Economics of Education Review 18 1999 405–415 www.elsevier.comlocateeconedurev
A comparison of conventional linear regression methods and neural networks for forecasting educational spending
Bruce D. Baker
a,
, Craig E. Richards
b
a
Department of Teaching and Leadership, 202 Bailey Hall, University of Kansas, Lawrence, KS 66045, USA
b
Department of Organization and Leadership, Teachers College, Columbia University, 525 West 120th Street, Box 16, Main Hall 212A, New York, NY 10027, USA
Received 1 June 1997; accepted 2 February 1998
Abstract
This study presents an application of neural network methods for forecasting per pupil expenditures in public elemen- tary and secondary schools in the United States. Using annual historical data from 1959 through 1990, forecasts were
prepared for the period from 1991 through 1995. Forecasting models included the multivariate regression model developed by the National Center for Education Statistics for their annual Projections of Education Statistics Series,
and three neural architectures: 1 recurrent backpropagation; 2 Generalized Regression; and 3 Group Method of Data Handling. Forecasts were compared for accuracy against actual values for educational spending for the period.
Regarding prediction accuracy, neural network results ranged from comparable to superior with respect to the NCES model. Contrary to expectations, the most successful neural network procedure yielded its results with an even simpler
linear form than the NCES model. The findings suggest the potential value of neural algorithms for strengthening econometric models as well as producing accurate forecasts. [JEL C45, C53, I21]
1999 Elsevier Science Ltd. All
rights reserved.
Keywords: Forecasting; Time series; Neural networks
1. Introduction
From 1940 to 1990, per pupil spending on public elementary and secondary education grew from US722
to US4622, a constant dollar increase of 540 Hanushek, 1994. At issue is whether educational
spending as one component of our economic system is outpacing the growth and eventually the carrying
capacity of the system as a whole. As a result, questions exist as to whether we can reasonably expect a continu-
ance of the current rate of growth into our near or distant future. Such questions point to the increasing importance
of developing and testing more sensitive forecasting methods for projecting educational expenditures.
Corresponding author. Tel.: 1 1-785-864-9844; fax: 1 1- 785-864-5076; e-mail: bdbakerukans.edu
0272-775799 - see front matter
1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 7 2 - 7 7 5 7 9 9 0 0 0 0 3 - 5
Over the past decade, neural network technologies have found their way into competitive industries from
the financial markets Lowe, 1994 to real estate Worzala, Lenk Silva, 1995 and health care
Buchman, Kubos, Seidler Siegforth, 1994. Neural networks are primarily touted for their prediction accu-
racy compared with conventional linear regression modeling methods. Ostensibly, neural networks are an
extension of regression modeling, occasionally referred to as flexible non-linear regression McMenamin, 1997.
Recently, social scientists have begun to assess the use- fulness of neural network methods for developing a
deeper understanding of trends and patterns in data, or “knowledge extraction from data,” in addition to the
usual emphasis in neural network research on prediction accuracy Liao, 1992.
The flexibility of neural network modeling makes it a theoretically appealing procedure for forecasting in gen-
406 B.D. Baker, C.E. Richards Economics of Education Review 18 1999 405–415
eral. Yet, future adoption of these methods in public fin- ance depends on our ability to establish standards for
neural network application compared with conventional methods and applied to public finance forecasting prob-
lems of interest. This study explores the potential value of using neural network methods alongside of more con-
ventional regression methods used by the National Center for Education Statistics for forecasting edu-
cational spending. A reasonable expectation, validated in other forecasting studies in public finance Hansen
Nelson, 1997, is that neural networks, by way of flex- ible, non-linear estimation, are likely to reveal changes,
or inflection points, in the general trend of education spending.
2. Neural networks
