Price and Income Elasticities of Demand: The Importance of Domestic Production

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1 Price and Income Elasticities of Demand: The Importance of Domestic Production Carla Canelas François Gardes Silvia Salazar January 31, 2014 Abstract In this article, we propose a new method to estimate price effects on micro crosssectional data using full prices derived from Household Budget and Time Use surveys. This method is applied to a matching of Ecuadorian surveys containing separately monetary and time expenditures, as well as to a Gutemalan survey containing both monetary and time expenditures. The estimated price elasticities perform well compared to other methods, and they can be computed for different sub-populations, which is an important question for policy design and simulation methods. Keywords: Price elasticity, income elasticity, time-use. 1 Introduction The study of consumers behavior has been for long time one of the most important concerns in economic theory. Indeed, it provides an important insight on how economic agents react to shocks in prices and/or income. Since its Marshallian beginning, the consumer demand model has evolved to more complex systems like the Rotterdam model, the Almost Ideal Demand System and many others. Becker has transform consumers into producers and metamorphose the household from a simple agent to a small company producing its own final goods thanks to monetary commodities and time as inputs. However, implementing the estimation of demand system Paris School of Economics, Université Paris 1, Centre d Economie de la Sorbonne, Bd de l Hôpital, Paris, France. addresses: carla.canelas@malix.univ-paris1.fr, gardes@univparis1.fr, silvia-marcela.salazar-cadena@malix.univ-paris1.fr 1

2 in developing countries has become a challenge since there are almost no reliable sources of local price data and even when such a data exist it is very likely to be incomplete for all commodities other than food. Welfare policies are concerned about targeting different sub-groups of the population. For instance, the population on the lowest decile of the income distribution will certainly not react in the same way to changes in commodities prices as those in the highest deciles. So, in order to correctly evaluate the effects of these policies, one needs pertinent demand elasticity estimates to the target population. Unfortunately, most available demand elasticities are estimated from macro time-series, in particular due to the lack of prices data at micro level. Time-series data is in general considered as being not robust to the specification of the demand system, its stationarity conditions are frequently rejected for long-term series, and they give no information on the change of price and income effects according to the household characteristics. Since most macroeconomic and microeconomic simulations models, including computable general equilibrium models, use elasticities estimates for the calibration procedure, it is necessary to provide consistent estimations of these parameters. The introduction of time in the households production function Becker (1965) allows us first, to take into account the domestic production in the estimation of the demand system, and secondly, it makes this estimation possible for different categories of aggregated goods. In this paper, we examine various methods to compute price elasticities applying micro data and propose a new one that overcomes the problem of price data availability and includes the households domestic production in the estimates. See Gardes (2014) So, the objectives of this paper are twofold: first, to provide a method for the computation of consistent demand elasticities using micro data, and second, to investigate the possible differences in price and income elasticities once domestic production has been incorporated in the analysis. The organization of the paper is as follows: Section 2 presents a quick review on the different methods to estimate price elasticities, while our new estimation method is presented on Section 3. Section 4 describes the data, and Section 5 contains the results of an application to Ecuadorian and Guatemalan surveys, with particular attention to the differences in consumer response by education level. 2 Methods to Estimate Price Elasticities Price elasticities can be estimated: first, by the estimation of demand systems under Slutsky constraints, which is generally applied to macro time-series (because price variability is uncommon in micro datasets). This estimation generates usual problems: co-linearity 2

