Student Member IEEE Nikola Besic
email: nikola.besic@gipsa-lab.grenoble-inp.fr

Member IEEE, Gabriel Vasile

Member IEEE Jean-Pierre Dedieu

Fellow IEEE Jocelyn Chanussot

Senior Member IEEE Srdjan Stankovic

J.-P Dedieu

Stochastic Approach in Wet Snow Detection Using Multitemporal SAR Data

Keywords: change detection, wet snow, stochastic approach, backscattering simulation

This paper introduces an alternative strategy for wet snow detection using multitemporal SAR data. The proposed change detection method is primarily based on the comparison between two X band SAR images acquired during the accumulation (winter) and the melting (spring) seasons, in the French Alps. The new decision criterion relies on the local intensity statistics of the SAR images by considering the backscattering ratio as a stochastic process: the probability that "the intensity ratio fits into the predetermined range of values" is larger than a defined confidence level. Both the conducted snow backscattering simulations and the state of the art measurements [1] indicate more complex relation between the backscattering properties of the two snow types, with respect to the conventional assumption of the augmented electromagnetic absorption associated to the wet snow. Therefore, rather than adopting the standard hypothesis, we analyse the wet/dry snow backscattering ratio as a function of the local incidence angle (LIA). After employing the multi-layer snow backscattering simulator, calibrated with scatterometer measurements in C band, we modify, to some extent, the range of ratio values indicating the presence of the wet snow, by including positive ratio values for lower LIA. By simultaneously accounting for the speckle noise, the proposed stochastic approach derives the refined wet snow probability map. The performance analyses are carried out both through the comparison with the ground air temperature map and by comparing two co-polarized channels processed separately.

I. INTRODUCTION

Depending on the liquid water content, snow can be considered as dry or wet. Dry snow is defined as snow consisted just of ice crystals embedded in air, without any liquid water. Its presence is characteristic for temperatures below 0 • C. Wet snow can be found during the melting season, when the temperature exceeds 0 • C. It contains a certain amount of liquid water introduced quantitatively through the wetness. These two snow types behave differently with respect to their dielectric properties: the wet snow contains liquid water with a dielectric constant differing significantly from the one of the ice. This fact points out to a difference in backscattering mechanisms [START_REF] Ulaby | Snowcover influence on backscattering from terrain[END_REF], and consequently that different feature extraction methods should be applied. Therefore, the estimation of any snow pack parameter by means of SAR remote sensing, requires firstly the proper identification of the snow cover type [START_REF] Shi | Snow mapping in alpine regions with synthetic aperture radar[END_REF].

Although studies on snow mapping by polarimetric SAR existed already [START_REF] Rott | Thematic studies in alpine areas by means of polarimetric sar and optical imagery[END_REF], it was not before the ERS-1 started providing repeat pass images that the idea of snow mapping based on SAR multitemporal data appeared [START_REF] Rott | Capabilities of ers-1 sar for snow and glacier monitoring in alpine areas[END_REF]. Further refinement on the initial change detection method leaded eventually to the compact algorithm based on the ratio of two C band SAR images introduced in [START_REF] Nagler | Retrieval of wet snow by means of multitemporal sar data[END_REF]. The Nagler and Rott method requires as inputs the SAR wet snow image and the reference SAR image of the dry snow (or the snow free terrain). After corregistration, either mutilooking or speckle filtering is applied on the two SAR intensities before constructing the backscattering ratio image. This ratio image is then georeferenced and an unique threshold of -3 dB is used to discriminate the wet snow from other surfaces. The expected difference in backscattering is justified by the increased electromagnetic absorption of the wet snow. The resulting maps are successfully validated by using snow terrain optical images. Subsequently, constraints concerning both sensor and target parameters with respect to the validity of the defined threshold have been introduced [START_REF] Magagi | Optimal conditions for wet snow detection using radarsat sar data[END_REF].

In this article, we propose an alternative change detection method with X-band SAR data for wet snow detection. The goal is to introduce an algorithm which is eventually more suited to the presence of the speckle noise and is based on a slightly modified hypothesis on a wet/dry snow backscattering ratio behaviour.

The first novelty is related to the choice of the reference image. It is supposed to be the image acquired in the winter season, when the dry snow assumption is valid.

The state of the art backscattering measurements [START_REF] Strozzi | Backscattering measurements of alpine snowcovers at 5.3 and 35 ghz[END_REF] indicate a complex relationship in terms of backscattering between the two types of snow, which cannot be simplified by assuming increased absorption and therefore lower backscattering of the wet snow, for all values of LIA. In order to account for this fact, we employ the multi-layer snow backscattering simulator (calibrated with the scatterometer measurements in C band) and analyse the wet/dry snow backscattering ratio as a function of LIA, in X band. Thereupon, we determine the range of ratio values, pointing to the presence of the wet snow. The derived range slightly differs with respect to the conventional assumption used in C band.

Further, the speckle noise statistics is introduced through the local estimation of the intensity ratio probability. This allows additional enhancement of the discrimination accuracy, which is illustrated through the matching of the independently obtained HH and VV maps. Finally, we analyse the performances by comparing snow maps obtained using TerraSAR-X data with interpolated temperature map. The paper is organized as follows. Section II is the core of the article, containing the description of the wet snow detection algorithm. Both the analysis of the wet/dry backscattering ratio and the stochastic approach are introduced in this section. In Section III, we present the results obtained with two TerraSAR-X dual-pol stripmap images acquired in the French Alps. This section provides the performance analyses, while Section IV concludes this article.

II. THE DETECTION ALGORITHM

The wet snow detection algorithm consists of five principal parts:

A. Input data

The approximate equivalence between the bare ground and the dry snow backscattering, perceived in C band, does not appear to be true for higher frequencies [START_REF] Strozzi | Backscattering measurements of snowcovers at 5.3 and 35 ghz[END_REF]. Therefore, in order to assure applicability in a wider range of frequencies, we compare directly the dry snow cover image with the mixed dry/wet snow cover one.

The following data are required as input:

• Winter SAR image, slant range geometry -image acquired during the winter season, when the dry snow assumption is fairly valid due to the air temperature at ground level; • Melting season SAR image, slant range geometry -image acquired at the end of the winter season, when an increase in the air temperature causes melting; • Digital Elevation Model (DEM) and Sensor & Orbit parameters (georeferencing and derivation of LIA map); • Approximate information about the snow cover in the region (verifying appropriateness of the proposed method);

B. SAR image processing

In this part, the input images are calibrated and corregistrated using the resampled SAR geometry intensity simulation. The slant range LIA is also derived.

C. Wet/Dry snow backscattering ratio

Given the fundamental role of both the snow surface and the underlying layer in snow backscattering, the local incidence angle (LIA) appears to be the most appropriate choice of an independent variable for the analysis of the wet/dry snow backscattering ratio. In order to both qualitatively and quantitatively analyse the backscattering ratio, we developed the multilayer backscattering simulator. The Integral Equation Model (IEM-B) [START_REF] Fung | Microwave Scattering and Emission Models for Users[END_REF] is used to simulate surface backscattering, while volume behaviour is modelled using the Quasi Crystalline Approximation with Coherent Potentials (QCA-CP) through the Dense Media Radiative Transfer (DMRT) [START_REF] Tsang | Scattering of Electromagnetic Waves[END_REF].

In the region of particular interest -the French Alps, the large multilayer snow cover occurs both in the accumulation and in the melting season, containing, in the former case, inevitably present ice crust. The analysis of dry snow have shown that most of the backscattering energy comes from the continuous ice crust, rather than from the underlying ground, as it is the case with the emissivity in the passive microwave remote sensing [START_REF] Matzler | Extension of the microwave emission model of layered snowpacks to coarse-grained snow[END_REF]. Therefore, we assumed the dominance of this underlying backscattering component in the case of a dry snow [START_REF] Besic | Dry snow backscattering sensitivity on density change for swe estimation[END_REF]. Consequently, the layers above the ice crust are considered to be the effective snow cover. We adopt the parameters of these layers as the multi-layer (ML) simulator input data. In the case of wet snow, the surface layer is considered as the most contributory [START_REF] Besic | Wet snow backscattering sensitivity on density change for swe estimation[END_REF]. Thus, the wet snow backscattering is simulated using a single-layer (SL) approach, by adopting the parameters of the surface layer.

The derived backscattering simulator is calibrated in C band (5.3 GHz) using the scatterometer measurements from [START_REF] Strozzi | Backscattering measurements of snowcovers at 5.3 and 35 ghz[END_REF] (Fig. 1). The applied calibration is essentially the optimization with respect to the surface parameters of both the underlying ice crust and the snow layers. After introducing in situ measured input parameters [START_REF] Strozzi | Backscattering measurements of alpine snowcovers at 5.3 and 35 ghz[END_REF] (density, depth, dielectric permittivity, wetness), we derive the surface parameters of the ice crust and the ones of the snow layers, by applying the optimization algorithm based on minimizing the mean square error between the simulator output in C band and the measurements (LIA ranging from 0 • to 70 • ). The HH simulation results have been modified by extrapolating the backscattering curves after LIA = 50 • . This is due to the observed anomaly of the IEM-B, related to the low values of dielectric permittivity, causing quite a radical increase of the surface backscattering for higher incidence angles, which is not fully consistent neither with the ground truth data, nor with the theoretical expectations.

