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Choice experiment assessment of public expenditure preferences.


Analysis of public preferences for government expenditures has taken a variety of forms. Research has addressed the scale of government spending (Gemmell et al., 2003; Preston & Ridge, 1995), preferences for 'redistribution' (Fong, 2001; Alesina & La Ferrara, 2005; Alesina & Giuliano, 2009), and whether expenditure on particular items should be More, the Same, or Less (MSL) than the existing allocation (e.g. Ferris, 1983; Lewis & Jackson, 1985; Hills, 2002; Delaney & O'Toole, 2007). Budget games provide another avenue for assessing public preferences. In these games people either reallocate expenditures without changing total spending (Bondonio & Marchese, 1994), allocate surplus funds (Alvarez & McCaffery, 2003; Blomquist et al., 2000, 2003; Israelsson & Kristrom, 2001) or cut portfolio budgets to meet a predetermined reduction in total spending (de Groot & Pommer, 1987, 1989). Psychologists have used category rating and magnitude estimation approaches (Kemp, 2002). Category ratings, which can be averages or can be at the margin, are evaluated on an integer scale ranging from 0 to 10, with 10 being the highest value. Magnitude estimation ascribes a standard score to a particular item and asks participants to evaluate other items relative to the standard. Kemp (2002) notes a high correlation between category ratings and logarithms of magnitude scores in an evaluation of government services.

The MSL approach is easy to apply, but provides relatively little information. MSL cannot identify the preferred scale of government expenditure, or the optimal allocation of spending between competing items. Budget games yield more information than MSL. Games with budget constraints can be useful for providing information about preferences for the distribution of small budget changes. Games in which the total budget is unrestricted can provide useful information about preferences for large budget changes, including optimal scale, but do not provide information on changes at the margin. Category rating and magnitude estimation can be useful for measuring total or marginal benefits (e.g. Kemp & Willetts, 1995), although negative values cannot be measured, even though they are feasible and relevant to optimal allocations. Category rating can be used to rank benefits from alternative expenditure categories. However, unlike MSL and unconstrained budget games, the interval measurement scale in category ranking precludes estimates of marginal rates of substitution between portfolios, which are required for optimally adjusting government expenditures.

Define the social welfare function as W([X.sub.1], [X.sub.2], ..., [X.sub.n], Z). [X.sub.i] is the amount of government funding allocated to portfolio i ([X.sub.i] [greater than or equal to] 0) and Z is the total amount of tax money spent on these portfolios (Z = [[summation].sub.i][X.sub.i]). Additional spending on any portfolio has two effects. It changes welfare because of the outcomes from spending on the specific portfolio ([delta]W/[delta][X.sub.i]), the sign of which will be positive if additional spending is perceived to produce 'goods', but is unknown a priori. The second effect arises from the source of the additional funds, which can come from two locations: increased taxes, which are expected to diminish community welfare directly ([delta]W/[delta]Z < 0), reduction in spending in other portfolios ([delta]W/[delta][X.sub.j], j [not equal to] i), or some combination of the two. Optimal budget allocation involves maximising W subject to the constraints that (i) all [X.sub.i] are non-negative, and (ii) the total budget equals Z, which can be fixed or variable. Trivially, the optimal first-order conditions for an internal solution (W must be twice-differentiable) are [delta]W/[delta][X.sub.i] = [delta]W/[delta][X.sub.i] [for all] i, j. In addition, when Z is a variable the optimal level of taxation requires [delta]W/[delta][X.sub.i] = [delta]W/[delta]Z [for all] i. Marginal welfare should be equated across portfolios and should offset the loss in welfare arising from appropriation of taxes.

The study

We explore a fresh approach towards providing information about preferences for government budget allocations. Choice experiments can inform government allocation decisions by deriving a welfare function, which can provide measures of (i) strength of preference for allocating marginal budget to specific portfolios, (ii) optimal total budget, and (iii) optimal allocation over portfolios.

Choice experiments are attribute based methods that present alternative products or policies that differ on a number of attributes. Experiment participants select their single preferred alternative, mimicking a political process. Each participant may make several choices between different sets of alternatives, which are designed to provide suitable data for application of random utility models to estimate the welfare function (Louviere et al., 2000; Bennett & Blamey, 2001; Hensher et al., 2005).

