Productivity convergence in

Keywords: Convergence, productivity, industrial sectors, spatial effects, mobility Convergence, productivity, industrial sectors, spatial effects, mobility

This paper analyses the evolution of the EU productivity between 1980 and 2003, both across regions and sectors. By making use of various techniques (cross-section, non-parametric and spatial approaches) it concludes that: 1) the regional and sectoral dispersion of productivity is quite high; 2) the gains experienced in aggregate productivity are due entirely to the sectors productivity growth effect; 3) there is a weak beta-convergence process at the aggregate and sectoral levels; 4) the accounting decomposition of the aggregate productivity convergence process reveals the sectoral productivity growth effect to be the only responsible for regional catching -up; 5) finally, there are clear signs of spatial dependence which, when properly addressed, increase the speed of convergence at the aggregate level.

I. Introduction

Productivity is undoubtedly a difficult concept to define, and consequently to measure [START_REF] Kitson | Regional competitiveness: An elusive yet key concept?[END_REF]. In spite of this, there is a broad consensus, both from the analytical and empirical point of view, that gains in productivity represent, in the long run, the main source of economic growth, wealth generation and welfare differences [START_REF] Krugman | The age of diminished expectations[END_REF]; as [START_REF] Ezcurra | Regional welfare disparities: The case of the European Union[END_REF] indicate "regional productivity differences prove to be the main determinant behind observed welfare inequality in the European context". Likewise, and although it must be recognised that it would be rather naive (and even wrong) to describe an economy's competitiveness solely in function of its productivity, it is no less true that productivity, along with the employment rate, is one of the most significant indicators of what might be termed "revealed competitiveness" of an economy, and therefore of its level of development and growth potential [START_REF] Gardiner | Competitiveness, Productivity and Economic Growth across the European Regions[END_REF]. This being the case, it is small wonder that in recent years politicians and economists in the European Union (EU) have expressed great concern about the persistent loss of dynamism of EU productivity, especially when compared with that of the United States (McGukin and van Ark, 2003). Hence the aim of the European Commission, launched in the Lisbon summit of 2000, to convert the EU by 2010 into "the most competitive and dynamic knowledge-based economy in the world, capable of sustainable economic growth with more and better jobs and greater social cohesion".

The issue of the aggregate productivity of an economy can be examined from a variety of different perspectives. One of the most interesting, illustrative and simple to carry out is however that which considers that aggregate productivity is simply the result of the joint behaviour of two vectors: one representing the sectoral productivities, and the other the sectoral distribution of the economic activity [START_REF] Bernard | Productivity and convergence across U.S. states and industries[END_REF]. Consequently, it seems clear that growth in aggregate productivity must be explained either by growth in the productivities of the individual sectors, or by a shifting in the above-mentioned sectoral distribution (better known as "structural change"), or, as often occurs, by a combination of both elements. This paper focuses on the analysis of industrial productivity of the EU from a regional (NUTS 2) 1 point of view. It draws on historic time series data (for the period between 1980 and 2003) compiled by "Cambridge Econometrics", which, for a broad definition of the industrial sector (including both energy and manufactured products), offers homogeneous information for a sectoral breakdown into ten branches of activity.

The paper is organised into three main sections plus a very brief one of conclusions. In Section II we deal with the aggregate productivity of the EU and its regions, analysing the external shape of the distribution and its internal mobility. Next, we examine the growth pattern of aggregate productivity, showing what part is due to improvements in the productivity of the sectors, and what part is the result of structural change. Section III is initially devoted to a classical betaconvergence analysis both at the aggregate and sectoral levels. Additionally it examines the contribution to the aggregate productivity convergence of the two components previously mentioned: the regional convergence (or divergence) between the productivity levels by sectors and the structural change. In Section IV, we carry out different tests of spatial dependence and, having detected its presence, we subsequently conduct a convergence analysis of regional productivity which takes into account this spatial dependence. As is usual, the paper closes with a summary and some concluding comments. Although there are different ways of interpreting productivity, the most conventional is that which refers to the productive efficiency of a particular workforce, that is to say the output (Gross Value Added) per worker employed 2 .

II. Productivity in the EU

According to this interpretation, Figure 1 shows the density functions representing the regional distribution of the relative aggregate productivity of the EU regions in the initial and final years of our sample period. Two features are particularly interesting: on the one hand, the number of regions with values similar to the mean is greater in 2003 than in 1980 which means convergence; and, on the other, there are some signs that the distribution presents not only a main mode but also two secondary ones in 2003, which implies a given degree of stratification. The mapping of the relative productivities of the EU regions in these two years (Figure 2) confirms these results to a certain extent, at the same time revealing some incipient signs of spatial dependence.

Figure 2 similarly shows that the relative situation of some regions has changed over time, this reflecting important differences in the regions' economic performance over time. Although this is repeatedly mentioned in the rest of the paper, for the moment it is worth pointing out (Table 1) that with the European aggregate productivity experiencing an average annual growth of 3.1%, this value 2 Another common interpretation refers to total factor productivity (TFP). As to the question of the changes in the ranking among the EU regions, the easiest way of analysing the importance of intra-distribution mobility is to calculate the well-known transition matrices. However, using these matrices leads to a clear problem in that the results critically depend on the number and length of the intervals considered for the original distribution. In view of this, some authors [START_REF] Quah | Empirics for growth and distribution: Stratification, polarisation, and convergence clubs[END_REF]Stokey and Lucas, 1989, among others) prefer to analyse the intradistribution dynamics by means of an approach based on the estimation of stochastic kernels. These are the equivalent of a transition matrix where the number of intervals tends to infinity. Therefore, we proceed to estimate a stochastic kernel for the aggregate relative productivity 3 . When interpreting the results of this estimation, which are shown in Figure 3, it must be borne in mind that in the 3-D graph the X and Y axes represent the relative productivity in the years 1980 and 2003, while the Z-axis measures the density (or conditioned probability) of each point in the X-Y plane.

The lines parallel to the Y-axis show the probability of moving from the point considered in the X-axis to any other point in the Y-axis. In turn, the 2-D graph shows the contour lines, obtained by taking a cut parallel to the X-Y plane for particular density values. The interpretation of the kernel is simpler if we look at this second graph. If the contour lines concentrate around the positive diagonal 3 A similar approach can be seen, among other recent papers, in [START_REF] Laurini | Income convergence clubs for Brazilian municipalities: A non-parametric analysis[END_REF]. (shown in the figure), the level of mobility is limited, while if they do not, there is some mobility, and the further these lines are from the diagonal, the greater the mobility degree.

As can be seen in Figure 3, the contour lines show at least two clearly different situations. Firstly, contour lines for regions with low values of initial relative productivity tend to concentrate around the diagonal, which indicates that, for these regions, intra-distributional mobility in total productivity levels has been relatively low. Secondly, looking at regions with higher levels of initial relative productivity we note that the contour lines diverge from the diagonal, meaning that some of these regions have substantially improved their relative position between 1980 and 2003.

Assuming the changes noted above were maintained over time, this would result in what is known as the "ergodic distribution"; this represents the long-term equilibrium distribution, which is obtained by iterating the stochastic kernel. As can be seen (Figure 4) this distribution presents a single mode, very close to the European mean. This suggests that, in the hypothetical long-term equilibrium, it is very unlikely to appear productivity poles or clusters among the European regions. Having looked at the main features of the aggregate productivity in the EU regions, in this section we explore the sources of its growth. Although there are various approaches that may help to provide a response to this question, we opted to apply one of the simplest and most illustrative: we aim to determine the role played by both the increase in productivity of the different sectors and by the structural change in the EU aggregate productivity growth.

Sectoral sources of productivity growth

Table 1 summarises industry productivity evolution in the EU over the sample period. Several results are apparent, the most interesting being the existence of a wide dispersion in productivity growth both across sectors and regions. At the EU level, it can be seen that "Transport equipment" and "Chemical products" were the most dynamic sectors, while "Paper and printing products" grew the least. At the regional level, it is also shown that industry variation is very large in all cases, with the "Ferrous and non-ferrous metals" providing the highest value of the coefficient of variation.

As far as the structural change in employment is concerned, we estimate this by calculating the degree of correlation between the productive structures corresponding to the initial and final years of the sample [START_REF] Jackson | Industrial performance under Transition: The impact of structure and geography, in The Development of the Balkan Region[END_REF]. Thus the coefficient of structural change (CSC) takes the form: CSC = Cor (s ik(t) ,s ik(t+T) )

(1) In order to consider the joint influence of the two aforementioned effects -the growth in the productivity within the various sectors and the structural change-in the evolution of the aggregate productivity, we make use of the approach applied by [START_REF] Bernard | Productivity and convergence across U.S. states and industries[END_REF]. This allows us to write the following expression:

( ) ( ) ( ) k k k k k k % P P T P P w T P P w T = + (2)
where k represents the sectors, P the productivity, w k the weight of the employment of sector k in the total employment, and a bar over a variable indicates its mean value over the sample period. The left-hand side of this expression denotes the rate of growth of the aggregate productivity, while on the right-hand side the first term represents the so-called "productivity growth effect (PGE)" while the second accounts for the structural change or "share effect (SE)". The PGE measures the contribution of within sector productivity growth for the region -with the average sectoral labour shares as weights-, whereas the SE effect captures the contribution of changing industry-mix to aggregate productivity growth.