3 between relative prices changes, and aggregation biases whenever individual agents face different prices changes or have different preferences. Almost all price elasticities, which are presented in the literature, are estimated on macro time-series. Second, arc-elasticity can be computed between two periods characterized by large changes in prices, see Gardes and Merrigan (2011) for such an estimation of the price-elasticity for tobacco. They allow the comparison of price effects for different types of households. For instance, recently divorced and young appear as more responsive to a decrease in the price of cigarettes. Third, prices for a set of products can be computed using the individual budget shares as weight of the products prices: these aggregate prices are therefore individualized and can be used to estimate price elasticities on a cross section survey. This method initiated in remarks by Hicks and Stone and was fully discussed by Lewbel. It has been recently applied by Ruiz and Trannoy (2008) on the French Household Expenditures surveys and proved efficient, but perhaps not very robust. Moreover, weighting individual goods in a group by the budget share of each household in the survey means that these groups do not correspond exactly to the same needs (whenever the individual goods are not perfectly substitutable). Finally, Deaton (1988) proposed a method to compute price elasticities on cross-sectional micro-data using unit values, for surveys containing information on the quantities consumed and the value of expenditures. These unit values may incorporate a quality effect (an expensive bread may have a higher quality), which is removed by comparing the unit prices with average local prices. In this paper, we present a method which consists of computing full prices for individual agents, defined as the sum of the monetary price and a shadow prices corresponding to non-monetary resources such as time (see the corresponding sub-section 3). 3 Methodology Demand System Specification We use an Almost Ideal specification (an estimation using the quadratic form on logincome, gives very similar results as concerns price coefficients with some complication in the estimation method, see Banks et al. (1997) and Gardes et al. (2005). The Almost Ideal Demand System is the most commonly used model to estimate demand elasticities. One of the model main advantages is that even is the model is nonlinear, one can use a Stone price index to approximate the AI model to its linearize version LAIDS, so as to facilitate estimation. Three main problems are derived from this approximation. First of all, as pointed out by Pashardes (1993), the errors coming from that approximation can result in biased parameter estimates, which can be seen as an omitted variable. The bias is bigger when the AI model is applied to micro-data, because in this case the expenditure effects 3

4 are highly correlated with the demographic characteristics of the household and thus is very heterogeneous between households. In order to correct this bias, Pashardes proposes a simple reparameterization of the price parameter that circumvents the problem created by the stone price index. The second problem comes from the fact the approximation made to linearize the model generates error-in-variable, which yields to inconsistent SUR and IV estimates Buse (1994) finds out that the SUR estimates when iterated to the ML solution are not consistent nor asymptotically efficient. Buse also detected a bias in the 3SLS estimator due to a simultaneity problem. This arises as the expenditures shares in the Stone price index are correlated with the disturbances, and therefore it will be the case of the instruments used. The third and last problem is identified by Moschini (1995), and it concerns the non commensurability of the Stone price index, meaning that the price index is not invariant to changes in units of measurement. The latter does notably affects the approximation properties of the model, generating a major inconvenient. As the problem arises because the Stone price index does not fulfill the commensurability property, the price index must be changed to another one that actually satisfies this property. Moschini proposes 3 price indexes that allows us to overcome this problem: the Tornqvist price index, a modified Stone index (Paasche-like index) and a second modified Stone index (Laspeyres-like index). We suppose that full expenditure follows an optimization program based either on an utility function or a cost function. We therefore estimate the linearize AIDS for each commodity group as follows: ( y ω i = α i + β i log + m) n γ i j logπ j + λ i Z + ε i, (1) j=1 where i = 1,..., n denotes the different commodity groups, ω i the full budget share, y the household expenditure, π the full price of the different commodities, Z some socioeconomic characteristics of the household, and m is the Stone s price index after the correction by Pashardes (1993). All the estimates are perform under homogeneity, additivity, and symmetry constraints. Note that the demand system is estimated for monetary, time, and full expenditures, separately. Estimated parameters for each system of equations are shown in the Appendix. Definition of Full Prices The way in which full prices are defined allow us to overcome problems associated with price data availability, and in particular, to estimate price elasticities for every good and service for which exists a corresponding time expenditure. 4

5 Full prices are defined as the ratio of full expenditure over the monetary expenditure: with monetary price for commodity (activity) i as p i, monetary expenditure is: p i x ih. The time-use price writes w h t ih or min wage t ih according to the time valuation by the average opportunity cost for household w h or by the minimum wage rate. The monetary expenditure is p i x ih and full expenditure: (p i + w h t ih ) x ih or (p i + min wage t ih ) x ih depends on households characteristics by means of its time participation to activity i: t ih and its opportunity cost for time w h. We can measure the full price for activity i by the ratio of full expenditures over their monetary component: π ih = (p i + w h t ih )x ih p i x ih = 1 + w ht ih p i, which no longer depends on the quantity consumed x ih. Note that, under the assumption of a common monetary price p i for all households, this ratio contains all the information on the differences of full prices through w h and t ih (for instance its logarithm in the AI specification is approximatively equal to w h t ih /p i for small values of this product). Possible endogeneity in the full demand equations (between full expenditure for i: (p i + w h t ih ) x ih and the vector of full prices π ih for all commodities k) is corrected by defining prices by the alternative time valuation, for instance, minimum wage when full expenditures are computed with the opportunity cost. Derivation of Demand Elasticities Income Elasticity To proceed with the estimation, we have to overcome two main problems: first, the demand system for full expenditure cannot be similar to the equations for monetary and time expenditures. For instance, if these expenditures are supposed to follow a Working model, the budget shares depending on log income, as a reduced form of two Piglog cost functions for money and time allocations, their sum cannot be written in the same form. Writing the full income elasticity E f in terms of monetary and time elasticities E im, E it affords the formula: E i f = E im ω im ω i f k + E ω it it ω i f k 1 + k, (2) 5

