Fugarolas Alvarez-Ude

Guadalupe ; Game

David Matesanz Gómez

Guadalupe Fugarolas Álvarez-Ude

Guadalupe Fugarolas Álvarez

Econometric Methods: Multiple/Simultaneous Equation Models < C -Mathematical and Quantitative Methods, F31 -Foreign Exchange < F3 -International Finance < F -International Economics, F43 -Economic Growth of Open Economies < F4 -Macroeconomic Aspects of International Trade and Finance < F -International Economics

Keywords: Argentina, Marshall-Lerner, J-Curve, Cointegration, Impulse Response Analysis, Variance Decomposition Argentina, Marshall-Lerner, J-Curve, cointegration and impulse response analysis JEL Classification: C22, C32, F31, F43 Argentina, Marshall-Lerner, J-Curve, cointegration, impulse response analysis and variance decomposition. JEL Classification: C22, C32, F31, F43

Using multivariate cointegration tests for non-stationary data and vector error correction models, this paper examines the determinants of trade balance for Argentina over the last forty to fifty years. Our investigation confirms the existence of long-run relationships among trade balance, Real Exchange Rate (RER) and foreign and domestic incomes for Argentina during different real exchange rate management policies. Based on the estimations, the Marshall-Lerner condition is examined and, by means of impulse response functions, we trace the effect of a one-time shock to the RER on the trade balance checking the J-curve pattern.

I. Introduction.

The management of the Exchange Rate has been a critical issue for the economic policy, especially in developing countries. In defining an exchange rate policy, one of the most important considerations is the responsiveness of Trade Balance (TB) to changes in terms of trade or, more generally, in Real Exchange Rate (RER). The effects of currency depreciation on a country's trade balance have centred an important and on-going debate in the international economic literature. Precisely, this issue has been traditionally studied in the Marshall-Lerner condition (ML) and the so called J-curve framework. According to the ML condition, currency devaluation improves the trade balance in the long run only if the sum of the absolute values of imports and exports demand price elasticities exceeds unit. However, due to the lag dynamics structure, TB can worsen in the short-run because of the inelastic demand for imports and exports in the immediate aftermath of an exchange rate change. In this case, TB is said to follow the J-curve pattern.

A wide number of papers has tested the ML condition and J-curve. Bahamani-Oskooee and Ratha ( 2004) is a good survey on ML and J-curve showing non conclusive results on this issue. In Bahamani-Oskooee and Niroomand (1998) the ML condition is addressed for almost thirty developed and developing countries over the period 1960-92. Gomes and Paz (2005) and [START_REF] Tsen | Is there a long-run relationship between trade balance and terms of trade? the case of Malaysia[END_REF] demonstrate the existence of a long run relationship among TB, real exchange rate, foreign and domestic income for Brazil in the nineties and for Malaysia during 1965-2002 respectively. Mahmud et al. (2004) suggest that, though during fixed exchange rates periods ML condition is supported, it is less probable in flexible exchange periods. Almost all these papers find support for the existence of the J-curve pattern except Narayan (2004) who does not confirm the ML condition in New Zealand.

As far as we know, there is only one paper that deals with ML condition in Argentina, namely Lopez y Cruz (2000). This study supports the relationship among TB, real exchange rate, foreign and domestic income for the argentine economy during the period 1965-1995, but it does not analyse the short-run adjustment through the J-curve phenomenon. In this paper, we test not only the validity of ML condition but also the existence of a J-curve pattern for the argentine economy from 1962 up to nowadays discerning three cut-off points due to different periods of exchange and trade policies implemented in Argentina: 1990 reveals a clear change in argentine exchange rate regime when the Convertibility Plan in April 1991 fixed the Argentine peso to US dollar in a currency board system; 2000 evidences a slowdown triggering the sharp crises in 2002 and the end of the fixed exchange rate regime period after an intense devaluation of the currency in the first days of 2002. Finally, we have analysed 1978-05 period to capture relationships during the change in Argentina's trade policy making towards a liberalization phase, away from the import substitution protectionism period in 1978. We note that three of the periods we have tested, 1962-2005, 1962-2000 and 1978-05, include the Convertibility Plan stage which implied a fixed exchange rate policy with US dollar. The other one, , showed more flexible options on the currency.

Hence, the aim of the paper consists on empirically verify the ML condition and the Jcurve pattern for Argentina. To this purpose, we exploit some econometric techniques using time series unit root tests to examine the stationary properties of the data and the Johansen and Juselius procedure (1991) to search for multivariate cointegrating relationships from a robust and stable vector autoregressive (VAR) modelling specification. Based on a vector error-correction (VECM) formulation and generalized impulse response function, we analyze the long and short term trade balance dynamic model for Argentina.

Taking into account the slow long run balance of payments constrained economic growth of Argentina suggested in several papers (see, for instance, López and Cruz (2000) and Perraton (2003) and the key role of the exchange rate rule on the Argentine development during the last decades, specially since 1991, we highlight the importance of this paper for policy-making decisions on exchange rate regime in the argentine economic development. The contributions of the paper are twofold. The first is to test ML and J-curve phenomenon for Argentina in different periods. The second is to provide new insights on the effects of fixed and flexible exchange rate regimes in the TB and, therefore, in the relationships between RER and long term economic growth.

The rest of the paper is organized as follows. Section 2 sets our model specification.

In Section 3 we present the econometric methodology and our empirical results for Argentina. Finally, Section 4 concludes the paper.

II. Theoretical framework

Following the straightforward modelling introduced by Rose and Yellen (1989) and Rose (1991), a country's trade balance behaviour is built into a reduced form function directly depending on the real exchange rate and the real domestic and foreign incomes.

( ) ε η * * t t t Y E P P X ⋅ ⋅ = (1) ( ) π γ t t t Y P E P M ⋅ ⋅ = * (2)
where X and M are the volume of exports and imports, E is the nominal exchange rate and . Precisely, the coefficient of t e ln indicates whether the ML condition is fulfilled. Note that here η and γ are assumed to be negative and ε and π are positive so ML holds whenever ϑ is positive indicating that a higher real exchange rate, that is, a real depreciation, appears to improve the trade balance over time.

Our major concern is focused on the time-path dynamics of the trade balance analyzing both the long run and short term impact of changes in the exchange rate of the Argentina's currency checking, in selected periods over the sample 1962-2005, whether it induced an upgrading or a worsening of the country' s trade position.

III. Methodology, empirical results and discussion.

In this section we present the estimation techniques as well as the empirical results

testing not only the long-and short-terms impacts of real exchange rate on the trade In keeping with the trade balance evolution encapsulated in equation ( 5), we assume that the long-run cointegrating testable relationship takes the following log-linear form

t t t t o t u RER Y Y TB + + + + = ln ln ln ln 3 * 2 1 β β β β (6)
where t u is the random error term. In this regard, likelihood-based inference in cointegrating vector autoregressive models is required in order to determine whether this linear combination of non-stationary data series of TB, real exchange rate and foreign and domestic incomes is stationary and, therefore, describes a stable and non-spurious regression.

In so doing, we run univariate Dickey-Fuller (DF) and the Augmented Dickey-Fuller (ADF) unit root tests for each variable that enters the multivariate model following the decision tree process proposed by Charemza and Deadman (1992) testing for the significance of trend and drift together with non-stationary and assuming that the choice of lags is based to guarantee non-residual autocorrelation. The results over the period 1962-2005 are reported in neither trends nor drifts should be entered in the cointegration space. Though not reported here, we have checked that all the variables are I(1) series for each of the short time spans considered. Note that, if the series have not contain a unit root, the cointegration test will lead to a number of cointegration vectors equal to four which is the number of endogenous variables.

Turning to cointegration analysis, we implement the cointegration test developed by Johansen (1988) and Johansen and Juselius (1990) which applies maximum likelihood to a VAR model assuming that the errors are Gaussian. Essentially, testing the existence of this long-run relationship requires a pth-order structural and dynamic VAR model on the variables under consideration which, in keeping with Granger representation theorem, can be written as an unrestricted VEC involving up to p lags

+ ∆ + ∆ + ∆ + ∆ + = ∆ - = = - = = - - j t p j k p j j t k p j p j j t k j t k t RER Y Y TB TB ln ln ln ln ln 1 1 * 1 1 0 φ ϕ γ θ δ [ ] t t t t o t RER Y Y TB ε β β β β λ + - - - - + - - - - 1 3 * 1 2 1 1 1 ln ln ln ln (7)
where ∆ is the first difference operator, λ provides information on the speed-ofadjustment coefficient to long-run equilibrium and t ε is a purely white noise term.

To this purpose, we firstly proceed by setting the appropriate lag-length in order to ensure the gaussian structure of the residuals in the VECM. We note that when the errors are not independent normal, it has been found that the Johansen method has a greater probability of rejecting the null of non cointegration even when there are no cointegrationg relations. In this fashion, we have selected the number of lags indicated by Schwartz (BIC) and Hannah-Quinn (HQ) criteria in all stages except for the term 1978-2005 where lags were chosen on the basis of the Akaike (AIC) criterion which has provided better results for Gaussian errors. On the basis of these information criteria, the best lag order is one year for the longer periods, 1962-2005 and 1962-2000, and two years for the shorter ones, 1978-2005 and 1962-1990. For brevity the results are not reported here. Following the Box and Jenkins (1970) 4) for every sample. We remark that the non-standard critical values are taken from Osterwald-Lenum (1992) which differ slightly from those reported in Johansen and Juselius (1990). Both statistics 1 confirm the existence of at most one cointegrating equilibrium relationship among the logarithms of TB, national and foreign income and real exchange rate at the 5% level. b , measures the trade balance elasticity with respect to the argentine income, the US income and the RER respectively, that is, the percentage change in TB for one unit percentage change in each of the explanatory variables. As expected, in all cases trade balance is negatively associated with domestic output and positively associated with international output. However, except for the sub-sample , in all periods trade balance and real exchange rate are found to be positively cointegrated and the elasticity coefficient 3 b is positive and statistically significant at the 95% confidence level.

