Estimation and Simulation of consumption behavior

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1 Estimation and Simulation of consumption behavior

2 Lecture outline Consumption choice theory Models of consumption Cobb Douglas (C D) Linear Expenditure System (LES) Constant Elasticity of Substitution (CES) Almost Ideal Demand Systems (AIDS) Estimation Estimation An Example of Simulation: the VAT reduction on restaurants t in France

3 Consumption theory Consumer theory is very simple. Consumer choses the most preferred object among a set of feasible objects. Microeconomic theory wants to put some structure on what the objects are, on feasible sets, on preferences and on the process of choice Objects x C They are N dimensional vectors C is the choice set x could be, for example, monthly consumption bundle (x i is consumption of good i) Vector of aggregate expenditure in periods 1,2,...,N Vector of time spent in N consumption or work activities Vector of N characteristics of complex goods (memory capacity, Mhz, monitor size..) Preference on C We define R as the relation of weak preferences (xry x is at least as good as y) I means is indifferent (xiy) P strictly preferred (xpy) R is complete, lt i.e. for all x and y in C either xpy, ypx or xiy R is transitive if xry and yrz then yrz

4 Consumption theory (2) Other assumptions on Preferencesmay be Weak monotonicity (if x y implies xry) Monotonicity (if x>y implies xpy) Local non satiation (can always find a bundle preferred to x (close to x) Convexity Utility function (Debreu Theorem) If preferences are rational (complete and transitive) and C contains a finite number of element, it exists a real valued function u() such that xpy implies u(x)>u(y) ypx implies u(y) > u(x) u() is the utility function and represent the preferences xiy implies u(x) = u(y) Feasible set, or opportunity set The consumer may have preference defined over C but may really chose among a subset B B is commonly defined as a list of constraints, eg. the budget constraint B{ B={x:p x m} }, where p is N-dimensional i vector of prices and m is the budget B is called the budget set

5 Consumption theory (3) Ifwe can represent preferences by the utility function u(), then consumer choice can be interpreted as the solution to a maximization problem Max u(x), s.t. st x B Or Max u x, s.t. p x m The problem can easily be solved by the standard Lagrange g technique

6 Consumption theory (4) Existence of a solution If p>0 and u() is continuous the problem has a solution. This is so because B is a compact set (closed and bounded) and a continuous function has always a maximum on a compact set Unique solution If u() is strictly quasi concave the solution is unique. This is the case of convex preferences Demand functions The solution can be expressed as functions of p and m x * =x(p,m) (Marshallian or Walrasian demand functions)

7 Consumption theory (5) Indirect utility function V(p,m) Is the maximum utility attained with prices p and income m V(p,m) = max u(x) s.t. p x=m V(p,m) = u(x*), where x * is Marsh. demand However, it is not necessary to start from u(x), (), v(p,m) can be autonomously defined without reference to direct utility. In this case, it must respect the following properties: Non increasing in p, non decreasing in m Homogeneous of degree 0 in p and m Quasi convex in p Continuous for positive prices and income

8 Consumption theory (6) Expenditure function e(p,u) Is the minimum expenditure needed to reach utility level U when facing prices p e(p,u) = min p x s.t. u(x)=u (dual problem w.r.t. max U) Call h * = h(p,u) the solution to the expenditure minimization problem (Hicksian demand), then e(p,u) = p h* = p h(p,u) As V(p,m), it can be define without defining u(x). Then, it must respect the following properties Non decreasing in p and U Homogeneous of degree 1 in p Continuous in p Concave in p

9 Consumption theory (7) Relationship between v(p,m) and e(p,u) e(p,v(p,m)) = m The expenditure function evalued for utility level equal to the indirect utility function corresponds to the income V(p,e(p,U)) = U The indirect utility function evalued for income level equal to the expenditure function retourns the utility level x i (p,m) = h i (p,v(p,m)) TheHicksianevalued evalued for utility level equal to theindirect utility function correspond to the Marshallian h i (p,u) = x i (p,e(p,u)) The Marshallian evalued for income level equal to the expenditure function correspond to the Hicksian

10 Consumption theory (8) Shephard s Lemma and Roy s Theorem and their budget share versions Shephard s Lemma Budget share demand function Roy s Theorem Can proved that Budget share demand function

