The authors look at eight models to forecast inbound tourist arrivals to Singapore, six of which were analyzed by Chan and by Chu. The authors explore model performance from a different perspective than either of these authors and arrive at different conclusions. Major suggestions are as follows: (1) a complete comparison among competing models during the estimation phase and a battery of performance statistics when evaluating these models sheds light on several top-performing models; (2) when evaluating the forecasting performance of competing models, different performance statistics may lead to different model selections; (3) among competing models, a model that performs best during the within-sample period does not necessarily perform best in the postsample period; (4) changing the length of the forecast horizon can have an effect on the choice of the best model; and (5) a combined model may be the one that provides the best forecasting performance.

No abstract

Planted wheat acreage supply elasticities are estimated for each of several leading wheat-producing states. Estimates of elasticities for the aggregate of these states are 0. 77, 0.45, and 0.52 for spring wheat, winter wheat, and all wheat, respectively, but there is considerable heterogeneity among states. Acreage allotments and marketing quotas appear to have destroyed the role of prices in allocating acreage between wheat and other crops during the years 1950 and 1954-64. Estimates were obtained using multiple regression analysis of time-series data for the period 194�74. This period was subdivided in order to take account of changing farm programs.

In the early 1940s, the Cowles Commission for Research (later, the Cowles Foundation) fostered the development of statistical methodology for application in economics and paved the way for large-scale econometric models to be used for both structural estimation and forecasting. This approach stood for decades. Vector autoregression (VAR), appearing in the 1980s, was a clear improvement over early Cowles Foundation models, primarily because it paid attention to dynamic structure. As a way of imposing long-run equilibrium restrictions on sets of variables, cointegration and error-correction modeling (ECM) gained popularity in the 1980s and 1990s, though ECMs have so far failed to deliver on their early promise. ARCH and GARCH modeling have been used with great success in specialized financial areas to model dynamic heteroscedasticity, though in mainstream econometrics, evidence of their value is limited and conflicting. Concerning misspecification tests, any model will inevitably fail some of them for the simple reason that there are many possible tests. Which failures matter? The root of the difficulty regarding all issues related to modeling is that we can never know the true data generating process. In the next 25 years, what new avenues will open up? With ever greater computational capacity, more complex models with larger data sets seem the way to the future. Will they require the automatic model selection methods that have recently been introduced? Preliminary evidence suggests that these methods can do well. The quality of aggregate data is no better than it was. Will greater use of more disaggregated data be sufficient to provide better forecasts? That remains an open question.

Multicollinearity among independent variables within a regress ion model is one of the most frequently encountered problems faced by the applied researcher. In a recent article in this Journal (Willis, e1 a/.) , a catalog of"remedies" for multicollinearity was presented to assist in reducing its level and associated adverse con sequences. One of these remedies-principal components-was suggested as a method oftransforming a set of collinear explanatory variables into new variables that are orthogonal to each other with the first few of these transformed va riables accounting for the majority of the variability in the origina l data set. In principal components regression , a transformed variable is determined to be important a nd included or unimportant and excluded in the regression model depending upon the size of the characteristic root (eigenvalue) associated with its corresponding characteristic vector (eigenvector) (Massy), the statistical significance of its regression coefficient (Mittelhammer and Baritelle), or some combination of eigenvalue size and correlation with the dependent variable (Johnson, et a/.). Unfortunately, this technique is widely abused and misunderstood by the applied researcher. Confusion exists with respect to (I) its relationship to other orthogonalization techniques; (2) the meaning of the orthogonalized components and the necessity of transforming the principal component estimators back to the original parameter space; (3) the implications of deleting components and the correspondence of this technique to a particular type of restricted least squares estimator; (4) the proper way to delete components and evaluate these implied restrictions; and (5) actual implementation of this estimation procedure via available computer routines. The purpose of this note, therefore, is to place the technique of principal components in perspective and to suggest a methodology for implementing this technique correctly. DEALING WITH MULTICOLLINEARITY Multicollinearity is the result of a lack of selective variation among the independent variables in a regression model. It is a problem associated with passively generated data, i.e. , data obtained from some outside source over which the investigator has no control or data characterized by lack of experimental design. Consequently, the problem of multicollinearity can never be cured; it can only be treated in an ad hoc manner.