The simulator is then applied in X band (10 GHz), using the extended set of parameters, reinforced by the derived surface parameters (Table I). By slightly varying the surface roughness parameters (RMS height and correlation length) we obtain the wet/dry snow backscattering ratio (Fig. 2a), allowing us, foremost, the following qualitative interpretation: the wet snow backscattering is not necessarily inferior in X band, neither.

Using the derived wet/dry snow backscattering ratio, we identify the ranges of values which should indicate the wet snow presence in the ratio image (Fig. 2b). Given that the I), red lines represent defined thresholds (Table II). Dashed grey lines represent simulation results, modified due to the observed IEM-B anomaly.

dry snow image is used as a reference, regions around 0 dB indicate dry snow presence (no change). Further, by adopting the standard hypothesis, negative regions (below -1.5 dB) are associated to the wet snow presence. However, believing that the positive backscattering difference for lower local incidence angles should also imply the wet snow, sooner than the dry one, we assign wet snow to the positive regions corresponding to the lower LIA, as well. Namely, the melting process which occurs in the upper layer gives rise to the snowpack surface backscattering, which eventually augments total snow backscattering at lower LIA.

D. Stochastic approach

Assuming the gaussianity of the SAR clutter, the intensity over homogeneous regions can be modelled by the Gamma probability density function (PDF), according to the fully developed speckle model [START_REF] Goodman | Some fundamental properties of speckle[END_REF]:

G(τ |ν, µ) = 1 Γ(ν) ν µ ν τ ν-1 e -νx µ , (1)
with µ being the texture intensity mean, ν -shape factor providing deviation with respect to the corresponding Gaussian distribution and Γ -the Gamma function. If the intensity is expressed as µ ν X, the random variable X follows the chisquared distribution χ 2 (ν) with ν degrees of freedom. The ratio of two chi-squared random variables, normalized with respect to the degrees of freedom, follows the Fisher-Snedecor distribution F(ν 1 , ν 2 ) [START_REF] Bombrun | Hierarchical segmentation of polarimetric SAR images using heterogeneous clutter models[END_REF]. This implies that the ratio of two Gamma random variables, having different shape factors but the same mean value is modelled using the Fisher-Snedecor distribution:

F(r|k, ν 1 , ν 2 ) = Γ(ν 1 + ν 2 ) Γ(ν 1 )Γ(ν 2 ) ν 1 kν 2 ( ν1r kν2 ) ν1-1 (1 + ν1r kν2 ) ν1+ν2 . (2)
The proposed stochastic approach is exactly based on the probability estimation relaying on the previously elaborated assumption. The algorithm uses the boxcar neighbourhood, coupled with the approximate maximum likelihood estimator (MLE), in order to obtain local statistics for each of the areas in the image. Due to the poor performances of the Fisher-Snedecor MLE, the estimation is performed rather on the normalized ratio intensity (ξ) than the ratio intensity itself (r = µξ). If the ratio intensity (r) follows the Fisher-Snedecor distribution, the normalized ratio intensity (ξ) is modelled by the Beta prime distribution:

B ′ (ξ|ν 1 , ν 2 ) = Γ(ν 1 + ν 2 ) Γ(ν 1 )Γ(ν 2 ) ξ ν1-1 (1 + ξ) ν1+ν2 . ( 3
)
For each local neighbourhood, we derive the mean value (µ), normalize the texture locally and estimate ν 1 and ν 2 parameters. This way, we define the probability density function (B ′ (i,j) ) for every region in the image. By integrating the obtained PDF with respect to the normalized texture, we get the cumulative distribution function (B ′ (i,j) ) for the normalized threshold of the central pixel:

i out (i, j) = B ′ (i,j) T 2 (i, j) µ(i, j) -B ′ (i,j) T 1 (i, j) µ(i, j) = = T 2 (i,j) µ(i,j) T 1 (i,j) µ(i,j) B ′ (i,j) (ξ)dξ. ( 4
)
This value is the probability of the ratio fitting the predefined range of values or exactly the wet snow probability. The thresholds {T 1 (dB), T 2 (dB)} ∈ {-1.5, 1.5, -∞, ∞}, can be deduced from Fig. 2b, as functions of the LIA.

E. Confidence level

The obtained wet snow probability map is transformed into the wet snow binary map by applying the confidence level. It reflects the level of certainty that the derived map indeed represents wet snow regions.

III. PERFORMANCE ANALYSES

The proposed algorithm is illustrated by the results obtained using two X-band TerraSAR-X stripmap images acquired over the Grandes Rousses massif near Grenoble, France: the winter image, acquired on the 8th of February, 2009, holding for the dry snow assumption (according to the local meteorological data and the DEM -88% of the area is at the altitude > 1500m); and the melting season image, acquired on the 2nd of March, 2009, in the presence of wet snow, according to the same source. The local incidence angle map is computed using the DEM (Datum: WGS-84, UL Geo:

5 • 57 ′ 3.64 ′′ E, 45 • 24 ′ 15.21 ′′ N ).
For comparison, we provide in Fig. 3 three pairs of binary maps (HH and VV) derived using different change detection methods. Firstly, we present the results obtained by using the criteria from Fig. 2b on the filtered ratio of original input images (Fig. 3a). Further, the same criteria is applied on the ratio of formerly speckle filtered input images (Fig. 3b). Finally, we include the proposed stochastic approach, and present the results obtained with the proposed method, using a very high confidence level -99% (Fig. 3c).

The quantitative correspondence between the independently obtained HH and VV maps (Fig. 3) significantly augments in the case of the proposed stochastic approach. By applying an unconstrained optimization technique, we estimate that the maps in Fig. 3a and Fig. 3b approximately correspond to the probability maps thresholded with 70% and 72% confidence level, respectively. Increase of confidence level decreases the fraction of wet snow, but augments the certainty.

The verification of the obtained results is performed using the local temperature measurements at the ground level. The measurements data, provided by the Électricité de France (EDF), are related to the area of interest (Grandes Rousses massif) at the same date (3rd of March, 2009), meaning that comparison with the available SAR images was possible. The single point measurements are acquired at 36 stations in the wider region (7 in the area of interest), and spatialized using the kriging interpolation method.

The procedure is based on the stated fact that wet snow presence is characteristic for the local ground temperature above 0 • C, while dry snow can be found below 0 • C. The temperature measurements are compared to the obtained wet snow probability map (Fig. 4). Quantitative evaluation of the comparison is done by calculating a spatial correlation, using a large sliding boxcar (Fig. 4c). This way, by calculating the correlation coefficient for each subregion, we get a more precise insight into the matching. The approximate overlapping between the high temperature regions and the high probability regions (two independent information), is pointing to the validity of the obtained results. Although this assessment, due to the heavily interpolated temperature and consequently quite a large boxcar used for calculating the correlation, cannot help us demonstrate all the subtleties of the proposed method, it remains an important indication of its validity.

In order to demonstrate that the estimated wet snow regions (Fig. 4a) are not confounded with a bare ground, we superpose to the wet snow binary map (99%) the mask derived from the DEM -Altitude > 1500m. This altitude is the least favourable assumption (highest value) of the snow line, for the area and the date of interest (Fig. 4d). Only 10.7% of the detected wet snow pixels risks to be misestimated.

IV. CONCLUSIONS Snow backscattering simulations, reinforced by the state of the art measurements, resulted in the conclusion that the difference in backscattering of wet and dry snow occurs to be significantly dependent on the local incidence angle and on the operating frequency. Consequently, we have proposed an alternative version of the conventionally used wet snow detection method, by analysing a wet/dry snow backscattering ratio in X band and moderately modifying the range of values in the ratio image pointing to the presence of wet snow. Also, we chose preferably the winter image as the reference, avoiding constraints related to the frequency dependent relation between dry snow and bare ground backscattering and therefore allowing application in wider frequency range. Finally, instead of directly thresholding the ratio of multitemporal images, by considering the spatial correlation, we rather estimated the probability of the wet snow occurrence, making the algorithm stochastic.

The plausibly modified assumption of the wet/dry snow backscattering ratio, the implicitly introduced spatial correlation between the wet snow areas, and the possibility to vary the level of confidence of the wet snow binary maps by thresholding the obtained probability map, are altogether the supplements brought by the introduced stochastic approach to the ensemble of change detection techniques in snow mapping.

Further refinements of the proposed detection method will assume the three main directions. First of all, in order to make it more solid, we intend investing efforts in improving the validation procedure. In the second direction, the quantitative interpretation of the wet/dry snow backscattering ratio will be improved, which should allow more accurate discrimination between different regions in Figure 2b, in terms of LIA. Concerning the third direction, further work will mostly consist in adjusting the proposed method to polarimetric SAR input data [START_REF] Lessard-Fontaine | Multi-temporal dry and wet snow mapping in alpine context using polarimetric radarsat-2 time-series[END_REF]. The idea is to exploit the dual-pol images in the probability derivation.

