Demand Dynamics Under Consumer Regret: An Empirical Analysis

Demand Dynamics Under Consumer Regret: AnEmpirical Analysis

Meisam Hejazi Nia

with Dr. Ozalp Ozer and Dr. Gonca SoysalUniversity of Texas at Dallas

[email protected]

April 23, 2014

Meisam Hejazi Nia (UTD) Demand Dynamics Under Consumer Regret April 23, 2014 1 / 33

Consumers are Regretful

(a) Fashion Goods (b) Mark Down(c) CounterfactualThinking


Motivation: Evidence from Press for Consumer Regret


Research Questions

Does the theory of emotionally rational consumer (consumer who regrets)describe consumer’s choice better than theory of rational forward lookingconsumer?

Are consumer’s more regretful for high price, or to fashion itemunavailablity?

Does the firm leave money on the table when it ignores consumer’semotion?

To what extend firm’s profitability increases, if it accounts for consumer’sregret, in its pricing decision (counterfactual)?

How can firm leverage bounded rationality of consumer through signalingto reap off more revenue (counterfactual)?


Every day Low price or Promotion Strategy?

Rational Consumers (FW LK) Emotionaly Rational Consumer (Re-gret) + Bounded Rationality

Pricing and MarkdownStudies

Soysal and Krishnamurthi (2012), Nair(2007),Li et al. (2009), Erdem and Keane(1996), Sun et al. (2003), , Song andChintagunta (2003), Erdem et al. (2003),Chevalier and Goolsbee (2009), Pazgal(2008),Cachon and Swinney (2009), Levinet al. (2009), Yin et al. (2009)

Pricing and MarkdownTheoretical Research(Behav. Econ., Dec.Sci., Manag. Sci.)

Ozer & Zhang(2013), Nasiry & Popescu(2009), Rotemberg (2010), Decidue etal. (2012), Heidhues and Koszegi 2008,Su 2009, Engelbrecht-Wiggans and Katok(2008), Qiu and Steiger 2011, Van de Kuilenand Wakker (2011)

Regret in Marketing andPsych. (Service, Productassortment, product cus-tomization, equity pur-chase, choice model)

Lemon, White & Winder (2002), Gourville& Soman (2005), Solnik (2008), Syam et al.(2008), Thiene et al. (2012), Peluso (2011),Pieters and Zeelenberg (2007), Zeelen-berg and Pieters (2007), Boles and Messik(1995), Tsiros and Mittaal (2000), Simon-son (1992), Zeelenberg et al. (2000), Inmanand Zeelenberg (2002), Roes (1994), Bell(1982), Keinan and Kivetz (2008), Loomesand Sugden (1982), Smith (1996) and Yaniv(2000), Gollier and Salanie (2006), Muer-mann et al. (2006), Braun and Muermann(2004),Barberis et al. (2006), Michenaudand Solnik (2008), etc.


Overview of This paper

Objectives

Model demand of emotionally rational consumer (consumer whoregrets) structurally and estimate regret parameters

Test theory of emotionally rational consumer against rational forwardlooking consumer theory

Analyze counterfactuals on pricing policy of the firm when consumersare emotionally rational

Analyze counterfactuals on profit impact of signaling strategies thataffect consumer’s misperception of time and depth of markdown, andavailablity

Test hypothesis on consumer regret coefficients across fashion itemcategories (i.e. cold vs. hot apparels, male vs. female apparels, simplevs. sophisticated items)


Overview

Data

Leading specialty fashion apparel retailer in US

Current category under analysis: Women’s coats over a course of Twoyears (105 SKU’s, PLC: 30 weeks)

Aggregate weekly sales, revenue, starting inventory, unit acquisitioncost

Methodology and Estimation

OLS for no heterogeneity

BLP and MPEC for latent type heterogeneity model (Static andDynamic Model)

Delta method for non-linear parameters

Fixed effect for product heterogeneity and Hierarchical Bayesian forcross category analysis


Overview of Paper

Firm’s Controls:

List Price

Markdown Depth

Markdown Time

Availablity Expectation

Contigency onSegments (Myopic,Static, Dynamic)

Product Heterogeneity

→

Consumer’s Ex-ante:

Valuation (Ownership,Consump. LC)

Price

Anticipated High PriceRegret

Anticipated Stock OutRegret

Bounded Rationality

Rejoice

→

Ex-Post:

Firm’s Profit

Consumer’s Utility

Consumer’s Regret(Cognitive Cost)


Evolution of Price and Sales


Basic Statistics: Average revenue and quantity sold atdifferent First Markdown Level

Relative Price (%) Revenue (%) Quantity sold (%)

70-100 0.896 1.23160-69 0.855 1.32550-59 0.671 1.22440-49 0.966 2.08730-39 1.193 3.19420-29 1.517 6.447< 20 0.081 0.490


