Anna Matas
email: anna.matas@uab.es

Josep-Lluis Raymond
email: josep.raymond@uab.es

C51 -Model Construction and Estimation < C5 -Econometric Modeling < C -Mathematical and Quantitative Methods, L62 -Automobiles|Other Transportation Equipment < L6 -Industry Studies: Manufacturing

Keywords:

published or not. The documents may come

Introduction

Quality improvements over time for some durable goods pose the long-discussed question of how to construct price indexes taking quality changes into account. As is well-recognised, the hedonic approach offers an adequate methodology to adjust prices for quality changes.

In this paper we address the issue of instability of coefficients of the hedonic equations over time, and present two alternative methodologies to deal with this problem. As is known, the hypothesis of parameter stability over time assumed by the traditional pooled regression approach is often rejected by the data. On the other hand, single period regression equations tend to estimate erratic coefficients, due, at least partly, to econometric problems. Our proposal builds on an intermediate solution between the two aforementioned approaches. We propose firstly to estimate the hedonic equation using a moving sample, and secondly, to compute the implicit price for the characteristics from a weighted moving average of the coefficients estimated in the single period regressions. Moreover, statistical tests are provided to test the simplifying assumptions.

The proposed methodologies are also compared with the frequently used adjacent year approach. Besides, the study offers a comparison of quality-adjusted price indexes constructed using each of the alternative methodologies.

We have applied the proposed methodology to the Spanish car market over the period . The choice of the car market is justified by the large number of quality improvements in the performance and characteristics of cars that has taken place as a result of technological changes. Quality improvements can be observed in different areas, such as comfort, safety, performance, reliability and fuel efficiency. In fact, the seminal papers on hedonic methodology by Court in 1939 and Griliches in 1961 are both applied to the car market.

On empirical grounds, the paper presents a decomposition of the variation in observed automobile price into the variation due to changes in the characteristics and a pure or quality-constant price effect. Moreover, the approach makes it possible to compute an index for the various quality dimensions. Finally, the paper shows a process of sigmaconvergence in quality-adjusted prices related to Spain's integration into the European Community (EC).

The hedonic methodology

Background

The first empirical research relating price and quality is attributed to the work of Waugh, who in 1928 estimated a price function on vegetables [START_REF] Berndt | The Practice of Econometrics: classic and contemporary[END_REF]. In 1939 Court estimated a multiple regression equation, which he named hedonic method, which related car prices to the relevant car characteristics, with the final objective of constructing a quality-adjusted price index for the automobile market in the US. However, it was not until Griliches's work in 1961, also applied to the car market, that the hedonic approach became widespread. Nowadays it is used by some statistical agencies to compute price indexes adjusted by quality, and there has been a renewed interest from empirical and theoretical research. In particular, this method is applied to the computer, automobile and housing markets. A recent and up to date review can be found in Triplett (2004). For the car market, see the studies by Otha and Griliches F o r P e e r R e v i e w (1986), [START_REF] Bajic | Automobiles and implicit markets: an estimate of structural demand model for automobile characteristics[END_REF], [START_REF] Arguea | Estimating consumer preferences using market data -an application to US automobile demand[END_REF], [START_REF] Raff | Quality adjusted prices for the American automobile industry: 1906-1940[END_REF], [START_REF] Murray | Price-quality relations and hedonic price indexes for cars in the United Kingdom[END_REF], [START_REF] Izquierdo | Mejoras de calidad e índices de precios del automóvil en España[END_REF], [START_REF] Reis | Hedonic prices indexes for new passenger cars in Portugal[END_REF], van Dalen and Bode (2004) and [START_REF] Requena-Silvente | Calculating hedonic price indices with unobserved product attributes: an application to the UK car market[END_REF].

The underlying hypothesis of the hedonic analysis is that goods can be viewed as a bundle of attributes or characteristics, and the demand for a good is really a demand for the attributes it contains. According to this hypothesis, the price of a good can be expressed as a function of its characteristics, and the relationship between price and characteristics is called the hedonic function. The estimation of a hedonic price equation makes it possible to distinguish between the variation in prices explained by a change in the characteristics and the variation that can be attributed to a pure price effect.

Initially, hedonic regressions were viewed as an ad hoc empirical instrument to construct a quality-adjusted price index. Its theoretical basis is found on the consumer theory developed among others by [START_REF] Houthakker | Compensated changes in quantities and qualities consumed[END_REF] and [START_REF] Lancaster | A new approach to consumer theory[END_REF] in the characteristics space. Later, [START_REF] Rosen | Hedonic prices and implicit markets: product differentiation in pure competition[END_REF] expanded the theoretical foundation 1 . In this study, we interpret the hedonic equation as an instrument to approximate the evolution of price indexes, taking into account the variation in product characteristics. Regression coefficients can be interpreted as implicit prices for characteristic. Despite the large literature devoted to the hedonic price function, some methodological problems have yet to be solved 2 . One of these problems is how to deal with the instability of coefficients over time. In the following section, two possible solutions to this issue are proposed.

Alternative proposals for estimating hedonic prices

Given that the coefficients in the hedonic equation can be interpreted as the result of the interaction of the demand and supply curves for characteristics, a shift in any curve might cause a change in the estimated coefficient over time. Thus, in empirical implementation, the stability of the parameters over time has to be tested. The most obvious alternative consists of estimating year-by-year equations and testing equality restrictions among coefficients.

The problem with single year equations is that the estimated coefficients tend to be very erratic due to the reduced number of degrees of freedom along with a high level of multicollinearity among characteristics. In that case, it is not possible to obtain a reliable valuation of individual characteristics or any group of them over time 3 .

2 See [START_REF] Diewert | Hedonic regressions: a review of some unresolved issues, 7 th Meeting of the Ottawa Group[END_REF]Triplett (2004, chapters V andVI). 3 Empirical evidence shows that the estimated coefficients in yearly equations are highly volatile. As long as these coefficients approximate implicit prices for characteristics, it seems desirable for both their magnitude and sign to behave according to the expected values. In our view, the volatility in the estimates can be largely explained by econometric problems. The main problems when estimating hedonic equations are multicollinearity and the reduced number of degrees of freedom which result in large variance of some of the estimated coefficients which in turn produce instability in their value. This view has however been recently disputed by Pakes in several provocative papers. In the context defined in footnote 2, this author argues that the coefficients in the hedonic function do not necessarily obey any of the restrictions associated with utility or costs functions [START_REF] Pakes | Hedonics and the consumer price index[END_REF]. As has been recognised [START_REF] Berndt | Hedonics for personal computers: a reexamination of selected econometric issues. R&D, Education and productivity[END_REF]Triplett, 2004, p.236-238), although some of the issues in Pakes's work are still controversial, it has made remarkable contributions to the hedonic theory. The issue we address in this paper is the econometric problems that arise when estimating yearly equations with limited sample size. The present paper proposes two alternative methodologies for improving the way the value of the characteristics is estimated. The first alternative is based on the estimation of the regression equations using a moving sample of the observations, and the second, on a weighted moving average of the estimated coefficients in the single period equations. In each case it is necessary to fix the best order for the averages. With the aim of validating the alternatives, the underlying hypothesis of equality of coefficients is tested for each specification. Additionally, the study shows how the new proposals improve the results obtained in the adjacent period approach, which is the common way to address the problem of coefficients instability.

Finally, our results corroborate the previous finding that instability of individual coefficients is not a problem for the construction of a hedonic price index. The adjusted quality price index is very similar for all alternatives approaches. This result confers robustness on the estimation of the hedonic price index. The five alternatives used in estimating the hedonic equations are set out below.

Time dummy variable method or pooled equation

This method assumes constant coefficients and includes time dummy variables. It has been widely used in empirical research in hedonic prices. All the observations are "pooled" into a single regression equation and the estimated coefficients are common to all periods. The estimated equation can be expressed as: The hypothesis of stability of coefficients over time can be tested using a conventional F test.

it it it t it Z X p + + + + = ' ' T t ,..., 2 , 1 = (1)

Single period equations

In the unconstrained approach, separate equations are specified for each time period:

i i i i Z X p + + + = ' '
(2)

Adjacent year equations

This approach combines data from two periods so that the characteristic coefficients are held constant only for two periods. A time dummy variable, , is included for the second year. This approach is also targeted to improve the problem of instability of coefficients and, hence, we will devote special attention to the comparison of its results with those of our proposals 4 .

it it it it Z X D p + + + + = ' ' t=t, t+1
where D is a dummy variable that takes value 1 for observations in the second year.

The F-test is used to test the constraint on equality of coefficients. 4 In this point we acknowledge the suggestion of an anonymous referee.

where the sub-index ms denotes that the parameter corresponds to a moving sample of h periods.

The regression equation is estimated for a centered moving sample of order h. A different vector of coefficients is estimated for each moving sample and, as in the previous case, an F-test allows us to test equality among coefficients and to establish the order of the moving sample.

5. Weighted moving average of the coefficients estimated in the single period regressions

The second new alternative put forward involves computing the implicit price for the product characteristics by constructing a weighted moving average of the coefficients estimated in the single period equations. This approach has the advantage that it makes it possible for the coefficient to take different values over time, while at the same time the erraticity found in annual estimates is smoothed out. Again, the restriction imposed on the coefficients and the order of the moving average can be tested. The basis for this procedure can be stated as follows. To fix ideas, let the order of the moving average be 3. We have three estimates for , i j , where i stands for a product characteristic and j for a year: , 1 ,0 , 1 ˆˆ, , i i i + . Let us assume that these are unbiased estimates. Then, the following estimator can be constructed5 :

1 , 1 0 ,0 1 , 1 1 , 1 0 ,0 1 0 , 1 ˆˆˆˆˆˆ• • • • • (1 )• i i í i i i i + + + = + + = + + (4)
Generally, the estimator can be written as:

ˆ• i i =
, where

, 1 ,0 , 1

ˆˆˆ( )

i i i i + = (5)
• 1 l = , where l is a unit vector.