These results hint us to conclude that, in these terms, the Marshall-Lerner condition is fulfilled and an increase in the real exchange rate has not only influenced but also has improved the Argentinean trade balance. Interestingly, ML condition only holds when the fix exchange rate period during Convertibility Plan in the nineties is included (observe that only in 2002 the fix parity dollar-peso was abandoned and ML holds in all periods counting the Convertibility Plan 2 ) and, on the contrary, it is not fulfilled in previous periods when the exchange rate policy has shown more flexible systems. In this sense, these results are aligned with those of Mahmud, et al. (2004) for developed countries and of Gomes and Paz (2005) for Brazil during Real crawling-peg exchange 1 Johansen and Juselius (1990) suggest that, in case that the statistics yield conflicting results, the maximum eigenvalue test may be better. 2 In fact, we have tested different periods and ML condition begins to be fulfilled after 1994. Moreover, in table (4), we can observe that when ML condition holds, the foreign and domestic income coefficients, 1 b and 2 b , are not statistically significant at the 5% level. However, in the 1962-90 period, when ML rule is not verified, income coefficients are significant indicating that during not fixed exchange rate periods, TB is more influenced by foreign and domestic income and therefore by foreign and domestic output growth rythms. From our point of view, these results are suggesting that currency devaluation in 2002 was necessary to improve the TB and recover an economic growth path more consistent with the balance of payments constraint that Argentine economy seems to bear in the long run (López and Cruz (2000) and Perraton (2003). Finally, we note that the significance of the parameter λ in all samples indicates that trade balance changes does not even up changes in past disequilibrium of either national and foreign income or real exchange rate during the same period.

We have checked that in all periods the estimated VEC models with one cointegrating relations are stable 3 and that the innovations are contemporaneously

RER ln

innovations. The results over the hold period are represented in figure 1 and suggest that for Argentina we do not find a negative effect of devaluation on the trade balance and the most important improvements on the TB have around four to five years of duration. However, for the period 1962-1990, Figure 2 shows that the effect is negative firstly from the fourth to the sixth year and again from the ninth to the eleventh year. We note that is precisely the unique sample where it is not verified the Marshall-Lerner condition. Hence, with the exception of the sub-period before the Convertibility Plan, no evidence in favour of the J-curve short term TB adjustment was found for Argentina, by using annual data. 3 The stability of the estimated VAR and VEC has been checked in each of the sub-periods from the inverse kp roots of the characteristic AR polynomial, where k is the number of endogenous variables and p is the largest one. The stability condition is verified if all the roots have modulus less than one. In a VEC estimation with r cointegration relations this implies that kr roots should be equal to unity, In this paper we assess the long and short run effects of real exchange rate on the Argentinean TB in a long period beginning in 1962. By using VAR-based cointegration tests and impulse response functions, we show that ML condition is fulfilled in the periods including fix exchange rate regime policy but not in those periods when exchange rate has shown more flexible policies. This result coincides with those reported by Mahmud et al. (2004) for developed countries. In the short run, Argentine TB has not usually followed the J-curve pattern of adjustment. Only before the Convertibility Plan launching in 1991, the impact of TCR is negative on the long-term and short-run TB showing that though the ML condition does not hold a J-curve-type phenomenon is observed.

A policy-making implication of our results suggests that, likely, currency devaluation in 2002 (and, therefore, the abandon of the currency board implemented in the Convertibility Plan) was necessary for improving TB and recovering a more sustainable economic growth path. In this sense, flexible exchange rate policies seems to be necessary to induce a balance of payments long run sustainability and, therefore, for argentine economic development. A wide number of papers have tested the ML condition and J-curve for developed and developing countries. There are two strands of the empirical literature on the issue depending on whether aggregate or bilateral trade information is used. On one hand, those works testing ML condition and J-curve pattern that have used country exports and imports aggregate data to assess the impact of currency depreciation on the trade balance.

F

0 : 0 = δ H 0 : 1 < δ H (i) t m i i t i t t y y t y ε α δ β β + ∆ + + + = ∆ = - - 1 1 2 1 ) ( (ii) t m i i t i t t y y y ε α δ β + ∆ + + = ∆ = - - 1 1 1 ) ( (iii) t m i i t i t t y y y ε α δ + ∆ + = ∆ = - - 1 1 ) ( variable k Model (i) Model (ii) Model (iii) 3 Φ tc t 1 Φ c t
Among this string of works, without searching for an exhaustive review, we could cite Mahmud et al. (2004) suggest that, though during fixed exchange rates periods ML condition is supported, it is less probable in flexible exchange periods. Narayan (2004) does not confirm the ML condition in New Zealand. On the other hand, there are studies that assessed the impact of currency depreciation of a country on their most important 2006) find mixed effects on the J-curve phenomenon and ML condition among the United Kingdom and their twenty major partners. [START_REF] Narayan | Examining the relationship between trade balance and exchange rate: the case of China' s trade with the USA[END_REF] finds evidence of ML condition between China and its trade flows with US but does not confirm the J-curve pattern. Finally, Bahamani-Oskooee and Ratha ( 2004) is a good survey on ML and J-curve showing non conclusive results on this issue.

As far as we know, there is only one paper that deals with ML condition in Argentina, namely Lopez y Cruz (2000). This study supports the relationship among TB, real exchange rate, foreign and domestic income for the Argentine economy during the period 1965-1995, but it does not analyse the short-run adjustment through the J-curve phenomenon. In this paper, we test not only the validity of ML condition but also the In particular, we address that, under the regime of managed float, foreign income has also been a crucial factor in the trade balance dynamics and, therefore, its variability should not be mainly attributed to real exchange shocks, as we demonstrate that it has occurred in those periods running over the fix-rate policy-making

The rest of the paper is organized as follows. Section 2 sets our model specification.

In Section 3 we present the econometric methodology and our empirical results for Argentina. Finally, Section 4 concludes the paper.

II. Theoretical framework

Following the straightforward modelling introduced by Rose and Yellen (1989) and Rose (1991), a country's trade balance behaviour is built into a reduced form function directly depending on the real exchange rate and the real domestic and foreign incomes.

We begin with a standard model specification for export and import demand functions indicates whether the ML condition is fulfilled. Note that here η and γ are assumed to be negative and ε and π are positive so ML holds whenever ϑ is positive indicating that a higher real exchange rate, that is, a real depreciation, appears to improve the trade balance over time.

( ) ε η * * t t t Y E P P X ⋅ ⋅ = (
Our major concern is focused on the time-path performance of the trade balance analyzing both the long-run and short term impact of changes in the exchange rate of the Argentina's currency checking, whether it induced an upgrading or a worsening of the country' s trade position.

III. Methodology, empirical results and discussion.

In this section we present the estimation techniques as well as the empirical results on the dynamics of trade balance for Argentina in selected sub-periods over the whole sample 1962-2005. Taking into account its interrelation with real exchange rate, the dynamic specification of the trade balance is assumed to be related to the lagged values of real exchange rate in addition to other income variables. As long as we are interested in examining the long-run as well as the short run effects of real depreciations, an error correction model is estimated. In keeping with the trade balance evolution encapsulated in equation ( 5), we assume that the long-run cointegrating testable relationship takes the following log-linear form

t t t t o t u RER Y Y TB + + + + = ln ln ln ln 3 * 2 1 β β β β (6)
where t u is the random error term. We note that it is expected that an estimate of 1 β will be positive as long as an increase in the Argentine income usually results in a higher demand for imports. By the same token, a raise in foreign growth uses to induce an increase in the exports demand so a negative estimate of 2 β is awaited. Depending on whether a higher RER improves or deteriorates the trade balance, the coefficient of 3 β will be positive or negative respectively.

2 Despite the USA has been the major trading partner for Argentina in the analysed period (for instance, in 1980 USA represent 31% of Argentinian exports and imports, in 2000 this percentage was 30,5%, only Brazil, during the nineties has been more important in the Argentinian trade balance), we have extended the same analysis by considering as "foreign income" the World GDP volume index from the data statistics provided by The World Bank. The long and the short-run analysis yield estimations which are lining up with these ones reported in this paper. These estimations can be obtained from the authors. In this regard, likelihood-based inference in cointegrating vector autoregressive models is required in order to determine whether this linear combination of nonstationary data series of TB, real exchange rate and foreign and domestic incomes is stationary and, therefore, describes an equilibrium and non-spurious regression.

In so doing, we run univariate Dickey-Fuller (DF) and the Augmented Dickey-Fuller (ADF) unit root tests for each variable that enters the multivariate model following the decision tree process proposed by Charemza and Deadman (1992) testing for the significance of trend and drift together with non-stationary and assuming that the choice of lags is based to guarantee non-residual autocorrelation. The results over the period 1962-2005 are reported in unit root in their levels form but not in their first differences form so they are integrated of order one, I(1), while TB ln is also stationary in levels3 . In addition, we find that neither trends nor drifts should be entered in the cointegration space. Though not reported here, we have checked that all the variables are I(1) series for each of the short time spans considered. Note that, if the series have not contain a unit root, the cointegration test will lead to a number of cointegration vectors equal to four which is the number of endogenous variables.

Turning to cointegration analysis, we implement the cointegration test developed by Johansen (1988) and Johansen and Juselius (1990) which applies maximum likelihood to a VAR model assuming that the errors are Gaussian. Essentially, testing the existence of this long-run relationship requires a pth-order structural and dynamic VAR model on the variables under consideration which, in keeping with Granger representation theorem, can be written as an unrestricted VEC involving up to p lags

+ ∆ + ∆ + ∆ + ∆ + = ∆ - = = - = = - - j t p j j p j j t j p j p j j t j j t j t RER Y Y TB TB ln ln ln ln ln 1 1 * 1 1 0 φ ϕ γ θ δ [ ] t t t t o t RER Y Y TB ε β β β β λ + - - - - + - - - - 1 3 * 1 2 1 1 1 ln ln ln ln (7) F o r P e e r R e v i e w 8
where ∆ is the first difference operator, λ provides information on the speed-ofadjustment coefficient to long-run equilibrium and t ε is a purely white noise term.

We remark that having estimating the cointegrating relationship (6), which yield the long-run elasticity parameters, the error correction modelling defined by equation ( 7) reflects the short-run dynamic behaviour model of the TB using the estimates of past disequilibrium.

