Marie Candito
email: marie.candito@linguist.univ-paris-diderot.fr

Matthieu Constant
email: matthieu.constant@u-pem.fr

Strategies for Contiguous Multiword Expression Analysis and Dependency Parsing

. Our work focuses on using an alternative representation of syntactically regular MWEs, which captures their syntactic internal structure. We obtain a system with comparable performance to that of previous works on this dataset, but which predicts both syntactic dependencies and the internal structure of MWEs. This can be useful for capturing the various degrees of semantic compositionality of MWEs.

Introduction

A real-life parsing system should comprise the recognition of multi-word expressions (MWEs1 ), first because downstream semantic-oriented applications need some marking in order to distinguish between regular semantic composition and the typical semantic non-compositionality of MWEs. Second, MWE information, is intuitively supposed to help parsing.

That intuition is confirmed in a classical but non-realistic setting in which gold MWEs are pregrouped [START_REF] Arun | Lexicalization in crosslinguistic probabilistic parsing: The case of french[END_REF][START_REF] Nivre | Multiword units in syntactic parsing[END_REF][START_REF] Güls ¸en Eryiǧit | Multiword expressions in statistical dependency parsing[END_REF]. But the situation is much less clear when switching to automatic MWE prediction. While [START_REF] Cafferkey | Multi-word units in treebank-based probabilistic parsing and generation[END_REF] report a small improvement on the pure parsing task when using external MWE lexicons to help English parsing, Constant et al. (2012) report results on the joint MWE recognition and parsing task, in which errors in MWE recognition alleviate their positive effect on parsing performance.

While the realistic scenario of syntactic parsing with automatic MWE recognition (either done jointly or in a pipeline) has already been investigated in constituency parsing [START_REF] Green | Multiword expression identification with tree substitution grammars: A parsing tour de force with french[END_REF]Constant et al., 2012;[START_REF] Green | Parsing models for identifying multiword expressions[END_REF], the French dataset of the SPMRL 2013 Shared Task [START_REF] Seddah | Overview of the spmrl 2013 shared task: A cross-framework evaluation of parsing morphologically rich languages[END_REF] only recently provided the opportunity to evaluate this scenario within the framework of dependency syntax. 2 In such a scenario, a system predicts dependency trees with marked groupings of tokens into MWEs. The trees show syntactic dependencies between semantically sound units (made of one or several tokens), and are thus particularly appealing for downstream semantic-oriented applications, as dependency trees are considered to be closer to predicate-argument structures.

In this paper, we investigate various strategies for predicting from a tokenized sentence both MWEs and syntactic dependencies, using the French dataset of the SPMRL 13 Shared Task. We focus on the use of an alternative representation for those MWEs that exhibit regular internal syntax. The idea is to represent these using regular syntactic internal structure, while keeping the semantic information that they are MWEs.

We devote section 2 to related work. In section 3, we describe the French dataset, how MWEs are originally represented in it, and we present and motivate an alternative representation. Section 4 describes the different architectures we test 2 The main focus of the Shared Task was on predicting both morphological and syntactic analysis for morphologically-rich languages. The French dataset is the only one containing MWEs: the French treebank has the particularity to contain a high ratio of tokens belonging to a MWE (12.7% of non numerical tokens).

for predicting both syntax and MWEs. Section 5 presents the external resources targeted to improve MWE recognition. We describe experiments and discuss their results in section 6 and conclude in section 7.

Related work

We gave in introduction references to previous work on predicting MWEs and constituency parsing. To our knowledge, the first works3 on predicting both MWEs and dependency trees are those presented to the SPMRL 2013 Shared Task that provided scores for French (which is the only dataset containing MWEs). [START_REF] Constant | The ligm-alpage architecture for the spmrl 2013 shared task: Multiword expression analysis and dependency parsing[END_REF] proposed to combine pipeline and joint systems in a reparser [START_REF] Sagae | Parser combination by reparsing[END_REF], and ranked first at the Shared Task. Our contribution with respect to that work is the representation of the internal syntactic structure of MWEs, and use of MWE-specific features for the joint system. The system of [START_REF] Björkelund | re)ranking meets morphosyntax: State-of-the-art results from the spmrl 2013 shared task[END_REF] ranked second on French, though with close UAS/LAS scores. It is a less language-specific system that reranks nbest dependency parses from 3 parsers, informed with features from predicted constituency trees. It uses no feature nor treatment specific to MWEs as it focuses on the general aim of the Shared Task, namely coping with prediction of morphological and syntactic analysis.

Concerning related work on the representation of MWE internal structure, we can cite the Prague Dependency Bank, which captures both regular syntax of non-compositional MWEs and their MWE status, in two distinct annotation layers [START_REF] Bejček | Annotation of multiword expressions in the prague dependency treebank[END_REF]. Our representation also resembles that of light-verb constructions (LVC) in the hungarian dependency treebank [START_REF] Vincze | Hungarian dependency treebank[END_REF]: the construction has regular syntax, and a suffix is used on labels to express it is a LVC [START_REF] Vincze | Dependency parsing for identifying hungarian light verb constructions[END_REF].

Data: MWEs in Dependency Trees

The data we use is the SPMRL 13 dataset for French, in dependency format. It contains projective dependency trees that were automatically derived from the latest status of the French Treebank [START_REF] Abeillé | Enriching a french treebank[END_REF], which consists of constituency trees for sentences from the newspaper Le Monde, manually annotated with phrase structures, morphological information, and grammatical functional tags for dependents of verbs. The Shared Task used an enhanced version of the constituency-to-dependency conversion of [START_REF] Candito | Statistical french dependency parsing : Treebank conversion and first results[END_REF], with different handling of MWEs. The dataset consists of 18535 sentences, split into 14759, 1235 and 2541 sentences for training, development, and final evaluation respectively.

We describe below the flat representation of MWEs in this dataset, and the modified representation for regular MWEs that we propose.

MWEs in Gold Data: Flat representation

In gold data, the MWEs appear in an expanded flat format: each MWE bears a part-of-speech and consists of a sequence of tokens (hereafter the "components" of the MWE), each having their proper POS, lemma and morphological features.

In the dependency trees, there is no "node" for a MWE as a whole, but one node per MWE component (more generally one node per token). The first component of a MWE is taken as the head of the MWE. All subsequent components of the MWE depend on the first one, with the special label dep_cpd (hence the name flat represen-tation). Furthermore, the first MWE component bears a feature mwehead equal to the POS of the MWE. An example is shown in Figure 1. The MWE en vain (pointlessly) is an adverb, containing a preposition and an adjective. The latter depends on former, which bears mwehead=ADV+.

