Dynamic Price Competition in Auto-Insurance Brokerage

Size: px
Start display at page:

Download "Dynamic Price Competition in Auto-Insurance Brokerage"

Transcription

1 Dynamic Price Competition in Auto-Insurance Brokerage Luis H. B. Braido Bruno C. A. Ledo March 5, 2015 Abstract We access Brazilian data on auto-insurance and document that: (a) about 20 percent of all policies are sold without brokerage commission; (b) over 40 percent of all policies are sold with the highest brokerage fee allowed for that contract; and (c) the remaining policies are associated with a spread-out distribution of positive fees. We develop a dynamic model of price competition with switching costs which reproduces these empirical findings. The equilibrium structure is used to estimate the model parameters and identify the distribution of switching costs. We also compute brokers life-time expected earns when dealing with regular and new customers. Keywords: Brokerage, fees, price competition, structural estimation, autoinsurance. JEL Classification: D4; L1. We are thankful for comments from Rodrigo de Losso Bueno, Marcelo Medeiros, Humberto Moreira, Mauricio Moura, Heleno Pioner, Bernard Salanié, Marcelo Sant Anna, and seminar participants at the EUI, FGV-SP, FUCAPE, IPEA-RJ, PUC-Rio, UFRJ, USP-RP, USP-SP, and at the following meetings: Econometric Society (Malaga 2012 and Shanghai 2010), European Economic Association (Glasgow 2010), and SBE (Salvador 2010). We are also grateful to Antero Alves Neto for computing support. FGV/EPGE, Rio de Janeiro, Brazil; University of Sao Paulo, Ribeirao Preto, Brazil; 1

2 1 Introduction This paper analyzes the brokerage activity in the Brazilian auto-insurance market. The standard auto-insurance policy lasts for one year. Automatic extensions are not available, and new contracts need to be signed after expiration. All contracts are required to be sold through a certified broker. 1 Auto-insurance brokers are considered experts who advise the insurees on details of the contract. They quote prices with different insurance companies and suggest the best deal for each consumer. They also represent the insuree during the policy duration, helping them to claim the contracted benefits in case of accidents. There are tens of auto-insurance companies and thousands of certified brokers. The typical broker runs a small local business, but the brokerage service is also offered by bank branches and internet companies. Each insurance company provides a standardized software program for brokers. This program computes the baseline insurance price for each given set of characteristics of the insuree, the insured vehicle, and the insurance contract. Brokers add a fee to the baseline price. Brokerage fees must not exceed a ceiling level defined by the insurance company. Ceilings vary from 15 to 50 percent of the policy final price, depending on observed and unobserved characteristics of the market and the contract. Our data document the coexistence of policies being sold with zero and positive brokerage fees. About 20 percent of all contracts are sold without brokerage commission. Positive fees vary smoothly within an interval that ranges from zero to over 900 BRL (equivalent to about 450 PPP USD). They reach a ceiling level for over 40 percent of the contracts. It is challenging to rationalize the economics behind this evidence. On the one hand, the mass of zero brokerage fees suggests that the brokerage market is very competitive. On the other hand, the mass of fees at ceiling levels suggests exactly the opposite. Moreover, our regression analysis shows that the variability in brokerage fees is poorly related to a large set of observable characteristics, suggesting that randomness may be an important element in brokerage pricing. We recall that mixed strategy is sometimes used to model equilibrium price dis- 1 This legislation is enforced under the supervision of a strong national association of insurance brokers with offices and elected representatives in all states of the country. 2

3 persion that is not related to observables see Varian [1980], Stahl [1989], Sharkey and Sibley [1993], and Braido [2009]. We notice however that Nash equilibrium requires that prices in the support of each player s mixed strategy generate the same expected payoff, given the other players strategies. Therefore, the usual static games do not generate zero and positive fees being simultaneously played in equilibrium. We introduce switching costs into a model of price competition. Costs to switch brokers generate an intertemporal value for brokerage. When dealing with a new client, brokers are tempted to set low fees in order to increase the probability of making a sale and becoming matched to the consumer for the following period. This type of loss leading generates a mass of contracts without brokerage commission. When dealing with a regular customer, brokers take advantage of the switching cost and only offer contracts with positive fees. They face a tension between extracting consumer surplus and risking to loose the customer to a competitor. This game has a symmetric stationary Nash equilibrium in which mixed strategies replicate the observed price dispersion. We use the equilibrium mixed-strategy distribution to derive a theoretical data generating distribution. We then perform a maximum likelihood estimation of the model parameters. This structural econometric procedure allows us to compute the brokerage present value of dealing with matched and unmatched insurees. These are important concepts in industrial organization which are difficult to obtain from data on prices. They are useful for analyzing mergers and acquisitions as they allow us to compute the value of a portfolio with regular customers and a stable flow of new potential clients. The remaining of this paper is organized as follows. We discuss related papers in Section 2 and describe the data recorded by the Brazilian Superintendence of Private Insurance (SUSEP) in Section 3. This thorough database conveys information about the population of auto-insurance contracts in the country. Section 4 formally describes our dynamic game of price competition and derives a symmetric stationary Nash equilibrium. In Section 5, we start to take the model to the data. We stress that the database does not record all quotations but only the contracted fees. We take the mixed-strategy equilibrium distribution and the individual decision rule to derive the theoretical data generating distribution. This distribution is used in Section 6 to identify the parameters of the model through a maximum 3

4 likelihood estimation. We compute the distribution of the switching costs and also find an average switching cost of BRL (approximately PPP USD). Additional implications of this structural analysis are presented in Section 7. We find, for instance, that brokers expected lifetime discounted profit is BRL when dealing with a regular (matched) customer and BRL when facing a new (unmatched) insuree. These values are economically meaningful. Concluding remarks are presented in Section 8. 2 Related Literature In frictionless competitive markets, all units of any given homogeneous good should be sold at the same price. Transaction costs for searching prices as well as for switching suppliers have being used to rationalize the fact that identical goods are sometimes sold at very different prices. We use this section to review some contributions in these areas. Search Costs In a seminal paper, Stigler [1961] pointed out the relation between price dispersion and the fact that consumers spend resources to gather information about prices. Since them, many authors in labor economics and industrial organization have contributed to this topic. In an important work, Varian [1980] develops a model of sales in which identical oligopolistic firms set prices for a homogeneous good produced at a constant marginal cost. There are two types of consumers, informed and uninformed. Informed consumers buy at the lowest available price, while uninformed consumers buy from a randomly selected firm. Firms face a tradeoff between lowering prices to increase the probability of making a sale to informed consumers and increasing prices to extract rent from randomly selected uninformed consumers. In order to balance these forces, firms end up using mixed strategies in equilibrium. This generates random sales and ex-post price dispersion. A natural concern about Varian s model is that uninformed consumers should be able to search for price information. To address this issue, Stahl [1989] introduces a searching model in which a fraction of (informed) consumers face zero search costs, while another fraction faces positive search costs. Similarly to Varian [1980], firms use mixed strategy to balance the tradeoff between selling to informed customers 4

5 and extracting rent from consumers with positive search costs. There is also a large empirical literature on the importance of searching costs to explain price dispersion in different markets such as: auto-insurance in Alberta, Canada (Dahlby and West [1986]); prescription drugs in New York drugstores (Sorensen [2000]); life insurance in the US (Brown and Goolsbee [2002]); retail items (such as refrigerator, chicken, coffee, and flour) selected from the Israeli CPI (Lach [2002]); hedge funds in the US (Hortaçsu and Syverson [2004]); on line books (Hong and Shum [2006]); and mortgage contracts (Allen et al. [2013]). There are also recent papers by De Los Santos et al. [2012] and De Los Santos et al. [2013] accessing the empirical relevance of non-sequential search models, as initially conceived by Stigler [1961]. These empirical works study environments with differentiated goods, where consumers hold preferences for brands or characteristics of the seller. Unlike them, we account for search in a fashion that is similar to Varian [1980]. We stress however that the static nature of the search friction is not able to rationalize the coexistence of zero and positive fees in equilibrium. The switching cost is the key element behind this equilibrium outcome in our approach, as it introduces an intertemporal value for selling today without a brokerage commission in order to become matched to the insuree for the next period. Switching Costs In a pioneering paper, Klemperer [1987] introduced a model in which two firms set prices over two periods of time, and consumers bear a fixed cost for switching from one firm to another in the second period. Prices are restricted to be the same for regular and new consumers, and the authors focus on computing a stationary mixed-strategy Nash equilibrium. Thus, the second-period pricing strategies depend on the firm s stock of regular customers. In equilibrium, firms charge identical prices and capture the same share of the market in each period. In other important contributions, Padilla [1995] and Anderson et al. [2004] extend this analysis to an environment with overlapping generations and infinitely many periods. 2 Like in Klemperer [1987], the two firms cannot price discriminate between regular and new consumers, and the equilibrium pricing depend on each 2 See Farrell and Shapiro [1988] and Beggs and Klemperer [1992] for alternative infinite-horizon frameworks. 5

