ECO 310: Empirical Industrial Organization Lecture 6 - Demand for Differentiated Products (III) The Almost Ideal Demand System

Transcription

1 ECO 310: Empirical Industrial Organization Lecture 6 - Demand for Differentiated Products (III) The Almost Ideal Demand System Dimitri Dimitropoulos Fall 2014 UToronto 1 / 29

2 References Deaton, A. and J. Muellbauer (1980). "An Almost Ideal Demand System," American Economic Review, Vol. 70(3), pp Hausman, J.A. and G.K. Leonard. (2002). The Competitive Effects of a New Product Introduction: A Case Study, Journal of Industrial Economics, Vol. 50(3), pp / 29

3 Demand For Differentiated Products: Motivation Most goods are differentiated, coming in a variety of brands, sizes, shapes, colors, flavours etc. With differentiated goods, we want to estimate the demand - in particular, the own-price and cross-price elasticity - for each product-variety. But this creates a "too-many parameters" problem. 3 / 29

4 Demand For Differentiated Products: Motivation We face a dimensionality problem in the estimation of demand for differentiated products. We seek ways to reduce the size of estimation problem Towards this end, we will impose structure on substitution patterns between goods so as two reduce the number of parameters The NEIO has focused on two different approaches to doing this: 1. Discrete Choice Models and the Characteristics Approach 2. Almost Ideal Demand Systems and A-Rriori Restrictions on Demand. 4 / 29

5 Demand For Differentiated Products: Motivation The Discrete Choice Models from the last set of lectures allowed us to estimate the demands for differentiated prodcut, under the assumption that these products only come in discrete units and consumers choose to consume at most one product But what about products that come in continuous units, or consumers purchase more than one product? The Almost Ideal Demand System will help for this later case 5 / 29

6 The Almost Ideal Demand Systems 6 / 29

7 AIDS One way to reduce the dimensionality of the estimation problem is to put more structure on the choice problem being faced by consumers. This is done by thinking about specific forms of the underlying utility functions that generate empirically convenient properties. Traditional approach is to use a model of multi-level budgeting Consider Good-Q which is offered in J different product varieties A consumer breaks his choice problem into two stages: 1. Decide how much to spend on Good-Q in total 2. Decide how to share this spending amongst the J different product varieties This two stage budgeting assumption places restrictions on substitution patterns, and thus greatly reduces the number of parameters. 7 / 29

8 AIDS - Economic Theory Consider a consumer who purchases L different goods, each good coming in many different product varieties Our focus is on the demand for the different product varieties of Good-Q Good-Q comes in J different varieties q 1,..., q J with prices p 1,..., p J Let X denote the Total Expenditure on Good-Q Let s j denote the Expenditure Share of Product j Let P denote the Price Index of Good-Q X = j p j q j s j = p j q j X log P = j s j log p j 8 / 29

9 AIDS - Economic Theory Stage 1. Expenditure on Goods In Stage 1 the consumer chooses the aggregate quantity of each of the L different goods to purchase The consumer is assumed to have "PIGLOG" preferences, and thus chooses the aggregate quantity of each good to minimize his expenditures while maintain his desired level of utility This results in a Top-Level Demand Function of the form log Q = δ 0 + δ 1 log Y + δ 2 log P where Q is the aggregate quantity of Good-Q Y is the total income/expenditre P is the price index of Good-Q 9 / 29

10 AIDS - Economic Theory Stage 2. Expenditure on Products In Stage 2, the consumer chooses how to allocate his chosen aggregate quantity of Good-Q amongst the J different product varieties. With "PIGLOG" preferences, the resulting Expenditure Share of Product j s j = α j + β j log X P + γji log pi i where s j is the expenditure share of Product j X is the total expenditure on Good-Q P is the price index of Good-Q p j is the price of Product j 10 / 29

11 AIDS - Economic Theory Stage 2. Expenditure on Products Note that, in the share equation s j = α j + β j log X J P + γ ji log p i the expenditure share of product j only depends on Good-Q variables. i=1 Moreover, economic theory imposes a number of parameter restrictions 1 Adding-Up: j α j = 1, j β j = 0, j γ ji = 0 Homoneity: i γ ji = 0 Symmetry: γ ji = γ ii The fact that the "bottom-level" demand for product j depends only on prices of the other products in its class, together with the parameter restrictions, significantly reduce the number of parameters to be estimated. 1 These formulas will not be tested 11 / 29

