Deregulation, Consolidation, and Efficiency: Evidence from the Spanish Insurance Industry

Transcription

1 J. DAVID CUMMINS MARIA RUBIO-MISAS Deregulation, Consolidation, and Efficiency: Evidence from the Spanish Insurance Industry This paper provides new information on the effects of deregulation and consolidation in financial services markets by analyzing the Spanish insurance industry. The sample period spans the introduction of the European Union s (EU) Third Generation Insurance Directives, which deregulated the EU insurance market. Deregulation has led to dramatic changes in the Spanish insurance market; the number of firms declined by 35%, average firm size increased by 275%, and unit prices declined significantly in both life and non-life insurance. We analyze the causes and effects of consolidation using modern frontier efficiency analysis to estimate cost, technical, and allocative efficiency, as well as using Malmquist analysis to measure total factor productivity (TFP) change. The results show that many small, inefficient, and financially underperforming firms were eliminated from the market due to insolvency or liquidation. As a result, the market experienced significant growth in TFP over the sample period. Consolidation not only reduced the number of firms operating with increasing returns to scale but also increased the number operating with decreasing returns to scale. Hence, many large firms should focus on improving efficiency by adopting best practices rather than on further growth. JEL codes: G2, G22, G28, L11 Keywords: insurance, data envelopment analysis, Malmquist index, mergers and acquisitions. Financial services markets have changed significantly over the past two decades, following the deregulation of banking, insurance, and other financial services in major industrialized nations. The introduction of the European Union s (EU s) Second Banking Directive (1993) and Third Generation Insurance Directive (1994) aimed at deregulating the EU banking and insurance markets, J. David Cummins is a professor at the Department of Insurance and Risk Management, The Wharton School, University of Pennsylvania ( cummins wharton.upenn.edu). Maria Rubio-Misas is an Associate Professor at Departamento de Finanzas y Contabilidad, Universidad de Malaga ( mrubiom uma.es). Received November 26, 2001; and accepted in revised form July 06, Journal of Money, Credit, and Banking, Vol. 38, No. 2 (March 2006) Copyright 2006 by The Ohio State University

2 324 : MONEY, CREDIT, AND BANKING respectively. Japan initiated financial system deregulation with the Big Bang financial reforms, launched in 1996; and U.S. regulations were relaxed in stages, culminating in the Gramm Leach Bliley Act of Common themes of these deregulatory efforts include the removal of restrictions on ownership of different types of financial services firms, the relaxation of geographical restrictions on branching and sales, and price deregulation. 1 The principal objective of financial services deregulation is to improve market efficiency and enhance consumer choice through increased competition. Efficiency gains can occur as a result of the market consolidation that has accompanied deregulation, particularly in Europe and the U.S. Consolidation has the potential to improve X-efficiency in an industry if it results in poorly performing firms exiting the market, either through voluntary or involuntary withdrawal or through mergers and acquisitions (M&As). Consolidation also can positively affect efficiency if it permits firms to take advantage of scale economies to reduce unit costs of production. In spite of the significant potential for efficiency gains from consolidation, the research evidence on the efficiency effects of consolidation has been mixed, with some studies showing efficiency gains and others showing no efficiency gains or efficiency losses (Berger and Humphrey 1997, Berger, Demsetz, and Strahan 1999, Grifell-Tatjé and Lovell 1996). The objective of the present paper is to provide additional information on the effects of deregulation and consolidation on financial services market efficiency by analyzing the Spanish insurance industry. The Spanish industry has been affected by the overall deregulation of European insurance markets, particularly through the EU s Third Generation Insurance Directives, implemented in July The Third Directives effectively deregulated the EU insurance market, with the exception of solvency regulation, which is carried out by the insurer s home country. The market changes have been particularly significant in Spain because the government began tightening solvency standards and encouraging M&As in the insurance industry even prior to the adoption of the Third Generation Directives, under a 1984 law and a 1985 Royal Decree. The 1980s Spanish deregulation was designed to create insurers who would be financially stronger, more efficient, and more competitive both nationally and internationally. As a result of these regulatory changes, the number of insurers operating in the Spanish market declined dramatically during both the 1980s and 1990s. Nevertheless, many small niche-market insurers remained in the market at the end of the 1990s, specializing in particular product lines and/or geographical regions within Spain. Government policies encouraging consolidation make sense economically if larger firms tend to be more X-efficient, if there are unrealized scale economies, and/or if consolidation leads to more vigorous competition that increases market efficiency. The purpose of this paper is to analyze scale economies and efficiency in the Spanish insurance industry to determine whether deregulation has had the intended effects. 1. For further discussion of deregulation of the U.S. banking industry, see Berger Kashyap, and Scalise (1995). European banking deregulation is discussed in Barth, Nolle, and Rice (2000); and Japanese financial deregulation is discussed in Hoshi and Patrick (2000). European insurance industry deregulation is discussed in Swiss Re (1996); and Japanese insurance deregulation is discussed in Swiss Re (2000a).

