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
Master’s thesis submitted on March 31st, 2014
No. of pages (characters): 70 (125.684)
Page
Executive Summary ... 4
1. Introduction ... 5
1.1 Problem formulation ... 6
1.2 Topic delimitation and methodological considerations ... 7
1.3 Previous research ... 8
1.4 Thesis overview ... 12
2. Switching Costs ... 13
2.1 Definition of consumer switching costs ... 13
2.2 Switching costs’ effect on firms and markets ... 15
2.3 Switching costs in the banking industry ... 16
3. Theoretical Models and Empirical Approaches ... 19
3.1 Shy’s model of consumer switching costs ... 19
3.2 Empirical approach to estimate consumer switching costs ... 23
3.3 Consumer switching costs and consumer characteristics ... 25
4. Data ... 27
4.1 Bank data ... 27
4.2 Firm data ... 31
4.2.1 Bank connections ... 31
4.2.2 Year of establishment ... 34
4.2.3 Financial data ... 35
4.2.4 Potential bias ... 38
5. Results ... 46
5.1 Estimating switching costs using Shy’s model ... 46
5.2 Switching costs estimated from firm’s bank connections ... 53
5.4.1 Issues of significance testing ... 61
5.4.2 Results of the estimation ... 62
5.4.3 Issues of non-‐normality ... 67
6. Conclusion ... 70
7. Bibliography ... 72
Appendix A ... 74
A-‐1 ... 74
A-‐2 ... 76
A-‐3 ... 77
In this thesis the switching costs of consumers in the Danish banking industry is examined. If consumers incur switching costs, each individual firm’s demand is more inelastic, and gives firms monopoly power over existing consumers.
The consumer switching costs are estimated using a simple theoretically derived model and an empirically based model. The theoretical model use market shares and prices offered to
consumers as input, and the empirical model examine the distribution of markets shares based on both new and existing consumers. New consumers do not incur switching costs, while the existing consumers potentially incur switching costs. If the distributions of market shares of new and existing consumers are identical, consumers incur no switching costs in the market.
The difference between the two distributions is used to proxy the consumer switching costs.
The relationship between consumer switching costs and consumers’ characteristics is examined using a linear regression model. Consumer characteristics are modeled using financial data on Danish firms.
The theoretical and empirical estimations are conducted on the same Danish banks. The estimated consumer switching costs, of both estimations, are consistent despite differences in methods and data. The level of switching costs is not examined, as the unit of measure is different for the two estimations, so the relative level of switching costs is used for comparison instead. Both estimations agree on the relative levels of consumer switching costs of the largest banks, and indicate that the largest banks generally serve the consumers with the highest switching costs. The linear regression of consumer switching costs on consumer characteristics reveals that the consumer characteristics do have some effect on the consumer switching costs, albeit not very large, as the consumer characteristics only explain a small part of the variance in consumer switching costs. There is a positive relationship between consumers’ size and
consumer switching costs, and a negative relationship between the consumers’ financial condition and consumer switching costs.
1. Introduction
Consumer switching costs are the costs consumers face if they switch to buying a functionally
identical product from another supplier. Switching costs can arise because consumers display brand-‐
loyalty or because consumers are locked in by the supplier. Switching costs can consist of many different elements, such as exit and entry costs related to the switching itself, as well as the more individual specific costs of searching and learning how to use a new product or brand. There can also be substantial risks involved with switching to a new supplier. Switching costs could for example occur when purchasing a new car, where the person have to invest time in learning how everything works and incur the risk that the new car does not live up to the expectations. It could also be
installation and start-‐up cost related to switching internet service provider. Firms can in some cases increase their consumer’s switching costs by rewarding consumers that purchase more, such as frequent-‐flyer benefits or supermarket coupons.
If consumers in a market incur switching costs, products that are ex ante homogeneous become, after the purchase of one of them, ex post heterogeneous (Klemperer 1987). Switching costs give firms market power over existing consumers, so that firms producing homogeneous goods can potentially earn monopoly profits (Klemperer 1995). If consumers incur switching costs, firms have to choose between charging a higher price that capitalizes on existing consumers, or a lower price to attract new customers. Switching costs undermine the basic principle of economic competition that consumers buy from the firm that offers the lowest price.
The banking industry is structurally different from many other industries, as either the banks or consumers carry a credit risk when lending money. The banking industry is also characterized by long relationships between the bank and the consumer. Due to this banks need to have substantial information about consumers, to offer a fair price given the consumers individual characteristics.