6 firm s market share. In a second front, there are papers analyzing environments with price discrimination. Chen [1997] and Taylor [2003] present models in which two firms set different prices for regular and new consumers over a finite number of periods. 3 Consumers face different switching costs in each period, according to i.i.d. draws from an exogenous distribution function. In equilibrium, the two firms offer the same price for their own regular customers and the same discount price for their rival s consumers. The exogenous distribution of switching costs determines the fraction of consumers who switch suppliers. 4 There are several differences between our work and those in the switching cost literature. 5 The most important is the type of price differentiation allowed in our model. Insurance brokers usually deal to one consumer at a time. It is then natural in our setting to allow for price differentiation between regular and new consumers as well as across insurees within each of these groups. Our equilibrium mixed strategies depend on whether the insuree is matched or not to the broker. They are unrelated to the broker s market share. Since brokers set prices to each consumer at a time, identical consumers end up facing different prices. 3 Data We use data recorded by the Brazilian Superintendence of Private Insurance (SUSEP), a federal institution responsible for regulating the insurance market in the country. Auto-insurance companies are commanded to provide detailed information on all active policies. The SUSEP database conveys cross-section information about the population of auto-insurance policies that have been active (for at least one day) during each semester. We use data relative to one-year policies that were active in the first semester of We focus our analysis on comprehensive 3 Fudenberg and Tirole [2000] and Villas-Boas [2006] also study dynamic models of price discrimination based on consumer s purchasing history. 4 In a relatively different context, Chen and Rosenthal [1996] derive a mixed-strategy equilibrium for a dynamic duopoly in which consumers are loyal to firms, but loyalty varies over time according to firms realized prices and an exogenous stickiness rule. 5 We refer the reader to Farrell and Klemperer [2007] for an extensive survey on this topic. 6

7 policies contracted by individuals. 6 For each policy, we access information about the characteristics of the insuree (such as gender and age), the insured vehicle (such as model and year), and the insurance contract (such as the insurance company, type of coverage, and deductible values). The insurance premium and the brokerage fee embedded on that price are also available. 7 broker. Table 1 defines all variables used along the paper. [Table 1] There is no information about the The insurance policies are associated with a wide range of brokerage fees. This feature is very robust, and a similar pattern is observed in different subsamples. Figure 1 presents histograms for nominal brokerage fees expressed in BRL, and Figure 2 displays the broker s percentage fees as a fraction of the policy final price. We report results for the following six different groups. Subsample A contains the fees paid to brokers across all insurance contracts in the country. Subsample B focuses on contracts in the metropolitan area of Sao Paulo (the largest in the country). Subsample C presents fees on policies covering nine comparable compact cars with identical power train in the metropolitan area of Sao Paulo. 8 Subsample D refines subsample C to include only contracts with positive bonus discount. Insurees with positive bonus discount are particularly interesting because they must have bought an insurance policy before and, then, they most likely conform our model assumption of being initially matched to a broker. (The insurees carry over the bonus status after changing the insurance company or the broker.) Subsamples E and F further refine subsample D to include only new compact cars and new Volkswagen Gol 1.0L, respectively. This vehicle model is the most popular within its class. On average, about 20 percent of the insurance policies are sold with zero fees. Furthermore, there is large dispersion in both nominal and percentage fees. The shapes of the histograms are surprisingly similar across the different subsamples. This suggests that there might be some relevant economic feature behind the dispersion in brokerage fees paid by consumers. 6 We do not analyze: (i) policy endorsements and cancelations; (ii) collective policies covering multiple vehicles; (iii) policies contracted by firms; and (iv) noncomprehensive contracts. 7 We also access files containing information on reported accidents, other claims, and disbursements. However, these files are not useful for the purpose of this paper. 8 The vehicle models are: Peugeot L, Clio 1.0L, Gol 1.0L, Fiesta 1.0L, Ka 1.0L, Uno 1.0L, Palio 1.0L, Corsa 1.0L, and Celta 1.0L. 7

8 [Figures 1-2] The class width of the histograms in Figure 2 is 0.50 percentage point, and there are contract fees in virtually all classes between zero and 42 percent. We notice a higher frequency of fees equal to 1, 5, 10, 15, 20, 25, 30, and 35 percent of the contract s final price. In addition to the fact that brokers round some numbers, the insurance companies impose percentage caps to brokerage fees. These percentage caps vary across companies and withing contracts of a given company. The most frequent caps are 15, 20, 25, 30, 35 percent. We stress however that policies associated with nonround percentage fees such as 12.9 and percent are not rare (they account, for instance, for 13.5 percent of subsample E). What Brokers Say We conducted structured interviews with 20 registered brokers in order to improve our understanding about institutional details of this market. The computer programs used by brokers record the contract final price, the brokerage nominal fee, and the percentage fee. Brokers argued they use these three pieces of information to make their pricing decisions. In many times, they round the percentage fee, the final price, or the monthly installment (when the sale is financed). They also mentioned that insurance companies impose ceilings on brokerage fees expressed in percentage terms. Selected Subsample We use subsample E in our quantitative analyses throughout the paper. The choice of analyzing a more homogeneous subsample is justified by the fact that we attempt to understand the economics behind the price dispersion that is not related to consumer heterogeneity. We recall that subsample E contains policies signed by insurees with positive bonus discount (and therefore not new in the market), covering new compact cars with identical power train, in the metropolitan area of Sao Paulo. This is the largest metropolitan area in the country and, according to SUSEP s categories, it includes 29 connected cities. Figure 3 lists these 29 cities with their respective zip codes. We stress that the city of Sao Paulo itself is indicated with number 1. It is subdivided in 99 neighborhoods in Figure 4. [Figures 3-4] 8

9 We perform reduced-form OLS regressions (using subsample E) for four different dependent variables: the insurance final price; the nominal brokerage fee; the percentage brokerage fee; and a dummy variable indicating whether the policy was sold without brokerage commission. Our econometric models use independent variables describing the policy coverage, the insuree s gender, age, and bonus category. Moreover, we divide the metropolitan area in 158 regions according to the first 3 digits of the zip code and introduce fixed effects for these subregions as well as for the vehicle model and the insurance company. The results are presented in Table 2. Its column zero lists the independent variables used in the estimation. The regression in column 1 analyzes the insurande final price. The R-squared in this regression shows that about 50 percent of the variability in the final price is explained by our model. This is a good fit considering that the insurance companies may use different models for pricing and are likely to access additional information that is not required to be reported to SUSEP. Next, we pursue a similar analysis with respect to the variables describing different aspects of the brokerage commission. The regressions presented in columns 2 to 4 show that our control variables account for: about 14% of the variation in brokerage fees; only 5% of the variation in the percentage fees; and about 15% of why policies are sold without brokerage commission. We conclude that differences in the observable variables are more relevant to explain the dispersion in the insurance price than the variability in the three variables measuring different aspects of the brokerage commission. This supports our view that an important part of the dispersion in brokerage fees is exogenously random. [Table 2] 4 A Recursive Model of Price Competition There are a few distinguishing features in the auto-insurance market. Policies last for one year and must be sold through an insurance broker. There is no automatic extension, and long-term contracts are not enforceable. Insurance companies define a positive baseline price b for each policy. Brokers add a fee q to that price. Insurance companies require that the brokerage fees do not exceed a percentage cap τ 9

