A New Approach for Testing Budgetary Incrementalism
Soumaya Tohamy
Hashem Dezhbakhsh
Peter H. Aranson*
February 1999
* The authors’ranks and affiliations are assistant professor, Berry College; associate professor,
Emory University; and full professor, Emory University, respectively. Please send inquiries to
Hashem Dezhbakhsh, Department of Economics, Emory University, Atlanta, GA 30322-2240,
Tel. (404) 727-4679, Fax (404) 727-4639.
A New Approach for Testing Budgetary Incrementalism
Abstract
Much of the extensive literature on testing for budgetary incrementalism originates from a
regression based method first suggested by Davis, Dempster, and Wildavsky (1966a; 1966b;
1971). This method is inappropriate, however, if the budgetary data are nonstationary.
Moreover, the method cannot detect a nonincremental period following (or preceding) an
incremental period. We present evidence suggesting that the U.S. Budgetary process is indeed
nonstationary and develop an alternative method that is valid even in nonstationary cases. The
method exploits both the cross sectional and time series characteristics of the budgetary data, to
identify statistically the occurrence of incremental decisions and to estimate incremental cycles
for each agency. We apply a Poisson regression model to the resulting series of counts to
examine how economic and political variables affect incremental outcomes. Our results suggest
that the Democrats’control over the political process, a switch in the party controlling the
White House or Congress, and presidential election year promises and political vulnerabilities all
cause departures from incremental budgeting. The public pressure resulting from a persistently
large deficit has a similar effect.
1- Introduction
The better part of a half century has passed since the publication of Simon’s (1955) essay on
“satisficing” and Lindblom’s (1959) essay on “the science of muddling through.” The burden of these
two justly famous works is that powerful forces lead decision makers in general, and legislatures in
particular, to adopt incremental strategies. For Simon, these forces originate in the informational and
computational complexity of choice, as well as the uncertainty arising from further search. For
Lindblom, these forces remain important, but decision makers also use incremental processes to reduce
political conflict. Political scientist were quick to employ these concepts. Wildavsky (1964), for
example, offered a theory of budgetary incrementalism and articulated a set of properties that
characterize incremental budgeting. Fenno (1966), similarly, addressed important sections of The
Power of the Purse to the issue of incremental choice in the U.S. Congress.
The principal empirical breakthrough in this literature came with the publication of Davis,
Dempster, and Wildavsky’s (DDW 1966a; 1966b; 1971; 1974) papers. In these contributions DDW
develop a regression based method to test for incrementalism in the U.S. federal budgetary process.
Many ensuing studies either apply DDW’s approach to data sets from different legislatures or offer
refinements to broaden the approach’s scope and enhance its effectiveness.1 By the late 1980s,
however, interest in incrementalism appeared to have waned. There remained a certain indeterminacy
in findings, indeterminacy enhanced by major political changes from the early 1980s, to the present day
period. We speculate that those who otherwise would be interested in the subject turned instead to
deductive models of legislative behavior growing out of the new institutionalism in economics.2
This essay is the first report in a research agenda focused on legislative budgetary incrementalism.3
Specifically, we review DDW’s contributions to bring its statistics to present technologies, and to
enlarge the data set and bring it current. In the process, we develop a new method for measuring and
1
See Berry (1990) for an excellent survey of this literature.
For representative works, see, e.g., Krehbiel (1992) and Shepsle and Weingast (1995). On the new
institutionalism in economics, see Furubotn and Richter (1997).
3 Other work now in progress involves the development of a rational choice model to explain the adoption of
incremental versus nonincremental choice strategies; incrementalism and Wagner’s Law; the effect of term limits
on incrementalism; and a reevaluation of incrementalism on normative grounds.
2
distinguishing between incremental and nonincremental outcomes. And, we report some results, to
explain when incremental legislative outcomes will happen and when they will not.
DDW's method involves estimating several linear regressions for each sampled agency. These
regressions estimate the time series process of agencies’budgets or the relationship between agencies’
funding requests and legislators’decisions.4 This method requires splitting the sample according to a
sample break-point, which may coincide with a change in budgeting priorities affecting the agency, and
then testing whether the coefficient estimates arising from the two sub-samples are equal. Equal
coefficients combined with a high multiple correlation coefficient, R2, suggest temporal stability in the
budgetary process for that agency. Scholars interpret such stability as an indication of incrementalism.
This method has several shortcomings that make it inappropriate for testing incrementalism. The
F-tests for equality of regression coefficients, for example, and some of the standard t-tests in these
regressions are invalid when the budget data are nonstationary.5 DDW (1971, p. 301) themselves
acknowledge this limitation, noting that "These models of the budgetary process … are unstable or
evolutionary [nonstationary], since appropriations tend to grow over time. … Econometric knowledge
concerning the evolutionary systems tends to be piece-meal and what is known is largely discouraging."
As if to presage recent developments, DDW (DDW 1966a, p. 540) assert that “the remedy for these
deficiencies must await the result of future theoretical research on explosive or evolutionary processes."
Nonetheless, no study of which we are aware has yet tested these budgetary data for stationarity.
In fairness to DDW and other scholars who use their method, we emphasize that much of the progress
in the still growing area of statistical inference for nonstationary data took place since the mid 1980s.6
Indeed, until Dickey and Fuller (1979;1981) proposed their tests, it remained impossible to test for even
the simplest form of nonstationarity. So, one could not find out whether the appropriation and request
4
The agency’s congressional appropriation, the appropriation requested by the Office of Management and Budget
(OMB), formerly the Bureau of the Budget, and the corresponding lagged values make up the dependent or
independent variables in various regression models.
5 A series is nonstationary if its mean, variance, or other moments change over the time period measured.
6 See, e.g., Hamilton (1994), chs. 15-20.
2
data are nonstationary. Such a diagnostic technique, moreover, would have been of little value in the
absence of appropriate statistical alternatives to estimate the models based on nonstationary data series.
This paper presents the first evidence suggesting that agency budget series are indeed
nonstationary. This nonstationarity arises from the presence of stochastic trends, shifting the series’
mean and variance over time. Our sample includes appropriations, requests, and spending (outlays) for
103 nondefense agencies that DDW originally considered.7 Our sampling period for the requests series
is 1946 through 1996 and for appropriations and outlays, 1946 through 1994, all fiscal years. Results
strongly suggest that the budgets of many agencies follow a nonstationary pattern.
If stochastic trend were the only source of nonstationarity in these series, one might maintain the
spirit of DDW's approach but adjust the estimation technique to accommodate for this kind of
nonstationarity.8 But another kind of nonstationarity seems likely to affect these series.9 Specifically,
during the sample period, there might be change(s) in slope coefficients of the autoregressive process
representing an agency's budget or the regression equations representing the relationship between
agencies’requests and legislators’decisions. Such temporal instability implies that the budgetary
process may be incremental for some periods and nonincremental for others. Dempster and Wildavsky
(1979, p. 375) themselves acknowledge this possibility in their later work: "The budgetary process
connecting a particular agency with Congress in a cycle of interaction may be incremental (regular) for a
period of time then become non-incremental (irregular) for a period, only to find a new stable pattern
that will at some time in the future again become unstable."
Most important, DDW's method assumes and tests incrementalism as an all-or-nothing proposition.
They select an ad hoc break-point and test whether the regression coefficient estimates pertaining to the
period before and after the break-point are equal. They then infer whether or not the coefficients are
stable (unchanged over time) and the budgetary process is incremental for the entire sample period.
7
Because of organizational restructuring, the number of agencies considered here is smaller than the 116 included
in the DDW studies.
8 See, Hamilton (1994), chs. 19 and 20, for details on regression with nonstationary series.
9 Another weakness of DDW's method, which seems less serious in comparison to the stationarity problem, is its
reliance on the multiple correlation coefficient, R2, as the criterion for validating regression models. The next
section addresses this problem.
3
This method obviously cannot identify cases where an incremental period follows (or precedes) a
nonincremental period.10 Indeed, even if one correctly prespecifies the break-point, a significant
statistic merely implies the presence of two stable subperiods separated by a break-point. This finding
is more an evidence “for,” rather than “against,” incrementalism because such a result suggests stability
over the two subperiods.
We develop an alternative method for analyzing budgetary time series that remains valid when the
data are nonstationary and the relationships between various budgetary actors are temporally unstable.
We initially draw on the cross sectional dimension of budgetary data statistically to identify incremental
instances. We identify accordingly the incremental years for each agency and construct a time series of
counts estimating the number of agencies with incremental budgets. We then use these counts in a
Poisson regression to explore some economic and political variables that may affect the frequency with
which incremental (or nonincremental) outcomes occur. We do not test for incrementalism as an all-ornothing proposition. Instead, we estimate the extent of incrementalism in the U.S. budgetary process
and examine factors that contribute to it. Our approach has two dimensions, one descriptive and the
other explanatory. The descriptive part of our study involves testing for nonstationarity, estimating
incremental instances, and constructing the time series of counts. The explanatory part includes the
Poisson regression analysis that explores factors that may affect the extent of incrementalism. Our
approach more generally provides a statistical framework for testing various propositions about
budgetary incrementalism.
Section 2 describes the DDW procedure and its variants and discusses its shortcomings. Section 3
presents results of nonstationarity tests applied to the budget time series and examines issues related to
testing for temporal stability in the budgetary process. Section 4 describes our method for identifying
incremental periods and presents time series of incremental counts for all sampled agencies. Section 5
reports and discusses the Poisson regression results that examine the relationship between our measure
10
The nonstationarity tests that we apply to budget data can pick up nonstationarity arising from temporal
instability as well. Our results suggest that such switches are quite common.
4
of incrementalism and various economic and political variables. Section 6 provides a summary, some
concluding remarks, and qualifications to our results.
Readers familiar with the literature on incrementalism may wonder why revisit an old question that
remains unsettled. We choose to return to the issue not as a statistical exercise but in an attempt to
reverse the presumption that legislators use incremental budgeting strategies because they cannot do
otherwise in an era of complexity, uncertainty, and conflict. Legislative incrementalism, we believe,
grows out of a “decision about how to decide.” If we can measure its occurrence more accurately, then
we should be able to discuss the contours of this metadecision. This work thus may contribute to our
understanding of legislative choice.
2- Regression Based Tests for Budgetary Incrementalism
DDW (1966a; 1966b; 1971) specify six equations to characterize the U.S. budgetary process.
