¹ See the Appendix for explanations of terms and concepts.

² The description which follows is taken from Wildavsky, Aaron, The Politics of the Budgetary Process (Boston, 1964)Google Scholar. Portions of the comments on the House Appropriations Committee are from Fenno, Richard, “The House Appropriations Committee as a Political System: The Problem of Integration,” this Review, 56 (1962), 310–324Google Scholar.

³ See Thiel, H., Linear Aggregation of Economic Relations (Amsterdam, 1954)Google Scholar.

⁴ Our subsequent discussion of “shift” or “break” points should also make clear that it is not realistic to expect meaningful time series of great length to be accumulated for most agencies in the United States government.

⁵ Since some readers may not be familiar with the notation we are using, a brief explanation may be in order. As a coefficient of the equation, β ₂ is an unknown number that must be estimated from the data, and this coefficient multiplies another number (y _t−1 — X _t−1) that may be computed by subtracting last year's request from last year's appropriation. We want the equation to say that the agency will try to counteract large changes in their appropriations by changing their normal requests in the next year. If the agency asks for much more than it thinks it will get and its request is cut, for example, the expression (y _t−1 — x _t−1) will be a negative number written in symbolic form as (y _t−1 — x _t−1) <0. A rule of multiplication says that a negative number multiplied by another negative number gives a positive number. If an agency pads its request, however, it presumably follows a cut with a new request which incorporates an additional amount to make allowance for future cuts. In order to represent this behavior, that is to come out with a positive result incorporating the concept of padding, the unknown coefficient β ₂ must be negative (β ₂ <0).

⁶ The agency that favors its own programs should increase its requests over time. In the absence of the stochastic disturbance (when the random variable is 0), the request in a given year should be larger than the request in the previous year so that x _t > x _t−1. Therefore, the unknown coefficient β ₃ must be larger than one (β ₃ > 1) since it multiplies last year's request.

⁷ Other gaming strategies are easily proposed. Suppose, for example, that a given agency believes that it knows the decision rule that Congress uses in dealing with it, and that this decision rule can be represented by one of (4), (7), or (8), above. Presume, for reasons analogous to those outlined for (8), that this agency desires to take into account that positive or negative portion of the previous year's appropriation y _t−1 that was not based on the previous year's request x _t−1 This consideration suggests

as an agency decision rule where Δ_t− is a dummy variable representing in year t − 1 the term not involving x _t−1 in one of (4), (7) or (8) above. If one believes that agency and Bureau of the Budget personnel are sufficiently well acquainted with the senators and congressmen to be able to predict the value of the current stochastic disturbance, then it becomes reasonable to examine a decision rule of the form

where Δ_t is defined as above. No evidence of either form of behavior was found, however, among the agencies that were investigated. We also estimated the parameters of the third order auto-regressive scheme for the requests of an individual agency

in an attempt to discover if naive models would fit as well as those above. In no case did this occur and generally the fits for this model were very poor. A similar scheme was estimated for the appropriations y _t of an individual agency with similar results with respect to qeuations (4), (7) and (8) above. Since the “d” statistic suggests that no higher order Markov process would be successful, no other rules for agency behavior were tried.

⁸ Agency proposals to the Bureau of the Budget are not reported to the public and could be obtained only for these eight sub-agencies.

⁹ Three interrelated difficulties arise in the analysis of the time series data x _t, y _t for an agency. The first problem is the choice of a technique for estimating the parameters of the alternate schemes in some optimal fashion. Given these estimates and their associated statistics, the second problem is the choice of criteria for selecting the model best specifying the system underlying the data. Finally, one is faced with the problem of examining the variability of the underlying parameters of the best specification. We believe that our solution to these problems, while far from optimal, is satisfactory given the present state of econometric knowledge. See our presentation in “On the Process of Budgeting: An Empirical Study of Congressional Appropriations,” by Davis, Otto, Dempster, M. A. H., and Wildavsky, Aaron, to appear in Tullock, Gordon (ed.), Papers on Non-Market Decision Making, Thoma Jefferson Center, University of VirginiaGoogle Scholar. See especially section 4 and the appendix by Dempster, which contains discussions and derivations of estimation procedures, selection criteria and test statistics for the processes in Section II of this paper.

¹⁰ We make the assumption that these two disturbances are independent throughout the paper. Notice, however, that dependence between the disturbances explicitly enters decision equation (8) of section II and those of footnote 7. For these equations, the assumption refers to the disturbance of the current year. That is, we allow the possibility that special circumstances may affect a single participant (Bureau of the Budget or Congress) as well as both. When the latter case occurred, our selection criteria resulted in the choice of equation (8) as best specifying Congressional behavior.

¹¹ We are estimating the unknown values of the coefficients (or parameters) of regression equations for each agency. All of our estimators are biased. We use biased estimators for the simple reason that no unbiased estimators are known. The property of consistency is at least a small comfort. All of our estimators are consistent. It might be noted that all unbiased estimators are consistent, but not all consistent estimators are unbiased.

¹² This statistic is known as the Durbin-Watson ratio. A description of the test may be found in Johnston, J., Econometric Methods (New York, 1963), p. 92Google Scholar.

