Javier Víctor

Ginés Cano-Fernández

María Guirao-Pérez

Margarita Esther Carolina Rodríguez-Donate

Romero-Rodríguez

Carolina Rodríguez-Donate

; Cano Fernández

Guirao Ginés

María Pérez

Rodríguez Carolina

Donate
email: cdonate@ull.es

Margarita Esther Romero Rodríguez

AN ANALYSIS OF COUNT DATA MODELS FOR THE STUDY OF EXCLUSIVITY IN WINE CONSUMPTION

Keywords: Count data models, Poisson regression model, Negative Binomial regression models, finite mixture models, number of wine types Count data models, Poisson regression model, Negative Binomial regression models, finite mixture models, number of wine types

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

Introduction

The worldwide wine scene has gone through significant changes lately, especially since the 90´s. Both producers and wine drinkers have taken turns as the main actors in these changes. The most significant event with respect to demand has been a decrease in worldwide wine consumption, or at least a certain amount of stagnation as a consequence of two opposite effects. On one hand, the increase in demand in countries with traditionally low wine consumption, and the other, a reduction of observed per-capita consumption in those countries where indeed there is greater wine production and tendency to drink wine. Life style changes have followed a parallel path. For instance, now an increase has been observed in the consumption of higher quality wines than before. Changes have also taken place in traditional family events and social occasions in general, where once daily wine consumption was typical but now has been replaced by an occasional status.

The supply side has also undergone changes. The international players have witnessed the entrance of new countries in a sharing role in two systems of harvesting, production, and commercialization. The first model belongs to the Old World countries and includes France, Italy, Germany, Portugal and Spain. A second type is made up of the New World countries, of which Australia, South Africa, Chile, Argentina and the United States are the major players. As a result there is saturation in the international wine market. The slowdown in demand is accompanied by an increase in the supply of quality wines. And in this environment of increasing competition many wine producers have sensed the need to construct their own image and create a concept of quality that can be perceived by consumers. This scenario can even be introduced, with certain overtones, to the Canary Archipelago, and specifically to the island of Tenerife. Vineyards and the wine community arouse analytical interest in this geographical area not only because of its tradition in the wine production process -present in the Archipelago since the 1400´s-but also because of the inherent peculiarity of these wines, namely the climatic conditions, the orography in the island, and the variety of grapes used1 . Vine growing is also an important asset of undeniable ecological value given its contribution to rural developments, one of the selling points for tourism on the island, which is the true motor of economic activity in the Archipelago.

Increased competition in the wine market, in addition to recent trends defined by consumers, such as the drop in per capita wine consumption and an increase in the demand by consumers for quality wines, have motivated the need for detailed studies regarding consumer behaviour. But these studies need to go beyond such questions as explaining the quantity or frequency of wine consumption, and must include the ways and means in which it is occurring. The characteristics that define the place of consumption or purchase, the origin or region from which the wine came from, and the brand or wine types, can be important when helping develop strategies to sufficiently differentiate wines under current circumstances. Some research indicates that it is difficult to obtain an appropriate economic forecast in the wine sector without a thorough study of demand. Either way it is possible to undertake a study of consumer behaviour using several approaches given the importance that brand loyalty has had in prior research.

This study recognizes the limited amount of available information in this regard. We In our case a special type of model is necessary to properly gather the characteristics of the phenomenon that is being explained, namely its discrete and non-negative nature. Several alternatives have been proposed in the econometric literature which can fall under the term count data regression models. These models allow us to undertake this type of analysis and also offer some alternatives when defining the structure of consumer preference.

The specific characteristics of this variable allow the study to cover two aspects. The first concerns methodology, which is evident by the variety of models that can be utilized and consists in comparing the alternatives which fit the type of count that is found. The second is eminently empirical, and its goal is to describe not only the most suitable decision making process but to identify which factors explain the increased or decreased diversity in wine consumption.

Given these objectives, the paper is divided into three sections. The first section develops the methodology used, including the different models, noting the most advantageous features of each. Section two describes the data and compares the obtained results from all the models used. The last section draws the most relevant conclusions.

2 Several studies which analyze the influence of socioeconomic characteristics on alcohol consumption are [START_REF] Nayga | Sample selectivity models for away from home expenditures on wine and beer[END_REF], [START_REF] Su | A censored system of cigarette and alcohol consumption[END_REF] and [START_REF] Selvanathan | Economic and demographic factors in Australian alcohol demand[END_REF].

Standard models for count data

In our paper the number of wine types is between zero (non consumers) and seven (those wine drinkers, hereafter consumers, who tried all of the wine types considered in the study). A linear regression model is not appropriate for a study of this type since it ignores the special characteristics of this variable and may lead to inefficient, inconsistent and biased estimators.

i i i i i i 2 1 0 = λ = = λ - [ ] ) ' x exp( x / y E i i i i β = = λ 3 .
Explanatory variables of the model collect the observed heterogeneity, since they are the only source which can be differentiated among the individual ones. The distinct observed values from the explanatory variables lead to different λ values, while all the individual ones with the same value of the explanatory variables produce the same value of λ.

The equality of the conditional mean and variance in the Poisson model is one of its main characteristics and reflects its heteroskedastic nature. Nevertheless, it is also 6 one its primary disadvantages, namely its inability to capture potential overdispersion4 which tends to be present in most data.

The search for greater flexibility has led to the introduction of other models, some of which are also based on the Poisson distribution. These models are better at capturing the overdispersion and other characteristics, such as the excess of zeroes or the existence of long tails on the right side (of the distribution), which are considered as signs of unobserved heterogeneity5 [START_REF] Mullahy | Heterogeneity, Excess Zeros and the Structure of Count Data Models[END_REF].

This
[ ] i i e e v v , x / y E ' x i i i i i * i ε β = λ = = λ .
One of these models is the negative binomial model6 . Its representation as a Poissongamma mixture model is obtained by assuming that the unobserved heterogeneity term7 , i v , distributed as gamma

( ) ( ) δ δ, Γ with α ≡ δ = σ 1 2 i v (dispersion parameter) and [ ] 1 = i v E [ ] 1 = i v E
, which leads to the negative binomial probability density8 :

( ) ( ) ( ) i y i i i i i i i i y y ) x / y Y ( P         λ + α λ         λ + α α + α + α = = - α - - - - - 1 Γ Γ Γ ,
with mean and variance defined as: Cameron and Trivedi (1986) propose a more general model, the NEGBIN k with variance [ ]

F o r P e e r R e v i e w [ ] [ ] ). ( x / y V , x / y E i i i i i i i λ α + λ = λ = 1
k i i i i x y V - λ α + λ = 2 . If 0 = k
, the resultant model is the NEGBIN II. In the case where 1 = k we have the NEGBIN I model.

These standard proposed models face two types of major limitations. The first limitation assumes a zero and positive observations are generated by the same data process. This is the case that we are analyzing, assuming the same preference structure for consumers and non-consumers. A second limitation is characterized by its rigid structure considering its unobserved heterogeneity and is based on known parametric distributions. Therefore it is useful to consider other models that offer greater flexibility regarding these issues.

Hurdle models

Hurdle models, also known as two parts models, are typical alternatives and have been used in a number of applications. These models were developed by [START_REF] Cragg | Some Statistical Models for Limited Dependent Variables with Application to the Demand for Durable Goods[END_REF] for continuous data in the Tobit model context. Nevertheless they are quite useful in data count analysis if we observe a number with many zeros and even cases where there are hardly any zeroes at all when compared to the Poisson model [START_REF] Winkelmann | Recent Development in Count Data Modelling: Theory and Applications[END_REF] 9 . 9 The data base in this study reveals that the number of zeros represents an important percentage (24%) of all observations. Early work with this class of count data models are described in [START_REF] Johnson | Discrete Distributions[END_REF]. Nevertheless not until [START_REF] Mullahy | Specification and Testing of Some Modified Count Data Models[END_REF] were economic applications seen and regression effects explained 10 .

The consideration of the individual decision making process is one of the principal characteristics of these models. In the first stage (hurdle part), the individual decides, for example, if he wants to consume a product or not, and in the second stage (called the parent-process), given an affirmative decision, he decides how much he wants to consume. As a consequence of this decision, the probability of a zero response is modelled separately of the probability of a positive result, that is:

... , , y , ) y ( f ) ( f ) ( f ) y ( f ) y Y ( P ) ( f ) Y ( P 2 1 0 1 0 1 0 0 2 2 1 2 1 = φ = - - = = = = where ( ) ⋅ 1 f and ( ) ⋅ 2 f
are probability density functions which may or may not be the same type, 1 f governs the hurdle part and 2 f the process once the hurdle has been passed. These models can be seen as a finite mixture compared to the Negative Binomial, which assumes a combination of continuous random variables, due to the combination of the zeros generated by a distribution and the positive values generated by a truncated distribution [START_REF] Cameron | Regression Analysis of Count Data[END_REF]. [START_REF] Mullahy | Specification and Testing of Some Modified Count Data Models[END_REF] 11 Although in this case the set of explanatory variables is the same, it is possible that it can differ.

F

i , i , i , i , j i , i i 2 1 1 1 0 2 2 1 1 2 = - λ - = = = = λ - λ - λ - λ -
The estimation of the parameters for maximum likelihood on this type of models can be carried out through separate optimization of both components, namely the binary process and the truncated one. On many occasions, the first part is represented by a logit or probit model. As pointed out by [START_REF] Trivedi | The Structure of Demand for Health Care: Latent Class versus two-part models[END_REF], this choice does not have significant effects on the estimated probabilities.

