\documentclass[a4paper]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx,color}
\usepackage{setspace}
\usepackage[a4paper, margin=1in, top=1.5in]{geometry}
\usepackage{url}
\usepackage{hyperref}
\hypersetup{colorlinks=true}
\hypersetup{linkcolor=blue}
\hypersetup{urlcolor=blue}
\hypersetup{citecolor=blue}
\usepackage[hang,flushmargin]{footmisc}
\usepackage{booktabs}
\usepackage{fixltx2e}
\usepackage{caption}
\usepackage{subcaption}
\usepackage{longtable}
\usepackage{rotating}
\usepackage{pdflscape}
\usepackage{indentfirst}
\usepackage{lscape}
\usepackage{tabularx}
\usepackage{float}
\usepackage{placeins}
\usepackage{breqn}
\usepackage{enumitem}
\usepackage{dcolumn}
\usepackage{cleveref}
\usepackage{microtype}
\usepackage{multirow}
\usepackage{xcolor,colortbl}
\usepackage{ragged2e}
\usepackage{bm}
\usepackage{array}
\usepackage{afterpage}
\usepackage{titling}
\usepackage{soul}
\setlength{\thanksmarkwidth}{0pt}
\thanksfootextra{\hspace*{-1em}}{}
\setlength{\thanksmargin}{0em}
\newcolumntype{C}[1]{>{\centering\arraybackslash}p{#1}}
% --------------------- The package for bibliography
\usepackage{natbib}
\newenvironment{mypar}[2]
{\begin{list}{}%
{\setlength\leftmargin{#1}
\setlength\rightmargin{#2}}
\item[]}
{\end{list}}
\begin{document}
\title{Infrastructure and Trade: A Meta-Analysis\thanks{The authors would like to thank the audience at the following paper presentations for valuable comments and discussions: 9th World Congress of Regional Science Association International; Timisoara, Romania, May 9-11, 2012; 12th PRSCO Summer Institute and the 4th International Conference of RSAI on Regional Science and Sustainable Regional Development, Renmin University, Beijing, China, July 3-6, 2012; Meta-analysis in Economics Research Network (MAER-Net) Colloquium, Edith Cowan University, Perth, Australia, September 18-20, 2012; New Zealand Productivity Commission, Wellington, New Zealand, September 28, 2012; Tinbergen Institute, Amsterdam, The Netherlands, November 26, 2012; Economics Department, University of Canterbury, Christchurch, New Zealand, May 24, 2013. Another version of this manuscript is also available online as a UNU-MERIT working paper with serial number 2013-032.}}
\date{}
\author{Mehmet Guney Celbis\thanks{UNU-MERIT, Maastricht Graduate School of Governance, Maastricht University. E-mail: celbis@merit.unu.edu}\and
Peter Nijkamp\thanks{Department of Spatial Economics, Free University of Amsterdam. E-mail: p.nijkamp@vu.nl} \and
Jacques Poot\thanks{National Institute of Demographic and Economic Analysis, University of Waikato. E-mail: jpoot@waikato.nz}}
\maketitle
\vspace{1cm}
\renewcommand{\arraystretch}{1.5}
\renewcommand\thesubsection{\alph{subsection})}
\renewcommand{\abstractname}{\large Abstract}
\begin{abstract}
\large
\noindent Low levels of infrastructure quality and quantity can create trade impediments through increased transport costs. Since the late 1990s an increasing number of trade studies have taken infrastructure into account. The purpose of the present paper is to quantify the importance of infrastructure for trade by means of meta-analysis and meta-regression techniques that synthesize various studies. The type of infrastructure that we focus on is mainly public infrastructure in transportation and communication. We examine the impact of infrastructure on trade by means of estimates obtained from 36 primary studies that yielded 542 infrastructure elasticities of trade. We explicitly take into account that infrastructure can be measured in various ways and that its impact depends on the location of the infrastructure. We estimate several meta-regression models that control for observed heterogeneity in terms of variation across different methodologies, infrastructure types, geographical areas and their economic features, model specifications, and publication characteristics. Additionally, random effects account for between-study unspecified heterogeneity, while publication bias is explicitly addressed by means of the Hedges model. After controlling for all these issues we find that a 1 percent increase in own infrastructure increases exports by about 0.6 percent and imports by about 0.3 percent. Such elasticities are generally larger for developing countries, land infrastructure, IV or panel data estimation, and macro-level analyses. They also depend on the inclusion or exclusion of various common covariates in trade regressions.
\
\noindent \textbf{Key words}: Infrastructure, Trade, Transportation, Communication, Public Capital, Meta-Analysis. \\
\textbf{JEL Classifications}: F10, H54, R53, C10, F1, R4.
\end{abstract}
\doublespacing
\newpage
\defcitealias{UN2010}{UNECA (2010)}
\defcitealias{Marquez2005}{M.-Ramos and M-Zarz. (2005)}
\defcitealias{Martinez2003}{M.-Zarz. and N.-Lehm (2003)}
\defcitealias{Coulibaly2005}{Coulibaly and Font. (2005)}
\defcitealias{Kurmanalieva2008}{Kurman. and Parp. (2008)}
\defcitealias{Iwanow2007}{Iwan. and Kirkpat. (2007)}
\defcitealias{Iwanow2009}{Iwan. and Kirkpat. (2009)}
\defcitealias{Hernandez2010}{Hernand. and Taning. (2010)}
\defcitealias{Portugal2012}{P.-Perez and Wilson (2012)}
\defcitealias{ABDC}{ABDC (2010)}
\defcitealias{COA2005}{Commission for Africa}
\large
\section{Introduction}
\label{sec:introduction}
Amid discussions and mixed results regarding the export-led growth hypothesis,\footnote{The export-led growth hypothesis argues that the growth of exports stimulates an economy through technological spillovers and other externalities \citep{Marin1992}} and the debates on the reasons and consequences of running persistent trade deficits, ways to increase competitiveness other than through exchange rate interventions, tariffs and quotas have been attracting interest. On the other hand, in the gravity model of trade, transport costs are seen as a determining factor in trade flows. Regarding this relationship between transport costs and trade, \citet[p.149]{Volpe2014} state that ``the extent to which these costs matter is, however, far less well-established." As a result, with respect to transport costs, the effects of trade-related infrastructure on trade flows have been increasingly become a focal point in studies examining the trade performance of countries and regions in recent years.
