years to 5 years, i.e., τ = 5, so that
the panel now consists of 6 data points per country. The subscripts 3 and 5 in Table 7 denote this
change. For brevity, all these modifications are denoted in terms of sub- and super-scripts for W in
Table 7. For example,
W
10
3 and τ = 3, while W tv
5 denotes the specification with the distance based binary weight matrix denotes the specification with the trade volume based weight matrix and
τ = 5.
We provide estimation results only for the Durbin specification with time fixed effects for each modification, since it corresponds to the theoretical convergence equation of the spatially augmented
Solow growth model. Furthermore, the Durbin model nests both the SAR and SE models so that it will produce unbiased coefficient estimates even when the true data generating process is
characterized as either the SAR model or the SE model (LeSage and Pace, 2009, p.158).
The first column of Table 7 provides estimation results based on the unified approach suggested
in Lee and Yu (2011). The coefficient estimates are very similar to the ones reported in column (3) of
Table 2. In particular, the FDI coefficient is statistically significant with an estimate of 0
.
2088. The performance of the bias corrected QMLE based on the unified approach is also investigated through
the Monte Carlo study described in Appendix B. The same bias properties that we described for
the bias corrected QMLE based on the transformation approach earlier are also prevalent for the
unified approach. The simulation results presented in Appendix B.2 shows that the estimator
imposes trivial bias. In terms of finite sample efficiency measured by RMSE, the estimator based on the unified approach is relatively inefficient in all cases. Note that the effective sample size is different for the unified approach as it involves different matrices. At the first stage, the SDPD model is transformed with spatial difference operator ( I n
− W n
). This transformation introduces
30

multicollinearity in the resulting disturbance term ( I n
− W n
) u nt
.
To remove multicollinearity, another transformation based on the eigenvectors of the covariance of ( I n
− W n
) u nt is employed.
The second transformation changes the effective sample size for the estimation.
As shown in
Section 4, the effective sample size is
n
?
= n − m n
, where m n is the number of unit eigenvalues of
W n
. Therefore the standard errors reported in the first column of Table 7 are relatively larger.
With the results reported in the second and the third columns of Tables 7, we examine whether
our results for the Durbin model in Table 2 change significantly when we replace the spatial weight
matrix with W d
3 and W
10
3
. As indicated by the log-likelihood function values in columns (2) and
(3) of Table 7, the original weight matrix specification
W fits the data better. The Wald test results indicate that null hypothesis of cointegration can be rejected around 5 percent level in both columns. The SAR model is rejected in both columns, but the SE model can only be rejected for the W
3 d specification. The estimated coefficients are somewhat similar to the ones in column (3) of
Table 2 in terms of sign, magnitude, and significance. The coefficient of FDI inflows is significant
at 5 percent level in both columns and has a similar magnitude as before. Interestingly though, the spatial lag of the human capital variable is now insignificant for the W
10
3 specification. This
results suggest that human capital spillovers may instead stem from non-immediate neighbors.
22
Turning to columns (3) and (4), we see that the spatial and spatial-time lags of the log output per capita are now insignificant. Furthermore, the SAR model cannot be rejected for W etv
3
. The SE model cannot be rejected for both W
3 tv and W etv
3 at 5 percent level. The main issue with using trade volume based weights is the potential endogeneity. The spatial econometrics literature has recently consider estimators that are robust to potential endogeneity in the weight matrix (Kelejian and
Piras, 2014; Qu and Lee, 2015). However, these estimators are suggested for cross-sectional models
and their panel data extensions are not yet available. Moreover, the form of endogeneity assumed in these papers have very strict forms, i.e., these estimators work under quite restrictive assumptions about the form of the endogeneity. Therefore, we choose not to place too much meaning to the results in the columns corresponding to the trade volume based weights. Despite this endogeneity
issue, the FDI variable in columns (3) and (4) is statistically significant.
23
As a final robustness exercise, we investigate the effect of changing the length of time intervals in constructing the panel data in columns (5) through (8). Focusing on the results in column (6), neither the SAR nor the SE model can be rejected at 5 percent level. We see that the time lag of the dependent variable now has a smaller coefficient as expected. However, its spatial lag is now insignificant. The coefficient of the physical capital variable is now higher, supporting the claim that physical capital elasticity of output is higher in the long-run. The coefficient of human capital variable has the correct sign now but is still insignificant. Interestingly though, the coefficient of the drag variable is now very small, casting doubt on its economic significance. The estimate of the
FDI variable are larger than the estimates reported for the 3 year interval cases in Table 2. The
coefficient is significant at 5 percent level in columns (5) and (6), but only significant at 10 percent level in the last column. The potential endogeneity in the weight matrix is still an issue to keep in mind here.
Overall, the parameter estimates in these robustness exercises generally imply the same set of
inference we obtained in column (3) of Table 2. In particular, the coefficient estimates for FDI
22
For the human capital variable, we also tried average total years of schooling for the population 15 and over from
Barro and Lee (2001). This specification yielded a negative significant coefficient for the human capital variable.
The negative sign is of course implausible, which underscores the functional misspecification issues regarding the role
of human capital in the production function (Benhabib and Spiegel, 1994; Kalaitzidakis et al., 2001; Kottaridi and
Stengos, 2010).
23
These specifications can be re-estimated using the unified approach. However, this approach is not robust to endogeneity in the weight matrix.
31

