Estimating the Effects of Non-Discriminatory Trade Policies within Structural Gravity Models

We propose a simple method to identify the effects of unilateral and non-discriminatory trade policies on bilateral trade within a theoretically-consistent empirical gravity model. Specifically, we argue that structural gravity estimations should be performed with data that include not only international trade flows but also intra-national trade flows. The use of intra-national sales allows identification of the effects of non-discriminatory trade policies on the importer side (e.g. most favored nation tariffs) and on the exporter side (e.g. export subsidies), even in the presence of exporter and importer fixed effects. An important byproduct of our approach is that it can be used to recover estimates of the export-supply elasticity and of the import-demand elasticity. We demonstrate the effectiveness of our techniques in the case of MFN tariffs and "Time to Export" as representative determinants of trade on the importer and on the exporter side, respectively. Our methods can be extended to quantify the impact on trade of any country-specific characteristics as well as any non-trade policies.


Introduction
Owing to its theoretical microeconomic foundations and remarkable predictive power, the structural gravity model has become the workhorse in the empirical trade literature that studies the eects of various determinants of bilateral trade ows and the impact of trade policies in particular. 1 However, as is evident from the opening quote of our study, despite its popularity and empirical success, the structural gravity equation cannot be used to identify the impact of any unilateral and non-discriminatory trade policies both on the importer side (e.g. MFN taris) and on the exporter side (e.g. export subsidies). General of the World Trade Organization (WTO) Pascal Lamy, 3 the world trade system has evolved from a state of protection (with the producer in mind) to a state of precaution (with the consumer 1 The structural gravity equation has been derived from a series of alternative theoretical foundations including, but not limited to, Armington-CES, Ricardian, Hekscher-Ohlin, monopolistic competition, heterogeneous rms, intermediate goods, and dynamic settings. The corresponding empirical gravity equation consistently delivers strong t (of 60 to 90 percent) with aggregate data but also with sectoral data for both goods and for services. We refer the reader to Anderson (2011), Costinot and Rodríguez-Clare (2014), Head and Mayer (2014),  for recent gravity surveys.
2 As pointed out by Head and Mayer (2014), the eects of such policies cannot be identied within the structural gravity model because they are perfectly collinear with and absorbed by the importer and/or by the exporter xed eects, which have to be included in gravity estimations to control for the multilateral resistance terms of Anderson and van Wincoop (2003).
Our most important result is that we can indeed identify the estimates of the eects of both non-discriminatory trade-policy variables (MFN taris and TTE), in the presence of importer and exporter xed eects, without any collinearity issues. In addition, we note that, in accordance with our intuition and despite the fact that our covariates were selected for methodological and demonstrative purposes, the estimates of the eects of MFN taris and Time to Export have the expected negative signs; they are statistically signicant; and they also have plausible economic magnitudes. In particular, our preferred econometric specications deliver estimates of the impact of MFN taris that are used to obtain structural values for the trade elasticity parameter of around 4.3 to 6.9, which are readily comparable to corresponding estimates from the existing literature. 6 Furthermore, our preferred estimates of the coecient on Time to Export reveal that an additional day of time to export reduces trade ows by around 3.5 percent.
The contribution of this paper is related to several strands of the literature. First, from a methodological perspective, our approach improves on three existing methods to identify the impact of unilateral policies and country-specic characteristics within the gravity literature: (i) Numerous papers have used country-specic variables directly in a-theoretic empirical gravity models that do not control for the multilateral resistances (MRs) and, therefore, deliver estimates that are potentially biased and subject to the critique of Anderson and van Wincoop (2003). In relation to these papers, our methods allow identication of the eects of country-specic variables even in the presence of exporter and importer xed eects, which control for the MRs; (ii) Some authors have constructed new dyadic variables as combinations of the country-specic variables of interest. 7 The coecients of the new bilateral variables can be estimated in the presence of exporter and importer xed eects. However, this approach does not allow for interpretation of the impact of the countryspecic variables. Our contribution in relation to this literature is that our methods allow for direct identication and clear interpretation of the eects of country-specic variables without the need of bilateral transformations; (iii) Finally, a third group of papers have implemented a two-stage 6 For example, Head and Mayer (2014) oer a summary meta-analysis estimate of the elasticity of substitution σ = 6.13. 7 For example, Rauch and Trindade (2002) identify the eects of ethnic networks on bilateral trade by the product of the ethnicity share in the two counties. Similarly, Anderson and Marcouiller (2002) construct a dyadic ratio variable for the strength of institutions for defending trade. Djankov et al. (2010) estimate the impact of the ratio of time to export of two countries exporting to a third country by using the ratio of the two countries' exports.
