Estimation of consumption choices with the EASI demand system: Application to Italian data

Transcription

1 Estimation of consumption choices with the EASI demand system: Application to Italian data Arianna Olivieri * Prometeia Associazione per le Previsioni Econometriche, Bologna This version: 30 August 2014 Abstract The literature has been enriched by a new model to estimate consumer demand functions, the Exact Affine Stone Index (EASI) demand system, an implicit Marshallian demand system, developed by Lewbel and Pendakur (2009). This article applies the EASI model to Italian household consumption data for the period , to estimate Engel curves by type of good, and perform a policy simulation exercise. The results show that, in Italy, certain goods, such as food and fuel, have decreasing Engel curves, while others, such as clothing and transport, have increasing curves. The policy simulation exercise shows that increases in the prices of food and fuel have a stronger negative impact on poorer households, while increases in the prices of education and recreation have a stronger impact on richer households. Keywords: EASI demand system, Engel curves, Household budget survey, Price indices. JEL codes: D11, D12, C36. * Address for correspondence: Prometeia Associazione per le Previsioni Econometriche, Via G. Marconi, 43, Bologna, Tel , Fax , arianna.olivieri@prometeia.com. This article is based on my master s degree dissertation supervised by Prof. Massimo Baldini (University of Modena and Reggio Emilia). The first draft was written during an internship at the Ministry of Economy and Finance in Rome under the supervision of Daniele Pacifico. I thank both my tutors for valuable suggestions and support. I am grateful also to Elena Giarda for comments and help. All remaining errors are my own responsibility.

2 Introduction and literature review During the crisis Italian household consumption has declined sharply, -5.3% in real terms between 2007 and 2012, with two significant falls in 2009 (-1.6%) and 2012 (-4.2%). This loss almost eroded the 6.3% real growth during and marked a departure from positive growth trend since the second half of the 1990s (around 1.5% annually). Household disposable income has fallen even more markedly, -9.6% in real terms between 2007 and 2012, wiping out the 7.8% growth achieved in Prices, income and demographics play important roles in explaining aggregate consumption patterns (Kutsam, 2013). Household size, geographic area and other demographic characteristics affect consumers decisions via their consumption preferences. In a simple model of consumer theory, income represents the budget constraint for household consumption, and households allocate their available resources to different goods and services subject to this expenditure ceiling. 1 Expenditure decisions depend also on prices, specifically they are affected by the price sensitivity of the goods on the market. Knowing how the consumer reacts to prices is necessary for the design of an effective tax system. Consumer behaviour is sensitive to prices, and taxes on consumption determine the final prices faced by consumers. When increasing the tax base, politicians prefer to increase taxes on goods with inelastic demand in order to create a more efficient taxation system. Thus, it is important for policymakers to know the structure of demand and the characteristics of consumers. The contribution of this article is to estimate the relationship between expenditure by type of good and income at household level (Engel curves) of the goods and services purchased via application of Lewbel and Pendakur s (2009) Exact Affine Stone Index (EASI) methodology to data from the Italian Family Expenditure Survey (ICF, Indagine sui Consumi delle Famiglie ) for the period To my knowledge this is the first application of this methodology to the Italian case. Applied work on the analysis of consumer demand demonstrates the importance of unobserved preference heterogeneity and the presence of complex Engel curve shapes (e.g. Blundell et al., 2003). However, it is difficult to incorporate these features into utility-derived Marshallian demand systems. The problem was addressed by Lewbel and Pendakur (2009) who specified demands in terms of prices and an affine function of Stone-index deflated expenditure (Stone, 1954), to develop the EASI family of demand systems, which provides the nice features of Hicksian 1 In an advanced economy, there is the possibility for the economic actors to find additional financial resources to extend their consumption capability. In this work this possibility is not considered; the resources used are those there really available to households without this extension. 2

