A new approach to estimating the metafrontier production function based on a stochastic frontier framework

This paper proposes a new two-step stochastic frontier approach to estimate technical efficiency (TE) scores for firms in different groups adopting distinct technologies. Analogous to Battese et al. (J Prod Anal 21:91–103, 2004), the metafrontier production function allows for calculating comparable TE measures, which can be decomposed into group specific TE measures and technology gap ratios. The proposed approach differs from Battese et al. (J Prod Anal 21:91–103, 2004) and O’Donnell et al. (Empir Econ 34:231–255, 2008) mainly in the second step, where a stochastic frontier analysis model is formulated and applied to obtain the estimates of the metafrontier, instead of relying on programming techniques. The so-derived estimators have the desirable statistical properties and enable the statistical inferences to be drawn. While the within-group variation in firms’ technical efficiencies is frequently assumed to be associated with firm-specific exogenous variables, the between-group variation in technology gaps can be specified as a function of some exogenous variables to take account of group-specific environmental differences. Two empirical applications are illustrated and the results appear to support the use of our model.     

A reexamination of the equity-premium puzzle: A robust non-parametric approach

Recent tests of stochastic dominance of several orders, proposed by Linton, Maasoumi and Whang [Linton, O., Maasoumi, E., & Whang, Y. (2005). Consistent testing for stochastic dominance under general sampling schemes. Review of Economic Studies, 72(3), 735–765], are applied to reexamine the equity-premium puzzle. An advantage of this non-parametric approach is that it provides a framework to assess whether the existence of a premium is due to particular cardinal choices of either the utility function or the underlying returns distribution, or both. The approach is applied to the original Mehra–Prescott data and more recent data that include daily yields on Treasury bonds and daily returns on the S&P500 and the NASDAQ indexes. The empirical results show little evidence of stochastic dominance among the assets investigated. This suggests that the observed equity premium represents compensation for bearing higher risk, taking into account higher-order moments such as skewness and kurtosis. There is some evidence of a reverse puzzle, whereby Treasury bonds stochastically dominate equities at the third order, a result which potentially reflects insufficient compensation to investors for bearing the negative skewness associated with the S&P500 index.     

A new approach to estimating earnings forecasting models: Robust regression MM-estimation

This study focuses on the impact of model estimation methods on earnings forecast accuracy. Compared with an ordinary least squares (OLS) regression combined with winsorization, robust regression MM-estimation improves the earnings forecast accuracy of all the models examined, especially for those with more variables. My findings indicate that the impact of outliers on the OLS regression increases with the number of variables in the models, alerting researchers who use OLS regressions for forecasting. My findings explain the puzzling negative relationship between earnings forecast accuracy and the number of model variables in prior research. Moreover, I demonstrate the valuation implications of earnings forecasted using robust regression MM-estimation. This study contributes to earnings forecasting, valuation, and influential observation treatment in forecasting.     

Forecasting Bitcoin risk measures: A robust approach

Over the last few years, Bitcoin and other cryptocurrencies have attracted the interest of many investors, practitioners and researchers. However, little attention has been paid to the predictability of their risk measures. This paper compares the predictability of the one-step-ahead volatility and Value-at-Risk of Bitcoin using several volatility models. We also include procedures that take into account the presence of outliers and estimate the volatility and Value-at-Risk in a robust fashion. Our results show that robust procedures outperform non-robust ones when forecasting the volatility and estimating the Value-at-Risk. These results suggest that the presence of outliers plays an important role in the modelling and forecasting of Bitcoin risk measures.     

Instrumental variable quantile regression: A robust inference approach

In this paper, we develop robust inference procedures for an instrumental variables model defined by Y=D^′α(U)$Y=D^{\prime }\alpha (U)$ where D^′α(U)$D^{\prime }\alpha (U)$ is strictly increasing in U and U is a uniform variable that may depend on D but is independent of a set of instrumental variables Z. The proposed inferential procedures are computationally convenient in typical applications and can be carried out using software available for ordinary quantile regression. Our inferential procedure arises naturally from an estimation algorithm and has the important feature of being robust to weak and partial identification and remains valid even in cases where identification fails completely. The use of the proposed procedures is illustrated through two empirical examples.     