Finite mixture models

The previous models can be seen as belonging to the finite mixture class, as indicated earlier, although they also assume certain restrictions which can be overcome. These restrictions include a sample that is divided into two subsets representing zero and positive observations, which can be generated by different processes and represent a special case of the finite mixture which incorporates a degenerate component. An alternative to this proposal is seen in the construction of finite mixture models which belong to family of latent class models [START_REF] Lindsay | Mixture Models: Theory, Geometry and Applications[END_REF]. These models show greater flexibility and other important advantages which allow for a combination of zero and positive values. Finite mixture models have been extensively used in statistics, but only recently have they achieved recognition due to their applications in various areas of research [START_REF] Leisch | FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R[END_REF].

12 Other authors have used different versions of this model, such as the negative binomial [START_REF] Gurmu | Excess of Zeros in Count Models for Recreational Trips[END_REF].

= ≥ π = π ∑ = .
The mixed density function is then expressed by:

n ,..., i ) / y ( f ) / y ( f C j j i j i 1 1 = θ π = θ ∑ = ,
where ( )

j i y f θ is the density function of each subpopulation j, C ,..., , , j 3 2 1 = .
These distributions can belong to different parametric families, although normally it is assumed that they belong to the same one (for example, Poisson, Negative Binomial, etc). In general, the j π are unknown parameters that must be jointly estimated with the rest of the parameters from the model, θ , with

∑ - = π - = π 1 1 1 C j j C
. These j π can be parameterized as a function of a group of explanatory variables, using a logit function (see, for example [START_REF] Wang | Analysis of Patent Data -A Mixed Poisson Regression Model Approach[END_REF], however identification problems can arise, hence in many cases these are estimated as simple constants 11 interesting, however, this is not essential since the finite mixture can be simply expressed in a flexible and parsimonious way of modelling the data [START_REF] Cameron | Regression Analysis of Count Data[END_REF].

Models for a subsample

In some instances, the range of the dependent variable is partially observable or only one subset of the population is of interest because it represents specific type of behaviour. For example, only those individuals who have tried at least a certain number of wine types are considered. This context reveals a truncated sample towards the left, typically with the truncation at zero, and in our case, only consumers.

The standard way of gathering this type of behaviour involves the use of Poisson or truncated Negative Binomial models 13 . These models coincide with the second part of the hurdle model discussed earlier. This case is characterized by the assumption that the behaviour of the dependent variable follows some of these distributions and that the observed counts are restricted to positive values.

An alternative way to deal with the truncation at zero is by changing the sample space. This approach is different then the one obtained by the conditional distribution, and the probability function would be given by: ( )

... , , y , )! y ( e x / y Y P i i y i i i i i i i 3 2 1 1 1 = - λ = = - λ -
where now 13 [START_REF] Gurmu | Test for Detecting Overdispersion in the Positive Regression Model[END_REF], [START_REF] Grogger | Models for Truncated Counts[END_REF], [START_REF] Gurmu | Overdispersion Test for Truncated Poisson Regression Models[END_REF], among others, have commented on these models. Recent application in order to look for some evidence of the presence of reputation in the return to tourist destination can be found in [START_REF] Ledesma | Return to tourist destination. Is it reputation, after all?[END_REF].

F o r P e e r R e v i e w 12 [ ] [ ] i i i i i i x / y V x / y E λ = + λ = 1
This distribution is known as the Displaced Poisson (Jonson and Kotz, 1969) and agrees with the one obtained by [START_REF] Shaw | On-site Samples Regression[END_REF] for the treatment of on-site sampling 14 .

Although the basis for the truncated distribution and the one obtained from this last distribution is the same, both are different (Cameron and Trivedi, 1998, p. 331).

Finally, our approach can be extended to the different versions of the Negative Binomial and the finite mixture model which were presented in previous sections.

The finite mixture model only requires an explanation of how new obtained distributions for the different classes are going to be considered. The optimization procedure follows the same steps as in the original.

Data and Results

Data

The data used in this study came from an exhaustive survey regarding wine consumption in Tenerife which took place during April and May, 2001. The survey included questions related to residents´ drinking habits and preferences with respect to wine consumption in general and specifically wine from Tenerife 15 . The variables that were used in our analysis include the type of wine consumed, the frequency of consumption and others of a socioeconomic nature. A description is included in table 1 of the appendix.

We thought it would be important to put together a descriptive analysis of the number of wine types. This analysis would give us an initial idea about the 14 See [START_REF] Englin | Estimating Social Welfare using Count Data Models: An Application to Long-run Recreation Demand under Conditions of Endogenous Stratification and Truncation[END_REF] for an extension to the Negative Binomial. 15 See [START_REF] Guirao | El consumo de vino en Tenerife[END_REF] for a detailed description of the survey. individuals. This variety is also greater among professionals, businessmen and civil servants, while housewives consume a smaller amount of wine types. An increase in income corresponds to an increase in the variety of wines consumed, although this is not the case for specific levels of education. For instance, university students and those individuals with primary school studies are those that consume the greatest amount of distinct wine types. Regarding consumption frequency we observe that, in general, as the frequency in wine consumption increases, so does the average number of wine types consumed. Specifically, those who seldom drink will consume on average approximately 2 different types of wine, while this figure rises to 2.5 for those who drink occasionally and 2.8 for those who drink often. Finally the average number of wine types for those who drink daily is 2.5, although the dispersion of these with respect to the average number of wine types is the highest of all the categories.

F

This relation among the number of wine types and consumption frequency suggests that frequency, along with other socioeconomic characteristics, can be a determining factor in the variety of wine types that the individual consumes and is the reason why it is included as an explanatory variable in the models used in the study. Both NEGBIN I and NEGBIN II models reveal that the parameter of dispersion ( ) α is not significant for the sample. This result suggests that the overdispersion present in the data is not very high (see table 2 in the appendix), which is reasonable given the relative nearness that exists between the mean and variance of the dependent variable, 1.8063 and 2.365, respectively.

Results

Several

In order to compare the Poisson model with the negative binomial approximations we began with the optimal regression-based test proposed by [START_REF] Cameron | Regression-based Tests for overdispersion in the Poisson Model[END_REF] to check for overdispersion or underdispersion in the Poisson model 16 . This test is based on the OLS auxilliary regression between

( ) [ ] i i i i i y y z µ - µ - = 2 2 and i i i ) ( g w µ µ = 2
, where ) ( i g µ is equal to µ or 2 i µ and in the posterior significance testing of the coefficient. In both cases, this coefficient is practically null and not significant, indicating scarce presence or absence of overdispersion in the data. We then use the common LR (likelihood ratios) 17 to compare nested models. In this case no evidence is found to reject the Poisson model against the NEGBIN I and

II models 18 . 16 ( )    µ α + µ = µ = i i i i i g ) y var( : H ) y var( : H 1 0 17 ) L Ln L Ln ( LR 1 0 2 - - = ~2 q χ
, where 0 L is the likelihood function for the restricted model and 1 L for the unrestricted model. 18 We previously studied the influence of certain socioeconomic characteristics of the individual on the number of wine types that are being consumed, but without considering the effect of consumption frequency. In this paper the Poisson model was rejected against the two negative binomial estimates using traditional overdispersion tests. This result leads us to consider whether the differences among individuals are not only due to observed heterogeneity but also to unobserved heterogeneity. The unobserved heterogeneity term included in the conditional mean of the negative binomial models can capture the effect of one explanatory variable which has been omitted in the model. The current study includes consumption frequency as the explanatory variable and has not lead to the rejection of the Poisson model against the two negative binomial models. Consequently we can consider that this Similarly the significance of j π confirms the hypothesis of the two subpopulations, whose estimated proportions would be 0.847 and 0.153.

Given that the Hurdle Poisson model and the FMPM models are not nested, two standard choice criteria are used in the comparison, namely the Akaike Information Criteria (AIC) and the Bayesian Information Criteria (BIC) 19 .

= ; ) N ln( k L ln 2 BIC + - =
, where L is the maximum likelihood function, k is the number of parameters that are estimated and N is the number of total sample observations. The nested models allow us to compare using likelihood ratio tests. In this case the statistic takes on a value of 39.766 which, at the 5% significance level, leads to the rejection of the Poisson model in favour of the latent class model. Fitted relative frequencies were calculated for each model, considering the entire sample or only consumers. For the first case (see table 3) our review reveals that all of the models under study tend to underestimate the number of zeros and overestimate the number of ones. Nevertheless good behaviour is observed when counts are greater than or equal to two. Most of the models adequately capture each one of the counts when only considering consumers (see table 4). In this situation the finite mixture model stands out. With regard to the subsample of wine drinkers, we followed the procedure described in section 2.4. As observed in

  approach not based strictly on one dimension but instead adopt a view which will at least allow us to observe consumption behaviour based on exclusivity or diversity. The study specifically aims to describe the socio-economic characteristics which best define the number of different wine types consumed by individuals based on a survey carried out with residents from the island of Tenerife 2 .