The algorithm to recover MWEs is: any node having dependents with the dep_cpd label forms a MWE with such dependents.

Alternative representation for regular MWEs

In the alternative representation we propose, irregular MWEs are unchanged and appear as flat MWEs (e.g. en vain in Figure 1 has pattern prepo-sition+adjective, which is not considered regular for an adverb, and is thus unchanged). Regular MWEs appear with 'structured' syntax: we modify the tree structure to recover the regular syntactic dependencies. For instance, in the bottom tree of the figure, biens is attached to the preposition, and the adjective sociaux is attached to biens, with regular labels. Structured MWEs cannot be spotted using the tree topology and labels only. Features are added for that purpose: the syntactic head of the structured MWE bears a regmwehead for the POS of the MWE (abus in Figure 1), and the other components of the MWE bear a regcomponent feature (the orange tokens in Figure 1). 4 With this representation, the algorithm to recover regular MWEs is: any node bearing regmwehead forms a MWE with the set of direct or indirect dependents bearing a regcomponent feature.

Motivations

Our first motivation is to increase the quantity of information conveyed by the dependency trees, by distinguishing syntactic regularity and semantic regularity. Syntactically regular MWEs (hereafter regular MWEs) show various degrees of semantic non-compositionality. For instance, in the French Treebank, population active (lit. active population, meaning 'working population') is a partially compositional MWE. Furthermore, some sequences are both syntactically and semantically regular, but encoded as MWE due to frozen lexical selection. This is the case for déficit budgétaire (lit. budgetary deficit, meaning 'budget deficit'), because it is not possible to use déficit du budget (budget deficit). Our alternative representation distinguishes between syntactic internal regularity and semantic regularity. This renders the syntactic description more uniform and it provides an internal structure for regular MWEs, which is meaningful if the MWE is fully or partially compositional. For instance, it is meaningful to have the adjective sociaux attach to biens instead of on the first component abus. Moreover, such a distinction opens the way to a non-binary classification of MWE status: the various criteria leading to classify a sequence as MWE could be annotated separately and using nominal or scaled categories for each criteria. For instance, déficit budgétaire could be marked as fully compositional, but with frozen lexical selection. Further, annotation is often incoherent for the MWEs with both regular syntax and a certain amount of semantic compositionality, the same token sequence (with same meaning) being sometimes annotated as MWE and sometimes not.

More generally, keeping a regular representation would allow to better deal with the interaction between idiomatic status and regular syntax, such as the insertion of modifiers on MWE subparts (e.g. make a quick decision).

Finally, using regular syntax for MWEs provides a more uniform training set. For instance for a sequence N1 preposition N2, though some external attachments might vary depending on whether the sequence forms a MWE or not, some may not, and the internal dependency structure (N1 → (preposition → N2)) is quite regular. One objective of the current work is to investigate whether this increased uniformity eases parsing or whether it is mitigated by the additional difficulty of finding the internal structure of a MWE.

Total

Nb of regular MWEs nb of (% of nouns, adverbs, MWEs prepositions, verbs) train 23658 12569 (64.7, 19.2, 14.6, 1.5) dev 2120 1194 (66.7, 17.7, 14.7, 0.8) test 4049 2051 (64.5, 19.9, 13.6, 2.0)

Implementation

We developed an ad hoc program for structuring the regular MWEs in gold data. MWEs are first classified as regular or irregular, using regular expressions over the sequence of parts-ofspeech within the MWE. To define the regular expressions, we grouped gold MWEs according to the pair [global POS of the MWE + sequence of POS of the MWE components], and designed regular expressions to match the most frequent patterns that looked regular according to our linguistic knowledge. The internal structure for the matching MWEs was built deterministically, using heuristics favoring local attachments. 5 Table 1 shows the proportions of MWEs classified as regular, and thus further structured. About half MWEs are structured, and about two thirds of structured MWEs are nouns.

For predicted parses with structured MWEs, we use an inverse transformation of structured MWEs into flat MWEs, for evaluation against the gold data. When a predicted structured MWE is flattened, all the dependents of any token of the MWE that are not themselves belonging to the MWE are attached to the head component of the MWE.

Integration of MWE features into labels

In some experiments, we make use of alternative representations, which we refer later as "labeled representation", in which the MWE features are incorporated in the dependency labels, so that MWE composition and/or the POS of the MWE be totally contained in the tree topology and labels, and thus predictable via dependency parsing. Fig- ure shows the labeled representation for the sentence of Figure 1.

For flat MWEs, the only missing information is the MWE part-of-speech: we concatenate it to the dep_cpd labels. For instance, the arc from en to vain is relabeled dep_cpd_ADV. For structured MWEs, in order to get full MWE account within the tree structure and labels, we need to incorporate both the MWE POS, and to mark it as 5 The six regular expressions that we obtained cover nominal, prepositional, adverbial and verbal compounds. We manually evaluated both the regular versus irregular classification and the structuring of regular MWEs on the first 200 MWEs of the development set. 113 of these were classified as regular, and we judged that all of them were actually regular, and were correctly structured. Among the 87 classified as irregular, 7 should have been tagged as regular and structured. For 4 of them, the classification error is due to errors on the (gold) POS of the MWE components. belonging to a MWE. The suffixed label has the form FCT_r_POS. For instance, in bottom tree of Figure 1, arcs pointing to the non-head components (de, biens, sociaux) are suffixed with _r to mark them as belonging to a structured MWE, and with _N since the MWE is a noun.

In both cases, this label suffixing is translated back into features for evaluation against gold data.

Architectures for MWE Analysis and Parsing

The architectures we investigated vary depending on whether the MWE status of sequences of tokens is predicted via dependency parsing or via an external tool (described in section 5), and this dichotomy applies both to structured MWEs and flat MWEs. More precisely, we consider the following alternative for irregular MWEs:

• IRREG-MERGED: gold irregular MWEs are merged for training; for parsing, irregular MWEs are predicted externally, merged into one token at parsing time, and re-expanded into several tokens for evaluation;

• IRREG-BY-PARSER: the MWE status, flat topology and POS are all predicted via dependency parsing, using representations for training and parsing, with all information for irregular MWEs encoded in topology and labels (as for in vain in Figure 2).

For regular MWEs, their internal structure is always predicted by the parser. For instance the unlabeled dependencies for abus de biens sociaux are the same, independently of predicting whether it forms a MWE or not. But we use two kinds of predictions for their MWE status and POS:

• REG-POST-ANNOTATION: the regular MWEs are encoded/predicted as shown for abus de biens sociaux in bottom tree of Figure 1, and their MWE status and POS is predicted after parsing, by an external tool.