6 where ω im and ω it are the monetary and time expenditures shares, k = Y t /Y m 1, and ω i f = Y m ω im + Y t ω it /Y m + Y t is the full budget share for good i, with Y t and Y m the total time and monetary mean expenditure respectively Second, quality effects are likely to exist in full prices and expenditures data as well as in unit-value data, since more time to consume the same quantity may induce a higher quality of the domestic production. Indeed, an increase (in the cross-section dimension i.e. between two households) of the full price for commodity/activity i may proceed either from the difference, between the two agents, of the opportunity cost w or from the difference of their time allocated to activity i. Both causes may increase the quality of this activity, by means of an increased productivity, which can be supposed to be positively related to w, or of the time devoted to i. Various methods have been proposed to correct this endogenous quality. In this paper we use the quality correction technique proposed by Cox and Wohlgenant (1986). Here, local prices are the individual full prices. Roughly speaking, the method consists on a regression of unit values on selected sociodemographic characteristics, such as region, household size, and household income. Quality adjusted prices for each commodity group, were then generated by adding the value of the constant to the residuals of the regression. Frisch Price Elasticity In absence of price data, Frisch (1959), has developed a method that allows to compute price elasticities derived from the values of the estimated income elasticities. The main drawback of this method lies on the assumption of strong separability among goods. Separability assumptions limit preferences but facilitate the estimation by restricting the substitutions between goods. The importance of this assumption relies on the fact that it is implicitly used in all demand system analysis based on a grouped set of commodities, such as the usual functional groups (food, transport expenditures, housing, etc). Strong separability is defined by an additive structure of, for instance, the direct utility: U(x) = n u i (x i ), i=1 corresponding to want-independent goods. The price elasticity for good i can be written in terms of the income elasticity of this good and of the Frisch income flexibility index ˇω 1 : E xi /π j = δ i j ˇω 1 ω i E xi /y ω j E xi /y(1 + ˇω 1 E x j /y), (3) 1 See Appendix for calibration of k 6

7 where δ i, j is the Kronecker index and the Frisch income flexibility index ˇω 1 equals the income elasticity of the marginal indirect utility. Hicks Own and Cross-Price Elasticity When prices or unit values are available, price elasticities can be directly calculated from price coefficients of the parameters of demand systems such as the Almost Ideal Demand System. Remark that when i = j we obtain the own-price elasticity. The formulas are as follows: Full Price Elasticity E xi /π j = ˆγ i j ω i + ω j δ i j (4) Monetary Price and Time Elasticities E xi /p j = E xi /π j p j x j π i x j (5) E xi /t j = E xi /π j w t j x j π i x j (6) Note that the full price elasticity is the sum of the monetary price and time elasticities. Valuation of Time In the economic literature, there is an ongoing discussion regarding the appropriated measure of the opportunity cost of time. We estimate our model using the minimum wage as the opportunity cost, which implies a uniform cost of domestic production for the whole population. Gardes (2014) presents a method to estimate the opportunity cost for time for each household using a domestic production scheme depending on the time and money used to produce each activity. 7

