Ranald Macdonald and statistical inference

Ranald Roderick Macdonald (1945-2007) was an important contributor to mathematical psychology in the UK, as a referee and action editor for British Journal of Mathematical and Statistical Psychology and as a participant and organizer at the British Psychological Society's Mathematics, statistics and computing section meetings. This appreciation argues that his most important contribution was to the foundations of significance testing, where his concern about what information was relevant in interpreting the results of significance tests led him to be a persuasive advocate for the 'Weak Fisherian' form of hypothesis testing.

Climate variability and human impact in South America during the last 2000 years: synthesis and perspectives from pollen records

An improved understanding of present-day climate variability and change relies on high-quality data sets from the past 2 millennia. Global efforts to model regional climate modes are in the process of being validated against, and integrated with, records of past vegetation change. For South America, however, the full potential of vegetation records for evaluating and improving climate models has hitherto not been sufficiently acknowledged due to an absence of information on the spatial and temporal coverage of study sites. This paper therefore serves as a guide to high-quality pollen records that capture environmental variability during the last 2 millennia. We identify 60 vegetation (pollen) records from across South America which satisfy geochronological requirements set out for climate modelling, and we discuss their sensitivity to the spatial signature of climate modes throughout the continent. Diverse patterns of vegetation response to climate change are observed, with more similar patterns of change in the lowlands and varying intensity and direction of responses in the highlands. Pollen records display local-scale responses to climate modes; thus, it is necessary to understand how vegetation–climate interactions might diverge under variable settings. We provide a qualitative translation from pollen metrics to climate variables. Additionally, pollen is an excellent indicator of human impact through time. We discuss evidence for human land use in pollen records and provide an overview considered useful for archaeological hypothesis testing and important in distinguishing natural from anthropogenically driven vegetation change. We stress the need for the palynological community to be more familiar with climate variability patterns to correctly attribute the potential causes of observed vegetation dynamics. This manuscript forms part of the wider LOng-Term multi-proxy climate REconstructions and Dynamics in South America – 2k initiative that provides the ideal framework for the integration of the various palaeoclimatic subdisciplines and palaeo-science, thereby jump-starting and fostering multidisciplinary research into environmental change on centennial and millennial timescales.

Inference for a skew extension of the Grubbs model

In this paper, we discuss inferential aspects for the Grubbs model when the unknown quantity x (latent response) follows a skew-normal distribution, extending early results given in Arellano-Valle et al. (J Multivar Anal 96:265-281, 2005b). Maximum likelihood parameter estimates are computed via the EM-algorithm. Wald and likelihood ratio type statistics are used for hypothesis testing and we explain the apparent failure of the Wald statistics in detecting skewness via the profile likelihood function. The results and methods developed in this paper are illustrated with a numerical example.

Common Features in Vector Nonlinear Time Series Models

This thesis consists of four manuscripts in the area of nonlinear time series econometrics on topics of testing, modeling and forecasting nonlinear common features. The aim of this thesis is to develop new econometric contributions for hypothesis testing and forecasting in these area. Both stationary and nonstationary time series are concerned. A definition of common features is proposed in an appropriate way to each class. Based on the definition, a vector nonlinear time series model with common features is set up for testing for common features. The proposed models are available for forecasting as well after being well specified. The first paper addresses a testing procedure on nonstationary time series. A class of nonlinear cointegration, smooth-transition (ST) cointegration, is examined. The ST cointegration nests the previously developed linear and threshold cointegration. An Ftypetest for examining the ST cointegration is derived when stationary transition variables are imposed rather than nonstationary variables. Later ones drive the test standard, while the former ones make the test nonstandard. This has important implications for empirical work. It is crucial to distinguish between the cases with stationary and nonstationary transition variables so that the correct test can be used. The second and the fourth papers develop testing approaches for stationary time series. In particular, the vector ST autoregressive (VSTAR) model is extended to allow for common nonlinear features (CNFs). These two papers propose a modeling procedure and derive tests for the presence of CNFs. Including model specification using the testing contributions above, the third paper considers forecasting with vector nonlinear time series models and extends the procedures available for univariate nonlinear models. The VSTAR model with CNFs and the ST cointegration model in the previous papers are exemplified in detail,and thereafter illustrated within two corresponding macroeconomic data sets.

