Intra-Household Distribution of Resources and Alcohol Consumption: the Passive Drinking Effect

Transcription

1 Intra-Household Distribution of Resources and Alcohol Consumption: the Passive Drinking Effect M. Menon F. Perali L. Piccoli August 21, 06 Abstract This paper aims at demostrating that an abuse in consumption of alcoholholic beverages may affect household distribution of resources. While household effects of alcohol abuse, such as violence, diseases, degrade, etc., are well known by everyday life experience, the economic effects of such a behavior reveals to be relevant as well, expecially when children are present. This gives even more emphasis on the necessity of a government intervention to reduce alcohol consumption. For the investigation of these issues we rely on a collective consumption framework, and estimate a collective quadratic almost ideal demand system. Form our estimates results that abuse of alcohol consumption influences the bargaining power in favour of the husband and significantly reduces the share of resources devoted to children respect to household in which alcohol is moderately consumed or not consumed at all. Very Preliminary Draft - Do not quote This work is part of the research project Dynamic Analysis of Addiction: Intra-household Resources Allocation, Social Welfare and Public Health 1. Researcher at University of Verona. Full Professor at University of Verona. Ph.D. Student at University of Verona

2 1 Introduction In analyzing alcohol consumption, and in general consumption of addictive goods, it have almost no sense to conduct an analysis at household level. The process of habit formation, which may evolve into addiction, is strictly personal, and depends on the quantities consumed by the person itself, and not by its household. However the majority of micro-data available today have little or no information about individual consumption, and also when some information is available it is quite unlikely to have the chance to construct a demand system. Since the our main aim is to analyze some household consequences of alcohol consumption, which is typically an individual question, the reference framework is that of Collective Choice models, introduced by Chiappori (1988) and Chiappori (1992). These models allow us to tell something about the distribution of resources within the household and on the bargaining power of each member of the couple. As shown in Peluso and Trannoy (06), the question of intra-household distribution is relevant for income distribution and well-baing analysis, and should be taken into strong consideration by public decisors. Moreover, we believe that these questions become more and more relevant if we look at poor household, which can be hardly affected by factors which would have scarce influence in other cases. Our working assumption is that a strong alcohol consumption may involve a perturbation of the equilibrium that would arise in households with moderate alcohol consumption or no consumption at all. This different allocation of resources, while being Pareto-efficient by assumption 2, may still be unsatisfactory for the policy maker, which should prefer a more equal choice in the Pareto-efficiency frontier. This is just one among many negative drawbacks of strong alcohol consumption at household level, such as episodes of violence, misunderstandings, lack of attention towards the other members and a possible bad example given to the children. There could also be negative individual effects, such as health problems or lack of concentration at work, along with social negative effects, such as the increased probability of car crashes, an increment on social costs due to higher public health costs and in general the costs related to intervention in many cases of troubles caused by drunk people. In this kind of situation, the decision to concentrate our attention on the distribution of resources within the household may seem much reductive, but it is still relevant for the wellbeing of the household members, and an unfair distribution may lead to a much lower level of well-being for some members of the household. If this is the case, there is an evident need for public intervention to re-establish a more fair distribution. Consider a poor household, where the husband is the only breadwinner and a wife and two children to maintain: if he is an alcoholic, there is a high probability that at least some of the resources that would normally be dedicated to other members are devoted to provide the daily measure of alcohol, with an evident shift from any socially desirable allocation. In our analysis, we use the Collective theory to handle two interesting questions: on one side, studying the sharing rule between husband and wife, we can infer something about the bargaining power. On the other hand, analyzing the sharing rule between adults and children (for the same households), we can shade some light on the distribution of resources. In both cases, we are particularly interested in analyzing how a strong alcohol consumption influences these mechanisms. The work is organized as follows. Section 2 introduces the theoretical framework of Collective Choice Models and the demand system specification. Section 3 deals with the 2 Pareto-efficiency of the decision on how resources have to be distributed is an essential assumption of collective models. 2

