Managerial economics and operating beta

We model a firm's unlevered beta in terms of elementary microeconomic variables. The source of uncertainty is a shock to demand. A firm decides on capital before the shock, and on labor, output, and price after the shock. Some insights are: (1) with decreasing returns to scale of production, beta has an inverse relation with price elasticity of demand, given the income elasticity of demand; (2) beta has a direct relation with the firm's returns to scale of production; (3) due to the impact of operating leverage, beta has an inverse relation with industry concentration; and (4) for a given returns to scale, beta has a direct relation with the capital–labor ratio that strengthens as industry concentration decreases. Copyright © 2011 John Wiley & Sons, Ltd.     

Returns to scale in the United States intercity bus industry

This paper has taken into account the a priori restrictions available from neoclassical cost theory in evaluating the relationship between cost and the level of output and input prices for U.S. intercity bus service. A general translog cost function is used which allows tests of the degree of returns to scale, homotheticity and non-constant elasticities of substitution among input pairs. Major empirical findings are: (i) the intercity bus service can be modeled by a homothetic production function, (ii) operators can substitute labor for capital by using vehicles more extensively, (iii) there are potential economies of scale in the provision of intercity bus service, and (iv) the Cobb-Douglas functional form used in earlier studies of the industry is inappropriate.     

The effects of uncertainty on investment and the expected long-run capital stock

This paper examines the effects of output price uncertainty on the optimal investment behavior of a risk-neutral competitive firm with a constant returns to scale production function. In the presence of convex costs of adjustment, investment is an increasing function of q, the shadow price of capital. Given the current price of output, we find that increased uncertainty will raise the current rate of investment. Increased uncertainty will also increase the expected long-run capital stock if the price of output is serially uncorrelated. However, if the price of output is serially correlated, then the direction of the effect of increased uncertainty on the expected long-run capital stock depends on the curvature of the marginal adjustment cost function. In this case, we obtain results which are directly opposite of the results in the literature and we locate the flaw in the existing analysis.     

On a linear stochastic differential equation

Summary Stochastic differential (s. d.) equations had been considered in [Nasr, 1960] and [Nasr]. We consider here, the s. d. equationf(D)x(t)=m(t)+v(t)z(t) wherem(t),v(t) are real functions oft,f(D) is a polynomial inD withD=d/dt, andz(t) is a random function. In particular,z(t) is assumed here, to be of the stationary type, while other types namely whenz(t) is of theGaussian or of thePoisson type, are considered in [Nasr]. A particular integral of the stated equation, and an associated covariance function of this integral are given in the form of generalized (g-)functions; [Nasr, 1965]. The equationdx/dt=v(t)z(t) wherez(t) is stationary in the wide sense is considered as a special case.     

A Cost System Approach to the Stochastic Directional Technology Distance Function with Undesirable Outputs: The Case of us Banks in 2001–2010

This paper offers a methodology to address the endogeneity of inputs in the directional technology distance function (DTDF)‐based formulation of banking technology which explicitly accommodates the presence of undesirable nonperforming loans—an inherent characteristic of the bank's production due to its exposure to credit risk. Specifically, we model nonperforming loans as an undesirable output in the bank's production process. Since the stochastic DTDF describing banking technology is likely to suffer from the endogeneity of inputs, we propose addressing this problem by considering a system consisting of the DTDF and the first‐order conditions from the bank's cost minimization problem. The first‐order conditions also allow us to identify the ‘cost‐optimal’ directional vector for the banking DTDF, thus eliminating the uncertainty associated with an ad hoc choice of the direction. We apply our cost system approach to the data on large US commercial banks for the 2001–2010 period, which we estimate via Bayesian Markov chain Monte Carlo methods subject to theoretical regularity conditions. We document dramatic distortions in banks' efficiency, productivity growth and scale elasticity estimates when the endogeneity of inputs is assumed away and/or the DTDF is fitted in an arbitrary direction. Copyright © 2015 John Wiley & Sons, Ltd.     

A study of multiple-output production functions: Klein's railroad study revisited

Using two sets of U.S. railroad data with two outputs and three inputs, we estimated production function parameters via the system of derived input demand functions, and via the dual cost function. The results indicate increasing returns to scale, and a violation of required convexity for the production function.     

Non-jointness and scope economies in the multiproduct symmetric generalized McFadden cost function

The multiproduct symmetric generalized McFadden cost function is increasingly prominent in empirical production analysis. Researchers should be aware that the scope for imposing and testing non-jointness in this model is limited. In the general version of the model non-jointness requires the non-testable maintained hypothesis of similar (in a sense we define) single-output production technologies, a maintained hypothesis for which there is not normally any basis. The apparent imposition and testing of non-jointness must be qualified accordingly. The attempt to impose non-jointness and global separability simultaneously necessarily imposes constant returns to scale and the implication that outputs are identical up to a scalar multiple. In this special case the model therefore effectively describes merely the production of a single output, and in this sense is only trivially multiproduct.     

