Uncertainty in measurement and control

Summary  Controlling is intervening in a situation on the basis of measurements. The three elements occurring in this definition may each contain an uncertainty that sets a limit to the control efficiency:
The measurements may be in error owing to both inaccuracies and sluggishness of the measurements. Proper and rapid data-processing is essential therefore.
The interventions may lose part of their effect through over-determinancy or dynamically unfavourable (sluggish) responses. In either case statistical calculations disclose the average control errors that are liable to be made, and also the way in which these can be minimized.
The situation may be unclear, i.e. the static and dynamic process characteristics are insufficiently known. In such cases regression and correlation techniques may aid in finding a solution.
Following a general review, we shall discuss in more detail those aspects that are bound up with the dynamics of the phenomena. Arguments from information theory reveal that the dynamic efficiency of control actions depends on correlation functions of time series (disturbances) and response curves of the systems (processes). The effects of disturbance correlation time, disturbance variance, sampling time, sample treatment, measuring errors, measuring time, rapidity of the intervention, etc., on the efficiency are elucidated by means of some formulae, graphs and examples.     

Mining the past to determine the future: Comments

In forecasting, data mining is frequently perceived as a distinct technological discipline without immediate relevance to the challenges of time series prediction. However, Hand (2009) postulates that when the large cross-sectional datasets of data mining and the high-frequency time series of forecasting converge, common problems and opportunities are created for the two disciplines. This commentary attempts to establish the relationship between data mining and forecasting via the dataset properties of aggregate and disaggregate modelling, in order to identify areas where research in data mining may contribute to current forecasting challenges, and vice versa. To forecasting, data mining offers insights on how to handle large, sparse datasets with many binary variables, in feature and instance selection. Furthermore data mining and related disciplines may stimulate research into how to overcome selectivity bias using reject inference on observational datasets and, through the use of experimental time series data, how to extend the utility and costs of errors beyond measuring performance, and how to find suitable time series benchmarks to evaluate computer intensive algorithms. Equally, data mining can profit from forecasting’s expertise in handling nonstationary data to counter the out-of-date-data problem, and how to develop empirical evidence beyond the fine tuning of algorithms, leading to a number of potential synergies and stimulating research in both data mining and forecasting.     

The Effect of Technological Change and Technical Inefficiencies on the Performance of Functional Forms

Technological change is one of the most important determinants of the technological structure of the firm. Unfortunately, this crucial factor is often unobserved and must therefore be approximated. It is also well recognized that firms are not necessarily located on their efficient production frontier, a phenomenon known as technical inefficiency. This paper compares the performance of three flexible functional forms (the Translog, Symmetric McFadden and Symmetric Generalized Barnett) to properly infer theoretical properties and technology measurements when: (i) unobserved technological change is approximated by a time trend in the variable-cost-function specification and, (ii) firms may be technically inefficient. Our results indicate that no functional form dominates and that measuring the shifts of the production (cost) function has a clear and negative effect on the performance of the functional forms. Furthermore, we find that technical inefficiencies have a significant and negative effect on the measurement of, notably, returns to scale and the implicit rental price of capital. However, all forms over-reject theoretical properties and provide adequate technology measurements only on a sample-average basis. In addition, the performance of the functional forms is closely related to the true underlying rate of technological change.     

Optimal allocation of measurements in a linear calibration process

A problem of allocation of measurements for a linear calibration process is considered in this article. It is assumed that a total of N measurements are made some of which may be measurements on two distinct standards, while the remaining measurements are on m different unknown specimens. We discuss allocation of the N measurements for the two standards and m unknown specimens based on A-optimality criterion, which is applied to asymptotic variances of maximum likelihood estimators for the true values of unknown specimens. It can be shown that the optimal allocation depends on the true values of unknown specimens. Hence, the user may resort to locally or Bayesian A-optimal measurement designs. Some practical solution is presented. Furthermore, the impact of prior on the allocation is also discussed.     

Summary Notes on the Statistics of Federal Affirmative Action Programs*

Abstract . In a review and critique of selected aspects of Federal requirements for use of statistical procedures to detect the absence of equal employment opportunity, seven statisticians find certain aspects capable of improvement. An overlap exists in protected groups between women and racelethnic groups which may lead to double-counting. Classification may be left to the employer. The Spanish-surname test may exclude 25 percent of people of Hispanic origin. Ethnic identification based on self-identification must be compared to identification by others (employer). The occupational categories required have but an imprecise relationship to available statistics. The statistics contain an unmeasurable data error. Chance factors may produce errors that are offsetting or additive, and which may be confused with data of significance. Recommendations are made for procedural improvements.     

