Estimating Consumer Switching Costs in the Danish Banking Industry

Transcription

1 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 31 st, 2014 No. of pages (characters): 70 ( )

2 Table of Contents Page Executive Summary Introduction Problem formulation Topic delimitation and methodological considerations Previous research Thesis overview Switching Costs Definition of consumer switching costs Switching costs effect on firms and markets Switching costs in the banking industry Theoretical Models and Empirical Approaches Shy s model of consumer switching costs Empirical approach to estimate consumer switching costs Consumer switching costs and consumer characteristics Data Bank data Firm data Bank connections Year of establishment Financial data Potential bias Results Estimating switching costs using Shy s model Switching costs estimated from firm s bank connections

3 5.3 Comparison of theoretical and empirical results Switching costs and firm characteristics Issues of significance testing Results of the estimation Issues of non- normality Conclusion Bibliography Appendix A A A A

4 Executive Summary 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. 4

5 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. 5

6 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? 6

7 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 7

8 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 examine 1. 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. 8

9 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- 9

10 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 10

11 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). 11

12 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. 12

13 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. 13

14 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. 14

15 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, 15

16 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 16

17 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. 17

18 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 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 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 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. 18

19 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! p! S U! p! S p! staying with brand A switching to brand B switching to brand A staying with brand B ( 3.1 ) ( 3.2 ) 19

20 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! = n! = 0 if p! > p! + S N! if p! S p! p! + S N! + N! if p! < p! S 0 if p! > p! + S N! if p! S p! p! + S N! + N! if p! < p! S ( 3.3 ) ( 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. 20

21 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). 21

22 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. 22

23 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! ) If (3.11) is treated as an equality, the switching costs of consumers at firm I are: S! = p!!!!!!!!!! ( 3.11 ) ( 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 23

24 theory to be reviewed. The merit of the model lies mainly in the logic of the method. The null hypothesis is if consumers in the Danish banking industry face switching costs. If the null hypothesis is true, the levels of the switching costs of consumers will be estimated. The follow method is similar to the one used in (Kézdi & Csorba 2011), but they look at the elasticities of market shares rather than actual market shares. The model distinguishes between existing consumers, and consumers entering the market hereafter called new consumers. Existing consumers have a current bank connection, while new consumers do not. It is assumed that the new and existing consumers are homogenously distributed, such that the characteristics that matter for demand changes are similar. It is also assumed that if banks price discriminate between new and existing consumers, they all do it to the same degree. If consumer j enters the market in period t, the probability that the consumer use bank i as their bank connection is denoted n!"#. Similarly if consumer j is an existing customer at bank i, defined as having bank i as a bank connection in period t 1, the probability that the consumers stay loyal to the bank in period t is denoted e!"#. The share of new and existing consumers choosing bank i in period t is respectively n!" and e!". In other words n!" is the market shares of banks based on the group for new consumers and e!" is the market shares of banks based on the group of existing consumers. If consumers do not face switching costs in the market, the existing consumers face the same choice as the new consumer. Since consumers are homogenously distributed, and banks price discriminate in the same way, the consumer s choice probabilities must be equal in the absence of switching costs n!"# = e!"#. If the choice probabilities are equal, then the market shares must be almost identical for the two group of consumers n!" e!". If there are switching costs in the market, and they are sufficiently high, then some existing consumers may not switch bank, even though they would if they did not have an existing bank connection. The existing consumers are therefore locked in at their current bank, as a consequence of switching costs. This is also called the lock- in effect of switching costs. The lock- in effect can be measured as: n!" e!" δ!" δ!" = e!" n!" ( 3.13 ) The indicator δ!" specify the fraction of existing consumers that are prevented from switching bank i in period t as a consequence of switching costs. The fraction of consumers δ!" would have switched if 24

25 there were no switching costs. It should be noted that δ!" is not the actual switching costs, but is a proxy of the switching costs. The results of δ!" can not be compared directly to the switching cost estimates in Shy s model, as the unit of measure are different. For comparisons it may sometimes be more correct to use a standardized version: θ!" =!!"!!!"!!" ( 3.14 ) Both δ!" and θ!" can be positive and negative. If they are positive there is a lock- in effect, if they are close to zero there is no lock- in effect and if they are negative, it essentially means there is a negative lock- in effect. This arises because the new consumers find the bank more attractive than the existing consumers, and the number of consumers is standardized in the market share calculation. If other banks have locked- in consumers, the consumers are prevented from switching to the more attractive banks in period t, and they will consequently have a negative lock- in effect. A negative lock- in effect should be interpreted as a low lock- in effect, or low switching costs of consumers, compared to the consumers of the other banks in the market. 3.3 Consumer switching costs and consumer characteristics In this section the regression of firms characteristics on the estimated consumer switching costs will be presented. The purpose of the regression is to examine the relationship between consumers switching costs and the consumers characteristics. A standard linear regression model is chosen to estimate the relationships. This method for estimating customers characteristics on computed switching costs is mentioned in (Chen & Hitt 2002), but is not used in the paper as the dataset was not large enough. The dataset available for this thesis is very large, and the interesting part of the estimation is to see if there is any relationship at all, and if there is, if it is a positively or negatively correlated relationship. The consumer switching costs estimated from firm s bank connections are a proxy based on the lock- in effect, which does not have a measure, so the actual magnitude of the parameter estimates are not of interest. The available data and the linear regression model can be seen below. 25

26 Variable Description and type Measure or code Balance Balance of firm Currency - DKK Capital Capital of firm Currency - DKK Profit Dummy variable indicating if the firm made a positive profit on the latest financial statement 1 Firm made a profit; 0 Firm did not make profit. Solvency Solvency ratio:!"#$%&!"#$%!""#$" Ratio capped at and 999 Debt Debt of firm Currency - DKK Equity Equity of firm Currency - DKK BankConnections Number of bank connections of the firm Integer registered in the dataset. YearEstablished Groups of dummy variables 7 dummy variables containing information about the year the firm were established Default category: <1950. Groups ; ; ; ; ; ; >2011 Table 1: Variables used for the linear regression. The linear regression model to be estimated is defined as follows: δ it = α + β 1 Log Balance + β 2 Log Capital + β 3 Profitable + β 4 Log Solvency + β 5 Log Debt + β 6 Log Equity + β 7 BankConnections + 14 k!8 β k YearEstablished ( 3.15 ) 26

27 4. Data In this paper data from two sources will be used. The first dataset is used as input to the theoretical model, and it contains financial data on all Danish banks. The theoretical model also use prices faced by consumers, these are found on a website where consumers can see all prices offered by the Danish banks. The second dataset contains data on all Danish firms, including their current bank connection, which will be used for the empirical estimation of switching costs. The first part of this section will present the data on the Danish banks, with focus on prices and market shares and the second part of this section will present the data on Danish companies. In the second part the variables will be reviewed and the important topics related to using the dataset will be discussed. 4.1 Bank data Most of the data on the banks in Denmark are from the database Bankscope. Bankscope is a global banking database that contains financial statements of all active banks in Denmark from 2006 to 2012, as well as some additional information about the banks. The database include all banks that has been operating any time in the time period, but not all banks publish comprehensive financial statements due to their size and some data might be incomplete, as many banks have been merged or acquired during the financial crisis. The banks that are included in the estimation, or equivalent the definition of the market, is based on the products the banks currently offer, which will be discussed later in this section. Shy s model use prices and market shares as input, so these are the two most important figures. Usually market shares would either be calculated using some unit measure or revenue, but banks do not produce goods in the usual sense, so a balance sheet figure is a more correct measure. The market shares should in this context be close to how consumers perceive them. The total balance is often used, but it includes many instruments that a private consumer are not concerned with, so only some part of the total balance is related to private consumers. To come closer to the market shares 27