The present study uses meta-analysis and meta-regression techniques to synthesize various ``quantitative opinions" \citep{Poot2014} that can be found in this literature. The type of infrastructure that we focus on is mainly public infrastructure in transportation and communication. Our meta-analysis has several objectives. Firstly, since all estimated effects are in the form of comparable elasticities, we can calculate precision-weighted averages of the likely impact of a given percentage increase in transportation infrastructure, broadly interpreted, on a country's trade. Secondly, we show that this likely impact is larger in developing countries and, moreover, likely to be trade balance enhancing. Thirdly, we show how such weighted average estimates from the literature are linked to a wide range of study features. Fourthly, the systematic analysis of all studies conducted to date can provide a platform for designing new primary studies. Fifthly, our meta-regression analysis is more transparent and replicable than a conventional narrative literature review. The data, Stata code and additional results can be downloaded.\footnote{They are available at \url{http://merit.unu.edu/staff/celbis/}.}
Infrastructure is a multidimensional concept and is measured in various ways, not just in relation to trade performance but also in estimating its impact on growth, welfare, efficiency, and other types of economic outcomes. As will be seen in our literature survey, empirical research often defines infrastructure as a portfolio of components, meaningful only in an integrated sense. Consequently, there exists a wide range of approaches in the literature regarding the conceptualization and classification of infrastructure. \citet[p.336]{Martin1995} define public infrastructure as ``any facility, good, or institution provided by the state which facilitates the juncture between production and consumption. Under this interpretation, not only transport and telecommunications but also such things as law and order qualify as public infrastructure." In this study, we focus exclusively on models that estimate the impacts of indicators of transportation and communication infrastructure. Recognizing the ``collective" nature of infrastructure, we pay specific attention to variation in effect size in terms of the way in which infrastructure is measured in the primary studies. Nonetheless, the remaining types of public infrastructure such as rule of law, regulatory quality, etc. are to some extent considered by controlling for such attributes in the meta-regression models employed in this study.
We collected a large number research articles that use regression analysis with at least one transportation and/or communication infrastructure-related factor among the explanatory variables, and a dependent variable that represents either export or import volumes or sales. These papers have been collected by means of academic search engines and citation tracking. Our search yielded 36 articles published between 1999 and 2012 which provided sufficiently compatible information for meta-analytical methods. These papers are broadly representative of the literature in this area. Section 5 describes the selection of primary studies and coding of data.
The rest of this paper is structured as follows. \Cref{sec:literature} provides a short narrative literature survey. The theoretical model that underlies most regression models of merchandise trade flows and the implications for meta-regression modeling are outlined in \Cref{sec:theory}. The meta-analytic methodology is briefly described in \Cref{sec:methodology}. The data are discussed in \Cref{sec:data}, which is followed by descriptive analysis in \Cref{sec:descriptive} and meta-regression modeling in \Cref{sec:regression}. \Cref{sec:conclusion} presents some final remarks.
\section{Literature review}
\label{sec:literature}
The broad literature on infrastructure and trade provides certain stylized facts: the relative locations of trade partners and the positioning of infrastructure, together with the trajectories of trade, can be seen as integral features that play a role in the relationship between infrastructure and trade flows. The location of physical infrastructure and the direction of trade strongly imply a spatial dimension to the relationship and can be subject to various costs that are closely linked with space, infrastructure quality and availability. Thus, the relationship in question is usually assessed in relation to space and trade costs. For instance, \citet[p.66]{Donaghy2009} states that ``trade, international or interregional, is essentially the exchange of goods and services over space. By definition, then, it involves transportation and, hence, some transaction costs." The analysis of the impact of transport costs on trade has a long history starting with \citet{Vonthunen1826}, and later elaborated by \citet{Samuelson1952,Samuelson1954} \citet{Mundell1957,Geraci1977,Casas1983,Bergstrand1985} and others. The specific role of infrastructure in trade has been attracting increasing attention more recently. Especially after seminal studies such as \citep{Bougheas1999} and \citet{Limao2001}, who empirically demonstrate that infrastructure plays an important role in determining transport costs, the relationship has become more prominent in the trade literature.
However, pinpointing the exact impact of infrastructure on trade remains a challenge. The range of estimates that can be found in the literature is wide. This may be due to numerous factors such as the relevant geographical characteristics, interrelations of different infrastructure types, infrastructure capacity utilization, and study characteristics. Additionally there are challenges in the ways in which infrastructure is defined. \citet[p.2]{Bouet2008} draw attention to this by stating:
\begin{mypar}{1cm}{1cm}
``Quantifying the true impact of infrastructure on trade however is difficult mainly because of the interactive nature of different types of infrastructure. Thus, the impact of greater telephone connectivity depends upon the supporting road infrastructure and vice versa. Most importantly, the precise way this dependence among infrastructure types occurs is unknown and there does not exist any a priori theoretical basis for presuming the functional forms for such interactions."
