An Investigation into Rule of Thumb Behaviour in New Zealand

<p>In recent times, macroeconomic models have begun to describe aggregate consumer and firm behaviour by allowing some proportion to behave in a rule of thumb manner. This dissertation attempts to address two main issues that are concurrent in the literature. First I test for the proportion of aggregate behaviour that deviates from Classical consumer allocation theory and New Keynesian firm pricing theory in New Zealand. Rule of thumb consumers are assumed to consume out of current income as opposed to obeying the Permanent Income Hypothesis, while rule of thumb firms set prices in a backward looking manner. Using the GMM estimation procedure, I examine the sensitivity of estimates across a range of instrumental variables. After positive GMM specification tests I find the proportion of rule of thumb consumers is 0.21 and the proportion of backward looking price setters is 0.82. These results suggest that specifications which fail to allow for rule of thumb behaviour cannot fully reflect consumer and firm decisions. The second main issue seeks to address how these estimates compare to those estimated in a small open economy DSGE model. Monte Carlo Markov Chain (MCMC) estimation finds an estimated degree of external habit persistence of 0.9, proportion of rule of thumb consumers of 0.34, and the proportion of backward looking price setters falls to 0.7. A full range of MCMC diagnostics is subsequently computed. The diagnostic tests are largely favourable.</p>

An Investigation into Rule of Thumb Behaviour in New Zealand

<p>In recent times, macroeconomic models have begun to describe aggregate consumer and firm behaviour by allowing some proportion to behave in a rule of thumb manner. This dissertation attempts to address two main issues that are concurrent in the literature. First I test for the proportion of aggregate behaviour that deviates from Classical consumer allocation theory and New Keynesian firm pricing theory in New Zealand. Rule of thumb consumers are assumed to consume out of current income as opposed to obeying the Permanent Income Hypothesis, while rule of thumb firms set prices in a backward looking manner. Using the GMM estimation procedure, I examine the sensitivity of estimates across a range of instrumental variables. After positive GMM specification tests I find the proportion of rule of thumb consumers is 0.21 and the proportion of backward looking price setters is 0.82. These results suggest that specifications which fail to allow for rule of thumb behaviour cannot fully reflect consumer and firm decisions. The second main issue seeks to address how these estimates compare to those estimated in a small open economy DSGE model. Monte Carlo Markov Chain (MCMC) estimation finds an estimated degree of external habit persistence of 0.9, proportion of rule of thumb consumers of 0.34, and the proportion of backward looking price setters falls to 0.7. A full range of MCMC diagnostics is subsequently computed. The diagnostic tests are largely favourable.</p>

Inference Using Simulated Neural Moments

This paper studies method of simulated moments (MSM) estimators that are implemented using Bayesian methods, specifically Markov chain Monte Carlo (MCMC). Motivation and theory for the methods is provided by Chernozhukov and Hong (2003). The paper shows, experimentally, that confidence intervals using these methods may have coverage which is far from the nominal level, a result which has parallels in the literature that studies overidentified GMM estimators. A neural network may be used to reduce the dimension of an initial set of moments to the minimum number that maintains identification, as in Creel (2017). When MSM-MCMC estimation and inference is based on such moments, and using a continuously updating criteria function, confidence intervals have statistically correct coverage in all cases studied. The methods are illustrated by application to several test models, including a small DSGE model, and to a jump-diffusion model for returns of the S&P 500 index.

Worth the effort? Comparison of different MCMC algorithms for estimating the Pareto/NBD model

The Pareto/NBD model is one of the best-known models in customer base analysis. Extant literature has brought up three different Markov Chain Monte Carlo (MCMC) procedures for parameter estimation of this model. Nevertheless, three main research gaps remain. Firstly, the issue of hyper parameter sensitivity for these procedures has been disregarded even though this is crucial when dealing with small sample sizes. Secondly, present research lacks a performance comparison between the different MCMC procedures as well as with Maximum Likelihood Estimates (MLE). Thirdly, existing minimal data set requirements for this model neglect MCMC estimation procedures as they only refer to MLE. To tackle these gaps, we perform two extensive simulation studies. We demonstrate that the algorithms differ in their sensitivity towards the hyper distributions and identify one algorithm that outperforms the other procedures in all respects. In addition, we provide deeper insights into individual level forecasts when using MCMC and enhance extant data set limitation guidelines by considering not only the cohort size but also the length of the calibration period.