3 J. DAVID CUMMINS AND MARIA RUBIO-MISAS : 325 We analyze the Spanish insurance industry over the ten-year period We measure efficiency by estimating best practice production and cost frontiers for each year of the sample period, using data envelopment analysis (DEA), a nonparametric technique (Cooper, Seiford, and Tone 2000). A production frontier gives the minimum inputs required to produce any given output vector, while the cost frontier measures the minimum costs to produce the output vector. Efficiency, which is measured for each firm in the sample in each year, ranges from 0 to 1, with firms operating on the frontier measured as fully efficient (efficiency of 1) and firms not operating on the frontier measured as inefficient (efficiency less than 1). Because the Spanish government s policies and the EU directives both have had the effect of facilitating the creation of larger and presumably more competitive insurers, we pay particular attention to the issue of economies of scale. Policies encouraging growth in firm size make sense on scale efficiency grounds only if there are or were many insurers operating with increasing returns to scale (IRS). If deregulation has had the intended effects, productivity should improve over the sample period. Accordingly, we also measure total factor productivity (TFP) growth using the Malmquist index approach (see Färe et al. 1994), an extension of the DEA methodology. 2 To provide additional information on the effects of consolidation, we analyze the characteristics of firms exiting the market due to M&As, firms exiting for other reasons such as voluntary or involuntary liquidation, and firms participating in M&As as acquirers of other firms. If consolidation has been beneficial, we expect firms exiting the market due to liquidation to be relatively inefficient in comparison with other firms in the market. There is a growing body of literature on efficiency in the insurance industry (for a review, see Cummins and Weiss 2000), including one prior paper on the Spanish insurance industry (Fuentes, Grifell-Tatjé, and Perelman 2001)). We extend their research by conducting a more extensive analysis of efficiency, using a different methodology to analyze TFP growth, and studying insurers that specialize in life or non-life insurance as well as diversified firms writing both types of insurance. 1. HYPOTHESES In this section, we discuss the hypotheses to be tested in this study. We begin with a discussion of the expected effects of recent regulatory policy changes on insurance market structure and competition. 1.1 Spanish Deregulation and the EU s Third Generation Insurance Directives As mentioned above, the Spanish government began tightening insurance solvency standards and encouraging M&As during the 1980s. As a result, the number of 2. We focus the present study on technical and cost efficiency in order to provide a thorough analysis of these topics, including the effects of M&As, as well as conducting the Malmquist productivity analysis. Extending this paper to consider other important issues such as the effect of consolidation on revenue efficiency, profit efficiency, and market power would have significantly lengthened the paper. We elected to present our results on those topics in subsequent papers.

4 326 : MONEY, CREDIT, AND BANKING insurers declined by about 25% from 1980 to 1990 as many firms exited the industry either through M&As or insolvency (Esteban-Jodar 1986, 1993). From 1980 to 1992, the number of mutual firms declined by almost 50% either through withdrawal from the market or conversion to the stock ownership form in order to gain access to equity capital (Esteban-Jodar 1993). As competition intensified in the 1990s, due in part to the entry of foreign insurers and banks into the insurance market, the number of insurers continued to decline, although the number of demutualizations fell dramatically (Figuereido-Almaça 1999). Between 1989 and 1998, the number of Spanish insurers declined by 35% and average firm size increased by 275% (Dirección General de Seguros 1999). In spite of the dramatic restructuring during the 1980s and 1990s, the Spanish insurance industry remains bifurcated between large national players and small regional niche players specializing in narrow product categories or geographical areas. For example, in 1998, 77% of firms accounted for only 15% of premiums. This market structure has important implications for the efficiency of the industry and provides a partial explanation for the low average efficiency scores reported below. Some of the smaller firms are well adapted to their market segments and are expected to remain in the market. However, others are clearly inefficient and their prospects for long-term survival are not good. Intermediate size insurers trying to compete in the national market are vulnerable to competition from the market leaders. In addition to local regulations and competitive conditions, the Spanish insurance industry is also affected by more general European developments. The insurance industry in Europe traditionally was subject to stringent regulation affecting pricing, contractual provisions, the establishment of branches, solvency standards, etc. A separate market existed in every European country, and cross-border transactions were rare, except for reinsurance and some commercial coverages. Competitive intensity was very low, with minimal price and product competition and stable profit margins (Swiss Re 1996, 2000b). The implementation of the EU s Third Generation Directives, beginning on July 1, 1994, represented a major step in creating conditions in the EU resembling those in a single deregulated national market. 3 The Third Generation Directives have three key components: (1) the establishment of a single EU license, whereby an insurer is required to obtain only one license to operate in the EU rather than being licensed in each member nation, (2) the principle of home country supervision, whereby an insurer is regulated only by the nation which issued its license and not by each host country where it operates, and (3) the abolition of substantive insurance supervision, meaning that regulation is limited to solvency control and that pricing, contracting, and other insurer operations are effectively deregulated. Thus, insurers 3. The First Generation Directives, adopted for reinsurance in 1964, for non-life insurance in 1973, and for life insurance in 1979, introduced freedom of establishment with host country control, giving insurers the right to establish subsidiaries and branches in each EU member state. The Second Generation Directives, adopted for large commercial risks in 1988 and for auto insurance and other coverages in 1990, established freedom of services, giving insurers the ability to conduct business outside of their home country without having to establish branches in host countries. For further discussion, see Swiss Re (1996).