To this purpose, we firstly proceed by setting the appropriate lag-length in order to ensure the gaussian structure of the residuals in the VECM. We note that when the errors are not independently normal, it has been found that the Johansen method has a greater probability of rejecting the null of non cointegration even when there are no cointegrationg relations. In this fashion, we have selected the number of lags indicated by Schwartz (BIC) and Hannah-Quinn (HQ) criteria in all samples except for the term 1978-2005 where lags were chosen on the basis of the Akaike (AIC) criterion which has provided better results for Gaussian errors. On the basis of these information criteria, the best lag order is one year for the longer periods, 1962-2005 and 1962-2000, and two years for the shorter ones, 1978-2005 and 1962-1990. For brevity the results are not reported here. Following the Box and Jenkins (1970) approach, the diagnostic checking listed in Table (2 Next, we apply Johansen and Juselius (1990) procedure testing for number and estimations of cointegrating relations. Let r be set from zero to 1 k , where 4 = k is the number of endogenous variables in our modelling. The procedure, which allows for interrelation effects among a set of variables, leads to two statistics for cointegration: the trace statistic, trace λ , tests the hypothesis that there are at most r cointegrating vectors while the maximal-eigenvalue statistic, max λ , tests that there are r cointegrating vectors against the alternative that 1 + r exists. The results of this sequential testing performance are reported in Table (3) for every sample. We remark that the non-standard critical values are taken from Osterwald-Lenum (1992) which differ slightly from those reported in Johansen and Juselius (1990). The null hypothesis of non cointegration ( b , measures the trade balance elasticity with respect to the Argentine income, the US income and the RER respectively, that is, the percentage change in TB for one unit percentage change in each of the explanatory variables. As expected, in all cases trade balance is negatively associated with domestic output and positively associated with international output. However, except for the sub-sample , in all periods trade balance and real exchange rate are found to be positively cointegrated and the elasticity coefficient 3 b is positive and statistically significant at the 95% confidence level.

These results hint us to conclude that, in these terms, the Marshall-Lerner condition is fulfilled. Hence, the long-run approach to estimate the ML condition reveals that an increase in the real exchange rate has not only influenced but also has improved the Argentinean trade balance. Interestingly, ML condition only holds when the fix exchange rate period during Convertibility Plan in the nineties is included (observe that only in 2002 the fix parity dollar-peso was abandoned and ML holds in all periods counting the Convertibility Plan5 ) and, on the contrary, it is not fulfilled in previous periods when the exchange rate policy has shown more flexible systems. In this sense, these results are aligned with those of Mahmud, et al. (2004) for developed countries and of Gomes and Paz (2005) for Brazil during Real crawling-peg exchange rate regime system in the nineties. As occurred in Brazil, real exchange rate in Argentina was supposed to be appreciated during the Convertibility Plan. 4), we can observe that when ML condition holds, the foreign and domestic income coefficients, 1 b and 2 b , are not statistically significant at the 5% level. However, in the 1962-90 period, when ML rule is not verified, income coefficients are significant indicating that, during floating exchange rate periods, TB is more influenced by foreign and domestic income and, therefore, by foreign and domestic output growth rythms. From our point of view, these results are suggesting that currency devaluation in 2002 was necessary to improve the TB and recover an economic growth path more consistent with the balance of payments constraint that the Argentine economy seems to bear in the long-run (López and Cruz (2000) and Perraton (2003). Finally, we note that the significance of the parameter λ in all samples indicates that trade balance changes does not even up changes in past disequilibrium of either national and foreign income or real exchange rate during the same period.

Moreover, in Table (

In addition, by employing error-correction modelling techniques we analyze the short-run impact of a RER depreciation on the trade balance.We have checked that in all periods the estimated VEC models with one cointegrating relations are stable 6 and that the innovations are contemporaneously uncorrelated. This enables us to analyze the Jcurve phenomenon for Argentina by taking into account the dynamic lag structure of the VEC formulation. For it, we use the full information estimates from Johansen's correction model and a one time shock to the real exchange rate is traced and the generalized impulse response function of TB ln are obtained for Cholesky one standarddeviation RER ln innovations. The results over the hold period are represented in Figure 1 7 and suggest that for Argentina we do not find a negative effect of currency devaluation on the trade balance and the most important improvements on the TB have around four to five years of duration and even holds relatively high for a long period after. However, for the period 1962-1990, Figure 2 shows that the effect is initially positive and becomes negative firstly from the fourth to the sixth year and again from the ninth to the eleventh year. We note that is precisely the unique sample where it is not verified the Marshall-Lerner condition. Hence, no evidence in favour of the J-curve short term TB adjustment was found for Argentina by using annual data for any of the considered periods. Our generalized impulse response function analysis suggests that in the whole period, 1962-2005, a continuous improvement of the trade balance is induced by currency depreciation. In that period ending just before the launching of the Convertibility Plan, we have found a cyclical pattern in terms of the responses of the trade balance to currency devaluation. This cyclical pattern hols over 14-18 years improving first and 6 The stability of the estimated VAR and VEC has been checked in each of the sub-periods from the inverse kp roots of the characteristic AR polynomial, where k is the number of endogenous variables and p is the largest one. The stability condition is verified if all the roots have modulus less than one. In a VEC estimation with r cointegration relations this implies that kr roots should be equal to unity. 7 Although, they have not been included in the Appendix, we note that the impulse response functions for the sub-periods 1962-2000 and 1978-2005 show a similar behaviour. phenomenon can be named cyclical converse S-curve pattern, contrary to that proposed by [START_REF] Backus | Dynamics of the trade balance and the terms of trade: The Jcurve?[END_REF] and similar to the converse J-curve effect (Boyd et al. 2001). In this fashion, we highlight that our results present an intense cyclical pattern in the flexible exchange rate period not usual in the literature (for similar results see, for instance, [START_REF] Narayan | Examining the relationship between trade balance and exchange rate: the case of China' s trade with the USA[END_REF] for New Zealand and the study by [START_REF] Bahmani-Oskooee | The J curve: China versus her trading partners[END_REF] for China and her major trading partners.)

All the reported results on the trade balance dynamic are suggesting the key role of the management and impact of RER. But how much of the variability of the trade balance can be explained by RER shocks and which proportion should be attributed to the income variables? Taking into account the whole time path dynamic of the trade balance described in estimating ( 7) and for each random innovation in affecting the variables in the VEC modelling, a variance decomposition analysis enables us to identify the importance of exchange rate innovations on the trade balance behaviour.

Table 5 shows for each sample the variance decomposition of the trade balance percentage of the forecast error-variance due to each innovation at different moments in a ten-step ahead analysis Based on the Cholesky factorization, standard errors are generated using Monte Carlo simulation method with 1000 replications. In all periods, it appears that RER plays a major role in determining the Argentine trade balance. We remark that in those long periods including the fix exchange rate policy making, the percentages that RER shocks innovations represent in the variance of TB are around ten percent for the one-year-ahead period but increase up to thirty percent at the ten-year horizon. The proportion of variability that can be attributed to RER impacts is even greater for that sub-period finishing in 2000, when Argentina began its drastic slowdown triggering the sharp crisis in 2002; in this case, and for the same forecast horizons, the variance of TB due to RER moves from around 18% to nearly 37%. In these periods, domestic income is the second main variable to explain the variability of TB. For Drawing to a close, we should remark that in this paper, and in step with Argentine real exchange policy-making events, the whole sample period has been exogenously sundered in three sub-periods. Nevertheless, it is well known that the existence of a long-run equilibrium relationship does not always result in stable coefficients. In our case, we note that it is clear that parameter stability must be tested as long as the volatility of the coefficients is extremely high, outstandingly in the case of income variables in those periods considering a fix exchange regime. To conclude, we checked the stability of both the long-run and the short-run parameters by applying the CUSUM and CUSUM of Squares Tests (CUSUMQ) proposed by [START_REF] Brown | Techniques for testing the the constancy of regression relations over time[END_REF] to the residuals of the equation ( 7) across each of the sub-samples. CUSUM and CUSUMQ are based on accumulative recursive residuals and represent its cumulative sum and its cumulative sum of squares against all subsample points respectively. Table (6

IV. Conclusions and policy implications

In this paper we assess the long and short-run effects of real exchange rate on the Argentinean TB in a long period beginning in 1962. By using VAR-based cointegration tests and impulse response functions, we show that ML condition is fulfilled in the periods including fix exchange rate regime policy but not in those when exchange rate has shown more flexible policies. This result holds even though there have been episodes

of RER overvaluation with relatively flexible exchange rate periods in the Argentine economy as have shown [START_REF] Richaud | Real exchange rate and openness in emerging economies: Argentina in the long run[END_REF]. Our results coincide with those reported by Mahmud et al. (2004) for developed countries where ML condition is more probably to be fulfilled when fixed exchange rate policies are implemented than in flexible currencies periods. In the short run, Argentine TB has not usually followed the J-curve pattern of adjustment. RER depreciation had shown permanent improvements on TB when the currency board in the Convertibility Plan is included in the analysed sample. Only before the Convertibility Plan launching in 1991, the impact of RER is negative on the longterm TB adjustment showing that the ML condition does not hold. In this period, we observe the cyclical converse S-curve pattern contrary to that proposed by [START_REF] Backus | Dynamics of the trade balance and the terms of trade: The Jcurve?[END_REF] during the first 14-18 periods. After that, real depreciation effects on TB disappeared suggesting that, in the very long-run, RER has no effects on TB when flexible exchange rate policies are adopted.

The variability of TB is highly due to RER and domestic income whenever the estimation is including the long fixed nominal exchange rate period after 1991. On the contrary, with flexible exchange rates before 1991, foreign income, proxied by US income, turns into the most important variable to explain TB variability. These variance decomposition results enable us to conclude that during the fixed exchange rate period, RER was the key variable to recover TB equilibrium. Because of its fixed parity with US dollar, domestic income was limited to growth if the TB wanted to be re-equilibrated; in any other case the currency board had to be abandoned.

Though all these findings are in line with other country studies, we remark that our analysis over different periods together with variance decomposition clearly improves dynamic previous results in the single country empirical literature on the TB effects of currency depreciation.

To sum up, in the results of these analysis for Argentina we find a strong policymaking implication: currency devaluation in 2002 (and, therefore, the abandon of the currency board implemented in the Convertibility Plan) was necessary for improving TB and recovering a more sustainable economic growth path according with long term balance of payments equilibrium. In this sense, flexible exchange rate policies seems to be necessary to induce a balance of payments long-run sustainability and, therefore, for Argentine economic development.

