Can LR Test Be Helpful in Choosing the Optimal Lag order in the VAR Model When Information Criteria Suggest Different Lag Orders?

Keywords: VAR, Lag length, Information Criteria, Likelihood Ratio Test, Monte Carlo Simulations JEL Classification: C32, C30 VAR, Lag length, Information Criteria, Monte Carlo Simulations, Likelihood Ratio Test JEL Classification: C32, C30 VAR, Lag length, Information Criteria, Monte Carlo Simulations, Likelihood Ratio Test

Can LR Test Be Helpful in Choosing the Optimal Lag order in the VAR Model When Information Criteria

Suggest Different Lag Orders?

Abdulnasser Hatemi-J, Scott Hacker

Introduction

One of the most applied models in the empirical economics is the vector autoregressive (VAR) model. In addition to its simplicity regarding estimation and interpretation, and its good forecasting capabilities, the VAR model treats all the variables of interest endogenesously. This property is important since in macroeconomics exogenous variables are rare. The VAR models also provide the possibility to investigate the causal relationship between the variables. It is also possible to transform the VAR model to a vector moving average (VMA) representation in order to trace the effects of the shocks on each variable in the system by calculating the impulse response functions and the variance decompositions. Due to the recent developments in dealing with integrated variables, the VAR model has been proven to be even more useful since it can be used to test for the long-run equilibrium relationship between the variables in combination with the short-run adjustment process. Obviously the VAR model is dynamic which accords with economic theory. However, economic theory is usually not much of help regarding the length of the dynamic process. In the literature several lag choosing criteria have been proposed for this purpose. Three of the most used information criteria are the Akaike (1969) information criterion, (AIC), the Schwarz (1978) Bayesian criterion (SBC) and the Hannan and Quinn (1979) criterion (HQC). These information criteria were originally developed for single equations. But they can be extended in vector form to determine the lag order of systems of equations, i.e. VAR models. However, the choice of these criteria for determining the lag order in the VAR model is usually arbitrary in the applied studies. Sometimes these information criteria do not agree in choosing the lag order. The question is then upon which information criteria one should rely. Hatemi-J (1999[START_REF]Time-Series Econometrics Applied to Macroeconomic Issues[END_REF] suggested using two of these criteria to choose the optimal lag length in the VAR model. If these two criteria choose different lag orders then the author suggested using the likelihood ratio (LR) test to choose between these two lags. It should be expressed that the LR test will be used only once in this case. 1 This means that the problem of mass-significance that occurs when the test is used sequentially can be avoided. 2 According to a simulation study performed by Hacker and Hatemi-J (2005) SBC 1 For an application of this approach see Hacker and Hatemi-J (2003). 2 See also Hatemi-J (2003). 3 has best performance in many cases. However, HQC has better performance in some cases. Thus, which criteria should be used is dependent on the data generating process for the variables. However, one cannot be sure about this issue when actual data is used because the true data generating process for the actual data cannot be known. This subject is important because inference in the VAR model is dependent on the choice of lag length.

The purpose of this article is to evaluate the lag choosing procedure suggested by Hatemi-J. Thus, the purpose of this study is to see whether the LR test can be useful in picking the optimal lag order of the VAR model when SBC and HQC suggest different lag orders. It should be pointed out that we will make use of many combinations of the parameters in the VAR model in the simulations in order to make the results as general as possible.

This paper is organized as follows. In the next section we will describe the VAR model and different criteria that can be used to determine the optimal lag order. Section 3 describes the design of our simulation. Section 4 presents the simulation results and conclusions.

The VAR Model and the Lag choosing Criteria

Let us define the following VAR model, consisting of n variables that is characterized by an order less-than or equal to K:

. , 1, 1 T t , Z D Z t k t K k k t t L = + + = = (1)
where t is a n×1 vector of disturbance terms that are assumed to be independently identically distributed errors with the distribution ( )

0, N n
, k is a matrix of coefficients for Z t-k , and D t represents non-stochastic components such as constant terms, linear trend, or seasonal dummies. The initial values,

0 - 1 , , Z Z K L
, are assumed to be fixed. Our objective is to choose the largest order for the time series, denoted by k l K, such that 0 l k and j = 0, j > k l .

To accomplish choosing the optimal lag length in the VAR model the following general form for an information criterion can be applied:

( ) ( ) , , 0, det K j , T T f j IC j L ) = + = ln (2) F o r P e e r R e v i e w 4
where j ˆ is the maximum likelihood estimate of the variance-covariance matrix when the lag order used in estimation is j. Logarithm is denoted by ln and det represents the determinant of the corresponding matrix.

The objective is to estimate k l by the j that minimizes the above criterion. Schwarz (1978) suggested ( )

T n T f ln 2 =
, whereas Hannan and Quinn (1979) preferred ( ) ( )

T n T f ln ln 2 2 = . 3
The lag order of the VAR model can also be determined by testing the significance of parameters for each specific lag order. The likelihood ratio (LR) test that can by applied for this purpose, due to Sims (1980), is defined as the following:

( )

2 1 log log = c T LR ( 3
)
where T is the sample size and c is the total number of parameters estimated in the VAR model under the alternative hypothesis. 1 is the maximum likelihood estimate of the variance-covariance matrix of the residuals in the VAR model under null hypothesis and 2 is the maximum likelihood estimate of the variance-covariance matrix of the residuals in the VAR model under alternative hypothesis. The LR test is chi-square distributed with the degrees of freedom equal to the number of restriction that are tested.

The Simulation Design

We make use of the following bivariate VAR model, which is of order two, in our simulations:

+ + + = t t t t t t t t z z z z z z 2 1 2 2 2 1 22 , 2 21 , 2 12 , 2 11 , 2 1 2 1 1 22 , 1 21 , 1 12 , 1 11 , 1 2 1 0 . 1 0 . 1 , (4)
The error terms vector t t 2 1 are designed to be independent or conditionally heteroscedastic.

More specifically, the simulations are also run when the variance of the error terms can be described by the following autoregressive conditional heteroscedasticity (ARCH): A central issue in a Monte Carlo simulation like the current one is choosing a variety of parameters that as a group has characteristics that fairly represent those of the infinite space of possible parameters. In order to obtain general results we consider all the combinations shown in Table 1 for the coefficient matrices. There are 12500 (5×5×5×5×4×5) possible combinations of the elements in this table. The VAR model is always of the second order since 2,22 is never zero.

× + = 2 1 2 2 1 1 2 2 2 1 5 . 0 0 0 5 . 0 0 . 1 0 . 1 t t t t , (5)
Table 1.

Parameter Values for VAR model of equation ( 4)

1,11 -1 0.5 0 0.5 1 1,22 -0.5 -0.25 0 0.25 0.5 1,12 = 1,21 -0.5 -0.1 0 0.1 0.5 2,11 -0.8 -0.2 0 0.2 0.8 2,22 -0.6 -0.1 0.1 0.6 2,12 = 2,21 -0.5 -0.1 0 0.1 0.5
To assure that we have stable cases we make sure that the modulus (the square root of the summed squares of the real and imaginary eigenvalue components) of each eigenvalue of the following companion matrix (B) is less than one.

B = 0 0 1 0 0 0 0 1 22 2 21 2 22 1 21 1 12 2 11 2 12 1 11 1 , , , , , , , , (6)
We run separate simulations based on small sample sizes (T = 40).4 Since VAR models are extensively used for forecasting purposes, we also investigate whether combining the LR test with the two information criteria can result in determining lag orders that can result in more accuracy in forecasts. Assume that

) z ( E h T , i +
is the forecast of variable z i , i = 1,2, for h periods into the future that we would make if we know the actual parameters of the VAR model (assuming errors are equal to zero for future periods). This forecast is equivalent to the expected value of h T , i z + based on the information available in the last observed period T. Let us denote h T , i z ˆ+ the forecast of variable z i for h periods into the future that we make using the estimated parameters based on the lag length chosen by the criterion. Finally, let h T , i z + denote the forecast of variable z i for h periods into the future that is made based on the estimated parameters using always the right lag length of two. Then, the sum of squared errors ratio, SSER, can be calculated for a particular case (set of parameters in a scenario) by the following equation:

( ) [ ] ( ) [ ] + + + + = S h T i h T i S h T i h T i z E z z E z SSER 2 , , 2 , , ˆ, (7)
where S denotes the set of 1000 simulations for a particular case, so in the numerator and denominator we are summing up over the simulations. In the numerator we show the systematic sum of squared errors of the forecasted variable based on forecasts using lags chosen by the criterion. 5 In the denominator we show the systematic sum of squared errors of a forecasted variable using always the correct lag length. The lower SSER is, the better the forecasting is in comparison to forecasts based on knowing the correct lag length. If the chosen criterion does just as well in forecasting as when the correct lag length is always chosen, then this ratio would be one. For any particular scenario we calculate the average SSER, i.e. the mean of the SSER over all the cases and over the two variables, z 1 and z 2 .

The Results of the Simulations and the Conclusions

5 Lütkepohl (1985Lütkepohl ( ,1991) ) handles his presentation of forecast capability in a different fashion. He focuses not on the systematic forecast error,

) z E( z ˆh T , i h T , i + + , but on the overall forecast error h T , i h T , i z z ˆ+ +
, where z i,T+h is an actualized outcome of z i for h periods into the future. He thus also includes in his focus the unsystematic (random) components of the forecast error, E(z i,T+h )z i,T+h , which injects additional randomness that we find undesirable for comparison since it is unsystematic. For his presentation in his 1985 article he normalizes (divides) an approximation of the mean squared overall forecast error with the theoretical variance of E(z i,T+h )z i,T+h . In Table 2 we present the frequency distributions in the presence and absence of conditional heteroscedasticity. We can see that the two criteria perform differently and which performance is better depends on the circumstances. However, when we combine these two criteria with the LR test for picking the true lag order in the VAR model the percentage choosing the optimal order increases significantly compared to cases when only one criterion is utilized, particularly for small sample sizes. This is true whether conditional heteroscedasticity is present or not. The same conclusion can be drawn regarding the forecasting properties (see Table 3). Using the LR test combined with SBC and HQC to choose the optimal lag order in the VAR model is going to result in choosing lag orders that are going to result in more precise forecasts compared to cases when only SBC and HQC are used.