11 Consumption theory (9) One of the most interesting implication of Shephard s Lemma and Roy s Theorem is that in order to specify demand functions consistent with utility maximization, we do not have to start with u(x) Instead we can start with e(p,m) or V(p,m) and obtain the demand functions applying Shephard s Lemmaor Roy s theorem They permit also deriving demands one by one, while starting with u(x) a system must usually be solved Moreover, only special forms of u(x) can have closed form solutions, while even very general forms of e(p,m) and V(p,m) will have well defined df dpartial derivatived d

12 Models of consumption Cobb Douglas LES Linear Expenditure System CES Constant Elasticity of Substitution

13 Models of consumption (2) Almost Ideal Demand System (AIDS) Start from expenditure function Use Shephard lemma to derive budget shares demand where Several extensions to the AIDS are possible

14 Models of consumption (3) The demand dequations of the previous models dlgive rise to closed dform demand systems which can usually be estimated. For example, suppose that we have 3 goods: food, clothing and other goods. If we model consumption following the Cobb Douglas model we will have the following system It is possible to estimate such a system provided that data about quantities, incomes and prices are available Since β sum up to 1 and p x=m, the third equation is redundant and only 2 equations need to be estimated, with β 3 =1 β 1 β 2 Adding an Error term to each of the two remaining equations allows to estimale it with a SUR (Seemingly Unrelated Regression)

15 Models of consumption (4) The example eampleof the previous slide is sufficient to understand what can be estimated and which are the problems that arise when estimating consumption models Estimating a demand system means estimating a value for the parameters of the utility function, which means estimating the characteristics of preferences for the representative consumer Heterogeneity can be introduced in several ways: one easy way is to introduce demographic variables and environmental characteristics. Once estimated the parameters it is possible to recover income and prices elasticities, which are the change in demand due to an infinitesimal change in prices and income Elasticities i i can be calculated l analytically ll from the demand dfunctions, but when the formulas become complicated it is rather common to calculate it numerically Knowing the elasticities, it becomes easy to include a behavioral response in a MSM model They allow both to evaluate the response to a policy of change in prices (for example a They allow both to evaluate the response to a policy of change in prices (for example a VAT reform) or, indirectly, the response due to a reform which affects available income in some way

16 Models of consumption (5) One of the most common problem in estimating consumption models is about data availability: often prices are not available Sometimes prices are estimated using prices index historical series, but this works very poorly There is a procedure by Lewbel to estimate pseudo unit values that have prooven to work quite well Another problem is the choice of goods aggregation: it may be driven from reform evaluation necessities but it is a good practice to keep in mind that there may be good reasons to keep some good disaggregated (alcohol, tobacco...) Also keep in mind that high complexity and flexibility of the models implies high number of parameters to be estimate t (exponential lincrease with the number of goods) d) It can happen that for several goods zero expenditures are observed: this may be due to household choice but also to data collection problems A common solution, with its pros and cons, is to use a sample selection model to correct the potential bias that would emerge from estimates obtained including the zeros

Models of consumption (6) Estimates t of simple AIDS for France (11 goods only α and elasticities) iti drinks tobacco clothing housing health energy comm leisure out other food alpha 0.2149 0.1535 0.

17 Models of consumption (6) Estimates t of simple AIDS for France (11 goods only α and elasticities) iti drinks tobacco clothing housing health energy comm leisure out other food alpha s.e Income Elasticities Compensated prices elasticities drinks tobacco clothing housing health energy comm leisure out other food

18 The Regressive Impact of a VAT Tax Cut on French Restaurants: Lessons from a Microsimulation Model. Nicolas Ruiz, Idep Alain Trannoy, EHESS, Greqam-Idep "Microsimulation as a tool for the analysis of public policies: i methods and applications" Paris School of Economics,Feb

19 Restaurant: three VAT rates The standard rate 19.6% on restaurants, The reduced rate 5.5% on take away food, corporate canteens, Exempted: school canteens, university college canteens, retirement home canteens Food when eaten on the premises: 19.6% Take away food 5.5% When a restaurant offers both types of food, it should charge a different price. If not, and it is often so, a 14% additional margin 2