8 4 Datasets The primary sources of data for this study are the ENEMDU Encuesta Nacional de Empleo y Desempleo-(National Survey of Employment and Unemployment) from 2007 and the Family Expenditure Survey from 2006 for Ecuador. The ENCOVI -Encuesta de Condiciones de Vida- (National Survey about Life Conditions) from 2000 for Guatemala. The sampling unit is a dwelling or housing structure, and information regarding the household or households occupying each dwelling is collected. We consider the household as the unit of analysis, and we work with a reduced sample of households that have either non-children or children aged less than 16 years old. We regroup time activities on nine categories for Ecuador, and eight categories for Guatemala, that are compatible with the monetary expenditure ones: Personal Care Time Personal Care Expenditure, Health Care Health Care Expenditure, Eating and Cooking Time - Food Expenditure, House Maintenance Time Dwelling Expenditures, Clothing Maintenance Time Clothing Expenditures, Education Time Education Expenditure, Transportation Time Transportation Expenditures, Leisure Time- Leisure Expenditures, and Miscellaneous Time - Miscellaneous Expenditures. Our key variables are defined as follows. The annual total expenditure of the household is divided by the square root of the number of persons in the household (to take into account possible economies of scale), as well as the total annual income, that we assumed as pooled within the household. The total expenditures per category is annualized for all of them by multiplying the expenditure of each item by the frequency of consumption reported. The demographic variables includes education and age of the head household, the logarithm of the household size to account for possible non linearities on demand, we also include a dummy variable equal to one for the families with kids and finally another dummy variable for the families living in couple. Prices were not provided in the corresponding surveys, but the definition of full price allowed us to obtain unit values for each commodity group. Since unit values are generally assumed to reflect quality effects, following Cox and Wohlgenant (1986), we adjusted for quality differences among households by regressing unit values on selected sociodemographic characteristics, such as region, household size, and household income. Since not all households purchased all commodities during the survey period, prices were not observed for non-consuming households. Whenever this was the case, the mean price was used instead. In order to value the time spent on domestic activities, we impute the wages for the nonworking individuals by the Heckman procedure, and we adjust all the wages for income tax. We compare the results with those ones obtained when the legal minimum wage is used. 8

9 Finally, aware of the possible endogeneity between total expenditure and the expenditure shares of the individual commodities that enter the demand model, we instrumented household total expenditure by household revenue. Ecuador Given data unavailability, we could not obtain monetary and time expenditures of the unit of analysis from the same source of information, so we proceeded with a matching of two different surveys by a Tobit regression (the selection equation concerns the households which have a positive time use of their activities) on similar characteristics in both datasets. For each activity on the Time Use survey, we impute time estimates for all the observation in the Family Expenditure Budget Survey 2. Summary statistics of household demographic characteristics are presented in table A.1 on the Appendix. On average, urban households represent 59% of the sample, and the average age of the household head is 42 years all. Level of education is low, with 53% of the household heads attaining primary education or less. Guatemala The Guatemalan survey contains both, the monetary expenditures made by the household and a record of its allocation of time over all types of activities. Any price distortions caused by the Guatemalan civil war that ended in 1996 are expected to have disappear by the year 2000 (when the survey takes place). Summary statistics of household demographic characteristics are presented in Table A.3 on the Appendix. On average, urban households represent 45% of the sample, the average age of the household head is 38 years all. Level of education is extremely low, with 77% of the household heads attaining primary education or less. Sample Statistics A quick look at the sample statics of Tables A.2 and A.4 on the Appendix (Section AppendixA) shows the differences between the Ecuadorian and Guatemalan population and sub-populations. Partitioning the data by educational attainment allow us not only to compare the parameter estimates between different income levels (lower levels of education are associated with lower levels of family income), but also gives us an interesting overview of the differences on the standard of living within each country. 2 See matching estimates on the Appendix 9

10 Roughly speaking, the richest group of the population, those with tertiary education, has on average an annual equivalent income of 5,072 american dollars in Ecuador, and of 56,278 quetzales in Guatemala, while the average annual equivalent income for the poorest group (primary education) is 1,578 dollars, and 9,640 quetzales, respectively. That is, a family with a household head that has attained some level of tertiary education has, in average, an equivalent income 3.2 times greater than a family on the group of primary education. The situation is more striking for Guatemala, where the difference in income between households on the tertiary and the primary education groups is 5.8 times greater. It is worth notice, that 53% and 77% of the population in Ecuador and Guatemala, respectively, have attained at most primary education, if any. These statistics reinforce the robustness of the estimates of the income elasticity on education for Guatemala, which point out that education is a luxury good for the poorest households in the sample. Important differences can also be observed in the residence region of the poverty group (primary education). For the case of Ecuador we found that 59% of this group resides in the rural area of the country against an 11% of the richest group. For Guatemala we found similar values: 66% of the poor are concentrated in this area, against 10% of the richest population. 5 Results Notice that the estimated elasticities are calculated on the base of full prices, which contain time and monetary expenditure. For interpretation of the results, we will assume that changes on prices refer to the monetary part of the price, while changes on income correspond to changes in others sources of income, and not wages, which otherwise will immediately change the cost of time. Interpretation for changes of wages should be done in the same way, that is, keeping the monetary part of the price constant. As mentioned above, we regroup time activities and monetary expenditure in nine different commodities for Ecuador, and eight for Guatemala. We also homogenize the sample as much as possible by withdrawing, for instance, extended families. However, problems regarding the estimation of certain goods still persist. For example, the aggregate good education may have a higher monetary expenditure, and it will probably be more time intensive for families with young children, than for a couple of seniors. Such problems should disappear by the correct identification of the target group, and the definition of aggregate goods (which is based in the good sense of the researcher). For the present analysis, we have decided to present the results for the whole sample, and different sub-populations for all the commodity groups, including the sensitive ones, so the interpretation of the estimates of such goods (i.e. education, health, etc) must be 10