Three of these equations have distinct specifications and the rest are variants of these three. The three
main equations are:
yt = β1 xt + ηt ,
(1)
xt = β2 yt − 1 + ζ t ,
(2)
xt = α 0 x t − 1 + v t ,
(3)
and
where yt is the appropriation Congress passes for an agency for the fiscal year t, xt is the appropriation
OMB requested for that agency, α and β's are parameters, ηt, ζ t, and vt are serially independent
regression errors, each with a zero mean and a time-invariant normal distribution. Given the structure
of the budgetary process and growth of the budget, one expects these inequalities to hold: β1<1;β2> 1;
and α0> 1. The other three equations are variants of equations (1)-(3) obtained by assuming a serially
correlated regression error or by augmenting the equation by the difference between the previous year's
appropriation and request.
5
DDW estimate these equations for all nondefense agencies for which the appropriation time series
are available. They then choose the two equations that best describe the appropriation and request
processes using the multiple correlation coefficient, R2, or the adjusted R2, as their selection criterion.11
DDW also define temporal stability as the lack of structural change in a regression parameter, and they
use an F-statistic developed by Chow (1960) to test whether the slope coefficient of each regression
equation changes at a specific point in time. The Chow test requires that such a point be exactly
identified. DDW subjectively locate the "most likely" break-point to implement the test. They then
interpret an insignificant F-statistic, along with a high R2, as evidence that the budgetary process is
temporally stable. DDW's earlier work does not state the link between temporal stability and
incremental budgeting in precise terms. Dempster and Wildavsky (1979, p. 371) acknowledge this
omission and explicitly state the link: "Our hope … is to give new meaning to the concept of
incrementalism applied to budgetary processes. This new meaning is central to our previous work and
can be operationally linked to it in precise terms. By identifying 'incremental' with the regular
relationship between Congress and bureaus, as expressed in our equations, non-incremental becomes
equivalent to a shift in these relations." The absence of a structural shift in the best equation, therefore,
constitutes evidence for incremental budgeting. DDW report such evidence for many agencies.
Reflecting the state of statistics when they wrote, DDW’s work has several shortcomings. Other
scholars have noted or tried to rectify some of these. Some argue that the regression equations should
include other explanatory variables that represent economic, political, and social environments.12 Gist
(1974) criticizes the exclusion of a constant term in DDW's original regression equations, and he shows
that including this term changes DDW's findings in some cases--a point that DDW acknowledge in their
1971 study. Gist (1974) and Ripley and Franklin (1975) also observe that ignoring the trend in the data
might bias DDW's results. Gist detrends the series, assuming a deterministic trend, before estimating
11
Choosing between an equation with serially correlated errors and one with independent errors is on the basis of
the Durbin-Watson test for serial correlation.
12 Among these are DDW themselves (1974), Jackson (1972), Bozeman (1977), Kamlet and Mowery (1985), and
Kamlet, et al. (1988) who add macro variables to the original equations, and Moreland (1975) and Ripley, et al.
(1975) who add agency-specific variables.
6
DDW's regressions. As we demonstrate later, these series contain a stochastic rather than a
deterministic trend; therefore, this procedure does not resolve the nonstationarity problem. Ripley and
Franklin (1975) and Ripley, et al. (1975) use regression models with the ratio of the current year to the
previous year's policy measure (appropriations or expenditures) as the dependent variable and a lagged
value of this ratio along with measures of institutional change as regressors. Dividing each data point in
one nonstationary series by that in another, however, does not render the ratio stationary. Hence,
Ripley, et al.’s analysis is subject to the same criticism as is DDW's.
Several other studies report that alternative measures of budgets can reduce considerably the
instances of incremental budgeting. Examples include Natchez and Bupp (1973), who use program
budgets instead of aggregated agency budgets, and Wanat (1974), who distinguishes between
mandatory requests and programmatic requests. 13 These refinements marginally may improve DDW's
method. But they do not resolve its serious statistical problems, some of which remain unexplored.
The rest of this section and the next contain a detailed discussion of these problems in an ascending
order of importance.
The reliance of DDW's method on the multiple correlation coefficient, R2, as the criterion for
validating regression models, is a weakness, particularly because the data are time series.14 Indeed, a
regression of one trended variable on another will produce a high R2 even if the two are not closely
related. Banerjee, et al. (1993, p. 76-83), show that in small samples (such as those under study in this
research) ordinary least squares regressions involving two unrelated trended series would lead to an
incorrect rejection of the hypothesis of no relationship thirty percent of the time. The percentage
exceeds sixty in large samples. Such spurious correlation is not informative, and it does not signify the
13 Other studies that offer refinements include: Lane, et al. (1981) who use residual diagnostics through the
CUSUM test to examine parameter stability and reject it; Mowery, et al. (1980); Bozeman and Straussman (1982);
Fischer and Kamlet (1984); Auten, et al. (1984); and Kamlet and Mowery (1987), who suggest imposing a fiscal
(top-down) constraint on the budgetary figures. The CUSUM test applies to the null hypothesis of no parameter
shift against the alternative of one or more shifts. The test is not very informative if the null is rejected, because
rejection does not shed any light on the frequency or timing of the shift.
14 Notice that such now well known criticisms apply equally to the adjusted multiple correlation coefficient, R 2 ,
which sometimes appears in this literature.
7
presence of a strong or stable relationship between the regressors and the regressand.15 With very few
exceptions, all budgetary series exhibit growth over time, indicating the presence of a trend. DDW
(1971, p. 302) seem themselves to doubt the adequacy of R2 as a criterion for model validation.
Regarding the use of this measure, they note, "although we are not completely satisfied with our
methods, we do argue that they are the best currently available." Berry (1986, p. 625), in a similar vein,
notes that "analysts can obtain nonzero statistical coefficients even in the absence of meaningful
relationships among the concepts themselves, and it is imperative that analysts consider alternative
explanations for their statistical results.”
3- Nonstationarity of the Budgetary Time Series
Magnifying the correlation between two trended variables is the least of the problems arising from
nonstationarity. Depending on the kind of nonstationarity in the data, the consequences for inference
could be quite serious. We focus on the nonstationarity issue and its implications for regression-based
tests of incrementalism. A data series is nonstationary if its distributional characteristics, such as mean,
variance, or correlation between variates in the multivariate case, change over time. We focus on two
kinds of nonstationarity that are likely to be present in budgetary data: one grows out of a stochastic
trend and the other arises from a change in parameter(s) of the underlying model. For notational
convenience, and following the statistical convention, we refer to the first as “nonstationarity” and to
the second as parameter instability, or simply, “instability.” In the rest of this section, we first discuss
stochastic trends and test the budgetary series for this problem. Then we discuss problems arising from
changing parameters and explain how these problems may affect DDW's results.
Consider a series {Zt} with this representation:
Zt = µ + γ
t + ρZt − 1 + ut ,
(4)
15
See Kennedy (1994), ch. 5, for a discussion of the inadequacies of R2, and Granger and Newbold (1974) for a
discussion of spurious correlations in time series regressions. Also, notice that there are problems with searching
for the highest R2, or adjusted R2, in cross sectional models as well. Such a strategy may lead to the inclusion of
insignificant variable(s), and therefore loss of efficiency; see, e.g., Pesaran (1974) and Maddala (1992), ch. 4.
8
where t is time and ut is a stationary zero mean error process, which is either independently and
identically distributed (i.i.d.) or autoregressive. For example,
ut = φ1ut − 1 + φ2 ut − 2 + L+ φput − p + εt ,
(5)
where the εt 's have zero mean and are i.i.d. and the φ's are parameters with values that ensure the
stationarity of the ut process.16 Parameters µ,γ
, and ρ determine whether Zt is trend stationary
(stationary around a deterministic trend) or nonstationary because of a stochastic trend. Zt is stationary
around a deterministic trend if | ρ |
< 1 and γ≠ 0. Zt contains a stochastic trend if ρ = 1, γ= 0, and µ ≠
0.17 The case Zt with a stochastic trend is sometimes referred to as an autoregression with a unit root
or a random walk with drift, where µ is the drift parameter.18
These null and alternative hypotheses formalize the preceding distinction:
H0: ρ = 1, γ= 0 and µ ≠ 0
Ha: | ρ |
< 1 and γ≠ 0.
Dickey and Fuller (1979; 1981) develop a test of the unit root hypothesis against Ha in the case of i.i.d.
errors. Said and Dickey (1984) extend the test to the case where the error terms follow equation (5);
the resulting test is known as the augmented Dickey-Fuller test.19 Both tests have the same asymptotic
distribution, and test statistics in either case are similar to the F-statistic for testing the preceding
restrictions.
To examine whether the budget data are nonstationary, we apply both the Dickey-Fuller and the
augmented Dickey-Fuller tests to the budgetary time series. Our sample includes most of the
nondefense agencies in the DDW studies but brought to 1994. DDW’s data set includes 116 agencies,
but ours includes the 103 agencies listed in Table 1.20 The discrepancy is the result of either
16
See, e.g., Hamilton (1994), p. 58.
Notice that Zt is still nonstationary, indeed explosive, if ρ > 1. Also, it is possible for a nonstationary series to
contain both stochastic and deterministic trends (e.g., ρ =1 and γ≠ 0). Our analysis equally applies to both cases,
which are detectable by the nonstationarity tests that we use here.
18 “Unit root” means that the root of the first degree polynomial in the lag operator for the nonstationary process is
unity. For example, we may write the nonstationary series as yt− yt-1 = µ+ut , or (1-L)yt = µ+u , where L is the lag
operator and 1-L is the polynomial in the lag operator.
19 Prior to the advent of these tests, visual inspection of the correlogram— the graph of the autocorrelation function
at various lags--was the common method for distinguishing between stationary and nonstationary series.
20 Similar to DDW (1971), we include supplemental appropriations in our measure of total appropriations.
17
9
institutional changes in the agencies— mergers, for example--or omission of data subcategories in the
source book (the Budget of the United States for fiscal years 1946-1996).21
Our sampling period for the requests series is 1946 through 1996; for appropriations and outlays it
is 1946 through 1994.22 The sampling period is shorter for 10 of the 103 agencies, because recent
observations are not available for them. For these ten agencies we apply the analysis of this section to
the portion of the data that remain available. We change the nominal series into real (inflation adjusted)
data using the Consumer price Index (CPI).23 Table 1 reports the Dickey-Fuller statistic, the
augmented Dickey-Fuller statistic with three autoregressive lags, and the corresponding five percent
critical values for all agencies and budget categories.24 In cases where the test statistic is smaller than
the corresponding critical value, we can reject the null hypothesis of nonstationarity in favor of the
alternative, that the series are stationary around a deterministic trend. Either a "*" or a "**" identifies
these cases, depending on whether we reject the null at the five percent or one percent significance
level. Using the augmented Dickey-Fuller test, we reject the null at the one percent level for only seven
series, and at the five percent level, for only sixteen series, out of a total of 309 series. The numbers of
such cases when we use the Dickey-Fuller test are forty and 58, respectively.25 The augmented test
results are usually more reliable, because overparameterizing (including extra autoregressive terms)
21
Our data set, however, includes actual outlays in addition to the agency requests and appropriations that DDW
use. We believe that outlays better measure an agency's capacity to spend than do appropriations, because
appropriations may be given for a period that extends over more than one year and thus do not accurately reflect
the promise of annual budget allocations. Given an occasional increasing concern about the total deficit, and
consequently spending, over time, the OMB might be tempted to increase agency appropriations in exchange for
agency acquiescence on lower levels of outlays. See, e.g., Mowery, et al. (1980).