F

= δ H 0 : 1 < δ H (i) t m i i t i t t y y t y ε α δ β β + ∆ + + + = ∆ = - - 1 1 2 1 ) ( (ii) t m i i t i t t y y y ε α δ β + ∆ + + = ∆ = - - 1 1 1 ) ( (iii) t m i i t i t t y y y ε α δ + ∆ + = ∆ = - - 1

  a standard model specification for export and import demand functions

  the validity of the ML condition for Argentina. In this fashion, we firstly examine whether there exists a long-run relationship between trade balance and real exchange rate, foreign income and domestic income for Argentina. Second, we test if a worsening of the RER results in a long-term improvement in the trade balance. Finally, we apply the impulse response analysis to determine whether shocks to RER induce the trade balance to follow a J-Curve. Annual data from the International Financial Statistics published by the International Monetary Fund (IMF) are used in our analysis covering the whole period 1962-2005. National (Y ) and foreign income ( * Y ) are defined by GDP volume index numbers and the US GDP is taken as the proxy for world output. TB is constructed as the rate volume of exports and volume of imports and the real exchange rate ) (RER is computed as the ratio of foreign price proxied by US consumer price to domestic consumer price multiplied by the nominal exchange rate of the domestic currency with US dollar. All the variables are expressed in logarithmic forms.

  in the nineties. As occurred in Brazil, real exchange rate in Argentina was supposed to be appreciated during the Convertibility Plan.

  uncorrelated. This enables us to analyze the J-curve phenomenon for Argentina by taking into account the dynamic lag structure of the VEC formulation. A one time shock to the real exchange rate is traced and the generalized impulse response function of TB ln are obtained for Cholesky one standard-deviation

  using similar econometric methods: Demirden and Pastine(1995) support the existence of the J-Curve for the US in the flexible exchange rate period after the collapse of Breton Wood system and so, indirectly, fulfilled the ML condition. In the same direction, the results by Gupta-Kapoor and Ramakrishnan (1999) support J-Curve for Japan during 1975-1996. In Bahamani-Oskooee and Niroomand (1998) the ML condition is addressed for almost thirty developed and developing countries over the period 1960-92.[START_REF] Lal | The J-curve: evidence from East Asia[END_REF] found evidences of J-curve patterns for seven Asian developing countries from 1980 to 1998.Gomes and Paz (2005) and[START_REF] Tsen | Is there a long-run relationship between trade balance and terms of trade? the case of Malaysia[END_REF] demonstrate the existence of a long-run relationship among TB, real exchange rate, foreign and domestic income for Brazil in the nineties and for Malaysia during 1965-2002 respectively.

  partners. For instance, in[START_REF] Nadenichek | The J-Curve Effect: An Examination Using a Structural Vector Error Correction Model[END_REF] bilateral trade flows among US and the other G7 countries are found to follow a J-curve pattern in the long period 1974-2004. On the contrary, Bahmani-Oskooee and Wang (2006) has found little evidence of J-curve hypothesis in China with their 13 major trade partners. Bahmani-Oskooee and Harvey (2006) results reveal short-run effects on Malaysian bilateral trade flows with most of their 14 major commercial partners but these effects do not hold on the long-run. Bahmani-Oskooee et al. (

  existence of a J-curve pattern for the Argentine economy from 1962 up to nowadays discerning three cut-off points accordingly to different periods of exchange and trade policies implemented in Argentina: 1990 reveals a clear change in Argentine exchange rate regime when the Convertibility Plan in April 1991 fixed the Argentine peso to US dollar in a currency board system; 2000 evidences a slowdown triggering the sharp crises in 2002 and the end of the fixed exchange rate regime period after an intense devaluation of the currency in the first days of 2002. Finally, we have analysed the 1978-05 period to capture relationships during the change in Argentina's trade policy making towards a liberalization phase, away from the import substitution protectionism period in 1978. We note that three of the periods we havetested -1962-2005, 1962-2000 and 1978-05- include the Convertibility Plan stage which implied a fixed exchange rate policy with US dollar. The other one, 1962-1990, showed more flexible options on the currency.Our major concern in this paper is to empirically estimate the all-out dynamic of the trade balance in relation to the exchange rate in addition to other income variables by discerning the long-run effects of currency depreciation on the trade balance for Argentina from its short-run impacts. To this purpose, we exploit some econometric techniques using time series unit root tests to examine the stationary properties of the data and the Johansen and Juselius procedure (1991) to search for multivariate a robust and stable vector autoregressive (VAR) modelling specification. Based on a vector error-correction (VEC) formulation and generalized impulse response function, we analyze the long and short term trade balance dynamic model for Argentina. To conclude, and in order to identified the determinants of the trade balance, we run a variance decomposition analysis examining how much percentage of the total forecast error variance of the TB is explained by each component.Taking into account the slow long-run balance of payments constrained economic growth of Argentina suggested in several papers (see, for instance,López and Cruz (2000) andPerraton (2003) and the key role of the exchange rate rule on the Argentine development during the last decades, specially since 1991, we highlight the importance of this paper for policy-making decisions on exchange rate regime in the argentine economic development. The contributions of the paper are twofold. The first is to test ML and J-curve phenomenon for Argentina in different periods. The second is to provide new insights on the effects of fixed and flexible exchange rate regimes in the TB and, therefore, in the relationships between RER and long term economic growth.

  , we firstly examine whether there exists a long-run relationship between trade balance and real exchange rate, foreign income and domestic income for Argentina. Secondly, we test if a worsening of the RER results in a long term improvement in the trade balance. Thirdly, we apply the impulse response analysis to determine whether shocks to RER induce the trade balance to follow a J-Curve. Finally, a variance decomposition allows us to quantify the influence of real exchange rate shocks on the trade balance variability. Annual data from the International Financial Statistics published by the International Monetary Fund (IMF) are used in our analysis covering the whole period 1962-2005. National ( Y ) and foreign income ( * Y ) are defined by gross domestic product (GDP) volume index numbers and the US GDP is taken as the proxy for foreign output 2 . TB is constructed as the rate volume of exports and volume of imports and the real exchange rate is computed as the ratio of foreign price proxied by US consumer price to domestic consumer price multiplied by the nominal exchange rate of the domestic currency with US dollar. All the variables are expressed in logarithmic forms.

  ) deals with residual Portmanteau (Q) and Breusch-Godfrey Lagrange Multiplier (LM) autocorrelation tests, White heterocedasticity and Jarque-Bera residual normality test via Cholesky (JB CHOL ) and Urzua (JB URZ ) factorizations and leads to wellbehaved residuals in all periods.

  that enter into the trade balance equation (6) can be rejected by the trace max λ test in each of the considered samples. Both statistics 4 confirm the existence of at most one cointegrating equilibrium relationship among the logarithms of TB, national and foreign income and real exchange rate at the 5% level of significance.Table (4) summarizes the estimated cointegrating vectors normalized on trade balance and the adjustment parameters, λ . By setting the estimated coefficient of TB ln at -1 we normalize the income and RER coefficients and, therefore, the estimates

  times in this long period. After 18 years, the cycle ends and RER becomes neutral or slightly negative suggesting a new short-run pattern of J-curve. This

  instance, in 1962-2000, variance of TB due to domestic income goes from 13% to 28% and from 8% to 18% in the whole sample, 1962-2005. However, once we move to the floating regime before the launching of the Convertibility Plan, we observe that RER and US income share the major proportion of variability of TB for the first five-year-ahead forecast and from the six year horizons respectively. We highlight that the variance decomposition result for the sample 1962-1990 is consistent with the high significance time series in the trade balance cointegrating equation and by the fact that ML condition does not hold in this period.

  )summarizes the results for both tests and Figure3displays for each of the considered periods the test statistic representation together with the 5% critical values. Concentrating on the plots, we observe that, in the majority of cases, the null hypothesis of parameter constancy cannot be rejected as long as both CUSUM and CUSUMQ statistics fall inside the area between the two critical lines. Only, the movement of the CUSUMQ test in 1978-2005 outside the 5 percent significance bounds is suggestive of parameter instability. To sum up, in each of the considered periods there is evidence of stability in both the long-run and the short-run coefficients.

Figure

  Figure 2.Trade response to a RER shock.1962-1990

  P , * P and Y , * Y denote the domestic and foreign price levels and incomes respectively; η and γ are the real exchange rate elasticities for exports and imports and ε and π are the income elasticities for imports and exports.

	where	Using logarithms, equation (1) and (2) become [ * ln ln ln ln ln t t t t E P P X ε η + --= ] [ t t t t P E P M ln Y t Y * t ln ln ln ln * π γ + -+ = ] [ ] t t t t P E P e ln ln ln ln * -+ = is the natural logarithm of real exchange rate. Let (3) (4)
	TB stand for the trade balance. Following common practice, TB is defined as the ratio
	between exports and imports so
						ln	TB	t	=	π	ln	t Y	+	ε	ln	t Y	*	+	ϑ	ln	e	t	(5)
	where	ϑ	=	-	( γ η +	)

Table ( 4

 ( ) summarizes the estimated cointegrating vectors normalized on trade balance and the adjustment parameters, λ . Each cointegrating coefficient,

11

  [START_REF] Tsen | Is there a long-run relationship between trade balance and terms of trade? the case of Malaysia[END_REF] Is there a long-run relationship between trade balance and terms of trade? The case of Malaysia, Applied EconomicsLetters, 13,[307][308][309][310][311]

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

Table 1 . Augmented Dickey-Fuller test (ADF). Argentina 1962-2005.

 1

Table 2 . VAR. Lags structure and residuals

 2

		Lag structure			Residuals-Diagnostic Views
				Ho: non autocorrelation Ho: normality Ho: homocedasticity
	Period
		Lag order Stability	Q	LM	JB Chol	JB Urz	White
	1962-2005	1	yes	215.25	13.51	9.07	62.78	89.95
	1962-2000	1	yes	185.77	11.82	7.91	61.14	88.13
	1978-2005	2	yes	102.12	11.59	12.34	33.51	164.36
	1962-1990	2	yes	93.76	9.16	10.62	41.66	170.83

Notes:

Lags for autocorrelation tests are taken as the third part of the observations . Results carried out by Eviews 4.1

Table 3 . Johansen and Juselius Cointegration Test

 3

	Johansen Test

Notes: Lag structure is drawn in each period from Table 3 results. *(**) denotes rejection of the hypothesis at the 5%(1%) level taking into account Osterwald-Lenum critical values. Trace and Max-eigenvalue test indicates 1 cointegrating equation(s) both 5% level levels.Results computed with Eviews 4.1

Table 4 . Johansen. Estimated cointegrating equation

 4 The management of the exchange rate has been a critical issue for the economic policy, especially in developing countries. In defining an exchange rate policy, one of the most important considerations is the responsiveness of Trade Balance (TB) to changes in terms of trade or, more generally, in Real Exchange Rate (RER). The effects of currency depreciation on a country's trade balance have centred an important and on-going debate in the international economic literature. Precisely, this issue has been traditionally studied in the Marshall-Lerner condition (ML) and the so called J-curve framework. According to the ML condition, currency devaluation improves the trade balance in the long-run only if the sum of the absolute values of imports and exports demand price elasticities exceeds unit. However, due to the lag dynamics structure, TB can worsen in the short-run because of the inelastic demand for imports and exports in the immediate aftermath of an exchange rate change. In this case, TB is said to follow the J-curve pattern. Precisely, both the short and the long-run relationships are considered the underlying model that policy makers use in formulating exchange rate policies.