Introduction

One of the most applied models in the empirical economics is the vector autoregressive (VAR) model. In addition to its simplicity regarding estimation and interpretation, and its good forecasting capabilities, the VAR model treats all the variables of interest endogenously.

This property is important since in macroeconomics exogenous variables are rare. The VAR models furthermore provide the possibility to investigate the causal relationship between the variables. It is also possible to transform the VAR model to a vector moving average (VMA)

representation in order to trace the effects of the shocks on each variable in the system by calculating the impulse response functions and the variance decompositions. Due to the recent developments in dealing with integrated variables, the VAR model has been proven to be even more useful since it can be used to test for the long-run equilibrium relationship between the variables in combination with the short-run adjustment process. Obviously the VAR model is dynamic which accords with economic theory on a variety of topics. However, economic theory is usually not much of help regarding the length of the dynamic process. In the literature several lag choosing criteria have been proposed for this purpose. Three of the most used information criteria are the Akaike (1969) information criterion, (AIC), the Schwarz (1978) Bayesian criterion (SBC) and the Hannan and Quinn (1979) criterion (HQC).

These information criteria were originally developed for single equations, but they can be extended in vector form to determine the lag order of systems of equations, i.e. VAR models.

However, the choice of which of these criteria to use for determining the lag order in the VAR model is usually arbitrary in applied studies. Sometimes these information criteria do not agree in choosing the lag order. The question is then upon which information criterion one should rely.

Hatemi-J (1999, 2001) suggested using two of these criteria to choose the optimal lag length in the VAR model. If these two criteria choose different lag orders then the author suggested using the likelihood ratio (LR) test to choose between these two lags. It should be expressed that the LR test will be used only once in this case. 1 This means that the problem of masssignificance that occurs when the test is used sequentially can be avoided. 2 According to a simulation study performed by Hacker and Hatemi-J (2005) SBC has best performance in 1 For an application of this approach see Hacker and Hatemi-J (2003).

2 See also Hatemi-J (2003Hatemi-J ( , 2006)), and Bahmani-Oskooee and Brooks (2003). 3 many cases. However, HQC has better performance in some cases. Thus, which criteria should be used is dependent on the data generating process for the variables. However, one cannot be sure about this issue when actual data is used because the true data generating process for the actual data cannot be known. This subject is important because inference in the VAR model is dependent on the choice of lag length. The purpose of this article is to evaluate the lag choosing procedure suggested by Hatemi-J (1999). Thus, the purpose of this study is to see whether the LR test can be useful in picking the optimal lag order of the VAR model when SBC and HQC suggest different lag orders. It should be pointed out that we will make use of many combinations of the parameters in the VAR model in the simulations in order to make the results as general as possible.

This paper is organized as follows. In the next section we will describe the VAR model and different criteria that can be used to determine the optimal lag order. Section 3 describes the design of our simulation. Section 4 presents the simulation results and conclusions.

The VAR Model and the Lag Choosing Criteria

Let us define the following VAR model, consisting of n variables that is characterized by an order less-than or equal to K:

. , 1, 1 T t , Z D Z t k t K k k t t L = + + = = (1)
where t is a n×1 vector of disturbance terms that are assumed to be independently identically distributed errors with the distribution ( )

0, N n
, k is a matrix of coefficients for Z t-k , and D t represents non-stochastic components such as constant terms, linear trend, or seasonal dummies. The initial values,

0 - 1 , , Z Z K L
, are assumed to be fixed. Our objective is to choose the largest order for the time series, denoted by k l K, such that 0 l k and j = 0, j > k l .

To accomplish choosing the optimal lag length in the VAR model the following general form for an information criterion can be applied:

( ) ( ) , , 0, det K j , T T f j IC j L ) = + = ln (2)
where j ˆis the maximum likelihood estimate of the variance-covariance matrix when the lag order used in estimation is j. Logarithm is denoted by ln and det represents the determinant of the corresponding matrix. The objective is to estimate k l by the j that minimizes the above criterion. Schwarz (1978) suggested ( )

T n T f ln 2 =
, whereas Hannan and Quinn (1979) preferred ( ) ( )

T n T f ln ln 2 2 = . 3
The lag order of the VAR model can also be determined by testing the significance of parameters for each specific lag order. The likelihood ratio (LR) test that can be applied for this purpose, due to Sims (1980), is defined as the following:

( )

2 1 log log = c T LR ( 3
)
where T is the sample size and c is the total number of parameters estimated in the VAR model under the alternative hypothesis. 1 is the maximum likelihood estimate of the errorterm variance-covariance matrix in the VAR model under the null hypothesis and 2 is the maximum likelihood estimate of the error-term variance-covariance matrix in the VAR model under the alternative hypothesis. Under the null hypothesis the LR test is chi-square distributed with the degrees of freedom equal to the number of restriction that are tested.

The Simulation Design

We make use of the following bivariate VAR model, which is of order two, in our simulations:

+ + + = t t t t t t t t z z z z z z 2 1 2 2 2 1 22 , 2 21 , 2 12 , 2 11 , 2 1 2 1 1 22 , 1 21 , 1 12 , 1 11 , 1 2 1 0 . 1 0 . 1 , (4)
The error terms vector t t 2 1 are designed to be independent and homoscedastic or conditionally heteroscedastic. In the conditionally heteroscedastic situation the simulations are run when the variance of the error terms can be described by the following autoregressive conditional heteroscedasticity (ARCH) 4 :

3 Nielsen (2001) shows that SBC and HQC are consistent regardless of the assumption about the characteristic roots in the VAR model. By consistency is meant that the criterion selects the true order of the VAR system with probability one asymptotically. 4 In this formulation of multivariate ARCH the conditional and unconditional variances are equal to each other asymptotically. This seems to be a necessary condition in order to make sure that the comparison of our simulation results for homoscedastic and conditionally heteroscedastic cases makes sense. A mathematical derivation of equation ( 5) is provided by [START_REF]Multivariate Tests for Autocorrelation in the Stable and Unstable VAR Models[END_REF]. For a test of multivariate ARCH effects in the VAR model the interested reader is referred to Hacker and Hatemi-J (2005).

F o r P e e r R e v i e w × + = 2 1 2 2 1 1 2 2 2 1 5 . 0 0 0 5 . 0 5 . 0 . 5 . 0 t t t t , (5)
where 2 it represents the conditional variance at time t for variable i (

. 2 , 1 = i
). To cancel the effect of starting up values, we generated 100 presample observations. This gives us the possibility to have the same number of observations in estimating the VAR model regardless of the number of lags.

A central issue in a Monte Carlo simulation like the current one is choosing a variety of parameters that as a group has characteristics that fairly represent those of the infinite space of possible parameters. In order to obtain general results we consider all the combinations shown in Table 1 for the coefficient matrices. There are 12500 (5×5×5×5×4×5) possible combinations of the elements in this table. The VAR model is always of the second order since 2,22 is never zero.

Table 1.

Parameter Values for VAR model of equation ( 4)

We run simulations based on small sample sizes (T = 40). It should be pointed out that we have run 10000 simulations for each combination of the parameters. This means that the total We investigate whether performance on lag length choice using either criterion can be improved by employing the LR test (with 5% significance for null hypothesis rejection) when the two criteria disagree. Since VAR models are extensively used for forecasting purposes, we also investigate whether combining the LR test with the two information criteria can result in determining lag orders that can result in more accuracy in forecasts. Assume that

) z ( E h T , i +
is the forecast of variable z i , i = 1,2, for h periods into the future that we would make if we know the actual parameters of the VAR model (assuming errors are equal to zero for future periods). This forecast is equivalent to the expected value of h T , i z + based on the information available in the last observed period T. Let us denote h T , i z ˆ+ the forecast of variable z i for h periods into the future that we make using the estimated parameters based on the lag length chosen by the criterion. Finally, let h T , i z + denote the forecast of variable z i for h periods into the future that is made based on the estimated parameters using always the right lag length of two. Then, the sum of squared errors ratio, SSER, can be calculated for a particular case (set of parameters in a scenario) by the following equation:

( ) [ ] ( ) [ ] + + + + = S h T i h T i S h T i h T i z E z z E z SSER 2 , , 2 , , ˆ, (7)
where S denotes the set of 1000 simulations for a particular case, so in the numerator and denominator we are summing up over the simulations. In the numerator we show the systematic sum of squared errors of the forecasted variable based on forecasts using lags chosen by the criterion. 6 In the denominator we show the systematic sum of squared errors of 5 Notice that SBC and HQC choose different lag orders more frequently in small sample sizes. In large sample sizes (asymptotically) both information criteria are expected to choose the same lag order and there will be no need for using the LR test in such cases. That is why we concentrate on small sample sizes in our simulations. However, we also conducted simulations for a sample size of 70. The results, not presented to save space, showed similar qualitative results. 6 Lütkepohl (1985, 1991) , where z i,T+h is an actualized outcome of z i for h periods into the future. He thus also includes in his focus the unsystematic (random) components of the forecast error, E(z i,T+h ) -z i,T+h , which injects additional randomness that we find undesirable for comparison since it is unsystematic. For his presentation in his 1985 article he normalizes (divides) an approximation of the mean squared overall forecast error with the theoretical variance of E(z i,T+h )z i,T+h . a forecasted variable using always the correct lag length. The lower SSER is, the better the forecasting is in comparison to forecasts based on knowing the correct lag length. If the chosen criterion does just as well in forecasting as when the correct lag length is always chosen, then this ratio would be one. For any particular scenario we calculate the average SSER, i.e. the mean of the SSER over all the cases and over the two variables, z 1 and z 2 .

