5 Trade impact of EU preferential policies: a

meta-analysis of the literature

Maria Cipollina and Filomena Pietrovito

Maria Cipollina: University of Molise, via de Sanctis, 86100 Campobasso, Italy. E-mail: cipollina@unimol.it. Filomena Pietrovito: University of Molise, via de Sanctis, 86100 Campobasso, Italy. E-mail: filomena.pietrovito@unimol.it.

Abstract

The gravity model has been regularly used to estimate the impact of EU’s Preferential Trade Agreements (PTAs) on trade flows. Studies report very different estimates since there are significant differences in datasets, sample sizes and independent variables. This chapter combines, explains and summarizes a large number of results using a meta-analysis approach. It provides pooled estimates, obtained from fixed and random effects models, of the preferential’s effect size on bilateral trade. The information collected on each estimate allows to test the sensitivity of the results to alternative specifications and differences in the control variables considered. After filtering out all potential biases, the meta-analysis confirms a robust and positive PTAs effect.

Acknowledgments

We acknowledge financial support from the “New Issues in Agricultural, Food and Bio-energy Trade (AGFOODTRADE)” (Small and Medium-scale Focused Research Project, Grant Agree-ment no. 212036) research project funded by the European Commission, and the “European Un-ion policies, economic and trade integration processes and WTO negotiations” research project funded by the Italian Ministry of Education, University and Research (Scientific Research Pro-grams of National Relevance 2007). The views expressed in this paper are the sole responsibility of the authors and do not necessarily reflect those of the European Commission.

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5.1 Introduction

It is generally asserted that PTAs positively affect the trade growth between countries or group of countries involved. However, the empirical literature has been much less successful in finding clear evidence that this is indeed the case. The aim of this chapter is to provide a survey of a range of empirical studies using the gravity model approach to estimate the impact of European Union (EU)’s PTAs on trade.1 From a methodological point of view, in reviewing this literature we mainly focus on those papers estimating the standard gravity equation augmented by a coefficient for preferences:

dcεdcγPTAdcXβ)dc(Distβ)c(Yβ)d(YββdcT ++++++= 4ln3ln2ln10ln 5.1

where Tdc is the trade flow between EU and country c; Yd(c) indicates the GDP of EU or country c; Distdc is the distance between EU and country c; PTAdc is a variable for preferential trade agreements between EU and c; Xdc are control variables; and εdc is the error term. As far as the impact of PTAs on trade is concerned, different ways adopted to measure preferences need be taken into account. For this reason, in conducting the MA we distinguish between papers using a dummy variables and papers using quantitative indicators to measure preferences between countries. To proxy for PTAs, most papers in our sample use a dummy variable which is equal to one if a preference exists between EU and country c (Oguledo and MacPhee 1994; Nilsson 2002; Peridy 2005; Caporale et al. 2009; Martìnez-Zarzoso et al. 2009). However, as highlighted by Cardamone (2007, 2009), the use of a dummy to capture the impact of PTAs on trade is not adequate because: (i) it also captures all other factors that are specific to the country-pair and contemporaneous to the PTAs; (ii) it does not discriminate among different instruments adopted for preferential trade policy; (iii) it does not discern the level of trade preferences. Among the articles

1 Regarding the estimated coefficients of the impact of preferences, comprehensive surveys are provided by Nielsen (2003) and Cardamone (2007). With respect to these surveys, the MA complement the qualitative analyses with a more accurate quantitative research synthesis. It has recently been growing in popularity in economics, and recently Cipollina and Salvatici (2010b) provide a meta-analysis of the literature on the impact of reciprocal trade agreements on trade flows between partners.

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published in academic journals, the only exceptions to the use of a dummy are provided by Francois et al. (2006) and Cipollina and Salvatici (2010a), who compute preferential margins, and by Manchin (2006) who use the potential value of the preferential scheme if all eligible trade would have requested and obtained preferential treatment. Moreover, there exists also a very recent and growing literature, still at a working paper stage, focusing on explicit measures of PTAs (Cardamone 2009; Demaria 2009; Nilsson and Matsson 2009; Aiello and Cardamone 2010; Aiello and Demaria 2010; Cipollina et al. 2010). Most of the papers adopting a dummy variable conduct the empirical analysis on aggregate data, whereas all papers adopting quantitative variables focus on disaggregated data on trade. Most published works using dummy variables and aggregated data confirm the role of preferences in fostering trade by finding highly significant positive coefficients ranging between 1% and more than 400%. Nevertheless, some of them find also significant negative coefficients implying a decline of trade ranging between 3% and more than 50% (Nilsson 2002; Martìnez-Zarzoso et al. 2009). Focusing on the literature using a quantitative variable for preferential policy and disaggregated data, among published papers, we survey an elasticity coefficient ranging between 0.004 and 15.9, that is an increase of 10% in preferences determines an increase in trade ranging between 0.04% and 159%. An exception is provided by Francois et al. (2006) finding also negative coefficients. In terms of the results for different agreements, the impact of the EU GSP scheme, estimated at the aggregate level only, is difficult to define since the dummy coefficients range between 1% to 290% (Oguledo and MacPhee 1994; Nilsson 2002). Moreover, Nilsson (2002) even finds a significant negative effect of the GSP preferences ranging between 3% and 50%. The impact of the GSP-Plus scheme on trade, analyzed only by unpublished papers (Demaria 2009; Aiello and Demaria 2010), seems to be both positive and negative over the period 2001-2004. Martìnez-Zarzoso et al. (2009) find mixed effects of Euro-Med on exports to the EU, depending on specification and sample. Several unpublished studies find that the EBA initiative and the Euro-Med scheme provide a significant boost to LDCs exports (Demaria 2009; Aiello and Cardamone 2010; Aiello and Demaria 2010) and to exports from