• REG-BY-PARSER: all regular MWE information (topology, status, POS) is predicted via dependency parsing, using representations with all information for regular MWEs encoded in topology and labels (Figure 2). We obtain four architectures, schematized in table 2. We describe more precisely two of them, the other two being easily inferable:

JOINT-REG architecture:

• training set: irregular MWEs merged into one token, regular MWEs are structured, and integration of regular MWE information into the labels (FCT_r_POS). • parsing: (i) MWE analysis with classification of MWEs into regular or irregular, (ii) merge of predicted irregular MWEs, (iii) tagging and morphological prediction, (iv) parsing

JOINT-IRREG architecture:

• training set: flat representation of irregular MWEs, with label suffixing (dep_cpd_ POS), structured representation of regular MWEs without label suffixing. • parsing: (i) MWE analysis and classification into regular or irregular, used for MWEspecific features, (ii) tagging and morphological prediction, (iii) parsing, We compare these four architectures between them and also with two simpler architectures used by [START_REF] Constant | The ligm-alpage architecture for the spmrl 2013 shared task: Multiword expression analysis and dependency parsing[END_REF] within the SPMRL 13 Shared Task, in which regular and irregular MWEs are not distinguished:

Uniform joint architecture: The joint systems perform syntactic parsing and MWE analysis via a single dependency parser, using representations as in 3.3.

Uniform pipeline architecture:

• training set: MWEs merged into one token • parsing: (i) MWE analysis, (ii) merge of predicted MWEs, (iii) tagging and morphological prediction, (iv) parsing For each architecture, we apply the appropriate normalization procedures on the predicted parses, in order to evaluate against (i) the pseudo-gold data in structured representation, and (ii) the gold data in flat representation.

Use of external MWE resources

In order to better deal with MWE prediction, we use external MWE resources, namely MWE lexicons and an MWE analyzer. Both resources help to predict MWE-specific features (section 5.3) to guide the MWE-aware dependency parser. Moreover, in some of the architectures, the external MWE analyzer is used either to pre-group irregular MWEs (for the architectures using IRREG-MERGED), or to post-annotate regular MWEs.

MWE lexicons

MWE lexicons are exploited as sources of features for both the dependency parser and the external MWE analyzer. In particular, two largecoverage general-language lexicons are used: the Lefff6 lexicon [START_REF] Sagot | The lefff, a freely available, accurate and large-coverage lexicon for french[END_REF], which contains approximately half a million inflected word forms, among which approx. 25, 000 are MWEs; and the DELA7 [START_REF] Courtois | Un système de dictionnaires électroniques pour les mots simples du franc ¸ais[END_REF][START_REF] Courtois | Dictionnaire électronique DELAC : les mots composés binaires[END_REF] lexicon, which contains approx. one million inflected forms, among which about 110, 000 are MWEs. These resources are completed with specific lexicons freely available in the platform Unitex8 : the toponym dictionary Prolex [START_REF] Piton | The prolex data base : Toponyms and gentiles for nlp[END_REF] and a dictionary of first names. Note that the lexicons do not include any information on the irregular or the regular status of the MWEs. In order to compare the MWEs present in the lexicons and those encoded in the French treebank, we applied the following procedure (hereafter called lexicon lookup): in a given sentence, the maximum number of non overlapping MWEs according to the lexicons are systematically marked as such. We obtain about 70% recall and 50% precision with respect to MWE spanning.

MWE Analyzer

The MWE analyzer is a CRF-based sequential labeler, which, given a tokenized text, jointly performs MWE segmentation and POS tagging (of simple tokens and of MWEs), both tasks mutually helping each other9 . The MWE analyzer integrates, among others, features computed from the external lexicons described in section 5.1, which greatly improve POS tagging [START_REF] Denis | Coupling an annotated corpus and a morphosyntactic lexicon for state-of-the-art POS tagging with less human effort[END_REF] and MWE segmentation [START_REF] Constant | Evaluating the impact of external lexical resources into a crf-based multiword segmenter and part-of-speech tagger[END_REF]. The MWE analyzer also jointly classifies its predicted MWEs as regular or irregular (the distinction being learnt on gold training set, with structured MWEs cf. section 3.2).

MWE-specific features

We introduce information from the external MWE resources in different ways: Flat MWE features: MWE information can be integrated as features to be used by the dependency parser. We tested to incorporate the MWE-specific features as defined in the gold flat representation (section 3.1): the mwehead=POS feature for the MWE head token, POS being the part-of-speech of the MWE; the component=y feature for the non-first MWE component. Switch: instead or on top of using the mwehead feature, we use the POS of the MWE instead of the POS of the first component of a flat MWE. For instance in Figure 1, the token en gets pos=ADV instead of pos=P. The intuition behind this feature is that for an irregular MWE, the POS of the linearly first component, which serves as head, is not always representative of the external distribution of the MWE. For regular MWEs, the usefulness of such a trick is less obvious. The first component of a regular MWE is not necessarily its head (for instance for a nominal MWE with internal pattern adjective+noun), so the switch trick could be detrimental in such cases.10 6 Experiments 6.1 Settings and evaluation metrics MWE Analysis and Tagging: For the MWE analyzer, we used the tool lgtagger 11 (version 1.1) with its default set of feature templates, and a 10-fold jackknifing on the training corpus.

Parser: We used the second-order graph-based parser available in Mate-tools 12 [START_REF] Bohnet | Top accuracy and fast dependency parsing is not a contradiction[END_REF]. We used the Anna3.3 version, in projective mode, with default feature sets and parameters proposed in the documentation, augmented or not with MWE-specific features, depending on the experiments.

Morphological prediction: Predicted lemmas, POS and morphology features are computed with Morfette version 0.3.5 [START_REF] Chrupała | Learning morphology with morfette[END_REF][START_REF] Seddah | Lemmatization and statistical lexicalized parsing of morphologically-rich languages[END_REF] 13 , using 10 iterations for the tagging perceptron, 3 iterations for the lemmatization perceptron, default beam size for the decoding of the joint prediction, and the Lefff [START_REF] Sagot | The lefff, a freely available, accurate and large-coverage lexicon for french[END_REF] as external lexicon used for out-of-vocabulary words. We performed a 10-fold jackknifing on the training corpus.

Evaluation metrics: we evaluate our parsing systems by using the standard metrics for dependency parsing: Labeled Attachment Score (LAS) and Unlabeled Attachment Score (UAS), computed using all tokens including punctuation. To evaluate statistical significance of parsing performance differences, we use eval07.pl 14 with -b option, and then Dan Bikel's comparator. 15 For MWEs, we use the Fmeasure for recognition of untagged MWEs (hereafter FUM) and for recognition of tagged MWEs (hereafter FTM).