	Period	b	0	Cointegrating coefficients 1 b 2 b	3 b	ECM λ
	1962-2005	0.1591	-0.3395	0.3339	0.6095	-0.8837
					[0.8281] [-1.362] [-5.51]	[-4.483]
	1962-2000	1.423		-0.6121	0.3295	0.3887	-0.692
					[1.541]	[-1.323]	[-3.336]	[-3.98]
	1978-2005	0.0128		-0.115	0.124	0.8231	-1.943
					[ 0.323]	[-0.769]	[-10.887]	[-3.683]
	1962-1990	-0.512		-0.8296	1.1224	-0.0283	-3.022
					[9.454]	[-15.149]	[0.863]	[-7.956]

Notes: The vectors are normalized for TB; 1 b , 2 b and 3 b denote the argentine GDP, USA GDP and TCR elasticties of trade balance, respectively. Figures in parentheses represent asymptotic p-values associated with the tests. Results carried out by Eviews 4.1.

  X and M are the volume of exports and imports, E is the nominal exchange rate and P , * P and Y , * Y denote the domestic and foreign price levels and incomes respectively; η and γ are the real exchange rate elasticities for exports and imports and ε and π are the income elasticities for imports and exports.

		M	t	=	P	P ⋅ *	E	γ t	⋅	( ) π t Y	(2)
	where	Using logarithms, equation (1) and (2) become [ * ln ln ln ln ln t t t t E P P X ε η + --= ] [ t t t t P E P M ln Y t Y * t ln ln ln ln * π γ + -+ = ] [ ] t t t t P E P e ln ln ln ln * -+ = is the natural logarithm of real exchange rate. Let (3) (4)
	TB stand for the trade balance. Following common practice, TB is defined as the ratio F between exports and imports so o t t t t e Y Y TB ln ln ln ln * ϑ ε π + + = (5) r where ) ( γ η ϑ + -= . Precisely, the coefficient of
					P
							e
								e r
										R e v
											i e
											w
											1)
											5

where t e ln

Table (

 (

	1) and indicate that Y ln ,	* lnY and RER ln	contain a

Table 1 . Augmented Dickey-Fuller test (ADF). Argentina 1962-2005.

 1

	o r
	P
	e
	e r
	R e v
	i e
	w
	14

Table 2 . VAR. Lags structure and residuals

 2 Lags for autocorrelation tests are taken as the third part of the observations . Results carried out by Eviews 4.1

		Lag structure			Residuals-Diagnostic Views
				Ho: non autocorrelation Ho: normality Ho: homocedasticity
	Period
		Lag order Stability	Q	LM	JB Chol JB Urz	White
	1962-2005	1	yes	215.25	13.51	9.07	62.78	89.95
	1962-2000	1	yes	185.77	11.82	7.91	61.14	88.13
	1978-2005	2	yes	102.12	11.59	12.34	33.51	164.36
	1962-1990	2	yes	93.76	9.16	10.62	41.66	170.83
	Notes:

Table 3 . Johansen and Juselius Cointegration Test

 3 Lag structure is drawn in each period from Table 3 results. *(**) denotes rejection of the hypothesis at the 5%(1%) level taking into account Osterwald-Lenum critical values. Trace and Max-eigenvalue test indicates 1 cointegrating equation(s) both 5% level. Results computed with Eviews 4.1

	Johansen Test

Table 4 . Johansen. Estimated cointegrating equation

 4

	Period	b	0	Cointegrating coefficients 1 b 2 b	3 b	ECM λ
	1962-2005	0.1591	-0.3395	0.3339	0.6095	-0.8837

Table 5 . Trade Balance Variance decomposition

 5 Notes: S.E indicates the forecast error of the variable at the given forecast horizon.Cholesky Ordering:

														Ahead forecast horizon
	Period												1	3	5	6	7	8	9	10
	1962-2005			S.E.					0.365	0.491	0.567	0.606	0.642	0.675	0.706	0.736
						ln	Y					8.589	15.168	15.990 16.515 16.960 17.275 17.514 17.720
						lnY	*			0.057	4.863	7.030 7.318	7.666	8.017	8.294	8.503
						ln	RER	12.337	27.385	27.637 28.040 28.566 28.933 29.166 29.355
	1962-2000			S .E.				0.322	0.414	0.454	0.474	0.495	0.514	0.533	0.551
						ln	Y					12.745	21.587	24.297 25.385 26.327 27.139 27.840 28.450
						lnY	*			0.763	1.736	3.878	4.358	4.693	4.979	5.242	5.481
						ln	RER	18.598	32.838	34.215 34.795 35.407 35.975 36.466 36.885
	1978-2005 S.E.					0.408	0.545	0.627	0.668	0.709	0.754	0.794	0.824
						ln	Y					4.126	6.751	11.665 12.028 11.617 11.124 11.116 11.663
						lnY	*			0.272	4.597	7.230	6.681	6.381	6.842	7.702	8.118
						ln	RER	7.134	27.861	26.140 23.823 24.069 26.940 29.029 28.997
	1962-1990 S.E.					0.323	0.369	0.427	0.446	0.448	0.452	0.459	0.472
						ln	Y					6.555	10.930	10.815 9.970	9.905	10.046 10.589 10.349
						lnY	*			24.399	24.777	26.970 30.762 30.465 31.299 30.374 31.149
						ln	RER	41.698	34.405	29.365 27.399 27.884 27.385 27.387 26.055
	ln	TB	,	ln	Y	,	ln	Y	*	,	ln	. RER	Results carried out with Eviews 4.1.

Table 6 . CUSUM and CUSUMQ tests. Stability results Period CUSUM CUSUMQ

 6

	1962-2005	Stable	Stable
	1962-2000	Stable	Stable
	1978-2005	Stable	Unstable
	1962-1990	Stable	Stable

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

Trade response to a RER shock.1962-2005

		Response of TB to Cholesky
		One S.D. RER Innovation
	.20
	.16
	.12
	.08
	.04
	.00
	5	10	15	20	25	30

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

The computed test statistics for the unit root null are greater than theMacKinnon (1996) critical values though at the 1 percent level the ADF test yields really close to the corresponding tabulated value. The ADF result coincides with the usual persistence of the variable and, therefore, the stationary consideration of the TB followed in the related literature. See[START_REF] Nadenichek | The J-Curve Effect: An Examination Using a Structural Vector Error Correction Model[END_REF] and[START_REF] Kim | Income Effects on the Trade Balance[END_REF] not only for a clear and brief discussion but also for examples on the stationary treatment of the trade balance.

Johansen and Juselius (1990) suggest that, in case that the statistics yield conflicting results, the maximum eigenvalue test may be better.

In fact, we have tested different periods and ML condition begins to be satisfied after 1994.


Behavior and Family Economics < D -Microeconomics, D46 -Value Theory < D4 -Market Structure and Pricing < D -Microeconomics, D80 -General < D8 -Information and Uncertainty < D -Microeconomics, D81 -Criteria for Decision-Making under Risk and Uncertainty < D8 -Information and Uncertainty < D -Microeconomics

Keywords: Cumulative Prospect Theory , Premium Bonds , Skewness Cumulative Prospect Theory, Exponential Value Function, Gambling JEL classification: C72, C92, D80, D84

Skewness of return has been suggested as a reason why agents might choose to gamble, ceteris paribus, in Cumulative Prospect Theory (CPT). We investigate the relationship between moments of return in two models where agents choices over uncertain outcomes are determined as in CPT. We illustrate via examples that in CPT theory, as with expected utility theory, propositions that agents have a preference for skewness may be invalid.

Introduction:

A preference for skewness of return, ceteris paribus, is often suggested as a reason why agents might choose to gamble in the context of cumulative prospect theory, (CPT), (see [START_REF] Kahneman | Prospect Theory: An Analysis of Decision Under Risk[END_REF], [START_REF] Tversky | Advances in Prospect Theory: Cumulative Representation of Uncertainty[END_REF]). For example [START_REF] Barberis | Stocks as Lotteries: The Implications of Probability Weighting for Security Prices[END_REF] write, "through the probability weighting function, cumulative prospect theory investors exhibit a preference for (positive) skewness. Whilst [START_REF] Taleb | Bleed or Blowups: What Does Empirical Psychology Tell Us About the Preference For Negative Skewness?[END_REF] suggests that "On the other hand, the value function of prospect theory documents a decreased sensitivity to both gains and losses, hence a marked overall preference for negative skewness".

A similar conjecture concerning skewness of return has also been made in the context of expected utility theory. For example Golec and Tamarkin (1998) assert "horse bettors accept low-return, high-variance bets because they enjoy the high skewness offered by these bets" and "we claim that bettors could be risk-averse and favour positive skewness, and primarily trade off negative expected return and variance for positive skewness.

In the context of expected utility theory the rationale for a positive skew preference is that the third derivative of the utility function of a globally risk-averse agent is positive, and approximation of the utility function to order three implies a valid trade-off between mean, variance and skewness of return, that is, preferring a higher third moment for two random variables having equal means and variances [START_REF] Kraus | Skewness Preference and the Valuation of Risky Assets[END_REF]).

In fact the argument is in general incorrect for the expected utility maximiser. [START_REF] Brockett | A Reexamination of the Relationship between Preference and Moment Orderings by Rational Risk Averse Investors[END_REF] show that one can always construct two distributions with a given moment ordering for which neither stochastically dominates the other at any degree of stochastic dominance i Given the conflicting statements concerning the preference of agents for skewness in cumulative prospect theory (and that the related conjectures in expected utility theory are incorrect), the purpose in this note is to investigate the relationship between moments of return, particularly skewness of return, in two models where agent's choices over uncertain outcomes are determined as in CPT.

The first model involves an agent undertaking a fixed stake gamble involving gains and losses. The second model is of a simple portfolio decision where the agent can purchase a safe asset paying an interest rate, h, or a bond that entitles you to participate in a lottery that pays X with probability p or zero otherwise. The key feature of the bond is that you do not loose your stake. You can cash in your holdings of the bond at any time. The UK government markets such a bond, called a National Premium Bond. It offers an expected rate of return that appears lower than the safe rate of return given by the interest rate paid on Treasury bills or Building Societies. ii Holdings of premium bonds are constrained by the UK government to a maximum of £30,000 and some 147,000 UK citizens hold this amount. Given the relatively large holdings by agents, with expenditure per year of some £2 billion, and a minimum purchase amount of £100, entertainment, as opposed to financial return, is, apriori, an unsatisfactory rationale for agents purchasing them. It is interesting to observe therefore that the UK government regards holdings of premium bonds as a form of saving but in the Budd report on Prevalence of Gambling in the UK (2001) they are considered as a component of gambling expenditure. Because the safe rate interest rate typically exceeds the expected rate of interest on bonds, we suggest that from the perspective of the standard expected utility model their holding constitutes an anomaly for many agents.