5 J. DAVID CUMMINS AND MARIA RUBIO-MISAS : 327 are allowed to engage in true price competition in personal lines for the first time and also to compete more freely in products and services. The Directives encouraged the entry of foreign firms and banks into the Spanish insurance market, making it more difficult for small, inefficient firms to survive. Although many such firms remained in the market in 1998, most will need to become more efficient to achieve long-term survival. 1.2 Hypothesized Effects of Regulatory Policy Changes Efficiency. The Third Generation Directives were expected to bring about price and product competition both within and across national boundaries. Given the degree of protectionism that existed in the past, such market liberalization has the potential to reduce prices and increase consumer choice. In addition, the level of efficiency in the industry is expected to improve as a result of market share gains by efficient firms, which were previously constrained from exploiting their efficiency advantage due to regulation. Inefficient firms are expected either to become more efficient or to exit the market. In addition, firms are expected to adopt new technologies and take other actions to improve productivity. 4 Consequently, it seems reasonable to expect that competition in the Spanish insurance market has intensified since deregulation, leading to efficiency gains and lower prices. Based on these arguments, we formulate the following hypotheses, both predicated on deregulation and increased competition. H1: Efficiency and productivity in the Spanish insurance industry have increased over the sample period. H2: Insurance prices declined in Spain during the sample period. Economies of scale. As suggested above, the Spanish government s policy of strengthening solvency standards and encouraging consolidation in the insurance industry was motivated by the presence of large numbers of small, undercapitalized insurers. These firms were believed to be scale inefficient and not sufficiently robust to compete effectively as the EU moved towards deregulation. It was argued that larger insurers would provide better value to insurance customers in Spain and would be more competitive with other EU insurers. Thus, the policy change was based on the implicit (and untested) assumption that there were significant unrealized scale economies in the industry and that creating larger firms would lead to more viable insurers and a more competitive market. Our tests are designed to provide information on whether these critical assumptions were correct and whether further consolidation is likely to be beneficial. 4. Prior research supports the idea that the Third Generation Directives have led to more aggressive competition among European insurers (Mahlberg and Url 2000, Swiss Re 2000b). Mahlberg and Url (2000) and Swiss Re (2000b) point out that intensified competition has occurred primarily in domestic markets (establishment of subsidiaries) rather than through true cross-border competition. One reason for this is that the Directives did not completely eliminate the ability of host countries to influence insurance markets through mechanisms such as taxation. In addition, there are significant differences in contract law across European nations (Swiss Re 1996), impeding contract standardization.

6 328 : MONEY, CREDIT, AND BANKING Economies of scale are present if average costs per unit of output decline as the volume of output increases. The usual source of scale economies is the spreading of the firm s fixed costs over a larger volume of output. Fixed costs are present for insurers due to the need for relatively fixed factors of production such as computer systems, managerial expertise, and financial capital. Economies of scale also can arise if operating at larger scale permits managers to become more specialized and therefore more proficient in carrying out specific tasks. Operating at a larger scale can reduce the firm s cost of capital if income volatility is inversely related to size. These arguments lead to the following hypothesis. H3: Insurance operations are subject to ranges of production characterized by IRS, permitting some insurers to reduce unit costs by increasing production. If IRS are present, increasing competitive intensity and market consolidation provide opportunities for firms to become more efficient by accessing economies of scale. Considering the growth in average firm size and the degree of consolidation in the Spanish market, the discussion of scale economies suggests the following hypothesis. H4: Consolidation during the 1990s has improved scale efficiency in the Spanish insurance market. Entry and exit. According to microeconomic theory, firms that do not succeed in minimizing costs will not be able to adequately compensate factors of production and will be forced to exit the market. Although several studies of financial institutions have shown that inefficient firms may be able to survive over periods of time as long as five to ten years (e.g., Berger et al. 2000, Cummins and Weiss 1993), we expect that inefficient firms eventually will be forced either to improve their performance or to exit the market, especially during a period of deregulation and increasing competitive intensity. Based on the theoretical prediction that inefficient firms will not be able to survive in the long run, we expect firms that exit the market due to voluntary or involuntary liquidation to be relatively inefficient and/or to exhibit signs of financial weakness. These predictions are formalized in the following hypotheses. H5: Firms exiting the market for reasons other than M&As are relatively inefficient. H6: Firms exiting the market for reasons other than M&As have relatively unfavorable financial performance characteristics. M&As also are expected to be efficiency-improving if targets and acquiring firms are more efficient than firms exiting the industry for other reasons or, minimally, no less efficient than the average firm remaining in the industry. Accordingly, we hypothesize a non-negative relationship between efficiency and participation in the M&A market as a target or acquirer. H7: Firms participating in the M&A market as targets and acquirers are no less efficient than non-m&a firms.