Fig. 1 :

 1 Fig. 1: Calibration of the backscattering simulator using scatterometer measurements in C band [1]: (a) VV, (b) HH.

Fig. 2 :

 2 Fig. 2: Wet/dry snow backscat. ratio for input paramet. in Table I (a) and backscat. ratio values indicating wet snow (grey) and dry snow (black) (b): (i) VV, (ii) HH. Grey lines are backscat. curves for different roughness paramet. (TableI), red lines represent defined thresholds (TableII). Dashed grey lines represent simulation results, modified due to the observed IEM-B anomaly.

Fig. 3 :

 3 Fig. 3: The comparison between HH (left) and VV (right) polarization maps obtained after: (a) filtering the thresholded ratio of input images, (b) thresholding the ratio of speckle filtered input images, (c) thresholding the probability map with 70%, 72% and 99% confidence level. (d) HH-VV matching.

Fig. 4 :

 4 Fig. 4: Georeferenced maps: (a) HH wet snow probability map; (b) interpolated ground level temperature map, (c) Correlation between the HH wet snow probability map and the ground level temperature map, (d) HH wet snow binary map (99%) superposed to the mask Altitude > 1500m: Classes I (no wet snow) and II (wet snow) -below 1500m, Classes III (no wet snow) and IV (wet snow) -above 1500m.

TABLE I

 I

	: INPUT PARAMETERS FOR THE SNOW BACKSCATTERING
	SIMULATION, USED IN THRESHOLDS DERIVATION. DIFFERENT
	SHADES OF GREY REPRESENT DIFFERENT DRY SNOW LAYERS.
	Input parameter		Dry snow (ML)		Wet snow (SL)
	Snow density	144 kg/m 3 185 kg/m 3 333 kg/m 3 315 kg/m 3
	Wetness	0 %	0 %	0 %	0.73 %
	Snow depth	0.24 m	0.12 m	0.24 m	1.77 m
	Frequency		5.3 GHz (C), 10 GHz (X)
	Particles effective radius		(• •), r ef f = 225 µm
	Water dielectric constant		55 + j40 (C), 38 + j40 (X)
	Snow layers RMS height		4.5 -6.5 mm
	Snow layers correlation length		42 -82 mm
	Ice crust dielectric constant		3.2
	Ice crust RMS height		8.4 mm
	Ice crust correlation length		24 mm

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ACKNOWLEDGEMENT

The authors would like to thank to the EDF and the Météo-France for providing us the ground truth temperature data and other input parameters of interest, and to the Institut national de l'information géographique et forestière (IGN France) for the DEM. We owe particular gratitude to anonymous reviewers whose comments and suggestions improved significantly the presented work.


Joachim Jarreau
email: joachim.jarreau@univ-amu.fr

James Anderson

Scott Baier

Lionel Fontagné

Kishore Gawande

Nuno Limao

Daniel Mirza

Marcelo Olarreaga

Joao Santos

Vincent Vicard

Keywords: International trade, Preferential trade agreements, Counterfactual Estimation, Trade creation and diversion. JEL classication: F13, F12, F47

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of trde poliy through the use of ountryEsetor (xed e'ets @fier nd fergstrndD PHHUAF yne rmed with these elstiity estimtes nd with our dt on pplied trE i' hngesD we ompute e e'ets y ounterftul estimtionF his llows us to ompute the trde nd rel inome impts implied trde poliies s implemented y world ountries during the periodF henD we use the method to onfront the e'ets of tul trde poliies to those of lterntive poliiesD nmely trde greements nd multilterl trde lierliztionsF e lrge literture hs studied the determinnts of trde poliyF he seminl pper y qrossmn nd relpmn @IWWSA uilds politil eonomy frmework where governments tke into ount oth voter9s interests nd industry speil interests in deiding over trde greementsF fy ontrstD we do not enter into the politil eonomy struture of ountriesD s we do not oserve whether groups re orgnized into loiesD nor whether there is oordintion ross setors in trying to in)uene trde poliyF therD we mke the impliit hypothesis tht net gins to eh groupD ggregted ross setorsD should mtter for the government9s deisionsF his should e the se if the possiility of trnsfers ross groups existsD so tht dversely impted groups n e ompensted for their lossesF yur results indite tht this is the se only in prtF yur results re lso relted to those in qolderg nd wggi @IWWWAD who run n empiril test of the model y qrossmn @IWWRAF hese uthors R quntify the weight of welfre in the government9s ojetive funtion nd (nd it to e very lose to I @HFWWAD implying tht the government is lose to eing perfet welfre mximizer in its design of tri' strutureF fy ontrstD our nlysis sed on the signing of es (nds roust evidene tht world ountries9 trde poliies sustntilly di'er from the welfreEmximizingD overweighting produers9 interests over those of onsumersF he use of n endowments model of trde sed on ermington di'erentition nd hixitE tiglitz preferenes ples our pper in the soElled struturl grvity literture @enderson nd otovD PHIIY igger et lFD PHIIAAF st hs een reognized tht di'erent oneEsetor models of trdeD sed on gi preferenesD suh s urugE mn @IWUWAY iton nd uortum @PHHPAY welitz @PHHQA hve in ommon to generte grvity eqution with similr struture for trde )owsF yne onsequene is tht these models generte the sme funtionl form for the impts of trde ost hnges on pries nd rel inome levelsD onditionl on trde elstiities nd on initil trde levels @erkolkis et lFD PHIPAF husD estimting trde elstiities eomes the key to predit prie movements in these modelsD s this prmeter enompsses the di'erE ent mrgins of djustment desried in these modelsF his motivtes our pprohD whih onsists in estimting setorElevel trde elstiitiesD in order to ompute the impts of vrious trde poliy senrios on prie nd rel inome levelsF he vlidE ity of these results eyond the ermington model will e disussed in detil in the textF sn dditionD relying on setorElevel elstiity estimtes insted of single e prmeter llows us to ount for heterogeneity in e e'ets due to the width nd depth of tri' redutionsF 1 pinllyD y ssuming (xed endowments the model fetures n inelsti export supply urveD similrly to models of termsEofEtrde mnipultion nd optiml tri's @frodD vimo nd einsteinD PHHVD vudem nd wydD PHIIAF hereforeD s in these modelsD there is positive ssoition etween mrket power nd tri'sX 1 Another dierence is that we solve the model in full general equilibrium, allowing for export prices to aect trade through countries' income, contrary to antecedents in which trade changes are computed while implicitly keeping countries' income as xed (Anderson and Wincoop, 2003;Anderson and Yotov, 2010a;Baier and Bergstrand, 2009;Egger et al., 2011). S ountries hve n inentive to set higher tri's on imports from prtner ountries in whih their mrket shre is higherD while opening trde in priority with those where their mrket power is lowerF 2 he rest of the pper is s followsF sn setion @PAD we present the modelD nd disuss its reltion to the lss of struturl grvity modelsD nd the possile generE liztion of our results in this frmeworkF e then use simpleD QEountry version of the model to nlyze its implitions for the e'ets of es on trdeD rel inome nd welfreF sn setion @RAD we estimte the trde elstiitiesF sn setion @SAD we ompute the prie nd rel inome impts of trde poliy implemented y world ountries during our period of studyF henD in setion @TAD we study the determinnts of the signing of esF etion @UA onludesF 2 Model his setion presents the multiEsetor ermington modelD nd the method used to lirte it nd to solve it in omprtive sttis simultion exerisesF e then disuss the reltionship etween this model nd other models of trde feturing dditionl mrgins of djustment to trde ost hngesD suh s the urugmn @IWUWAD iton nd uortum @PHHPA nd welitz @PHHQA modelsF e mke the point tht the hnges in pries nd rel inome levels whih we ompute in our model nD under some onditionsD e generlized to these riher frmeworksF Model structure he model fetures multiple setorsD overing griultureD mining nd mnufturing tivitiesF 3 e model preferenes with goEhougls struture ross setors nd gi @onstnt elstiity of sustitutionA ross vrieties within eh setorF qoods in eh setor k re produed using spei( ftorD of whih eh ountry i hs (xed endowment L i k F ithin eh setorD we mke the ermington ssumption tht goods re di'erentited y ountry of origin @onsumers pereive vrieties produed in di'erent ountries s imperfet sustitutesAF hemnd is thus given yX

c k ij = (p k i ) -σ k . τ k ij P k j 1-σ k .E k j , @IA
where c k ij is the demnd of ountry j9s onsumers for the i vriety of good kD p k i is the fFoF @free on ordA prie of tht vrietyD τ k ij is the ieerg trde ost on trde from i to j in setor k @whih is to inlude geogrphi nd trde poliy omponents of trde ostsAD P k j is ountry j9s prie index in tht setor nd σ k is the elstiity of sustitution etween vrieties of tht goodF E k j is ountry j9s expenditure on good kD given y E k j = α k .Y j D where α k is the goEhougls prmeter shre of expenditure on good k nd Y j is ountry j9s totl inome 4 F etors re thus modeled s lrgely independent in the modelX lor nnot e relloted ross setorsD nd onsumers spend (xed shre of their expenditure on eh setor @goEhougls ssumptionA 5 F e thus strt from ftorEsed omprtive dvntge e'etsD s well s from interEsetorl linkges @eFgF vertil reltionsAF yne reson for doing this is thtD s doumented elowD results on prie responses to trde ost hnges in the oneEsetor ermington model reD under some onditionsD vlid under lrger lss of oneEsetor modelsF his is still true of prie responses in eh setor of our modelD whih funtions like superposition of oneEsetor ermington modelsF his restritive ssumption llows to estimte prie responses to trde poliy hnges using limited list of sttistis @trde elstiityD trde levelsD tri' hngesAY whih would not e possile if ounting for interE setorl linkgesF he nominl ilterl trde )ow etween i nd j in setor k is given y