Product placement in movies: a cross cultural study between Brazil and the USA

The broader objective of this study undertaking can briefly be articulated in particulate aims as follows: to measure the attitudes of consumers regarding the brand displayed by this strategy as well as to highlight recall, recognition and purchase intentions generated by product placement on consumers. In addition, check the differences and similarities between the behavior of Brazilian and American consumers caused by the influence of product placements. The study was undertaken targeting consumer audience in Brazil and the U.S. A rang3 modeling set ups were performed in order to realign study instruments and hypothesis towards the research objectives. This study gave focus on the following hypothesized models. H1: Consumers / Participants who viewed the brands / products in the movie have a higher brand / product recall compared to the consumers / participants who did not view the brands / products in the movie. H2: US Consumers / Participants are able to recognize and recall brands / products which appear in the background of the movie than Brazil. H3: Consumers / participants from USA are more accepting of product placements compared to their counterparts in Brazil. H4: There are discernible similarities in consumer / participant brand attitudes and purchase intentions in consumers / participants from USA and Brazil in spite of the fact that their country of origin is different. Cronbach’s Alpha Coefficient ensured the reliability of survey instruments. The study involved the use of the Structural Equation Modeling (SEM) for the hypothesis testing. This study used the Confirmatory Factor Analysis (CFA) to assess both the convergent and discriminant validities instead of using the Exploratory Factor Analysis (EFA) or the Principal Component Analysis (PCA). This reinforced for the use of the regression Chi Square and T statistical tests in further. Only hypothesis H3 was rejected, the rest were not. T test provided insight findings on specific subgroup significant differences. In the SEM testing, the error variance for product placement attitudes was negative for both the groups. On this The Heywood Case came in handy to fix negative values. The researcher used both quantitative and qualitative approach where closed ended questionnaires and interviews respectively were used to collect primary data. The results were additionally provided with tabulations. It can be concluded that, product placement varies markedly in the U.S. from Brazil based on the influence a range of factors provided in the study. However, there are elements of convergence probably driven by the convergence in technology. In order, product placement to become more competitive in the promotional marketing, there will be the need for researchers to extend focus from the traditional variables and add knowledge on the conventional marketplace factors that is the sell-ability of the product placement technologies and strategies.

Wald tests for IV regression with weak instruments

This dissertation deals with the problem of making inference when there is weak identification in models of instrumental variables regression. More specifically we are interested in one-sided hypothesis testing for the coefficient of the endogenous variable when the instruments are weak. The focus is on the conditional tests based on likelihood ratio, score and Wald statistics. Theoretical and numerical work shows that the conditional t-test based on the two-stage least square (2SLS) estimator performs well even when instruments are weakly correlated with the endogenous variable. The conditional approach correct uniformly its size and when the population F-statistic is as small as two, its power is near the power envelopes for similar and non-similar tests. This finding is surprising considering the bad performance of the two-sided conditional t-tests found in Andrews, Moreira and Stock (2007). Given this counter intuitive result, we propose novel two-sided t-tests which are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test of Moreira (2003).