  11 , leading to the Hurdle Poisson model,10 Yen (1999) compares continuous and count data hurdle models to study cigarettes consumption by women in the US finding similar demand elasticities with respect to continuous explicative variables.

  in this type of model is assumed to be taken from a population which is an additive mixture of C distinct subpopulations in proportions

(

  Deb and Trivedi, 1997, among others).Finite mixture models offer a natural and intuitively attractive representation of the heterogeneity in a finite number of usually small, latent classes, where each one of which can be considered as a type or a group. The choice of the number of components of the mixture determines the number of types. If these components have a natural interpretation, then a characterization of the finite mixture is

  models have been tested for all individuals and for the sub-sample of consumers with the aim of analyzing the role of exclusivity in the consumption of wine. Both cases initially used the Negative Binomial and Poisson models. Two assumptions are made with respect to the Negative Binomial: one, that the variance is considered to be proportional to the mean, leading to the NEGBIN I model, and the variance is defined as a quadratic function of the mean, resulting in the NEGBIN II model.

  model (HPM) and Finite Mixture Poisson Model (FMPM) (see table 2 in appendix) are also included with the prior estimates. The Hurdle model separately models the probability of individual decision to not drink from the one where he decides to drink a specific number of wine types, while the finite mixture model considers two components (latent classes) that could initially be interpreted in relation to the level of exclusivity in the consumption. The dichotomy between these two groups would be characterized by a mean and variance of the number of wine types consumed where the first model has a lower value than the second. In our study the means are, respectively, 1,70 and 2,55, with variances of 0.974 and 6.15.

  preferred according to the AIC and the Poisson model is favoured by the BIC.

  several approaches regarding the analysis of wine type consumption by the residents in Tenerife have been presented. Standard approximations (Poisson, NEGBIN I and NEGBIN II) have been compared with more flexible ones (Hurdle Poisson Model and the Finite Mixture Poisson Model with two components). These last two have been proposed as alternatives in the data count context which normallyshows relatively high means and long tails, thus producing greater advantages than those found in typical parametric versions[START_REF] Guo | Flexible Parametric Models for Long-tailed Patent Count Distributions[END_REF]). In our case, the count type showed different characteristics than those mentioned, and motivated the interest in exploring these alternatives from an empirical point of view. Based on some traditionally used criteria in model selection for count data it can be concluded that Negative Binomial models are not superior to the Poisson model. A comparison of the Poisson model with the other two models which do not assume the same preference structure for consumers and non-consumers (Hurdle Poisson Models), or those that assume the presence of subpopulations with different response (Finite Mixture Poisson Model) is carried out. In our study the Poisson model or the Finite Mixture Poisson Model is chosen according to the criteria utilized. Nevertheless our results indicate that these models can be, marginally at least, more appropriate when including this particular type of count. At any rate other semiparametric and non-parametric alternatives are open to further research in this area. A summary of the results obtained from our study regarding the determining factors based on the level of exclusivity in the consumption of wine shows that, in general, the age of the individual -where a smaller variety of wine types remain as individuals age-, the individuals residence -in this case the most exclusive consumption occurs in the northern part of the island-and drinking frequency are

  factors. In addition income and education are exceptionally relevant for certain models. These factors also show behaviour patterns which are differentiated according to the group of individuals considered in the Finite Mixture Poisson Model, providing this model perhaps with a more realistic and useful approach to represent the heterogeneity of the observed phenomena.

Table 1 . Frequency Distribution: number of wine types Number of types Frequency Overall % % of those that consumer

 1

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

(33.7%), imported bottled wine with A.O. (16.3%) and self produced local table wine (12.6%). In addition, 20.67% drink three different types of wines. The most common combination among this three type group was imported table wine, local bottled wine with A.O. and imported bottled with A.O., representing 38%.

Table 2 . Model selection (Information Criteria) Criteria/Model Poisson Hurdle Poisson model

 2 Based on the results from the prior table we conclude that the Hurdle Poisson model should be rejected in favour of the other alternatives, where the Finite Mixture variable has assisted in explaining the individual differences that were initially attributed to unobserved heterogeneity, and specifically, to overdispersión.

	Finite
	mixture
	Poisson
	model

Table 3 . Actual and fitted distributions: (Relative frequencies for different models) N=1172 Number of types

 3 Age generally influences the number of wine types chosen by the consumer. This finding is consistent with the Finite Mixture Poisson Model (FMPM). As a result the number of variety of wine consumed decreases as the individual gets older. This characteristic is also present in the rest of the models. Other determining factors in the rest of the models are geographical area and consumption frequency. There is a wide range among consumption in the southern part of the island, and especially in the metropolitan area, when compared to the northern part of the island. Nonetheless, its influence in the finite mixture model is different for both considered classes. For instance, a significant impact is noted in the southern area for the group of less exclusive wine drinkers, and for the metropolitan area, it is the most exclusive.

		Observed	Poisson	Hurdle Model Finite Mixture
	0	0.24	0.16	0.15	0.16
	1	0.21	0.30	0.28	0.29
	2	0.27	0.27	0.27	0.27
	3	0.16	0.16	0.17	0.16
	4	0.06	0.07	0.08	0.07
	5	0.03	0.03	0.03	0.03
	6	0.02	0.01	0.01	0.01
	7	0.01	0.00	0.00	0.00
			Table 4.
	Actual and fitted distributions: (Relative frequencies for different models)
			N=890
	Number of types	Observed	Poisson	Truncated Poisson	Finite Mixture
	1	0.28	0.25	0.33	0.29

  Table2, the obtained results for the choice of models are the same as those for the complete sample. That is, according to the AIC criteria the FMPM is preferred, while the BIC criteria points to the Poisson model. The statistical value of the likelihood ratio test among these nested models is 64.64, rejecting the Poisson model against the Finite Mixture Model at the 5% significance level. The proportions for each class are significant for the Finite Mixture Model, estimated at 0.758 and 0.242, respectively. As we mentioned earlier, this can be an indication of the presence of two subpopulations that show a different response with respect to the greater or lesser exclusivity in consumption.The obtained results are, in some aspects, similar to those obtained for the entire sample (see table 3 in the appendix). That is, for the standard Poisson model, age, geographical location and consumption frequency are seen as relevant factors, but not educational level. The greatest variability is found in the set of individuals with university studies. This last result is also generated by both groups in the finite mixture model. Occupation is also not relevant in this model for the least exclusive group. Note, however, that income has a positive effect in the most exclusives, even when the negative impact for the first group is obtained. Finally the remaining factors, which include age, geographical area and consumption frequency, reveal similar behaviour to that obtained from our entire sample, although in this case the impact of consumption frequency is lesser for both groups.

Table 3 . Estimation results for the consumer subsample (N=890)

 3

				Finite Mixture Model (Latent Class)
	Variables	Poisson Coeff. p-value	Class I Coeff. p-value	Class II Coeff. p-value
	Constant	-0.924	0.000	-0.969	0.017	-0.903	0.257
	S2	-0.086	0.207	-0.052	0.604	-0.129	0.512
	E1	0.598	0.004	0.425	0.174	1.371	0.158
	E2	0.638	0.001	0.566	0.052	0.889	0.069
	E3	0.564	0.002	0.349	0.229	0.874	0.058
	E4	0.596	0.001	0.493	0.103	0.762	0.114
	E5	0.265	0.144	-0.079	0.786	0.827	0.057
	A2	0.193	0.008	-0.085	0.533	0.713	0.000
	A3	0.201	0.009	0.287	0.013	0.063	0.796
	SF2	0.113	0.242	0.256	0.078	-0.607	0.199
	SF3	-0.068	0.534	-0.016	0.922	-0.285	0.345
	MUF	0.036	0.130	-0.010	0.759	0.063	0.301
	O2	-0.097	0.468	-0.209	0.248	-0.038	0.932
	O3	-0.063	0.569	-0.032	0.854	0.252	0.436
	O4	0.003	0.978	-0.229	0.219	0.455	0.192
	O5	0.119	0.233	-0.167	0.367	0.563	0.084
	O6	0.136	0.233	-0.082	0.657	0.352	0.261
	O7	-0.014	0.906	-0.237	0.222	0.470	0.194
	ED2	0.093	0.502	0.203	0.452	-0.041	0.908
	ED3	-0.041	0.784	-0.276	0.341	0.585	0.145
	ED4	0.129	0.418	0.044	0.884	0.412	0.353
	I2	-0.018	0.874	0.295	0.127	-0.696	0.018
	I3	-0.030	0.796	0.415	0.040	-0.866	0.012
	I4	-0.161	0.228	0.332	0.155	-0.988	0.012
	I5	-0.098	0.480	0.461	0.051	-1.075	0.006
	FC α	0.185	0.000	0.180	0.000	0.242	0.007
	Ln L	-1337.968		-1305.646

A significant amount of grape diversity is present in the Canary Archipelago, due to several reasons, one of which is the absence of phylloxera.

Note that the log-linear formulation of the parameter i λ ensures the positive nature of the mean of

1 1 1 1 1

Overdispersion means that the conditional variance is greater than the conditional mean.

The problem of unobserved heterogeneity occurs in application in which behavioural differences among individuals can not properly "captured" by the group of explanatory variables in the conditional mean function of the model.

This type of model can also be inspired by different approaches. See[START_REF] Boswell | Chance Mechanisms Generating the Negative Binomial Distributions[END_REF].

This term can pick up a specification error, such as the omission of some explanatory variable(Gourieroux et al, 1984a, b) or by the intrinsic random process(Hausmann et al, 1984).

This probability function refers specifically to the NEGBIN II model.