3 econometric method which will be applied and describes the data used. Section 4 shows results, with particular emphasis on the implication of alcohol consumption and on the differences observed between the bargaining power analysis and the income distribution analysis. Section 5 concludes the work and suggests for further developments. 2 The Model of Collective Choice In literature, there is much attention to the issue of identifying the sharing rule within a collective model. Consider the case of a household composed by the husband and the wife. Since data are collected at the household level itwillingeneralnotbepossibletodistinguish the preferences of the single member of the household, and hence it will not be possible to identify the sharing rule. However, it is often possible to overcome this difficult using available data, and in the literature there are mainly three suggestions for this. The first is proposed by Chiappori itself and many successive works, and consists in assuming that time is an exclusive good which a member of the household may devote, to work, leisure and household activities. Thus, observing how each member devotes his/her time it is possible to identify the sharing rule. On the other hand, as proposed by Browning et al. (05) 3, assuming that there is no change in preferences when passing from a status of single to that of married, it is possible to use informations on singles to identify the sharing rule. In their paper they state that it is possible to relax the assumption of invariance of preferences, but then it is not clear if other information is necessary to identify the sharing rule. In our opinion, this is an interesting solution which should be undertaken with extreme care. In fact, if on one hand the assumption of invariance of preference is rather implausible, on the other hand this method could provide information on the preference change itself, given that the sharing rule and the household consumption technology are identified by other ways. The last opportunity to overcome the issue of identification consists in the use of exclusive/assignable goods. The availability of data on expenditure of goods that are consumed by just one member of the household, it is possible to identify the sharing rule. To clarify the point, it is useful to give a definition of what an ordinary, an assignable and an exclusive good are. A good is ordinary when private consumption of that good is not observed or deducible. This is the common case in household expenditure surveys. Examples are numerous, but just for the sake of clarity, think about food. It will be consumed by each member of the household, but it is impossible to know in which proportion it will be consumed. Even if a survey were designed to account for individual information, for some goods it is very difficult to trace individual consumption. A good is assignable when it is consumed in observed proportions by each member of the household. A good is exclusive when a strictly private good is consumed by one identifiable member of the household only. According to Bourguignon et al. (1994), the distinction between exclusive and assignable goods is relevant in relation to prices. For exclusive goods a price is available for each household consumer, while for assignable goods price is the same for each household member. For our analysis we choose this latter case, since the dataset we use have information on an exclusive good, namely clothing, which is recorded as males clothing, females clothing, children clothing and other kind of clothing. If we keep just household with husband, wife and children below a certain age, we can reasonably assume that observed expenditure for clothing of each kind is exclusive to that member of the household. Moreover, this 3 And in some labor supply models by Barmby and Smith (01) and Bargain et al. (06). 3

4 assumption allows us to reasonably assume that alcohol is consumed only by parents, and not by children. In our work we are both interested on two kind of the sharing rule: the first is the sharing rule of husband and wife, which in our view represents the bargaining power of each member of the household, assuming that it is the couple that, given the needs of the household takes decisions on the distribution of resources. The second sharing rule we are interested in is that of adults and children. In this case, interpretation is purely distributive, which is to give an idea of the weight given to children felicity in determining household choices. In both cases our attention is particularly devoted in the effects that a excessive alcohol consumption produces to the sharing rules. The hypothesis that we aim at investigating is that addictive substances consumption can lead to a modification of the bargaining power between husband and wife, and that the main losers of this may be children. 2.1 Theoretical Framework For the exposition of the model we consider a couple without children, hence composed by husband and wife, which we will refer to as m (male) and f (female). The model applies straightforward if we consider adults and children, while a model in which the three members of the household are jointly considered is planned for a future development. Household members consume for their private use the vector of good x. This vector is composed by ordinary goods o and exclusive goods e i,fori = {m, f}, and is additively separable in x = x m + x f. Individual consumption x m and x f is not observed. Prices (in our case unit values) of the exclusive goods are observable and exogenous. We assume that household is not engaged in production and that labor supply is fixed (which is the case of full time employment in Italy). As a consequence household income is exogenous and assumed to be approximated by total expenditure of households y. The information set available in this framework is n o e m,e f,o; y;(p m,p f ; p) and the collective household decision problem is max U i (e i,o) s.t. p i e i + o φ i (p m,p f,y) e i 0,o>0,i= m, f; (1) where φ i is the sharing rule governing the intra-household allocation of resources, represented as the amount of resources devoted to member i. The existence of a sharing rule implies that we can recover individual consumption x m and x f. Marginal propensities to consume here are proportional to each other because they involve the sharing rule which is the same for all goods. Identification of the sharing rule from the structural specification is obtained thanks to techniques used to modify demand functions incorporating demographic variables or exogenous factors (Pollak and Wales (1981) and Lewbel (1985)), and to studies estimating household technologies (Bollino et al. (00)). In general, demographic functions interact with exogenous prices or income and can be identified provided that there is sufficient information in the data. The analogy steams from the fact that in order to identify the sharing rule from a structural specification, we use an 4