Applying expression (2) to the EU as a whole for both 1980 and 2003 leads to the results shown in Table 3. From these results we can conclude that:

1. The main cause of aggregate productivity growth in the EU is productivity growth at the sectoral level. In fact, the within-sector effect dominates the share effect for our sample of regions, accounting for 100.49% of total productivity growth. This means, logically, that the share effect -i.e., the reallocation of employment between the different sectors-has played a completely marginal (as well as negative) role in the aggregate productivity growth experienced in Europe.

2. As it was observed earlier, Table 3 confirms that all sectors have contributed positively to the growth in the aggregate productivity, with "Metal products"

and "Textiles, clothing and footwear" being the sectors that contributed the most and least, respectively.

3. The PGE was positive in all sectors, although it was particularly important in that of "Metal products". In contrast, the SE offered a positive contribution in only half the cases. Finally, we should mention that, although the relative contribution of this effect on the aggregate productivity growth in the EU has been very small in all sectors, there are some examples where the contribution to the total productivity growth in the sector itself has been considerable. This is the case of the "Textiles, clothing and footwear", for example, in which the share effect has reduced its productivity growth by more than 56%. Likewise, in the "Paper and printing products" sector, the contribution of the share effect to the productivity growth (both the aggregate and that of the sector itself) was much higher than the contribution of the sectoral productivity growth effect. In all the other cases the predominance of this latter effect over the share effect was considerable.

III. Convergence in EU productivity

Having presented the main features of EU productivity in the previous section, we devote the next two to analyse whether a convergence process has taken place between the European regions and, this being the case, which factors are behind this process 4 .

Convergence in productivity: an aggregate and sectoral perspective

To begin with, we carry out a classical analysis of beta-convergence regressions, so that for every sector and the aggregate, the growth rate of productivity for each region between 1980 and 2003 ( i ) is regressed on its initial level (P i0 ) 5 and a 4 For a different but complementary approach to the analysis of convergence in productivity, see [START_REF] Tsionas | Real convergence in Europe. How robust are econometric inferences?[END_REF]. 5 As is usual in the analysis of beta convergence, we have introduced the variable object of analysis -in this case, productivity -in relative terms. In fact, we have taken the value of each region with respect to the mean value for EU-15 without considering the value registered by a As can be seen in the first column of (Table 4), there appears to have been a weak process of absolute 6 convergence in aggregate productivity between the EU regions, since the coefficient associated with the initial productivity is, although low (-0.009), negative and statistically significant.

In this table we have included, apart from the direct results of the estimation, another two typical indicators generally provided by the studies of convergence.

On the one hand, the speed of convergence 7 , whose informative content goes further than the value of the beta coefficient and, on the other, the number of years that would be necessary to cover half the distance separating the European regions from their steady state (half-life) 8 , providing that the current convergence rate is maintained. It can be seen that the speed of convergence is 1% per year, which implies a half-life of 75 years.

As for the sectoral convergence process, the results are also shown in Table 4. We note first that there appears to have been some convergence in all branches of activity. The sectors in which the convergence process has been most intense are "Chemical products" and "Other manufacturing", which have registered annual convergence rates of 2 and 1.8%, respectively, this meaning that the number of years required to halve the distance from the steady state is 42 years for the first sector and 46 for the second. In contrast, the convergence speed is lowest among "leader" region (as is done in other papers). Here the degree of disaggregation is so high that in our opinion this second option is not advisable. 6 We have also carried out a conditional beta-convergence analysis. The results are available upon request. 7 To calculate this we use the following expression: the "Metal products", "Paper and printing products" and "Ferrous and nonferrous metals " sectors (1% for the first two and 0.9% for the third).

Sectoral contributions to productivity convergence

In the final part of Section II we decomposed the aggregate productivity growth into two elements: one measuring the growth of the sectoral productivities, and the other representing the structural change. In order to complete our analysis of the convergence process, in this section we try to disentangle the contribution of each one of these two factors to the convergence pattern that has been detected in relation to both the aggregate and sectoral productivities. With this aim, we apply again the method proposed by [START_REF] Bernard | Productivity and convergence across U.S. states and industries[END_REF] and used recently by [START_REF] Van Ark | ICT and productivity in Europe and the United States. Where do the differences come from?[END_REF]. As we have already indicated, this approach is based on building a measure of the productivity growth for each region in relation to the productivity growth in the EU globally. Starting from Equation (2) it can be found that if this relation is maintained both for each region and for the EU as a whole, the difference between the annualised variation of the aggregate productivity in region i and in the EU, in percentages, can be expressed as follows:

(

) [ ]

T P P % i -( ) [
] 13 when the initial productivity of region i is less than that of the EU 9 . The results obtained by applying Equation (3) to our databank are shown in Table 5, from which we can draw the following conclusions 10 :

T P P % UE = k (PGE k,i -PGE k,UE ) + k (SE k,i -SE k,UE ) (3)
1. The convergence process is entirely due to the within-sector effect, which represents 110.49% of the total. This means, logically, that the contribution from the share effect has been negative (-10.49%), which testifies that variations in the industrial mix have not been a factor of convergence. Far from it: they have actually generated an (albeit small) increase in regional disparities in Europe.

2. If we break down the analysis by sectors, we observe that all of them, with the sole exception of "Transport equipment" (with a negative contribution of 6.14%), have contributed to reducing the imbalances in aggregate productivity. In order of importance, the most substantial contributions to the convergence process have been those from "Food, beverages and tobacco"

and "Fuel and power products", with contributions of 35% and 30%, respectively, followed at some distance by "Metal products" (just over 10%).

3. Finally, the sectoral contributions of the productivity growth and share effects to convergence show that the most striking results are, on the one side, the negative within-sector effect corresponding to "Transport equipment" 11 and, on the other, the positive (although very weak) share effect in the "Ferrous 9 When the initial productivity of region i exceeds that of the EU, the expression to apply is as follows:

( ) [ ]

T P P % UE -( ) [
] 10 We should point out that the results shown are weighted by the share of the GVA in each region with respect to the EU as a whole. 11 Also negative is the effect of "Paper and printing products", but its value is practically zero. and "Other manufacturing" sectors.

T P P % i= k (PGE k,UE -PGE k,i )+ k (SE k,UE -SE k,i )

IV. Convergence in EU productivity: a spatial approach

Spatial dependence in the regional distribution of productivity At the beginning of Section II we made a passing reference to the presence of some spatial dependence between certain regions (see again Figure 2). If this were to be confirmed, the results from a conventional beta-convergence analysis would be inconsistent. In order to solve this potential problem, in the first part of this section we analyse this phenomenon of spatial dependence in the regional productivity distribution in more detail 12 . Spatial dependence refers to the coincidence of value similarity with geographical similarity. The presence of global spatial dependence (or autocorrelation) 13 in a given distribution can be tested using, among others, the statistic known as Moran's I. Applying this test to the aggregate mean relative productivity for the initial and final year of our sample (see the "Total" row of Table 6), using as the distance matrix the inverse of the standardised distance, offers the expected and statistically significant results (0.1721 in 1980 and 0.1626 in 2003). This testifies 12 For this, we used the programs ArcView GIS 3.2 and SpaceStat 1.90. Other recent studies that have used spatial econometric techniques are, for example, [START_REF] López-Bazo | The regional distribution of Spanish unemployment: A spatial analysis[END_REF], [START_REF] Toral | Measuring distance in the Spanish regional convergence process[END_REF], [START_REF] Villaverde | Desigualdades regionales y dependencia espacial en la Unión Europea[END_REF], [START_REF] Maza | Regional disparities in the EU: Mobility and polarisation[END_REF] and [START_REF] Villaverde | A new look to convergence in Spain. A spatial econometric approach[END_REF]. 13 Spatial autocorrelation can be of two types: substantive, which, through phenomena such as technological diffusion, externalities and factor mobility, links the behaviour of a particular variable in various different spaces; and noise, which comes from a poor specification of the model, and refers to the residuals of the estimated regression. 15 that many of the regions with high (low) productivity levels are surrounded by regions with similar productivities. Thus, the European regions should not be treated as independent observations, since there is a global tendency to form geographical groups in function of its productivity.

A slightly more precise procedure to visualize the presence of spatial dependence is offered by representing the Moran scattermap, since this allows us to identify the situation of each region and the formation of the different groups. This map divides the regions into four groups: group I comprises relatively highproductivity regions surrounded by high-productivity neighbours (High-High); II contains those regions with a low productivity that have high-productivity neighbours (Low-High); III comprises low-productivity regions surrounded by equally low-productivity regions (Low-Low); and IV comprises high-productivity regions surrounded by low-productivity regions (High-Low). When the majority of observations are among groups I and III, the spatial dependence is positive, while when the majority are in groups II and IV, it is negative. If the regions are about evenly distributed among these four groups there is no spatial association of any type, in which case considering the observations (regions) as independent entities -as we have done up to this point-would be correct.

The results obtained (Figure 5) reveal the existence of two large groups: one made up of regions with relatively high productivity levels and the other of regions with relatively low productivity. Thus, and in spite of the important changes that have occurred between 1980 and 2003, the homogeneity observed allows us to confirm 16 that a region's productivity is directly associated with the productivity of its neighbouring regions. Nevertheless, we should not ignore the presence of some outliers -i.e., regions whose productivity differs markedly from that of their neighbours. For example, and looking at the year 2003, some regions have much higher productivity than their neighbours (among which we might mention some Spanish regions, and the south of France), while others have a considerably lower productivity than their neighbours (such as Denmark, and various Dutch and German regions).