3 demands in an empirically practical framework. The EASI system also allows the presence of unobserved preference heterogeneity, innovating on previous empirical models of consumer demand that do not allow model error terms to be interpreted as unobserved heterogeneity (i.e. McFadden and Richter, 1990; Brown and Matzkin, 1998; Lewbel, 2001; Beckert and Blundell, 2004). The EASI demand system is an important instrument for policy evaluation and analysis of consumer choices. It is an implicit Marshallian demand system that combines the desirable features of various demand systems, and allows the estimation of consumer budget shares as functions of total household expenditure. It is more advanced than the previous generation of demand systems and is similar to the Almost Ideal Demand System (AIDS) because the budget shares are linear in parameters, given real expenditures. A problem common to many models of consumer demand is the absence of unobserved heterogeneity in consumer preferences or the difficulty to include it in a coherent fashion. Deaton and Muellbauer s (1980) Almost Ideal Demand (AID) model, which has linear Engel curves and does not incorporate unobserved heterogeneity, is very popular, in part, because alternative models involve nonlinear functions of numerous prices and parameters, which often are difficult or numerically impossible to implement. The AID model also has a very convenient approximate form which can be estimated using linear methods. For these reasons the AIDS has been applied extensively in different countries and contexts, for example, as a new approach based on the chain price index (Brown and Lee, 2011) or an application to the elasticity of medicine prices (Filippini et al., 2007). As in the AIDS, EASI budget shares are linear in parameters up to the construction of real expenditure. However, in contrast to the AID system, EASI Engel curves for each good are almost completely unrestricted; they can have any rank and be polynomials or splines of any order in real expenditures. In addition, EASI error terms correspond to unobserved preference heterogeneity random utility parameters. The EASI model is used because it provides several advantages compared to older systems. For example, the configuration of budget shares and households consumption choices do not depend only on relative prices and spending power, that is, the household income available for spending, but also consider household social and demographic characteristics. EASI demand functions can be estimated using Generalized Method of Moments (GMM), and, as in the AIDS, an approximate model can be estimated using linear regression methods. The EASI demand system is as flexible in price responses and as close to linear in parameters as the 3

4 AIDS, but also allows for flexible interactions between prices and expenditures, and permits almost any functional forms of the Engel curves. As explained by Lewbel and Pendakur (2009), the EASI model is an application of a new general methodology to construct demand systems, which they describe as pseudo-marshallian demands. These types of demand functions are basically Hicks demands associated with cost functions that have the property that utility can be represented by a simple function of observables. In EASI demands, this function is an affine transformation of total expenditure deflated by a Stone index. The EASI demand system is recent and, therefore, has yet to be applied as extensively as the AIDS. Wood et al. (2012) estimate a food demand system with GMM using Mexican household data, and demonstrate that information on how households substitute goods in response to price increases is needed to predict households income variations when prices vary. Magaña-Lemus et al. (2013) also use Mexican household data to estimate the impact of rising food prices on poverty and welfare for different types of households, using a linearized approximation of the model, while Song et al. (2013) study the rank of the demands and investigate the profile of Chinese households consumption. In this paper, I estimate the EASI demand system for Italy, using ISTAT (Italian National Statistical Institute) Family Expenditure Survey data for the period The EASI demand system can be estimated using GMM, but in this work an approximate model is estimated using the Three-Stage Least Squares (3SLS) linear regression method. Estimation of the EASI demand system for Italy shows that certain goods, such as food and fuel, have decreasing Engel curves, while others, such as clothing and transport, have increasing curves. This is in line with previous studies of consumption (Banks et al., 1997; Blundell and Robin, 1999). I also perform a policy simulation exercise by quantifying the changes in consumption deriving from a 5% increase in prices. Computation of the cost-of-living index proposed by Lewbel and Pendakur (2009), defined as the difference between two cost functions associated with two price levels, shows that a 5% increase in the prices of Food and non-alcoholic beverages and Fuel and energy have a stronger negative impact on poorer households, while a 5% increase in the price of Education, culture and recreation has a stronger impact on richer households. The paper is structured as follows. Section 1 describes the datasets used in the analysis. Section 2 presents an overview of the consumer s utility optimization problem and the structure of the EASI demand system. Section 3 presents the results of Engel curves estimates by expenditure 4

5 category. Section 4 discusses a policy simulation exercise of a price increase and Section 5 concludes with a summary of the main findings. 1. Theoretical framework: consumer theory and the EASI demand system 1.1 Consumer theory The central assumption in consumer theory is optimization: given a feasible set of consumption bundles, the consumer chooses the one he/she prefers. This theory is the instrument offered by microeconomics to understand how the consumer, whether an individual or a household, allocates its income for the purchase of goods and services. Thus, the allocation decisions of all consumers determine the overall demand for goods and services, which, in turn, is influenced by changes in prices and incomes. Consumer theory entails the concept of utility, which refers to the numerical value of the level of satisfaction or well-being obtained by the consumer from purchasing a specific bundle of goods. A utility function ( ) assigns a level of utility to each bundle of goods. It is based on the concept of preference ordering. The consumer orders the bundle of goods according to his/her preferences: given two bundles and, if, then the consumer prefers to and ( ) ( ); if, instead,, then is said to be preferred over or the consumer is indifferent to and ( ) ( ). Another important element of consumer theory is definition of the feasible set which constrains consumers choices by setting a limit to their available income, that is, the budget constraint. Given a fixed amount of income x and n goods among which the consumer can allocate his/her expenditure, the budget line represents the geometrical position of all combinations of goods for which total expenditure is equal to income. This rests on the assumption that the consumer expends all his/her income. Therefore, the consumer will choose a bundle that is on his/her budget line. Given these assumptions, the consumer s problem related to choosing the preferred bundle from those available, can be formally stated as a problem of constrained utility maximization (the original problem) as follows: ( ) ( ) (1) 5