28 consumers perceive the total customer deposits in each bank is used to calculate the market shares 2. Market shares for each bank are illustrated graphically below, indexed by size. Figure 2: Market shares for each bank in the Danish banking market, based on retail consumer deposits in Figure 2 shows that there are very large size differences of the banks in the market. The two largest banks account for around 70% of the market, while the smallest banks have an almost insignificant part of the total market. Prices offered to consumers are much harder to obtain than market shares. It is not straight forward to find a single uniform price that consumers face. Banks compete on multiple markets, and consumers use multiple products, so there is no ideal uniform price offered by each bank. The price 2 Market shares calculated using total customer deposits, total balance and both gross and net loans are highly correlated, and the results are very similar for each measure. 28

29 of a loan to consumption and a loan to a house, in which the bank has collateral, can be significantly different. The price consumers face can also be both a lending rate or a deposit rate, depending on the product, with different contractual obligations. There is also a chance that consumers only compare prices on a limited number of products, and make a conclusion about the bank s general prices on that basis. Retail banking is however characterized by third degree price discrimination, while commercial banking is often characterized by personal pricing, so it does make sense to proxy the price offered by banks to all retail consumers. A proxy of prices offered to consumers could be an interest income or interest rate figure on the financial statements, but it is a very rough estimation of the actual prices offered to consumers, as it is an average over all products and all consumers, as well an average over the financial year. An alternative proxy is to use the current prices, of a unique product, offered by each bank. These prices can be retrieved from the Danish website It is a website made in collaboration with The Danish Bankers Association and The Danish Consumer Council that gives consumers opportunity to compare prices of Danish banks. It is the banks own responsibility to update the information, and the prices are guiding. The website comes very close to the actual prices consumers currently face for each individual products. The product of which prices will be used is a 5- year annuity of DKK with no collateral. It should be a decent proxy for a uniform price faced by consumers, but it is still a proxy, as only one product is considered and the prices offered by banks on the website are indicative. The product is chosen because it is one of the most common products, and it is expected to have a high correlation with the prices on other products offered by each bank. An average of the prices on all products on the website could also be used, but there is no indication that this is more accurate estimate of the price consumers base their decisions on. The distribution of prices are illustrated below. 29

30 Figure 3: Prices offered to retail consumers by each bank in the market. There is a quite large spread between the prices offered by the 32 banks. The spread between the largest and the fifth largest bank is around 4%. There seems to be no general trend in the prices, but the variation increase as the banks get smaller, which is expected as some of them are niche banks that targets certain groups of people. The banks that should be included in the estimation have to be considered. In accordance with the theoretical model, a market has to be defined, where each firm produces or offer the same product. The Bankscope database have data for most banks, but there are many banks that are specialized in some way, such that they focus on particular customers or products. An initial condition for a bank to be included in the estimation is that they have to offer a simple loan of the type mentioned earlier. Therefore all banks that can be found on pengepriser.dk are considered. This limits the estimations to banks that are active and have contributed to the website. Some smaller and specialized banks have chosen not to participate on the website, but they are not competing for the same customers as 30

31 the other on the website, so it seems reasonable that they are not included in the market. In a market where consumers use many products from one or more banks, the product offered to the consumer is harder to define. If a bank only offer loans to consumers, then a consumer that only need a loan might use that bank, but consumers that need a full line of banking services cannot use that bank alone. This issue becomes more complex when the consumer switching costs are considered. It is hard to predict the effect it would have if banks that only offer a limited line of products are included in the estimation, so the market is limited to banks that offer all products on the aforementioned website. That adds up to six different lending products and two deposit products. A total of 32 banks satisfy this condition. This restriction does not limit the market significantly. To test how the results change if the market definition is modified, another market is defined, where each bank must have at least a two- percent market share. This rules out the many small banks that characterize the Danish banking market as seen on Figure 2. This limits the market to six banks. Both estimations will be presented for both markets. 4.2 Firm data Data on firms are acquired from the CD- Direct database supplied by KOB. In Shy s theoretical model firms are producers, while firms in this section are consumers, as the firms are customers in the banks. The database has information about all Danish firms that are registered for VAT. The database includes financial and accounting data, number of employees, industry and bank connections. The database contains new as well as historical public financial reports for all Danish firms. The primary data that will be used for the estimation of consumer switching costs, are bank connections of firms and year of establishment. For the estimation of firm characteristics influence on consumer switching costs, the figures; balance, capital, equity, debt, profit, solvency ratio, number of bank connections, and the year of establishment are used Bank connections 50% of all Danish companies have at least one registered bank connection in the database, which corresponds to observations, after all criteria has been applied. In the estimations only firms that have registered bank connections will be considered. The missing bank connections seem to be 31

32 evenly distributed among all firms and considering the large amount of data it should not bias the estimations. Firms can have more than one bank connection, which is also registered in the database. Firms usually only have one primary bank for day- to- day activities, but the distinction between primary and secondary bank is not available in the database. Therefore each bank connection is treated equally, so firms that have more than one bank connection will contribute more to the total number of bank connections. The database does not include foreign firms, so there is no information about any banks foreign operations. This will most likely not bias the estimations, as the banks with substantial foreign operations in other countries than Denmark usually have foreign subsidiaries due to regulatory considerations. There is however the possibility that banks that operate in other countries than Denmark are structurally different than the banks that only operates in Denmark. This heterogeneity may be reflected in the estimations and can potentially bias the switching cost estimates, unfortunately this is not possible to control for using this dataset. The banks considered in Shy s model have been defined as banks that offer a full line of products to retail consumers. To be able to compare the results of the empirical estimation with Shy s model, the same banks are considered, with the same indexation. This will decrease the statistical power of the estimation, as the number of observations is limited, but will not bias the estimations. Below is the bank connections of each bank considered earlier, indexed according to descending market share calculated on the basis of private deposits. 32

33 Figure 4: Registered bank connections for each bank. It is evident that the market shares do not correspond to those that were calculated using consumer deposits. Some banks have different market shares, so the indexation by size is not consistent on the commercial banking market. Bank number 23 is not present in the commercial market and is therefore not included on the horizontal axis. The two main reasons for these differences are that commercial customers rather than private customers are considered and the market shares are based on respectively a number of bank connections and the monetary amount of deposits. So differences occur both because of the proportion of private and commercial customers as well as differences in the average size of deposits in each bank. This should not affect the estimations, but it is clear that the two market shares are not perfectly correlated, which should be kept in mind when comparing the consumer switching cost estimates of the theoretical and empirical model. 33

34 4.2.2 Year of establishment The year of establishment is used to group the firms into two groups. The groups proxy respectively new firms entering the market, and thus face no switching costs, and existing firms in the market that face switching cost. The two distributions that will be compared are the bank connections of firms established before 2011 and the bank connections of firms established in 2011 and after, corresponding to the last group in Figure 5. Below is a graphical illustration of the year each firm in the database were established and the amount of bank connections that those firms have. Figure 5: Number of registered bank connections. The majority of the firms in the dataset were established in the past decades. The dataset includes many observations of firms established between 1990 and 2010, which is a significant advantage, as firms established around the same time are likely to be similar and will therefore reduce the heterogeneity of firms in the two groups. There is a significant size difference between the group of 34