A choice experiment was applied to test optimality of New Zealand budget allocation amongst four portfolios: health, education, income support (support), and conservation and environmental management (environment). Data were collected as part of a self-completed mail survey of registered voters that sought perceptions of the state of the New Zealand environment (Hughey et al., 2002). The response rate to the March 2002 survey was 45% (n = 836), with 736 responses to the choice experiment question (88% of respondents).

Nine choice sets, each composed of three alternatives for spending on the four portfolios, were derived using an orthogonal design. The full factorial design for four attributes at three levels entails 81 different combinations of attribute levels. Utilisation of all possible combinations in the full factorial design was logistically infeasible, so the smallest partial factorial design in the Hahn and Shapiro (1966) catalogue that permitted estimation of the main effects (nine different choice profiles) was used. Design orthogonality ensures that the attribute levels are uncorrelated, permitting estimation of the statistical model (Hensher et al., 2005). (1) The original design profile in each choice set was used as a starting point in a shifted-triple design to obtain choice sets of three alternatives (Louviere et al., 2000). The final experimental design is shown in Table 1. The alternatives covered selected combinations of $50 million more, the same, or $50 million less annual spending on each of the portfolios. Options entailed total budget changes across the range of [+ or -] $200 million relative to the existing budget for these portfolios.

Common choice experiment practice obtains information from several choice sets for each participant, adopting panel estimation models to account for correlations amongst each individual's responses. While Caussade et al. (2005) indicate minimum error variance with about nine choice sets for each participant, survey space limitations dictated a single choice question in this application. The nine choice sets were evenly distributed across the survey sample so that each respondent was presented with only one choice set. Respondents identified the single alternative that they preferred from the three alternatives in the choice set presented to them. An alternative approach that can yield more information from each participant is ranking of the alternatives in each choice set. However, providing a full ranking is a cognitively more demanding task than simply identifying a single preferred alternative, which has resulted in higher variance in ranking-based models and inconsistencies with underlying theoretical models (Morrison et al., 1996; Louviere et al., 2000). In view of the already large burden of the omnibus survey the simplest possible budget choice question was utilised, requiring participants to indicate their single preferred alternative. Figure 1 shows one of the choice sets. Information was provided on government spending on each of the budget items on the expectation that survey participants would be unaware of such matters (Kemp, 2009).

Statistical methods

Modelling assumed a linear welfare function, which is limited because it does not accommodate diminishing marginal welfare, which is necessary for an internal solution to the budget allocation problem. However, for small changes it is possible to approximate the welfare function using a linear form. Relative to the current budget, proposed changes were 0.4% (Support), 0.7% (Education and Health), and 10% (Environment). Further support of the linear utility function assumption is provided by Kemp and Willetts (1995), who found no significant difference in ratings for a 5% increase or a 5% decrease in provision of specific New Zealand government services.

The underlying linear welfare function is:

W = [[beta].sub.1] [X.sub.1] + [[beta].sub.2] [X.sub.2] + [[beta].sub.3] [X.sub.3] + [[beta].sub.4] [X.sub.4] + [[beta].sub.5] Z (1)

The total welfare effect of a purely tax-funded change in spending on portfolio i is:

dW = d[X.sub.1] = d([[beta].sub.1] d[X.sub.1] + [[beta].sub.2]d[X.sub.2] + [[beta].sub.3]d[X.sub.3] + [[beta].sub.4] d[X.sub.4] + [[beta].sub.5]dZ/d[X.sub.1] = [[beta].sub.1] + [[beta].sub.5]

Because Z is a linear function of the other variables, it is not possible to identify (1). However, it is possible to identify (2):

W = [[alpha].sub.1] [X.sub.1] + [[alpha].sub.2] [X.sub.2] + [[alpha].sub.3] [X.sub.3] + [[alpha].sub.4] [X.sub.4] (2)

where [[alpha].sub.i] = [[beta].sub.i] + [[beta].sub.5] = d W/d[X.sub.i] and [[alpha].sub.i] is net marginal welfare of spending on portfolio i, which includes the benefits obtained from spending on the portfolio, as well as the disutility of paying higher taxes to fund that additional spending. This welfare model was fitted to the data using the 'workhorse' multinomial logit model (Alberini et al., 2007), which estimates welfare function parameters that maximise the probability of concurrently observing the 736 actual participant choices from the nine different choice sets. For any individual m, utility associated with alternative k is a function of the vector of characteristics of alternative k ([X.sub.k]) and a vector of characteristics of the individual ([Y.sub.m]) such as age, income, education and gender.