¹³ Theil, H. and Nagar, A. L., “Testing the Independence of Regressional Disturbances,” Journal of the American Statistical Association, 56 (1961), 793–806CrossRefGoogle Scholar. These significance points were used to construct further significance points when necessary. See Davis, Dempster and Wildavsky, op. cit.

¹⁴ The test is described in Anderson, T. W., An Introduction to Multivariate Analysis (New York, 1958) pp. 69–71Google Scholar. See Dempster's appendix to Davis, Dempster, and Wildavsky, op. cit., for some justification of the use of the test.

¹⁵ See Davis, Dempster, and Wildavsky, op. cit.

¹⁶ Chow, G. C., “Tests of Equality between Sets of Coefficients in Two Linear Regressions,” Econometrica, 28 (1960), 591–605CrossRefGoogle Scholar, and the appendix to Davis, Dempster, and Wildavsky, op. cit.

¹⁷ In a few instances an inspection of the residuals indicated that a shift point occurred so early or so late in the series that it was not possible to compute a meaningful stationarity F-Statistic. In these few cases the deviant observations were dropped and the usual analysis performed on the shortened time series. Thus we “forced” a break in every case in order to perform subsequent operations.

¹⁸ The apparent discrepancy between the latter part of Table 3 and Table 1 is caused by the fact that for two agencies, the Bureau of the Census and the Office of Education, although the Agency-Bureau of the Budget decision equations are temporally stable and best specified as (1), when a shift point is forced, the criteria indicate (3) for the latter period.

¹⁹ Some of the shift points appeared to occur so early in the series that it was not possible to calculate a correlation coefficient.

²⁰ The importance of analyzing deviant cases is suggested in: Gordon, Milton M., “Sociological Law and the Deviant Case,” Sociometry, 10 (1947)CrossRefGoogle Scholar; Kendall, Patricia and Wolf, Katharine, “The Two Purposes of Deviant Case Analysis,” in Lazarsfeld, Paul F. and Rosenberg, Morris (eds.), The Language of Social Research, (Glencoe, 1962), pp. 103–137Google Scholar; Horst, Paul, The Prediction of Personal Adjustment: A Survey of the Logical Problems and Research Techniques (New York, 1941)Google Scholar; and Lipset, Seymour, Trow, Martin, and Coleman, James, Union Democracy (New York, 1960)Google Scholar.

²¹ We are indebted to Rose M. Kelly, a graduate student in the Department of Political Science, University of California, Berkeley, who did the research on the deviant cases and provided the data for Tables 6 and 7.

²² See Wildavsky, op. cit., pp. 64–68, for a discussion of clientele and confidence. In his forthcoming book, The Power of the Purse (Boston, 1966)Google Scholar, Richard Fenno provides further evidence of the usefulness of these categories.

²³ Clarkson, Geoffrey P. E., Portfolio Selection: A Simulation of Trust Investment (Englewood Cliffs, N. J., 1962)Google Scholar; Clarkson, G. P. E. and Simon, H. A., “Simulation of Individual and Group Behavior,” American Economic Review, 50 (1960), 920–932Google Scholar; Cyert, Richard and March, James (eds.) A Behavioral Theory of the Firm (Englewood Cliffs, N. J., 1963)Google Scholar; Newell, Allen, “The Chess Machine: An Example of Dealing with a Complex Task by Adaptation,” Proceedings of the Western Joint Computer Conference (1955), pp. 101–108Google Scholar; Newell, Allen, Shaw, J. C., and Simon, H. A., “Elements of a Theory of Human Problem Solving,” Psychological Review, 65 (1958), 151–166CrossRefGoogle Scholar; Newell, Allen and Simon, H. A., “The Logic Theory Machine: A Complex Information Processing System,” Transactions on Information Theory (1956), 61–79Google Scholar; Reitman, W. R., “Programming Intelligent Problem Solvers,” Transactions on Human Factors in Electronics, HPE-2 (1961), pp. 26–33Google Scholar; Simon, H. A., “A Behavioral Model of Rational Choice,” Quarterly Journal of Economics, 60 (1955), 99–118CrossRefGoogle Scholar; and Simon, H. A., “Theories of Decision Making in Economics and Behavioral Science,” American Economic Review, 49 (1959), 253–283Google Scholar.

²⁴ Braybrooke, David and Lindblom, Charles, A Strategy of Decision (New York, 1964)Google Scholar.

²⁵ Wildavsky, op. cit., pp. 8–63.

²⁶ March, James, “The Power of Power,” in Easton, David, editor, Varieties of Political Theory (Etiglewood Cliffs, N. J., 1966), pp. 39–70Google Scholar.

²⁷ See the forthcoming studies by John P. Crecine on budgeting in Pittsburgh, Detroit and Cleveland, and by Donald Gerwin on the Pittsburgh School District. Aaron Wildavsky will attempt to apply variations of the models in this paper to Oakland, California.

²⁸ Wildavsky, Aaron, “Private Markets and Public Arenas,” The American Behavioral Scientist vol. 9 no. 7. (09 1965) pp. 33–39Google Scholar.