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

Appendix Table 1. Variables included in the models

 -1760.601 -1760.499 -1760.602 -565.248 -1338.331 -1740.718


P Garcia-Del-Barrio

L A Gil-Alana

Pedro Garcia

PERSISTENCE IN SPAIN. (Time series and panel data approaches using regional data)

Keywords: J64 -Unemployment: Models, Duration, Incidence, and Job Search < J6 -Mobility, Unemployment, and Vacancies Unemployment persistence, Regional unemployment JEL Classification: J64 Unemployment persistence; Regional unemployment

This paper aims to re-examine the persistence of unemployment in Spain. For this purpose, we use time series and cross-section analysis. From a time series viewpoint we disaggregate unemployment by regions, and use unit root tests, AR coefficients and fractional differencing parameters as indicators of persistence. For the cross-section approach, we first estimate mean regressions of regional unemployment rates. Then, using a panel of 114 periods and 50 provinces, we estimate pooled, fixed and random effects models. Finally, following some recent developments, we implement several panel data unit root tests. Previous studies had already shown the strong persistence of Spanish unemployment. Our disaggregated analysis extends that finding to reveal that the persistence is greater in the most industrialised regions. The results also suggest that a structural break took place in 1994, implying a decline in the unemployment persistence since then.

Introduction

The high persistence of unemployment in the developed countries since the first oil shock has produced an intense debate about the different theories explaining unemployment behaviour. On the one hand, some traditional theories [START_REF] Friedman | The Role of Monetary Policy[END_REF][START_REF] Phelps | [END_REF], 1968) assume that fluctuations in unemployment are stationary around a natural rate. Occasionally, these fluctuations may be permanently changing the natural rate of unemployment from one level to another. On the other hand, the hysteresis hypothesis [START_REF] Blanchard | Spanish unemployment: Is there a solution?[END_REF]Summers, 1986, 1987) assumes that shocks in unemployment have a permanent effect on the level of the variable, implying that unemployment is nonstationary.

The concept of persistence might be considered somehow a conciliating theory.

Persistence implies mean reversion, even if the speed of adjustment towards the equilibrium level is slow, thereby being a special case of the natural rate hypothesis. At the same time, the hysteresis theory is also closely related to the concept of persistence, insofar as it takes long time for the shocks to disappear completely. In this context, the unemployment series is modelled by autoregressions (with the roots close to the unit circle) or by some other techniques like fractional integration. The sources of European unemployment persistence have been examined in a number of papers. Some of them highlight the presence of persistence mechanisms that lead the current equilibrium unemployment rate (UR) to be positively related to previous realizations of unemployment (Cf. [START_REF] Bean | The role of demand management policies in reducing unemployment, Chapter 4 in Snower DJ and G de la Dehesa[END_REF][START_REF] Jimeno | Regional unemployment persistence (Spain, 1976-1994[END_REF] for the case of Spain). The goal of this paper is not to explain those mechanisms, but simply to examine the degree of aggregate and regional UR persistence in Spain, for the period 1976-2004. Previous studies have examined the unemployment persistence from an aggregate approach, using time series techniques. The degree of persistence has been usually measured through the estimated coefficients of AR(I)MA models. ( [START_REF] Blanchard | Hysteresis and the European unemployment problem[END_REF][START_REF] Barro | The persistence of unemployment[END_REF]. More recently, new developments in econometrics have studied unemployment persistence through fractionally integrated (ARFIMA) models. (See, i.e., [START_REF] Tschernig | Illusive persitence in German unemployment[END_REF][START_REF] Crato | Measuring hysteresis in unemployment rates with long memory models[END_REF][START_REF] Caporale | Unemployment and input prices. A fractional cointegration approach[END_REF]andGil-Alana, 2001a, 2002).

The study of unemployment persistence also requires accounting for regional disparities. As stated by [START_REF] Blanchard | Spanish unemployment: Is there a solution?[END_REF], the most striking fact in Spanish regional trends is not just the difference in unemployment rates across regions, but rather the persistence of these differences. In fact, regional considerations might help us to understand more deeply the nature of unemployment persistence.

The interest for revisiting the Spanish case is unquestionable given its high UR.

More importantly, Spain is an obvious laboratory where to apply our regional approach, since regional discrepancies of rates between provinces are enormous. In the last quarter of 2004 various southern provinces (like Badajoz, Córdoba, Jaén and Cádiz) had UR above 20%, whereas others (Navarra, Lleida, Rioja, Soria and Teruel) presented rates of less that 5%, far below the average UR in Europe (which in 2004 was 9.2% for the EU-25 zone).

In summary, this paper aims not just to analyse thoroughly the Spanish experience, but to do it in a comprehensive way by adopting different perspectives and using a broad array of empirical devices. Should the same result be achieved from diverse approaches, the conclusion could be stated in a very consistent way. Hence, this study is challenging as far as it can be used to validate the accuracy of some recent empirical methods that we have employed. The outline of the paper is as follows: Sections 2 and 3 address the concept of persistence in time series and cross-section / panel data models respectively. Section 4 describes the data and presents the empirical results, while Section 5 concludes.

Time series persistence

From a time series viewpoint a classic model of persistence is the unit root case, where the effect of the shocks persists forever. To illustrate this point, consider the simplest case: the random walk model,

, ... , 2 , 1 , ) 1 ( = = t v u L t t (1)
where u t is the UR series we observe; L is the lag-operator (Lu t = u t-1 ) and v t is i.i.d.

Note that after recursive substitutions, (1) can be re-written as:

= = = t j j t t v u 1 , .... , 2 , 1 , (2)
and thus, a 1-unit shock has a 1-unit effect on the future path of the series.

Let us suppose now that v t in ( 1) is an ARMA(p, q) process of form:

..., ,

( = = t L v L t q t p 2 , 1 , ) ( )
(3) with all the roots of p (L) within the unit circle and all the roots of G q (L) within or in the unit circle. In such a case, v t can also be expressed in terms of a MA(H) representation,

= = = 0 , .... , 2 , 1 , j j t j t t b v (4)
and the coefficients b j will slowly (in fact, exponentially) decay to zero. These coefficients are usually associated with the short run dynamics of the series. In light of this, it is crucial to correctly determine the order of integration of the series. Thus, if it is 1 (i.e, a unit root with or without ARMA components) the series is said to be persistent as opposed to the case of simple stationary ARMA structures, where the effect of shocks disappears in the future. In the latter case the series is said to be I(0) since the order of integration is 0. Note that here persistence is measured by the impulse responses in (4) (the b j -coefficients). Thus, i.e., if u t is a stationary AR(1) process:

, ... , 2 , 1 , 1 = + = t u u t t t
(5) the model can also be expressed as

j j t j t t u (6)
and the higher is the AR coefficient , the higher is the persistent behaviour of the series, though disappearing in the long run as long as . 1 < Among the many procedures for testing unit roots, the tests of Dickey and Fuller (ADF, 1979) are the most widely used. These tests involve the regression of the firstdifference of the series on its lagged level and k lagged first differences. To select the value of k, the [START_REF] Ng | LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power[END_REF] procedure is applied. The starting upper bound, k max , is then determined by applying the [START_REF] Schwert | Test for unit roots; A Monte Carlo investigation[END_REF] criterion. In addition to ADF tests, we can also employ a DF-GLS test, which is a modified Dickey-Fuller test in which the series has been transformed by GLS regressions. For the latter tests, we can use the interpolated critical values proposed by [START_REF] Elliot | Efficient tests for an autoregressive unit root[END_REF].

In view of the previous discussion the classic approach to the time series persistence consists of determining if the series is nonstationary I(1) or stationary I(0), and, in the latter case, examining the coefficients that are associated with the short run dynamics. However, in the last twenty years a new model has emerged that avoids the strong dichotomy produced by the I(0) and I(1) specifications. This is because the number of differences required to get I(0) stationarity may not necessarily be an integer value (usually 1) but is possibly a real value.

We define a I(0) process {v t , t = 0, ±1, …} as a covariance stationary process with spectral density that is bounded and bounded away from zero at the zero frequency. In such a case, u t is I(d) if:

, ... , 2 , 1 , ) 1 ( = = t v u L t t d (7)
where d can be any real value. Note that using the Binomial expansion:

.... 2 ) 1 ( 1 ) 1 ( ) 1 ( 2 0 + = = = L d d L d L j d L j j j d
= = + = 1 , ... , 2 , 1 , j t j t j t t v y a u
and similarly, (if d > -0.5), using the expansion of (1-L) -d , u t admits a MA(H) representation:

= = = 0 , ... , 2 , 1 , j j t j t t v c u
with c 0 = 1, and c j decaying to zero at a hyperbolic "slow" rate (if d < 1). Therefore the parameter d also plays a crucial role in describing the time series persistence: the higher the d is, the greater is the persistent behaviour or the series. Similar to the unit root case (d = 1), v t in (7) can be extended to allow for short run dynamics, decaying exponentially to zero.