It holds:

ˆvar( ) •cov( )• i i = (6)
By using the Lagrange multiplier method, the expression to minimise is:

1 •cov( )• •(1 • ) 2•cov( )• • 0 1 •cov( ) • • 2 i i i l l l µ µ µ = + = = = (7)
Multiplying by l :

1 1 1 1 ˆ• 1 • •cov( ) • • 2• •cov( ) • 2 i i l l l l l µ µ = = = (8)
We have:

1 1 1 1 1 1 1 ĉov( ) • 1 ˆˆ• cov( ) • • cov( ) • • •cov( ) • 2 •cov( ) • i i i i i l l l l l l l µ = = = (9)
Hence, the estimator of that minimises the variance of ˆ is:

F o r P e e r R e v i e w 1 1 ĉov( ) • • cov( ) • i i l l l = (10) If ĉov( )
i is a diagonal matrix, as can be expected in our case given that we run separate estimates, the weighting for ĉov( ) i will be:

, , 1 var( ) 1 var( )

i j i j i j = (11)
Finally, we propose a procedure to determine the number of periods to be included in the moving average. Let us again assume that we have a 3-moving average. To guarantee that the estimated average has sense, we need the following assumption for the underlying population:

, 1 ,0 , 1

i i i i + = = = If 1 ,
ˆ i is the estimated price for characteristic i using the sample for year -1, 0 , ˆi is the estimated price for characteristic i using the sample for year 0, and 1 , ˆ+ i is the estimated price for characteristic i using the sample for year +1, the following hypotheses must be satisfied:

2 , 1 1 ˆ( , ) i i N 2 ,0 0 ˆ( , ) i i N (12) 2 , 1 1 ˆ( , ) i i N + +
Assuming temporal independence in ˆi , under the null hypothesis it must be verified that:

F o r P e e r R e v i e w 2 2 2 , 1 ,0 , 1 2 3 1 0 1 ˆˆî i i i í i + + + + (13)
This distribution is still asymptotically satisfied when the population is substituted by its estimates. The proposed criterion would be similar for testing higher order moving averages.

Accordingly, the order of the moving average can be tested for each characteristic. The higher the selected order of the moving average, the higher will be the smoothing imposed on the parameters, but at the same time the higher the number of t lost (a 3moving average implies losing the for the first and last year in the sample, whereas a 5-moving average implies losing two at the beginning and two at the end), and the lower the adjustment capacity of the underlying price model.

The data

The data set for our study covers a 24-year period from 1981 to 2005. Over this period we collected data for car models with higher sales figures in Spain, coming to roughly 90% of total registrations. The total number of observations is 1970, with an average of 82 models per year, although the number of models increases for more recent years6 . In our opinion, the sample gathered is a representative sample of market trends. The prices and characteristics of the car models were obtained from specialist magazines. The price used thus corresponds to list prices, as is often the case in hedonic analysis. In addition, car prices include VAT and special car tax. Table A.1. in the appendix offers descriptive statistics for the dependent variable.

A relevant issue in hedonic analysis is the selection of the explanatory variables in the model. These variables should reflect the set of characteristics that consumers look for when choosing a new car. In this study, the selection of the variables to be included as regressors was based on the results reported in the literature 7 , taking into account the limitation of our data source. We expect that the characteristics used are a reasonable approximation to the consumer's price determinants. The variables are grouped into six categories and summarised in Table 1.

Dummy variables for car manufacturers were included in order to account for unobservable attributes that are related to characteristics like reliability or other unobserved attributes. Finally, annual dummy variables on imported cars entered the equation to capture the effect of tariffs. It should also be mentioned that we tried a number of other explanatory variables in preliminary analyses that did not prove to be statistically significant 8 .

Estimation issues

7 We draw heavily on [START_REF] Raff | Quality adjusted prices for the American automobile industry: 1906-1940[END_REF]. 8 For instance, number of gears, maximum speed, number of airbags and central locking. The first issue to be considered is the functional form for the hedonic regression. Given that economic theory does not restrict the functional form for hedonic functions 9 , we proceeded by choosing the functional form that best fits the data. The starting point was the Box-Cox formulation, transforming the dependent variable and independent variables with a different parameter, which nests the most common functional forms used in hedonic regressions. To select the final specification we computed the likelihood function after taking into account the transformation of the dependent variable in order to guarantee that its value could be compared among the different specifications. Table 2 presents the value of the likelihood function for the Box-Cox and semi-log formulation using the time dummy variable approach 10 . Although the likelihood function was maximised for a Box-Cox, the semi-log formulation (taking logs of the dependent variable) could not be rejected and it was also the preferred option in terms of the Schwarz criterion. Given these results, and taking into account that the semi-log formulation is simple to estimate and easy to interpret, this was the selected specification 11 .

A second issue to be considered is whether the hedonic regression should be weighted or unweighted 12 . Our preferred option has been not to weight. In fact, as [START_REF] Deaton | The analysis of households surveys: A microeconometric approach to development policy[END_REF] remarks, under the standard assumptions of the linear regression model weighting leads 9 Rosen (1974) established that the hedonic functional form is an empirical issue. Subsequent studies showed that only under very restrictive assumptions is it possible to restrict the functional form. 10 It should be noted that the same result was reached by the single year equations approach. Nevertheless, it would be too cumbersome to present all the estimations year by year. 11 The semi-log functional form has been widely used with automobile data; see, for instance, [START_REF] Bajic | Automobiles and implicit markets: an estimate of structural demand model for automobile characteristics[END_REF], [START_REF] Murray | Price-quality relations and hedonic price indexes for cars in the United Kingdom[END_REF], van Dalen and Bode (2004) and Requena-Silvente and Walker (2006).

12 A clear distinction should be made between weighting the hedonic regression and weighting the hedonic price index (see, Triplett 2004, pp.189-193). to a loss of efficiency. Even if those assumptions are not satisfied, weighting will not generally be the appropriate solution 13 .

Once the functional form had been selected, we proceeded to estimate the hedonic equation according to the five alternatives set out in section 2. All the equations have been estimated in current prices. This decision does not affect the estimated coefficient for the characteristics, it only affects the coefficient of the time dummy variables.

First, the estimation results for the pooled regression model, presented in Table A.2 in the appendix, show a good fit. In addition, the estimated coefficients take the expected sign and are statistically significant. Since some heteroskedasticity was observed, the variance-covariance matrix was computed using the White procedure. However, the standard errors were very similar in both formulations; i.e., under the standard approach or using White formulation. It is interesting to test whether disturbance heteroskedasticity is present over time. In order to test this possibility we followed the procedure suggested by [START_REF] Berndt | Hedonics for personal computers: a reexamination of selected econometric issues. R&D, Education and productivity[END_REF]. Thus, we regressed the squared residuals on a constant and a set of annual dummy variables, and computed the F-test 13 A frequently discussed issue in the literature is whether in order to estimate the hedonic price equations the variables must be weighted or not. In fact, under the usual regression model hypothesis, weighting the observations by the market shares of car models has not a conceptual justification. As it is well known, in this case weighting must lead to a loss of efficiency meanwhile not weighting must lead to a BLU estimation. Also, under these hypotheses, both weighted least squares and unweighted least squares must be consistent. So, if the model specification satisfies the standard hypothesis, it could be expected that weighted and unweighted least squares will lead to similar values for the estimated coefficients. Nonetheless, for the exposed reasons, the not weighted least squares is the preferred alternative. In our case, using a sample for the period 1987-2004 for which data on sales by car model are available, the estimated parameters in the weighted and not weighted alternatives are rather similar. Computing a 95% confidence interval for the valuation of the characteristics that results from the two options the two intervals always overlap, and taking as a reference the unweighted estimates, the percentage of overlapping is 47% for the variable displacement, 74% for H.P/weight, 92% for size, 84% for fuel consumption, 84% for diesel, 54% for minivan, 67% for number of doors, 94% for air conditioned, 87% for climate control, 88% for ABS, 63% for assisted steering, 94% for electric windows and 100% for automatic gear. The estimated coefficients for the dummy variables can be interpreted as the percentage increase in car price derived from the introduction of a new attribute. For instance, those cars with a climate control system are 13% more expensive, holding the rest of the characteristics constant. Brand effects are computed with respect to Seat, probably the most representative Spanish car manufacturer. The significance of the estimated coefficients shows that there is a brand-quality effect over and above the included car attributes. Mercedes cars appear as the most expensive brand, once the characteristics have been controlled for. In the semi-log formulation, the coefficient for the time dummy variables reveals the variation in the log of the price adjusted by quality change.

That is, the antilogarithm of the estimated coefficient for year t can be interpreted as the percentage change in the car price between the base period and period t, maintaining quality constant. In our case, the coefficient estimated for year 2005 implies that, holding constant the characteristics, nominal car prices have increased by a factor of 2.31 between 1981 and 2005.