X k ij = p k i .τ k ij P k j 1-σ k .E k j .
@PA with P k j the idel prie index for j9s onsumers in ountry kD given yX

(P k j ) (1-σ k ) = i (p k i .τ k ij ) 1-σ k . @QA
e quntity Q k i of good k is produed y representtive (rm in ountry iD using spei( ftor L k i whih is in (xed supplyF ithout loss of generlityD one n set the ftor requirement to ID whih yields identity etween setorElevel wges w k i nd the fFoFF prie of the goodX

w k i = p k i @RA
he mrket lering ondition for eh vriety of eh good is written sX

j X k ij = p k i .Q k i , @SA
where the sum is over ll destintionsD inluding domesti sles of the goodF pinllyD eh ountry9s totl inome Y j is equl to the totl vlue of sles in ll setorsX

Y j = k p k j .Q k j @TA
The structural gravity equation enderson nd inoop @PHHQA de(ne the ggregte of demndEweighted trde osts fed y n exporter s the exporter9s multilterl resistne9F his multilterl prie @we use here oth terms interhngelyA is de(ned sX

(Π k i ) 1-σ k = j τ k ij P k j 1-σ k E k j Y k w , @UA V
where Y k w is the totl nominl vlue of world prodution of good kX Y k w = i p k i Q k i F sing this de(nition nd eqution SD one otins the reltionship etween fFoF pries nd multilterl resistne terms sX

(p k i ) σ k = Y k w Q k i .(Π k i ) 1-σ k . @VA
gomining this expression with the trde demnd eqution PD one otins the grvity eqution for nominl trde )owsX

X k ij = τ k ij P k j Π k i 1-σ k . E k j Y k i Y k w . @WA
whih expresses ilterl trde s funtion of ilterl trde ostsD multilterl pries @Π k i A nd @P k j A @leled exporter nd importer multilterl resistne termsD respetivelyD y enderson nd inoop @PHHQAAD nd the inome nd expenditure levels of the exporter nd importerD E k j nd Y k i F yne dvntge of this expression is tht its struture is ommon to distint trde modelsF wore preiselyD trde models suh s urugmn @IWUWAD iton nd uortum @PHHPA nd welitz @PHHQAD ll yield grvity eqution for trdeD where ilterl trde )ows re onstntEelstiity funtion of ilterl trde osts nd of multilterl prie terms for the exporting nd importing ountriesF eross modelsD the trde elstiity @equl to 1 -σ k in the se onsidered hereA will depend on di'erent prmeters of the modelF 6 husD the trde elstiity n e estimted using eqution WD using mesure of timeEvrying ilterl trde osts nd ountryEsetor (xed e'ets whih ontrol for the exporter nd importer terms P k j nd E k j D Π k i nd Y k i F his otined estimte of the trde elstiitiesD σk D should thus e viewed not s spei( to the ermington used hereD ut vlid under more generl ssumptions whih re omptile with the struturl grvity equtionF sn turnD the reltive prie hnges in response to trde ost hngesD re lso 6 For example, in the Armington model used here, as in the Krugman (1979) model, it is simply a function of the CES elasticity of substitution. In Eaton andKortum (2002) andin Melitz (2003), it depends on the CES elasticity and on the parameter governing the distribution of rms productivities.

W invrint ross lss of modelsD onditionl on the vlue of trde elstiities nd initil trde vluesF his motivtes our empiril strtegyX we (rst estimte setorE level trde elstiitiesD then ompute prie nd inome hnges resulting from trde ost hnges @preferentil greementsAD in omprtive sttis exerise whose vE lidity extends eyond the ermington modelF his result is disussed in the setion PFIF Resolution method yne estimtes of the trde elstiities for eh setor re otined @setion RAD the omprtive sttis exerises in setions S nd T re rried y solving the model (rst in the referene yer PHHI with dt for pplied tri's in tht yer nd totl prodution y ountry nd setor 7 Y then in lterntive senrios where hnges in tri's re ppliedD while prodution vlues nd nonEtri' omE ponents of trde osts re mintined onstntF por eh set of tri' vluesD the model is solved using n itertion lgorithmF iqutions VD Q nd T re solved in the vriles p k i D P k j nd Y j D iterting until the reltive error in eh omponent of the equtions is lower thn HFI7F he system dmits unique equilirium one normliztion is imposedX we set Y w = j Y j = 1F sn eh senrioD hnges in pries nd inome levels re then mesured s the reltive hnge etween the equilirium in enhmrk yer PHHI nd the new equiE lirium fter tri' hnges re ppliedF IH ountryD resulting from hnge in trde ostsD will e driven y the onstntE elstiity dependene of trde to priesF husD the reltive hnges in priesD conditional on the trade elasticity @s well s on initil trde levelsA will e unhnged ross these modelsF xote tht this does not imply equivlene ross these modelsD ut rtherD tht the trde elstiity is su0ient sttisti to ompute numer of prie hngesF erkolkis et lF @PHIPA present set of onditions de(ning lss of models where this result holdsF hese inlude the urugmn @IWVHA model of trde with symmetri (rms in monopolisti ompetition in eh ountryY the iton nd uortum @PHHPA model of irdin omprtive dvntgeD nd the welitz @PHHQA model with heterogeneity in (rm produtivityF he three required mroElevel restritions reX tht trde is lnedY tht the shre of pro(ts in ountry9s totl revenues is onstntY nd tht the import demnd system is of the formX

X ij = ξ ij .N i .(w i τ ij ) . Y j i ξ i j .N i .(w i τ i j ) @IHA
where X ij is trde vlue from ountry i to jD N i is the numer of (rms operting in ountry iD ξ ij is funtion of prmeters distint from τ Y Y j is ountry j9s inome levelY nd is the trde elstiityD whih is funtion of di'erent prmeters in di'erent models 8 st is reltively strightforwrd to show tht this set of onditions leds to the following system of equtionsX Arkolakis et al. (2012) and is more restrictive than condition R3 under which their most central result on the welfare gains from trade is derived. This central result states that welfare change from a shock to trade costs, conditional on the change in import penetration, is constant across a class of models. This does not mean that these models generate the same welfare changes from a given trade policy shock, as the import penetration reaction can dier across models. Thus, in order to derive the stronger result, of interest to us, that relative price changes, for a given shock on trade costs, are invariant, condition R3' is necessary.

ŵi = l λ il ŵl Y l ( ŵi τil ) Y i r λ rl ( ŵr τrl ) @IIA nd 8 Condition 10 is called R3' in
II Pj = [ i λ ij ( ŵi τij ) ] -1/ @IPA
where ẑ denotes the rtio of (nl to initil vlue of vrile zD z /zD resulting from ritrry hnge in trde ostsY nd λ ij = X ij E j is the initil shre of imports from i in ountry j9s totl expenditureF his system de(nes the reltive hnge in wges ŵi s n impliit funtion of initil trde shres nd reltive hnges in trde ostsF yur ermington model of trde veri(es these ssumptionsX trde is lnedY pro(ts re zeroD due to the hypothesis of perfet ompetitionY nd trde )ows re given y the expression IHD with the numer of (rms nd the prmeter ξ eing uniformly oneY nd = 1 -σD with σ our gi elstiity of sustitutionF his ensures tht the reltive hnges in wges @or equivlentlyD fFoFF priesA ŵi nd in the onsumption prie index Pj re given y onditions II nd IPD in this lss of modelsD nd thus tht these hngesD onditionl on trde elstiities nd trde shresD re invrint ross these modelsF hese models inlude some of the models often used in the trde litertureF yne importnt ommon hrteristi of these models is tht they ssume gi preferenes 9 F sn prtiulrD this implies tht mrkups will e onstntX proE or ntiEompetitive e'ets of trde openness re thus not ounted forF 10 3 Impact of a PTA on prices: a simple example sn this setionD we use simple exmple with threeEountryD oneEsetor version of the ermington modelD to illustrte the impts of preferentil trde lierliztion on prodution pries nd rel inome in this modelF e onsider the following stylized model with three ountries denoted eD f nd gD produing nd trding di'erentited vrieties of the sme one goodF e ssume 9 In principle, condition 10 does not imply that preferences are CES, as this condition charac- terizes the import demand function as a result of both preferences and supply side responses. In practice, commonly used models verifying 10 all assume CES preferences.

10 See e.g. Neary and Mrazova (2013) for a discussion of the relation between demand elasticities and pro-competitive eects in a more general framework.