12 AIDS - Econometrics Suppose we have data from M markets on which we will estimate the demand for the differentiated products: To derive an econometric model through which we can estimate the various demands, we translate the economic model into a statistical model Our data: where {Y m, q 1m,...q Jm, p 1m,...p Jm : m = 1, 2,...M } Ym Total Income/Expenditure in City m qjm Quantity of Product j Sold in City m pjm Price of Product j in City m 12 / 29

13 AIDS - Econometrics Suppose we have data from M markets on which we will estimate the demand for the differentiated products: To derive an econometric model through which we can estimate the various demands, we translate the economic model into a statistical model Our data: {X m, (q 1m,...q Jm ), (p 1m,...p Jm ) : m = 1, 2,...M } From these we can construct Xm Total Expenditure on Good-Q in City m Qm Total Consumption of Good-Q in City m sjm Expenditure Shrare of Product j. in City m Pm Price Index of Good-Q in in City m 13 / 29

14 AIDS - Econometrics Stage 1:. Expenditure on Good-Q Top-level demand is specified in terms of the total quantity of Good-Q The Demand for Good-Q in Market m log Q m = δ 0 + δ 1 log Y m + δ 1 log P m + η m where the unobservable demand shock η m captures all other random factors which cause consumer spending on Good-Q to differ from the average. Note that this is a traditional linear demand function. Stage 2. Share Equations Bottom-level demand is specified in terms of the expenditure shared The Expenditure Share for Product j in Market m s jm = α j + β j log Xm P m + J γ ji log p im + ε jm where the unobservable product shock ε jm captures all other random factors which cause consumer spending on Product j to differ from the average. Note that sjm depends on the prices off all product varieties of Good-Q. i=1 14 / 29

15 AIDS - Econometrics Of course, what we are really interested is in elasticities: The own-price elasticity of demand for product j is 2 e jj = γjj βj sj + (sj + βj )(1 + δ2)sj s j 1 The cross-price elasticity of demand for product j w.r.t product i is 3 e ji = γji βj si + (sj + βj )(1 + δ2)si s j Note that these elasticities depend on parameters from both the "Top-Level" and "Bottom-Level" specifications. Nevertheless, ejj depends only on outcomes for product j, and e ji depends only on outcomes for products j and i 2 This formula will not be tested 3 Neither will this one 15 / 29

16 AIDS - Econometrics An issue which we will have to deal with in estimating this demand system is the usual simultaneity problem The demand shocks in the share equations capture the existence of factors unobserved to the econometrician but affect consumer demand However, these factors are observable both to consumers, and to firms in the industry. Now, prices and quantities are jointly determined by the interactions of consumers and producers in the market place. But demand depends explicitly on these demand shocks And firms will set prices by reacting optimally to demand Thus, prices in the demand equations are likely to be correlated with the demand unobservables The usual method to account for this potential simultaneity problem is they use of an instrumental variables. However, there are many products, with each s demand depending on the prices of all products So we will need many instruments. a different instument for the price of 16 / 29 each product variety

17 Hausman and Leonard (JIE, 2002) 17 / 29

18 Hausman and Leonard (2002) - Motivation Hausman and Leonard (2002). "The Competitive Effects of a New Product Introduction: A Case Study". Hausman and Leonard (HL) analyze the competitive effect of a new product introduction: namely, the introduction of "Kleenex Bath Tissue" into the toilet paper industry The empirical question set forth in the paper: "How much do consumers benefit from the introduction of a new product." To estimate the additional consumer surplus associated with the new availability to consumer of "Kleenex Bath Tissue", Hasuman and Leonard must first estimate the demand for bath tissue. 18 / 29

19 Hausman and Leonard (2002) - The Bath Tissue Industry In the 80s, the US bath tisse industry was an oligopoly of 4 major players vs. a competitive fringe Major Players: P&G, James River, Georgia Pacific, Scott Fringe: Supermarket "private labels" Bath tissue (BT) products fell into several quality tiers 1. Premium - Angel Soft (Georgia Pacific), Cottonel (Scott), Charmin (P&G), Nothern (James River) 2. Economy - Scott Tissue (Scott) 3. Private Label - Supermarket "No-Name" brands In 1991, Kimberly-Clark introduced Klenex Brand Tissue (KBT), a brand already associated with facial tissue, as new premium bath tissue 19 / 29

20 Hausman and Leonard (2002) - The Data HL make use of Panel Data to estimate the demand for bath tissue. The paper uses panel data Products: 7 brands of bath bissue Time: Weekly data - Jan. 92 to Sept. 95 (196 weeks) Markets: 30 Major U.S. Cities The data on bath-tissue sales and prices come from scanner data In each major U.S city, sample a number of supermarkets. From each supermarket, gather data from point-of-sale scanners. Scanning device records price and UPC code (identifying brand, style, size, etc.) of all sales transactions. 20 / 29