MWE-specific feature prediction

In all our experiments, for the switch trick (section 5.3), the POS of MWE is always predicted using the MWE analyzer. For the flat MWE features, we experimented both with features predicted by the MWE analyzer, and with features predicted using the external lexicons mentioned in section 5.1 (using the lexicon lookup procedure). Both kinds of Table 3: Baseline and best results for the four MWE+parsing architectures on the dev set (see text for statistical significance evaluation). The UAS for the structured representation is the same as the one for the labeled representation, and is not repeated.

prediction lead to fairly comparable results, so in all the following, the MWE features, when used, are predicted using the external lexicons.

Tuning features for each architecture

We ran experiments for all value combinations of the following parameters: (i) the architecture, (ii) whether MWE features are used, whether the switch trick is applied or not (iii) for irregular MWEs and (iv) for regular MWEs. We performed evaluation of the predicted parses using the three representations described in section 3, namely flat, structured and labeled representations. In the last two cases, the evaluation is performed against an instance of the gold data automatically transformed to match the representation type. Moreover, for the "labeled representation" evaluation, though the MWE information in the predicted parses is obtained in various ways, depending on the architecture, we always map all this information in the dependency labels, to obtain predicted parses matching the "labeled representation". While the evaluation in flat representation is the only one comparable to other works on this dataset, the other two evaluations provide useful information. In the "labeled representation" evaluation, the UAS provides a measure of syntactic attachments for sequences of words, independently of the (regular) MWE status of subsequences. For the sequence abus de biens sociaux, suppose that the correct internal structure is predicted, but not the MWE status. The UAS for labeled representation will be maximal, whereas for the flat representation, the last two tokens will count as incorrect for UAS. For LAS, in both cases the three last tokens will count as incorrect if the wrong MWE status is predicted. So to sum up on the "labeled evaluation", we obtain a LAS evaluation for the whole task of parsing plus MWE recognition, but an UAS evaluation that penalizes less errors on MWE status, while keeping a representation that is richer: predicted parses contain not only the syntactic dependencies and MWE information, but also a classification of MWEs into regular and irregular, and the internal syntactic structure of regular MWEs.

The evaluation on "structured representation" can be interpreted as an evaluation of the parsing task plus the recognition of irregular MWEs only: both LAS and UAS are measured independently of errors on regular MWE status (note the UAS is exactly the same than in the "labeled" case).

For each architecture, Table 3 shows the results for two systems: first the baseline system without any MWE features nor switches and immediately below the best settings for the architecture. The JOINT baseline corresponds to a "pure" joint system without external MWE resources (hence the minus sign for the first three columns). For each architecture except the PIPELINE one, differences between the baseline and the best setting are statistically significant (p < 0.01). Differences between best PIPELINE and best JOINT-REG are not. Best JOINT has statistically significant difference (p < 0.01) over both best JOINT-REG and best PIPELINE. The situation for best JOINT-IRREG with respect to the other three is borderline (with various p-values depending on the metrics).

Concerning the tuning of parameters, it appears that the best setting is to use MWE-features, and switch for both regular and irregular MWEs, except for the pipeline architecture for which results without MWE features are slightly better. So overall, informing the parser with independently pre- Table 4: Final results on test set for baseline and the best system for each architecture.

dicted POS of MWE has positive impact. The best architectures are JOINT and JOINT-IRREG, with the former slightly better than the latter for parsing metrics, though only some of the differences are significant between the two. It can be noted though, that JOINT-IRREG performs overall better on MWEs (last two columns of table 3), whereas JOINT performs better on irregular MWEs: the latter seems to be beneficial for parsing, but is less efficient to correctly spot the regular MWEs.

Concerning the three distinct representations, evaluating on structured representation (hence without looking at regular MWE status) leads to a rough 2 point performance increase for the LAS and a one point increase for the UAS, with respect to the evaluation against flat representation. This quantifies the additional difficulty of deciding for a regular sequence of tokens whether it forms a MWE or not. The evaluation on the labeled representation provides an evaluation of the full task (parsing, regular/irregular MWE recognition and regular MWEs structuring), with a UAS that is less impacted by errors on regular MWE status, while LAS reflects the full difficulty of the task. 16

Results on test set and comparison

We provide the final results on the test set in table 4. We compare the baseline JOINT system with the best system for all four reg/irreg architectures (cf. section 6.3). We observe the same general trend as in the development corpus, but with tinier differences. JOINT and JOINT-IRREG significantly outperform the baseline and the PIPELINE, on labeled representation and flat representation. We can see that there is no significant difference between JOINT and JOINT- 16 The slight differences in LAS between the labeled and the flat representations are due to side effects of errors on MWE status: some wrong reattachments performed to obtain flat representation decrease the UAS, but also in some cases the LAS. IRREG and between JOINT-REG and JOINT-IRREG. JOINT slightly outperforms JOINT-REG (p < 0.05). On the structured representation, the two best systems (JOINT and JOINT-IRREG) significantly outperform the other systems (p < 0.01 for all; p < 0.05 for JOINT-REG). Moreover, we provide in table 5 a comparison of our best architecture with reg/irregular MWE distinction with other architectures that do not make this distinction, namely the two best comparable systems designed for the SPMRL Shared Task [START_REF] Seddah | Overview of the spmrl 2013 shared task: A cross-framework evaluation of parsing morphologically rich languages[END_REF]: the pipeline simple parser based on Mate-tools of Constant et al. (2013) (Const13) and the Mate-tools system (without reranker) of Björkelund et al. (2013) (Bjork13). We also reimplemented and improved the uniform joint architecture of [START_REF] Constant | The ligm-alpage architecture for the spmrl 2013 shared task: Multiword expression analysis and dependency parsing[END_REF], by adding MWE features and switch. Results can only be compared on the flat representation, because the other systems output poorer linguistic information. We computed statistical significance of differences between our systems and Const13. On dev, the best system is the enhanced uniform joint, but differences are not significant between that and the best reg/irreg joint (1st row) and the Const13 pipeline. But on the test corpus (which is twice bigger), the best system is Const13 pipeline, with statistically significant differences over our joint systems. So the first observation is that our architectures that distinguish between reg/irreg MWEs do not outperform uniform architectures. But we note that the differences are slight, and the output we obtain is enhanced with regular MWE internal structure. It can thus be noted that the increased syntactic uniformity obtained by our MWE representation is mitigated so far by the additional complexity of the task. The second observation is that currently the best system on this dataset is a pipeline system, as results on test set show (and somehow contrary to results on dev set). The joint systems that integrate MWE information in the labels seem to suffer from increased data sparseness.