In the next section we set out our two models and analyse their implications. The final section of the note is a brief conclusion.

2.Some Analysis

We specify the value function as having the expo-power form which is a generalization of the power form employed by [START_REF] Tversky | Advances in Prospect Theory: Cumulative Representation of Uncertainty[END_REF] iii . . Defining reference point utility as zero, for a gamble to occur in CPT we require expected utility or value (EU) to be non-negative. For the expo-power value function expected value is given by

EU w p e p e r s o s

n n n = + ( )( ) ( ) 1 0 w 1-) (1- - (1)
where the win-probability is given by p, and the functions w p + ( )and w p ( ) 1 are non-linear s-shaped probability weighting functions, o are the odds and s the stake. r n , , and are positive constants with 0 1 < n . The agent is riskaverse over gains and risk seeking over losses as assumed in CPT.

The value function in (1) has upper and lower bounds, as is required to resolve the St.Petersburg Paradox (see e.g. [START_REF] Bassett | The St. Petersburg Paradox and Bounded Utility[END_REF]). The expo-power function also has the convenient property that as 0, the value function approximates the power form employed by Tversky and Kahneman.

The degree of loss aversion, (LA) is defined by the ratio of the value of gain to the value of loss from a symmetric gamble, o = 1 and is given by

LA e e r s s n n = ( ) ( ) 1 1 (2)
From (2), as stake size approaches zero loss aversion would require that r < 1.

and for large stake size 1 1 < . In order to ensure that the degree of loss aversion increases with stake size, we also require r 1. We assume that the probability weighting functions over gains and losses are as employed by [START_REF] Tversky | Advances in Prospect Theory: Cumulative Representation of Uncertainty[END_REF] and given by where and are constants.

. The expected return from a one-unit stake gamble is defined by, µ 1 , where µ µ

1 1 1 = + po p ( )( ) or = p(1+ o) (4)
so that the return from an s stake gamble is

s pos p s µ 1 1 = + ( )( ) (5)
Skewness of return is given by

µ µ 3 3 3 2 1 1 2 = s p p p ( )( ) (6)
where µ µ = + ( ) 1 1 and an actuarially fair bet is defined when µ µ

1 0 1 = = or .
We assume that stake size is fixed at 10 units. We set the values of the parameters in the probability weighting functions at = 0 61 . and = 0.69 , those reported by [START_REF] Tversky | Advances in Prospect Theory: Cumulative Representation of Uncertainty[END_REF].

We let n = 088 . , r = 20, k = 45 = 0.00001.

As noted above as 0 , we obtain precisely the same specification of CPT and parameter values as reported by [START_REF] Tversky | Advances in Prospect Theory: Cumulative Representation of Uncertainty[END_REF]. Because our choice of is small our specification will exhibit the same features as that of Tversky and Kahneman for almost all of the probability range.

Substituting (4) and ( 3) into (1) we can write expected value solely as a function of expected return and win probability. Also using (6) we can write expected value solely as a function of skewness and expected return.

We plot the indifference curves between expected return and win probability and expected return and skewness of return for EU=0 in Figures 1(a) to 1(g). In Figures 1(a) and 1(b) we observe that the indifference curve exhibits a maximum in the range of actuarially fair bets and that the agent requires around $30 to stake. $10 at a probability of 0.5. These figures are the same as those reported by students in [START_REF] Kahneman | Prospect Theory: An Analysis of Decision Under Risk[END_REF] experiments. We also note that due to probability distortion the agent will gamble at actuarially unfair odds on long shots.

+ = + = + ( ) ( ( ) ) ( ) ( ) ( ( ) ) 1 1 1 1 1 1 , (3)
In Figure1(c) we observe that at low enough probabilities the indifference curve exhibits a minimum and an asymptote. This is a resultant of the bounded ness of the value function. Ultimately boundedness implies that the agents will only take very long shot bets at actuarially fair odds and will ultimately reject some long shot bets regardless of the rate of return. This behaviour differs from that with a power function. It is discussed further in [START_REF] Cain | Cumulative Prospect Theory and Gambling[END_REF].

The indifference curve between expected return and skewness is plotted in Figures 1(d) to 1(g). The indifference curve has properties that reflect that for expected return and win probability. The important point to note is that the trade-off changes sign. For probabilities close to a half the trade-off is positive as shown in (1d) as the probability declines the trade-off exhibits a maximum and then a negative trade-off.

For very low probabilities (very high positive skewness) the trade-off exhibits a minimum and the trade-off becomes positive as shown in Figure (1e). Clearly in some regions of positive skewness the agent requires a higher expected return to compensate for higher positive skewness. For probabilities between 0.5 and 2/3 the trade-off is negative, so the agent accepts more negative skewness and lower expected rates of return. For probabilities between 2/3 and 1 this is reversed, the agent exhibiting indifference between lower expected returns and less negative skewness. The Figures illustrate that there is no simple relationship between expected return and skewness of return for a fixed stake gamble in CPT.

In model 2 we assume that the agent has wealth of one unit to invest in a safe asset yielding h% and a premium bond yielding b%. The agent invests a and 1-a in the safe asset and premium bond respectively. In this model we assume that n=1 so as to allow a tractable analytic solution. The premium bond pays X with probability p so that b pX =

.

= + + + + ( )( ) ( ( ))( ) ( ( ) ) 1 1 1 1 (7)
The expected return of the portfolio is ER p ah a X p ah

= + + ( ( ) ) ( ) 1 1 the variance, 2 2 2 1 1 = ( ) ( ) a b p p
and skewness, 3

3 3 2 1 1 2 1 = ( ) ( )( ) a b p p p .
The optimal share of the portfolio in the safe asset, where

= < EU a EU a 0 0 2 2 , , is
given by

a w p X h w p h X = + 1 1 ln ( ){ } ( ( )) (8)
We assume the parameters = = = = 0 61 0 3 0 05 0 3 . , . , . , . . h

Portfolio A has X p = = 250 0 0001 , .
and aq value of a = 0.9613805, which is optimal.

This gives the following moments for the portfolio;.

. with EU = 0 0153266 .

Comparing portfolio's A and B we observe that they have identical means and variances but that B exhibits a higher positive skewness of return than portfolio A.

Conclusions.

We have demonstrated with examples that in CPT, as with expected utility theory, it is not true to state that agents will prefer gambles that exhibit more positive skewness. In fact in model one we show that the agent can require a higher expected return to compensate for greater positive skewness. In the model two we

show that a portfolio that has the same expected return and variance as another but lower positive skewness is preferred. relating is often characterized by arguments invoking a "ceteris paribus" condition, which is intended to separate out the effect of higher order moments (and thus to focus solely upon the utility differences resulting from changes in skewness alone). [START_REF] Cain | Skewness as an Explanation of Gambling by Locally Risk-Averse Agents[END_REF] and [START_REF] Cain | Cumulative Prospect Theory and Gambling[END_REF] illustrate the logical fallacy in the context of simple mixed gambles in non-CPT models.

. ዊhዊh National Premium bonds are tax-free and the expected return was recently raised to 3.2 per cent. A higher-rate taxpayer would have to earn a gross rate of around 5.33 per cent to exceed this and a standard rate taxpayer around 4%. The safe rate of interest always appears higher than the rate for a standard rate taxpayer and for many periods also for a higher ratepayer. Premium bonds have multiple prizes (like a lottery ticket with N prizes). The chances of winning any prize are 24,000 to 1 since 1 September 2004. The top prize is one million. The minimum purchase is £100

iii Tversky and Kahneman (1992) assumed the value function was of the power form with the same exponent over gains and losses. This specification is not appropriate for analyzing mixed gambles. For equal exponents stake size is indeterminate. With appropriately different exponents the agent becomes infinitely gain loving rather than loss averse over small (and also optimal stake gambles) violating the loss aversion assumption in CPT.

  Figures 1(a)-1(c) Indifference Curves between Expected Return and Win Probability 1(a) 0.05< p 1 1(b) 0 001 0 05 . . < < p

  comparison the expected utility or value of the portfolio with a=1 and a=0 are EU = 0 01489 . and EU = 0.0036 respectively.Consider now a Portfolio B. This has X

  Consequently the example demonstrates that a KT agent can optimally prefer a portfolio with lower skewness than another when both exhibit the same expected return and variance.

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

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


Yasmin Nazirizadeh

Friederike Vogel

Wolfgang Bader

Ekkehard Haen

Bruno Pfuhlmann

Gerhard Gründer

Michael Paulzen

Markus Schwarz

Gerald Zernig

Christoph Hiemke
email: hiemke@mail.uni-mainz.de

: M Paulzen

Serum concentrations of paliperidone versus risperidone and clinical effects

Keywords: Antipsychotic drug, Inter-individual variation, Paliperidone, Pharmacokinetics, Risperidone, Therapeutic drug monitoring, Trough serum concentrations Y, Nazirizadeh :

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Paliperidone is an atypical antipsychotic drug [START_REF] Kane | Treatment of schizophrenia with paliperidone extended-release tablets: A 6-week placebo-controlled trial[END_REF][START_REF] Kramer | Paliperidone extended-release tablets for prevention of symptom recurrence in patients with schizophrenia[END_REF]. It is identical to 9-hydroxyrisperidone, the pharmacologically active metabolite of risperidone, and has a similar pharmacological profile as risperidone, exhibiting high affinities for the dopamine D 2 and the serotonin 5-HT 2 receptor [START_REF] Leysen | Biochemical profile of risperidone, a new antipsychotic[END_REF][START_REF] Leysen | Risperidone: a novel antipsychotic with balanced serotonindopamine antagonism, receptor occupancy profile, and pharmacologic activity[END_REF]. Paliperidone has been made commercially available as a new antipsychotic treatment option in an extended-release (ER) formulation using OROS technology from ALZA Corp (Vacaville, CA). This delivery profile allows treatment to be started with therapeutically effective doses without the need of initial dose-escalation for acceptable tolerability. The administration of paliperidone ER results in small 24-h peak-to-trough fluctuations in paliperidone plasma concentrations at steady state [START_REF] Karlsson | Pharmacokinetics, dopamine D2 and serotonin 5-HT2A-receptor occupancy and safety profile of paliperidone extended-release in healthy subjects: two open-label, single-dose studies[END_REF], thereby avoiding the rapid raise and fall in concentrations characteristic for immediate-release oral formulations. Since paliperidone does not undergo significant hepatic metabolism [START_REF] Vermeir | Absorption, metabolism, and excretion of paliperidone, a new monoaminergic antagonist, in humans[END_REF], it is also well tolerated by patients with poor hepatic function, and it is not susceptible to metabolic drug interactions.