7 J. DAVID CUMMINS AND MARIA RUBIO-MISAS : 329 We analyze the last three hypotheses by examining the efficiency and other financial characteristics of the firms in the industry by M&A status. 2. DATA AND METHODOLOGY 2.1 The Data, Outputs, and Inputs The database. The database for our study consists of financial statements for all insurers operating in Spain over the period that report to the Spanish regulatory authority, the Dirección General de Seguros, Ministerio de Economía y Hacienda. 5 The database thus includes all insurers in the Spanish market supervised by the Spanish regulatory authority except for social benefit institutions. 6 Some firms were eliminated from the sample because of data problems such as zero or negative premiums or net worth. The firms remaining in the sample account for at least 90% of premium volume in the Spanish insurance market in each year of the sample period. To provide an accurate picture of the evolution of the entire Spanish market during the sample period, our sample includes firms specializing in life and nonlife insurance as well as diversified firms offering both types of insurance. Because diversified firms and specialists, each account for about half of the total premium revenues in Spain, to exclude either group would be to overlook a significant component of the market. 7 In addition, because specialized and diversified firms compete against each other in the product market, specialist firms can be dominated by joint firms and vice versa. 8 Our non-parametric DEA methodology lends itself to this analysis because DEA permits zeros in the output vector, a characteristic not possessed by some parametric specifications such as the translog function. Outputs. Insurers are analogous to other financial firms in that their outputs consist primarily of services, many of which are intangible. Consistent with most of the recent literature on financial institutions, we adopt a modified version of the value-added approach to output measurement, which counts as important outputs those that have significant value added, as judged using operating cost allocations (Berger and Humphrey 1992). Insurers provide three principal services: 5. The sample primarily consists of Spanish insurers and Spanish subsidiaries of insurers headquartered in other EU countries. As in other EU nations, the primary method for foreign insurers to enter the Spanish market has been through the formation of Spanish-licensed and regulated subsidiaries rather than through branches or agencies. Consequently, the sample consists of firms writing the vast majority of insurance sold in Spain. 6. Social benefit institutions (mutualidades de prevision social) are non-profit private mutual insurers providing coverage complementary to social security schemes. We omitted these firms because of their specialized objective and because we wanted to focus on the for-profit segment of the insurance market. 7. On average by year for the sample period, there were 78 diversified firms offering both life and non-life insurance, 55 life insurance specialist firms, and 249 non-life specialist firms. In 1998, there were 64 diversified firms, 46 life specialists, and 183 non-life specialists. In 1998, the diversified firms accounted for 44.6% of life insurance premium revenues and 49.7% of non-life premium revenues. 8. The approach differs from that taken by Fuentes, Grifell-Tatjé, and Perelman (2001) who include only diversified Spanish firms in their sample. However, the primary objective of their empirical analysis was to illustrate the parametric Malmquist methodology developed in their paper rather than to measure the overall performance of the Spanish insurance market as is the case in our paper.

8 330 : MONEY, CREDIT, AND BANKING Risk pooling and risk-bearing. Insurance provides a mechanism through which consumers and businesses exposed to losses can engage in risk reduction through pooling. The actuarial, underwriting, and related expenses incurred in risk pooling are important components of value added in the industry. Insurers also add value by holding equity capital to bear the residual risk of the pool. Real financial services relating to insured losses. Insurers provide a variety of real services for policyholders including financial planning, risk management, and the provision of legal defense in liability disputes. Intermediation. For life insurers, financial intermediation is a principal function, accomplished through the sale of asset accumulation products such as annuities. For non-life insurers, intermediation is an important but incidental function, resulting from the collection of premiums in advance of claim payments. Insurers value added from intermediation is reflected in the net interest margin between the rate of return earned on invested assets and the rate credited to policyholders. Transactions flow data such as the number of policies issued, the number of claims settled, etc. are not publicly available for insurers. However, a satisfactory proxy for the amount of risk pooling and real insurance services provided is the value of real losses incurred (Berger, Cummins, and Weiss 1997). 9 Losses incurred are defined as the losses that are expected to be paid as the result of providing insurance coverage during a particular period of time. Because the objective of risk pooling is to collect funds from the policyholder pool and redistribute them to those who incur losses, proxying output volume by the amount of losses incurred seems quite appropriate. Losses are also a good proxy for the amount of real services provided since the amount of claims settlement and risk management services also are highly correlated with loss aggregates. Because the types of services provided differ between the principal types of insurance, we use as separate output measures the value of life and non-life insurance losses incurred. Losses incurred are a satisfactory measure of output for coverage provided during any given year. However, insurers also perform services in connection with claims occurring in prior years or claims expected to occur in the future. As a proxy for these services, we use the real value of policy reserves. 10 Because the services provided by reinsurers differ from those provided by primary insurers, we include as separate outputs the real values of reinsurance reserves and reserves for primary insurance contracts. Our final output variable, which proxies for the intermediation function, is the real value of invested assets. All monetary values used in the study are expressed in 1986 monetary units by deflating the Spanish Consumer Price Index (Indice de Precios al Consumo, from the Instituto Nacional de Estadística (INE)). 9. The use of premiums generally is not considered appropriate because premiums represent price times quantity of output, i.e., insurance revenues (Yuengert 1993). 10. Reserves in insurance represent the insurer s best estimate of claims to be paid in the future as a result of past events (non-life insurance) or future contingencies (life insurance).

