Discriminating Dispersion in Prices

Transcription

1 Discriminating Dispersion in Prices Greg Kaplan Princeton University Leena Rudanko FRB Philadelphia Guido Menzio University of Pennsylvania Nico Trachter FRB Richmond (preliminary and incomplete) December 2014

2 Motivation Significant interest in flexibility of prices over time Micro data allows direct look at how frequently prices adjust Various issues come up: Sales: If some consumers can adjust by making use of sales, how to treat sales when thinking about price flexibility? Switching stores: If some consumers can adjust by switching stores, how to deal with this in thinking about price flexibility? Switch to cheaper store or shop in multiple stores Both represent price discrimination by sellers, to take advantage of heterogeneity among consumers We focus on latter less-studied phenomenon

3 This paper Study spatial price discrimination in cross section Evidence on prices of multiple goods in multiple stores Theory of prices of multiple goods in multiple stores Features of theory to reflect data: Systematic differences in overall price-level across stores stores take advantage of some consumers being more informed about prices (standard price dispersion mechanism) Systematic differences in individual prices from store average stores take advantage of some consumers being able to purchase different goods from different stores (new relative price dispersion mechanism)

4 Related Literature Idea of consumers adjusting to macro shocks by switching sellers: Coibion, Gorodnichenko and Hong (2014), Jaimovic, Rebelo, Wong (2014), Menzio and Kaplan (2014) Evidence of price dispersion: Stigler (1961), Pratt, Wise, Zeckhouser (1979),..., Eden (2013), Menzio and Kaplan (2014) Theories of price dispersion: Burdett and Judd (1983), Burdett and Mortensen (1998), and others Theories of multiproduct search: Burdett and Malueg (1981), Carlson and McAfee (1984), Gatti (1999), McAfee (1995), Rhodes (2014), Zhou (2014) Empirical approach: Gottschalk and Moffitt (1994), Blundell and Preston (1998) and others

5 Outline of talk Evidence Theory

6 Evidence

7 Questions To what extent does the overall price-level vary across stores? How much of this variation is very temporary (sales) and how much more persistent? To what extent do individual goods prices differ from the store average? How much of this variation is very temporary (sales) and how much more persistent? Goal: Show significant degree of persistent dispersion in both

8 Questions To what extent does the overall price-level vary across stores? How much of this variation is very temporary (sales) and how much more persistent? To what extent do individual goods prices differ from the store average? How much of this variation is very temporary (sales) and how much more persistent? Goal: Show significant degree of persistent dispersion in both New approach to treat price data, motivated by literature studying income/earnings (Gottschalk and Moffitt 1994, Blundell and Preston 1998)

9 Data Kilts-Nielsen Retail Scanner Data Weekly pricing, volume, and store environment information for 2.6 mi UPCs for More than 35,000 grocery, drug, mass merchandiser, and other stores, nationwide: cover more than half the sales of US grocery and drug stores Current working sample Minnesota, Arizona 1000 UPCs with largest sales in 2010 Restrictions: at least 250 UPCs per store, at least 50 stores

10 Data Product group Number of UPCs Percentage of UPCs (%) Dairy Deli Dry Grocery Fresh Produce 60 6 Frozen Foods General Merchandise Health and Beauty Non-Food Grocery Packaged Meat 40 4

11 Decomposing variation in prices Express price of good j in store s at time t as: log p jst = µ jt }{{} good + y st }{{} store + z jst }{{} store-good

12 Construction Average price-level of good: ˆµ jt = 1 S S log p jst s=1

13 Construction Average price-level of good: ˆµ jt = 1 S S log p jst s=1 Demeaned prices: ˆp jst = log p jst ˆµ jt

14 Construction Average price-level of good: Demeaned prices: ˆµ jt = 1 S S log p jst s=1 ˆp jst = log p jst ˆµ jt Relative price-level of store: (store component) ŷ st = 1 J J ˆp jst j=1

15 Construction Average price-level of good: Demeaned prices: ˆµ jt = 1 S S log p jst s=1 ˆp jst = log p jst ˆµ jt Relative price-level of store: (store component) ŷ st = 1 J J ˆp jst j=1 Relative price of good in store: (store-good component) ẑ jst = ˆp jst ŷ st

16 Decomposing variation in prices Express price of good j in store s at time t as: log p jst = µ jt }{{} good + y st }{{} store + z jst }{{} store-good

17 Auto-covariance function of store component ŷ st Empirical Auto-Covariance FuncAon: Store Component Lag Minnesota Arizona Store prices vary 6-7% around market average Substantial persistence, but also transitory variation