3 estimation approach where, in the rst step, the appropriate set of exporter and importer xed eects are included in the gravity regression, and then, in the second step, the tted values of the xed eects are regressed on the policy variables of interest which could not be included in the rst step. 8 Even if the rst-stage xed eects are estimated consistently, 9 the two-step approach has been criticized because its asymptotic properties have not yet been established formally. Furthermore, if the rst-stage gravity estimates are obtained with the PPML estimator, which has become the standard for gravity regressions (see Santos Silva and Tenreyro, 2006), then the xed eects can be predicted perfectly in the second stage by the the structural gravity terms (i.e. by size and the MRs, see Fally, 2015) and, therefore, identication of other country specic variables in the second stage is not possible.
Second, from a practical perspective and as emphasized above, our methods allow for identication of the impact of non-discriminatory and unilateral trade policies on the exporter side and on the importer side. Thus, our work contributes to the literature on the trade eects of MFN taris (see for example Augier et al., 2005) as well as to the literature concerning trade facilitation (see for examples Wilson et al., 2005;Martinez-Zarzoso and Márquez-Ramos, 2008;Djankov et al., 2010) by allowing for estimation of the eects of such policies directly within the structural gravity model.
While the focus of the analysis in this paper is on trade policies, our methods can be extended and applied more broadly to obtain estimates of the eects on trade of any country-specic characteristics (e.g. size and institutions) as well as any non-trade policies (e.g. value added taxes and exchange rates), thus having much broader implications and contributing to a much wider literature.
Third, a potentially important byproduct of our approach is that it can be used to obtain estimates of the elasticity of substitution, which is the single most important parameter in the international trade literature, see Arkolakis et al. (2012). Since MFN taris are a direct price-shifter, gravity theory can be used to recover the elasticity of substitution directly from the estimate of the coecient on MFN taris. 10 Thus, we contribute to the literature that aims at estimating trade 8 Examples include Eaton and Kortum (2002), Head and Ries (2008), Anderson and Yotov (2012), and Head and Mayer (2014). 9 Only recently the consistency of the model parameter estimates in nonlinear panel models with two types of xed eects has been shown by Fernández-Val and Weidner (2016). 10 We refer the reader to Heid and Larch (2016) for a formal derivation of the structural gravity system with taris. 4 elasticities. 11 While bilateral measures of eectively applied taris have previously been used to identify the trade elasticity in structural gravity frameworks, e.g. de Sousa et al. (2012), Egger and Larch (2012), Aichele et al. (2014), and Heid and Larch (2016) to date MFN taris have not been used as the literature so far has focused on estimating gravity models using inter national trade data only and, as noted above, the eects of MFN taris in such settings are absorbed by the importer or importer-time xed eects in structural gravity models. The ability to use MFN taris has several practical advantages. Specically, MFN taris are the predominant form of non-discriminatory trade policy. In addition, MFN tari data are widely accessible and available over a long period of time and for a wide range of countries.
Fourth, with appropriate data on export support (e.g. with data on export subsidies, which may also take the form of direct price shifters), our methods can also be used to recover estimates of the export supply elasticities, which have been of signicantly lower interest to the trade profession. Exceptions to this include Kee et al. (2004), Broda et al. (2006), Tokarick (2014), Imbs and Mejean (2015), and Imbs and Mejean (2017). The ability of our method to recover estimates of the import demand elasticities and of the export supply elasticities has broader implications for trade policy analysis because our approach enables researchers to perform general equilibrium simulation experiments with elasticity parameters that have been obtained within the same theory-consistent structural estimation framework.
Finally, our work is related to a literature that already has capitalized on some of the benets of using intra-national trade ows within the structural gravity model. 12 For example: Anderson andvan Wincoop (2003), de Sousa et al. (2012) and Anderson et al. (2015) use intra-national trade data to estimate border eects; Anderson and Yotov (2010) use intra-provincial and inter-provincial sales 11 See for example Eaton and Kortum (2002), Anderson and van Wincoop (2003), Broda et al. (2006), Kee et al. (2008 and Simonovska and Waugh (2014). Costinot and Rodríguez-Clare (2014) and Head and Mayer (2014) provide discussions of the available estimates of the elasticity of substitution and trade elasticity parameter.