The Results of the Simulations and the Conclusions

In Table 2 we present the frequency distributions in the presence and absence of conditional heteroscedasticity. We can see that the two criteria perform differently and which performance is better depends on the circumstances. However, when we combine these two criteria with the LR test for picking the true lag order in the VAR model the percentage choosing the optimal order increases substantially compared to cases when only one criterion is utilized, particularly for small sample sizes. This is true whether conditional heteroscedasticity is present or not. The same conclusion can be drawn regarding the forecasting properties (see Table 3). Using the LR test combined with SBC and HQC to choose the optimal lag order in the VAR model is going to result in choosing lag orders that are going to result in more precise forecasts compared to cases when only SBC and HQC are used.

  effect of starting up values, we generated 100 presample observations. This gives us the possibility to have the same number of observations in estimating the VAR model regardless of the number of lags.

  simulations is 125000000. The simulations are performed by a program procedure written by the authors in GAUSS.5

Table 2 .

 2 Results for picking the optimal lag order based on simulations for a VAR(2) model with and without autoregressive conditional heteroscedasticity (ARCH).

	Info criterion	Lag	0	1	2	3	4	5	6	7
	& variance	length
	situation
			Frequency distribution of estimated VAR orders, without ARCH
	HQC,		0.019 0.031 0.860	0.056 0.018	0.007 0.005 0.004
	SBC		0.066 0.070 0.850	0.013 0.001	0.000 0.000 0.000
	HQC, SBC and LR	0.021 0.050 0.908	0.018 0.003	0.000 0.000 0.000
				Frequency distribution of estimated VAR orders, with ARCH
	HQC,		0.018 0.032 0.833	0.078 0.022	0.008 0.005 0.004
	SBC		0.060 0.069 0.846	0.022 0.002	0.000 0.000 0.000
	HQC, SBC and LR	0.019 0.051 0.897	0.028 0.004	0.000 0.000 0.000

Table 3 .

 3 Results for forecasting performance (SSER) based on simulations for a VAR(2) model with and without autoregressive conditional heteroscedasticity (ARCH).

	Forecasting Period	Forecasting Error for HQC
	Forecasting Period	Without ARCH	With ARCH
	1	1.249	1.334
	2	1.267	1.422
	3	1.240	1.403
	4	1.229	1.453
	5	1.194	1.877
	Forecasting Period	Forecasting Error for SBC
	1	1.283	1.254
	2	1.285	1.257
	3	1.139	1.149
	4	1.111	1.149
	5	1.063	1.181
	Forecasting Period	Forecasting Error for HQC, SBC and LR
	1	1.141	1.162
	2	1.147	1.176
	3	1.089	1.131
	4	1.073	1.148
	5	1.049	1.18

Table 2 .

 2 Results for picking the optimal lag order based on simulations for a VAR(2) model with and without autoregressive conditional heteroscedasticity (ARCH).

	Lag length

Table 3 .

 3 Results for forecasting performance (average SSER) based on simulations for a VAR(2) model with and without autoregressive conditional heteroscedasticity (ARCH).

	Forecasting Period	Forecasting Error for HQC
	Forecasting Period	Without ARCH	With ARCH
	1	1.249	1.334
	2	1.267	1.422
	3	1.240	1.403
	4	1.229	1.453
	5	1.194	1.877
	Forecasting Period	Forecasting Error for SBC
	1	1.283	1.254
	2	1.285	1.257
	3	1.139	1.149
	4	1.111	1.149
	5	1.063	1.181
	Forecasting Period	Forecasting Error for HQC, SBC and LR
	1	1.141	1.162
	2	1.147	1.176
	3	1.089	1.131
	4	1.073	1.148
	5	1.049	1.18

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Nielsen (2001) shows that SBC and HQC are consistent regardless of the assumption about the characteristic roots in the VAR model. By consistency is meant that the criterion selects the true order of the VAR system with probability one asymptotically.

It should be pointed out that we have run 10000 simulations for each combination of the parameters. This means that the total number of the simulations is 125000000 for each sample size. The simulations are performed by using GAUSS.

Acknowledgment

We would like to thank the editor of this journal and an anonymous referee for useful comments and suggestions that resulted in an improvement of this paper. However, the usual disclaimer applies.


Roberto Basile

Sergio De Nardis

Alessandro Girardi

PRICING TO MARKET OF ITALIAN EXPORTING FIRMS

Keywords: Pricing to market, survey data, panel-VAR models

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

A large body of empirical studies shows that price differentiation across destination markets is the rule, rather than the exception, in the pricing behaviour of exporters of industrial countries. [START_REF] Adolfson | Swedish Export Price Determination: Pricing to Market Shares?[END_REF] Exchange rate swings induce firms, endowed with some degree of market power, to adopt optimal (short run) price strategies, consisting in pricing the same good differently according to the markets where it is sold. Dornbusch (1987) investigates this phenomenon drawing on models of industrial organization, while Krugman (1987) formalizes it with the concept of pricing-to-market (PTM): if the domestic currency appreciates, a firm can react by reducing the domestic currency price of the good sold abroad to restrain the rise of the corresponding foreign price and the consequent fall of the (volume) market share. Motives behind the attempt at limiting the market share loss relate to the long-run investment made to establish in the market and the adjustment costs the firm has to incur when reducing volume of sales (these may be both reputation/brandswitching costs, as in Froot and Klemperer, 1989, and proper fixed costs in entering and exiting the market, as in Kasa, 1992). Relevant macroeconomic consequences of PTM are incomplete exchange rate pass-through (ERPT) and deviations from the law of one price (LOP), such that the classical textbook reaction of the current account to exchange rate modifications (based on the Marshall-Lerner requirements on export and import price elasticities) can be considerably diluted.

Irrespective of whether a general equilibrium framework (Betts and Devereux, 1996, among others) or a partial equilibrium model is concerned (Dornbusch, 1987; Krugman, 1987; Marston, 1990), necessary conditions for price discrimination, consequent on exchange rate movements, involve market-structure characteristics, functional forms of demand faced by firms in the various destination markets and degree of integration of [START_REF] Adolfson | Swedish Export Price Determination: Pricing to Market Shares?[END_REF] For a comprehensive survey, see Goldberg and Knetter (1997). [5] major advantage to provide empirical testable predictions on the key variable measuring the degree of PTM behaviour (i.e. the export-domestic price margin given by the ratio of the price of a good set by a firm for sale abroad relative to the price of the same good set for sale at home, converted to a common currency), which is indeed properly captured by a section of the survey we use. Moreover, explicit conditions under which an exchange rate change translates into a rise or a fall in the export-domestic price margin are discussed.

Third, in order to deal with the above-mentioned "intrinsic" endogeneity of the variables involved, the empirical analysis is based on the panel Vector AutoRegression (VAR) methodology (Love, 2001). Such quite a novel technique seems to be particularly well suited for our purposes, since it applies the traditional VAR approach, where all variables in the system are treated as endogenous, within a panel data framework, which allows for unobserved individual heterogeneity.

Estimations results as well as dynamic simulation exercises suggest that while cost competitiveness factors have represented the major driving force for the sample of Italian firms in setting export prices over the period from 1999 to 2001, demand conditions in the domestic and in the foreign markets have exerted a relevant role in the most recent years, leading to an anomalous behaviour of the export-domestic price margin which was increasing in a period of rising competitive pressures. Sector analysis indicates that this phenomenon was mainly related to traditional industries, that is those that suffered the most because of foreign competition. This evidence notwithstanding, the peculiar pricing policy of Italian exporting firms turned to be limited in timing and in intensity. These findings seem to contrast PTM-based argumentations in explaining long-run deviations from the LOP.

The paper is structured as follows. In section 2 we introduce the theoretical framework used to model PTM behaviour of exporting firms. Dataset characteristics are illustrated in section 3. Sections 4 and 5 report the empirical specification and estimation results. In F o r P e e r R e v i e w [6] section 6 we present dynamic simulation exercises. Section 7 concludes.

Theoretical framework

Formalization of the theoretical framework to test PTM of Italian exporting firms is based on the model originally proposed by Marston (1990). We consider a firm operating in sector i endowed, for whatever reason, with some degree of market power. [START_REF] Brander | A "Reciprocal Dumping" Model of International Trade[END_REF] As in Giovannini (1988) and Marston (1990), the firm sells its product in two distinct markets, labelled respectively as Home ( H ) and Foreign ( F ) destinations. The two markets are segmented, so that the firm is potentially able to practice different prices in each of them.

Moreover we assume, for the sake of simplicity, that the good sold to the two markets is produced in the Home country by a single-plant firm. This makes marginal costs independent of the destination markets; yet, marginal costs may respond to changes in total sales (caused by modifications of either domestic or foreign sales). The imperfectly competitive firm will set prices in each market in order to maximize its profit.

Let j it P be the domestic currency price practiced by the firm of sector i at time t in each market j ( , j H F = ), j it X be the volume of sales to each market, t E the exchange rate of H 's currency per unit of F 's. We consider, moreover, a cost function, C , a price index of production inputs, it W , the price of competitors expressed in the currency of market F, C it P , and the demand of each market for all possible varieties of the considered product, j it V . Profit maximization of firm i at each time t

(1) ( ) ( ) max , j it j j j it it it it j j X P X C X W , with ( / ; ; ) j j j C j it it it t it it X X P E P V =
leads to the first-order conditions which define the price set in each destination market as a [START_REF] Brander | A "Reciprocal Dumping" Model of International Trade[END_REF] It might derive from monopolistic competition and product differentiation or from any other market imperfection. ( ) ( )

j j j j j it it it it it X P P X =
indicate, respectively, the marginal cost and the price elasticity of demand faced by firm i in H and F markets.

