Among the independent variables, we consider the competitiveness variable as well as other control variables. We use Lerner index as a proxy of competitiveness level. Lerner index (LernerIndex) represents the markup of price over marginal costs. A large Lerner index implies insurers have high market power and are very competitive. For a perfectly competitive firm, the index equals 0 where the price equals the marginal costs implying such a firm has no market power. For a monopolistic firm, the index is close to 1 as the price is far from its marginal costs. It is calculated as:
𝐿𝑒𝑟𝑛𝑒𝑟𝐼𝑛𝑑𝑒𝑥𝑖𝑡 =𝑃𝑇𝐴𝑖𝑡𝑃−𝑀𝐶𝑇𝐴𝑖𝑡
𝑇𝐴𝑖𝑡 (2)
where TAit represents a proxy for firm output for insurer i at time t. As only one output is used in equation (2), we follow past literatures such as Berg and Kim (1994), Fernandez de Guevara et al. (2005) to use total assets as the output. P𝑇𝐴𝑖𝑡 is the price of the output for firm i at time t and we use two different methods to define it.
Following Tennyson (1997) and Cummins, Phillips and Tennyson (2001), we define output price as the inverse of loss ratio3. In addition, we define output price as the
3 We also consider the effect of loss adjustment expenses incurred and redefine the output price equal to inverse of (loss incurred and loss adjustment expenses incurred / premiums earned) and the result of
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ratio of firm revenue relative to its total assets following banking literatures such as Bikker and Haaf (2002) and Claessens and Laeven (2004), and we define the revenue of the insurance industry as the sum of net written premiums and net investment income earned4. 𝑀𝐶𝑇𝐴𝑖𝑡 is the marginal cost of total assets for firm i at time t.
𝑀𝐶𝑇𝐴𝑖𝑡 is derived from the following translog cost function:
𝑙𝑛 𝑇𝐶𝑖𝑡 = 𝛽0+ 𝛽1𝑙𝑛 𝑇𝐴𝑖𝑡 +12𝛽2(𝑙𝑛 𝑇𝐴𝑖𝑡)2+ ∑4𝑗=1𝜆𝑗ln 𝑊𝑗,𝑖𝑡 +
1
2∑4𝑗=1∑4𝑘=1𝜆𝑗𝑘ln 𝑊𝑗,𝑖𝑡ln 𝑊𝑘,𝑖𝑡+ ∑4𝑗=1𝛾𝑗ln 𝑇𝐴𝑖𝑡ln 𝑊𝑗,𝑖𝑡+ 𝜃1𝑇𝑟𝑒𝑛𝑑 +
𝜃212𝑇𝑟𝑒𝑛𝑑2+ 𝜃3𝑇𝑟𝑒𝑛𝑑 ln 𝑇𝐴𝑖𝑡 + ∑4𝑗=1∅𝑗𝑇𝑟𝑒𝑛𝑑 ln 𝑊𝑗,𝑖𝑡+ 𝜇𝑖 + 𝜂𝑖𝑡 , ∀𝑖, 𝑡 (3)
where 𝑇𝐶𝑖𝑡 reflects the total costs of the firm, 𝑊𝑘,𝑖𝑡 are the four input prices used, and Trend represents the technological change measured by time trend. The Trend variable equals 1 to 16 for year 1996-2011. The equation (3) must be homogeneous of degree one in input prices, and we also impose the symmetry restrictions.
Four inputs and their input prices are discussed belows. Following the insurance literature (e.g. Cummins and Weiss, 2012), we define the four inputs used in the calculation of marginal cost as: labor (X1), business services (X2), equity capital (X3) and debt capital (X4). Labor accounts for about two-thirds of total non-loss insurer expenses, with the remaining insurer expenses including computers and business services expenses. We also consider both equity and debt as two sources of capital. The labor cost is defined as the sum of salaries and payroll taxes as well as employee relations welfare, and the business service expenses includes agent commissions as well as loss adjustment expenses. Applying the banking literature (e.g.
Altunbas, et.al, 2001) which consider it a common practice to use total assets as the
marginal cost is not materially different.
4 We replace net investment income earned by net investment income gain as an alternative to calculate the output price and the results are not materially different.
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proxy of number of employees, we use total net written premium as the proxy of number of employees and quantity of business services accordingly5. We believe that total premium is a better proxy of number of employees or quantity of business services than total assets for the property liability insurers. The labor price thus equals to labor cost divided by total net premium, and business service input price equals to business service expense divided by total net premium.
The third input capital is measured by book value of equity capital. The ideal cost of capital measure is expected market return on equity capital. However, expected market returns cannot be calculated for most insurers because the majority of them are not publicly traded. Following Cummins and Xie (2008), we use a proxy for the expected return on equity, the size adjusted capital asset pricing model expected return, based on data from Ibbotson Associates (2005)6. The final input is debt capital and is measured by borrowed fund and deposits from reinsurers (Cummins and Rubio-Misas, 2006). The cost of debt capital is estimated as the ratio of total expected investment income minus expected investment income attributed to equity capital divided by average debt capital (e.g., Berger, Cummins, and Weiss, 1997). Finally, marginal cost is then computed as:
𝑀𝐶𝑖𝑡 = 𝜕𝑇𝐶𝑖𝑡
5 While the amount of labor costs and business service expenses are both available in the financial statements of insurance firms, past literatures such as Cummins and Weiss (2012) consider salary deflator as the input price because data for the number of employees and for the quantity of business services are not available. The salary deflators used in the past literatures include average weekly wages for Standard Industrial Classification (SIC) sector 6411, insurance agents and for SIC sector 7300, business services using U.S. Department of Labor data. However, as Lerner index measure is the key variable used in our study, it is not appropriate to use the same input price for every sample observation to calculate marginal cost. We thus use alternative measures to calculate the prices for labor and business services inputs.
6 The cost of capital for year t is calculated as the 30-day Treasury bill rate at the end of year t-1, plus the long term (1926 to the end of year t-1) average market risk premium on large company stocks, plus the long term (the 1926 through end of year t-1) average size premium by size category from Ibbotson Associates. We follow Ibbotson in grouping the insurers in our sample into four size categories based on equity capital. Details please see Cummins and Xie (2008).
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