35 new firms, consisting of firms established in 2011 and after, and the group of existing firms, consisting of all firms established before is chosen as a cut- off point for new firms, both to ensure a decent sample size and to ensure that the firms have not changed bank connection after entering the market. There are very few registered observations of firms established in 2012 and 2013 in the dataset and it is not very likely that firms have changed bank connection within the first few years, so 2011 seems like a good cut- off point Financial data The various financial data chosen for the estimation reflects characteristics of consumers that the switching costs could be affected by. Rather than just financial figures, the variables should be seen as characteristics of the firms. Each variable is reviewed below. The database includes financial reports of firms that are not active anymore, as well as historical financial reports. The bank connections are not registered with a date, so they are all assumed to be the current bank connections. It is not clear how the bank connections are registered, but it is unlikely that they are all collected on the same day and updated daily. The financial data used, has to be the latest available to reflect the current bank connections, and the time the switching costs are estimated. The financial report also has to be for 2011 or later, to ensure that the characteristics of the firm are current. The dependent variable of the estimation is the consumer switching costs estimated empirically from the firms bank connections. All customers at each bank thus have the same switching costs. The variable will be extensively reviewed in section 5.2. The balance and capital of the firms are included in the estimation to model the size of the firms. Both figures are non- negative and have a high amount of variance across individual firms, and is often highly dependent on the industry of the firm as well as the firms financial policy. The balance of the firm is sensitive to accounting methods, and items that may not be relevant for the size of the firm can also be included in the balance. Capital of the firm can also vary between otherwise similar firms. One can be undercapitalized while the other can be overcapitalized. The high variance across otherwise identical firms can decrease the predictive power of the variables. The variance across time is on the other hand not very large compared to other financial figures that may change 35

36 significantly from one year to another. Both of the variables are skewed across firms, due a small amount of very large firms with very high balance and capital. To reduce this skewedness, both variables are logarithmically transformed. Alternative measures of market size could be output of the firm, market capitalization or revenue, which may be more suitable for some subgroups of firms. Output and market capitalization is however not available for all firms in the dataset. Revenue is registered for around 50% of firms, but it is optional for firms if they want it published, so it is not included in the estimation. Firms profit are available through the financial reports and possibly has influence on the switching cost of the firm. Firms profit provides some indication of the current financial situation of the firm, and thus its ability to pay back its loans. Banks are generally not interested in acquiring new customers with high credit risk. The profit itself is not particularly interesting, when it is not related to another financial figure that contains information about the base upon which the profit is earned. The hypothesis being examined is concerned with the switching costs of good and bad customers, so it is not interesting to estimate exactly how much switching costs change when the profit change. Therefore a dummy variable that is 1 if the firm earned a positive profit and 0 otherwise is used instead of the original variable. The profit of firms also varies considerably across firms, most likely more than the balance and capital, but also over time. A firm s profit, especially in a distressed economic environment as the one the firms in this thesis operate in, can vary significantly from year to year. Using the dummy variable, instead of the actual profit, should reduce this effect. The equity of firms is included in the estimation because it is a central financial figure. It is dependent on the assets and liabilities, as well as the size of the firm and the profit over time. It is therefore possible that the amount of equity a firm has is correlated with some of the other variables in the estimation. While it is related to many factors, the amount of equity a firm has is a financing decision, and can vary from firm to firm. Large outliers characterize the data, as the balance and capital figure, so a logarithmic transformation is applied to reduce the effect the of outliers. Equity can be negative, and there are both positive and negative outliers. Since the logarithm of negative numbers or zero is not defined, the lowest equity in the dataset plus one is added to all equity figures. It obviously does not make sense to interpret the parameter value, but since the concern of 36

37 this estimation is only the dependencies and not the actual parameters, there is no loss of generality due to the logarithmic transformation. The total amount of debt each firm has is also included in the estimation. It is calculated as the sum of the short- term and long- term debt for each firm. The debt is related to equity and balance by the accounting identity that says debt and equity must equal assets. Including debt could thus possibly cause multicollinearity, which could affect the parameters estimations of individual variables. Multicollinearity cannot reduce the predictive power or reliability of the estimation, but should be avoided to reduce the standard errors of the parameter estimates. In the real world, the accounting identity is not that simple. There are other instruments such as subordinated loan capital and other instruments that are not short- or long- term debt and not equity. These instruments are therefore not included in the dataset variables used for the estimation. Including the debt in the estimation should therefore not cause multicollinearity. Like many of the other variables, the calculated variable debt is skewed to the right with many large outliers. A logarithmic transformation of the variable is therefore used in the estimation. The solvency ratio is the only financial ratio included in the estimation. It is defined as equity divided by total assets. The solvency ratio is an expression for a firm s ability to incur losses. It measures the percentage of capital the firm can lose before the more senior financing is affected. The solvency ratio is negative if the equity is negative, which is a clear sign of financial distress. The solvency ratio has a tendency to be very negative when it is negative. In the database the solvency ratio is capped at and 999, which is relevant for some firms in the dataset. The solvency ratio is very sensitive in its nature, with many outliers and high variation, so the solvency ratio is logarithmically transformed in the estimation to reduce these effects. The solvency ratio can be negative, so the database cap plus one is added to all solvency ratios. It could be preferred to use a dummy variable to proxy firms with a good solvency ratio and a bad solvency ratio. It is however not obvious what a high and low solvency ratio is for the entire population of firms, so a continuous scale seems like the better choice 3. 3 Using a dummy variable yield equivalent results. 37

38 The dataset used for the estimation contains all available bank connections of firms that satisfy the requirements. If firms have more than one bank connection, then they appear more than once in the dataset. It is interesting to examine if it has an effect on the firms switching costs. A simple variable that contains the number of bank connections each firm has in the dataset is therefore included in the estimation. The last variable that is included in the dataset is the year of establishment. It is not a continuous variable and there are too many years to include each year as a dummy. Therefore the seven groups used in Figure 5 are used. The groups are included in the estimation as six dummy variables, with the group of firms established before 1950 as the default group. Each dummy thus represents the switching costs of the firms that were established in the time period, compared to firms that were established before Potential bias The simple nature of the estimation of switching costs has the implication that the estimates are potentially biased. Basically the estimation of consumer switching costs is based on the difference of two market shares, which is assumed to be the lock- in effect, without controlling for any other effects. If there are other effects affecting the difference in the market shares the estimation of consumer switching costs may be biased. If the other effects that are not controlled for have the same impact on both new and existing consumers, the estimations will not be biased, as the difference is not influenced. If however the effects impact one group of firms more than the other, the estimation is potentially biased. The viability of the method depends on the market share differences ability to proxy the actual switching costs. The market share differences are partly due to locked in consumers, called the lock- in effect of switching costs, but the market share differences may also be caused by other factors. If the market share differences are only due to the lock- in effect, then the market share differences are a very good proxy of the switching costs. If there are other effects than the lock- in effect that affects demand and supply of new and existing firms differently, then the market share differences are not a good proxy for the switching costs of consumers. Demand and supply typically do not depend on the 38

39 year a firm were established, but rather on other characteristics of the firms. In the following size of firms will be examined, as it should be highly correlated with the other characteristics. The size of the firm is thus used a proxy of the firms demand. The relevancy of the examination depends on how well the size of the firm explain the demand of the firms. The supply of credit is based on the firms ability to fulfill their credit commitments. This is mostly depending on future factors and therefore hard to measure. Usually a subjective assessment by each bank decides the terms of the contract. It is not possible to observe the individual contracts, so a formal examination of this is not possible. The subjective assessment is however partly based on financial figures, so it is likely to be correlated to the observed figures in the estimation. If the newly established firms have different preferences than the existing firms, observed differences in the market shares can be caused by consumer heterogeneity and not the lock- in effect. The preferences of consumers are likely to depend on the size of the consumer, it is therefore important that the two distributions of markets shares that are compared are based on a homogenous distribution of firms. The first examination looks at the distribution of both the median balance and median capital of each group depending on year the firms were established. The median is presented instead of the average, because the switching cost estimates are based on the absolute number of firms that each bank serve in each period. Thus each firm has identical weights, independent of their characteristics, when estimating the switching costs 4. The amount of firms in each category is also added to the graph, to illustrate the weight each group has in the estimations. The financial figures approximate the size of the firm. If the sizes of firms are independent of the year the firms were established, the median financial figures would be the same for each group of firms. Below are the two aforementioned graphs. 4 The averages are similar but influed by the large firms, most notably in the groups consisting of the oldest firms. 39

