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Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

Statistical inference (estimation and testing) for the stochastic volatility (SV) model Taylor (1982, 1986) is challenging, especially likelihood-based methods which are difficult to apply due to the presence of latent variables. The existing methods are either computationally costly and/or inefficient. In this paper, we propose computationally simple estimators for the SV model, which are at the same time highly efficient. The proposed class of estimators uses a small number of moment equations derived from an ARMA representation associated with the SV model, along with the possibility of using “winsorization” to improve stability and efficiency. We call these ARMA-SV estimators. Closed-form expressions for ARMA-SV estimators are obtained, and no numerical optimization procedure or choice of initial parameter values is required. The asymptotic distributional theory of the proposed estimators is studied. Due to their computational simplicity, the ARMA-SV estimators allow one to make reliable – even exact – simulation-based inference, through the application of Monte Carlo (MC) test or bootstrap methods. We compare them in a simulation experiment with a wide array of alternative estimation methods, in terms of bias, root mean square error and computation time. In addition to confirming the enormous computational advantage of the proposed estimators, the results show that ARMA-SV estimators match (or exceed) alternative estimators in terms of precision, including the widely used Bayesian estimator. The proposed methods are applied to daily observations on the returns for three major stock prices (Coca-Cola, Walmart, Ford) and the S&P Composite Price Index (2000–2017). The results confirm the presence of stochastic volatility with strong persistence.

A semiparametric stochastic frontier model is proposed for panel data, incorporating several flexible features. First, a constant elasticity of substitution (CES) production frontier is considered without log-transformation to prevent induced non-negligible estimation bias. Second, the model flexibility is improved via semiparameterization, where the technology is an unknown function of a set of environment variables. The technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs, environment variables, and/or inefficiency determinants. Furthermore, the technology function incorporates a single-index structure to circumvent the curse of dimensionality. Third, distributional assumptions are eschewed on both stochastic noise and inefficiency for model identification. Instead, only the conditional mean of the inefficiency is assumed, which depends on related determinants with a wide range of choice, via a positive parametric function. As a result, technical efficiency is constructed without relying on an assumed distribution on composite error. The model provides flexible structures on both the production frontier and inefficiency, thereby alleviating the risk of model misspecification in production and efficiency analysis. The estimator involves a series based nonlinear least squares estimation for the unknown parameters and a kernel based local estimation for the technology function. Promising finite-sample performance is demonstrated through simulations, and the model is applied to investigate productive efficiency among OECD countries from 1970–2019.

The standard method to estimate a stochastic frontier (SF) model is the maximum likelihood (ML) approach with the distribution assumptions of a symmetric two-sided stochastic error v and a one-sided inefficiency random component u. When v or u has a nonstandard distribution, such as v follows a generalized t distribution or u has a χ2 distribution, the likelihood function can be complicated or untractable. This chapter introduces using indirect inference to estimate the SF models, where only least squares estimation is used. There is no need to derive the density or likelihood function, thus it is easier to handle a model with complicated distributions in practice. The author examines the finite sample performance of the proposed estimator and also compare it with the standard ML estimator as well as the maximum simulated likelihood (MSL) estimator using Monte Carlo simulations. The author found that the indirect inference estimator performs quite well in finite samples.

This chapter examines the effect of the division of labor from a Bayesian viewpoint. While organizational reforms are crucial for cost reduction in the Japanese water supply industry, the effect of labor division in intra-organizational units on total costs has, to the best of our knowledge, not been examined empirically. Fortunately, a one-time survey of 79 Japanese water suppliers conducted in 2010 enables us to examine the effect. To examine this problem, a cost stochastic frontier model with endogenous regressors is considered in a cross-sectional setting, because the cost and the division of labor are regarded as simultaneously determined factors. From the empirical analysis, we obtain the following results: (1) total costs rise when the level of labor division becomes high; (2) ignoring the endogeneity leads to the underestimation of the impact of labor division on total costs; and (3) the estimation bias on inefficiency can be mitigated for relatively efficient organizations by including the labor division variable in the model, while the bias for relatively inefficient organizations needs to be controlled by considering its endogeneity. In summary, our results indicate that integration of internal sections is better than specialization in terms of costs for Japanese water supply organizations.

We consider a semiparametric panel stochastic frontier model where one-sided firm effects representing inefficiencies are correlated with the regressors. A form of the Chamberlain-Mundlak device is used to relate the logarithm of the effects to the regressors resulting in a lognormal distribution for the effects. The function describing the technology is modeled nonparametrically using penalized splines. Both Bayesian and non-Bayesian approaches to estimation are considered, with an emphasis on Bayesian estimation. A Monte Carlo experiment is used to investigate the consequences of ignoring correlation between the effects and the regressors, and choosing the wrong functional form for the technology.

Purpose – This chapter explores the basic characteristics of stochastic frontier estimation, discusses advantages of the method that make it conducive to research in international marketing, and provides an application to demonstrate its use. Potential applications in international marketing research are also discussed.

Methodology – Stochastic Frontier Estimation.

Findings – Stochastic frontier estimation models, prevalent in other fields, are very limited in the international marketing literature. Many potential opportunities exist for its use in the context of international marketing.