12 While the current literature review focuses on the most closely related papers from a methodological perspective, we also note that our work is related to a recent and more broad literature that recognizes the importance of intra-national trade frictions. For example, Ramondo et al. (2016) demonstrate that the standard ndings (i) that larger countries should be richer than smaller countries and (ii) that real income per capita increases too steeply with country size, disappear when intra-national trade costs are taken into account. Donaldson (2016) studies the implications of intra-national trade costs in the form of railroad network in India for productivity and welfare. Co³ar and Demir (2016) and Co³ar and Fajgelbaum (2016) consider the impact improvements in transportation infrastructure and internal geography when trade must pass through gateway locations.
to study the impact of trade liberalization within Canada; Yotov (2012) uses intra-national trade ows to resolve`the distance puzzle' in international trade; Dai et al. (2014) employ domestic sales in order to identify the impact of free trade agreements; nally, Bergstrand et al. (2015) rely on intranational trade ows in order to identify the impact of globalization and the evolution of international borders over time. A common feature of all of these studies is that they use intra-national trade ows data in order to identify the impact of bilateral variables within the structural gravity model.
Thus, the analysis in none of the above-mentioned studies is subject to the challenges from the motivational quote of our paper. Instead, the contribution of our work is exactly to address these challenges by recognizing and highlighting the ability of the structural gravity model to identify the impact of unilateral and non-discriminatory trade policies.
The rest of the paper is organized as follows. Section 2 briey reviews the structural gravity theory (in Section 2.1) and illustrates our identication strategy (in Section 2.2). Section 3 introduces our econometric specication (in Section 3.1), describes our data (in Section 3.2), and presents the empirical applications to MFN taris and TTE (in Section 3.3). Finally, Section 4 concludes with summary remarks and directions for possible extensions and future work.

Theoretical Foundation and Identication Strategy
We start with a brief review of the theoretical foundations of the structural gravity model. Then, more importantly, in Section 2.2 we discuss the issues with the identication of the eects of nondiscriminatory trade policies within the structural gravity model and we oer a simple solution to overcome these challenges.

Theoretical Foundation
As demonstrated in the seminal paper of Arkolakis et al. (2012), and as summarized in the survey articles of Head and Mayer (2014) and Costinot and Rodríguez-Clare (2014), a large class of trade models lead to the following structural gravity equation for bilateral trade ows X ij from country 6 i to j: were T ij is a function of bilateral trade costs between i and j, including both taris and non-tari trade costs. Structural gravity models impose the condition that the value of production in country i equals its total sales to all countries, including domestic sales, Y i = j X ij , and that expenditure in country j equals the sum over all imports, E j = i X ij . Ω i and P j are outward and inward multilateral resistance terms which are dened by the following system of equations: The same equations apply at the aggregate and sector level when according measures of sectoral production and expenditure are used.
The nal step in dening an operational structural gravity model is to dene bilateral trade costs T ij . In general, T ij can be decomposed into two parts: where τ ij is a direct demand shifter, for example MFN taris, in which case τ ij is equal to 1 + the ad-valorem MFN tari rate. 1 is a direct measure of the demand elasticity with respect to price. In the Anderson and van Wincoop (2003) structural gravity framework, 1 is equal to −σ, the elasticity of substitution between varieties from dierent countries. T ij is a measure of non-tari barriers. Many researchers specify non-tari barriers as a function of, inter alia, bilateral (log) distance between countries, whether countries share a common border, language, colonial history or trade agreement membership. In general, where t ij,f denotes individual measures of non-tari barriers as mentioned above, and δ f is the corresponding tari equivalent trade cost elasticity of barrier f . Again, in the Anderson and van Wincoop (2003) framework, 2 equals (1−σ). The dierent elasticities between taris and non-tari barriers stem from the fact that taris are paid by the consumer and hence are applied to the price of goods including trade costs, whereas non-tari trade costs are borne by the producer.
13 As is well known by now (see e.g. Arkolakis et al., 2012 andMayer, 2014), using the Eaton and Kortum (2002) framework replaces (1 − σ) by −θ, a parameter which measures the variability of productivity across countries. For expositional convenience, we will stick to the Anderson and van Wincoop (2003) framework from now on. However, we note that our methods to identify the impact of non-discriminatory trade policies are independent of the specic theoretical micro-foundations of the structural gravity model. Thus, for example, the elasticity of substitution between varieties that we will obtain in the empirical analysis below can also be interpreted as a method to estimate the technology parameter θ.