Table 7: Robustness Exercises: Bias Corrected QML Estimation Results ln ln ln ln(
FDI
W
W
W
W
W
W
λ
Y s s n
× n,t − 1 k h
×
×
×
×
×
+ ln ln ln ln
.
ln(
FDI
Half-life
05)
Y
Y s s n k h
Wald-test nt n,t
+
−
.
(Cointegration)
Wald-test (SAR)
F-test (time)
1
05)
(convergence)
Wald-test (SE)
Uni. App.
0.9456
∗∗∗
(0.0186)
0.0819
∗∗∗
(0.0139)
-0.0056
(0.0121)
-0.0946
∗∗∗
(0.0172)
0.2088
∗∗
(0.1037)
0.2666
∗∗∗
(0.0745)
-0.2552
∗∗∗
(0.0892)
-0.0402
(0.0413)
0.1204
∗∗∗
(0.0407)
-0.0695
(0.0647)
0.1857
(0.3490)
0.0187
∗∗∗
(0.0066)
37.1637
0.6454
[0.4217]
11.9945
W d
3
0.9253
(0.0175)
0.0812
∗∗∗
(0.0137)
-0.0058
(0.0122)
-0.0875
∗∗∗
(0.0169)
0.2325
∗∗
(0.1040)
0.2492
(0.0474)
-0.2230
(0.0514)
-0.0296
(0.0235)
0.0800
∗∗∗
(0.0247)
0.0146
(0.0389)
0.2354
(0.1758)
0.0259
∗∗∗
(0.0063)
26.7801
3.8085
∗∗∗
∗∗∗
[0.0510]
12.5164
∗∗∗
W 10
3
0.9276
-0.0023
0.2362
∗∗∗
(0.0179)
0.0860
∗∗∗
(0.0136)
(0.0118)
-0.0899
∗∗∗
(0.0171)
∗∗
(0.1018)
0.3299
∗∗∗
(0.0665)
-0.3097
∗∗∗
(0.0681)
0.0057
(0.0373)
0.0424
(0.0342)
-0.0565
(0.0654)
0.0874
(0.2946)
0.0251
∗∗∗
(0.0064)
27.6588
3.4945
[0.0616]
3.3139
W tv
3
0.8802
0.0075
∗∗∗
(0.0161)
0.0986
∗∗∗
(0.0135)
0.0089
(0.0119)
-0.0915
∗∗∗
(0.0173)
0.2250
∗∗
(0.1034)
-0.0021
(0.0145)
-0.0017
(0.0088)
(0.0315)
0.0410
∗
(0.0245)
0.1013
∗∗
(0.0483)
-0.3462
(0.2201)
0.0425
∗∗∗
(0.0061)
16.3024
30.0336
[0.0000]
9.0086
W etv
3
0.8853
0.0895
∗∗∗
(0.0179)
0.0003
-0.0725
∗∗
(0.0305)
0.2450
∗∗∗
∗∗
(1.0082)
-0.5962
(1.5671)
1.7473
(2.1059)
0.2401
0.1776
[0.6734]
1.1868
W
0.8815
0.1278
0.4068
(0.0606)
0.1258
∗∗
(0.0573)
0.0255
(0.0528)
0.5263
(1.4856) (0.5946)
0.0406
∗∗∗
0.0252
∗∗∗
(0.0064) (0.0066)
17.0639
27.4741
0.7046
[0.4013]
6.5122
5
∗∗∗
(0.0169) (0.0292)
∗∗∗
(0.0243)
-0.0027
(0.0221) (0.0232)
-0.0081
(0.0164)
∗∗
(0.1099) (0.2048)
0.2901
0.4337
∗∗∗
(0.5035) (0.0652)
0.0205
-0.3525
∗∗∗
(0.2530) (0.0772)
-0.4130
-0.0755
W tv
5
0.7985
0.0247
0.4117
∗∗∗
0.1385
∗∗∗
-0.0071
(0.0172)
∗
W etv
5
0.8011
0.0305
0.6564
∗∗∗
(0.0264) (0.0271)
(0.0243) (0.0553)
0.1602
∗∗
(0.0229) (0.0731)
0.3225
∗∗
(0.1454)
∗∗∗
(0.2132) (0.2520)
-0.0067
0.3327
(0.0249) (0.6487)
0.0336
∗∗
-0.4341
(0.0136) (0.3517)
-0.0910
∗
-9.1290
∗∗
(0.0533)
0.0511
(4.1036)
11.4933
∗∗
(0.0449) (5.7796)
0.1432
∗
27.8738
∗∗
(0.0840) (12.1310)
0.0655
19.3637
∗∗
(0.3826) (8.8574)
0.0450
∗∗∗
0.0444
∗∗∗
(0.0066) (0.0068)
15.4048
15.6266
19.9058
0.2947
[0.0000]
6.5424
[0.5872]
5.6591
[0.0174]
11.1971
[0.0476]
[0.0139]
12.5914
[0.0275]
[0.5067]
6.7900
[0.2367]
[0.0609]
9.1115
[0.1047]
[0.8803]
2.2579
[0.8124]
[0.1640]
6.8020
[0.2358]
[0.1621]
9.2525
[0.0994]
[0.2261]
3.1422
[0.6781]
12.1193
[0.0000]
2.9539
[0.0012]
3.7583
[0.0001]
3.7036
[0.0001]
1.3843
[0.1828]
0.8529
[0.5297]
3.4604
[0.0024]
0.7579
[0.6035]
1208.1367
1252.6629
1250.9838
2161.2817
2157.0732
640.3620
1188.4544
1185.4256
log-likelihood
Note:
Standard errors are in parentheses and p -values are in brackets.
∗∗∗ if p < 0 .
01 ,
∗∗ if 0 .
01 ≤ p < 0 .
05, and
∗ if
0 .
05 ≤ p < 0 .
10. Column 1 presents the results from the unified approach corresponding to column 3 in Table 2. In columns
3 through 8, the subscripts denote the length of time intervals chosen to generate the panel. The superscripts denote how the weights are generated: d stands for the inverse of the great-circle distance, 10 stands for the nearest 10 neighbors, tv denotes trade volume, and etv denotes exponent of the scaled trade volume. Wald-test (Cointegration), Wald-test (SAR), Wald-test
(SE) denote, respectively, the Wald test for the null hypotheses H
0
: λ
0
+ γ
0
+ ρ
0
= 1, H
0
: η
0
= 0, and H
0
: ρ
0
= − γ
0
λ
0
, and
η
0
= − λ
0
β
0
.
32