A multiproduct Symmetric Generalized McFadden cost function

This paper introduces a flexible multiproduct cost function that permits zero values of one or more of the outputs and can impose restrictions quite easily, if not automatically satisfied, to ensure global concavity property. It satisfies linear homogeneity (in prices) property and is flexible in the output space. Thus the function is ideal for estimating, for example, economies of scope, cost complementarity, product-specific returns to scale, etc., without worrying about zero values of output(s) and extrapolations to points far from the point of approximation. As an empirical application, we use panel data (1978–1985) on 12 Finnish foundry plants to estimate technical progress, overall returns to scale, product-specific returns to scale and economies of scope.     

AN EMPIRICAL GROWTH MODEL FOR MAJOR OIL EXPORTERS

This paper develops a long‐run output relation for a major oil‐exporting economy where the oil income‐to‐output ratio remains sufficiently high over a prolonged period. It extends the stochastic growth model developed in Binder and Pesaran (1999) by including oil exports as an additional factor in the capital accumulation process. The paper distinguishes between the two cases where the growth of oil income, g^o, is less than the natural growth rate (the sum of the population growth, n, and the growth of technical progress, g), and when g^o ≥ g + n. Under the former, the effects of oil income on the economy's steady growth rate will vanish eventually, while under the latter oil income enters the long‐run output equation with a coefficient which is equal to the share of capital if it is further assumed that the underlying production technology can be represented by a Cobb–Douglas production function. The long‐run theory is tested using quarterly data on nine major oil economies. Overall, the test results support the long‐run theory, with the existence of long‐run relations between real output, foreign output and real oil income established for six of the nine economies considered. Copyright © 2012 John Wiley & Sons, Ltd.     

Het statistische verband tussen arbeidsproduktiviteit en produktie

The statistical relation between labour-productivity and production.
Rising labour productivity can be induced by increases in output, or result from "autonomous" factors. Many induced increases will be irreversible, in particular those associated with "learning" processes. Under conditions of continuous economic growth the learning curve hypothesis leads to a simple exponential relation between labour demand and output in the long run.
In the short run, current and past profits and the profitability of import substitution join output as explanatory factors of labour demand.
In the long run, the effect of growth of capital must be taken into account. Autonomous factors can be represented by an exponential trend. With United States data, increasing returns to scale are still found. Under conditions of a constant savings ratio and continuous population growth a production function, which takes account of all these factors, can be shown to be compatible with a constant labour-output elasticity, however.     

The measurement of productivity in the nonmarket sector

In many sectors of the economy, governments either provide various services at no cost or at highly subsidized prices. Examples are the health, education and general government sectors. The System of National Accounts 1993 recommends valuing these nonmarket outputs at their costs of production but it does not give much guidance on exactly how to do this. In this paper, an explicit methodology is developed that enables one to construct these marginal cost prices. However, in the main text, an activity analysis approach is taken in order to simplify the analysis, so in particular, constant returns to scale, no substitution production functions for the specific activities in the nonmarket sector are assumed. It is shown that it is possible to obtain meaningful measures of Total Factor Productivity growth in this framework. An “Appendix” relaxes some of the restrictive assumptions that are used in the main text.     

Decompositions of profitability change using cost functions

The paper presents a decomposition of a production unit’s cost ratio over two periods into explanatory factors. The explanatory factors are growth in the unit’s cost efficiency, output growth, changes in input prices and technical progress. In order to implement the decomposition, an estimate of the industry’s best practice cost function for the two periods under consideration is required. Profitability at a period of time is defined as the value of outputs produced by a production unit divided by the corresponding cost. Using the earlier work by Balk and O’Donnell, the paper provides a decomposition of profitability growth over two periods into various explanatory factors that are similar to the cost ratio decomposition except that change in outputs explanatory factor is replaced by two separate factors: an index of output price growth and a measure of returns to scale.     

Optimal process parameters under LINEX loss function with general input quality characteristic

In this paper we generalize the quality and cost trade-off problem of Chang and Hung (Qual Quant 41: 291–301, 2007) under the LINEX loss function. We consider the general input characteristic given by the random variable X with moment generating function m _X (t) and output characteristic given by the deterministic transformation Y  =  g(X). The two cases we consider are when g(X) is an affine function of X and X follows (1) the gamma distribution, and (2) the double exponential distribution.     