9 J. DAVID CUMMINS AND MARIA RUBIO-MISAS : 331 Inputs and input prices. We follow the recent insurance efficiency literature in defining four inputs labor, business services (including materials and physical capital), financial debt capital, and equity capital. The price of labor is the average monthly wage for employees in the insurance sector, provided by the INE. The INE s Spanish business services deflator is used as the price of business services. Because data on the number of employees in the Spanish insurance industry are not available, we follow other insurance efficiency researchers (e.g, Cummins and Weiss 1993, Berger, Cummins, and Weiss 1997, Cummins and Zi 1998) in measuring the quantity of labor by dividing labor expenditures by the insurance sector wage rate. The quantity of business services is defined similarly. Our other inputs are the quantity of financial equity capital and debt capital (borrowed funds). Financial equity capital is an important input in insurance because insurers must hold equity to ensure policyholders that they will receive payment if claims exceed expectations and to satisfy regulatory requirements. Debt capital provides another source of funds, consisting of borrowed funds as well as deposits from reinsurance companies. Measuring the cost of capital in the Spanish insurance industry is difficult because few insurers have traded shares. As a proxy for the cost of equity capital, we use the rate of total return on the Madrid Stock Exchange Index for each year of the sample period; and for debt capital we use the one-year Spanish Treasury bill rate. 11 Summary. To summarize, we use five outputs and four inputs. The outputs are nonlife insurance losses incurred, life insurance losses incurred, reinsurance reserves, reserves for primary insurance contracts, and invested assets. The inputs are labor, business services, debt capital, and equity capital. 2.2 Frontier Efficiency Concepts To measure efficiency in the Spanish insurance industry, we utilize modern frontier efficiency analysis. This technique involves measuring the performance of each firm in the industry relative to best practice efficient frontiers. Efficiency scores vary between 0 and 1, with fully efficient firms having efficiencies equal to 1 and inefficient firms having efficiencies less than 1. We estimate efficient production and cost frontiers, providing measures of technical, cost, and allocative efficiency for each firm in our sample. Technical efficiency is defined as the ratio of the input usage of a fully efficient firm producing the same output vector to the input usage of a specified firm. Technical efficiency can be decomposed into pure technical efficiency and scale efficiency. The decomposition is illustrated in Figure 1, which shows production frontiers for a firm producing one output (Y) using one input (X). The discussion in this section focuses on the production frontiers for period t. 11. It would be preferable to vary both the cost of equity and the cost of debt capital by insurer depending upon capital structure and portfolio risk. However, the data to do this are not available. As a robustness check, we also estimated efficiency by creating three tiers of insurers, with differing costs of debt capital based upon their capital to asset ratios, giving insurers with lower capital to asset ratios higher costs of debt. The results indicated that the efficiency scores and efficiency rankings are not substantially affected by the interest rate assumption.

10 332 : MONEY, CREDIT, AND BANKING Fig. 1. Efficiency and Productivity Measurement: Single Input-Single Output Firm Figure 1 shows three frontiers for period t a constant returns to scale (CRS) frontier (V t CRS), a variable returns to scale (VRS) frontier (V t VRS), and a non-increasing returns to scale (NIRS) frontier (V t NIRS). The CRS frontier is the straight line 0V t CRS, the VRS frontier is the solid line EBCDV t VRS, and the NIRS frontier is the dashed line 0CDV t NIRS. Pure technical efficiency is measured relative to the VRS production frontier. Firms operating on the VRS frontier have achieved pure technical efficiency, whereas firms operating to the right of the VRS frontier are inefficient in the pure technical sense. For example, firm A, operating with input output vector (x t A,y t A) is inefficient because it could reduce its input usage from 0a to 0b if it were to operate on the VRS frontier. Its pure technical efficiency is the ratio 0b/0a. The firm could further reduce its input usage to 0c if it could attain CRS, i.e., by moving to the CRS frontier represented by the solid line 0V t CRS. Thus, its scale efficiency is given by the ratio 0c/0b. Technical efficiency, the product of pure technical and scale efficiency, is equal to 0c/0a for firm A. Cost efficiency for a given firm is defined as the ratio of the costs of a fully efficient firm (i.e., a firm operating on the efficient cost frontier) with the same output quantities and input prices to the given firm s actual costs. Firms achieve cost efficiency by adopting the best practice technology (technical efficiency) and choosing the optimal mix of inputs (allocative efficiency), conditional on outputs and input prices. Cost efficiency is the product of technical and allocative efficiency. 2.3 Estimation Methodology We estimate efficiency using DEA (Cooper, Seiford, and Tone 2000), a nonparametric approach that computes efficient best practice production and cost