Since the marginal cost is independent of j (destination markets), price differences in the two markets (and hence geographical differences of the mark-ups) depend only on the price elasticity of demand in the two destination markets. In turn, such elasticities reflect the characteristics (degree of convexity) of the demand schedules. Models of price discrimination leading to PTM hence require particular functional forms of the demand curves, such that the price elasticity of the demand schedule, j it , is not constant in at least one destination market. [START_REF] Bugamelli | Le strategie di prezzo delle imprese esportatrici italiane[END_REF] In general, demand functions must be less convex (or more linear) than the constant price elasticity demand schedule in order to have positive PTM elasticities (with respect to the exchange rate). Under this condition, an appreciation of the domestic currency leads to an increase of the foreign currency price practiced in the export market less than proportional to the exchange rate appreciation; with variable demand price elasticities, incomplete ERPT is always the rule whatever the behaviour of the marginal [START_REF] Bugamelli | Le strategie di prezzo delle imprese esportatrici italiane[END_REF] If both demand curves in the two markets have constant price elasticities -as in a log-linear demand schedule -then the mark-ups in each destination market are constant; in this case prices practiced in H and F are affected by a common marginal cost and the ratio between the price made in F and the price made in H (expressed in the same currency) is invariant to currency movements. This means that there may be a constant wedge between the two prices, but PTM does not change in response to variations of the exchange rate. Whether ERPT is complete or not depends, in this case, on the behaviour of the marginal cost: if the latter is increasing in output (total sales), ERPT is partial (i.e. an appreciation of the domestic currency, negatively affecting total sales, gives rise to a decrease of the marginal cost and, hence, to a reduction of both the domestic and foreign prices expressed in the home currency). As a consequence, the export price expressed in the foreign currency increases less than proportionally to the exchange rate change (see the Appendix).

F o r P e e r R e v i e w [8] cost in response to total sales changes. [START_REF] Caves | World Trade and Payments[END_REF] Former considerations can be succinctly described as follows. Labelling by

/ F H it it it
R P P = the export-domestic price margin (in the spirit of Marston, 1990), the elasticity

( / ) F H it it t
P P E of it R with respect to the exchange rate is given by (3)

( ) H F H F it t it t it it t it t P E P E P P E t it R E E R = =
where both terms

F it t P E
and

H it t P E
are positive, as shown in the Appendix. On the grounds of these signs, the elasticity of R it with respect to the exchange rate is positive and less than 1, such that an appreciation (depreciation) of the domestic currency leads to a less than proportional reduction of the export-domestic price margin (and vice versa, see the Appendix).

In the empirical specification of the model we focus on the level of the exportdomestic price margin, it R . This implies that, while levels of common marginal costs wipe out, it R will depend on the influences activated by both exchange rate changes and movements of all the other factors, which include, as described in (1), the price of competitors C it P , named in the F 's currency, and the cyclical conditions of demand in the domestic and foreign markets, indicated by j it V .

To make explicit the model for empirical testing, we take the logarithmic transformation of (2), linearise the mark-up in the two markets around respective average values through a first order Taylor approximation and take the difference between the logarithms of prices in the Foreign and Home markets (see Adolfson, 1999). All this yields [START_REF] Caves | World Trade and Payments[END_REF] In the model by Caves and Jones (1977), the phenomenon of "dumping" in international trade arises when a monopolistic profit maximizing firm, facing a higher elasticity of demand abroad than at home, is able to discriminate between foreign and domestic markets. As a consequence, it will charge a lower price abroad than at home. Conversely, Brander and Krugman (1983) show how dumping may arise for "systematic" reasons associated with oligopolistic behaviour rather than "accidental" differences in country demands. (4)

p P = , ln F it it f V = , ln H it it h V =
and the constant, grouping the time independent terms (average values) that come from the linearisation, is omitted.

In (4), the PTM behaviour of firms is captured by the parameter 1 which measures the response of the export-domestic price margin to changes in competitors' prices expressed in domestic currency. Since price setting, described in (4), bases export prices on the overall competitive conditions in foreign markets (rather than just the nominal exchange rate), this formulation allows to consider the possibility of PTM behaviour in markets (and with respect to competitors) with which exporting firms share fixedexchange rate regimes or even the same currency. 9

Data

Data are taken from the quarterly ISAE (Institute for Studies and Economic Analyses) survey. It covers a representative sample of Italy-based manufacturing exporting firms with more than 10 employees. The sample (around 2,000 firms) is random and stratified according to the number of employees, the sector and the regional location of the firm. We base our analysis on quarterly data covering the period between January 1999 and June 2005. Survey data not only constitute a valuable complement to statistical sources, which involve typically quantitative variables, but also provide a reliable (and direct) picture of agents' opinions about the dynamics of variables influencing their position in the markets.

Moreover, the use of survey data makes it possible to work with a panel dimension [START_REF] Coibion | Equilibrium Demand Elasticities across Quality Segments[END_REF] In the empirical specification, we hence follow Marston (1990) (information are set at region/sector and at time level) which is largely precluded by other statistical sources.

Table 1 reports the distribution of sample firms by sector and by region. [START_REF] De Nardis | How Intense is Competition in International Markets of Traditional Goods? The Case of Italian Exporters[END_REF] The number of firms entering in our panel dataset represents more than four-fifth of the total (1,275 out of 1,525), excluding sector "DF-Manufacture of coke, refined petroleum products and nuclear fuel", which contains numerous missing values in all regions.

[TABLE 1]

As for the variables involved in the empirical analysis, the most relevant one, from the point of view of the PTM analysis, is the answer concerning the export-domestic price margin practiced by the firm. Particularly, firms are asked to indicate whether the prices charged in foreign markets are higher than, equal to, or lower than those practiced in the domestic market. Individual answers are aggregated by computing an indicator which takes values ranging between -100 and 100. In this work, relative prices are argued to fit the testing of the economic hypotheses discussed in section 2 much better than the information obtainable from traditional sources for several reasons. First, survey data on export-domestic price margins allow dealing with proper export price rather than EUV, which are an inaccurate measure of export prices, being affected by important composition effects. Second, as stressed by Goldberg and Knetter (1997), indeed, it is important that the relevant variable in the analysis is the export/domestic price for the same good produced by the same firm, since it allows capturing price differences from two different transactions. [START_REF] Devereux | Real Exchange Rates Movements and Macroeconomics: Evidence and Theory[END_REF] As an illustrative example, Figure 1 shows a comparison of the EUV/producer prices ratio [START_REF] De Nardis | How Intense is Competition in International Markets of Traditional Goods? The Case of Italian Exporters[END_REF] In the empirical investigation, firms belonging to the South of Italy (Sicilia, Sardegna, Calabria, Puglia, Basilicata, Molise, Campania, Abruzzo) are not included because of the scant relevance of several sectors in that region. [START_REF] Devereux | Real Exchange Rates Movements and Macroeconomics: Evidence and Theory[END_REF] Consider, for instance, Italian footwears. Comparing domestic prices to those charged abroad by the same "shoe-firm" makes undoubtedly more sense than comparing the prices of footwear produced by different firms at home and abroad.

F o r P e e r R e v i e w [11] and its survey qualitative counterpart ( / F H it it P P ), over the period 1991q1-2005q2. Even though both series present similar behaviours over time (correlation equal to 0.63), exportdomestic price margins seem to anticipate the quantitative series. Moreover, in the most recent years, the qualitative indicator exhibits a slightly higher volatility.

[FIGURE 1]

Another relevant source of information coming from the ISAE survey regards the domestic and foreign demand levels. Firms are asked to indicate whether the domestic (foreign) demand level increased, remained unchanged or decreased over the period of reference. The qualitative variable is constructed as the difference between the relative frequency of firms that declare an increase and the relative frequency of those indicating a decline in the domestic (foreign) demand levels. Accordingly, the values of the two indicators range from -100 to 100. In terms of our theoretical model, domestic and foreign orders are used as proxies of the cyclical demand conditions in the two markets, which are the other factors affecting the behaviour of the export-domestic price margin.

Finally, we use the survey variables referring to competitiveness obstacles. Out of the different kinds of impediments faced by exporters, we consider price and non-price competitiveness factors. [START_REF] Dornbusch | Exchange Rates and Prices[END_REF] The price competitiveness indicator is represented by the share of firms that declare to have experienced impediments in foreign markets due to price competitiveness from foreign exporters. Within the class of non-price impediments, aimed at capturing the notion of trade costs, we consider the indications of firms about exporting obstacles due to "delivery", "financial", "administrative" and "other" costs. All of the above discussed obstacles are bounded to belong to the interval between 0 and 100.

Figure 2 illustrates the evolution of the export-domestic price margin and the price [START_REF] Dornbusch | Exchange Rates and Prices[END_REF] Even though the theoretical model does not explicitly involve non-price obstacles to export, we extend our dataset in order to control for possible effects of these forms of trade costs on the export-domestic price margin.

F o r P e e r R e v i e w [12] competitiveness indicator, it Q , over the period 1991q1-2005q2 for the aggregate Italian manufacturing sector as a whole.

[FIGURE 2]

A strong negative correlation (-0.37) between the two series characterizes the entire period considered, even though they co-move in the last four years (the correlation turns to be positive and equal to 0.86), when the perception of increasing competitive pressures in foreign markets was accompanied by a rise in the export-domestic price margin. [

TABLE 2]

All series take values consistent with the range within which they are expected to fall. More interestingly, the mean value of export-domestic price margins is positive and statistically significant, [START_REF] Engel | Real Exchange Rates and Relative Prices: An Empirical Investigation[END_REF] suggesting the existence of some degree of price differentiation and of market segmentation, despite the fact that a large share of exports was sold in EMU countries.

Empirical specification and estimation of the baseline model

Survey data have been properly transformed in order to perform the econometric analysis. For those variables constructed as differences between positive and negative outcomes from multiple-choice-answers in the survey ( /

F H it it P P , F it V , H it V
) the following transformation is used [START_REF] Engel | Real Exchange Rates and Relative Prices: An Empirical Investigation[END_REF] The 95% confidence interval of a standard t-test ranges from 3.

Q , time it X , fin it X , adm it X or oth it X .

