Academic journal article Atlantic Economic Journal

Incorporating Risk into the Analysis of Production

Academic journal article Atlantic Economic Journal

Incorporating Risk into the Analysis of Production

Article excerpt


A number of mysteries have survived intensive investigation. Though the question of whether the Loch Ness creature is elusive or simply illusive is better known, no less baffling is the case of commercial banking's missing scale economies. The story of these missing economies is a cautionary tale about the importance of accounting for risk in modeling production.

In the last two decades commercial banks in the U.S. have merged in record numbers to create banks of record size. The bankers involved in these mergers invariably claim to see scale economies in their merged institutions, which provide an important economic justification for consolidation. Banking textbooks implicitly confirm these sightings as they hypothesize about the sources of such economies. However, when the empirical evidence is sent to the academic laboratory for confirmation, the econometric tests applied to it usually conclude that smaller banks enjoy only slight economies of scale while larger banks experience slight diseconomies of scale.(1) Thus, the empirical evidence usually contradicts the testimony of bankers and textbook authors. Where, then, are the scale economies?

The standard textbook explanation usually focuses on the relationship of scale to diversification and to the ability to spread the costs of various centralized functions over a larger scale. The investment in information technology, for example, does not increase in proportion to the size of the bank. In addition, as the number of a bank's loans and deposits increases with its size, the bank's exposure to credit risk and to liquidity risk can be reduced by better diversification of assets and liquid liabilities. In turn, the potential that an increase in size can better diversify risk implies the potential for economies of scale in risk management and for a lower risk premium on the cost of uninsured, borrowed funds, ceteris paribus.

However, other things are not constant, which may provide an important clue to the whereabouts of the missing scale economies. By reducing the risk attached to any given production plan, better diversification can decrease the marginal cost of risk-taking and provide an incentive for banks to take additional risk to earn a higher expected return. For example, in response to better diversification of deposits that diminishes liquidity risk, banks may reduce their holdings of liquid government securities and increase the proportion of their assets held in illiquid, but more profitable, loans. Similarly, in response to better diversification of loans that diminishes banks' exposure to credit risk and, hence, to insolvency risk, they may make riskier loans and reduce the ratio of equity capital to total assets to improve the return on their equity. Of course, this additional risk-taking is costly both in terms of the additional resources required to manage the risk and the higher risk premium that must be paid for uninsured, borrowed funds. This additional cost may obscure the scale economies generated by better diversification when no account is taken of risk. On one hand, an increased scale of operations that improves diversification may result in a less-than-proportionate increase in cost, ceteris paribus. However, on the other hand, the additional cost of increased endogenous risk may cause cost to increase proportionately with scale or even more than proportionately and give the appearance that there are no scale economies.

If accounting for endogenous risk is critical to detecting risk-related scale economies, is it possible, then, that the assumptions made about risk by the standard techniques of measuring scale economies yield their generally negative result? I shall answer, "Yes," to this question and argue that the standard dual cost and profit functions usually neglect important relationships among the firm's production choices, its financial structure, and its exposure to market-priced risk. …

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