11 J. DAVID CUMMINS AND MARIA RUBIO-MISAS : 333 frontiers based on linear combinations of firms in the industry. DEA has been widely used in recent years to estimate efficiency in a variety of industries and national markets. We consider DEA appropriate to analyze insurance because a paper by Cummins and Zi (1998) provides evidence that DEA estimates of efficiency for U.S. life insurers are more highly correlated with conventional performance measures such as expense to premium ratios and return on assets than are the estimates obtained using econometric production and cost functions. A second reason for choosing DEA as our estimation methodology is that the Malmquist approach, which has become a standard methodology for estimating the evolution of productivity and efficiency over time, is conveniently implemented using DEA. 12 Thus, relying on DEA permits us to use the same methodology consistently throughout the paper rather than using the non-parametric approach for some of our estimates and the econometric approach for others. A third important reason for using DEA is that it provides a particularly convenient method for decomposing cost efficiency into allocative, pure technical, and scale efficiency, facilitating our analysis of scale economies. Technical efficiency. We measure technical efficiency using the input distance function introduced by Shephard (1970). Suppose firm i uses input vector x t i (x 1it, x 2it,, x Kit ) T K to produce output vector y t i (y 1it, y 2it,, y Nit ) T N in period t, where K is the number of inputs, N is the number of outputs, and T denotes vector transpose. The production technology of period t, which transforms inputs into outputs, is modeled by an input correspondence y t V t r (y t ) 4 K. For any y t N, V t r (y t ) denotes the subset of all input vectors x t K which yield at least y t, using a production technology characterized by returns to scale of type r, where r c CRS, r v VRS, and r n NIRS. The input-oriented distance function is given by D t r (x s i, y s i) sup{ θs i: ( xs i, yi) s θ s Vt r (yi)} s (inf{θs i:(θ s i x s i, y s i) V t r (y s i)}) 1, (1) i where (x s i, y s i) is the input output vector for firm i in time period s. Notice that the input output vector does not have to come from the same time period as the reference technology (i.e., s t and s t are both possible in Expression 1). As explained below, by letting s and t represent different time periods, it is possible to use distance functions to measure productivity changes over time. When s and t represent the same time period (s t), the distance Function (1) is the reciprocal of the minimum equi-proportional contraction of the input vector x t i, given outputs y t i Farrell s (1957) radial measure of input technical efficiency. Technical efficiency TE t r (x t i, y t i) is thus defined as TE t r (x t i, y t i) 1 D t r (x t i, y t i). CRS 12. Although a parametric distance function approach has been developed by Fuentes, Grifell-Tatjé, and Perelman (2001), their approach is based on the translog functional form. Use of the translog for our data would create problems in dealing with specializing firms that have zero values for some outputs. Zero outputs are not a problem in DEA.

12 334 : MONEY, CREDIT, AND BANKING technical efficiency is estimated for each firm in the sample by solving a linear programming problem: (D t c (x t i, y t i)) 1 TE t c (x t i, y t i) min θ t i (2) Subject to: Y t λ t i y t i X t λ t i θ t i x t i λ t i 0 where X t is a K I input matrix and Y t an N I output matrix for all sample firms, x t i is a K 1 input vector and y t i an N 1 output vector of firm i, λ t i is an I 1 intensity vector (the inequalities are interpreted as applying to each row of the relevant matrix), and I the number of firms in the sample (i 1, 2,, I). This estimation (with the λ t i only constrained to be non-negative) produces a CRS (r c CRS) frontier. The frontiers are estimated year by year, producing a best practice production frontier for each year of the sample period. The next step is to decompose technical efficiency into pure technical efficiency and scale efficiency, where TE t c(x t i, y t i) TE t v (x t i, y t i)se t (x t i, y t i),te t v(x t i, y t i) technical efficiency relative to a VRS frontier (pure technical efficiency), and SE t (x t i, y t i) scale efficiency. Pure technical and scale efficiency are separated by solving Equation (2) with the additional constraint: Σ i λ i 1 for a VRS frontier, and again with the constraint Σ i λ i 1 for a NIRS frontier. Pure technical efficiency (TE t v) is the solution to the VRS problem, and scale efficiency is then obtained as SE t (x t i, y t i) TE t c(x t i, y t i) TE t v(x t i, y t i). IfSE t (x t i, y t i) 1, CRS are indicated. If SE t 1 and NIRS efficiency TE t v, decreasing returns to scale (DRS) are present; and if SE t 1 and NIRS efficiency TE t v, then IRS are present. Cost efficiency. To estimate cost efficiency, we use a two-step procedure. For firm i, let w t i (w 1it, w 2it,, w Kit ) T denote the input price vector. Then, we first solve the following problem: min x t i K w t ki x t ki k 1 Subject to: Y t λ t i y t i X t λ t i x t i (3) λ t i 0. As in the case of technical efficiency, constraining the λ t i only to be non-negative produces estimates of cost efficiency relative to a CRS frontier. The solution vector x t* i is the cost minimizing input vector for the input price vector w t i and the output vector y t i. Second, calculate the ratio CE t c(x t i, y t i) (w tt i x *t i ) (w tt i x t i) to obtain CRS