\end{mypar}
Thus, the infrastructure effects may be non-linear and may need to be explored through taking account of the interactions of different types of infrastructure. In addition to this, \citet{Portugal2012} draw attention to the possibility of infrastructure satiation by pointing out that, based on their results from a sample of 101 countries, the impact of infrastructure enhancements on export performance is decreasing in per capita income while information and communication technology is increasingly influential for wealthier countries, implying diminishing returns to transport infrastructure.
Another question that arises in assessing the impact of infrastructure on trade is the asymmetry in the impact of infrastructure in the two directions of bilateral trade. In this regard, \citet{Martinez2003} examine the EU-Mercosur bilateral trade flows and conclude that investing in a trade partner's infrastructure is not beneficial because only exporter's infrastructure enhances trade but not the importer's infrastructure. This result is not universal, however. \citet{Limao2001} consider importer, exporter, and transit countries' levels of infrastructure separately and conclude that all these dimensions of infrastructure positively impact on bilateral trade flows. Similarly, \citet{Grigoriou2007} concludes that, based on results obtained from a sample of 167 countries, road construction within a landlocked country may not be adequate to enhance trade since transit country infrastructure, bargaining power with transit countries, and transport costs also play very important roles in trade performance.
Additionally, the impact of infrastructure may not be symmetric for trade partners who have different economic characteristics. For example, \citet{Longo2004} find that both exporter and importer infrastructure play a very significant role in intra-African trade. However, these authors do not find a significant infrastructure impact regarding trade flows between Africa and major developed economies. In another study on intra-African trade, \citet{Njinkeu2008} conclude that port and services infrastructure enhancement seem to be a more useful tool in improving trade in this region than other measures.
Another issue is that infrastructure that is specific to one geographical part of an economy may impact on exports or imports at another location within the same economy. If the two locations are relatively far apart, then this may yield unreliable results when broad regions are the spatial unit of measurement. Smaller spatial units of analysis may then be beneficial. However, sub-national level studies on the impact of infrastructure on trade are relatively rare. \citet{Wu2007} provides evidence from Chinese regions and finds a positive impact of infrastructure (measured as total length of highways per square kilometer of regional area) on export performance. Similarly, in another sub-national level study, \citet{Granato2008} examines the export performance of Argentinean regions to 23 partner countries. The author finds that transport costs and regional infrastructure are important determinants of regional export performance.
In the trade literature, infrastructure is usually measured in terms of stock or density, or by constructing a composite index using data on different infrastructure types. Adopting a broad view of infrastructure, \citet{Biehl1986} distinguishes the following infrastructure categories: transportation, communication, energy supply, water supply, environment, education, health, special urban amenities, sports and tourist facilities, social amenities, cultural amenities, and natural environment. The transportation category can be classified into subcategories such as roads, railroads, waterways, airports, harbors, information transmission, and pipelines \citep{Bruinsma1989}. \citet{Nijkamp1986} identifies the features that distinguish infrastructure from other regional potentiality factors (such as natural resource availability, locational conditions, sectoral composition, international linkages and existing capital stock) as high degrees of: publicness, spatial immobility, indivisibility, non-substitutability, and monovalence. Based on the methods employed in the primary studies, we distinguish two main approaches regarding the measurement of infrastructure: the usage of variables measuring specific infrastructure types, and/or employing infrastructure indices. This point is further elaborated in \Cref{sec:data}.
\section{The theory of modeling trade flows}
\label{sec:theory}
An improvement in infrastructure is expected to lower the trade hindering impact of transport costs. Transport costs have a negative impact on trade volumes as trade takes place over space and various costs are incurred in moving products from one point to another. Such costs may include fuel consumption, tariffs, rental rates of transport equipment, public infrastructure tolls, and also time costs. A very convenient way to represent such costs is the ``iceberg melting" model of \citet{Samuelson1954} in which only a fraction of goods that are shipped arrive at their destination. In this regard, \citet{Fujita1999} refer to von Thunen's example of trade costs where a portion of grain that is transported is consumed by the horses that pull the grain wagon. \citet{Fujita1999} model the role of such trade costs in a world with a finite number of discrete locations where each variety of a product is produced in only one location and all varieties produced within a location have the same technology and price. The authors show that the total sales of a variety particular to a specific region depends, besides factors such as the income levels in each destination and the supply price, on the transportation costs to all destinations.