Productivity differences in multiple output industries: An empirical application to electricity distribution

Given that electricity distribution is undertaken via a network, it is expected that costs of production are affected both by the nature of the network and the volume of physical output distributed via the network. This two-dimensional concept of firm size, that is involving network size (number of customers) and the level of physical output (kWh), also corresponds to the distinction between productivity measures of returns to density and returns to scale.This approach has been used to specify a restricted multioutput cost function and to estimate this function for the Norwegian electricity distribution industry through the use of a flexible functional form (translog). The results indicate that no economies of scale are present in the industry even for small plants when measured correctly, but that economics of density are present.     

Scale economies in electricity distribution: a semiparametric analysis

We estimate the costs of distributing electricity using data on municipal electric utilities in Ontario, Canada for the period 1993–5. The data reveal substantial evidence of increasing returns to scale with minimum efficient scale being achieved by firms with about 20,000 customers. Larger firms exhibit constant or decreasing returns. Utilities which deliver additional services (such as water/sewage), have significantly lower costs, indicating the presence of economies of scope. Our basic specifications comprise semiparametric variants of the translog cost function where output enters non‐parametrically and remaining variables (including their interactions with output) are parametric. We rely upon non‐parametric differencing techniques and extend a previous differencing test of equality of non‐parametric regression functions to a panel data setting. Copyright © 2000 John Wiley & Sons, Ltd.     

Second‐Price Auctions with Different Participation Costs

This paper studies equilibria of second‐price auctions in independent private value environments with different participation costs. Two types of equilibria are identified: monotonic equilibria in which a bidder with a lower participation cost results in a lower cutoff for submitting a bid, and nonmonotonic equilibria in which a lower participation cost results in a higher cutoff. We show that there always exists a monotonic equilibrium, and further, that the monotonic equilibrium is unique for either concave distribution functions or strictly convex distribution functions with nonincreasing reverse hazard rates. There exist nonmonotonic equilibria when the distribution functions are strictly convex and the difference of the participation costs is sufficiently small. We also provide comparative static analysis and study the limiting properties of equilibria when the difference in bidders’ participation costs approaches zero.     

A General Procedure to Recover the Marginal Products of a Cost Minimizing Firm

Inthis paper we develop a new method, based on generalized inverse,to recover the first derivatives of the production function.This allows us to retrieve returns to scale, technological progressand, in a dynamic setting, a measure of the adjustment cost.The method is general and systematic and it applies in caseswhere the traditional method does not. It is especially relevantwhen examining dynamic models or regulated firms.     

Distinguishing external from internal scale effects: The case of public infrastructure

The recent applied production theory literature focusing on the economic performance of firms has increasingly recognized the importance of scale effects on costs and therefore efficiency. These scale effects may include short run returns due to fixity of privately demanded inputs (i.e., capital, long run internal returns to scale, and external factors affecting costs. Since these different types of scale effects can be thought of as shifts in and movements along cost curves, the different cost effects of such factors can be identified in a framework which explicitly takes them into account in the definition ofscale.In this article we formalize such a framework, and then use it to measure short run, long run (internal) and external scale effects from fixity of private capital, nonconstant returns to scale and public infrastructure. We then use these measures to identify the impacts of these different scale factors on productivity growth. The focus on public infrastructure as an important external scale factor is motivated by the current theoretical and policy interest in this issue; we show how a structural production theory model provides a rich basis for the analysis of the cost effects of infrastructure investment.     

超越对数函数要素替代弹性公式修正与估计方法比较

对超越对数函数要素替代弹性估计方法进行专门研究,修正了超越对数生产函数要素替代弹性公式错误,梳理超越对数成本函数各类替代弹性定义,综合考虑数据易得性、估计可靠性、定义合意性以判定各类估计方法的相对优劣。研究发现,受困于共线性难题,基于超越对数生产函数计算替代弹性效果不佳;基于超越对数成本函数计算替代弹性更具优势,影子替代弹性凭借出色的理论性质与强稳健性成为首选。     

On certainty equivalent

Riassunto Come noto, una funzione continua e strettamente monotona individua una media associativa di una variabile aleatoria (v.a.)X.Nel presente lavoro si confrontano due medie associativeM _f eM _g , indotte da due diverse funzionif eg, allo scopo di individuare, nella classe delle v.a.X limitate, l'estremo superiore della loro differenza in modulo.Sotto alcune ipotesi, in particolare chef sia una trasformazione crescente e concava dig, si forniscono condizioni necessarie e/o sufficienti di estremo superiore della differenza in questione.Da un punto di vista applicativo, qualoraf eg siano interpretabili come funzioni di utilità e quindi le medie associative considerate assumano il significato di certi equivalenti, l'estremo superiore della loro differenza può rappresentare il margine di contrattazione (sul prezzo) che un venditore ed acquirente potenziali hanno a disposizione. Se poig è lineare ef è concava allora la differenza considerata è il premio di rischio.

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Partially supported by M.U.R.S.T. and C.N.R.