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REVISITING THE TRADE-GROWTH NEXUS: ANONPARAMETRIC APPROACH∗
Ali Raza
Department of Economics, University of Manchester†
This Draft: June 13th, 2016
Abstract
Applying parametric models, empirical studies of the trade-growth nexus have arrived
at the consensus that the relationship is largely homogeneous and positive. This study ex-
tends this literature by identifying relevant trade proxies which are then modelled in an en-
vironment that, unlike parametric models, is not subject to functional form misspecification.
Using 7 measures of trade, we perform nonparametric regressions on TFP and GDP growth
rates since 1990. We find trade to be more relevant for the former than the latter. We also find
significant heterogeneities with greater openness being correlated with higher TFP growth.
Lastly, we find trade liberalisation to be insignificant for resource dependent countries sup-
porting the findings of Arezki and van der Ploeg (2010). Our formal tests reject traditional
parametric techniques in favour of our nonparametric models though linearities still exist.
JEL Classification: F13, F14, O13, O47.
Key Words: Trade Openness, Nonparametric Regression, Nonlinearities, Economic
Growth.
∗I am grateful to my supervisors, Dr. Emranul Haque and Dr. Simon Peters, for their guidance towards thecompletion of this study. Furthermore, Dr. Christopher Parmeter, Prof. Daniel Henderson, and Prof. ThanasisStengos have also provided valuable assistance in the estimation of the nonparametric techniques applied in thisstudy.
†Ph.D. Candidate, School of Social Sciences, Department of Economics, University of Manchester, e-mail:[email protected].
1 Introduction
Though a government has at its disposal a number of tools to enhance its population’s wellbeingfew are more important than trade policy. For instance, despite dominating academic and policycircles for almost four decades after the Second World War, protectionist policies, emphasis-ing “infant industry” arguments to development, slowly lost their appeal in the face of growingevidence that more open economies outperformed those pursuing closed policies. Through amixture of theoretical, historical and statistical evidence - coupled with the strong performanceof “open” East Asia against that of “closed” Latin America, beginning from the early 1980s,policy recommendations led to developing nations adopting (to varying degrees) more outward-looking policies. Driven by this favourable evidence, institutions such as the IMF and the WorldBank have promoted such policies by insisting that developing nations seeking assistance liber-alise their trade regimes and external sectors (Edwards, 1993; Dornbusch, 1992). As a result ofthis increasing tendency towards liberalisation1, the world economy experienced rapid institu-tional reconcilement which culminated with the establishment of the World Trade Organisationin 1995.
The channels through which increased openness may generate economic growth are many2 butit is generally accepted that markets must be unrestricted and free from government interven-tion such that resources can flow to their most efficient use. If markets are not free and tradeis restricted then, according to advocates of greater openness, economic growth is stunted sinceagents, individuals or otherwise, cannot reap the benefits of costless contractual arrangements.Thus, greater openness invariably leads to an improvement in living standards and overall eco-nomic wellbeing. That said, there has not been a consensus on how trade liberalisation shouldbe measured with studies adopting different measures as proxies. This has led to different con-clusions about the magnitude and direction of the impact of trade liberalisation on growth withthere being a growing doubt over the validity of the perceived benefits of trade liberalisation.Theory positing a favourable impact of trade on growth through technological diffusion (Gross-man and Helpman, 1991; Krueger, 1997) has been challenged by models predicting the oppositeeffect (Krugman, 1994; Redding, 2002). The body of empirical research has also not settled ona definitive conclusion with papers by Edwards (1998) and Greenaway et al. (2002) finding apositive relationship contrasted with papers by Rodriguez and Rodrik (2001) and Kneller et al.(2008) that do not.
Two key explanations have been offered for why the empirical literature has delivered conflictingresults. Firstly, the heterogeneity in findings has been attributed to omitted variable bias withconditioning variables such as education, corruption, and macroeconomic stability having beenproposed as possibly having interaction affects with trade (Winters, 2004). Secondly, and more
1In this paper, trade liberalisation, trade and openness are used interchangeably.2See Dornbusch (1992, pg. 73-75) for some prominent examples.
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relevant to this paper, it has been argued that papers that have found a positive relationshipbetween trade and growth are sensitive to model specification and/or the proxy used to measureopenness (Rodriguez and Rodrik, 2001). This paper attempts to revisit the debate by focusing onthe second concern. It does so by applying recently developed nonparametric kernel estimatorson a variety of measures capturing both trade openness and trade policy. These estimators allowus to determine the relevance of trade in a particular growth process as well as uncovering anynonlinearities in the trade-growth nexus. Since the lack of a consensus rests partly on how agrowth regression is specified (Durlauf et al., 2008), our methodology overcomes this concernas it does not explicitly model the trade-growth relationship a-priori.
That said, this paper is connected to three strands of the empirical growth literature. Firstly, itprovides further empirical evidence on the relationship between trade and growth. Secondly, itadds to the nascent literature applying nonparametric techniques to macroeconomic data. Lastly,it offers preliminary evidence of the impact of trade and trade policy across resource dependentand resource independent economies.
In this respect, our results indicate the following. Trade is more relevant for productivity growththan for real GDP per capita growth. Given that the literature has primarily focused on the latter,this suggests further work on determining the impact of trade on the former is necessary. Interms of impact, we find trade, and trade policy, to have a positive and significant effect on pro-ductivity growth - more trade intensity, lower non-tariff barriers, and a more liberal trade policyare especially beneficial. We also find a strong heterogeneity in the impact of these measuresacross resource dependent and resource independent economies. These findings generally holdwhen endogeneity is controlled for - a first application of nonparametric instrumental variablestechniques to trade data.
The remainder of the paper is structured as follows. Section 2 motivates our work by reviewingthe existing literature on the trade-growth nexus. Section 3 describes the data used in this study.Thereafter, Section 4 explains our econometric methodology. Section 5 discusses our findings.Section 6 summarises.
2 Existing Literature
Here, we review the existing empirical studies on trade so as to place our contribution withinthe current body of research. We separate our review into two distinct parts: traditional studieson trade and growth that assume a linear, parametric relationship with those that try to uncovernonlinearities, for instance threshold effects, in the impact of trade on growth. That said, weselectively review studies and other, more comprehensive reviews by Santos-Paulino (2002) andWinters (2004) of the existing literature may also be referred to.
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Early studies testing the trade-growth nexus attempt to construct indices reflecting trade restric-tiveness which are then regressed on growth rates. The earliest example is the paper of Dollar(1992) in which two indices of trade distortions, based on exchange rates, are shown to be nega-tively correlated with growth for a sample of 95 developing economies. Both indices are meant tocapture the idea that highly protectionist regimes would be more likely to have sustained higherprice levels over time. In the same vain, Sachs and Warner (1995) look at a longer time periodand construct a single index capturing trade openness. The presence of multiple indicators oftrade in a single regression can be troublesome if they are correlated among themselves. TheSachs-Warner index tries to solve this measurement issue by combining 5 aspects of trade policy- tariff barriers, non-tariff barriers, black market premia, the existence of an export marketingboard, and whether an economy is socialist - into a single dummy indicating whether an econ-omy is open (1) or closed (0). They apply arbitrary rules on the components of the index toclassify countries into each category. Their regression results indicate that open economies ex-perienced growth rates 2.5 percentage points highers than those that were closed. Sala-i-Martin(1997) confirms this finding through a sensitivity analysis.
However, researchers have criticised the appropriateness of such indices as measures of tradeopenness. Rodriguez and Rodrik (2001) cast doubt on their suitability by subjecting them tofurther robustness analyses. By including covariates which are now standard in empirical growthstudies, such as initial income and education, they show that only one of the two indices in Dollar(1992) remains robust and unchanged. Likewise, they deconstruct the Sachs-Warner index intoits 5 components and perform separate growth regressions of each finding only 2, black marketpremia and an exchange board dummy, to be significant. Consequently, they construct a newindex using only the 2 significant components and show that openness classifications remainlargely unchanged. They summarise their findings by stating that these studies suffer from modelmisspecification and/or that the indices do not truly reflect openness. Nevertheless, a key messagefrom these early studies is that further empirical work should include measures reflecting tradepolicy.
However, these early studies ignored the possibility that trade may be endogenous to growth.Two prominent examples which control for this possible endogeneity are Frankel and Romer(1999) and Yanikkaya (2003). The former treat geographical characteristics, such as distancefrom the equator and whether a country is landlocked, as potential factors and instrument tradewith fitted values from a gravity equation. They show that trade positively, and significantly,affects per income growth. However, they only use a single measure of trade which reflects tradeintensity rather than trade policy. The latter goes further by regressing a plethora of trade proxiesmeasure both intensity and trade policy. OLS, SUR and 3SLS regressions are performed andthe conventional view - that openness fosters growth - is confirmed. Two differences do arise,however: trade barriers tend to be positively correlated with growth, and the impact of trade ongrowth is weaker, in some cases insignificant, when panel methods are applied. This confirms
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the benefit of applying nonparametric kernel estimators since any resulting estimates are notcontingent on model specification.
A number of papers have also attempted to assess the impact of trade on growth by recognis-ing the importance of country fixed effects. Greenaway et al. (2002) investigate the impact ofopenness in a dynamic panel context. They use 3 dummy indicators, including the Sachs-Warnerindex, reflecting openness and perform growth regressions using the GMM estimator of Arrelanoand Bond (1991). They find that, while it has a favourable impact, trade affects growth with a lag.They uncover a J-curve type effect which lasts approximately 5 years: openness reduces growthin the short run, but increases it over time. They do argue, however, that the long-run payoffs offurther openness may be substantial. That said, noting the Rodriguez-Rodrik critiques, Wacziargand Welch (2008) construct an updated index, based on case studies and the Sachs-Warner in-dex, reflecting trade liberalisation. They argue that, since their measure is based on liberalisationdates, it is less susceptible to the criticisms leveled by Rodriguez and Rodrik (2001). Their fixedeffects analysis shows that liberalised economies experienced growth rates 1.5 percentage pointshigher post-liberalisation. They also regress their dummy on de jure openness and find that lib-eralisation raised intensity by 5 percentage points. In terms of its impact over time, they findthat trade liberalisation had a significant effect after the 1970s - a finding echoed by Vamvakidis(2002) who finds an insignificant impact of de jure openness before the 1970s. Despite this,Kneller et al. (2008) use the same index, turning it on 5 years before and after a liberalisationepisode, to find no conclusive evidence when using a difference-in-differences approach. Theycast doubt on the ability of simple dummy indicators at capturing heterogeneities in the impactof trade.
Investigating parameter heterogeneities has been the subject of the papers applying more recentlydeveloped quantile regression techniques. Foster (2008) finds that, for a sample of 75 economies,the relationship between trade and growth is generally positive and significant across the distri-bution of growth rates. This effect is particularly strong for economies at the lower quartile ofthe distribution. However, it mainly used the Wacziarg-Welch index, alongside de jure openness,without considering alternative measures. Dufrenot et al. (2010) do include more measures andreinforce the finding that economies with the lowest growth rates tend to benefit from trade themost. However, they also suggest that countries that stand to gain the most from trade in the longrun are also those that, as a result of being more open, may suffer in the short run. Nevertheless,they support the argument that openness can be a vehicle for economic convergence.
The idea that trade openness affects economic growth in a non-linear way has been fostered byliterature which has suggested that empirical findings are sensitive to country characteristics andsample size (see Rodriguez and Rodrik, 2001). An early example which focuses on the impactof trade on productivity growth is Edwards (1998). He argues that, given the inherent difficultiesin constructing trade indices, research should focus on determining whether findings are robustto alternative proxies. Performing WLS regressions on 9 different measures of trade, he finds
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that trade is beneficial, and statistically significant, for productivity growth. Adding quadraticterms to the continuous trade indicators, he finds evidence of nonlinearities although the impactis largely insignificant. In a linear framework, Miller and Upadhyay (2000) do offer evidence ofa positive impact of trade and make a stronger conclusion that openness significantly increasesproductivity growth with more outward orientated economies experiencing higher productivitygrowth over and beyond the impact of trade.
Other papers have analysed non-linearities by searching for thresholds in the impact of tradeon growth with the goal being to classify countries according to a particular regime. An earlyexample of such work is the study of Michaely (1977) which examines the link between exportgrowth and economic growth finding that a statistically significant, positive correlation is contin-gent on a country’s level of development. Other studies which consider a similar question in thecontext of policy formulation find that technological progress and its growth effects also hingeon development levels (Tyler (1981)). Such early work treats threshold effects in a superficialsense and relatively recent developments in econometric modelling have allowed the estimationof thresholds to move away from ad-hoc sample splitting to more robust estimation techniques.These threshold models are attractive in that, unlike earlier studies, they treat the threshold to beestimated as unknown prior to estimation rather than impose it onto the data. A growing liter-ature has utilised such models in varying contexts to determined thresholds in the convergencedebate with the vast majority being based on the seminal works of Hansen (1999, 2000), andCaner and Hansen (2004).
Papageorgiou (2002) employs Hansen’s (2000) data-sorting methodology to classify countriesinto “trade clubs” according to their trade share finding that openness matters little for high andlow income countries, that is, that openness is instrumental in determining the growth path (lowor high income) for middle income countries. This suggests that further research has to be un-dertaken to determine which variables can safely be classified as threshold variables (Durlauf et
al. (2005)). It has also been found that levels of development act as a threshold in determiningwhether greater trade benefits growth. Using various definitions of trade, Kim and Lin (2009)find that countries above an initial income level of $780 to $820 per capita in 1960 have benefitedmore from increased openness. Increased trade has distortionary effects depending on the chan-nels it functions through. They suggest investigating the role of geographical variables whichmay be correlated with such channels. Taking on board this suggestion, Henry et al. (2012)provide evidence that natural barriers - geographical, trade costs and market access based - havedifferent threshold effects on openness and growth. For example, countries with lower geograph-ical barriers experience lower growth as a result of increased openness whereas those with highertrade cost barriers experience the opposite effect. The important question of the timing of tradeliberalisation has also been touched upon in the literature. In particular, the convenience of un-dertaking trade liberalisation, packaged within overall policy reform, in times of crises is a pointof concern for policy makers. Treating crises as a threshold variable, Falvey et al. (2009) present
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evidence towards this end by finding that liberalisation in times of external crises - such as cur-rent account deficits - amplifies growth while in times of internal crises - such as exchange ratedepreciation - it impedes it. Their results also confirm the earlier finding of Greenaway et al.(2002) that trade liberalisation and economic growth follow a J-curve relationship.