\citet{AvW2003} show that bilateral trade flows between two spatial trading units depend on the trade barriers that exist between these two traders and all their other trade partners. The authors start with maximizing the CES utility function:
\begin{equation}
\left( \sum_i\beta_i^{(1-\sigma)/\sigma} c_{ij}^{(\sigma-1)/\sigma} \right)^{\sigma/(\sigma-1)}
\label{eq:utility}
\end{equation}
\noindent with substitution elasticity $\sigma>1$ and subject to the budget constraint
\begin{equation}
\sum_ip_{ij}c_{ij}=y_j
\label{eq:constraint}
\end{equation}
\noindent where subscripts $i$ and $j$ refer to regions and each region is specialized in producing only one good. $c_{ij}$ is the consumption of the goods from region $i$ by the consumers in region $j$, $\beta_i$ is a positive distribution parameter, and $y_j$ is the size of the economy of region $j$ in terms of its nominal income. $p_{ij}$ is the cost, insurance and freight (cif) price of the goods from region $i$ for the consumers in region $j$ and is equal to $p_it_{ij}$ where $p_i$ is the price of the goods of region $i$ in the origin (supply price) and $t_{ij}$ is the trade cost factor between the origin $i$ and the destination $j$, and $p_{ij}$ $c_{ij}=x_{ij}$ is the nominal value of exports from $i$ to $j$. The income of region $i$ is the sum of the values of all exports of $i$ to the other regions:
\begin{equation}
y_i=\sum_jx_{ij}
\label{eq:market}
\end{equation}
\noindent Maximizing (\ref{eq:utility}) subject to (\ref{eq:constraint}), imposing the market clearing condition (\ref{eq:market}), and assuming that $t_{ij}=t_{ji}$ (i.e. trade barriers are symmetric) leads to the gravity equation:
\begin{equation}
x_{ij}=\frac{y_iy_j}{y^W} \left( {\frac{t_{ij}}{P_iP_j}}\right)^{1-\sigma}
\label{eq:gravity}
\end{equation}
\noindent where $y^W\equiv\sum_jy_j$ is the world nominal income. \citet{AvW2003,AvW2004} refer to $P_i$ and $P_j$ as ``multilateral resistance" variables which are defined as follows:
\begin{equation}
P_i^{1-\sigma}=\sum_jP_j^{\sigma-1}\theta_jt_{ij}^{1-\sigma}, \ \ \forall i
\label{eq:resistance1}
\end{equation}
\begin{equation}
P_j^{1-\sigma}=\sum_iP_i^{\sigma-1}\theta_it_{ij}^{1-\sigma}, \ \ \forall j
\label{eq:resistance2}
\end{equation}
\noindent in which $\theta$ is the share of region $j$ in world income, $\frac{y_j}{y^W}$. Therefore, the authors show in equations (\ref{eq:resistance1}) and (\ref{eq:resistance2}) that the multilateral resistance terms depend on the bilateral trade barriers between all trade partners. Moreover, the gravity equation (\ref{eq:gravity}) implies that the trade between $i$ and $j$ depends on their bilateral trade barriers relative to the average trade barriers between these economies and all their trading partners. \citet{AvW2003} finalize their development of the above gravity model by defining the trade cost factor as a function of bilateral distance ($d_{ij}$) and the presence of international borders: $t_{ij}=b_{ij} d_{ij}^\rho$; where if an international border between $i$ and $j$ does not exist $b_{ij}=1$, otherwise it is one plus the tariff rate that applies to that specific border crossing.
Infrastructures can be interpreted as the facilities and systems that influence the \textit{effective} bilateral distance, $d_{ij}$. Lower levels of infrastructural quality can increase transportation costs. Consider for example, increased shipping costs in a port when there is congestion due to insufficient space; higher fuel consumption due to low quality roads; and more time spent in transit because of shortcomings in various types of facilities. Within the context of the iceberg melting model mentioned earlier, \citet{Bougheas1999} construct a theoretical framework in which better infrastructure increases the fraction that reaches the destination through the reduction of transport costs. By including infrastructure variables in their empirical estimation using a sample of European countries, the authors find a positive relationship between trade volume and the combined level of infrastructure of the trading partners. In many other studies on bilateral trade flows, specific functional forms of the bilateral trade barriers (trade costs) that take the level of infrastructure into account have been constructed.
An important assumption in the derivation of the gravity model (\ref{eq:gravity}) is that $t_{ij}=t_{ji}$, which leads to $x_{ij}=x_{ji}$ (balanced bilateral trade). In practice, every trade flow is directional and infrastructure conditions at the origin of trade (the exporting country) may impact differently on the trade flow than conditions at the destination of trade (the importing country). Defining $k_i$ ($k_j$) as the infrastructure located in origin $i$ (destination $j$), referred to in the remainder of the paper as exporter infrastructure and importer infrastructure, this implies that $\partial d_{ij}/\partial k_i \neq \partial d_{ij}/\partial k_j$. At the same time, there are also empirically two ways to measure the trade flow: as export at the point of origin or as import at the point of destination. This implies that from the perspective of any given country $i$, there are in principle four ways of measuring the impact of infrastructure on trade:
\begin{itemize}
\item[--] The impact of $k_i$ on $x_{ij}$ (own country infrastructure on own exports)
\item[--] The impact of $k_i$ on $x_{ji}$ (own country infrastructure on own imports)
\item[--] The impact of $k_j$ on $x_{ij}$ (partner country infrastructure on own exports)
\item[--] The impact of $k_j$ on $x_{ji}$ (partner country infrastructure on own imports)
\end{itemize}
\noindent Logically, with a square trade matrix, $i$ and $j$, can be chosen arbitrarily and the impact of $k_i$ on $x_{ij}$ must therefore be the same as the impact of $k_{j}$ on $x_{ji}$ (and the impact of $k_i$ on $x_{ji}$ the same as the impact of $k_j$ on $x_{ij}$). Thus, in a cross-section setting, a regression of world trade on infrastructure gives only two effect sizes in theory. Such a regression equation, when estimated with bilateral trade data, may look like: $ln(x_{ij}) = a + b_o ln(k_i) + b_d ln(k_j) + othervars + e_{ij}$ where a is $a$ constant term, $b_o$ is the origin infrastructure elasticity of trade (exporter infrastructure), $b_d$ is the destination infrastructure elasticity of trade (importer infrastructure) and $e_{ij}$ is the error term. With $n$ countries, $i=1,...,n$ and $j=1,...,n-1$ and the number of regression observations is $n(n-1)$.