Identication Strategy
Our identication strategy is best demonstrated by an example. We rst show that our method works in a cross-section setting, then we discuss an extension to applications with panel data.
Consider a cross-sectional bilateral trade data set that consists of trade ows between three countries {A, B, C}, including both domestic sales as well as international trade ows. The goal is to demonstrate that we can estimate the eect of MFN taris on trade ows while controlling for the structural multilateral resistance terms by including a full set of exporter and importer xed eects.
The following is a representative relevant excerpt of the data matrix: 13 The actual incidence of trade costs and taris is a dierent matter, see Anderson and Yotov (2010).
Column one identies the observations. Columns exporter and importer denote the respective exporting and importing country. η 1 to η 3 are the exporter dummies/exporter xed eects, while µ 1 to µ 3 are the importer dummies/importer xed eects. I is an indicator variable which is one if the trade ow is international, and zero for intra-national trade ows. The last column is our regressor of interest, i.e., the non-discriminatory unilateral MFN tari vector τ M F N , which, by denition, is set to zero for all intra-national trade ows.
Note that when estimating structural gravity models we have to drop one of the exporter or importer dummies due to perfect collinearity. This is a standard collinearity concern, which is independent of trying to identify non-discriminatory trade policy. Without loss of generality, our choice in the subsequent analysis is to drop the xed eect η 3 . We note, however, that our methods apply regardless of this normalization choice.
We start with a brief demonstration of why standard gravity analyses are unable to identify the impact of non-discriminatory trade policies. Typically, researchers only use international trade ows, i.e. observations one to six. Hence, the corresponding data matrix can be represented as follows: Inspection of the relationships in matrix (6) reveals that the non-discriminatory MFN tari vector, ln τ M F N , is perfectly collinear with the set of vectors of the importer dummies, µ 1 , µ 2 , and µ 3 : Thus, due to perfect collinearity, it is impossible to identify the impact of MFN taris in a typical gravity specication that only uses international trade data and employs a proper set of exporter and importer xed eects to control for the unobservable multilateral resistance terms. This is exactly the reason that motivated the opening quote in our paper by Head and Mayer (2014).
Next, we oer a simple (and theoretically consistent) adjustment to structural gravity specications that will enable us to identify the eects of non-discriminatory trade policies, such as MFN taris, even in the presence of exporter and importer xed eects. Specically, we demonstrate that adding intra-national trade ow observations breaks the perfect multicollinearity from our previous example. Adding intra-national trade ows to matrix (6) obtains: Here, observations 7-9 represent the additional observations for intra-national trade. If MFN taris were perfectly collinear with the rest of the variables in matrix (8), then there would have to exist a non-zero solution, α * 1 , α * 2 , ..., α * 7 , for the following system of equations: In other words, if MFN taris were perfectly collinear with the rest of the variables in matrix (8), then the vector ln τ M F N × I could be expressed as a linear combination of the dummies: We now prove that non-discriminatory taris are linearly independent from the dummies by contradiction.
14 Focus on observation 9 in matrix (8). To express the last column as a linear combination of the remaining columns, α 5 has to be equal to zero. In addition, to fulll Equation (10) for observation 8, it follows that α 2 = −α 4 . Similarly, it follows from observation 7 that α 1 = −α 3 . We then can re-express Equation (10) in matrix form as: 14 The remaining analysis is performed under the realistic assumption that there is sucient variation in the MFN taris and they do take non-zero and dierent values, i.e., we exclude the trivial cases of multicollinearity.

11
It is clear from system (11) that the equations corresponding to observations 7 to 9 fulll the condition for perfect collinearity.
Next, focus on observations 1 and 6. From these two lines we see that they can only sum up to ln τ M F N B if α 1 = 0. This, in turn, implies that, from equations corresponding to observations 2 and 4, α 2 has to be equal to zero for perfect multicollinearity. Now we are left with α 6 , which would have to take three dierent values in order to fulll equations 1 to 6. Thus, the only solution for the system of equations in (10) is the trivial solution that α * 1 = ... = α * 7 = 0, implying that a non-discriminatory MFN tari is linearly independent from the set of exporter and importer dummies when including intra-national trade ows.
The MFN tari is an example for a non-discriminatory trade policy which is identical across all exporting countries for a specic importer. A similar line of reasoning can be applied to show that a non-discriminatory trade policy on the exporter side, such as export subsidies or time-to-export, can be identied. For brevity of exposition we delegate the detailed analysis of the collinearity issues on the exporter side to Appendix A.