6 The optimal solution to the system of equations (1) is the set of Marshallian demands ( ), which are a function of x and p. In the two-good case, the solution to the maximization problem is a tangency solution where the optimal bundle q* is such that the highest attainable indifference curve is tangent to the budget line. Substitution of the optimal values set of ( ) into system (1) gives: ( ) ( ) [ ( ) ( )] ( ) (2) where ( ) is defined as indirect utility function since it depends indirectly on prices and income, as opposed to direct utility which depends directly on income. This function gives us the maximum possible utility given x and p. It is possible to reformulate this issue in a symmetric way. The expenditure function is derived from the problem of minimizing the total expenditure necessary for the consumer to achieve a specific level of utility u (the dual problem). Therefore, the expenditure minimizing problem consists of moving along the indifference curve until the lowest iso-expenditure line is reached (the consumer chooses the lowest expenditure line tangential to a given indifference curve). The dual problem is formulated as follows: s.t.: ( ) ( ) ( ) (3) The solution to the system of equations (3) is the set of Hicksian or compensated demand functions, ( ) which are expressed in terms of u and p. These functions show that the purchased quantities are affected by their prices, given a certain level of utility. To each price variation there is a corresponding variation of the expense which, thus, is "compensated" in order to maintain the same level of utility. Similar to what we did above, if we substitute the optimal quantities ( ) in system (3), we obtain: ( ) ( ) (4) where ( ) is the expenditure function. 6

7 The indirect utility function and the expenditure function are closely connected: in fact we can invert ( ) in order to have u as a function of x and p, thus obtaining ( ). The same result can be obtained starting from the indirect utility function. Now, if we take as the constraint in the utility maximization problem the level of expenditure resulting from solving the expenditure minimization problem, then the optimal values of both problems, the Marshallian and Hicksian demand functions, will be identical: ( ) ( ) ( ( )) for i = 1,, n (5) Alternatively, if the utility level of the dual problem coincides with the solution to the original problem, the bundle of goods chosen by the consumer will be the same in both problems, and the expenditure minimized in the dual problem will be equal to the available income in the original problem. Now let us consider two goods, i and j. If we differentiate eq. (5) with respect to the jth price, use Shepard s lemma and then rearrange, we obtain the Slutsky equation (Gravelle and Reese, 1993): (6) which links the Marshallian and the Hicksian demand functions. Taking, that is, considering the effect of a price change on its demand, the slope of the Marshallian demand is the sum of the substitution effect (the first term of eq. 6) and the income effect (the second term of eq. 6). Finally Roy's identity allows us to obtain the Marshallian demands from the indirect utility function as follows: ( ) ( ) (7) 1.2 The EASI demand system and Engel curves The EASI demand system has the particular advantage that it allows any shape of Engel curves. An Engel curve describes how the quantity of a good bought by a consumer varies as his total financial resources, such as income or total expenditure, vary. In most work, including the present paper, total expenditure is used to separate the problem of resource allocation from the decision of how much of current income to save. Engel curves can be used to calculate the income elasticity of a good, and they may depend also on demographic variables and other consumer 7

8 characteristics. Engel curves frequently are expressed in the form of budget shares [ ( ) ] where is the share of total expenditure that is spent buying the good j, x is the available resources and z is a vector of other consumer characteristics such as household composition. The EASI model is used because it allows us to maximize utility without restrictions in the rank of demand and, therefore, each Engel curve might have a different shape, which is closer to reality. 2 There is another important issue which is that the configuration of budget shares and households consumption choices do not depend only on relative prices and spending power, that is, the income available for spending; they depend also on household social and demographic characteristics. These characteristics affect the household s consumption preferences and demand for each good, which are different for each household. This is the problem of heterogeneity in consumer preferences. Given that certain household characteristics are observable, but others are not, there exists a type of preference heterogeneity that can be observed and another type that cannot. A problem common to many models of consumer demand is the absence of unobserved heterogeneity in consumer preferences or the difficulty of including it in a coherent fashion. In these systems, the observed variables, such as price, expenditure and household demographics, often explain less than half the variation in budget shares, leaving the rest to errors and unobserved preference heterogeneity, which latter cannot be represented by error terms interpreted as random utility parameters. The EASI demand system solves the problems of the shape of the Engel curves and the unobserved preference heterogeneity, maintaining the simplicity of the AID model family, but gaining flexibility. The strategy followed by Lewbel and Pendakur (2009) is to define Hicksian budget-share functions in the right side of the equation and to find an observable function of prices, expenditure and budget-shares that equals utility, and to substitute that function in the Hicksian demand. Define x as the nominal total expenditure of the consumer, and ( ) as the vector of prices faced by the consumer. Assume the consumer chooses a bundle of goods, described by the vector of budget shares ( ), that maximizes his/her utility u given the budget constraint. Consider also a vector of the consumer s demographic characteristics ( ), and a vector of unobserved consumer preference parameters ( ) to be considered as the error term in the cost function. 2 The rank of a demand system can be seen as the dimension of space crossed by its Engel curves. Gorman s (1981) rule says that utility is maximized if demands have rank three or lower. Gorman was referring to exactly aggregable demand systems, but over time the rule has been applied to all demand systems. It has been demonstrated (Lewbel, 1991, 2003) that utility maximization is not violated at higher ranks. 8

