Consider the class of two parameter marginal logistic (Rasch) models, for a test of m True-False items, where the latent ability is assumed to be bounded. Using results of Karlin and Studen, we show that this class of nonparametric marginal logistic (NML) models is equivalent to the class of marginal logistic models where the latent ability assumes at most (m + 2)/2 values. This equivalence has two implications. First, estimation for the NML model is accomplished by estimating the parameters of a discrete marginal logistic model. Second, consistency for the maximum likelihood estimates of the NML model can be shown (when m is odd) using the results of Kiefer and Wolfowitz. An example is presented which demonstrates the estimation strategy and contrasts the NML model with a normal marginal logistic model.

Using an infinite item test framework, it is argued that the usual assumption of local independence be replaced by a weaker assumption, essential independence. A fortiori, the usual assumption of unidimensionality is replaced by a weaker and arguably more appropriate statistically testable assumption of essential unidimennsionality. Essential unidimennsionnality implies the existence of a “unique” unidimensional latent ability. Essential unidimensionality is equivalent to the “consistent” estimation of this latnet ability in an ordinal scaling sense using any Balanced empirical scaling. A variation of this estimation approach allows consistent estimation of ability on the given latent ability scale.

Randomization tests are often recommended when parametric assumptions may be violated because they require no distributional or random sampling assumptions in order to be valid. In addition to being exact, a randomization test may also be more powerful than its parametric counterpart. This was demonstrated in a simulation study which examined the conditional power of three nondirectional tests: the randomization t test, the Wilcoxon–Mann–Whitney (WMW) test, and the parametric t test. When the treatment effect was skewed, with degree of skewness correlated with the size of the effect, the randomization t test was systematically more powerful than the parametric t test. The relative power of the WMW test under the skewed treatment effect condition depended on the sample size ratio.

Political polarization has become an increasingly salient issue worldwide, but a systematic examination of the variation and sources of mass polarization across countries is limited by current measurement methods. This work proposes a nonparametric, entropy-based measure of mass political polarization. It exploits the specific structure of ordinal distributions in public opinion data, makes no prior assumptions about the form and spacing of the data, and can still draw reliable measures of issue-based polarization. We demonstrate the theoretical and practical superiority of the measure with analytical comparisons and simulations. We then apply the proposed measure to questions about mass polarization in the USA, the relationship between radical parties and polarization in Europe, and cross-country trends in affective and ideological polarization.

Difference-in-differences is a widely used evaluation strategy that draws causal inference from observational panel data. Its causal identification relies on the assumption of parallel trends, which is scale-dependent and may be questionable in some applications. A common alternative is a regression model that adjusts for the lagged dependent variable, which rests on the assumption of ignorability conditional on past outcomes. In the context of linear models, Angrist and Pischke (2009) show that the difference-in-differences and lagged-dependent-variable regression estimates have a bracketing relationship. Namely, for a true positive effect, if ignorability is correct, then mistakenly assuming parallel trends will overestimate the effect; in contrast, if the parallel trends assumption is correct, then mistakenly assuming ignorability will underestimate the effect. We show that the same bracketing relationship holds in general nonparametric (model-free) settings. We also extend the result to semiparametric estimation based on inverse probability weighting. We provide three examples to illustrate the theoretical results with replication files in Ding and Li (2019).

Synthetic seed banks are a useful tool for tracking how weed populations change over time. By sowing a known number of seeds of a given species within a quadrat with defined boundaries, an investigator can measure the number remaining and thereby calculate demographic rates (e.g., mortality). The alternative is to use in situ seeds and estimate their initial population density via sampling. To make a synthetic seed bank approach useful within an agricultural system subjected to soil disturbances such as tillage, one would need a way to account for seeds leaving the initial quadrat (i.e., a way to follow how the area encompassing the sown seeds changes over time). Without accounting for the change in location/extent of the synthetic seed bank, any field operation moving soil will create additional uncertainty in population size. Depending on the “aggressiveness” of specific field operations and the initial size of the quadrat, this effect might be negligible or so large as to be intractable. Here, we describe a method for following a synthetic seed bank over time using a “living boundary” of nondormant seeds, which effectively play the role of tracers used in the study of dynamics in other scientific disciplines. Study quadrats in East Lansing, MI, and Arlington, WI, were sown with giant foxtail and velvetleaf at a rate of 2,000 seeds m−2. The study quadrats were marked on the perimeter and diagonals using nondormant seeds of three marker species: kale, radish, and rye. The areas were then subjected to tillage and planting operations. Spatial coordinates of seedling locations for the marker and weed species were obtained through digital image processing. A nonparametric comparison of the spatial displacement of marker and weed species indicated that their empirical spatial distributions did not differ. The marker species quadrats described by the 50th, 90th, and 99th quantiles of movement contained all velvetleaf seedlings in Wisconsin, all velvetleaf seedlings in Michigan, and all giant foxtail seedlings in Michigan, respectively. The results suggest a simple rule for applying the method to field demography studies: after the original quadrat is deformed and seedlings have emerged, flag the polygon containing all marker seedlings to obtain the expanded quadrat containing the study weed population.