22 Like DDW, we do not include the period before 1946 because of the effect WWII had on decreasing non-defense
agency budgets as a share of the total budget, to allow increased funding to defense functions. DDW use data on
agency requests (as indicated by the figures in the president’s budget) and agency appropriations.
23 All budget series are from the Budget of the United States for fiscal years 1946-1996. CPI data for 1946-1960
are from Historical Statistics of the U.S: Colonial Times to 1970, and CPI data for 1960-1996 are from Statistical
Abstract of the U.S.
24 We also use the augmented Dickey-Fuller test with six autoregressive lags as well as other formulations of the
Dickey-Fuller test that focus on a single parameter, e.g. ρ. Results are remarkably similar to those in Table 1. We
do not report these results for brevity, but they are available upon request.
25 The only budget item that is stationary, based on both tests and across all three categories, is the Emergency
Fund for the President. Appropriations, requests, and outlays for this item have changed very little over time.
Their lack of variation perhaps contributes to the series being identified as stationary. Budget items pertaining to
the Maritime Administration, the Agricultural Conservation Program, and the Bureau of the Census are the other
stationary series with very little variation.
10
affects the standard errors of the estimates, while underparameterizing renders the parameter estimates
biased in addition to affecting the standard errors. The results in Table 1 suggest that the majority of
the budgetary series (appropriations, requests, and outlays) are nonstationary--or, in other words, they
have a stochastic trend.
One implication of the observed nonstationarity is the change in variance of the autoregressive
process. Notice that under the null hypothesis of nonstationarity, the variance of the process changes
with time. This variance partly parameterizes what DDW (1966b) call “special circumstances.’ These
are factors that may affect the decision making process, but they are not known to the researcher
modeling this process. Hence, they are represented by a stochastic error term. Changes in special
circumstances can contribute to changes in variance. Another implication of the nonstationarity is that
the coefficient of the autoregressive process that generates the budgetary series may change over time.
We refer to this phenomenon as parameter (coefficient) instability. The nonstationarity tests that we
use here are known to pick up cases with unstable parameters. These test are also better than the Chow
test, which DDW use, in ascertaining whether the parameters change during the sample period.
DDW use the Chow (1960) test to examine whether the budgetary process, characterized by
equations (1)-(3) and their variants, is temporally stable. This regression based test and its extensions
apply to the null hypothesis, that regression coefficients do not change over the sample, and to the
alternative hypothesis that they do change at a pre-specified point. The Chow test involves partitioning
each series according to a pre-specified break-point, estimating two sets of coefficients, and using an Ftest to examine whether the two sets of estimates are statistically equal. DDW interpret an insignificant
test statistic as evidence of no structural change in parameters. This finding, in turn, implies temporal
stability, which indicates the presence of incrementalism.
The Chow test has several limitations as used in this literature. First, the distributional
characteristics of the test under the null hypothesis relate to stationary cases. The nonstationarity of the
regressors and the regressand in DDW's models, therefore, casts doubt on the validity of the test.
Second, the test is predicated on estimates from dynamic models that are justified only asymptotically
and, thus, require each of the two subsamples to be large. Given the annual frequency of the data and
11
that the starting observation postdates WWII, neither DDW's sample nor ours meets such a size
requirement. Third, the test requires a correct identification of a break-point in the sample. If one
incorrectly specifies the break-point, then the two sets of estimates are biased and the test is invalid.
Given the ad hoc manner in which DDW and other authors choose break-points, the test appears not to
be valid. Fourth, and most important, even if there is a single break-point and one correctly identifies it,
the test's rejection of the null hypothesis of stability implies the presence of two stable subperiods
disjointed by a break-point. This finding does not constitute evidence against incrementalism. Finally,
the test is not applicable in cases where an incremental period follows (or is followed by) a
nonincremental period. Such a switching case, however, is a possibility that DDW themselves
acknowledge is very likely.
Using the Chow test to detect incrementalism, in sum, is statistically unfounded. The alternative
method that we propose in the next two sections is designed to serve three purposes: to allow an
analysis of non-stationary budget data series; to provide a way to detect nonincremental outcomes
without relying on R2 or subjectively chosen break-points; and to accommodate testing various
hypotheses about incremental budgeting.
4- A New Approach for Estimating Incremental Budgeting
The concept of incrementalism in the budgetary process has various meanings, each appropriate to
a different scholarly concern. Berry (1990) identifies twelve distinct meanings of incrementalism, some
used in descriptive and others in explanatory contexts. Confirming or refuting the presence of
incrementalism in each case may depend on the meaning invoked. Following DDW, we identify
incrementalism with regularity in the annual change in a budget category and closeness to existing
levels (see, e.g., Dempster and Wildavsky (1979). This meaning of incrementalism is compatible with
six of the meanings that Berry (1990) lists: lack of attention to the base26; smallness of the ultimate
26
“Lack of attention to the base” means, for example, that zero-base budgeting is not under consideration. The
base, outlays in year t become like an entitlement. The legislature only decides how much to increase outlays in
year t+1.
12
change; simple decision rules; regularity of the relationships; restricting the number of alternatives; and
the restriction to noninnovative alternatives. The first three meanings are the most common, among
which lack of attention to the base is the initial definition of incrementalism in public budgeting that
emerges from Wildavsky (1964) and DDW (1966a; 1966b). Smallness of the ultimate change focuses
on the result of the process. Wildavsky (1964) and Sharkansky (1968) are the first to introduce this
meaning, which Wanat (1978) suitably terms "descriptive incrementalism." "Simple decision rule" is a
meaning often used interchangeably with phrases such as "aids to calculation," "standard operating
procedure," and "rule of thumb." The last two meanings, which define incrementalism in relation to
relevant alternatives, follow from Lindblom (1959) and Braybrooke and Lindblom (1963).
Our statistical procedure focuses on regularity in the budgetary process and closeness to existing
levels. The procedure accommodates the notion that the budgetary process for a particular agency may
be incremental for one period of time but nonincremental for another, and each period may be long or
short, depending on political and economic circumstances. Contrary to this notion, DDW's method and
its variants test incrementalism as an all or nothing proposition; they use "temporal stability over the
entire sample" as the null hypothesis and "two stable periods separated by a break-point" as the
alternative.27 We believe that a scheme containing cycles of change (from incremental to
nonincremental and vice versa) better characterizes the budgetary process. We estimate the cycles of
change for each agency in two steps, one examining the closeness of the budget choice to the existing
level and the other examining the regularity of such close instances.
More specifically, in our first step we exploit the cross sectional dimension of the data to infer
whether the budget of an agency is statistically close to the previous level. We make this inference on a
statistical basis, where we evaluate each agency's annual rate of budget change (in real terms) in
comparison to rates for other agencies. When testing for incrementalism, some authors select an
arbitrary cut off percentage point to identify small incremental changes in agency budgets.28 An
27
Although none of the studies in this area explicitly state the alternative hypothesis, the statement is quite clear
given the way they formulate the test for parameter stability.
28 Fenno (1966), for example, uses both ±10 percent and ±20 percent, while Kemp (1982) uses a ±10 percent
annual change in appropriations as a cut off point; Sharkansky (1968) refers to ±10 percent, and Kanter (1972), to
13
arbitrarily predetermined and time invariant cut off point, to distinguish between the incremental and the
nonincremental, is inappropriate and misleading. It may result in identifying a change as small without
considering either similar changes in the budgets of other agencies or cross agency variations in such
changes for particular time periods. Changes in fiscal considerations and special circumstances,
moreover, may affect how legislators appropriate budgets over time.29 These possibilities make a time
invariant cut off point even more inappropriate, because when comparing the annual budget changes
among agencies, a given percentage change deemed small in one year may be considered large in
another, and vice versa.
To avoid such problems, we construct a statistical band that uses the annual variation in budget
change (in real terms) across agencies, to identify small percentage changes. The size of the band varies
from year to year as the cross-agency variance of the annual change in the budget varies over time. It
contains zero but is not symmetric around it. Formally stated, the band is
(−
c′
σ∃t , + cσ∃t ) ,
(6)
$t is the cross-agency standard deviation of the annual percentage change in budget, t is time, and
where σ
c and c' are the critical values from the standardized distribution of the annual budget changes. We
obtain this distribution by pooling the annual rate of change in the budget choice (in real terms) for all
agencies and all years together; we standardize the rates by subtracting from the median and dividing by
the standard deviation of the pooled rates; we then tabulate the resulting frequency distribution.30
We use four pairs of critical values to make it possible to check our results for robustness to
different specifications of the statistical band. The first pair consists of the forty percentile point above
zero and the forty percentile point below zero, leaving ten percent mass in each tail. Notice that because
±5 percent as the potential range for incremental changes; Gist (1974) uses 0 percent to +20 percent; Baily and
O'Connor (1975) use 0 percent to +10 percent to define incrementalism; Wanat (1974) considers a 10 percent
increase as the appropriate limit.
29 As DDW (1966a; 1966b) point out, special circumstances, such as a new president occupying the White House,
some agencies acting with special zeal, changing priorities, and so forth affect budgetary allocations. Such effects,
however, may not be uniform across all agencies.
30 We use the median rather than the mean to standardize the distributions because the distributions are skewed to
the right as the rate of decrease is limited to 100 percent while rate of increase may exceed 100 percent. The shape
of the distributions also make it impossible to use convenient critical values from a standard normal distribution.
14
the distribution is not symmetric, the two percentiles are not equidistance from the center of the
standardized distribution, which is zero. The second pair of critical values includes the 45 percentile
point above zero and the 45 percentile point below zero, leaving five percent mass in each tail.