Evaluating the double task with respect to simpler tasks

In this section, we propose to better evaluate the difficulty of combining the tasks of MWE analysis and dependency parsing by comparing our systems with systems performing simpler tasks: i.e. MWE recognition without parsing, and parsing with no or limited MWE recognition, simulated by using gold MWEs. We also provide a finer evaluation of the MWE recognition task, in particular with respect to their regular/irregular status. We first compare our best system with a parser where all MWEs have been perfectly pre-grouped, in order to quantify the difficulty that MWEs add to the parsing task. We also compare the performance on MWEs of our best system with that achieved by the CRF-based analyzer described in section 5.2. Next, we compare the best JOINT-REG system with the one based on the same architecture but where the irregular MWEs are perfectly pre-identified, in order to quantify the difficulty added by the irregular MWEs. Results are given in table 6. Without any surprise, the task is much easier without considering MWE recognition. We can see that without considering MWE analysis the parsing accuracy is about 2.5 points better in terms of LAS. In the JOINT-REG architecture, assuming gold irregular MWE identification, increases LAS by 1.3 point. In terms of MWE recognition, as compared with the CRFbased analyzer, our best system is around 2 points below. But the situation is quite different when breaking the evaluation by MWE type. Our system is 1 point better than the CRF-based analyzer for irregular MWEs. This shows that considering a larger syntactic context helps recognition of irregular MWEs. The "weak point" of our system is therefore the identification of regular MWEs.

Conclusion

We experimented strategies to predict both MWE analysis and dependency structure, and tested them on the dependency version of French Treebank [START_REF] Abeillé | Enriching a french treebank[END_REF], as instantiated in the SPMRL Shared Task [START_REF] Seddah | Overview of the spmrl 2013 shared task: A cross-framework evaluation of parsing morphologically rich languages[END_REF]. Our work focused on using an alternative representation of syntactically regular MWEs, which captures their syntactic internal structure. We obtain a system with comparable performance to that of previous works on this dataset, but which predicts both syntactic dependencies and the internal structure of MWEs. This can be useful for capturing the various degrees of semantic compositionality of MWEs. The main weakness of our system comes from the identification of regular MWEs, a property which is highly lexical. Our current use of external lexicons does not seem to suffice, and the use of data-driven external information to better cope with this identification can be envisaged.

Figure 1 :

 1 Figure 1: French dependency tree for L'abus de biens sociaux fut dénoncé en vain (literally the misuse of assets social was denounced in vain, meaning The misuse of corporate assets was denounced in vain), containing two MWEs (in red). Top: original flat representation. Bottom: Tree after regular MWEs structuring.

Figure 2 :

 2 Figure 2: Integration of all MWE information into labels for the example of Figure 1.

Table 1 :

 1

Total number of MWEs and number of regular MWEs in training, development and test set (and broken down by POS of MWE).

Table 2 :

 2 The four architectures, depending on how regular and irregular MWEs are predicted.

	Name	prediction of	prediction of
		reg MWEs	irreg MWEs
	JOINT	irreg-by-parser reg-by-parser
	JOINT-REG	irreg-merged	reg-by-parser
	JOINT-IRREG irreg-by-parser reg-post-annot
	PIPELINE	irreg-merged	reg-post-annot

Table 5 :

 5 Comparison on dev set of our best archi-

	tecture with reg/irregular MWE distinction (first
	row), with the single-parser architectures of (Con-
	stant et al., 2013) (Const13) and (Björkelund et
	al., 2013) (Bjork13). Uniform joint is our reimple-
	mentation of Const13 joint, enhanced with mwe-
	features and switch.

Table 6 :

 6 Comparison with simpler tasks on the flat representation of the development set.

		Tasks		LAS	UAS	ALL MWE	REG MWE	IRREG MWE
	System	Parsing MWE			FUM FTM	FUM FTM	FUM FTM
	Our best system (best JOINT)	+	all	85.15 88.78	77.6	74.5	70.8	67.8	85.4	82.6
	Uniform pipeline/gold MWEs	+	-	88.73 90.60	-	-	-	-	-	-
	CRF-based MWE analyzer	-	all	-	-	78.8	76.3	73.5	71.9	84.2	80.8
	JOINT-REG	+	all	84.58 88.34	76.3	73.2	69.3	66.5	84.1	80.7
	JOINT-REG/gold irreg. MWE	+	reg.	85.86 89.19	82.9	78.8	70.0	67.2	-	-

Multiword expressions can be roughly defined as continuous or discontinuous sets of tokens, which either do not exhibit full freedom in lexical selection or whose meaning is not fully compositional. We focus in this paper on contiguous multiword expressions, also known as "words with spaces".

Concerning non contiguous MWEs, we can cite the work of[START_REF] Vincze | Dependency parsing for identifying hungarian light verb constructions[END_REF], who experimented joint dependency parsing and light verb construction identification.

The syntactic head of a structured MWE may not be the first token, whereas the head token of a flat MWE is always the first one.

We use the version available in the POS tagger MElt (Denis and[START_REF] Denis | Coupling an annotated corpus and a morphosyntactic lexicon for state-of-the-art POS tagging with less human effort[END_REF].

 7 We use the version in the platform Unitex (http://igm.univ-mlv.fr/˜unitex). We had to convert the DELA POS tagset to that of the French

Treebank. 8 http://igm.univ-mlv.fr/˜unitex

Note that in our experiments, we use this analyzer for MWE analysis only, and discard the POS tagging prediction. Tagging is performed along with lemmatization with the Morfette tool (section 6.1).

 10 We also experimented to use POS of MWE plus suffixes to force disjoint tagsets for single words, irregular MWEs and


Abdul Aleem
email: aaleem@dal.ca

Amine Lahiani
email: amine.lahiani@univ-orléans.fr

A Threshold Vector Autoregression Model of Exchange Rate Pass-through in Mexico

Keywords: Exchange rate pass-through, prices, threshold vector autoregression. JEL classification: E31, F31, F47

Considering nonlinearities in the exchange rate pass-through to domestic prices, this paper estimates exchange rate pass-through in Mexico. We examine responses of domestic prices to a positive one unit exchange rate shock by estimating a Threshold Vector Autoregression (TVAR) model. A monthly rate of inflation of 0.79% acts as a threshold. The exchange rate pass-through to domestic prices is statistically significant above the threshold level of the inflation rate and statistically insignificant below it.

Introduction

The credibility of monetary policy to stabilize inflation in the economy determines the degree of exchange rate pass-through. A way to measure monetary policy's credibility is the rate of inflation. Economic agents change inflationary expectations if the rate of inflation is higher than a threshold level. Firms perceive any increase in the cost of production beyond a certain threshold to be more persistent in the presence of high inflation rates. Therefore, in a high inflationary environment, they choose a higher frequency of price adjustment for a given menu cost. Firms transfer the effects coming from shocks on costs in order to maintain their mark up.