More flexible have recently been applied to address the issue of whether trade, in the larger con-text of macroeconomic policy, is a relevant explainer of growth. Anteceded by the seminal paperof Levine and Renelt (1992) which tried to identify robust determinants of growth, these papershave revisited this issue by applying either Bayesian Model Averaging (BMA) or, as in this study,nonparametric kernel estimation. Durlauf et al. (2008) apply the former in their assessment of“theory open endedness”: the idea that given the abundance of growth theories, each is logicallyconsistent with another. They examine a host of variables, combining them as separate theories,against growth and productivity growth and, for our purposes, find that the posterior probabilityof including macroeconomic policy - trade, inflation, and government size - is nearly 1, but it isvery low for productivity growth. We take this disparity as the initial motivation of determiningthe relevance of our macroeconomic policy variables to both growth and productivity growthin a nonparametric framework. That said, their subsequent 2SLS regressions show that tradepositively and significantly affects growth, but also has a positive impact on productivity growth.
A small, but growing, literature revisits the empirical growth literature through the lens of non-parametric regression. The key strength of these papers is that their findings do not hinge onfunctional form and, hence, they are immune to potential misspecification criticisms. The semi-nal paper of Maasoumi et al. (2007) bridges the gap between the theoretical literature regardingkernel estimation and applied work, especially using macroeconomic data3. Though it is primar-ily concerned with the evolution of growth distributions over time, it demonstrates the reliabilityof nonparametric techniques - known to be demanding in their data requirements - to relativelysmall samples common in macroeconomic data. Stemming from this paper, Henderson andMillimet (2007) perform a model selection exercise, comparing parametric to nonparametric es-timators, for US bilateral trade flows. Their aim is to determine whether the gravity model oftrade, typically used as instrument (see Frankel and Romer, 1999), is best represented by a linearsetup. They apply the estimator of Racine and Li (2004) against OLS and conclude that it is.The weakness of their study, however, is that they fail to account for cross-country differencesby focusing only on national data.
Henderson et al. (2012) do consider cross-country evidence when applying the nonparametricestimator of Racine and Li (2004). They attempt to assess the validity of common growth theoriesin the same vain as Durlauf et al. (2008). In particular, they focus on macroeconomic policyand conclude that it is a relevant determinant of growth. In terms of its impact, they find that
3Other examples of nonparametric techniques being taken to macroeconomic data are Henderson et al. (2013)and Delgado et al. (2014). The former focuses on the relationship between financial development and growth, whilethe latter assesses the relevance of education in the growth process.
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trade affects growth positively and the relationship is likely to be linear. Interestingly, they alsoperform a Monte Carlo simulation of their nonparametric estimator and show that it performswell in replicating their macroeconomic, panel dataset. That said, we contribute to this studyby considering a wider range of trade measures, by focusing on a more recent sample, and byfocusing on productivity growth. More importantly, we control for the endogeneity of trade in anonparametric setup - a first in the literature.
The preceding literature review has highlighted a number of points. The overall empirical evi-dence suggests that trade causes growth, but its impact may be conditional on other variables.Parametric regressions have delivered mixed evidence due to differences in modelling strategy.Studies have not adequately determined whether trade is more relevant for productivity growththan for GDP growth. There is a need for the parametric literature to be assessed against coun-terfactual estimations using nonparametric techniques. This paper aims to add to the existingliterature by addressing all of these points.
3 Data
We study the relationship between trade and growth on a constructed panel of 99 countries span-ning the period 1990-20144. Given that the majority of the literature studies this relationshipwith historical data up to the millennium, our panel offers up to date evidence which covers thetrade liberalisation of the nineties and recent global economic downturns. We use data on growthrates of total factor productivity (TFP), measured as a Torqvist index, and real GDP per capita asour dependent variables.
3.1 Trade Proxies
Offering a suitable proxy for trade openness has been a contentious issue in the literature witha drawback of many studies being their focus on a single measure. With this in mind our dataconsists of 7 measures which reflect trade in two aspects: trade intensity and trade restrictive-ness/policy. We measure intensity as the ratio of exports and imports to GDP with respect toworld trade, and the same ratio with respect to advanced economies. The latter measure cap-tures the idea of the perceived benefits of trade with more technologically advanced economies(Yanikkaya, 2002). Trade restrictiveness is proxied by the ratio of taxes on international tradeto GDP, the simple average tariff ratio on all goods, a score reflecting the size of black marketpremia (hence the size of the shadow economy), a score measuring the extent to which non-tariffbarriers permeate trade policy. As a comprehensive measure of trade policy we also include atrade freedom score taken from the Fraser Institute (2015).
4A detailed explanation of the data and its sources is given in table 1 in the appendix.
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3.2 Covariates
In a parametric framework, Arezki and van der Ploeg (2010) find that countries endowed withlarge natural resource stocks can attenuate the so called “resource curse” by adopting more lib-eral trade policies. Motivated by this suggestion, we also assess the dichotomy between theimpact of trade in resource dependent and resource independent countries, respectively. In do-ing so, we contribute to exisiting nonparametric studies which, though following a similar logic,concern themselves with regional subsamples or OECD vs. non-OECD countries. We create ourtwo subsamples by constructing a dummy variable indicating whether a country can be perceivedas resource dependent or otherwise. Specifically, we use the minimum of total resource rents asa share of GDP for members of OPEC - highly resource dependent countries - as a benchmarkand define a country as being resource dependent if its respective resource rents are greater thanor equal to this value throughout the sampling period. Our reference to this being a measure ofresource dependence is supported by Brunnschweiler and Bulte (2008) who argue that resourceexports as a share of GDP are at best a proxy for resource dependence rather than abundance.That said, despite its simplicity, in the absence of established indices, we believe it offers anacceptable measure of resource dependency. Our definition results in 20 countries being clas-sified as resource dependent with a number of oil producing nations, such as Saudi Arabia andVenezuela, being among them. Table 2 in the appendix presents the complete classification.
Besides our main variables of interest, we also control for omitted variable bias by incorporatinga number of relevant covariates. Initial Income, measured as real GDP per capita at the begin-ning of each 5 year period, tests for conditional convergence. Gross capital formation acts as ameasure of investment and population growth proxies demographic trends. Historical empiricalresearch has shown these variables to have a significant impact on economic growth and theirinclusion in our framework allows the Solow hypothesis to be tested. We also include averageinflation rates and government spending as a share of GDP as measures of macroeconomic sta-bility. As a final covariate, we include an index of human capital, based on average years ofschooling, created by Feenstra et al. (2015). Despite Durlauf et al. (2005) identifying over100 potential regressors in the debate over convergence, we restrict our additional covariates tothese five measures for two reasons. Firstly, by judiciously including every available regressorwe increase the probability of colliniarities between explanatory variables and the likelihood ofover-fitting our model. Secondly, and more importantly, nonparametric techniques are exhaus-tive in their data requirements and are not immune to the curse of dimensionality which requiresthat we, similar to Henderson et al. (2012, 2013), adopt a parsimonious approach that focusesour attention to the effects of trade on growth and productivity growth.
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4 Methodology
The following sections outline our empirical methodology beginning with our baseline paramet-ric estimation before explaining our nonparametric estimation in relative detail.
4.1 Parametric Estimators
Common with the empirical literature, we transform our panel dataset into five non-overlapping5-year periods - 1990-1994, 1995-1999, 2000-2004, 2005-2009, 2010-2014 (inclusive)5 - andbegin by estimating parametric models of the form:
git = β0 +∑T−1t=1 β1Dt +β2Drd
i +β3ln(yit)+β4ln(tradeit)+β5ln(kit)
+β6ln(govtit)+β7ln(πit)+β8ln(nit)+β9ln(hcit)+ εit(4.1)
where git is the growth rate of real GDP per capita or TFP for country i at time t; Drdi is our
resource dependence dummy, ln(yit) measures initial income at the beginning over every five yearperiod, ln(tradeit) are our trade proxies, ln(kit) measures capital investment measure, ln(govtit)
measures government size, ln(πit) measures inflation, ln(nit) measures population growth, andln(hcit) is a composite human capital index; εit is an additive error term distributed with zeromean.
4.1.1 Correct Parametric Specification
The workhorse functional form test in a parametric framework is the Reset test based on Ramsey(1969, 1974). It rests on specifying a parametric model with higher order terms and performingan F-test on these terms to determine their significance. However, given that we wish to deter-mine non-linearities and not specify them a-priori, this test is inappropriate. For this reason,the nonparametric literature has developed a number of correct specification tests in a more gen-eral framework. Examples are the works of Zheng (1996), Li and Wang (1998), and Fan andLi (2001). In this paper, we apply the correct specification test of Hsiao et al. (2007) whichextends these studies to include discrete and continuous independent variables. Denoting equa-tion (4.1) as git = m(xit ,β ), where β is a k dimensional parameter vector, and its conditionalmean as E(git |xit), this test amounts to a test of H0 : pr.[E(git |xit) = m(xit ,β )] = 1 for some β
vs. HA : pr.[E(git |xit) = m(xit ,β )] 6= 1 for any β where H0 implies that equation (4.1) is correct
5Since liberalisation episodes are typically gradual, and given the prevalence of business cycle fluctuations, ourtransformation allows us to focus on the medium term impact of this relationship. This follows the suggestion ofWinters (2004) with supporting evidence from Greenaway et al. (2002) that such J-curve effects last approximatelyfive years.
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versus a nonparametric alternative. The resulting test statistic is defined as
Jn = n|h|1/2 In
σn∼ N(0,1)
where In =1
n(n−1) ∑ni=1 ∑
nj=1, j 6=i uiu jwi jx and σ2
n = 2n(n−2)|h|∑
ni=1 ∑
nj=1, j 6=i u2
i u2jw
2i jx where w is a
weighting matrix and ui = git−m(xit , β ) are the residuals obtained by estimating equation (4.1).Under the null, Jn converges to a standard normal distribution.
Hsiao et al. (2007) demonstrate the test’s relative robustness, in terms of size and consistency,and applicability to mixed data. A rejection of the null hypothesis provides evidence againstequation (4.1) being correctly specified.
4.2 Nonparametric Estimators
Equation (4.1) implicitly assumes that the conditional mean of growth is linear in the explanatoryvariables. If this is the case then, under additional Gauss-Markov assumptions, its coefficientestimates are suitable for inference. However, if the true conditional mean is in fact nonlinearin its arguments, equation (4.1) would deliver coefficient estimates that would ultimately leadto misleading policy conclusions. Furthermore, a growth process modelled as in equation (4.1)delivers a single coefficient estimate for each regressor implying that the effects on growth of thatparticular regressor are homogeneous. This ignores the possibility of heterogeneity in the partialeffects of, for instance, trade. Since part of our analysis is concerned with the impact of tradein resource dependent countries, such an approach may lead to incorrect policy prescriptions.Quantile regression techniques, examples of which are mentioned earlier or fitting higher orderpolynomials to trade offer solutions but nevertheless rest on assuming a functional form for thegrowth process. We let our data determine the relationship and estimate our nonparametric modelas:
gi = m(xi)+ui; i = 1, ...,n (4.2)
where gi is the growth rate of real GDP per capita or TFP for country i; m(.) is a smooth functionwhose functional form is ambiguous; xi is our matrix of covariates; ui is an additive error termdistributed with zero mean.
Though equation (4.2) is ambiguous in its functional form, it can be interpreted as the condi-tional mean of gi. This forms the basis of the two nonparametric estimators we apply in thispaper: local-constant least squares (LCLS) and local-linear least squares (LLLS). Both of theseestimators do not require a specific assumption for the conditional mean nor for the distributionof ui in equation (4.2). Furthermore, they allow us to tackle the issue of the type of growth pro-cess trade is relevant for, if any, and to determine the shape of its impact on growth. We describeboth in the following sections.
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4.2.1 Local-Constant Least Squares
We begin by estimating our nonparametric regressions by LCLS which, in essence, calculatesa locally weighted average of gi. Formally, the LCLS estimator of equation (4.2) is (in matrixform)
m(xi) = [i′k(xi)i]−1i′k(xi)gi (4.3)
where git is a vector of growth rates, i is a (n×1) vector of ones, and
k(xi) =
kh(x1,xi) 0 . . . 0
0 kh(x2,xi) · · · 0...
... . . . ...0 0 · · · kh(xn,xi)
is a weighting matrix of kernel functions with a bandwidth vector, h, based on a Gaussian kernelfor the continuous variables and the Li-Racine kernel for the discrete variables.
The LCLS estimator works by locally averaging values of gi which are close to those taken onby a particular independent variable. The closeness is determined by the size of h - the choiceof which we describe later. The rationale behind applying the LCLS estimator first is that itwill allow us to determine whether trade is more relevant for real GDP growth per capita and/orTFP growth. Given that parametric estimations have found trade to have a stronger relationshipwith TFP growth, but with a lower posterior inclusion probability, and mixed results for realGDP growth, but with relevance, our initial estimation is the first to determine whether our tradeproxies are relevant in explaining TFP growth. It will also allow our subsequent estimation to bemore focused.
4.2.2 Local-Linear Least Squares
In order to determine the partial impact of trade on growth we estimate equation (4.2) by LLLS.This estimator performs weighted least-squares around a point xit with weights determined bythe kernel function and bandwidth vector outlined previously. A larger weight is given to obser-vations closer to xit and a lesser weight to those further away. Formally, the LLLS estimator ofequation (4.2) is determined by taking its first-order Taylor series expansion with respect to thecontinuous explanatory variables, xc
it , as
gi = m(xi)+ui ≈ m(xi)+(xci −xc)β (xc)+ui (4.4)
where β represents the partial derivative/gradient of m(xi) with respect to xci .