The
third and fourth pairs are similar to the first and second, respectively, except that they include zero
instead of the lower percentile point, so that the resulting bands count only budget increases as possible
nonincremental events. In choosing forty and 45 percentile points, we follow the statistical convention
of allowing the one tail significance level to be either ten percent or five percent. We include the last
two measures in response to the argument that incrementalism should only characterize situations where
an agency’s budget increases.31 We refer to the bands based on the forty percentile points as “the small
bands” and those based on the 45 percentile points as “the large bands.” We use the terms “positive”
and “two-sided” to indicate whether a band contains only positive or positive as well as negative
changes.
$t changes. But in any given year, the
Notice that each of these bands changes from year to year as σ
band is the same for all agencies regardless of their size. Small agencies, however, may experience
exceptionally large growth rates, particularly soon after their inception. We adjust the band to allow for
heterogeneity of the variance of the budget change across various size agencies. We first divide the
sample into three sets according to agency size in each year. Then, we construct three different bands
for the three different sizes, using the three different sample variances and three different pairs of critical
values. Critical values come from the three frequency distributions, each corresponding to one size.
Figure 1 presents these three distributions, which appear to have different shapes, both in terms of the
range and curvature. The distribution of annual real growth rate of outlays for medium size agencies
appear to be more condensed (less dispersed) than those for the smaller or the larger size agencies. The
center of all three distributions seem to be between 0 and .1 percent.
As we note earlier, we use outlays (in real terms) as the budgetary choice. Tables 2 and 3 contain
results of this counting procedure on real outlays applied to the 93 agencies for which data for the
31
See, e.g., Wanat (1974; 1978); Gist (1977); Bunce and Echols (1978); Lauth (1980); and Kamlet and Mowery
(1980).
15
entire period 1946-1994 are available. A “zero” in a cell (Table 2) indicates that the percentage change
pertaining to that cell (a particular agency in a given year) falls inside the band for that size agency. So,
the annual change in outlays for that agency is statistically small, incremental, in that year. Table 2
presents the results based on the small positive band and Table 3 contains the results based on the large
two-sided band.32
Using a small positive band to measure incremental outcomes (Table 2), total deviations from
incrementalism in a given year range from 37 (for 1950) to 83 (for 1964). Also, the total number of
deviations from an incremental outcome for each agency over time ranges from nineteen to 47. Using a
large two-sided band to measure incremental outcomes (Table 3), total deviations from incrementalism
range from twelve (in 1950) to 64 (in both 1962 and 1992). The number of deviations for specific
agencies over time ranges from two to 43.
Our second step involves using the time series dimension of the data to identify cases where small
budgetary changes are repeated with regularity. A departure from a maintained pattern of small
changes suggests nonincremental budgeting. To operationalize this concept of incrementalism, we also
must define how long a sequence of small changes must persist before we can classify budget outcomes
as incremental. We use a four year period as the minimum length because it matches the duration of an
administrative term. To identify the incremental periods for each agency, we use the row
corresponding to that agency in Table 2 or Table 3. We classify a year as an incremental year for an
agency if it places in a chain of at least three other adjacent years with statistically small changes
(marked by zeros). This technique allows us to estimate incremental cycles, each consisting of several
incremental years following (or followed by) several nonincremental years.33 Tables 4 and 5 report the
results. Table 4 draws on Table 2, which is based on the small positive band. Table 5 draws on Table 3
and the larger two-sided band, so it reflects more incremental cases. Strings of I's indicate incremental
32
The number of zeros for each of the two bands not reported here fall between those in Tables 2 and 3.
Instead of discarding the first and the last few observations to accommodate four year cycles, we use a window
of two years for the first (1946-47) and the last two years (1993-94). So, two zeros in the first two years means two
incremental years, and the same is true for the last two years. This treatment seems reasonable, particularly
because the first and the last two sample years are each a part of an administrative term for which we do not have
four years of data.
33
16
cases. Notice that the estimates of the incremental cases based on the other two bands, which we do
not report here, fall between the ones reported.
Table 5 as compared with Table 4 shows a larger number of agencies experiencing incremental
budgeting because of a broader band of incremental outcomes. These tables suggest two general
conclusions. First, the total number of incremental budgeting decisions varies widely among agencies.
Second, in the mid-sample years there are fewer instances of incremental budgeting. This pattern is
clearer in Table 4, which uses a narrower band to identify incremental outcomes. In the next section we
explore the determinants of such patterns and examine factors that contribute to incremental budgeting.
5- Poisson Regression for Modeling Incrementalism
The classification in section 4 reflects a definition of incrementalism that involves closeness of the
budget to existing levels and regularity in annual changes. This statistical classification, like many
others in this area, is descriptive. Here we offer an explanatory analysis to ascertain how economic and
political variables affect the frequency with which incremental outcomes occur. We use estimates of
incremental cycles to construct a measure of departure from incrementalism in the budgetary process.
We do this by summing the number of nonincremental outcomes of all agencies in each year, and
repeating this for every year. The resulting variable, Dt, represents the number of sampled agencies in a
given year whose budgets deviate from an incremental path. By constructing Dt based on cross
sectional inference, we avoid the statistical problems mentioned earlier. We compute this measure
using Table 4, Table 5, and the results based on the other two bands that we do not report here.
We base our inference on a regression of the dependent variable Dt on a set of plausible
explanatory variables, Xt. Because the dependent variable is integer valued, least squares analysis
would be inappropriate: the resulting estimates would be inefficient; standard errors would be
inconsistent; and thus hypothesis testing would be invalid (see, e.g., King 1989; Hausman, et al. 1984).
One appropriate alternative is the Poisson regression model, which is an extension of the simple Poisson
probability model. The specification of this model in the present context is
17
e − λt ( X t ) ( λt ( X t ))
dt
Pr( Dt = d t ) =
dt !
,
dt=0,1, .... ,
t=1,2, .... T,
(7)
where λt(.) is finite and positive and Xt is a set of explanatory variables.34 These variables are
sometimes referred to as covariates. We wish to estimate E(DtXt) = λt(Xt), which is the moment
conditional on the explanatory variables. Following statistical convention, we assume that λt(.) is loglinearly dependent on the model’s explanatory variables. The regression equation is, therefore,
ln E ( Dt X t ) = βX t ,
(8)
where β is a vector of regression coefficients.
We use several political and economic variables as regressors. Because the budget is decided a
year in advance, we lag all explanatory variables by one period. Political variables include a party
variable (DEMOCRATS) that takes a value of three if the Democrats have control of the White House,
Senate, and the House of Representatives; the variable takes values of two, one, or zero if Democrats
control two, one, or none of these three institutions.35 Because Democrats perceive a more active role
for the government than do Republicans, we expect this variable to be positively related to the number
of nonincremental outcomes.36 We include two other political variables that reflect a switch in political
control, each taking values of 1 for a switch and 0 otherwise. One variable (CONG-SWITCH)
indicates if the congressional majority party changes and the other (PRES-SWITCH) indicates if the
White House changes hands (from one party to another). Ripley and Franklin (1975) argue that the
Democrats seem particularly to favor some agencies while the Republicans favor others. One then
would expect a switch in the political party in charge to reduce incremental decisions, as the switch
leads to a reallocation of resources, which in turn disturbs the regularity of the budget change for some
agencies. Finally, we include a presidential election year (ELECTION YEAR) dummy (binary) variable
34
The Poisson model imposes the restriction that the conditional mean and variance of the count variable are
equal. King (1989) and Cameron and Trivedi (1990) explain that the model is inappropriate if the data exhibits
overdispersion--variance exceeding the mean. In such cases one should use the negative binomial model or other
mixture models, as discussed in King (1989) and Gurmu and Trivedi (1994). We apply a test proposed by
Cameron and Trivedi, and the results suggest no overdispersion in our data. So, we proceed with the Poisson
model.
35 Separating out political control of each institution by the use of distinct dummy variables does not materially
affect our results.
36 This explanation might change if our analysis included budgets for agencies related to national defense.
18
that takes a value of one in presidential election years and zero otherwise. This variable captures the
effects of election year promises and political vulnerabilities on the budgeting process; we expect it to
have a positive effect on the frequency of nonincremental outcomes. This reasoning accords with most
of the political business cycle literature. See, e.g., Mueller (1989), p. 277-306.
The regressors also include five economic variables: inflation rate (INFL-RATE); discount rate
(DISC-RATE); the rate of growth of government revenue (REV-GROWTH); the budget deficit
(DEFICIT); and a measure of the attitude toward the budget deficit (DEFICIT-DUMMY). We expect
increases in the growth rate in government revenue to have a negative effect on the frequency of
deviations from an incremental path, because high growth of revenues makes it easier for politicians to
build a high common increase in the base expenditure; so legislators can maintain their previously made
promises even if they wish to budget more expansively in a few cases. Increases in inflation would have a
similar effect on nonincremental outcomes. We have no intuitive explanation for the effect of inflation on
instances of incrementalism other than the possibility that a high inflation rate both increases uncertainty
and reduces the real discount rate. The (nominal) discount rate affects the present value of any expected
payoffs from political (legislative) commitments. A higher discount rate, therefore, reduces the appeal of
longer term commitments in favor of single-period budgeting. Single-period budgeting, in turn, increases
the frequency of nonincremental outcomes. We expect the corresponding coefficient, therefore, to have a
positive sign.
The deficit should have a constraining effect on government expenditure, making it costly for the
legislators to keep their promises. The frequency of nonincremental outcomes would decline, therefore,
leading to a negative coefficient on the variable DEFICIT. The adverse effect of budget deficit,
however, may be constraining only when voters and their representatives view the deficit as a problem.
Before the 1980s the deficit was not large as a share of the budget, and budgeters tended to ignore it.
During the 1980s the deficit grew larger and gradually became an issue of public concern. To account
for this asymmetric effect, we use an interactive dummy variable consisting of deficit multiplied by a
binary variable taking a value of 1 if the share of the deficit in the total budget is greater than ten
19
percent for two consecutive years, and 0 otherwise.37 The justification for creating this dummy variable
is that budgeters' attitudes toward the deficit change over the sample period. We expect this variable to
have a positive effect on the occurrence of nonincremental cases, therefore, because increased public
concern over the deficit makes it more difficult for politicians to keep previous promises of perpetual
budget funds.
We estimate four versions of equation (8), each with one of the four measures of nonincremental
cases. The four dependent variables are D1t which is a measure of nonincremental cases estimated using
the positive small band. D2t, D3t, and D4t are similar measures, but they correspond to the small twosided band, the large positive band, and the large two-sided band, respectively. The method of estimation
is maximum likelihood (ML). Table 6 reports the results.
