Econometric estimation of distance functions and associated measures of productivity and efficiency change

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change.     

单侧公差及非对称公差过程能力指数

本文在已发表的过程能力指数4个基本特性基础上,通过引入“目标值M”,将单侧公差问题科学地转化为对称公差求解,不仅推导出单侧公差无偏情况下的CpUr和CpLr公式,而且推导出单侧公差有偏情况下的CpUk和CLk公式;通过设置辅助线U或L将非对称公差问题科学地转化为对称公差求解,不仅推导出非对称公差无偏情况下的Cpa公式,而且还推导出有偏情况下的Cpak公式。此外,列举典型案例详细分析和比较。     

Diversity Analysis of Structural Change Based on the Canadian Input–Output Tables

This article presents some of the results of a study conducted at Statistics Canada that involved the analysis of the variability through time of input–output structures. All structures have been analyzed in current and constant prices over the period 1961–84, but only the results about the industries' input structures in current prices are reported in this article. Structural changes are assessed over time horizons of 1, 2 and 5 years, using the Kullback, cross-entropy index formula. Structural changes in the current prices input structure are decomposed into a price and a quantity component, following a new decomposition of the entropy formula. It is shown from that decomposition that the traditional analysis of the variability of constant prices input–output structures may be quite misleading. The authors have found that structural changes generally follow a smooth path through time and tend to be cumulative in the long run, with some cyclical fluctuations in the short term. Some of the structural changes appear to be due to statistical events (establishment moves across industries, changes in methodologies, etc.) rather than reflecting real phenomena. The quantity component of structural change appears to be more important than the price component in almost all time periods and time spans, except when the Canadian economy was subjected to important price shocks during the 1970s.     

Managing hedonic housing price indexes: The French experience

Despite their theoretical advantages, hedonic housing price indexes are not so commonly computed by statistical agencies or real estate professionals. Many published indexes still rely on mean or median prices, or favor repeat-sales methods, which require less information about the attributes of the housing units and less econometric expertise on the part of the index compilers, but may be less accurate and robust. In France as in other countries where housing sales have to be recorded in front of a notary, data on transaction prices and characteristics of dwellings are available. Such data have been centralized since 1994, and quarterly hedonic housing price indexes have been computed for more than 10 years. This paper describes the institutional setting of housing transactions in France, and the collaboration between the notaries and the national statistical agency (INSEE). The former are responsible for data collection and regular computation, whereas the latter takes scientific responsibility for the method. The detailed information on the individual properties transacted remains proprietary data, but disaggregated indexes are publicly and freely available. This organization and assignment of roles has proven effective and might be extended to countries with similar institutional settings.     

Forecasting the volatility of asset returns: The informational gains from option prices

A new class of forecasting models is proposed that extends the realized GARCH class of models through the inclusion of option prices to forecast the variance of asset returns. The VIX is used to approximate option prices, resulting in a set of cross-equation restrictions on the model’s parameters. The full model is characterized by a nonlinear system of three equations containing asset returns, the realized variance, and the VIX, with estimation of the parameters based on maximum likelihood methods. The forecasting properties of the new class of forecasting models, as well as a number of special cases, are investigated and applied to forecasting the daily S&P500 index realized variance using intra-day and daily data from September 2001 to November 2017. The forecasting results provide strong support for including the realized variance and the VIX to improve variance forecasts, with linear conditional variance models performing well for short-term one-day-ahead forecasts, whereas log-linear conditional variance models tend to perform better for intermediate five-day-ahead forecasts.     

住房流动性对房价指数的影响及其定量分析

目前中国城市住房市场不稳定程度较高,这不仅体现为房价的迅速变化,而且反映在交易量的大幅波动上,后者就是住房流动性的变化。有学者研究指出,以实际交易价格为基础的房价指数可能会低估住房市场的波动程度。为了更准确地把握住房市场的运行状态,本文借鉴美国MIT的相关技术,分析了住房流动性（交易活跃程度）对房价指数的影响,并尝试将流动性信息引入房价指数当中。我们发现,住房流动性对于房价指数有较大影响,且符合人们对于市场走势的直观判断,能够较好地反映市场转折点。     

有关过程能力指数基准的若干问题

基准是过程能力指数的一个重要属性，对有关过程能力指数基准的若干问题作出详尽阐述，可为进一步纠正过程能力指数公式错误（诸如Cpk、CpU、CpL等）提供了理论基础。     

Why elementary price index number formulas differ: Evidence on price dispersion

Most countries use either the Dutot or Jevons index number formula for the compilation of their consumer price index at the elementary level of aggregation. The difference between the formulas is shown to be accounted for by changes in price dispersion. In turn, some of this difference is shown to be explained by product heterogeneity. Scanner data on television sets (TVs) are used to calculate Dutot and Jevons indexes. The difference between them is successfully explained in terms of changes in price dispersion and much reduced using an hedonic, heterogeneity-controlled Dutot index.     