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The LLLS estimator is then defined as the estimator of δ (xi) =
[m(xi)
β (xci )
]which is (in matrix
form)δ (xi) = (x
′ik(xi)xi)
−1x′ik(xi)gi (4.5)
where xi is a matrix with typical row xi = [1,(xci −xc)], k(xi) is the kernel matrix outlined previ-
ously with a bandwidth vector h.
This particular form of estimation is due to Racine and Li (2004) who extend earlier estimatorsto admit both categorical and continuous data. Applying the LLLS estimator to determine partialeffects is appealing for a number of reasons. Firstly, the LLLS, for a given variance, estimatesequation (4.2) with less bias and hence a lower mean-square-error. Secondly, if the underlyingnature of equation (4.2) is indeed linear, then the LLLS estimator results in zero bias which isnot the case for the LCLS estimator. Lastly, unlike the LCLS estimator, the LLLS estimatorreadily delivers information on the function itself in addition to (approximate) gradients for eachvariable in xi.
4.2.3 Bandwidth Estimation
The optimal bandwidths, h, which are used in our LCLS and LLLS estimators are determined byleast-squares cross-validation (LSCV) which minimises
h = Σni=1 [gi− m−i(xi)]
2 (4.6)
where h is the bandwidth and m−i(xit) is the leave-one-out estimator of m(xit) defined as
m−i(xi) =∑
nj=1, j 6=i g jk(x j,xi)
∑nj=1, j 6=i k(x j,xi)
Under LSCV, m(.) is replaced by gi as we only observe gi = m(xi)+ui. Assuming E(u|xi) = 0we can assume on average that gi = m(xi). The presence of m−i(xi) ensures that h > 0 suchthat we have enough observations for smoothing. It also ensures a balance between the bias andvariance of our estimates (Henderson and Parameter, 2015).
Henderson and Parmeter (2015) mention that the choice of a particular kernel function matterslittle for the estimation of equation (4.2) and that optimal bandwidth selection is the most salientpoint to consider. In nonparametric estimation, continuous variables are smoothed and the extentof this smoothing is controlled by their bandwidths. For instance, larger bandwidths mean moresmoothing which, despite reducing variance, increase the bias of the gradient estimates whilesmaller bandwidths have the opposite effect. As such, optimally determining the bandwidthplays a crucial role in a nonparametric setup. Instead of a simple rule-of-thumb estimation for
13
the bandwidths, automated estimation of equation (4.6) is the most popular route irrespectiveof its computationally intensive nature. Under LCLS, a particular independent variable shouldbe deemed irrelevant in explaining gi if its resulting bandwidth is equal to, or larger than, aparticular upper-bound.. Likewise, a particular independent variable should be specified linearlyunder LLLS for the same reason. The idea being that as h→ ∞, LCLS smooths the variableout of the regression (k(xi) = 0), and LLLS fits a regression line using all observations in theneighborhood of a particular regressor which is constant for any observation hence linear. Sincein practice h cannot approach infinity, to determine relevance and linearity, we follow Hall et
al. (2007)6 in specifying two standard deviations of the independent variable as its upper-bound.For instance, a bandwidth larger than this under LLLS implies that the variable’s impact on gi
is linear. Even under the presence of linearity, however, Henderson and Parmeter (2015) notethat subsequently using a semi-parametric approach would ignore potential interactions betweena variable deemed linear and the remaining explanatory variables.
4.3 Endogeneity
To control for endogeneity, we apply the local-polynomial least squares estimator developed bySu and Ullah (2008), and extended by Henderson et al. (2013) to include discrete regressors. Toour knowledge, this study is the first to apply this technique to determine the causal impact oftrade and this is a key contribution of our work. A thorough explanation of this estimator can befound in Henderson and Parmeter (2015) so we describe only its key elements. To begin with werewrite equation (4.2) to include a single endogenous regressor as
gi = m(xi,z1i)+ εi
xi = f (zi)+µi(4.7)
where xit is endogenous, in our case trade, zi = (d1×1) vector of exogenous variables, f (zi) isan unknown smooth function of the instruments, εi and µi are error terms with the assumptionsE (µi|zi) = 0 and E (εi|zi,µi) = E (εi|µi). Henderson and Parmeter (2015) mention that theseassumptions are more general than zi being independent of (µi,εi) and allow both error terms tobe heteroskedastic.
The second term in equation (4.7) allows for the identification of m(xi) and requires that E(µi)
depends on xi only through εi. Su and Ullah (2008) show that m(xi,z1i) can be identified by
6Hall et al. (2007), Henderson et al. (2012), and Parmeter et al. (2009) show that for small n, LSCV performswell in removing irrelevant independent variables.
14
observing thatE(g|x,z,ε) = m(x,z1)+E(ε|x,z,µ)
= m(x,z1)+E(ε|x− f (z),z,µ)= m(x,z1)+E(ε|z,µ)= m(x,z1)+E(ε|µ)
which, following iterated expectations, implies that w(x,z1,µ)≡E(g|x,z,µ)=m(x,z1)+E(ε|µ).
The estimation procedure is as follows:
1. Run a LCLS regression of ln(tradei) = m(xi,zi)+ui with a kernel function k1,h(.) (h1 is itsbandwidth vector). Denoting (consistent) estimates of f (zi) as f (zi), obtain its residualsas ui = xi− f (zi) for i = 1, ...,n.
2. Defining w(xi,zi,µi) = m(xi,zi)+E (εi|µi), run a LLLS regression of git on xi,zi and ui
with a kernel function k2,h(.) (h2 is its bandwidth vector) and denote its fitted values asw(xi,zi,µi).
3. Assuming that E (εi) = 0, we obtain a consistent estimate of gi as:
m′(xi,zi) =1n
n
∑i=1
w′ (xi,zi, µi) . (4.8)
where w′ (xi,zi, µi) is the derivative of m(xi,zi)+E (εi|µi).
The intuition behind this estimator is that in the first stage we run a nonparametric regression ofthe endogenous regressor on all exogenous variables. The second stage requires a nonparametricregression of gi on each of the exogenous variables in the model, including the endogenousregressor itself, and, because we do not observe the realisations of µi in practice, the residualsfrom the first stage. Marginal integration is performed as a final step to ensure that E (εit) = 0holds. In order to satisfy the exclusion restriction, a LCLS regression is performed in the firststage since if any bandwidths hit their upper-bound for a regressor that particular regressor isdeemed irrelevant in explaining the dependent variable. In our case, if its correlation with gi iszero and with ln(tradei) it is non-zero it can be deemed to be a valid instrument. Hendersonand Parmeter (2015) also describe alternative approaches to this estimator but nevertheless itsapplicability using the nonparametric estimators described earlier means we apply it in our case.
5 Results
We discuss the findings, presented in tables and plots, of our parametric and nonparametricregressions in the following sections.
15
5.1 Parametric Estimates
We begin by presenting - in tables 1 and 2 - the results of our parametric models - pooled OLSand within-country fixed effects - for TFP and real GDP growth, respectively. We do so to de-termine the suitability of our dataset and to consider any differences across techniques. Table1 shows that, for TFP growth, our trade proxies are generally insignificant in a cross-sectionalsetup though their signs are as expected whereas switching to panel methods results in substan-tial differences. Five out of the seven measure are now statistically significant. For instance,openness and the Fraser Index ranking now have a significantly positive impact on TFP growthwhereas having lower NTBs does not. The impact of trading with advanced economies is alsoinsignificant across both methods suggesting that the perceived benefits of technological transferdo not affect TFP growth. On the other hand, table 2 shows that openness is insignificant acrossboth techniques with its impact being negative in a panel framework. The remaining covariatesdo not change in sign compared to table 1 except now the impact of a more liberalised traderegime is significant in both frameworks.
16
Tabl
e1:
Para
met
ric
Est
imat
esof
Equ
atio
n(4.1)
Dep
ende
ntV
aria
ble:
TFP
Gro
wth
Pool
edO
LS
Fixe
dE
ffec
ts
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
RD
Dum
my
0.33
2(0.2
73)
0.33
9(0.2
73)
0.73
4b(0.3
53)
0.03
7(0.2
83)
0.02
7(0.3
37)
0.02
8(0.3
63)
0.18
2(0.2
73)
--
--
--
-
In.I
ncom
e−
0.43
8a
(0.1
01)
−0.
453a
(0.1
02)
−0.
372a
(0.1
46)
−0.
479a
(0.1
17)
−0.
561a
(0.1
26)
−0.
476a
(0.0
98)
−0.
514a
(0.1
05)
−3.
017a
(0.6
98)
−3.
031a
(0.7
07)
−4.
720a
(1.2
66)
−3.
413a
(0.7
53)
−5.
737a
(1.0
10)
−2.
381a
(0.7
32)
−3.
415a
(0.7
30)
Ope
nnes
s0.
236
(0.2
03)
1.50
2b(0.6
39)
Adv
.Tra
de0.
172
(0.1
79)
0.40
7(0.4
34)
Trad
eTa
xes
−0.
108
(0.0
75)
−0.
329b
(0.1
61)
Ave
.Tar
iffs
−0.
106
(0.1
75)
−0.
689b
(0.3
48)
NT
Bs
1.64
9b(0.6
46)
1.44
8(0.9
94)
BM
P−
0.09
3(0.5
23)
0.91
8c(0.5
54)
Fras
erIn
dex
0.58
7(0.3
59)
0.82
8b(0.4
12)
Inve
stm
ent
0.09
0(0.4
02)
0.05
5(0.4
08)
1.15
6b(0.5
34)
0.39
6(0.4
22)
0.32
2(0.4
88)
−0.
158
(0.3
89)
0.15
1(0.3
86)
−0.
407
(0.5
50)
−0.
174
(0.5
50)
1.15
7(0.9
43)
−0.
306
(0.6
35)
1.13
1(0.8
54)
−0.
397
(0.5
29)
−0.
559
(0.5
72)
Infla
tion
−0.
214b
(0.0
98)
−0.
210b
(0.1
00)
−0.
135
(0.1
20)
−0.
265b
(0.1
07)
−0.
224c
(0.1
20)
−0.
262a
(0.0
95)
−0.
312a
(0.0
96)
−0.
431a
(0.1
22)
−0.
419a
(0.1
27)
−0.
278c
(0.1
57)
−0.
510a
(0.1
39)
−0.
354b
(0.1
64)
−0.
290b
(0.1
16)
−0.
389a
(0.1
24)
Gov
t.Si
ze−
0.49
9(0.3
23)
−0.
475
(0.3
25)
−1.
074a
(0.4
16)
−0.
713b
(0.3
53)
−0.
823b
(0.3
87)
−0.
402
(0.3
20)
−0.
394
(0.3
18)
−1.
227c
(0.6
78)
−1.
237c
(0.6
83)
−0.
471
(1.1
19)
−2.
002a
(0.7
43)
−2.
474b
(1.0
59)
0.07
0(0.7
62)
−1.
589b
(0.7
30)
Pop.
Gro
wth
−0.
062
(0.6
22)
0.00
5(0.6
24)
−0.
348
(0.7
41)
0.57
7(0.6
53)
−0.
195
(0.7
37)
−0.
811
(0.6
18)
−0.
594
(0.6
36)
−1.
681
(1.3
46)
−2.
207
(1.3
52)
−2.
273
(1.8
68)
−1.
236
(1.4
33)
−1.
804
(2.0
79)
−3.
674b
(1.4
61)
−3.
194b
(1.5
99)
Hum
anC
apita
l2.
006a
(0.6
89)
2.11
5a(0.6
80)
1.48
0c(0.8
89)
2.63
3a(0.7
05)
2.28
4a(0.8
35)
2.10
1a(0.6
68)
1.83
3a(0.6
94)
1.10
6(3.3
28)
2.07
8(3.4
08)
3.49
1(5.5
25)
1.79
7(3.7
40)
9.91
3c(5.9
10)
−3.
725
(3.3
30)
1.17
3(3.5
08)
NR
Dum
my/
Yea
rY
esY
esY
esY
esY
esY
esY
es-
--
--
--
Cou
ntry
--
--
--
--
--
--
--
Cou
ntry
/Yea
r-
--
--
--
Yes
Yes
Yes
Yes
Yes
Yes
Yes
n45
545
327
140
730
940
541
945
545
327
140
730
940
541
9
R2
0.11
50.
113
0.11
20.
122
0.09
20.
136
0.11
10.
116
0.10
70.
116
0.14
10.
198
0.09
90.
134
Whi
test
d.er
rors
inpa
rent
hese
s.a
bc
repr
esen
tsig
nific
ance
at1%
,5%
and
10%
.Yea
rDum
mie
sin
c.in
allm
odel
s.
17
Tabl
e2:
Para
met
ric
Est
imat
esof
Equ
atio
n(4.1)
Dep
ende
ntV
aria
ble:
GD
PG
row
th
Pool
edO
LS
Fixe
dE
ffec
ts
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
RD
Dum
my
0.25
0(0.2
76)
0.24
3(0.2
75)
0.52
6(0.3
63)
0.10
4(0.2
92)
0.48
6(0.3
30)
0.45
5c(0.2
71)
0.46
5c(0.2
72)
--
--
--
-
In.I
ncom
e−
0.58
4a
(0.1
02)
−0.
628a
(0.1
03)
−0.
509a
(0.1
51)
−0.
643a
(0.1
20)
−0.
767a
(0.1
24)
−0.
603a
(0.0
97)
−0.
718a
(0.1
05)
−4.
989a
(0.7
56)
−5.
300a
(0.7
57)
−8.
186a
(1.3
40)
−5.
300a
(0.7
90)
−6.
624a
(0.9
80)
−5.
018a
(0.7
72)
−5.
361a
(0.7
26)
Ope
nnes
s0.
154
(0.2
06)
−0.
675
(0.6
92)
Adv
.Tra
de0.
394b
(0.1
81)
1.24
0a(0.4
65)
Trad
eTa
xes
0.02
5(0.0
77)
0.18
7(0.1
71)
Ave
.Tar
iffs
−0.