The estimated coefficients for the dummy variables on imported cars clearly showed the process of tariff reductions that took place once Spain joined the European Community in 1986 14 . The coefficients were no longer significant after 1992, when the tariff reached zero for Europeans cars. In the preliminary estimations, we include a dummy on imported cars for those years after 1992. However, the coefficients were not 14 The process of tariff reduction started in 1986 and finished in 1992. Over those years taxes on European cars fell from 65% to zero. The main problem with the time dummy variable method is that it assumes parameter stability over time. With the aim of relaxing this assumption, we proceeded according to the proposals detailed in section 2. We began by estimating the most general model, i.e., the yearly regression equations, followed by the adjacent year approach. We then estimated the hedonic function for a moving sample of order 3 and 5, and finally we calculated the coefficients on car attributes as a moving average of the estimated coefficients in the single year equations. Again the order of the moving average was limited to 3 and 5. Table 3 summarises the results of yearly, adjacent year and moving sample estimations15 .

As is usual, the estimated coefficients in the single year regressions varied considerably from one year to another, and their observed behaviour could not be explained either on economic or on technical grounds. The adjacent period approach reduced the instability of coefficients but still the erratic behaviour of the coefficients could be observed.

However, the estimations using order 3 and 5 moving samples smoothed out the changes in the estimated coefficients. To illustrate this fact, in Figure 1 we plotted the estimated coefficients in the adjacent year and order 5 moving sample specifications for two car attributes: engine power (horsepower/weight) and car size.

In order to provide more formal evidence about the advantage of the moving sample approach over the yearly equations and the adjacent year ones we constructed three approaches. These criteria have been computed for the continuous variables in the equation. We report the standard error of the elasticities, and not directly the standard error of the coefficients, in order to make comparisons between variables meaningful.

Table 4 shows the results. It can be observed that the moving sample will always be the selected approach under the three criteria.

Additionally, we have constructed a normal distribution for the elasticity of the continuous variables estimated according to the adjacent year approach and the order 3 and 5 moving samples. Figure 2 shows how the precision of the estimation increases when we change from year equations to the moving sample 16 .

The validity of the new proposals needs to be tested against the yearly equation model.

Thus, the hypotheses regarding the temporal stability of the characteristic coefficients with respect to the single year equations were tested using the F-test. The results are presented in Table 5. Comparing the yearly regressions with the pooled model, the hypothesis of parameter stability over time is rejected. In contrast, at a 5% significance level, the hypothesis of equality restrictions both for the adjacent year approach and for 16 A normal distribution has been generated for each estimated elasticity, the mean being the average of the estimated elasticities for each year in the sample and the standard deviation the average of the estimated standard errors. It is interesting to remark that the mean value of the estimated elasticities under the three estimation approaches are very similar but the standard deviations substantially differ. the order 3 moving sample was not rejected in any of the cases, whereas that for the order 5 moving sample was marginally rejected only in three cases out of 21.

The second proposal to correct for erraticity in the estimated coefficients consists of calculating the weighted average of annual coefficients, using the inverse of the variance as weights. As was previously stated, when deciding on the order for the moving average, a trade-off exists between the degree of smoothing and the flexibility of the coefficients in accommodating structural changes over time. Given the time span for our data, we propose to use order 3 and order 5 moving averages and test the equality constraints. In this case the test on equality restrictions entails testing equality among coefficients according to the proposal detailed in section 2. For the order 3 moving average, the null hypothesis of stability of the slope coefficients was rejected only in 5 cases out of 745 computed averages, at a significance level of 5%. For the order 5 moving average, the hypothesis was rejected in 12 cases from 667.

At the usual significance levels, the results on equality restrictions support the alternative methodologies suggested in this paper. That is, the procedures based either on moving samples or on moving averages of coefficients allow for temporal changes in the estimated coefficients, as demand or supply curves shift over time, while avoiding the situation where the erratic variation in the coefficients, tied to the multicollinearity problem and to the reduced sample size, hinders their economic interpretation. In the previous section we provided support for alternative methodologies to estimate hedonic equations. Now we turn to the essential objective of hedonic equations; i.e.

Results

Computation of quality-adjusted prices

computing quality-adjusted price indexes or hedonic indexes. The question is: does the methodology used make a difference to the price index in our case? To answer this question we computed the rate of change of the price index applying each alternative procedure.

The hedonic regression in period t has the following form:

it it it t it Z X p + + + = ' ' ) ln( (14)
The semi-log formulation makes it possible to define the mean variation of quality adjusted prices as the difference between the variation in the average observed prices minus the variation that can be attributed to the changes in the mean values of each of the X characteristics and each of the Z brands for different time periods. Thus, the variation in the index for periods t and t-1 will be given by: In accordance with expression 15, we computed the price index variation rate for six of the hedonic formulations employed: adjacent year; 3-moving sample; 5-moving sample;

3-moving average of the coefficients of single period estimates, 5-moving average of the coefficients of single period estimates and pooled equation 18 . As can be observed in Figure 3, our findings are that all indexes are remarkably close across alternative methodologies 19 .

The fact to be stressed is that, although the marginal prices for characteristics differ substantially depending on the methodology employed, the rate of variation of the quality-adjusted price index is very similar for all six alternative formulations. The reason for this apparent paradox is that the multicollinearity and the reduced degrees of freedom distort the yearly regression coefficients. However, when adding up the contributions of all explanatory variables, the differences cancel out, so that the behaviour of quality adjusted prices is very similar, irrespectively of the formulation employed to estimate the characteristics.

The previous result can be tested in a more formal way as follows. By comparing the price index for two alternatives, we have: ln( ) ln( )

ijt it jt d I I = (16)
Where, i and j denote different estimation methods. Thus, ( )

ij ijt N d , 0 (17)
18 When computing the index for the single year equation between years t and t-1, it is necessary to choose the reference year. A common option suggested in the literature [START_REF] Diewert | Hedonic regressions: a review of some unresolved issues, 7 th Meeting of the Ottawa Group[END_REF]) is to use the arithmetic average of the coefficients estimated in t and t-1. This procedure offers very similar results to those obtained when estimating according to adjacent year method. In fact, as Triplett (2004, p.63) argues, one of the earliest empirical regularities found in the hedonic literature is that the adjacent period regression often yields coefficients that are approximately the average of the coefficients estimated from a separate regression in the two periods. This is the reason why the single year approach is not presented. 19 The moving sample and moving average formulations do not allow the index for the latest years in the sample to be calculated. These values have been forecast by using an AR model. Table 6 summarises the statistic computed for all possible pairs of combinations between alternative estimations. In all cases, the null hypothesis could not be rejected at a high significance level.

To sum up, our contribution to hedonics is a new strategy that can be defined as a compromise solution for estimating the marginal prices for characteristics between two polar alternatives: the time dummy variable model -which assumes that marginal prices for characteristics are constant over time -and single period estimations -that allow estimated coefficients to vary freely year-by-year. In any event, in our study the price indexes based on models with different assumptions about parameter stability are robust to the specified hypothesis.

Price indexes behaviour

Once the methodological issues have been dealt with, this section focuses on the empirical results yielded by the study. The reported results are based on an order 3 moving average equation. Taking into account that equality restriction among the price indexes has not been rejected, the selection of this equation is due to the fact that it provides smoothed coefficients, at the cost of losing only two observations. First, we present an analysis of the decomposition of the observed prices for cars according to the different components included in the hedonic equation. Specifically, price variation between period t and t-1, ) ln (ln

1 t t p p
, can be decomposed into the sum of the following terms:

= ) ln (ln 1 t t p p ) ( ' ˆ1 t t X X + ) ( ' ˆ1 t t Z Z + ) ln( t I (19)
Where,

) ( ' ˆ1 t t X X
is the variation that can be attributed to the characteristics

) ( ' ˆ1 t t Z Z
is the variation that can be attributed to the brands ) ln( t I is the hedonic variation computed as in ( 15)

The hedonic variation in real terms is computed as ) ln( ) ln(

CPI I t

The indexes were computed for each year at the mean value of the explanatory variables. Table 7 provides the results. The first and third columns illustrate the rise of the nominal and real (CPI-deflated) car prices. Thus, according to our sample, over the 1981-2005 period, nominal car prices in Spain increased by a factor of 4.4; in real terms the factor falls to 1.2. However, part of the price growth is explained by quality improvements. As can be seen in the fourth column, the quality index, measured by the characteristics included in the equation, increased by a factor of 1.9. The effect of changes in brand composition (fifth column) was almost nil. As a result, it can be seen that the real quality-adjusted price index fell by 40%.

It should be noted that changes in car taxes are included in our hedonic index. The most important changes in taxation were a 9 point increase in the tax rate in 1986 and a 5 point reduction in 1992, which coincided with a fall in the average nominal car price. Our approach gives a lower rate of quality-adjusted price increases compared with the rates used by the Spanish statistical agency. This is a common result when applying hedonic regressions. Van Dalen and Bode (2004) estimated a hedonic model for new passenger cars in the Netherlands over the period 1990-1999 that lead to quality corrected price increases between 7.3 and 17.7 percentage points below the official CPI index for new passengers cars, although the latter partially corrects for quality changes.

A similar result has been found by [START_REF] Izquierdo | Mejoras de calidad e índices de precios del automóvil en España[END_REF] in their study of car prices in Spain during the 1997-2000 period.