An issue that arises in practice is that regressions may yield different results when estimated with export data as compared with import data. Hence, referring to $b_{ox}$ and $b_{dx}$ as $b_o$ and $b_d$ estimated with export data (and $b_{om}$ and $b_{dm}$ similarly defined with import data), in theory $b_{ox}=b_{om}$ and $b_{dx}=b_{dm}$, but we shall see that in our meta-regression analysis $b_{ox}>b_{om}$, while $b_{dx} 0.05$ respectively. We use the method proposed by \citet{Ashenfelter1999} to formulate a likelihood function to estimate $\omega_2$ and $\omega_3$. These parameters should equal to 1 if publication bias is not present. \Cref{tab:hedges} presents the estimates associated with the Hedges publication bias procedure. In part (a) of \Cref{tab:hedges} we consider the case in which there is no observed heterogeneity assumed, i.e. there are no study characteristics that act as covariates. In part (b) of \Cref{tab:hedges}, covariates have been included. The model is estimated under the restriction that the probabilities of publication are all the same on the RHS of the table, while the LHS of the table estimates the relative probabilities with maximum likelihood.
On the LHS of \Cref{tab:hedges} (a) we see that less significant estimates are less likely to be reported. The corresponding weights for $0.01 < p < 0.05$ and $p > 0.05$ are 0.739 and 0.137 for exporter's infrastructure, and 0.280 and 0.120 for imports. The RHS shows the results of the restricted model which assumes $\omega_2 = \omega_3 = 1$ (no publication bias). The chi-square critical value at 1 percent level with two degrees of freedom is 9.21. Two times the difference between the log-likelihoods of assuming and not assuming publication bias is 63.28 for exporter's infrastructure without study characteristics and 51.2 with study characteristics, in both cases greatly exceeding the critical value and providing evidence for publication bias at the 1 percent level. Similarly, evidence for the existence of publication bias is observed for importer infrastructure as well, with test statistics of 53.62 and 151.8 for without and with covariates respectively.
We can also see that residual heterogeneity considerably decreases upon the introduction of study characteristics for both exporter and importer infrastructure (from 0.341 to 0.255 and from 0.231 to 0.0302 respectively). Accounting for publication bias and study heterogeneity (\Cref{tab:hedges}b) lowers the RE estimate of the exporter infrastructure elasticity from 0.300 to 0.254 but leaves the RE estimate of the importer infrastructure elasticity relatively unaffected (0.256 and 0.259 respectively). This is consistent with the result of the extended Egger test reported above.
Taking into account the heterogeneity that is apparent in our data set (as demonstrated formally by the Q-statistic) we now conduct MRA in order to account for the impact of study characteristics on study effect sizes.
The simplest MRA assumes that there are \textit{S} independent studies $(s=1,2,...,S)$ which each postulate the classic regression model $\bm{y}(s)=\bm{X}(s)\bm{\beta}(s)+\bm{\epsilon}(s)$, with the elements of $\bm{\epsilon}(s)$ identically and independently distributed with mean 0 and variance $\sigma^2(s)$. Study $s$ has $N(s)$ observations and the vector $\bm{\beta}(s)$ has dimension $K(s)\times1$. The first element of this vector is the parameter of interest and has exactly the same interpretation across all studies (in our case it is either the exporter infrastructure elasticity of trade or the importer infrastructure elasticity of trade).
\begin{sloppypar}
Under these assumptions, a primary study would estimate $\bm{\beta}(s)$ by the OLS estimator $\bm{\hat\beta}(s)=[\bm{X}(s)^'\bm{X}(s)]^{-1}[\bm{X}(s)^'\bm{y}(s)]$, which is best asymptotically normal distributed with mean $\bm{\beta}(s)$ and covariance matrix $\sigma^2(s) [ \bm{X}(s)^'\bm{X}(s) ] ^{-1}$. The $S$ estimates of the parameter of interest are the effect sizes. We observe the effect sizes $\hat\beta_1(1),\hat\beta_1(2),...,\hat\beta_1(s)$. Given the data generating process for the primary studies,
\end{sloppypar}
\begin{equation}\label{eq:one}
\displaystyle
\large
\hat\beta_1(s)=\beta_1(s)+ [ [ \bm{X}(s)^'\bm{X}(s) ]^{-1}\bm{X}(s)^'\bm{\epsilon}(s) ]_1
\end{equation}
\begin{sloppypar}
\noindent which are consistent and efficient estimates of the unknown parameters $\beta_1(1),\beta_1(2),...,\beta_1(S).$ These effect sizes have estimated variances $v(1),v(2),...,v(S)$. In study $s$, $v(s)$ is the top left element of the matrix $\hat\sigma^2(s)[\bm{X}(s)^'\bm{X}(s)]^{-1}$ with $\hat\sigma^2(s)=[\bm{e}(s)^'\bm{e}(s)]^'/N(s)$, and $\bm{e}(s)=\bm{y}(s)-\bm{X}(s)\bm{\hat\beta}(s)$ is the vector of least square residuals.