The Bayesian Susceptible-Exposed-Infected-Recovered model for the outbreak of COVID-19 on the Diamond Princess Cruise Ship

The outbreak of COVID-19 on the Diamond Princess Cruise Ship provides an unprecedented opportunity to estimate its original transmissibility with basic reproductive number (R0) and the effectiveness of containment measures. We developed an ordinary differential equation-based Susceptible-Exposed-Infected-Recovery (SEIR) model with Bayesian underpinning to estimate the main parameter of R0 determined by transmission coefficients, incubation period, and the recovery rate. Bayesian Markov Chain Monte Carlo (MCMC) estimation method was used to tackle the parameters of uncertainty resulting from the outbreak of COVID-19 given a small cohort of the cruise ship. The extended stratified SEIR model was also proposed to elucidate the heterogeneity of transmission route by the level of deck with passengers and crews. With the application of the overall model, R0 was estimated as high as 5.70 (95% credible interval: 4.23–7.79). The entire epidemic period without containment measurements was approximately 47 days and reached the peak one month later after the index case. The partial containment measure reduced 63% (95% credible interval: 60–66%) infected passengers. With the deck-specific SEIR model, the heterogeneity of R0 estimates by each deck was noted. The estimated R0 figures were 5.18 for passengers (5–14 deck), mainly from the within-deck transmission, and 2.46 for crews (2–4 deck), mainly from the between-deck transmission. Modelling the dynamic of COVID-19 on the cruise ship not only provides an insight into timely evacuation and early isolation and quarantine but also elucidates the relative contributions of different transmission modes on the cruise ship though the deck-stratified SEIR model.

Explaining Variability in Response Style Traits: A Covariate-Adjusted IRTree

Contamination of responses due to extreme and midpoint response style can confound the interpretation of scores, threatening the validity of inferences made from survey responses. This study incorporated person-level covariates in the multidimensional item response tree model to explain heterogeneity in response style. We include an empirical example and two simulation studies to support the use and interpretation of the model: parameter recovery using Markov chain Monte Carlo (MCMC) estimation and performance of the model under conditions with and without response styles present. Item intercepts mean bias and root mean square error were small at all sample sizes. Item discrimination mean bias and root mean square error were also small but tended to be smaller when covariates were unrelated to, or had a weak relationship with, the latent traits. Item and regression parameters are estimated with sufficient accuracy when sample sizes are greater than approximately 1,000 and MCMC estimation with the Gibbs sampler is used. The empirical example uses the National Longitudinal Study of Adolescent to Adult Health’s sexual knowledge scale. Meaningful predictors associated with high levels of extreme response latent trait included being non-White, being male, and having high levels of parental support and relationships. Meaningful predictors associated with high levels of the midpoint response latent trait included having low levels of parental support and relationships. Item-level covariates indicate the response style pseudo-items were less easy to endorse for self-oriented items, whereas the trait of interest pseudo-items were easier to endorse for self-oriented items.

Efficient Estimation of Large-Scale Spatial Capture-Recapture Models

Capture-recapture methods are a common tool in ecological statistics, which have been extended to spatial capture-recapture models for data accompanied by location information. However, standard formulations of these models can be unwieldy and computationally intractable for large spatial scales, many individuals, and/or activity center movement. We provide a cumulative series of methods that yield dramatic improvements in Markov chain Monte Carlo (MCMC) estimation for two examples. These include removing unnecessary computations, integrating out latent states, vectorizing declarations, and restricting calculations to the locality of individuals. Our approaches leverage the flexibility provided by the nimble R package. In our first example, we demonstrate an improvement in MCMC efficiency (the rate of generating effectively independent posterior samples) by a factor of 100. In our second example, we reduce the computing time required to generate 10,000 posterior samples from 4.5 hours down to five minutes, and realize an increase in MCMC efficiency by a factor of 25. We also explain how these approaches can be applied generally to other spatially-indexed hierarchical models. R code is provided for all examples, as well as an executable web-appendix.

Variational Bayes Inference for the DINA Model

In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables much faster computation than the existing Markov chain Monte Carlo (MCMC) method, while still offering the benefits of a full Bayesian framework. A simulation study revealed that the proposed VB estimation adequately recovered the parameter values. Moreover, an example using real data revealed that the proposed VB inference method provided similar estimates to MCMC estimation with much faster computation.

Bayesian estimation of IVW and MR-Egger models for two-sample Mendelian randomization studies

We present our package, mrbayes, for the open source software environment R. The package implements Bayesian estimation of IVW and MR-Egger models, including the radial MR-Egger model, for summary-level data Mendelian randomization analyses. We have implemented a choice of prior distributions for the model parameters, namely; weakly informative, non-informative, a joint prior for the MR-Egger model slope and intercept, and a pseudo-horseshoe prior, or the user can specify their own prior. We show how to use the package through an applied example investigating the causal effect of BMI on insulin resistance. In future work, we plan to provide functions for alternative MCMC estimation software such as Stan and OpenBugs.AvailabilityThe package is freely available, under the MIT license, on GitHub here https://github.com/okezie94/mrbayes.It can be installed in R using the following commands.There is a website of the package helpfiles at https://okezie94.github.io/mrbayes/.