Attempting to summarize some of the literature on hysteresis and persistence on unemployment, [START_REF] Gordon | Hysteresis in history. Was there ever a Phillips curve?[END_REF] defined full hysteresis as the case of a unit root and persistence as stationarity AR. In that study, he concludes that no evidence of full hysteresis was found in five countries (France, Germany, USA, Japan and the UK) for the time period 1873[START_REF] Blanchard | Hysteresis and the European unemployment problem[END_REF][START_REF] Graafland | On the causes of hysteresis in long term unemployment in the Netherlands[END_REF] stated that, in the 80s, the labour market in the Netherlands was characterized by high and persistent level of unemployment. [START_REF] Lopez | Explaining the dynamics of Spanish unemployment[END_REF] reported that monthly unemployment in Spain (1976m6-1994m10) was consistent with hysteresis. On the other hand, [START_REF] Nott | Hysteresis in the Canadian labour market[END_REF] did not find evidence of hysteresis in Canada, while [START_REF] Wilkinson | A micro approach to the issue of hysteresis in unemployment; evidence from the 1988-1990 labour market activity survey[END_REF] did. [START_REF] Mitchell | Testing for unit roots and persistence in OECD unemployment rates[END_REF] examines hysteresis for the OECD countries, and [START_REF] Leon-Ledesma | Unemployment hysteresis in the US states and the EU. A panel approach[END_REF] analyses the case of the US states and the EU countries. Other studies on unemployment hysteresis are [START_REF] Song | Hysteresis in unemployment. Evidence from 48 states[END_REF], [START_REF] Roed | Does unemployment cause unemployment? Micro evidence from Norway[END_REF] and [START_REF] Roed | A note on the macroeconomic modelling of unemployment[END_REF], who proposes an alternative way of modelling unemployment hysteresis in which permanency is viewed as a continuous phenomenon. Cross-section and Panel data persistence Cross-sectional techniques may help to examine if regional UR are persistent of not. In the context of regional convergence, unemployment persistence could be evaluated by computing mean regressions of regional UR. In the regressions, the dependent variable is obtained after taking differences of the UR, where the length of the spell for which the differences are taken changes. This procedure was employed by [START_REF] Blanchard | Regional evolutions[END_REF] and [START_REF] Bertola | Wage Inequality and Unemployment: US vs Europe[END_REF]. The estimated models are of the form:

t u i = + u i q + (8)
where u i q is the UR in region i at the starting period q, and t u i is the change in the UR in that region over the following t periods. If the cross-sectional coefficient of the initial UR ( ) becomes more negative when the length of the spell increases, it means that regional UR are not persistent (since their reversion towards the aggregate mean is stronger over longer intervals).

Regarding panel data methods, some developments can also be implemented so that we may benefit from the better statistical properties associated with large samples. Panel data analysis permits us extracting greater information from the data and, more importantly, taking into account the possible influence of individual heterogeneity components. In particular, by isolating the unobservable individual heterogeneity, the fixed and random effects models filter the impact that these unobservable elements have upon the dependent variable.

Given the temporal dimension of the data and the nature of unemployment persistence itself, it seems imperative to specify and estimate the dynamic structure of the

Data and results

Data on unemployment were obtained from the EPA (Encuesta de Población Activa.

INE, Spain). The sample consists of quarterly (seasonally unadjusted) data for the time period 1976q3 -2004q4. Although there were some methodological changes over this period, the data series provided by the INE has been conveniently homogenized according to the methodological guidelines given by EPA-2002. 2 The time series 1 Arellano and Bond (1991) derived a Generalized Method of Moments (GMM) estimator using lagged levels of the dependent variable and the predetermined variables and differences of the strictly exogenous variables. This methodology assumes that there is no autocorrelation in the error term.

2 The ongoing nature of the EPA has allowed the INE, since the 3 rd quarter of 1976, to compute homogeneous data on the main characteristics of the labour market. In order to ensure such homogeneity in the results, it was required to carry out retrospective adaptations (from 1994 untill the 2 nd quarter of 1987) as well as to incorporate to the survey some improvements applied since 1999. For a detailed description of changes affecting EPA-2002, To measure unemployment persistence at the regional level, the analysis can be based on absolute regional UR or, alternatively, on regional relative UR. (The latter uses differentials; that is, the regional UR minus the national UR rate). Given our interest for examining unemployment persistence in Spain as a whole, we have chosen the first route. Other results based on the two approaches can be found in [START_REF] Jimeno | Regional unemployment persistence (Spain, 1976-1994[END_REF].

Results based on time series approaches

According to the classic (time series) perspective we first determine if the unemployment series is stationary or not. A visual inspection at the series, displayed in Nevertheless, these features might also be the result of a stationary AR process with the roots close to the unit circle.

[Insert Figure 1 about here]

Several methods have been proposed for testing the hypothesis of a unit root. Table 1 displays the results of the ADF and DF-GLS tests for the whole country as well as for each of the 17 regions. The latter were computed using Elliott- [START_REF] Elliot | Efficient tests for an autoregressive unit root[END_REF] efficient test for an autoregressive unit root, which has a better overall statistical 3 Spain is divided into 50 provinces, which are gathered in 17 regions, with different cultural traditions and political autonomy: Andalucía, Aragón, Asturias, Baleares, Canarias, Cantabria, Castilla-Mancha, Castilla-León, Cataluña, Valencia, Extremadura, Galicia, Madrid, Murcia, Navarra, País Vasco and Rioja. performance. The procedures were carried out for the model with and without trend, and they include as many lagged first differences as indicated by k in columns ( 1) and ( 4). The tests provide no evidence against the unit root hypothesis: the unit root null cannot be rejected for any of the 17 regions at the 1%, and not even at the 5% significance level.

[Insert Table 1 about here] However, the method presented above has very low power if the alternative is an AR process with the roots close to the unit circle [START_REF] Campbell | Pitfalls and opportunities. What macroeconomists should known about unit roots[END_REF][START_REF] Dejong | The power problems of unit root tests in time series with autoregressive errors[END_REF], but also if they are of a fractional form [START_REF] Diebold | On the power of Dickey-Fuller tests against fractional alternatives[END_REF][START_REF] Hassler | On the power of unit root tests against fractional alternatives[END_REF][START_REF] Lee | On the power of the KPSS test of stationarity against fractionally integrated alternatives[END_REF]. 4 Hence, we also use as a measure of persistence the fractional differencing parameter d, as described in Section 2.

The first two values in the first row in Table 2 display the estimates of the AR parameter assuming that d = 0 and that y t follows a non-seasonal and a seasonal AR(1) process. 5 We observe that in both cases the coefficients are very close to 1: it is 0.9944 in the non-seasonal case, and 0.9518 with a seasonal AR(1) process. In the right hand side of the table we display the estimates of d based on a parametric approach of [START_REF] Robinson | Efficient tests of nonstationary hypotheses[END_REF]. (See Appendix A for a full description of this procedure). The latter method uses a Whittle function, which is an approximation to the likelihood function.

Since it is parametric, we have to specify the functional form of the I(0) disturbances u t in (7). We try with white noise, Bloomfield and seasonal AR(1) v t . The model of [START_REF] Bloomfield | An exponential model in the spectrum of a scalar time series[END_REF] is a non-parametric way of modelling v t that produces autocorrelations decaying exponentially as in the AR case (See, e.g., Gil-Alana, 2001b).

We observe that for the three cases the values of d are much higher than 1, ranging 4 See also [START_REF] Cook | Spurious rejection using Dickey-Fuller tests[END_REF] for spurious rejections using Dickey-Fuller tests. [Insert Table 2 andFigure hypothesis. It is semiparametric in the sense that we do not specify any functional form for the I(0) disturbances v t . We see that practically all values are above the I(1) interval, implying orders of integration higher than 1, which is consistent with the results based on the parametric approach.

Next, we wonder if the unemployment persistence in Spain has experienced any substantial alteration along the last three decades. In other words, we are concerned with the possibility of a structural break in the data, since a number of institutional changes have taken place during this period. Various techniques can be applied in order to test structural shifts in regional UR (see, e.g., [START_REF] Baddeley | The impact of the early 1980s recession on British regional unemployment[END_REF], who studies the impact of the 1980s recession on regional unemployment in Britain). We employ here a methodology suggested by [START_REF] Hsu | Long memory or structural change: Testing method and empirical examination[END_REF], testing simultaneously the order of integration (d)

and the time of the break, which, in this context, is a single mean shift. (Appendix C).

[Insert Figure 3 about here]

The upper part of Figure 3 displays the estimates of the time break across the bandwidth number m. We see that in all except two cases, the break takes place at the fourth quarter in 1993. The lower part of the figure refers to the order of integration of the series and the results are to some extent ambiguous. If the bandwidth number m is smaller than T/4, the order of integration is strictly higher than 1, however, if m > T/4, the values are within the I(1) interval. Thus, it seems that once the break is taken into account the evidence of orders of integration higher than 1 is not as clear as before. In any case, from the analysis of the results presented so far it seems that unemployment, at an aggregate level, is 11 nonstationary, with an order of integration equal to or larger than 1, supporting thus the hysteresis hypothesis in the unemployment series for Spain.

Next, we examine the persistence of UR at a regional level. Starting with the AR coefficients, we see (Table 2) that all values are very close to 1. The lowest values are those referring to Baleares, with the coefficients smaller than 0.90 in the two cases. At the other end, Cataluña and PaísVasco are two of the areas with the highest coefficients.

Performing the parametric procedure of [START_REF] Robinson | Efficient tests of nonstationary hypotheses[END_REF] (in the right hand side of the table) the most noticeable features are first the fact that for Baleares, the unit root null hypothesis is rejected in favour of smaller orders of integration. This may be related to the tourism sector, which is highly predominant in this region. On the opposite side we find that Cataluña, País Vasco and Madrid, precisely among the most industrialized areas of Spain, are the regions where d is found to be higher than 1. 6

[Insert Figure 4 and the remaining regions, with values of d within the unit root interval in most of the cases. Thus, the results based on the semiparametric approach are completely in line with the parametric method: Baleares presents the smallest degree of UR persistence, while the most industrialized areas are those with the highest degree of persistence.

