Returns to Scale and Scale Elasticity in Farrell,Russell and Additive Models

This research extends the Farrell-based returns to scale methodology into Russell and Additive models in three ways with the focus of relationships between interior points and projected points. First, we present and prove four theorems that identify the scale nature. Second, we compare these results with the scale elasticity results. Third, we present techniques for estimating upper and lower bounds for the scale elasticities.     

Returns to scope: a metric for production synergies demonstrated for hospital production

Knowledge of the production function’s scope properties can provide insights for firms choosing their operating strategy, policy-makers considering industry structure, and analysts determining appropriate tools. We introduce a new property, returns to scope, which is distinct from scale properties and does not rely on price information. Based on desirable characteristics of an estimator of returns to scope, we propose two methods for assessment. We present examples using simulated data and hospital production data from the 2008 National Inpatient Sample of the Agency for Healthcare Research and Quality’s Healthcare Cost and Utilization Project. We find that hospitals experience negative returns to scope (productivity losses) from the joint production of minor and major diagnostic procedures. Based upon our results we conclude that the new returns to scope property allows sharper insights than classic economies of scope approaches.     

Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies

Thepurpose of this short article is to simplify goodness-of-fitmethods to obtain qualitative information about returns to scalefor individual observations. Traditional and new goodness-of-fitmethods developed for estimating returns to scale on nonparametricdeterministic reference technologies are reviewed. Using compositionrules for technologies with specific returns to scale assumptions,we show how these goodness-of-fit methods can be simplified inthe case of convex technologies (Data Envelopment Analysis (DEA)models).     

Returns-to-scale and the equity premium puzzle

A model of heterogenous firms facing idiosyncratic risk is proposed which generates an equity premium of 6 per cent and a risk-free rate of 1.5 per cent even if aggregate returns are risk-free. The premium in this model reflects diminishing returns-to-scale and the fact that equity shares are equal claims to firm output. In the bond market, the risk-free rate reflects trade in assets at marginal rates of return with a linear technology and thus the equity premium in excess returns reflects a comparison of average returns with marginal returns. In the model, credit constraints lower the equity premium and, absent such constraints, the equity premium would roughly double. Since the model may be interpreted as a model of entrepreneurship, this paper also presents estimates from a structural model of entrepreneurship using data from the Survey of Consumer Finances and also finds only a modest level of risk aversion is sufficient to replicate entrepreneurial returns.     

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.     

Anomalies and Unusual Patterns in Reported Earnings: Japanese Managers Round Earnings

Using Benford's law, this study documents pervasive evidence that managers of Japanese firms tend to engage in earnings manipulative activities of rounding earnings numbers to achieve key reference points. Similar to Carslaw (1988) and Thomas (1989) , we find that the first digit of earnings numbers is often emphasized by the management. We also find that key reference points are not limited to the first digit. The second, third, or even fourth digits are sometimes used as the reference points of the rounding earnings behavior. Finally, our results show that the incentives of rounding earnings numbers are negatively associated with the distance of pre‐rounded earnings to the next reference point.     

Assessing and valuing the nonlinear structure of hedge fund returns

Several studies have put forward that hedge fund returns exhibit a nonlinear relationship with equity market returns, captured either through constructed portfolios of traded options or piece‐wise linear regressions. This paper provides a statistical methodology to unveil such nonlinear features with respect to returns on benchmark risk portfolios. We estimate a portfolio of options that best approximates the returns of a given hedge fund, account for this search in the statistical testing of the nonlinearity, and provide a reliable test for a positive valuation of the fund. We find that not all fund categories exhibit significant nonlinearities, and that only a few strategies provide significant value to investors. Our methodology helps identify individual funds that provide value in an otherwise poorly performing category. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Downside risk and defaultable bond returns

This paper analyzes the influence of downside risk on defaultable bond returns. By introducing a defaultable bond-trading model, we show that the decline in market risk tolerance and information accuracy leads to trading loss under downside conditions. Our empirical analysis indicates that downside risk can explain a large proportion of the variation in yield spreads and contains almost all valid information on liquidity risk. As the credit level decreases, the explanatory power of downside risk increases significantly. We also investigate the predictive power of downside risk in cross-sectional defaultable bond excess returns using a portfolio-level analysis and Fama-MacBeth regressions. We find that downside risk is a strong and robust predictor for future bond returns. In addition, due to the higher proportion of abnormal transactions in the Chinese bond market, downside risk proxy semi-variance can better explain yield spreads and predict portfolio excess returns than the proxy value at risk.     

Time-varying leverage effects

Vast empirical evidence points to the existence of a negative correlation, named ”leverage effect”, between shocks to variance and shocks to returns. We provide a nonparametric theory of leverage estimation in the context of a continuous-time stochastic volatility model with jumps in returns, jumps in variance, or both. Leverage is defined as a flexible function of the state of the firm, as summarized by the spot variance level. We show that its point-wise functional estimates have asymptotic properties (in terms of rates of convergence, limiting biases, and limiting variances) which crucially depend on the likelihood of the individual jumps and co-jumps as well as on the features of the jump size distributions. Empirically, we find economically important time-variation in leverage with more negative values associated with higher variance levels.     

Unconventional monetary policy and the stock market’s reaction to Federal Reserve policy actions

We examine the change in the effect of Federal Reserve’s policy actions on stock returns after the Fed started to use unconventional policy actions. We find that the response of stock returns to monetary policy actions are almost seven times higher after the federal funds rate hit the zero lower bound. We conduct additional analysis to examine the underlying causes of the increase in the impact of monetary policy actions of stock returns. We show that investors rebalance their portfolios towards equity after selling Treasury securities to the Federal Reserve during large scale asset purchases.     