Empirical specification

For the empirical implementation of model ( 4), we consider the possibility that omitted variables may contribute to determine export-domestic price margins. Firstly, some of these variables may be constant over time but vary across sectors/regions, and others may be fixed between sectors/regions but vary over time. Secondly, we try to control for all potential endogeneity sources: simultaneity and measurement errors. We start from the following model ( 5)

1 2 3 R R R R R R R it it it it i t it it r q f h m = + + + + + + , 1 R R R R it i t it v v e = + , 1 R < , ( ) , ~0 R R it it e m MA
where R i is a sector/region-specific intercept, R t is a time-specific intercept and R it v is a possibly autoregressive shock. We are interested in consistent estimations of the parameters

( 1 2 3 , , , R R R R
), maintaining that both the price competitiveness factor it q and (foreign and domestic) demand levels are potentially correlated with the sector/region-specific effects ( R i ), and with both sector/regional shocks ( R it e ) and serially uncorrelated measurement Price competitiveness factors are explained by no other variables, except for unobserved sector/region-specific and time effects ( 6)

Q Q Q Q it i t it it q m = + + + , 1 Q Q Q Q it i t it v v e = + , 1 Q < , ( ) , ~0 Q Q it it e m MA
while foreign demand depends on price competitiveness factors ( 7)

1 F F F F F it it i t it it f q m = + + + + , 1 F F F F it i t it v v e = + , 1 F < , ( ) , ~0 F F it it e m MA .
Finally, domestic demand is influenced by current price competitiveness factors as well as foreign demand ( 8)

1 2 H H H H H H it it it i t it it h q f m = + + + + + , 1 H H H H it i t it v v e = + , 1 H < , ( ) , ~0 H H it it e m MA .
In ( 6), ( 7) and ( 8) the parameters 's, 's, 's as well as the disturbances e 's and m 's have the same interpretation of those in equation (5). As usual, the structural model ( 5)-( 8)

admits the dynamic representation

1 2 3 ( ) ( ) ( ) ( ) R R R R R R it it it it i t it R L r R L q R L f R L h m = + + + + + % % % ( ) Q Q Q it i t it Q L q m = + + % % % 1 ( ) ( ) F F F F it it i t it F L f F L q m = + + + % % % 1 2 ( ) ( ) ( ) H H H H H it it it i t it H L h H L q H L f m = + + + + % % %
where L denotes the lag operator and with ( )

( ) 1 L L = , ( ) t t L = % , ( )
1 i i = % , ( ) it it it m e L m = + % , , , , R Q F H = .
More compactly, the model can be written as follows (9)

{ 0 , 1 1 , 1 , 1 1 1 , 1 1 2 1 2 , 1 1 2 3 1 2 3 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 1 it i t Q Q i t it i F F F F i t it H H H H H H H i t it R R R R R R R R R R i t it q q f f h h r r = + y A y A % 144244 3 123 1444 424444 3 { { { i it t Q Q it t F F F i it t H H H i it t R R R i it t m m m m + + e % % % % % % % % % % %
under the assumption that measurement errors exist but are constant over time. [START_REF] Fabiani | The pricing behaviour of Italian firms: New survey evidence on price stickiness[END_REF] Recasting the model in matrix form, we have

1 1 1 1 0 1 , 1 0 0 0 it i t i t it = + + + y A A y A A A e or ( 10
) 1 , 1 it i t i t it = + + + y y a d
where

1 1 0 1 = A A , 1 0 i i = a A , 1 0 t t = d A
and

1 0 it it
= A e have appropriate dimensions. [START_REF] Froot | Exchange Rate Pass-Through when Markets Share Matters[END_REF] In order to estimate the multivariate dynamic system (10) we employ the panel data VAR methodology (Love, 2001). This technique applies the traditional VAR approach, where all variables in the system are modelled as endogenous, within a panel data framework, where unobserved individual heterogeneity is allowed. It seems to be particularly well suited for purposes of this study, because of the "intrinsic" endogeneity of the variables involved in the analysis (i.e. the "same" individual firm provides all the requested information on its exporting activity). However, in using the VAR approach to panel data, we need to impose the restriction that the underlying structure is the same for each cross-sectional unit by introducing fixed effects ( i a ). Since the fixed effects are correlated with the regressors due to lags of the dependent variables, the mean differencing procedure might lead to biased coefficients estimates. To avoid this problem we use the [START_REF] Fabiani | The pricing behaviour of Italian firms: New survey evidence on price stickiness[END_REF] This assumption also holds when measurement errors do not exist at all and implies that var( ) 0 it m = and ( ) Helmert transformation (Arellano and Bover, 1995), which removes only the forward mean, i.e. the mean of all future observations available for each sector/region-quarter.

~1 it m MA % otherwise.
Since such a transformation preserves the orthogonality between transformed variables and lagged regressors, we use the latter as instruments and estimate the coefficients by GMM. 16 Finally, model ( 10) also admits region-specific time dummies ( t d ) in order to capture aggregate macro shocks that may affect all sectors in the same way. These dummies are eliminated subtracting the means of each variable calculated for each sector/region-quarter.

Estimation results

The starting point of the empirical analysis is the estimation of model (10). The order of autoregression is set equal to one, according to the conventional general to specific model reduction procedure. [START_REF] Ghosh | Pricing in International Markets: Lessons from The Economist[END_REF] Finding an exhaustive explanation for all effects of lagged variables in a vector autoregression is often both difficult (Sims, 1980) and unnecessary for the purposes of the analysis. In this work, instead, all estimated coefficients have a clear economic interpretation. Testing the structural model ( 9) from the reduced form (10) implies that only coefficients above the main diagonal of level (lower part of the Tables), corroborating our economic priors.

Since the focus of the analysis is on the behaviour of the export-domestic price margins, the rest of the work is devoted to discuss the role of their determinants over time.

As far as the entire period (1999q1-2005q2) is concerned, lagged values of q, f and h do not affect current values of r, while traces of persistence can be detected. Conversely, the statistical significance of the parameter of 1 t r suggests that past export-domestic price margins influence current relative prices. Predetermined variables have the expected signs, but their lack of statistical significance might suggest that market forces mainly drive the pricing behaviour of Italian exporting firms, without any room for price differentiation policies. However, that conclusion seems to stand out against the stylised facts in section 3.

[TABLE 3]

Extensions and robustness checks

The role of non-price obstacles

Though the estimations of the baseline model provides no evidence of an impact of the cost competitiveness indicator and of the demand levels on the export-domestic price margin, it is premature to conclude that these effects do not exist without considering possible sources of model misspecification. Particularly, we consider the omission of relevant regressors (e.g. non-price competitiveness obstacles or trade costs) in the baseline system as a major candidate of the empirical failure of our theoretical model. To this end, we employ a five-dimensional panel-VAR in order to assess the role of each additional trade obstacle taken from the survey. The empirical evidence suggests that the inclusion of non-price competitiveness factors does not help in explaining the pricing behaviour of Italian exporters over the period considered. The only exception concerns the administrative obstacles, which enter with expected sign and turn to be statistically significant at the 10% level. Exclusion tests provide mixed results. On the one hand, the causal linkage implied by relations ( 5)-( 8) is supported in the four specifications. On the other hand, the exogeneity for non-price competitiveness indicators is rejected in the case of "time" and "other" obstacles.

Parameter instability

A key assumption in previous estimations concerns the temporal stability of parameters. If this hypothesis is not supported by the data, the estimates may be questionable. In other words, the driving forces predicted by the theoretical model may evolve over time, but remain stable in a short sample period. In order to investigate whether the relationship between the export-domestic price margin and its determinants is stable over time, model (10) is estimated for all sub-periods of 12 quarters. Thus, 15 sets of regressions have been run over the sample period in order to test the stability of regression coefficients. [START_REF] Giovannini | Exchange Rates and Traded Goods Prices[END_REF] Results from the fixed-window rolling estimation (not reported) indicate a strong instability of all coefficients, but the one of the export-domestic price margin.

Interestingly, price competitiveness coefficients turn to be positive (negative) and statistically significant in the last estimations (first sub-samples). A related question deals with the dating of such a change in the pricing behaviour of Italian exporters. We try to address this issue by using an estimation window of increasing size. In this exercise, all windows end in the last observation of the sample, but they have different starting quarters.

The smallest window covers the last three years (as in the fixed-window rolling estimation), while the largest window embraces the entire sample span (i.e. it coincides with the baseline [START_REF] Giovannini | Exchange Rates and Traded Goods Prices[END_REF] The decision to use 12-quarter sub-periods was the result of a compromise between maximizing the number of regressions and maintaining a reasonable sample size for each regression. estimation). Table 5 shows that the effects of the lagged export-domestic price margin is substantially stable over time, while lagged demand levels enter with the expected sign, albeit they are not statistically significant in most of the regressions. Finally, the effects of the lagged cost competitiveness is positive and statistically significant in the first three regressions (i.e. up to the window 2002q1-2005q2), while the progressive extensions of the sample size translates into a loss of statistical significance and into a change in the sign of the coefficient of 1 t q .

[TABLE 5]

On the grounds of these indications, consistent with the stylised facts discussed in section 3, we split the time span into two sub-samples (1999q1-2001q4 and 2002q1-2005q2). As far as the first period (1999q1-2001q4) is concerned (Table 6), while foreign and domestic demand variables turn to be statistically insignificant, the effect of price competitiveness factors results statistically significant: a 10% increase in the perceived price competition translates into a 0.4% drop for the margin between export and domestic prices. This finding seems to indicate a PTM-type behaviour of Italian exporters that have set prices differently in the Home and Foreign markets according to the fluctuations of price competitiveness, due to both exchange rate movements and cost pressures of competitors.

[TABLE 6]

As far as the second period (2002q1-2005q2) is concerned (Table 7), the estimates depict remarkable differences. Lagged demand variables have the expected signs, while the cost competitiveness indicator becomes positive, albeit statistically not significant. This finding is somewhat surprising, in that it suggests that Italian exporters did not use the price channel to offset the negative consequences coming in this period from the appreciation of the euro and the growing competitive pressure of products of the emerging economies (China and other Far-East countries). Moreover, foreign demand (and to a lesser extent the F o r P e e r R e v i e w [20] domestic one) seems to significantly affect export-domestic price margins, indicating a procyclical pricing policy in the most recent period.

[TABLE 7]

Robustness check

As a check of robustness of our results, we have applied the same econometric procedure but imposing the symmetry and proportionality condition on foreign and domestic demand variables, i.e. using a relative (foreign minus domestic) demand indicator, g . A closer look to the estimated demand coefficients in the baseline model reveals that lagged h and f enter in the export-domestic price margin equation with the opposite sign but similar magnitude (Table 3). Thus, it is possible that the dynamics of export-domestic price margin actually reacts to developments in the domestic and foreign economies in a symmetric way. g coefficient turns to be very similar to (the absolute value of) demand levels coefficients in Table 3.