Quality indexes for groups of characteristics

Following the same procedure as in price indexes, we have computed quality indexes for the six categories established in Table 1: performance, ease of drive, size, comfort, fuel consumption and safety. Figure 4 has to be related to the small size of Spanish cars in 1981, as well as to the existence of other non-observed quality attributes that improve with size. Secondly, the increase in fuel cosnumption has also had a positive effect on quality (1.16 in 2005). The time profile of this variable can be related to the fuel price. Thus, up to 1988 the quality index rose very sharply as a consequence of technical changes introduced by car manufacturers after the energy crises of 1973 and 1979. However, the decline in oil prices in the second half of the eighties slowed down efficiency gains, which picked up again after 1997. Thirdly, during the eighties a steep increase in the quality index related to engine power was observed followed by much lower rates thereafter. This result agrees with the findings of previous studies, and can be explained by the improvements in engine efficiency, that allowed far better performance without increasing engine power. Finally, the substantial contribution of those variables representing comfort to the quality of cars should be mentioned. In this case, a certain relationship with Spanish income growth can be observed.

Price convergence and economic integration

Spain joined the European Community in 1986. One of the main arguments put forward to favour the process of economic integration is the consequent increase in competition which in turn translates into efficiency gains. Although it is difficult to find situations where this hypothesis can be directly tested, we should expect a convergence in qualityadjusted prices favoured by a higher level of market competition. We address this issue by computing the sigma convergence for different definitions of car prices. Figure 5 provides the results.

For observed real prices, no clear pattern emerges. Despite the process of economic integration, price dispersion oscillates without a defined trend. However, when adjusting prices for quality changes, a clear process of convergence can be seen between 1986 and 1992, corresponding to the period of tariff reduction. This result is even clearer when prices are adjusted for both quality and brand changes. Hence, while for observed prices there was no process of convergence, for hedonic prices, which are the relevant ones in terms of measuring the degree of market competition, a clear reduction of price dispersion emerged. The reason lies in the substantial increase in high quality car imports with significant quality improvements with respect to Spanish cars, which The effects of economic integration on the level of market competition can also be analysed by re-estimating the pooled regression equation including annual dummy variables on imported cars to capture its impact on prices 20 . The estimated coefficients for these variables can be interpreted as the effect of market integration, and as such can be related to the degree of dispersion in the price variable. A simple scatter diagram illustrates the correlation between the effect of tariff reduction, through the estimated coefficients, and the -convergence. Figure 6 shows a weak relationship between tariff reduction and -convergence for observed car prices, while a strong negative correlation appears when prices are adjusted for quality changes.

Conclusions

The aim of this paper has been to estimate hedonic prices for a manufactured good -the car-that has been subject to significant technical change.

From a methodological point of view, we have addressed one of the limitations of hedonic regressions, the instability of coefficients over time. As long as the estimated coefficients can be interpreted as marginal prices for characteristics, an accurate estimation of them is needed. It is common in the literature to consider two polar assumptions. On the one hand, the pooled regression model assumes constant coefficients over time. In this case, the coefficients usually take the expected sign and 20 In the original specification these variables were limited to the 1981-1992 period. are precisely estimated, but parameter equality is very often rejected by the data. On the other hand, unrestricted single year equations are estimated, which frequently generate very erratic and poorly estimated coefficients. The adjacent year is the usual approach to address this problem. Nonetheless, erraticity is still present. Our study proposes two solutions consisting in constructing a moving sample of the observations and a weighted moving average of the coefficients estimated in the single year equations. In both cases, the new alternative makes it possible to allow for annual changes in marginal prices of characteristics without imposing constraints that would be rejected by the data.

In relation to the empirical results, two issues can be emphasised. Firstly, CPI deflated car prices in Spain rose by 20% between 1981 and 2005. However, once quality improvements are taken into account, real car prices fell by 40%. This result is common in the literature that computes hedonic prices for goods subject to rapid technological progress and quality improvements. Additionally, it has to be stressed that the 40% drop is robust to the alternative estimation procedures employed in the study.

Secondly, for observed car prices there is no general trend of sigma convergence over the sample period; however, once quality improvements are taken into account, a clear trend in -convergence emerges between 1986 and 1992. This result has to be related to the tariff reduction following Spain's integration in the EC, which led to a more competitive market. Ease of drive

  of the residual variances across all years. The null hypothesis of homoskedasticity over time was not rejected (F=1.299, p-value=0.151).

  the final equation therefore, the dummy for imported cars was limited to the 1981-1992 period.

  the standard error of the estimated elasticities, a measure of the degree of predictability of the coefficients and the number of wrong signs for the estimated coefficients. We construct a measure of predictability by adjusting an autoregressive model to the series formed by the estimated elasticities for the characteristic variables for each year in the sample. The standard error of this model is interpreted as an indicator of predictability of the estimated elasticities under the four alternative

  plots the temporal profile. The variables representing size show the highest contribution to quality improvement of cars. The index takes value 1 in 1981 and it increases up to 1.19 in 2005. The growth of this index

  wider dispersion of observed prices, whereas the dispersion in qualityadjusted prices narrowed.

  . (2004) Handbook on hedonic indexes and quality adjustments in price indexes: special application to information technology products. Paris: OECD, STI Working Paper 2004/9.

Figure 2 .

 2 Figure 2. Normal density functions for the estimated elasticities

  Where it p is the price of car model i in period t;

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

it X is the vector of car characteristics it Z is the vector of car brands t annual dummy variables

Page 7 of 41 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

	4. Moving sample of order h
	This is the first of the new alternatives suggested in this work. The estimated equation
	can be expressed as:
	ih p	=	msh	h + +	'	msh	X	ih	+	'	msh ih Z	+	ih	h	=	,.. 2 , 1	H
					F o r
									P
											e
											e r
													R
													e
													v i e
																w

Page 12 of 41 Editorial

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

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

Page 13 of 41 Editorial

	Submitted Manuscript
	F o r
	P
	e
	e r
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Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 1 .

 1 Variable definition for vehicle characteristics

	Performance	Displacement (CID, cubic inch displacement)
		Horsepower / weight
	Ease of drive	Power assisted steering (dummy variable)
		Automatic gear (dummy variable)
	Size	Volume (length*width*height)
		Minivan (dummy variable)
	Comfort	Number of doors
		Air conditioning (dummy variable)
		Climate control (dummy variable)
		Electric windows (dummy variable)
	Fuel efficiency	Fuel consumption (litres per 100 km / horsepower)
		Diesel (dummy variable)
	Safety features	Antilock Braking System (ABS) (dummy variable)
	Table 2. Selection of the functional form
	Functional form		L*-value	Schwarz criterion
	Box-Cox ( l.h.s =0.03)	-26403.48	-26699.33
	( r.h.s =1.05)
	Semi-log		-26404.79	-26696.84
	Schwarz criterion has been computed as

Table 3 . Estimation results

 3

	Page 31 of 41							Submitted Manuscript
		Yearly equations			Adjacent year			Third order sample average	Fith order sample average
		No.	No.sign.	Standard	No.	No.	No.sign.	Standard	No.	No.	No.sign.coef	Standard	No.	No.	No.sign.	Standard	No.
		regressors	coef	error	obs.	regressors	coef (5%)	error	obs.	regressors	(5%)	error	obs.	regressors	coef	error	obs.
			(5%)												(5%)
	1981	20	10	0.05425 47	-	-	-	-	-	-	-	-	-	-	-	-
	1982	22	12	0.06895 58	24	15	0.05991 105	28	19	0.06504 168	-	-	-	-
	1983	24	13	0.06757 63	26	16	0.06709 121	28	21	0.07150 189	33	26	0.07241	301
	1984	24	12	0.07629 68	26	18	0.06927 131	29	22	0.06793 196	35	28	0.07076	318
	1985	25	13	0.06671 65	27	17	0.06890 133	31	24	0.06831 197	36	29	0.06773	329
	1986	27	15	0.06162 64	29	20	0.06531 129	32	24	0.06454 198	36	29	0.06829	332
	1987	28	11	0.06485 69	30	19	0.05843 133	32	23	0.06158 199	37	31	0.06575	331
	1988	27	13	0.07175 66	30	19	0.06299 135	33	22	0.06223 202	37	28	0.06307	329
	1989	28	15	0.06490 67	30	19	0.06261 133	32	22	0.06201 196	38	27	0.06240	335
	1990	27	12	0.06650 63	30	21	0.06084 130	33	22	0.06136 200	39	30	0.06457	337
	1991	28	15	0.05830 70	29	17	0.06202 133	34	23	0.06051 204	39	29	0.06126	342
	1992	30	15	0.06581 71	32	19	0.05776 141	34	25	0.05547 212	38	30	0.05884	350
	1993	29	20	0.05253 71	31	25	0.05640 142	34	27	0.05662 217	40	32	0.05607	364
	1994	31	18	0.05947 75	32	25	0.05322 146	36	29	0.05269 223	40	32	0.06127	374
	1995	34	18	0.06007 77	35	25	0.05449 152	37	27	0.06281 232	39	33	0.06598	387
	1996	35	11	0.07541 80	36	22	0.06693 157	37	27	0.07050 241	42	34	0.06871	409
	1997	35	14	0.08161 84	36	23	0.07289 164	40	28	0.07061 257	42	34	0.06852	429
	1998	38	20	0.06002 93	37	26	0.06994 177	40	29	0.06514 272	42	32	0.06881	449
	1999	38	22	0.06057 95	39	25	0.05609 188	40	26	0.06093 285	43	30	0.06848	472
	2000	38	15	0.07541 97	39	23	0.06384 192	41	26	0.06728 295	43	31	0.06455	492
	2001	39	14	0.07738 103	40	21	0.07109 200	41	24	0.06678 304	43	29	0.06488	505
	2002	39	17	0.06486 104	40	22	0.06656 207	41	22	0.06370 313	43	25	0.06599	523
	2003	39	20	0.06513 106	40	24	0.05968 210	41	26	0.06256 323	43	26	0.06770	527
	2004	39	19	0.06846 113	40	22	0.06480 219	41	22	0.06709 320	-	-	-	-
	2005	36	15	0.07580 101	37	20	0.07097 214	-	-	-	-	-	-	-	-
					Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 4 .

