Signal Extraction in Economics

Transcription

1 Signal Extraction in Economics Tamura, Masaoki Institute of Innovation Research, Hitotsubashi University July 17, / 51

2 Introduction 2 / 51

3 I study four types of economic environments in which economic agents send or extract signals. Economic Agents: Firms, consumers (Ch.2), donors (Ch.3), politicians and voters(ch.4). 3 / 51

4 Ch.1 Firm s prize promotions to solve time-inconsistency. Ch.2 Donors signaling to maximise their utility including social image. Ch.3 Politicians signaling to reveal their hidden types to voters. Ch.4 Empirical analysis on quality change and inflation rate. 4 / 51

5 Chapter 1 Prize Promotions as Costless Commitment 5 / 51

6 Introduction Prize Promotions: Firm attaches a lottery ticket to its product. Example: USD 100 cashback for 100 buyers. In Management (Kotler and Keller (2012)): stimulate quicker or greater purchase of particular products, similarly to coupons, free trials, and/or product warranties. In Economics: work the same as Price Cut in a static case. 6 / 51

7 My Questions and Contributions My Questions: What is the economic role of prize promotions? When are they profitable and better than other ways? Contributions: Find the economic role of prize promotions. Investigate a dynamic property of lottery Provide the best way to solve firm s inconsistency 7 / 51

8 General Model of Firm s Inconsistency 1 Assumptions: One Monopoly Firm and Many Consumers Two Periods Model Sequential Model Quasi-linear Utility Atomless Consumers 8 / 51

9 General Model of Firm s Inconsistency 2 Consumers Problem: U i( x 1 i,x 2 i,m i) = u i( x 1 i,x 2 i ) + M i, x t i : consumer i s demand at period t P t : price at period t M i : monetary gain w i : income P 1 x 1 i + P 2 x 2 i + M i = w i, Demand functions: i X 1 = x ( ) 1 P 1,P 2 i i X 2 = x ( 2 P 2 {x i 1 } ). i 9 / 51

10 General Model of Firm s Inconsistency 3 Firm s total profit: π = π 1 + π 2 = P 1 X 1 C 1 (X 1 ) + P 2 X 2 C 2 (X 2 ) 1st best policy ( X 1,X 2 ) solves max X1,X 2 π ( X 1,X 2 ) Inconsistency arises when X 2 argmax X2 π 2 ( X2 X 1 ) Examples: Switching Cost Model (Farrell and Gallini (1988)), Experience Goods Model (Cremer (1984)), Network Externality Model. 10 / 51

11 Introducing Prize Promotion 1 Time 1 Time 2 Firm: Announce Prize Sell Goods Sell Goods Allocate Prize Consumers: Buy Goods Buy Goods 11 / 51

12 Introducing Prize Promotion 2 Demand functions: Firm s total profit: X 1 = ( i x 1 P 1 Prize,P 2 Prize ) i X 1 + X 2 X 1 + X 2 X 2 = ( i x 2 P 2 Prize ) {x i 1 }. i X 1 + X 2 π = π 1 + π 2 Prize = P 1 X 1 C 1 (X 1 ) + P 2 X 2 C 2 (X 2 ) Prize. 12 / 51

13 Main Theorem Theorem (Costless Commitment by Prize Promotion) If expansionary commitment is needed for the inconsistent first best X 1 and X 2, there exists a Prize level that makes X 1 and X 2 consistent and yields the first best profit. 13 / 51

14 Brief Sketch of the Proof 1 Prize = 0 vs Prize > 0 Inverse Demand: ) P 1 (X 1,X 2 Prize = 0 ) P 2 (X 1,X 2 Prize = 0 ) vs P 1 (X 1,X 2 Prize = 0 ) vs P 2 (X 1,X 2 Prize = 0 + Prize X 1 +X 2 + Prize X 1 +X 2 Total Profit: Neutral Not depend on the level of Prize, but only on X 1 and X / 51

15 Brief Sketch of the Proof 2 Consistency: 1st best: (X 1,X 2 ) ) π 2 = P 2 (X 1,X 2 Prize = 0 X 2 C(X 2 ) X 2 > X 2 = argmax X 2 π 2 vs ( ) π 2 = [P 2 X 1,X 2 Prize = 0 + Prize X 1 + X 2 ] X 2 C(X 2 ) ) = P 2 (X 1,X 2 Prize = 0 X 2 C(X 2 ) + X 2 X Prize 1 + X 2 X 2 = X 2 = argmaxπ 2 X 2 15 / 51

16 Interpretations ) π 2 = P 2 (X X 2 1,X 2 Prize = 0 X 2 C(X 2 ) + X } {{ } Prize 1 + X } {{ 2 } Prize=0 Prize>0 If the firm increases X 2, then Benefit: X 2 X X 1 +X 2 Increases. ( 2 X 1 +X 2 : Prob. of t = 2 consumers winning) Cost: Constant. (Fixed total amount of Prize is Sunk Cost!) 16 / 51

