Classification-based model selection in retail demand forecasting

Retailers supply a wide range of stock keeping units (SKUs), which may differ for example in terms of demand quantity, demand frequency, demand regularity, and demand variation. Given this diversity in demand patterns, it is unlikely that any single model for demand forecasting can yield the highest forecasting accuracy across all SKUs. To save costs through improved forecasting, there is thus a need to match any given demand pattern to its most appropriate prediction model. To this end, we propose an automated model selection framework for retail demand forecasting. Specifically, we consider model selection as a classification problem, where classes correspond to the different models available for forecasting. We first build labeled training data based on the models’ performances in previous demand periods with similar demand characteristics. For future data, we then automatically select the most promising model via classification based on the labeled training data. The performance is measured by economic profitability, taking into account asymmetric shortage and inventory costs. In an exploratory case study using data from an e-grocery retailer, we compare our approach to established benchmarks. We find promising results, but also that no single approach clearly outperforms its competitors, underlying the need for case-specific solutions.     

Demand for education, and its estimation

Since education produces major externalities and has important merit want characteristics, the estimation of a demand schedule is extremely difficult. Demand estimation for higher education is made somewhat easier because of the great importance of the associated costs and the relevant private substitutes, i.e. private colleges and universities. Therefore higher education is a good candidate for the application of the individual (economic) preference approach, which is based on the assumption that individuals are aware of their need for education about as they are aware of their needs for products provided by the open market.

The estimation of demand for primary and secondary education can rely only to a minor extent on the individual (economic) preference approach. The voter's behavior approach analysis is likely to be more directly applicable. Study of the behavior of voters and the behavior of legislators and members of school boards can shed light on the demand for education. Analytic insight can be gained also by the “voting with one's feet”, and the “calculus of consent” methods.

Finally, benefit-cost analysis can be applied in situations where education gives an extremely weak demand signal. In education we often are less interested in overall benefit-cost estimates than in the benefit-cost positions in which different important interest groups find themselves with regard to education. Such analysis requires the identification of significant interest groups, bargaining strategies, and bargaining patterns, as well as of ways in which education decision makers respond to group pressures.     

Estimating economic relationships subject to firm‐ and time‐varying equality and inequality constraints

Applied econometricians often fail to impose economic regularity constraints in the exact form economic theory prescribes. We show how the Singular Value Decomposition (SVD) Theorem and Markov Chain Monte Carlo (MCMC) methods can be used to rigorously impose time‐ and firm‐varying equality and inequality constraints. To illustrate the technique we estimate a system of translog input demand functions subject to all the constraints implied by economic theory, including observation‐varying symmetry and concavity constraints. Results are presented in the form of characteristics of the estimated posterior distributions of functions of the parameters. Copyright © 2001 John Wiley & Sons, Ltd.     

THE DEMAND FOR GASOLINE: EVIDENCE FROM HOUSEHOLD SURVEY DATA

In this paper we investigate the demand for gasoline in Canada using recent annual expenditure data from the Canadian Survey of Household Spending, over a 13‐year period from 1997 to 2009, on three expenditure categories in the transportation sector: gasoline, local transportation, and intercity transportation. In doing so, we use three of the most widely used locally flexible functional forms, the Almost Ideal Demand System (AIDS) of Deaton and Muellbauer (1980), the quadratic AIDS (QUAIDS) of Banks et al. (1997)—an extension of the simple AIDS model that can generate quadratic Engel curves—and the Minflex Laurent model of Barnett (1983), which can also generate quadratic Engel curves. We pay explicit attention to economic regularity, argue that unless regularity is attained by luck, flexible functional forms should always be estimated subject to regularity as suggested by Barnett (2002), and impose local curvature to produce inference consistent with neoclassical microeconomic theory. Our findings indicate that the curvature‐constrained Minflex Laurent model is the only model that is able to provide theoretically consistent estimates of the Canadian demand for gasoline. Our estimates show that the own‐price elasticity for gasoline demand in Canada is between ? 0.738 and ? 0.570 —less elastic than previously reported in the literature. Copyright © 2013 John Wiley & Sons, Ltd.     