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Mediterranean countries (Demaria 2009; Nilsson and Matsson 2009; Aiello and Demaria 2010), even if some specifications report highly negative coefficients for both schemes. Positive results have been also obtained for the ACP countries, with an elasticity coefficient ranging between 0.04 and 0.18 (Francois et al. 2006; Manchin 2006). Finally, several studies analyze the impact of PTAs on trade without distinguishing among different agreements and find positive coefficients of the dummy variables for preferences ranging between 2% and more than 400% (Nilsson 2002; Peridy 2005; Caporale et al. 2009), and an elasticity coefficient of the variable preference margin equal on average to 5 (Cipollina and Salvatici 2010a). Some authors focus on specific products and/or sectors, using highly disaggregated data. Here we highlight some recent studies. For instance, Cardamone (2009) find that the GSP scheme seems to be effective in increasing exports of apples and mandarins to the EU, while the Cotonou agreement is successful in making EU imports of fresh grapes and mandarins grow. Furthermore, regional trade agreements seem to be effective in expanding EU imports of all fruits but oranges from eligible countries. More recently, Cipollina and Salvatici (2010a) find that the largest coefficients of the impact of PTAs on trade are registered by tropical products, beverages and tobacco sectors. At the end of the day, the results of these studies show disconcerting variance: the estimates of γ̂ , which is the coefficient of our variable

of interest (PTA), are not stable, with widely varying estimates across studies and some worrying rankings of trade-creating agreements. Consequently, it is not easy to summarize the results of the large literature assessing the impact of preferences on trade since studies report very different estimates, due to the fact that they differ greatly in data sets, sample sizes, independent variables and estimation methods used in the empirical analysis. In order to combine and analyze the trade effects highlighted in the literature we use the Meta-Analysis (MA) approach.2 The MA is an appealing technique for evaluating empirical results from different studies (Rose and Stanley 2005). The central concern of MA is to

2 Empirical economists have increasing employed MA methods: in 2005, the Journal of Economic Surveys dedicated a Special Issue (Vol.19, No. 3) to this approach..

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test the null hypothesis that different point estimates, treated as individual observations i of the jth study ( jiγ̂ ), are equal to zero

when the findings from this entire area of research are combined. MA has recently been growing in popularity in different fields of economic research. The rest of this chapter is articulated as follows: in section 5.2 we describe the construction of the sample and the MA regression and explanatory variables; in section 5.3 we comment the main results; and, finally, in section 5.4 we draw some conclusions.

5.2 MA model

5.2.1 MA sample

In evaluating and combining empirical results, there is a risk to analyze completely different outcome variables or different explanatory variables (the “Apples and Oranges Problem” as referred to by Glass et al. 1981). In this respect, the first step of any MA , namely the construction of a database of estimates, is crucial. In this application, we only use papers written in English. Papers were selected via extensive search in Google Scholar and in databases, such as EconLit, Web of Science and Scopus. With the search in Google Scholar, we get papers and working papers that are not published in academic journals. EconLit provides coverage since 1969 to the economics literature including 750 journals. Web of Science provides access to current and retrospective multidisciplinary information from approximately 8,700 of the most prestigious, high impact research journals in the world (199 journals in the field of economics), covering the time period from 1992 to the present. Whereas Scopus includes the abstracts and references of 15,000 peer-reviewed journals from more than 4,000 international publishers, ensuring broad interdisciplinary coverage. Finally, we traced some specific papers cross-referenced in other works. The keywords searched for are: “preferential trade agreements”, “gravity equation or gravity model” in the title, the abstract or the text of the paper. The first keyword permits to get papers dealing with PTAs, while the second keyword sorts out papers using a gravity approach. Among the first group we select papers analyzing PTAs and focusing on trade flows to the EU; in the second group,

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we selected those studies including PTAs as the key explanatory variable in the gravity equation. The final sample includes 36 papers (10 published in academic journals and 26 working papers or unpublished studies) providing 638 point estimates based on a dummy variable for PTAs and 338 point estimates based on quantitative variables for PTAs, i.e. the coefficient γ in equations (5.1) (see table 5.1 for details). Table 5.2 shows the structure of the dataset in our MA. It accounts the number of estimates of the impact of preferential schemes on sectoral trade and on total trade. For each group we distinguish the number of estimated coefficients of dummies for trade policies and of explicit measures for preference margins. Most of studies that focus on sectoral trade obtain estimates of the preference effect by using an explicit measure of the margin for specific agreements. Whereas most of studies that estimate the preference impact on total trade use dummy variables as proxy of the trade policy. The information collected on each estimate allows us to test the sensitivity of the results to alternative specifications and differences in the control variables considered, as well as the impact of the publication selection process. We provide pooled estimates, obtained from fixed and random effects models of the PTAs’ effect size on EU imports: the hypothesis that there is no effect of PTAs on trade is robustly rejected at standard significance levels.

5.2.2 MA regression

In the sample considered, it happens quite often that a study provides multiple estimates of the effect under consideration. Pooling different estimates into a large sample for MA raises the question of within-study versus between-study heterogeneity. In order to take this into account, fixed effects and random effects models can be used: the former assume that differences across studies are only due to within-variation; the latter considers both within-study and between-study variability, assuming that the estimates are a random sample from the universe of all possible results (Sutton et al. 2000). Following Higgins and Thompson (2002), the fixed effects model calculates the “true” effect ( Fγ̂ ) underlying every study as a

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weighted average of all the studies' estimates, using the precisions as weights:

∑

∑=

ji ji

ji jijiF

w

wγγ

ˆˆ 5.2

where jiγ̂ is the reported estimate i of the PTAs effect in the jth

study and the weights, wji, are inversely proportional to the square of the standard errors, so that studies with smaller standard errors have greater weight than studies with larger standard errors. However, a field of the literature showing high heterogeneity cannot be summarized by the fixed effects estimate under the assumption that a single “true” effect underlies every study. As a consequence, the fixed effects estimator is inconsistent and the random effects model seems to be more appropriate. The random effects model assumes that there are real differences between all studies in the magnitude of the effect. Unlike the fixed effects model, the individual studies are not assumed to be estimating a true single effect size, rather the true effects in each study are assumed to have been sampled from a distribution of effects, assumed to be Normal with mean 0 and variance σ2. The weights incorporate an estimate of the between-study heterogeneity, σ2, so that the random effects estimate ( ˆ

Rγ ) is

equal to (Higgins and Thompson 2002):

∑

∑=

ji ji

ji jiji

Rw

w

*

*ˆˆ

γγ 5.3

where the weights are equal to 1)2ˆ1(* −+−= σjiwjiw . Allowing for the

between-study variation has the effect of reducing the relative weighting given to the more precise studies. Hence, the random effects model produces a more conservative confidence interval for the pooled effect estimate. A general belief is that publication bias occurs when researchers, referees, or editors have a preference for statistically significant results. The publication bias may greatly affect the magnitude of the