Other things held constant, the exchange rate pass-through to domestic prices is higher during high inflationary episodes than low inflationary episodes. Using micro data for Argentina, [START_REF] Alvarez | From hyperinflation to stable prices: Argentina's evidence on menu cost models[END_REF] found that the frequency of price adjustment is uncorrelated with current inflation for inflation rates below 10% and that this frequency has an elasticity close to 2/3 for higher inflation rates.

It is worth noting that the exchange rate pass-through literature has seen the use of three econometric techniques i.e., the single equation regression, stationary Vector Autoregression (VAR) and cointegration. In the univariate process, the domestic prices are assumed to be exogenously determined by the exchange rate shocks. The VAR methodology has the advantage of measuring simultaneous relationships between exchange rate and other variables. This methodology has been widely used to examine the exchange rate pass-through. 1 Given the presence of nonlinearities in the exchange rate pass-through, linear modelling techniques may 1 [START_REF] Mccarthy | Pass-through of exchange rates and import prices to domestic inflation in some industrialised economies[END_REF], [START_REF] Choudhri | Explaining the exchange rate pass-through in different prices[END_REF], [START_REF] Takatoshi | Exchange rate pass-through and domestic inflation: A comparison between East Asian and Latin American countries[END_REF], [START_REF] Zorzi | Exchange rate pass-through in emerging markets[END_REF]. [START_REF] Bhundia | An empirical investigation of exchange rate pass-through in South Africa[END_REF], [START_REF] Leigh | Exchange rate pass-through in Turkey[END_REF], [START_REF] Billmeier | Exchange rate pass-through and monetary policy in Croatia[END_REF], [START_REF] Korhonen | A note on exchange rate pass-through in CIS countries[END_REF], and [START_REF] Sek | Pass-through of exchange rate into domestic prices: The case of four Asian countries[END_REF].

give imprecise exchange rate pass-through coefficients. A more realistic approach would be to recognize that the inflationary environment also affects the responses of economic agents to an exchange rate shock. It follows that domestic prices may not respond to an exchange rate shock due to the low and stable inflation. But they respond to the same shocks if the inflation is above its threshold level. Therefore, in this paper we use a multivariate process, the Threshold Vector Autoregression (TVAR) model, to study the exchange rate pass-through. The TVAR model is in line with the fact that movements in the exchange rate could alter the responses of economic agents to those changes and consequently these responses may correspond to different regimes depending on the rate of inflation. During 1990s, a series of monetary policy reforms and subsequent transition to new policy regimes in post-crisis Latin American emerging economies increased the importance of nonlinear models. We estimate a TVAR model consisting of a set of variables that determine the exchange rate pass-through to domestic prices in Mexico. In December 1994, Mexico suffered from a currency crisis and it adopted a floating exchange rate regime. In 1996, the Central Bank of Mexico started a gradual transition towards an inflation targeting policy to control inflationary expectations, and it switched completely to inflation targeting policy in January 1999. interval of +/-1%. During this time period, significant changes in the rate of inflation in terms of its volatility and its mean level make Mexico particularly suitable to examine the exchange rate pass-through using a TVAR model.

We estimate the nonlinear responses of domestic prices to an exchange rate shock by taking into account the threshold levels of the rate of inflation. The contributions of this paper are threefold. First we estimate a nonlinear multivariate model by using the threshold level of inflation. The threshold level of inflation is determined endogenously. To our knowledge there is no work done in the context of exchange rate pass-through using endogenously determined threshold level of inflation. Second, we allow for a simultaneous regime switching in our TVAR model. Third, we allow for the presence of more than two regimes and test for the presence of three regimes.

We review the previous literature to find possible causes of nonlinear exchange rate passthrough in the next section. In section 3, we present the TVAR model to estimate the nonlinear exchange rate pass-through to domestic prices. In section 4, we present the estimation methodology. In section 5, we present the empirical findings. Finally, we set out our conclusions in section 6. Data definitions and sources are summarized in the appendix.

Nonlinearities in exchange rate pass-through

Previous empirical studies show a positive relationship between the exchange rate passthrough and the inflationary environment. [START_REF] Taylor | Low inflation, pass-through and the pricing power of firms[END_REF] found that the responsiveness of prices to fluctuations in the exchange rate depends positively on the level of inflation. He argued that low exchange rate pass-through in low inflation countries is a result of the low inflation environment. [START_REF] Choudhri | Explaining the exchange rate pass-through in different prices[END_REF] found that countries having high rates of inflation are often characterised by high exchange rate pass-through coefficients. [START_REF] Baqueiro | Fear of floating or fear of inflation? The role of the exchange rate pass-through[END_REF] examined the exchange rate pass-through in different countries by splitting the sample period of each country into high and low inflation regimes. They found that the exchange rate pass-through is higher in high inflationary episodes than in low inflationary episodes. These findings suggest that the relationship between the degree of exchange rate pass-through to domestic prices and inflationary environment is nonlinear. The exchange rate depreciation increased from -15.3% in August 1998 to -20.2% in December 1998 and the inflation increased from 14.5% to 17.1% during the same period. However, the inflation rose from 5.5% in October 2008 to 5.9% in March 2009 when the exchange rate depreciation increased from -13.8% to -25.3%. The relationship between inflation and exchange rate depreciation is positive in two episodes, but the change in inflation is negligible in the latter episode of exchange rate depreciation. Previous empirical studies explain the nonlinear relationship between exchange rate and inflation in several ways. [START_REF] Al-Abri | Re-examining the exchange rate pass-through into import prices using non-linear estimation techniques: Threshold cointegration[END_REF] argued for a significant threshold cointegration relationship between the nominal effective exchange rate and import prices. They showed that the degree of exchange rate pass-through improves from the 50% average documented in the literature once a threshold is detected. [START_REF] Pollard | Size matters: asymmetric exchange rate pass-through at the industry level[END_REF] found that most firms respond asymmetrically to large and small changes in the exchange rate with pass-through positively related to the size of the change. [START_REF] Josip | Threshold Autoregressive model of exchange rate pass-through effect: The case of Croatia[END_REF] employed the Threshold Autoregressive model to estimate the exchange rate pass-through in Croatia, and showed that a certain level of devaluation acts as a threshold between the two regimes. They found that below the threshold, there is no exchange rate passthrough to prices and above the threshold there is a complete pass-through to prices. But, the historical data on exchange rate depreciation and inflation in Mexico shows that the inflation responds significantly to exchange rate depreciation if the rate of inflation only if the rate of inflation is above certain level. As long as, the rate of inflation is below that level, the response of inflation to exchange rate depreciation remains insignificant. It necessitates the estimation of the threshold levels of inflation in the first step, and the analysis of the responses of domestic prices to exchange rate shocks in different inflationary regimes in the second step.