18 Auto-covariance function of store-good component ẑ jst 0.03 Empirical Auto-Covariance FuncAon: Store-Good Component Lag Minnesota Arizona Good prices vary 14-16% around store average Stronger transitory variation, but also persistent

19 Decomposing variation in prices Express price of good j in store s at time t as: log p jst = µ jt }{{} good + y st }{{} store + z jst }{{} store-good

20 Decomposing variation in prices Express price of good j in store s at time t as: log p jst = µ jt Express store component as: }{{} good y st = y F s }{{} fixed Express store-good component as: z jst = z F js }{{} fixed + y st }{{} store + y P st }{{} AR + zjst P }{{} AR + z jst }{{} store-good + y T st }{{} MA + z T jst }{{} MA

21 GMM parameter estimates Store component Store-good component MN AZ MN AZ MA(1) parameter Var of transit shock AR(1) parameter Var of pers shock Var of fixed effect Half-life of AR(1): Store component: weeks one year or more Store-good component: weeks six months

22 Variance decomposition Store component Store-good component MN AZ MN AZ MA(1) 4% 3% 63% 67% AR(1) 20% 97% 20% 17% FE 76% 0% 17% 16% Persistent 96% 97% 37% 33%

23 Variance decomposition Store component Store-good component MN AZ MN AZ MA(1) 4% 3% 63% 67% AR(1) 20% 97% 20% 17% FE 76% 0% 17% 16% Persistent 96% 97% 37% 33% Almost all price differences across stores persistent 30-40% of price differences from store average persistent

24 Next: theory to formalize ideas Construct theory of stores selling multiple products Capturing persistent dispersion in store price levels and in goods prices from store average Based on stores discriminating among heterogeneous buyers Multi-stop shoppers vs one-stop shoppers

25 Theory

26 Outline Static model Two goods Continuum identical stores, each selling both goods Continuum heterogeneous households Frictional product market: build on Burdett and Judd (1983)

27 Households Measure h households per store Can purchase neither, only one, or both goods Learn prices of one store with probability α, two with 1 α Measure b busy, measure 1 b frugal: Frugal can visit two stores, busy only one Frugal have lower willingness to pay U F < U B for each good

28 Household problem Get one or two price offers (p 1, p 2 )

29 Household problem Get one or two price offers (p 1, p 2 ) Frugal: (multi-stop shoppers) max (U F p 1 )1 {buy at p1 } + (U F p 2 )1 {buy at p2 } s.t. can buy from two stores

30 Household problem Get one or two price offers (p 1, p 2 ) Frugal: (multi-stop shoppers) max (U F p 1 )1 {buy at p1 } + (U F p 2 )1 {buy at p2 } s.t. can buy from two stores Minimize price independently across goods

31 Household problem Get one or two price offers (p 1, p 2 ) Frugal: (multi-stop shoppers) max (U F p 1 )1 {buy at p1 } + (U F p 2 )1 {buy at p2 } s.t. can buy from two stores Minimize price independently across goods Busy: (one-stop shoppers) max (U B p 1 )1 {buy at p1 } + (U B p 2 )1 {buy at p2 } s.t. can only buy from single store

32 Household problem Get one or two price offers (p 1, p 2 ) Frugal: (multi-stop shoppers) max (U F p 1 )1 {buy at p1 } + (U F p 2 )1 {buy at p2 } s.t. can buy from two stores Minimize price independently across goods Busy: (one-stop shoppers) max (U B p 1 )1 {buy at p1 } + (U B p 2 )1 {buy at p2 } s.t. can only buy from single store Tend to minimize bundle price across stores

33 Store problem Each store sets (p 1, p 2 ) to maximize profit, taking as given distribution of prices in market Distribution of single good prices: F (p j ) for j = 1, 2 Bundle price q := p 1 + p 2 Distribution of bundle prices: F q (q)

34 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q]

35 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B

36 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B Top of distribution is q = 2U B (if top below 2U B, deviate)

37 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B Top of distribution is q = 2U B (if top below 2U B, deviate) Profit at top: π = hbα2u B (sell only to busy with one offer)

38 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B Top of distribution is q = 2U B (if top below 2U B, deviate) Profit at top: π = hbα2u B (sell only to busy with one offer) Profits below: (q [q, 2U B ]) π(q) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles

39 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B Top of distribution is q = 2U B (if top below 2U B, deviate) Profit at top: π = hbα2u B (sell only to busy with one offer) Profits below: (q [q, 2U B ]) π(q) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles In equilibrium, π(q) π