9 Let ( ) be the cost function giving the minimum total expenditure for a consumer with observed heterogeneity (included in the characteristics z) and unobserved heterogeneity (included in characteristics ) to attain a utility level u facing price p. Combining these elements we obtain the EASI cost function as follows: ( ) ( ) ( ) (8) where are the Hicksian budget share functions, J is the number of goods categories and relative budget shares and u is the utility. 3 Through Shephard s Lemma, the Hicksian functions of budget shares are found to be: ( ) ( ) ( ) (9) where ( ) ( ) for all j, k. After some substitutions, we obtain the implicit EASI Marshallian budget shares: ( ( ) ) ( ) (10) These budget share functions have the distinctive property of not being constrained by Gorman s rank restrictions and, therefore, can have any shape over y. This means that the demand system can have any rank, that is, each Engel curve may be a different shape. Lewbel and Pendakur (2009) propose an extension to the EASI model that includes interactions among utility, demographic characteristics and prices. With the inclusion of the interaction terms, the new EASI cost function becomes: ( ) ( ) ( ) (11) Using Shephard s Lemma the implicit utility is derived as: 3 Subscripts j and k identify two different categories and show that the budget share of a category depends also on the prices of the other categories. 9

10 ( ) (12) After parameterizing the system and simplifying, the implicit Marshallian budget shares are as follows: (13) where: (14) is relative implicit utility. The EASI demand system can be estimated efficiently using GMM. However, I use the 3SLS linear endogenous estimation method which is a good linear approximation of GMM. 4 I follow Lewbel and Pendakur s (2009) choice of instrumental variables and, thus, include the log of prices, demographic variables and the log of total expenditure. The budget shares in equation (13) are used to build the Engel curves, which are the object of the empirical Section 3.1. An Engel curve describes how consumer s purchases of a good vary with his total resources (income or total expenditure). They are frequently expressed in budget share form (Lewbel, 2006). The main characteristic of the Engel curves estimated with the EASI system is that they are very flexible in the tails of the distribution where the sample dimension is small, unlike the AIDS model which obtains good results for the centre of the distribution, but is not accurate if there is non-linearity in the tails. Finally, since EASI demands are derived from a cost function model, given the estimated parameters, the model gives simple closed form expressions for consumer surplus calculations, such as the cost-of-living index for large price changes. The cost-of living index is defined as the difference between two cost functions (eq. 11) associated with a price change from to : 5 ( ) ( ) (15) 4 The endogeneity problem arises from the presence of budget shares in both sides of equations (9) and (12). 5 For more details see Lewel and Pendakur (2009, p. 835). 10

11 2. The data Estimation of the EASI demand system requires information on expenditure and prices by type of good. Italy s ICF provides very detailed data on household expenditure and a number of household socio-economic characteristics. Similar to other budget surveys, it does not provide indications of the prices paid by consumers. Prices for each category of goods are available from national statistical offices in the form of price indices. These price indices are the input used to build the overall Harmonised Consumer Price Index (HCPI). The two datasets, ICF and the HCPI series, need to be linked, so that each category of expenditure can be associated with its price index. The following two subsections describe these datasets and the problems encountered in linking them. 2.1 The Household Budget Survey The ICF is the most important source of data for analyses of household expenditure on goods and services. It provides detailed data on expenditure items and the characteristics of household members. The survey provides a satisfactory picture of changes in the level and structure of expenditure by households social and economic characteristics, housing choices and spending habits. The unit of the survey is the household, and is administered each year to some 28,000 households in approximately 480 Italian municipalities (the smallest Italian administrative territorial grouping) of different demographic sizes. The objective of the survey is collecting the costs incurred by households resident in Italy to buy consumption goods and services, such as food, housing costs, furniture, appliances, clothing, footwear, health, transport, communications, leisure, entertainment, education, holidays, etc. In addition to information on individual expenditure, the survey asked about household characteristics such as household size, age and professional status of its components, and area of residence, all of which elements might influence household spending behaviour. These and other characteristics constitute the set of household socio-economic variables, which are important for explaining the different choices related to the allocation of the family budget. The period covered by this study is 2005 to 2010, and includes a total of 140,820 households. This time frame was chosen first because it is reasonably long and, therefore, provides a good overview of the evolution of consumption, and second because during this period there were no substantial changes to data collection and data processing methods, which ensures comparability 11