Firm and Consumer Decisions’ Timing

Note: Consumer’s have finished search, and now they are only decideabout the Fashion good to purchase (Soysal and Krishnamurthi 2012)


First Model:Basic

Model

Ui1 = αi + (0.5di1 + ridi2)θ + βppi1

+αpai2(pi1 − pi2) + ξi1 + εi1

i = 1..105, t = 0..2 ,

ri = 11.0025

di1

εit ∼ EV 1(0, π2

6 ) , ξit ∼ N(0, σ2ξ )

Ui2 =

ri (ai2(αi + 0.5di2θ + βpPi2)

+(1− ai2)βr (0.5di1 + ridi2)θ) + ξi2 + εi2

Ui0 = εi0

Assumption: Two period as consumer’s are ra-tionally bounded

i :Product index

t:Period index (0 for not purchase)

Uit :Utility of Consumer for Purchasein period (t = 0 not purchase)

Pit :Price of product i at period t

ait :Probability that product i is avail-able in t: Distribution factor

ri :Discount factor for product i

dit :Duration of period t for product i

ξit:Unobserved aggregate demandshock

αi : Ownership utilityθ: Weekly consumption Utilityβp: Price Sensitivityαp: High Price Regret


First Model:No Consumer Heterogeneity

Model



i = 1..105, t = 0..2 ,

ri = 11.0025

di1

εit ∼ EV 1(0, π2

6 ) , ξit ∼ N(0, σ2ξ )

Ui2 = ri (ai2(αi + 0.5di2θ + βpPi2)


Ui0 = εi0

Assumption Counterfactual Thinkingi :

Product indext:

Period index (0 for not purchase)Uit :

Utility of Consumer for Purchasein period (t = 0 not purchase)


ait :Probability that product i is avail-able in t: Distribution factor




αi : Ownership utilityθ: Weekly consumption Utilityβp: Price Sensitivityαp: High price regretβr : Stock Out Regret


Second Model: Aggregate Demand with UnobservedDemand Shocks (BLP)

Model

Uij1 = αi + (0.5di1 + ridi2)θ + βpjpi1

+αpjai2(pi1 − pi2) + ξi1 + εi1

i = 1..105, t = 0..2 , j = 1, 2

ri = 11.0025

di1

εit ∼ EV 1(0, π2

6 ) , ξit ∼ N(0, σ2ξ )

Ui2 = ri (ai2(α + 0.5di2θ + βpjPi2)

+(1− ai2)βrj(0.5di1 + ridi2)θ) + ξi2 + εi2

Ui0 = εi0

Assumption: Only two segment (H and L) forease of exposition (j = 1, 2)



ait :Availability of product i at periodt




α: Ownership utilityθ: Weekly consumption Utilityβpj : Price Sensitivityαpj : High price regretβrj : Stock Out Regret


Third Model: Add Rejoice to the Model

Model

Uij1 = αi + (0.5di1 + ridi2)θ + βpjpi1


i = 1..105, t = 0..2 , j = 1, 2

ri = 11.0025

di1

εit ∼ EV 1(0, π2

6 ) , ξit ∼ N(0, σ2ξ )

Ui2 = ri (ai2(α + 0.5di2θ + βpjPi2+

αhj(pi1 − pi2)) + (1− ai2)

βrj(0.5di1 + ridi2)θ) + ξi2 + εi2

Ui0 = εi0

Assumption: Only two segment (H and L) forease of exposition (j = 1, 2)



ait :Availability of product i at periodt




α:Ownership utility

θ:Weekly consumption Utility

βpj :Price Sensitivity

αpj :High price regret

βrj :Stock Out Regret

αhj :Rejoice coefficient


Fourth Model: Misperception, Product Fixed Effect, NewConsumer’s Segments

Model

αi = α + α1 ∗ ci + α2 ∗mi + α3 ∗ cli + α4 ∗ api

dei1 = di1 + κi

pei2 = pi2 + ηi

aei2 = ai2 + µi

κi , ηi , µi ∼ N(0,Σ)

α:Ownership utility intercept parameter

αk :Ownership utility parameter for mate-rial, color and cloth (k = 1..3)

κi :Misperception error for the time ofmarkdown

ηi :Misperception error for the price ofitem i after markdown

µi :Misperception error for the availablityof fashion item i after markdown

Assumption: We can have segment of Static,Dynamic and Myopic decisionmakers

ci :per unit cost of acquistion of fash-ion item i

mi :material of fashion item i (i.e.Wool, Nylon, Fur, others)

cli :color of fashion item i (i.e. Dark,Bright, texture, others)

api :Type of apparel of fashion item i(i.e. coat, jacket, suit, short, oth-ers)

dei1:Expectation time of markdown forproduct i

pei2:Expected price of fashion item iafter markdown

aei2:Expected availablity of fashionitem i after markdown


Estimation: Aggregate Logit

Basic Model (Demand Side)