 4 Comparison of coefficients' instability for different estimation approaches

													Page 32 of 41
		Standard error of the characteristic elasticity	Standard error of the AR model for the	Number of wrong signs for the estimated
							estimated elasticities			coefficients
		Yearly	Adjacent	3rd	5th	Yearly	Adjacent	3rd	5th	Yearly	Adjacent	3rd	5th
		equations	years	order	order	equations	years	order	order	equations	years	order	order
	Displacement	0.1098	0.0703	0.0555 0.0426	0.0963	0.0673	0.0563 0.0330	1	0	0	0
	H.P./weight	0.1263	0.0804	0.0633 0.0483	0.1091	0.0858	0.0515 0.0312	1	1	0	0
	Volume	0.1734	0.1110	0.0877 0.0671	0.1516	0.0990	0.0671 0.0390	0	0	0	0
	Fuel consumption	0.0980	0.0612	0.0496 0.0376	0.0925	0.0661	0.0441 0.0235	2	0	0	0

Table 7 .

 7 Decomposition of car price index into different components

		Price	CPI	Price	Characteristics	Brand	Hedonic	Hedonic
		(nominal)		(real)	index	index	index	index (real)
	1981	1.000	1.000	1.000	1.000	1.000	1.000	1.000
	1982	1.168	1.144	1.021	1.026	1.013	1.125	0.983
	1983	1.449	1.283	1.129	1.050	1.033	1.336	1.041
	1984	1.621	1.428	1.135	1.076	1.043	1.446	1.012
	1985	1.811	1.554	1.165	1.105	1.052	1.558	1.002
	1986	1.960	1.691	1.159	1.133	1.050	1.647	0.974
	1987	2.156	1.780	1.212	1.171	1.043	1.765	0.992
	1988	2.379	1.866	1.275	1.212	1.067	1.841	0.987
	1989	2.467	1.992	1.238	1.247	1.066	1.856	0.932
	1990	2.603	2.126	1.224	1.282	1.080	1.880	0.884
	1991	2.661	2.252	1.181	1.339	1.072	1.852	0.822
	1992	2.700	2.386	1.132	1.394	1.080	1.794	0.752
	1993	2.818	2.495	1.129	1.404	1.079	1.859	0.745
	1994	2.947	2.613	1.128	1.426	1.077	1.919	0.734
	1995	3.110	2.735	1.137	1.438	1.054	2.050	0.750
	1996	3.246	2.832	1.146	1.475	1.046	2.104	0.743
	1997	3.336	2.888	1.155	1.500	1.049	2.120	0.734
	1998	3.393	2.941	1.154	1.559	1.051	2.072	0.705
	1999	3.532	3.009	1.174	1.602	1.057	2.086	0.693
	2000	3.525	3.112	1.133	1.626	1.048	2.069	0.665
	2001	3.745	3.224	1.162	1.727	1.044	2.077	0.644
	2002	3.939	3.323	1.185	1.793	1.046	2.101	0.632
	2003	4.048	3.424	1.182	1.825	1.044	2.124	0.620
	2004	4.171	3.528	1.182	1.878	1.043	2.131	0.604
	2005	4.351	3.614	1.204	1.934	1.045	2.153	0.596
	From equation (15) price indexes were obtained by adding cumulative log differences of prices and then
	taking antilogs.

Table A .2. Estimation results for the pooled equation

 A

		YEAR82 Figure 1. Estimated coefficients for two alternative specifications 0.106147 0.018453 5.752221	0.0000
	YEAR83 Dependent Variable: LOG(Price) Included observations: 1970 YEAR86 White Heteroskedasticity-Consistent Standard Errors & Covariance 0.261728 0.017167 0.498870 0.017538 YEAR84 0.339597 0.016736 YEAR85 0.406745 0.017252 6 .12 Estimated coeficients for engine power Estimated coefficients for volume 15.24589 28.44517 20.29105 23.57620	0.0000 0.0000 0.0000 0.0000
	5	YEAR87	0.567498	.11	0.016520	34.35153	0.0000
	4	Variable YEAR88	Coefficient 0.624455		Std. Error 0.018241	t-Statistic 34.23388	Prob. 0.0000
	3	C YEAR89 YEAR90	12.33359 0.645247 0.679791	.10	0.049774 0.018856 0.018422	247.7927 34.22006 36.90009	0.0000 0.0000 0.0000
	2	DISPLACEMENT YEAR91	0.000222 0.683766	.09	1.08E-05 0.017354	20.49526 39.40096	0.0000 0.0000
	1	H.P./WEIGHT YEAR92	2.301612 0.679761		0.247389 0.019555	9.303607 34.76090	0.0000 0.0000
	VOLUME FUEL CONSUMPTION YEAR94 0 YEAR93	0.091077 -2.067027 0.763649 0.731340	.08	0.003050 0.183303 0.017163 0.017146	29.85688 -11.27656 44.49353 42.65282	0.0000 0.0000 0.0000 0.0000
	-1	DIESEL YEAR95 MINIVAN Nº DOORS AIR CONDITIONED CLIMATE CONTROL ABS F o r 0.069964 0.818267 0.039537 0.029148 0.053243 0.127339 0.046201 YEAR96 0.840995 YEAR97 0.846782 YEAR98 0.810593 YEAR99 0.809771 YEAR00 0.798102 82 84 86 88 90 92 94 96 98 00 02 04 Order 5 moving sample F r o Adjacent year	.07	0.008492 0.017397 0.016749 0.005915 0.006215 0.007673 0.006698 0.017872 0.018356 0.017363 0.017577 0.017887 82 84 86 88 90 92 94 96 98 00 02 04 8.238396 47.03626 0.0000 0.0000 2.360549 0.0183 4.928121 0.0000 8.566656 0.0000 16.59570 0.0000 6.897887 0.0000 47.05540 0.0000 46.13110 0.0000 46.68580 0.0000 46.07055 0.0000 44.61910 0.0000 Order 5 moving sample Adjacent year
	ASSITED STEERING ELECTRIC WINDOWS YEAR01 YEAR02	0.067912 0.025584 P 0.800529 0.813099 P		0.006651 0.006178 0.018220 0.018027	10.21149 4.141281 43.93748 45.10523	0.0000 0.0000 0.0000 0.0000
		AUTOMATIC GEAR ALFA ROMEO AUDI AUSTIN BMW YEAR03 YEAR04 YEAR05 YEAR81*IMPORT YEAR82* IMPORT CHRYSLER CITROEN YEAR83* IMPORT YEAR84* IMPORT DAEWOO FIAT FORD HONDA HYUNDAI KIA LANCIA MAZDA YEAR85* IMPORT YEAR86* IMPORT YEAR87* IMPORT YEAR88* IMPORT YEAR89*IMPORT YEAR90* IMPORT YEAR91* IMPORT YEAR92* IMPORT	0.085218 0.091467 0.258700 -0.074346 0.346397 e e r 0.825567 0.829190 e 0.837513 0.264849 0.264331 e r -0.233620 0.043901 R 0.017102 0.017487 0.011970 0.025075 0.010389 0.018300 0.018550 0.018972 0.042542 0.034747 0.021121 0.009586 0.271647 0.024829 0.272940 0.024230 R -0.114095 0.015723 0.008876 0.011847 0.034471 0.008564 0.089910 0.018446 -0.142778 0.011942 -0.267411 0.044292 0.098621 0.012422 0.035517 0.015353 e v i e w 4.982959 5.230558 21.61241 -2.964914 33.34168 45.11407 44.69939 44.14556 6.225597 7.607373 -11.06121 4.579825 10.94067 11.26461 -7.256535 0.749286 4.024977 4.874273 -11.95573 -6.037499 7.939430 2.313313 0.253548 0.021787 11.63772 0.173231 0.020021 8.652421 e 0.137589 0.017780 7.738514 0.113397 0.020192 5.615971 0.091651 0.018818 4.870388 0.053550 0.017336 3.088959 v i e 0.045937 0.015027 3.056973 0.019186 0.018042 1.063358 w	0.0000 0.0000 0.0000 0.0031 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.4538 0.0001 0.0000 0.0000 0.0000 0.0000 0.0208 0.0000 0.0000 0.0000 0.0000 0.0000 0.0020 0.0023 0.2878
		MERCEDES	0.414736		0.011592	35.77729	0.0000
	MITSUBISHI R-squared	0.054551 0.982608	0.023226 Mean dependent var	2.348656	0.0189 14.58690
	NISSAN Adjusted R-squared	0.030624 0.981910	0.011925 S.D. dependent var	2.568030	0.0103 0.561995
	OPEL S.E. of regression	0.082621 0.075588	0.008827 Akaike info criterion	9.360237	0.0000 -2.288733
	PEUGEOT Sum squared resid	0.057520 10.81578	0.008135 Schwarz criterion	7.070261	0.0000 -2.070406
	RENAULT Log likelihood	0.007337 2331.402	0.007427 F-statistic	0.987918	0.3233 1407.247
		ROVER	0.043062		0.015401	2.796093	0.0052
		SAAB	0.197645		0.015198	13.00467	0.0000
		SKODA	-0.061187		0.020247	-3.021983	0.0025
		TALBOT	-0.020536		0.009720	-2.112741	0.0348
		TOYOTA	0.045968		0.012418	3.701838	0.0002
		VOLVO	0.227725		0.013648	16.68590	0.0000
		VOLKSWAGEN	0.118445		0.008642	13.70599	0.0000
							38