026
(0.1
80)
0.57
3(0.3
65)
NT
Bs
1.89
3a(0.6
34)
3.61
7a(0.9
64)
BM
P0.
986c
(0.5
20)
1.70
4a(0.5
85)
Fras
erIn
dex
1.33
6a(0.3
57)
1.42
3a(0.4
09)
Inve
stm
ent
4.13
1a(0.4
07)
3.99
8a(0.4
11)
4.14
0a(0.5
50)
4.29
8a(0.4
35)
4.54
3a(0.4
79)
4.17
2a(0.3
86)
4.40
0a(0.3
84)
4.24
6a(0.5
97)
4.23
1a(0.5
89)
4.68
0a(0.9
98)
4.31
2a(0.6
67)
6.76
3a(0.8
29)
4.57
0a(0.5
58)
4.35
9a(0.5
69)
Infla
tion
−0.
389a
(0.0
99)
−0.
353a
(0.1
00)
−0.
204c
(0.1
24)
−0.
416a
(0.1
10)
−0.
103
(0.1
18)
−0.
107
(0.0
95)
−0.
236b
(0.0
95)
−0.
736a
(0.1
32)
−0.
637a
(0.1
36)
−0.
346b
(0.1
66)
−0.
753a
(0.1
46)
−0.
366b
(0.1
59)
−0.
302b
(0.1
22)
−0.
408a
(0.1
24)
Gov
t.Si
ze−
1.50
2a
(0.3
28)
−1.
428a
(0.3
27)
−1.
645a
(0.4
28)
−1.
530a
(0.3
64)
−0.
969b
(0.3
80)
−1.
126a
(0.3
18)
−1.
252a
(0.3
17)
−2.
133a
(0.7
35)
−2.
022a
(0.7
32)
−2.
282c
(1.1
85)
−2.
659a
(0.7
80)
−0.
050
(1.0
27)
−0.
849
(0.8
04)
−1.
538b
(0.7
27)
Pop.
Gro
wth
−2.
534a
(0.6
31)
−2.
457a
(0.6
28)
−3.
973a
(0.7
63)
−2.
474a
(0.6
74)
−3.
261a
(0.7
24)
−3.
211a
(0.6
14)
−2.
892a
(0.6
33)
−4.
379a
(1.4
60)
−4.
436a
(1.4
47)
−4.
179a
(1.9
78)
−3.
993a
(1.5
05)
−8.
745a
(2.0
17)
−7.
607a
(1.5
42)
−6.
716a
(1.5
91)
Hum
anC
apita
l1.
359a
(0.6
99)
1.38
9b(0.6
85)
0.58
1(0.9
16)
1.73
5b(0.7
27)
1.26
6(0.8
20)
1.75
8a(0.6
64)
1.59
8b(0.6
91)
1.51
4(3.6
08)
2.74
0(3.6
50)
0.47
6(5.8
48)
3.93
1(3.9
26)
10.6
10c
(5.7
32)
3.43
3(3.5
14)
0.52
8(3.4
90)
RD
Dum
my/
Yea
rY
esY
esY
esY
esY
esY
esY
es-
--
--
--
Cou
ntry
--
--
--
--
--
--
--
Cou
ntry
/Yea
r-
--
--
--
Yes
Yes
Yes
Yes
Yes
Yes
Yes
n45
545
327
140
730
940
541
945
545
327
140
730
940
541
9
R2
0.36
00.
369
0.38
80.
379
0.42
00.
422
0.42
10.
295
0.30
40.
294
0.31
20.
417
0.34
60.
357
Whi
test
d.er
rors
inpa
rent
hese
s.a
bc
repr
esen
tsig
nific
ance
at1%
,5%
and
10%
.Yea
rDum
mie
sin
c.in
allm
odel
s.
18
Tabl
e3:
Con
sist
entS
peci
ficat
ion
Test
sof
Equ
atio
n(4.1)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
TFP
Gro
wth
:p-
Val
ue<
2.22
e−16
<2.
22e−
160.
0150
38<
2.22
e−16
<2.
22e−
160.
0050
125
0.00
7518
8J-
Stat
istic
3.29
715
2.96
8667
0.51
9970
33.
3010
314.
1075
321.
2294
251.
3550
14
GD
PG
row
th:
p-V
alue
<2.
22e−
16<
2.22
e−16
<2.
22e−
16<
2.22
e−16
<2.
22e−
16<
2.22
e−16
<2.
22e−
16
J-St
atis
tic9.
1218
939.
5788
974.
3343
587.
8375
138.
1759
768.
8991
317.
0830
04
Boo
tstr
ap:W
ild.R
eplic
atio
ns:3
99.
19
Our resource dependence dummy (RD Dummy) suggests that the raw growth rates for such coun-tries are higher than their counterparts though the coefficient is by-and-large insignificant. Theremaining covariates behave as expected. Initial income is negative and significant in all casesthereby proving the convergence hypothesis and, following Islam (1995), its impact is greater ina panel framework. Investment is positively significant at the 1% level for real GDP growth butits impact becomes (insignificantly) negative when applying the fixed-effects estimator for TFPgrowth. Population growth has a negative impact for both growth measures though it is largelyinsignificant for TFP growth. The impact of human capital is positive for both growth mea-sures though it is more significant for TFP growth. This follows existing literature which findsstronger effects for TFP growth using semiparametric techniques in contrast to irrelevance usingnonparametric estimators (see Mamuneas et al., 2007; Delgado et al., 2014). The remainingmacroeconomic policy variables, inflation and government size, are, as expected, negative andare, on the whole, significant across both measures. The only exception to this is for governmentsize where significance depends on the parametric model applied.
Taken as a whole, our parametric results attest to the suitability of our datasets since none ofthe variables have unusual estimated coefficients. They also show that the role of trade in thegrowth process is heavily dependent on the type of growth measure and the type of parametricspecification used. This is also true, to a lesser extent, for the remaining covariates. In order todetermine whether our parametric specifications are correct, we present, in table 3, the results -for both growth measures - of the Hsiao et al. (2007) test described earlier. The null of correctspecification is rejected at the 1% level for all variants of our parametric model. In line withprevious studies, this suggests that, without alterations, our linear specification do not completelycapture the dynamics modeled in equation (4.1). As such, there is considerable scope for ournonparametric estimation, the results of which we discuss in the following sections.
5.2 Nonparametric Estimates
Tables 4 and 5 present the bandwidth estimates using both the LCLS and LLLS estimators forTFP and GDP growth respectively. In brackets below each variable, we also present the upper-bound for that variable as two-times its standard deviation. An asterisk against a variable in-dicates that its bandwidth exceeds the variable’s upper-bound. For the LCLS estimation thisimplies that the variable is smoothed out of the regression - it is irrelevant in explaining the de-pendent variable whereas for the LLLS estimation it implies that the variable enters linearly inthe regression. Our parametric results showed that the effects of trade on TFP growth were moresensitive to model choice than the effects of trade on GDP growth suggesting we could ignorethe latter in nonparametric analysis. Our LCLS bandwidths support this view as 5 out of 7 tradeproxies are relevant in explaining TFP growth while only 1 (Adv. Trade) is relevant in explainingGDP growth. Importantly, the commonest measure - openness - is only relevant in explaining
20
TFP growth which suggests that traditional studies using GDP growth rates need to be comple-mented with further work using TFP growth. In terms of linearity, the LLLS bandwidths implythat trade affects growth in a linear fashion as the majority of bandwidths exceed their upper-bound. This does not necessarily mean that the effects are homogeneous across the distributionof growth rates and nor does it mean the absence of potential interactions, such as thresholdeffects, with the remaining covariates. Rather, it means that, if modelled parametrically, tradeenters linearly regardless of the nature of the dependent variable.
21
Tabl
e4:
Ban
dwid
ths
Obt
aine
dus
ing
LSC
VA
pplie
dto
the
LC
LS
and
LL
LS
Reg
ress
ions
Dep
ende
ntV
aria
ble:
TFP
Gro
wth
LC
LS
Ban
dwid
ths
LL
LS
Ban
dwid
ths
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Yea
rDum
my
0.99
9[1.0
00]
0.91
5[1.0
00]
0.69
7[1.0
00]
0.69
5[1.0
00]
0.99
9[1.0
00]
0.89
7[1.0
00]
0.93
0[1.0
00]
0.93
8[1.0
00]
0.99
9[1.0
00]
0.83
2[1.0
00]
1.00
0∗[1.0
00]
0.97
6[1.0
00]
0.88
8[1.0
00]
0.93
0[1.0
00]
RD
Dum
my
1.19
1e−
16[0.5
00]
3.39
1e−
08[0.5
00]
0.49
9[0.5
00]
0.49
9[0.5
00]
0.36
8[0.5
00]
0.49
9[0.5
00]
0.50
0[0.5
00]
0.09
7[0.5
00]
0.19
7[0.5
00]
0.46
1[0.5
00]
0.39
9[0.5
00]
0.03
0[0.5
00]
0.00
5[0.5
00]
0.00
6[0.5
00]
In.I
ncom
e0.
597
[3.2
99]
0.57
0[3.2
93]
5328
990∗
[3.0
13]
0.74
8[3.2
67]
0.65
1[3.1
26]
0.68
8[3.2
21]
0.70
2[3.2
23]
0.59
9[3.2
99]
0.57
7[3.2
93]
3.29
2∗[3.0
13]
1.29
9[3.2
67]
0.48
7[3.1
26]
1.45
8[3.2
21]
2.44
7[3.2
23]
Ope
nnes
s0.
290
[1.0
44]
3478
67.3∗
[1.0
44]
Adv
.Tra
de68
7895
.9∗
[1.3
36]
1777
619∗
[1.3
36]
Trad
eTa
xes
3.54
1[4.5
76]
1954
60.8∗
[4.5
76]
Ave
.Tar
iffs
0.34
5[1.7
91]
1.20
4[1.7
91]
NT
Bs
0.07
5[0.4
62]
0.40
3[0.4
62]
BM
P0.
248
[0.3
76]
4112
74.3∗
[0.3
76]
Fras
erIn
dex
7050
17.5∗
[0.7
03]
0.83
1∗[0.7
03]
Inve
stm
ent
0.38
4[0.5
10]
0.35
1[0.5
11]
0.34
7[0.4
79]
0.27
2[0.4
88]
0.58
8∗[0.4
57]
0.69
1∗[0.4
98]
0.55
2∗[0.5
10]
3.39
9∗[0.5
10]
3858
21.9∗
[0.5
11]
2328
167∗
[0.4
79]
1.08
7∗[0.4
88]
1.62
6∗[0.4
57]
9467
9.28∗
[0.4
98]
8563
55.9∗
[0.5
10]
Infla
tion
2.95
8∗[2.5
36]
2794
095∗
[2.5
41]
8741
609∗
[2.6
24]
2.36
8[2.3
69]
7329
553∗
[2.1
57]
2.37
0∗[2.3
65]
0.53
5[2.4
35]
3748
004∗
[2.5
36]
6109
204∗
[2.5
41]
6060
702∗
[2.6
24]
2143
20.7∗
[2.3
69]
4580
23.6∗
[2.1
57]
2001
497∗
[2.3
65]
1326
6303∗
[2.4
35]
Gov
t.Si
ze0.
154
[0.7
13]
0.16
3[0.7
14]
0.27
5[0.6
86]
0.18
0[0.6
89]
0.23
9[0.6
65]
0.22
1[0.6
76]
0.23
3[0.6
90]
0.33
7[0.7
13]
0.30
4[0.7
14]
8338
0.93∗
[0.6
86]
0.29
7[0.6
89]
0.29
4[0.6
65]
0.30
9[0.6
76]
0.23
3[0.6
90]
Pop.
Gro
wth
0.54
4∗[0.4
15]
0.45
2∗[0.4
16]
4517
190∗
[0.4
44]
3025
110∗
[0.4
08]
1291
928∗
[0.3
78]
7.48
4∗[0.3
87]
1344
68.9∗
[0.3
88]
0.22
9[0.4
15]
0.57
5∗[0.4
16]
6750
94.7∗
[0.4
44]
0.12
2[0.4
08]
0.13
3[0.3
78]
2203
883∗
[0.3
87]
7725
95.9∗
[0.3
88]
Hum
anC
apita
l0.
133
[0.5
07]
0.14
8[0.5
08]
0.16
9[0.4
68]
0.16
6[0.4
87]
0.07
2[0.4
20]
0.14
6[0.4
81]
0.13
0[0.4
81]
7985
66.9∗
[0.5
07]
0.25
0[0.5
08]
0.10
1[0.4
68]
3202
6.11∗
[0.4
87]
4469
7.09∗
[0.4
20]
5134
2∗[0.4
81]
4233
56.6∗
[0.4
81]
n45
545
327
140
730
940
541
945
545
327
140
730
940
541
9
Con
tinuo
usV
aria
ble:
[UB]
isth
eup
per-
boun
dof
the
band
wid
than
dis
2tim
esva
riab
le’s
stan
dard
devi
atio
n.C
ateg
oric
alV
aria
ble:
[UB]
isth
etr
ueup
per-
boun
dof
the
vari
able
.
Not
es:F
orco
ntin
uous
vari
able
s,w
eus
ea
seco
nd-o
rder
Gau
ssia
nke
rnel
.For
fact
orva
riab
les,
we
use
the
Aitc
hiso
nan
dA
itken
kern
el.T
heL
i-R
acin
eke
rnel
isus
edfo
rthe
orde
red
vari
able
.