εit ∼ EV 1(0, π2

6 ) , ξit ∼ N(0, σ2ξ )

Ui2 =

ri (ai2(αi + 0.5di2θ + βpPi2)


Ui0 = εi0

Estimation

Ui1 = Vi1 + εi1

Ui2 = Vi2 + εi2

Ui0 = εi0

Sit = eVit∑2s=0 e

Vis

Vi1 = ln(Si1)− ln(Si0)

Vi2 = ln(Si2)− ln(Si0)

Sit = salesitMi

Mi = 1.25Invi


Estimation: Aggr. demand with unobs. demand shock(static)

BLP type Model (Demand Side)

Ui1 = αi + (0.5di1 + ridi2)ciθ + βpjpi1


εit ∼ EV 1(0, π2

6 ) , ξit ∼ N(0, σ2ξ )

Ui2 = ri (ai2(α + 0.5di2ciθ + βpjPi2)

+(1− ai2)βrj(0.5di1 + ridi2)ciθ) + ξi2 + εi2

Ui0 = εi0L(Ω) =

∏Tt=1 fξ(D

−1t (qt ; Ω)) ‖J‖

‖J‖ =∥∥∥∂D−1

t (qt ;Ω)∂qit

= | ∂ξit∂qit|

= | − ∂G/∂qit∂G/∂ξit

= | − −1∑2k=1 NkitPikt(qt |Ω)[1−skit(qt |Ω)]

|

Estimation

Ω = (α, c , β, π, σxi )

δi1 = α + c + γc + βp1pi1

αp1ai2(pi1 − pi2) + ξi1

δi2 = ri (ai2(α + c + βp1pi2)

+(1− ai2)βr1((0.5di1 + ridi2)ciθ) + ξi2

β2 = (β2 − β1), , β2 = (β2p, α2p, β2r )

MSi1 = π1iexp(δi1)∑2t=0 exp(δit)

+(1− π1i )exp(δi1+βp2pi1+αp2ai2(pi1−pi2))∑2

t=0 exp(Uit2)

MSi2 = π2iexp(δi1)∑2t=0 exp(δit)

+ (1− π1i )

exp(δi2+ri (ai βp2pi2+(1−ai )βr2ai2(0.5di1+ridi2)ciθ))∑2t=0 exp(Uit2)


MPEC (Constraint) versus BLP (Fixed Point)

Objective Function

BLP (Fixed Point): maxβ2L(ξ1, ξ2)

Subj. to sit = sit, k < 1−10

β2 = (π,∆βp,∆αp,∆βr )

MPEC (constraint): maxβ2,δ1,δ2L(ξ1, ξ2)

Subj. to sit = sit

We need to supplement analytically calculated Gradient and Hessian:

G = (G1, . . . ,G4) = (∂LL∂π , . . . ,∂LL∆βr

)

H =( ∂G1∂π

...∂G1βr

.... . .

...∂G4∂π

...∂G4βr

)

Dynamic Model

Consumer decides whether to buy now or wait:

Wijt = γait ln[exp(δj ,t+1) + exp(Wijt+1)]

Wijt(St) = 1N(ξit+1)

∑N(ξit+1)n=1 Wijt

WijTj= 0, Gausian Quadrature

Segments:

Sit =∑s

j=1 πjsijt∑sj=1 πj = 1

On myopic case:sijt+1 = Mi (p + qsijt)(1− sijt)

On Multiple Period, high price regret:

αp(Pt − 1(Ti−t)

∑Tτ=t iaiτPiτ )

On Multiple Period, stock out regret:βr (1 + τ)θ


Estimation:Delta Method to Identify Stock Out RegretCoefficient

Basic Model

Ui1 = α + (0.5di1 + ridi2)θ + βppi1


εit ∼ EV 1(0, π2

6 ) , ξit ∼ N(0, σ2ξ )

Ui2 =

ri (ai2(α + 0.5di2θ + βpPi2)


Ui0 = εi0

Estimation

η = θβr

V

(θη

)=

(σ11 00 σ22

)

βr = η

θ

µ =

(1θ

− η

θ2

)V (βr ) = µ′V

(θη

)µ


Sources of Variation for Identification

High Price Regret: Availablity of the product (exogenous), and themarkdown amount (endogenous) → Best effort: control for remaininginventory?

Stock out Regret: Availablity of the product (exogenous), Time ofthe markdown (endogenous)→ Best effort: control for the ratio ofremain.Inv

remain.Period ?

Price sensitivity: Variation in price (endogenous) → Best effort:control for remaining amount in inventory

Consumption utility: Length of the season (exogenous), Time of themarkdown (endogenous)→ Best effort: control for the ratio ofremain.Inv

remain.Period ?