inflows are positive and significant, confirming our conclusion from the previous section.
Despite the notion that FDI should have a positive significant impact on the economic growth of host countries, the empirical studies have shown no substantial evidence for the positive effect. As an increasing number of countries implement policies designed at promoting FDI inflows, we think that it is important to identify the missing positive effect in the data. We think that the culprit for inconclusive findings so far is the textbook Solow model which is often the choice of underlying theoretical model to derive the regression specifications to study the relationship between FDI and economic growth. The assumptions of the Solow model yield a major shortcoming for the resulting regression specification: an isolated and closed economy of the Solow growth model cannot reflect the real world in which countries interact in various ways.
In this study, we overcome this shortcoming by implementing a modified version of the textbook
Solow model, which allows for interactions among countries via a modified total factor production function. We use the corresponding empirical equation (SDPD) of the theoretical convergence equation of the spatially augmented growth model to investigate the effect of FDI on economic growth. The main characteristic of the new estimation equation is that the spatial dependence among countries is incorporated into the estimation equation. As a result, the output per-worker of a country not only depends on its domestic pertinent variables but also on the output per-worker and exogenous variables of other countries. Our empirical results based on this new specification indicate that FDI indeed has a significant positive effect on the output per worker of host countries.
We close by making some suggestions for future research. The model specification and estimation approach presented in this paper can also be used to study the growth impact of FDI at a disaggregated level by using regional or even sectoral level data. By disaggregating the FDI data across sectors, the industry-specific differences can be properly controlled to allow more precise and nuanced estimation results for the growth impact of sectoral FDI in host countries. Besides the sectoral growth impacts, the sectoral FDI spillovers across different sectors can also be explored in disaggregated studies. All these issues remain to be studied in future.
33