Finally, neither lagged price competitiveness nor lagged relative demand levels are statistically significant, with magnitudes almost identical to the ones obtained in the baseline model.

[TABLE 8]

Controlling for the role of non-price competitiveness factors, the robustness check confirms their negligible impact in the explanation of the pricing behaviour of Italian exporters. Moreover, it is worthwhile to stress that the recursive structure of the model is now strongly supported in all of the four different specifications (Table 9), corroborating the choice of imposing non-price competitiveness factors as the less endogenous variable F o r P e e r R e v i e w [21] in each system.

[TABLE 9]

Tables 10 and 11 report the estimation of the tri-variate model over the first and the second sub-sample, respectively. In both regressions, exclusion F tests give strong support to our economic priors. Consider the model estimated over the period 1999q1-2001q4, first. Lagged price competitiveness has a negative and statistically significant coefficient, while lagged relative demand is substantially irrelevant. Moreover, the estimated 1 t g coefficient turns to be very close to (the absolute value of) lagged demand levels coefficients reported in Table 4.

[TABLE 10]

Conversely, results from the most recent period (2002q1-2005q2) show that the 1 t g coefficient is statistically significant, with a magnitude (0.137) roughly nine times the one estimated over the period 1999q1-2001q4 (0.016). Furthermore, the price competitiveness indicator enters with the positive sign, albeit it is weakly statistically significant.

[TABLE 11]

Impulse response analysis

Estimated models can be used to assess the relative contribution of mutually orthogonal (structural) factors in explaining the dynamics of export-domestic price margins to support previous interpretations. In the following, structural residuals are extracted from reduced-form disturbances through an identification scheme based on the recursive structure discussed in section 4.1. Dynamic simulations are based on the analysis of impulse response functions (IRFs), which allow revealing the dynamic effects of one-time structural shocks on the export-domestic price margin. The simulation horizon is set equal to eight quarters and conducted over the two sub-samples 1999q1-2001q4 and 2002q1-F o r P e e r R e v i e w [22] 2005q2.

Evidence from the baseline model

Figures 3 and4 illustrate the response of relative prices to a positive shock to price competitiveness, foreign demand, domestic demand and export-domestic price margin from the model estimated over the first and the second sub-sample, respectively.

Confidence bounds at the 95% significance level (dashed lines) are also reported.

Consider the period 1999q1-2001q4, first. The export-domestic price margin reacts negatively one quarter after a cost competitiveness shock; then, the response decreases over time. Since confidence bounds include the baseline path (the horizontal axis), deviations from the pre-shock level after four quarters cannot be judged as statistically relevant at the chosen significance level. Foreign and domestic demand shocks produce negligible effects, while the response to an export-domestic price margin shock is fully absorbed within the third quarter of the simulation horizon, with a half-life of the response equal to one quarter. [START_REF] Goldberg | Goods Prices and Exchange Rates: What Have We Learned?[END_REF]

[FIGURE 3]

The simulation exercise for the period 2002q1-2005q2 produces results rather different from those in Figure 5. While the export-domestic price margin remains substantially inelastic to changes in the domestic demand, a foreign demand shock shifts upward the export-domestic price margin in the first year of simulation. The response is statistically significant and a certain degree of sluggishness in the deviation relative from the pre-shock level can be detected. More interestingly, the effects of a cost competitiveness shock are now positive (but not statistically significant). This would confirm that, during the most recent years, Italian exporters' pricing policy was mainly influenced by cyclical conditions of foreign demand rather than by exchange rate and price competitiveness factors.

Evidence from the trivariate model

Focusing on the first sub-sample (Figure 5), the indications from the IRFs relative to the baseline model (Figure 3) are fully supported by the simulations from its tri-variate counterpart. Conversely, the evidence relative to the period 2002q1-2005q2 (Figure 6)

indicates that the response of export-domestic price margin is positive and statistically significant not only to a relative demand shock but also to a price competitiveness shock. [START_REF] Goldberg | Measuring the Intensity of Competition in Export Markets[END_REF]

[FIGURE 5] [FIGURE 6]

IRFs analysis from the baseline and the tri-variate model allows us to conclude that unanticipated changes in cost competitiveness and relative demand levels appear to exert non-negligible effects on export-domestic price margins. While a typical PTM behaviour emerges over the period 1999q1-2001q4, the influence of cyclical demand conditions seem to prevail during the most recent years. A possible explanation of this quite odd behaviour can be related to an upgrading of the price/quality mix of goods sold abroad following fiercer price competition from low-cost producers and an appreciated exchange rate (the "qualitative barrier" discussed in de Nardis and Pensa, 2004). Such pro-cyclical price policies on foreign markets could have acted as a buffer to compensate the fall of profits in the domestic market, characterized by an extremely weak demand in the last years.

Evidence from a more disaggregate analysis

Dissecting the analysis in two sub-periods allowed us shedding light onto pricing [START_REF] Goldberg | Measuring the Intensity of Competition in Export Markets[END_REF] Lagged reactions to price competitiveness shocks (Figures 3,4 [24] behaviour of Italian exporting firms. We now further investigate on the determinants of pricing policies in order to test a possible heterogeneity across sectors. In doing that, we distinguish between traditional sectors (i.e. those usually referred as "Made-in-Italy", which include sub-sections DB, DC, DI e DN indicating respectively textile products, leather products, non metallic mineral products and furniture) and other sectors (i.e. the remaining sectors included in Table 1). Accordingly, our datasets consist of: 1) a panel of 12 crosssectional observations (4 sectors and 3 regions) and 26 time points for the "traditional sectors" model; 2) a panel of 27 cross-sectional observations (9 sectors and 3 regions) and 26 time points for the "other sectors" model. We compare IRFs from the two models and calculate their differences ("traditional sectors" minus "other sectors") with respect to the sub-samples 1999q1-2001q4 and 2002q1-2005q2 (Figures 7 and8). 21

[FIGURE 7] [FIGURE 8]

We observe a strong heterogeneity not only between the two sub-periods, as discussed previously, but also across sectors. More in details, the increase in export-domestic price margins consequent, in the second sub-period, to a rise in cost competitiveness obstacles turns to be higher in the "traditional sectors" model. Conversely, the export-domestic price margins reactions in the "other sectors" model appear to be more elastic to unanticipated changes in demand levels, albeit the results relative to a domestic demand shock are not significant in the second sub-sample, indicating a homogeneous reaction to this kind of disturbance in both of models. The fact that traditional sectors were those that mainly drove, in the second sub-period, the anomalous response of pricing polices to price [START_REF] Haskel | The Law of One Price -A Case Study[END_REF] Results from the two models (not reported for sake of brevity) indicate that a deterioration of price competitiveness translates into a decrease (increase) of the export-domestic price margin in the first (second) sub-sample, while the time profile of the responses relative to other shocks are consistent with our economic priors. Given that the two samples are independent, IRFs of the differences are equivalent to the difference of IRFs. The same argument holds for the confidence bounds. [25] competitiveness shocks may be indicative of some modification in the specialization of the Italian economy. Traditional sectors were harshly affected by the sharp increase of foreign competition at the beginning of the decade (with the entry of China in the WTO). Rising competitive pressures may have caused within-sector shifts towards upper quality segments of production. As analysed by Coibion et al. (2006), these segments are typically characterised by lower price sensitivity of consumers, more scope for product differentiation and higher sunk costs (including those related to brand investment); all elements that determine a reduction of demand elasticities with respect to lower quality products. It can hence be drawn that, in line with the past adjustment patterns that had characterised Italian specialisation (see de Nardis and Pensa, 2004), surviving exporters in traditional industries were "shielded" from foreign competition thanks to quality differentiation and were hence able to adopt, in the first half of the current decade, pricing policies in international markets (partly) independent of competitors' behaviour.

From a micro to a macroeconomic perspective

A discussion focused only on a firm-based level may tell part of the whole story.

Looking at the macroeconomic consequences of the observed pricing policy in our panel of firms allows interpreting the results in (at least) two additional ways. First, PTM policies are often evoked as a primary source of the empirical rejection of the LOP (Engel, 1993).

The empirical evidence presented in sections 4 and 5 seems to contrast with this view. Short-lived deviations from the baseline path emerging from the IRFs exercise suggest that PTM policies may be pursued only in the very short-run. Moreover, there are no statistically significant responses of the export-domestic price margin to the various shocks when a longer simulation horizon is taken into account. Finally, the extent of the deviations from the baseline path in the IRFs is indeed well below the level predicted by theoretical models based on translog preferences, such as the one proposed by Bergin and Feenstra (2001). As shown in Haskel and Wolf (2001) [26] taxes, and tariffs as well as in other additional factors may allow firms to vary mark-ups over time, although the convergence between prices may be restored in the long-run. In this sense, the results from our study conforms recent findings on threshold mean reversion for sector goods (see Obstfeld and Taylor, 1997; Sarno and Taylor, 2002). Second, a reduced incompleteness of ERPT associated to a limited PTM should have no dramatic consequences on the classical textbook reaction of the current account to exchange rate modifications based on the Marshall-Lerner requirements on export and import price elasticities. Under this point of view, the results of the present study are consistent with the evidence of improvements of the trade balance to real exchange rate depreciations as discussed in Boyd, Caporale and Smith (2001) for the G7 economies.

Conclusions

We revisited the model proposed by Marston (1990) to test PTM of Italian exporting firms over the period 1999q1-2005q2. The model was augmented in the empirical testing to allow for possible influence of non-price obstacles to trade. We looked at the average behaviour of a sample of Italian exporting industrial firms, during a very critical period (the EMU years, since 1999) when a significant reduction of the aggregate Italian market share took place in volume terms.

The use of survey data made it possible to use as relevant variable in the analysis an indicator of the export-domestic price margin for the "same" good produced by the "same" firm, permitting to capture effective price differences from two different transactions made by the same production unit. This is a significant step forward with respect to an analysis based on export unit values, which are affected by unavoidable composition effects and are not consistent with the domestic price indicator adopted as comparison (usually, producer prices). The empirical investigation used panel data VAR F o r P e e r R e v i e w [27] models, which treat all variables in the system as endogenous within a framework allowing for unobserved individual heterogeneity. Impulse-response analysis helped assessing the reaction of export-domestic price margins to unanticipated changes in cost competitiveness and demand levels.