Next, we extend the analysis to demonstrate that our methods can be used to identify simultaneously both, non-discriminatory importer policies as well as non-discriminatory exporter policies in the presence of the full set of exporter and importer xed eects. The corresponding representative data matrix takes the form: Following the exposition of the previous case, we rst note that perfect collinearity would exist if ln τ M F N × I can be expressed as a linear combination of the dummies and τ T T E × I, i.e., if: Focus on observation 9 in matrix (12). To express the last column as a linear combination of the remaining columns, α 5 has to be equal to zero. In addition, to fulll Equation (13) for observation 8, it follows that α 2 = −α 4 . Similarly, it follows from observation 7 that α 1 = −α 3 . We then can re-express Equation (13) in matrix form as: System (14) implies that the equations corresponding to observations 7 to 9 fulll the condition for perfect collinearity. Next, focus on observations 1 and 6. Assuming that = 0, we nd the following solution (which can be checked by plugging in into observations 1 to 6): Thus, in theory, there could exist a realization of the data for which perfect collinearity would not allow identication of the impact of MFN taris and TTE simultaneously. Note however, that this would only happen if there were a specic functional dependence between the exporter-specic non-discriminatory trade policies across countries. This is unlikely to hold in practice as trade policies like taris are typically not set in such a systematic manner across countries. 15 In sum, we attach zero probability to the existence of a combination of data that satises these conditions, which implies that MFN taris are not perfectly collinear with the rest of the variables in (14). 16 Thus, we have demonstrated that it is possible to identify the eects of non-discriminatory 15 Compare this to the typical dummy variable trap, where e.g., the dummy F EM ALE is a function of 1 − M ALE.
In each of these cases to hold, there would either have to be one or more of the variables to be zero and/or the variables would have to take the same values for some of the observations. Therefore, with sucient variation in the regressors of interest, we can rule these scenarios out.
14 export and import trade policy at the same time.
The arguments for identication of the eects of non-discriminatory MFN taris and TTEs in a cross-section setting that we presented thus far translate to the panel case, where the main dierence is that controlling for the unobservable multilateral resistance terms requires the use of exporter-time and importer-time xed eects. Intuitively, the panel setting can be decomposed into a sequence of cross-section matrices. Furthermore, our methods apply even in the presence of bilateral xed eects.
To demonstrate the validity of our approach we consider a panel with only two time periods, however, it is straight-forward to extend the analysis to more years. With the twoperiod panel data, we can apply a rst-dierence strategy. This will wipe out all of the bilateral xed eects and also requires us to express all remaining variables in changes. The system in changes that corresponds to Equation (9) is: Due to its identical structure, it is clear from Equation (15) that all of the arguments and steps that we took in order to demonstrate the validity of our methods in the cross-section case apply here as well.

Empirical Analysis
This section demonstrates the empirical validity of our methods with applications to actual data. Specically, we consider two non-discriminatory trade policies. On the importer side, we obtain estimates of the eects of MFN taris within the structural gravity model. On the exporter side, we obtain estimates of the impact of`Time To Export' as a representative country-specic and non-discriminatory trade determinant.

Econometric Specication
To implement our methods, we capitalize and extend on recent developments in the empirical gravity literature. Our departing point is the following estimating equation, which is based on Equation (1): Here, X ijt denotes nominal trade ows from exporter i to importer j at time t. In order to be as general as possible, we set up the estimating equation under the assumption that it will be implemented with panel data. However, in order to demonstrate the validity and robustness of our methods, we also implement Equation (16)  The regressors enter (16) exponentially because we follow Santos Silva and Tenreyro (2006) to estimate the gravity model with the Poisson Pseudo Maximum Likelihood (PPML) estimator. Santos Silva and Tenreyro (2006) demonstrate that, since trade ows exhibit a large degree of heteroscedasticity, estimating a log-linearized version of (16) leads to inconsistent parameter estimates due to Jensen's inequality. Therefore, they propose the use of PPML as an alternative that overcomes this deciency of the standard OLS estimator. An additional advantage of the PPML estimator is that, since the gravity model is estimated in multiplicative form, PPML enables us to take advantage of the information that is contained in the zero trade ows. The use of any specic estimator does not play a role for the implementation of our methods and does not aect their eectiveness. However, in order to demonstrate the robustness of our approach, in the sensitivity analysis we also obtain estimates using the OLS estimator.