10 of the policy final price p := b + q. The condition q τp is therefore equivalent to q r, where r := τ 1 τ b is a nominal ceiling for brokerage fees. Remark 1. The baseline price b and the percentage cap τ are random variables, in the sense that they take different values for each observation in the data. We assume brokers are well-informed and take as given the values of b and τ associated with each insuree. Game Structure Brokers are allowed to set a different fee for each quotation. This is as if they competed for each insuree at a time. We therefore model an environment with a single ensuree, a continuum of identical brokers, and an infinite sequence of periods t T := {0, 1,...}. The insuree demands one insurance policy every period and seeks to minimize the expected lifetime discounted costs. He starts each period matched to a broker and faces a fixed cost c > 0 for switching to another broker. 9 The switching cost c is heterogeneous across insurees, but it is taken as given by brokers when dealing with each insuree. In each period, the insuree faces an i.i.d. shock on the oportunity cost of time. With probability µ (0, 1), he is too busy to shop around and only accesses the price quotation from the matched broker. Alternatively, with probability (1 µ), he costlesly accesses another price quotation from an unmatched broker, randomly selected from the continuum set of brokers. Brokers select a price offer for each period they are called to play. They cannot commit to prices in the future. They maximize expected lifetime discounted profits, and share the same intertemporal discount factor δ (0, 1). Brokerage fees cannot exceed the ceiling r > 0. In principle, fees are not allowed to be negative. However, when dealing with a new insuree, the broker can offer assistance services that reduces the consumer switching cost. To represent this possibility, we allow the unmatched broker to set negative fees down to c. Hence, brokerage fees q must lie in the interval [0, r] when the broker deals with a regular (matched) insuree, and in [ c, r] when the broker deals with a new (unmatched) insuree. The timing of the game is as follows. Nature moves first. It selects an unmatched broker out of the continuum of brokers and determines whether the insuree meets 9 In period t = 0, the matched broker is randomly selected. After that, the insuree stays matched to the last broker he purchased from. 10

11 this broker or not. This latter event occurs with probability 1 µ. It is private to the insuree and cannot be credibly revealed to the matched broker. Second, the two selected brokers choose their pricing strategies. Then, the insuree purchases one policy. The broker who makes the sale becomes matched to the insuree, and the game ends for the other broker. An identical game starts next period. Strategies Brokers payoffs depend on their matched/unmatched statuses. Conditional on this status, the payoffs do not directly depend on the history of the game or on the broker s name. Although strategies could still depend on this information, we will focus on equilibria in which all players select the same stationary strategy (σ m, σ u ), where σ m is a probability distribution over [0, r] to be used when playing under the matched status, and σ u is a distribution over [ c, r] to be used when unmatched. Brokers Payoff Functions For a given strategy σ u followed by the unmatched broker, we denote by π m (q, σ u ) the probability that the matched broker sells the policy when she poses the fee q. The expected life-time discounted payoff of a broker facing a matched insuree is implicitly defined by the following equation: V m (σ m, σ u ) = r 0 π m (q, σ u ) (q + δv m (σ m, σ u )) dσ m (q), where δv m (σ m, σ u ) is the equilibrium continuation value of becoming matched to the consumer next period, after selling a policy today. 10 Similarly, for a given strategy σ m, we let π u (q, σ m ) represent the probability that the unmatched broker after being selected to play sells the contract when her fee is q. The expected life-time discounted payoff of a broker selected to play under the unmatched status is V u (σ m, σ u ) := r c π u (q, σ m ) (q + δv m (σ m, σ u )) dσ u (q). We impose a tie-breaking rule that favors the matched broker in case of a tie. 10 Throughout the paper, we use θ θ to represent the Lebesgue integral over the set of real numbers larger than θ and smaller than θ. In cases where θ < θ, this set is empty and the integral is zero. 11

12 When the distribution σ u is atomless, we obtain π m (q, σ u ) = µ + (1 µ)(1 σ u (q c)) (1) and π u (q, σ m ) = 1 σ m (q + c). (2) In equation (1), the fraction µ stands for the probability that the insuree has no other option but to take the offer from his matched broker, and (1 µ)(1 σ u (q c)) is the probability that the insuree meets a second (unmatched) broker but this broker poses a fee that does not beat offer q posed by the matched broker. In equation (2), the term 1 σ m (q + c) is the probability that the fee offered by the matched broker exceeds q + c and turns to be less attractive than the fee q posed by the unmatched broker. Remark 2. The unmatched broker infers that she only plays after nature has promoted a meeting with the insuree. For this reason, the probability (1 µ) does not affect definition of π u and V u. The value of being called to play under the unmatched status before nature decides whether the insuree will or will not access the unmatched offer is (1 µ)v u (σ m, σ u ). Definition 1 (Equilibrium Concept). A symmetric stationary Nash equilibrium is described by a strategy (σ m, σ u ) for which there is no profitable one-period deviation that is, there is no pair of probability distributions σ m over [0, r] and σ u over [ c, r] such that either V m (σ m, σ u ) < r 0 π m (q, σ u ) (q + δv m (σ m, σ u )) dσ m(q) or V u (σ m, σ u ) < r c π u (q, σ m ) (q + δv m (σ m, σ u )) dσ u(q). Remark 3. We focus on independent one-period deviations and this is without loss of generality. In a stationary equilibrium, players strategies do not relate their current actions to past information that is not summarized by their current matching status. In principle, deviations are allowed to depend on it, but no broker can profit from conditioning behavior on the history of this game given that no other player does 12

13 so. In this, we follow Duffie et al. [1994]. 4.1 Mixed Strategy Equilibrium Consider a deviation strategy in which the matched broker always charges the ceiling fee r. Since the insuree meets no other broker with probability µ > 0, the lifetime expected payoff associated with this strategy is at least t=0 (δµ)t µr = µr 1 δµ. In economies with µr 1 δµ c, there is a pure-strategy equilibrium in which σ m degenerates to min {(1 δ)c, r} and σ u degenerates to min{ δc, r c}. The matched { } r broker sells the policy every period and earns a lifetime payoff of min c, 1 δ. 11 All others earn zero from this insuree. This pure strategy is not a Nash equilibrium when the matched broker can deviate and collect analyze. µr 1 δµ > c. We take this case to Assumption 1. The model parameters are such that δ (0, 1), µ (0, 1), and µr > (1 δµ)c > 0. Let σ u be an atomless probability distribution with support given by [ a, r c), where c < a < r c. Similarly, let σ m be a probability distribution with support given by [c a, r], which is atomless in [c a, r) and has a mass point at r. The lifetime expected payoff associated with an action q [0, r] taken by the matched broker is v m (q) := [µ + (1 µ)(1 σ u (q c))] (q + δv m (σ m, σ u )). (3) Analogously, the lifetime expected payoff associated with a fee q [ c, r] for the broker called to play under the unmatched status is v u (q) := (1 σ m (q + c)) (q + δv m (σ m, σ u )). (4) Strategy when Unmatched We define v m := µr 1 δµ (5) 11 Recall that our tie-breaking rule favors the matched broker. 13

14 and set σ u ( ) to be such that v m (q) = v m, q [c a, r]. (6) If we take v m (q) and v m from equations (3) and (5) and solve condition (6) for σ u, we obtain the following expression for the strategy of brokers under the unmatched status: σ u (q) = 1 µ ( ) r 1 µ δµr + (1 δµ)(q + c) 1, q [ a, r c). (7) By setting σ u ( a) = 0, we obtain a = c (1 δ)µr 1 δµ. (8) It is simple to verify that c < a < r c, 0 σ u ( ) 1, and lim σ u(q) = 1. q r c Strategy when Matched define σ m to be such that Using an analogous reasoning, we take v u > 0 and v u (q) = v u, q [ a, r c). (9) We set σ m (c a) = 0 and evaluate equation (9) at the point q = a. By using equations (4), (5), and (8), we obtain v u = µr c. (10) 1 δµ It follows from Assumption 1 that v m > v u > 0. From our previous derivation, we also obtain σ m (q) = 1 µr (1 δµ)c δµr+(1 δµ)(q c), for q [c a, r); 1, for q = r. Notice that σ m (c a) = 0 as initially set. The distribution σ m is continuous at any q < r and has a mass at the point r. We also have 0 σ m ( ) 1. Moreover, (11) 14