11 done it carefully. We present the results for the price and income elasticity for the Ecuadorian and Guatemalan surveys in the Tables underneath. Table 1 shows the monetary and full income elasticities whereas Table 3 presents the Frisch price elasticities estimated under separability, and the compensated direct elasticities obtained from the estimation of the demand system under symmetry constraints. The Frisch estimation is calibrated by the inverse of the income flexibility at -0.5 (as predicted by Frisch and estimated by Theil. SeeSelvanathan (1993)), and the compensated price estimation presented in the table below is corrected from quality effects according to the method developed by Cox and Wohlgenant (1986). Two important results come out from the estimations. First, all income and price elasticities are significantly different from zero and range from -1.5 to 0. The value and magnitude of the estimates, is consistent with the others microeconomic elasticities estimates. Secondly, as expected the quality correction decreases the magnitude of the price elasticities by 15-20% in both countries (not shown in tables). Indeed, as explained above, when the quality effect is corrected, the price elasticity becomes smaller as the quality effect that was incorporated in the price is now cleared out. Since the analysis of welfare policies is concerned about different sub-groups of the population, i.e. income and price elasticities may change at different levels of income, we reestimate the model by educational attainment, which is a consistent exogenous way of regrouping the population. Table 1: Income Elasticities, Whole Sample Commodity Groups Income Elasticities Ecuador Guatemala Monetary Full Monetary Full Food Housing Transport Clothing Personal Care Health Education Leisure Others Regarding monetary and full income elasticities, Table 1 shows the different behaviour between Ecuadorian and Guatemalan societies. Ecuadorian income elasticities are higher 11

12 than those of Guatemala, indicating the bigger dynamism of the Ecuadorian population. Most of its goods have an unitary demand that is, an increase in income generates a proportional increase of demand for goods and vice-versa. Finally, only food, health, and education are necessary goods, while for Guatemala just transport and leisure are luxury goods, implying a more inelastic demand for the rest of commodities. It is worth noticing that at the population level, for both countries, food is a necessary good, as expected from theory, and leisure is mostly a luxury good. In general, the Ecuadorian full expenditure for goods is more time intensive than those of Guatemala. We observe that the income elasticities are smaller for the time intensive goods once the domestic production is taken into account. This is explained by the fact that the domestic production allows for an exchange between time and monetary goods. Indeed, if family revenue decreases, the income lost can be compensated by an increase in the time spent in domestic production and a decrease in monetary goods expenditure. Guatemala being a poorer country than Ecuador the substitution may be feasible only for the richest population (those in the group with tertiary education), since the monetary constraint is stronger for poorer households. Commodity Groups Table 2: Full Income Elasticities by Education Level Education Level Ecuador Guatemala Primary Secondary Tertiary Primary Secondary Tertiary Food Housing Transport Clothing Personal Care Health Education Leisure Others The Guatemalan income elasticities for each education level deserve particular attention. The estimates of the households that have attained at most primary education, are considerably bigger than the ones from secondary and tertiary education. As it can be seen on Table A.4 on the Appendix, the population having attained at most primary education is the poorest one, so it is not surprising that education and leisure has become 12