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estimated effect. Several meta-regressions and graphical methods have been envisaged in order to differentiate genuine empirical effect from publication bias (Stanley 2005). The simplest and conventional method to detect publication bias is by inspection of a funnel graph diagram. The funnel graph is a scatter diagram presenting a measure of sample size or precision of the estimate on the vertical axis, and the measured effect size on the horizontal axis. The most common way to measure precision is the inverse of the standard error. Asymmetry is the mark of publication bias: in the absence of such a bias, the estimates will vary randomly and symmetrically around the true effect. The diagram, then, should resemble an inverted funnel, wide at the bottom for small-sample studies, narrowing as it rises.3 A Meta-Regression Analysis (MRA) can also be used to investigate and correct publication bias. The model regresses estimated coefficients ( jiγ̂ ) on their standard errors (Card and Krueger 1995;

Ashenfelter et al. 1999). Since the studies in the literature may differ greatly in data sets, sample sizes, independent variables, variances of these estimated coefficients may not be equal. As a consequence, meta-regression errors are likely to be heteroschedastic, though the Ordinary Least Square (OLS) estimates of the MRA coefficients remain unbiased and consistent. A Weighted Least Squares (WLS) corrects the MRA for heteroschedasticity and the regression equation becomes:

jiejiSe

jitjiSe

ji++==

110

ˆββ

γ 5.4

where tji is the conventional t-value for jiγ̂ the intercept and slope

coefficients are reversed and the independent variable becomes the inverse of Seji. The potential for heteroschedasticity, then, causes the meta-analyst to direct his attention towards the reported t-statistics (Stanley and Jarrell 2005). Equation (5.4) is the basis for the Funnel Asymmetry Test (FAT), and it may now be estimated by OLS. In

3 An additional graphical method is the Egger test that detects funnel plot asymmetry by determining whether the intercept significantly deviates from zero in a regression of the standardized effect estimates against their precision.

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the absence of publication selection the magnitude of the reported effect will be independent of its standard error, then β0 will be zero. Although it is true that the peer-review process can greatly affect the magnitude of the estimated effect, whether or not this impact should be considered a bias is a moot point. Since in MA, notwithstanding the wide variation in the quality of the point estimates included in the study, each estimate in the sample is weighted equally; it could be argued that there is a nonpublication bias due to the lower quality of unpublished research. In the following we assess the conse-quences of the peer-review process, but refer to a general “publica-tion impact” (rather than a “bias”) for the above reasons (Cipollina and Salvatici 2010b). The standard meta regression model includes a set of explanatory variables (X) to integrate and explain the diverse findings presented in the literature:

jieK

k jiSe

jikXk

iSejit

jiSe

ji+∑

=++==

1

110

ˆ αββ

γ 5.5

where β1 expresses the true value of the parameter of interest, Xjik is

the independent variable which measures relevant characteristics (k) of an empirical study and explains its systematic variation from other results in the literature, αk is the regression coefficient which reflects the biasing effect of particular study characteristics, and εji is

the disturbance term.

5.2.3 Explanatory variables

The set of explanatory variables Xjik in equation (5.5) can be partitioned into two groups: the first includes dummies explaining the diversity in the results from a methodological point of view and the second includes dummies regarding structural features of the studies considered. The methodological dummies included in the MRA are based on a recent survey of the errors in the empirical literature applying gravity equations carried out by Baldwin and Taglioni (2006). The “gold medal” of classic gravity model mistakes arises from the correlation between possible omitted variables and the trade-cost terms leading to endogeneity and, consequently, biased estimates. In particular, the estimated trade impact will be upward biased if the

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omitted variables and the variable of interest (PTAs, in our case) are positively correlated. Possible solutions to the “gold medal” problem include country effects (a dummy that is one for all trade flows that involves a particular country) and pair effects (a dummy that is one for all observations of trade between a given pair of countries). Country dummies remove the cross-section bias, but not the time-series one. This is a serious shortcoming since omitted factors affecting bilateral trade costs often vary over time. Accordingly, pair dummies perform better with panel data, but they cannot be used with cross-section data, since the number of dummies equals the number of observations) and, in any case, they provide a partial answer to the “gold medal” bias (Baldwin and Taglioni 2006). In the MRA, in order to control for any possible bias due to the “gold metal” mistake, we adopt the dummy “No-country effects” which is equal to 1 if the original studies do not use country fixed effects to remove

the cross-section bias. 4 The “bronze medal” mistake refers to the (quite common) practice of deflating nominal trade values by an aggregate price index. Since there are global trends in inflation rates, inclusion of this term probably creates a spurious correlation (Baldwin and Taglioni 2006). When the bilateral trade flow is divided by the same price index, a time dummy corrects the mistaken deflation procedure and possible spurious correlation. In our analysis the “No-time effects” equal to 1 if the original studies do not use time fixed effects to account for common shocks affecting all trade flows equally across-countries. Concerning the typologies of data used, it is worth noting that point estimates in our sample are obtained from different datasets: cross-section data, or panel data. Some authors (Baier and Bergstrand 2005; Baldwin 2006) find that the best method for estimating the effect of PTAs on bilateral trade flows is through panel data, since cross-sectional and pooled regression models may be affected by the exclusion or mismeasurement of trading pair–specific variables. For

4 The “silver medal” mistake arises from the fact that gravity models are usually estimated in log form: in this case, computing the wrong average trade (the arithmetic average corresponding to the log of the sums, rather than the geometric average corresponding to the sum of the logs) tends to overestimate the trade effects. In our sample, we find that no study employs the log of average bilateral trade flows in place of the average of the logs of the trade flows and, for this reason, we do not control for this bias.

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this reason, the most recent gravity model estimations tend to use panel data regression techniques.5 We introduce a dummy “Cross-section” which is equal to 1 if the original studies use cross-section or pooled data. With regard to the second group of dummies describing different features of the studies considered, we expect PTAs and their impact on trade to change over a period of time. Accordingly, we use four dummies “1970s”, “1980s”, “1990s” and “2000s”, in order to collect studies using data related only to specific time periods and see whether most recent estimates differ from the earlier ones.6 Most of the empirical analyses use the gravity model with aggregated data both in terms of products and in terms of countries. As far as the product aggregation is concerned, it is well-know that it is inconsistent to use aggregate export flows to analyze the effects of trade preferences applied at product level. Indeed, the few works using disaggregated data confirm that the aggregation produces a significant estimation bias (Aiello et al. 2006). In order to correct for this we add a dummy for papers using “Aggregated data”. Moreover, Engel (2002) criticizes the use of elasticities of substitution estimated without considering the number of countries involved. We add a dummy “Aggregated EU” in order to take into account differences in results for the EU as a whole with respect to those obtained considering each EU member country separately. In addition, since we expect to find different effect sizes in studies that attempt to assess the various determinants of bilateral trade at sectoral level and since most of them focus on the agricultural sector, we add the dummy “Agriculture” to distinguish the PTAs impact on this sector. The use of disaggregated data implies the presence of a high percentage of zero trade flows. It creates obvious problems for the log-linear form of the gravity equation. Several methods have been proposed to deal with this issue: many empirical studies simply drop from the dataset the pairs with zero trade, and estimate the log-linear form using OLS estimator. However, when the zero values are excluded, we face a selection bias problem. In our MRA a dummy “No-zero treatment” is included for estimates

5 The most of papers using panel techniques rely on static panel gravity models.

6 Dummies for years 1970s, 1980s and 1990s are not included in the MRA considering studies adopting preference margins since all of them are focused only on the 2000s.