5 interaction with income alabarten (Barten (1964) and Perali (03)), with the estimation problem similar to that of estimating a regression containing unobservable independent variables (Goldberg (1972)). When this approach is feasible, it reveals itself simpler than the reduced form approach (Chiappori et al. (02)), which, on the other hand, is useful when the source of identification problems arise from insufficient information in the data. The estimation of an individual demand function, as it is implied by a collective representation of the household decision process, requires the estimation of the sharing rule. The minimal information required for the identification of the sharing rule is the observability of at least one assignable good, or, equivalently, two exclusive goods. If a good is exclusive, and there are no externalities, for a given observed demand e(p, y) satisfying the Collective Slutsky property (Chiappori (1988), Chiappori (1992), Chiappori and Ekeland (02b) and Chiappori and Ekeland (02a)), and such that the Jacobian D p e(p, y) is invertible, then the sharing rule φ m (p m,p f,y)=φ(p m,p f,y), φ f (p m,p f,y)=y φ(p m,p f,y) is identified. The sharing rule can be recovered by integrating back from the derivatives of the decision process. It is then possible to derive each member s demand for private goods, and the associated utility functions. 2.2 The Collective Quadratic Almost Ideal Demand System In this section we specify the identifiable model associated with the collective preferences described in Section 2. The chosen demand system is an extension to the Almost Ideal Demand System originally proposed by Deaton and Muellbauer (1980). The model is extended introducing a quadratic income term, following Banks et al. (1997), and the choice is motivated in the following section, which provide some evidence for a rank 3 demand system. Moreover, for the sake of generality, demographic characteristics interact multiplicatively both with prices and income in a theoretically plausible way (Lewbel (1985)). The interaction with prices captures Barten-like substitution effects (Barten (1964)), while interaction with income captures Gorman-like fixed costs (Gorman (1976)). The model is called collective because it incorporates the sharing rule. The budget shares demand functions for a Quadratic AIDS form are usually specified as follows w i = α i + X j γ ji ln p j + β i (ln y ln a(p)) + λ i b(p) (ln y ln a(p))2, (2) where α i, γ ij, β i and λ i are parameters, p j is price of good j and y is total expenditure. a(p) and b(p) are two price indexes, defined as ln a(p) =α 0 + X α i ln p i + 1 X X i 2 γ i j ij ln p i ln p j ln b(p) = X i β i ln p i, or b(p) = Y i pβ i i. When demographic modifications alabarten-gorman are introduced, then the budget shares are modified as follows w i (y, p, d) =t i (d)+s i (d)w i (y(p, d),p,d), where t(d) is a translating function, s(d) is a scaling function and d is a vector of demographic variables. 5

6 Similarly to the Slutsky decomposition of income and substitution effects, the Barten- Gorman specification translates the budget line through the fixed cost element (translating) and rotates the budget constraint by modifying the effective prices with the related substitution effects via demographic characteristics (scaling). Applying this transformation to equation (2), we obtain the following demographically modified budget shares equation where w i = α i + t i (d)+ X j γ ji ln p j + β i (ln y ln a(p )) + t i (d) = X r τ ir ln d r ln p =lnp i +lns i (d) ln s i (d) = X r δ ir ln d r or s i (d) = Y r dδ ir r ln y =lny X i t i(d)lnp ln a(p )=α 0 + X i α i ln p i X i X ln b(p )= X i β i ln p i, or b(p )= Y i (p i ) β i. j γ ij ln p i ln p j λ i b(p ) (ln y ln a(p )) 2, It is important to note that this budget share demand function is subject to a number of restrictions on the parameters. To satisfy linear homogeneity in p of the expenditure function and Slutsky symmetry X α X i =1; β X i i i =0; λ X i =0; γ X i i ij =0; γ j ij =0; γ ij = γ ji must hold, while, as proven in Perali (03), to ensure that the Barten-Gorman modified cost function maintains the homogeneity property, demographic parameters must respect X τ X ir =0; δ ir =0. i i It is important to note that these restrictions do not imply homogeneity of degree 0, and since they are essentially a normalization derived from the homogeneity requirement of the cost function, they do not alter the economic content of the model. The next step to obtain a Collective QAIDS is to introduce the sharing rule. This is straightforward in the light of equation (1) since it is evident that for each household member, the sharing rule determines the (natural logarithm of the) total amount of resources devoted to each member. In the Collective framework the decision process is individual rather than centralized, then, each member decides how to allocate his share of total expenditure, and the observed household budget share will be equal to w i = α i + t i (d)+ X γ j ji ln p j + β m i (ln y m ln a(p )) + λm i b m (p ) (ln ym ln a(p )) 2 (3) ³ +β f i ln y f ln a(p ) + λf ³ i b m (p ln y f ln a(p ) 2. ) Here household income ln y have been divided into the husband assigned income ln y m and the wife assigned income ln y f. Being the only household members, their incomes sum up to the household income, i.e. ln y =lny m +lny f. Being the sharing rule the portion 6