IP tht e is t n equl distne from f nd gD with lrger distne etween f nd gF sn prtieD we set initil trde osts sX

τ ij = 1 if i = j τ AB = τ AC = 1.5 τ BC = 2 tradecost ij = (1 + AV ij ).τ ij @IQA
where AV is the dEvlorem equivlent of trde poliy rriers pplied y j on imports from iF ht isD ilterl trde osts result from omintion of geogrphil omponent nd of poliy rriers pplied y ountriesF 11 e initilly set the size of ountries eD fD g to ID IH nd SY ountry9s size eing here equl to its lor endowmentD or equivlently to the volume of its produtionF e ssume tht ountries initilly pply wpxD nonEdisrimintory tri' to ll importsD nd set it to QH7F e onsider the se of ilterl e signed etween ountries e nd fD whih sets tri's etween these two ountries to HF e fous on the impt of the e on pries in ountry eF he questions of interest to usD here nd in the rest of the pperD re the impt of the e on the produer prie p A Y the onsumer prie index P A Y nd the ountry9s rel inome

Y A = p A .Q A P A F 12
pigure I represents the reltive hnge in prodution prie p A X we hve here two prmeters vryingD the size of the prtner ountry fD whih goes from I to PHY nd the elstiity of sustitution σD whih vries etween I nd IHF he (gure shows tht the impt of the e on prodution prie hnges sign 11 This is similar to the functional form which will be used to model trade costs in the empirical part, where the geographic component will account in particular for distance and contiguity.

12 In the case of policy barriers being in the form of taris, the real income of a country includes the share of revenues from trade barriers which is rebated:

Y A = p A .Q A +ρ. i=B,C AViX iA P A
with ρ the share of revenue rebated. We will check that modifying ρ does not modify qualitatively our results. IQ depending on these two prmetersF sn prtiulrD in the low sustitution seD the impt is positiveD while it eomes mostly negtive in the highEσ regionF his re)ets two ompeting e'etsX on one hndD the e grnts preferentil ess to ountry f9s mrketD whih llows e9s produers to rise their prodution prieD the more soD the more inelsti the demnd for their vriety isF yn the other hndD the e entils reiprol tri' redutionsD whih implies ompetition e'et on e9s domesti mrketX this tends to ring the prie of e9s vriety lowerD with this e'et eing lrger if ompeting vrieties from e nd f re more sustitutleF hese two e'ets re generlly lrger when the size of the prtner ountry inE resesF husD in lowEσ setorD one would expet produers in ountry e to prefer e with lrge prtner @ll else equlAY while in highEσ where import ompetition domintesD they would prefer e with smller prtner ountryF pigure P displys the impt of the e on ountry e9s onsumer prie index @the gi idel prie indexAF he impt is negtive s the e lowers the ggregte prie of onsumption in the ountryY it is displyed in solute vlue hereF he (gure shows tht onsumers stnd to gin from the eD the more so when σ is low nd the size of the prtner ountry inresesF snterestinglyD the grdient of the impt is not ligned with tht of the prodution prie imptX for exmpleD in the highEσ regionD the gin inreses with the prtner9s sizeD while the impt on prodution prie eomes more negtiveF his illustrtes the divergene of interests in trde poliyX in ountry trding good with high trde elstiityD poliy foused on mximizing prodution pries would prefer e with smll prtner ountryD while fvoring the gins to onsumers would led to hoose e with lrge ountryF pigure Q displys the impt of the e on ountry e9s rel inomeF st shows tht the lrger gins in rel inome re otined in the highEσD highE regionF he e lowers the onsumer prie index in ountry eD through heper imports from prtner ountry f nd through the import ompetition e'etD whih lso lowers the domesti vriety9s prieF hese e'ets re lrger in the highEσ region nd dominte the negtive impt on domesti priesD using lrger rel inome ginF his illustrtes the divergene etween the ojetives of mximizing prodution pries

Y k i Y k W + ln E k j Y k W + (1 -σ k ).(ln τ k ij -ln(P k j .Π k i )).
@IRA e funtionl form of trde osts is needed to estimte this equtionF sn line with the ommon prtie in the litertureD we ssume the following logEliner stohsti formX

τ k ij = (1 + ri' k ij ).d ρ k ij .e α k gontig ij .e β k gomlng ij .e u k ij , @ISA
where ri' k ij is the dEvlorem equivlent of tri' rriers on i9s produts exported to j in setor kD d ij is the distne etween i nd j nd u k ij represent unoserved ilterl trde ost determinntsF e lso dd two dummy vrilesX gontig ij D whih is unity if ountriesGregions i nd j re ontiguousD nd gomlng ij D whih is unity if i nd j shre n o0il lngugeF lugging the funtionl form of trde osts into @IRA nd dding time susripts to stress the point tht some of the vriles re time vrying give usX

ln X k ijt = ln Y k it Y k W t + ln E k jt Y k W t + (1 -σ k ).(ln(1 + T arif k ijt ) -ln(P k jt ) -ln(Π k it )) + (1 -σ k ).(ρ k .d ij + αContig ij + βComlang ij ) + k ijt , @ITA
where k ijt is the stohsti error termF e estimte this eqution seprtely for eh setorF e introdue exporterEtime @λ it A nd importerEtime @λ jt A (xed e'etsD whih enles us to ontrol fully for unoserved setorElevel ountry shres of world prodution nd expenditureD s well s for ountry multilterl prie terms for eh setorF hus our spei(tion is the followingX PV fefore thisD we wish to sk whether world trde is eoming s whole more or less preferentilD iFeF whether trde etween e prtners is growing fster or

ln X k ijt = β k ln(1+ri' k ijt )+γ k ln d ij +δ k gontig ij +η k gomlng ij +λ it +λ jt + k ijt . @
A ij = 1] = F (β 1 . p ij j + β 2 . P ij j + β 3 . (Y j /P j ) M L ) @IVA
where F is the logisti funtionY P r[P T A ij = 1] is the proility of e eing signed etween ountries i nd jY p ij j nd P ij j re the predited impts @reltive prie hngesA of e with ountry i on ountry j9s ggregte prodution prie p j nd onsumer prie index P j D respetivelyF (Y j /P j ) M L ) represents the predited impt of multilterl redution of tri' rriers for ountry i @expressed in reltive termsAF his ltter vrile is intended to test whether the options of preferentil versus multilterl trde lierliztion pper s sustitutes in trde poliyF rospetive impts p ij j D P ij j re omputed y strting from the oserved level of protetion for ll ountries in our model in PHHID nd simulting the impt of ll potentil ilterl es etween ny pir ountriesD while mintining sttus quo on ll other trde rriersF es re modeled s desried t the eginning of this setionF (Y j /P j ) M L ) is omputed s the result of multilterl opening of ountry j9s trdeD modeled s uniform ut of SH7 on ll tri's rriersF he dependent vrile is inry inditor of e eing signed etween two ountries fter PHHIF QI sn lterntive spei(tionsD we rerrnge this funtionl form sX

P r[P T A ij = 1] = F (β 1 . p ij j + β 2 . (Y j /P j ) ij + β 3 . (Y j /P j ) M L ) @IWA
whih is equivlent if one rells thtD in the modelD ntionl inome is the sum of prodution pries multiplied y (xed volumes X Y j = k p k j Q k j F his expression llows to mesure with β 2 D the impt of expeted rel inome gins on the proE ility of signingY while β 1 tests whether the impt on prodution prie hs ny explntory powerD fter ontrolling for rel inomeF esults re shown in tle SF hese results inditeD ressuringlyD tht the rel inome gins tht ountry n expet from signing ilterl e in)uene trde poliy in the right diretionD inresing the proility of signing the greementF st lso shows tht the potentil gins from opening multilterlly derese the proE ility of signing eX this indites tht ountries with higher expeted gins from multilterl opening @due to eFgF more diversi(ed trde ross prtnersD ndGor higher verge distne from trde prtnersA tend to engge less in preferentil delsF heomposing the rel inome gins from es into prodution pries on one hndD nd domesti ggregte prie index impts on the other @olumn PA revels tht these two vriles do not rry the sme weight in explining trde poliyF he reltive gins in prodution pries hve n impt on the proility of signing whih re more thn two times tht of onsumer prie ginsF his di'erene is signi(nt nd roust ross spei(tionsF golumn R further deomposes the gins from multilterl opening into their prodution prie nd onsumer prie index omponentsF he spei(tion in olF S uses ountry (xed e'etsD whih ontrol for the gins from multilterl opening @invrint ross prtner ountriesA s well s for other potentil ftors impting e hoies t the level of ountriesF hese my relte to eFgF ountries9 sizeD tehnology levelD trde sophistitionD whih my 'et the gins from es through hnnels not ounted for in our modelF yur min resultD the lrger impt of produer gins over rel inome gins is holding in these spei(tionsF le T tests the relevne of our mesures of e e'ets for explining trde QP poliyF sn seminl pperD fier nd fergstrnd @PHHRA develop model of trde whih they use to derive list of determinnts of the potentil gins from eY they then show tht this list llows to orrely predit numer of the greements whih were tully signedF heir model inludes severl dimensions of the gins from esD inluding speiliztion ginsF fy ontrstD our pproh is restrited to more spei( gins from esD nmely termsEofEtrde ginsY ut we mesure these gins struturllyF o test if our model dds some elements to ther understnding of ountries9 poliyD we run in tle T regressions inluding the two lists of vrilesF Natural is dummy for two ountries eing on the sme ontinentF st ptures the gins from singing es with soElled nturl prtners9D yielding higher gins euse of the more intense trde reltionsF Remote is proxy mesure of the distne of two prtners from the rest of the world ountriesD distne whih inreses the e gins s diversion e'ets re reduedF pinllyD drgdp is mesure of the gp in inome levels etween two ountries nd ptures the similrity etween two eonomiesF esults show tht lthough these vriles hve some power to explin esD they do not exhust the determinnts of ountries9 trde poliyY in prtiulrD our mesures of e prie impts remin signi(ntF pinllyD tle U introdues mesure of the losses fed y ountry if one of its trde prtners engges with e with third ountryF fldwin @IWWQA hs proposed tht ontgion or domino e'ets my explin the prolifertion of preferentil greementsD s trde diversion from es retes n inentive for nonEmemers to join existing greementsD or to form new onesF rere we test this hypothesis y using proxy mesure of the loss to third ountriesX for eh pir @eDfA of ountriesD we ompute the rel inome hnges for e in senrios where f signs n greement with third ountryF hese hnges re negtiveD due to diversionF e tke the mximum loss inurred y e ross ll potentil es signed y fD nd use this s proxy mesure of the diversion thretF his mesure is introdued in our spei(tion in olumn ID nd deomposed in olumn P into the prodution nd prie index omponentsF esults indite tht the mgnitude of this potentil QQ loss reltes to the proility of signing n greementD whih tends to on(rm the ontgion hypothesisF golumn Q we uild the e net impts on priesD de(ned s the impt of signing n greementD minus the loss in the se no greement is signed nd the prtner ountry engges in nother eF he lrger imp le SX heterminnts of e signing @IA @PA @QA @RA @SA P r[P T A = 1] el inome impt of ilterl e HFTQ a HFTQ a HFVI a @HFIHA @HFIHA @HFIRA e impt on prodution pries IFRP a HFUW c IFRR a IFQP b @HFRVA @HFRUA @HFRWA @HFSPA e impt on domesti prie index EHFTQ a EHFTQ a @HFIHA @HFIHA el inome impt of multilterl opening EHFPS a EHFPR a EHFPR a @HFHTA @HFHTA @HFHTA wv openingX prodF pries The American Economic Review 89@SAD IIQS!IISSF qrossmnD qF @IWWRAF 4Import