40 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B Top of distribution is q = 2U B (if top below 2U B, deviate) Profit at top: π = hbα2u B (sell only to busy with one offer) Profits below: (q [q, 2U B ]) π(q) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles In equilibrium, π(q) π F q (q)

41 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B Top of distribution is q = 2U B (if top below 2U B, deviate) Profit at top: π = hbα2u B (sell only to busy with one offer) Profits below: (q [q, 2U B ]) π(q) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles In equilibrium, π(q) π F q (q) F q (q) = 0

42 Constructing equilibrium 1: targeting top Consider market where stores target busy (who buy bundles): Look for continuous bundle price distribution on [q, q] The highest bundle price stores can charge is 2U B Top of distribution is q = 2U B (if top below 2U B, deviate) Profit at top: π = hbα2u B (sell only to busy with one offer) Profits below: (q [q, 2U B ]) π(q) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles In equilibrium, π(q) π F q (q) F q (q) = 0 q

43 Constructing equilibrium 1: targeting top U B + U F 2U F U F U F 2U F U B + U F

44 Store customer base U B + U F 2U F Price in top: Busy buy bundles, if second offer has higher bundle price U F U F 2U F U B + U F

45 Household behavior U B + U F Busy: Buy bundle at cheapest bundle price 2U F U F U F 2U F U B + U F

46 Household behavior U B + U F Busy: Buy bundle at cheapest bundle price 2U F U F Frugal: Buy nothing U F 2U F U B + U F

47 Price distributions U B + U F 2U F Bundle distribution: pinned down over [q, 2U B ] U F U F 2U F U B + U F

48 Price distributions 1 Cumulative F q (q) Tractability: (C 0, C 1 constants) Cumulative: F q (q) = C 0 C 1 /q Density: f q (q) = C 1 /q 2 Bottom: q = C 1 /C 0 0 q :[q, q]

49 Price distributions 1 Cumulative F q (q) Tractability: (C 0, C 1 constants) Cumulative: F q (q) = C 0 C 1 /q Density: f q (q) = C 1 /q 2 Bottom: q = C 1 /C 0 Mean: µ q = C 1 log(q/q) Variance: σ 2 q = C 1 (q 2µ q log(q) mu 2 q/q) C 1 (q 2µ q log(q) mu 2 q/q) 0 q :[q, q]

50 Price distributions 1 Cumulative F q (q) Tractability: (C 0, C 1 constants) Cumulative: F q (q) = C 0 C 1 /q Density: f q (q) = C 1 /q 2 Bottom: q = C 1 /C 0 Mean: µ q = C 1 log(q/q) Variance: σ 2 q = C 1 (q 2µ q log(q) mu 2 q/q) C 1 (q 2µ q log(q) mu 2 q/q) Variance of store component 0 q :[q, q]

51 Price distributions 1 Cumulative F q (q) Tractability: (C 0, C 1 constants) Cumulative: F q (q) = C 0 C 1 /q Density: f q (q) = C 1 /q 2 Bottom: q = C 1 /C 0 Mean: µ q = C 1 log(q/q) 0 q :[q, q] Variance: σ 2 q = C 1 (q 2µ q log(q) mu 2 q/q) C 1 (q 2µ q log(q) mu 2 q/q) Variance of store component Bounds on distance from store average: [0, U B q/2] Bounds on variance of store-good component

52 Constructing equilibrium 2: price discrimination Some stores target busy, some sell one good to frugal: Drop price of one good enough to sell it to frugal capture mass of frugal buyers

53 Constructing equilibrium 2: price discrimination Some stores target busy, some sell one good to frugal: Drop price of one good enough to sell it to frugal capture mass of frugal buyers Look for bundle distribution on [q, U B + U F ] [q, 2U B ]

54 Constructing equilibrium 2: price discrimination Some stores target busy, some sell one good to frugal: Drop price of one good enough to sell it to frugal capture mass of frugal buyers Look for bundle distribution on [q, U B + U F ] [q, 2U B ] Profit at top and just below as before (q [q, 2U B ])

55 Constructing equilibrium 2: price discrimination Some stores target busy, some sell one good to frugal: Drop price of one good enough to sell it to frugal capture mass of frugal buyers Look for bundle distribution on [q, U B + U F ] [q, 2U B ] Profit at top and just below as before (q [q, 2U B ]) Profit further down: (q [q, U B + U F ], p [p, U F ]) π(q, p) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles + h(1 b)[α + 2(1 α)(1 F (p))]p }{{} frugal buy cheaper good only