Estimates of the coefficient for DEMOCRATS are positive and highly significant in all case,
suggesting that an increase in the Democrats’control over the political process leads to more deviations
from an incremental path (more nonincremental outcomes). This result is not surprising considering
how Democrats tend to view governmental nondefense responsibilities. The other three political
variables, PRES-SWITCH, CONG-SWITCH, and election year dummy, all have coefficient estimates
that are positive, as expected, and statistically significant. These estimates suggest that a switch in the
party that has control over the Congress or Presidency all contribute to nonincremental budgeting and
increase the number of agencies whose budgets deviate from an incremental path in the following year.
Among the economic variables, three have the expected signs and are significant in all four
regression equations. These are the inflation rate (negative), discount rate (positive), and the interactive
deficit dummy (positive). This positive estimate of the coefficient of the deficit dummy reflects the
public pressure on the government to reduce the deficit when it is large in consecutive periods.
Responding to such pressure leads to a reassessment of budgetary promises and a consequent increase
in the number of nonincremental cases. The deficit itself does not have such an effect when we use it to
estimate the relationship over the entire period. One reason could be lack of public interest in the
37
The dummy equals one for the years 1972, 1976, 1977, 1978, and 1981-1994.
20
deficit issue for a good portion of the sample period. In the absence of public pressure, the deficit trend
can reduce budgetary discipline and lead to more nonincremental behavior. When deficit spending is
used to stimulate the economy, its effect on budgeting decisions would be similar to the effect of real
revenue growth. The estimated coefficient of revenue growth is negative as expected only in one case,
D4t, which allows a broader definition of marginal (small) outcomes, and positive in the other three.
These estimates are statistically insignificant however.
The insignificant coefficients may be the result of our inability to separate the sample period into
two different subperiods. In the earlier period, revenues, their growth, or the size of the deficit did not
place a binding constraint on budget expansion because politicians relied on deficit financing without
facing any political opposition. In the later period, deficit financing generated political opposition as a
result of an increase in the deficit.
The remarkable similarity of the coefficient signs and significance levels for the four measures of
nonincremental outcomes suggests that these results are highly robust to the choice of the statistical
band used to identify incremental budgeting. The results are also largely consistent with our hypotheses
about the frequency of incremental choice. Incremental choice, it follows, is not a constant feature of
budgetary politics. Legislators, by contrast, sometimes decide incrementally and sometimes
nonincrementally, over nearly all agencies and for any particular agency. Hence, the metadecision to
decide incrementally or to decide nonincrementally is itself a matter of choice.
6- Summary and Conclusion
We present evidence here that suggests that the U.S. budgetary data are nonstationary--they
contain a stochastic rather than a deterministic trend. This finding implies that the least squares
regressions and autoregressions used previously to examine incrementalism in the budgetary process are
inappropriate, and their results may be suspect. DDW introduce these widely used regression models in
their pioneering work (1966a; 1966b; 1971). This regression based method has several other
shortcomings, the most notable being its inability to identify cases where the budgetary process may be
incremental for a period of time and then become non-incremental, or vice versa. This is a relevant
21
possibility that DDW acknowledge. Moreover, the method requires choosing a break-point to test if
model estimates are the same before and after this point. Even if one correctly chooses this breakpoint, however, the test merely can detect the presence of two stable periods that are separated by a
break-point. This finding would provide more evidence for, rather than against, incrementalism over
the two sub-periods.
We offer an alternative method for identifying incrementalism in the budgetary process. This
method is valid even if the data are nonstationary; it provides estimates of incremental cycles for each
agency; and it offers a framework for testing hypotheses about incremental budgeting. The method
includes three distinct steps, the first two involving descriptive analysis and the last one explanatory.
The first step builds on cross agency variations in budgetary changes to identify statistically cases with a
marginal outcome. The second step examines the regularity of such outcomes, to identify incremental
cycles. These estimates provide a time series measure of the pervasiveness of incremental outcomes in
terms of agency counts. The third step involves a Poisson regression of the constructed series of
nonincremental counts to ascertain how economic and political variables may affect the extent of
incrementalism or nonincrementalism in the budgetary process.
We apply this method to U.S. budgetary data for 1946 through 1994, including 93 of the agencies
in DDW's original sample. We identify cases with a statistically small budgetary change, estimate
incremental cycles for these agencies, and examine the political and economic determinants of these
cycles. The political variables include measures of the extent of Democrats' administrative and
legislative control, switch in the party occupying the White House or controlling each house in
Congress, a presidential election year dummy that captures the effects of election year promises and
electoral vulnerability on the budgeting process. The economic variables include the inflation rate, the
discount rate, the rate of growth of government revenue, the budget deficit, and a measure of the
attitude toward the budget deficit.
Our results suggest that the extent of the Democrats’control over the political process, a switch in
the party controlling the White House or one or both houses of Congress, and the presence of an
election year all cause departures from incremental budgeting. This analysis also indicates that the
22
Democrats pursue a more active nondefense role for the government than do Republicans. Because
Democrats seem particularly to favor some agencies, moreover, while Republicans favor others, the
observed effect accords well with the theory that the switch leads to an increased nonincremental
reallocation of resources, which disturbs the regularity of the budget change for some agencies.
Political business cycle theories also point to an effect of the election year on the budgeting process.
Among economic variables, three have the expected signs and are significant under all
specifications of incrementalism. These are the inflation rate (positive), the discount rate (negative),
and the interactive deficit dummy, which captures the effect of public pressure resulting from a
persistently large deficit (positive). We expect inflation to have a negative effect on the frequency of
deviations from an incremental path, because a high inflation rate makes the real discount rate smaller.
A lower (nominal) discount rate, or a higher inflation rate, reduces the appeal of a longer term
commitment in favor of single period budgeting, thereby increasing the frequency of nonincremental
outcomes.38 Finally, the positive estimate of the coefficient of the deficit dummy indicates that political
pressure arising from persistently large deficits leads to a reassessment of budgetary promises and a
subsequent increase in the number of nonincremental cases. Consistency of these results with our prior
expectations about the budgetary process reflects the statistical effectiveness of our method.
We used four measures of nonincremental counts and find a remarkable similarity between the
coefficient signs and significance levels for all four measures. This similarity indicates that the results
are highly robust to the choice of the statistical band used to estimate the incremental periods.
38
Such promises may offer agency funds in perpetuity. The only budgetary choices would be responses to inflation
and changing factor costs, to keep service levels constant. These two considerations doubtless make up most of the
incrementalism in incremental budgeting.
23
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Wildavsky Aaron D. 1964. The Politics of the Budgetary Process. 1st ed. Boston: Little, Brown.
27
Table 1: Unit Root Test Results for Budgetary Data
Department or Agency
Agriculture
Agricultural Research Service
Extension Service
Soil Conservation Service
Commodity Stabilization Service
Agricultural Conservation Program
Agricultural Marketing Service
Foreign Agricultural Service
Commodity Exchange Authority
Rural Electrification Administration
Farmer's Home Administration
Federal Crop Insurance Corp.
Forest Service
Commerce
B of Census+ Offic. of Bus. Econ.
Environmental. Science Serv. Adm.
Domest. & Int'l Bus.
Patent Office
National Bureau of Standards
Maritime admin.
Bureau of Public Roads
Health
Public Health Service
Social Security Admin.
Food and Drug admin.
Office of Education
Office of Vocational Rehabilitation
Allergy Infectious Disease Actv.
Arthritis and Metabolic Disease Act.
General Research and Services
National Cancer Institute
National Heart Institute
National Institute of Dental Research
Neurology and Blindness Actv.
Mental Health Activities
Independent
Civil Aeron. Admin/FAA
Civil Aeronautics Board
National Labor Relations Board
Army Corps of Engineers
Nat'l Adv Com. for Aeron./ NASA
American Battle Monuments Com.
AEC/ Nuc. Reg. Com.
Civil Service Com.
Nat’l Capital Planning Com.
Federal Communication Com.
Federal Power Com.
Federal Trade Com.
General Accounting Office
General Services Admin.
Housing and Home Finance Agn.
Indian Claims Com.
Nat’l Capital Housing Authority
Tax Court of U.S.
Nat’l Science Foundation
Renegotiation Board
Interstate Commerce Com.
Securities and Exchange Com.
Selective Service System
Tariff Com.