Finally, analysing the presence of spatial dependence under the sectoral perspective simply confirms the result obtained at the aggregate level: all sectors without exception present a positive spatial dependence that is statistically different from zero. Notwithstanding this, there are differences between them (see again Table 6). The sectors with the highest degree of spatial dependence are "Metal products", "Chemical products", "Paper and printing products" (with coefficients in 2003 of 0.17, 0.15 and 0.12, respectively) while those with the lowest spatial autocorrelation are "Other manufacturing", "Textiles, clothing and footwear" and "Transport equipment" (0.06, 0.06 and 0.08 respectively). In terms of evolution we should point out that all sectors have experienced a decline in their spatial dependence, with this reduction being most extreme for "Nonmetallic mineral products", "Transport equipment" and "Other manufacturing". The previous analysis has shown that there is spatial dependence in the regional distribution of productivity, so it is necessary to test for the presence of possible problems of spatial autocorrelation in the classical beta-convergence equations.

Regional convergence in productivity: a spatial aggregate analysis

To this effect, table 7 presents a battery of statistics, most of them (the Lagrange multipliers) are based on the principle of maximum likelihood (for more details on these tests, see [START_REF] Rey | US regional income convergence: A spatial econometric perspective[END_REF]. Specifically, the test known as the Lagrange multiplier for spatial errors (or LM-ERR), along with the associated robust LM-EL, test for the absence of residual spatial autocorrelation, which would be caused by not including a structure of spatial dependence in the error term. However, the test known as the Lagrange multiplier for spatial lags (or LM-LAG), and its associated robust LM-LE, test for the absence of substantive spatial autocorrelation, which would be due to the spatial correlation in the endogenous variable. In this respect, if the tests are significant, changes should be made to the classical beta-convergence equations. There are two possibilities: introduce an autoregressive structure in the error term if there is residual spatial dependence, or include a spatial lag of the endogenous variable if there is substantive spatial autocorrelation 14 . When both types of spatial autocorrelation are present, we decide which is predominant, comparing the value of the tests in the two cases.

As can be seen, for the aggregate productivity (see the "Total" column in Table 7) all the tests are statistically significant, this meaning that the productivity of each region does not depend exclusively on its own factors. In addition, and given that the value of the LM-ERR test (77.48) is greater than that of LM-LAG (45.50), it 14 As well as other possibilities, such as including spatial lags of the explanatory variables. Thus, the spatial error beta-convergence model can be defined in the following generic form:

u W P i i i o i i + = + + = , ln (4)
where again i is the growth rate of the aggregate productivity of region i between the years 1980 and 2003, denotes the constant term of each equation, P i.0 the relative productivity of region i in 1980, i is the error term, and is the additional parameter which quantifies the spatial autocorrelation between the errors.

The first column in Table 8 shows the results obtained from Equation (4), estimated by means of maximum likelihood, since doing so by ordinary least squares is inconsistent [START_REF] Anselin | Spatial Econometrics: Methods and models[END_REF]. From these results we can draw a number of conclusions. First of all, different goodness-of-fit measures -the logarithm of maximum likelihood (LIK), Akaike's information criterion (AIC) and the Schwartz criterion (SC)-show that the spatial equation achieves a better fit than 19 the traditional one15 ; in addition, the coefficient associated with the spatial error is significant. Second, and with regard to the speed of convergence, the most noteworthy finding is that this substantially increases (passing from 1 to 1.3% annually), so that the period required to cover half the gap to the steady state falls from 75 to 60 years.

Regional convergence in productivity: a spatial analysis by sectors

Following the same approach that with aggregate productivity, we have also tested for the presence of spatial autocorrelation in the classical beta-convergence equations by sectors. Table 7 shows that , with the sole exception of "Transport equipment", there appear to be problems of spatial dependence in all sectors.

Specifically, we can see that in the "Ferrous and non-ferrous metals", "Metal products" and "Other manufacturing" sectors higher values are achieved in the tests for the presence of residual spatial dependence than in those testing for substantive spatial dependence, so that again a spatial error model needs to be estimated. The suitability of this type of model is even clearer in the sectors "Fuel and power products", "Chemical products", "Food, beverages and tobacco", "Textiles, clothing and footwear" and "Paper and printing products", for in all of them the LM-LE test is not even significant at the 95% level. In contrast, the "Non-metallic mineral products" sector does not follow the same pattern, since here the LM -LAG test achieves a higher value than the LM-ERR. In addition, the robust associate of this latter, the LM-EL test does not differ statistically from zero. Thus, in this case it is clearly necessary to include a spatial lag in the convergence equation, without changing the structure of the error term.

In short, we need to correct the spatial dependence problems in the classical betaconvergence equations for all sectors except "Transport equipment". More specifically, we need to estimate a spatial error model such as the one shown in Equation ( 4) for all these sectors, apart from the "Non-metallic mineral products", in which the following spatial lag model must be estimated instead:

i i o i i W P + + + = _ ln , (5)
where, in addition to the variables considered in the classical convergence equation, we include the term " i W _ ", which measures the spatial lag of the endogenous variable. To build this lag, the variable i is pre-multiplied by the socalled spatial weights matrix, W , defined in terms of the inverse of the standardised distance, and whose elements j i w , reflect the intensity of the interdependence between the regions i and j . Thus, each element of this spatially-lagged variable represents the weighted average of the values of this variable in the rest of the regions, a weighting that declines as the distance between the regions grows. 8. As can be seen, the presence of spatial dependence in the distribution of regional productivity in all sectors, except one, modifies the beta coefficients of the regressions although not to a great extent. However, in some branches of activity there are important differences between the results of classical and spatial analysis: this is especially the case of the "Non-metallic mineral products" and "Chemical products", where the rate of convergence declines (respectively by 35 and 40%) and, in the other extreme, that of the "Other manufacturing" sector, which shows a higher speed of convergence (10%) once the spatial dependence is included in the model.

V. Conclusions

In this paper, we have provided new insights as to the nature of the productivity convergence patterns in Europe between 1980 and 2003, both across regions and sectors. By using a variety of approaches, mainly spatial econometric techniques, key conclusions can be summarised as follows:

First, we observe a high degree of dispersion in productivity, both from the spatial and the sectoral perspectives. At the same time, there has been some mobility in the relative position of the European regions, especially important across regions with productivity levels around or above average. Third, a weak process of classical beta-convergence has taken place both at the aggregate and sectoral levels. At the aggregate level, this convergence has been caused, in its totality, by the sectoral productivity growth effect ; on the other side, the contribution of the share effect has been negative. Likewise, the results reveal that "Food, beverages and tobacco" and "Fuel and power products" are the sectors that have most contributed to reducing the disparities in productivity.

Fourth, the analysis has revealed a clear (although declining) relationship between the aggregate productivity of each region and its geographic location, allowing us to conclude that relatively more (less) efficient regions tend to concentrate spatially. Once this spatial dependence is corrected, analysis of the beta convergence reveals that the speed of convergence at the aggregate level increases by 30%. From a sectoral point of view, this same analysis shows again the presence of spatial dependence and, when this dependence is inte grated in the classical beta-convergence equations, important changes in some sectors can be found, mainly in the "Chemical products", "Non-metallic mineral products" and "Other manufacturing".

  a minimum of -2.5% in Ionia Nisia (Greece), to a maximum of 8.8% in Southern and Eastern (Ireland).

  share of the employment from sector k in region i in the total employment of that region, t is the base year and T a (distinct) year for which the coefficient is calculated. Naturally, the closer this value to 1, the less intense the structural change, while a value equal to or close to -1 would reflect a complete turnaround in the productive structure. The results obtained are displayed in Table2, and in general indicate that very little structural change has occurred. However, it should be mentioned some "atypical" performances, with the most noteworthy occurring in the Valle d'Aosta (Italy), a region in which the CSC achieves its minimum, although positive value (0.460). The maximum value in contrast corresponds to the region of Stockholm (0.999).

8

  If this number of years is denoted h, it can be easily calculated according to the expression:

  ferrous metals", "Metal products", "Paper and printing products"

  most appropriate to re-estimate the model including a structure of spatial dependence in the error term. As this result is confirmed if we observe their associated robust tests, it is necessary to estimate a spatial error model, which includes a parameter measuring the intensity of spatial dependence between the residuals.

  estimating spatial beta-convergence equations by sectors are shown in Table

  growth in the aggregate productivity of the EU is due entirely to productivity gains across sectors. The so-called structural change (share effect) offers a negative, although quantitavely insignificant, contribution to the growth of aggregate productivity. By sectors, this effect is positive in half of the cases and negative in the other half.

Fig. 2 .

 2 Fig. 1. Density functions of aggregate productivity

FigFig. 4 .