21 Hausman and Leonard (2002) - The Data HL make use of Panel Data to estimate the demand for bath tissue. Products: 7 brands of bath bissue Time: Weekly data - Jan. 92 to Sept. 95 (196 weeks) Markets: 30 Major U.S. Cities The data: 4 where {Y mt, (q 1m,...q 7m ), (p 1m,...p 7m ) : m = 1,..., 30, t = 1,..., 196} Ymt - total expenditure in city m during week t qjmt - quantity of brand j sold in city m during week t pjmt - price of Product j in city m during week t 4 Note: My notation differs slightly from the paper. 21 / 29

22 Hausman and Leonard (2002) - Specification As with any differentiated product, Hausman and Leonard face a dimensionality problem in the estimation of the demand for bath tissue. Hausman and Leonard get around the too-many parameters problem by using the two-stage budgeting framework of the AIDS model Stage 1: Expenditure on Bath Tissues Top-level demand is specified in terms of the total quantity of Bath Tissue log Q mt = µ m + µ y log Y mt + µ p log P mt + Z mtδ + η mt where Q mt - Total quantity of BT for city m in week t Y mt - Total disposable income for city m in week t P mt - Price Index of BT for city m in week t µ m - City m fixed effect Z mt - Vector of controls 22 / 29

23 Hausman and Leonard (2002) - Specification As with any differentiated product, Hausman and Leonard face a dimensionality problem in the estimation of the demand for bath tissue. Hausman and Leonard get around the too-many parameters problem by using the two-stage budgeting framework of the AIDS model Stage 2: Share Equations The lower level demand specification for the share of brand j is where s jmt = α jm + β j log Xmt P mt + J γ ji log p imt + Z mtθ j + ε jmt s jmt - Expenditure share of product j for city m in week t i=1 p jmt - Price of product j for city m in week t X mt - Total expenditure on bathroom tissue for city m in week t P mt - Price Index of BT for city m in week t α jm - City-Product Fixed Effect Z mt - Vector of controls 23 / 29

24 Hausman and Leonard (2002) - IV Strategy Of course, Hausman and Leonard must deal with the simultaneity problem For example, in the share equation s jmt = α jm + β j log X mt P mt + J γ ji log p imt + Z mt θ j + ε jmt i=1 prices are likely to be correlated with the error. Usual way of dealing with the endogeneity of prices is to apply instrumental variables in the form of cost-shifters However while plant-specific variable cost data for each manufacturer would be helpful [...] we do not have access to such data 24 / 29

25 Hausman and Leonard (2002) - IV Strategy The only data available to the authors is price, quantity and expenditure. Thus, at first glace appears that they have no available instruments. Hausman and Leonard use a unique set of instruments: "To get around this problem, we attempt to utilize the panel structure of the underlying data. [... ] We use the prices from one city as the instruments for other cities Intuition: Prices in each city reflect both underlying product costs and city-specific factors that vary over time. To the extent that the stochastic city-specific factors are independent of each other, prices from one city can serve as instruments for another city. 25 / 29

26 Hausman and Leonard (2002) - IV Strategy Is the price of Product j in city n a valid instrument for the price of Product j in city m? Suppose we want to estimate the demand for Kleenex Bath Tissue (KBT) in Montreal - and so we will need an instrument for KBT s price in Montreal For KBT s price in New York to be a valid instrument, it must: (First Stage) Correlated with KBT s price in Montreal cov (P jn, P jm ) 0 (Exclusion Restriction) Not correlated with unobserved factors affecting demand for KBT in Montreal cov (P jn, ε jm ) = 0 26 / 29

27 Hausman and Leonard (2002) - IV Strategy First Stage is satisfied since prices in both New York and Montreal will reflect the production costs for KBT (which are similar across cities) cov(mc jn, MC jm ) 0 cov(p jn, P jm ) 0 The exclusion restriction will be satisfied so long as the unobserved demand factors in New York are independent from those in Montreal cov(ε jn, ε jm ) = 0 cov(p jn, ε jm ) = 0 27 / 29

28 Demand for BT - Results 28 / 29

29 Demand for BT - Results Consider the first row in Table III What is the interpretation of ? Can we infer that the demand for Kleenex is inelastic? Is this statistically significant? What is the interpretation of 0.679? Can we infer that Kleenex and Charmin are substitutes? Is this statistically significant? Which is the best substitute for Kleenex? Worst? Can we infer that the worst substitute is in fact not a substitute at all? 29 / 29