The Dynamics of Self-Esteem and Physical Self: Between Preservation and Adaptation

The aim of this study was to model and characterize the psychologicalprocesses that underlie the dynamics of global self-esteem and physicalself over time. Twice a day for 228 consecutive days, seven participantscompleted a short inventory (PSI-6, Ninot et al., 2001) measuring sixsubjective dimensions: global self-esteem, physical self-worth, physicalcondition, sport competence, physical strength, and attractive body.Each series was modeled by means of ARIMA procedures. The resultsshowed that a simple moving average model provided a satisfactoryaccount for the dynamics of all series. This model suggests that acombination of two opposite processes underlies the dynamics ofself-concept: preservation, which tends to restore the previousvalue after a disturbance, and adaptation, which tends to inflectthe series in the direction of the perturbation.     

Bias in dynamic panel estimation with fixed effects,incidental trends and cross section dependence

Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N→∞$N\to \infty$. The results extend earlier work by Nickell [1981. Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426] and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.     

Farm heterogeneity and technical efficiency: Some results from Swedish dairy farms

This paper introduces farm-heterogeneity in measuring technical efficiency of Swedish dairy farms using farm-level data. In calculating technical efficiency which is allowed to vary over time and across farms, we control for farm-specific effects. This is possible only when panel data is available. Furthermore, we separate technical efficiency from technical change—the presence of which is indicated by a shift in the production function over time,ceteris paribus. We also calculate percentage change in technical efficiency to examine whether farm efficiencies have improved over time. Finally, a comparison of technical efficiency, elasticities of different inputs, and technical change is made across different years and panels. The data includes four panels of dairy farms observed during the period 1976–1988, excluding 1985.We thank two anonymous referees, Anders Klevmarken and Lennart Hjalmarsson for valuable comments. Financial support from SJFR, the Gothenburg Economic School Foundation, Jan Wallender and Tore Browaldh Research Foundations is gratefully acknowledged.     

Asymptotic distributions of some scale estimators in nonlinear models

Often in the robust analysis of regression and time series models there is a need for having a robust scale estimator of a scale parameter of the errors. One often used scale estimator is the median of the absolute residuals s ₁. It is of interest to know its limiting distribution and the consistency rate. Its limiting distribution generally depends on the estimator of the regression and/or autoregressive parameter vector unless the errors are symmetrically distributed around zero. To overcome this difficulty it is then natural to use the median of the absolute differences of pairwise residuals, s ₂, as a scale estimator. This paper derives the asymptotic distributions of these two estimators for a large class of nonlinear regression and autoregressive models when the errors are independent and identically distributed. It is found that the asymptotic distribution of a suitably standardizes s ₂ is free of the initial estimator of the regression/autoregressive parameters. A similar conclusion also holds for s ₁ in linear regression models through the origin and with centered designs, and in linear autoregressive models with zero mean errors.  This paper also investigates the limiting distributions of these estimators in nonlinear regression models with long memory moving average errors. An interesting finding is that if the errors are symmetric around zero, then not only is the limiting distribution of a suitably standardized s ₁ free of the regression estimator, but it is degenerate at zero. On the other hand a similarly standardized s ₂ converges in distribution to a normal distribution, regardless of the errors being symmetric or not. One clear conclusion is that under the symmetry of the long memory moving average errors, the rate of consistency for s ₁ is faster than that of s ₂.     

Tests of asset pricing with time‐varying factor loads

This paper proposes an empirical asset pricing test based on the homogeneity of the factor risk premia across risky assets. Factor loadings are considered to be dynamic and estimated from data at higher frequencies. The factor risk premia are obtained as estimates from time series regressions applied to each risky asset. We propose Swamy‐type tests robust to the presence of generated regressors and dependence between the pricing errors to assess the homogeneity of the factor risk premia and the zero intercept hypothesis. An application to US industry portfolios shows overwhelming evidence rejecting the capital asset pricing model, and the three and five factor models developed by Fama and French (Journal of Financial Economics, 1993, 33, 3–56; Journal of Financial Economics, 2015, 116, 1–22). In particular, we reject the null hypotheses of a zero intercept, homogeneous factor risk premia across risky assets, and the joint test involving both hypotheses.     