 4 Fig. 3. Stockastic kernel of aggregate productivity

Table 1 . Productivity growth

 1

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

Table 2 . Coefficient of structural change in employment

 2

	Minimum (Valle d'Aosta)	0.460
	Maximum (Stockholm)	0.999
	EU-15	0.987
	Standard Desv.	0.080
	Coefficient of Variation	0.081

Table 3 . Sources of productivity growth

 3

			Total			%
	Sectors	P.G.E.	S.E	Total Effect	P.G.E.	S.E	Total Effect
	Total	4.36	-0.02	4.34	100.49	-0.49	100.00
	1.-Fuel and power products	0.69	-0.10	0.59	15.90	-2.37	13.53
	2.-Ferrous and non-ferrous metals	0.15	-0.03	0.12	3.51	-0.71	2.80
	3.-Non-metallic mineral products	0.14	-0.01	0.13	3.22	-0.14	3.08
	4.-Chemical products	0.67	0.10	0.78	15.53	2.34	17.87
	5.-Metal products	1.39	0.02	1.40	31.91	0.41	32.31
	6.-Transport equipment	0.59	-0.05	0.53	13.52	-1.20	12.31
	7.-Food, beverages and tobacco	0.39	0.07	0.46	9.07	1.59	10.66
	8.-Textiles, clothing and footwear	0.16	-0.09	0.07	3.63	-2.12	1.50
	9.-Paper and printing products	0.05	0.07	0.12	1.12	1.70	2.82
	10.-Other manufacturing	0.13	0.00	0.13	3.09	0.01	3.10

Table 5 . Sources of convergence

 5

			Total			%
	Sectors	P.G.E.	S.E	Total Effect	P.G.E.	S.E	Total Effect
	Total	0.32	-0.03	0.29	110.49	-10.49	100.00
	1.-Fuel and power products	0.11	-0.02	0.09	38.30	-7.91	30.38
	2.-Ferrous and non-ferrous metals	0.01	0.01	0.02	2.77	3.29	6.06
	3.-Non-metallic mineral products	0.03	-0.00	0.02	8.70	-1.32	7.38
	4.-Chemical products	0.02	-0.01	0.01	7.44	-3.43	4.01
	5.-Metal products	0.03	0.00	0.03	9.91	0.37	10.28
	6.-Transport equipment	-0.02	-0.00	-0.02	-5.91	-0.23	-6.14
	7.-Food, beverages and tobacco	0.12	-0.01	0.10	40.02	-5.00	35.02
	8.-Textiles, clothing and footwear	0.02	-0.00	0.01	5.64	-0.72	4.92
	9.-Paper and printing products	-0.00	0.01	0.00	-0.78	1.88	1.10
	10.-Other manufacturing	0.01	0.01	0.02	4.40	2.59	6.99

Table 6 . Moran's I statistic

 6

	Sectors	Year	Moran's I	Mean	Stand.	Z	Probability
					Desv.
	Total	1980 2003	0.1721 0.1626	-0.005 -0.005	0.0077 0.0077	23.04 21.82	0.00 0.00
	1.-Fuel and power products	1980 2003	0.1261 0.0918	-0.005 -0.005	0.0077 0.0077	17.06 12.60	0.00 0.00
	2.-Ferrous and non-ferrous metals	1980 2003	0.0962 0.0795	-0.005 -0.005	0.0077 0.0077	13.16 10.99	0.00 0.00
	3.-Non-metallic mineral products	1980 2003	0.2009 0.0987	-0.005 -0.005	0.0077 0.0077	26.80 13.49	0.00 0.00
	4.-Chemical products	1980 2003	0.1818 0.1461	-0.005 -0.005	0.0077 0.0077	24.31 19.66	0.00 0.00
	5.-Metal products	1980 2003	0.1813 0.1712	-0.005 -0.005	0.0077 0.0077	24.24 22.93	0.00 0.00
	6.-Transport equipment	1980 2003	0.1411 0.0768	-0.005 -0.005	0.0077 0.0077	19.01 10.64	0.00 0.00
	7.-Food, beverages and tobacco	1980 2003	0.1649 0.1107	-0.005 -0.005	0.0077 0.0077	22.11 15.05	0.00 0.00
	8.-Textiles, clothing and footwear	1980 2003	0.0931 0.0634	-0.005 -0.005	0.0077 0.0077	12.76 8.90	0.00 0.00
	9.-Paper and printing products	1980 2003	0.1374 0.1213	-0.005 -0.005	0.0077 0.0077	18.53 16.43	0.00 0.00
	10.-Other manufacturing	1980 2003	0.1064 0.0581	-0.005 -0.005	0.0077 0.0077	14.49 8.21	0.00 0.00

31 Fig. 5. Moran'

s scattermaps Page 31 of 32 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i e w 32Table 7 . Diagnosis for spatial dependence

 7

	Test	Total	1. Fuel and power products	2. Ferrous and non-ferrous metals	3. Non-metallic mineral products	4. Chemical products	5. Metal products	6. Transport equipment	7. Food, beverages and tobacco	8. Textiles, clothing and footwear	9. Paper and printing products	10. Other manufacturing
	I-Moran	12.92*	15.11*	17.53*	13.87*	14.46*	14.25*	3.13*	15.80*	11.69*	8.64*	11.77*
	LM-ERR	77.48*	108.16*	144.69*	88.95*	100.03*	94.25*	2.91	117.59*	63.36*	32.47*	63.14*
	LM-EL	43.22*	21.67*	51.88*	2.98	10.98*	31.27*	1.05	24.91*	8.74*	7.19*	39.47*
	LM-LAG	45.50*	87.54*	99.84*	92.57*	90.61*	68.20*	1.88	92.73*	54.64*	25.53*	29.18*
	LM-LE	11.24*	1.05	7.03*	6.59*	1.57	5.22*	0.02	0.05	0.02	0.25	5.50*
	Note: *= 95% significant

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

It should be pointed out that the traditional measure of fitness (R 2 ) is unreliable because of the inclusion of spatial errors. For the sake of comparison, the values of these coefficients in the estimation of the traditional beta convergence are as follows: LIK=601.15,AIC=-1198.30 and SC=-1191.65.

Acknowledgements

The research was partly funded by the Spanis h Institute for Fiscal Studies


David Aristei

Luca Pieroni
email: lpieroni@unipg.it

-Luca Pieroni

A Double

Keywords: double-hurdle models, tobacco consumption, limited dependent variables, Box-Cox transformation J.E.L. classification: C24, D12 tobacco consumption, double-hurdle models, limited dependent variables, Box-Cox transformation

HAL is

Introduction

In the last years the empirical literature has produced a large body of evidence on the price and non-price determinants of tobacco demand. One strand of literature has adopted an aggregate time series approach to provide empirical support to the rational addiction model proposed by [START_REF] Becker | A Theory of Rational Addiction[END_REF] [START_REF] Chaloupka | Rational Addictive Behavior and Cigarette Smoking[END_REF][START_REF] Becker | An Empirical Analysis of Cigarette Addiction[END_REF][START_REF] Bask | Rationally addicted to drinking and smoking?[END_REF]. On the other hand, the growing availability of microdata from household expenditure surveys has allowed to model tobacco consumption accounting for zero observations and simultaneously exploiting the richness of survey data information to control for heterogeneous individual (or household) behaviour [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF][START_REF] Jones | A note on computation of the double-hurdle model with dependence with an application to tobacco expenditure[END_REF][START_REF] Blaylock | U.S. Cigarette consumption: The Case of Low-Income Women[END_REF][START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF]Yen, 2005a). From a policy perspective, cross-sectional surveys enables to improve the knowledge of the impacts of socio-demographic variables on tobacco expenditure and help the design of public health programs to achieve smoking-reduction objectives.

While it would be interesting to obtain simultaneous empirical responses concerning addiction, censoring and heterogeneity in tobacco consumption decisions in Italy, the absence of a true panel data does not enable us to account for addictive behaviours while controlling for demographic and socio-economic characteristics 1 . Thus, in this paper we investigate household tobacco expenditures, addressing the issues connected to limited dependent variable models by an approach based on a double-hurdle specification [START_REF] Cragg | Some statistical models for limited dependent variables with application to the demand for durable goods[END_REF][START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF][START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF][START_REF] Su | A censored system of cigarette and alcohol consumption[END_REF].

Several empirical studies [START_REF] Blundell | Bivariate Alternatives to the Univariate Tobit Model[END_REF][START_REF] Blaylock | Wine consumption by US men[END_REF]; 3 [START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF][START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF] have shown the inadequacy of the standard Tobit model [START_REF] Tobin | Estimation of relationships for limited dependent variables[END_REF] in cross-sectional analysis of tobacco consumption, connected with its failure in accounting for differences concerning the generation of zero observations. Since it is implausible that all zero observations in tobacco consumption arise from standard corner solutions generated by a constrained budget, we emphasize the importance of a double-hurdle specification distinguishing between abstentions and corner solutions.

As shown by [START_REF] Arabmazard | An Investigation of the Robustness of the Tobit Estimator to non-normality[END_REF], maximum likelihood estimates are sensitive to misspecification issues and they will be inconsistent if the bivariate normality assumption is violated. One way to correct for the non-normality of the error terms, providing to generalize the standard double-hurdle model, consists in applying a Box-Cox transformation on the dependent variable [START_REF] Yen | Working wives and food away from home: the Box-Cox double hurdle model[END_REF][START_REF] Jones | A Box-Cox double-hurdle model[END_REF].

In this way we can encompass, besides the standard double-hurdle model, a wide range of specifications, that differ for the distributional assumptions on the error terms, and test the best model to rationalize the data.

Standard Tobit model, standard Double-hurdle model with independence and Box-Cox Tobit model seem to be restrictive specifications, confirming both the violation of the bivariate normality assumption and the existence of separate individual decisions on participation and consumption. Moreover, the independence of the errors for the Box-Cox double-hurdle is not rejected by the data, concluding that the non-normal specification with independent errors is the best model to account for household behaviours on tobacco expenditures.

The remainder of the paper is organized as follows: the next section outlines the theoretical framework upon which the empirical models are based. In Section 3 we Survey, are discussed and factors influencing participation and consumption equations are examined. In Section 5 specification and estimation results are presented and discussed, with specific attention devoted to the nested strategy used to derive the best specification and to the analysis of the estimated parameters and elasticities. Section 6 offers some concluding comments.