Sources of Variation for Identification

Ownership utility: Accounts for product heterogeneity (productquality)

Rejoice: Availablity of the product (exogenous), and the markdownamount (endogenous) → Best effort: control for remaining inventory?

Unobservables: Control with market time dummy (Unobserveddemand shocks)

Consumer heterogeneity: Static, dynamic, and myopic decisionmakers with different price sensitivity through BLP model


BLP estimation with sample size of 270K (Duration 1-2days)

First Simulation

α θ βp αp βr

1st segment Real Parameter 2.9410 0.4640 -2.0130 -5.1110 -0.5600Estimate (BLP) 2.8150 0.4400 -1.9230 -4.8900 -0.5710Estimate (OLS) 2.4350 0.4060 -1.9200 -4.7700 -0.9720

2nd segment Real Parameter 2.9410 0.4640 -2.3700 -5.4220 -1.5220Estimate (BLP) 2.8150 0.4390 -2.2740 -5.0670 -1.5270Estimate (OLS) 2.4350 0.4060 -1.9200 -4.7700 -0.9720

Seg. size (π) Real Parameter 0.2000Estimate 0.1960



Second Simulation

α θ βp αp βr






Third Simulation

α θ βp αp βr





MPEC estimation with sample size of 105 (Less than 5minues)

First Simulation

α θ βp αp βr

1st segment Real Parameter 2.331 2.9486 -2.1827 -0.6108 -1.4496Estimate (BLP) 2.3271 2.9281 -2.178 -0.58 -1.4251

2nd segment (Hetrog) Real Parameter -0.9165 -4.293 -2.6808Estimate (BLP) -0.9165 -4.293 -2.6995




Second Simulation

α θ βp αp βr






Third Simulation

α θ βp αp βr






Fourth Simulation

α θ βp αp βr

1st segment Real Parameter 2.00E+00 1.82E+00 -7.78E-02 -1.95E+00 -0.1109Estimate (BLP) 2.0563 1.789 -0.0904 -1.8997 -0.0938




Model EStimation Performance

Model Estimation LL AIC BIC

BLP (Dynamic) 151.95 −293.91 −280.64BLP (Static) 300.14 −590.27 −577.004OLS -631.9 1273.8 1287.1MPEC (Static) 7712 −1541 −1540

MPEC algorithm of estimation outperforms BLP Model estimationalgorithms

Static Model fits the data better than dynamic model (so far)

No heterogeneity model performs worse than static and dynamicmodel with heterogeneity


Parameter Estimate

α θ βp αp βr

First segment Dynamic(BLP)

parameter esti-mate

-0.0077 0.025 -1.5963 0.1563 -174.4532

t-stat -1.0551 1.9099 -562.8402 21.857 -2.8659Static Model(BLP)

parameter esti-mate

-0.0003 0.0742 -1.5955 0.1658 -56.5262

t-stat -0.037 5.9756 -592.4332 24.4085 -9.0029Static Model(MPEC)

parameter esti-mate

-0.0581 -0.0428 0.0101 0.0078 -3.4788

t-stat -0.4943 -0.2029 0.2212 0.0674 -0.3275Second segment Dynamic

(BLP)parameter esti-mate

-0.0077 0.025 0.0086 -0.0412 1.1854

t-stat -1.0551 ”1.9099 ” 15513i -816 -232iStatic Model(BLP)

parameter esti-mate

-0.0003 0.0742 0.0094 -0.0317 2.5927

t-stat -0.037 5.9756 0.0004 0 0Static Model(MPEC)

parameter esti-mate

-0.0581 -0.0428 -0.4958 -0.4411 56.2505

t-stat -0.4943 -0.2029 -73.8071 -0.3552 6.0364Segment size (π) Dynamic

(BLP)parameter esti-mate

0.1779

t-stat 588Static Model(BLP)

parameter esti-mate

0.1789

t-stat 19.119Static Model(MPEC)

parameter esti-mate

0

t-stat 0


Still A lot to do ....

Estimate model of fixed effects, rejoice, dynamic multiperiod using MPECestimation

Add 3 types of misperception (Markdown time and depth and availablity)

Allow model to decide on size of segment of static, dynamic and myopicconsumers

Counterfactual analysis on pricing policy when consumers are regretful,higher regretful consumer (signaling of firm), and availablity misperception


Still A lot to do ....

Counterfactual analysis on pricing policy when consumers are regretful,higher regretful consumer (signaling of firm), and availablity misperception

Robustness check on the markdet size coefficient (1.25), more segments,only one type of regret, reduced model

Test hypothesis on product category level regret (cold vs hot apparels,men vs women apparels, simple vs. sophisticated items)


Thank You


Demand Dynamics Under Consumer Regret: An Empirical Analysis

Data & Analytics

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