12 of the results over these years. Also important is that this time frame includes the years before the economic crisis, its onset, and the first signs of its persistence. Aggregation of goods into clearly defined, non-overlapping categories in the ICF is needed to merge this dataset with the HCPI and proceed with the analysis. The aggregation of the goods in the ICF is constrained by the breakdown in HCPI by type of good, which follows the COICOP (Classification of Individual Consumption by Purpose). We conform to the COICOP to aggregate expenditure items in the ICF. The main limitation of this classification is that, since it was designed to compute the price index, it has no one-to-one correspondence with the goods covered by the ICF. However, this classification is the best available instrument to associate expenditure items with prices and allows also for comparability over time. 2.2 Price indices and their association with the ICF The next important - and delicate - step is to find the best possible association between the goods and their prices. For prices we use the sub-indices that comprise the HCPI. The HCPI is compiled by Eurostat and national statistics institutes in accordance with harmonized statistical methods, to monitor inflation in Europe. I decided to adopt this index because it reflects the price actually paid by consumers as opposed to indices that reflect the total sales price. This distinction is important in the case of medical care, for example, where the HCPI registers only out-of-pocket expenses, excluding the amount charged to the National Health System (an important component in the case of some medicines, which could bias the estimates). Breaking down the HCPI by purpose of consumption or type of good, is done following the COICOP, the nomenclature developed by the United Nations to classify and analyse individual consumption expenditure by households, non-profit institutions serving households, and government, according to its purpose. It was adapted to enable compilation of the HCPI for the European Union. Expenditure is categorized into 14 divisions. The first 12 are related to household consumption: 1. food and non-alcoholic beverages; 2. alcoholic beverages and tobacco; 3. clothing and footwear; 4. housing, water, electricity and fuel; 5. furniture, items and services for the home (furniture, electric appliances, glassware tableware and utensils, tools and equipment for house and garden, goods and services for ordinary house maintenance etc.); 12

13 6. health services and health care expenses (medicinal and pharmaceutical products, nonhospital medical services, hospital services); 7. transport (purchase transportation, operating costs of transportation, transport services); 8. communication (postal services, telephone equipment, telephone services); 9. recreation and culture (audio-visual and photographic equipment, other durables for recreation and culture, books, all- inclusive package holidays, etc.); 10. education; 11. accommodation and food services (restaurants, canteens, hotels, etc.); 12. other goods and services (toiletries and cleaning goods and services, personal services, insurance and financial services, etc.). In 2005, to conform to the Eurostat standard, the structure of the Consumer Price Index (CPI) changed from a fixed base where the base year remains unchanged for a certain number of years, to a chain structure where the base year changes every period, thus, changing the weight system annually. In order to associate each item of the ICF to each price index, I follow the association table provided by ISTAT which is based on the COICOP classification. However, as already noted, the two datasets have no item-to-item correspondence and, therefore, 36 goods are excluded. These goods also cannot be associated with a price index either because they are not included in the price index basket or because the definition of the categories does not find exact correspondence in the two datasets making them not uniquely or directly connectable. There are other goods that are excluded from the analysis. Since imputed rents are not included because they are not part of the price domain, we need also to exclude the real rents for main and secondary dwellings. Durable goods are also excluded because of their nature 6. First, they are an exceptional outlay, which makes it difficult to analyse the evolution of their purchase over time, and they are characterized by a particular sensitivity to price changes. In addition, since they relate to a relatively substantial share of the household budget, their inclusion in the estimates would produce peaks in a particular time frame and in a particular category of goods that could hide the dynamics of expenditure on all other goods. All these factors would bias the estimates. 6 The exclusion of durable goods and rents requires an intervention in the chain price index because this is built and weighted for a bundle of goods that includes durable goods and rents. 13