7 of income assigned to i th member of the household, we can write φ m (p m,p f ; y) =y m, and, taking natural logarithms, ln φ m (p m,p f ; y) = lny m. Hence, in equation (3), ln y m and ln y f are defined as ln y m =lnφ m (p m,p f ; y) X i t i(d)lnp, ln y f =lnφ f (p m,p f ; y) X i t i(d)lnp. (4) The sharing rule φ m,canbedefined, in analogy with Barten s scaling, as a demographically scaled income φ m (p m,p f ; y; s) =m m (p m,p f ; s)y m, which in natural logarithms is ln φ m (p m,p f ; y; s) =lny m +lnm m (p m,p f ; s). In the last equation m(p m,p f ; s) is the scaling function, definedoverpricesandaset of demographic variables s, which in the literature are often called distribution factors, since they affect the distribution of income within the household. The identifying assumption in our model is that the portion of income relative to each member y i can be determined by the observed expenditures in exclusive or assignable goods. In other words we define personal income by means of the ratio of expenditures of the exclusive goods. For instance, husband income is defined as his expenditure in his exclusive good e m plus half of expenditure in ordinary goods o. This, in mathematical terms, is equivalent to write ln y i = w i ln y, with w i defined as w m = 1 µ e m + 1 ³y f e m e, (5) y 2 with e m and e f being expenditure on the exclusive goods for husband and wife. We can then write the sharing rules as ln φ m (p m,p f ; y; s) =w m ln y +lnm m (p m,p f ; s) ln φ f (p m,p f ; y; s) =w f ln y +lnm f (p m,p f ; s) Since ln φ m (p m,p f ; y; s) +lnφ f (p m,p f ; y; s) = lny must hold, and, by construction, w m ln y + w f ln y =lny, the following constraint must hold ln m m (p m,p f ; s) = ln m f (p m,p f ; s). (6) To save on notation, we can, without loss of generality, set ln m m (p m,p f ; d) =lnm( ), ln m f (p m,p f ; d) = ln m( ), ln φ m (p m,p f ; y; d) =lnφ( ) and ln φ f (p m,p f ; y; d) =lny ln φ( ). Substituting into equations (4) we obtain ln y m = w m ln y +lnm( ) X i t i(d)lnp ln y f = w f ln y ln m( ) X i t i(d)lnp. In analogy to function t i (d), function m( ) =m(p m,p f ; s) is identified provided that there is enough variation in distribution factors s, and as long as the distribution factors s 7