40 Figure 6: Median capital of firms distributed according to year of establishment. 40

41 Figure 7: Median balance of firms distributed according to year of establishment. It is clear that firms are not homogenously distributed according to size over the year they were established. Firms established a longer time ago are generally larger than newly established firms, which can be seen from the larger median capital and median balance. The median capital of firms, illustrated by Figure 6, is largest for the two groups containing the oldest firms. It is constant for the group of firms established in , but considerably smaller for the group of firms established in 2011 and after. The median balance of firms, illustrated by Figure 7, is continuously decreasing from the group of firms established the longest time ago, to the group of firms established in 2011 and after. These graphs are not surprising, as firms are likely to either grow or go out of business. This can unfortunately potentially bias the observations, if the sizes of the firms are also correlated with the choice of bank. As mentioned before firms are not weighted according to their size in the switching cost estimations, but all count equally towards the market shares. In Figure 7 and Figure 8 the number of firms in each group are also graphed. The number of firms displays how much each group contribute to the estimations. The graph of the number of firms is in line with the tendency for 41

42 firms to either grow or go out of business. While the medians indicate that the estimation is potentially biased, the number of firms in each group reduces this effect. The groups with the largest medians that potentially bias the estimation are very small compared to the groups with medians most similar to those of the new firms. The groups most similar to the newest firms are the largest groups and because firms are not weighted, this suggest that while the estimation does have potential to be biased, the issue is not as severe as the medians suggest without taking the size of the groups into account. One way to reduce the potential bias that arise because of firm heterogeneity, could be to use another group of firms that consists of firms that has been established after 1990, or some other year, and compare that group to the group of new firms. The same method for estimating the consumer switching costs could then be applied to the two distributions of market shares. As the two groups of firms are more similar than the total population of firms, it would reduce the potential bias. The group is not more correct than the original but will contain firms that are more similar to the newly established firms and still have a significant number of observations. The disadvantage of this approach is that many firms that could potentially have large switching costs, due to a longer lasting relationship with a bank, will be excluded. The alternative group definition yields very similar results, but with lower statistical power as would be expected. The results are not reported independently. It is evident that the size of the firms are correlated with the year the firms were established. It will bias the estimations if the sizes of the firms have an affect on the firms choice of bank. If all banks serve consumers of the same size, the market share differences will not be biased as a consequence of size differces of firms. To examine if the size of the firms are correlated with the choice of bank, the median capital and median balance are graphed for each bank. The interesting aspect is the difference of the medians across banks. If some banks banks serve customers with low medians, ie small firms, the market share of new firms will be to high compared to the situation with homogenous firms, and likewise will banks that serve firms with high medians have a high market share among the existing firms. This means that the switching cost estimates of banks that serve small firms will be biased such that their switching cost estimates are too low, and similarly will the switching cost estimations of banks that serve large firms will be too high. Below are the median 42

43 capital and median balance of firms that are customers at the ten largest banks graphed on separate graphs. The ten largest banks accounts for the majority of the market, so for a better overview the smallest banks are left out. Graphs including all banks can be found in appendix A- 1. Figure 8: Median capital of firms served by the ten largest banks. Figure 8 illustrates that there are differences in the amount of capital that the customers of the banks have. Bank number three and bank number five to ten serve customers with the same median capital, while other banks serve customers with a higher median capital. The fourth largest bank serves customers with much larger capital than the other banks, while the two largest banks are also quite a bit above the other banks. These banks, especially bank number four, will have a tendency to have a too high market share among existing customers, compared to new customers, as they generally serve larger customers. This will bias their switching costs upwards. The amount of firms these banks serve accounts for a large part of the market, which suggest that the switching costs of those banks could be upwards biased. Generally however it seems that there is not much difference 43

44 between the sizes of customers that most of the banks serve. So while Figure 6 and Figure 7 suggests that there are significant size differences between the groups, Figure 8 suggests that there is not a general tendency for banks to serve customers of different size. Figure 9: Median balance of firms served by the ten largest banks. The median balance of firms served by each bank has more variance than the median capital. The four largest banks serve firms with comparable balance, but there seems to be a general tendency for smaller banks to serve firms with a smaller balance. This problem is enhanced as the large banks serve most of the market, so a large part of the market is affected by potentially biased switching costs. Figure 7 shows that the existing firms are generally larger and Figure 9 shows that the larger banks generally serve larger customers. As before this has the consequence that the switching costs of the larger banks are potentially upwards biased. 44

45 The potential bias ascending because of heterogeneity of firms cannot be controlled for in the estimations conducted in this thesis, and is therefore an unavoidable downside to using this method to estimate consumer switching costs. The potential bias is of less importance when doing the regression of firm characteristics on switching costs, as the switching cost estimates are all potentially upwards biased, but the concern of the estimation, is only the sign and significance of the parameters. The sign of the parameters will not change if the switching cost estimates are increased, but their individual significance may be overestimated. Chen and Hitt estimate consumer switching costs with and without controlling for consumer heterogeneity and find no substantial differences between the two estimations (Chen & Hitt 2002). This suggests that their estimation of consumer switching costs is not very sensitive to consumer heterogeneity. If the estimation in this thesis yields the same traits, the estimates should be practically unbiased. 45

46 5. Results In this section the results of the thesis will be presented. The first two sections will cover the results of Shy s model and the empirically estimated switching costs, respectively. The third section will compare the two results. The last section will present the results of the regression of firm characteristics on switching costs. 5.1 Estimating switching costs using Shy s model Switching costs of consumers of each bank are calculated using equation (3.10) and (3.12), using the prices and market shares introduced in section 4. First Shy s unmodified model is applied to both the market consisting of all banks that offer a full line of products, and then the same calculations are done on the market where only the six largest banks compete. The switching costs are in the same unit as the price, and since the prices each banks offer are interest rates, the switching costs are also reported as an interest rate. Below is a graphical illustration of the calculated switching costs estimated using Shy s model. 46

47 Figure 10: Switching costs of consumers calculated using Shy s model. The blue graph shows that consumers have varying switching costs, but are all in an interval of 10%. The switching costs of consumers of the largest banks seem to vary less than the switching costs of consumers of the smaller banks. Generally it seems as the largest banks serve consumers with the highest switching costs. The same picture can be seen if the market where only the six largest banks compete is considered. So according to the model, the largest banks serve the consumers with the highest costs of switching; similarly does the smallest banks serve the consumers with the lowest costs of switching. From Figure 10 it is obvious that the two definitions of the market on which the banks operates yields very different results. Intuitively this seems reasonable, as the banks pricing methods should depend heavily on the firm 5 they compete with or in the model framework, the one firm they fear will undercut them. The smallest firm in the market with the six largest banks have retail customer 5 Each firm only fears being undercut by one firm according to Definition 3. 47

48 deposits, which is used to calculate market shares, that is 250 times larger than the smallest firm in the model with all banks, so it is not surprising that the results are significantly different. The most obvious difference between the two models is the estimation of the switching costs of consumers of bank five and six. The main reason is that they go from being large banks in the model with all banks, and does not have an incentive to undercut the other banks, to being small banks in the model with only six banks and therefore have a larger incentive to undercut the other banks. The overall result that larger banks serve the customers with the largest switching costs, are equivalent for both market definitions. Measuring the switching costs, as an interest rate can be hard to put in perspective, since the actual costs also depends on the unobserved principal and number of payments. Using an interest rate as the unit of measure can also be misrepresentative since switching costs is a onetime cost, while an interest rate is usually associated with repeated payments. It can however be related to the observed price of the bank. If the switching costs are measured as a percentage of the bank s price, the switching costs dependency on the principal and number of payments is eliminated. The measure is also independent of the price level and can be used if the price of the bank is not measured as an interest rate. The graph below illustrates the result. 48