17 Effective Prize Promotions Effective Prize Promotions: USD 100 cashback for 100 consumers Ineffective Prize Promotions: USD 1 cashback for every purchase 17 / 51

18 Applications: Network Externality Total amount of good has a positive effect on each good owner. If generation 1 buys good, it can derive utility in both period 1 & 2. Generation 1 : U i = u i( x i,x 1 ) + u i ( x i,x 1 + X 2 ), Generation 2 : U i = u i( x i,x 1 + X 2 ). In general, X 2 > argmax X2 π 2 ( X2 X 1 ). At t = 2, the firm does not pay attention to the external benefit from X 2 to t = 1 consumers. 18 / 51

19 Concluding Remarks Prize promotions work as costless expansionary commitment, and the firm can implement the 1st best. Many other ways have been suggested to achieve second-best. Dixit (1980) excess capacity, Farrell and Gallini (1988) second-sourcing. = Prize promotions are the best way to solve time-inconsistency. 19 / 51

20 Chapter 2 Anonymous Giving as a Vice: An Application of Image Motivation 20 / 51

21 Introduction 1 The more anonymity experimenters provide, the less altruistic the examinees become. This paper focuses on Anonymity controlled by the donors themselves, Who? What effect on other donors? Virtue? Paradoxically, this paper proves that anonymous giving is a vice, even if the donors themselves desire anonymity. 21 / 51

22 Introduction 2 Donate Online Amount: $ Anonymous: Name: Address: Credit #: I prefer to make this donation anonymously. Figure : Online Donation Page 22 / 51

23 Introduction 3 Contributions: Heterogenous image motivation, Homogenous: Benabou and Tirole (2006) Endogenous anonymous giving. Exogenous: Andreoni and Petrie (2004), Rege and Telle (2004), and Soetevent (2005) 23 / 51

24 Structure of the Model 1 The utility function for consumer i: c i : consumption, x i : donation, ˆα i : social image. U(c i,x i, ˆα i ) = (1 α i )lnc i + α i lnx i + β i lni( ˆα i ). The budget constraint for i: c i + x i = y i, x i = D i x ki + (1 D i )x ai. 24 / 51

25 Structure of the Model 2 Social image ˆα i = others belief for α i. ˆα i = E[α i x ki,y i ]. Individuals form beliefs based on known giving (x k ), not anonymous giving (x a ). 25 / 51

26 Structure of the Model 3 α = ᾱ > 0: Altruistic β = β > 0: Image Conscious Table : 4 Individual Types Type α β Impure Altruist ᾱ β Pure Altruist ᾱ 0 Hypocrite 0 β Selfish / 51

27 β = 0 case: Separating Equilibrium 1 Hypocrites Mimic Who? β > 0 case: Type α β x i Impure Altruist ᾱ β ᾱyi Pure Altruist ᾱ 0 ᾱy i Hypocrite 0 β 0 Selfish Type α β x i Impure Altruist ᾱ β ᾱyi + ε Pure Altruist ᾱ 0 ᾱy i Hypocrite 0 β 0 or ᾱyi Selfish / 51

28 Separating Equilibrium 2 Introducing Anonymous Giving Q. Who gives anonymously? A. Pure Altruists. Q. What is the effect? A. It dilutes hypocrites incentive to make a giving. decrease effect blend effect 28 / 51

29 Separating Equilibrium 3 Numerical Simulation x i x s +x p +x h +x i Amount of Donation Hypocrites Impure Altruists K Total Amount of Donation K Figure : Numerical Simulation 29 / 51

30 Policy Implications Fund-raisers should not exaggerate the number of anonymous donors. Remove the check box and implement small foot cost. (e.g. send an to fundraisers) 30 / 51

31 Chapter 3 A Signaling Explanation for Political Parties and Advertisements 31 / 51

32 Introduction 1 This chapter studies the situation in which politicians make signals to voters under uncertainty of politicians types. Two types of signaling tools: political parties political advertisements 32 / 51

33 Introduction 2 Extend Snyder and Ting (2002) to a multi-period model with possibility of reelection My Question: What is the role of political advertisements and political parties? 33 / 51

34 Payoff The policy space is between [ 1,1]. The payoff of a politician with an ideal point z who is affiliated with party i and wins office is w α(x i z) 2 c (1) where w: rent of taking office, c [0,w): cost of running for election, x i : policy of political party i, and coefficient α > 0. The expected payoff of the median voter y if party i s candidate wins is E [ (y z) 2] = (y µ i ) 2 σ 2 i (2) 34 / 51

35 Timing without Political Advertisements The last three stages are added to Snyder and Ting (2002). 1. Platform Selection. 2. Candidate Nomination and Selection. 3. 1st Voting. 1st Term of Office. 4. Decision of Running for Reelection. 5. Candidate Nomination and Selection. 6. 2nd Voting. 2nd Term of Office. 35 / 51