Table 8: Variable Definitions and Descriptive Statistics
Number of observations: N=85, T=10
Variables
Output per-worker
(ln Y nt
(ln( n
)
Investment rate (ln
Human capital (ln
Pop. growth rate
+ 0 .
05))
Inward FDI Flows s s h k
)
)
Definition logarithm of real GDP per-worker logarithm of the share of gross investment in GDP logarithm of secondary school enrollment rate logarithm of the growth rate of working age population
The share of inward
FDI flows in GDP mean std.
min max overall 9.3419
1.3328
6.2167
11.524
between within
1.3263
0.1896
6.7417
8.6634
11.2512
10.0420
overall -1.6116
0.4509
-3.5279
-0.4158
between 0.3959
-3.3523
-0.8597
within 0.2197
-2.4309
0.2335
overall -0.7638
0.8115
-3.5468
0.4549
between within
0.7580
-2.9225
0.1690
0.2999
-2.4896
0.9494
overall -2.6437
0.2184
-4.2674
-1.6785
between within
0.1459
0.1632
-2.9632
-4.2267
-2.3746
-1.8063
overall 0.0237
0.0381
-0.3425
0.4104
between 0.0232
-0.0269
0.1316
within 0.0304
-0.2918
0.3257
1. The variables in the table are constructed from a panel data set over the period 1980-2010 for 85 countries.
We choose three-year time intervals to construct the variables so that we have ten data points over the whole period. Then, the variables are constructed by taking averages over non-overlapping time-spans.
2.
For the Pop.
growth rate variable, we calculate the number of workers for a country i at time t by
RGDP CH it
× P OP it
/RGDP W it
, where RGDP CH it is real GDP per-capita computed by the chain method,
P OP it is the total population, and RGDP W it is real GDP per-worker computed by the chain method.
Argentina, Australia, Austria, Bangladesh, Belgium, Benin, Bolivia, Botswana, Brazil, Burundi,
Cameroon, Canada, Central African Republic, Chile, Colombia, Congo, Congo Democratic, Costa
Ghana, Greece, Guatemala, Honduras, Hong Kong, India, Indonesia, Ireland, Israel, Italy, Jamaica, Japan, Jordan, Kenya, Korea Rep., Malawi, Malaysia, Mali, Mauritania, Mauritius, Mexico, Morocco, Mozambique, Nepal, Netherlands, New Zealand, Nicaragua, Niger, Norway, Pakistan, Panama, Papua New Guinea, Paraguay, Peru, Philippines, Portugal, Rwanda, Senegal, Sierra
Leone, Singapore, South Africa, Spain, Sri Lanka, Sweden, Switzerland, Syrian Arab Republic, Tanzania, Thailand, Togo, Trinidad and Tobago, Tunisia, Turkey, Uganda, United Kingdom, United
States, Uruguay, Venezuela RB, Zambia, Zimbabwe.
34