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obtained by OLS models that do not deal with the presence of zero trade flows. When the dependent variable is zero for a substantial part of the sample but positive for the rest of the sample, the econometric theory suggests the use of Tobit models. However, this procedure relies on rather restrictive assumptions that are not likely to hold since the censoring at zero is not a “simple” consequence of the fact that trade cannot be negative (Cipollina and Salvatici, 2007). Zero flows, as a matter of fact, do not reflect unobservable trade values but they are the result of economic decision making based on the potential profitability of engaging in bilateral trade at all. Recently there has been a long debate concerning what is the best econometric approach in order to avoid the bias that would be implied by dropping of the observations with zero flows. Even if most of the authors suggests the Heckman two-step estimator as the best procedure (Linders and de Groot 2006; Helpman et al. 2008; Martin and Pham 2008), others claim that, because of the presence of heteroskedasticity, estimates of the log-linear form of the gravity equation are biased and inconsistent, then they strongly recommend that gravity type models, as well as other constant-elasticity models, should be estimated in multiplicative form. They suggest a simple quasi-maximum likelihood estimation technique based on Poisson regression (Santos-Silva and Tenreyro 2006; Proenca et al. 2008; Siliverstovs and Schumacher 2009). However, the standard Poisson model is vulnerable for problems of overdispersion and excess number of zero flows. A way to overcome both heteroskedasticity (in the case of the log-normality assumption) and overdispersion (in the case of the standard Poisson specification) is to use the Zero-Inflated Poisson (ZIP) or the Negative Binomial models, recently suggested by Burger et al. (2009). In our multivariate MRA, different methodological dummies (GMM, Hausman-Taylor, Heckman, Poisson, Tobit, Zip/Negative Binomial) are included to deal with the selection bias and the presence of zero trade flows. Regarding (possible) publication bias, we distinguish published from unpublished studies. Since we believe that published and very specific studies tend to include more accurate econometric analyses, we introduce a dummy “Unpublished” equal to 1 for unpublished papers. Furthermore, in order to detect the existence of extreme values, we consider the descriptive statistics for the sample of estimates obtained by using dummy variables and preference

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margins for PTAs and we find 23 extreme values corresponding to the first and the last percentile of the distribution. Since the removal of these extreme values could bias the meta-results (Cipollina and Salvatici 2010b), we prefer to deal with them by inserting a dummy variable “Outlier” (equal to 1 for outliers) in the MRA. Finally, since some studies do not specify the type of agreement, while others include different dummies for each agreement, we add the dummy “PTAs” taking the value 1 if the original paper does not use a variable for each type of agreement. Alternatively, we introduce five dummy variables controlling for the specific agreement: “ACP”, “EBA”, “Euro-Med”, “GSP” and “GSP-Plus”.

5.3 Econometric results

The Fisher test suggests that the null hypothesis of no effect of PTAs on trade should be easily rejected at any standard significance level (χ2 is equal to 6,509 and to 7,536 for estimates coming from papers using dummies and preference margins for trade policy, respectively).7 The fixed and random effects model provide a synthetic measure of such impact. Table 5.3 shows combined meta-estimates of jiγ̂ together with the

p-values associated with the tests for the lack of any effect. The null hypothesis is easily rejected, confirming the existence of an impact of PTAs on EU bilateral trade. Looking at the fixed effects estimate, in the case of coefficients obtained by papers using a dummy variable as proxy for trade policy, we get that PTAs increase trade by around 2% (e0.02 - 1 = 0.02), while in the case of estimates associated to papers adopting quantitative variables for the measure of preferences, results indicate that an increase of 10% in preference margins implies an increase in trade of around 0.6%. However, considering the high heterogeneity in our sample of estimates8, we should look at the more appropriate random effects results. The

7 Under the null hypothesis of no effect (γ = 0), no publication selection and independence, the statistic minus twice the sum of the logarithms of the p-values is distributed approximately as a χ

2 with 2n degrees of freedom (Fisher 1932).

8 The last column of table 5.3 shows p-values of the Q statistic providing a test of homogeneity (for a detailed description, see Higgins and Thompson 2002). As expected, in all cases, we strongly reject the null hypothesis of estimates homogeneity.

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random effects estimate indicates an increase up to 22% (e0.20 - 1 = 0.22) when the dummy variable is used in the analysis, and an elasticity coefficient of 0.7% if the preference margin increase of 10%, when an explicit measure for the preferential policy is used. The results of the studies using dummies seems to be higher, in absolute term, than those obtained by studies using some measures of margins. However, the two analyses are not comparable: the estimated coefficient of dummy refers to total effect, while the estimated effect size of the preference margin is an elasticity. Table 5.4 shows combined meta-estimates of jiγ̂ by distinguishing

different PTAs. In general, PTAs have an effect on trade which is statistically significant, except for GSP-Plus and Euro-Med. Such effect is positive in all cases, apart from EBA when the dummy variable is used as proxy for the policy. If we look at the sample of estimates obtained using the dummy for the presence of PTAs, the smaller random effect in the case of EBA indicates that such scheme decrease trade by 28%, whereas the largest effect estimate of the Cotonou agreement for ACP countries indicates an increase in trade of more than 90%. When we consider the sample of estimates obtained using an explicit measure for margin of preference, the null hypothesis is easily rejected in three out five PTAs, confirming the existence of an impact of GSP, ACP and EBA on bilateral trade with an elasticity coefficient ranging between 0.02 and 0.03, implying that a 10% increase in the preference margin increases trade by around 2-3%. The funnel test for detecting the presence of publication bias is represented in figures 5.1 and 5.2. When the trade policy is proxied by a dummy variable, the mean PTAs effect is 0.02 and the median is 0.18. Even though the graph in figure 5.1 (panel a) slightly resembles a funnel, it does not present the symmetry that is crucial to exclude publication bias. Estimates of PTAs effects seem to indicate a positive effect on trade, also the Egger test (panel b in figure 5.1) shows that the intercept deviates significantly from zero in a regression of the standardized effect estimates against their precision. Figure 5.2 (panel a) represents the funnel graph of individual estimates obtained by using preference margins for PTAs. It clearly shows that the plot is overweighted on the right side, with a mean equal to 0.08 and a median equal to 0.4. Such direction is