The banking market is also characterized by very high complexity, with many banks offering a very wide range of products. A simple loan in one bank can thus be very different from a simple loan in another bank, due to additional products offered by the banks. This indicates that switching costs might be relatively high in the banking industry compared to other industries.
An analysis by the Danish Competition and Consumer Authority using data from 2012 concludes that the Danish retail banking industry is not competitive enough. Only 16% of Danish banks assess interest rates and fees as important competition parameters (Konkurrence-‐ og Forbrugerstyrelsen 2013). Another report from the Danish Competition and Consumer Authority finds that when Danish consumers has to borrow money, 78% contacts only one bank, and that is the bank they usually choose (Konkurrence-‐ og Forbrugerstyrelsen 2011). This competitive inefficiency may be partially caused by consumer switching costs.
This thesis is organized as follows: in the rest of this section the problem formulation, a topic delimitation, a presentation of the previous research and a graphic overview of the thesis will be presented. In section 2 a formal definition of switching costs, as well as the market and industry will be considered. In section 3 the theoretical models and approaches will be described, and in section 4 the data used in the models will be presented. In section 5 the results of the thesis will be presented, and in section 6 the conclusion of the thesis will be presented.
1.1 Problem formulation
The main focus of this thesis will be to analyze the switching costs of consumers in the Danish
banking industry, by estimating the switching costs of consumers, using both theoretical models and empirical estimations.
The problem formulated above will be studied by answering the following research questions:
• How can consumer switching costs be estimated theoretically from publicly available data?
• Which empirical methods can be used to estimate the switching costs of consumers, if the individual switches of consumers are not observed?
• What is the theoretical and empirically estimated switching costs of consumers at each bank and how does the theoretical and empirically estimated switching costs compare?
• How does the switching costs vary across consumers of individual banks, and does the characteristics of consumers have an influence on the switching costs?
1.2 Topic delimitation and methodological considerations
This thesis seeks to examine the switching costs of consumers in the Danish banking industry. The consumers considered are both individual retail consumers and commercial consumers, respectively in the theoretical and empirical part of the thesis. Switching costs of consumers in other countries or industries will not be considered. While alternative countries and industries are both very
interesting for comparison of the estimated switching costs, the focus will be on the comparison between the theoretical and empirical estimations. The switching costs of consumers are assumed to be exogenous, and no inferences about how switching costs can be affected by suppliers will be offered. There are many ways that the switching costs of consumers can be affected, and they may be endogenous by nature, but it is too large a subject to be covered in this thesis. The focus will be on the actual estimations of switching costs, but the methods used are of equal importance, as they ensure the legitimacy and reproducibility of the results.
The thesis is limited by the data available, which is the main challenge of estimating consumer switching costs. Estimating consumer switching costs, if data on individual switches is available, is not very complicated, as each choice of the consumer can be replicated. If the individual switches are not observed, as they rarely are, the task is much more complex. This thesis will assume that
individual switches are unobservable and will therefore have to proxy the choices of consumers.
Formally the scientific method that will be used in the thesis is the hypothetico-‐deductive model. The scientific method is characterized by forming a hypothesis theoretically, and examine if the
theoretical results can be replicated using empirical models. This scientific method is chosen to offer the best overview of the subject, since consumer switching costs are very complicated to measure without data on each consumer’s switch. The entire thesis is based on strict assumptions and the ability of variables to proxy the underlying effects. This is a consequence of the problem studied, which essentially tries to estimate micro-‐effects based on macro-‐data. As a consequence thereof, all models and theories are kept as simple as possible. Complicated and complex models can be
advantageous in some cases, but can switch the focus of the thesis to the models, rather than the results and empirical relationships. More complex models may have been preferred if the data available were more comprehensive, in contrast to the aggregated data used in this thesis. Using
complex models to investigate this subject, given the data available, may additionally give the impression that the results are more exact than they actually are.
1.3 Previous research
In this section a short review of the previous research done on consumer switching costs, with focus on empirical estimations will be offered. The review serves as an overview of the challenges and issues related to estimating consumer switching costs. The predominant challenge when studying consumer switching costs is that the data available to researchers does not include the actual switches of consumers. As a consequence of this, the amount of empirical research on the subject is limited. Many papers attempt to estimate switching costs across some groups of consumers, but without quantification of the magnitude or significance of the consumer switching costs. The previous research will in the following be presented in order of their subject. First the theoretical research will be presented, then the empirical research on switching costs, and at last the empirical research on consumers in the financial sector will be presented. Practically all published papers find evidence of switching costs in the markets the have chosen to examine1.