Theoretical Framework

Standard consumer choice theory assumes that every individual (or household) is a potential consumer of all goods. However, for commodities like tobacco this may not be true and, regardless of price and income levels, some individuals cannot be induced to smoke. In these cases, zero observations are not the result of economic nonconsumption, but they may be determined by other behavioural factors apart from prices and income. Following [START_REF] Pudney | Modelling Individual Choice: The Econometrics of Corners, Kinks and Holes[END_REF], alternative models of tobacco demand have been derived by using discrete random preferences regimes. According to this approach, smokers are hypothesized to have a different preference structure than non-smokers.

Observed zero expenditure then reflect either the decision to not smoke or a standard corner solution and hence only potential smokers determine the parameters of tobacco Engle curve [START_REF] Blaylock | Wine consumption by US men[END_REF].

Given this setting, individual's utility function takes the following form: Equation ( 1) can be alternatively rewritten as:

1 2 2 ( , ,..., ; ) (1 ) ( ,..., ; )

s n s n n U dU c c c w d U c c w = + (2)
where s U is the utility function of smokers (actual and potential) and ns U for nonsmokers. For a non-smoker, given that 1 c does not enter 2 ( ,..., ; )

ns n U c c w and 1 p is in any case positive, the optimal tobacco consumption level is 1 0 c = . For actual and potential smokers, the optimal level of 1 c is determined by solving the following constrained utility maximization: U c c c w to be continuous, increasing, and quasi-concave, then the notional demand for tobacco can be expressed as a demand function ( , ; ) f p m w and the corresponding expenditure equation can be denoted as ( ; ) g m w . As price information was not collected in the ISTAT Italian Household Budget Survey, we assume that all households face the same relative prices [START_REF] Yen | Determinants of household expenditures on alcohol[END_REF]. The notional demand and expenditure have been derived as the results of utility maximization with only the budget constraint, given individual (or household) In the next section, alternative empirical models are developed in order to account for the presence of different zero-generating mechanisms in tobacco consumption.

Econometric Specification

Recent empirical analyses have shown the inadequacy of the standard Tobit model in cross-sectional analysis of tobacco consumption, stressing the relevance of a doublehurdle approach for microeconomic analysis of tobacco consumption [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF][START_REF] Blaylock | U.S. Cigarette consumption: The Case of Low-Income Women[END_REF][START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF][START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF][START_REF] Labeaga | A double-hurdle rational addiction model with heterogeneity: estimating the demand for tobacco[END_REF]. The main feature of the double-hurdle model is that participation and consumption decisions are assumed to stem from two separate individual choices and the determinants of the two decisions are allowed to differ.

The double-hurdle model, originally proposed by [START_REF] Cragg | Some statistical models for limited dependent variables with application to the demand for durable goods[END_REF], assumes that two separate hurdles must be passed before a positive level of consumption can be observed.

In the context of tobacco consumption analysis, the first hurdle involves the decision of whether or not to smoke (participation decision). It is reasonable to assume that the choice of smoking is not only an economic decision, but also influenced by social and demographic factors which are independent of the quantity consumed. The second hurdle concerns the level of tobacco consumption to choose (consumption decision). We now turn to the econometric specification of the model. Both hurdles are assumed to be linear in the parameters ( , ), with disturbance terms u and v randomly distributed with a bivariate normal distribution. The matrices z and x include the variables that are assumed to influence participation and consumption decisions, respectively. Formally, following [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF] and [START_REF] Pudney | Modelling Individual Choice: The Econometrics of Corners, Kinks and Holes[END_REF], the bivariate model can be written as:

i) Observed consumption: i i y d y = (4)
ii) Participation equation:

i i i w z u = + (0,1) i u N (5) 1 if 0 0 otherwise w d > = iii) Consumption equation: i i i y x v = + , 2 (0, ) i v N (6) if 0 0 otherwise i i i y y y > =
A positive level of tobacco consumption y is observed only if the individual (or the household) is a potential smoker ( 1 d = ) and actually consumes tobacco ( y ). For this reason, in double-hurdle models, differently from Heckman selection model [START_REF] Heckman | Sample selection bias as a specification error[END_REF], in which zeros are not affected by the consumption decision, observed zero expenditures are the result of either participation or consumption decisions and potential smokers may have zero tobacco expenditure.

In the present analysis, different double-hurdle models are used to analyze household tobacco expenditure patterns, with particular attention devoted to the specification of the stochastic structure of the model by testing whether the assumptions of bivariate To account for the presence of heteroscedasticity, the variance of the error terms specified it as a function of a set of continuous variables: exp( )

i i z h = (7)
where i z is a vector of continuous variables included in i x ( i i z x ) and h is a conformable vector of coefficients [START_REF] Yen | Working wives and food away from home: the Box-Cox double hurdle model[END_REF][START_REF] Yen | Determinants of household expenditures on alcohol[END_REF][START_REF] Newman | A double-hurdle model of Irish household expenditure on prepared meals[END_REF].

The assumption of correlated error terms allows for the possibility that participation and consumption decisions are simultaneously taken. In particular, we assume that u and v are distributed as a bivariate normal:

( , ) (0, ) u v BVN , 2 1 = (8)
where is the correlation coefficient.

Denoting zero consumption as 0 and positive consumption as +, the likelihood function for the full double-hurdle model with heteroscedasticity correction and dependence between u and v can be written as:

a) Heteroscedastic Double-hurdle model with dependent error terms [ ] ( ) 2 0 1 1 ( , , ) ( ) 1 ( ) i i i i i i i i i i L z x z y x y x + = + ! " ! " # $ % % (9)
where denotes the standard normal CDF (univariate or multivariate) and is the univariate standard normal PDF.

In empirical applications it is common to assume that u and v are independent (i.e. 0 = ).

Under this hypothesis we obtain the original formulation proposed by [START_REF] Cragg | Some statistical models for limited dependent variables with application to the demand for durable goods[END_REF].

] ( ) 0 1 1 ( ) ( ) ( ) ( ) i i i i i i i i L z x z y x + = % % (10)
This model hypothesizes that the participation and consumption decisions are made separately and that there is a feedback effect from the level of consumption to the participation decision [START_REF] Atkinson | Household expenditure on tobacco 1970-1980: evidence from the Family Expenditure Survey[END_REF][START_REF] Deaton | Statistical models for zero expenditures in household budgets[END_REF][START_REF] Blaylock | Wine consumption by US men[END_REF]. In the present analysis we do not make any a priori assumption on the correlation structure of the error terms; differently from other studies [START_REF] Yen | Determinants of household expenditures on alcohol[END_REF][START_REF] Moffatt | Hurdle models of loan default[END_REF][START_REF] Newman | A double-hurdle model of Irish household expenditure on prepared meals[END_REF], the independence of error terms is not assumed as a maintained hypothesis, but its significance is tested by means of a Wald test. Moreover, it is worth noticing that the standard Tobit model is a nested version of the Cragg model, when

0 j = for 0 j & and 0 = ' , that is when ( ) 0 i p u z > = (i.e. ( )
1 i z = )
, and a likelihood ratio test can be used to distinguish between the Tobit and the independent double-hurdle model.

A limitation of the standard double-hurdle specification is that it is built on the assumption of bivariate normality of the error terms. If the normality assumption is violated the maximum likelihood estimates of the model will be inconsistent. This may be particularly relevant when the model is applied to a dependent variable with a highly skewed distribution, as is often the case with survey data on tobacco expenditures.

As suggested by [START_REF] Yen | Working wives and food away from home: the Box-Cox double hurdle model[END_REF] and [START_REF] Jones | A Box-Cox double-hurdle model[END_REF], one way to correct for the nonnormality of the error terms consists in applying a Box-Cox transformation to the dependent variable, which gives:

1

T i i y y ( ( = , with 0 1 ( < * (11)
T i i i i y y w y ( > > = ( 12
)
where i w and i y are defined as in ( 7) and ( 8).

This specification relaxes the normality assumption on the conditional distribution of i y and still allows stochastic dependence between the error terms of participation and consumption equations. The likelihood functions for dependent and independent double-hurdle models with heteroscedasticity correction can be written as:

c) Box-Cox Heteroscedastic Double-hurdle model with dependent error terms ( ) 0 2 ( 1 ) 1 1 , , 1 ( 1) 1 ( 1) i i i i i i i i i i i i x L z z y x y y x ( ( ( ( ( ( +
+ = × ! " # $ - × + ! " . ! " / # $ % % (13) d) Box-Cox Heteroscedastic Double-hurdle model with independent error terms ( ) ( ) ( 1) 0 1 1 ( ) ( 1 ) ( ) ( 1) i i i i i i i i i L z x z y y x ( ( ( ( + = + % % (14)
Model (c) is a general model that nests all the other three double-hurdle specifications presented and also encompasses a wide range of standard limited dependent variable models [START_REF] Jones | A Box-Cox double-hurdle model[END_REF]. implied by the nested specifications.