22
Tabl
e5:
Ban
dwid
ths
Obt
aine
dus
ing
LSC
VA
pplie
dto
the
LC
LS
and
LL
LS
Reg
ress
ions
Dep
ende
ntV
aria
ble:
GD
PG
row
th
LC
LS
Ban
dwid
ths
LL
LS
Ban
dwid
ths
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Yea
rDum
my
0.60
9[1.0
00]
0.60
5[1.0
00]
0.77
9[1.0
00]
0.60
0[1.0
00]
0.70
2[1.0
00]
0.68
5[1.0
00]
0.71
4[1.0
00]
0.84
1[1.0
00]
0.86
1[1.0
00]
0.80
0[1.0
00]
0.94
1[1.0
00]
0.77
8[1.0
00]
0.82
4[1.0
00]
0.83
9[1.0
00]
RD
Dum
my
0.18
0[0.5
00]
0.17
5[0.5
00]
0.50
0∗[0.5
00]
0.46
2[0.5
00]
0.49
9[0.5
00]
0.49
9[0.5
00]
0.46
7[0.5
00]
0.30
2[0.5
00]
0.27
9[0.5
00]
0.27
9[0.5
00]
0.42
6[0.5
00]
0.47
6[0.5
00]
0.49
9[0.5
00]
0.31
9[0.5
00]
In.I
ncom
e0.
565
[3.2
99]
0.55
8[3.2
93]
0.70
6[3.0
13]
0.62
5[3.2
67]
0.46
1[3.1
26]
1.02
4[3.2
21]
0.53
8[3.2
23]
1.08
3[3.2
99]
1.95
8[3.2
93]
1.02
3[3.0
13]
0.83
4[3.2
67]
1.45
5[3.1
26]
2.26
5[3.2
21]
3.57
3∗[3.2
23]
Ope
nnes
s1.
366∗
[1.0
44]
4321
64.9∗
[1.0
44]
Adv
.Tra
de2.
416∗
[1.3
36]
0.68
9[1.3
36]
Trad
eTa
xes
7158
780∗
[4.5
76]
1708
3.85∗
[4.5
76]
Ave
.Tar
iffs
0.41
0[1.7
91]
2.49
1∗[1.7
91]
NT
Bs
2044
336∗
[0.4
62]
0.48
8∗[0.4
62]
BM
P0.
700∗
[0.3
76]
1.66
1∗[0.3
76]
Fras
erIn
dex
5871
13.4∗
[0.7
03]
3.31
8∗[0.7
03]
Inve
stm
ent
0.17
1[0.5
10]
0.16
7[0.5
11]
0.18
9[0.4
79]
0.19
5[0.4
88]
0.13
2[0.4
57]
0.14
1[0.4
98]
0.17
0[0.5
10]
0.25
5[0.5
10]
0.30
1[0.5
11]
0.27
1[0.4
79]
0.20
6[0.4
88]
0.22
9[0.4
57]
0.32
0[0.4
98]
0.32
7[0.5
10]
Infla
tion
1.10
1[2.5
36]
1.08
8[2.5
41]
0.54
2[2.6
24]
1.05
6[2.3
69]
0.60
2[2.1
57]
0.65
6[2.3
65]
0.61
5[2.4
35]
1.17
6[2.5
36]
2.49
1[2.5
41]
1.06
7[2.6
24]
1.29
2[2.3
69]
0.84
0[2.1
57]
0.46
1[2.3
65]
0.53
0[2.4
35]
Gov
t.Si
ze0.
280
[0.7
13]
0.27
2[0.7
14]
0.37
5[0.6
86]
0.39
9[0.6
89]
2545
88.5∗
[0.6
65]
0.54
7[0.6
76]
2052
662∗
[0.6
90]
0.74
0∗[0.7
13]
7699
8.8∗
[0.7
14]
0.46
6[0.6
86]
0.55
1[0.6
89]
1000
58.9∗
[0.6
65]
1268
8.99∗
[0.6
76]
7.84
0∗[0.6
90]
Pop.
Gro
wth
0.19
2[0.4
15]
0.19
6[0.4
16]
0.15
4[0.4
44]
0.13
6[0.4
08]
0.16
3[0.3
78]
0.13
6[0.3
87]
0.14
4[0.3
88]
0.67
2∗[0.4
15]
0.18
4[0.4
16]
0.58
7∗[0.4
44]
0.21
1[0.4
08]
3825.5
35∗
[0.3
78]
0.36
2[0.3
87]
0.17
4[0.3
88]
Hum
anC
apita
l0.
237
[0.5
07]
0.23
1[0.5
08]
7307
41.8∗
[0.4
68]
0.24
3[0.4
87]
0.19
4[0.4
20]
9175
88.1∗
[0.4
81]
0.27
8[0.4
81]
1491
38.8∗
[0.5
07]
6083
1.34∗
[0.5
08]
901.
0325∗
[0.4
68]
2127
9.59∗
[0.4
87]
0.24
5[0.4
20]
6483.8
47∗
[0.4
81]
0.74
9∗[0.4
81]
n45
545
327
140
730
940
541
945
545
327
140
730
940
541
9
Con
tinuo
usV
aria
ble:
[UB]
isth
eup
per-
boun
dof
the
band
wid
than
dis
2tim
esva
riab
le’s
stan
dard
devi
atio
n.C
ateg
oric
alV
aria
ble:
[UB]
isth
etr
ueup
per-
boun
dof
the
vari
able
.
Not
es:S
eeno
tes
fort
able
4.
23
Interestingly, the LCLS bandwidth on the resource dependence dummy is far below its upper-bound in all specifications for TFP growth and six out of seven for GDP growth. In contrast to theparametric estimates, the nonparametric estimation suggests that there are significant differencesbetween growth rates in resource dependent economies and their counterparts. This providesevidence against readily accepting the results of parametric models without determining the cor-rectness of their functional form. The remaining bandwidths show that initial income is highlyrelevant and nonlinear for both growth rates as the vast majority of bandwidths are less thantheir upper-bounds. The nonlinear nature of initial income supports the findings of Durlauf et al.(2005) and Mamuneas et al. (2007) and imply that it should enter as a polynomial in any para-metric framework. In terms of the remaining covariates, we find that the bandwidths are sensitiveto the choice of dependent variable. For TFP growth, investment and human capital are foundto be generally relevant and linear whereas population growth is irrelevant and its linearity isdependent on model choice. On the other hand, for GDP growth, investment enters non-linearlywhile population growth is now a relevant variable. Regarding macroeconomic policy, inflationis irrelevant and linear for TFP growth while relevant and nonlinear for GDP growth. Govern-ment size is a relevant variable for both growth rates but its impact is nonlinear only for TFPgrowth. Taken together with the bandwidths for our trade measures, these policy bandwidthssuggest that one should consider the nature of the dependent variable before deciding whether toinclude trade and/or inflation as independent variables and whether to include government sizeas polynomial.
In summary, we find that the trade-growth nexus since 1990 is more relevant for TFP growththan for GDP growth while the relevance and impact of macroeconomic policy as a whole variesacross across specifications. Furthermore, we find, in contrast to our parametric results, thatthere exists a significant difference in growth rates across resource dependent economies andtheir counterparts. This might be explained by differences in trade policy (or interactions withour continuous covariates) which cannot be captured by intercept shifts (Henderson et al. 2012).Therefore, we relegate our remaining analysis on the affects of trade on TFP growth while alsooffering a preliminary analysis of heterogeneities in its impact based on our resource dependentclassification.
5.2.1 Partial Effects at Quartiles
We now consider the partial effects of our trade measures on TFP growth using the LLLS es-timator described earlier. Since nonparametric regression provides an estimated partial effectfor each observation, tables 6 and 7 present partial effects alongside their corresponding wildbootstrapped errors7 in parentheses at the 25th, 50th, and 75th percentiles (Q1,Q2,Q3) of the
7We obtain estimates for our standard errors using 399 replications of a wild bootstrap since it is robust toheteroskedasticity (Henderson and Parmeter 2015).
24
estimated partial effects. Statistical significance can be determined by performing a T-test atthese fixed points.
Tables 6 and 7 indicate clear heterogeneities in our trade measures (and remaining covariates)that a parametric model would not immediately highlight. Furthermore, compared to our para-metric results, the nonparametric regressions explain far more of the variation in TFP growthrates which indicates that they perform comparatively better at fitting the data. Our gradient esti-mates reveal that our volume based measures of trade (openness and adv. trade) are insignificantacross all quartiles. This does not imply overall insignificance which will be determined througha graphical analysis of all partial effects. The negative impact at the 25th percentile for opennessis in line with previous studies (see Henderson et al. 2012, 2013). Our LLLS bandwidths impliedlinearity which is supported by the interquartile range of openness which is less than its largeststandard error (0.48 < 0.520). Our remaining measures relating to trade policy reveal the follow-ing. The impact of higher tariffs is significant and positive at the 50th and 75th quartiles, and isnonlinear since its interquartile range is now larger than its largest standard error (0.72 > 0.359).Lower NTBs and lower BMP are associated with higher TFP growth rates though, at our fixedpoints, the effects are insignificant. Our overall measure of trade policy, the Fraser Index, indi-cates that trade liberalisation promotes TFP growth with significant effects at the 50th and 75thquartiles. Its interaction with TFP growth contains non-linearities as its interquartile range largerthan the largest standard error.
25
Tabl
e6:
Part
ialE
ffec
tsat
Qua
rtile
sus
ing
LL
LS
Reg
ress
ion
Dep
ende
ntV
aria
ble:
TFP
Gro
wth
(1)
(2)
(3)
(4)
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
In.I
ncom
e−
0.87
2a
(0.2
51)−
0.33
0(0.3
23)−
0.02
4(0.3
96)−
0.69
3a
(0.2
69)−
0.26
2(0.3
31)−
0.10
6(0.4
12)−
0.46
1b
(0.1
89)
−0.
272
(0.2
20)−
0.14
5(0.2
75)−
0.72
8a
(0.1
70)−
0.22
4(0.2
05)
0.12
5(0.2
58)
Ope
nnes
s−
0.13
5(0.2
91)
0.16
7(0.4
04)
0.34
5(0.5
20)
Adv
.Tra
de−
0.27
0(0.2
84)−
0.00
3(0.3
37)
0.17
6(0.3
87)
Trad
eTa
xes
−0.
138
(0.0
88)
−0.
057
(0.1
07)
0.00
1(0.1
51)
Ave
.Ta
riff
s−
0.05
1(0.2
72)
0.55
8c(0.3
11)
0.66
9c(0.3
59)
Inve
stm
ent−
0.52
9(0.6
02)
0.31
7(0.8
23)
1.30
4(1.0
27)−
0.61
2(0.7
14)
0.44
1(0.8
83)
1.37
1(1.0
52)
0.01
3(0.7
66)
0.82
9(0.8
43)
1.62
2(1.0
12)−
0.30
5(0.5
91)
0.62
3(0.7
66)
1.28
8(0.9
32)
Infla
tion
−0.
450a
(0.1
58)−
0.27
7(0.1
86)−
0.08
5(0.2
16)−
0.44
6b
(0.1
77)−
0.28
2(0.1
95)−
0.07
5(0.2
25)−
0.35
4b
(0.1
60)
−0.
190
(0.1
75)−
0.03
9(0.2
01)−
0.38
1a
(0.1
37)−
0.25
5(0.1
56)−
0.14
0(0.1
88)
Gov
t.Si
ze−
1.51
9b
(0.6
40)−
0.89
2(0.7
44)
0.07
5(0.8
88)−
1.58
7b
(0.6
89)−
0.84
9(0.8
03)
0.24
6(0.9
45)−
2.21
5a
(0.6
33)−
1.82
7b
(0.7
12)−
0.00
4(0.7
97)−
1.08
2c
(0.6
06)−
0.55
9(0.7
31)
0.00
8(0.9
27)
Pop.
Gro
wth
−1.
494
(1.2
16)−
0.38
3(1.4
50)
0.83
5(1.8
78)−
1.43
2(1.1
15)−
0.67
1(1.2
65)
0.19
8(1.6
14)−
2.47
2a
(0.9
42)
−1.
301
(1.0
61)
0.78
2(1.4
57)−
2.82
6c
(1.4
46)−
1.40
6(1.6
39)−
0.18
5(2.0
84)
Hum
anC
apita
l−
2.00
1c
(1.1
60)
0.08
5(1.3
44)
2.31
4c(1.5
41)−
2.07
0(1.3
35)−
0.03
2(1.5
04)
2.49
3(1.6
82)−
1.74
9(1.7
33)
0.03
0(2.0
68)
1.45
5(2.7
44)−
3.35
2a
(0.9
52)−
1.13
9(1.2
30)
1.41
7(1.4
79)
R2
0.61
40.
502
0.47
00.
520
n45
545
327
140
7
Boo
tstr
appe
dSt
d.E
rror
sin
Pare
nthe
ses.
ab
cre
pres
ents
igni
fican
ceat
1%,5
%an
d10
%.Y
earD
umm
ies
inc.
inal
lmod
els.
26
Tabl
e7:
Part
ialE
ffec
tsat
Qua
rtile
sus
ing
LL
LS
Reg
ress
ion
Dep
ende
ntV
aria
ble:
TFP
Gro
wth
(5)
(6)
(7)
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
In.I
ncom
e−
1.16
5a
(0.3
44)
−0.
321
(0.4
03)
0.04
4(0.5
84)−
0.58
5a
(0.1
33)−
0.34
4b
(0.1
59)−
0.17
1(0.2
00)−
0.63
8a
(0.1
23)−
0.39
4a
(0.1
41)−
0.31
6c
(0.1
88)
NT
Bs
0.63
5(0.9
63)
1.72
9(1.2
16)
2.65
8(1.6
80)
BM
P−
0.90
5(1.2
46)
1.44
3(1.6
27)
2.55
8(1.9
88)
Fras
erIn
dex
0.74
7(0.6
80)
1.67
6b(0.7
67)
2.49
5a(0.9
04)
Inve
stm
ent−
0.90
5(0.7
96)
0.29
9(0.9
66)
2.42
9b(1.1
61)
0.16
1(0.5
36)
0.72
2(0.6
23)
1.06
0(0.8
13)
0.33
9(0.4
97)
0.84
1(0.5
56)
1.10
4(0.7
32)
Infla
tion
−0.
803a
(0.2
06)
−0.
341
(0.2
67)
−0.
147
(0.3
56)−
0.41
7a
(0.1
20)−
0.25
6c
(0.1
39)−
0.13
8(0.1
76)−
0.40
4a
(0.1
14)−
0.26
6b
(0.1
24)
−0.