These factors appeared to exert non-negligible effects. Specifically, for the period 1999q1-2001q2 a typical PTM behaviour emerged, while during the period 2002q1-2005q2 the influence of cyclical demand conditions prevailed, inducing exporting Italian firms to increase their export-domestic price margins to take advantage of a more favourable foreign demand in face of a strong deterioration of their cost competitiveness. However, IRFs exercises showed low persistent reactions of variables once shocked, suggesting short-lived PTM policies. Moreover, taking into account sector heterogeneity, we found indications that the anomalous price setting in the second sub-period was mainly due to traditional ("Made-in-Italy") sectors, i.e. those most hit by external competitive pressures; a phenomenon that we relate to likely quality upgrading (with shifts in quality segments characterised by lower demand elasticities) induced by increased foreign competition.

From a macroeconomic point of view, consequences of a limited PTM (not only in timing but also in intensity) are at least twofold. First, PTM policies should not be relevant in explaining long-run deviations from the LOP. Second, no dramatic effects on the classical textbook reaction of the current account to exchange rate modifications should be observed. Both results are consistent with the most recent empirical literature.

H F H F it t it t it t it it t P E P E P P E t it R E E R = =
Indicating by F it M the variable mark-up over marginal cost in the Foreign market, explicit formulations of the elasticities on the R.H.S. of (A1) are the following where

( ) ( ) ( ) ( ) 1 F F F F F F it it t it it it it t it it F it t F F F F F F it it t it it it it t it it M P E MC X X P E P MC P E M P E MC X X P E P MC = ( ) ( 1)
H F F F F H it t it
( ) F F it it t M P E
is the elasticity of the mark-up practiced in the Foreign market with respect to the (foreign currency) price made in that market (

F it t P E ).
This elasticity is negative, provided the demand schedule is less convex than a constant elasticity curve (such that the mark-up reduces when the price rises and the quantity falls).

As for the other terms in the expressions,

F it it MC X
is the (positive) elasticity of marginal costs with respect to foreign sales,

( ) F F it it t X P E
is the (negative) elasticity of foreign sales with respect to foreign currency prices practiced in the Foreign market, and

F it it
P MC and

H it it P MC
are the (positive) elasticities of (domestic currency) prices practiced in Foreign and Home markets with respect to the (common) marginal cost. Given these signs, both

F it t
P E and H it t P E are positive (and less than 1), indicating positive reactions of the (domestic currency) prices in the Foreign and Home markets to exchange rate changes.

As to the sign of the elasticity of the export-domestic price margin to exchange rate changes, expression (A1) can be written as Note. See Table 3. Note. See Table 6. Note. See Table 6.

F F F F F H F it it t it it it it it it it it t H F it t it F F F F F F H F F F it it it it it it it it it it it it it it t t ( ) ( ) ( ) (1 )(1 )

  , 5 and 6) might be considered as consistent with models based on sticky prices adjustment due to menu-cost-driven pricing behaviour or other nominal rigidities (see, among others,Ghosh and Wolf, 1994), although in the study conducted in a different context (pricing behaviour of Italian firms in the domestic market),Fabiani et al. (2004) find the price inertia in manufacturing relates mainly to the existence of nominal contracts and to coordination failures.

Figure 1 .

 1 Figure 1. Export unit values (solid line) and export-domestic price margin (dashed line). Italy: 1991q1-2005q2.

Figure 2 .

 2 Figure 2. Price competitiveness indicator (solid line) and export-domestic price margin (dashed line). Italy: 1991q1-2005q2.

Figure 3 .

 3 Figure 3. Baseline Panel VAR model. Impulse response analysis: 1999q1-2001q4.

Figure 4 .

 4 Figure 4. Baseline Panel VAR model. Impulse response analysis: 2002q1-2005q2.

Figure 5 .

 5 Figure 5. Tri-variate Panel VAR model. Impulse response analysis: 1999q1-2001q4.

Figure 6 .

 6 Figure 6. Tri-variate Panel VAR model. Impulse response analysis: 2002q1-2005q2.

Figure 7 .

 7 Figure 7. Sector Panel VAR models. Differences in impulse-responses ("Traditional sectors" minus "Other sectors"): 1999q1-2001q4. Percentage values.

Figure 8 .

 8 Figure 8. Sector Panel VAR models. Differences in impulse-responses ("Traditional sectors" minus "Other sectors"): 2002q1-2005q2. Percentage values.

Table 2

 2

presents some descriptive statistics of the four qualitative series we use to test relation (4). The indicators refer to the full post-euro period 1999q1-2005q2 (upper panel) as well as the two sub-samples 1999q1-2001q4 and 2002q1-2005q2 (central and lower panel).

Table 8

 8

presents GMM estimates for the tri-variate panel VAR model, over the full sample. Three main findings emerge. First, exclusion tests indicate that the theoretical structure of reference is not rejected by the data. Second, the magnitude of 1 t

  , differences in local distribution costs, local

	F o r
	P
	e
	e r
	R e v
	i e
	w

Table 1 -ISAE survey on exporting firms.

 1

	(a) Number of firms by sector and by region	North West	North East	Centre	Total by sector
	DA -Food products, beverages, tobacco	24	40	15	79
	DB -Textile, textile products	59	61	68	188
	DC -Leather, leather products	7	25	43	75
	DD -Wood, wood products	8	22	10	40
	DE -Pulp, paper, paper product, publishing, printing	13	21	17	51
	DG -Chemicals, chemical products, man-made fibres	25	15	21	61
	DH -Rubbers and plastic products	32	27	17	76
	DI -Other non-metallic mineral products	20	35	23	78
	DJ -Basic metals, fabricated metal products	61	73	27	161
	DK -Machinery and equipment n.e.c.	47	94	39	180
	DL -Electrical and optical equipment	41	35	25	101
	DM -Transport equipment	31	19	13	63
	DN -Furniture, n.e.c.	18	64	40	122
	Total by region	386	531	358	1275
	(b) Definition of the regions
	North West	Piemonte, Lombardia, Liguria, Valle D'Aosta
	North East	Friuli-Venezia Giulia, Veneto, Emilia Romagna, Trentino Alto-Adige
	Centre	Lazio, Toscana, Marche, Umbria
	Note. Classification by sector according to NACE (rev. 1.1) -ATECO 2002.

Table 2 -

 2 Descriptive statistics.

	Percentile

Table 3 -Baseline Panel VAR model. Estimation results: 1999q1-2005q2.

 3

				t q	f	t	t h	t r
	t q	1	0.3449 (0.0331)	-0.0496 (0.0127)	-0.0465 (0.0108)	-0.0037 (0.0131)
	f	t	1	-0.1640 (0.1009)	0.5593 (0.0388)	0.1523 (0.0328)	0.0449 (0.0400)
	t h	1	0.0184 (0.1147)	0.0842 (0.0441)	0.4583 (0.0373)	-0.0561 (0.0454)
	t r	1	0.0903 (0.0804)	0.0159 (0.0309)	0.0045 (0.0262)	0.2794 (0.0318)
	Number of Observations F-test	936 29.08 [0.00]	936 119.40 [0.00]	936 121.92 [0.00]	936 19.96 [0.00]
	Single-equation	ft-1=ht-1=rt-1=0 F(3,3728)=1.82 [0.14]	Exclusion Tests ht-1=rt-1=0 F(2,3728)=1.91 [0.15]	rt-1=0 F(1,3728)=0.03 [0.86]	. .
	System			F(6,3728)=1.55 [0.16]
	Note. The system includes price competitiveness (q), foreign demand level (h), domestic demand level (h) and
	export-domestic price margin (r). Standard errors (p-values) are reported in parentheses (square brackets). In single equation (system) exclusion tests, under the null hypothesis, lagged variables are deleted separately
	(contemporaneously) in each equation of the system.

Table 4 -Baseline Panel VAR model augmented by trade costs. Export-domestic price margin equation. Estimation results: 1999q1-2005q2.

 4

	Panel [A]		Specification of the non-price competitiveness obstacle i
				time	fin	adm	oth
	i t x	1	-0.0019 (0.0128)	0.0094 (0.0134)	-0.0254 (0.0129)	-0.0189 (0.0119)
	t q	1	-0.0036 (0.0131)	-0.0046 (0.0132)	-0.0033 (0.0131)	0.0010 (0.0131)
	f	t	1	0.0455 (0.0402)	0.0454 (0.0400)	0.0548 (0.0401)	0.0372 (0.0403)
	t h	1	-0.0557 (0.0455)	-0.0569 (0.0454)	-0.0585 (0.0454)	-0.0704 (0.0460)
	t r	1	0.2793 (0.0319)	0.2777 (0.0319)	0.2797 (0.0318)	0.2801 (0.0318)
	Panel [B]		Exclusion Tests
				time	fin	adm	oth
	Single equation
	qt-1=ft-1=ht-1=rt-1=0 F(4,4655)	8.51 [0.00]	1.08 [0.36]	2.45 [0.04]	16.5 [0.00]
	ft-1=ht-1=rt-1=0 F(3,4655)	1.64 [0.18]	1.75 [0.15]	1.80 [0.14]	0.96 [0.41]
	ht-1=rt-1=0 F(2,4655)	1.63 [0.20]	1.93 [0.14]	2.04 [0.13]	0.54 [0.58]
	rt-1=0 F(1,4655)	0.05 [0.83]	0.05 [0.83]	0.03 [0.86]	0.04 [0.84]
	System
	F(10,4655)	4.23 [0.00]	1.35 [0.20]	1.93 [0.04]	6.99 [0.00]
	Note. Panel [A]: GMM-estimates of the export-domestic price margin equation. The system includes non-price competitiveness (x), price competitiveness (q), foreign demand level (h), domestic demand level (h) and
	export-domestic price margin (r). Standard errors (p-values) are reported in parentheses (square brackets).
	Panel [B]: exclusion tests. In single equation (system) exclusion tests, under the null hypothesis, lagged
	variables are deleted separately (contemporaneously) in each equation of the system.