13 a luxury good for them (both in the monetary as well as in the full dimension). What is striking is that as expenditure is considered at the household level (this commodity mostly comprises the expenses on children education), when income decreases kids are directly affected, leading to a downward spiral for the poorest population. As expected, the non-compensated price elasticities (not shown in tables) are bigger than the ones compensated of the income effect. The cross price elasticities shown on Tables A.5 and A.6 of the Appendix, are pretty low and positive in general. The small substitution across different groups of commodities is not unusual on the literature, this effect can be accentuated by the incorporation of domestic production as we are also taking into account the substitution between goods and time. However, given the small coefficients of cross price elasticities, the separability hypothesis may hold for this kind of data. The estimates of price elasticities under the separability assumption (Frisch elasticities) are much lower compared to the compensated price elasticities. The former ones oscillate around 0.5, while the latter ones around 1, this gap is even more important and clear in the case of Ecuador. Therefore, we have a strong suspicion of non separability between the different groups of commodities. If the Frisch price elasticities are estimated under the separability assumption and the compensated ones are not, one can run a Hausseman test on separability between the two estimates, to see if separability holds in the dataset. Since the difference in the two estimates is smaller for Guatemala, we computed this test on the Guatemalan dataset 3 and as expected, we conclude on the non-separability among commodities groups. Table 3: Full Own-Price Elasticities, Whole Sample Commodity Groups Full Own-Price Elasticities Ecuador Guatemala Frisch Compensated Frisch Compensated Food Housing Transport Clothing Personal Care Health Education Leisure Others See test results on the Appendix 13

14 On the other hand, the compensated price elasticities are bigger in Ecuador than in Guatemala, both being around 1. The Ecuadorian population seems to have a bigger dynamism and the demand is more elastic to price than in Guatemala. Ecuador shifted currencies from Ecuadorian sucres to dollars in the year 2000, after 3 years of crisis characterized by a high volatility and inflation of prices. This might explain the differences in dynamism and higher price elasticities compared to those of Guatemala. It is interesting to see that just food and leisure are inelastic to price for Ecuador. If we see the estimates from income elasticity, food is the only commodity that is inelastic with respect to changes in income and price. The case of Guatemala is different, the demand for all goods but transport, personal care, and health is price inelastic. But what is interesting to see is that in both countries, leisure is a superior good, so its consumption increases with income, but when prices change, the demand for it is inelastic. This can be explained by the fact that in Ecuador and Guatemala, in average, leisure is more time intensive compared to others goods. So, when income increases, its monetary expenditure increases as well; but when prices change, demand is little sensitive since time may still be consumed by the same amount. That is, time consumption on a good i does not necessarily imply a monetary expenditure, it all depends on the elasticity of substitution for each good between time and money. Therefore, one can imagine that the elasticity of substitution for leisure is small. Table 4: Compensated Own-Full Price Elasticities by Education Level Commodity Groups Education Level Ecuador Guatemala Primary Secondary Tertiary Primary Secondary Tertiary Food Housing Transport Clothing Personal Care Health Education Leisure Others When we have a look at the full price elasticities for the different education level, we observe that the more educated people (i.e the wealthiest ones) are more sensitive to price variation than its counterparts, this is mainly due to the importance of the monetary 14

15 constraint of the poorest population. The wealthiest population has a bigger maneuver concerning its monetary expenditure than the poorest one. The latter population has a binding expenditure constraint. Table 5: Decomposition of Compensated Own-Price Elasticities Commodity Groups Decomposition Ecuador Guatemala Full Monetary Time Full Monetary Time Food Housing Transport Clothing Personal Care Health Education Leisure Others Table 5 presents the results of the compensated price elasticity decomposed in monetary and time elasticities, for Ecuador and Guatemala respectively. It is interesting to see how the Ecuadorian results present a clear patter where the monetary elasticities represent in average one third of the full elasticities for all commodity groups. This pattern is not found in the Guatemalan case where the proportion of monetary and time elasticities change from one good to another. Common characteristics are found in transport, personal care, education, and leisure, where the values of the monetary elasticity are smaller than those of time elasticity for both countries. Tables A.9 and A.10 on the Appendix present the same results by educational attainment. The results from Guatemala show an interesting pattern. From primary to tertiary education, the monetary price elasticities are increasing in value for all goods but health, while the time elasticities are decreasing in value for all goods but leisure. Results from Ecuadorian sample concerning monetary price elasticities are quite similar. From primary to tertiary education, the elasticities are increasing in value for all goods but health and food. The pattern is less clear for the time elasticities. While food and education present and increasing pattern, other goods like transport, health, and others present a decreasing one. The rest of the goods remain more or less constant, with very small changes in values if any, for the three education categories. 15