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also confirmed by the Egger approach (panel b). As far as we consider graphical test, the publication selection assumes a particular path for estimates obtained both by using dummy variables and preference margins for preferences. We explore the publication bias more rigorously by estimating equation (5.4): the results are reported in table 5.5. Columns 1 and 2 show the results for the sample of estimates based on dummy variable and those based on preference margins, respectively. In both cases, the estimated intercept, β0, is significantly positive confirming the apparent asymmetry of the funnel graphs (column 1). Considering the magnitude of the reported effect (the parameter β1), results are lower than pooled estimates obtained by the random-effects model (table 5.3). In order to filter out publication impact and other biases, and to control for the different features of studies surveyed, we estimate the multivariate meta regression (equation (5.5)) using an OLS approach. However, the presence of more than one estimate reported per study is problematic, because the OLS estimator may be consistent but inefficient if the dependence among estimates obtained in the same study is not taken into account. In order to get correct standard errors, we adopt a “robust with cluster” procedure, adjusting standard errors for intra-study correlation (Cipollina and Salvatici 2010b). Each cluster identifies the study the estimate belongs to: this changes the variance-covariance matrix and the standard errors of the estimators, but not the estimated coefficients themselves. Tables 5.6 and 5.5 present the results for the sample of estimates based on dummy variable and those based on preference margins, respectively. With respect to table 5.6, in table 5.7 we drop some variables because of multicollinearity. In particular, papers estimating the PTAs effects through an explicit measure of preference margin are based on very disaggregated data and always addresses the issue of zero flows. Indeed, since these papers are more recent, they tend to include the most advanced choices from a methodological point of view. In each table, models 1 and 2 present the estimated coefficients with and without the introduction of a fixed effect for each type of agreement. Comparing the two models it appears that the results are largely robust. The statistically significant estimates of β0 in table 5.6 confirm the apparent asymmetry of the funnel graph, since the

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reported effect is not independent of its standard error, whereas the β1 estimate provides evidence of a significant general PTAs effect on trade of 0.17 (model 1) and 0.53 (model 2), indicating a positive impact of preferences on trade of around 20% and 70%, respectively. The dummy “No-country effects” is used to correct for the “gold medal” mistake pointed out by Baldwin and Taglioni (2006). Its statistically insignificant coefficient suggests that the omitted variable bias does not seriously affect the estimation of the PTAs trade impact. The dummy “No-time effects” is introduced to offset the “bronze medal” error implied by the mistaken deflation procedure. The negative sign associated with this variable shows that uncorrected studies tend to underestimate the PTAs impact on trade. Coming to the variables related to each study characteristics, we find significant and negative coefficients associated with the dummy for period 2000s: the effect size tends to be smaller in the studies focusing on recent preferential schemes. Such a result is much more evident in the case of estimations using explicit variables for preference margins, where the effect size have a tendency to become negative. Regarding the typologies of data used, the negative coefficient suggests that the product aggregation bias leads to a serious underestimation of the PTAs trade impact. In this respect, it is worth recalling that all papers based on aggregated data use a dummy variables for the presence of preferences. By comparing the results for the EU as a whole with those obtained taking into account the differences in the import structure of the EU members, the positive and statistically significant coefficients of dummy “Aggregated EU”. It confirms the overestimation consequences of the geographical aggregation bias. Apparently, the estimation problems make the overestimation bias even larger when all EU importers are lumped together. Moreover, estimates that refer to the impact on trade of EU preferences in the agricultural sector tend to be lower. It is not surprising since the role of the agricultural sector is crucial because it accounts for a large share of developing countries and is heavily protected in the European market (Cipollina and Salvatici 2010a).

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As far as the estimation methods are concerned, the treatment of “zeros” seems to be a problem: studies that do not deal with the problem of zeros in the trade matrix get higher coefficients for the PTA effect. However, when the estimate is carried out using dummies for preferential policies, papers that address the issue of zero flows by adopting the Tobit and GMM estimators find lower effects, whereas Hausman-Taylor, Poisson and Zip/Negative Binomial estimators produce higher coefficients. Looking at the coefficient of the dummy “Unpublished”, it is statistically insignificant implying that the peer-review process do not play any role in affecting the magnitude of the estimated effect. As it was mentioned in the previous section, we handle the extreme values in the sample adding a dummy called “Outliers”. The estimated coefficient of this variable is clearly positive, since most outliers indicate a positive and very high effect size of PTAs. In any case, the removal of this dummy does not significantly affect the results. Finally, we find a positive and highly significant coefficient for the “PTAs” dummy taking the value 1 if the original estimates do not focus on a specific type of preferential scheme, implying a general effect on trade of 0.40 (0.23+0.17); that is preferences raise trade by 50%. Studies focusing on specific PTAs tend to estimate much lower impacts on trade. In particular, the dummies for the “EBA” and “GSP-Plus” regimes imply a negative overall impact on trade. Conversely, studies focusing on “Euro-Med” and the “GSP” preferential agreements get lower but still positive impact on trade.. Concerning estimates obtained by using preference margins (table 5.7), the intercept β0 is not significant, then there is not evidence of asymmetry in distribution of econometric results. Conversely, the coefficient β1 suggests that an increase of preferences by 10% fosters trade by about 4%. With respect of table 5.6, coefficients of control variables used in the MRA in table 5.7 are quite consistent. The positive and statistically significant estimate for the dummy “Cross-section” confirms that results from cross-section and pooled models may be affected by the exclusion or mismeasurement of trading pair-specific variables (Baldwin 2006). If we look at the PTAs effects for papers using an explicit measure of preference margin, the results suggest the existence of a “geographical aggregation bias” that can lead to an underestimation

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of the preference impact, since the coefficient of dummy “Aggregated EU” is negative and statistically significant. All studies that estimate the PTAs effect with the preference margin variable use disaggregated data and have to deal with the zero-value in trade flows. Among the possible approaches used, the Heckman two step procedure tends to halve the estimated impact of PTAs. The positive coefficient for the dummy “Unpublished” in table 5.7 may be a good news, suggesting that editors do a pretty good job in excluding the highest (and possibly less realistic) results. Usually, papers that compute a measure for the preference margin, in order to estimate its potential impact on trade flows, are particularly interested at this issue. However, the negative coefficient of the “PTAs” dummy says when the original estimates do not focus on a specific type of preferential scheme their size is slightly lower. Conversely, the estimated impact of EBA and GSP is higher, while the impact of the GSP-Plus is lower but still positive. This result hints to the existence of a “psychological bias”, since authors interested in estimating the effect of preferential trade policy tend to report larger results.