[] = W [X.sub.k], [Y.sub.m]

From the analyst's perspective, welfare derived from each alternative has two components, observable and random. Letting the observable portion of welfare be V(.), then:

[] = V([X.sub.k], [Y.sub.m]) + [epsilon]([X.sub.k], [Y.sub.m])

Individual i will choose alternative k over all others if alternative k is expected to yield the most welfare. The probability of choosing alternative k is:

[P.sub.k] = Prob {[V.sub.k] + [[epsilon].sub.k] > [V.sub.j] + [[epsilon].sub.j] [[for all].sub.j] [not equal] k }

The probability of choosing any option can only be modelled after assumptions have been made about distributions of the error terms. The assumption that the errors are Gumbel distributed leads to the multinomial logit model, which has choice probabilities:


The scale parameter ([mu]) is typically assumed to equal unity for all alternatives, implying constant variance. Model parameters are estimated by substituting for V with a parametric utility function that is dependent on the vector of attribute levels (X). For example, a linear welfare function takes the form:

[V.sub.k] = V ([V.sub.k]) = [[alpha].sub.0] + [[alpha].sub.1] [X.sub.1] + [[alpha].sub.2] [X.sub.2] + ... [[alpha].sub.n] [X.sub.n] = [alpha]X'

This is equation (2). Data analysis entails selection of the coefficient vector [alpha] that maximises the probability of obtaining the observed choices.


Multinomial logit model estimates of the linear welfare function parameters in equation (2) and their standard errors are reported in Table 2. Polynomial and logarithmic welfare functions were estimated, but provided no improvement over the simple linear model, which is unsurprising given the small scale of expenditure changes. Latent class and random parameters models failed to improve model fit.

These models have only moderate predictive ability. However, the independent variables are all highly significant. The SUPPORT coefficients are negative, with asymptotic Z-scores ([Z.sub.i] = [[alpha].sub.i]/SE([[alpha].sub.i])) of -7.0, indicating a definite preference for reduced spending on income support. The three other portfolio coefficients are all significantly positive, indicating preferences for increased spending on those items. Model B is preferred to Model A on all three statistical criteria reported in Table 2, a conclusion that is confirmed by a likelihood ratio test ([chi square] = 47.72, 4 dof). Unlike the other portfolios, marginal welfare from health spending did not differ significantly by age.

Policy analysis

For efficiency, as judged by the public, whenever marginal welfare net of tax ([[alpha].sub.i]) is positive, taxes should be increased to allow additional spending on portfolio i and vice versa. Additional taxes are justified to support increased spending on HEALTH, EDUCATION and ENVIRONMENT. On the other hand, efficiency is enhanced by reducing expenditure on SUPPORT in order to lower taxes. However, the linear utility function approximation precludes identification of optimal magnitudes of expenditure and tax changes.

Another possibility is reallocation of existing expenditures without change to the total tax take. Any increase of spending in one portfolio requires reductions in spending in at least one other portfolio. When spending on one item ([X.sub.j]) is reduced to allow increased spending on another ([X.sub.i]) with a balanced budget (d[[X].sub.j] = -d[X.sub.i]), the change in welfare is dW= [[beta].sub.i]d[X.sub.i] + [[beta].sub.j]d[X.sub.j]. Hence: dW/d[X.sub.i] = [[beta].sub.i]-[[beta].sub.j] = [[alpha].sub.i]-[[alpha].sub.j]. Efficiency is enhanced whenever expenditure is transferred from lower marginal welfare to higher marginal welfare portfolios. With a linear welfare function all spending should be transferred to the item with the largest marginal welfare net of tax ([[alpha].sub.i]). Table 3 provides estimates of differences in marginal welfares and their significance, estimated using a Monte Carlo procedure (Krinsky & Robb, 1986).

The marginal welfare differences ([[beta].sub.i]-[[beta].sub.j]) allow the items to be ranked. A positive difference indicates that marginal spending on portfolio i yields more welfare than spending on portfolio j. Welfare would be improved by transferring spending from item j to item i in such cases. Two marginal welfare differences in Model B are not significantly different from zero, so Model B is unable to provide a full ranking of HEALTH, EDUCATION and ENVIRONMENT for the 50 year old in the example. HEALTH spending is significantly more valuable than ENVIRONMENT spending, but the differences between HEALTH and EDUCATION and between EDUCATION and ENVIRONMENT are unclear. Expenditure on any other portfolio provides more marginal welfare than spending on SUPPORT.