The theoretical foundation of the literature on consumer switching costs is summarized in
(Klemperer 1995). Klemperer has written many widely cited articles on consumer switching costs, and is one of the leading researchers on the subject. In the paper Klemperer defines a model where consumer switching costs give firms monopoly power over their existing consumers. In a two period model, he shows that prices in the first period are lower if consumers incur switching costs than in the absence of switching costs. The model is subsequently extended to a many period model, to examine the competitiveness of markets where consumers have switching costs. In the model firms must balance the incentive to charge a high price to exploit its locked-‐in consumers, against the opposing incentive to charge a low price to increase its market share that will be valuable in the future. From the model Klemperer also derives that consumer switching costs will most likely raise prices of both new and existing consumers, when firms cannot discriminate between them. He also reasons that switching costs may discourage new entry, and in turn reduce competitiveness further.
In a discussion of multiproduct competition Klemperer suggest a rationale for multiproduct firms. He
1 This does not imply that consumers in all markets incur switching costs.
argues that if consumers value variety, but have switching costs, then a firm that does not offer a full line of products force consumers to either forgo variety or force consumers to incur switching costs.
This is highly relevant for the banking industry.
(Chen & Hitt 2002) estimate the switching costs of consumers of online brokers. They use a proxy for the individual switches of consumers, based on their internet behavior. They measure the switching costs of consumers of each broker, and find significant variation in switching costs of consumers across brokers, with as much as a factor two variation. They examine the brokers and consumers’
characteristics, and find that customers’ demographic characteristics have very little effect on switching, while the product usage and quality seem to be associated with reduced switching.
One of the more popular papers on consumer switching costs in the banking industry is (Kim, Klinger og Vale 2003). They set up an empirical model where customers transition probabilities, embedded in firms’ value maximization are used to derive equations of a first-‐order condition, market share (demand), and supply equations that can be estimated. They use panel data of the entire Norwegian banking sector. Their model is very complex and require many derivations and estimations to reach the final equations. The model defines the transition probabilities of consumers and model the probabilities, and consequently market shares of banks. The model is dependent on a time lag that specifies the period over which switching of bank can take place. They find that their estimation is significant if a time lag of three years are used, but time lags of one and two years does not yield significant switching costs. Using a three year time lag they find evidence of consumer switching costs. The point estimate of the average switching costs of consumers is 4.1% or about one-‐third of the average price used in the estimation. From the parameters of the estimation, they can infer that about a third of the average bank’s market share is due to locked-‐in customers. The robustness of the estimation can be questioned, as they work with several market definitions and time lags, but only some combinations are reported.
(Hannan & Adams 2011) examine consumer switching costs, by observing the bank’s deposit rates, as well as in-‐ and out-‐migration of various geographical areas. They argue that the trade-‐off
mentioned in (Klemperer 1995), between attracting new customers and exploiting new customers, should theoretically cause banks to offer higher deposit rates (lower prices) in areas with more in-‐
migration. Similarly should banks in areas with high out-‐migration offer lower deposit rates (higher prices), as customers are customers at the bank for a shorter amount of time on average. They find strong evidence to support their hypotheses. (Sharpe 1997) applies the same method, but uses migration as a proxy for consumer switching costs. He also finds significant evidence that switching costs affects the level of deposit interest rates.
(Barone, Felici & Pagnini 2010), a paper published by the Bank of Italy, investigate switching costs of commercial consumers on four local Italian credit markets. Using a mixed logit model they find that firms tend to iterate their choice of main bank over time, and conclude that switching bank is costly for the consumers. They also find evidence that banks price discriminate between new and existing consumers.
Consistent with theory they find that banks offer lower interest rates (lower prices) to new customers, to cover their switching costs and attract new customers, and higher interest rates (higher prices) to existing customers to exploit that they incur switching costs if they switch to a competing bank. The discount
offered to new customers amounts to, on average, 44 basis points or around 7% of the average interest rate.