Change point estimation in panel data with time-varying individual effects

Existing panel data methods remove unobserved individual effects before change point estimation through data transformations such as first-differencing. In this paper, we show that multiple change points can be consistently estimated in short panels via ordinary least squares. Since no data variation is removed before change point estimation, our method has better small-sample properties compared to first-differencing methods. We also propose two tests that identify whether the change points found by our method originate in the slope parameters or in the covariance of the regressors with individual effects. We illustrate our method via modeling the environmental Kuznets curve and the US house price expectations after the financial crisis.     

Technology choice in an evolutionary oligopoly game

In this paper, we propose and analyze a two-stage oligopoly game in which firms first simultaneously choose production technologies and in the second stage simultaneously choose production quantities. After characterizing the Nash equilibrium of the game, we cast our static model in a dynamic setting exploring the stability properties of the market equilibrium in two different cases: (i) exogenously distributed technologies and Cournot adjustments and (ii) endogenously distributed technologies in an infinite population game with Cournot–Nash equilibrium outputs. The main aim of the paper is that of extending the results about Cournot oligopoly stability in an evolutionary setting of heterogeneous decreasing returns-to-scale technologies. We show how the interplay between production decisions and R&D decisions can generate endogenous market fluctuations leading to complex dynamic phenomena.     

Calculation of scale elasticities in DEA models: direct and indirect approaches

The qualitative characterisation of returns to scale in DEA has been a research issue the last decade. However, quantitative information provides the ultimate information. This paper presents two ways of obtaining numerical values of scale elasticity by an indirect approach using efficiency scores and dual variables for radial projections of inefficient points to the frontier, and a direct approach that is more general and powerful and directly evaluates numerically scale elasticity at any point on the DEA surface along intersections with planes. The direct and indirect approaches are compared using real data and a very high correspondence is found.     

The evolution of scale economies in US banking

Continued consolidation of the US banking industry and a general increase in the size of banks have prompted some policymakers to consider policies that discourage banks from getting larger, including explicit caps on bank size. However, limits on the size of banks could entail economic costs if they prevent banks from achieving economies of scale. This paper presents new estimates of returns to scale for US banks based on nonparametric, local‐linear estimation of bank cost, revenue, and profit functions. We report estimates for both 2006 and 2015 to compare returns to scale some 7 years after the financial crisis and 5 years after enactment of the Dodd–Frank Act with returns to scale before the crisis. We find that a high percentage of banks faced increasing returns to scale in cost in both years, including most of the 10 largest bank holding companies. Also, while returns to scale in revenue and profit vary more across banks, we find evidence that the largest four banks operate under increasing returns to scale.     

Aspects of growth in a system of cities

This paper explores and develops the modeling of growth in a system of cities in two alternative settings. First, we examine a large growing economy with a fully developed system of cities with perfectly malleable private and public capital. Local scale economies in production and diseconomies in consumption in equilibrium offset each other at the margin so that from a national point of view we have a constant returns to scale economy. We show that at the steady state the number of cities grows exponentially at the rate of growth of the population. We then examine the impact of technological change, considering a case where public capital is not perfectly malleable. In the second setting, we consider the problem of growth for a small economy and discuss problems associated with the transition to the steady state. We modify the previous model to describe a system of cities that is just starting to develop. Investment in public infrastructure capital is subject to sharp indivisibilities and as a result new cities are built at discrete points in time.     

Threshold effect of scale and skill in active mutual fund management

In this paper, we apply threshold estimation techniques to study the size-performance relationship in the US mutual fund industry. Existing studies have found diseconomies of scale, and we add our contribution to this by considering possible non-linear decreasing returns to scale caused by fund age and manager tenure. We find significant threshold effects of both fund age and manager tenure at approximately three to four years in the size-performance relationship. Compared with younger funds, older funds have more severe decreasing returns to scale as the industry size increases.     

The impact of the disposition effect on asset prices: insight from the NBA

In this paper we examine the price movements of contracts that represent bets on NBA games and find that the disposition effect causes significant deviations between contract prices and values. The contracts under examination are listed on Tradesports, a prediction market which provides an ideal venue for testing this and other behavioral theories because of its asset properties, market structure, and the absence of the joint hypothesis problem. In our analysis, we forecast the projected final combined scores of both teams in a contest based on observed within-game scores and game time remaining. At all points in time throughout each game, mean future returns (measured as Ticks to Expiry) should be no different than zero. However, we find that contracts which have fallen off pace to exceed the stated contract total become overpriced and experience negative future returns. Likewise, we provide evidence that contracts on games in which teams are on pace to exceed the stated total become underpriced and experience significantly positive future returns. These findings are consistent with the disposition effect in which traders tend to hold losing positions to avoid realizing losses yet prematurely unwind winning positions to realize gains.     

Causality effects in return volatility measures with random times

We provide a structural approach to identify instantaneous causality effects between durations and stock price volatility. So far, in the literature, instantaneous causality effects have either been excluded or cannot be identified separately from Granger type causality effects. By giving explicit moment conditions for observed returns over (random) duration intervals, we are able to identify an instantaneous causality effect. The documented causality effect has significant impact on inference for tick-by-tick data. We find that instantaneous volatility forecasts for, e.g., IBM stock returns must be decreased by as much as 40% when not having seen the next quote change before its (conditionally) median time. Also, instantaneous volatilities are found to be much higher than indicated by standard volatility assessment procedures using tick-by-tick data. For IBM, a naive assessment of spot volatility based on observed returns between quote changes would only account for 60% of the actual volatility. For less liquidly traded stocks at NYSE this effect is even stronger.