Dickey-Fuller Statistic
(5% critical Value)
Appropriations
Requests
Outlays
(1946-1994)
(1946-1996)
(1946-1994)
Augmented Dickey-Fuller Statistic
(5% critical Value)
Appropriations
Requests
Outlays
(1946-1994)
(1946-1996)
(1946-1994)
-1.30
-1.91
-2.38
-2.86
-5.8**
-2.76
-5.4**
1.29
-4.02*
-3.01
-2.75
-1.89
(-3.50)
(-3.50)
(-3.50)
(-3.52)
(-3.50)
(-3.50)
(-3.50)
(-3.58)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-1.19
-2.50
-3.25
-3.01
-5.4**
-4.3**
-6.2**
0.68
-5.9**
-2.15
-0.80
-1.75
(-3.50)
(-3.50)
(-3.50)
(-3.52)
(-3.50)
(-3.50)
(-3.50)
(-3.58)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-0.86
-1.71
-3.78*
0.44
-6.3**
-1.97
5.83
-0.89
-5.9**
-2.76
-1.85
-1.97
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.57)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-1.14
-2.22
-0.68
-2.32
-3.99*
-2.46
-3.29
1.94
-3.03
-2.51
-2.35
-1.56
(-3.51)
(-3.51)
(-3.51)
(-3.53)
(-3.51)
(-3.51)
(-3.51)
(-3.60)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
-0.85
-2.52
-0.23
-1.66
-3.22
-2.48
-3.49
2.44
-2.17
-2.77
-1.22
-3.06
(-3.50)
(-3.50)
(-3.50)
(-3.53)
(-3.50)
(-3.50)
(-3.50)
(-3.61)
(-3.50)
(-3.51)
(-3.51)
(-3.50)
-0.93
-1.98
-1.08
3.38
-3.14
-2.53
2.22
-1.87
-2.75
-2.05
-0.84
-2.23
(-3.51)
(-3.51)
(-3.51)
(-3.52)
(-3.51)
(-3.51)
(-3.51)
(-3.59)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
-4.4**
0.18
-1.84
-4.05*
6.10
-5.3**
-4.12*
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-4.45**
0.02
-0.57
-5.1**
3.81
-7.2**
-3.54*
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-4.8**
0.24
0.52
-3.45
-4.14*
-7.6**
-2.70
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-3.71*
0.26
-2.11
-1.82
2.28
-3.73*
-2.83
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
-3.38
0.95
-0.92
-2.63
0.98
-3.58*
-2.31
(-3.50)
(-3.50)
(-3.51)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
-3.45
0.59
0.34
-11.6**
-1.60
-3.66*
-2.12
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
2.17
-3.08
2.14
-1.51
3.44
1.12
-1.36
-1.88
-0.74
-0.40
-0.05
-0.65
-2.27
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.65)
(-3.53)
(-3.52)
(-3.50)
(-3.50)
(-3.51)
(-3.51)
(-3.52)
(-3.50)
0.75
-1.83
0.55
-1.71
-0.91
-3.07
-2.16
-2.60
-1.98
-2.02
-1.73
-2.06
-2.48
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.64)
(-3.53)
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.51)
(-3.50)
-1.56
-2.59
1.08
-1.65
3.26
0.64
-0.72
-2.02
-0.36
-0.84
-1.79
-0.78
-1.46
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.65)
(-3.53)
(-3.52)
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.52)
(-3.50)
2.04
-2.46
0.95
-0.76
1.58
-0.34
-1.00
-2.51
-0.84
-0.26
1.23
-0.55
-2.02
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.71)
(-3.54)
(-3.53)
(-3.51)
(-3.51)
(-3.52)
(-3.52)
(-3.53)
(-3.51)
0.37
-1.69
0.88
-1.40
3.43
-2.29
-0.76
-2.07
-1.24
-1.14
-0.72
-1.15
-1.61
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.69)
(-3.54)
(-3.52)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.52)
(-3.51)
-0.61
-2.48
0.50
-0.46
1.74
-0.53
1.05
-2.15
-0.51
-0.49
0.28
-0.65
-1.70
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.71)
(-3.54)
(-3.53)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.53)
(-3.51)
-5.8**
-6.8**
-1.56
-4.9**
-0.93
-2.06
-3.85*
-1.18
-3.30
-2.24
3.90
-1.34
-1.04
-5.08*
-3.71*
(-3.50)
(-3.52)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.56)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
-5.6**
-1.93
-1.73
-2.53
-1.31
-1.48
-2.55
-1.34
-4.7**
-4.6**
1.96
-1.51
-1.37
-4.4**
-2.90
(-3.50)
(-3.52)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.55)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
-5.6**
-0.07
-1.32
-1.72
-0.71
0.05
-2.34
-1.12
-2.88
-2.19
1.35
-1.76
-0.62
-3.48*
-2.56
(-3.50)
(-3.52)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.56)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
-3.43
-0.98
-2.23
-2.68
-1.68
-0.07
-2.30
-1.68
-0.34
-1.82
1.53
-1.97
-0.16
-3.60*
-2.02
(-3.51)
(-3.53)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.58)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
-3.05
-1.73
-2.67
-2.22
-2.41
-1.08
-2.58
-1.79
-1.93
-1.87
-0.21
-1.66
-1.47
-2.28
-2.45
(-3.50)
(-3.53)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.57)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
-3.63*
-1.30
-2.01
-2.16
-1.69
-0.23
-2.40
-1.67
-1.10
-1.95
1.17
-2.05
-0.62
-2.80
-0.81
(-3.51)
(-3.53)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.58)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
1.03
-2.16
-2.48
2.65
-2.12
-3.09
-7.0**
-1.97
1.64
(-3.56)
(-3.64)
(-3.50)
(-3.51)
(-3.58)
(-3.50)
(-3.50)
(-3.50)
(-3.58)
-1.44 (-3.57) -0.76 (-3.54)
0.44 (-3.58)
0.52 (-3.59)
-4.33* (-3.64) -4.46* (-3.64) -3.49 (-3.69) -1.60 (-3.69)
-2.52 (-3.50) -0.88 (-3.50) -0.95 (-3.51) -1.01 (-3.50)
0.38 (-3.50)
1.89 (-3.51)
3.22 (-3.52)
0.94 (-3.51)
-2.02 (-3.58) -1.57 (-3.56) -2.39 (-3.61) -4.5** (-3.61)
-1.40 (-3.50) -3.54* (-3.50) -1.49 (-3.51) -2.34 (-3.50)
-0.72 (-3.50) -4.8** (-3.50) -3.65* (-3.51) -1.30 (-3.50)
-2.07 (-3.50) -1.63 (-3.50) -2.59 (-3.51) -3.41 (-3.50)
3.43 (-3.57)
0.67 (-3.58)
0.13 (-3.61)
0.47 (-3.59)
29
-2.35 (-3.55)
-7.8** (-3.69)
-1.02 (-3.51)
2.52 (-3.52)
-2.47 (-3.58)
-1.83 (-3.51)
0.07 (-3.51)
-2.83 (-3.51)
-0.02 (-3.61)
Table1: Continued
Department or Agency
Subversive Actv. Control Brd.
National Mediation Brd.
Federal Med. and Concil. Serv.
Tennessee Valley Authority
U.S. Information Agency
Veterans' Admin.
Smithoninan Institute
Interior
South Eastern Power Admin.
Bonneville Power Admin.
Bureau of Land Manag.
Bureau of Indian Affairs
Bureau of Reclamation
Geological Survey
Bureau of Mines
National Park Serv.
Fish and Wildlife Serv.
Office of Territories
Justice
Federal Bureau of Investigation
Imm. and Naturalization Office
Federal Prison System
Legal Actv. and General Admin.
General Admin. Sal. & Exp.
Gen. Legal Actv. Sal. & Exp.
Antitrust Division Sal. & Exp.
US Attrn. & Marsh., Sal. & Exp.
Fees and expenses of Witnesses
Clms. of Per. of Jap. An., S.& E.
Labor
Off of Secr. +off of Solic.
Bureau of Labor Standards
Bureau of Vet. Reemply. Rts.
Bureau of Appr. & Training
Bureau of Emply. Security
Bureau of Employee Comp.
Bureau of Labor Statistics
Wage and Hour Division
Presidential
Exec. Office of the President
Emr. Fnd for the Pres. (Nat'l Def)
Off. of Em. Plan. (civ. def. mob.)
National Security Council
Post Office Department
Treasury
Bureau of Accounts
Bureau of Public Debt
Bureau of Customs
Internal Revenue Service
Bureau of Narcotics
U.S. Secret Service
Bureau of the Mint
Dickey-Fuller Statistic
(5% critical Value)
Appropriations
Requests
(1946-1994)
(1946-1996)
-3.01 (-3.63)
-4.41* (-3.63)
-0.04 (-3.50)
-2.16 (-3.50)
-1.77 (-3.50)
-2.27 (-3.50)
-7.6** (-3.50)
-7.5** (-3.50)
-0.81 (-3.52)
-1.40 (-3.52)
-0.97 (-3.50)
-1.68 (-3.50)
-0.36 (-3.50)
-0.28 (-3.50)
Outlays
(1946-1994)
-0.83 (-3.62)
-0.65 (-3.50)
-1.34 (-3.50)
-2.61 (-3.50)
1.00 (-3.53)
-0.54 (-3.50)
2.22 (-3.50)
Augmented Dickey-Fuller Statistic
(5% critical Value)
Appropriations
Requests
Outlays
(1946-1994)
(1946-1996)
(1946-1994)
-1.56 (-3.67)
-2.69 (-3.67)
-1.28 (-3.65)
-0.33 (-3.51)
-0.38 (-3.50)
0.14 (-3.51)
-2.74 (-3.51)
-2.32 (-3.51)
-2.87 (-3.51)
-2.75 (-3.51)
-2.47 (-3.50)
-1.97 (-3.51)
-1.47 (-3.53)
-1.75 (-3.53)
1.20 (-3.56)
-2.20 (-3.51)
-1.13 (-3.50)
-2.02 (-3.51)
1.49 (-3.51)
1.32 (-3.50)
2.01 (-3.51)
-3.30
-6.3**
-2.33
-0.55
-3.08
-1.84
-5.7**
-1.39
-0.91
-3.05
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-2.88
-2.71
-2.35
-0.57
-2.16
-2.30
-2.13
-0.55
-0.66
-2.12
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-1.68
-3.70*
-2.23
-0.48
-1.48
-1.70
-3.39
-1.58
-0.54
-2.79
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-0.76
-3.79*
-2.76
-0.52
-2.03
-3.18
-2.71
-0.78
-1.16
-1.89
(-3.52)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
-1.75
-1.51
-2.76
-1.43
-1.80
-2.61
-1.54
0.54
-0.97
-2.18
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-0.40
-2.80
-2.81
-1.30
-2.21
-2.68
-2.21
-1.35
-0.13
-1.96
(-3.52)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
0.79
1.49
-1.13
0.50
0.40
-0.86
-1.62
-0.62
0.16
-2.81
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-4.08)
0.00
3.51
2.50
1.76
-1.91
-3.54*
-2.05
-0.16
-1.09
-2.28
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-4.08)
2.41
1.10
3.58
-0.03
0.25
0.81
-1.85
0.41
1.78
-4.25*
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.51)
(-3.50)
(-3.51)
(-3.50)
(-3.99)
0.85
1.67
-0.36
2.46
0.61
0.90
-2.18
1.78
2.95
-3.E+3**
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.52)
(-3.51)
(-3.51)
(-3.51)
(-4.58)
1.52
6.68
1.71
5.29
-2.66
-2.24
-1.96
0.41
0.97
2.E+3
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-4.58)
3.01
2.38
3.11
1.77
2.20
3.15
-2.16
3.73
1.93
-3.48
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.52)
(-3.52)
(-3.51)
(-3.52)
(-3.51)
(-4.35)
-1.18
-2.38
-2.02
-2.14
-4.07*
-3.35
-0.74
-1.39
(-3.50)
(-3.50)
(-3.79)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.64)
-3.22
-2.02
-5.91**
-2.51
-3.28
-2.46
-0.06
-1.63
(-3.50)
(-3.50)
(-3.73)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.61)
-0.85
-1.97
-2.88
-0.89
-3.50*
-3.33
-0.67
-1.27
(-3.50)
(-3.50)
(-3.67)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.63)
-1.626
-1.907
-2.50
-3.19
-1.98
-1.88
2.29
-0.95
(-3.51)
(-3.51)
(-3.92)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.69)
-2.09
-1.88
-2.36
-2.64
-3.46
-1.57
2.92
-1.03
(-3.50)
(-3.50)
(-3.82)
(-3.51)
(-3.50)
(-3.50)
(-3.50)
(-3.64)
-1.13
-2.04
-1.35
-1.00
-2.15
0.42
-1.27
-0.71
(-3.51)
(-3.51)
(-3.73)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.67)
-3.25
-6.1**
-2.20
-1.38
-6.4**
(-3.50)
(-3.50)
(-3.58)
(-3.51)
(-3.50)
-3.18
-6.3**
-3.22
-2.08
-3.32
(-3.50)
(-3.50)
(-3.58)
(-3.50)
(-3.50)
-0.94
-4.4**
-2.55
-2.01
-5.1**
(-3.50)
(-3.50)
(-3.56)
(-3.50)
(-3.50)
-1.35
-8.8**
-2.38
-1.45
-3.15
(-3.51)
(-3.51)
(-3.60)
(-3.51)
(-3.51)
-2.97
-4.4**
-1.79
-1.83
-1.55
(-3.50)
(-3.51)
(-3.61)
(-3.51)
(-3.50)
-1.01
-4.8**
-2.70
-1.78
-2.056
(-3.51)
(-3.51)
(-3.58)
(-3.51)
(-3.51)
-7.1**
-2.04
-0.30
2.69
0.77
-0.47
-5.4**
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-3.49
-2.20
0.02
4.23
0.49
-2.63
-5.1**
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-1.84
-1.67
-0.23
2.79
0.16
-0.12
-6.3**
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
-2.98
-1.08
-1.64
2.69
2.60
1.73
-2.53
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
-1.59
-1.74
-0.34
2.70
0.34
-0.99
-1.34
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
(-3.50)
1.56
-1.03
-0.74
2.62
-1.83
3.17
-2.26
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
(-3.51)
Notes: Five percent critical values are in parentheses. Null of unit root is rejected if the test statistic is smaller than the corresponding
critical value. Notice that critical values depend on the number of observations and the lag structure of error terms. “*”and “**” indicate
rejection of the null hypothesis at the five percent and one percent levels, respectively
30
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 2: Cases with a Small Budget Change - Small Positive Band
Agricultural Research Service
1
Federal Crop Insurance Corp.