For Model A, it is possible to conclude that HEALTH spending provides more benefits than either ENVIRONMENT or EDUCATION spending. The following hierarchy of marginal welfares applies with better than 95% confidence: HEALTH > {EDUCATION, ENVIRONMENT} > 0 > SUPPORT.

Predictions from Model B vary significantly with respondent age (Table 4). Marginal welfares for HEALTH, EDUCATION and ENVIRONMENT are larger than for SUPPORT for all age groups, except for 70 year olds who no longer have a clear preference for ENVIRONMENT spending over SUPPORT. There are no significant differences in marginal welfare for ENVIRONMENT and EDUCATION for any age group. However, younger respondents were more likely to value ENVIRONMENT and EDUCATION spending more highly than HEALTH spending. This outcome is similar to results from the category rating of New Zealand health budget preferences (Kemp & Burt, 2001).


This preliminary study addressed budget allocations for a narrow range of government services and for small changes in portfolio expenditures. Results nevertheless indicated preferences for reduced spending on income support, a strong desire to spend more on health, and a willingness to support additional spending on education and the environment, consistent with category rating studies. The highest marginal value ratings in New Zealand category rating studies are achieved by health, education and police, with environment ranking in the middle range, and spending on income support always rated lowly (Kemp & Willetts, 1995; Kemp, 1998, 2003; Kemp & Burt, 2001).

Choice experiments allow application of mathematical models of preferences, which provide opportunities to statistically derive estimates of marginal utility, which are of value for estimating optimal budget allocations based on preferences-an advantage over other approaches. This suggests that further use of the approach on a broader range of services should be considered as well as including a broader range of demographic factors (Delaney and O'Toole, 2008a), as well as larger expenditure changes and designs suitable for estimating non-linear welfare functions. Results then could be compared directly with budget game outcomes. SUPPORT incorporates a large number of sub-categories (e.g. pensions, unemployment benefit, single parent support), which may be judged quite differently (Lewis and Jackson, 1985; Delaney and O'Toole, 2008b). This within-portfolio diversity has two potential effects: first, it hides preferences for particular components of the portfolio; and second, respondent focus on any one of those components to the exclusion of others may have biased parameter estimates. (2) Disaggregation of SUPPORT may provide guidance about relative desirability of components within this portfolio. Further enhancement would be provided by increasing the number of choices faced by each participant, allowing use of panel models.

The choice experiment approach to identification of efficient budget allocation is novel. This preliminary study has successfully estimated marginal welfare differences between portfolios within relatively narrow confidence intervals. There is potential to use choice experiments to identify marginal benefits as well as optimal budget allocations. This gives the choice experiment approach a theoretical advantage over category rating, budget games and MSL. This preliminary trial of the choice approach to modelling community preferences, along with the potential advantages the approach offers, indicates the method has strong potential and suggests that further research into design improvements is warranted.

DOI: 10.1080/00779954.2010.522163


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(1.) Recent experimental design literature has questioned the need for orthogonality, and has illustrated advantages of alternative design strategies (Scarpa & Rose, 2008).

(2.) The authors are grateful to an anonymous reviewer for the latter point.

Geoffrey N. Kerr *, Ross Cullen and Kenneth F.D. Hughey

Environmental Management, Lincoln University, PO Box 84, Lincoln University, Lincoln, Canterbury 7647, New Zealand

(Received 21 July 2009; final version received 5 March 2010)

* Corresponding author. Email:
Table l. Experimental design.

Choice set   Alternative   Health   Education   Support   Environment

                  1          -50       -50        -50         -50
1                 2           50        50         50          50
                  3            0         0          0           0
                  1          -50         0          0          50
2                 2           50       -50        -50           0
                  3            0        50         50         -50
                  1          -50        50         50           0
3                 2           50         0          0         -50
                  3            0       -50        -50          50
                  1            0       -50          0           0
4                 2          -50        50        -50         -50
                  3           50         0         50          50
                  1            0         0         50         -50
5                 2          -50       -50          0          50
                  3           50        50        -50           0
                  1            0        50        -50          50
6                 2          -50         0         50           0
                  3           50       -50          0         -50
                  1           50       -50         50          50
7                 2            0        50          0           0
                  3          -50         0        -50         -50
                  1           50         0        -50           0
8                 2            0       -50         50         -50
                  3          -50        50          0          50
                  1           50        50          0         -50
9                 2            0         0        -50          50
                  3          -50       -50         50           0

Table 2. Multinomial logit model utility functions.