20 The ten-year VAT battle The argument of an unfair competition between big corporations and small restaurants The «musketeer» André Daguin boss of a powerful lobby : professional union of restaurateurs Before 2001, all canteens were exempted. In 1999, he prosecuted the GVT for exemption of all canteens (a decision of 1943!) and he won in 2001 (opposite to the European laws) The GVT refused to comply with and was finally condemned to pay penalties to the Restaurant Unions. New regime of tax rates for canteens 3

21 The European dimension Chirac in his presidential campaign in 2002 promised the application of the reduced rate of 5.5% to restaurants. But he was not able to do so without the permission of European Commission and a unanimity agreement among all the 27 countries Chirac did not obtain the permission. At least, Germany and Denmark vetoed. Sarkozy during his presidential campaign: «I have not promised it and yet, I will get it» A first «victory» : In July 2008, the European Commission has recommended to lower the VAT taxes for labor intensive services. A second «victory» 20th January : A pre-agreement between France and Germany about the list of services among which restaurants are included 4

22 «Laisse faire le temps, ta vaillance et ton roi» Le Cid, Corneille «Let time your courage and your King do the job» According to Daguin, the measure will be effective in 2011 The measure will cost about 3 Billion Euros to the Treasury What about the redistribution ib ti effects of these measures, including the behavioural responses? Lessons from a microsimulation model 5

23 Outline 1.The microsimulation model 2. Application to the VATrestaurant reform 6

24 The data basis Data basis : French Household Budget Survey every five years, 2006, 2000, 1995, 1989, 1985, households Non durable Expenditures: reported in a notebook during two weeks for every household member older than 14 Durables: face-to-face questionnaire Yearly expenditures, incomes, income sources and sociodemographics Weakness: no available quantities 7

25 The good list Build up a common list of goods and services for all surveys 71 items Two main determinants The same tax regime (VAT, excise duties) Individual price index available since the beginning of the survey Aggregate list of 8 items, Eating at home, Tobacco-alcohol Clothing Housing and energy Motorcar and transportation Leisure Eating out Miscellaneous 8

26 Ad valorem and excise taxes VAT, Insurance tax Excise on alcohol, petrol, Specific regime on tobacco We are able to compute the implicit equivalent ad valorem tax for every excise duty. Expression which gives the former in function of the latter for the aggregated expenditure reported in the survey 9

27 Two parameters 1) Value of VAT shifting rate on prices Depends on the degree of competition in the market Carbonnier : 77% for housing repair services 52% for new cars The parameter is free 2) Underestimation of expenditures according to Household survey with respect to national accounts Adjustment of aggregate expenditures to compute the correct impact on the GVT budget 10

28 What does the microsimulation model do? The gain or loss to each household resulting from the reform The Theil and Gini indexes and the Lorenz curve for the distribution of total household expenditure and taxes, before and after The total cost of the reform for the Treasury Introducing behavourial responses 11

29 Estimation of price and income elasticities Identification problem for price effects since no much price variability Utilisation of «Stone-Lewbel cross section prices» for identification of price elasticities Independently, Nicolas Ruiz in his thesis 2006 and Hoderlein and Mihaleva 2007 forthcoming in Journal of Econometrics. «Increasing the Price Variation in a Repeated Cross Section» We construct individualized prices, exploring individual specific variation in the composition of the bundles of goods. 12

30 The econometric model of demandd QAIDS model with sample selection for the presence of non consumers at the aggregate level (8 bundles of goods). Heckit estimation. Instrumentation of the total expenditure by income Correction for heterocedasticity 15

31 Precise formulation (except the selection) w, is the budget share of bundle i for the household h h i w ijh is the budget share of good j in bundle i for household h p ij is the price index of good j in bundle I N i ' X h X h w h, i = X h, iβ = αh, i + γ i wijh ln pijh lnp + βi ln + λr + u j P ln P = 1 α h, i = αi 0 + h m α h 2 i avec age of family head, occupation of family head, household composition, = m h location, season 16

32 Estimated elasticities at the sample average point (2000) Direct Price Elasticity Income Elasciticy Mills Ratio Eating at -0,81 0,721-0,426 home 0,169 0,057 0,32 Tobacco and - 0,522 0,398-0,117 Alcohol 0,097 0,062 0,059 Clothing - 0,527 0,888 0,031 0,066 0,026 0,014 Housing and - 0,383 0,67-0,269 Energy 0,15 0,059 0,167 M otorcar and , , ,015 Tranportation 0,01 0,016 0,128 Leisure - 1,306 1,212 0, , , ,018 Miscellaneous Eating out - 0,953 1,085-0,992 0,142 0,051 1,606-0,512 1,22 0,043 0,066 0,024 0,01 17

