Melvin J. Hinich

The spatial theory of voting: an introduction.

Preface 1. Spatial voting models: the behavioural assumptions 2. The unidimensional spatial voting model 3. A two-dimensional spatial model 4. A general spatial model of candidate competition 5. The influence of candidate characteristics and abstention on election outcomes 6. Voting on budgets 7. Models of voter uncertainty 8. Institutions 9. Empirical testing of the spatial theory of elections 10. Concluding observations References Answers to selected problems Index.

Evidence of Nonlinearity in Daily Stock Returns

This article applies a newly developed statistical technique to time series of daily rates of return of 15 common stocks. The technique involves estimating the bispectrum of the observed time series. The bispectrum is defined as the double Fourier transform of the third-order cumulant function. If the process generating rates of return is linear with independent innovations, then the skewness of the bispectrum will be constant. The article describes a test that can detect nonconstant skewness in the bispectrum. Hence if the test rejects constant skewness, a nonlinear process is implied. As a consequence, the test can distinguish between white noise and purely random noise. The results suggest that daily stock returns are generated by a nonlinear process.

SOCIAL PREFERENCE ORDERINGS AND MAJORITY RULE

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Some comparisons of tests for a shift in the slopes of a multivariate linear time series model

Abstract Our objective is to find a simple, robust, reasonably powerful test for a shift in one or more of the slopes in a linear time series model at some unknown point of time. Two such tests are ‘Chows test’ (1960) for a shift at the midpoint of the record and the ‘Farley-Hinich test’ (1970b); both can be performed easily with standard regression programs. In section 2, we compare the asymptotic properties of these tests when the disturbance variance is known. As expected, Chows test is superior when the true shift is near the middle of the record; with a single, uniformly-distributed explanatory variable, the Farley-Hinich tests dominates over the remaining eighty-four percent of the record. In section 3, we describe the results of some Monte Carlo experiments with a finite sample, which can be summarized as follows. (i) The asymptotic results of section 2 were appropriate for finite sample power comparisons. (ii) The relative performance of the two tests does not depend appreciably on whether the variance is known. (iii) The likelihood ratio test, which is far more costly to perform than the other two tests, does not dominate either Chows test or the Farley-Hinich test; it has moderately more power at the ends of the record, moderately less in the middle. The conclusion is clear: at low cost (in terms of computer cost and lost power), one can reduce the probability of over- looking a structural shift by routinely performing Chows test or the Farley-Hinich test.

A Test for a Shifting Slope Coefficient in a Linear Model

Abstract A locally most powerful test is developed for the hypothesis that a slope coefficient in a linear time series model is stable, against the alternative that the slope shifts exactly once somewhere in the series. Analysis of the procedure using artificial data indicates good power characteristics even when the ratio of the shift size to the error variance is moderate—especially if the shift does not occur very near either end of the series. Power also depends on the pattern of the independent variables and on whether the error variance is known or must be estimated using the residuals about the regression line.

Testing for dependence in the input to a linear time series model

This paper presents a simple test for dependence in the residuals of a linear parametric time series model fitted to non gaussian data. The test statistic is a third order extension of the standard correlation test for whiteness. but the number of lags used in this test is a function of the sample size. The power of this test goes to one as the sample size goes to infinity for any alternative which has non zero bicovariances c e3(r,s)= E[e(t)e(t + r)e(t + s)] for a zero mean stationary random time series. The asymptotic properties of the test statistic are rigorously determined. This test is important for the validation of the sampling properties of the parameter estimates for standard finite parameter linear models when the unobserved input (innovations) process is white but not gaussian. The sizes and power derived from the asymptotic results are checked using artificial data for a number of sample sizes. Theoretical and simulation results presented in this paper support the proposition that the test wi...

A New Approach to Voter Uncertainty in the Downsian Spatial Model

A new model of voter uncertainty about candidate positions is presented in which voters simplify the issue positions of the candidate by representing them as a random variable on an underlying evaluative dimension. It is further assumed that the degree of voter uncertainty depends upon the mean location of this random variable. It is demonstrated that this type of spatially dependent uncertainty results in a shift of each voters ideal point on the underlying dimension. We discuss two types of shifts, one in which voter ideal points are shifted toward the extremes and the other in which they are shifted toward the center and comment on the consequences of these shifts for two-candidate electoral competition. Finally, we relate our model to earlier work on the subject by Downs (1957) and Shepsle (1972).

Nonspatial Candidate Characteristics and Electoral Competition

BASIC TO MODELS of electoral competition is the assumption that candidates adopt positions on policy issues as a means of attracting votes. However, candidates are also judged on the basis of human qualities and other attributes not related to the policies they espouse in a campaign. The spatial theory of electoral competition has, in the past, treated such attributes as part of the policy space over which candidates compete. However, certain difficulties attend such an interpretation. For example, it is difficult to view a candidates personality as something which can be altered to please the voters. The mistakes that an incumbent has committed in office are not things he can erase to compete more effectively for votes. A candidates religion cannot be abandoned because it is a political liability. In short, there are nonspatial attributes that affect voter evaluations of each candidate, which are beyond that candidates immediate control. It is the purpose of this paper to incorporate these nonspatial attributes into the spatial model of electoral competition to show how the policy outcome of two candidate electoral competition is af-

A single-blind controlled competition among tests for nonlinearity and chaos

Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and nonchaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by e-mail, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The results of this competition provide much surprising information about the power functions of some of the best regarded tests for nonlinearity or noisy chaos.

A New Approach to the Spatial Theory of Electoral Competition

In his unidimensional model of electoral competition, Downs argues that voters use party ideology as an informational short cut for forecasting the policies that a party will pursue if elected. Parties are perceived by voters as points on an ideological axis. In the Davis-Hinich multidimensional model, on the other hand, the axes are real issues, and the principal actors are politicians who are modeled as points in the multi-issue space. This paper reformulates spatial voting theory in terms of a model that connects what we call predictive dimensions with political issues that are salient during a given election campaign. This model is both a synthesis and an extension of the Downs and Davis-Hinich spatial models. We obtain a median voter result for one predictive dimension that is similar to the Downs result but with important differences. We also obtain results showing the electoral advantage of incumbency and the tendency for incremental change when there is a great deal of heterogeneity in voter perceptions about the candidates.