5.4 Conclusions

Recent empirical studies attempt to assess the impact of EU PTAs on trade flows in a gravity framework. The interest on this field of literature is likely to increase in the immediate future due to the deeper involvement of the EU in a web of preferential trade relations with other countries or regional groupings. One way to carry out a comparative study of empirical results on this field is to simply tabulate authors, countries, methodology and results. However, from a policy perspective it is useful to complement qualitative analyses with a more precise quantitative research synthesis. For this reason, the aim of this chapter is to provide a MA approach to summarize the trade effect highlighted in the literature. As far as the impact of PTAs on trade is concerned, the different ways adopted to measure preferences need be taken into account. In particular, in conducting the MA we distinguish between estimates coming from papers adopting dummy variables and estimates obtained by using quantitative measures of preferences. Accordingly, by means of MA techniques we summarize 638 point

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estimates based on dummy variables and 338 based on preference margins, collected from a set of 36 studies. The pooled fixed and random effect estimates reveal an impact ranging between 2% and 22%, respectively, for studies using dummy variables for trade policies, and an elasticity of0.06 and 0.07, respectively, for studies using explicit preference margins. However, considering the heterogeneity of estimates included in the sample, in terms of econometric methodologies and specific features, the MA conducted by using the more appropriate random effect method confirms a robust, positive effect of PTAs on trade which remains significant and economically relevant even after considering most specific agreements between EU and other countries. By looking also for publication selection, the results suggest a specific path since the magnitude of the reported estimates obtained by using dummy variables will depend on its standard error, while the elasticity coefficients of preference margins do not seem to be affected by publication bias. However, even after correcting for publication bias, the magnitude of the trade effect remains economically and statistically significant for coefficients of dummy variables, equivalent to an increase in trade of around 88%. As far as the methodological choices are concerned, and compared to the general effect of preferences on trade, the MRA provides evidence that the bias due to the omitted variable problem (“gold medal” mistakes) is not an issue in our sample of estimates, while the small problem deriving from the inappropriate deflation of nominal trade values (“bronze medal” mistakes) confirm a downward bias for estimates not considering time effects. Moreover, concerning the typology of data used, the MRA highlights that cross-sectional models are affected by the exclusion or mismeasurement of trading pair-specific variables in estimates using preference margins. Concerning the specific features of each study, results reveal a decreasing magnitude effect for the most recent years and for products’ aggregated data . Conversely, extreme values and unpublished studies in the sample produce an upward bias in the estimated impact of preferences through dummy variables and preference margins, respectively. In conclusion, all combined estimates of PTAs imply a substantial increase in trade, but they vary a lot depending on the estimation

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method. It should be emphasized that the MA is a methodology for reviewing the literature, not an alternative approach to studying the trade effects of PTAs. The goal is not to discover the “true” value of the parameter under investigation, but rather to explain why there is so much variation in the empirical results reported in the economic studies that supposedly investigate the same phenomenon. Our results shed some light on the role played by some research characteristics in explaining the variation in reported estimates. References

Aiello F, Agostino MR, Cardamone P (2006) Reconsidering the impact of trade preferences in gravity models. Does aggregation matter? TradeAG Working Paper

Aiello F, Cardamone P (2010) Analysing the effectiveness of the EBA initiative by using a gravity model. Pue&Piec Work. Pap.n. 10/7

Aiello F, Demaria F (2010) Do preferential trade agreements enhance the exports of developing countries? Università della Calabria, Dipartimento di Economia e Statistica, Working Paper n. 02/2010

Ashenfelter O, Harmon C, Oosterbeek, H (1999) A Rev of estimates of the schooling/earnings relationship, with tests for publication bias. Labour Economics 6:453-470

Baier SL, Bergstrand JH (2005) Do free trade agreements actually increase members’ international trade? Federal Reserve Bank of Atlanta Working Paper n. 2005-3

Baldwin R (2006) The Euro’s trade effects. European Central Bank Working Paper n. 594 Baldwin R, Taglioni D (2006) Gravity for dummies and dummies for gravity equations. NBER

Working Paper n. 12516 Caporale GM, Rault C, Sova R, Sova A (2009) On the bilateral trade effects of free trade

agreements between the EU-15 and the CEEC-4 countries. Rev. of World Economy 145:189-206

Card D, Krueger AB (1995) Time-series minimum-wage studies: a meta-analysis. Am. Econ. Rev. 85:238-43

Cardamone P (2007) A survey of the assessments of the effectiveness of preferential trade agreements using gravity models. TradeAg Working Paper n. 07/09

Cardamone P (2009) Preferential trade agreements granted by the European Union: an application of the gravity model using monthly data. Pue&Piec Working Paper n. 09/6

Cipollina M., Laborde D., Salvatici L. (2010), Do Preferential Trade Policies (Actually) Increase Exports? A comparison between EU and US trade policies, Working Paper presented at ETSG 2010 in Lausanne, Switzerland, 9-11 September..

Cipollina M, Salvatici L (2010a) The impact of European Union agricultural preferences. J. of Econ. Policy Reform, Vol. 13:87-106.