8 differ from the demographic variables d. The proof is very similar to proving that function t i (d) is identified, for which we suggest to refer to Gorman (1976), Lewbel (1985) or Perali (03). It is worth noting that, at the moment, in our empirical exercise, we do not apply the price scaling function to the demand system, because of scarce variability in the data which causes heavy difficulties in the estimation process. 3 Empirical Strategy 3.1 Data Description The data used in this work are drawn from the Italian ISTAT 04 cross-sectional household expenditure survey. We selected household composed by married couples with dependent children aged 0-14 with an observed positive consumption for clothing 4. The sample includes 2999 households. In this dataset, several goods are consumed exclusively by a male, a female or the children. This feature, together with the choice of keeping only couples with children, allows us to assign some of these goods respectively to the husband, to the wife and to children. In particular clothing can be assigned to the husband, to the wife and to the children; education can be assigned to children and alcohol can be assigned to adults. We consider only expenditure on non durable goods, and deliberately exclude health expenditure, which could seems of interest when analyzing alcohol related issues, because Italy have an almost completely public health system, and the remaining expenditure would be on cosmetics and other somewhat non-relevant goods. The expenditure cathegories considered are food, alcohol, clothing, education and recreation, and other consumption. Household-specific prices are assigned following the procedure described below. Table 1 and Table 2 report the descriptive statistics of the sample for the estimates of the sharing rule of both husband & wife, and adults & children. We use slightly different sets of demographic variables and distribution factors in the two estimates, since the main determinants of the sharing rule between adults and children need not to be the same than for husband and wife, unless in particular cases. The set of demographic variables include the macro regions (north and south, and by difference center of Italy), number of children, a dummy variable for the presence of children and one for babies (children aged 0-5 years old), a dummy variable which is 1 if at least one of the couple is a pensioner, a dummy variable December to capture seasonalities, and in particular for Christmas time, a dummy variable to indicate that the household do not live in urban areas (rural), a dummy variable indicating that husband is an employee (i.e. he is not an entrepreneur or private worker), husband age, a dummy variable equal to 1 if at least one in the couple smokes, a dummy equal to 1 if at least one in the couple is aged 45 or above (called mature), a dummy indicating that household head have at least an high school education, a variable which measure the difference in schooling years between the husband and the wife, and a dummy indicating that the wife has a work. A separate citation is needed for variable habits, which is equal 0 if alcohol and tobacco are not consumed by the household, equal 1 if one between alcohol and tobacco is consumed, equal 2 if both alcohol and tobacco are consumed and equal 3 if both are consumed and expenditure on tobacco is greater than 0, which is more or less equivalent to cigarettes/day 5. The actual 4 We restrict to positive clothing expenditures because this is the main source of identification for the sharing rule. Adding also observations with no xlothing expenditure would not mean to add useful information for the identification of the sharing rule. 5 This variable is at least in part endogenously determined, and may lead to biased results. However, 8

9 choice of demographic variables and distribution factors for each estimate are reported in details in Table 4 and Table 6, which are discussed in Section 4, where results are exposed. 3.2 Nonparametric Engel Curves and Rank Test Engel curves 6 are a widely used tool to assess the relationship between good consumption and income. Despite of the long time since this relationship have been studied, there is still no agreement on which functional is best suited to this extent. According to the early work of Working (1943) and Leser (1963) the Engel curves could be considered linear in the log of income, but later studies (among which Atkinson et al. (1990), Bierens and Pott-Buter (1987), Blundell et al. (1993), Hausman et al. (1995), Härdle and Jerison (1988), Hildebrand (1994), and Lewbel (1991) have shown that this specification is rather poor in describing Engel Curves for some goods. To be pragmatic, the general evidence on micro-data is for a quadratic relationship between budget shares and log of total expenditure 7,i.e.arank3 demand system 8. Even if there is some general agreement on the use of quadratic Engel curves, we use nonparametric technique to verify the rank of the demand system. To this aim, we use single equation non-parametric 9 Engel curve estimation, and model the budget share of each good to be a non-linear function of the natural logarithm of total expenditure. In doing this we follow Banks et al. (1997) and Perali (03), and plot, in Figure 1, the non-parametric estimates of the Engel curves (orange line) along with its 99% confidence interval (blue dashed lines) and a quadratic polynomial regression (violet line). Along with the Engel Curves, we present nonparametric kernel bivariate density estimates and contour plots. From a graphical analysis appears evident that food shows a linear-like relationship, while all other goods exhibit a quadratic-like relationship, however we prefer to deepen the analysis by using a non-parametric rank test for the system as a whole. This test does not need the specification of a functional form for the demand system, and hence permits to avoid specification errors. We use the non-parametric rank test proposed by Gill and Lewbel (1992). This test is based on the estimated pivots of a matrix associating shares to function of total expenditure. The data matrix is decomposed using the Lower-Diagonal-Upper (LDU) Gaussian elimination with complete pivoting (Golub and Loan (1983)). The rank of each matrix equals the number of non-zero elements of the diagonal matrix of pivots. The null hypothesis is tested against the alternative that the rank is greater than r, and that the rank test is conducted sequentially, starting with r =1. The test consists in evaluating the hypothesis that only pivot d 1 is significantly different from 0, and consequentially all remaining p r pivots are zero. The results of the rank test, summarized in Table 3, show that the system can be considered a rank 3 demand system, and a p-value of indicates that the choice of a while we have intention to explore the way of an endogenously determined sharing rule as proposed by Basu (06), at the moment we stick to the assumed exogeneity of this constructed variable. 6 Engel (1895). 7 Total expenditure is often used in cross section analysis when no reliable information on income is available. This is also the case for our study, since ISTAT does not record income information. 8 Following Lewbel (02), we define the rank of a demand system as the maximum dimension of the function space spanned by the Engel curves. 9 We use a local polynomial regression of first degree with a bandwidth set to 0.3. This value is the same for all the goods and is slightly larger than the Silverman and Silverman (1986) Rule-of-thumb for the larger bandwidth good. The analysis is conducted using the Nonparametrix package for Mathematica provided by Bernard Gress, which refer to Pagan and Ullah (1999). 9