Forecasting (aggregate) demand for US commercial air travel

We analyze whether it is better to forecast air travel demand using aggregate data at (say) a national level, or to aggregate the forecasts derived for individual airports using airport-specific data. We compare the US Federal Aviation Administration’s (FAA) practice of predicting the total number of passengers using macroeconomic variables with an equivalently specified AIM (aggregating individual markets) approach. The AIM approach outperforms the aggregate forecasting approach in terms of its out-of-sample air travel demand predictions for different forecast horizons. Variants of AIM, where we restrict the coefficient estimates of some explanatory variables to be the same across individual airports, generally dominate both the aggregate and AIM approaches. The superior out-of-sample performances of these so-called quasi-AIM approaches depend on the trade-off between heterogeneity and estimation uncertainty. We argue that the quasi-AIM approaches exploit the heterogeneity across individual airports efficiently, without suffering from as much estimation uncertainty as the AIM approach.     

Bayesian analysis of random coefficient logit models using aggregate data

We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry et al. [Berry, Steven, Levinsohn, James, Pakes, Ariel, 1995. Automobile prices in market equilibrium. Econometrica. 63 (4), 841–890], which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a reparameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who are willing to trade off one additional distributional assumption for increased efficiency in estimation.     

Mixed MNL models for discrete response

This paper considers mixed, or random coefficients, multinomial logit (MMNL) models for discrete response, and establishes the following results. Under mild regularity conditions, any discrete choice model derived from random utility maximization has choice probabilities that can be approximated as closely as one pleases by a MMNL model. Practical estimation of a parametric mixing family can be carried out by Maximum Simulated Likelihood Estimation or Method of Simulated Moments, and easily computed instruments are provided that make the latter procedure fairly efficient. The adequacy of a mixing specification can be tested simply as an omitted variable test with appropriately defined artificial variables. An application to a problem of demand for alternative vehicles shows that MMNL provides a flexible and computationally practical approach to discrete response analysis. Copyright © 2000 John Wiley & Sons, Ltd.     

Estimation of spatial autoregressive panel data models with fixed effects

This paper establishes asymptotic properties of quasi-maximum likelihood estimators for SAR panel data models with fixed effects and SAR disturbances. A direct approach is to estimate all the parameters including the fixed effects. Because of the incidental parameter problem, some parameter estimators may be inconsistent or their distributions are not properly centered. We propose an alternative estimation method based on transformation which yields consistent estimators with properly centered distributions. For the model with individual effects only, the direct approach does not yield a consistent estimator of the variance parameter unless T is large, but the estimators for other common parameters are the same as those of the transformation approach. We also consider the estimation of the model with both individual and time effects.     

Exact computation of max weighted score estimators

We show that exact computation of a family of ‘max weighted score’ estimators, including Manski’s max score estimator, can be achieved efficiently by reformulating them as mixed integer programs (MIP) with disjunctive constraints. The advantage of our MIP formulation is that estimates are exact and can be computed using widely available solvers in reasonable time. In a classic work-trip mode choice application, our method delivers exact estimates that lead to a different economic interpretation of the data than previous heuristic estimates. In a small Monte Carlo study we find that our approach is computationally efficient for usual estimation problem sizes.     

Estimation Methods and Related Systems at Statistics Canada

This paper provides an overview of research in estimation techniques, their application, and the development of generalized estimation systems at Statistics Canada. In Canada, the demand for more detailed and better quality cross-sectional data related to various sodo-economic issues has increased significantly in recent years. Also, there has been increasing interest in longitudinal data to better understand and interpret the relationships among variables, necessitating the implementation of a number of large scale panel surveys by Statistics Canada. The paper briefly discusses estimation for longitudinal data and a weighting approach developed for cross-sectional data Prom these surveys. For cross-sectional household and business surveys, as well as the census of population, appropriate dibration estimators developed for each situation are briefly discussed. In addition, regression composite estimation, a method developed to improve the quality of cross-sectional estimates from rotating panel surveys such as the Canadian Labour Force Survey, is presented. With regard to more detailed cross-sectional estimates at sub-provincial levels, different approaches to small area estimation developed for various programs are also presented. We SUmmarize the various modules developed lor the GeneraIiized Ektimation System. important new developments within the system include two-phase estimation as well as the estimation of variance for a number of imputation procedures. We briefly review the status of current estimation research on selected topics as well as the direction of future research.     