Experimental designs for estimating plateau-type production functions and economically optimal input levels

Estimation of nitrogen response functions has a long history and yet there is still considerable uncertainty about how much nitrogen to apply to agricultural crops. Nitrogen recommendations are usually based on estimation of agronomic production functions that typically use data from designed experiments. Nitrogen experiments, for example, often use equally spaced levels of nitrogen. Past agronomic research is mostly supportive of plateau-type functional forms. The question addressed is if one is willing to accept a specific plateau-type functional form as the true model, what experimental design is the best to use for estimating the production function? The objective is to minimize the variance of the estimated expected profit maximizing level of input. Of particular interest is how well does the commonly used equally-spaced design perform in comparison to the optimal design. Mixed effects models for winter wheat (Triticum aestivium L.) yield are estimated for both Mitscherlich and linear plateau functions. With three design points, one should be high enough to be on the plateau and one should be at zero. The choice of the middle design point makes little difference over a wide range of values. The optimal middle design point is lower for the Mitscherlich functional form than it is for the plateau function. Equally spaced designs with more design points have a similar precision and thus the loss from using a nonoptimal experimental design is small.     

The measurement of productive efficiency: A robust minimax approach

Some applied aspects of robustness are formulated and empirically tested so as to generalize the Farrell efficiency measure for the frontier production function. A minimax method is used to develop a Chebyshev efficiency measure along with a stochastic production frontier. The relative insensitivity of such a measure in respect of sample size variations and outliers are illustrated by an empirical application to educational production functions.     

A bias in estimating urban population density functions

This paper demonstrates that because of the rules used to delineate census tracts, unweighted estimation of an urban population density function using census tract observations leads to a severe upward bias in the estimated function. A weighted estimation procedure which leads to an unbiased estimate is proposed. The paper also points out that if one computes the integral of an unbiased estimate of a density function over the area of a city, that integral is not necessarily an unbiased estimate of total population. The paper thus explains the “disturbing” empirical results concerning density functions reported by McDonald and Bowman.     

A robust asymptotically optimal sequential estimation procedure for the Poisson process

The problem of estimating sequentially the intensity parameter of a homogeneous Poisson process with quadratic loss and fixed cost per unit time is considered within the Bayesian framework. Without using both the prior information and any auxiliary data, this paper proposes a sequential procedure as that suggested by Vardi (Ann Statist 7:1040?C1051, 1979) in classical non-Bayesian sequential estimation. The proposed sequential procedure is robust in the sense that it does not depend on the prior. The second order approximations to the expected sample size and the Bayes risk of the proposed sequential procedure are established for a large class of prior distributions.     

A heterogeneous coefficient approach to the knowledge production function

Past literature has used conventional spatial autoregressive panel data models to relate patent production output to knowledge production inputs. However, research conducted on regional innovation systems points to regional disparities in both regions’ ability to turn their knowledge inputs into innovation and to access external knowledge. Applying a heterogeneous coefficients spatial autoregressive panel model, we estimate region-specific knowledge production functions (KPFs) for 94 NUTS-3 regions in France using a panel covering 21 years from 1988 to 2008 and four high-technology industries. A great deal of regional heterogeneity in the KPF relationship exists across regions, providing new insights regarding spatial spillin and spillout effects between regions.     

A new approach to estimating a profit frontier using the censored stochastic frontier model

The translog profit functional form is widely used to study technical efficiency for banks. Although this functional form is known as being flexible, it is not applicable to those banks incurring economic losses. The recently developed approach, i.e., the censored stochastic frontier model (CSFM), by Tsay et al. (2013) appears to be superior to existing approaches, since CSFM does not need to transform negative profit into positive profit before taking the natural logarithm. The transformation with respect to the profit variable tends to bias the parameter estimates of the profit frontier and the subsequent profit efficiency measure. We show that the parameter estimates of CSFM have the desirable statistical properties. Moreover, empirical results reveal that the mean profit efficiency of CSFM is more robust than those models using transformed profits across the sub-periods 1991–1998 and 1999–2009.     