Studies on the pharmacokinetics of risperidone have revealed large inter-individual variation in the concentrations of the active moiety risperidone plus 9hdroxyrisperidone [START_REF] Heykants | The pharmacokinetics of risperidone in humans: a summary[END_REF]. Since the response to antipsychotic drugs needs sufficient D 2 receptor blockade, which correlates well with the plasma concentrations of most antipsychotics [START_REF] Medori | Plasma antipsychotic concentration and receptor occupancy, with special focus on risperidone long-acting injectable[END_REF], the efficacy and tolerability can be improved by therapeutic drug monitoring (TDM). For risperidone, it has been reported that concentrations of the active moiety of 20-60 ng/ml should be attained for optimal clinical outcome [START_REF] Baumann | The AGNP -TDM expert group consensus guidelines: therapeutic drug monitoring in psychiatry[END_REF]. Because of almost identical pharmacodynamic profiles, the therapeutic range of paliperidone is expected to be identical to that of the risperidone active moiety. Data from patients which verify or refute this assumption, however, are lacking to date. The constant delivery formulation of paliperidone has a positive impact on peakto-trough fluctuations which may lead to a better tolerability and possibly explain why the usual daily doses of paliperidone are 6-9 mg and thus higher than those for risperidone (4-6 mg). It may also be expected that intraand inter-individual variations in drug concentrations in the blood are less pronounced in patients taking paliperidone ER than in those given risperidone.

In the study reported here, we analyzed serum trough concentrations of paliperidone in patients treated with paliperidone in association with clinical effects and compared the drug concentrations with those reported in the literature for risperidone [START_REF] Aravagiri | Plasma concentrations of risperidone and its 9-hydroxy metabolite and their relationship to dose in schizophrenic patients: simultaneous determination by a high performance liquid chromatography with electrochemical detection[END_REF][START_REF] Lane | Risperidone in acutely exacerbated schizophrenia: dosing strategies and plasma levels[END_REF]. For comparison, we also analyzed intra-individual variability in the trough serum concentrations in patients being treated with either the paliperidone ER formulation or risperidone.

Subjects and methods

Subjects

Data were obtained from patients of four psychiatric hospitals (Mainz, Munich, Regensburg, and Würzburg) between 2007 and 2009. Serum concentrations of paliperidone were recorded for treatment optimization by TDM. Blood was drawn under steady state conditions, namely, from patients who had been treated with paliperidone for at least 5 days, in the morning before the first dose of the day.

This naturalistic study was carried out in accordance with current German law (PsychKG), and retrospective analysis of TDM data was approved by the local Ethics Committee.

The Clinical Global Impressions (CGI) scale [item one, 1-8 points, for severity (CGI-S); item two, 1-5 points, for improvement (CGI-I)] was used to assess the patient's state [START_REF] Guy | ECDEU assessment manual for psychopharmacology[END_REF]. Side effects were assessed using a modified UKU scale [START_REF] Lingjaerde | The UKU side effect rating scale. A new comprehensive rating scale for psychotropic drugs and a cross-sectional study of side effects in neuroleptic-treated patients[END_REF]. The CGI and UKU scores were rated on the day of blood sampling and entered into the request form for the TDM measurements [START_REF] Baumann | The AGNP -TDM expert group consensus guidelines: therapeutic drug monitoring in psychiatry[END_REF].

Analysis of serum paliperidone and risperidone concentrations

Drug measurements were performed in four different laboratories of the TDM group of the Arbeitsgemeinschaft für Neuropsychopharmakologie und Pharmakopsychiatrie (AGNP, see: www.agnp.de). All four laboratories used chromatographic methods, and all were continuously checked using internal and external quality assurance programs to attain comparable results. The assay specifications, precision, accuracy, limit of detection, and linearity were similar in the different laboratories. Risperidone and paliperidone were determined by established highperformance liquid chromatography methods [START_REF] Kirschbaum | LC with column-switching and spectrophometric detection for determination of risperidone and 9-OH-risperidone[END_REF][START_REF] Riedel | Risperidone plasma levels, clinical response and side-effects[END_REF]. For these assays, the inter-and intra-coefficients of variance were <15%. The limit of detection was about 2 ng/ml for both risperidone and paliperidone [START_REF] Kirschbaum | LC with column-switching and spectrophometric detection for determination of risperidone and 9-OH-risperidone[END_REF]. The quality of the analyses was controlled by participation in an external quality control program to assure similar results in different laboratories.

Statistical analysis

Data were given as arithmetic means with the corresponding standard deviation (SD). The inter-and intra-individual variabilities were given as the percentage coefficient of variance (CV%) which was based on a minimum of three measurements. The Pearson correlation was used to determine the relationship between the daily dose of paliperidone, therapy improvement according to CGI-I, and the measured serum concentrations. Student's t-test and the Mann-Whitney U test were used to determine statistical significance between groups.

Results

For paliperidone, we analyzed a total of 303 blood samples obtained from 217 psychiatric patients at four psychiatric hospitals (Mainz, n=100; Regensburg, n=77; Würzburg, n = 30; Munich, n = 10). Among the 217 patients, 106 (48.8%) were receiving paliperidone as antipsychotic monotherapy. We used the first measurement under steady state conditions for each patient. Complete information on treatment efficacy and co-medication was available for each patient.

According to the International Classification of Diseases, Tenth Edition (World Health Organization, ICD-10), most of our patients suffered from schizophrenia spectrum psychoses (67.4%), with 16.4% suffering from a schizoaffective disorder, 5.2% from a bipolar affective disorder, 6.1% from depression, and 3.8% from other psychiatric disorders. The patient cohort comprised 54% males and 46% females, with a mean age of 38.1±12.3 (range 18-89) years.

The patients were, on average, markedly ill [CGI-S (mean ± SD) 5.9±0.9] and showed highly variable responses to paliperidone treatment (CGI-I 2.6±1.0). The average number of additional medications administered to each patient was 2.4±2.0 (range 0-8 concomitant medication).

The oral daily dose of paliperidone ranged between 3 and 18 mg/day, and the mean daily dose was 7.8±2.9 mg/ day, which yielded a mean paliperidone serum concentration of 35.7±25.2 ng/ml (range 0-213 ng/ml; 25th-75th percentiles 19.5-46.0 ng/ml). The mean dose-corrected paliperidone concentration (C/D, concentration/dose ratio) was 4.7±2.9 ng/ml/mg. The dose-dependent serum concentrations are shown as box plots in Fig. 1. The Pearson correlation between the prescribed daily dose and resulting serum concentrations was r 2 =0.452 (p<0.001).

The mean serum concentration of paliperidone was 35± 29 ng/ml (25th-75th percentiles 18-44 ng/ml) in the 106 patients receiving paliperidone as antipsychotic monotherapy. Among the 63 patients for whom GCI scores of improvement were known, 32 were very much or much improved (Fig. 2). The mean paliperidone serum concentration of these patients was 43±39 ng/ml (25th-75th percentiles 20-52 ng/ml). Among patients who showed minimal or no improvement (n=31), the mean paliperidone serum concentration was 33±24 ng/ml (25th-75th percentiles 19-41 ng/ml). Co-medications in patients receiving antipsychotic monotherapy with paliperidone included antidepressants (27%), mood stabilizers (17%), anxiolytic or hypnotic drugs (31%), or non-psychiatric drugs (38%). Drugs with an inhibiting or inducing potential on the cytochrome P450 3A4 (CYP3A4) isoenzyme, which is involved to some extent in the metabolism of paliperidone, were not present.

Analysis of the complete patient sample for side effects revealed that more than half of the patients (62.3%) were free from side effects according to the physician's report (UKU scale), with 28% developing mild adverse events, 8.5% moderate adverse events, and 1.5% severe adverse events. The most frequently reported adverse events were somnolence (18.9%), extrapyramidal disorder (16.8%), and agitation (3.2%). There was no observable correlation between dose or serum concentrations of paliperidone and side effects (Fig. 3). In a separate analysis, we compared patient intra-and inter-individual variabilities in paliperidone serum concentrations with those of patients treated with risperidone using data from a single medical center (Mainz). A total of 30 patients were included in this analysis, 13 of whom received paliperidone and 17 risperidone. A mean of 4.3± 1.5 (range: 3-8) measurements were made on each patient, and a total of 134 samples were analyzed. Of this group of 40 patients, 45% were male and 55% female, and the mean age was 39.4±10.6 years (Table 1). We found no significant differences between the coefficients of variance of serum concentrations. Intra-individual variability was 35±15% for paliperidone and 32±19% for the risperidone active moiety (Table 1).

Discussion

In this study we analyzed paliperidone serum concentrations in psychiatric patients treated with paliperidone, and we compared variabilities in the trough serum levels in patients receiving paliperidone or risperidone as antipsychotic therapy. In patients receiving paliperidone as antipsychotic monotherapy and showing at least a much improvement level (according to the CGI-I scale), the 25th-75th percentiles of paliperidone serum levels were 20-52 ng/ml. This range was almost identical with the recommended optimal plasma concentration of 20-60 ng/ml for the risperidone active moiety [START_REF] Baumann | The AGNP -TDM expert group consensus guidelines: therapeutic drug monitoring in psychiatry[END_REF]. The intra-individual variabilities of trough serum concentrations were similar for paliperidone and risperidone plus 9-hydroxyrisperidone. The concentrations of risperidone and 9-hydroxyrisperidone measured in these patients are very similar to those reported previously by other investigators [START_REF] Riedel | Risperidone plasma levels, clinical response and side-effects[END_REF][START_REF] Aichhorn | Influence of age and gender on risperidone plasma concentrations[END_REF].