An Econometric Analysis of Brand-Level Strategic Pricing Between Coca-Cola Company and PepsiCo.

We investigate market structure and strategic pricing for leading brands sold by Coca-Cola Company and PepsiCo. in the context of a flexible demand specification (i.e., nonlinear AIDS) and structural price equations. Our flexible and generalized approach does not rely upon the often used ad hoc linear approximations to demand and profit-maximizing first-order conditions, and the assumption of Nash-Bertrand competition. We estimate a conjectural variation model and test for different brand-level pure strategy games. This approach of modeling market competition using the nonlinear Full Information Maximum Likelihood (FIML) estimation method provides insights into the nature of imperfect competition and the extent of market power. We find no support for a Nash-Bertrand or Stackelberg Leadership equilibrium in the brand-level pricing game. Results also provide insights into the unique positioning of PepsiCo.'s Mountain Dew brand.     

On solving bias‐corrected non‐linear estimation equations with an application to the dynamic linear model

In a seminal paper, Mak, Journal of the Royal Statistical Society B, 55, 1993, 945, derived an efficient algorithm for solving non‐linear unbiased estimation equations. In this paper, we show that when Mak's algorithm is applied to biased estimation equations, it results in the estimates that would come from solving a bias‐corrected estimation equation, making it a consistent estimator if regularity conditions hold. In addition, the properties that Mak established for his algorithm also apply in the case of biased estimation equations but for estimates from the bias‐corrected equations. The marginal likelihood estimator is obtained when the approach is applied to both maximum likelihood and least squares estimation of the covariance matrix parameters in the general linear regression model. The new approach results in two new estimators when applied to the profile and marginal likelihood functions for estimating the lagged dependent variable coefficient in the dynamic linear regression model. Monte Carlo simulation results show the new approach leads to a better estimator when applied to the standard profile likelihood. It is therefore recommended for situations in which standard estimators are known to be biased.     

Bayesian estimation of labor demand by age: theoretical consistency and an application to an input–output model

Extended input–output models require careful estimation of disaggregated consumption by households and comparable sources of labor income by sector. The latter components most often have to be estimated. The primary focus of this paper is to produce labor demand disaggregated by workers’ age. The results are evaluated through considerations of its consistency with a static labor demand model restricted with theoretical requirements. A Bayesian approach is used for more straightforward imposition of regularity conditions. The Bayesian model confirms elastic labor demand for youth workers, which is consistent with what past studies find. Additionally, to explore the effects of changes in age structure on a regional economy, the estimated age-group-specific labor demand model is integrated into a regional input–output model. The integrated model suggests that ceteris paribus ageing population contributes to lowering aggregate economic multipliers due to the rapidly growing number of elderly workers who earn less than younger workers.     

基于贝叶斯结构方程模型的城际铁路客运需求影响因素分析

作为城市群区域间的连接纽带,城际铁路是社会经济快速发展的基础。研究城际铁路客运需求的影响机理,对于掌握城际铁路客运量分布特征和变化规律具有十分重要的现实意义。通过分析城际铁路客运需求的相关影响因素及相互作用关系,建立基于贝叶斯参数估计的结构方程模型。以长三角与珠三角地区城市群为案例,分析交通运输设施、运输成本以及经济状况等潜在变量对城际铁路客运需求的影响。结果显示,在直接影响层面,经济状况对两地区城际铁路客运需求影响最为显著,而在综合影响层面,交通运输设施对城际铁路客运需求的影响最为显著。     

Kernel estimation for disequilibrium models for floorspace efficiency in retailing