Optimality and efficiency of small chessboard designs for correlated errors

Optimal p × q row–column designs are obtained via complete enumeration of all possible designs for two treatments in some fixed effects models with errors specified by a doubly geometric covariance structure. This is done, in part, by a computer search, for a finite set of sizes of the correlation coefficients and in cases where p and q are small enough to make such a search feasible.     

An adjustment procedure for predicting systematic risk

This paper looks at the currently available beta adjustment techniques and suggests a multiple root-linear model to adjust for the regression tendency of betas. Our empirical investigate on indicates that cross-sectional betas are not normally distributed, but their distribution tends to normal after a square-root transformation. The evidence from the Box-Cox regression model and the multivariate normality observed among betas after the transformation, make the functional form of our model correct. Also, we observe that the disturbance term of the multiple root-linear model is well behaved. These findings make the ordinary least squares estimates unbiased and efficient. Finally, the mean square and extreme errors are found to be lower when our adjustment procedure is used vis-à-vis the existing procedures.     

Nonparametric transformation to white noise

We consider a semiparametric distributed lag model in which the “news impact curve” m is nonparametric but the response is dynamic through some linear filters. A special case of this is a nonparametric regression with serially correlated errors. We propose an estimator of the news impact curve based on a dynamic transformation that produces white noise errors. This yields an estimating equation for m that is a type two linear integral equation. We investigate both the stationary case and the case where the error has a unit root. In the stationary case we establish the pointwise asymptotic normality. In the special case of a nonparametric regression subject to time series errors our estimator achieves efficiency improvements over the usual estimators, see Xiao et al. [2003. More efficient local polynomial estimation in nonparametric regression with autocorrelated errors. Journal of the American Statistical Association 98, 980–992]. In the unit root case our procedure is consistent and asymptotically normal unlike the standard regression smoother. We also present the distribution theory for the parameter estimates, which is nonstandard in the unit root case. We also investigate its finite sample performance through simulation experiments.     

Measures in DEA with an Application to the Malmquist Index

This paper shows the importance of goal vectors G in measuring and dealing with DEA inefficiencies. It emphasizes the advantages of the family of additive relative to the traditional oriented DEA models and shifts the primary emphasis to measuring inefficiency rather than efficiency. This new (raw) inefficiency measure RIN incorporates both the traditional DEA efficiency and the DEA slacks and provides the background for a new approach to the Malmquist Index. The final section points out some deficiencies in existing computational procedures for selecting G and calls for continued research on the selection process, as well as showing a role for G in returns to scale studies.     

Projection properties of certain three level orthogonal arrays

Two orthogonal arrays based on 3 symbols are said to be isomorphic or combinatorially equivalent if one can be obtained from the other by a sequence of row permutations, column permutations and permutations of symbols in each column. Orthogonal arrays are used as screening designs to identify active main effects, after which the properties of the subdesign for estimating these effects and possibly their interactions become important. Such a subdesign is known as a ``projection design'. In this paper we have identified all the inequivalent projection designs of an OA(27,13,3,2), an OA(18,7,3,2) and an OA(36,13,3,2) into k=3,4 and 5 factors. It is shown that the generalized wordlength pattern criterion proposed by Ma and Fang [23] can distinguish between most, but not all, inequivalent classes. We propose an extension of the Es² criterion (which is commonly used for measuring efficiency of 2-level designs) to distinguish further between the non-isomorphic classes and to measure the efficiency of the designs in these classes. Some concepts on generalized resolution are also discussed.     

Heteroskedasticity, autocorrelation, and spatial correlation robust inference in linear panel models with fixed-effects

