Liquidity Constrains and Ricardian Equivalence in Estonia

This paper aims to find evidence of the influence of government deficit on private consumption in Estonia. The data only shows some support for Ricardian equivalence. Two approaches were used in the empirical tests. The Haque and Montiel (1989) equation of consumption was estimated using an instrumental variables technique. The Aschauer (1985) system of equations was estimated with the full information maximum likelihood method. Formal tests based on macro data could neither reject nor confirm the existence of liquidity constraints or Ricardian equivalence. There remains a lot of room for testing both of these hypotheses in Estonia. Further efforts to test liquidity constraints should concentrate on using micro data.Ricardian equivalence, liquidity constraints, Estonia

The equivalence of information-theoretic and likelihood-based methods for neural dimensionality reduction

Stimulus dimensionality-reduction methods in neuroscience seek to identify a low-dimensional space of stimulus features that affect a neuron's probability of spiking. One popular method, known as maximally informative dimensions (MID), uses an information-theoretic quantity known as "single-spike information" to identify this space. Here we examine MID from a model-based perspective. We show that MID is a maximum-likelihood estimator for the parameters of a linear-nonlinear-Poisson (LNP) model, and that the empirical single-spike information corresponds to the normalized log-likelihood under a Poisson model. This equivalence implies that MID does not necessarily find maximally informative stimulus dimensions when spiking is not well described as Poisson. We provide several examples to illustrate this shortcoming, and derive a lower bound on the information lost when spiking is Bernoulli in discrete time bins. To overcome this limitation, we introduce model-based dimensionality reduction methods for neurons with non-Poisson firing statistics, and show that they can be framed equivalently in likelihood-based or information-theoretic terms. Finally, we show how to overcome practical limitations on the number of stimulus dimensions that MID can estimate by constraining the form of the non-parametric nonlinearity in an LNP model. We illustrate these methods with simulations and data from primate visual cortex

Relational models for contingency tables

The paper considers general multiplicative models for complete and incomplete contingency tables that generalize log-linear and several other models and are entirely coordinate free. Sufficient conditions of the existence of maximum likelihood estimates under these models are given, and it is shown that the usual equivalence between multinomial and Poisson likelihoods holds if and only if an overall effect is present in the model. If such an effect is not assumed, the model becomes a curved exponential family and a related mixed parameterization is given that relies on non-homogeneous odds ratios. Several examples are presented to illustrate the properties and use of such models

Statistical considerations of noninferiority, bioequivalence and equivalence testing in biosimilars studies

In recent years, the development of follow-on biological products (biosimilars) has received increasing attention. The dissertation covers statistical methods related to three topics of Non-inferiority (NI), Bioequivalence (BE) and Equivalence in demonstrating biosimilarity. For NI, one of the key requirements is constancy assumption, that is, the effect of reference treatment is the same in current NI trials as in historical superiority trials. However if a covariate interacts with the treatment arms, then changes in distribution of this covariate will result in violation of constancy assumption. We propose a modified covariate-adjustment fixed margin method, and recommend it based on its performance characteristics in comparison with other methods. Topic two is related to BE inference for log-normal distributed data. Two drugs are bioequivalent if the difference of a pharmacokinetics (PK) parameter of two products falls within prespecified margins. In the presence of unspecified variances, existing methods like two one-sided tests and Bayesian analysis in BE setting limit our knowledge on the extent that inference of BE is affected by the variability of the PK parameter. We propose a likelihood approach that retains the unspecified variances in the model and partitions the entire likelihood function into two components: F-statistic function for variances and t-statistic function for difference of PK parameter. The advantage of the proposed method over existing methods is it helps identify range of variances where BE is more likely to be achieved. In the third topic, we extend the proposed likelihood method for Equivalence inference, where data is often normal distributed. In this part, we demonstrate an additional advantage of the proposed method over current analysis methods such as likelihood ratio test and Bayesian analysis in Equivalence setting. The proposed likelihood method produces results that are same or comparable to current analysis methods in general case when model parameters are independent. However it yields better results in special cases when model parameters are dependent, for example the ratio of variances is directly proportional to the ratio of means. Our research results suggest the proposed likelihood method serves a better alternative than the current analysis methods to address BE/Equivalence inference

The Generalized Method of Moments in the Bayesian Framework and a Model of Moment Selection Criterion

While the classical framework has a rich set of limited information procedures such as GMM and other related methods, the situation is not so in the Bayesian framework. We develop a limited information procedure in the Bayesian framework that does not require the knowledge of the likelihood function. The developed procedure is a Bayesian counterpart of the classical GMM but has advantages over the classical GMM in practical applications. The necessary limited information for our approach is a set of moment conditions, instead of the likelihood function, which has a counterpart in the classical GMM. Such moment conditions in the Bayesian framework are obtained from the equivalence condition of the Bayes' estimator and the GMM estimator. From such moment conditions, a posterior probability measure is derived that forms the basis of our limited information Bayesian procedure. This limited information posterior has some desirable properties for small and large sample analyses. An alternative approach is also provided in this paper for deriving a limited information posterior based on a variant of the empirical likelihood method where an empirical likelihood is obtained from the moment conditions of GMM. This alternative approach yields asymptotically the same result as the approach explained above. Based on our limited information method, we develop a procedure for selecting the moment for GMM. This moment selection procedure is an extension of the Bayesian model selection procedure to the Bayesian semi-parametric, limited information framework. It is shown that under some conditions the proposed moment selection procedure is a consistent decision rule.