(Stango 2002) examines consumer switching costs, by looking at prices on the credit card market. He uses panel data of credit card issuers, and find evidence that consumer switching costs have a
significant influence on commercial banks’ pricing. He examine banks’ customer bases and find that banks with riskier customers bases yields stronger results, and suggest that there is a correlation between probability of default and switching costs. (Ausubel 1991) studies the same market in the 1980s and claims that the market resembles the theoretical model of perfect competition, but
contrary to theory, prices are sticky relative to cost of funds and credit card issuers have persistently earned three to five times the ordinary rate of return in the banking industry. Ausubel argues that switching costs, and primarily search costs, may explain the high interest rates and profits.
Many of the papers on the subject are concerned with consumer switching costs’ distortion of prices.
Regulative authorities are especially interested in the subject, as they want to reduce the economic inefficiency that consumer switching costs can cause. (Matthews 2009) writes that the importance of switching costs lies in their impact on market operation, allocative inefficiency, monopolistic profits and barriers to entry. In (Konkurrence-‐ og Forbrugerstyrelsen 2013) the Danish Competition and
Consumer Authority finds evidence of inefficient price competition on the Danish retail banking market and suggest various initiatives to increase price competition in the market.
Several papers on consumer switching costs focus on the financial sector. This may be because it is a sector with high information asymmetry and high complexity, which makes it plausible that
consumers incur switching costs. Information asymmetry is especially prevalent when switching bank. High quality borrowers or consumers may be pooled with low quality borrowers and consumers, and as a consequence is offered a worse contract than an informed bank would have offered (Thadden 2001). The current banks of high quality borrowers are therefore able to offer better contracts than competing banks, which will contribute to the consumer’s switching costs. The focus on relationship banking in modern banking, where consumers have account managers and are offered packages with many products, may also increase the consumer switching costs (Boot 2000).
1.4 Thesis overview
Several datasets, methods, and results are included in the thesis. For a better overview of the thesis, the following flowchart outline the methods applied to estimate consumer switching costs, the data used for each estimation, and the result of each estimation. Each box represent a sub-‐section in the thesis.
Figure 1: Thesis overview.
2. Switching Costs
This section offers an introduction to the basic definitions that will be used in this thesis. The section serves as a foundation for the later investigations of consumer switching costs. The real life effects of switching costs are important to keep in mind when doing the more formal examinations, as it is those effects that the thesis seeks to replicate and estimate. The first part of this section offer a definition of consumer switching costs, and what factors that contribute to consumer switching costs. The next section offers a description of the effects of switching costs on markets, and the following section looks at the switching costs of consumers in the banking industry. The last section offers a general outline of the Danish banking industry.
2.1 Definition of consumer switching costs
Consumers switching costs can be defined as the onetime costs that customers associate with the process of switching from one provider to another (Burnham, Frels og Mahajan 2003). The switching costs are the costs perceived by the consumers and not limited to the actual monetary costs. The switch has to be from one functionally identical product to another, otherwise the switching costs cannot be isolated from the utility of switching to a different product. Functionally identical products can be defined as products that are not differentiated except for switching costs, thus the products does not have to be strictly identical (Klemperer 1987). If consumers has not made a previous
purchase, i.e. are entering the market, then they cannot switch supplier. Consumers therefore have to have made a previous purchase from a supplier in the market to incur switching costs. If the
switching costs are zero, then the choice of buying a product is the same as the choice consumers that enters the market face. As per the definition switching costs are a onetime cost, in contrast to an ongoing cost associated with using a product after the switching has occurred. The entire cost of switching does not have to be incurred at the time of the switch, but the switching costs that are realized after the switch must be related to the switching process. Consumer switching costs are asymmetric, as a consequence of the psychological or non-‐economic costs associated with a switching process. For example the costs of searching and learning about a technical product will depend on the consumer’s technical knowledge.
Three different groups or types of switching costs can be defined: transaction costs, learning costs, and artificial or contractual costs (Klemperer 1987). Each of these groups consists of different elements that potentially affect the cost of switching.
Transaction costs are related to the financial loss incurred when switching to a functionally identical product. These costs will mostly be onetime financial outlays that are incurred when switching providers, other than the funds used to purchase the product itself (Burnham, Frels og Mahajan 2003). That could be costs associated to equipment that has to be returned or rented, or the cost of cancelling and starting a new subscription. There may also be certain products or additional
equipment related to the brand that has to be replaced, for example accessories for a new mobile phone. These additional costs are also a part of the switching costs.
Learning costs are related to the time and effort aspect of switching to a functionally identical product. Even though the products are functionally identical, they may not require the same skills.