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis–Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models—a fixed effects model and a random effects model—are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed.     

A household production approach to the evaluation of transportation system change

This paper intends to present a model for evaluating nationwide and interregional transportation system change from the viewpoint of the user's welfare. The model stems primarily from an adaptation of the household production approach, and thereby represents a departure from traditional methods of evaluation. In the development of our model, the transportation system changes are regarded as technical changes in the trip production function. With proper assumptions regarding the specified utility and trip production functions, it is possible to empirically evaluate the transportation system change and to measure the technical change in trip production function.     

Money and production: A stochastic frontier approach

Considerable controversy surrounds the role of money in the production of goods and services. Previous empirical research has appeared to find that the real money stock affects aggregate output, holding other, more conventional inputs constant. However, the theoretical literature offers no convincing explanation for this empirical finding. One interpretation is that real money balances reduce the extent to which labor and capital are diverted into exchange-related activities instead of being used in production defined in a more narrow sense. To investigate this hypothesis, we estimate a production function augmented with real money balances as an input, using time-series data for the aggregate U.S. economy. A stochastic production frontier is then estimated without real money balances. We use these estimates to establish the presence of technical inefficiency. Finally, we show that the extent of technical inefficiency is negatively correlated with the real money stock. Our results provide a reconciliation between the empirical literature, which finds that real money balances affect output in a production function framework, and the theoretical literature, which suggests that real money balances enhance the technical efficiency of the economy.     

Long-term wealth growth portfolio allocation under parameter uncertainty: A non-conservative robust approach

The Kelly portfolio, which is documented to have the highest wealth growth rate of any other portfolio in the long run, has highly risky and unstable performance in the short term. This paper offers a hybrid approach to address this problem by integrating the concept of ridge regression and shrinkage estimation into a robustly modified Kelly portfolio. The proposed approach is a two-stage optimization process that not only takes into account the effect of estimation error but also solves the notoriously conservative problem introduced by the robust optimization method. By extending the worst-case scenarios considered by the robust Kelly portfolio, our approach significantly improves its out-of-sample performance without compromising risk reduction. In an extensive out-of-sample analysis with simulated and empirical data sets, we also characterize the impacts of the robustness level and the length of the rolling window on the final result. Moreover, we conduct a comparative study to confirm the validity of the proposed approach, and our model allows the investor to have a better risk-return trade-off than other traditional models.     

Mapping the innovation production process from accumulative advantage to economic outcomes: A path modeling approach

The research about the innovation production process (IPP) is burgeoning. Our understanding of the interdependent interactions between functionally distinct innovation activities during it from a systemic perspective is rather unclear, yet, which is beneficial to empirical innovation management. This study, based on systems thinking, presents a novel analytical framework to empirically and quantitatively map the IPP jointly associated with a path modeling approach, which helps in untangling the interactive mechanism between stage-specific innovation activities with distinct functions within an IPP from accumulative advantage to economic outcomes. We use the attractive analytical framework to guide an empirical investigation to the China's high-tech industries' IPP at the macro-regional level. Our empirical study confirms the dominant role of previous innovation capital accumulation in the whole IPP embedded into regional innovation systems of China's high-tech industries. That is, we prove the existence of accumulative advantage phenomenon in the regional IPP. The examination results show that there is a significant Matthew effect of technological innovation accumulation on technological innovation inputs as well as the Path dependence of technological innovation outputs/outcomes on technological innovation accumulation. This indicates that the innovation-practitioners should promote innovation capital accumulation for sustainable innovations and economic profits in a long time. At the same time, our findings suggest that, in order to alleviate the cross-regional unbalance of innovation development and promote radial innovations in China's high-tech industries, both policy-makers and innovation-practitioners should try to get rid of the dependence on the previous accumulated innovation capital.