10 quadratic demand system is likely to be correct. 3.3 Econometric Model Econometricians working with household micro-data often are faced to the zero expenditures problem, especially when working with a disaggregate goods, which is the case, for example, of alcohol consumption, tobacco and clothing. It is known that estimates of coefficients are inconsistent when only observed positive purchase data are used, then a correction technique must be used. Zero s correction methods differ for the different assumptions related to the zero expenditures. For example the Tobit model simply captures the corner solutions for utility maximization problem, which imply that the observation is zero just because household decided to consume zero on the basis of disposable income prices and preferences. This could be the case for some goods, but for some other not, as for semi-durable goods (for example cloths) which may not be purchased in the reference period simply because they give utility for more than one period and a household needs to buy them only once in, say, 6 months. This situation is called Infrequency of Purchases, and cannot be captured by a Tobit model. The Double-Hurdle model 11 instead assumes that zero expenditures are explained by a decision process that arise from not observed latent variables which drive consumer choice. The model allow for separate parameter estimation for participation and expenditure choices. This is the case of alcohol, which may be not consumed because of moral conviction or health problems, which are not observable in the survey. Again this model is not useful when we consider semi-durable goods, as cloths. An alternative to the Double-Hurdle model is the Heckman two-step,which assumes that zero expenditures are due to the well known sample selection bias (Heckman (1979)) and are treated as a mispecification error. This approach allows to obtain different estimates for participation and expenditure parameters, but the participation choice is dependent from other observable variable which does not enter the main regression. In the original model, the first stage determines the participation probability using a probit regression, and then, in the second stage, Heckman propose a specification for the omitted variable which can be used to correct the sample selection bias, if present. The omitted variable is the inverse Mill s ratio, which is the ratio between density and cumulative probability function of the standard normal distribution. In this paper we use a two-stage generalization of Heckman model which overcomes the issues which emerge with the Generalized Heckman model proposed by Amemiya (1978) and Amemiya (1979), and applied by Heien and Wessells (1990). In particular, we refer to the work of Shonkwiler and Yen (1999), which shows the inconsistency of the Generalized Heckman estimator and proposes a consistent, though still simple, two-step estimator for a censored system of equations. Following Shonkwiler and Yen (1999), consider the following general limited dependent variables system of equations yit = f(x it,β i )+ it, d it = zitα 0 i + υ it, (7) ½ 1 if d d it = it > 0 0 if d it 0 y it = d it yit, (i =1, 2,...,m; t =1, 2,...,T), See Amemiya (1985) and Maddala (1983). 11 Yen (1993).

11 Engel Curve for Food Food shar e Tot exp Food Share Ln of total expenditure Engel Curve for Alcohol Alcohol shar e Tot exp Alcohol Share Ln of total expenditure Engel Curve for Clothing Clothing shar e Tot exp 0.1 Clothing Share Ln of total expenditure Engel Curve for Education and Recreation 0.25 Education an d Recreatio n shar e Tot exp Ln of total expenditure Edu Rec Share 0.5 Engel Curve for Other goods 0.45 Other good s shar e Tot exp Others Share Ln of total expenditure Figure 1: Engel curves, unconditional joint p.d.f. and contour maps 11