16 Conclusions The effect of public policies on households consumption is primarily determined by the resulting changes in incomes and prices. Using Ecuadorian and Guatemalan surveys, aggregated commodity groups were analyzed from two different perspectives: a purely monetary one, and a second one (full expenditure) that allows to take into account the domestic production of the household through the incorporation of time on family expenditures. One of the goals of this paper is to provide consistent parameters estimates that can be used to calibrate macro and microeconomic simulations models, such as computable general equilibrium models. The method used in this article provide such estimates for different commodity groups in absence of real price data, solving in this way the problem of price data availability in most developing countries. Parameter estimates were used to obtain own-price and income elasticities for the different sub-samples divided by educational level. For most of the commodities, own-price elasticities are similar between the different educational level groups. Compensated price elasticities range from -1.5 and 0 which seems as correct estimations, but they are bigger in Ecuador than in Guatemala. Indeed, the Ecuadorian demand is more elastic to changes in price than the Guatemalan one, where just three commodities are price-elastic against seven for the Ecuadorian case. Full price elasticities were also decomposed in monetary price and time elasticities. In general terms, monetary price elasticities are smaller than time elasticities. In the case of Ecuador, they represent, in average, one third of the full elasticities for all commodity groups, while for the case of Guatemala no clear patter could be found. Regarding income elasticities, roughly speaking, the demand for the different goods is pretty elastic for Ecuador and inelastic for Guatemala. In general, the income elasticity is smaller once the domestic production is taken into account. This is explained by the fact that the domestic production allows for an exchange between time and monetary goods. That is, if the income of the family decreases, the aggregated good i that has become, in monetary terms, less affordable, can still be consumed if it is compensated by an increase of domestic production i.e, consumptions of meals at home increases while consumption away home decreases. All in all, results indicate that full elasticities differ from the monetary ones in a significant way, suggesting that the consideration of domestic production through the incorporation and valuation of time into the design of public policy can have a relevant impact on it. 16

17 References Banks, J., Blundell, R., and Lewbel, A. (1997). Quadratic Engel Curves and Consumer Demand. Review of Economics and Statistics, 79(4): Becker, G. S. (1965). A Theory of the Allocation of Time. The Economic Journal, 75(299): Buse, A. (1994). Evaluating the Linearized Almost Ideal Demand System. American Journal of Agricultural Economics, 76(4): Cox, T. L. and Wohlgenant, M. K. (1986). Prices and Quality Effects in Cross-Sectional Demand Analysis. American Journal of Agricultural Economics, 68(4): Deaton, A. (1988). Quality, Quantity, and Spatial Variation of Price. The American Economic Review, pages Frisch, R. (1959). A Complete Scheme for Computing All Direct and Cross Demand Elasticities in a Model with Many Sectors. Econometrica: Journal of the Econometric Society, pages Gardes, F. (2014). Full Price Elasticities and the Value of Time: A Tribute to the Beckerian Model of the Allocation of Time. Cahiers du Centre d Economie de la Sorbonne. Gardes, F., Duncan, G., Gaubert, P., Gurgand, M., and Starzec, C. (2005). Panel and Pseudo-Panel Estimation of Cross-Sectional and Time Series Elasticities of Food Consumption: The Case of US and Polish Data. Journal of Business & Economic Statistics, 23(2): Gardes, F. and Merrigan, P. (2011). Revisiting an Important Canadian Natural Experiment with New Methods: an Evaluation of the Impact of the 1994 Tax Decrease on Smoking, wp cirpée. Université du Québec à Montréal. Moschini, G. (1995). Units of Measurement and the Stone Index in Demand System Estimation. American Journal of Agricultural Economics, 77(1): Pashardes, P. (1993). Bias in Estimating the Almost Ideal Demand System with the Stone Index Approximation. The Economic Journal, 103(419): Ruiz, N. and Trannoy, A. (2008). Le caractère régressif des taxes indirectes: les enseignements d un modèle de microsimulation. Economie et statistique, 413(1):

18 Selvanathan, S. (1993). A System-Wide Analysis of International Consumption Patterns. Number 29 in Advanced Studies in Theoretical and Applied Econometrics. Kluwer Academic. 18