49 Figure 11: Switching costs calculated using Shy s model expressed as a percentage of the price. Figure 11 shows that in the model with all banks, the largest banks consumers switching costs are essentially the prices that the individual banks offer. This ratio decreases for the smaller banks, but the consumers switching costs are still above 50% of each bank s price. This seems very high compared to other research, as well as general knowledge about markets. That the banks with the largest market share serve the costumers with the largest switching costs makes sense, as having consumers with high switching costs will for obvious reasons often result in a high market share. Shy s definition of market competition is not appropriate to use on markets where there are large differences in the size of the competitors, and therefore large differences in the competition between the individual competitors. The results of the model are highly dependent on the smallest firm in the market, as the smallest firm is the one most likely to undercut the price of the other firms. The other firms in the market are therefore essentially setting their price according to the smallest firm in the 49

50 market. If the smallest firm is significantly smaller than the larger firms, it is unrealistic that the larger firms will price according to the smallest firm, and the assumption is not suitable. The problem arises because of the utility function of consumers and subsequently the demand structure of firms. The market shares are a function of the prices, and if a single firm undercuts the price of the others, and compensate the consumer s switching costs, the firm will capture the entire market share. This is a simplified assumption, and is not in line with empirical observations. Instead of modifying the market assumptions, the demand structure of the model could be modified or the consumers switching costs are allowed to be asymmetric. For example could construction of a model where each firm face downward- sloping demand curves be constructed. In this thesis the underlying theoretical assumption of the model are intact, while the market assumptions are modified. Two different modifications to Shy s market conditions will be imposed. The purpose is to examine, if a more suitable assumption for the Danish banking industry can be found. The general idea is that the firms in the market do not set their prices according to the smallest firm in the market, but rather the firms with market shares similar to themselves. The assumptions are meant as a benchmark, and are not necessarily an improvement, or more correct. The first modification is that each bank only considers undercutting bank i + 1, still using an index where banks are ranked by decreasing market share, i.e. each bank only consider undercutting the one bank with higher market share just above itself. In the second modification a moving average of both market shares and prices for bank i + 3, i + 2, i + 1, i 1, i 2, i 3, i.e. the three banks with market share just above or below bank i, is used as input in equation (4.10). For the three largest and smallest banks, where some of these do not exist, a moving average of the available banks are used. Below is a graphical presentation of the results. 50

51 Figure 12: Switching costs calculated using Shy s model with modified market conditions. The two modified estimations of switching costs are quite similar. They are both lower than the estimations using Shy s assumption of undercutting on the market consisting of all banks. So if markets are defined as above, with different competitors for each bank, the switching cost of the consumers they serve are estimated to be lower. The market with the six largest banks cross both the new lines, implying that the switching cost variation of consumers is higher than in the two benchmark cases. Overall it seems that the four models yield estimated consumer switching costs with similar characteristics, but of different magnitude. Below is the switching costs given as a percentage of the each banks price illustrated. 51

52 Figure 13: Switching costs calculated using Shy s model with modified market conditions expressed as a percentage of the price. The two estimations using Shy s market assumption are quite different than the estimations with modified assumptions. Shy identify one bank that is most likely to undercut the others and the rest set their price relative to that bank, which usually leads to continuously decreasing switching costs of consumers. In the benchmark models the bank or banks that are most likely to undercut are different for each bank, which leads to switching costs of consumers that vary for each bank, and there is no uniform trend across the entire market. The tendency that large banks, serve consumers with high switching costs, does also seem to be existent with the modified market conditions. The model is very simplified as it only considers prices and market shares, and makes some strong assumptions about which firms that potentially undercut each other. It is however an easy method to assess the level of consumer switching costs of each supplier in a market. Another disadvantage of the model is that switching costs are estimated on the basis of observed prices and market shares. 52

53 Prices and market shares will always be historical, and so will the consumer switching costs. This may not be an issue if switching costs of consumers are fairly constant over time, which is an interesting topic for further research. 5.2 Switching costs estimated from firm s bank connections The first hypothesis to be tested is the existence of switching costs in the market. The hypothesis is tested by comparing the market shares for new and existing consumers. The consumers are Danish firms, as described in section 4.2. If the market share differences are significantly different, they will be used as an estimate for the switching costs of the consumers of each bank. Below is a graphical illustration of the banks distribution of market shares and the absolute differences in market shares for both new and existing firms. The graphs offer a visual presentation of the market shares in the two periods. A chi square test will be used to make formal conclusions about the two distributions. 53

54 Figure 14: Distribution of market shares in the two time periods. Figure 14 show that the largest banks serve most of the market. Especially the two largest banks have a much higher market share then the rest. The graph illustrates some differences in the two market share distributions. As it is the absolute market shares that are of interest, the banks with the largest market shares also seems to have the largest differences between the two distributions. The absolute differences in market shares rather than the relative differences in market shares are reported in the following. The smaller banks with fewer bank connections displays larger relative than absolute differences. The opposite is true for the larger banks. There is a much larger amount of data on the bank connections of the large banks, which favors using the absolute differences, as market shares will be more precise. The relative differences may be the theoretically preferred choice, but there are very few registered bank connections in the dataset for the smallest banks, which distorts the estimate. The choice of using either the absolute or relative differences will only affect the magnitude of the switching cost estimates but not the direction, so the results will be similar. Figure 15 illustrates both the absolute and relative differences between the two market 54

55 share distributions. The actual market share is presented as a percentage, as can be seen on the left vertical axis, while the relative differences are actual percentage deviations, as can be seen on the right vertical axis. Figure 15: Differences in market shares Figure 14 and Figure 15 shows that the largest four banks have a higher market share among the existing firms than the newly established firms. Similarly does the following banks generally have a lower market share among the existing firms that newly established firms. The magnitude of the absolute market shares is decreasing as the banks get smaller, but this is primarily because they have the largest market shares. Generally if the magnitude of the difference in market share for a single bank is large and positive, the consumers of the banks have relatively high switching costs. If the difference in market share is close to zero, the consumers have average switching costs. If the difference is negative, it means that 55

56 consumers of other banks have high switching costs, as the current consumers do not switch from their current bank to the now more attractive bank. Thus a negative difference does not imply negative switching costs, but rather relatively low switching costs compared to the other customers in the market. A chi square test is conducted to formally test if the two samples are different. The chi square test is applied to the two distributions of market shares for the 31 banks 6. Below is a preview of the chi square table, showing the observed frequency, expected frequency and the cell chi square values. The full table can be found in appendix A- 2. The cell chi square test considers each cell in the table and tests whether it is significantly different from its expected value in the total table. The cell chi square values are meant to discover and specify the cells, i.e. the bank and group that are furthest away from the expected values and indicate how much each cell contributes to the overall chi square value compared to the other cells. Table 2: Frequency table for the first 10 banks. The preview table shows the two groups of firms that make up the two distributions. The first row is the group of existing firms and the second row is the group of the newly established firms. The 6 Bank number 23 has no commercial customers. 56

57 original table contains 31 columns, each representing a bank, while the preview only show the first 10 banks. The bottom row show the totals of the two groups. From Table 2 it is clear that the group of existing firms have observed bank connections very close to their expected values. This is a consequence of the size difference between the group of new firms and the group of existing firms. The expected values depend on the total distribution, of which the existing firms are a large proportion. If the expected and observed values are close to each other, the cell chi square values are subsequently low and vice versa. The group of new firms is generally further away from their expected values and this is also where some of the large cell chi square values are observed. A large cell chi square value does not necessarily correspond to a large market share difference and consequently a large switching cost estimate. They are only meant to give an indication of the banks that contribute most to the total chi- square value. In the complete table, the smallest banks have very few customers, which result in very low expected frequencies. A chi square test should not have too many cells with expected frequencies less than five and none less than one. Bank 23 have no customers and are therefore left out of the test, but many of the smaller banks have expected frequencies less than one. The usual strategy would be to reduce the amount of cells with low expected frequencies by grouping some of the cells or leave them out of the test. Both strategies would be reasonable in this case, but the chi square tests give similar results and are therefore not reported. Below is a table presenting the result of the chi square test for the two distributions of market shares for the entire sample of 31 banks. Table 3: Chi square test values. The chi square test has 30 degrees of freedom and yields a P- value of 88, which corresponds to a probability that the two distributions are the same are less than 0.01%. The hypothesis that the 57