12 where i represent the ith equation and t the tth observation, y it and d it are the observed dependent variables, y it and d it are the latent variables, x it and z it are vectors of exogenous variables, β i and α i are parameters, and, it and υ it are random errors. Without entering into details of derivation (refer to the authors for details), system (7) can be written as y it = Ψ(z 0 itα i )f(x it,β i )+η i ψ(z 0 itα i )+ξ it, where Ψ( ) and ψ( ) are univariate standard normal cumulative distribution function and probability density function. The system can be estimated by means of a two-step procedure, where α i are are estimated using Maximum Likelihood probit estimator, and then used to calculate Ψ(z 0 it α i) and ψ(z 0 it α i), and successively estimate β i and η i in the system y it = Ψ(z 0 itˆα i )f(x it,β i )+η i ψ(z 0 itˆα i )+ξ it by Maximum Likelihood. This correction method applies to zero expenditures observed in the demand functions. In this particular framework, however, it happens that the zero expenditures reveals to be particularly noisy since it affects also the determinants of the sharing rule, which in the case of husband and wife are clothing for man and clothing for women. In a future development we will try to correct for these zero observation both using a variant of the Shonkwiler-Yen and using a particular technique which is under development right now. Since the ISTAT survey records only expenditure information, the lack of information about quantities purchased preclude the possibility to derive household specific unit values. ISTAT s price index, which have the same aggregation level of the survey, is not sufficient to provide plausible estimates. For this reason, we use a procedure, originally proposed by Lewbel (1989) and applied by Atella et al. (03), to construct pseudo unit values. Atella et al. (03) propose to use informations that come from the national and regional price indexes to raise variability of pseudo unit values, but given that our period of analysis is quite short ( ), and keeping in mind that the main aim of our work is to identify the proper demographic variables to construct a pseudo-panel, we rely on the original procedure as proposed by Lewbel, except for the fact that we express pseudo unit values in levels rather than in relative terms. The method proposes to estimate the cross-sectional variability of actual unit values by exploiting the demographic information included in generalized within-group equivalence scales, or, more generally, demographic functions. Without entering into details 12, we estimate pseudo unit values by means of n i ˆP i = 1 Y ki j=1 w w ij ij y i, where y i is expenditure for i-th group of goods, w ij is the subgroup 13 budget share and k i is a scaling factor defined as n i Y ki = j=1 k k ij ij where k ij = mean(w ij ) is the mean subgroup budget share. 12 See Lewbel (1989) for details. 13 For clarity, suppose one want to estimate a demand system with i goods from micro-data. Each good is in turn an aggregation of other j goods, from here the definition of group i and subgroup j. 12

13 4 Results 14 This section describes the estimate for the sharing rule between husband and wife, which in our view represent the bargaining power in the decision process of allocating household resources, and the sharing rule between adults and children, which can be seen as an index of the relative well-being of children within the household. The sharing rules are the outcome of two separated and independent estimation processes. This is the case since the identification of a three-sided sharing rule is still an open question. Estimation of the sharing rule comes from maximum likelihood estimates of a Collective Quadratic Almost Ideal Demand System, as described in Section 2, in which zero observed expenditures are corrected applying the methodology proposed by Shonkwiler and Yen (1999). This zero correction technique is not applied (yet) to exclusive and assignable goods, since these goods do not enter directly the demand system, and much attention should be posed in manipulating these variables. The system s properties of symmetry and homogeneity are ensured by construction, with the Slutsky matrix having in each estimate two individual income term which sum up to the household income effect, because of the symmetry of the individual transfers shown in equation (6). Results of the estimates of the sharing rule between husband and wife are reported in Table 4 and 5 and are discussed in the following paragraph, results for the sharing rule between adults and children are reported in Table 6 and 7, and are discussed later on. 4.1 The Sharing Rule between Husband and Wife The estimates of the sharing rule and of all other parameters of the CQAIDS are presented in Table 4. In general the demand related parameters are almost all significative, with the exception of very few parameters. Also the η i parameters are significative, indicating that the observed zero expenditure do not come from Kuhn-Tucker corner solutions, but rather from other sources of error, like sample selection or infrequent purchases. Among demographic variables, the general trend is towards small parameters values, even if many are still significantly different from 0. An exception is husband age, which is not significant in most cases, and for alcohol demand equation, which is insensible to any demographic variable, except to the habits variable, which have a negative sign, while we expected a positive one. Parameters of the sharing function tell us that the sharing rule (husband s share of total expenditure) is not influenced by the price of males and females clothing, that the differential in education in the couple have a scarce influence and that having a small children is not significant as well. This last parameter however reflects the whole sample, while from figure 3, it seems that for low income household it has a greater influence. Note that figures 2 through 5 represent the relative sharing rule, expressed as the ratio between wife expenditure and total expenditure (φ f /y). The other parameters have a stronger impact, especially wife working and high education parameters (see also figures 4 and 5), which reduces the bargaining power of husbands. The habits parameter is significantly positive, implying an enforcement of the bargaining of power of men. This is reflected also by figure 2 which shows how wives living in households with high alcohol consumption have a lower bargaining. 14 Please consider that this work is still in an early stage, and as a consequence results are still very preliminary. In particular we do dot implement price scaling: it seems that data variability is not sufficient for the identification of all parameters. 13