Turning to the covariates in (16) GRAV ijt is a vector of variables which includes all standard time-invariant gravity covariates (e.g. the log of bilateral distance, common language, etc.) as well as time-varying determinants of trade (e.g. regional trade agreements (RTAs)). We will experiment by replacing the time-invariant bilateral gravity variables with a full set of pair xed eects.
Finally, η it denotes the set of exporter xed eects, which will control for the unobserv-17 In our data set, we apply the MFN tari to all countries to ensure that it really is non-discriminatory across countries. However, we recognize that countries may apply dierent taris, e.g. various preferential rates. Furthermore, in principle, WTO-MFN taris only apply to WTO member states. However, many countries apply their MFN tari also to non-WTO members, and non-WTO member countries report MFN, i.e., non-preferential, tari rates in TRAINS. and Ethiopia are included. We make sure that the MFN tari rates are non-discriminatory in our data set. able outward multilateral resistances and also will absorb any other country-specic trade determinants on the exporter side. Similarly, µ jt denotes the set of importer xed eects, which will control for the unobservable inward multilateral resistances and also will absorb any other country-specic trade determinants on the importer side. ε ijt is a remainder error term.

Data
In order to perform the empirical analyses, we construct an unbalanced panel data set for 19 To create our data set, we keep every country pair observation which we observe at least twice such that the bilateral xed eects do not perfectly predict bilateral trade ows by construction. We focus on manufacturing trade.
The reason is the need to construct proper intra-national trade ows, which we discuss next.
Intra-national Trade Flows. Availability of intra-national trade ows data is crucial for the implementation of our methods. We construct domestic trade ows as apparent consumption, i.e. as the dierence between the value of domestic production minus the value of total exports. While it is tempting to obtain aggregate domestic sales as the dierence between GDP and total exports, we do not recommend this approach due to the inconsistency between the measure of GDP as value added and the measure of total exports as gross value.
18 A list of the countries in our data set appears in Section B of the Appendix.
In other words, in order to construct consistent intra-national trade ows, we need gross production value data. Therefore, we rely on the UNIDO's Industrial Statistics Database (INDSTAT2), which oers cross-country gross production manufacturing data. 20 We also note that, recently, more and more data sets include consistently constructed international and intra-national trade ows. Thus, the implementation of our methods is not limited to the data set that we use for the current analysis. Other Data. We also use a series of control variables. In order to perform the main analysis with panel data, we employ bilateral xed eects that absorb all time-invariant bilateral determinants of trade. However, we cannot use directional bilateral xed eects in our cross-section regressions. Therefore, in this case, we rely on the set of standard gravity variables from the literature. Specically, we use data on bilateral distance, common language, contiguity, and colonial ties, which are taken from CEPII's Distances Database (see Mayer and Zignago, 2011). An important advantage of CEPII's Distances Database for our analysis is that it provides population-weighted distances, which can be used to calculate consistently both bilateral distances as well as internal distances. Finally, our measure of regional trade agreements comes from Mario Larch's Regional Trade Agreements Database from Egger and Larch (2008). 24

Estimation Results and Analysis
We demonstrate the eectiveness of our methods in several steps. We start with a standard cross-section specication, where the only non-discriminatory trade policy variable of interest is MFN taris. Then, we extend the specication to a panel setting, which is estimated with standard gravity variables and with bilateral xed eects. In the next step we obtain simultaneously estimates of MFN taris, as a representative non-discriminatory trade policy on the importer side, and of TTE, as a representative non-discriminatory trade policy on the exporter side. The empirical analysis concludes with a series of sensitivity experiments, 23 For a description of the data, see Djankov et al. (2010) (2).
The most important result from column (2) is that, as was the case with cross-section data, 25 We refer the reader to Head and Mayer (2014) who oer a meta analysis study of more than 2500 gravity estimates from 159 papers.
26 In addition, we note that the structural value of the trade elasticity parameter that is recovered from the estimate on the coecient on taris in the gravity model depends on the interpretation of taris in the denition of trade costs. Studies that treat taris as iceberg trade costs would deliver structural values of 11.042 and −11.042 of the elasticity of substitution and of the import-demand elasticity, respectively. We refer the reader to Larch and Yotov (2016) for a detailed discussion of the structural interpretation of the estimates on taris in gravity equations.