(Figure 1 about here)

The economic interpretation of limited dependent variable models frequently focuses on the analysis of the marginal effects of regressors on the expected value of i y [START_REF] Jones | A Box-Cox double-hurdle model[END_REF], which can be decomposed into an effect on the probability of purchase and an effect on the conditional level of expenditure2 . The unconditional mean of i y in the Box-Cox Double-hurdle model can be written as:

( ) ( 0) ( | 0) i i i i E y P y E y y = > > (15)
The conditional expectation of i y is:

1 ( | 0) ( | , ) i i i i i i i E y y E y w z y x ( > = > > (16)
and, assuming independence between error terms of participation and consumption3 , can be written as:

1 0 1 ( | 0) T i i i i i i i i i i x y y x E y y dy ( ( ' + > = ! " ! " # $ # $ 0 (17)
Given independence, the probability of a positive consumption level is: Marginal effects can be obtained by differentiating equations ( 16), ( 17) and ( 18) with respect to each explanatory variable 4 . From these marginal effects, elasticities can be derived. In particular, using equation ( 15), the elasticity of the conditional mean with respect to regressor ij x can be written as:

1 ( 0) ( ) i i ii i x P y w ( + > = ! " # $ (18)
( ) ( 0) ( | 0) ( ) ( 0) ( | 0) ij ij ij i i i i j ij i ij i ij i i x x x E y P y E y y e x E y x P y x E y y 1 1 > 1 > = = + 1 1 > 1 > ( 19
)
where the two addends are the elasticity of the probability of observing a positive expenditure ( P j e ) and the elasticity of conditional consumption ( cc j e ). For continuous variables, the elasticities are computed at the sample means. For categorical explanatory variables, marginal effects are used to compute percentage changes in probability, conditional level and unconditional level when the value of the variable shifts from zero to one, holding all the other variables constant [START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF][START_REF] Newman | A double-hurdle model of Irish household expenditure on prepared meals[END_REF].

Data and Variables

The data used in the empirical analysis are taken from the 2002 Italian Household [START_REF] Yen | Working wives and food away from home: the Box-Cox double hurdle model[END_REF] and [START_REF] Jones | A Box-Cox double-hurdle model[END_REF]. 13 goods and services over a one-week period and is subsequently expressed on a monthly basis. No price or quantity information is reported and consumption of each good or service is measured as reported expenditure. Moreover, data refer to the household rather than to individuals, providing no information on intra-household income allocation and making it necessary to account for family composition effects when analysing the demand for certain non-durable goods.

In this analysis, household monthly expenditure on cigarettes and tobacco is used as the dependent variable. As already underlined, the ISTAT survey only records the value of household expenditures and so quantity and quality effects cannot be identified and analyzed. Since the survey does not provide any information on the presence of smokers in the household, inference on participation in tobacco consumption has to be made on the basis of recorded expenditure, identifying non-smoking households as those with zero tobacco expenditure. Expenditures on tobacco, as all expenditures on commonly used non durable goods, are monitored for only one week. The fact that the collection of information only covers a seven-day period, with a 33.4 percent of consuming households, introduces some room for undetected infrequency of purchases. However, for commodities like tobacco, it is unlikely that observed zero expenditures capture infrequent purchases and they probably stem from abstentions or corner solutions [START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF]. Using household data to model tobacco consumption, which is mainly the result of an individual decision, may generate some bias in the analysis of consumption behaviours. For this reason, it is necessary to correctly account for family size and composition effects as well as for the socio-economic characteristics of the household, since the household situation plays an active role in modifying individual preferences. Household tobacco expenditures are assumed to be expressible as a linear combination of explanatory variables that are assumed to separately affect participation and consumption decisions. The explanatory variables selected, together with their sample statistics, are presented and fully described in Table 1. They include household income (proxied by total expenditure), alcohol consumption, the head of the household's age, and dummy variables indicating education, marital status, gender and working status of the household's head, the percentage of adult male members, the presence of children under fourteen years old, home ownership, and participation in alcohol consumption.

All expenditure variables are expressed in real terms, by deflating current values using ISTAT regional price indexes, in order to account for price variability across regions. Moreover, in order to obtain a per-equivalent adult measure of household consumption, all expenditure variables are adjusted for family size by using the modified OECD equivalence scale, which assigns a weight equal to one to the first adult in the household, 0.5 to each other adult and 0.3 to each child under fourteen years of age.

(Table 1 about here)

Results

In this section, estimation results are presented and discussed, with specific attention devoted firstly to the choice of the most appropriate model specification and then to the analysis of the effects of explanatory variables by calculating and decomposing elasticities. All the double-hurdle specifications discussed in Section 3 have been estimated by maximizing the logarithm of the likelihood functions ( 9), ( 10), ( 13) and ( 14). One parameter estimation issue in double-hurdle models concerns the choice of the regressors for participation and consumptions equations. As it is known, the choice of the explanatory variables to be included in the two hurdle does not rest on any a priori theory and may be somewhat arbitrary. Given that the inclusion of the same set of regressors in each hurdle makes the parameters identification difficult, exclusion restrictions must be imposed 5 . In empirical applications the first hurdle is usually assumed to be a function of non-economic factors affecting household's smoking decision, so that economic variables can be excluded from the first equation [START_REF] Newman | A double-hurdle model of Irish household expenditure on prepared meals[END_REF]. Their exclusion is motivated by the discrete random preference theory, according to which sample selection is determined exclusively by non-economic factors [START_REF] Pudney | Modelling Individual Choice: The Econometrics of Corners, Kinks and Holes[END_REF]Yen, 2005a).

The foregoing arguments require, before presenting estimation results, a discussion of the explanatory variables included in the model. The independent variables considered are intended to encompass the determinants of both smoking participation and tobacco consumption decisions and their choice rests on suggestions taken from previous empirical literature (Jones, 1989; Blaylock and Blisard, 1992; Garcia and Labeaga, 1996; 5 In estimating the final model we started with a specification that included all explanatory variables in both hurdles; insignificant variables were gradually dropped, with exclusion restrictions giving identification higher reliability. 16 [START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF]Yen, 2005a) and on more specific issues connected with identification problems. Their inclusion in either participation or consumption equations is justified by economic, demographic and sociological factor, such as habit formation, information and social awareness on damages and health risks connected with smoking and restriction to smoking due to security reasons or to health guidelines for public places.

In this study, both participation and consumption decisions are postulated to be influenced by the presence of children under fourteen years old within the household (Child014), the percentage of adult male members (PercMale), age (Age), gender (MaleHH), marital status (Single), education level (Highedu) and occupation (Whitecollar) of the household's head.

A dummy variable indicating the presence of children is included in the model postulating that the household would not smoke or at least would attempt to moderate tobacco consumption when small children are present [START_REF] Blaylock | Wine consumption by US men[END_REF][START_REF] Kerr | Age, period and cohort influences on beer, wine and spirits consumption trends in the US National Alcohol Surveys[END_REF]. The percentage of adult male members in the household (PercMale) is included to account for gender differences in tobacco consumption and to test for the presence of gender-differentiated smoking habits [START_REF] Angulo | The demand for alcoholic beverages in Spain[END_REF]. The education variable (equal to one if the household's head has at least a high school education, zero otherwise) has been often used in previous empirical studies [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF]Blaylock andBlisard, 1992, 1993;Yen, 2005b;[START_REF] Yen | Determinants of household expenditures on alcohol[END_REF][START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF][START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF], suggesting that individuals with better education may be more aware of the health risks connected with consumption of unhealthy goods such as tobacco and alcohol. Being a white-collar worker reflects the individual's social class and may help in explaining how smoking habits vary among different social groups.

Age is considered to assess how age-related health problems affect smoking behaviours and to verify the existence of a significant lifecycle pattern for both tobacco participation and consumption decisions6 .

In the participation equation, we include an additional binary variable indicating whether the household displays a high expenditure level (over the 75 th percentile of the observed distribution) on alcoholic beverages (HighAlc), as a proxy for habit formation tendencies [START_REF] Blaylock | Wine consumption by US men[END_REF].

Specific variables accounting for economic conditions have been introduced in consumption equation. Total household expenditure (Income) is included as a proxy for current income. A variable indicating whether the household lives in a home that is owned or being bought (OwnerOcc) is included, following the suggestions of [START_REF] Atkinson | Household expenditure on tobacco 1970-1980: evidence from the Family Expenditure Survey[END_REF] and [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF], as a proxy for wealth and economic stability. Further, household alcohol expenditure (Alcohol) is included as a proxy to verify the presence of complementary relationships with household expenditures on alcoholic beverages. The consumption equation also includes quadratic terms of age and income to capture possible non-linear relationships with tobacco expenditure [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF][START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF].

Statistical Tests and Estimation Results

In [START_REF] Vuong | Likelihood ratio test for model selection and non-nested hypotheses[END_REF]) likelihood ratio tests. However, it should be underlined that the validity of the LR tests strongly rests on the assumption that the general model is not misspecified [START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF]; in particular homoscedasticity and normality assumptions should not be violated.

Distributional assumptions assume crucial relevance in limited dependent variable models, since maximum-likelihood estimation will lead to inconsistent parameter estimates when normality and homoscedasticity are not fulfilled [START_REF] Maddala | Specification Errors in Limited Dependent Variable Models[END_REF][START_REF] Arabmazard | An Investigation of the Robustness of the Tobit Estimator to non-normality[END_REF]. For these reasons, preliminary tests for the validity of the distributional assumptions are necessary. To this end LR test for homoscedasticity and Pagan and Vella's (1989) moment base test for normality have been carried out on both Tobit and double-hurdle specifications 7 ; the results are presented in Table 2.