Regarding the similar intra-individual variability in serum concentrations of paliperidone and risperidone, it should be noted that TDM measures trough levels. The ER formulation of paliperidone reduces the peak-to-trough fluctuations of drug concentrations in blood under steady state conditions [START_REF] Karlsson | Pharmacokinetics, dopamine D2 and serotonin 5-HT2A-receptor occupancy and safety profile of paliperidone extended-release in healthy subjects: two open-label, single-dose studies[END_REF]. According to the summary of product characteristics (SPC), the peak-trough fluctuation index is 38% for paliperidone and 125% for the immediate-release formulation of risperidone [17]. Flattening of the pharmacokinetic profile can be obtained by decreasing peak levels, by increasing trough levels, or by both. Our measurements conducted under the naturalistic conditions of the TDM indicate that an increase in trough levels was unlikely since dose-and weight-corrected trough concentrations of paliperidone and risperidone plus the active metabolite were similar in patients receiving the ER formulation of paliperidone or the immediate-release formulation of risperidone. This result is consistent with data from a pharmacokinetic study on five healthy male subjects [START_REF] Vermeir | Absorption, metabolism, and excretion of paliperidone, a new monoaminergic antagonist, in humans[END_REF]. Moreover, a pharmacokinetic characterization of OROS and immediate-release amitriptyline has shown that acute doses of the OROS formulation affect primarily peak concentrations without affecting the elimination halflife of the antidepressant drug [START_REF] Gupta | Pharmacokinetic and pharmacodynamic characterization of OROS® and immediaterelease amitriptyline[END_REF]. Similarly, our data provide evidence that steady state trough concentrations of paliperidone and risperidone are controlled by the metabolic and secretory capacities of the liver and the kidneybut not by the formulations of the drugs. In both drugs, the CYP3A4 isoenzyme is involved in the metabolic pathways [START_REF] Jung | Cytochrome P450 3A inhibitor itraconazole affects plasma concentrations of risperidone and 9-hydroxyrisperidone in schizophrenic patients[END_REF]. For risperidone, CYP2D6 plays the predominant role in the formation of 9-hydroxyrisperidone [START_REF] Ereshefsky | Pharmacokinetics and drug interactions: updates for new antipsychotics[END_REF]. Since CYP2D6 activity can be compromised due to a genetic deficiency or co-medication with a CYP2D6 inhibitor, the variability in plasma concentrations should be higher for risperidone than for paliperidone. However, when the "active moiety" of risperidone is taken into consideration and its elimination is compared with that of paliperidone, CYP2D6 becomes of minor importance [START_REF] Vermeir | Absorption, metabolism, and excretion of paliperidone, a new monoaminergic antagonist, in humans[END_REF] as concentrations of the active moiety of risperidone are not significantly different in individuals with an active or inactive CYP2D6 isoenzyme, respectively [START_REF] Scordo | Cytochrome P450 2D6 genotype and steady state plasma levels of risperidone and 9-hydroxyrisperidone[END_REF]. Another factor that contributes to pharmacokinetic variability of the two drugs is the efflux transporter P-glycoprotein (P-gp), which is expressed in several organs, especially in the intestinal epithelia and in the blood-brain barrier. Both risperidone and 9-hdroxyrisperidone/paliperidone are substrates of P-gp [START_REF] Doran | The impact of p-glycoprotein on the disposition of drugs targeted for indications of the central nervous system: evaluation using the MDR1A/1B knockout mouse model[END_REF][START_REF] Gunes | ABCB1 polymorphismus influence steady-state plasma levels of 9hydroxyrisperidone and risperidone active moiety[END_REF][START_REF] Kirschbaum | Pharmacodynamic consequences of P-glycoprotein-dependent pharmacokinetics of risperidone and haloperidol in mice[END_REF]. The expression of P-gp may vary due to genetic abnormalities and from inhibition or induction by co-medications. The unlikelihood of CYP3A4 and P-gp differing in their contribution to the elimination of either risperidone or paliperidone [17] provides a good explanation for why our observed variabilities in drug concentrations were not different for the two drugs.

In patients who were very much or much improved according to the CGI-score, the 25th-75th percentiles of paliperidone serum levels were 20-52 ng/ml. In an earlier TDM study on amisulpride, we defined patients with at least a level of much improvement as "res-ponders" and thus calculated optimal plasma concentrations of amisulpride based on clinical effects [START_REF] Müller | Therapeutic drug monitoring of optimizing amisulpride therapy in patients with schizophrenia[END_REF]. In this study, however, the power of our data was not sufficient to evaluate a therapeutic range for paliperidone. Nevertheless, the 25th-75th percentile range of serum levels was found to be similar to the clinically defined optimal target range (20-52 ng/ml) and thus was very similar to the therapeutic range reported for the sum of concentrations of risperidone plus 9-hydroxyrisperidone (20-60 ng/ml) [START_REF] Baumann | The AGNP -TDM expert group consensus guidelines: therapeutic drug monitoring in psychiatry[END_REF]. This observation suggests that paliperidone and risperidone exhibit similar optimal serum concentrations. The 20-60 ng/ml range can be considered as a preliminary target range of paliperidone when applying TDM for treatment optimization and is slightly higher than the one derived from a recent positron emission tomography (PET) study with paliperidone [START_REF] Arakawa | Dose-finding study of paliperidone ER based on striatal and extrastriatal dopamine D2 receptor occupancy in patients with schizophrenia[END_REF]. In that study, paliperidone serum concentrations in the range between 16 and 27 ng/ml led to 65-80% striatal dopamine D 2 receptor occupancy, which is the D 2 occupancy range considered to be optimal for antipsychotic treatment [START_REF] Farde | Positron emission tomographic analysis of central D 1 and D 2 dopamine receptor occupancy in patients treated with classical neuroleptics and clozapine. Relation to extrapyramidal side effects[END_REF][START_REF] Kapur | Relationship between dopamine D(2) occupancy, clinical response, and side effects: a double-blind PET study of first-episode schizophrenia[END_REF][START_REF] Gründer | Mechanism of new antipsychotic medications: occupancy is not just antagonism[END_REF]. PET studies on patients receiving risperidone also suggest that optimal (striatal) D 2 receptor occupancy levels are achieved with serum concentrations of approximately 15-40 ng/ml [START_REF] Medori | Plasma antipsychotic concentration and receptor occupancy, with special focus on risperidone long-acting injectable[END_REF][START_REF] Nyberg | Suggested minimal effective dose of risperidone based on PETmeasured D2 and 5-HT2A receptor occupancy in schizophrenic patients[END_REF] or probably somewhat higher [START_REF] Remington | A PET study evaluating dopamine D2 receptor occupancy for long-acting injectable risperidone[END_REF]. The striatal median effective dose (ED 50 ) values calculated from PET studies are surprisingly similar for paliperidone (6.65 ng/ml) [START_REF] Arakawa | Dose-finding study of paliperidone ER based on striatal and extrastriatal dopamine D2 receptor occupancy in patients with schizophrenia[END_REF] and the risperidone active moiety (6.87 ng/ml) [START_REF] Nyberg | Suggested minimal effective dose of risperidone based on PETmeasured D2 and 5-HT2A receptor occupancy in schizophrenic patients[END_REF], which supports the view that the relationship between serum levels and D 2 receptor occupancy is very similar for both compounds. Further PET studies on the relationship between serum levels, brain receptor occupancy, clinical effects, and side effects in larger patient samples are needed to resolve the slight discrepancies between the optimal therapeutic ranges suggested by PET studies and TDM surveys, respectively.

The side effects observed in our study were not significantly related to the doses or serum concentrations of paliperidone. This lack of correlation may be explained by the small number of patients. Side effects occurred only in a limited number of patients which reduces the power of the statistical analysis.

Our approach used a retrospective analysis of data without a fixed dose design, as we considered the latter to be the optimal approach to define therapeutic concentrations of a drug [START_REF] Baumann | The AGNP -TDM expert group consensus guidelines: therapeutic drug monitoring in psychiatry[END_REF]. Therefore, this study has a number of limitations. Data were obtained from routine TDM surveys. Data on clinical improvement or side effects were missing for a significant number of patients and, therefore, the total number of patients who could be used in the various pharmacokinetic and pharmacodynamic analyses differed. The patients included for analysis were real life patients. As such, they were treated under naturalistic conditions which allowed co-medications which also affected clinical outcomes. The treatment duration of each patient receiving paliperidone as medication was not standardized. Variability due to pharmacokinetic interferences would seem to be unlikely since the data did not include patients under co-medications that may have given rise to interaction, namely, inducers inhibitors of CYP3A4. Despite the marked limitations of our experimental conditions, the two antipsychotic drugs paliperidone and risperidone behaved in a rather similar manner in terms of the serum concentrations considered to be optimal when using TDM for dose optimization. A similarity was also observed for the variability of the trough levels of the drugs. We suggest that the clinically relevant differences between medication with paliperidone or risperidone, which differ in galenic formulation and phase-I metabolism, are likely attributable to the phase of absorption rather than to the phase of elimination of the drugs. Based on these results, we conclude that TDM is useful for treatment optimization of patients with paliperidone. The target range of 20-60 ng/ml recommended for risperidone [START_REF] Baumann | The AGNP -TDM expert group consensus guidelines: therapeutic drug monitoring in psychiatry[END_REF] seems likely to be the target plasma concentration for paliperidone as well.

Fig. 1 Fig. 2

 12 Fig. 1 Box plot of the correlation of paliperidone serum concentrations with the given dose

Fig. 3

 3 Fig. 3 Box plot of the tolerability (as measured by the UKU scale) and serum concentrations of paliperidone

Table 1

 1 Mean ± SD doses (mg) and drug concentrations (ng/ml) and intra-individual coefficients of variance (CV%) in patients treated under naturalistic conditions with either paliperidone or risperidone who were supervised by repeated therapeutic drug monitoring

	Variable	Paliperidone mean ± SD	Risperidone mean ± SD	p value
	Number of patients	13	17	-
	Daily dose (mg/day)	9.1±2.2	5.1±2.3	0.000 a
	Number of samples per patient taken for TDM	4.2±1.7; range 3-8; median 3	4.4±1.3; range 3-7; median 4	NS b
	Age (years)	37.1±12.4	41.1±8.9	NS a
	Number of dose changes	1.0 ± 0.7; range 1-2; median 1	1.5 ± 1.4; range 0-4; median 1	NS b
	Gender (% male)	58	35	NS b
	Total serum concentration (ng/ml)	54.8±38.6	31.6±14.4	NS b
	Dose-corrected serum concentration (ng/ml/mg)	6.2±4.1	7.1±3.0	NS b
	Dose and weight-corrected serum concentration	5.0±3.6	6.5±3.1	NS b
	[(ng/ml/mg)/weight × 70 kg]
	CV% of total serum concentration (ng/ml)	32.2	33.8	NS b
	CV% of dose-corrected serum concentration (ng/ml/mg)	34.6	32.4	NS b
	CV% of weight and dose-corrected serum concentration	30.3	32.4	NS b
	((ng/ml/mg) /weight × 70 kg)

TDM, Therapeutic drug monitoring; CV%, coefficients of variance; NS, not significant Where appropriate, values are given as the mean ± standard deviation a t test b Mann-Whitney U test