Cipollina M, Salvatici L (2010b) Reciprocal trade agreements in gravity models: A Meta-Analysis. Rev of International Econs. 18:63-80

Demaria F (2009) Empirical analysis on the impact of the EU GSP scheme on the agricultural sector. Dissertation, University of Calabria

Engel C (2002) Comment on Anderson and van Wincoop. In: Collins S and Rodrik D (eds) Brookings Trade Forum 2001. The Brookings Institution, Washington

Fisher RA (1932) Statistical methods for research workers. Oliver and Boyd, London Francois J, Hoekman B, Manchin M (2006) Preference erosion and multilateral trade

liberalization. The World Bank Econ. Rev. 20:197-216 Glass GV, McGaw B, Lee Smith M (1981) Meta-Analysis in social research. Sage, Beverly

Hills, CA

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Higgins JPT, Thompson SG (2002) Quantifying heterogeneity in a meta-analysis. Statistics in Med. 21:1539-58

Manchin M (2006) Preference utilisation and tariff reduction in EU imports from ACP countries. The World Economy 29:1243-1266

Martínez-Zarzoso I, Nowak-Lehmann DF, Horsewood N (2009) Are regional trading agreements beneficial? Static and dynamic panel gravity models. North American J. of Economics and Finance, 20:46-65

Nielsen CP (2003) Regional and preferential trade agreements: a literature Rev and identification of future steps. Fodevareokonomisk Institut, Copenhagen, Report n. 155.

Nilsson L (2002) Trading relations: is the roadmap from Lomé to Cotonou correct? Appl. Economics 34:439-452

Nilsson L, Matsson N (2009) Truths and myths about the openness of EU trade policy and the use of EU trade preferences. DG Trade European Commission Nijkamp Poot Work Pap

Oguledo VI, MacPhee CR (1994) Gravity models: a reformulation and an application to discriminatory trade arrangements. Appl. Economics 26:107-120

Péridy N (2005) The trade effects of the Euro-Mediterranean partnership: what are the lessons for ASEAN countries? J. of Asian Economics 16:125-139

Proenca I, Fontoura MP, Martìnez-Galàn E (2008) Trade in the enlarged European Union: a new approach on trade potential. Portuguese Econ. J. 7:205-224

Rose AK, Stanley TD (2005) Meta-analysis of the effect of common currencies on international trade. J. of Econ. Surveys 19:347-365

Santos Silva JMC, Tenreyro S (2006) The log of gravity. The Review of Economics and Statistics, Vol. 88, 641-58.

Siliverstovs B, Schumacher D (2009) Estimating gravity equations: to log or not to log? Empirical Economics 36:645-669

Stanley TD (2005) Beyond publication bias. J. of Econ. Surveys 19:309-346 Sutton AJ, Abrams KR, Jones DR, Sheldon TA, Song F (2000) Methods for meta-analysis in

medical research. John Wiley, Chichester

Table 5.1 Papers included in the MA

Authors and References N. of estimates

Mean Min Max

Published studies using dummy variable

Agostino M, Demaria F, Trivieri F (2010). Journal of Agricultural Economics 61

27 0.19 -0.30 0.80

Caporale GM, Rault C, Sova R, Sova A (2009). Rev. of World Economy 145

7 0.21 0.67 15.9

De Benedictis L, De Santis R, Vicarelli C (2005). The European J. of Comparatice Economics 2

1 0.11 -0.48 0.68

Martínez-Zarzoso I, Nowak-Lehmann DF, Horsewood N (2009). North Ame. J. of Econ. and Finance 20

14 0.02 -0.68 1.68

Nilsson L (2002). Appl. Economics 34 142 0.25 1.37 1.37

Oguledo VI, MacPhee CR (1994). Appl. Economics 26 1 1.37 0.12 1.65

Péridy N (2005). J. of Asian Economics 16 6 0.5 0.12 1.65

Published studies using preference margins

Cipollina M, Salvatici L (2010a). J. of Econ. Policy Reform 13 10 5.32 -1.40 0.18

Francois J, Hoekman B, Manchin M (2006). The World Bank Econ. Rev. 20

4 -0.53 0.00 0.12

Manchin M (2006). The World Economy 29 28 0.05 -0.35 0.30

Working papers and unpublished studies using dummy variable

Amurgo-Pacheco A (2006). Graduate Institute of International Studies, Geneva. HEI Working Paper n. 18/2006

6 0.18 -0.01 0.01

De Santis R, Vicarelli C (2006). Mimeo 22 0.40 0.15 0.58

De Santis R, Vicarelli C (2007). Istituto di Analisi Economica, Working Paper n. 79, March 2007

4 0.41 -50.9 20.46

De Wulf L, Maliszewska M (2009). Center for Social and Economic Research. Final report, September 2009.

8 0.08 -5.99 4.07

García-Alvarez-Coque JM, Marti Selva ML (2006) MPRA Working Paper n. 4124

54 -1.58 -0.29 1.08

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Gasiorek et al., (2010). Report for the European Commission 11 1.07 2.97 -5.60

Gaulier G, Jean S, Ünal-Kesenci D (2004). CEPII Working Paper n. 2004-16, November

10 0.433 -1.83 -1.58

Gradeva K, Martinez-Zarzoso I (2009). Ibero America Institute for Econic Research (IAI) Discussion Paper n. 197, August 2009

5 -1.65 -1.77 1.93

Leite JC (2008). Dessarrollo y Sociedad, Primier semester 2008 112 0.25 0.00 0.63

Nilsson (2005). Mimeo 8 0.52 -0.70 0.88

Nilsson (2009). European Commission, Directorate General for Trade

12 0.20 -0.26 5.41

Nugent JB, Yousef TM (2005). EUI Working Paper RSCAS n. 2005/26

6 -0.55 -3.31 0.52

Persson E (2008). Bachelor thesis University of Lund - Department of Economics

40 -0.49 -0.67 0.74

Persson M, Wilhelmsson F (2005). Lund University, Sweden 32 0.16 -0.69 0.43

Persson M, Wilhelmsson F (2006). Lund University, Sweden 25 0.07 -1.51 -0.30

Pishbahar E, Huchet-Bourdon M (2007). Working Paper presented at PhD Workshop, EAAE 2007, Rennes, France

6 -0.99 0.09 0.73

Pusterla F (2007). IDB-SOE Working Paper, January 2007 9 0.39 -0.82 0.47

Ruiz JM, Vilarrubia JM (2007). Banco de Espana. Documentos de Trabajo n. 0720

25 -0.08 -0.94 1.96

Verdeja L (2006). Working Paper presented at ETSG 2005 in Dublin, Ireland

45 0.38 -0.94 1.06

Unpublished studies using preference margins

Aiello F, Demaria F (2010). Università della Calabria. Dipartimento di Economia e Statistica. Working Paper n. 02/2010