  Validity of our results in more complex models esults for reltive prie hnges in response to trde ost hngesD otined in the ermington model presented ove n e generlized to roder lss of models of trdeF he si intuition ehind this result is tht numer of oneEsetor models of trde generte trde equtions with the sme grvity struture for the trde equtionD where the trade elasticity E the elstiity of trde with respet to trde osts nd wges E is funtion of di'erent prmeters of the modelD re)eting di'erent mrgins of djustment to trde shoksF sn turnD hnges in the fFoFF pries of vriety nd the idel prie index in eh 7 See section 4 for details on the data used.

  price index (abs. value) sigma Relative price change pigure PX e impt on ountry e9s onsumer prie index enother exmple of this divergene is given on (gure RD whih fouses on hnges in prodution pries nd in the onsumer prie indexD in the se σ = 8D s funtion of the prtner ountry9s size QF he (gure highlights the nonElinerities in prie IS pigure QX e impt on ountry e9s rel inome hnges in this model nd shows tht the mxim of the two prie funtions do not oinideF his highlights gin the divergene etween the two ojetivesX ssuming tht ountry would fe the lterntive of signing e with two ountries di'ering only y their sizeD the optiml hoie would di'er depending on whether poliymkers fvor the ojetive of mximizing prodution priesD or onsumers9 rel inome levelF he rest of the pper will ttempt to use the informtion on the es signed y world ountries s inditive of the underlying ojetive pursued y signing govE ernmentsF he sme ermington modelD ut with more ountriesD multiple setors will e usedF ritions in initil trde level nd setorl ompositionD distne to potentil e prtners nd third ountriesD will generte vritions in the potentil impt of e on signing ountries9 prodution pries nd rel inomeF yur pE proh onsists in onfronting these impts to the oserved hoie of es to infer informtion on the ojetive funtions governing trde poliy hoiesF IT PTA impact on price index, production price prod. price impact Price index impact pigure RX snidene on importer9s prie index IU 4 Estimation of sector elasticities Empirical specication he estimtion of the e'ets of es is done in two stepsF sn this setion we estimte elstiities of sustitution t setor level to prmetrize the modelF xext we estimte the e'ets of trde poliy hngesF king the log of eqution @WA yields ln X k ij = ln

  IUAIV sn this equtionD oe0ient β k gives us diretly the estimte of (1 -σ k )D while γ gives us the estimte of the produt (1 -σ k ).ρ k D of whih we n dedue ρY we n similrly otin the e'ets of ontiguity nd ommon lnguge on trde ostsF Data e estimte the setorElevel grvity eqution using nominl ilterl trde vlues from the fegs trde dtseF 13 rde dt t produt rrmonized ystem @rAET digit level re ggregted t the snterntionl tndrd sndustril glssi(E tion @ssgA revFP level @UW setorsAF e see this level of ggregtion s onsistent with the de(nition of setors in the modelF 14 ell world trde is onsideredD ggreE gting )ows into TV ountriesGregions to keep the model trtleF his estimtion strtegyD whih redues the high dimensionlity of dtD is ommon in the literture @see enderson nd vn inoopD PHHQ nd enderson nd otovD PHIHAF ht on distneD ontiguity nd lnguges re tken from the distne giss dtseF 15 ri' dt re otined from the giss wwp dtse @fouet et al.D PHHVAF his dt set ontins dt on ilterl pplied tri' protetion for the yers PHHID PHHR nd PHHUF ht on ad-valorem nd spei( tri'sD nd on tri' quotsD re onverted into ad-valorem equivlents using unit vlues dt for the yer PHHIF husD our tri' vrile is omprehensive mesure of pplied tri' protetionD whih enles us to trk hnges in tri' protetion due to preferentil greementsF 16 smportntlyD this enles us to oserve preisely the ontent of esD nd to oserve vritions ross es in setor overgeD extent of tri' redutions nd time period of implementtionF 17 xote tht running our estimtes on threeEyer intervls llows us to otin stle estimtesD while the use of yerly dt hs een shown to yield unstle grvity estimtesD due to delys in the djustment to trde shoks @ylivero nd otovD PHIPAF his lso llows to (lter out usiness yle e'etsF sn estimting eqution @IUAD we fe the prolem of endogeneity of trde poliyD here of the tri' vrileF roweverD this prolem is signi(ntly redued y the use of detiled tri' dtD insted of ggregte trde poliy inditors suh s e dummiesF sndeedD tri' dt t setor level o'er onsiderly more vritionF e exploit the ft tht trde poliy is deided t ggregte level @through multilterl nd preferentil greementsA so tht most tri' hnges t setor level n e seen s exogenous from the point of view of the industryF 18 his vrition omes from di'erenes @IA in initil preEe tri' levelY @PA in overge of es @tht implement prtil redution of tri's ross produtsAY nd @QA in implementtion of tri' redutions over timeF xote lso tht our use of detiled tri' dt llows for more diret estimtion of elstiitiesD in ontrst to studies fousing on the e'et of distne or orders on trde @see eFgF enderson nd otovD PHIID rummelsD IWWWAF rere setor elstiities re diretly otined from the oe0ients on tri' vriles @the oe0ients re 1 -σ k AD so tht the knowledge of the elstiity of trde osts to distne nd other vriles is not neededF Estimation method e use n yrdinry vest qures estimtor with gountryE er pixed i'ets @yvEgpiA to estimte the UP setorElevel elstiitiesF he ountryEyer (xed e'ets @λ it nd λ jt A ontrol fully for importer nd exporter timeE vrying vrilesX import prie indiesD exporter fFoF priesD exporter nd importer shres of prodution nd expenditure demnd in world totlY nd ny other omitted vrile suh s those relted to institutionsF Results. le @VA in ppendix e displys the estimtion resultsF he tle disE plys the vlue of the tri' oe0ient @orresponding to 1 -σ k in the modelAD the ssoited stndrd error nd the numer of oservtions used for the estimtionF gonsistently with the gi preferenes in our modelD whih imply tht σ k ≥ 1 in ll setorsD we (nd negtive oe0ients in ll setorsF he vlues we otin re in the rnge IDPHY IQFWD with men vlue t SFQUF his is onsistent with estimtes from other studiesY for instneD the peenstr @IWWRA method pplied to ST ssg setors yields estimtes rnging from QFI to PVD with men TFU @sms nd wejenD PHHWAF en dditionl hek of the onsisteny of our setorElevel estimtes onsists in ompring our results with the lssi(tion of trded goods in homogeneous versus di'erentited goodsD proposed y uh @IWWWAF sndeedD the elstiity of sustiE tution σ k is in verge QFTW higher mong homogeneous setors thn mong the di'erentited ones 19 19 Our ISIC rev.2 sectors are classied as homogeneous if they contain more SITC products classied as homogenous than dierentiated. PI 5 Price and real income impacts of PTAs, 2001-2007 ermed with our estimtes of the prmeters of the modelD we strt in this setion y estimting the imptD on prodution pries nd rel inome levelsD of the trde poliy tht ws implemented y world ountries during the PHHIEPHHU periodF sn the next setionD we will estimte the impts of lterntive trde poliiesF 5.1 Price impacts of PTAs pirstD we sk whether es ene(t t ll to ountries whih sign themF heoretil insights hve shown tht ountry my fe loss from distortions reted in import priesD so tht preferentil trde opening my in some ses e detrimentl to domesti welfreF e use our model nd dt on tri' protetion hnges for the PHHIEPHHU period to ompute the implied impts of es tive in this periodD looking t hnges in rel inome of signing ountriesF ell tht this exerise gives us lower ound estimte of the totl e'et of preferentil lierliztion on rel inomeD s these estimtes only tke into ount the hnges in tri' rriers implemented y e prtnersF woreoverD the model fouses on the e'ets of hnging termsEofEtrdeD while dditionl potentil gins through hnges in speiliztion nd produtivity improvements re not tken into ountF eondD we deompose those hnges in rel inome into two omponentsX proE dution pries nd the onsumption prie indexF 20 his deomposition ims to distinguish the two soures of ene(ts from esX on one hndD it lowers import priesD s well s domesti pries through the ompetition e'etF his ene(ts onsumers in the ountryD y rising their inome in rel termsF yn the other hndD reiprol tri' redutions in the prtner ountry inreses ess to this mrketD whih llows domesti produers to rise their mill prieF les I nd P disply the results of this exerise for the list of ll tive greeE 20 Production prices and the consumption price index are aggregated across sectors. The aggre- gate production price is the average of sector prices weighted by the sector share in total production value. The aggregate ideal price index is the Cobb-Douglas aggregate of sector-level CES price indices. PP ments during the periodF 21 hese results show lrge vrition in the rel inome impts of es nd in the distriution of these impts ross gents within prtner ountriesF gonsumer gins E in the form of redution of the domesti prie index E vry etween EHFVP nd PFP7F roduer gins E inresed mrket essD llowing rise in prodution pries E vry etween EHFIS nd IFST7F he mplitude of the prie impts of es is vrying with trde shres etween prtnersD trde ompositionD preEgreement tri' levelsD nd with the mgnitude of tri' redutionsF sn prtiulrD setion Q illustrtes how the trde elstiity nd the reltive size of trde prtners modify the prie imptsF 21 We use the data for the list of signed PTAs which is maintained by José de Sousa, http://jdesousa.