14 Sharing Rule Strong Drinkers Sharing Rule Small Children Sharing Rule Sharing Rule Ln of Total Expenditure Reduced Sample Scatter Plot Astemious Figure 2 Sharing Rule Wife Working Strong Drinkers Ln of Total Expenditure Reduced Sample Scatter Plot No children < 5 years old Figure 3 Sharing Rule by Schooling Children < 5years old Sharing Rule Sharing Rule Ln of Total Expenditure Reduced Sample Scatter Plot Wife not working Figure 4 Wife working Ln of Total Expenditure Reduced Sample Scatter Plot less educated Figure 5 High school or more Finally, numerically calculated uncompensated price elasticities seem to respect consumption theory statements, i.e. negativity of own price elasticities, which are the diagonal elements in Table The Sharing Rule between Adults and Children Speaking about resources devoted to children, there are similar results for the demand parameters. Parameters are in general significative with exception to the alcohol related demographic parameters and to husband age as in the previous estimate. Things change when we consider the sharing rule. The small child parameter that was present in the estimation of the bargaining power have been substituted by the number of children which seems more likely to influence resources devoted to children. By the way, it resulted the only significant parameter, and still with a quite limited influence. A graphical analysis of the sharing rule tells a quite different story. In fact, figure 6 through 8, which show the relative sharing rule expressed as the ration of children expenditure on total expenditure (φ c /y), all show a quite relevant shift, except for the wife working parameter. 5 Conclusions and Further Developments In this work we presented some evidence of how an excessive alcohol consumption may affect the distribution of resources within the household. Results, even if very preliminary seems relatively strong, even for a country (Italy), which is supposed to have a relatively advanced society. Nevertheless, these estimates should be taken with some caution, since are very preliminary and needs several improvement and checks. 14

15 Sharing Rule Strong Drinkers Sharing Rule Number of Children Sharing Rule Sharing Rule Ln of Total Expenditure Reduced Sample Scatter Plot Astemious Figure 6 Sharing Rule Wife Working Strong Drinkers Ln of Total Expenditure Reduced Sample Scatter Plot 3 children or Figure 7 Sharing Rule by Schooling < 3 Children Sharing Rule Sharing Rule Ln of Total Expenditure Reduced Sample Scatter Plot Wife not working Fogure 8 Wife working Ln of Total Expenditure Reduced Sample Scatter Plot less educated Figure 9 High school or more One of the biggest issues relies on the estimation of a quadratic demand system. The convergence of estimate depends heavily on the choice of the starting values and the surface of the objective function seems to be relatively flat, so that estimates should not be considered definitive in any way. In fact, even if advantages of a quadratic demand system may seem evident, the numerical complications that derive from the applications of such a model, may overwhelm its advantages. We are trying to evaluate which model is to prefer between AIDS and QAIDS. Moreover, we are investigating whether it more convenient to estimate the system as a whole, with restrictions on parameters which come from the theory, or if it would be better to estimate equation by equation via Maximum Likelihood and successively recover parameters estimates by means of a Minimum Distance Estimator. This last technique would be really useful when classic estimation takes too long (a question of hours is what usually happens) or whenever usual numeric techniques run into difficulty. Another big issues relates on the observed zero expenditures. If from one side this issue is partly solved by the Shonkwiler-Yen procedure, which is rather largely accepted by the literature, part of the problem remains for the exclusive and assignable goods, with relevant percentages. On this side, we are trying to proceed by pre-imputing expected expenditure. The procedure is similar to that of Shonkwiler-Yen, but should allow for a more flexible application, so that it could be applied also to those goods which are not part of the demand system. In our paper, to say something about the bargaining power and on the distribution of resources, we had to provide two separate estimates: one for the sharing rule between husband and wife, and one for the sharing rule between adults and children. We are trying to prove that a three-sided sharing rule would be identified, so that the sharing rule between the three members of the household could be estimated at once. The usefulness of such a specification is evident in all that cases in which the winners and the losers from 15

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