21
we are able to identify the impact of MFN taris even in the presence of the exporter-time and importer-time eects in a panel setting. The estimate of the coecient on MFN taris is again highly statistically signicant. In terms of economic magnitude, with a value of −9.703, our MFN tari estimate is a bit smaller in absolute magnitude than the corresponding estimate from column (1), however, it is still in the upper tail of comparable estimates from the existing literature. 27 A possible explanation for the large MFN tari estimate may be that trade policies, such as taris or whether two countries sign a regional trade agreement, are not randomly assigned across countries. 28 Therefore, both the RT A regressor as well as our measure for the non-discriminatory trade policy, τ M F N it , are potentially endogenous. Matching techniques to correct for the selection bias are hampered by violations of the stable unit treatment value assumption (SUTVA) as trade policy has by denition general equilibrium and third country eects via its impact on trade creation and diversion (see e.g. Viner, 1950 andImbens andWooldridge, 2009). Instrumental variables which fulll the necessary exclusion restriction are hard to come by at the country or industry level. We therefore follow Baier and Bergstrand (2007) and include bilateral (directed) country-pair eects to control for the endogeneity of trade policy in column (3).
As discussed in the analytical identication Section 2.2, the inclusion of pair xed eects does not prevent identication of the impact of unilateral and non-discriminatory trade policies in structural gravity equations. Accordingly, once again, in column (3) of Table 1 we are able to identify the estimate of the coecient of MFN taris. The estimate on MFN taris is still highly statistically signicant. Furthermore, consistent with the endogeneity analysis from Baier and Bergstrand (2007), when we control for the unobserved directional bilateral 27 Existing elasticity estimates from the related literature usually vary between 2 and 12. Head and Mayer (2014) oer a summary meta-analysis estimate of σ = 6.13. We refer the reader to Eaton and Kortum (2002), Anderson and van Wincoop (2003), Broda et al. (2006) and Simonovska and Waugh (2014), Costinot and Rodríguez-Clare (2014), and Head and Mayer (2014) for discussion of the available estimates of the elasticity of substitution and trade elasticity parameter.
28 See e.g. the arguments in Treer (1993) and Magee (2003). For example, countries which are closer have a signicantly higher probability of signing an RTA, see e.g. Baier and Bergstrand (2004) and Egger et al. (2011). eects, the estimate drops to −6.854, which is readily comparable to the corresponding estimates of the elasticities of substitution and the import demand elasticities, which we summarized in Footnote 27.
The last two columns of Table 1 oer results from two robustness experiments. Specifically, in column (4) we use 3-year intervals instead of each year. The motivation for this experiment is that trade ows may need time to adjust in response to trade policy changes, c.f. Cheng and Wall (2005). As can be seen from Table 1, the specication with 3-year intervals is still able to identify an estimate of the coecient on MFN taris, but delivers an estimate that is larger than the corresponding index from column (3). The last column of Table 1 reports estimation results that are obtained by treating non-reported trade ows as missing values instead of replacing them with zeros as in the previous columns. This leads to a loss of 901 observations. However, with a point estimate of −6.851, the coecient on MFN taris is virtually identical to the −6.854 value from column (3).
The results that we present in Table 2 replicate the specications from Table 1, but after adding as an additional regressor time-to-export (TTE), which is our representative non-discriminatory unilateral trade policy on the exporter side. Two main ndings stand out from Table 2. First, and most important from an econometric perspective, we are able to identify an estimate of the impact of TTE in each column of Table 2, while, at the same time, we are still able to identify estimates of the impact of MFN taris. Second, from an economic and policy perspective, we obtain negative and highly statistically signicant estimates of the impact of TTE across all specications in Table 2. As with MFN taris, the estimates from the panel specication with bilateral xed eects lead to smaller TTE estimates in absolute value. In terms of economic magnitude, our preferred estimate from column (3) of Table 2 (−0.035, std.err. 0.005), suggests that an additional day of time to export reduces trade ows by 3.5 percent.
We nish the analysis with several robustness experiments. Panels A and B of Table 3 reproduce the results from the specications from Tables 1 and 2, respectively, but using the OLS estimator and logarithmized trade ows as dependent variable instead of the PPML estimator and trade ows in levels. Since the OLS estimator automatically eliminates all zero trade ows, there is no need to report separately the estimates that treat non-reported values as zeros or as missing, because those estimates are identical by construction. Therefore, we do not reproduce the results from the last columns of Tables 1 and 2 in Table 3. Most importantly, the estimates from Table 3 conrm that we can identify the eects of unilateral and non-discriminatory trade policies on the importer and on the exporter side. In addition, we nd that, overall, both non-discriminatory policies are signicant and have negative eects on trade ows. Generally, the estimates for the MFN taris become larger in absolute values, as do the time-to-export coecients. The latter, however, are not consistently statistically signicant across all specications.