15 thanks to Assumption 1, we have µr (1 δµ)c 0 < 1 lim σ m (q) = < 1. (12) q r r (1 δµ)c Proposition 1. The strategy (σ m, σ u ) defined by conditions (7), (8), and (11) is a symmetric stationary Nash equilibrium under Assumption 1. Proof. The matched broker is indifferent to any action in supp σ m = [c a, r]. Moreover, it follows from conditions (3), (5), and (8) that fees smaller than c a generates a payoff smaller than v m. Analogously, the unmatched brokers are also indifferent to any action in supp σ u = [ a, r c), and fees outside this interval cannot increase this broker s payoff. Remark 4. Notice from equation (8) that c a > 0. Therefore, the fees posed by the matched broker are always positive. When a < 0, there is a positive probability that the unmatched broker offers assistance services to alleviate the switching cost. 5 Taking the Model to Data In our recursive model, brokers pose prices for each insuree at a time. They share the same discount factor δ (0, 1) and are assumed to know the values of r, c, and µ associated with each insuree. When taking the model to data, we assume that µ is a constant parameter in (0, 1) and let r and c vary across insurees. We recall that r := τ b. (13) 1 τ The insurance baseline price b takes a different value for each observation, and these realizations are available from the data. Unfortunately, this is not the case for the percentage ceiling τ. The realizations of τ are known by the brokers, but they are not recorded in our data. We model τ as a latent random variable following a conditional distribution ϕ(τ x), where x represents a vector of observed characteristics. We also notice that, since our parameters are connected to each other through Assumption 1, we can write the random variable c as follows: c = α µr 1 δµ, (14) 15

16 where α is a constant parameter in (0, 1). Under this modeling strategy, we end up with three parameters (δ, µ, α) and one conditional distribution ϕ(τ x) to estimate. 5.1 Data Generating Probability We do not observe all price quotations but only the contracted fees. Our theoretical data generating probability must then combine the equilibrium strategy (σ m, σ u ) with the insurees selection rule. According to our model, each insuree observes a matched offer q m drawn from σ m. Moreover, with probability (1 µ), he also observes an unmatched offer q u drawn from σ u. When observing two offers, the insuree accepts the fee q m if q m q u + c, and he takes q u otherwise. Let y R + denote the brokerage fee recorded in the data (i.e., the winning offer). The conditional probability Pr (y b, τ) represent the data generating distribution of y given (b, τ). Recall that negative fees represent the situation in which the unmatched broker charges zero and offers assistance services to alleviate the switching costs. Since assistance services are not recorded in the data, our observations of y are censored at zero. Moreover, nonpositive fees must be drawn from the distribution σ u. Each insuree accesses an unmatched offer with probability 1 µ and takes it whenever it exceeds the quotation posed by the matched broker plus the switching cost. This implies Pr (0 b, τ) = (1 µ) min{0,r c} a (1 σ m (q + c)) dσ u (q). 12 (15) The distribution Pr (y b, τ) has no mass point over the open interval (0, r). For y (0, r), we have: y Pr (y b, τ) = (1 µ) a (1 σ m (q + c)) dσ u (q) + (1 µ) y c a (1 σ u (q c)) dσ m (q) + µσ m (y). (16) The first two terms in this equation are associated with the scenario in which the insuree accesses two offers. This occurs with probability 1 µ. In this case, with 12 Notice from equation (8) that a < r c. Moreover, recall from footnote 10 than this integral is zero when a > 0. 16

17 probability 1 σ m (q +c), the insuree takes the offer posed by the unmatched broker. Alternatively, with probability 1 σ u (q c), the insuree takes the offer drawn from the matched-broker strategy σ m. The last term in equation (16) accounts for the fact that, with probability µ, the insuree accesses only one offer q < y drawn from the matched-broker strategy σ m. We also recall that: σ m (q) = dσ m (q) = 0, q c a; (17) and dσ u (q) = 0, q r c. (18) This means that fees in (0, c a) are never generated from the distribution σ m which support is [c a, r], while fees in (r c, r) are never generated from the distribution σ u which support is [ a, r c). We conclude by pointing out that the distribution Pr ( b, τ) has a second mass point at the ceiling fee r := τ 1 τ b. Since the support of σ u is [ a, r c), fees equal to r can only be taken by insurees who do not meet an unmatched broker. This is to say that ( ) µr (1 δµ)c 1 lim Pr (y b, τ) = µ. 13 (19) y r r (1 δµ)c 6 Estimation Procedure We estimate the the parameters (α, δ, µ) in two steps. We first model the unobserved percentage ceiling imposed by the insurance company as a latent random variable τ. We use an ordered logit model to represent the conditional distribution ϕ(τ x) given the observed characteristics x. Next, we use this distribution to construct a likelihood model and estimate the structural parameters (α, δ, µ). 6.1 Ordered Logit for ϕ(τ x) We accessed documents from the insurance companies and reports from the broker s association mentioning ceilings on brokerage fees at five different per- 13 We notice that r c (1 σm(q + c)) dσu(q)+ r (1 σu(q c)) dσm(q) = 1. This is because, a c a for any independent realizations of q u and q m, respectively draw from σ u and σ m, we have that q m > q u + c if and only if q u < q m c. This implies r c (1 σm(q + c)) dσu(q) = r σu(q c)dσm(q). a c a 17

18 centage levels, namely:.15,.20,.25,.30, and.35 of the policy final price. about 99.88% of observations in subsample E, the observed percentage fees do not exceed the.35-percentage cap. There are, however, 15 observations with percentage fees in (.35,.42]. To account for that, we also include the value.42 as a percentage ceiling. According to our model, the conditional probability of observing a percentage fee equal to τ is given by ϕ(τ x) (1 lim y r Pr (y b, τ)). By replacing equation (14) into (19), we find that this mass point is given by For 1 lim y r Pr (y b, τ) = 1 α 1 αµ µ2. (20) Since the term 1 α 1 αµ µ2 is constant across all observations, we can estimate the distribution ϕ(τ x) by using the subsample of observations for which the percentage fee reach one of the possible ceiling levels τ {.15,.20,.25,.30,.35,.42}. Subsample E has 6,200 observations with percentage fees equal to one of those percentage caps. We use this reduced subsample to estimate an ordered logit model for ϕ(τ x). The results from this estimation appear in Table 3. We then take these estimates to predict values for ˆϕ τ,j for all observations of Subsample E (including those not used in this estimation step). These values are used next to estimate the parameter vector (α, δ, µ) through a maximum likelihood procedure using the entire subsample E. [Table 3] 6.2 Maximum Likelihood Estimation for α, δ, and µ We adapt the maximum likelihood procedure for censored data described in Meeker and Escobar [1994] to estimate the parameter vector (α, δ, µ). Each observation j is associated with one realization of the vector of characteristics x j and baseline price b j. Moreover, each observation j is generated from one of six possible games, indexed by τ. We fix an observation j and a game τ to define an auxiliary likelihood function L j,τ (α, δ, µ) as follows. For policies sold without brokerage commission (censored observation), we take 18

19 equation (15) and define L j,τ (α, δ, µ) := Pr (0 b j, τ). (21) Similarly, for censored observations associated with a brokerage fee at the percentage ceiling τ, we take equation (20) and write L j,τ (α, δ, µ) := 1 α 1 αµ µ2. (22) Next, we take equations (13) and (14) and write r j,τ = τ 1 τ b j and c j,τ = α µr j,τ 1 δµ. For observations associated with a brokerage fee y j (0, r j,τ ), we derive equation (16) to find a density probability and write L j,τ (α, δ, µ) := (1 µ) (1 σ m (y j + c j,τ )) dσ u (y j ) + [(1 µ) (1 σ u (y j c j,τ )) + µ] dσ m (y j ). (23) We stress that conditions (8) and (17) imply σ m (y j ) = dσ m (y j ) = 0, (24) for every y j (1 δ)µr j,τ 1 δµ. Moreover, condition (18) implies dσ u (y j ) dy = 0, (25) for every y j r j,τ c j,τ. Given the assumption that each τ is independently withdrawn with probability ϕ(τ x), the likelihood function associated with a given observation j is L j (α, δ, µ) = τ ˆϕ τ,j L j,τ (α, δ, µ). (26) To conclude, we write our final likelihood function as L(α, δ, µ) = j L j (α, δ, µ), (27) 19