[Insert Table 3 about here] 6 Though not reported in the paper we also examined the orders of integration of unemployment disaggregating the series by sectors. It was found that the lowest degree of integration was obtained for the Services sector. On the other extreme, Industry had the highest levels of persistence. [START_REF] Tolvi | Unemployment Persistence of Different Labour Force Groups in Finland[END_REF] found that unemployment in Finland is less persistent for females and young people. We leave for future research the analysis of persistence for groups of age and sex in Spain. 12

In view of the potential presence of a break taking place at 1993q4, we compute again, in Table 3, the parametric approaches but using now data ending at 1993q4. We see here that values of d higher than 1 are once more obtained for Cataluña, Valencia, Aragon, Madrid and País Vasco. However, for the aggregate as well as for most of the regions, the order of integration is higher in this period compared with the whole sample, meaning that persistence might have been reduced since 1993q4 onwards.

We can summarize the previous results by saying that unemployment in Spain is highly persistent, a result that is inferred from the ADF and DF-GLS tests. More significantly, when using autoregressions, the coefficients are very close to 1, while when adopting fractionally integrated approaches, the values of d are higher than 1 in all cases. Besides, if a break is taken into account, it seems to take place at 1993q4, and the level of persistence declines from that period onwards. From a regional perspective, Baleares presents the lowest degree of persistence, due possibly to the influence of the tourism sector, predominant in this region. On the contrary, some of the most industrialized areas (Cataluña, Madrid and País Vasco) are those with the highest levels of persistence.

Our results are so far consistent with other previous studies on unemployment in Spain (e.g. Jimeno and Bentolilla, 1998), finding evidence of high levels of persistence at both aggregate and regional level. One explanation to this evidence might be the low geographical labour mobility observed in Spain during the considered period (e.g. [START_REF] Garcia-Rubiales | Unemployment in Spain: An analysis of labor mobility and young adult unemployment[END_REF]. This idea is congruent with the results for Baleares, which is presumably the region with the highest labour mobility and the lowest UR persistence.

Results based on cross-section and panel data approaches

The analysis made so far is based exclusively on time series approaches. Yet, the nature of unemployment persistence can be better understood exploiting the information Once the temporal dimension comes into the scene, we need to pay attention to the periods in which institutional features have taken place in Spain. For this reason, and for the sake of simplicity, we have arranged the cross-sectional analysis considering homogeneous periods of 6 years each (starting at 1976 and attending specially to 1982, 1988, 1994 and 2000). Following the lines of previous studies [START_REF] Jimeno | Regional unemployment persistence (Spain, 1976-1994[END_REF][START_REF] Wu | The persistence of regional unemployment: evidence from China[END_REF] etc.), we offer an initial flavour of Spanish unemployment persistence in Figure 5. This scatter graph represents provincial UR (annual averages from quarterly data), for different years, against the corresponding records for the year 1976. The positive slope in all the graphs of Figure 5 means that the ranking of provinces according to their UR has remained noticeable stable over the years. This fact suggests a high degree of persistence of regional unemployment differentials, which is noticeable broader than expected within an integrated economy.

[Insert Figure 5 and Table 4 about here]

To get a more accurate perception of this issue, Table 4 gathers the estimated coefficients for several regressions between provincial UR for two different years. In all cases, the significance of the estimated coefficients is remarkably strong as well as the 7 Some major economic and political events in Spain are summarized by [START_REF] Bentolila | Spanish unemployment[END_REF] onwards the trend of regional UR persistence has been reverted, inasmuch as the estimated coefficients (the slopes) experience a decline after that year. From inspection of the whole table, we can conclude that regional UR persistence in Spain increased between 1982 and 1988, remained high and stable between 1988 and 1994, and declined consistently since 1994. Note that the decline experienced since 1994 is congruent with the above results.

In addition, we also compute mean regressions of regional UR. The results vary depending both on the length of the spell for which the differences were taken (indicated in rows) and on the starting period (in columns). The results in Table 5 report the point estimates and t-statistics of [ from cross-sectional regressions starting at different time periods. The estimations were computed for the annual averages obtained from quarterly data. The constant is not shown and absorbs the effects of aggregate UR changes.

[Insert Table 5 about here]

The results manifest an interesting contrast. If we take 1976 as the starting year, the values are positive and statistically significant up to the point in which we have a spell of length 24 years. (In fact, we have to wait 28 years to find a negative sign). It means that extremely high persistence exists, since reversion towards the aggregate mean takes long time to occur. The analysis of column (2) suggests that strong persistence still exists, at least, until 1996, whereas the negative signs right from the first row of columns (3), ( 4) and

(5) indicates a change of behaviour in the unemployment persistence. It is certainly the case for the starting year 1994, in which reversion towards the aggregate mean is much faster than in previous periods. When considering the starting years 1988 and 1994, we realise

that the negative coefficients become significant after 10 and 4 years respectively, suggesting that regional unemployment persistence is lower since 1998 onwards. This result In summary, the previous results allow us to conclude that the dispersion of regional UR has persistently increased in Spain during the 80s, but it has experienced a reverted trend at the mid of the 90s. It has declined perhaps since 1994, and undeniably since 1998.

Up to now, we have studied unemployment persistence either adopting time series or cross-sectional methodologies. Next, we focus on panel data results. Table 6 collects the OLS and GLS estimates for the pooled model. Given that the estimations may have problems of heteroskedasticity, the former estimates were computed for robust standard errors, while the GLS estimations were performed specifying a heteroskedastic error structure.

[Insert Table 6 about here]

The results in Table 6, columns (3) and ( 6), include 17 dummies corresponding to the regions. The magnitude of the AR(1) coefficient, close to one in all the models, corroborates the strong persistence of Spanish unemployment, which is slightly lessen whenever regional dummies are present. More interestingly, the temporal dummies, that were included to explore breaks in unemployment behaviour, suggest a positive variation in 1982, whereas they manifest a significant decrease in 1994 and 2000. Note that this is again consistent with a break taking place in the last quarter of 1993, as time series analysis pointed out. It is also consistent with the conclusions reached from the cross-sectional results of Table 5.

In any case, the information contained in the data has not yet been fully exploited, and could be enhanced by applying the fixed and random effects models. Table 7 collects, in columns ( 7) and ( 8), the results for the fixed effects model, while columns ( 9) and ( 10) 8 First, in 1994 a number of changes took place. Economic circumstances were included in the reasons justifying individual dismissal procedures, which made it easier to occur. Unemployment benefit would come to be considered as taxable income and a range of issues on working conditions were no longer regulated. In that year the principle of causality was also re-established as a general rule for fixed-term contracts. Then, in 1997 a new permanent contract with lower dismissals costs was approved. refer to the random effects model. The results are basically consistent with the others already obtained, meaning that high persistence unemployment exists even after controlling for the elements of heterogeneity of the Spanish provinces.

[Insert Table 7 about here]

Table 7 also shows, in Columns ( 11) and ( 12), the estimates obtained through the GMM technique of [START_REF] Arellano | Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations[END_REF] described in Section 3. The results were computed using robust standard errors to avoid heteroskedasticity.9 Given that we deal with quarterly data, we have included in the model, as instruments, four lags of the dependent variable. We also display in Table 7 the statistics for the first-and second-order autocorrelation of the residuals (m 1 and m 2 , respectively). As expected, the residuals of the estimated equation show first-but not second-order autocorrelation. 10In summary, panel data analysis enables us to state that UR persistence in Spain has remained remarkably high in the last decades: the AR(1) coefficient is hovering around 0.95 for the majority of the estimated panel data models. It also suggests that the persistence might have experienced a substantial decline in 1994. A drawback of applying [START_REF] Arellano | Some tests of specification for panel data: Monte Carlo evidence and an application to employment equations[END_REF] procedure to our data set is that it is designed under the "classical" panel setting, where T is small and N is large, which is not the case in the present work.

Moreover, it imposes stationarity, while previous results presented in this work indicated that unemployment was nonstationary.11

Finally, we perform panel unit root tests, which provide dramatic improvements in power compared to performing separate unit root tests for each individual series. In 7, exhibited important differences between regions and, therefore, a common constant for the whole panel should not be included. Instead, the estimations allow for heterogeneous intercepts.

[Insert Table 8 about here]

Recall that the ADF and DF-GLS tests for time series failed to reject the unit root null for all regions. However, the low power of these tests against the stationary alternative, when the process is near-integrated, is a well-known problem (see, for instance, León-Ledesma and McAdam, 2004). Now, using a panel data set, we apply more powerful procedures and benefit from a reasonable large panel, collecting 50 provinces and 114 time periods. The degree of persistence for each individual regression error is allowed to vary freely across the 50 provinces.

The LLC (2002) paper proves that their t-star statistic is standard normal under the null of nonstationarity. We have included in equation ( 10) as many lagged first differences, for each province, as indicated by k in Table 7. Since Table 7 was computed for the regions, we assume here the same k for all the provinces comprised in the same region. 12 The results in Table 8 indicate that, once again, we cannot reject the unit root null for aggregate Spanish unemployment, implying that the question about unemployment persistence in Spain finds

again an affirmative answer. Next, we make up panels gathering all the provinces which belong to the same region, 13 even if most of them do not reach to the 8 or 10 individuals, 12 The estimations based on different k for each individual (instead of enforcing the same k for all the provinces within the same region) yielded very similar results and are not shown. 13 The devise of grouping "ad hoc" sub-panels for particular purposes, has been applied even for the case of just a few individuals (Cf. [START_REF] Culver | Is there a unit root in the inflation rate? Evidence from sequential break and panel data models[END_REF]. The shorter is the panel, the more difficult is that the cross-section variation helps to reject the unit root null, but whenever it happens, the result is very strong. Note also that LLC ( 2002) test is to some extent accurate for small panels, since "the normal distribution provides a good approximation to the empirical distribution of the test statistic in relatively small samples". which is a minimum required to make an accurate implementation of the test. Then, we gather the provinces in groups of 8 or 9, attending mainly to the value of k in Table 1.