In this section, we provide some evidences on the performance of bias corrected QML estimators
suggested in Lee and Yu (2010a) and Lee and Yu (2011). We consider the following model
Y nt
= λ
0
W n
Y nt
+ γ
0
Y n,t − 1
+ ρ
0
W n
Y n,t − 1
+ X nt
β
0
+ W n
X nt
η
0
+ c n 0
+ α t 0 l n
+ u nt
.
(B.1)
We consider two data generating processes for the above model. Both data generating processes are based on the same parameter values. Based on our estimation results, we set ( λ
0
, γ
0
, ρ
0
)
0
=
(0 .
3 , 0 .
8 , − 0 .
2)
0
β
0
. In our application X nt
= (0 .
1 , 0 .
01 , − 0 .
08 , 0 .
4)
0 and η
0
= (ln s k
, ln s h
, ln( n + g + δ ) , F ) is n × 4 matrix and we set
= ( − 0 .
05 , 0 .
06 , 0 .
01 , 0 .
3)
0
. For the first data generating process
(Model 1), the elements of X nt
, c n 0
α t 0 and u nt are generated from i.i.d Normal(0 , 1). Following
Lee and Yu (2010a), we generate the spatial panel data with 20 +
T periods and then take the last
T periods as our sample. In the second data generating process (Model 2), we use sample moments of our data set to generate exogenous and fixed effects. The country and time fixed effects are not identified in this model therefore we cannot separately estimate them from the model. The identification problem is present since a common constant can be added to country effects and subtracted from the time effects without changing the model. Therefore, we can only estimate demeaned country or time fixed effects. Let d ˆ n be the demeaned estimate of the country fixed
effects. By using the results in (4.7) and (4.8) , we recover the demeaned country fixed effects from
the estimation of (B.1) according to
d ˆ n
= J n
( I n
− ˆ n
W n
) Y nT
− ˆ n
W n
Y nT , − 1
− ˆ n
Y nT , − 1
− X nT
β n
− W n
X nT
η n
.
(B.2)
Then the estimates of the time fixed effects can be recovered from
ˆ tn
=
1 n l
0 n
( I n
−
ˆ n
W n
) Y nt
− ˆ n
W n
Y n,t − 1
− ˆ n
Y n,t − 1
− X nt
ˆ n
− W n
X nt
ˆ n
− d ˆ n
(B.3)
Following Hauk and Wacziarg (2009), we stack the sample data and the estimated country fixed
effects into an n × (4 T + 2) matrix in the following way:
D n
=
 ln s k
11

 ln s k
21



 ln s k
31
.
..
ln s k n 1 ln s k
12 ln s k
22 ln s k
32
.
..
ln s k n 2
. . .
ln s k
1 T
. . .
ln s k
2 T
. . .
ln s k
3 T
. ..
.
..
. . .
ln s k nT
. . .
F
11
. . .
F
21
. . .
F
31
. ..
..
.
. . .
F n 1
. . .
F
1 T
. . .
F
2 T
. . .
F
3 T
. ..
..
.
. . .
F nT
Y
10
ˆ
1 n

Y
20
Y
30
.
..
c
2 n c
3 n
.
..






.
Y n 0
ˆ nn
(B.4)
We calculate the sample mean and covariance of the variables in the above matrix. Let µ
D n and Ω
D n be, respectively, the sample mean vector and covariance matrix of
D n
. Then, we generate our variables from a multivariate normal distribution with mean µ
D n and covariance Ω
D n
. Then
the dependent variable is generated according to (B.1). Finally, for both data generating processes,
we generate the elements of u nt from i.i.d Normal(0 , 1). We consider ( n, T ) = (85 , 6) and ( n, T ) =
(85 , 10) in both cases. In the second case (Model 2), where ( n, T ) = (85 , 10), we average our sample data over 3 years periods so that we have 10 data points. We use the distance based weight matrix
described in Section 2 in this simulation. Re-sampling is done 10,000 times.
The simulation results are presented in the following tables. In Tables 9 and 10, the empirical
mean (mean), the bias (Bias), the empirical standard error (Std.Err.), and the root mean square error (RMSE) of parameter estimates are presented.
35