Time and effort invested in learning one product might not be transferrable to other products. The consumer thus has to spend time and effort to learn the new product, as well as making the
consumers current knowledge obsolete. The costs associated with searching for alternative products are also included in this category. A textbook example is a consumer choosing a cake mix. Even though the products are of identical quality, it is less costly for the consumer to choose the one he or she purchased before and knows how to make.
The last category, artificial costs, is characterized by the absence of natural cost related to the switching. They arise entirely as a consequence of firm’s decisions. They are related to business practices that ensure repeat purchases, such as rewards when a customer buys a certain amount of goods from the firm. An example of such benefits is supermarket stamps earned by shopping, which can eventually be traded in for other goods. It could also be costs created by a contract between a consumer and a supplier, where the consumer commits one self to one supplier. This is seen on a large scale with mobile phone subscriptions and business-‐to-‐business relations.
The three categories do not cover all types of switching costs. It is difficult to make a comprehensive list, as all costs associated with switching from one supplier to another constitute switching costs.
One category that can be very significant is the relationship to the firm’s employees, and can in certain cases contribute to a very large part of the consumer switching costs. This is especially the case when the product is highly related to the employees of the firm, for example when an employee of the firm has private knowledge about the consumer. This type of switching costs could likely be prevalent in service industries. Some consumers may also identify themselves with the brand, in such a way that affective losses can be incurred when breaking those bonds of identification. Both can be very significant in some industries and completely irrelevant in other industries. Another facet that does not fit into these categories is the risk involved in switching. Even though the products are functionally the same, personal preferences may cause the products to yield different utility. The consumer cannot know for certain if the switch will improve his or hers utility unless the consumer has perfect information about both products. Empirically this aspect is very important, as there is uncertainty involved in practically all real life decisions and consumers display bounded rationality. Common to all aspects of switching costs is that if switching costs are present, rational consumers in a market display brand loyalty when faced with a choice between functionally identical products (Klemperer 1987).
Many of the costs consumers incur when switching to a new supplier have parallels in firms’ costs of serving new customers (Klemperer 1995). If consumers face costs of opening and closing a new account, it is likely that firms also face the same cost of completing that transaction. If consumers face a cost of learning to work with a new firm, then the firm might also incur costs when learning to work with the customer as well. A firm and a consumer can allocate their total costs of switching in numerous ways; therefore the total switching costs can be defined as the consumers’ switching costs plus the suppliers’ switching costs.
2.2 Switching costs’ effect on firms and markets
Existence of consumer switching costs in a market can have a wide range of consequences. Consumer switching costs make each individual firm’s demand more inelastic, such that firms that increase their price experience a decrease in demand of less magnitude than in markets without switching costs (Klemperer 1987). Switching costs make otherwise homogenous products heterogeneous after consumers have made their first purchase, which essentially segment the market into submarkets,
and thus reduce competition. In regular models with differentiated products, the social cost of firms’
increased monopoly power is mitigated by the benefit of increased consumer choice, while perceived differentiation as a consequence of switching costs does not yield any benefits for consumers to offset the cost of restricted output (Klemperer 1987). The products are per definition functionally identical, so the differentiation only increases firms’ market power, and do not increase consumers’
choices, as would normally be the case.
The higher the switching costs, the higher is the monopoly power that firms gain over their existing customers, and the more intense is the competition for consumers and market share before
consumers are attached to a supplier. Brand loyalty and in turn switching costs are important aspects of the firms’ focus on building market share. It might also be part of the reason why market share is sometimes used as a measure of corporate success. The increased market power over existing customers does not necessarily increase firms overall profit and make them better off. As firms’ realize that they can get comparatively more money out of customers that have purchased the product before, which increases the competition for new customers. The increased competition for new customers might offset the monopolistic profits that firms can achieve. Therefore the effect of consumer switching costs on firms profit is unambiguous, but it is evident that competition for new customers and switching costs are positively correlated. So consumers’ benefit from low switching costs, it is not clear if suppliers’ benefit from high switching costs.
2.3 Switching costs in the banking industry
The banking industry is a very important part of the economy, as all persons and firms need a bank for financial intermediation and transaction services. The price of banks’ products and services can have a big impact on consumers’ economy, and it is thus important for the economy that the financial markets are efficient. This section will first consider the banking industry in general, and then the Danish banking industry.