58 distributions of market shares comes from the same distribution can be rejected on a significance level of 99.99%, and it can subsequently be rejected that there are no switching costs in the market. The chi square test support the use of the market share differences as an expression of the switching costs in the market. 5.3 Comparison of theoretical and empirical results The switching costs of consumers has both been estimated theoretically using Shy s model and empirically using data on firms bank connections. Naturally these two can be compared, to see if they are similar. The switching costs are not in the same unit of measure, as the empirical switching costs are a proxy of the actual switching costs. The levels of switching costs across consumers of banks can still be compared. A graphical illustration of the two switching cost estimated will be offered, but no formal comparison will be made. The two estimations are both methodically different, but they also differ in the data used in the estimations. The theoretical switching costs are calculated using data on the retail banking market, while the empirical switching costs are estimated using data on the commercial banking market. This difference will certainly result in differences in the actual consumer switching costs that are being estimated, so some differences between the two estimates are expected. Four different estimations were made using Shy s model, as can be seen in Figure 13. Shy s original market assumption that each bank only feared being undercut by one bank, namely the smallest bank in the market, did not seem to be applicable to the Danish banking industry. The two modified market assumptions seem to be superior across the entire market, therefore is the market assumption that banks fear being undercut only by the bank with market share directly below itself reported. From the empirical estimations it can be inferred that the large banks generally serve consumers that have large costs of switching, as firms entering the market choose these banks relatively less than the group of existing firms, and vice versa. Especially the four largest banks contribute to this with large positive market share differences. This is consistent with the theoretical results from Shy s model that also estimated that the largest banks generally served the customers with the highest switching costs. Below is a graphical comparison of the two estimations, as well as simple linear 58

59 regression lines for both estimations. Only the ten largest banks are displayed for a better overview and because the banks are not weighted. So each the customers of each bank s switching cost estimate count for the same when doing the linear regression, but there are a much larger sample of firms for the larger banks, so the statistical uncertainty is considerably lower. The same graph for all 32 banks can be found in appendix A- 3. Figure 16: Theoretically estimated switching costs using Shy s model with one competitor and empirically estimated switching costs using firm data. The graph has Shy s estimate on the left vertical axis and the empirical estimate on the right vertical axis. As mentioned before, the focus is not on actual measure, but on how the switching costs of the consumers of banks compare. In both estimations bank number one serves the consumers with the highest switching costs, bank number two serves the consumers with the second largest switching costs, bank number three serves the customers with the fourth largest switching costs and bank number four serves the customers with the third highest switching costs. Overall both estimations 59

60 seem to agree on the customers of banks relative switching costs compared to the customers of other banks. The linear regression lines offer a more general interpretation of consumers switching costs of each bank. Since banks are ranked by size it relates the customers switching costs to the size of the banks they choose. The regression lines are very similar and almost parallel. They both predict an inverse relationship between consumer switching costs and size of bank. The customers of large banks typically have high switching costs, and customers of small banks typically have low switching costs. This result is very logical, as having customers with high switching costs will typically lead to a high market share, unless the banks exploit the customers so much that they switch to competing banks. There is a possibility of a spurious relationship between the two estimations. Spurious relationships can be caused by raw coincidence or factors that are not controlled for. A spurious relationship between the two estimations can be caused because the theoretical model is too simple and is constructed to replicate the empirically expected positive relationship between market share and consumer switching costs. The empirical model is also very simple and there is an almost build- in size effect in the market share differences, as larger banks have the possibility of larger market share differences. There do nonetheless seem to be a very high correlation between the two estimations. 5.4 Switching costs and firm characteristics The switching costs of consumer of each bank in the market have been estimated empirically in the previous section. The validity of the estimation is based on the accuracy and correctness of the empirical switching cost estimates. The empirical switching cost estimations are consistent with the theoretical estimations, which favors the accuracy of the estimates. The objective of this section is to examine if consumers switching costs are dependent on the consumers characteristics and if they are, the relationships between the consumer characteristics and the switching costs. The consumers considered are the Danish firms that were also used for the estimation of the switching costs. The main concern of the estimation is the significance of the variables, so the actual parameter estimates are not of interest, but only the signs and standard errors are of the estimates. There are two main concerns when doing the estimation. The main concern is that the residuals of the estimation are not normally distributed, which is a central assumption of linear regression models, or equivalently that 60

61 the switching cost estimates are not normally distributed, conditional on the independent variables. The other concern is the significance test applied to the parameter estimations. If the test is applied to very large datasets, all variables have a tendency to become significant. In the first part of this section the issues of significance testing will be outlined, then the results of the estimation will be presented and thereafter will the issues of non- normality be discussed Issues of significance testing The usual convention when testing for significance of variables is to set up a test of the null hypothesis, which results in a P- value. If the P- value is below 5% then the null hypothesis is rejected, and the parameter estimate is said to be significant, and contrary will a P- value above 5% lead to a null hypothesis that cannot be rejected and the parameter estimate is said to be significant. There is however one very large issue when using the method above on estimations based on very large datasets. The P- value is calculated as the difference between the observed values and the null hypothesis multiplied by the sample size. If the null hypothesis is indeed true, as most tested hypotheses are, increasing the number of observations will increase the P- value. In a dataset with over fifty thousand observations, the P- values are almost inevitably very small. The usual convention of using 5% as the cutoff value will cause many variables that would not be considered significant using a smaller dataset, to become significant in estimations based on large datasets. Using other tests for significance can circumvent this issue or the estimations can be repeated on smaller subsets of the original dataset, and the t- values can be compared to those of the full dataset. In (Good 1982) it is suggested that one could also standardize the P- values to a sample of 100. Standardizing the P- values to a sample of 100 would mean that all P- values in this estimation should be multiplied by around 23. This will be used as a rule of thumb when the results are discussed, as it is a simple improvement and sufficient for the purposes of this estimation. The conventional cutoff point of 5% will be used on the standardized P- values, but more as a guideline than a cutoff point. 61

62 5.4.2 Results of the estimation Table 4: Estimation of firms switching costs dependency on firms characteristics. Table 4 shows the results of the regression. The first column shows the name of the variable, the third and fourth show the actual parameter estimate, of which only the sign is of interest. The last two columns show the t value and corresponding P- value. Below will individual interpretations of each parameter estimate be presented. The intercept of the estimation is not of interest, both because the level of switching costs is not interesting in this estimation, but also because it does not make economic sense to consider the switching costs of a firm where independent variables are zero. Generally most of the variables appear to be significant and the standard errors are quite low, which is most likely because of the large dataset used for the estimation. 62

63 The parameter estimates of the balance and capital are both positive and very significant compared to the other variables. Firms with a larger balance or capital are thus predicted to have larger switching costs. So the size of the firms and their switching costs are, according to the estimation, positively correlated. It seems reasonable that both parameters have the same sign, as both variables are expressions of size of the consumers. The positive relationship is also what would be expected from theory. The parameter of capital is larger and more significant than balance. This could be because capital is a better measure for firm size than the balance. The balance includes all the firm s operations and can easily be affected by both the firm s accounting and financial policies. The capital is more narrowly defined, and therefore better at predicting the level of switching costs of the firm. The reason for this positive correlation can be found on both the supply and demand side. Larger firms are likely to require more banking services and are therefore relatively more important for the banks. Therefore banks put more effort into keeping the larger customers. The high volume of business probably also makes it more inconvenient to switch, but may also increase the firms incentive to choose the best current contract. The last effect seems to be offset by the others. All in all, these effects and maybe other effects, reduce the likelihood of firms switching bank. The variable profit is a dummy variable that is one if a firm made a profit in their latest financial report. The parameter is negative and significant. According to the estimation, profitable firms have lower switching costs than firms that did not make a profit. This result is in line with the theoretical prediction. Unprofitable firms are generally not desirable customers in banks, as they have a higher risk of defaulting on their loans. The most obvious reason for the relationship between switching costs and firms profitability is that the firms and the banks have obligations to each other through a contract, and that there is very low supply of credit for unprofitable firms. Competing banks are not likely to offer loans to unprofitable firms, let alone attractive contracts, so the firms often have to stay with their current bank connection. The current bank often have an interest in continuing the relationship with the firm if it is unprofitable, to lower the risk of the firm defaulting on its loans. If the bank stop supplying credit to the firm, and the firm is unable to get financing elsewhere, the firm may default and be unable to pay back its debt in full. The debt of firms is correlated with the other variables through the size of the firm, but it is also the product being traded between the firm and the bank. This makes it hard to predict the variables 63