[START_REF] Rosen | Hedonic prices and implicit markets: product differentiation in pure competition[END_REF] developed a theoretical framework for hedonic prices as equilibrium prices for supply and demand functions, both defined on the characteristics of products. Under this framework, the characteristic coefficients in the hedonic equation are the result of the interaction between the consumer's marginal valuation and the producer's marginal cost. As has been demonstrated by many authors, only under very restrictive assumptions is it possible to identify estimated coefficients as consumers' preferences or producers' costs. However, this problem does not affect the possibility of computing the hedonic index as an approximation to the exact hedonic index. Moreover, several publications by A. Pakes(Pakes,

2003;[START_REF] Pakes | Hedonics and the consumer price index[END_REF] have recently revived the interest in the economic rationale of hedonic prices. This author derives the hedonic framework from the industrial organization theory in the context of technological change, differentiated product markets and heterogeneous consumers. Under his approach producers' mark-ups are a function of the characteristics and costs of all goods and of the distribution of consumer attributes, and vary over time and depending on products. Under this approach, the coefficients in the hedonic equation may vary quickly over time and do not necessarily have to take the expected sign. Pakes's formulation has received great attention in hedonic literature. It has however generated some still unresolved controversies (see, for instance,Triplett, 2004, p. 159).

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

[START_REF] Granger | Forecasting economic time series[END_REF] made a similar proposal for combining individual forecasts derived from separate models.

The information on sales volumes was provided by the Instituto de Estudios de Automocion (Spanish motor vehicle manufacturers' association). Unfortunately, no data was available for the different model versions. Our choice was to select a middle-range model.

We estimated 93 different equations. Since presentation of all equations would be too cumbersome, the results are summarised in Table3.

Acknowledgements

This work has benefited from a research grant from the Spanish Ministerio de Educación y Ciencia (SEJ 2006-14849). The authors thank A.I. Guerra for her support in collecting the data and the Instituto de Estudios de Automoción for providing the information on automobile sales and to J. Asensio for his comments.


Jarko Fidrmuc
email: jarko.fidrmuc@lrz.uni-muenchen.de

Keywords: money demand, panel unit root tests, panel cointegration, direct inflation targeting, CEECs Money demand, panel unit root tests, panel cointegration, direct inflation targeting, CEECs. JEL Classification: E41, E58, C23

A panel data set for six countries (Czech Republic, Hungary, Poland, Romania, Slovakia, and Slovenia) is used to estimate money demand with panel cointegration methods over the recent disinflation period. The basic money demand model is able to convincingly explain the long-run dynamics of M2 in the selected countries. However, money demand is found to have been significantly determined by the euro area interest rates and the exchange rate against the euro, which indicates possible instability of money demand functions in the CEECs. Therefore, direct inflation targeting is an appropriate monetary regime before the eventual adoption of the euro.

Introduction

Inflation in Central and Eastern European countries (CEECs) has figured prominently in current research (see, for example [START_REF] Fischer | Modern hyper-and high inflations[END_REF]. More recently, disinflation received increased attention as a part of the fulfillment of Maastricht criteria. As the CEECs have joined the European Union (EU) 1 and as five of them (Slovenia and Slovakia, as well as Estonia, Latvia and Lithuania, which are not analyzed here) have already entered the Exchange Rate Mechanism II (ERM II), the environment conditions for monetary policy in these countries are becoming increasingly important. From this perspective, the determinants and the stability of money demand are crucial. Stable money demand and a transmission mechanism similar to that in the euro area are likely to create good preconditions for the eventual introduction of euro by new member states (see [START_REF] Elbourne | Financial structure and monetary policy transmission in transition countries[END_REF]. [START_REF] Calvo | Money demand, bank credit, and economic performance in former socialist economies[END_REF] and [START_REF] Budina | Money demand and seigniorage in transition[END_REF] provide an early comparative study on determinants of money demand in selected CEECs, while other authors offer insights on individual countries: [START_REF] Buch | Money demand in Hungary and Poland[END_REF] estimated money demand for Hungary and Poland, [START_REF] Komárek | Currency substitution in a transitional economy with an application to the Czech Republic[END_REF] for the Czech Republic, [START_REF] Ross | Post Stabilization Dynamics in Slovenia[END_REF] for Slovenia, [START_REF] Slavova | Money demand during hyperinflation and stabilization: Bulgaria, 1991-2000[END_REF] for Bulgaria, and Mehrota (2006) for China. Similarly, [START_REF] Crespo-Cuaresma | The Monetary Approach to Exchange Rates in the CEECs[END_REF] show that the monetary model of exchange rates is able to explain the long-run dynamics of nominal exchange rates vis-à-vis the euro in CEECs. However, the analyses of money demand are available only for the highinflation episodes during the early years of the economic transition, but not for the F o r P e e r R e v i e w 3 current period of successful disinflation during and after accession to the EU (see Figure 1). This paper aims to fill this surprising gap in the current literature by estimating money demand functions for a panel of relatively homogenous CEECs (Czech Republic, Hungary, Poland, Romania, Slovakia, and Slovenia).

Besides this, our paper is also relevant for countries using direct inflation targeting as a framework for their monetary regime (see [START_REF] Svensson | Open-economy inflation targeting[END_REF][START_REF] Orlowski | From inflation targeting to the euro-peg: a model of monetary convergence for transition economies[END_REF]and 2005), even more so as several CEECs have recently adopted direct inflation targeting as a tool for disinflating to EU rates. [START_REF] Nelson | The future of monetary aggregates in monetary policy analysis[END_REF] argues that the monetary aggregates provide important information for central banks in inflation targeting countries. By contrast, [START_REF] Dotsey | Should monetary policymaker look at money?[END_REF] see unstable money demand as a possible source of shocks. [START_REF] Fraga | Inflation Targeting in Emerging Markets Economies[END_REF] also point out that unstable money demand may trigger unexpected monetary shocks, posing new challenges for direct inflation targeting in emerging economies. 2 The paper is structured as follows. The next section describes the disinflation process and the panel data set for six CEECs (Czech Republic, Hungary, Poland, Romania, Slovakia, and Slovenia). Section 4 contains a set of unit root tests, while section 5 presents several estimates of money demand. The final section offers concluding remarks. Six Central and Eastern European countries are included in our data sample (Czech Republic, Hungary, Poland, Romania, Slovakia, and Slovenia). During the sample period, several countries in our sample have moved from monetary regimes characterized by adjustable pegged exchange rates to direct inflation targeting accompanied by managed or free floating exchange rates, and towards ERM II participation (in Slovenia and Slovakia) after the EU accession (omitted from the later analysis). These changes could have some implications for monetary policy and money demand functions, although the CEECs had significant de-facto flexibility of exchange rates during the whole analyzed period (see [START_REF] Reinhart | The Modern History of Exchange Rate Arrangements: A Reinterpretation[END_REF]. 3 The degree of monetization of the economy and the degree of development of the banking sector differ also across countries (see [START_REF] Hainz | Are Transition Countries Overbanked? The Effect of Institutions on Bank Market Entry[END_REF]. Therefore, the countries in our sample do not [START_REF] Buch | Money demand in Hungary and Poland[END_REF] for Hungary and Poland, we found no indications for structural breaks in our time series. However, in the Czech Republic and Slovakia, the variance of several nominal variables was higher around the periods of policy changes (see Figure 1).

The variables in our data set comprise the real broad money stock (M2), consumer prices, real industrial production, and interest rates (deposit rates) in the CEECs. All variables except interest rates were seasonally adjusted and indexed to the base year of 1995 as 100 %, and they were all converted into natural logarithms.

Wherever possible, time series data are taken from the International Financial Statistics of the IMF. The remaining variables are taken from national sources and publications of the Vienna Institute for Comparative Economics (WIIW).

The monetary variables are strongly influenced by the achieved degree of disinflation (see Figure 1). In the mid-1990s, all CEECs reported two-digit annual inflation rates, with the exception of Romania, whose annual inflation rate exceeded 100% in 1994, 1995, and 1997. By the time of the EU accession, the Czech Republic and Poland had stabilized their inflation rates at the historically lowest figures below 2%. The only country to report double-digit inflation rates (15.3% in 2003) at the end of our sample period was Romania. However, there was a revival of inflation in some CEECs immediately before and after the accession to the EU, while Romania continued its disinflation process to one-digit annual inflation rates at the end of 2005. (2002) proposed a new more general test (LLC test), which is appropriate also for panels of moderate size (N between 10 and 250 individuals and T between 25 and 250 periods).

These dimensions are close to our panel.

The generality of the Levin-Lin type tests has made them a widely accepted panel unit root test. However, Levin and Lin have an important homogeneity restriction of the autoregressive parameter in their tests, as the null hypothesis assumes that i = = 0 against the alternative i < 0 for all cross-section units i. As far as this result also reflects the possible speed of convergence, the Levin and Lin type tests are likely to reject the panel unit root. 5 The results of the Augmented Dickey Fuller test (ADF test) and of the test according to [START_REF] Kwiatkowski | Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root?[END_REF] for all variables are available from the authors on request. For the interest rate in the euro area, which is used in the subsequent analysis, the ADF test with two lags is -1.236 for the levels and -4.889

for the first differences (critical values are -2.889 at 5% and -3.493 at the 1% significance level).