146
(0.1
50)
Gov
t.Si
ze−
2.37
7a
(0.7
05)
−1.
704b
(0.8
43)
−0.
703
(1.1
75)−
1.33
2a
(0.4
97)
−0.
719
(0.5
90)−
0.16
6(0.7
95)−
1.23
5b
(0.5
50)
−0.
462
(0.6
44)
0.16
3(0.9
64)
Pop.
Gro
wth
−1.
721
(1.5
15)
−0.
165
(1.8
62)
2.12
1(2.6
28)−
1.84
7b
(0.8
59)
−0.
893
(0.9
75)−
0.16
0(1.2
32)−
1.41
3c
(0.7
78)
−0.
301
(0.8
81)
0.19
5(1.2
52)
Hum
anC
apita
l−
3.03
3a
(1.3
76e−
6 )0.
168a
(2.0
48e−
6 )2.
504a
(2.8
39e−
6 )−
2.86
4a
(0.8
94)
0.28
5(1.0
44)
1.93
4(1.3
25)−
2.88
5a
(0.8
71)
0.94
4(0.9
64)
2.22
3c(1.2
01)
R2
0.81
10.
747
0.79
9n
309
405
419
See
note
sfo
rtab
le6.
27
The partial impact of our remaining covariates is as expected. Initial income is generally nega-tive and significant across our seven specifications. Investment is generally insignificant acrossspecifications though its impact is positive at the 50th and 75h percentiles. The impact of humancapital is generally positive but significant largely at the 25th percentile - existing nonparametricstudies have found significance using TFP rates (Mamuneas et al. 2007) but irrelevance us-ing GDP growth (Delgado et al. 2014). The partial effects of the remaining policy variablesare also as expected with higher inflation rates and larger governments generally having signifi-cantly, negative partial effects. The interquartile ranges for government size is also greater thanthe largest standard error across specifications which indicates heterogeneities not captured in asimple parametric framework.
All in all, our analysis of partial effects at quartiles supports the findings presented in tables 4and 5. Less restrictive trade policy generally has a positive impact on TFP growth at our chosenfixed points with the effect being particularly significant for our comprehensive measure of tradeliberalisation. That said, our analysis has not controlled for endogeneity and it is tied to thefixed points chosen - it only covers 50% of all observations. We account for both caveats in thefollowing sections.
5.3 Nonparametric Instrumental Variables Estimates
The previous discussion of our nonparametric regression was based on correlations without par-ticularly accounting for causation. We now focus on four of our trade measures (openness, ave.tariffs, NTBs, Fraser Index) and apply the estimator of Su and Ullah (2008) described earlier.The most important issue in any instrumental variable regression is determining instrument va-lidity and, following Henderson et al. (2013), we present an intuitive nonparametric method ofdoing so. We return to our bandwidth estimates in table 4 and note that the LCLS bandwidthfor population growth exceeds its upper-bound across all specifications. We interpret this as im-plying that it is uncorrelated with TFP growth and could potentially be an instrument for trade;we could alternatively use the lags of the endogenous regressor as an instrument due to theirpredetermined nature.
28
Table 8: First Stage (LCLS) and Second Stage (LLLS) Bandwidths using the Su and Ullah (2008)Regression
First Stage Second Stage
Dependent Variable: TFP Growth
(1) (2) (3) (4) (1) (2) (3) (4)
Year Dummy 0.909[1.000]
0.764[1.000]
0.762[1.000]
0.610[1.000]
0.917[1.000]
0.782[1.000]
0.901[1.000]
0.938[1.000]
RD Dummy 0.008[0.500]
0.007[0.500]
1.708e−5[0.500]
0.447[0.500]
0.064[0.500]
0.414[0.500]
0.448[0.500]
0.222[0.500]
In. Income 0.149[3.299]
0.217[3.293]
0.138[3.013]
0.493[3.223]
0.698[3.299]
0.899[3.293]
5.784[3.013]
3.897[3.223]
Openness - 1177571∗[1.044]
Ave. Tariffs - 0.467[1.336]
NTBs - 0.384[4.576]
Fraser Index - 0.952∗[0.703]
Investment 0.139[0.510]
0.375[0.511]
0.072[0.479]
0.102[0.498]
0.843∗[0.510]
0.885∗[0.511]
195538∗[0.479]
2288996[0.498]
Inflation 0.917[2.536]
0.515[2.541]
0.510[2.624]
0.476[2.435]
6524349∗[2.536]
119231.4∗[2.541]
2025664∗[2.624]
6045191∗[2.435]
Govt. Size 0.090[0.713]
0.112[0.714]
0.247[0.686]
0.305[0.690]
0.368[0.713]
0.334[0.714]
0.370[0.686]
0.198[0.690]
Pop. Growth 0.064[0.415]
0.231[0.416]
0.033[0.444]
0.103[0.388]
- - - -
Human Capital 0.044[0.507]
0.036[0.508]
0.035[0.468]
0.069[0.481]
0.370[0.507]
0.460[0.508]
0.622∗[0.468]
0.701∗[0.481]
u - - - - 138754.3[0.168]
1306.071[0.121]
1177627[0.033]
15859.71[0.060]
Table 8 presents both stages of our instrumental variables regression which attempts to determineinstrument validity. In this stage we perform a LCLS regression of each of our trade measureson the remaining covariates in equation (4.1). Columns 1 to 4 present the resulting bandwidthswhich show that population growth is a relevant variable for each of our trade measures as itsbandwidth is now less than its upper-bound. We take this as evidence for the exclusion restrictionbeing satisfied and, given that we have one instrument for one endogenous regressor, our modelis just identified. Having obtained valid regressions for our first stage, we include their residualsas additional regressors in nonparametric regressions of trade on TFP growth. The remaining4 columns of table 8 present the resulting estimates using the LLLS estimator. We see that theresulting bandwidths are qualitatively similar to those presented in table 4.
5.3.1 Partial Effects at Quartiles
As previously, table 9 presents the partial effects of our instrumental variables regression atquartiles. The signs of the partial effects for each trade measure change somewhat from table
29
4: openness has a negative impact at the 25th and 50th percentiles though having a more liberaltrade policy remains positive at all quartiles. However, we now find that that having a lowercoverage of NTBs has a statistically positive impact on TFP growth at all quartiles. Moreover,the significance of our trade policy measure now increases to the 1% level at the 50th and 75thpercentiles. The other covariates remain largely unchanged with initial income, higher inflationand larger governments all having negative affects on TFP growth. In terms of fit, we see that theR2 is smaller than before for 3 of our trade measures8. For instance, though the standard errors arelarger, the instrumental variables regressions have removed some of the variation for openness,ave. tariffs, and trade policy but the opposite is true for NTBs. That said, the instrumentalvariables regressions have confirmed, and in some cases strengthened, our earlier nonparametricfinding that greater openness fosters TFP growth.
8Here, R2 is defined as [∑ni=1(git−g)(git−g)]
2
∑ni=1(git−g)∑
ni=1(git−g) . It is analogous to the R2 in parametric models and always lies in
[0,1].
30
Tabl
e9:
Part
ialE
ffec
tsat
Qua
rtile
sus
ing
LL
LS
Reg
ress
ion
Dep
ende
ntV
aria
ble:
TFP
Gro
wth
(1)
(2)
(3)
(4)
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
In.I
ncom
e−
0.85
8a
(0.2
09)−
0.37
8(0.2
78)−
0.12
9(0.3
63)−
0.64
2a
(0.2
31)
−0.
265
(0.2
65)
0.04
9(0.3
44)−
0.61
0a
(0.1
40)−
0.50
9a
(0.1
47)−
0.42
0a
(0.1
58)−
0.64
2a
(0.1
24)−
0.42
9a
(0.1
36)−
0.36
7b
(0.1
54)
Ope
nnes
s−
0.45
5(0.3
13)−
0.12
2(0.4
16)
0.17
8(0.5
49)
Ave
.Ta
riff
s−
0.22
1(0.4
38)
0.22
3(0.5
10)
0.71
2(0.6
18)
NT
Bs
1.55
0b(0.7
78)
1.75
4b(0.8
20)
2.02
4b(0.8
78)
Fras
erIn
dex
1.02
2c(0.6
14)
2.08
8a(0.7
07)
2.92
6a(0.8
63)
Inve
stm
ent−
0.24
6(0.6
57)
0.36
9(0.8
56)
1.09
8(1.0
63)−
0.62
0(0.7
48)
0.80
6(0.9
70)
2.06
4c(1.1
55)
0.45
2(0.5
25)
0.72
7(0.5
56)
0.99
2c(0.5
95)
0.32
3(0.4
90)
0.73
4(0.5
46)
0.95
6(0.6
41)
Infla
tion
−0.
501
(0.1
53)−
0.28
9(0.1
77)−
0.12
2(0.2
20)−
0.59
7a
(0.1
78)−
0.37
8c
(0.2
08)−
0.09
8(0.2
53)−
0.26
8b
(0.1
26)−
0.24
8c
(0.1
34)
−0.
188
(0.1
44)−
0.31
8a
(0.1
08)
−0.
197
(0.1
21)
−0.
107
(0.1
39)
Gov
t.Si
ze−
1.19
9b
(0.6
09)−
0.67
8(0.7
19)
0.05
0(0.9
01)−
1.22
6c
(0.7
31)
−0.
299
(0.8
75)
0.67
2(1.0
48)−
1.60
4a
(0.4
65)−
1.48
0a
(0.4
95)−
1.29
5b
(0.5
49)−
1.17
8b
(0.5
87)
−0.
554
(0.6
58)
0.06
9(0.8
11)
Hum
anC
apita
l−
2.90
2a
(1.0
75)−
0.52
2(1.3
63)
1.97
0(1.5
78)−
2.95
2b
(1.2
17)
−1.
328
(1.4
91)
1.30
2(1.7
08)−
2.72
6a
(0.8
51)
−1.
285
(0.9
05)
−0.
038
(0.9
90)−
2.94
0a
(0.7
94)
−0.
099
(0.8
58)
1.79
8c(0.9
46)
R2
0.72
70.
833
0.54
10.
552
n45
540
730
941
9
See
note
sfo
rtab
le6.
31
5.4 Kernel Density Plots
Though presenting partial effects at quartiles can reveal heterogeneities, it is only informative toa certain extent since doing so does not indicate the overall impact of our independent variables.In order to capture heterogeneities more accurately, we plot the kernel densities of the partialeffects of our 4 trade measures obtained from our nonparametric and nonparametric instrumentalvariables regressions. Plotting these effects together allows us to visualise any differences acrossthe two estimators in order to see the extent to which they deliver similar results. Alongside eachof the trade measures, we also plot corresponding partial effects for initial income, inflation andgovernment size to analyse the impact of macroeconomic policy as a whole. The solid black linein figures 1 to 4 depicts the density of partial effects of our nonparametric regression while thedashed red line depicts the partial effects of our nonparametric instrumental variables regression.
The densities for openness for both estimators follow each other closely and the mass of partialeffects lie to the right of zero suggesting an overall positive impact on TFP growth. Further-more, the distribution is unimodal supporting our earlier bandwidth estimates which, alongsideHenderson et al. (2012, 2013), point to a linear relationship between de jure openness and TFPgrowth.The densities of average tariffs, depicted in figure 2, varies slightly across the estimatorswith an element of bimodality supporting the bandwidth estimate in table 4. The overall impactdiffers across the two estimators as, though the mass of effects lie to the right of zero for thenonparametric instrumental variables regression, it is not clear as to where the mass of effectslies for our nonparametric regression. The densities of NTBs are relatively unimodal and themass lies to the right of zero confirming the finding of our nonparametric regressions at the meanwhich indicate a positive impact of lower NTBs on TFP growth. Lastly, the densities of our mea-sure of overall trade policy indicate that its overall impact is positive - more liberal trade regimesare increase TFP growth - and contains and element of non-linearity. Though the LLLS band-width presented in table 4 indicated linearity, its closeness to its upper-bound does not rule outthe bimodality depicted in figure 4. The densities of the remaining variables support the definitenegative impact of initial income, higher inflation, and larger government size on TFP growth asthe mass of partial effects lie to the left of zero.
In summary, our kernel density plots indicate that greater openness promotes TFP growth and theassumption of linearity in the trade-growth nexus rests on the trade measure used. We also findthat higher inflation rates and larger governments hurt TFP growth. Despite this, these kerneldensity plots do not indicate whether the impact of each variable is significant.
32
Figure 1: Kernel Density Plot of Partial Effects of Openness
Figure 2: Kernel Density Plot of Partial Effects of Ave. Tariffs
33
Figure 3: Kernel Density Plot of Partial Effects of NTBs
Figure 4: Kernel Density Plot of Partial Effects of the Fraser Index
34
5.5 45◦ Gradient Plots
Our final metric of assessment is the 45◦
gradient plot proposed by Henderson et al. (2012).Traditional nonparametric studies resort to kernel density plots and/or partial mean plots to high-light partial effects. In the latter, the partial effects of a variable, say trade, are plotted against thedependent variable holding all other variables constant at a particular point - usually the mean.However, in a multivariate context, holding other variables at such fixed points is an arbitrarychoice which the resulting plots are contingent upon. 45
◦plots overcome this issue while allow-
ing the direction, and significance, of partial effects to be objectively determined. Figures 5 to 20present plots of our trade measures, including initial income and the remaining macroeconomicpolicy variables, for both nonparametric regressions. To begin with, each # represents a pointestimate of the partial effect for a particular variable for each observation. For example, in thecase of openness, there are 455 point estimates overall which include insignificant and signif-icant partial effects. Each upper and lower 4 represent upper and lower confidence intervals(constructed using our bootstrapped errors) for each point estimate. When both 4 are in theupper-right-quadrant of the plot the estimated partial effect is positive and significant. Likewise,when both 4 are in the lower-left-quadrant estimated partial effect is negative and significant.When both4 straddle the horizontal axis the partial effect is not statistically different from zero.A clustering of partial effects indicates a larger degree of homogeneity in the overall impact of avariable whereas a greater degree of dispersion indicates heterogeneity.