64 relationship with the firms switching costs. The estimation reveals that the parameter is negative and very significant. Thus the more debt a firm has, the lower is its switching costs. There are at least two effects that contribute to the parameter estimation. The first is the size effect of the firm. The larger a firm is, the larger is their debt generally. Other variables, such as balance and capital that are also linked to the size of the firm, revealed a positive correlation between size of the firm and switching costs of firm. The other effect is a consequence of the increased size of the contract between the bank and the firm. The larger a potential contract is, the more incentive does the competing banks have to offer a good contract to the firm, which can make firms incentive to switch larger. The firms also have a larger monetary incentive to get the best possible contract, due to the large volume. The current bank connection of the firm obviously has the same incentive to offer the firm a good contract, but the increased competition between banks and the strong incentive for the firm to choose the best current contract seems to exceed this effect. The size effect, that definitely is present in the estimation, is offset either by the before mentioned effect or by other unknown effects. The equity of the firm is estimated to be positively correlated with the switching costs of the firm. The larger a firm s equity is, the larger is the estimated switching costs of the firm. Equity is also positively correlated with the size of the firm, which is positively correlated with switching costs. But equity is also an indication of firms ability to absorb losses. A high equity is therefore also a sign of a healthy firm, which is negatively correlated with switching costs as with the profit variable. According to the sign of the parameter, the size effect is the dominating factor. This is likely because the variable does not compare the equity level to other factors, so it is not possible to infer if the equity for a given firm is high or low. The solvency ratio does exactly that. It relates equity to the assets and therefore excludes the effect of the size of the firm from the variable. The solvency ratio is a continuous logarithmically transformed variable. The estimated parameter is negative and significant. It is one of the least significant variables with a standardized P- value around 0.7%, which is still well below the conventional cutoff value of 5%. According to the estimation the higher a firm s solvency ratio is, the lower is the firm s switching costs. The solvency ratio is an expression for a firm s ability to meet its obligations. It is related to the profitability measure, as both variables measure the firms health. It is therefore not surprising that both have the same sign. 64

65 Generally the estimation reveals that healthier firms have lower switching costs, most likely because they are more attractive customers to competing banks. The reason for the low significance of the variable is most likely due to high variation in solvency ratios of otherwise similar firms. This variation is caused by sector and industry differences, as well as the nature of the ratio. If a firm has few assets, which is the denominator of the fraction, the equity has a high impact on the total ratio, and vice versa. The number of bank connections that each firm has in the dataset is not a financial figure like the other variables. It is mainly included to reduce the effect of some firms weighting more than others in the estimation, if they have more than one bank connection. The parameter is negative, but not very significant. The adjusted P- value is slightly above 10%, so the variable would usually be considered insignificant. The standard error does however reveal that the parameter estimate with a high probability is negative, which is an interesting result. The number of bank connections a firm has is possibly correlated to the size of the firm, but it is not clear how strong this effect is. Most firms can get their demand fulfilled by one bank, but larger firms may want more bank connections, to spread their risk and dependency across several banks. The logical relationship between the number of bank connections that a firm has, and the switching costs of the firm, is negative. Multiple bank connections indicates that the firm is not loyal to one bank and therefore have lower costs of switching. If a firm has more than one bank connection, then it will be easier to close a bank connection with a bank, which in the dataset will be interpreted as a switch. This is not a desired feature, but it is the disadvantage of including firms with more than one bank connection. The last mentioned effect dominates the size effect in the dataset, according to the estimation. The last parameter estimates are those of the dummy variables containing information about the year of establishment. The default category is the group consisting of firms established before All parameter estimates are therefore in relation to this group. All the parameter estimates related to the year of establishment are negative, meaning that the other groups of firms has lower switching costs than the default group. It is expected that, if there is a significant relationship, then it is a positive correlation between the number of years a firm has existed and the switching costs of the firm. The parameter estimations are thus in line with the expectations. The group of firms established between 1950 and 1959 has a P- value of 0.23%, which yields a standardized P- value 65

66 slightly above 5%. The group of firms established between 1960 and 1969 also has a standardized P- value above 5%, which suggest that the parameter estimates are not significant, and consequently that the switching costs of the firms established between 1950 and 1969 are not significantly different from the switching costs of firms established before The three groups are arbitrarily composed and they all contain firms that are very mature, it is therefore reasonable to accept that they do not have different switching costs. The other groups have parameter estimates that decrease as the ages of the firms decreases. According to the estimation, the more recently a firm was established, the lower switching costs does it have, which is also in line with the expectations of the relationship. The relationship can be partly explained by the likely correlation between the amount of time a firm has been a customer at a bank and the year a firm were established, caused by the fact that firms generally do not switch banks very often. The longer a firm has been a customer at a bank, the higher switching costs are the firm expected to have. The variables of the estimation are generally all relatively highly correlated, as firms characteristics are all related to size of the firms, which may lead to multicollinearity. The issue of multicollinearity would be an important issue if a smaller sample size were used for the estimation. Multicollinearity increases the standard errors, because it is not clear which of the independent variables that are responsible for the variation in the dependent variable. This effect is mitigated by the large sample size, as can be seen from the standard errors of the estimation. The coefficient of determination, R!, is slightly above 2%. It is very low, which means that the model does not do a very good job at predicting the observed values. Thus the characteristics of firms, used in the estimation, are not good predictors of the firms switching costs. It was not expected that the firm characteristics could explain very much of the variation in the consumer switching cost, so a low coefficient of the determination was expected. The dataset include all firms, without controlling for outliers, other than transforming the variables. Looking at the data, it is evident that there are many large outliers, as well as significant variation across industries. This may also contribute to a low the coefficient of the determination. The focus of the estimation was not to set up a model to predict the consumer switching costs on the basis on consumers characteristics, but to examine if there were some relationship between the characteristics and the switching costs. If the model was constructed to predict the switching costs of consumers, the coefficient of determination could most likely be 66

67 increased if outliers were removed from the dataset, and the industry of the firms were controlled for. Generally the parameter estimates are all very reasonable, and are consistent with both theory and expectations. The most important result of the estimation is that almost all of the variables are significant. While the variables does not explain very much of the variation in the switching costs, it is still notable that they have an influence on the switching costs of the firm Issues of non- normality There are three assumptions to consider in the regression. First the independence assumptions, then equality of variance and at last the normality assumption. There seem to be no violations of the two first assumptions, but the residuals of the estimation are not normally distributed. It has become the norm to assume normality of the dependent variable, conditional on the independent variables, or equivalent that residuals are normally distributed, when doing least square linear regression. This is a consequence of the independent variables, i.e. the firm data, being distributed equally across banks, and the banks having a non- normal distribution of switching costs. Especially the large switching costs of the customers of bank number 1 are causing this non- normality. The Q- Q plot below illustrates the non- normality of the residuals. 67