6 Banarjee (1999) provides detailed surveys of panel unit root tests. Finally, [START_REF] Hadri | Testing for stationarity in heterogenous panel data[END_REF] presents an extension of the test of [START_REF] Kwiatkowski | Testing the null hypothesis of stationarity against the alternative of a unit root: how sure are we that economic time series have a unit root?[END_REF] to a panel with individual and time effects and deterministic trends (PKPSS test), which has as its null the stationarity of the series.

In general, our estimates of the panel unit root tests confirm that the variables contain a unit root (see Table 1). The panel version of the KPSS does not reject the null hypothesis of stationarity for any of the variables. A similar result pertains for the IPS test although this test (with time dummies) rejects the null of unit root for interest rates.

Individual country results show that this ambiguous outcome is influenced mainly by the Romanian interest rates. The IPS test confirms that all differenced variables are stationary. However, the KPSS test rejects the null of stationarity again for first differences of real money and industrial production. Despite some ambiguity of the results, we conclude that the variables are I(1).

Estimation of the Long-Run Money Demand

The money demand function in the CEECs is analyzed using a general two-country portfolio balance model described in [START_REF] Leventakis | Modelling money demand in open economies over the modern floating rate period[END_REF]. The assets held by residents in the home country and the foreign country include domestic money, foreign money, domestic bonds, and foreign bonds. The home country residents' demand for domestic money is assumed to depend on a scale variable and the rates of return to the four assets. The Following these arguments, the open-economy version of money demand can be summarized as follows (see [START_REF] Chowdhury | The Demand for Money in a Small Open Economy: The Case of Switzerland[END_REF],

it it it i it it R y p m µ + + + = 2 1 , ( 1
)
where m, p, y and R are defined as money, prices, output and domestic interest rates, respectively. This specification assumes that the nominal money demand is homogenous in prices. Sensitivity analysis confirms this assumption. Various specifications of the model include fixed effects (denoted by µ) or a common intercept.

Equation (1) represents the desired or long-run real money demand function under the assumption of a long-run unitary elasticity of the nominal cash balances with respect to the price level. We tested the assumption of price homogeneity (see also [START_REF] Buch | Money demand in Hungary and Poland[END_REF], which is confirmed for our sample.

Several authors have included wealth-related additional variables as further determinants of money demand (see recent surveys by Knell and[START_REF] Knell | The income elasticity of money demand: A meta analysis of empirical results[END_REF][START_REF] Mehrotra | Demand for Money in Transition, Evidence from China's Disinflation[END_REF]). An increase in wealth is expected to lead to an increase in the demand for financial assets, including money. As monthly data are used for estimation, we can not include any variable representing this effect because possible proxies tend to be strongly correlated with the scale variable. Nevertheless, fixed effects in panel estimations are likely to cover a substantial part of time-invariant cross-section differences in wealth across countries. The Finally, the exchange rate and the euro area interest rates (see [START_REF] Leventakis | Modelling money demand in open economies over the modern floating rate period[END_REF] are included in the open-economy formulation of the money demand,

it it t it it i it it e R R y p m µ + + + + + = 4 * 3 2 1 , (2)
where, in addition to the previous variables, R * stands for the euro area interest rates and e is the nominal exchange rate (in logs) defined on the basis of nominal exchange rate (expressed as units of domestic currency per 1 euro). Correspondingly, depreciation or devaluation is displayed as an upward movement of e. We expect that external weakness of the currency will lower domestic demand, for example through a higher demand for foreign currency.

The previous section showed that money demand and the right-hand side variables in the money demand equations ( 2) and (3) are I(1). Furthermore, the standard money demand models predict that these variables should be cointegrated. Therefore, we consider several approaches to estimating the long-run (cointegrating) relationship between the variables. [START_REF] Kao | On the estimation and inference of cointegrated regression in panel data[END_REF] show that the panel OLS estimator is asymptotically normal, but it is still asymptotically biased. Although they propose a correction for this bias, it has been found that this correction does not tend to perform well at reducing the bias in small samples. Therefore, alternative methods of panel cointegration estimation have been proposed. [START_REF] Pedroni | Fully Modified OLS for Heterogenous Cointegrated Panels and the Case of Purchasing Power Parity[END_REF]2001) proposes the fully modified OLS estimator (FMOLS), while [START_REF] Kao | On the estimation and inference of cointegrated regression in panel data[END_REF] recommend the dynamic OLS (DOLS). Both approaches take into account the potential endogeneity of involved variables. Pedroni's FMOLS corrects for the endogeneity and serial correlation to the OLS estimator non- 2, with and without fixed effects. Furthermore, we present a DOLS specification accounting for the contemporaneous correlation in the errors across countries by a seemingly unrelated regression (SUR).

Already the estimation of a standard money demand function for a closed economy yields comparably good results. All variables have correct signs and nearly all of them are highly significant (see Table 2). The coefficient of industrial production is significantly different from unity in all specifications, with the exception of FMOLS, where the coefficient is insignificant. Thus, the output elasticity of money demand is lower than values typically found for the euro area, although [START_REF] Stracca | The functional form of the demand for euro area M1[END_REF] finds output elasticities of M3 close to our estimates. Furthermore, we use industrial production as a proxy for the scale variable, which grew much faster than GDP (used in comparable studies for other regions). We have also to take into account the formulation of our econometric specification. In particular, Knell and[START_REF] Knell | The income elasticity of money demand: A meta analysis of empirical results[END_REF][START_REF] Mehrotra | Demand for Money in Transition, Evidence from China's Disinflation[END_REF] show that time series with higher frequencies and the inclusion of wealth variables (e.g. by fixed effects here) are likely to lead to relatively lower estimates of output elasticities. In a panel of OECD countries, [START_REF] Mark | Cointegration Vector Estimation by Panel DOLS and Long-Run Money Demand[END_REF] [START_REF] Leventakis | Modelling money demand in open economies over the modern floating rate period[END_REF] and [START_REF] Chowdhury | The Demand for Money in a Small Open Economy: The Case of Switzerland[END_REF].

The inclusion of the exchange rate and of euro area interest rates confirms the robustness of the basic model of money demand in CEECs (see Table 4). The The euro area interest rates have significantly shaped money demand in the CEECs, which indicates that the capital mobility effect plays an important role in the CEECs. Somewhat surprisingly, the coefficient estimated for the interest rate in the euro area is much larger than the coefficient of domestic interest rates. The semi-elasticities of money demand with respect to the foreign interest rates are generally reported to be slightly higher than those for the domestic interest rates (see [START_REF] Leventakis | Modelling money demand in open economies over the modern floating rate period[END_REF].

Furthermore, our results may reflect the different definition of the euro area and domestic interest rates, which are treasury rates and deposit rates, respectively. For the shorter period with both types of interest rates available for the euro area, we can see that treasury rates are usually lower than the deposit rates. As expected, the exchange rate is revealed to have negative effects on money demand, but the estimated elasticity Finally, we test whether the estimated relationships truly represent cointegrating vectors in Tables 3 and5. Following the Engle and Granger's approach, [START_REF] Kao | Spurious regression and residual-based tests for cointegration in panel data[END_REF] proposed All tests reveal nearly the same picture (see Table 3 andTable 5). On the one hand, the panel cointegration tests for FMOLS, DOLS and to a lesser extent for DOLS with SUR errors confirm the stationarity of the residuals. The methods suggested in the literature seem to perform similarly in our data sample. At the same time, the majority of the tests rejects cointegrating relationship for the OLS specification.

Conclusions

The analyses of money demand in the CEECs have gained an increased importance recently as the new EU Member States have started the preparation for a full participation in the monetary union. This reflects that the monetary policy of the European Central Bank puts a strong emphasis on the development of monetary 13 aggregates (in particular M3), which constitute the so-called 'monetary pillar' of its monetary strategy. Correspondingly, there are a large number of studies analyzing money demand for euro area countries (see Stracca, 2003, Brand and[START_REF] Brand | A money demand system for euro area M3[END_REF]. In contrast, there are virtually no comparative studies for the new member states in Central and Eastern Europe with regard to the recent period of disinflation and preparation for the euro adoption.

Filling this gap in the literature, the empirical estimation presented in this paper provides the following conclusions. First, we document the relatively fast and successful process of disinflation in the CEECs. Second, we show that a simple money demand model is able to explain the long-run dynamics of broad money in the CEECs.

Furthermore, the euro area interest rates are found to have a significant impact on money demand in the CEECs, which confirms the importance of capital substitution in these countries. The exchange rate is also significant, but the estimated elasticity is relatively low, which implies that currency substitution is playing a less important role in these countries.

We find parameters of money demand in the new member states to be close to those in developed countries, especially with regard to domestic interest rates. This may create good preconditions in these countries for the eventual adoption of euro. However, our estimates of output elasticities are somewhat lower than comparable estimates for the euro area. Nevertheless, the difference may reflect the different formulation of our econometric specifications (monthly data, definition of the scale variable, and the use of the panel data models). Finally, our results imply that the euro area interest rates are already important determinants of monetary developments in the new member states As a result, the policy of direct inflation targeting, which nearly all countries in the sample adopted during the period instead of direct targets for the monetary aggregates, has been an appropriate monetary regime during disinflation and may remain appropriate until the eventual adoption of the euro.

  access to monthly data from 1994 to the end of 2005 (see Figure 1), our analyses concentrate on the period between September 1994 and June 2003. This allows us to use panel cointegration methods for estimating the money demand function in a balanced sample. At the same time, this avoids any structural break related to the accession to the European Union in May 2004 (given also possible anticipatory effects before the Eastern enlargement of the EU).