13 J. DAVID CUMMINS AND MARIA RUBIO-MISAS : 335 cost efficiency for firm i. The measure of cost efficiency, 0 CE t c (x t i, y t i) 1, is the proportion by which the firm could multiply its costs and still produce no less of any output. We then can obtain an estimate of CRS allocative efficiency by utilizing the relationship: CE t c(x t i, y t i) AE t c(x t i, y t i)te t c(x t i, y t i). We solve Equation (3) for each firm in the sample for each year, producing a CRS best practice cost frontier for each year of the sample period. CRS efficiency is the ultimate benchmark because it implies that a firm has achieved pure technical efficiency, optimal scale, and allocative efficiency. However, for completeness, we also report some results based on VRS. VRS cost efficiency is estimated by solving Equation (3) with the additional constraint Σ i λ i 1, producing estimates of VRS cost efficiency: CE t v(x t i, y t i). VRS allocative efficiency is then estimated using the relationship: CE t v(x t i, y t i) AE t v(x t i, y t i)te t v(x t i, y t i). VRS allocative efficiency will not equal CRS allocative efficiency unless scale efficiency equals 1. Consequently, the input proportions implied by the solution of the VRS problem are not generally interpretable as the optimal input combinations that would be achieved under the CRS benchmarking standard, i.e., they impound some elements of scale inefficiency for firms not operating with CRS. Malmquist analysis. If consolidation in the Spanish insurance industry has been beneficial, we would expect to observe improvements in TFP during the sample period. To measure TFP, we utilize input-oriented Malmquist productivity indices. In working with Malmquist indices, it is important to adopt an assumption with respect to the returns to scale of the underlying technology, with the choices generally being CRS and VRS. As shown by Ray and Desli (1997), this assumption does not affect the overall Malmquist productivity index, which is correctly measured by the ratio of CRS distance functions even when the underlying technology exhibits VRS. However, the returns to scale benchmark does affect the decomposition of the index, which can be decomposed into indices representing pure efficiency change, technical change, and scale change. This decomposition is likely to provide useful information about the effects of consolidation in the Spanish insurance industry. Because many firms in our sample are operating with increasing or decreasing returns to scale during the sample period, we adopt the VRS benchmark technology to perform the Malmquist index decomposition. The decomposition we use was originally developed by Ray and Desli (1997). However, our decomposition differs from theirs in that we adopt an input-orientation rather than an output-orientation, consistent with our approach in the DEA analysis of firm efficiency. To provide intuition into the Malmquist approach, we consider an industry consisting of four single input, single output firms, A, B, C, and D, operating in periods t and t 1. Firms B, C, and D are efficient and hence determine the frontiers, while firm A is inefficient. The CRS and VRS frontiers for this industry for periods t and t 1 are shown in Figure 1. The CRS frontiers are the lines 0V t CRS and 0VCRS, t 1 respectively; and the VRS frontiers are the lines EBCDV t VRS and E B C D VVRS, t 1 respectively. The efficient firms operate at points B, C, and D in period t and at B,

14 336 : MONEY, CREDIT, AND BANKING C, and D in period t 1. Firm A has input output vector (x t A, y t A) in period t and input output vector (x t 1 A, ya t 1 ) in period t 1. We first illustrate TFP change using the CRS frontiers, considering the case of firm A. The improved technology represented by 0V t 1 CRS enables CRS efficient firms to produce any level of output using less of the input than under the technology of 0V t CRS. For firm A, two principal changes have occurred between periods t and t 1. First, because of technical progress, the firm produces more output per unit of input in period t 1. In fact, its input output combination in period t 1 would have been infeasible using period t technology. Thus, technical change has taken place. Second, the firm has experienced technical efficiency change because it is operating closer to the CRS frontier in t 1 than it was in period t. Malmquist TFP impounds both improvements in technology and changes in efficiency relative to the frontiers. 13 The input-oriented Malmquist index for firm A based on the CRS technology is obtained by estimating the distances from its period t and t 1 input output vectors to both the period t and the period t 1 CRS production frontiers. In terms of Equation (1), we estimate the following distance functions: D t c(x t i, y t i), D t c(xa t 1, ya t 1 ), Dc t 1 (x t A, y t A), and Dc t 1 (xa t 1, ya t 1 ), where D t c(dc t 1 ) represents the distance function relative to the CRS frontier at time t (t 1), and x t A and y t A (xa t 1 and ya t 1 ) are the input and output vectors at time t (t 1). In Figure 1, D t c(x t A, y t A) 0a 0c, D t c(xa t 1, ya t 1 ) 0a 0c, Dc t 1 (x t A, y t A) 0a 0e, and D t 1 c (x t 1 A, ya t 1 ) 0a 0e. The distance functions that compare the period t (t 1) input output vector to the same period s production frontier must be 1. However, if the frontiers shift over time, the distance function D t c(x t 1 A, ya t 1 ) or Dc t 1 (x t i, y t i) can be 1, implying that a given period s operating point is infeasible using the other period s technology. Malmquist indices can be defined relative to the technology in either period t or period t 1: M t c Dt c(x t A, y t A) D t c(xa t 1, y t 1 A ) or M t 1 c Dt 1 Dc t 1 (x t 1 A c (x t A, y t A), ya t 1 ), (4) where M t c measures productivity growth between periods t and t 1 using the CRS technology in period t as the reference technology, while Mc t 1 measures productivity growth with respect to the CRS reference technology in period t 1. To avoid an arbitrary choice of technology, the input-oriented Malmquist TFP index is defined 13. Technical change and technical efficiency change cannot be measured accurately using trends in annual average efficiency scores because the average scores are based on separate frontiers estimated for each year of the sample period. The Malmquist approach avoids this problem by also measuring each firm s position in year t j (t) relative to the frontier of period t (t j). It would be possible, for example, for year t j s frontier to dominate that of year t but for the average score to be higher in year t than in year t j, i.e., firms could be positioned closer to the frontier in period t but that frontier could be dominated by the frontier for period t j.