The banking industry is characterized by high complexity and products that goes far beyond lending and borrowing. The large banks offer many different products, such as day-‐to-‐day accounts with or without a line of credit, savings accounts, pension accounts, investment and insurance. Banks thus
compete for consumers on many different markets, and often have consumer programs that offer benefits to consumers if they use more products. Using more than one product will likely increase consumer switching costs, as consumers either have to incur the inconvenience of switching only part of their products with the bank, or switch all their products and incur the switching costs for multiple products. Banks that does not offer all products that a consumer demand will be at a serious disadvantage, as they force consumers to either incur switching costs related to the unavailable products or do without those products. The high complexity of the financial sector makes the learning costs higher than other more simple sectors. If consumers want to switch they have to be able to compare their current product with alternative products, which means that they have to know the prices and services of the different products. This task can be difficult for the average consumer (Konkurrence-‐ og Forbrugerstyrelsen 2011).
The banking market is also characterized by information asymmetry, namely adverse selection. This is especially the case when firms or individuals want to borrow money. A customer’s current bank has private or inside knowledge about the firm or individual that cannot be directly transferred to competitors. The initial situation of symmetric informed competitors turns into one of asymmetric information after the bank has dealt with the customer (Thadden 2001). This is much like the normal switching cost situation where ex-‐ante homogenous products become ex-‐post heterogeneous after a purchase. In this case the products themselves does not necessarily change, but the price rival banks offer may change due to information asymmetry. A high quality borrower that wants to switch to an uninformed competitor, may be pooled with low quality borrowers and thus is offered a contract inferior to a contract offered by an informed bank (Thadden 2001).
The Danish banking industry is characterized by a few large banks as well as a large number of smaller banks. At the moment there are 108 active banks in Denmark. There are two banks with markets shares above 15 percent, 5 banks with market shares between 2 and 10 percent, and the last 101 banks has a market share under 2 percent (Konkurrence-‐ og Forbrugerstyrelsen 2013). A large part of these banks are specialized, and only operate on some markets, thus not all banks are
relevant in this thesis. Only eight banks have a nationwide branch network, and nine out of ten Danish citizens has a bank close their home or work. So while there are many banks in Denmark, most consumers only have a limited number of banks to choose from due to banks’ branch network.
Contracts in the Danish banking industry, as well as the financial sector in general, are often characterized by a mutual counterparty risk – a risk that the counterparty will not meet its contractual obligations. “The Deposit Guarantee Fund” guarantee all deposits held by all Danish banks, up to 100.000 euro per depositor. It is also customary that larger strong banks in Denmark acquire distressed banks before they go bankrupt. For the depositors with deposits under 100.000 euro, there is a relatively low risk of a financial loss if their bank defaults. There is however other costs related to being a customer in a bank that defaults. The depositors that prefer to have more than 100.000 euro in a single bank will probably choose a bank with a low perceived probability of default, which may create an asymmetry of consumer types across banks.
3. Theoretical Models and Empirical Approaches
In this section the theoretical foundation and empirical approach for estimating consumer switching costs is presented. In the first part of this section Shy’s theoretical model will be presented, then the method for estimation the empirical switching costs will be reviewed. Finally the regression of consumer characteristics on the empirically estimated consumer switching costs will be outlined.
3.1 Shy’s model of consumer switching costs
In this section Shy’s method for calculating consumer switching costs will be presented (Shy 2002).
The model is extremely simple, which is both a strength and weakness of the model. It is
nevertheless a good foundation for further research. The model uses firms’ observed market shares and prices and maps these onto the switching costs of consumers of the firm. Shy starts off by introducing the model in a duopoly and then extends the model to a multiform industry and then solve for the unobserved switching costs.
Consider a market with two firms denoted A and B, producing two identical products also denoted A and B. Initially consumers are distributed such that 𝑁! consumers already purchased brand A, and 𝑁! already purchased brand B. The first group of consumers is represented by 𝛼 and the second group 𝛽. The prices charged by the firms are 𝑝! and 𝑝!, respectively. It is not possible for firms to price discriminate between consumers. The cost of switching from one brand to another is denoted 𝑆. Shy make the assumption that switching costs have to be positive, 𝑆> 0. The switching costs are assumed to be known by each firm, but unobserved by the researcher.