Figures 5 to 8 depict the partial effects from our nonparametric regression. We can see that thelocation of partial effects is as expected for all variables. The majority of partial effects for open-ness are positive and there is a degree of heterogeneity since they are dispersed. Thus, despitethe partial effects at quartiles being insignificant, the overall impact of greater openness on TFPgrowth is positive and significant. The average tariff rate does not seem to have a significantimpact on TFP growth as almost all of the partial effects straddle the horizontal axis. Neverthe-less, the majority of these partial effects are precisely estimated as the confidence intervals arerelatively tight. Thus, despite the partial effects at the quartiles being positive and significant atthe 10% level, plotting all effects does not indicate so. The impact of non-tariff barrier is a lotmore heterogeneous with many partial effects having a negative impact. However, the overallimpact of lower NTBs looks to be positive. This supports the results presented in table 7 wherewe found positive effects at the 50th and 75th quartiles with significance for the latter. Lastly,we see from figure 8 that a more liberal trading regime generally fosters TFP growth as the vastmajority of partial effects lie in the upper-right-quadrant of the plot. The overall partial effectsof the remaining covariates follow convention. The majority of partial effects for initial income,government size, and inflation are negative suggesting that poorer countries grow faster than theircounterparts, and higher inflation and larger governments hurt TFP growth.
We also plot the partial effects from the nonparametric instrumental variables regression in fig-
35
ures 9 to 12. We see from figure 13 that the plot of partial effects for openness is almost identicalto that of figure 5. This is not surprising since the kernel densities of partial effects of bothregressions were very similar (see figure 1). Where the kernel densities differed we also see adifference in the 45
◦plots across regressions. The partial effects of average tariffs are now more
varied and a large degree of heterogeneity is visible; they are not so clustered around zero com-pared to figure 6. In terms of NTBs we see somewhat of an opposite picture. The effects are notas extreme as before, especially for those partial effects which are negative, and the partial effectsdo not straddle the horizontal axis as much as figure 7. We do not see an obvious change in theimpact of overall trade policy as the majority of partial effects still lie in the upper-right-quadrant.
Figure 5: 450 Plot of Partial Effects of Openness
36
Figure 6: 450 Plot of Partial Effects of Ave. Tariffs
Figure 7: 450 Plot of Partial Effects of NTBs
37
Figure 8: 450 Plot of Partial Effects of Fraser Index
Figure 9: 450 Plot of Partial Effects of Openness - Su and Ullah (2008) Regression
38
Figure 10: 450 Plot of Partial Effects of Ave. Tariffs - Su and Ullah (2008) Regression
Figure 11: 450 Plot of Partial Effects of NTBs - Su and Ullah (2008) Regression
39
Figure 12: 450 Plot of Partial Effects of Fraser Index - Su and Ullah (2008) Regression
5.5.1 Significant Effects
As a robustness check, we extract the significant partial effects and present 45◦
gradient plotsin figures 13 to 16, nonparametric regression, and figures 17 to 20, nonparametric instrumentalvariables regression, respectively. The conclusions derived from the preceding analysis generallyhold as the majority of the partial effects for initial income, inflation, and government size liein the lower-left quadrant. Hence, we can interpret this as applying that the conventional viewregarding the negative impact of these variables holds. Regarding our trade measures, openness,lower NTBs, and a more liberal trade policy significantly, and positively boost TFP growth. Thenegative partial effects when controlling for endogeneity also point to the same conclusion.
Therefore, when considering all our metrics for assessment - and controlling for endogeneity,our nonparametric regressions suggest that openness promotes TFP growth. Additionally, theysuggest that a more liberal macroeconomic policy also has the same effect.
40
Figure 13: 450 Plot of Significant Partial Effects of Openness
Figure 14: 450 Plot of Significant Partial Effects of Ave. Tariffs
41
Figure 15: 450 Plot of Significant Partial Effects of NTBs
Figure 16: 450 Plot of Significant Partial Effects of Fraser Index
42
Figure 17: 450 Plot of Significant Partial Effects of Openness - Su and Ullah (2008) Regression
Figure 18: 450 Plot of Significant Partial Effects of Ave. Tariffs - Su and Ullah (2008) Regression
43
Figure 19: 450 Plot of Significant Partial Effects of NTBs - Su and Ullah (2008) Regression
Figure 20: 450 Plot of Significant Partial Effects of Fraser Index - Su and Ullah (2008) Regression
44
5.6 Comparing Resource Dependent and Resource Independent Economies
Existing nonparametric studies assess heterogeneities in the impact of regressors by consideringestimates based on time, estimates either side of cutoffs, or by region. This typically involvessplitting samples based on a criteria and assessing the partial effects of each subsample. For ex-ample, one could split a sample between countries above and below median levels of a covariate,say initial income, and then use any of our metrics as forms of assessment. We, however, lookat another issue: the impact of openness across resource dependent and resource independenteconomies. To do so, we split the estimates of the partial effects, discussed previously, of ourfour chosen trade measures based on our resource dependence dummy. Note, we are not re-estimating our models on each subsample. We separate our analysis into comparing the partialeffects at quartiles and via kernel density plots of the two groups.
5.6.1 Partial Effects at Quartiles
Tables 10 and 11 present the partial effects of our trade measures without controlling for endo-geneity, while tables 12 and 13 present their counterparts. We see from tables 10 and 11 that ourtrade policy measure only has a significant impact for resource independent economies. More-over, its impact is positive across all 3 quartiles whereas it is only positive at the 50th and 75thquartile for resource dependent economies. In order to explain this difference, further work onthe framework of trade policy in resource dependent economies is warranted. Unsurprisingly,trade intensity has a positive impact at all 3 quartiles for resource dependent economies with sig-nificance at the 50th and 75th percentiles. However, it does not have a significant impact at anyfixed point for resource independent economies. Given that these economies are more diversifiedin terms of exports, de jure openness may not be important for productivity growth. One mayconclude from this that trade intensity is more important for resource dependent economies untilthey become resource independent. There may be a threshold effect at play between trade andresource dependency. With respect to trade policy, the difference could be explained by the im-pact of ave. tariffs and NTBs across the two groups. The former consistently lower TFP growthfor resource dependent economies and the effect is significant at the 25th and 50th percentiles.However, for resource independent economies, ave. tariffs have a positive and significant effectat the 75th percentile.
The remaining covariates impact TFP growth as expected. Initial income, higher inflation rates,and larger governments all have a negative impact on productivity growth. However, we do seethat higher rates of population growth have a stronger, negative impact for resource dependenteconomies. The effect is far weaker for resource independent economies which indicates thepossibility that population growth is a threshold variable which separates the two groups (seeMaasoumi et al., 2007).
45
When we separate the partial effects of our nonparametric instrumental variables regression inthe same manner, we notice similarities and differences. The magnitude, and direction, of tradeintensity and trade policy do not change greatly. Rather, trade policy now has a more significantlypositive impact for resource independent economies. However, the impact of Ave. Tariffs is nowinsignificant but lower NTBs now have a positive and significant impact across the two groups.That said, the estimates from both regressions are qualitatively the same.
46
Tabl
e10
:Par
tialE
ffec
tsat
Qua
rtile
sfo
rRes
ourc
eD
epen
dent
Eco
nom
ies
usin
gL
LL
SR
egre
ssio
nD
epen
dent
Var
iabl
e:T
FPG
row
th
(1)
(2)
(3)
(4)
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
In.I
ncom
e−
1.11
5a
(0.3
40)
−0.
647
(0.4
13)−
0.00
1(0.5
66)−
1.13
3a
(0.1
78)
−0.
918a
(0.2
06)−
0.59
4b
(0.2
94)−
1.66
3a
(0.6
35)
−1.
080
(0.7
67)
0.84
1(1.1
98)−
0.20
7(0.2
72)
0.08
8(0.2
94)
−0.
227
(0.3
32)
Ope
nnes
s0.
270
(0.5
35)
1.35
6b(0.5
81)
2.40
5a(0.7
79)
Ave
.Ta
riff
s−
0.94
2a
(0.2
84)
−0.
692b
(0.3
24)
−0.
431
(0.4
17)
NT
Bs
−2.
480
(1.7
05)
2.02
7(2.4
07)
3.27
1(4.0
33)
Fras
erIn
dex
−0.
459
(0.7
41)
0.30
7(0.8
23)
1.01
6(0.9
37)
Inve
stm
ent−
0.84
5(0.8
96)
0.17
8(1.0
56)
1.63
9(1.4
13)
2.79
4a(0.5
97)
3.88
6a(0.7
09)
4.47
0a(0.9
75)−
4.20
3b
(1.6
91)
−1.
607
(1.9
98)−
0.31
7(2.5
44)−
0.25
8(1.0
82)
1.01
6(1.1
94)
1.69
6(1.3
40)
Infla
tion
−0.
450b
(0.2
06)
−0.
076
(0.2
30)
0.30
9(0.3
29)−
0.48
2a
(0.1
37)
−0.
240
(0.1
60)
−0.
169
(0.2
15)−
0.76
4c
(0.4
11)
−0.
246
(0.4
89)
0.11
1(0.6
39)−
0.53
4b
(0.2
58)
−0.
418
(0.2
74)
−0.
316
(0.3
03)
Gov
t.Si
ze−
1.45
4c
(0.8
55)
−0.
723
(0.9
79)
1.75
2(1.2
22)−
1.54
8b
(0.6
32)
−0.
944
(0.7
38)
−0.
546
(0.9
67)−
6.16
0a
(1.6
67)−
3.19
8c
(1.8
13)−
0.80
1(2.1
60)−
2.36
2c
(1.2
16)
−1.
059
(1.4
13)
−0.
305
(1.6
79)
Pop.
Gro
wth
−6.
164a
(1.6
94)−
3.51
6c
(2.0
45)−
1.38
0(2.5
27)−
11.1
63a
(1.5
67)
−7.
112a
(1.9
50)
−2.
693
(2.6
19)−
6.86
4b
(3.0
84)
−3.
625
(3.8
54)−
0.92
7(4.7
24)−
6.42
5a
(1.7
20)−
5.82
9a
(1.8
12)−
4.64
7b
(2.0
72)
Hum
anC
apita
l−
1.38
1(1.3
71)
1.24
8(1.8
60)
2.64
6(2.2
70)
−1.
512
(0.9
41)
−0.
678
(1.1
07)
0.08
3(1.4
61)−
4.58
4b
(2.2
48)
−1.
177
(2.9
38)
0.61
0(3.4
25)
0.64
5(2.1
13)
2.21
7(2.2
61)
3.44
7(2.5
87)
n84
7145
67
See
note
sfo
rtab
le6.
47
Tabl
e11
:Par
tialE
ffec
tsat
Qua
rtile
sfo
rRes
ourc
eIn
depe
nden
tEco
nom
ies
usin
gL
LL
SR
egre
ssio
nD
epen
dent
Var
iabl
e:T
FPG
row
th
(1)
(2)
(3)
(4)
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
In.I
ncom
e−
0.78
9a
(0.2
42)
−0.
291
(0.2
93)−
0.02
7(0.3
75)−
0.98
5a
(0.1
69)−
0.78
0a
(0.2
04)−
0.55
0b
(0.2
49)−
0.94
2a
(0.3
37)
−0.
317
(0.3
90)
0.01
4(0.4
76)−
0.67
3a
(0.1
22)−
0.41
3a
(0.1
36)−
0.34
7b
(0.1
55)
Ope
nnes
s−
0.17
4(0.2
75)
0.12
0(0.3
81)
0.27
1(0.4
49)
Ave
.Ta
riff
s−
0.46
4c
(0.2
69)
0.12
2(0.3
09)
0.64
1c(0.3
51)
NT
Bs
0.71
4(0.9
48)
1.71
1(1.1
47)
2.56
7c(1.4
26)
Fras
erIn
dex
1.04
9(0.6
69)
1.94
7b(0.7
60)
2.58
0a(0.8
95)
Inve
stm
ent−
0.45
4(0.5
54)
0.32
9(0.7
75)
1.21
7(0.9
86)
2.25
8a(0.5
88)
3.55
3a(0.7
84)
4.29
1a(0.9
26)
−0.
296
(0.7
61)
0.50
7(0.9
33)
2.69
8a(1.0
31)
0.36
1(0.4
90)
0.79
8(0.5
29)
1.06
8c(0.6
09)
Infla
tion
−0.
450a
(0.1
54)−
0.29
2c
(0.1
76)−
0.13
7(0.2
01)−
0.47
6a
(0.1
37)
−0.
248
(0.1
55)
−0.
134
(0.1
85)−
0.80
3a
(0.2
01)
−0.
345
(0.2
50)−
0.17
5(0.3
04)−
0.37
7a
(0.1
13)−
0.22
4c
(0.1
21)
−0.
135
(0.1
33)
Gov
t.Si
ze−
1.51
9b
(0.6
16)
−0.
919
(0.7
04)−
0.19
8(0.8
16)−
1.89
7a
(0.6
04)−
1.40
4c
(0.7
30)
−0.
922
(0.9
25)−
2.28
0a
(0.6
98)−
1.66
7b
(0.7
91)−
0.71
4(0.9
49)−
1.11
0b
(0.5
32)
−0.
412
(0.6
10)
0.20
7(0.7
29)
Pop.
Gro
wth
−1.
115
(1.1
68)
0.02
3(1.3
93)
1.03
8(1.6
90)−
5.97
2a
(1.4
21)−
2.63
9c
(1.6
03)
−1.
430
(1.9
95)
−1.
147
(1.4
80)
0.29
3(1.7
52)
2.41
6(2.2
25)−
0.62
3(0.7
62)
−0.
128
(0.8
44)
0.31
2(1.0
27)
Hum
anC
apita
l−
2.43
8b
(1.1
09)
−0.
126
(1.3
09)
2.26
7(1.4
64)−
1.93
5b
(0.9
55)
−1.
159
(1.2
62)
−0.
540
(1.4
78)
−2.
166
(1.3
30)
0.70
5(1.4
69)
2.55
0(1.7
33)−
3.18
6a
(0.8
56)
0.49
8(0.9
30)
2.03
1c(1.0
39)
n37
133
626
435
2
See
note
sfo
rtab
le6.