19 AppendixA Table A.1: Descriptive Statistics (Ecuador, Whole Sample) Socio-Economic Variables Variables Obs Mean Std. Dev Min Max Income per Capita ,962 2, ,134 Household Size Age Household Head Percentage Urban Households Ave. Number of Children Percentage Couples Primary Education Secondary Education Tertiary Education Ecuador data is shown in local currency, US dollars Table A.2: Descriptive Statistics (Ecuador, Subsamples) Socio-Economic Variables Variables Q1 Q2 Q3 Q Primary Secondary Tertiary Income per capita 553 1,320 2,258 5,673 2,073 2,664 2,104 1,577 2,599 5,071 Household Size Age Household Head Percentage Urban Households Ave. Number of children Percentage Couples Primary Education Secondary Education Tertiary Education Observations 1,871 1,889 1,852 1,870 1,607 4,688 1,187 3,988 2,302 1,192 Ecuador data is shown in local currency, US dollars Data shown in mean values 19

20 Table A.3: Descriptive Statistics (Guatemala, Whole Sample) Socio-Economic Variables Variables Obs Mean Std. Dev Min Max Income per Capita ,729 40, ,524,248 Household Size Age Household Head Percentage Urban Households Ave. Number of Children Percentage Couples Primary Education Secondary Education Tertiary Education Guatemala data is shown in local currency, Quetzales Table A.4: Descriptive Statistics (Guatemala, Subsamples) Socio-Economic Variables Variables Q1 Q2 Q3 Q Primary Secondary Tertiary Income per Capita 2,720 5,902 10,583 39,739 12,568 15,807 14,789 9,640 23,234 56,278 Household Size Age Household Head Percentage Urban Households Ave. Number of children Percentage Couples Primary Education Secondary Education Tertiary Education Observations ,127 2, , Guatemala data is shown in local currency, Quetzales Data shown in mean values 20

21 Table A.5: Ecuador: Full Cross-Price Elasticities. Minimum Wage, Whole Sample Cross-Price Elasticities Commodity Groups Food Housing Transport Clothing Personal Care Health Education Leisure Others Food Housing Transport Clothing Personal Care Health Education Leisure Others All respective elasticities are calculated using the sample means of the data Price elasticities are estimated under symmetry and homogeneity constraints Table A.6: Guatemala: Full Cross-Price Elasticities. Minimum Wage, Whole Sample Cross-Price Elasticities Commodity Groups Food Housing Transport Clothing Personal Care Health Education Leisure Food Housing Transport Clothing Personal Care Health Education Leisure All respective elasticities are calculated using the sample means of the data Price elasticities are estimated under symmetry and homogeneity constraints 21

22 Table A.7: Monetary Income Elasticities by Education Level Commodity Groups Monetary Income Elasticities by Education Level Ecuador Guatemala Primary Secondary Tertiary Primary Secondary Tertiary Food Housing Transport Clothing Personal Care Health Education Leisure Others Table A.8: Price Elasticities under Separability by Education Level Commodity Groups Education Level Ecuador Guatemala WS Primary Secondary Tertiary WS Primary Secondary Tertiary Food Housing Transport Clothing Personal Care Health Education Leisure Others

23 Table A.9: Compensated Own-Price Elasticities by Education Level Commodity Groups Ecuador Monetary Time Primary Secondary Tertiary Primary Secondary Tertiary Food Housing Transport Clothing Personal Care Health Education Leisure Others Table A.10: Compensated Own-Price Elasticities by Education Level Commodity Groups Guatemala Monetary Time Primary Secondary Tertiary Primary Secondary Tertiary Food Housing Transport Clothing Personal care Health Education Leisure

24 Table A.11: Ecuador: Time Imputation Variable Mean Std. Dev. Min. Max. Food Family Food Female wd Food Female we Food Male wd Food Male we Transport Family Transport Female wd Transport Female we Transport Male wd Transport Male we Personal Care Family Personal Care Female wd Personal Care Female we Personal Care Male wd Personal Care Male we Housing Family Housing Female wd Housing Female we Housing Male wd Housing Male we Clothing Family Clothing Female wd Clothing Female we Clothing Male wd Clothing Male we Health Family Health Female wd Health Female we Health Male wd Health Male we Education Family Education Female wd Education Female we Education Male wd Education Female we Leisure Family Leisure Female wd Leisure Female we Leisure Male wd Leisure Male we Other Family Other Female wd Other Female we Other Male wd Other Male we Data shown in local currency US dollars. wd: week day, we: weekend 24