Consumers who has purchased brand A and B has utility 𝑈! and 𝑈!, respectively. The utility function for each consumer is given by
𝑈! ≡ −𝑝! staying with brand A
−𝑝!−𝑆 switching to brand B ( 3.1 ) 𝑈! ≡ −𝑝!−𝑆 switching to brand A
−𝑝! staying with brand B ( 3.2 )
Let 𝑛! denote the number of people buying brand A on their next purchase and 𝑛! denote the number of people buying brand B on their next purchase. Both are endogenously determined in the model. If Bertrand competition is assumed, then the market shares will be
𝑛! =
0 if 𝑝! >𝑝!+𝑆
𝑁! if 𝑝!−𝑆≤𝑝! ≤𝑝!+𝑆
𝑁! +𝑁! if 𝑝! <𝑝!−𝑆 ( 3.3 )
𝑛! =
0 if 𝑝! >𝑝!+𝑆
𝑁! if 𝑝!−𝑆≤𝑝!≤ 𝑝!+𝑆
𝑁! +𝑁! if 𝑝! <𝑝!−𝑆 ( 3.4 )
In models without switching costs the firm that set the lowest price will capture the entire market.
In this model each firm will capture the entire market if they set a price lower than the other firm, minus the switching costs of consumers. If the firm sets a price in the interval between the other firm’s price minus switching costs and the other firm’s price plus the switching costs, then the firm will keep their existing market share. In a standard Bertrand model with homogenous goods, the results are often a theoretical benchmark, as products almost always are differentiated in some sense and consumers almost always incur search costs and therefore switching costs. This model tries to get closer to reality by including switching costs, and therefore including the almost unavoidable costs such as search costs and risk related to switching.
For simplicity it is assumed that the firms’ production costs are zero, and their respective profits are straightforward
𝜋! 𝑝!,𝑝! = 𝑝!𝑛! ( 3.5 )
𝜋! 𝑝!,𝑝! = 𝑝!𝑛! ( 3.6 )
With these definitions the prices that the two firms will choose can be examined. First it is attempted to find a Nash-‐Bertrand equilibrium that is a pair of nonnegative prices, as the firms marginal costs are zero, where both firms choose prices that maximize their profits given the other firms price. If neither firm has an incentive to deviate, then a Nash-‐Bertrand equilibrium exist.
According to equation (3.3) and (3.4) firm A can set a maximal price of 𝑝! = 𝑝!+𝑆 without losing any of its customers 𝑁!. Similarly can firm B set a maximal price of 𝑝!= 𝑝!+𝑆 without losing any customers. If firm B choses any price 𝑝!∗, then firm A’s best response is price 𝑝! = 𝑝!∗ +𝑆, and firm B will have incentive to deviate as 𝑝! = 𝑝!∗ +2𝑆. Thus the two equations are inconsistent, and there is no equilibrium where either firm does not have an incentive to deviate.
As no Nash-‐Bertrand equilibrium exists, Shy goes on to introduce his own equilibrium concept called undercutting. In his paper he defines undercutting as follows:
Definition 1
Firm i is said to undercut firm j, if it sets its price to 𝑝! <𝑝!−𝑆,𝑖=𝐴,𝐵 and 𝑖≠𝑗. That is, if firm i
‘subsidizes’ the switching cost of firm j’s customers.
If either firm undercuts the other, then the firm captures the entire market, and leaves the other firm with 𝑛! = 0. Shy’s equilibrium property, called the undercut-‐proof property, is based on the premise that neither firm should have an incentive to undercut the other and capture the entire market. Both firms earn zero profit if they does not have a market share, and are thus limited in their liability.
Profits of each firm are 𝜋!!! =𝑝!𝑁! if each firm only sells to their existing customers and 𝜋!!!!!! = 𝑝!−𝑆 𝑁! +𝑁! ,𝑖 ≠𝑗 if either firm undercut the other and captures the entire market share. In the undercut-‐proof equilibrium the pair of prices satisfies 𝜋!!! ≥𝜋!!!!!!,𝑖≠ 𝑗.
Shy formally defines the undercut-‐proof property as follows:
Definition 2
A par of prices (𝑝!,𝑝!) is said to follow the Undercut-‐proof Property (UPP) if (a) For given 𝑝!! and 𝑛!!, firm A chooses the highest price 𝑝!! subject to 𝜋!! = 𝑝!!𝑛!! ≥(𝑝!−𝑆)(𝑁! +𝑁!)
(b) For given 𝑝!! and 𝑛!!, firm B chooses the highest price 𝑝!! subject to 𝜋!! = 𝑝!!𝑛!! ≥(𝑝!−𝑆)(𝑁!+𝑁!)