  become more or less discriminatory? he results just presented doument the impts of preferentil trde poliyF his represents only shre of overll trde poliyD s mny ountries lso implement trde rriers redutions outside of trde greementsF his n tke the form of wpx tri' redutionsD of redutions of pplied tri's elow the ound level @for y memersAD or more generlly of unilterl rrier redutions grnted on nonE preferentil importsF he theory predits di'erent impts from preferentil versus nonEpreferentil tri' redutionsX preferentil trde opening n e detrimentl to the ountry9s welfreD if trde diversion previlsF woreoverD we expet multilterl opening to e generlly more ene(il in rel inome termsD ut less positive for prodution priesD s it generlly does not entil n esier ess to prtner ountries9 mrketsF et this pointD we would like to know whether world trde tends to evolve rther preferentilly or multilterllyY nd whether we n understnd wht ftors led ountry to opt rther for the preferentilD or the multilterl optionF e strt y exmining this question t the level of ntionl trde poliiesF por eh ountry in our modelD we onsider its unilterl trde poliy E iFeFD ll hnges in its tri' struture E nd sk wht would hve een the impt all else equalF esults in tle Q show ontrsted pro(les ross ountriesF yut of the RP ounE tries we onsiderD PQ hve hd trde poliy tht fvored the preferentil mode of lierliztionD in the sense tht it mde their trde grow fster with their preferentil prtnersF he other IW ountries hve hd trde poliy tht oriented their trde reltively more towrd multilterlismF he tle lso displys the rel inome impts of eh ountry9s trde poliyF yne oservesD ressuringlyD tht most ountries hve implemented poliy tht yielded rel inome ginsF sn prtiulrD this is the se lso for ountries tht mostly led preferentil poliy still otined positive gin from itD on(rming tht detrimentl e'ets due to diversion re generlly smll ompred to the gins of preferentil openingF husD these results o'er more ontrsted piture of the evolution of trde poliyD thn sul look t the explosion of es might sugE PT gestF wost ountries implement preferentil nd multilterl trde rrier redutions onurrentlyD with the reltive importne of the two proesses vrying ross ounE triesF esults on rel inome e'ets of these poliies suggest tht these ountries re hoosing their trde poliy in their est interestX there is no signi(nt di'erE ene in the rel inome impts of trde poliies etween the preferentilist nd multilterlist ountriesF 22 he reltive ttrtiveness of opening trde multiltE erlly or preferentilly vries ross ountries with the struture of their trdeD the importne of trde diversion to e expeted from signing eD nd the levels of tri's in the ountry nd in its prtnersY this should result in di'erent trde poliy hoiesF esting the optimlity of these hoies will e the ojetive of next setionF

  slower thn tht with nonEe prtnersF o exmine this questionD we perform ounterftul estimtion of the impt of the two proesses seprtelyX in other wordsD we study two senriosD one inluding ll tri' redutions etween e prtE nersD the seond inluding ll other tri' redutionsD thus eing the omplementry of the (rstF le RX rde impts of esX tretment e'ets 7hnge in world trde es nonEes qlol xonEpreferentil trde EHFWT PFRW HFQI referentil trde PFHR EHFRI IFHT le R shows the resultsF sf only preferentil trde rrier redutions hd een implemented in PHHIEPHHUD world trde would hve inresed y PFHR7 etween eD while ontrting y lmost I perentge point mong nonEprtnersF gonverselyD llowing only nonEpreferentil tri' redutions would hve resulted in n derese in the reltive weight of preferentil trdeF ht is interesting is thtD overllD tri' hnges in tht period hve mde world trde more preferentil thn notX preferentil trde hs grown y I perentge pointD more thn three times more thn nonEpreferentil trdeF his my e surprising given the lne etween the orienttion of trde poliies ross ountriesD ut results from the ft tht higher numer of lrge ountries hve implemented prefereneEoriented trde poliies in the periodX the ountries with prefereneEoriented poliies represented TU7 of totl world trde in PHHIF PW 6 Do countries sign the most benecial PTAs? e now use our model to exmine the following questionsX mong ll possile trde greementsD how do ountries hoose the ones they signc hih of the ojetives of inresing the ountry9s rel inome levelD or the level of its prodution priesD is eing est served y these hoiesc pinllyD do they optimlly hoose etween the options of preferentil nd multilterl trde lierliztionc o nswer these questionsD we perform simultion exerise in whih we ompute the imptsD for eh ountry in our smpleD of ll possile ilterl trde greements with eh other ountryF e model these greements s followsX the two ountries gree to redue their tri's to hlf the lowest of their two tri's in eh setorF his is intended to pture the reiproity tht pplies to most greementsF yur pproh here rests on severl hypothesesF pirstD we ssume tht the ontent of e is su0iently onstrined y rulesD so tht the pro(le of tri' redutions in ny prospetive greementD onditionl on initil protetion levelsD n e predited with reltive degree of uryF he most prominent suh rule is rtile sD prgrph V of the qe @now yAD whih requires tht in e duties and other restrictive regulations of commerce (...) are eliminated on substantially all the trade between the constituent territoriesF sn prtieD this mens tht two ountries my not sign prtil greementD whih would over only numer of seleted setorsF ixeptions re D howeverD generlly dmitted to this ruleD y whih smll numer of produt lines re eing exempted from tri' dismntlement following negotitions etween prtiesF he numer of exeptions is generlly smllD oth euse of the qeGy rule nd euse of on)iting interests etween negotiting governmentsD s eh ountry ttempts to preserve protetion for its strtegi industriesD while trying to gin mrket ess for ll its exportersF eondD our simultion exerise fouses on one spei( spet of e imptsX the termsEofEtrde e'ets of preferentil lierliztionF otentil determinnts of trde poliy lso inlude eonomi ftors not ounted for in our frmeworkX in prtiulr speiliztion ginsY s well s nonEeonomi ftorsF por exmpleD es my fvorD or e filitted yD politil links nd llines etween prtnersF QH egrding eonomi determinntsD our hypothesis is tht termsEofEtrde e'ets ptured in our model onstitute the most immedite e'ets of hnging trde rriE ersY while speiliztion or produtivity gins my tke longer to mterilizeF essumE ing tht governments hve shortEterm horizonD one n thus expet termsEofEtrde e'ets to ply role in their deisionsF sn order to test tht our results re not driven y orreltion etween these two omponents of e ginsD we will perE form roustness heks where vriles pturing speiliztion gins re inluded s ontrols in our regressionsF es for politil determinntsD we do not oserve themF yur working ssumption is tht suh politil links re not systemtilly orrelted with our estimted prie imptD whih re funtions of trde osts nd initil trde nd protetion levelsF Empirical specication e model the proility of two ountries signing e with the following funtionl formX P r[P T