33 2. Impact of VAT tax cuts on restaurants The eating out bundle comprises 4 items (not the same as in 2000) Restaurant (eating on the premises) 19.6% Drinking on the premises (19.6%) Take away food (5.5%) Canteens (5.5% 5% when you work, 0 otherwise) We assume that the tax cuts will affect the first two items 18

34 Expenditure and taxes for each 4 goods Mean Min Max STD Spending on food at restaurant Spending on take away Spending on canteen Spending on drinks outside Taxes on food at restaurant Taxes on take away Taxes on canteen Taxes on drinks outside

35 Budget shares in the aggregate Shares wrt food Share wrt total spending away total spending Spending on food outside 2,08% 37,50% Spending on food outside to take away 0,29% 5,17% Spending on canteen 2,78% 50,18% Spending on drinks outside 0,40% 7,15% 20

36 The microeconomic impact of the reform Assumption that the decrease will be fully shifted to consumers Assumption not at tune with what restaurateurs said 1/3 for consumers 1/3 for investment 1/3 for employees. This assumption will at least maximize the distributional impact of the reform 24

37 Impact of the reform in the aggregate Agregated amounts After tax After tax Variation in % Before taxe changes Variation in % with changes with without changes without behaviour behaviour behaviour behaviour Spending on food at restaurant % -4% Spending on take away % 0% Spending on canteen % 0% Spending on drinks outside % -4% Taxes on food at restaurant % -70% Taxes on take away % 0% Taxes on canteen % 0% Taxes on drinks outside % -70% 25

38 Expenditure per decile Spending on food at restaurant Spending on drinks outside Deciles of income per consumption units Before After without After with Before behaviour behaviour After without behaviour After with behaviour ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% ,79% -4,15% -11,79% -4,15% 26

39 Distribution ib ti of total t tax gains per deciles Total Tax Gain Restaurant Total Tax Gain Drinking Decile of living standard Withou Elas With Elas Without Elas With Elas Total

40 Distribution of Average tax gain per household Average tax gain per household Restaurant Average tax gain per household Drinking Décile of livng standard 1 Without Elas -21 With Elas -20 Without Elas -8 With Elas Total

41 Distribution of average tax gain per household by socio-economic status Socio-economic status Farmer Independent workers Intermediary Executive Workers Non-employed Taxes on food outside Taxes on drinks outside After After After with Before without behaviour Before After with without behaviour behaviour behaviour ,94% -69,51% -71,94% -69,51% ,94% -69,51% -71,94% -69,51% ,94% -69,51% -71,94% -69,51% ,94% -69,51% -71,94% -69,51% ,94% -69,51% -71,94% -69,51% ,94% -69,51% -71,94% -69,51% 29

42 Distribution ib ti of total t tax gain by family size Types of households Single Single with children(s) Couples without children Couples with children(s) Spending on food at restaurant Spending on food outside to take away Spending on canteen Spending on drinks outside After After After After After with Before without behaviour Before After with without behaviour Before After with without behaviour Before After with without behaviour behaviour behaviour behaviour behaviour ,79% -4,15% 0,00% 00% 0,00% 00% 0,00% 00% 0,00% 00% -11,79% -4,15% ,79% -4,15% 0,00% 0,00% 0,00% 0,00% -11,79% -4,15% ,79% -4,15% 0,00% 00% 0,00% 00% 0,00% 00% 0,00% 00% -11,79% -4,15% ,79% -4,15% 0,00% 0,00% 0,00% 0,00% -11,79% -4,15% 30

Lecture 5. Varian, Ch. 8; MWG, Chs. 3.E, 3.G, and 3.H. 1 Summary of Lectures 1, 2, and 3: Production theory and duality

Lecture 5. Varian, Ch. 8; MWG, Chs. 3.E, 3.G, and 3.H. 1 Summary of Lectures 1, 2, and 3: Production theory and duality Lecture 5 Varian, Ch. 8; MWG, Chs. 3.E, 3.G, and 3.H Summary of Lectures, 2, and 3: Production theory and duality 2 Summary of Lecture 4: Consumption theory 2. Preference orders 2.2 The utility function