It is meaningful the fact that there are some regional panels for which the unit root null is not rejected.14 Not surprisingly, they correspond precisely to those regions for which fractional integration methods reported a greater degree of UR persistence: Cataluña, País

Vasco and Madrid. The corresponding P-value, for the model without time trend in column

(3), indicates that there is a certain significant probability of failure of rejecting the unit root null, which is consistent with the finding that these three regions present the strongest unemployment persistence. More significantly, the P-value for the panel gathering these three regions together is as high as [0.031] for the model without trend.

Note, on one hand, that LLC ( 2002) test has been criticised for assuming, under the alternative of stationarity, that all cross-sections converge to the equilibrium at the same speed of adjustment. That should not be a serious problem in the present paper as far as we are precisely interested in the cases in which we fail to reject the null hypothesis of unit roots. On the other hand, if some degree of heterogeneity between panels exists, the prescribed test procedure is the IPS ( 2003) unit root test. Even though the properties of both types of tests depend upon the independence assumption across individuals, we venture that they may be of some help in some applied studies like this. 15 The results of these tests, shown in Table 9, yield basically the same conclusions than those in Table 8. In all the models we have included 8 lagged first differences. 16 The tests clearly fail to reject the unit 19 root null both in the case of the national aggregate UR and for the panel that gathers the three mentioned regions. Furthermore, this result occurs regardless whether the trend is included or not. By comparing the last two rows of Table 9, IPS ( 2003) tests teach us that the unit root for Valencia can be discarded.

Concluding comments

In this paper we have examined the persistence of Spanish unemployment in the last three decades, paying especial attention to the regional unemployment persistence.

From a time series viewpoint, we first computed ADF and DF-GLS unit root tests.

Then, we also measure UR persistence through the AR coefficients and by fractional differencing parameters. The cross-section analysis consisted basically of running mean regressions of regional UR. For the panel data methodology, we have employed a panel of 114 periods and 50 provinces. We run regressions for the pooled model as well as for the fixed and random effects models. The Arellano and Bond method for estimating dynamic panels was applied too. Finally, we performed LLC (2002) and IPS (2003) panel data unit root tests.

Among other findings, this empirical analysis has taught us three major lessons.

First, that UR persistence (in aggregate as well as in regional terms) has been very

strong in Spain throughout the last 25 years. Second, that it experienced a decline around 1994. Finally, that some of the most industrialized areas, like Cataluña, Madrid and País Vasco, endure the greatest unemployment persistence across the sample. These three regions are also the areas that present the smallest share of the labour force in agriculture and where the proportion of population living in large cities is among the greatest across the country.

Regarding the first conclusion, the high level or persistence at both aggregate and regional level in Spain is probably similar to the Italian experience, whereas it is in , 1998). This feature might suggest that there are some types of idiosyncratic factors (common to other Southern European countries) that explain the high persistence of unemployment. Even considering the reforms carried out in the Spanish labour market in 1994 and 1997, rigidities might have prevailed due to the inertia of legislation that has only recently been annulled.

However, other authors consider that institutional factors are not the main sources provoking high unemployment. [START_REF] Bertola | Wage Inequality and Unemployment: US vs Europe[END_REF] argue that, since institutional rigidities already existed in the past, other factors ought to be invoked to explain the high UR experienced in Europe since the middle 1980s. On their view, both the high unemployment in Europe and the increasing wage dispersion in the US must stem from the same cause. Then, institutional rigidities would have only triggered the process leading to high UR, but other forces (like a more rapid idiosyncratic shocks between sectors, suggested by [START_REF] Lilien | Sectoral Shifts and Cyclical Unemployment[END_REF]) must be the ultimate cause of it.

For the case of Spain, geographic labour mobility should certainly be taken into account. Since the time in which Spain became a democratic country in 1975, a persistent characteristic of its labour market has been the low rate of interregional immigration, despite of the disparities in the UR across regions [START_REF] Jimeno | Regional unemployment persistence (Spain, 1976-1994[END_REF]. Garcia-Rubiales (2005) moves along the same position when states that Spanish unemployment is more closely linked to the lack of labour mobility than to institutional rigidities. 17 We venture that the lack of labour mobility across Spanish regions could be the root of not just of high UR level but also of high unemployment persistence. Note that they are different concepts, since high persistence in a region can be experienced 17 This can be related to the number of temporary jobs too. Spain is the EU member with the highest level of temporary employment, which affects the duration distribution of unemployment (Cf. [START_REF] Guell | Fixed-Term Contracts and the Duration Distribution of Unemployment[END_REF]. Other meaningful finding of this study is the lower unemployment persistence experienced in Spain from the middle 1990s onwards. Why did such a decline in unemployment persistence occur around 1994? We have already mentioned that important labour market reforms were introduced precisely in that year. Besides that, by 1994 Spain had already had time enough to accommodate its integration into the EU (1986) and the EMS (1989). Besides, note that other important institutional changes took placed at that time, linked to government changes coming from the European, regional and general elections of 1994, 1995 and 1996, respectively. According to the report for Spain of the European Commission (2005, p. 5):

"High and persistent unemployment prompted a labour market reform in 1984, which was instrumental to job creation. During the economic boom in the second half of the eighties, the UR went down to around 16% in 1991. Labour rigidities, which enhanced the persistence of adverse shocks [START_REF] Dolado | The causes of Spanish unemployment; a structural VAR approach[END_REF] coupled with the incorporation of the baby boom cohorts and women into the labour market in the late 80s and the early 90s, pushed the UR above 20% in the 1993 slowdown. Since the second half of the 90s the UR fell significantly below 15% to nearly 11% in 2003 (…). Moreover, the resilience of employment growth has been particularly impressive during the last ten years. Since 1995, more than 25% of the total net job creation in the euro area was registered in Spain. Such (un)employment performance could point to a major structural change with respect to the past".

The previous comments are basically consistent with our empirical findings.

Since 1995, the Spanish employment rate has increased briskly by more than 13%, standing now close to 60%. This might be the main reason for the structural break that we have found around 1994. Moreover, the UR in Spain, although still the highest in the Euro-area, has been steadily falling from its peak of around 23% in 1994 to slightly above 11% in 2003. The positive change in labour market outcomes with respect to past trends might also be explained by: (i) the stability-oriented policies associated to the EMU membership; (ii) the labour market reforms as well as the moderation in nominal Note that z t in (A1) is a (kx1) vector of deterministic variables that might include an intercept (i.e. z t = 1) or an intercept and a linear time trend. Also, a ˆand A ˆin the above expressions are obtained through the first and second derivatives of the log-likelihood function with respect to d (see [START_REF] Robinson | Efficient tests of nonstationary hypotheses[END_REF]Robinson, , page 1422, for further details). I( j ) is the periodogram of u t evaluated under the null, i.e.:

Appendix B

The Whittle estimate of [START_REF] Robinson | Gaussian semi-parametric estimation of long range dependence[END_REF] is implicitly defined by:

, log 1 2 ) ( log min arg ˆ1 = = m j j d m d d C d (B1) . 0 , 2 , ) ( 1 ) ( ; ) 2 / 1 , 2 / 1 ( 1 2 = = = T m T j I m d C d for j m j d j j
where m is a bandwidth parameter number. The large sample standard error under the null hypothesis of no autocorrelation is 1/#T. The periodogram was computed based on the discrete Fourier frequencies fj = 2gj/T.

FIGURE 2

Estimates of d based on the Whittle semiparametric approach of Robinson (1995)

0 0,5 1 1,5 2
The horizontal axe refers to the bandwidth number while the vertical one corresponds to the estimates of d.

FIGURE 3

Estimates of the time break and the fractional differencing parameter The horizontal axe refers to the bandwidth number m while the vertical is the estimated time break in the upper plot and the estimated values of d in the lower plot. In the latter, we also include the 95% confidence interval of the I(1) hypothesis. The horizontal axe refers to the bandwidth number while the vertical one corresponds to the estimates of d. Mean regression of UR for provinces in Spain: t u i = + u i q + (1)

(2) (3) (4) (5)

After: q = 1976 q = 1982 q = 1988 q = 1994 q = 2000 i denotes province, u i q is the UR in the starting period q, and t u i is the variation of the UR over the following t periods.

1

Figure 1 ,

 1 Figure 1, does not produce clear conclusions. The first 50 sample autocorrelation values are also displayed in Figure 1, and they show a very slow decay to zero. Moreover, the periodogram presents the highest value at the lowest frequency. This may be an indication that first differences are required, implying thus nonstationarity I(1).

  5 A seasonal AR(1) process can be defined as (1-L s )u t = Y t , where s is the number of time periods within a year. 318 and 1.381. Moreover, the unit root hypothesis (d = 1) is rejected in the three cases in favour of higher orders of integration.

Figure 2

 2 Figure2displays the estimates of d based on a semiparametric approach[START_REF] Robinson | Gaussian semi-parametric estimation of long range dependence[END_REF] See Appendix B) along with the 95% confidence interval corresponding to the I(1)

  Figure 4 displays the estimates of d based on the Whittle semiparametric approach of Robinson (1995). The results here can be grouped into three different categories: Baleares, with values smaller than one in most of the cases; Cataluña, País Vasco, Madrid, Aragón and Valencia, with values of d strictly above 1 in many cases;

  panel data set. Applying the empirical methods that were described in Section 3, we examine, from different perspectives, the persistence of Spanish UR. The sample includes quarterly data for 114 periods and 50 provinces.