Exact decomposition of the Fisher ideal total factor productivity index

Decompositions of total factor productivity (TFP) shed light on the driving factors behind productivity change. We develop the first exact decomposition of the Fisher ideal TFP index which contains no debatable mixed-period components or residuals. We systematically isolate five effects of (1) technical change, (2) technical efficiency, (3) scale efficiency, (4) allocative efficiency, and (5) price effect. The three efficiency components (2–4) represent the efficiency of achieving a given target point. Components (1) and (5) capture the changes of the target point. While the technical change component is well-established, changes in the relative input–output prices can have real effects on the scale and scope of the target. Such changes are captured by the new price effect component (5). The new decomposition is compared with existing decompositions both in theory and by means of an empirical application to a panel data of 459 Finnish farms in years 1992–2000.

Lower bound of cost efficiency measure in DEA with incomplete price information

The conventional cost efficiency model assumes that all the input prices are fixed and known exactly at each decision making unit. In practice, however, exact knowledge of prices is difficult and prices may be subject to variations over very short periods of time. In this paper, we develop a new DEA model, which can be transformed into a special case of bi-level linear program, to calculate the lower bound of CE efficiency from the pessimistic viewpoints based on the shortcomings of the existing approaches. As the input (price) cone of the pessimistic CE model tightens, the objective function converges to the traditional Farrell cost efficiency measure. Numerical examples are used to demonstrate the proposed approach and compare the results with those obtained with the existing approaches.     

Een prijsindex van nieuwe personenauto's, 1950–1965*

Summary In constructing a price index of new motorcars the main problem is how to deal with the introduction of new models and with quality variation generally. The first difficulty is turned by compiling year-to-year indices based on models that each account for 2 per cent or more of total sales in either year. The shifting basis of these indices comprises from 7 to 15 models which together account for 45 to 70 per cent of total registrations. All models are subject to minor improvements; this quality variation is taken into account by representing increases in horse power and overall length by equivalent price reductions. The elasticity coefficients involved in this translation are derived from a cross section analysis of prices and technical characteristics of some fifty widely ranging models in 1964. A price index for the period from 1950 to 1965 is then obtained by linking successive year-to-year indices. Over the whole period list prices have risen by a third, to a large extent as the result of changes in purchase tax; this price rise is just about offset by imporvements in quality of some 2 per cent per annum.     

Chain indices of the cost-of-living and the path-dependence problem: An empirical solution

This paper proposes a new method for estimating true cost-of-living (Konüs) indices, for large numbers of commodities, using data only on prices, aggregate budget shares and aggregate expenditure. Conventional chain indices are path-dependent unless income elasticities are (implausibly) all equal to 1. The method allows this difficulty to be overcome. I show that to estimate a Konüs index, only income and not price elasticities are required. The method is applied to estimate a Konüs price index for 70 products covering nearly all the UK's Retail Prices Index over 1974–2004, using the Quadratic Almost Ideal Demand System. The choice of base year for utility has a significant effect on the index.     

Variance trading and market price of variance risk

This paper develops a new approach for variance trading. We show that the discretely-sampled realized variance can be robustly replicated under very general conditions, including when the price can jump. The replication strategy specifies the exact timing for rebalancing in the underlying. The deviations from the optimal schedule can lead to surprisingly large hedging errors. In the empirical application, we synthesize the prices of the variance contract on S&P 500 index over the period from 01/1990 to 12/2009. We find that the market variance risk is priced, its risk premium is negative and economically very large. The variance risk premium cannot be explained by the known risk factors and option returns.     

An Implicit Törnqvist Index of Real GDP

Recently much attention has been devoted to superlative indexes in the context of the national accounts. In this paper we advocate the use of the implicit Törnqvist quantity index to measure real GDP. This index, which has been proposed by Diewert and Morrison (1986), has never received serious consideration in the literature. Yet, compared to the better-known Fisher index, the implicit Törnqvist index of real GDP has a number of advantages. Thus, it can be shown to be exact for the Translog GDP function, it allows for a complete multiplicative decomposition of nominal and real GDP, and it is consistent with state-of-the-art measures of total factor productivity that typically rely on the Törnqvist aggregation. Estimates for a sample of 26 countries are reported. We find that the Laspeyres quantity index still used by the statistical agencies of most countries tends to underestimate real growth. Over the 1960–1996 period, the cumulated shortfall was as much as 13.4% of GDP in the case of Japan.     

The adaptive approach for storage assignment by mining data of warehouse management system for distribution centres

Among distribution centre operations, order picking has been reported to be the most labour-intensive activity. Sophisticated storage assignment policies adopted to reduce the travel distance of order picking have been explored in the literature. Unfortunately, previous research has been devoted to locating entire products from scratch. Instead, this study intends to propose an adaptive approach, a Data Mining-based Storage Assignment approach (DMSA), to find the optimal storage assignment for newly delivered products that need to be put away when there is vacant shelf space in a distribution centre. In the DMSA, a new association index (AIX) is developed to evaluate the fitness between the put away products and the unassigned storage locations by applying association rule mining. With AIX, the storage location assignment problem (SLAP) can be formulated and solved as a binary integer programming. To evaluate the performance of DMSA, a real-world order database of a distribution centre is obtained and used to compare the results from DMSA with a random assignment approach. It turns out that DMSA outperforms random assignment as the number of put away products and the proportion of put away products with high turnover rates increase.     