Essays on Spatial Econometrics

Esta dissertação concentra-se nos processos estocásticos espaciais definidos em um reticulado, os chamados modelos do tipo Cliff & Ord. Minha contribuição nesta tese consiste em utilizar aproximações de Edgeworth e saddlepoint para investigar as propriedades em amostras finitas do teste para detectar a presença de dependência espacial em modelos SAR (autoregressivo espacial), e propor uma nova classe de modelos econométricos espaciais na qual os parâmetros que afetam a estrutura da média são distintos dos parâmetros presentes na estrutura da variância do processo. Isto permite uma interpretação mais clara dos parâmetros do modelo, além de generalizar uma proposta de taxonomia feita por Anselin (2003). Eu proponho um estimador para os parâmetros do modelo e derivo a distribuição assintótica do estimador. O modelo sugerido na dissertação fornece uma interpretação interessante ao modelo SARAR, bastante comum na literatura. A investigação das propriedades em amostras finitas dos testes expande com relação a literatura permitindo que a matriz de vizinhança do processo espacial seja uma função não-linear do parâmetro de dependência espacial. A utilização de aproximações ao invés de simulações (mais comum na literatura), permite uma maneira fácil de comparar as propriedades dos testes com diferentes matrizes de vizinhança e corrigir o tamanho ao comparar a potência dos testes. Eu obtenho teste invariante ótimo que é também localmente uniformemente mais potente (LUMPI). Construo o envelope de potência para o teste LUMPI e mostro que ele é virtualmente UMP, pois a potência do teste está muito próxima ao envelope (considerando as estruturas espaciais definidas na dissertação). Eu sugiro um procedimento prático para construir um teste que tem boa potência em uma gama de situações onde talvez o teste LUMPI não tenha boas propriedades. Eu concluo que a potência do teste aumenta com o tamanho da amostra e com o parâmetro de dependência espacial (o que está de acordo com a literatura). Entretanto, disputo a visão consensual que a potência do teste diminui a medida que a matriz de vizinhança fica mais densa. Isto reflete um erro de medida comum na literatura, pois a distância estatística entre a hipótese nula e a alternativa varia muito com a estrutura da matriz. Fazendo a correção, concluo que a potência do teste aumenta com a distância da alternativa à nula, como esperado.

A unit root test based on partially adaptive estimation

This paper constructs a unit root test baseei on partially adaptive estimation, which is shown to be robust against non-Gaussian innovations. We show that the limiting distribution of the t-statistic is a convex combination of standard normal and DF distribution. Convergence to the DF distribution is obtaineel when the innovations are Gaussian, implying that the traditional ADF test is a special case of the proposed testo Monte Carlo Experiments indicate that, if innovation has heavy tail distribution or are contaminated by outliers, then the proposed test is more powerful than the traditional ADF testo Nominal interest rates (different maturities) are shown to be stationary according to the robust test but not stationary according to the nonrobust ADF testo This result seems to suggest that the failure of rejecting the null of unit root in nominal interest rate may be due to the use of estimation and hypothesis testing procedures that do not consider the absence of Gaussianity in the data.Our results validate practical restrictions on the behavior of the nominal interest rate imposed by CCAPM, optimal monetary policy and option pricing models.

Improved combinations of parametric and nonparametric Regression estimators

This paper provides a systematic and unified treatment of the developments in the area of kernel estimation in econometrics and statistics. Both the estimation and hypothesis testing issues are discussed for the nonparametric and semiparametric regression models. A discussion on the choice of windowwidth is also presented.

Asymptotic efficiency in an instrumental variable model

Esta dissertação se propõe ao estudo de inferência usando estimação por método generalizado dos momentos (GMM) baseado no uso de instrumentos. A motivação para o estudo está no fato de que sob identificação fraca dos parâmetros, a inferência tradicional pode levar a resultados enganosos. Dessa forma, é feita uma revisão dos mais usuais testes para superar tal problema e uma apresentação dos arcabouços propostos por Moreira (2002) e Moreira & Moreira (2013), e Kleibergen (2005). Com isso, o trabalho concilia as estatísticas utilizadas por eles para realizar inferência e reescreve o teste score proposto em Kleibergen (2005) utilizando as estatísticas de Moreira & Moreira (2013), e é obtido usando a teoria assintótica em Newey & McFadden (1984) a estatística do teste score ótimo. Além disso, mostra-se a equivalência entre a abordagem por GMM e a que usa sistema de equações e verossimilhança para abordar o problema de identificação fraca.

Inference in differences-in-differences with few treated groups and heteroskedasticity

Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we can model the heteroskedasticity of a linear combination of the errors. We show that this assumption can be satisfied without imposing strong assumptions on the errors in common DID applications. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative inference method that relies on strict stationarity and ergodicity of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment periods. We extend our inference methods to linear factor models when there are few treated groups. We also derive conditions under which a permutation test for the synthetic control estimator proposed by Abadie et al. (2010) is robust to heteroskedasticity and propose a modification on the test statistic that provided a better heteroskedasticity correction in our simulations.