75 0.00 -0.41 0.52

Aiello F, Cardamone P (2010). Analysing the effectiveness of the EBA initiative by using a gravity model. Pue&Piec Working Paper n. 10/7

94 0.02 -0.20 0.09

Cipollina M, Laborde D, Salvatici L (2010). Working Paper presented at ETSG 2010 in Lausanne, Switzerland

18 0.33 -0.13 0.61

25

Cipollina M, Salvatici L (2007). TradeAg Working Paper n. 2007/11

32 1.36 0.11 0.11

Demaria F (2009). On the impact of the EU GSP scheme. Dissertation, Università della Calabria

71 -1.47 -0.50 0.75

Manchin M (2004). Tinbergen Institute Discussion Paper 2004 - 132/2

40 0.12 0.23 0.78

Nilsson L, Matsson N (2009). European Commission, Directorate General for Trade

16 1.70 -1.34 0.97

Table 5.2 Structure of the dataset

Trade\Policy (number of estimates)

Specific agreements PTAs Dummy variable

Preference Margin

Dummy variable

Preference Margin

Sectoral trade 164 217 83 0 Total trade 330 38 144 50

Table 5.3 MA of estimates of PTAs effect on trade

Sample Effects Pooled Estimate

Lower Bound of 95% CI

Upper Bound of 95% CI

p-value for

H0: no effect

Q-test

(p-value)

Dummy for PTAs

Fixed effects 0.02 -0.01 0.02 0.00 0.00

Random effects 0.20 0.17 0.23 0.00 0.00

Preference margin

Fixed effects 0.06 0.06 0.06 0.00 0.00

Random effects 0.07 0.06 0.07 0.00 0.00

Table 5.4 MA of estimates of different PTAs effect on trade

Sample Random effects

ACP EBA Euro-Med GSP GSP-Plus

Dummy for PTAs 0.66*** -0.33** 0.05 0.14*** 1.32

Preference margin 0.03*** 0.02** 0.01 0.02*** -0.01

Note: (*) significant at 10% level; (**) significant at 5% level; (***) significant at 1% level.

Table 5.5 MRA of PTAs effect

Coefficient

Variables Dummy for PTAs Preference Margins

β0: Intercept 0.36 *** 1.00 *** (0.05) (0.10)

β1: 1/Se 0.13 *** 0.04 *** (0.00) (0.01)

N. of studies 638 388

Note: Standard errors in parenthesis; (*) significant at 10% level; (**) significant at 5% level; (***) significant at 1% level.

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Table 5.6 MRA of PTAs effects for papers using dummies for PTAs

Model 1 Model 2 β0: Intercept 0.53* 0.51 (0.28) (0.38) β1: 1/Se 0.17* 0.53*** (0.09) (0.09) No-country effects -0.04 0.13 (0.22) (0.21) No-time effects -0.28** -0.41*** (0.13) (0.08) Cross-section 0.06 -0.01 (0.13) (0.12) 1970s 0.19 0.21 (0.20) (0.21) 1980s 0.27 0.20 (0.20) (0.19) 1990s 0.28 0.20 (0.20) (0.19) 2000s -0.39** 0.11 (0.15) (0.32) Aggregated data -0.55*** -0.67*** (0.12) (0.13) Aggregated EU 0.31* 0.25 (0.16) (0.21) Agriculture -0.49*** -0.43*** (0.15) (0.14) No-zero Treatment 0.37*** 0.35*** (0.10) (0.08) GMM -0.08* -0.06 (0.04) (0.04) Hausman-Taylor 0.16 0.29* (0.15) (0.16) Heckman -0.01 -0.02 (0.09) (0.09) Poisson 0.69* 0.98 (0.40) (0.58) Tobit -1.67*** -1.97*** (0.20) (0.19) ZIP/Negative Binomial 0.61 6.35** (0.39) (2.97) Unpublished 0.02 -0.07 (0.07) (0.07) Outliers 3.67*** 4.87*** (0.10) (0.44) PTAs 0.23*** (0.08) ACP 0.05 (0.18) EBA -0.90*** (0.30) Euro-Med -0.24*** (0.05) GSP -0.12* (0.07) GSP-Plus -7.01** (3.13)

Adjusted R2 0.46 0.61

Note: No. of obs. (no. of clusters) = 638 (26); (*) significant at 10% level; (**) significant at 5% level; (***) significant at 1% level. Standard errors adjusted for studies/clusters are reported in parentheses.

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Table 5.7 MRA of PTAs effects for papers using preference margins for PTAs

Model 1 Model 2 β0: Intercept -0.24 -0.24 (0.73) (0.75) β1: 1/Se 0.42* 0.41* (0.18) (0.19) No-country effects 0.03 0.03 (0.03) (0.03) No-time effects -3.48*** -3.47*** (0.58) (0.60) Cross-section 4.25*** 4.23*** (0.76) (0.78) 2000s -0.47** -0.46** (0.18) (0.19) Aggregated EU -0.44** -0.44** (0.18) (0.18) Heckman -0.25*** -0.25*** (0.03) (0.03) Poisson -0.01 -0.01 (0.01) (0.01) ZIP/Negative Binomial -0.01 -0.01 (0.02) (0.02) Unpublished 0.07*** 0.06*** (0.00) (0.00) Outliers 16.16*** 16.16*** (3.69) (3.75) PTAs -0.01*** (0.00) ACP -0.00 (0.00) EBA 0.01** (0.01) Euro-Med 0.00 (0.00) GSP 0.02*** (0.00) GSP-Plus -0.03*** (0.00) Adjusted R2 0.68 0.69

Note: No. of obs. (no. of clusters) = 338 (10); (*) significant at 10% level; (**) significant at 5% level; (***) significant at 1% level. Standard errors adjusted for studies/clusters are reported in parentheses.

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Figure 5.1: Funnel graph of individual estimates obtained by paper using dummies for

PTAs 1

/se

ga

mm

a

Funnel plot Dummy_policy=1gamma

-10 -5 0 5 10

.262398

1000

Egger's publication bias plot

sta

nda

rdiz

ed e

ffe

ct

precision0 500 1000

-50

0

50

29

Figure 5.2: Funnel graph of individual estimates obtained by papers using preference

margins for PTAs

1/s

ega

mm

a

Funell Plot Dummy_policy=0gamma

-60 -40 -20 0 20

.011776

1000

Egger's publication bias plot

sta

nda

rdiz

ed e

ffe

ct

precision0 500 1000

0

100

200