This paper examined the value of different estimating procedures for an econometric model. Specifically it forecasted the number of U.S. visitors to Hawaii using real airfare to Honolulu and U.S. real per capita income. Data fro 1961-73 were used to calibrate the model with ordinary least squares (OLS), generalized lease squares (GLS) and ridge regression. Conditional forecasts were then made for five years (1974-78). Ridge regression produced more 'reasonable' coefficients (because, they say, the signs were correct and the standard errors of the coefficients were smaller) than did either OLS or GLS. Ridge regression also tended to produce the most accurate forecasts, while GLS was worst. This study would have been more valuable had the sample been used more effectively for validation (that was possible had backcasting and successive updating been used) and had unconditional forecasts also been examined. The authors failed to mention previous studies showing that the magnitude of the estimated coefficients has little impact of forecast accuracy; ballpark estimates are adequate providing that the signs are correct.
Response by E. J. Fujii and J. Mak
The authors feel the above review to be incorrect in a number of aspects:
1. The focus if the paper is methodological, not empirical. hence, the comment with respect to the data set seems misplaced.
2. The issue of a potentially larger sample size ignores a number of salient facts about the Hawaiian economy. The tourist industry in Hawaii developed in earnest only after the Korean War and was profoundly disrupted and changed with the advent of Statehood in 1959. Hence, the decision was made to begin the time series with 1961.
3. The year 1978 was the last year for which data were available as the paper was written in 1979.
4. the statement: "The authored failed to mention the studies showing that the magnitude of the estimated coefficients had little impact on forecast accuracy,' is contradicted directly in p. 76 of the paper. As the quote below indicates, the magnitude of the coefficients does matter if the pattern of collinearity changes.
The inability to isolate the separate effects of the income and airfare variables stemming from multicollinearity, however, is not a problem in forecasting with OLS provided that the pattern of collinearity, i.e., the approximately linear relationship among the independent variables, which existed in the estimation period, persists in the forecast period. This condition holds, however, as Farrar and Glaube1r (1967) note, only in a situation in which the forecasting problem is all but trivial.
Farrar and Glauber (1967, p. 95) note, 'Successful forecasts with multicollinear variables require not only the perpetuation of a stable dependency relationship between y and X, but also the perpetuation of stable interdependency relationships within X. Both conditions are met, unfortunately, only in a context in which the forecasting problem is all but trivial.'
With the world-wide oil crisis and the passage by Congress of the Airline Deregulation Bill (1978), there is strong reason to believe that the pattern of collinearity between airfares and income (Table 1 of the article) will not be the same as in the past. If so, successful forecasting of visitor flows will depend on the degree of accuracy with which the separate effects of the explanatory variables can be estimated.
Editor's notes: Some of the disagreements mentioned by the authors have been corrected in the revised version published.
Farrar, D. E. and Glauber, R. R. (1967), "Multicollinearity in regression analysis: the problem revisited," Review of Economics and Statistics, 49, 92-107.