A dual measure of economies of scope

Abstract

Information on the economies of scope (or cost complementarities) between two or more output variables is traditionally obtained from the second derivative properties of an econometrically estimated multi-output cost function. However, in some instances the econometric estimation of a cost function may not be viable, because cost or input price data are not readily available or because the assumption of cost minimising behaviour is not appropriate in the industry at hand, perhaps due to government ownership or regulatory controls. In this paper we address this issue by utilising the duality between the cost and input distance functions in deriving an expression for a measure of economies of scope in terms of the derivatives of an input distance function. We derive expressions for the special cases of the CES and translog functional forms, and then provide an empirical illustration using sample data on Australian aged care facilities, an industry which is currently undergoing a major pricing and regulatory review. Our empirical results indicate that there is some evidence for existence of economies of scope between high care and low care patients, a result which is of particular interest to policy makers in this industry.

Examining the relationship between farm size and productive efficiency: a Bayesian directional distance function approach

“…The coefficient estimates for the Bayesian DTDF are presented in Table . As expected, the estimates have positive first‐order coefficients for inputs and negative first‐order coefficients for outputs, implying that monotonicity conditions are satisfied (Feng and Serletis, ; Hajargasht et al., ). The highest posterior density intervals for all first‐order coefficients are either on the left‐side of zero (for outputs) or on the right‐side of zero (for inputs).…”

“…The productivity effect of durable capital (0.03) and material inputs (i.e., an index of seed and nonfertilizer chemicals) (0.02) were the lowest elasticities, relative to the other three inputs. The positive (negative) input (output) elasticities in the directional distance function imply that, consistent with the monotonicity conditions imposed, TI would increase with the level of input use (Feng and Serletis, ; Hajargasht et al., ). That is, increasing the input bundle required to produce a fixed amount of crop output could increase the distance to the frontier.…”

“…The highest posterior density intervals for all first‐order coefficients are either on the left‐side of zero (for outputs) or on the right‐side of zero (for inputs). Since our data were mean‐scaled prior to model estimation, these coefficients can be interpreted as elasticities evaluated at the mean of the sample (Hajargasht et al., ; Khataza et al., ). For example, the mean elasticities with respect to land, fertilizer, and labor are 0.50, 0.24, and 0.29, respectively.…”

Analyzing Bank Efficiency: Are “Too-Big-to-Fail” Banks Efficient?

“…The elasticity estimates do not vary significantly across quantiles, but the estimates on Credit Risks and Liquidity Risks have displayed a distinctive increasing pattern. 14 Economies of scope, displayed in Table 5.3, are constructed following Hajargasht, Coelli and Rao (2008), who derive the expression for economies of scope in terms of the derivative of the distance functions, utilizing the duality between the cost and input distance functions. The economies of scope between outputs i and j can be calculated using the derivatives of the output distance function as follows:…”

Using a Bayesian approach to evaluate the accuracy of economies of scope: Examples from Australian public universities

“…Choosing a significance level of 5%, we can draw the 95% confidence intervals for the point estimates evaluated at 50% to 300% of output mean in Figure 1. Notice that the positive figure of in Table 3 implies sufficient condition of diseconomies of scope (Hajargasht, Coelli, & Rao, 2008;Pulley & Humphrey, 1993). Negative values of degree of economies of scope are therefore expected.…”