14 Table 1 Monthly expenditure (euro) before and after the ICF-HCPI merge and relative loss (%) average original data (HBS) after the merge HBS-HICP loss from the merge (%) Table 1 reports the loss in terms of monthly expenditure imputable to the exclusion of nonconnectable goods, rents and durable goods: the loss is significant since it represents around 33% of total expenditure. Unfortunately the structure of the data does not allow a different outcome. 2.3 Descriptive statistics After merging the two datasets we obtain a sample of 103,600 observations for the period , and an average value of expenditure of 1,652 (Table 1). As we can see the monthly average expenditure was increasing before the crisis broke in 2007, and continued to rise up to The first signs of the effect of the crisis on household consumption emerge in 2009 when it began to fall. Table 2 Budget shares by category of expenditure (%) average Food and non-alcoholic beverages Alcoholic beverages and tobacco Clothing and footwear Housing, water, electricity and fuel Furniture, items and services for the home Health services and health care expenses Transport Communication Recreation and culture Education Accommodation and food services Other goods and services Total expenditure Table 2 shows budget shares by category during the years Basic needs (the categories including food and non-alcoholic beverages and housing expenses) slightly increased between 2005 and 2010 relative to the other categories. Most of the other categories remain 14

15 constant over the years, with luxury goods (clothing and footwear, recreation and culture) slightly decreasing. 3. Estimation results This section presents the estimations of the Engel curves represented as budget shares (see equation 13) derived from the EASI model using Italian ICF data for the period Some goodness-of-fit measures are discussed. A preliminary round of estimates was performed on all 12 expenditure categories. The estimated Engel curves of two categories Education and Culture and recreation have the same shape (spending behaviour on these categories is homogeneous) and, therefore, are grouped together. The category Expenditure on food services is included in the residual category because the spending pattern is highly variable among the population. Healthcare requires a separate discussion. The National Health Service finances the majority of health care costs, leaving individuals responsible only for a small portion of the total price. So demand is very much influenced by exogenous factors and less by the structure of the service and its actual price. For this reason, the Engel curve for health services is included in the residual group, the ninth category. This led me to group the original ISTAT divisions into nine categories of expenditure: (1) Food and nonalcoholic beverages, (2) Tobacco and alcoholic beverages, (3) Clothing and footwear, (4) Housing and furniture, (5) Fuel and energy, (6) Transport, (7) Communications, (8) Education, culture and recreation, and (9) Other goods and services. The budget shares in eq. (13) are a function of the following variables (see Table 3 for descriptive statistics): - demographic characteristics: age class of the older household component (15 age classes); a dummy variable to identify one-person households; average years of education of the parents; geographic area (North, Centre, South and Islands), with North as the reference category; a dummy variable to identify household with mortgage or rent; number of components; number of underage components; a time variable which identifies the year and month of the interview; - total expenditure; 15

16 - prices of the 9 categories of goods; - interactions between prices and demographic characteristics; - interactions between utility and demographic characteristics; - interactions between utility and prices. Estimation of the EASI demand system on nine categories of expenditure generated 800 estimated coefficients. This large number of coefficients is caused by their being 100 explanatory variables in each of the eight equations, 80 of which are interaction terms. To ease their reading and interpretation, the tables present only the estimates of the Engel curves (Section 3.1) and some measures of goodness of fit (Section 3.2), but not all the estimated coefficients. Table 3 Descriptive statistics of the variables used in the estimation No. of obs. Mean Standard deviation Minimum Maximum Dependent variables: budget shares Food and non-alcoholic beverages Tobacco & alcoholic beverages Clothing & footwear Housing expenses Fuel and energy Transport Communication Education, culture & services Other goods & services Explanatory variables: price indices of the expenditure categories Food and non-alcoholic beverages Tobacco & alcoholic beverages Clothing & footwear Housing expenses Fuel and energy Transport Communication Education, culture & services Other goods & services Explanatory variables: demographic characteristics Total expenditure (euro) Age class of the older component age age age One-person households Average years of education Geographic area Mortgage or rent Number of components Number of underage components