36 Equilibrium without Political Advertisements Two parties set x i = 0. 3 types of politicians: cannot win at all, if z [ 1,θ 1] or z [1 θ,1], where θ (w c)/α. can win the first election, but not get reelected, if z [θ 1, 3 3 θ] or z [ 3 3 θ,1 θ]. can win the first election, and get reelected, if z [ 3 3 θ, 3 3 θ]. Implication: Some incubents are not favourable to the voters in reality even though they are elected in the first election. 36 / 51

37 Timing with Political Advertisements 1. Platform Selection. 2. Candidate Nomination and Selection. 3. Advertisement 4. 1st Voting. 1st Term of Office. 5. Decision of Running for Reelection. 6. Candidate Nomination and Selection. 7. 2nd Voting. 2nd Term of Office. 37 / 51

38 Equilibrium with Political Advertisements 3 types of politicians: not join the party, not make advertisement, and not win at all, if z [ 1,θ 1] or z [1 θ,1]. join the party, not make advertisement, win or lose the 1st election and not get reelected, if z [θ 1, 3 3 θ] or z [ 3 3 θ,1 θ]. join the party, make advertisement 1 2 (w αz j 2 c), win the 1st election, and get reelected, if z [ 3 3 θ, 3 3 θ]. Implication: Political advertisements work as signals that differentiate a two-time winner from a one-time winner, while joining a party works as signals that differentiate a one-time winner from a loser. 38 / 51

39 Conclusion Making political advertisements in addition to joining a party enables promising candidates to reveal their hidden types, and voters to elect their favourable candidates adequately. 39 / 51

40 Chapter 4 Measuring Quality Changes for Consumer Goods through Quality Engel Curves in the Japanese Economy 40 / 51

41 Introduction Mkt Price Change = Pure Inflation + Quality Change CPI prices are quality-adjusted prices which aim to measure pure inflation. Ideally, CPI price change = Pure inflation. My Objective: Measuring the extent to which the Japanese CPI controls for the quality changes (without using the hedonic approach) 41 / 51

42 Introduction (cont d) Key Idea: To divide pure inflation and quality change, we want some variables correlated with quality change and uncorrelated with pure inflation. Related Literature: Hedonic Approach Bils and Klenow (2001) AER Boskin et al (1996) 42 / 51

43 Estimation Equation Two basic equations: x i = q i + z i p i = z i + µ q i x i : mkt price, q i : quality, z i : pure inflation rate, p i : quality-adjusted price, and overbar: time average of each variable. Substituting out q i yields p i = µ x i + (1 µ) z i (3) We regard (1 µ) z i as the error term. Problem: z i is the endogenous regressor. 43 / 51

44 A Candidate for an Instrument We want some instrument variable which is correlated with x i and NOT correlated with z i. A candidate: Slopes of Quality Engel Curves. price automobile socks income Figure : Quality Engel Curve 44 / 51

45 Are the data available? To obtain the slopes of quality Engel curves, we need price data of purchased goods with respect to income classes. = The Japanese Family Income and Expenditure Survey (FIES) provides not only the expenditures data, but also prices and quantities data! 45 / 51

46 Estimation for Slopes of Quality Engel Curves For each good i, we obtain the panel data of prices at time (t) with respect to income class ( j). logx i jt = α it + θ i logy j (4) θ i is the slope of quality Engel curve for good i. Our estimator is the Fixed-Effect Estimator. Data is obtained from the FIES. Observations: 72 for each good TV Sets (0.16), Automobiles (0.32), Handbags (0.34), Refrigerators (0.008), Blankets (0.01), Haircut Charges (0.01), Men s Socks (0.12). 46 / 51

47 Valid Instrument? Estimation Equation: p i = µ x i + (1 µ) z i (1) Instruments: θ i (and θ i ) Necessary Conditions: Cov (θ i, x i ) 0, Cov (θ i, z i ) = 0 Figure : Correlation Between x i and θ i. Correl = / 51

48 Correlation between θ i and x i Why does θ i display such a positively high correlation with x i? Hypothesis: when new and high-quality goods enter the market, only wealthy households purchase these high-priced goods. = New goods entries make quality Engel curves steeper. 48 / 51

49 Data To obtain θ i we make use of the FIES as the panel data. x i is from FIES. p i is from CPI Price. We select the samples from the FIES that have corresponding goods listed in the CPI. (excluding food-related goods from the samples) Sample Periods: / 51

50 Results Our estimation equation: p i = µ x i + (1 µ) z i The estimation is based on GMM using θ i and θ i as instrumetal variables. Observations: 43 instrument set µ adjusted R 2 θ i (0.134) t = 4.70 θ i, θ i (0.126) t = 5.01 Our instrumental variables pass the orthogonality test with H = 1.61, 1.73 respectively. 50 / 51

51 Conclusion We make use of the noticeable features of the panel data in the Japanese FIES: reporting the prices and quantities of purchased goods separately! Two advantages: We can simultaneously consider a wide variety of goods. We can apply our method even to those goods whose quality is unclear. 51 / 51