1
Forest Service
0
Extension Service
0
Soil Conservation Service
1
Commodity Stabilization Service
0
Agricultural Conservation Program
1
Agricultural Marketing Service
1
Foreign Agricultural Service
0
Rural Electrification Admin. (costs)
1
Farmer's Home Admin. (costs)
1
B of Census+ Offic. of Bus. Econ.
1
C&G Surv+Weath. B -- Env. Sc. Serv. Ad. 1
Domest. & Int'l Bus.
1
Patent Office
1
National Bureau of Standards
1
Maritime Admin.
1
Bureau of Public Roads
1
Civil Aeron. Admin/Federal Aviation Agency0
Federal Communication Commission
1
Federal Power Commission
1
Federal Trade Commission
1
General Accounting Office
1
General Services Admin.
0
Housing and Home Finance Agency
1
Indian Claims Commission
0
Tax Court of U.S.
0
National Science Foundation
0
Renegotiation Board
0
Civil Aeronautics Board
1
Interstate Commerce Commission
1
Securities and Exchange Commission
1
Selective Service System
1
National Mediation Board
1
Federal Mediation and Conciliation Service 0
Tennessee Valley Authority
1
Veterans' Admin.
1
Smithonian Institute
1
National Labor Relations Board
1
Army Corps of Engineers
1
Nat'l Adv Com. for Aeron./ NASA
1
American Battle Monuments Commission 1
AEC/ Nuc. Reg. Comm
0
Civil Service Commission
1
National Capital Planning Commission
1
Public Health Service
1
National Institute of Dental Research
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
31
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 2: Continued
Neurology and Blindness Activities
0
Mental Health Activities
0
Social Security Admin.
1
Food and Drug admin.
1
Office of Education
0
Allergy Infectious Disease Activities
0
Arthritis and Metabolic Disease Activities 0
General Research and Services
0
National Cancer Institute
1
National Heart Institute
0
South Eastern Power Administration
0
Office of Territories
1
Bonneville Power Administration
1
Bureau of Land Management
1
Bureau of Indian Affairs
1
Bureau of Reclamation
1
Geological Survey
1
Bureau of Mines
1
National Park Service
1
Fish and Wildlife Service
1
Federal Bureau of Investigation
1
Immigration and Naturalization Office
1
Federal Prison System
1
Legal Activities and General Admin.
1
General Admin. Salaries and Expenses
0
Gen. Legal Activities Salaries and Expenses 0
Antitrust Division Salaries and Expenses
0
U.S. Attorneys and Marshalls, Sal. & Exp. 0
Fees and expenses of Witnesses
1
Off of Secr. +off of Solic.
1
Bureau of Labor Standards
1
Bureau of Apprenticeship and Training
1
Bureau of Employment Security
1
Bureau of Employee Compensation
1
Bureau of Labor Statistics
1
Executive Office of the President
1
Emergency Fund for the President (Nat'l Def)1
National Security Council
0
Total Post office Department
1
Bureau of Accounts
1
Bureau of Public Debt
1
Bureau of Customs
0
Internal Revenue Service
1
Bureau of Narcotics
1
U.S. Secret Service
1
Bureau of the Mint
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
Notes: A "0" indicates that the percentage change falls inside the statistical band and a "1" indicates otherwise. The band used here is based on the 40 percentile p
32
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 3: Cases with a Small Budget Change – Large Two-Sided Band
Agricultural Research Service
1
Federal Crop Insurance Corp.
1
Forest Service
0
Extension Service
0
Soil Conservation Service
0
Commodity Stabilization Service
0
Agricultural Conservation Program
0
Agricultural Marketing Service
1
Foreign Agricultural Service
0
Rural Electrification Admin. (costs)
1
Farmer's Home Admin. (costs)
1
B of Census+ Offic. of Bus. Econ.
1
C&G Surv+Weath. B -- Env. Sc. Serv. Ad. 0
Domest. & Int'l Bus.
1
Patent Office
1
National Bureau of Standards
1
Maritime Admin.
1
Bureau of Public Roads
1
Civil Aeron. Admin/Federal Aviation Agency0
Federal Communication Commission
1
Federal Power Commission
1
Federal Trade Commission
1
General Accounting Office
0
General Services Admin.
0
Housing and Home Finance Agency
1
Indian Claims Commission
0
Tax Court of U.S.
0
National Science Foundation
0
Renegotiation Board
0
Civil Aeronautics Board
1
Interstate Commerce Commission
1
Securities and Exchange Commission
0
Selective Service System
1
National Mediation Board
0
Federal Mediation and Conciliation Service 0
Tennessee Valley Authority
1
Veterans' Admin.
1
Smithonian Institute
1
National Labor Relations Board
1
Army Corps of Engineers
0
Nat'l Adv Com. for Aeron./ NASA
0
American Battle Monuments Commission 1
AEC/ Nuc. Reg. Comm
0
Civil Service Commission
1
National Capital Planning Commission
0
Public Health Service
1
National Institute of Dental Research
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
33
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 3: Continued
Neurology and Blindness Activities
0
Mental Health Activities
0
Social Security Admin.
1
Food and Drug admin.
1
Office of Education
0
Allergy Infectious Disease Activities
0
Arthritis and Metabolic Disease Activities 0
General Research and Services
0
National Cancer Institute
1
National Heart Institute
0
South Eastern Power Administration
0
Office of Territories
1
Bonneville Power Administration
1
Bureau of Land Management
1
Bureau of Indian Affairs
0
Bureau of Reclamation
1
Geological Survey
1
Bureau of Mines
0
National Park Service
1
Fish and Wildlife Service
1
Federal Bureau of Investigation
1
Immigration and Naturalization Office
0
Federal Prison System
0
Legal Activities and General Admin.
0
General Admin. Salaries and Expenses
0
Gen. Legal Activities Salaries and Expenses 0
Antitrust Division Salaries and Expenses
0
U.S. Attorneys and Marshalls, Sal. & Exp. 0
Fees and expenses of Witnesses
1
Off of Secr. +off of Solic.
1
Bureau of Labor Standards
1
Bureau of Apprenticeship and Training
1
Bureau of Employment Security
0
Bureau of Employee Compensation
1
Bureau of Labor Statistics
1
Executive Office of the President
1
Emergency Fund for the President (Nat'l Def)1
National Security Council
0
Total Post office Department
0
Bureau of Accounts
1
Bureau of Public Debt
1
Bureau of Customs
0
Internal Revenue Service
1
Bureau of Narcotics
0
U.S. Secret Service
1
Bureau of the Mint
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
Notes: A "0" indicates that the percentage change falls inside the statistical band and a "1" indicates otherwise. The band used here is two-sided and based on the
34
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 4: Incremental Cases - Small Positive Band
Agricultural Research Service
Federal Crop Insurance Corp.
Forest Service
I
Extension Service
Soil Conservation Service
Commodity Stabilization Service
I
Agricultural Conservation Program
Agricultural Marketing Service
Foreign Agricultural Service
Rural Electrification Admin. (costs)
Farmer's Home Admin. (costs)
B of Census+ Offic. of Bus. Econ.
C&G Surv+Weath. B -- Env. Sc. Serv. Ad.
Domest. & Int'l Bus.
Patent Office
National Bureau of Standards
Maritime Admin.
Bureau of Public Roads
Civil Aeron. Admin/Federal Aviation AgencyI
Federal Communication Commission
Federal Power Commission
Federal Trade Commission
General Accounting Office
General Services Admin.
I
Housing and Home Finance Agency
Indian Claims Commission
Tax Court of U.S.
National Science Foundation
I
Renegotiation Board
I
Civil Aeronautics Board
Interstate Commerce Commission
Securities and Exchange Commission
Selective Service System
National Mediation Board
Federal Mediation and Conciliation Service I
Tennessee Valley Authority
Veterans' Admin.
Smithonian Institute
National Labor Relations Board
Army Corps of Engineers
Nat'l Adv Com. for Aeron./ NASA
American Battle Monuments Commission
AEC/ Nuc. Reg. Comm
I
Civil Service Commission
National Capital Planning Commission
Public Health Service
National Institute of Dental Research
I
I I I I
I
I I I I I I I
I I I I I I I I
I
I I I I
I I I I
I I I
I I I I I I
I I I I
I I I I
I I I I I
I I I I
I
I I I I I
I I I I I
I I
I
I I I I I
I I I
35
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 4: Continued
Neurology and Blindness Activities
I
Mental Health Activities
I
Social Security Admin.