\FloatBarrier
\input{Hedges.tex}
\FloatBarrier
MRA assumes that there are $P$ known moderator (or predictor) variables $M_1,M_2,...,M_P$ that are related to the unknown parameters of interest $\beta_1(1),\beta_1(2),...,\beta_1(S)$ via a linear model as follows:
\end{sloppypar}
\begin{equation}\label{eq:two}
\displaystyle
\large
\beta_1(s)=\gamma_0+\gamma_1M_{s1}+...+\gamma_PM_{sP}+\eta_s
\end{equation}
\vspace{1cm}
\begin{sloppypar}
\noindent in which $M_{sj}$ is the value of the $j$th moderator variable associated with effect size $s$ and the $\eta_s$ are independently and identically distributed random variables with mean 0 and variance $\tau^2$ (the between-studies variance). Thus, equation (\ref{eq:two}) allows for both observable heterogeneity (in terms of observable moderator variables) and unobservable heterogeneity (represented by $\eta_s$). Combining (\ref{eq:one}) and (\ref{eq:two}), the MRA model becomes
\begin{equation}\label{eq:three}
\displaystyle
\large
\hat\beta_1(s)=\gamma_0+\gamma_1M_{s1}+...\gamma_PM_{sP}+\left\lbrace \underbrace{{\eta_s+[[\bm{X}(s)^'\bm{X}(s)]^{-1}\bm{X}(s)^'\epsilon(s)]_1}}_{\text{Error term of MRA}} \right\rbrace
\end{equation}
\vspace{1cm}
\noindent with the term in the curly brackets being the error term of the MRA. The objective of MRA is to find estimates of $\gamma_0,\gamma_1,...\gamma_P$ that provide information on how observed estimates of the coefficients of the focus variable are linked to observed study characteristics. Typically, the meta-analyst observes for each $s=1,2,...,S:\hat\beta_1(s)$; its estimated variance $\hat\sigma^2(s)[[\bm{X}(s)^'\bm{X}(s)]^{-1}]_{11}$; the number of primary study observations $N(s)$, and information about the variables that make up $\bm{X}(s)$, possibly including means and variances, but not the actual data or the covariances between regressors.\footnote{If covariances are known, \citet{Becker2007} suggest an MRA that pools estimates of all regression parameters, not just of the focus variable, and that can be estimated with feasible GLS.} The $P$ known moderator variables $M_1,M2,...M_P$ are assumed to capture information about the covariates and the estimation method in case the estimations were obtained by techniques other than OLS. Clearly, the error term in regression model (\ref{eq:three}) is heteroskedastic and generates a between-study variance due to $\eta_s$ and a within-study variance due to $[[\bm{X}(s)^'\bm{X}(s)]^{-1}\bm{X}(s)^'\bm{\epsilon}(s)]_1$.
We apply two different estimation methods for equation (\ref{eq:three}):\footnote{For robustness checks we also ran OLS and WLS regressions with standard errors clustered by primary study (with weights being the number of observations from each primary regression equation) and variables transformed to deviations from means, so that the estimated constant term becomes the estimated mean effect size. The results are reported in \Cref{tab:robustfinal} in the online Appendix.}
\begin{enumerate}[label=\alph*.]
\item Restricted Maximum Likelihood (REML): In REML the between-study variance is estimated by maximizing the residual (or restricted) log likelihood function and a WLS regression weighted by the sum of the between-study and within-study variances is conducted to obtain the estimated coefficients \citep{Harbord2008}. The standard error does not enter as an individual variable into this specification.
\item The publication bias corrected maximum likelihood procedure proposed by \citet{Hedges1992} and outlined above.
\end{enumerate}
\end{sloppypar}
\noindent The results of the estimation of equation (\ref{eq:three}) with the REML and Hedges estimators are shown in \Cref{tab:regressionsfinal}. All explanatory variables are transformed in deviations from their original means. We analyze the results separately for each category of variables.
\FloatBarrier
\afterpage{
\newgeometry{left=1cm}
\input{Regressionsfinal.tex}
\restoregeometry
}
\FloatBarrier
\clearpage
\subsection{Methodology}
Results from estimation with the Hedges model suggest which studies that take zero trade flows into account by using Heckman sample selection, Tobit, or Probit models, on average, estimate a lower effect size for exporter infrastructure, and a higher effect size for importer infrastructure. For robustness checks, OLS and WLS estimates are reported in the Appendix. On the matter of sample selections, the results are not consistent across MRAs. In what follows, we will pay most attention to the results of the Hedges model since this is the only model that accounts for publication bias but emphasize those results that are found in the other MRAs as well.
According to both the REML and Hedges results, studies that use instrumental variable methods to deal with potential endogeneity observe a larger impact of exporter infrastructure on trade. Consequently, econometric methodology can be seen as an important study characteristic that affects the results. Not accounting for endogeneity of exporter infrastructure leads to an underestimation of its impact on trade. This is not the case for importer (consumer) infrastructure.
The primary study using a gravity model or not does not seem to have an influence. For importer infrastructure this variable drops out. This is because, naturally, there are no effect sizes in our sample resulting from a regression where the importing partner's infrastructure is included and the model is not in gravity form. Implicitly, the inclusion of the \textit{Gravity \ model} dummy also asks the question if the distance between trade partners has been considered in the primary estimations, as distance is an essential component of a gravity specification.
\subsection{The Point at Which the Trade is Measured}
In both the REML and Hedges estimations, the coefficient on the dummy \textit{Dependent variable is exports} is significant and positive for exporter infrastructure, suggesting that own infrastructure has a greater impact when trade is measured by export data rather than by import data. This is also found in the OLS and WLS MRAs in the Appendix. As discussed in Section 3, in a primary study where all bilateral trading partners would be included and all trade is measured with transaction costs included (cif), the two effect sizes ought to be equal. However, data on any trade flow may differ dependent on measurement at the point of shipment or at the point of importation. Moreover, as noted previously, trade matrices may not be square, such as in an analysis of developing country exports to developed countries. For the same variable, the Hedges model yields a significant and negative coefficient for importer infrastructure, suggesting that the impact of the infrastructure located in the importing economy is lower when measured with respect to the exports of its partner than with respect to its own imports.
Using the Hedges model, we can predict the overall impacts of exporter (producer) infrastructure and importer (consumer) infrastructure by combining these coefficients with the constant terms, which measure the overall average effects. The results can be directly compared with the ``raw" averages reported in \Cref{tab:direction}. We get:
\begin{itemize}
\item[--] The own infrastructure of country $i$ has an average effect size of $0.254+0.345=0.599$ on the exports of $i$;
\item[--] The own infrastructure of country $i$ has an average effect size of $0.259$ on the imports of $i$;
\item[--] The infrastructure in the partner country $j$ of the exporting country $i$ has an average effect size of $0.254$ on the imports of $i$;
\item[--] The infrastructure in the partner country $j$ of the exporting country $i$ has an average effect size of $0.259-0.126=0.133$ on the exports of $i$.