Table 9: SDPD Monte Carlo Results
λ γ ρ β
1
β
2
β
3
β
4
Model 1 : (n,T)=(85,6)
Mean
Bias
Std.Err.
RMSE
Model 1 : (n,T)=(85,10)
Mean
Bias
Std.Err.
RMSE
Model 2 : (n, T)=(85,6)
Mean
Bias
Std.Err.
RMSE
Model 2 : (n,T)=(85,10)
Mean
Bias
Std.Err.
RMSE
0.288
0.714
-0.175
0.096
0.010
-0.008
0.387
-0.012
-0.086
0.025
-0.004 0.000
0.000
-0.013
0.063
0.061
0.107
0.048
0.048
0.048
0.049
0.064
0.293
-0.007
0.046
0.046
0.305
0.005
0.062
0.062
0.105
0.758
-0.042
0.037
0.056
0.655
-0.145
0.064
0.159
0.110
-0.187
0.013
0.066
0.067
-0.071
0.129
0.095
0.160
0.048
0.099
-0.001
0.037
0.037
0.103
0.003
0.226
0.226
0.048
0.010
0.000
0.036
0.036
0.047
0.037
0.226
0.229
0.048
-0.008
0.000
0.036
0.036
-0.003
0.005
0.160
0.160
0.051
0.395
-0.005
0.036
0.037
0.402
0.002
2.052
2.052
0.302
0.728
-0.131
0.105
0.019
-0.004
0.350
0.002
-0.072
0.069
0.005
0.009
0.004
-0.050
0.046
0.040
0.059
0.163
0.149
0.210
1.276
0.046
0.083
0.091
0.164
0.149
0.210
1.277
Note:
β
1
, β
2
, β
3
, and β
4 correspond to ln s k
, ln s h
, ln( n + g + δ ), and F , respectively.
The simulation results for the unified approach are provided in Table 10. The same pattern about
the bias properties is also prevalent for the unified approach. In terms of finite sample efficiency
measured with RMSE, the bias corrected QMLE of Table 9 is more efficient since the effective
sample size is smaller in the unified approach. The transformation in the unified approach reduces the sample size from 510 to 468 in this Monte Carlo study.
36

Table 10: SDPD Monte Carlo Results (Unified Approach)
λ γ ρ β
1
β
2
β
3
β
4
Model 1 : (n,T)=(85,6)
Mean
Bias
Std.Err.
RMSE
Model 1 : (n,T)=(85,10)
Mean
Bias
Std.Err.
RMSE
Model 2 : (n, T)=(85,6)
Mean
Bias
Std.Err.
RMSE
Model 2 : (n,T)=(85,10)
Mean
Bias
Std.Err.
RMSE
0.288
-0.012
0.069
0.070
0.293
-0.007
0.050
0.050
0.304
0.004
0.068
0.068
0.715
-0.085
0.066
0.107
0.757
-0.043
0.039
0.057
0.646
-0.154
0.068
0.168
-0.173
0.027
0.117
0.120
-0.186
0.014
0.074
0.075
-0.062
0.138
0.103
0.173
0.097
-0.003
0.051
0.051
0.099
-0.001
0.037
0.037
0.106
0.006
0.237
0.237
0.009
-0.001
0.050
0.050
0.009
-0.001
0.037
0.037
0.041
0.031
0.239
0.241
-0.007
0.001
0.050
0.050
-0.008
0.000
0.037
0.037
-0.007
0.001
0.166
0.166
0.390
-0.010
0.052
0.053
0.395
-0.005
0.038
0.039
0.379
-0.021
2.163
2.163
0.305
0.723
-0.128
0.104
0.016
-0.001
0.332
0.005
-0.077
0.072
0.004
0.006
0.007
-0.068
0.049
0.043
0.065
0.171
0.154
0.219
1.331
0.050
0.088
0.097
0.171
0.155
0.219
1.333
Note:
β
1
, β
2
, β
3
, and β
4 correspond to ln s k
, ln s h
, ln( n + g + δ ), and F , respectively.
37

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