A dynamic-stochastic model is developed to evaluate preferences among alternative countercyclical payment programs for representative farms producing corn or soybeans in Iowa and cotton or soybeans in Mississippi. Countercyclical payment programs are found to not necessarily be preferred to fixed payment programs.

Extension faculty have been educating cow-calf producers about value-added calf management programs and the premiums available at auction from these management practices for years. Despite these efforts, producers express doubt regarding the likelihood of premiums and the profitability of value-added management practices. We use matching pairs to calculate the difference in premiums and net returns between adopters and nonadopters and calculate the likelihood of positive net returns (and premiums) for individual practices and practice bundles. The probability of positive net returns ranges from 57% for dehorning to 79% for a certified vac-45 program (calves certified by a third party to be preconditioned for a minimum of 45 days, vaccinated, and dehorned) and probabilities increase with more practices adopted.

We consider a sequential rule, where an item is chosen into the group, such as a university faculty member, only if his/her score is better than the average score of those already belonging to the group. We study four variables: the average score of the members of the group after k items have been selected, the time it takes (in terms of the number of observed items) to assemble a group of k items, the average score of the group after n items have been observed, and the number of items kept after the first n items have been observed. We develop the relationships between these variables, and obtain their asymptotic behavior as k (respectively, n) tends to ∞. The assumption throughout is that the items are independent and identically distributed with a continuous distribution. Though knowledge of this distribution is not needed to implement the selection rule, the asymptotic behavior does depend on the distribution. We study in some detail the exponential, Pareto, and beta distributions. Generalizations of the ‘better than average’ rule to the β better than average rules are also considered. These are rules where an item is admitted to the group only if its score is better than β times the present average of the group, where β > 0.

Using U.K. data that are consistent with utility maximizing behavior by consumers, we construct aggregates for both consumption goods (nondurables and services) and monetary assets that are consistent with economic aggregation theory. Using these aggregates and the stock of durable goods, we estimate the elasticities of substitution between various consumption goods and monetary assets. These estimates are compared to the corresponding results from conventional monetary and consumption aggregates. The results give important information for monetary policy and the monetary transmission mechanism. In particular, these substitution estimates provide insight into the recent changes in expenditure on durable goods. We also show that the use of conventional U.K. consumption and monetary aggregates often give incorrect estimates of substitution and can provide misleading policy insights.

Specification tests reject a linear inflation forecasting model over the period 1959–2002. Based on this finding, we evaluate the out-of-sample inflation forecasts of a fully nonparametric model for 1994–2002. Our two main results are that: (i) nonlinear models produce much better forecasts than linear models, and (ii) including money growth in the nonparametric model yields marginal improvements, but including velocity reduces the mean squared forecast error by as much as 40%. A threshold model fits the data well over the full sample, offering an interpretation of our findings. We conclude that it is important to account for both nonlinearity and the behavior of monetary aggregates when forecasting inflation.

We propose inference tools to analyse the concordance (or correlation) order of random vectors. The analysis in the bivariate case relies on tests for upper and lower quadrant dominance of the true distribution by a parametric or semiparametric model, i.e. for a parametric or semiparametric model to give a probability that two variables are simultaneously small or large at least as great as it would be were they left unspecified. Tests for its generalisation in higher dimensions, namely joint lower and upper orthant dominance, are also analysed. The parametric and semiparametric settings are based on the copula representation for multivariate distribution, which allows for disentangling behaviour of margins and dependence structure. A distance test and an intersection-union test for inequality constraints are developed depending on the definition of null and alternative hypotheses. An empirical illustration is given for US insurance claim data.

We examine whether annual, quarterly, and monthly U.S. aggregate consumption data could have been generated by a utility-maximizing representative agent with intertemporally separable utility. The model appears inapplicable over the full time periods covered by the NIPA data, which are the sample periods often used in the literature. The model does appear applicable, however, over long subsamples. The data also are inconsistent with separability assumptions routinely made in the literature. In particular, the main categories of consumption (nondurables, services, and durables) are not mutually separable. We consider the implications of our results for inference about consumption based on the representative-agent model.