  Given the catching-up of the CEECs, we would expect the real money and industrial production series to display a clear trend pattern. Standard unit root tests for single time series (not reported here) confirm that the majority of individual time series are I(1) processes.5 Adding a cross-section dimension to unit root tests can potentially improve the quality of these tests significantly by increasing their power.6 Levin and Lin (1992) have significantly influenced the discussion of panel unit root tests for a panel of N individuals, where each individual contains T time series observations. They proposed a panel version of the Dickey-Fuller test (DF test) with fixed effects, individual deterministic trends and serially correlated errors.Levin et al.

  et al. (2003) address this homogeneity issue, proposing a heterogeneous panel unit root test (IPS test) based on individual ADF tests. They propose average ADF statistics. By construction of the heterogeneous panel unit root test, the rejection of the null of panel unit root does not necessarily imply that the unit root is rejected for all cross-sectional units, but only for a positive share of the sample.

  return on domestic money is zero, while the expected rate of return on foreign money is the expected depreciation of the domestic currency. The domestic interest rate represents the nominal rate of return on domestic bonds, while the foreign interest rate measures the nominal rate of return on foreign bonds. Therefore, depreciation of the domestic currency lowers the demand for domestic money by leading to its substitution with foreign money and foreign bonds.

  true for expected differences in financial development (e.g. the size of the banking sector, the use of credit cards, etc.).

  the DOLS uses the future and past values of the differenced explanatory variables as additional regressors. Kao and Chiang show that both estimators have the same (normal) limiting properties, although they are shown to perform differently in empirical analyses. The FMOLS does not improve the properties of the simple OLS estimator in finite samples. Correspondingly, DOLS can be considered to be more promising for the estimation of panel cointegration. The results for the individual estimators of money demand are listed in Table

  coefficient estimated for the domestic interest rates remains nearly unchanged, but the size of coefficient estimates for the industrial production is lower in the open economy specification of money demand than in the previous models. All coefficient estimates of the industrial production are now below one. The DOLS estimate of the output elasticity, for example, drops from approximately two-thirds in the closed economy specification to approximately one-third in the open economy formulation of the money demand.

  This indicates that currency substitution does not play an important role in the CEECs.

  several tests based on a homogenous panel version of the residual Dickey-Fuller test. Kao's panel cointegration tests are based both on the autoregressive coefficient (denoted by DF ) and on the corresponding t-statistic (DF t ). Furthermore, they consider the endogeneity relationship between the regressors and residuals, which is adjusted by the long-run conditional variance of the residuals. The corresponding test statistics for the autoregressive coefficients and the t-statistics are denoted by DF * and DF t * , respectively. Finally, Kao proposes a panel version of the residual ADF test, which is again corrected for a possible endogeneity relationship between the regressors and the residuals.

  , which may present a possible source of instability of money demand functions in the CEECs.

  Figure 1: Disinflation in Selected CEECs (Inflation, M2 Growth, and Deposit Interest Rates), in Per Cent

  Furthermore, the long-run semi-elasticity with respect to the domestic interest rate is very close to the values reported by

	across the specifications.
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
	11

find output elasticities relatively close to our estimates (0.860). In turn, the effect of the interest rate is estimated at similar values

Table 1 : Panel Unit Root Tests, 1994:9-2003:6

 1 TD denotes the inclusion of time dummies. IPS test with 2 lags (based on the maximum number of lags implied by SIC for the individual tests); PKPSS test with lag truncation of 5 lags. The panel includes the Czech Republic, Hungary, Poland, Romania, Slovakia and Slovenia. All variables except interest rates

	A. Levels
		Real Money	Industrial	Domestic	Exchange
		(M2)	Production	Interest Rate	Rate
	IPS-test	-0.152	2.122	0.162	-0.778
	IPS TD -test	-0.697	-0.584	-3.375 ***	-0.200
	LLC-test	-3.227 ***	-0.324	-0.324	-2.529 ***
	LLC TD -test	-2.141 **	-1.348 *	-1.811 **	-2.900 ***
	PKPSS-test	9.790 ***	12.782 ***	10.457 ***	19.468 ***
	PKPSS TD -test	10.992 ***	13.575 ***	10.563 ***	15.782 ***
	B. First Differences
		Real Money	Industrial	Interest	Exchange
		(M2)	Production	Rate	Rate
	IPS-test	-5.357 ***	-10.388 ***	-8.664 ***	-8.398 ***
	IPS TD -test	-6.632 ***	-11.159 ***	-13.771 ***	-8.528 ***
	LLC-test	0.651	7.396	0.421	-3.329 ***
	LLC TD -test	-0.435	6.227	-6.885 ***	-3.170 ***
	PKPSS-test	8.079 ***	1.609*	-1.589	0.167
	PKPSS TD -test	8.829 ***	2.308 **	-1.673	0.306
	Notes: are in logs. Variables are seasonally adjusted if necessary (money supply, industrial production). */**/***
	denote significance at the 10%/5%/1% level.

Table 2 : Panel Cointegration Estimation of Money Demand (Closed Economy Formulation), 1994:9-2003:6

 2

		Submitted Manuscript
		OLS	FE	FMOLS	DOLS	DOLS-SUR
	Industrial production	0.470	0.726	1.059	0.644	0.664
		(9.457)	(18.266)	(0.932)	(15.086)	(52.480)
	Interest rates	-0.002	-0.003	-0.009	-0.006	-0.005
		(-5.038)	(-6.079)	(-15.147)	(-8.290)	(-12.235)
	No. of observations per country	106	106	106	106	106
	Total no. of observations	636	636	636	636	636
	Fixed effects	no	yes	yes	yes	yes

Notes: The panel includes the Czech Republic, Hungary, Poland, Romania, Slovakia and Slovenia. All variables except interest rates are in logs. Variables are seasonally adjusted if necessary (money supply and industrial production). t-statistics are in parentheses. Page 21 of 23 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3 : Residual Panel Cointegration Tests (Closed Economy Formulation),

 3 Notes: See Table2. */**/*** denote significance at the 10%/5%/1% level.

		Submitted Manuscript			Page 22 of 23
	1994:9-2003:6
		OLS	FE	FMOLS	DOLS	DOLS-SUR
	DF test	1.919	-1.507 *	-3.988 ***	-2.389 ***	-1.899 **
	DF t test	2.814	-2.109 **	-5.593 ***	-3.367 ***	-2.670 ***
	DF * test	0.036	-6.007 ***	-10.306 ***	-7.508 ***	-6.684 ***
	DF t * test	0.453	-2.159 **	-4.126 ***	-2.879 ***	-2.472 ***
	Panel ADF test	0.486	-2.029 **	-2.485 ***	-2.199 **	-2.021 **

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

Table 4 : Panel Cointegration Estimation of Money Demand (Open Economy

 4 The panel includes the Czech Republic, Hungary, Poland, Romania, Slovakia and Slovenia. All variables except interest rates are in logs. Variables are seasonally adjusted if necessary (money supply and industrial production). t-statistics are in parentheses.

	Formulation), 1994:9-2003:6 Industrial production Domestic interest rates Foreign interest rate Exchange rate No. of observations per country Total no. of observations Fixed effects Notes: Page 23 of 23 Submitted Manuscript OLS FE 0.227 0.433 (4.426) (9.869) -0.002 -0.003 (-4.460) (-6.400) -0.062 -0.050 (-10.013) (-11.587) -0.032 -0.040 (-2.023) (-2.626) 106 106 636 636 no yes	FMOLS 0.539 (7.841) -0.009 (-21.407) -0.032 (-8.767) -0.025 (-27.789) 106 636 yes	DOLS 0.312 (6.167) -0.007 (-9.690) -0.056 (-11.386) -0.071 (-4.106) 106 636 yes	DOLS-SUR 0.393 (17.856) -0.005 (-10.514) -0.048 (-20.224) -0.055 (-5.783) 106 636 yes

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

Table 5 : Residual Panel Cointegration Tests (Open Economy Formulation),

 5 Notes: See Table4. */**/*** denote significance at the 10%/5%/1% level.

						Page
	1994:9-2003:6
		OLS	FE	FMOLS	DOLS	DOLS-SUR
	DF test	2.119	-0.938	-4.521 ***	-3.293 ***	-1.794 **
	DF t test	3.086	-1.499 *	-6.679 ***	-4.960 ***	-2.774 ***
	DF * test	0.385	-5.006 ***	-11.083 ***	-8.979 ***	-6.488 ***
	DF t * test	0.587	-1.828 **	-4.892 ***	-3.864 ***	-2.533 ***
	Panel ADF test	0.595	-1.711 **	-3.155 ***	-2.737 ***	-1.989 **

24 of 23 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

The changes in the monetary regime took place in the CzechRepublic in 1997, in Slovakia in 1998, in Poland in 2000, and finally in Hungary in 2001.

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

Estimations with the longer, unbalanced sample were used in order to check the robustness of the parameter estimates to the inclusion of earlier transition periods (available upon request from author). In general, the parameters remain in the range of those presented for the balanced sample.

Acknowledgments

I benefited from comments by Abdur Chowdhury, Ronald MacDonald, Lucjan Orlowski, Jesús Crespo-Cuaresma, Iikka Korhonen, Robert Kust, and Doris Ritzberger-Grünwald.