17 3.1 The Engel curves Fig. 1a shows the estimated Engel curve for Food and non-alcoholic beverages and the average budget shares computed on the sample. The horizontal axis shows the percentiles of the distribution of total household expenditure and the vertical axis shows the budget shares for the expenditure category. We can immediately see a decreasing shape of the Engel curve for food and non-alcoholic beverages. This tells us that households allocate an absolute value of expenditure to this category which is almost fixed (resulting in budget shares decreasing in total expenditure) and does not increase if total expenditure increases or increases less than the increase in total expenditure (and by extension, with the increase in total family resources). This is consistent with empirical evidence: when available resources increase, households do not need more food and drink - the amount consumed depends on the number of individuals in the household and on their physiological needs. If these stay constant, then food needs remain unchanged. There is a certain degree of freedom in the choice of quality and variety of food, but this has only a small effect on total household expenditure on this category. These results are in line with those obtained by Lewbel and Pendakur (2009), and with the most important literature on this topic (i.e. Perthel, 1975, and Chai and Moneta, 2010) and the empirical analysis conducted by Ernst Engel which allowed identification of the relationships that characterize the famous Engel's law of food consumption. The first category is a good example of the power of the EASI model; the budget share is not completely linear with respect to total expenditure and the tails of the distribution present some peculiarities that only the EASI system is able to capture. The budget share for Tobacco and alcoholic beverages is small, but the increase in this expenditure category is higher than the increase in total expenditure up to the 40 th percentile when its budget share slightly decreases while total expenditure keeps increasing (Fig. 1b). This result suggests that the expenditure on tobacco and alcoholic beverages depends very much on the available household budget: it is a luxury good when total expenditure is very low, increases more than proportionally with respect to total income or expenditure, then becomes a basic need for medium and high levels of total expenditure. For Clothing and footwear (Fig. 1c), we see that the budget share increases a lot compared to total expenditure. This may be due to the fact that although it is a basic necessity of life, it is also an instrument of social and self-affirmation and people choose clothing according to both their income and their needs. This reasoning applies particularly to Italy whose the textile and fashion industry imposes its law across the world and certainly affects the spending habits of Italians. 17

18 With regard to the fourth category, Housing expenses (excluding durables), the relative budget share decreases slightly up to about the 60 th percentile (Fig.1d), and increases in the right tail of the distribution. This result is consistent with the reality because spending on home accessories is highly dependent on the available household income. In contrast, expenditure on Fuel and energy for the household dwelling represents a higher burden more those on lower incomes since it is a fixed cost for all households, which is apparent in its Engel curve which is decreasing with respect to the log of total expenditure (Fig. 1e). Fig. 1 Estimated Engel curves (a) Food and non-alcoholic beverages (b) Tobacco & alcoholic beverages (c) Clothing & footwear (d) Housing expenses (e) Fuel and energy (f) Transport (g) Communication (h) Education, culture & services (i) Other goods & services The Engel curve for Transport increases significantly with expenditure (Fig. 1f): this might be because people travel more if financial resources allow it, although there is a fixed 18

19 proportion of expenditure for necessary transfers. In addition, this category includes the operating costs of household transportation means, which are related to the household s spending capacity. The Engel curve for Communications is decreasing (Fig. 1g), explained by the fact that an increase in total expenditure does not necessitate more letters or more telephone calls; these costs may be linked to job type and, thus, only indirectly to income. The estimated budget share for Education, culture and recreation grows with the increase in total expenditure (Fig. 1h), which is as expected given the nature of these goods, which are not considered basic necessities and in some cases are luxury goods. The ninth category, the residual category, includes very different goods and services (financial services, health care expenses, etc.) making it difficult to define a law that regulates the Engel curve (Fig. 1i). In general, it is clear that this category includes luxury items. 3.2 Goodness of fit Table 4 presents some measures of goodness of fit. Five of the eight estimated equations have an R-squared varying from a maximum of 0.32 in the first equation ( Food and non-alcoholic beverages ) to a minimum of a 0.13 in the eighth ( Education, culture and services ). These values could be considered low, but recall that a low R-squared for regressions using microdata is not uncommon. Therefore, we can define these R-squared values as satisfactory. However, for three equations ( Tobacco and alcoholic beverages, Clothing and footwear and Housing expenses ) the R-squared is lower than 0.1, which is very low and not satisfactory. We cannot consider only the R-squared because on its own it does not provide sufficient evidence of regression quality. 7 The Chi-squared tests on the joint significance of all the parameters in each equation provide further evidence of the model s goodness of fit: for all eight equations the test is significant at the 99% significance level. Table 4 Goodness-of-fit: R-squared and Chi-squared tests of the 3SLS estimates Equation Obs Parms RMSE R-squared CHI-squared P-value s s s s s s s s Students who are first learning econometrics tend to put too much weight on the size of the R-squared in evaluating regression equations (Wooldridge, 2009, p. 41). 19