Table 5 -Baseline Panel VAR model. Export-domestic price margin equation. Rolling estimation results.

 5

		t q	1	f	t	1	t h	1	t r	1
	2002q3-2005q2	0.0317	(0.0187)	0.1879		(0.0581)	-0.0987	(0.0708)	0.1763	(0.0481)
	2002q2-2005q2	0.0293	(0.0174)	0.1494		(0.0555)	-0.0909	(0.0680)	0.1712	(0.0438)
	2002q1-2005q2	0.0293	(0.0164)	0.1451		(0.0536)	-0.1139	(0.0662)	0.2384	(0.0428)
	2001q4-2005q2	0.0152	(0.0156)	0.1010		(0.0520)	-0.0869	(0.0649)	0.2855	(0.0409)
	2001q3-2005q2	0.0187	(0.0154)	0.0861		(0.0502)	-0.0959	(0.0619)	0.2710	(0.0405)
	2001q2-2005q2	0.0054	(0.0147)	0.0523		(0.0481)	-0.0781	(0.0593)	0.2810	(0.0382)
	2001q1-2005q2	-0.0025	(0.0145)	0.0548		(0.0475)	-0.1042	(0.0587)	0.2776	(0.0383)
	2000q4-2005q2	-0.0039	(0.0141)	0.0494		(0.0444)	-0.0907	(0.0559)	0.2900	(0.0366)
	2000q3-2005q2	-0.0075	(0.0138)	0.0538		(0.0405)	-0.1014	(0.0525)	0.2916	(0.0359)
	2000q2-2005q2	-0.0100	(0.0135)	0.0371		(0.0403)	-0.0603	(0.0489)	0.2858	(0.0347)
	2000q1-2005q2	-0.0070	(0.0132)	0.0378		(0.0388)	-0.0718	(0.0472)	0.2855	(0.0335)
	1999q4-2005q2	-0.0060	(0.0129)	0.0505		(0.0382)	-0.0620	(0.0469)	0.2860	(0.0329)
	1999q3-2005q2	-0.0042	(0.0128)	0.0465		(0.0378)	-0.0462	(0.0458)	0.2761	(0.0327)
	1999q2-2005q2	-0.0026	(0.0124)	0.0542		(0.0369)	-0.0564	(0.0442)	0.2716	(0.0323)
	1999q1-2005q2	-0.0037	(0.0131)	0.0449		(0.0400)	-0.0561	(0.0454)	0.2794	(0.0318)
	Note. The system includes price competitiveness (q), foreign demand level (h), domestic demand level (h) and
	export-domestic price margin (r). The estimation horizon is indicated in the first column. Standard errors are reported in parentheses.

Table 6 -Baseline Panel VAR model. Estimation results: 1999q1-2001q4.

 6

				t q	f	t	t h	t r
	t q	1	0.1990 (0.0500)	-0.0503 (0.0194)	-0.0165 (0.0171)	-0.0420 (0.0206)
	f	t	1	-0.0780 (0.1456)	0.5293 (0.0564)	0.1613 (0.0497)	0.0122 (0.0601)
	t h	1	0.2670 (0.1582)	0.1116 (0.0613)	0.4387 (0.0541)	-0.0223 (0.0653)
	t r	1	0.1380 (0.1140)	0.0244 (0.0442)	0.0256 (0.0390)	0.1917 (0.0471)
	Number of Observations F-test	390 5.59 [0.00]	390 61.09 [0.00]	390 60.12 [0.00]	390 5.58 [0.00]
	Single-equation	ft-1=ht-1=rt-1=0 F(3,1544)=1.80 [0.14]	Exclusion Tests ht-1=rt-1=0 F(2,1544)=1.78 [0.17]	rt-1=0 F(1,1544)=0.43 [0.51]	. .
	System			F(6,1544)=1.57 [0.15]

Table 7 -Baseline Panel VAR model. Estimation results: 2002q1-2005q2.

 7

				t q	f	t	t h	t r
	t q	1	0.2818 (0.0412)	-0.0153 (0.0155)	-0.0343 (0.0127)	0.0293 (0.0164)
	f	t	1	0.1650 (0.1344)	0.4063 (0.0507)	0.0959 (0.0414)	0.1451 (0.0536)
	t h	1	-0.3159 (0.1658)	-0.0618 (0.0626)	0.2186 (0.0511)	-0.1139 (0.0662)
	t r	1	0.0313 (0.1073)	-0.0165 (0.0405)	-0.0477 (0.0331)	0.2384 (0.0428)
	Number of Observations F-test	468 13.85 [0.00]	468 20.78 [0.00]	468 16.75 [0.00]	468 11.94 [0.00]
	Single-equation	ft-1=ht-1=rt-1=0 F(3,1856)=1.34 [0.26]	Exclusion Tests ht-1=rt-1=0 F(2,1856)=0.52 [0.59]	rt-1=0 F(1,1856)=2.08 [0.15]	. .
	System			F(6,1856)=1.19 [0.31]
	Note. See Table 3.

Table 8 -Tri-variate Panel VAR model. Estimation results: 1999q1-2005q2.

 8

				t q	g	t	t r
	t q	1	0.3284 (0.0304)	-0.0074 (0.0102)	-0.0028 (0.0120)
	g	t	1	-0.1819 (0.0879)	0.4161 (0.0295)	0.0527 (0.0348)
	t r	1	0.0716 (0.0756)	0.0232 (0.0254)	0.2828 (0.0299)
	Number of Observations F-test	936 40.77 [0.00]	936 67.97 [0.00]	936 31.46 [0.00]
	Single-equation	gt-1=rt-1=0 F(2,2799)=2.46 [0.09]	Exclusion Tests F(2,2799)=0.84 [0.36] rt-1=0	. .
	System		F(3,2799)=1.92 [0.12]
	Note. The system includes price competitiveness (q), relative demand level (g), and export-domestic price
	margin (r). Standard errors (p-values) are reported in parentheses (square brackets). In single equation (system) exclusion tests, under the null hypothesis, lagged variables are deleted separately
	(contemporaneously) in each equation of the system.

Table 9 -Tri-variate Panel VAR model augmented by trade costs. Export-domestic price margin equation. Estimation results: 1999q1-2005q2.

 9

	Panel [A]		Specification of the non-price competitiveness obstacle i
				time	fin	adm	oth
	i t x	1	-0.0026 (0.0125)	0.1306 (0.2302)	-0.0476 (0.0620)	0.0345 (0.0306)
	t q	1	-0.0034 (0.0131)	-0.0157 (0.0255)	-0.0031 (0.0131)	-0.0125 (0.0154)
	g	t	1	0.0487 (0.0385)	0.0571 (0.0432)	0.0626 (0.0428)	0.0500 (0.0388)
	t r	1	0.2794 (0.0319)	0.2560 (0.0534)	0.2799 (0.0319)	0.2784 (0.0322)
	Panel [B]		Exclusion Tests
				time	fin	adm	oth
	Single equation
	qt-1=gt-1=rt-1=0 F(3,3728)	3.23 [0.02]	0.56 [0.64]	0.59 [0.62]	1.55 [0.20]
	gt-1=rt-1=0 F(2,3728)	1.30 [0.27]	0.54 [0.58]	0.79 [0.45]	0.60 [0.55]
	rt-1=0 F(1,3728)	0.22 [0.64]	0.66 [0.41]	0.14 [0.71]	0.17 [0.68]
	System
	F(6, 3728)	2.09 [0.05]	0.57 [0.75]	0.58 [0.75]	1.00 [0.42]
	Note. Panel [A]: GMM-estimates of the export-domestic price margin equation. The system includes non-price competitiveness (x), price competitiveness (q), relative demand level (g) and export-domestic price
	margin (r). Standard errors (p-values) are reported in parentheses (square brackets). Panel [B]: exclusion tests.
	In single equation (system) exclusion tests, under the null hypothesis, lagged variables are deleted separately
	(contemporaneously) in each equation of the system.

Table 10 -Tri-variate Panel VAR model. Estimation results: 1999q1-2001q4.

 10

				t q	g	t	t r
	t q	1	0.2097 (0.0497)	-0.0315 (0.0167)	-0.0426 (0.0204)
	g	t	1	-0.1448 (0.1402)	0.3535 (0.0471)	0.0158 (0.0577)
	t r	1	0.1514 (0.1139)	0.0017 (0.0383)	0.1909 (0.0469)
	Number of Observations F-test	390 6.51 [0.00]	390 19.74 [0.00]	390 7.44 [0.00]
	Single-equation	gt-1=rt-1=0 F(2,1161)=1.33 [0.26]	Exclusion Tests F(1,1161)=0.00 [0.96] rt-1=0	. .
	System		F(3,1161)=0.89 [0.45]

Table 11 -Tri-variate Panel VAR model. Estimation results: 2002q1-2005q2.

 11

				t q	g	t	t r
	t q	1	0.2870 (0.0409)	0.0180 (0.0136)	0.0282 (0.0163)
	g	t	1	0.2065 (0.1283)	0.3022 (0.0426)	0.1365 (0.0512)
	t r	1	0.0385 (0.1070)	0.0298 (0.0355)	0.2370 (0.0427)
	Number of Observations F-test	468 18.11 [0.00]	468 18.93 [0.00]	468 15.84 [0.00]
	Single-equation	gt-1=rt-1=0 F(2,1395)=1.46 [0.23]	Exclusion Tests F(1,1395)=0.70 [0.40] rt-1=0	. .
	System		F(3,1395)=1.21 [0.31]

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The inclusion of non competitiveness factors (or trade costs) in system (9) is modelled by treating that variable as the most exogenous, in order to preserve the causal linkage implied by relations (5)-[START_REF] Caves | World Trade and Payments[END_REF].

In all models, lagged coefficients, of order greater than one, turn to be not statistically significant at the usual significance levels.

Half-life is defined as the number of quarters which have to pass before the deviation from the steady-state falls to half the size of the initial shock.

Appendix

The elasticity of the export-domestic price margin with respect to the exchange rate is given by (A1)