Conclusions In this paper we have proposed new techniques for simplifying the estimation of disequilibrium models by avoiding constrained maximum likelihood methods (which cannot avoid numerous theoretical and practical difficulties mentioned above) including an unrealistic assumption of the independence of errors in demand and supply system of equations. In the proposed first stage, one estimates the relative magnitude of the residuals from the demand and supply equations nonparametrically, even though they suffer from omitted variables bias, because the coefficient of the omitted variable is known to be the same in both equations. The reason for using nonparametric methods is that they do not depend on parametric functional forms of biased (bent inward) demand and supply equations. The first stage compares the absolute values of residuals from conditional expectations in order to classify the data points as belonging to the demand or the supply curve. We estimate the economically meaningful scale elasticity and distribution parameters at the second stage from classified (separated) data.We extend nonparametric kernel estimation to the r = 4 case to improve the speed of convergence, as predicted by Singh's [1981] theory. In the first stage, r = 4 results give generally improved R² and ¦t¦ values in our study of the Dutch data—used by many authors concerned with the estimation of floorspace productivity. We find that one can obtain reasonable results by our approximate but simpler two stage methods. Detailed results are reported for four types of Dutch retail establishments. More research is needed to gain further experience and to extend the methodology to other disequilibrium models and other productivity estimation problems.This paper was processed by W. Eichhorn.     

基于消费结构分析的扩大内需对策研究——以上海城镇居民为例

消费是拉动经济的三驾马车之一,在当前依靠投资和出口拉动经济战略受阻的背景下,扩大内需、刺激消费成为推动我国经济发展的关键因素。作为反映居民消费本质的重要概念,消费结构与扩大内需是密不可分的。本文以上海城镇居民消费结构为研究对象,分析其在1995～2008年间演变规律;运用ELES模型探究居民消费支出与可支配收入的关系;测算商品需求收入弹性系数并进行比较分析。在此基础上,提出从稳定商品价格、提高居民收入、完善社会保障制度和优化供给结构等方面政策刺激消费,扩大内需。     

Slowdown of credit flows in Jordan in the wake of the global financial crisis: Supply or demand driven?

This paper estimates a disequilibrium model of credit supply and demand to evaluate the relative role of these factors in the slowdown of credit flows in the Jordanian economy in the wake of the global financial crisis. The empirical analysis suggests that the credit stagnation is mainly driven by the restricted credit supply amid tighter monetary policy conditions in Jordan relative to the United States, as evidenced by the widened interest differential between the Central Bank of Jordan (CBJ) re-discount and the U.S. Federal Reserve funds rates. Although it appears that demand side factors related to the slowdown of economic activity have also had an impact, their role has been relatively modest. The estimation results imply that economic policies targeted towards stimulating the supply of credit are likely to be a more effective tool for expanding credit flows relative to demand stimulating policies.     

Robust estimation for structural spurious regressions and a Hausman-type cointegration test

This paper analyzes an approach to correcting spurious regressions involving unit-root nonstationary variables by generalized least squares (GLS) using asymptotic theory. This analysis leads to a new robust estimator and a new test for dynamic regressions. The robust estimator is consistent for structural parameters not just when the regression error is stationary but also when it is unit-root nonstationary under certain conditions. We also develop a Hausman-type test for the null hypothesis of cointegration for dynamic ordinary least squares (OLS) estimation. We demonstrate our estimation and testing methods in three applications: (i) long-run money demand in the U.S., (ii) output convergence among industrial and developing countries, and (iii) purchasing power parity (PPP) for traded and non-traded goods.     

Analysing I(2) Systems by Transformed Vector Autoregressions*

We characterize the restrictions imposed by the minimal I(2)‐to‐I(1) transformation that underlies much applied work, e.g. on money demand relationships or open‐economy pricing relationships. The relationship between the parameters of the original I(2) vector autoregression, including the coefficients of polynomially cointegrating relationships, and the transformed I(1) model is characterized. We discuss estimation of the transformed model subject to restrictions as well as the more commonly used approach of unrestricted reduced rank regression. Only a minor loss of efficiency is incurred by ignoring the restrictions in the empirical example and a simulation study. A properly transformed vector autoregression thus provides a practical and effective means for inference on the parameters of the I(2) model.     

Environmental Preservation Demand

Abstract . When the demand for environmental preservation is not explicitly revealed in markets, motivating attitudes toward environmental preservation become important. A survey approach allows revelation and measurement of demand for environmental preservation. Indices which measure the altruistic, bequest, intrinsic, and option to use motives and other attitudes are utilized as determinants in a model that measures the demand for environmental preservation. Demand is more likely with greater preservation motives. Preservation demand also depends on individual preferences for economic development, perceptions of affordability and responsibility for preservation of the wetlands.