\end{itemize}
We see that after controlling for heterogeneity and publication bias, the exporter infrastructure effect continues to be larger when measured with export data than with import data, ($0.599$ versus $0.254$ above, compared with $0.50$ and $0.15$ respectively in \Cref{tab:direction}), while for importer infrastructure the opposite is the case ($0.133$ versus $0.259$ above, and $0.22$ versus $0.09$ respectively in \Cref{tab:direction}). The most important result from this analysis is that from any country perspective, the impact of own infrastructure on net trade (assuming roughly balanced gross trade) is $0.599-0.259=0.340$. Alternatively, if we take the average of the exporter infrastructure elasticities $0.599$ and $0.254$, and subtract the average of the importer infrastructure elasticities ($0.133$ and $0.259$), we get a net trade effect of $0.23$. Averaging the calculations from both perspectives, an increase in own infrastructure by $1$ percent increases net trade by about $0.3$ percent. We address the macroeconomic implication of this finding in \Cref{sec:conclusion}.
\subsection{Infrastructure category}
As earlier discussed, infrastructure is defined as a collection, or portfolio of various components. As a result, in our estimations, four common measurements of infrastructure are accounted for (land, maritime or air, communication, and a composite index).
Except the REML model for importer infrastructure, all our estimations suggest that land transport infrastructure is, on average, estimated to have a larger effect size on trade than the other infrastructure categories. The Hedges model suggest that maritime and air transportation infrastructure and communication infrastructure on the importer side are found to yield higher average effect sizes compared to elasticities obtained from composite infrastructure indexes.
\subsection{Development level of the economy in which the infrastructure is located}
Both the REML and Hedges results suggest that exporter infrastructure matters more for trade if the exporting economy is developing rather than developed (also shown by the OLS model in the Appendix). This result was already noted previously and is commonly found in the literature. Moreover, importer infrastructure is less influential in trade when the importing economy is a developed one (also shown with the WLS model in the Appendix).
\subsection{Sample structure}
The Hedges, REML, OLS and WLS MRAs all suggest that estimates obtained in studies where the units of analysis were sub-regional or firm level, a lower infrastructure elasticity of trade has been observed for importer infrastructure. The same is found for exporter infrastructure, but only in the Hedges model. Sub-regional samples force the location where trade takes place and the location of infrastructure to be measured spatially more closer to one another. Therefore, such samples do not capture spillovers to the rest of the economy. The negative result on the variable \textit{Sub-national or firm level} suggests that the estimated macro effects are larger than the micro effects.
\subsection{Model specification}
The dummy variables are defined such that they are equal to unity when a particular covariate has been omitted from the primary regression. Consequently, the coefficients provide an explicit measure of omitted variable bias. The Hedges model results show some evidence that estimations which do not control for other infrastructure types (for example, if only road infrastructure is considered), the impact of importer infrastructure on trade is likely to be overestimated. The REML and Hedges models suggest that similar positive omitted variable bias arises for the importer infrastructure elasticity of trade when exporter infrastructure is not jointly considered (this is also found in the OLS and WLS MRAs).
Both models also suggest that excluding income and tariff or trade agreement variables can bias the estimate on exporter infrastructure downwards, while based on the Hedges results, an upward bias for importer infrastructure can result if tariffs or trade agreements are not controlled for. Both models suggest that omitting variables for education or human capital can cause a downward bias in the estimation of the importer infrastructure elasticity of trade (also found in the OLS and WLS MRAs). The same can be said for the estimation of both the exporter and importer infrastructure effect size based on the results of both models if governance-related variables such as rule of law and corruption are omitted. Not considering population can cause the effect size of importer elasticity to be overestimated according to the Hedges results. Omitting the exchange rate in the trade regression leads to upward bias in the estimate for exporter infrastructure (also confirmed by the OLS and WLS MRAs).
\subsection{Nature of publication}
Some evidence is provided by the Hedges model that studies which were published in highly ranked journals have estimated a larger effect size of importer infrastructure compared to other studies. A similar result is also the case for the advocacy variable: research published by institutes with potential advocacy motives for announcing a larger infrastructure effect have estimated, on average, a higher effect size for importer infrastructure. All advocacy coefficients are positive, but for exporter infrastructure, only the result of the WLS estimation reported in the Appendix is statistically significant.
\subsection{Model prediction}
A final useful exercise is to consider the goodness of fit of an MRA with respect to the set of effect sizes reported in the original studies. For this purpose we predicted for each study the mean squared error (MSE) of the comparison between the observed effect sizes and those predicted by the REML model (predictions by the Hedges model are more cumbersome). For each study, the MSE is reported in \Cref{tab:mse1} for exporter infrastructure and \Cref{tab:mse2} for importer infrastructure. Among the studies that contributed to both MRAs, the REML describes the studies of \citet{Raballand2003}, \citet{Grigoriou2007}, \citet{Bandyopadhyay1999}, \citet{Carrere2006} and \citet{Brun2005} really well. On the other hand, the studies of \citet{Iwanow2009}, \citet{Fujimura2006} and \citet{Marquez2005} yielded results that were not closely aligned with what the REML MRAs suggested.