56 Constructing equilibrium 2: price discrimination Some stores target busy, some sell one good to frugal: Drop price of one good enough to sell it to frugal capture mass of frugal buyers Look for bundle distribution on [q, U B + U F ] [q, 2U B ] Profit at top and just below as before (q [q, 2U B ]) Profit further down: (q [q, U B + U F ], p [p, U F ]) π(q, p) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles + h(1 b)[α + 2(1 α)(1 F (p))]p }{{} frugal buy cheaper good only In equilibrium π(q, p) π

57 Constructing equilibrium 2: price discrimination Some stores target busy, some sell one good to frugal: Drop price of one good enough to sell it to frugal capture mass of frugal buyers Look for bundle distribution on [q, U B + U F ] [q, 2U B ] Profit at top and just below as before (q [q, 2U B ]) Profit further down: (q [q, U B + U F ], p [p, U F ]) π(q, p) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles + h(1 b)[α + 2(1 α)(1 F (p))]p }{{} frugal buy cheaper good only In equilibrium π(q, p) π F q (q), F (p)

58 Constructing equilibrium 2: price discrimination Some stores target busy, some sell one good to frugal: Drop price of one good enough to sell it to frugal capture mass of frugal buyers Look for bundle distribution on [q, U B + U F ] [q, 2U B ] Profit at top and just below as before (q [q, 2U B ]) Profit further down: (q [q, U B + U F ], p [p, U F ]) π(q, p) = hb[α + 2(1 α)(1 F q (q))]q }{{} busy buy bundles + h(1 b)[α + 2(1 α)(1 F (p))]p }{{} frugal buy cheaper good only In equilibrium π(q, p) π F q (q), F (p) F q (q) = 0 q, F (p) = 0 p

59 Constructing equilibrium 2: price discrimination U B + U F 2U F U F U F 2U F U B + U F

60 Store customer base U B + U F Price in top: Busy buy bundles, if second offer has higher bundle price 2U F U F U F 2U F U B + U F

61 Store customer base U B + U F Price in top: Busy buy bundles, if second offer has higher bundle price 2U F U F Price in sides: Busy buy bundles, if second offer has higher bundle price Frugal buy cheaper good, if second offer has higher price U F 2U F U B + U F

62 Household behavior Busy: Buy bundle at cheaper bundle price (one-stop shopper) U B + U F 2U F U F U F 2U F U B + U F

63 Household behavior Busy: Buy bundle at cheaper bundle price (one-stop shopper) U B + U F 2U F U F U F 2U F U B + U F Frugal: Ignore top offers If one offer from sides, buy one good If two offers from same side, buy one good at cheaper price If offers from both sides, buy both goods (multi-stop shopper)

64 Price distributions U B + U F Bundle distribution: pinned down over [q, U B + U F ] [q, 2U B ] 2U F U F Single distribution: over [p, U F ] pinned down U F 2U F U B + U F

65 Price distributions 1 Cumulative F q (q) 1 Cumulative F(p) 0 q :[q, q] 0 p :[p,ue]

66 Constructing equilibrium 3: top, discrimination, bottom U B + U F 2U F U F U F 2U F U B + U F

67 Equilibrium behavior Proposition (stores matter) Suppose some stores sell both bundles and single goods. Pricing the two goods independently is not consistent with equilibrium.

68 Distribution and variance decomposition Proposition (shape of distributions) Cumulative and density of bundle and single prices take form: F q (q) = C 0 C 1 /q, f q (q) = C 1 /q 2, F (p) = D 0 D 1 /p, and f (p) = D 1 /p 2 (defined over the appropriate regions). Proposition (store component) Variance of bundle prices can be solved in closed form. Proposition (store-good component) Upper and lower bounds for variance of distance of individual goods from store average can be solved in closed form.

69 Distribution of purchased prices i.e. price index Proposition (distributions) Cumulative and density of purchased prices can be solved in closed form. Proposition Variance of purchased prices can be solved in closed form.

70 Conclusions/Directions Documented significant and persistent dispersion in both store and store-good component in current sample of Kilts-Nielsen scanner price data Robustness Other tests of theory: posted vs purchased prices, regional differences in heterogeneity vs pricing Proposed new multi-product search theory generating price dispersion both across stores and within a store formalizes idea of price discrimination between one-stop and multi-stop shoppers Develop theoretical side Testable predictions Quantify dispersion