The Threshold Vector Autoregression (TVAR) model

We estimate the following three regime TVAR model:

     > + + ≤ < + + ≤ + + = 2 3 3 3 2 1 2 2 2 1 1 1 1 ) ( ) ( ) ( γ ε α γ γ ε α γ ε α t t t t t t t t t t q if y L A q if y L A q if y L A y (1)
where the vector of variables (y t ) consists of the rate of inflation (π), the output gap, the nominal effective exchange rate (NEER) and an indicator of the stance of monetary policy (i). The output gap captures the effects of the real sector on exchange rate pass-through. We include an indicator of the stance of monetary policy in the vector of variables to take into account the effects of the monetary policy on exchange rate pass-through.

[ ] i NEER Outputgap y t π = t q is the threshold variable, and 1 γ and 2 γ are the threshold values. We treat the rate of inflation as the threshold variable in our model. ' i α , i=1,...,3, is a 1 3× is vector of constants while the lagpolynomial

p ip i i i L A L A L A L A + + + = ... ) ( 2 2 1 with a p 4 4 × matrix p j A ij ,..., 2 , 1 , =
; L is the lag operator.

A more compact form of the three regime ) ( p TVAR model is as follows:

( ) ( ) ( ) ( ) ( ) (
)

2 3 3 1 31 3 2 1 2 2 1 21 2 1 1 1 1 11 1 ) ( ... ) ( ) ( ... ) ( ) ( ... ) ( γ ε α γ γ ε α γ ε α > + + + + + ≤ < + + + + + ≤ + + + + = - - - - - - t t p t p t t t p t p t t t p t p t t q I y L A y L A q I y L A y L A q I y L A y L A y
where ( ) .

I

takes the value 1 if its argument is satisfied and 0 otherwise.

It is worth noting that when 2 1 γ γ = , the three regime TVAR model reduces to a two regime TVAR model.

Defining

) , , ,

1 3 2 1 3 2 1 γ γ α α α θ A A A = , , , , ( 2
as the vector of parameters of interest, we use the ordinary least square (OLS) method to minimise the following function:

( ) ( ) ( ) ( ) ( ) ( )                         > + + + + - ≤ < + + + + - ≤ + + + + - = ∑ = - - - - - - T t t t p t p t t t p t p t t t p t p t t q I y L A y L A q I y L A y L A q I y L A y L A y 1 2 3 3 1 31 3 2 1 2 2 1 21 2 1 1 1 1 11 1 ) ( ... ) ( ) ( ... ) ( ) ( ... ) ( min arg ˆγ ε α γ γ ε α γ ε α θ θ

Estimation methodology

Data description

We use monthly seasonally adjusted data from January 1994 to November 2009. The exchange rate is the nominal effective exchange rate computed by the Bank for International Settlements (BIS) 3 . We define a shock to the exchange rate as a positive variation of the exchange rate. Thus, a positive variation of the exchange rate represents an appreciation of the domestic currency. The rate of inflation is measured by the Consumer Price Index (CPI). It is a widely used indicator by both financial analysts and policy makers to examine developing price trends and is generally considered as an indicator of the inflationary process in the economy. 4 The exchange rate affects import prices which in turn affect production costs and consequently the CPI. The output gap is created by taking the deviations of the logarithm of real GDP from the trend estimates 5 . The overnight interbank rate has been shown to be a good indicator of the monetary policy stance. 6 The Bank of Mexico has been using the target for overnight interbank rate as policy instrument since January 2008.

3 We use the broad index of the nominal effective exchange rate. It is calculated as a geometric weighted average of bilateral exchange rates comprising of a basket of 42 countries. The weights are based on trade in 2005-07. 4 Brière and Signori (2012); [START_REF] Granville | Does inflation or currency depreciation drive monetary policy in Russia[END_REF]. 5 To calculate the trend estimates, we decompose the real GDP ( t y ) into two components; the trend component ( . We extract the trend component by minimizing

( ) ( ) ( ) [ ] ∑ ∑ = - - - = - - - + - T t t t t t T t t t t t g g g g g y g Min 1 2 2 1 1 1 2 λ .
10 Before testing for thresholds in the Vector Autoregression representation of the data7 , we select the optimal lag order by estimating the linear VAR model. The optimal lag order is determined by using the Akaike Information Criterion (AIC) which is the most widely used information criterion in the empirical literature of model selection. The AIC selects 3 as the optimal lag for the TVAR model.

The nonlinearity test

We run a nonlinearity test for a threshold VAR model against a linear VAR model by using the rate of inflation as threshold variable. The rate of inflation below the threshold level constitutes a low inflation regime, and above the threshold level it constitutes a high inflation regime. The threshold values are the turning points at which either a significant exchange rate pass-through takes the place of an insignificant exchange rate pass-through, or an insignificant exchange rate pass-through takes the place of a significant exchange rate pass-through. To test the null hypothesis of linearity (m = 1 regime) against the alternative of nonlinearity (m = 2, 3 regimes), we use a multivariate extension of the linearity test by [START_REF] Hansen | Testing for Linearity[END_REF], and [START_REF] Lo | Threshold cointegration and nonlinear adjustment to the law of one price[END_REF]. The test makes use of the covariance matrix of each model (models 0 and 1), i.e., model 0 is the simple VAR model (under the null of linearity) and model 1 is the TVAR model with one and two regimes, respectively. The LR test statistic is written as follows: 1. Results are obtained by using the middle 70% of sorted observations, based on [START_REF] Hansen | Inference when a nuisance parameter is not identified under the null hypothesis[END_REF] result that the optimal trimming is 15%.

Results in table 1 show that the simultaneous dynamics of the Mexican economy are well described by a 3-regime TVAR model8 . Hence, we accept the 3-regime TVAR model. Of course all the previous analyses examine the exchange rate pass-through dynamics by looking at the coefficient of nominal effective exchange rate in the inflation equation in different regimes.

Empirical results

Table 2 reports the results of the TVAR model with the rate of inflation (π) as a threshold variable. Although the econometric tests select a three-regime VAR model, the exchange rate pass-through is negative and statistically significant only in the upper regime (π > 0.783) at the third lag. In the lower regime (π ≤ 0.167) and the middle regime (0.167 < π ≤ 0.783), the exchange rate pass-through is statistically insignificant.