\FloatBarrier
\input{MSE1.tex}
\input{MSE2.tex}
\FloatBarrier
\clearpage
\section{Concluding Remarks}
\label{sec:conclusion}
In this study we have applied meta-analytic techniques to estimate the impact of exporter and importer infrastructure on trade and to examine the factors that influence the estimated elasticities of this impact. The initial data set consisted of $542$ estimates obtained from $36$ primary studies. We observe evidence that publication (or file drawer) bias exists in this strand of literature in question and apply the Hedges publication bias procedure.
The key result of our research is that the own infrastructure elasticity of the exports of a country is about 0.6 and own infrastructure elasticity on the imports of a country is about 0.3. This finding suggests that exports would respond to an improvement in the overall trade-related infrastructure more than imports and that an expansion of the interrelated and integrated components of total trade-related infrastructure may have an attractive return through its impact on the external trade balance.
This result can be further elaborated. Assume that in a given economy, infrastructure is valued at about 50 percent of GDP. \footnote{This is a fairly conservative estimate that refers, for example, to the case of Canada. The report by \citet{Dobbs2013} suggests that infrastructure is valued at around 70 percent of GDP.} The resource cost of a 1 percent increase in infrastructure would be therefore about 0.5 percent of GDP. As the Hedges MRA results suggest that such an increase in infrastructure will increase exports by about 0.6 percent and imports by about 0.3 percent, starting from a situation of exports and imports being of similar magnitude, net exports will then increase by about 0.3 percent of the value of exports. The impact of this on GDP clearly depends on the openness of the economy (as measured by the exports to GDP ratio) and the short-run and long-run general equilibrium consequences. In turn, these will depend on the assumptions made and the analytical framework adopted. In any case, even under conservative assumptions the additional infrastructure is likely to have an expansionary impact in the short-run (although the size of any multiplier remains debated, see e.g. \citealt{Owyang2013}) but also in the long-run through increasing external trade. For reasonable discount rates and sufficiently open economies, it is easy to construct examples that yield attractive benefit-cost ratios for such infrastructure investment. Additionally, it has often been argued that such an expansionary policy may yield further productivity improvements.
The question remains of course what causes this differential impact of infrastructure on exports vis-a-vis imports. Consider the export demand function as presented by \citet{AvW2003}:
\begin{equation}
x_{ij}=\left( {\frac{\beta_{i}p_it_{ij}}{P_j}}\right)^{1-\sigma}y_j
\label{eq:demandlast}
\end{equation}
\noindent equation (\ref{eq:demandlast}) implies that a decline in $t$ due to improved infrastructure raises the demand for a country $i$'s (or region's) exports. Given that an exporting firm is a price taker in the foreign market and bears the transportation costs to compete there, increases in the stock or quality of origin infrastructure raise the profitability of exports to all possible destinations. On the other hand, from the point of view of a foreign firm that supplies imports to country $i$, this infrastructure enhancement in the home economy lowers the cost of transportation to one destination only. Thus, an increase in infrastructure affects all exports of the local firm but it affects only a proportion of the exports of the foreign firm. Because imports may be more income elastic than price elastic, the effect of the decrease in the price of imports (which already included the foreign freight and insurance) relative to the domestic price will be small. Consequently, the change in infrastructure in country $i$ impacts the behavior of the foreign firm that produces the imports less than that of the domestic firm that produces exports (assuming the infrastructure in other countries remained constant). Therefore, the marginal impact is at least initially larger on exports than on imports. It is important to underline that this conclusion is based on the \textit{ceteris paribus} assumption. On average, infrastructural investment in a certain country may only be expected to improve if all its trading partners do not improve their infrastructures in similar proportions. Trade is a zero-sum game and an the trade balance of an economy will only improve given that all economies in the rest of the world do not improve their infrastructures in similar proportions.
Moreover, there may also be structural asymmetries and intangible aspects adding to this difference in the exporter and importer infrastructure elasticities of trade. Infrastructure may be tailored more towards exports and not be neutral to the direction of trade. Even if the quality and stock of infrastructure is identical, the way it is utilized may differ between incoming and outgoing traffic of goods. Differences between the two functions of the same infrastructure can be due to choices such as the amount of personnel allocated or prices charged for infrastructure utilization. Another possibility that causes this asymmetry may be due to political factors. If exporters have politically more lobbying power than importers, new infrastructure approved by governments may be biased to benefit exporters more than importers. The literature would therefore benefit from further research on microeconomic mechanisms that yield the ``stylized facts" that we have uncovered in this meta-analysis.
Finally, our research provides crucial synthesized evidence for developing economies or even low-income economies where infrastructure deprivation is a fact. For instance, the 2005 report of the \citetalias{COA2005} emphasizes on the need of a functioning transport and communications system for Africa and states that the continent's transport costs ``local, national, and international - are around twice as high as those for a typical Asian country" and ``to improve its capacity to trade Africa needs to make changes internally. It must improve its transport infrastructure to make goods cheaper to move." \citep[p.14, 102]{COA2005}. Our meta-analytic evidence adds useful evidence to back the argument that areas with poor infrastructure, such as certain parts in Africa, could greatly benefit from trade-enhancing infrastructure oriented policy measures.
\iffalse
\afterpage{
\newgeometry{left=1cm}
\newpage
\raggedright
\appendix
\renewcommand\thefigure{\thesection.\arabic{figure}}
\renewcommand\thetable{\thesection.\arabic{table}}
\section{Appendix}
\label{sec:Appendix}
\setcounter{figure}{0}
\setcounter{table}{0}
\FloatBarrier
\input{Robustfinal.tex}
\restoregeometry
}
\FloatBarrier
\fi
\clearpage
\bibliographystyle{chicago}
\bibliography{References2}
\end{document}