(Table 2 about here)

As can be noted, all equations present severe problems of non-normality and heteroscedasticity, with LR test values well above the relevant critical values in both Tobit and double-hurdle models. The violation of homoscedasticity requires allowance for heteroscedastic error terms in the univariate and bivariate specifications. Following [START_REF] Yen | Working wives and food away from home: the Box-Cox double hurdle model[END_REF], we relax homoscedasticity assumption by specifying standard deviation 2 i as a function of the continuous variables of the model, as in equation ( 7), and allowing it to vary across observations. For this reason, all the models considered in the 7 Details on distributional tests in censored and limited dependent variable models can be found in [START_REF] Bera | Testing the Normality Assumption in Limited Dependent Variable Models[END_REF], [START_REF] Pagan | Diagnostic tests for models based on individual data: A survey[END_REF] and double-hurdle models may lead to inconsistent results, supporting the necessity of a non-normal generalization of these models. As previously introduced in Section 3, following [START_REF] Yen | Working wives and food away from home: the Box-Cox double hurdle model[END_REF] and Yen andJones (1996, 2000), we consider a Box-Cox transformation of the dependent variable that relaxes normality assumption on the conditional distribution of i y and includes as special cases linear and logarithmic transformations. The results of the normality tests also can be interpreted as a strong indication of the superiority of the univariate and bivariate Box-Cox generalizations with respect to their standard counterparts.

Once the diagnostics of the model have been analyzed, we now turn to the choice of the most appropriate model. As previously shown in Figure 1, all restricted models can be obtained by placing the relevant restrictions on the likelihood function ( 13) and can be interpreted as special cases of the Box-Cox double-hurdle model with dependent error terms 9 .

The specification tests carried out are reported in Table 3. Firstly, we tested the hypothesis of independent errors between participation and consumption equations; the issue of dependency in double-hurdle models is a problem of great relevance, but it has often been disregarded in previous empirical works (Newman et al, 2003; Moffatt, 8 In principle all explanatory variables can be included in the heteroscedasticity specification; however, doing so would considerably increase the number of parameters to be estimated. So we focused our attention only on the variables that are more likely to cause heteroscedasticity and then we tested alternative specification excluding those variables that are not significantly different from zero. 9 The Heckman sample selection model can also be obtained as a restricted specification, assuming that participation decision dominates consumption decision. (1989), [START_REF] Blaylock | Wine consumption by US men[END_REF] and [START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF] and demonstrates that the independent Box-Cox double-hurdle model is an acceptable alternative to the dependent model 10 . On the basis of the results of Vuong specification test for nested models [START_REF] Vuong | Likelihood ratio test for model selection and non-nested hypotheses[END_REF], all the other restricted specifications are rejected, each with a pvalue of less than 0.0001. The interpretation of these results is twofold. Firstly, they suggest the inadequacy of the univariate Tobit specification in modelling tobacco consumption behaviours, given the existence of separate participation and consumption decisions. On the other hand, the results give further support to the generalized specification to account for non-normal and heteroscedastic error terms. Thus, the model that best rationalizes tobacco expenditure data is the independent Box-Cox double-hurdle model.

(Table 3 about here)

Maximum-likelihood estimates are presented in Table 4. In order to account for differences in estimated parameters, we report the results of both standard and Box-Cox independent double-hurdle models, even if the discussion is focused only on the latter.

Analyzing the estimated parameters, it is possible to highlight that all the coefficients, with the exception of that of education in the consumption equation and that of occupational status in the participation equation, are significant at the one 10 Smith (2003) puts into question the relevance of the dependent double-hurdle model itself, asserting that this model contains too little statistical information to support estimation of dependency, even when dependency is truly present. (Table 4 about here)

Turning to explanatory variables, income has a positive effect on household tobacco consumption, while income squared, which accounts for non-linearity relationships, is negative. These outcomes are in line with the findings of [START_REF] Garcia | Alternative Approaches to Modelling Zero Expenditure: An Application to Spanish Demand for Tobacco[END_REF] and imply that tobacco expenditure rises as household income increases, but at a decreasing rate. The estimated age effects are negative and significant in both participation and consumption equations, indicating the existence of a strong lifecycle pattern [START_REF] Kerr | Age, period and cohort influences on beer, wine and spirits consumption trends in the US National Alcohol Surveys[END_REF][START_REF] Aristei | Cohort Analysis of Alcohol Consumption: a Double-Hurdle Approach[END_REF]. As in [START_REF] Yen | Individual Cigarette Consumption and Addiction: a Flexible Limited Dependent Variable Approach[END_REF] and Yen (2005b), the probability of smoking and tobacco expenditure levels decrease with the age; moreover, the estimated age squared parameter shows a positive non-linear relationship between consumption levels and age.

The estimated parameters of the variables included in both hurdles have the expected 22 the existence of differentiated behaviours, with female headed households presenting both a higher probability of smoking and higher tobacco expenditures. On the other hand, the variable indicating the percentage of adult male members within the household (PercMale) exerts a significant and positive effect on both participation and consumption decisions. These evidences highlight the existence of important gender differences in tobacco consumption patterns. Moreover, it is worth noticing that the marital status variable exerts opposite effects on participation and consumption. In particular, being a single reduces the likelihood to smoke but, conditional on smoking, it increases tobacco expenditure.

Home ownership seems to negatively affect tobacco consumption levels; this result, previously found by [START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF] and Yen (2005a), suggests that belonging to wealthier social groups may induce moderate consumption.

Finally, the positive coefficient of the dummy variable indicating a high level of alcohol expenditure (HighAlc) reveals that the probability of being a smoker is higher for those households that are strong drinkers. Moreover, tobacco expenditure is also found to be positively correlated with the level of alcohol expenditure, showing the existence of a complementarity relationship in the consumption of addictive and habitgenerating goods.

Elasticities

In assessing the impact of explanatory variables, the presence of parameter estimates with opposite signs in the two hurdles and the Box-Cox transformation complicate the interpretation of the estimated effects. Thus, the impact of explanatory variables can be better explored by computing elasticities. The elasticities of probability, conditional level and unconditional level with respect to explanatory variables are calculated by using the formulas in equation ( 19). For statistical inference, standard errors are computed using the delta method [START_REF] Su | Microeconometric Models of Infrequently Purchased Goods: An Application to Household Pork Consumption[END_REF][START_REF] Spanos | Probability Theory and Statistical Inference: Econometric Modeling with Observational Data[END_REF].

(Table 5 about here)

Estimated elasticities and discrete effects for the categorical variables, along with their standard errors, are presented in Table 5. Analysing the effects of the continuous variables, income has a positive effect on the conditional level of tobacco consumption;

the elasticity are both significant, with a net effect on unconditional mean equal to 0.2638, a value which is in line with the empirical findings of Yen (2005a). This finding shows that economic factors play an important role in determining smoking decision and indirectly suggest that observed zero consumption may well be the result not only of abstention but also of standard corner solution, confirming the validity of the doublehurdle specification for modelling tobacco expenditure.

The elasticities with respect to age suggest that households with older heads are less likely to smoke and, conditional on smoking, consume less tobacco than younger households. This result is consistent with previous studies, even if the estimated effect on the unconditional level is lower than that found by [START_REF] Yen | Gaussian versus count-data hurdle models: cigarette consumption by women in the US[END_REF].

The level of alcohol consumption positively affects the unconditional level of tobacco consumption, revealing the existence of significant complementarities between smoking and drinking, with tobacco consumption rising as expenditures on alcoholic beverages grow. The elasticities with respect to PercMale are all positive and significant, with an overall effect on the unconditional level equal to 0.0443. This result highlights how men and women exhibit different consumption patterns in relation to tobacco, with both smoking probability and conditional level increasing as the ratio of male to female members increases.

The analysis of the effects of binary variables gives further support to the evidence highlighted in the discussion of parameters estimates. In particular, it is worth noticing that education plays a negative and significant role only on the probability but not on the conditional level of smoking. The impact of education on the unconditional level of tobacco consumption is negative and significant at the 10 percent significance level (equal to -0.347) as the negative effect on probability obviously dominates. These evidences suggest that more educated individuals are more aware of the health risks associated with smoking and they are less likely to participate to tobacco consumption.

The occupational variable does not influence the probability of smoking, but whitecollar workers are found to consume less tobacco conditional and unconditional on smoking.

The marital status variable exerts opposite effects on probability and conditional expenditure; more precisely, being a single reduces tobacco consumption probability by about 3 percent, but significantly increases the level of expenditure conditional on the smoking households sub-sample (the estimate effect is equal to 3.1230). However,

given that the positive effect on conditional level dominates the negative effect on probability, the net effect on unconditional expenditure is clearly positive and equal to 1.3693. Analysing the effect of household's head gender, it can be pointed out that the female-headed households are more likely to smoke and tend to consume more tobacco than the male-headed ones. The effects on probability, conditional and unconditional level are negative and significant, with an overall effect on the unconditional effect of equal to -0.7942. This result is not in contrast with the evidences connected to the effect of the percentage of male members and it is mainly connected to the structure of the female-headed households. In fact, the female-headed families in our sample are mainly single adult and single adult with adult children households and the effect exerted by this particular household structure may interact with the effect of household's head gender, making the separate identification of the two effects difficult.

Moreover, it should be noted that the categorical variable indicating the presence of children is characterized by a negative elasticity of probability (equal to -1.7%).

However, conditional on smoking, the elasticity of consumption is positive and offsets the negative effect of probability.

Finally, heavy alcohol drinking households are characterized by positive and significant elasticities of probability, conditional and unconditional levels. In particular, this result suggests that the probability of smoking is higher (of about 5%) for those households displaying habit generation tendencies and less aware of the health risks connected with tobacco and alcohol consumption.

Concluding Remarks

In The results based on the estimated parameters and elasticities confirm that decisions to smoke are related to income and demographic characteristics. In particular, income positively affects tobacco expenditure, indirectly showing the presence of habit-related behaviours in low income households which lead towards a lower income elasticity.