20 and the associated log-likelihood function as lnl(α, δ, µ) = j ln (L j (α, δ, µ)). (28) 6.3 Numerical Estimation Our optimization problem is not simple since the log-likelihood function is not continuous. We have managed to reduce the model to depend only on three parameters (α, δ, µ), each of them lying in the unit interval (0, 1). This allows us to set a comprehensive grid search and considerably reduces concerns about global optimality. We use the software Wolfram Mathematica to compute closed-form solutions for the integral in equation (15), used in definition of the function (21). The optimization code is written in Matlab. We evaluate the log-likelihood function over a grid with 8 million points. More precisely, our grid includes 200 equally spaced points for each unit interval of the domain. Each block with a million points take about 11 hours to be computed in a high performance server. We select the 50,000 highest values obtained from the grid computation and use their respective parameter values as initial seeds for the Matlab patternsearch optimization algorithm. This algorithm performs a numerical search using fixeddirection vectors (GPS method) and randomly-selected vectors (MADS method). For robustness, we also make this same optimization for 50,000 random initial seeds. Our results are presented in Table Brokers discount factor is This factor accounts for the intertemporal cost of money as well as for the probability that the brokerage relationship is interrupted for unmodeled motives: for instance, when the insuree moves to another city. Our estimate for µ is This means that about percent of the insurees see a price quotation from a new (unmached) broker in addition to the quotation from the regular (matched) broker. The estimated value for α is.4997, which implies an average switching cost of BRL (i.e., approximately PPP USD), where the average is taken over different models indexed by τ and observations indexed by j. Moreover, Figure 5 displays the distribution of switching costs across insurees (averaged over τ). 14 The optimal parameter values were rounded to 4 decimal places. 20

DynamicPriceCompetitioninAuto-InsuranceBrokerage

DynamicPriceCompetitioninAuto-InsuranceBrokerage DynamicPriceCompetitioninAuto-InsuranceBrokerage BrunoAurichio LuisH.B.Braido June 23, 2010 Abstract Auto-insurance data present an intriguing fact: the coexistence of policies sold with zero and positive

More information

Dynamic Price Competition in Auto-Insurance Brokerage

Dynamic Price Competition in Auto-Insurance Brokerage Dynamic Price Competition in Auto-Insurance Brokerage BrunoLedo LuisH.B.Braido February 15, 2012 Abstract Auto-insurance data present an intriguing fact: the coexistence of policies sold with zero and

More information

Price Dispersion. Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK. November, 2006. Abstract

Price Dispersion. Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK. November, 2006. Abstract Price Dispersion Ed Hopkins Economics University of Edinburgh Edinburgh EH8 9JY, UK November, 2006 Abstract A brief survey of the economics of price dispersion, written for the New Palgrave Dictionary

More information

Estimation of Search Frictions in the UK Electricity Market

Estimation of Search Frictions in the UK Electricity Market Estimation of Search Frictions in the UK Electricity Market Monica Giulietti Nottingham University Business School Nottingham United Kingdom Michael Waterson Department of Economics University of Warwick

More information

SERVICE. user guide. Version 1.0 FLM 030004

SERVICE. user guide. Version 1.0 FLM 030004 Version 1.0 FLM 030004 index INTRODUCTION SERVICE DEFINITION BASIC REQUIREMENTS RECOMMENDATIONS REGISTERING THE FLIP SERVICE PLACING CALLS RECEIVING CALLS CALL FORWARDING PLANS AND CALLING RATES VIRTUAL

More information

THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING

THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING THE FUNDAMENTAL THEOREM OF ARBITRAGE PRICING 1. Introduction The Black-Scholes theory, which is the main subject of this course and its sequel, is based on the Efficient Market Hypothesis, that arbitrages

More information

Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets

Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Unraveling versus Unraveling: A Memo on Competitive Equilibriums and Trade in Insurance Markets Nathaniel Hendren January, 2014 Abstract Both Akerlof (1970) and Rothschild and Stiglitz (1976) show that

More information

Simultaneous or Sequential? Search Strategies in the U.S. Auto. Insurance Industry

Simultaneous or Sequential? Search Strategies in the U.S. Auto. Insurance Industry Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance Industry Elisabeth Honka 1 University of Texas at Dallas Pradeep Chintagunta 2 University of Chicago Booth School of Business September

More information

Direct Marketing of Insurance. Integration of Marketing, Pricing and Underwriting

Direct Marketing of Insurance. Integration of Marketing, Pricing and Underwriting Direct Marketing of Insurance Integration of Marketing, Pricing and Underwriting As insurers move to direct distribution and database marketing, new approaches to the business, integrating the marketing,

More information

Switching Cost, Competition, and Pricing in the Property/Casualty Insurance Market for Large Commercial Accounts

Switching Cost, Competition, and Pricing in the Property/Casualty Insurance Market for Large Commercial Accounts Switching Cost, Competition, and Pricing in the Property/Casualty Insurance Market for Large Commercial Accounts Lisa L. Posey * Abstract: With large commercial accounts, a small number of insurers negotiate

More information

Imperfect information Up to now, consider only firms and consumers who are perfectly informed about market conditions: 1. prices, range of products

Imperfect information Up to now, consider only firms and consumers who are perfectly informed about market conditions: 1. prices, range of products Imperfect information Up to now, consider only firms and consumers who are perfectly informed about market conditions: 1. prices, range of products available 2. characteristics or relative qualities of

More information

Chapter 7. Sealed-bid Auctions

Chapter 7. Sealed-bid Auctions Chapter 7 Sealed-bid Auctions An auction is a procedure used for selling and buying items by offering them up for bid. Auctions are often used to sell objects that have a variable price (for example oil)

More information

Hierarchical Insurance Claims Modeling

Hierarchical Insurance Claims Modeling Hierarchical Insurance Claims Modeling Edward W. (Jed) Frees, University of Wisconsin - Madison Emiliano A. Valdez, University of Connecticut 2009 Joint Statistical Meetings Session 587 - Thu 8/6/09-10:30

More information

Modeling Competition and Market. Equilibrium in Insurance: Empirical. Issues

Modeling Competition and Market. Equilibrium in Insurance: Empirical. Issues Modeling Competition and Market Equilibrium in Insurance: Empirical Issues Pierre-André Chiappori Bernard Salanié December 2007 In the last decade or so, numerous papers have been devoted to empirical

More information

Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance Industry

Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance Industry Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance Industry Current version: April 2014 Elisabeth Honka Pradeep Chintagunta Abstract We show that the search method consumers use when

More information

Simultaneous or Sequential? Search Strategies in the U.S. Auto. Insurance Industry

Simultaneous or Sequential? Search Strategies in the U.S. Auto. Insurance Industry Simultaneous or Sequential? Search Strategies in the U.S. Auto Insurance Industry Elisabeth Honka 1 University of Texas at Dallas Pradeep Chintagunta 2 University of Chicago Booth School of Business October

More information

Estimating Consumer Switching Costs in the Danish Banking Industry

Estimating Consumer Switching Costs in the Danish Banking Industry Copenhagen Business School 2014 MSc in Business Administration and Management Science Estimating Consumer Switching Costs in the Danish Banking Industry by Frederik Vrangbæk Jensen Supervisor: Cédric Schneider

More information

Equilibrium: Illustrations

Equilibrium: Illustrations Draft chapter from An introduction to game theory by Martin J. Osborne. Version: 2002/7/23. Martin.Osborne@utoronto.ca http://www.economics.utoronto.ca/osborne Copyright 1995 2002 by Martin J. Osborne.

More information

A Simple Model of Price Dispersion *

A Simple Model of Price Dispersion * Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No. 112 http://www.dallasfed.org/assets/documents/institute/wpapers/2012/0112.pdf A Simple Model of Price Dispersion

More information

Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole

Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole Market Power and Efficiency in Card Payment Systems: A Comment on Rochet and Tirole Luís M. B. Cabral New York University and CEPR November 2005 1 Introduction Beginning with their seminal 2002 paper,

More information

An Empirical Analysis of Insider Rates vs. Outsider Rates in Bank Lending

An Empirical Analysis of Insider Rates vs. Outsider Rates in Bank Lending An Empirical Analysis of Insider Rates vs. Outsider Rates in Bank Lending Lamont Black* Indiana University Federal Reserve Board of Governors November 2006 ABSTRACT: This paper analyzes empirically the

More information

How to Win the Stock Market Game

How to Win the Stock Market Game How to Win the Stock Market Game 1 Developing Short-Term Stock Trading Strategies by Vladimir Daragan PART 1 Table of Contents 1. Introduction 2. Comparison of trading strategies 3. Return per trade 4.