                                   Model A (Standard errors)

[[alpha].sub.HEALTH]                1.088 E-2 *** (0.l05 E-2)
[[alpha].sub.EDUCATION]             8.259 E-3 *** (l.050 E-3)
[[alpha].sub.SUPPORT]              -6.996 E-3 *** (l.001 E-3)
[[alpha].sub.ENVIRONMENT]           6.859 E-3 *** (l.029 E-3)
[[alpha].sub.AGE x EDUCATION]
[[alpha].sub.AGE x SUPPORT]
[[alpha].sub.AGE x ENVIRONMENT]
Akaike Information Criterion                  1.873
Bayesian Information Criterion                1.898
Adjusted [[rho].sup.2]                        0.093

Significance levels * (10%), ** (5%), *** (1%).

                                   Model B (Standard errors)

[[alpha].sub.HEALTH]                1.163 E-2 *** (0.110 E-2)
[[alpha].sub.EDUCATION]             2.222 E-2 *** (0.375 E-2)
[[alpha].sub.SUPPORT]              -2.460 E-2 *** (0.350 E-2)
[[alpha].sub.ENVIRONMENT]           2.137 E-2 *** (0.368 E-2)
[[alpha].sub.AGE x EDUCATION]      -2.635 E-4 *** (0.685 E-4)
[[alpha].sub.AGE x SUPPORT]         3.353 E-4 *** (0.650 E-4)
[[alpha].sub.AGE x ENVIRONMENT]    -2.782 E-4 *** (0.675 E-4)
Akaike Information Criterion                  1.810
Bayesian Information Criterion                1.855
Adjusted [[rho].sup.2]                        0.126

Significance levels * (10%), ** (5%), *** (1%).

Table 3. Marginal utility differences.


     i             j          Model A         Model B (#)

HEALTH        EDUCATION     0.0026 **         0.0025 *
HEALTH        ENVIRONMENT   0.0040 ***        0.0041 ***
EDUCATION     ENVIRONMENT   0.0014            0.0016
HEALTH        SUPPORT       0.0179 ***        0.0194 ***
EDUCATION     SUPPORT       0.0153 ***        0.0170 ***
ENVIRONMENT   SUPPORT       0.0139 ***        0.0153 ***

# Differences are age-dependent. The marginal utility differences
are for a 50 year old. Significance levels * (10%), ** (5%), *** (1%).

Table 4. Marginal utility differences by age, Model B.

      HEALTH--      HEALTH--      EDUC--    ENVIRON--    HEALTH--

20    -0.0042       -0.0053 **    0.0011    0.034 ***    0.030 ***
30    -0.0014       -0.0027       0.0013    0.028 ***    0.026 ***
40     0.0014        0.0000       0.0014    0.021 ***    0.023 ***
50     0.0041 ***    0.0026 *     0.0016    0.015 ***    0.019 ***
60     0.0070 ***    0.0052 ***   0.0017    0.0092 ***   0.016 ***
70     0.0097 ***    0.0079 ***   0.0019    0.0030       0.013 ***


20    0.035 ***
30    0.029 ***
40    0.023 ***
50    0.017 ***
60    0.011 ***
70    0.0049 **

Significance levels * (10%), ** (5%), *** (1%).

Figure 1. Example of a choice question.

The New Zealand government spends about $36 billion each year on
a range of public services.

Suppose the government were thinking about changing the amount it
spent on health, education, income support, and conservation and
environmental management. Any increase in total spending on these
items would result in a tax increase, but reduced spending could
lower taxes. You arc asked for your opinion on the following
options. You might think there are better options than these
ones, but they are the only options you can choose from for now.
Which option do you prefer?

Area of public   Approximate   Change in spending each year million
spending         amount
                 spent in      Option 1      Option 2      Option 3

                 ($ million)

Health           $7,000 m.     no change     $50 m. less   $50 m. more

Education        $6,733 m.     $50 m. more   no change     $50 m. less

Income support   $13,000 m.    $50 m. less   $50 m. more   no change

Conservation     $500 m.       $50 m. more   no change     $50 m. less

Change in                      $50 m. more   no change     $50 m. less
total taxes

[] I like option 1 best

[] I like option 2 best

[] I like option 3 best
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Author:Kerr, Geoffrey N.; Cullen, Ross; Hughey, Kenneth F.D.
Publication:New Zealand Economic Papers
Article Type:Report
Geographic Code:8NEWZ
Date:Dec 1, 2010
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