A substantial decline in the participation is found when the age of the household's head increases, together with an important lifecycle pattern in consumption. Estimation results highlight the presence of significant gender differences in both smoking participation and tobacco consumption patterns. High education and white collar occupation are found to reduce the likelihood of smoking and tobacco expenditure levels, suggesting that households with low educational levels and belonging to lower social classes have not yet benefit from policies concerning health consequences of smoking. Again, the data show that being a single determines a lower probability on smoking initiation, but conditional on smoking, the consumption level is higher.

Finally, complementarities between tobacco and alcoholic beverages consumption are present in both the probability and the level of smoking. This relationship is consistent with a wide body of empirical evidences and suggests that anti-smoking policies and public health strategies aimed at reducing alcohol abuse should be jointly addressed towards those households with higher levels of alcohol and tobacco expenditures.

F

  . In particular, both the standard double-hurdle model and the extended specification based on the Box-Cox transformation are presented. In Section 4 data used in the empirical analysis, taken from 2002 Italian Household Budget

  , as the quantity and expenditure are also subject to a nonnegativity constraint, the optimal level of tobacco expenditure ( -hurdle specification for modelling tobacco consumption, since it jointly accounts for both abstentions and corner solutions.

  and independence of the error terms across participation and consumption equations are acceptable.

  Double-hurdle model with independent error terms

[

(

  an unknown parameter. It is worth noticing that the Box-Cox transformation includes, as special cases, a straightforward linear transformation ( 1 , but normally we would expect the parameter ( to lie between these two extremes.The Box-Cox double-hurdle model implies the following relationship between the transformed dependent variable and the latent variables, w and y :

  Figure1summarizes the relationships between all the showing the relevant restrictions on the likelihood function(13)

  One of the main objective of this paper is to test whether univariate or bivariate models are adequate for analysing tobacco consumption behaviour of Italian households.

  different from one and zero; this implies a Box-Cox transformation that is different from both a linear transformation and a logarithm specification.

  signs and indicate that having a high education and being a white collar worker reduce the probability of smoking and the level of tobacco expenditure. The presence of children under fourteen years old significantly reduces the likelihood of smoking, indicating that households tend to refrain from smoking when small children are present. However, limited to the smokers sub-sample, the presence of children under fourteen years old increases the level of tobacco expenditure. The estimated coefficients for the dummy variable indicating the gender of the household's head (MaleHH) reveal

  Figures

  order to correctly analyze the determinants of tobacco expenditures and to model

	the other bivariate and univariate models discussed in Section 3, against its nested
	alternatives, by means of conventional and adjusted
	F o r
	P
	e
	e r
	R e v
	i e
	w
	household smoking behaviour, one first task relates to the choice of the most
	appropriate specification. Our selection strategy consists in testing the bivariate model
	with dependent error terms, which is the most general specification and encompasses all
	18

  this paper a Box-Cox double-hurdle model has been applied to data on tobacco expenditure from the Italian Household Budget Survey. The test strategy to obtain the best specification that out-perform nested models was carried out by means of a

	general-to-particular approach. The results obtained show that independence in the Box-
	Cox double-hurdle model is a non-restrictive assumption, while Tobit model, standard
	double-hurdle model with independence and Box-Cox Tobit model seem to be
	restrictive specifications, since they failed to account for non-normality in the bivariate
	distribution and for separate individual decisions on smoking participation and tobacco
	consumption.
	F o r
	P
	e
	e r
	R e v
	i e
	w

Table 1 -

 1 Variable definitions and descriptive statistics

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

Table 2 -

 2 Diagnostic testsNote: the degrees of freedom of each 2 2 statistic are reported in round brackets while the p-value of each test is in squared brackets.

	Model	Homoscedasticity	Normality
	Tobit	90.82 (2) [0.000]	134.603 (2) [0.000]
	Double-hurdle	825.2 (3) [0.000]	138.122 (2) [0.000]

Table 3 -

 3 Specification testsNote: the degrees of freedom of the 2 2 statistic of the LR test are reported in round brackets while the corresponding p-value is in squared brackets. In the Vuong tests, the asterisk indicates that the null hypothesis of model equivalence is rejected at the 1% significance level.

	Model	Test type	Test value
	Box-Cox dependent double-hurdle vs. Box-Cox independent double-hurdle	LR	0.78 (1) [0.3771]
	Box-Cox independent double-hurdle vs. Box-Cox Tobit	Vuong	21.074*
	Box-Cox independent double-hurdle vs. Independent double-hurdle	Vuong	38.428*
	Independent double-hurdle vs. Tobit	Vuong	12.311*

Table 4 -

 4 Heteroscedastic double-hurdle estimatesNote: the absolute value of each t-statistic is reported in round brackets.

			Submitted Manuscript			Page 32 of 34
			Heteroscedastic		Box-Cox Heteroscedastic
		Double-Hurdle Model	Double-Hurdle Model
	Variable	Participation Consumption	Het.	Participation	Consumption	Het.
	AGE	-0.0032	-0.9120	-	-0.0101	-0.0560	-
		(5.60)	(7.08)		(16.42)	(9.02)
	AGESQR	-	0.0067	-	-	0.0004	-
			(5.66)			(7.84)
	MALEHH	-0.0453	-2.2069	-	-0.0704	-0.0884	-
		(4.48)	(2.26)		(6.52)	(2.13)
	HIGHEDU	-0.0354	0.0886	-	-0.0327	-0.0297	-
		(4.43)	(0.14)		(3.91)	(0.98)
	WHITECOLLAR	-0.0035	-2.5902	-	-0.0182	-0.1666	-
		(0.39)	(3.48)		(1.78)	(4.86)
	PERCMALE	0.1764	3.2854	-	0.2461	0.1646	-
		(8.49)	(2.59)		(11.93)	(2.66)
	SINGLE	-0.1071	23.5328	-	-0.0804	1.1662	-
		(8.57)	(33.75)		(8.28)	(30.94)
	CHILD014	-0.0451	1.6787	-	-0.0435	0.1237	-
		(4.36)	(2.36)		(3.87)	(3.89)
	OWNEROCC	-	-4.6780	-	-	-0.2355	-
			(8.07)			(8.46)
	INCOME	-	12.8827	0.2489	-	0.6113	0.0476
			(8.05)	(15.00)		(14.34)	(2.77)
	INCOMESQR	-	-3.1280	-0.0078	-	-0.0819	0.0047
			(6.22)	(6.55)		(8.75)	(1.97)
	ALCOHOL	-	0.0994	0.005	-	0.0077	-
			(2.84)	(5.49)		(9.40)
	HIGHALC	0.1014	-	-	0.1309	-	-
		(8.51)			(11.67)
	CONSTANT	0.0261	27.1526	-	0.6647	4.5645	-
		(1.21)	(7.57)		(16.70)	(26.40)
	Box-Cox parameter ( ( )					0.1864 (17.50)
	Log Likelihood		-50881.02			-31097.36

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

Table 5 -

 5 Elasticities with respect to continuous variables and effects of binary variablesNotes: Asymptotic standard errors of estimated elasticities and discrete effects are reported in round brackets.Asterisks indicate levels of significance: *** = 0.01, ** = 0.05 and * = 0.10.

	Variables	Probability	Conditional level	Unconditional level
	Continuous variables
	AGE	-0.2551*** (0.0155)	-0.0748*** (0.0040)	-0.3299*** (0.0134)
	PERCMALE	0.0339*** (0.0042)	0.0104*** (0.0022)	0.0443*** (0.0011)
	INCOME	-	0.2638*** (0.0184)	0.2638*** (0.0184)
	ALCOHOL	-	0.0025*** (0.0003)	0.0025*** (0.0003)
	Discrete variables
	MALEHH	-0.0272*** (0.0104)	-0.8969*** (0.0561)	-0.7942*** (0.0426)
	HIGHEDU	-0.0127*** (0.0058)	-0.2952 (0.2460)	-0.3470* (0.2015)
	WHITECOLLAR	-0.0071 (0.0088)	-1.4820*** (0.4940)	-0.5296** (0.2493)
	SINGLE	-0.0313*** (0.0094)	3.1230*** (0.0919)	1.3693*** (0.0437)
	CHILD014	-0.0169** (0.0085)	1.2554*** (0.0523)	0.7603*** (0.0335)
	OWNEROCC	0.0462*** (0.0067)	-2.1037*** (0.0915)	-0.5305*** (0.0286)
	HIGHALC	0.0506*** (0.0062)	2.0469*** (0.1279)	1.0921*** (0.0341)

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

This decomposition follows the approach proposed by[START_REF] Mcdonald | The Uses of Tobit Analysis[END_REF] for the decomposition of the unconditional mean of the dependent variable in the Tobit model.

Here, for simplicity, we focus on the Independent Box-Cox Double-Hurdle model. Details on the derivation of the conditional mean for the Box-Cox Double-Hurdle model with dependent errors can be found in[START_REF] Jones | A Box-Cox double-hurdle model[END_REF].

[START_REF] Jones | A double-hurdle model of cigarette consumption[END_REF] included the individual's age and its square as explicative variables, while[START_REF] Yen | Determinants of household expenditures on alcohol[END_REF] used both household age composition and the age of the household head, showing significant lifecycle patterns for both participation and consumption decisions.

Acknowledgement. We would like to thank Federico Perali and Luca Piccoli for their useful comments and suggestions. This paper is part of the research project "Dynamic

Analysis of Addiction: Intra-household Resources Allocation, Social Welfare and Public

Health", University of Verona.

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