This paper develops an asymptotic theory for test statistics in linear panel models that are robust to heteroskedasticity, autocorrelation and/or spatial correlation. Two classes of standard errors are analyzed. Both are based on nonparametric heteroskedasticity autocorrelation (HAC) covariance matrix estimators. The first class is based on averages of HAC estimators across individuals in the cross-section, i.e. “averages of HACs”. This class includes the well known cluster standard errors analyzed by Arellano (1987) as a special case. The second class is based on the HAC of cross-section averages and was proposed by Driscoll and Kraay (1998). The ”HAC of averages” standard errors are robust to heteroskedasticity, serial correlation and spatial correlation but weak dependence in the time dimension is required. The “averages of HACs” standard errors are robust to heteroskedasticity and serial correlation including the nonstationary case but they are not valid in the presence of spatial correlation. The main contribution of the paper is to develop a fixed-b asymptotic theory for statistics based on both classes of standard errors in models with individual and possibly time fixed-effects dummy variables. The asymptotics is carried out for large time sample sizes for both fixed and large cross-section sample sizes. Extensive simulations show that the fixed-b approximation is usually much better than the traditional normal or chi-square approximation especially for the Driscoll-Kraay standard errors. The use of fixed-b critical values will lead to more reliable inference in practice especially for tests of joint hypotheses.     

Efficiency vectors, efficiency and performance measures: new methods for ranking efficient organizational units

We present and discuss measures for analyzing productivity in deterministic frontier models. A new efficiency measure is introduced allowing for discrimination among efficient organizational units. In addition, a new performance measure for analyzing productivity of organizational units is presented. This measure fulfills various properties of efficiency measures but relaxes the indicator property. Both new approaches are based on the development of efficiency vectors which is a new vector measure for measuring efficiency. The vector components are efficiency measures related to subsets of a production possibility set. The new approaches are applied in the context of data envelopment analysis.

Asymptotic properties of the efficient estimators for cointegrating regression models with serially dependent errors

In this paper, we analytically investigate three efficient estimators for cointegrating regression models: Phillips and Hansen’s [Phillips, P.C.B., Hansen, B.E., 1990. Statistical inference in instrumental variables regression with I(1) processes. Review of Economic Studies 57, 99–125] fully modified OLS estimator, Park’s [Park, J.Y., 1992. Canonical cointegrating regressions. Econometrica 60, 119–143] canonical cointegrating regression estimator, and Saikkonen’s [Saikkonen, P., 1991. Asymptotically efficient estimation of cointegration regressions. Econometric Theory 7, 1–21] dynamic OLS estimator. We consider the case where the regression errors are moderately serially correlated and the AR coefficient in the regression errors approaches 1 at a rate slower than 1/T$1/T$, where T$T$ represents the sample size. We derive the limiting distributions of the efficient estimators under this system and find that they depend on the approaching rate of the AR coefficient. If the rate is slow enough, efficiency is established for the three estimators; however, if the approaching rate is relatively faster, the estimators will have the same limiting distribution as the OLS estimator. For the intermediate case, the second-order bias of the OLS estimator is partially eliminated by the efficient methods. This result explains why, in finite samples, the effect of the efficient methods diminishes as the serial correlation in the regression errors becomes stronger. We also propose to modify the existing efficient estimators in order to eliminate the second-order bias, which possibly remains in the efficient estimators. Using Monte Carlo simulations, we demonstrate that our modification is effective when the regression errors are moderately serially correlated and the simultaneous correlation is relatively strong.     

Optimal migration policies: an analytical approach. Part I

This paper explores the analytical features of population distribution or human settlement policies. It proposes a methodology for quantitative policy analysis and policy design based on optimal control and system theory. The paper consists of two parts. This part shows how policy models may be derived from demographic and demoeconomic or demometric models by adding a new dimension: the goals-means relationship of population distribution policy. It examines a large class of relevant policy models and demonstrates their relationship to the original Tinbergen Theory of Policy, which provides a paradigm for static and dynamic policy analysis. Problems of existence and of design of optimal population distribution policies are studied analytically. In designing optimal policies, use may be made of the minimizing properties of generalized inverses.     

An algorithm for panel ANOVA with grouped data

In this paper, we present an algorithm suitable for analysing the variance of panel data when some observations are either given in grouped form or are missed. The analysis is carried out from the perspective of ANOVA panel data models with general errors. The classification intervals of the grouped observations may vary from one to another, thus the missing observations are in fact a particular case of grouping. The proposed Algorithm (1) estimates the parameters of the panel data models; (2) evaluates the covariance matrices of the asymptotic distribution of the time-dependent parameters assuming that the number of time periods, T, is fixed and the number of individuals, N, tends to infinity and similarly, of the individual parameters when T → ∞ and N is fixed; and, finally, (3) uses these asymptotic covariance matrix estimations to analyse the variance of the panel data.