20 To obtain additional information on the goodness of fit of the model, I tested the statistical significance of the model by group of coefficients, via the Chi-squared tests. The tests are applied to each equation and to the following groups of coefficients: utility functions, demographic characteristics, prices, interaction between prices and demographics, interaction between utility and demographics and interaction between prices and utility. The choice to test the coefficients by group is driven by the fact that checking the statistical significance of all the 800 estimated coefficients would be impractical and difficult to understand. Table 5 Goodness of fit: joint CHI-squared tests Equation utility demo char. prices price*demoutility*demo utility*price S1 S2 S3 S4 S5 S6 S7 S8 CHI-squared p-value CHI-squared p-value CHI-squared p-value CHI-squared p-value CHI-squared p-value CHI-squared p-value CHI-squared p-value CHI-squared p-value Table 5 summarizes the results. We see that the coefficients are jointly significant with the exception of prices in equation S2 ( Tobacco and alcoholic beverages ). This is possible despite the presence of single non-significant coefficients because, within each category of coefficients, there is at least one that is very significant with a very high value of z which then cancels out the nonsignificance of all the other coefficients with a much smaller z in the joint test. For example, in the first equation, in the utility-prices interaction terms there are only two significant coefficients, ynp1 and ynp7 (interactions between the utility and the prices of Food and non-alcoholic beverages and Communication ), which, however, have z test values of respectively 8.91 and 8.39, compared to the other categories which have z values ranging from to Overall, we can be satisfied about the quality of the model and its estimates. 20

21 4 A policy simulation exercise: the cost-of-living index The EASI model is an efficient method to evaluate the effects on household consumption and consumption choices of changes to the tax system. For instance, we can simulate an increase in the prices of some goods in order to see which households are more affected by these variations. Here I propose an experiment to evaluate the economic significance of the model and compute the cost-of-living index of equation (15) in two cases: (i) a simultaneous 5% price increase in the categories of Food and non-alcoholic beverages and Fuel and energy ; (ii) a 5% price increase in the category Education, culture and recreation. Fig. 2 Cost of living index: increase in food and fuel prices In case (i), the increase weighs more on the lower part of the expenditure distribution, that is, on households with lower expenditure power (Fig. 2). The regressive nature of a price increase in these categories, which contain goods that represent an important share of the budgets of households with low total expenditure, is clear. These results suggest caution when contemplating for example an increase in VAT rates, because of the equity consequences, particularly if the increase applies to goods in the categories of Food and non-alcoholic beverages and Fuel and energy. In case (ii), we see that the increase is heavier in the right tail of the distribution, that is, for richer households (Fig. 3). If an increase in VAT rates was focused concentrated on these kinds of goods, this would reduce the regressive effect of the tax change. 21

22 Fig. 3 Cost of living index: increase in culture and recreation prices 5. Conclusions This paper applied the Exact Affine Stone Index demand system proposed by Lewbel and Pendakur (2009), to Italy s Household Budget Survey for the period , with the objective of investigating the relationship between expenditure by type of good and household total expenditure, through the Engel curves. Estimation of the equation system was carried out using a 3SLS procedure, a linear approximation of the GMM. The advantages of this demand system are several. It is flexible, it supports all Engel curve shapes, it considers unobserved preference heterogeneity, it adapts well to the data, and it produces statistically significant estimation results. The model can be used also to evaluate the effects of fiscal policy variations, allowing their impacts on household consumption to be checked. R-squared and Chi-squared tests give satisfactory results in terms of goodness of fit of the model. The model estimations provided interesting results that confirm previous studies of demand systems and Engel curves, for example, a greater weight of food, fuel and energy in the total expenditure of poorer households. The shape of the Engel curve for Food and non-alcoholic beverages is decreasing because households allocate an absolute, almost fixed, value of expenditure to this category, which is consistent with the empirical evidence. This category demonstrates one of the advantages of the EASI model, flexibility in the tails of the distribution. 22

23 Certain estimated budget shares such as Clothing and footwear and Education and culture increase greatly compared to total expenditure, while the Engel curve for Tobacco and alcoholic beverages is convex, increasing for poor households and decreasing for high levels of total expenditure. The Engel curve for the category Housing expenses is slightly decreasing up to the 60 th percentile and is increasing in the right tail of the distribution while the Engel curve for Transport is significantly increasing with total expenditure, and for Communications it is decreasing. Knowing the structure of household consumption and how consumers react to price changes is important for policymakers to build an equal and efficient system of indirect taxation. The EASI model turns out to be a good instrument for analysis and evaluation of indirect fiscal policies. The policy experiment with the cost-of-living index demonstrates the greater weight borne by the poorer sections of the population in response to a rise in the prices of food and fuel, which then causes a deterioration in the living conditions of these households which are already in a situation of economic hardship. This confirms the regressivity of an increase in the prices of these goods. In the context of further research, the analysis could be extended by adding the most recent waves of the survey, 2011 and 2012, and estimating the model for sub-periods (e.g , and ) to test whether the Engel curves changed before and during the different stages of the crisis. The analysis could be enhanced by creating groupings of goods more closely related to the Italian VAT structure which involves three different rates applied to as many groups of goods, in order to discuss and analyse the option to move goods from one group to another and tax them accordingly, an old debate amongst Italy s policy makers which resurfaced in 2012 when one of the tax rates was modified. 23