Figure 4 depicts the accumulated impulse responses of output gap, domestic prices and interest rate to a positive one unit exchange rate shock. In regimes 1 and 2, a positive one unit exchange rate shock results in positive output gap. In regime 3, it is negative. However, the responses of output gap are not statistically significant in any regime.

In regime 1, a positive one unit exchange rate shock leads to a decrease in domestic prices. In regime 2, domestic prices increase after a positive one unit exchange rate shock. But the response of domestic prices is statistically insignificant in the two regimes. In regime 3, domestic prices decline after a positive one unit exchange rate shock. The response of domestic prices is statistically significant in the third regime.

The empirical estimates suggest that the exchange rate pass-through dynamics are rather described by two regimes i.e., a lower inflation regime with statistically insignificant and weak exchange rate pass-through and a higher inflation regime with statistically significant and strong exchange rate pass-through. In other words, a monthly rate of inflation of 0.79% acts as a threshold between two regimes.9 When the rate of inflation is above the threshold level, the exchange rate pass-through is significant, and when the rate of inflation is below the threshold level, the exchange rate pass-through is insignificant.

16 A monthly rate of inflation of 0.17% acts as a threshold between two regimes. The response of monetary policy to an exchange rate shock is insignificant in the lower regime and significant in the middle and high regime, respectively.

Conclusion

The presence of menu costs and the adjustment of profit margins alters the reaction of economic agents to an exchange rate shock above and below a certain threshold level of the rate of inflation. We examine the exchange rate pass-through to domestic prices in Mexico by This empirical analysis provides important implications for policy makers and financial analysts. First, the Central Bank of Mexico should keep the inflation below 9.48% to insulate domestic prices from exchange rate shocks. Second, the expected inflation is an important determinant of investment in securities markets. Inflation regimes in the TVAR model serve as leading indicator of exchange rate pass-through to domestic prices. As long as the annual rate of inflation is less than 9.48%, the response of inflation to exchange rate shocks will be statistically insignificant. So, the expected inflation will not change significantly, ceteris paribus.

2 4Figure 1 .

 21 Figure 1. Annual rate of inflation and inflation targets in Mexico

Figure 2 .

 2 Figure 2. Exchange rate depreciation and inflation in Mexico

Figure 2

 2 Figure2shows the exchange rate devaluation and inflation in Mexico from 1994 to 2009.

Figure 3 :Figure 3

 33 Figure 3: Overnight interbank rate and the monetary policy stance

  estimated covariance matrix of the model under the null hypothesis and 1 Σ is the estimated covariance matrix under the alternative. The calculation of the p-value is done by simulation. The bootstrap distribution is based on resampling the residuals from the null model, estimating the threshold and computing the test. For all computations we use 1000 bootstrap replications.

Figure 4 .

 4 Figure 4. Accumulated impulse responses of output gap, inflation and monetary policy to a positive one unit exchange rate shock

  estimating a threshold vector autoregression (TVAR) model. The nonlinearity test for a TVAR model against a linear VAR model suggests the presence of three regimes with two threshold values of inflation. The threshold values of inflation are estimated endogenously. Based on the estimates of the TVAR model, we reduce three regimes with two threshold values of inflation to two regimes with one threshold value of inflation. The monthly rate of inflation of 0.79% acts as a threshold level between two regimes. We find that domestic prices in Mexico react strongly to a positive one unit exchange rate shock only above the threshold level of the rate of inflation.

Table 1 :

 1 LR test results

	Panel A: LR test for linearity against 2 regimes
	LR Statistic	253.492
	p-value	[0.000]
	Estimated threshold	0.171
	Panel B: LR test for linearity against 3 regimes
	LR Statistic	405.706
	p-value	[0.000]
	Estimated thresholds	0.171; 0.789
	Panel C: LR test for 2 regimes against 3 regimes
	LR Statistic	138.674
	p-value	[0.000]
	Estimated Threshold	0.171; 0.789
	Results of the threshold test are reported in Table

Table 2 :

 2 Estimation results of the TVAR model: - γ variable: π

	Re	: gime π 1	(	) 1 -	≤	0	171 .				Re	gime	2	:	0	171 .	<	π	(	-	) 1	≤	. 0	789	Re	: gime π 3	(	-	) 1	>	. 0	789
	Percentage	of	ns observatio	=	. 18	% 7	Percentage	of	ns observatio	=	. 62	% 6	Percentage	of	ns observatio	=	. 18	% 7
	Constant					0.181										0.072									0.702
						(0.1455)										(0.072)								(0.251)**
	Output gap (-1)					-0.033										0.023									0.008
						(0.0289)										(0.010)*							(0.027)
	π(-1)					0.133										0.725									0.277
						(0.3800)									(0.159)***						(0.244)
	NEER(-1)					-0.005										-0.014								0.001
						(0.0120)										(0.011)								(0.004)
	i(-1)					0.051										0.008									0.010
						(0.039)										(0.017)								(0.007)
	Output gap (-2)					-0.055										0.030									-0.006
						(0.033).										(0.012)*							(0.028)
	π (-2)					-0.3684										-0.136								-0.376
						(0.222)										(0.111)								(0.239)
	NEER(-2)					0.016										-0.004								-0.0003
						(0.014)										(0.011)								(0.004)
	Note: Values in the brackets are the standard errors. * represents the 1% level of significance, ** represents 5% level of significance, *** represents 10% level of
														significance

[START_REF] Schemidt-Hebbel | Inflation targeting in Brazil, Chile, and Mexico: Performance, credibility, and the exchange rate[END_REF],[START_REF] Levin | The macroeconomic effects of inflation targeting[END_REF]

[START_REF] Bernanke | The Federal funds rate and the channels of monetary transmission[END_REF] for United States,[START_REF] Aleem | Transmission mechanism of monetary policy in India[END_REF] for India.

Johansen cointegration test shows that the cointegrating matrix is a full rank matrix. Thus, variables are stationary, and a TVAR model is estimated to examine the exchange rate pass-through.

p-values = 0 in table 1 indicates the rejection of the null of linearity.

A monthly rate of inflation of 0.79% equals an annual rate of inflation of 9.48%

Acknowledgements

Earlier version of this paper was presented in the ACEA conference at the University of Prince Edward Island, Canada, on October 15, 2011, and doctoral workshop of CEPN at the University of Paris XIII, on April 11 th , 2008. We are grateful to the participants of the ACEA conference for their constructive comments.

Appendix. Data sources

Data on the Consumer Price Index (CPI) and the industrial production index are taken from the International Financial Statistics, International Monetary Fund. The data on the nominal effective exchange rate (NEER) are taken from the Bank for International Settlements (BIS). Data on overnight money market rate are taken from datasteam.