(c) The distribution of consumers between the firms is determined in (3.3) and (3.4).
From this definition it can be inferred that firms charge a higher price if their competitor charge a high price. It is also clear that large switching costs allows firms to charge a higher price, which is a very desirable property of the model.
Point (a) and (b) states that each firm choose the highest possible price, which means that both equations must hold with equalities in equilibrium. The two equations can be solved for a unique pair of prices:
𝑝!! = !!!!!! !!!!!! !
! !!!!!!!!! ! ( 3.7 )
𝑝!! = !!!!!! !!!!!! !
! !!!!!!!!! ! ( 3.8 )
The only unknown variable in equation (3.7) and (3.8) is the consumer switching costs, 𝑆. It is clear that there is a positive relationship between the firm’s prices and the switching costs, while the relationship between the firm’s prices is unambiguous.
Shy then extends the model to a multifirm industry. In the following, it is assumed that prices and market shares of each firm are observed. There are 𝐼≥ 2 firms in the market, indexed 𝑖=1,…,𝐼 and each firm sets a price 𝑝!,𝑖=1,…,𝐼. Shy use the undercut-‐proof property from Definition 2, by
making the assumption that each firm only consider undercutting exactly one competitor. He
justifies this assumption by the real world observation that most ‘price wars’ are generally triggered between only two brands. If all prices satisfy the undercut-‐proof property, market shares are an expression for the profitability of a firm, so the larger market share a firm has, the more profitable is the firm. The smallest firm will then have the largest incentive to undercut, and is therefore most likely to undercut all other firms in the market. Without loss of generality firms can be indexed by decreasing market share 𝑁! > 𝑁! >⋯ >𝑁!. Shy then assumes the competitive behavior of each firm are as follows:
Definition 3
• Each firm 𝑖 ≠𝐼 fears to be undercut by firm 𝐼, and hence sets its price, 𝑝!, in reference to the price charged by firm 𝐼.
• Firm 𝐼 itself fears that it is targeted by firm 1 and therefore sets its price, 𝑝!, in reference to 𝑝! so firm 1 will not find it profitable to undercut its price.
The unobserved consumer switching costs can now be calculated for each firm in the market. Shy define 𝑆! as the switching costs of a brand 𝑖 consumer that has previously purchased brand 𝑖. This is assumed known to all firms and consumers, but not known to the researcher. Each firm 𝑖≠ 𝐼 takes 𝑝! as given, and sets the maximal 𝑝! to satisfy
𝜋! = 𝑝!𝑁! ≥ 𝑝!−𝑆! 𝑁!+𝑁! ( 3.9 )
The condition is very similar to that of the duopoly case, but now firms only fear being undercut by the smallest competitor, 𝐼, and thus maximizes their prices so only firm 𝐼 will not find it profitable to undercut. Equation (3.9) is solved for the unobserved switching costs, in the case of equality.
𝑆! =𝑝!−!!!!!
!!!! ,𝑖∈ 1,…,𝐼−1 ( 3.10 )
Thus the consumers at firm 𝑖’s switching costs are equal to price firm charges, subtracted some market share weighting of the price firm 𝐼 charge. The switching costs of firm 𝑖’s consumers, 𝑆!, are high if firm 𝑖 charge a high price or if firm 𝑖 has a large market share relative to firm 𝐼. Similarly, are the consumer’s switching costs low if firm 𝐼 charge a high price, or if firm 𝐼 has a large market share relative to firm 𝑖.
The switching costs of consumer’s of brand 𝐼 also have to be determined. Shy assume that the smallest firm find firm 1 most likely to undercut, and therefore choose a price, such that firm 1 does not have incentive to undercut.
𝜋! =𝑝!𝑁! ≥(𝑝! −𝑆)(𝑁!+𝑁!) ( 3.11 )
If (3.11) is treated as an equality, the switching costs of consumers at firm 𝐼 are:
𝑆! = 𝑝!−!!!!!
!!!! ( 3.12 )
The switching costs of consumers at each firm can be calculated from equation (3.10) and (3.12).
Before the calculations can be carried out using empirical data, the size of the market, prices, and market shares has to be defined.
3.2 Empirical approach to estimate consumer switching costs
In this section the theoretical framework for the empirical estimation of consumer switching costs will be reviewed. The method for estimating switching costs is very simple, and there is not much