68 Figure 17: Q- Q plot of the residuals of the estimation A normal distribution of residuals would be on the straight line. It is clear that the residuals of the estimations are far from normal. The residuals seem to constitute two straight lines, with a horizontal jump between those. Each of the straight lines that the residuals form resemble two approximately Gaussian distributions. This suggest that there are two different distributions in the estimation, one which is most likely the firms that are customers at bank number 1 and has much larger estimated switching costs than the remaining firms, and other group is firms with bank connections at the remaining banks. The problem arises both because the switching costs are so different from the other firms, but the problem is magnified because bank number 1 has so many customers. It is not good practice to include a dummy to control for these customers, as there is no theoretical basis to exclude all customers of bank number 1. It would also most likely reduce the statistical power of the estimation considerably. Having a large dataset, as the one used for this estimation, is an advantage when dealing with non- normal data. In (Johnson and Wichern 2007, p. 382), a textbook for colleges and universities, it is stated that if the number of observations is large, minor departures from normality will not greatly affect inferences about the parameter estimates. It is, as it often is in statistics, a subjective assessment about what a large number of observations is and what minor departures from normality 68

69 is. The data used in this estimation would probably be at the very high end of the scale when it comes to number of observations, but the results do probably depart very much from normality. It is hard to say how much the latter affect the parameter estimates, but this suggests that the estimation in this thesis is viable even though it departs from normality. (Lumley, et al. 2002) considers the importance of the normality assumption in large public health datasets. They argue that normality is not required to fit a linear regression, but normality of the coefficient estimates is needed to compute confidence intervals and perform tests. The coefficient estimate is a weighted sum of the dependent variable, illustrated below. β = (X! X)!! X! y Where β is the coefficient estimates, X is the design matrix for the model and y is the vector of responses. The central limit theorem states that the arithmetic mean of a sufficiently large number of iterations of independent random variables will be approximately normally distributed. Thus, if the sample size is large enough, the t statistic can be calculated correctly, despite departures from normality, and tests and confidence intervals can be based thereon. If the sample size on the other hand is small, the outcome variable has to be normally distributed for t- test and linear regression model to be appropriate. The most important indication of the estimations usefulness is the fitted parameter estimations. They are consistent with the theory, and what would be logically expected. If the variables were biased or incorrectly estimated, then this would most likely not occur. Therefore the validity of the estimations lies mostly in the result of the relationship between the firm characteristics and estimated switching costs. It may not be the most accurate model, but the simplicity of the linear regression model and the purpose of the estimation favors using linear regression instead of more complicated models. It is evident that firms characteristics do have some influence on the switching costs, but it does not seem to be very strong effects. There are most likely much more important things than firms characteristics that influence the consumer switching costs. 69

70 6. Conclusion In this thesis, consumer switching costs have been estimated using both Shy s theoretical model and an empirical estimation of a proxy of consumer switching costs. Both models use data where consumers individual switches are not observed. Shy s theoretical model use market shares and prices as the only inputs. The results depend considerably on the definition of the market, but the model indicates a general tendency for large banks to serve consumers with high switching costs. The market definitions that Shy s suggest are not appropriate for the Danish banking market. He assumes that only the smallest bank considers undercutting the other banks in the market, which is not appropriate for a market with many competitors of substantially different sizes. Modifying his assumption about the undercutting firm results in more realistic switching costs between 20 and 60 percent of the total price faced by consumers. The empirical method used to proxy consumer switching costs is also very simple, and is based on the market shares of new consumers that do not face switching costs and existing consumers that may face switching costs. The empirical estimations show clear evidence of consumer switching costs in the Danish banking industry. The proxy of switching costs of consumers of each bank is very similar to the estimated switching costs of consumers of each bank in Shy s model, so the empirically and theoretical estimations are consistent. The tendency for large banks to serve consumers with high switching costs is also present in the empirical estimations. The relationship between consumer switching costs and consumer s characteristics is examined by a linear regression of the characteristics of Danish commercial bank consumers and the empirically estimated proxy of switching costs. The characteristics of the consumers are related to the switching costs, but the effect is not very strong. The regression reveals that larger firms generally incur higher switching costs, while profitable firms and firms with a high solvency ratio incur lower switching costs. The level of debt is negatively related to switching costs, regardless of its correlation with size. There also seem to be a positive relationship between the age of the firm and the switching costs. The findings are in line with the theoretically expected relationships, but the characteristics of consumers can only explain a small part of the variance in consumer switching costs. 70

71 The overall conclusion is that consumers in the Danish banking industry face significant switching costs. There is strong theoretical and empirical evidence that the larger banks generally serve the customers with the highest switching costs, but only a small part of the consumer switching costs can be explained by the characteristics of consumers. 71

72 7. Bibliography Akerlof, George A. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism." The Quarterly Journal of Economics, Ausubel, Lawrence M. "The failure of competition in the credit card market." The American Economic Review 81, 1991: Barone, Guglielmo, Roberto Felici, and Marcello Pagnini. "Switching costs in local credit markets." Bank of Italy, Boot, Arnoud W. A. "Relationship Banking: What Do We Know?" Journal of Financial Intermediation 9, 2000: Borenstein, Severin. "Selling costs and switching costs: explaining retail gasoline margins." RAND Journal of Economics, 1991: Burnham, Thomas A., Judy K. Frels, and Vijay Mahajan. "Consumer Switching Costs: A Typology, Antecedents, and Consequences." Academy of Marketing Science, Chen, Pei- Yu, and Lorin M. Hitt. "Measuring Switching Costs and the Determinants of Customers Retention in Internet- Enabled Businesses: A Study of the Online Brokerage Industry." Information Systems Research, Vol. 13, No. 3, 2002: Dijk, Bureau Van. Bankscope. Good, I. J. "Standardized tail- area probabilities." Journal of Statistical Computation and Simulation, Hannan, Timothy H., and Robert M. Adams. "Consumers Switching Costs and Firm Pricing: Evidence of Bank Pricing of Deposit Accounts." The Journal of Industrial Economics, 2011: Johnson, Richard A., and Dean W. Wichern. Applied Multivariate Statistical Analysis. 6th Edition. Pearson International Edition, Kézdi, Gábor, and Gergely Csorba. "Estimating the Lock- in Effects of Switching Costs from Firm- Level Data." Kim, Moshe, Doron Klinger, and Bent Vale. "Estimating switching costs: the case of banking." Journal of Financial Intermediation 12 (2003): Klemperer, Paul. "Competition when Consumers have Switching Costs: An Overview with Applications to Industrial Organization, Macroeconomics, and International Trade." The Review of Economic Studies 62, no. 4 (Oct 1995):

73 Klemperer, Paul. "Entry Deterrence in Markets with Consumer Switching Costs." The Economic Journal 97 (1987): Klemperer, Paul. "Markets with consumer switching costs." The Quarterly Journal of Economics, Konkurrence- og Forbrugerstyrelsen. "Konkurrencefremmende Forbrugeradfærd." Konkurrence- og Forbrugerstyrelsen. "Konkurrencen på bankmarkedet for privatkunder." Lumley, Thomas, Paula Diehr, Scott Emerson, and Lu Chen. "The Importance of the Normality Assumption in Large Public Health Data Sets." Matthews, Claire. "Switching Costs in Banking: The Regulatory Response." Centre for Banking Studies, Massey University, Sharpe, A. Steven. "The Effect of Consumers Switching Costs on Prices: A Theory and its Application to the Bank Deposit Market." Review of Industrial Organization, 1997: Shy, Oz. "A quick- and- easy method for estimating switching costs." International Journal of Industrial Organization, 2002: Stango, Victor. "Pricing with Consumer Switching Costs: Evidence from the Credit Card Market." The Journal of Industrial Economics, Vol. 50, Issue 4, 2002: Thadden, Ernst- Ludwig von. "Asymmetric Information, Bank Lending and Implicit Contracts: The Winner s Curse." Finance Research Letters,

74 Appendix A A- 1 Figure A.1: Median capital of firms served by all largest banks. 74

75 Figure A.2: Median balance of firms served by all largest banks. 75

76 A- 2 76

77 A- 3 Figure A.3: Theoretically estimated switching costs using Shy s model with one competitor and empirically estimated switching costs using firm data. 77