Originality/value of paper – The intent of this chapter is to show that stochastic frontier estimation is a potentially valuable tool for international marketing research. We show this by demonstrating the use of the tool and by providing examples of potential research studies.

The purpose of this paper is to estimate the China’s outward FDI efficiency and it determinants in 69 countries along the Belt and Road over the period of 2003-2013.

This paper defines the extent of the Belt and Road in terms of geographical boundaries, justifying the application of the stochastic frontier gravity model to the FDI analysis, and then constructing a frontier regression model to assess the China’s outward FDI efficiency and it determinants in countries along the Belt and Road.

Regarding the core gravity parameter estimates, China’s outward FDI was highly consistent with the gravity model. As far as policy parameters are concerned, China’s outward FDI was significantly restricted by some man-made barriers in host countries. According to the estimated FDI efficiency scores, China has huge outward FDI potential in countries along the Belt and Road. In general, China’s outward FDI efficiency demonstrated a consistent uptrend from the perspectives of both FDI flows and stocks over the period of 2003-2013. Although China’s outward FDI performance indicated a very uneven pattern across different countries and periods, there were no significant performance differences between the Road and Belt.

The Belt and Road initiative can be largely beneficial to China’s outward FDI, but the specific framework of cooperation should be designed on the basis of determinants of China’s outward FDI. The regional cooperation with the Road countries should mainly focus on the removal of business barriers and financial barriers. The regional cooperation with the Belt countries should mainly concern the improvement of local intellectual property protection, the reduction of local tax burden, and removal of business barriers and financial barriers.

To the authors’ best knowledge, no existing literature has specifically examined the efficiency of China’s outward FDI in the countries along the Belt and Road and its determinants.

The purpose of this paper is to measure technical efficiency and examine its determinants while disentangling unobserved time-invariant heterogeneity from actual inefficiency using comprehensive household-level panel data.

This paper estimates technical efficiency based on the true random-effects stochastic production frontier estimator with a Mundlak adjustment. By utilising comprehensive panel data with 4,694 observations from 39 districts of four major maize-producing regions in Ethiopia, the author measures technical efficiency and examine its determinants while disentangling unobserved time-invariant heterogeneity from technical inefficiency. By using competing stochastic production frontier estimators, the author provides insights into the influence of farm heterogeneity on measuring farm efficiency and the subsequent impact on the ranking of farmers based on their efficiency scores.

The study results indicate that ignoring unobservable farmer heterogeneity leads to a downwards bias of technical efficiency estimates with a consequent effect on the ranking of farmers based on their efficiency scores. The mean technical efficiency score implied that about a 34% increase in maize productivity can be achieved with the current input use and technology in Ethiopia. The key determinants of the technical inefficiency of maize farmers are the age, gender and formal education level of the household head, household size, income, livestock ownership, and participation in off-farm activities.

While the findings of this study are critical for informing policy on improving agricultural production and productivity, a few important things are worth considering in terms of the generalisability of the findings. First, the study relied on secondary data, so only a snapshot of environmental factors was accounted for in the empirical estimations. Second, there could be other sources of unmeasured potential sources of heterogeneity caused by persistent technical inefficiency and endogeneity of inputs. Third, the study is limited to one country. Therefore, future research should extend the analysis to ensure the generalisability of the empirical findings regarding the extent to which unmeasured potential sources of heterogeneity caused by persistent technical inefficiency, endogeneity of inputs and other unobservable country-specific features – such as geographical differences.

This paper contributes to the literature on agricultural productivity and efficiency by providing new evidence on the influence of unobservable heterogeneity in a farm efficiency analysis. While agricultural production is characterised by heterogeneous production conditions, the influence of unobservable farm heterogeneity has generally been ignored in technical efficiency estimations, particularly in the context of smallholder farming. The value of this paper comes from disentailing producer-specific random heterogeneity from the actual inefficiency.

Using a panel of 1,122 UK firms listed on the London Stock Exchange over the period of 1981-2009, corporate efficiencies are predicted in this paper as inverse proxies of agency cost and the agency cost hypotheses are tested. The paper aims to discuss this issue.

Stochastic frontier analysis is used to estimate corporate efficiency of firms, but from two different perspectives. The long-run and short-run corporate efficiencies are predicted focussing on modern approach of value maximization and traditional approach of profit maximization, respectively.

The estimation results reveal that, an average firm in the sample achieves 74.5 percent of its best performing peer's market value and 86.6 percent of its best performing peer's profit and both of them are highly significant in the analysis. The long-run market value efficiency supports the agency cost of outside equity and the short-run profit efficiency supports the agency cost of outside debt hypothesis. Also there is a positive rank correlation between these two efficiencies which confirms that an average firm in the UK suffers from inefficiency or agency conflicts to a certain extent, no matter whether the firm is driven by short-run or long-run growth perspectives.

The predicted broad measures of agency costs in the paper have wider implications in enhancing the understanding of the UK firms’ corporate performance especially when they operate under a relatively free and market based governance and financial system.

The work is distinguished by the large panel of UK firms and a long period of time that is considered. Emphasizing on the empirical implications of the distinctions between short-run and long-run efficiency is also novel.