More information

Warranty Designs and Brand Reputation Analysis in a Duopoly

Warranty Designs and Brand Reputation Analysis in a Duopoly Warranty Designs and Brand Reputation Analysis in a Duopoly Kunpeng Li * Sam Houston State University, Huntsville, TX, U.S.A. Qin Geng Kutztown University of Pennsylvania, Kutztown, PA, U.S.A. Bin Shao

More information

Game Theory: Supermodular Games 1

Game Theory: Supermodular Games 1 Game Theory: Supermodular Games 1 Christoph Schottmüller 1 License: CC Attribution ShareAlike 4.0 1 / 22 Outline 1 Introduction 2 Model 3 Revision questions and exercises 2 / 22 Motivation I several solution

More information

Lecture notes: single-agent dynamics 1

Lecture notes: single-agent dynamics 1 Lecture notes: single-agent dynamics 1 Single-agent dynamic optimization models In these lecture notes we consider specification and estimation of dynamic optimization models. Focus on single-agent models.

More information

Working Paper Series

Working Paper Series RGEA Universidade de Vigo http://webs.uvigo.es/rgea Working Paper Series A Market Game Approach to Differential Information Economies Guadalupe Fugarolas, Carlos Hervés-Beloso, Emma Moreno- García and

More information

Intellectual Property Right Protection in the Software Market

Intellectual Property Right Protection in the Software Market Intellectual Property Right Protection in the Software Market Yasuhiro Arai Aomori Public College 153-4, Yamazaki, Goushizawa, Aomori-city, Aomori 030-0196, Japan March 01 Abstract We discuss the software

More information

Foreclosure, Entry, and Competition in Platform Markets with Cloud

Foreclosure, Entry, and Competition in Platform Markets with Cloud Foreclosure, Entry, and Competition in Platform Markets with Cloud Mark J. Tremblay Department of Economics Michigan State University E-mail: trembl22@msu.edu August 27, 2015 Abstract Platforms in two-sided

More information

Testing Cost Inefficiency under Free Entry in the Real Estate Brokerage Industry

Testing Cost Inefficiency under Free Entry in the Real Estate Brokerage Industry Web Appendix to Testing Cost Inefficiency under Free Entry in the Real Estate Brokerage Industry Lu Han University of Toronto lu.han@rotman.utoronto.ca Seung-Hyun Hong University of Illinois hyunhong@ad.uiuc.edu

More information

Customer Service Quality and Incomplete Information in Mobile Telecommunications: A Game Theoretical Approach to Consumer Protection.

Customer Service Quality and Incomplete Information in Mobile Telecommunications: A Game Theoretical Approach to Consumer Protection. Customer Service Quality and Incomplete Information in Mobile Telecommunications: A Game Theoretical Approach to Consumer Protection.* Rafael López Zorzano, Universidad Complutense, Spain. Teodosio Pérez-Amaral,

More information

ANNUITY LAPSE RATE MODELING: TOBIT OR NOT TOBIT? 1. INTRODUCTION

ANNUITY LAPSE RATE MODELING: TOBIT OR NOT TOBIT? 1. INTRODUCTION ANNUITY LAPSE RATE MODELING: TOBIT OR NOT TOBIT? SAMUEL H. COX AND YIJIA LIN ABSTRACT. We devise an approach, using tobit models for modeling annuity lapse rates. The approach is based on data provided

More information

Momentum Traders in the Housing Market: Survey Evidence and a Search Model

Momentum Traders in the Housing Market: Survey Evidence and a Search Model Federal Reserve Bank of Minneapolis Research Department Staff Report 422 March 2009 Momentum Traders in the Housing Market: Survey Evidence and a Search Model Monika Piazzesi Stanford University and National

More information

Momentum traders in the housing market: survey evidence and a search model. Monika Piazzesi and Martin Schneider

Momentum traders in the housing market: survey evidence and a search model. Monika Piazzesi and Martin Schneider Momentum traders in the housing market: survey evidence and a search model Monika Piazzesi and Martin Schneider This paper studies household beliefs during the recent US housing boom. The first part presents

More information

1 Portfolio Selection

1 Portfolio Selection COS 5: Theoretical Machine Learning Lecturer: Rob Schapire Lecture # Scribe: Nadia Heninger April 8, 008 Portfolio Selection Last time we discussed our model of the stock market N stocks start on day with

More information

Department of Agricultural & Resource Economics, UCB

Department of Agricultural & Resource Economics, UCB Department of Agricultural & Resource Economics, UCB CUDARE Working Papers (University of California, Berkeley) Year 2006 Paper 1020 Learning, Forgetting, and Sales Sofia B. Villas-Boas University of California,

More information

Prices versus Exams as Strategic Instruments for Competing Universities

Prices versus Exams as Strategic Instruments for Competing Universities Prices versus Exams as Strategic Instruments for Competing Universities Elena Del Rey and Laura Romero October 004 Abstract In this paper we investigate the optimal choice of prices and/or exams by universities

More information

A revisit of the hierarchical insurance claims modeling

A revisit of the hierarchical insurance claims modeling A revisit of the hierarchical insurance claims modeling Emiliano A. Valdez Michigan State University joint work with E.W. Frees* * University of Wisconsin Madison Statistical Society of Canada (SSC) 2014

More information

Joint Product Signals of Quality. James E. McClure and Lee C. Spector. Ball State University Muncie, Indiana. September 1991.

Joint Product Signals of Quality. James E. McClure and Lee C. Spector. Ball State University Muncie, Indiana. September 1991. Joint Product Signals of Quality By James E. McClure and Lee C. Spector Ball State University Muncie, Indiana September 1991 Abstract In the absence of other information about the quality of an experience

More information

2. Information Economics

2. Information Economics 2. Information Economics In General Equilibrium Theory all agents had full information regarding any variable of interest (prices, commodities, state of nature, cost function, preferences, etc.) In many

More information

Chap 3 CAPM, Arbitrage, and Linear Factor Models

Chap 3 CAPM, Arbitrage, and Linear Factor Models Chap 3 CAPM, Arbitrage, and Linear Factor Models 1 Asset Pricing Model a logical extension of portfolio selection theory is to consider the equilibrium asset pricing consequences of investors individually

More information

Loyalty Rewards Programs in the Face of Entry

Loyalty Rewards Programs in the Face of Entry Loyalty Rewards Programs in the Face of Entry Ross A. Brater January 03 Abstract consider a two-period model of a horizontally differentiated product market which features an incumbent firm and a potential

More information

Buyer Search Costs and Endogenous Product Design

Buyer Search Costs and Endogenous Product Design Buyer Search Costs and Endogenous Product Design Dmitri Kuksov kuksov@haas.berkeley.edu University of California, Berkeley August, 2002 Abstract In many cases, buyers must incur search costs to find the

More information

Two Papers on Internet Connectivity and Quality. Abstract

Two Papers on Internet Connectivity and Quality. Abstract Two Papers on Internet Connectivity and Quality ROBERTO ROSON Dipartimento di Scienze Economiche, Università Ca Foscari di Venezia, Venice, Italy. Abstract I review two papers, addressing the issue of

More information

9.1 Cournot and Bertrand Models with Homogeneous Products

9.1 Cournot and Bertrand Models with Homogeneous Products 1 Chapter 9 Quantity vs. Price Competition in Static Oligopoly Models We have seen how price and output are determined in perfectly competitive and monopoly markets. Most markets are oligopolistic, however,

More information

Why do merchants accept payment cards?

Why do merchants accept payment cards? Why do merchants accept payment cards? Julian Wright National University of Singapore Abstract This note explains why merchants accept expensive payment cards when merchants are Cournot competitors. The

More information

Forthcoming in Research Papers Series, SU- HSE, Research in Economics and Finance, May 2010

Forthcoming in Research Papers Series, SU- HSE, Research in Economics and Finance, May 2010 Forthcoming in Research Papers Series, SU- HSE, Research in Economics and Finance, May 2010 How Does Income Inequality Affect Market Outcomes in Vertically Differentiated Markets? Anna V. Yurko State University

More information

Marketing Mix Modelling and Big Data P. M Cain

Marketing Mix Modelling and Big Data P. M Cain 1) Introduction Marketing Mix Modelling and Big Data P. M Cain Big data is generally defined in terms of the volume and variety of structured and unstructured information. Whereas structured data is stored

More information

Cournot s model of oligopoly

Cournot s model of oligopoly Cournot s model of oligopoly Single good produced by n firms Cost to firm i of producing q i units: C i (q i ), where C i is nonnegative and increasing If firms total output is Q then market price is P(Q),

More information

Markups and Firm-Level Export Status: Appendix

Markups and Firm-Level Export Status: Appendix Markups and Firm-Level Export Status: Appendix De Loecker Jan - Warzynski Frederic Princeton University, NBER and CEPR - Aarhus School of Business Forthcoming American Economic Review Abstract This is