Finally, Panels A and B of Table 4 reproduce the regression results from the specications given in Tables 1 and 2, respectively, after replacing the average MFN tari with weighted MFN taris, where the weights are the observed levels of trade. It is well known that using weighted trade ows may lead to an endogeneity problem if policy makers set taris as a reaction to the level of trade ows. Still, weighted taris are often used as an alternative measure of taris. As can be seen from the estimates in Table 4, using weighted instead of simple average taris does not change any of our results qualitatively and hardly matters quantitatively. Mainly, estimates of the MFN tari become a little bit larger in absolute values.
To summarize, the empirical analysis in this section demonstrate that our proposed method works well, produces sensible estimates, and can be fruitfully applied in realistic gravity data sets.

4 Conclusion
The eects of unilateral or non-discriminatory trade policies are interesting and important both for academics as well as for policy makers. In this paper we propose a simple method to identify the trade eects of such policies within structural gravity models, which employ complete sets of theoretically-motivated xed eects on the importer and on the exporter side. We demonstrate the validity of our methods and illustrate the eectiveness of our (3) * for p < 0.05, ** for p < 0.01, and *** for p < 0.001. See main text for further details.
(3)   Panel A: Replication of the Estimates from Table 1 Panel B: Replication of the Estimates from Table 2 (1) (3)  (1) and (5)  In addition, columns (3), (4), (7) and (8) also include directional country-pair xed eects. Standard errors are robust for the cross-sectional regression and clustered at the country-pair for the panel regressions and are reported in parentheses. * for p < 0.05, ** for p < 0.01, and *** for p < 0.001. See main text for further details.  Table 1 Panel B: Replication of the Estimates from Table 2 (1) (3) (8)   (1) and (6)  Columns (4) and (9)  if COMTRADE reports both imports and exports; if only imports or exports are observed, these are used. Non-reported international trade ows are set to zero except in columns (5) and (10). Constructed domestic trade ows are set to missing if negative. All regressions include exporter(-year) and importer-(year) xed eects. In addition, columns (3) to (5) and (8) to (10) also include directional country-pair xed eects. Standard errors are robust for the cross-sectional regressions and clustered at the country-pair for the panel regressions and are reported in parentheses. * for p < 0.05, ** for p < 0.01, and *** for p < 0.001. See main text for further details.
33 Appendix A Non-Discriminatory Export Policy In this Appendix we show that we can identify a non-discriminatory trade policy on the exporter side, such as export subsidies or time-to-export (TTE), when using international and intra-national trade ows. TTE is chosen to illustrate our methods in the current analysis because the same variable is used as a representative non-discriminatory policy on the exporter side in the empirical analysis. The methods that we develop here apply equally to any non-discriminatory policy on the exporter side, e.g. export subsidies, export promotion fairs, etc. The following is the corresponding representative data matrix that only includes observations for international trade ows: Inspection of the relationships in the data set matrix (17) supports the claim of Head and Mayer (2014) that the non-discriminatory time to export is perfectly collinear with the set of dummies, as η 1 τ T T E Similar to the case of MFN taris, adding observations for intra-national trade ows breaks the perfect multicollinearity in the case of a representative non-discriminatory trade policy on the exporter side. Adding intra-national trade ows to matrix (17) results in the following data matrix: # exporter importer η 1 η 2 µ 1 µ 2 µ 3 I τ T T E × I where the observations for intra-national trade ows are observations 7-9. If TTE were perfectly collinear with the rest of the variables in matrix (18), then there has to exist a non-zero solution, α * 1 , α * 2 , ..., α * # exp. imp. α 1 η 1 + α 2 η 2 + α 3 µ 1 + α 4 µ 2 + α 5 µ 3 + α 6 I = τ T T E × I System (21) reveals that the equations corresponding to observations 7 to 9 fulll the condition for perfect collinearity.
Now focus on observations 1 and 2. These two lines can only sum up to τ T T E A if α 2 = 0.
This in turn implies that, from the equations corresponding to observations 3 and 4, α 1 has to be equal to zero for perfect multicollinearity. Now we are left with α 6 , which would have to take three dierent values to fulll equations 1 to 6. Hence, the only solution for the system of equations in (21) is the trivial solution that α * 1 = ... = α * 7 = 0, implying that a non-discriminatory export policy is linearly independent from the set of exporter and importer dummies when including intra-national trade ows. 36