48
Tabl
e12
:Par
tialE
ffec
tsat
Qua
rtile
sfo
rRes
ourc
eD
epen
dent
Eco
nom
ies
usin
gL
LL
SR
egre
ssio
n-S
uan
dU
llah
(200
8)R
egre
ssio
nD
epen
dent
Var
iabl
e:T
FPG
row
th
(1)
(2)
(3)
(4)
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
In.I
ncom
e−
1.08
7a
(0.3
46)−
0.71
4c
(0.3
91)−
0.17
4(0.4
98)−
0.67
6a
(0.2
15)
−0.
211
(0.2
51)
0.12
1(0.3
95)−
0.61
2a
(0.1
38)−
0.56
1a
(0.1
42)−
0.47
8a
(0.1
53)−
0.49
6a
(0.1
37)−
0.44
3a
(0.1
46)−
0.34
5b
(0.1
56)
Ope
nnes
s−
0.26
5(0.5
77)
1.21
8c(0.6
27)
2.53
2a(0.7
74)
Ave
.Ta
riff
s−
0.19
5(0.4
37)
0.22
0(0.5
14)
0.78
9(0.6
50)
NT
Bs
1.45
1c(0.7
80)
1.72
4b(0.8
14)
2.02
0b(0.8
55)
Fras
erIn
dex
0.04
7(0.5
72)
0.66
1(0.6
18)
1.16
5(0.7
10)
Inve
stm
ent−
0.81
9(1.0
52)
0.58
3(1.1
43)
1.57
8(1.4
35)−
0.74
5(0.6
97)
0.37
5(0.8
60)
1.56
0(1.0
34)
0.32
4(0.5
15)
0.66
3(0.5
40)
0.93
8c(0.5
69)
0.26
8(0.5
45)
0.48
5(0.5
92)
0.82
0(0.6
73)
Infla
tion
−0.
203
(0.2
26)
0.04
8(0.2
51)
0.34
4(0.2
95)−
0.42
6a
(0.1
64)
−0.
238
(0.1
97)
6.00
e−4
(0.2
55)−
0.23
2c
(0.1
21)
−0.
185
(0.1
30)
−0.
161
(0.1
39)−
0.25
0c
(0.1
31)
−0.
181
(0.1
36)
−0.
105
(0.1
48)
Gov
t.Si
ze−
1.17
3(1.0
07)
−0.
143
(1.0
83)
1.13
3(1.2
56)−
1.89
7a
(0.6
91)
−0.
518
(0.8
13)
0.46
5(1.0
11)−
1.60
1a
(0.4
51)−
1.47
2a
(0.4
69)−
1.33
2a
(0.5
09)−
1.09
1c
(0.6
24)
−0.
832
(0.7
04)
−0.
470
(0.8
21)
Hum
anC
apita
l−
2.33
3c
(1.3
83)
−1.
423
(1.6
06)
0.16
5(1.8
45)−
3.62
0a
(1.1
51)−
2.57
4c
(1.3
73)−
1.03
2(1.5
81)−
2.89
7a
(0.8
32)−
2.04
1b
(0.8
71)
−1.
257
(0.9
14)−
2.86
6a
(0.8
58)−
2.12
3b
(0.9
29)
−0.
065
(1.0
26)
n84
7145
67
See
note
sfo
rtab
le6.
49
Tabl
e13
:Par
tialE
ffec
tsat
Qua
rtile
sfo
rRes
ourc
eIn
depe
nden
tEco
nom
ies
usin
gL
LL
SR
egre
ssio
n-S
uan
dU
llah
(200
8)R
egre
ssio
nD
epen
dent
Var
iabl
e:T
FPG
row
th
(1)
(2)
(3)
(4)
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
Q1
Q2
Q3
In.I
ncom
e−
0.77
6a
(0.2
00)
−0.
341
(0.2
47)−
0.12
8(0.3
15)−
0.63
2a
(0.2
33)
−0.
282
(0.2
70)
0.02
0(0.3
37)−
0.60
7a
(0.1
40)−
0.49
6a
(0.1
47)−
0.41
4a
(0.1
60)−
0.69
5a
(0.1
22)−
0.42
3a
(0.1
32)−
0.36
9b
(0.1
52)
Ope
nnes
s−
0.46
4(0.3
04)
−0.
169
(0.3
99)
0.11
0(0.4
67)
Ave
.Ta
riff
s−
0.23
0(0.4
38)
0.22
4(0.5
09)
0.68
0(0.6
10)
NT
Bs
1.56
0b(0.7
77)
1.75
4b(0.8
22)
2.04
5b(0.8
82)
Fras
erIn
dex
1.34
5b(0.6
26)
2.36
0a(0.7
28)
3.07
6a(0.8
81)
Inve
stm
ent−
0.13
2(0.6
32)
0.34
6(0.7
90)
1.00
8(0.9
58)−
0.58
2(0.7
60)
0.90
9(0.9
95)
2.16
6c(1.1
84)
0.46
6(0.5
30)
0.73
7(0.5
59)
0.99
3c(0.6
00)
0.36
1(0.4
83)
0.77
4(0.5
33)
0.96
3(0.6
32)
Infla
tion
−0.
513a
(0.1
50)−
0.36
7c
(0.1
66)−
0.19
0(0.1
90)−
0.62
4a
(0.1
80)−
0.38
9c
(0.2
11)−
0.13
1(0.2
51)−
0.27
0b
(0.1
27)−
0.25
2c
(0.1
35)
−0.
209
(0.1
47)−
0.32
2a
(0.1
07)−
0.20
4c
(0.1
17)
−0.
109
(0.1
36)
Gov
t.Si
ze−
1.19
9b
(0.5
74)
−0.
751
(0.6
73)−
0.18
6(0.7
88)−
1.15
4(0.7
46)
−0.
231
(0.8
78)
0.73
9(1.0
50)−
1.60
5a
(0.4
67)−
1.48
0a
(0.5
01)−
1.29
2a
(0.5
50)−
1.19
9b
(0.5
68)
−0.
475
(0.6
54)
0.11
9(0.8
11)
Hum
anC
apita
l−
3.50
4a
(1.0
23)
−0.
318
(1.2
83)
2.04
4(1.5
03)−
2.49
8b
(1.2
26)
−0.
783
(1.5
22)
1.35
4(1.7
32)−
2.66
1a
(0.8
57)
−0.
966
(0.9
14)
0.10
5(1.0
07)−
2.93
3a
(0.7
86)
0.68
5(0.8
48)
1.96
3b(0.9
28)
n37
133
626
435
2
See
note
sfo
rtab
le6.
50
5.6.2 Kernel Density Plots
In order to visualise differences across our two groups, we present kernel density plots of thepartial effects of the macroeconomic policy variables. We also plot the mean partial effect foreach group. The solid black line and the dashed blue line plot the kernel densities for resourcedependent and resource independent economies respectively. The mean effect is represented bythe dashed red line (resource dependent economies) and dashed green line (resource independenteconomies). In general, the mass of partial effects for initial income, inflation, and governmentsize - including the mean effect - lie to the left of zero. This indicates that there are no hetero-geneities in their impact based on natural resource dependency.
Turning to our trade measures, however, highlights the differences presented in tables 10 and 11.The impact of trade intensity is strongly unimodal for resource independent economies while thespread of partial effects is far greater for their counterparts. Comparing this to figure 1 revealsfar more heterogeneity for a subgroup, resource dependent, than for the whole sample. Fur-thermore, though the mean impact of trade intensity is indistinguishable from zero for resourceindependent economies, we see a strongly positive impact for resource dependent economies.The density of partial effects for Ave. Tariffs is more dispersed but has a negative mean effect forresource dependent economies. There is less of a difference in the density of partial effects forNTBs. Trade policy can clearly be seen to have impacted both groups differently with the ma-jority of partial effects for resource independent economies being positive; the mass for resourcedependent economies is equally centered around zero. While this may suggest that trade policyhas been insignificant for resource dependent economies, it also implies that the negative effectsof natural resources (typically a part of trade policy) may be linked to ineffective trade policy insuch economies.
51
Figure 21: Kernel Density Plot of Partial Effects of Openness - RD vs. NRD Economies
Figure 22: Kernel Density Plot of Partial Effects of Ave. Tariffs - RD vs. NRD Economies
52
Figure 23: Kernel Density Plot of Partial Effects of NTBs - RD vs. NRD Economies
Figure 24: Kernel Density Plot of Partial Effects of Fraser Index - RD vs. NRD Economies
53
6 Conclusion
Does trade cause growth? This paper revisits this question by considering common criticisms ofexisiting empirical growth studies on a relatively large sample of countries for the period 1990 to2014. We begin by determining the growth process, TFP or GDP, for which trade is more relevantfor. Then, without specifying the functional form of the trade-growth nexus, we determine themagnitude and shape of the impact of trade on our chosen growth process. We ensure that ouranalysis is comprehensive by considering a wide range of trade measures covering trade intensityand trade policy. As a preliminary analysis, we also compare the performance of trade and tradepolicy in resource dependent and resource independent economies.
Our investigation yields a number of findings. Firstly, our nonparametric bandwidths suggestthat openness, and more broadly trade policy, is more relevant for TFP growth than for GDPgrowth. This is contrary to the findings in Durlauf et al. (2008) who find the posterior inclusionprobability for openness with respect to TFP growth to be low. This suggests that our resultsneed to be complemented with further work using a larger sample. Secondly, we find that open-ness has a positive and significant impact on TFP growth: more open economies tend to be moreproductive. Our nonparametric bandwidths also imply that this relationship generally linear andcan be best represented by a modified parametric model. Applying a nonparametric instrumentalvariables regression lends further support for these findings. Since authors have suggested thatopenness may be a tool in potentially attenuating the resource curse, our initial evidence regard-ing the impact of trade in resource dependent and resource independent economies suggests thattrade intensity has a positive and significant effect for the former whereas the impact of tradepolicy is insignificant. Given that we also find the opposite effect in the case of resource inde-pendent economies, further investigation as to why trade policy has not been effective in resourcedependent economies may determine whether it can be a panacea for the resource curse.
This paper can be extended in a number of directions. Firstly, it ignores heterogeneities in thetrade-growth nexus over time and across different development levels. With this in mind, amore closer examination of such heterogeneities in the impact of trade intensity and trade pol-icy in our nonparametric setup is needed. Secondly, in terms of model specification we findsupport for a parametric representation of the trade-growth nexus. Therefore, identifying an effi-cient parametric macroeconomic policy model should be an immediate point of research. Lastly,our nonparametric techniques could identify the true impact, referred to as a “red herring” byBrunnschweiler and Bulte (2008), of natural resource trade on growth. We leave these areas forfuture research.
54
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A Appendix
Table 14: Data and SourcesVariable Description Source
Total FactorProductivity(TFP) Growth
Growth Rate of Total Factor Productivity - Calculated as aTorqvist Index.
The ConferenceBoard : TotalEconomyDatabase (2014)
GDP Growth Growth Rate of GDP per Capita. World Bank(2015)
Openness Log of Imports and Exports as % of GDP. World Bank(2015)
Adv. Trade Log of Imports and Exports to Advanced Economies as %of GDP.
IMF-DOTS(2014)
Trade Taxes Log of Taxes on Import and Export Duties, Profits ofExport or Import Monopolies, Exchange Profits, andExchange Taxes as a % of Revenue.
World Bank(2015)
Ave. Tariffs Log of Ave. Tariff Rate on all Goods (Simple Mean). World Bank(2015)
NTBs Log of Non-Tariff Barriers Score. Fraser Institute(2015)
BMP Log of Black Market Premia Score. Fraser Institute(2015)
Fraser Index Log of Trade Freedom Index (Original Range: 0-100). Fraser Institute(2015)
Initial Income Log of Initial GDP per Capita. World Bank(2015)
PopulationGrowth
Log of Annual Population Growth + 0.05. World Bank(2015)
Investment Log of Gross Capital Formation as a % of GDP. World Bank(2015)
Inflation Log of Annual % CPI Inflation Rate. World Bank(2015)
Govt. Size Log of Net Government Expenditures as a % of GDP. World Bank(2015)
Human Capital Log of Composite Human Capital Index. Feenstra et al.(2015)
Natural ResourceRents
Total Natural Resource Rents as a % of GDP. World Bank(2015)
RD Dummy Resource Dummy indicating dependence (1) andindependence (0).
Author’scalculation basedon NaturalResource Rents
60
Table 15: Resource Dependent and Resource Independent Country Groupings (n = 455)Resource Dependent(RD)
Resource Independent (NRD)
Bahrain, CameroonEcuador, Iran, IslamicRep., Iraq, Kazakhstan,Kuwait, Malawi,Malaysia,Mozambique, Norway,Qatar, RussianFederation, SaudiArabia, Syrian ArabRepublic, Trinidad andTobago, Uganda,Venezuela, RB, Yemen,Rep.
Albania, Argentina, Armenia, Australia, Austria,Bangladesh, Belgium, Bolivia, Brazil, Bulgaria,Cambodia, Canada, Chile, China, Colombia, Costa Rica,Cote d’Ivoire, Croatia, Cyprus, Czech Republic, Denmark,Dominican Republic, Egypt, Arab Rep., Estonia, Finland,France, Germany, Ghana, Greece, Guatemala, Hungary,India, Indonesia, Ireland, Israel, Italy, Jamaica, Japan,Jordan, Kenya, Korea, Rep., Kyrgyz Republic, Latvia,Lithuania, Luxembourg, Mali, Mexico, Moldova,Morocco, Netherlands, New Zealand, Niger, Pakistan,Peru, Philippines, Poland, Portugal, Romania, Senegal,Singapore, Slovak Republic, Slovenia, South Africa,Spain, Sri Lanka, Sudan, Sweden, Switzerland, Tajikistan,Tanzania, Thailand, Tunisia, Turkey, Ukraine, UnitedKingdom, United States, Uruguay, Vietnam, Zambia,Zimbabwe
61