More information

Moral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania

Moral Hazard. Itay Goldstein. Wharton School, University of Pennsylvania Moral Hazard Itay Goldstein Wharton School, University of Pennsylvania 1 Principal-Agent Problem Basic problem in corporate finance: separation of ownership and control: o The owners of the firm are typically

More information

Pricing and Persuasive Advertising in a Differentiated Market

Pricing and Persuasive Advertising in a Differentiated Market Pricing and Persuasive Advertising in a Differentiated Market Baojun Jiang Olin Business School, Washington University in St. Louis, St. Louis, MO 63130, baojunjiang@wustl.edu Kannan Srinivasan Tepper

More information

3 Introduction to Assessing Risk

3 Introduction to Assessing Risk 3 Introduction to Assessing Risk Important Question. How do we assess the risk an investor faces when choosing among assets? In this discussion we examine how an investor would assess the risk associated

More information

Research Article Pricing Model for Dual Sales Channel with Promotion Effect Consideration

Research Article Pricing Model for Dual Sales Channel with Promotion Effect Consideration Mathematical Problems in Engineering Volume 06 Article ID 80403 0 pages http://dxdoiorg/055/06/80403 Research Article Pricing Model for Dual Sales Channel with Promotion Effect Consideration Chuiri Zhou

More information

Essays on Consumer Search

Essays on Consumer Search Essays on Consumer Search Inaugural-Dissertation zur Erlangung des Grades Doctor oeconomiae publicae (Dr. oec. publ.) an der Ludwig-Maximilians-Universität München 2013 vorgelegt von Sergey Kuniavsky Referent:

More information

Fixed-Effect Versus Random-Effects Models

Fixed-Effect Versus Random-Effects Models CHAPTER 13 Fixed-Effect Versus Random-Effects Models Introduction Definition of a summary effect Estimating the summary effect Extreme effect size in a large study or a small study Confidence interval

More information

6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games

6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games 6.254 : Game Theory with Engineering Applications Lecture 2: Strategic Form Games Asu Ozdaglar MIT February 4, 2009 1 Introduction Outline Decisions, utility maximization Strategic form games Best responses

More information

Chapter 9 Experience rating

Chapter 9 Experience rating 0 INTRODUCTION 1 Chapter 9 Experience rating 0 Introduction The rating process is the process of deciding on an appropriate level of premium for a particular class of insurance business. The contents of

More information

OPTIMAL DESIGN OF A MULTITIER REWARD SCHEME. Amir Gandomi *, Saeed Zolfaghari **

OPTIMAL DESIGN OF A MULTITIER REWARD SCHEME. Amir Gandomi *, Saeed Zolfaghari ** OPTIMAL DESIGN OF A MULTITIER REWARD SCHEME Amir Gandomi *, Saeed Zolfaghari ** Department of Mechanical and Industrial Engineering, Ryerson University, Toronto, Ontario * Tel.: + 46 979 5000x7702, Email:

More information

Why High-Order Polynomials Should Not be Used in Regression Discontinuity Designs

Why High-Order Polynomials Should Not be Used in Regression Discontinuity Designs Why High-Order Polynomials Should Not be Used in Regression Discontinuity Designs Andrew Gelman Guido Imbens 2 Aug 2014 Abstract It is common in regression discontinuity analysis to control for high order

More information

LIFE INSURANCE AND PENSIONS by Peter Tryfos York University

LIFE INSURANCE AND PENSIONS by Peter Tryfos York University LIFE INSURANCE AND PENSIONS by Peter Tryfos York University Introduction Life insurance is the business of insuring human life: in return for a premium payable in one sum or installments, an insurance

More information

Pacific Life Insurance Company Indexed Universal Life Insurance: Frequently Asked Questions

Pacific Life Insurance Company Indexed Universal Life Insurance: Frequently Asked Questions Pacific Life Insurance Company Indexed Universal Life Insurance: Frequently Asked Questions THE GROWTH CAP, PARTICIPATION RATE, AND FLOOR RATEE 1. What accounts for the gap in indexed cap rates from one

More information

ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE

ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE ECON20310 LECTURE SYNOPSIS REAL BUSINESS CYCLE YUAN TIAN This synopsis is designed merely for keep a record of the materials covered in lectures. Please refer to your own lecture notes for all proofs.

More information

Interpreting Data in Normal Distributions

Interpreting Data in Normal Distributions Interpreting Data in Normal Distributions This curve is kind of a big deal. It shows the distribution of a set of test scores, the results of rolling a die a million times, the heights of people on Earth,

More information

Supplement to Call Centers with Delay Information: Models and Insights

Supplement to Call Centers with Delay Information: Models and Insights Supplement to Call Centers with Delay Information: Models and Insights Oualid Jouini 1 Zeynep Akşin 2 Yves Dallery 1 1 Laboratoire Genie Industriel, Ecole Centrale Paris, Grande Voie des Vignes, 92290

More information

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay

Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Information Theory and Coding Prof. S. N. Merchant Department of Electrical Engineering Indian Institute of Technology, Bombay Lecture - 17 Shannon-Fano-Elias Coding and Introduction to Arithmetic Coding

More information

Online Appendix to Are Risk Preferences Stable Across Contexts? Evidence from Insurance Data

Online Appendix to Are Risk Preferences Stable Across Contexts? Evidence from Insurance Data Online Appendix to Are Risk Preferences Stable Across Contexts? Evidence from Insurance Data By LEVON BARSEGHYAN, JEFFREY PRINCE, AND JOSHUA C. TEITELBAUM I. Empty Test Intervals Here we discuss the conditions

More information

When to Use the Open Business Model for Software Products under Network Effects?

When to Use the Open Business Model for Software Products under Network Effects? When to Use the Open Business Model for Software Products under Network Effects? Lizhen Xu, Marius F. Niculescu and D. J. Wu Scheller College of Business, Georgia Institute of Technology, Atlanta, GA 30308

More information

Betting with the Kelly Criterion

Betting with the Kelly Criterion Betting with the Kelly Criterion Jane June 2, 2010 Contents 1 Introduction 2 2 Kelly Criterion 2 3 The Stock Market 3 4 Simulations 5 5 Conclusion 8 1 Page 2 of 9 1 Introduction Gambling in all forms,

More information

FINANCIAL ECONOMICS OPTION PRICING

FINANCIAL ECONOMICS OPTION PRICING OPTION PRICING Options are contingency contracts that specify payoffs if stock prices reach specified levels. A call option is the right to buy a stock at a specified price, X, called the strike price.

More information

Combining player statistics to predict outcomes of tennis matches

Combining player statistics to predict outcomes of tennis matches IMA Journal of Management Mathematics (2005) 16, 113 120 doi:10.1093/imaman/dpi001 Combining player statistics to predict outcomes of tennis matches TRISTAN BARNETT AND STEPHEN R. CLARKE School of Mathematical

More information

Price Discrimination in Oligopoly: Evidence from Swedish Newspapers*

Price Discrimination in Oligopoly: Evidence from Swedish Newspapers* Price Discrimination in Oligopoly: Evidence from Swedish Newspapers* Marcus Asplund London Business School and CEPR Rickard Eriksson Stockholm School of Economics Niklas Strand Stockholm School of Economics

More information

Vieira Ceneviva, Almeida, Cagnacci de Oliveira & Costa Advogados Associados

Vieira Ceneviva, Almeida, Cagnacci de Oliveira & Costa Advogados Associados Vieira Ceneviva, Almeida, Cagnacci de Oliveira & Costa Advogados Associados PCS In Brazil One More Time! On September 11 th Anatel issued a new draft edital in the hopes that the unsold regions that were

More information

Regret and Rejoicing Effects on Mixed Insurance *

Regret and Rejoicing Effects on Mixed Insurance * Regret and Rejoicing Effects on Mixed Insurance * Yoichiro Fujii, Osaka Sangyo University Mahito Okura, Doshisha Women s College of Liberal Arts Yusuke Osaki, Osaka Sangyo University + Abstract This papers

More information

Econometric analysis of the Belgian car market

Econometric analysis of the Belgian car market Econometric analysis of the Belgian car market By: Prof. dr. D. Czarnitzki/ Ms. Céline Arts Tim Verheyden Introduction In contrast to typical examples from microeconomics textbooks on homogeneous goods