A superlative index number formula for the Hicks-Moorsteen productivity index

The Malmquist and Hicks-Moorsteen productivity indexes are the two most widely used theoretical indexes for measuring productivity growth. Since these productivity indexes are defined by unknown distance functions, it is necessary to estimate the distance functions to compute them in principle. On the other hand, the Törnqvist productivity index is an empirical index number formula that is directly computable from the prices and quantities of the inputs and outputs alone. Caves et al. (1982) imply that the Malmquist index coincides with the Törnqvist index under profit maximizing behaviour and constant returns to scale technology. The purpose of the present paper is to point out that the Hicks-Moorsteen productivity index coincides with the Törnqvist productivity index under the same condition. We emphasize that the condition of constant returns to scale is indispensable for deriving the equivalence between the two indexes. Moreover, even when this condition is relaxed to the α returns to scale, the equivalence between the Hicks-Moorsteen and Törnqvist productivity indexes is shown to hold true.     

Markov-switching and the Beveridge–Nelson decomposition: Has US output persistence changed since 1984?

We show that, for a class of univariate and multivariate Markov-switching models, exact calculation of the Beveridge–Nelson (BN) trend/cycle components is possible. The key to exact BN trend/cycle decomposition is to recognize that the latent first-order Markov-switching process in the model has an AR(1) representation, and that the model can be cast into a state-space form. Given the state-space representation, we show that impulse-response function analysis can be processed with respect to either an asymmetric discrete shock or to a symmetric continuous shock. The method presented is applied to Kim, Morley, Piger’s [Kim, C.-J., Morley, J., Piger, J., 2005. Nonlinearity and the permanent effects of recessions. Journal of Applied Econometrics 20, 291–309] univariate Markov-switching model of real GDP with a post-recession ‘bounce-back’ effect and Cochrane’s [Cochrane, J.H., 1994. Permanent and transitory components of GNP and stock prices. Quarterly Journal of Economics 109, 241–263] vector error correction model of real GDP and real consumption extended to incorporate Markov-switching. The parameter estimates, the BN trend/cycle components, and the impulse-response function analysis for each of these empirical models suggest that the persistence of US real GDP has increased since the mid-1980’s.     

Pricing To Signal Product Line Quality

This paper offers a general characterization of the optimal product line prices for a monopolist whose quality of products is initially unknown to consumers. In the focal equilibrium, a monopolist signals a high-quality product line by pricing as if quality were known to be high, but costs of production were higher than they truly are. In a rich set of environments, this characterization implies that the prices of all products are initially distorted upward, with the price distortion being largest for products with the most inelastic demands and/or quality-sensitive production costs. These implications yield predictions for the time path of prices flint are broadly consistent with evidence from the marketing literature. The multidimensional signaling problem is made tractable by the satisfaction of a very simple and powerful single crossing property.     

Correcting Standard Errors in Two‐stage Estimation Procedures with Generated Regressands*

Feenstra and Hanson [NBER Working Paper No. 6052 (1997)] propose a procedure to correct the standard errors in a two‐stage regression with generated dependent variables. Their method has subsequently been used in two‐stage mandated wage models [Feenstra and Hanson, Quarterly Journal of Economics (1999) Vol. 114, pp. 907–940; Haskel and Slaughter, The Economic Journal (2001) Vol. 111, pp. 163–187; Review of International Economics (2003) Vol. 11, pp. 630–650] and for the estimation of the sector bias of skill‐biased technological change [Haskel and Slaughter, European Economic Review (2002) Vol. 46, pp. 1757–1783]. Unfortunately, the proposed correction is negatively biased (sometimes even resulting in negative estimated variances) and therefore leads to overestimation of the inferred significance. We present an unbiased correction procedure and apply it to the models reported by Feenstra and Hanson (1999) and Haskel and Slaughter (2002) .     

Yield measure for the process with multiple streams

Process capability indices, such as C _pk , have been widely used in the manufacturing industry to provide common quantitative measures for process performance. The index C _pk only provides an approximate rather than an exact measure of the process yield. To obtain an exact measure of the process yield, Boyles proposed a yield index S _pk . Capability measures for processes with single stream have been investigated extensively; however, multiple streams processes often occur in practice. Bothe presented a capability index for multiple streams process. In the present paper, a new index that is able to provide an exact measure of yield for a multiple streams process is developed. Three examples are given for illustration. From the results of the yield measure in the three examples, the conventional approach, using the arithmetic average of the estimated yield indices of all streams, will certainly over-estimate the process yield.