15 J. DAVID CUMMINS AND MARIA RUBIO-MISAS : 337 as the geometric mean of M t c and M t 1 c, M c (x t 1 i, yi t 1, x t i, y t i) [M t c M t 1 c ] 1 2. A Malmquist index 1( 1) implies TFP growth (decline). 14 In Figure 1, the Malmquist TFP index is: M c (xi t 1, y t 1 i, x t i, y t i) [(0a 0c)(0c 0a )(0a 0e)(0e 0a )] 1 2. Recall that this equation gives TFP under both the CRS and VRS technologies. Utilizing VRS as the benchmark technology to allow for the possibility that some firms have not achieved CRS, we decompose the input-oriented Malmquist index into pure efficiency change (PEFFCH), pure technical change (TECHCH), and scale change (SCH), where M c (x t 1 i, yi t 1, x t i, y t i) PEFFCH*TECHCH*SCH. The components for the input-oriented Malmquist index are given by the following formulas: PEFFCH*TECHCH ( D t v(x t A, y t A) [ SCH Dt c(x t A, y t A) D t v(x t A, y t A) D t 1 v D t 1 v D t 1 c (xa t 1 (xa t 1 (xa t 1, y t 1 A, y t 1 ))[ D A ), y t 1 t 1 v (xa t 1 A ) D t 1, y t 1 D t v (x t 1, y t 1 A D t 1 c (x t A, y t A) A ) D t 1 v (x t A, y t A) A ) v (x t A, y t A) D t v(x t A, y t A) D t v(xa t 1, y t 1 A ) D t c(xa t 1, ya t 1 )]1 2 ]1 2. (5). (6) The pure efficiency change component (PEFFCH), the expression in parentheses in Equation (5), compares the firm s distance from the VRS frontier in period t to its distance from the VRS frontier in period t 1. If the firm has moved closer to the frontier in period t 1, the ratio will be 1. In terms of Figure 1, PEFFCH [(0a/0b)/(0a /0d )]. The technical change component (TECHCH) in Equation (5) measures the shift in the VRS frontier between periods t and t 1 with respect to the operating points of firm A in the two periods. If the operating point in period t 1 is further from the frontier in period t 1 than in period t, the implication is that the frontier has shifted to the left, implying that technology has improved, and likewise for the period t operating point. In Figure 1, TECHCH {[(0a /0d )/ (0a /0b )][(0a/0d)/(0a/0b)]} 1/2. The scale change component of the input-oriented Malmquist index is somewhat complicated but can be envisioned intuitively as measuring the ratio of the distances between the VRS and CRS frontiers in periods t and t 1, with respect to the operating points of firm A in the two periods. If the geometric mean distance between the CRS and VRS frontiers with respect to the period t operating point is greater than the geometric mean distance between the CRS and VRS frontiers with respect to the period t 1 operating point, the ratio will be 1, i.e., the firm s period t 1 operating point is closer to CRS than its period t operating point. For example, the ratio D t c(x t A, y t A) D t v (x t A, y t A) (0a 0c) (0a 0b) 0b 0c measures the distance 14. Some authors define the input-oriented Malmquist index as the reciprocal of the index reported in this paper (e.g., Färe and Grosskopf, 1996, p. 55). In that definition, a Malmquist index value 1 ( 1) implies productivity growth (decline). Our definition is consistent with the recent literature (e.g., Althin 2001), and we consider the interpretation of an index value 1 as representing growth to be more intuitive than the alternative approach.

16 338 : MONEY, CREDIT, AND BANKING between the period t VRS and CRS frontiers with respect to the period t operating point, and the ratio Dc t 1 (x t A, y t A) Dv t 1 (x t A, y t A) (0a 0e) (0a 0d) 0d 0e measures the distance between the period t 1 VRS and CRS frontiers with respect to the period t operating point. The geometric mean of these two distances is [(0b/0c) (0d/0e)] 1/2. The comparable ratios for the t 1 operating point appear in the denominator, accounting for their being reciprocated in Equation (6). The overall scale efficiency component in Figure 1 is given by: SCH [(0b/0c)(0d/0e)]/[(0b /0c ) (0d /0e )] 1/2. The product of the three components equals the overall input-oriented Malmquist productivity index M c (x t 1 i, yi t 1, x t i, y t i). 3. RESULTS This section presents our results. We begin by discussing market concentration and efficiency trends and then turn to the analysis of scale economies and the Malmquist TFP analysis. The section concludes with a discussion of the efficiency effects of M&As. 3.1 Concentration and Efficiency Trends The number of firms in the Spanish insurance industry fell dramatically over the sample period, due to firm retirements, insolvencies, and M&As. The number of firms offering non-life insurance fell from 436 to 280, the number offering life insurance declined from 159 to 116, and the total number of firms fell by 35% (from 508 to 331) over the sample period. 15 The 20-firm concentration ratio in the Spanish non-life insurance industry increased from 47.3% in 1989 to 59.6% in In contrast, concentration declined in the life insurance segment of the Spanish insurance industry, with the four-firm concentration ratio falling from 40.9% in 1990 to 21.4% in The decline in life insurance concentration is attributable to market share gains by new entrants, including de novo Spanish firms, bank-owned firms, and foreign firms. Summary statistics on outputs, inputs, and input and output prices are shown in Table 1. The table shows averages for 1998 and the average annual growth rate from 1989 to 1998 as well as the total percentage growth for the period Total market output and average firm size increased significantly over the sample period. For example, total invested assets grew by 142.3% (10.3% per year) and average invested assets per firm grew by 275.5% (15.8% per year). Total input usage generally increased by smaller percentages than output over the sample period. As a first indicator of improved market efficiency due to competition and consolidation, Table 1 reports trends in non-life and life insurance prices during the sample 15. The total number of firms does not equal the sum of the number life firms and non-life firms because the sample includes diversified firms offering both types of insurance as well as specialists. The firm count omits six depository firms, a somewhat unusual organizational form which disappeared from the market by 1994.