More information

Persuasion by Cheap Talk - Online Appendix

Persuasion by Cheap Talk - Online Appendix Persuasion by Cheap Talk - Online Appendix By ARCHISHMAN CHAKRABORTY AND RICK HARBAUGH Online appendix to Persuasion by Cheap Talk, American Economic Review Our results in the main text concern the case

More information

Mixing internal and external data for managing operational risk

Mixing internal and external data for managing operational risk Mixing internal and external data for managing operational risk Antoine Frachot and Thierry Roncalli Groupe de Recherche Opérationnelle, Crédit Lyonnais, France This version: January 29, 2002 Introduction

More information

ECON 312: Oligopolisitic Competition 1. Industrial Organization Oligopolistic Competition

ECON 312: Oligopolisitic Competition 1. Industrial Organization Oligopolistic Competition ECON 312: Oligopolisitic Competition 1 Industrial Organization Oligopolistic Competition Both the monopoly and the perfectly competitive market structure has in common is that neither has to concern itself

More information

Decline in Federal Disability Insurance Screening Stringency and Health Insurance Demand

Decline in Federal Disability Insurance Screening Stringency and Health Insurance Demand Decline in Federal Disability Insurance Screening Stringency and Health Insurance Demand Yue Li Siying Liu December 12, 2014 Abstract This paper proposes that the decline in federal disability insurance

More information

Discussion of Momentum and Autocorrelation in Stock Returns

Discussion of Momentum and Autocorrelation in Stock Returns Discussion of Momentum and Autocorrelation in Stock Returns Joseph Chen University of Southern California Harrison Hong Stanford University Jegadeesh and Titman (1993) document individual stock momentum:

More information

On Compulsory Per-Claim Deductibles in Automobile Insurance

On Compulsory Per-Claim Deductibles in Automobile Insurance The Geneva Papers on Risk and Insurance Theory, 28: 25 32, 2003 c 2003 The Geneva Association On Compulsory Per-Claim Deductibles in Automobile Insurance CHU-SHIU LI Department of Economics, Feng Chia

More information

Optimal proportional reinsurance and dividend pay-out for insurance companies with switching reserves

Optimal proportional reinsurance and dividend pay-out for insurance companies with switching reserves Optimal proportional reinsurance and dividend pay-out for insurance companies with switching reserves Abstract: This paper presents a model for an insurance company that controls its risk and dividend

More information

Chapter 6: The Information Function 129. CHAPTER 7 Test Calibration

Chapter 6: The Information Function 129. CHAPTER 7 Test Calibration Chapter 6: The Information Function 129 CHAPTER 7 Test Calibration 130 Chapter 7: Test Calibration CHAPTER 7 Test Calibration For didactic purposes, all of the preceding chapters have assumed that the

More information

EDUCATION AND EXAMINATION COMMITTEE SOCIETY OF ACTUARIES RISK AND INSURANCE. Copyright 2005 by the Society of Actuaries

EDUCATION AND EXAMINATION COMMITTEE SOCIETY OF ACTUARIES RISK AND INSURANCE. Copyright 2005 by the Society of Actuaries EDUCATION AND EXAMINATION COMMITTEE OF THE SOCIET OF ACTUARIES RISK AND INSURANCE by Judy Feldman Anderson, FSA and Robert L. Brown, FSA Copyright 25 by the Society of Actuaries The Education and Examination

More information

Hedonic prices for crude oil

Hedonic prices for crude oil Applied Economics Letters, 2003, 10, 857 861 Hedonic prices for crude oil Z. WANG Department of Economics, Monash University, PO Box 197, Caulfield East, Victoria 3145, Australia Email: Zhongmin.Wang@BusEco.monash.edu.au

More information

IBM SPSS Direct Marketing 23

IBM SPSS Direct Marketing 23 IBM SPSS Direct Marketing 23 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 23, release

More information

INTERNATIONAL COMPARISON OF INTEREST RATE GUARANTEES IN LIFE INSURANCE

INTERNATIONAL COMPARISON OF INTEREST RATE GUARANTEES IN LIFE INSURANCE INTERNATIONAL COMPARISON OF INTEREST RATE GUARANTEES IN LIFE INSURANCE J. DAVID CUMMINS, KRISTIAN R. MILTERSEN, AND SVEIN-ARNE PERSSON Abstract. Interest rate guarantees seem to be included in life insurance

More information

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering

Engineering Problem Solving and Excel. EGN 1006 Introduction to Engineering Engineering Problem Solving and Excel EGN 1006 Introduction to Engineering Mathematical Solution Procedures Commonly Used in Engineering Analysis Data Analysis Techniques (Statistics) Curve Fitting techniques

More information

An Example of Non-Existence of Riley Equilibrium in Markets with Adverse Selection

An Example of Non-Existence of Riley Equilibrium in Markets with Adverse Selection An Example of Non-Existence of Riley Equilibrium in Markets with Adverse Selection Eduardo M Azevedo Daniel Gottlieb This version: February 7, 06 First version: January, 06 Rothschild and Stiglitz [976]

More information

Quality differentiation and entry choice between online and offline markets

Quality differentiation and entry choice between online and offline markets Quality differentiation and entry choice between online and offline markets Yijuan Chen Australian National University Xiangting u Renmin University of China Sanxi Li Renmin University of China ANU Working

More information

Inflation. Chapter 8. 8.1 Money Supply and Demand

Inflation. Chapter 8. 8.1 Money Supply and Demand Chapter 8 Inflation This chapter examines the causes and consequences of inflation. Sections 8.1 and 8.2 relate inflation to money supply and demand. Although the presentation differs somewhat from that

More information

WARWICK ECONOMIC RESEARCH PAPERS

WARWICK ECONOMIC RESEARCH PAPERS Estimation of Search Frictions in the British Electricity Market Monica Giulietti Michael Waterson and Matthijs R. Wildenbeest No 940 WARWICK ECONOMIC RESEARCH PAPERS DEPARTMENT OF ECONOMICS Estimation

More information

Internet Advertising and the Generalized Second Price Auction:

Internet Advertising and the Generalized Second Price Auction: Internet Advertising and the Generalized Second Price Auction: Selling Billions of Dollars Worth of Keywords Ben Edelman, Harvard Michael Ostrovsky, Stanford GSB Michael Schwarz, Yahoo! Research A Few

More information

Oligopoly: Cournot/Bertrand/Stackelberg

Oligopoly: Cournot/Bertrand/Stackelberg Outline Alternative Market Models Wirtschaftswissenschaften Humboldt Universität zu Berlin March 5, 2006 Outline 1 Introduction Introduction Alternative Market Models 2 Game, Reaction Functions, Solution

More information

Competition and Fraud in Online Advertising Markets

Competition and Fraud in Online Advertising Markets Competition and Fraud in Online Advertising Markets Bob Mungamuru 1 and Stephen Weis 2 1 Stanford University, Stanford, CA, USA 94305 2 Google Inc., Mountain View, CA, USA 94043 Abstract. An economic model

More information

STOCK MARKET VOLATILITY AND REGIME SHIFTS IN RETURNS

STOCK MARKET VOLATILITY AND REGIME SHIFTS IN RETURNS STOCK MARKET VOLATILITY AND REGIME SHIFTS IN RETURNS Chia-Shang James Chu Department of Economics, MC 0253 University of Southern California Los Angles, CA 90089 Gary J. Santoni and Tung Liu Department

More information

IBM SPSS Direct Marketing 22

IBM SPSS Direct Marketing 22 IBM SPSS Direct Marketing 22 Note Before using this information and the product it supports, read the information in Notices on page 25. Product Information This edition applies to version 22, release

More information

INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition)

INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition) INDIRECT INFERENCE (prepared for: The New Palgrave Dictionary of Economics, Second Edition) Abstract Indirect inference is a simulation-based method for estimating the parameters of economic models. Its

More information

Consumer Search and Pricing Behavior in Internet Markets

Consumer Search and Pricing Behavior in Internet Markets Consumer Search and Pricing Behavior in Internet Markets Maarten C.W. Janssen Erasmus University and Tinbergen Institute José Luis Moraga-González Erasmus University, Tinbergen Institute and CESifo Matthijs

More information

Non-Exclusive Competition in the Market for Lemons

Non-Exclusive Competition in the Market for Lemons Non-Exclusive Competition in the Market for Lemons Andrea Attar Thomas Mariotti François Salanié October 2007 Abstract In order to check the impact of the exclusivity regime on equilibrium allocations,

More information