  These impacts are decomposed into eects on production prices, domestic CES price index and overall real income impact. Net impacts are the dierence between the impact of signing a PTA, and the impact if the partner country signs with a poliy hs een reurrent question in the litertureF sn this pper we hve proposed n originl pproh to itD sed on oserving trde poliies in the dt nd looking t the implied trde nd inome e'etsF pirstD we looked t ll tri' hnges implemented y world ountries during PHHIEPHHUD nd used generl equilirium model to ompute the implied impts on trde ptternsD nd on ountry rel qh nd welfre levelsF elthough simpleD our model essentilly ptures termsEofEtrde e'ets of preferentil nd multilterl trde lierliztionD thus llowing to quntify trde retion nd diversion e'etsF his exerise revels tht oth preferentil nd multilterl lierliztions re eing implemented onE urrently y most world ountriesY overllD out hlf the ountries in our smple hve een running trde poliy more multilterl thn preferentilD thus reduing distorsions in their tri' strutureF xextD we found tthe hoie of trde poliy to e strongly relted to oth produer nd onsumer interestsD with the former hving weight out two times lrgerF sn ontrst to previous estimtes in the litertureD this result shoows the presene of importnt distorsions in the setting of trde polE iyF st suggests tht the exessive weight put on mrket ess gins leds ountries to exhiit is in fvor of preferentil trde lierliztionD despite lrger expeted gins from multilterl openingF QU iggerD FD wF vrhD uF iF tuD nd F inkelmnn @PHIIAF he trde e'ets of endogenous preferentil trde greementsF American Economic Journal: Economic Policy 3@QAD IIQâRQF qoldergD F uF nd qF wggi @IWWWAF rotetion for sleX en empiril investigtionF

  Logit regression on the probability of a PTA being signed between two countries in or after 2001.Impact of each PTA on production f.o.b. prices and on the domestic price index (CES price index) are used in % variation. They are computed at sector level, then aggregated consistently with the model structure. See text for the denition of PTAs in the simulation exercise.Regressions in this table add to the former specication used in table 5 the determinants of PTAs as identied inBaier and Bergstrand (2004). Natural is 1 if the two countries are on the same continent. Remote is the average distance of the two partners to other countries outside the pair.Drgdp is the absolute value of the dierence of the log of real GDPs of the two partners.Regressions in this table add estimates of the potential losses by diversion faced by one country if the partner country implements another PTA with a third country.

	le UX heterminnts of esX diversion e'ets @IA @PA	@QA
	P r[P T A = 1] le TX heterminnts of esX roustness heks @IA @PA el inome impt of ilterl e HFRU a HFRW a P r[P T A = 1] @QA @HFIPA @HFIQA
	e imptX prodution pries hiversionX rel inome impt	IFPI b IFPI b @HFRVA @HFRVA ETFVP a @PFRWA	IFIU b @HFRVA
	e imptX domesti prie index hiversionX prodution pries	EHFTR a EHFTR a @HFIHA @HFIHA ERFQQ a @IFQIA	EHFSU a @HFIIA
	el inome impt of multilterl opening EHFPR a EHFPS a @HFHTA @HFHTA hiversionX domesti pries @QFRSA HFIR	EHFPR a @HFHTA
	xturl rodution priesX net impt wv openingX domesti prie index emote homesti priesX net impt gountry (xedEe'ets yservtions seudo R 2 hrgdp el inome impt of multilterl opening EHFPR a EHFPP a HFRW b HFSH b @HFPIA @HFPIA EHFIS @HFSRA IUPP IUPP IUPP HFHSQ HFHST HFHST HFHST HFIQT HFST a IFQT a @HFPPA @HFQWA EHFQQ @HFPTA EHFIS EHFSW a @HFSRA @HFIHA HFPR a @HFHTA yes IUPP IIRV HFHW EHFPQ a @HFHTA yservtions IUPP IUPP @HFHTA @HFHTA @HFHTA IUPP seudo R 2 HFHTP HFHTP yservtions IUPP IUPP IUPP HFHTS seudo R 2 HFHTH HFHTS HFHTH
	Standard errors in parentheses. Standard errors in parentheses. c p<0.1, b p<0.05, a p<0.01 c p<0.1, b p<0.05, Standard errors in parentheses. a p<0.01 c p<0.1, b p<0.05, a p<0.01
	QR QS

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		le VX etor elstiities estimtes
	etors goe'F stdF ysF etors goe'F stdF	ysF
	ssg		error		ssg		error
		@IA	@PA	@QA		@IA	@PA	@QA
	IHI	EQFUS PFVV ITHP	PSI	ESFWU HFSS	UVQQ
	IHP	ERFI	PFSP IPSH	PSP	EUFWV HFSV	VQWH
	IHQ	ERFI	PFSP IPSH	PTI	EVFHT HFTQ	TVUI
	III	EIFPR HFPP VHPS	PTW	EQFPP HFUU	UTSI
	IIP	EHFQQ HFPW SSVR	PUI	ERFIW HFUV	UTQR
	IIQ	EIFWS HFPT UVQW	PUP	EUFIS HFWQ	UHWU
	IPI	EHFVT HFRV PHST	PVI	ERFTQ HFUQ	SWVI
	IPP	EHFPI HFPW RTWU	PVW	ERFIW HFSV	VVVS
	IQI	EIHFV PFRI QWPR	PWI	ETFQI HFUP	WHHT
	IQP	EIHFV PFRI QWPR	PWP	ESFRT IFPT	VWTU
	IRI	ESFWT HFWW RQPI	PWQ	ESFIR HFSW	TQTU
	IRP	ERFWT IFPQ SQST	QHH	ETFV	IFRR	UVIW
	ISI	EIFWQ HFPR VVII	QII	ETFRV HFWW	UPQT
	ISP	EIFQR HFQI RQIP	QIP	ESFQ	HFVQ	UIRU
	ISQ	EIFHQ HFIU SWRP	QIQ	EUFU	HFVQ	SVIV
	ISR	EHFVV HFPI VHSW	QIR	ERFS	HFUS	SQSW
	ISS	EHFQR HFII SVPT	QIS	ERFHP HFSW	TQIQ
	ITH	EHFTT HFPI QUWR	QIW	ERFRQ HFVR	TUQR
	IUI	EPFUT HFSV UUUP	QPI	EWFRR	IFQ	TQRI
	IUP	EQFTT HFSI VISH	QPP	EHFUT HFTP	TSRV
	IUQ	EPFUP HFSW UIRR	QPQ	EQ	HFTS	TWTV
	IVI	EPFV	HFQV VRHH	QQI	ESFUI	I	VPHQ
	IVP	EIFIT HFVU PRRV	QQP	EPFHW HFVP	SVHI
	IWI	ERFWV HFSU TWPW	QQQ	EPFSQ HFVQ	RSHV
	IWP	EQFT	HFRV TQWH	QRI	EQFWT HFRU	TTQQ
	PHH	EIFSV	HFS SSRP	QRP	EPFVR HFTQ	RSUP
	PHI	ERFIQ	IFI SIIP	QRQ	ETFWR HFTU	UPTP
	PHP	EQFTP HFST UHWW	QSI	ERFI	IFR	QSWT
	PIH	EU	HFTW URRS	QSP	EIPFWU PFHI	PSUI
	PPI	ETFUI HFUR TWWV	QSQ	EUFWW IFTT	RSRI
	PPP	ERFRV HFSW SUWW	QSW	EPFST HFST	SHQP
	PQI	ERFUS RFHQ IITR	QTI	ESFHU HFRW	UQRV
	PQP	EQFTW HFWW THHR	QTW	EHFUW HFPI	VUSW
	PQQ	ESFIW PFSW IUIQ	QUP	EPFQV IFPQ	IVQT
	PRI	EVFUU HFVU WHSW	SHH	EIFP	HFT	RQUH
	PRP	EIFQI HFRQ WSQS	URP	ETFTQ QFPU	IQTT
	PRQ	ERFRU IFHS RUUP	URW	EWFWI IFSU	IUTQ
	Appendices			WPI	EQFPU HFUT	RQTP
	A Estimation of sector elasticities
				QW

Notes

However, contrary to those models, there is no optimal positive tari, because the gain to consumers always dominates over losses to domestic producers. This is due to the hypothesis of imperfect substitution between domestic and imported goods. Thus, issues related to negotiations over taris are not considered here.

In the empirical application, each sector corresponds to one code in revision 3 of the Interna- tional Standard Industrial Classication (ISIC), maintained by the UN.T

Note: parameters of the demand function α k and σ k are assumed to be identical across countries.

5 This modeling choice is motivated by the fact that our sectors (as dened by ISIC codes) are suciently distinct to allow little substitution. U

The BACI trade data set is built by the CEPII (see www.cepii.fr/anglaisgraph/bdd/baci. htm).

Recall that the model assumes a Cobb-Douglas structure of demand over sectors. Estimating the model at a product level (e.g. HS-6 classication) would thus implicitly impose a substitution elasticity of 1 over HS-6 products, while the ne level of detail of this classication implies that this elasticity is certainly higher.

See http://www.cepii.fr/francgraph/bdd/distances.htm.

Tari values at product level are aggregated at the level of ISIC-sectors using the `Regions of Reference' method, thus weighting tari lines by trade values for the region to which the importer belongs. This mitigates biases in simple trade-weighted aggregates. For more on this seeBouet et al. (2008).

PTAs.

Note that this is true in particular for manufacturing sectors which are considered here, given that all trade agreements considered apply a quasi-total tari dismantlement in manufacturing.