Food and Drug admin.
Office of Education
I
Allergy Infectious Disease Activities
I
Arthritis and Metabolic Disease Activities I
General Research and Services
I
National Cancer Institute
National Heart Institute
I
South Eastern Power Administration
I
Office of Territories
Bonneville Power Administration
Bureau of Land Management
Bureau of Indian Affairs
Bureau of Reclamation
Geological Survey
Bureau of Mines
National Park Service
Fish and Wildlife Service
Federal Bureau of Investigation
Immigration and Naturalization Office
Federal Prison System
Legal Activities and General Admin.
General Admin. Salaries and Expenses
I
Gen. Legal Activities Salaries and Expenses I
Antitrust Division Salaries and Expenses
I
U.S. Attorneys and Marshalls, Sal. & Exp. I
Fees and expenses of Witnesses
Off of Secr. +off of Solic.
Bureau of Labor Standards
Bureau of Apprenticeship and Training
Bureau of Employment Security
Bureau of Employee Compensation
Bureau of Labor Statistics
Executive Office of the President
Emergency Fund for the President (Nat'l Def)
National Security Council
I
Total Post office Department
Bureau of Accounts
Bureau of Public Debt
Bureau of Customs
Internal Revenue Service
Bureau of Narcotics
U.S. Secret Service
Bureau of the Mint
I I I I I I I
I
I I I I I I
I I
I I I I I I I I I
I I I I I I I
I
I I I
I I I I
I I I I I
I I I I
I I I I I
I I I I
I
I I I I
I I I I I
I I I I I I
I
I I I I I
I I I I
I I I I I
Notes: A string of I's indicates an incremental cycle. The band used here is based on the forty percentile point and it covers only positive changes.
36
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 5: Incremental Cases – Large Two-Sided Band
Agricultural Research Service
Federal Crop Insurance Corp.
Forest Service
I
Extension Service
Soil Conservation Service
I
Commodity Stabilization Service
I
Agricultural Conservation Program
I
Agricultural Marketing Service
Foreign Agricultural Service
I
Rural Electrification Admin. (costs)
Farmer's Home Admin. (costs)
B of Census+ Offic. of Bus. Econ.
C&G Surv+Weath. B -- Env. Sc. Serv. Ad. I
Domest. & Int'l Bus.
Patent Office
National Bureau of Standards
Maritime Admin.
Bureau of Public Roads
Civil Aeron. Admin/Federal Aviation AgencyI
Federal Communication Commission
Federal Power Commission
Federal Trade Commission
General Accounting Office
I
General Services Admin.
I
Housing and Home Finance Agency
Indian Claims Commission
Tax Court of U.S.
I
National Science Foundation
I
Renegotiation Board
I
Civil Aeronautics Board
Interstate Commerce Commission
Securities and Exchange Commission
Selective Service System
National Mediation Board
I
Federal Mediation and Conciliation Service I
Tennessee Valley Authority
Veterans' Admin.
Smithonian Institute
National Labor Relations Board
Army Corps of Engineers
I
Nat'l Adv Com. for Aeron./ NASA
I
American Battle Monuments Commission
AEC/ Nuc. Reg. Comm
I
Civil Service Commission
National Capital Planning Commission
I
Public Health Service
National Institute of Dental Research
I
I I I I I I I
I
I I I I I I
I I I I I I I I I I I
I
I I I I I I I I I I I I I
I I I I I I I I
I
I I I I I I
I I I I
I I I I I
I I I I I I I I I
I I I I I I
I I I I I
I I I I I I
I I I I
I I I I I
I I I I I I I I I I I I I
I I I
I I I I
I I I I I I I I
I I I
I I I
I I I I I I I
I I I I I I I I
I
I
I
I
I I I I
I I I I I
I I I I I I I
I I I I I I
I I I I I I I I
I I I
I I I I I I
I I I
I I I I I I I I I I I I
I I I I I
I I
I I
I I I I
I
I I
I I
I I
I
I
I
I
I
I
I
I
I
I
I I
I I I I I I I
I I I I
I I I I
I I I I I I I I I I
I I
I
I I I I
I I I I
I I
I
I
I
I
I I I I I
I I I I I
I
I
I
I
I
I
I
I
I
I
I I I I
I I I I
I I I I
I I I
I
I I I I I I
I
I I I I
I I I I I I I I
I
I
I I I I I I
I I I I
I I I I
I I
I
I I I I I I I I I I I I
I I I I I I I I I I I I
I I I I
I I I I I I
I I I I I I I I I I I I I I
I I I I I I I I I I I I I I I I I I I
I
I I I I I I I I I I I I I I
I I I I I I I I I I
I I I I I I
I I I I I I I I I
I I I I I
I I I I I I
I I I I
I I I
I
I I I I I I
I I I I I
I
I
I I I I I
I I I I I I I I
I I I I I I I I
I I I I
I
I I I I
I I I I I I I
I I I I
I I I
I I I I
I I I I I I
I I I I I I
I I I I
I I I I I I I
I I I I I
37
I I
I
I I I I I
I I
I
I I I
I I
I
I
I I
I
I
I
I
I
I
I
I
I
Agency
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
Table 5: Continued
Neurology and Blindness Activities
I
Mental Health Activities
I
Social Security Admin.
Food and Drug admin.
Office of Education
I
Allergy Infectious Disease Activities
I
Arthritis and Metabolic Disease Activities I
General Research and Services
I
National Cancer Institute
National Heart Institute
I
South Eastern Power Administration
I
Office of Territories
Bonneville Power Administration
Bureau of Land Management
Bureau of Indian Affairs
I
Bureau of Reclamation
Geological Survey
Bureau of Mines
National Park Service
Fish and Wildlife Service
Federal Bureau of Investigation
Immigration and Naturalization Office
Federal Prison System
Legal Activities and General Admin.
General Admin. Salaries and Expenses
I
Gen. Legal Activities Salaries and Expenses I
Antitrust Division Salaries and Expenses
I
U.S. Attorneys and Marshalls, Sal. & Exp. I
Fees and expenses of Witnesses
Off of Secr. +off of Solic.
Bureau of Labor Standards
Bureau of Apprenticeship and Training
Bureau of Employment Security
Bureau of Employee Compensation
Bureau of Labor Statistics
Executive Office of the President
Emergency Fund for the President (Nat'l Def)
National Security Council
I
Total Post office Department
I
Bureau of Accounts
Bureau of Public Debt
Bureau of Customs
I
Internal Revenue Service
Bureau of Narcotics
I
U.S. Secret Service
Bureau of the Mint
I I I I I I I
I
I I I I I
I
I I I I
I
I I I I I I I
I I I I I I I
I
I
I
I
I
I I I I I I I
I I I
I I I I I I I
I
I I I I
I I I
I I I I
I
I I I I
I I I I I I I I
I I I I I I I I I I I I I
I I I I
I I I I I I
I I
I I I I I
I I I I
I I I I I
I I I I
I I I
I I I I I I I I
I I I I I I
I I I I
I I I I I I I I I I I
I I I I I I
I
I I I I
I
I I I I I I
I I I I
I
I I I I I
I I I I
I I I I I I
I
I I I I
I
I
I
I I I I
I I I I
I I I I I I I I I I I I I I I I I I I
I I I I I I I I
I I I I I I
I I I I
I I I I I I I I I I I I I
I I I I I I
I I I I I
I I I I I I
I I I I
I I I I I I I
I I I
I I I I I
I I I
I I I I I I I I I I
I I I I I I I I
I I I
I I I I
I I I I I I I
I I I I I I
I I I I
I
I I I I
I I I I I
I
I I I I I
I I I I I
I I I I
I I I I
I I I I I I
I I I I
I I I I I I I I I I I
I I I I I I I I
I I
I I I
I I I I I I
I
I
I
I
I
I
I
I
I I
I I I
I I I
I
I I I I I I I
I I I I
Notes: A string of I's indicates an incremental cycle. The band used here is two-sided and based on the 45 percentile point.
38
I I
I I I I
Table 6: Poisson Regression Results Based on Various Time Series of Counts
Explanatory Variable
Dependent Variable
D2t
D3t
D1t
D4t
POLITICAL
VARIABLES:
DEMOCRATS
1.244***
(0.0127)
1.217***
(0.0133)
1.218***
(0.0131)
1.163***
(0.0151)
PRES-SWITCH
0.196***
(0.0562)
0.189***
(0.059)
0.183***
(0.058)
0.206***
(0.066)
CONG-SWITCH
1.356***
(0.055)
1.300***
(0.058)
1.351***
(0.057)
1.181***
(0.066)
ELECTION YEAR
0.581***
(0.0442)
0.561***
(0.0462)
0.573***
(0.0456)
0.560***
(0.0516)
INFL-RATE
-4.843***
(0.781)
-4.691***
(0.812)
-4.542***
(0.799)
-4.151***
(0.897)
DISC-RATE
21.579***
(0.925)
21.47***
(0.962)
21.394***
(0.946)
19.722***
(1.065)
0.507
(0.320)
0.176
0.342
0.453
(0.333)
-0.203
(0.386)
DEFICIT
0.000017***
(0.000002)
0.000017***
(0.000002)
0.000017***
(0.000002)
0.000017***
(0.000002)
DEFICIT-DUMMY
0.000032***
(0.000002)
0.000031***
(0.000002)
0.000031***
(0.000002)
0.000030***
(0.000002)
Log-likelihood
Number of observations
-1750.08
47
-1593.13
47
-1607.00
47
-1166.23
47
ECONOMIC
VARIABLES:
REV-GROWTH
Notes: ‘***’ indicate significance at the one percent level.
D1t measures the number of incremental cases using a small positive band.
D2t measures the number of incremental cases using a small two-sided band.
D3t measures the number of incremental cases using a large positive band.
D4t measures the number of incremental cases using a large two-sided band.
39
Figure 1: Frequency Distribution for Various Agency Sizes
Small Agencies
500
Frequency
400
300
200
100
26
More
26
>30
>30
21
25
21
16
19
11
6
1
0.7
0.5
0.2
0
-0.2
-0.5
-0.7
-1
0
annual real growth rate of outlays
Medium Agencies
500
Frequency
400
300
200
100
13
7
1
0.7
0.4
0.1
0
-0.1
-0.4
-0.7
-1
0
annual real growth rate of outlays
Large Agencies
500
300
200
100
annual real growth rate of outlays
40
16
11
6
1
0.7
0.5
0.2
0
-0.2
-0.5
-0.7
0
-1
Frequency
400