  Note that Spain joined the European Union (EU) in 1986 and the European Monetary System (EMS) in 1989. After some initial transitional years, the Socialist Party (PSOE) formed the government from 1982 until 1996. Since then, and almost until the end of the sample period, the conservative (right-wing) Popular Party (PP) has been driving the country. 7

  the mentioned structural break and could be explained by the labour market reforms introduced in Spain in the years1994 and 1997. 8

  other European countries or with the US (Cf.Jimeno and Bentolila

  UR. And yet, the fact is that high UR become more harmful as long as it coexists with high UR persistence.

  ; and (iii) the expansion of some labour-intensive sectors (construction and some services), which have significantly contributed to sustain employment growth.Finally, we have found greater persistence in some regions, namely: Cataluña,Madrid and País Vasco (and, in a minor extent, in Valencia and Aragón). The reasons for this evidence are not straightforward. In any case, the issue must be placed into the context of regional unemployment divergence between regions, since there are large disparity in the geographical distribution of UR. Andalucía and Extremadura recorded the highest UR in 2004, around 18%; whereas the opposite geographical and socioeconomic extremes, Navarra and La Rioja, registered rates about 5%. Madrid exhibited a rate of 6.5% and Cataluña and País Vasco of about 9%.The study accomplished by the European Commission (2005) justifies the disparities across regions on the bases of low geographical mobility of the labour force, which in turn is amplified by the characteristics of the housing market (poor development of rental housing, etc.). However, regardless of the origin of such persistence in regional unemployment dispersion, it does not explain why Madrid, Cataluña and País Vasco are the regions with greater unemployment persistence. The first one is by far the region in which a bigger proportion of the population lives in large cities, while the other two are among the most industrialized regions in Spain. These are also the three regions in which the smallest percentage of labour force is enrolled in the agriculture sector. Further study must be done to explain the causes behind this facts.

  FIGURE 1Unemployment rate in Spain, with its corresponding correlogram and periodogram a) Original time series

  FIGURE 4Estimates of d based on the semiparametric approach of[START_REF] Robinson | Gaussian semi-parametric estimation of long range dependence[END_REF] a) Baleares

  FIGURE 5Provincial UnemploymentRates for 1988Rates for , 1994Rates for , 2000Rates for and 2004Rates for with respect to 1976

  the regressions. The results in the first row in Table4seem to indicate increasing divergence of unemployment persistence in Spain until 1994. From that year

	explanatory power of
	F o r
	P
	e
	e r
	R e v
	i e
	w
	14

, p.238. The reforms of the Spanish labour market are described in European Commission (2005), p.49.

Table 8

 8 we report the results of computing LLC (2002) procedure, while Table9shows the IPS (2003) unit root tests. The estimated coefficients of the intercepts, in the single-equation models in Table

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

TABLE 3

 3

	Unemployment persistence: Aggregated and disaggregated by regions with data ending at 1993q4
			d = 0		Estimates of d
		AR (1)	Seasonal AR(1)	White noise	Bloomfield (1)	Seasonal AR(1)
	TOTAL	0.9976	0.9668	1.402	1.342	1.336
	ANDALUCIA	0.9945	0.9629	1.02	1.25	0.97
	ARAGON	0.9880	0.9204	1.06	1.30	1.00
	ASTURIAS	0.9937	0.9631	1.00	0.90	0.97
	BALEARES	0.8728	0.8888	0.55	0.29	0.56
	CANARIAS	0.9925	0.9640	0.97	0.95	0.93
	CANTABRIA	0.9926	0.9560	0.94	1.00	0.94
	CASTILLA-LEON	0.9946	0.9747	0.97	0.73	0.98
	CASTILLA-MANCHA	0.9883	0.9480	0.97	0.82	0.91
	CATALUÑA	0.9939	0.9237	1.38	1.51	1.29
	COM.VALENCIANA	0.9957	0.9588	1.19	1.48	1.12
	EXTREMADURA	0.9788	0.9424	0.67	0.53	0.64
	GALICIA	0.9964	0.9777	0.99	0.76	0.91
	MADRID	0.9884	0.8967	1.20	1.33	1.14
	MURCIA	0.9891	0.9449	0.91	0.83	0.91
	NAVARRA	0.9631	0.9138	0.89	0.98	0.78
	PAIS VASCO	0.9962	0.9691	1.12	1.49	1.04
	RIOJA	0.9759	0.8994	0.93	1.20	0.87

TABLE 4

 4 Regressions of Unemployment Rates for provinces with respect to previous yearsEstimations computed for the annual average unemployment rates. Coefficients in bold at the 95% level. (t-statistic) in parenthesis.

			Dependent variable: UR (annual averages for provinces)
		1982	1988	1994	2000	2004
		1.288 (8.44)	1.914 (10.5)	1.925 (8.93)	1.449 (6.60)	0.960 (5.89)
	1976	R 2 = 0.597	R 2 = 0.696	R 2 = 0.624	R 2 = 0.475	R 2 = 0.419
			1.176 (11.4)	1.146 (8.77)	0.715 (4.78)	0.474 (4.36)
	1982		R 2 = 0.731	R 2 = 0.615	R 2 = 0.322	R 2 = 0.284
				0.978 (16.3)	0.751 (9.91)	0.487 (7.94)
	1988			R 2 = 0.847	R 2 = 0.671	R 2 = 0.567
					0.744 (11.8)	0.516 (11.0)
	1994				R 2 = 0.745	R 2 = 0.719
						0.650 (16.5)
	2000					R 2 = 0.850

TABLE 5

 5

TABLE 6

 6

			Spanish unemployment persistence. Panel data estimations (1976q3-2004q4)
			(1)	(2)	(3)	(4)	(5)	(6)
	Variables	OLS	OLS	OLS	GLS	GLS	GLS
	AR(1)		0.9663 (269.2)	0.9655 (217.5)	0.9285 (152.4)	0.9735 (373.8)	0.9776 (308.4)	0.9607 (230.7)
	Break1982		0.0628 (0.86)	0.4108 (4.72)		0.0698 ( 1.11)	0.0887 (1.31)
	Break1988		0.0149 (0.19)	0.0205 (0.27)		0.0075 ( 0.14)	0.0123 ( 0.22)
	Break1994		0.4628 ( 5.92)	0.3832 ( 4.88)		0.4933 ( 9.04)	0.4575 ( 8.28)
	Break2000		0.1892 ( 2.11)	0.0494 ( 5.12)		0.0267 ( 0.42)	0.1675 ( 2.50)
	Constant	0.5572 (11.70)	0.7171 (15.02)	0.6255 (5.24)	0.4133 (10.29)	0.6114 (13.21)	0.5553 (4.67)
	Reg.dummies			Yes			Yes
	R 2		0.9456	0.9467	0.9476
	Nº periods	113	113	113	113	113	113
	Nº provinces	50	50	50	50	50	50
	Nº		5650	5650	5650	5650	5650	5650
	b	i

Coefficients in bold at the 95% level. (t-statistic) in parenthesis.

[P-value]

in brackets.

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

On the other hand, the Sargan test from the one-step homoskedastic estimator rejected the null hypothesis that the over-identifying restrictions are valid, but this could be due to heteroskedasticity.

The presence of first-order autocorrelation in the differenced residuals does not imply that the estimates are inconsistent, while it would be the case if the second-order autocorrelation were found. SeeArellano and Bond, 1991, pp. 281-2.

Note, however, that even with the novel techniques used here, it is still statistically difficult to distinguish between nonstationarity (with a unit root) and stationarity with AR coefficients close to the unit circle.

That is not the case for the majority of the regions, implying that the individual unemployment series included in those regions should be considered I(0). This panel-based test could not be carried out for the case of regions containing a number of provinces smaller that 3.

As stressed by[START_REF] Strauss | Shortfalls of Panel Unit Root Testing[END_REF], subtracting cross-sectional means to remove common time specific effects is a quite common procedure but, if there is heterogeneity in the cross sectional correlation, it will only partially reduce the problem. Regarding the LLC test, it requires independence across individuals, assumption that can be somewhat relaxed to allow for some degree of dependence by including timespecific intercepts, which does not affect the limiting distributions of the test(Cf.: LLC, 2002, p. 13).

 16 Note thatIPS (2003) pointed out that the tests perform better if the orders of the underlying ADF regressions are correctly chosen or over-estimated.

Ministerio de Ciencia y Tecnologia (SEC2005-07657, Spain).

Appendix A

The LM test of [START_REF] Robinson | Efficient tests of nonstationary hypotheses[END_REF] 8) is:

where T is the sample size and:

Appendix C

The starting model in [START_REF] Hsu | Long memory or structural change: Testing method and empirical examination[END_REF] is:

where T b is unknown and x t is given by (1). The procedure is simple. For each hypothetical change point (T b ) we estimate first µ 1 and µ 2 in (C1) from the pre-and post-change observations, i.e

The residuals are

and the periodogram of t x ˆ, (evaluated at the discrete Fourier frequencies, j =2 j/T) is given by: 5650 5650 5650 5650 5600 5600

Individual effects

Coefficients in bold at the 95% level. (t-statistic) in parenthesis. [P-value] in brackets.

a: F-test that all u i = 0 (H0: no fixed effects). b: likelihood ratio test of u = 0 (H0: no random effects).

m i: (i-order correlation test): Arellano-Bond test that average autocovariance in residuals of order i is 0. (H0: no autocorrelation). a Indicates the number of provinces included in each panel. b The t-bar statistic, derived by Im-Pesaran-Sin (2003), converges in probability to a standard normal distribution.