Inference in differences-in-differences with few treated groups and heteroskedasticity

Differences-in-Differences (DID) is one of the most widely used identification strategies in applied economics. However, how to draw inferences in DID models when there are few treated groups remains an open question. We show that the usual inference methods used in DID models might not perform well when there are few treated groups and errors are heteroskedastic. In particular, we show that when there is variation in the number of observations per group, inference methods designed to work when there are few treated groups tend to (under-) over-reject the null hypothesis when the treated groups are (large) small relative to the control groups. This happens because larger groups tend to have lower variance, generating heteroskedasticity in the group x time aggregate DID model. We provide evidence from Monte Carlo simulations and from placebo DID regressions with the American Community Survey (ACS) and the Current Population Survey (CPS) datasets to show that this problem is relevant even in datasets with large numbers of observations per group. We then derive an alternative inference method that provides accurate hypothesis testing in situations where there are few treated groups (or even just one) and many control groups in the presence of heteroskedasticity. Our method assumes that we know how the heteroskedasticity is generated, which is the case when it is generated by variation in the number of observations per group. With many pre-treatment periods, we show that this assumption can be relaxed. Instead, we provide an alternative application of our method that relies on assumptions about stationarity and convergence of the moments of the time series. Finally, we consider two recent alternatives to DID when there are many pre-treatment groups. We extend our inference method to linear factor models when there are few treated groups. We also propose a permutation test for the synthetic control estimator that provided a better heteroskedasticity correction in our simulations than the test suggested by Abadie et al. (2010).

Theoretical and empirical essays on microeconometrics

This Master Thesis consists of one theoretical article and one empirical article on the field of Microeconometrics. The first chapter\footnote{We also thank useful suggestions by Marinho Bertanha, Gabriel Cepaluni, Brigham Frandsen, Dalia Ghanem, Ricardo Masini, Marcela Mello, Áureo de Paula, Cristine Pinto, Edson Severnini and seminar participants at São Paulo School of Economics, the California Econometrics Conference 2015 and the 37\textsuperscript{th} Brazilian Meeting of Econometrics.}, called \emph{Synthetic Control Estimator: A Generalized Inference Procedure and Confidence Sets}, contributes to the literature about inference techniques of the Synthetic Control Method. This methodology was proposed to answer questions involving counterfactuals when only one treated unit and a few control units are observed. Although this method was applied in many empirical works, the formal theory behind its inference procedure is still an open question. In order to fulfill this lacuna, we make clear the sufficient hypotheses that guarantee the adequacy of Fisher's Exact Hypothesis Testing Procedure for panel data, allowing us to test any \emph{sharp null hypothesis} and, consequently, to propose a new way to estimate Confidence Sets for the Synthetic Control Estimator by inverting a test statistic, the first confidence set when we have access only to finite sample, aggregate level data whose cross-sectional dimension may be larger than its time dimension. Moreover, we analyze the size and the power of the proposed test with a Monte Carlo experiment and find that test statistics that use the synthetic control method outperforms test statistics commonly used in the evaluation literature. We also extend our framework for the cases when we observe more than one outcome of interest (simultaneous hypothesis testing) or more than one treated unit (pooled intervention effect) and when heteroskedasticity is present. The second chapter, called \emph{Free Economic Area of Manaus: An Impact Evaluation using the Synthetic Control Method}, is an empirical article. We apply the synthetic control method for Brazilian city-level data during the 20\textsuperscript{th} Century in order to evaluate the economic impact of the Free Economic Area of Manaus (FEAM). We find that this enterprise zone had positive significant effects on Real GDP per capita and Services Total Production per capita, but it also had negative significant effects on Agriculture Total Production per capita. Our results suggest that this subsidy policy achieve its goal of promoting regional economic growth, even though it may have provoked mis-allocation of resources among economic sectors.

Evolutionary Changes in the Complexity of the Tectum of Nontetrapods: A Cladistic Approach

Background: The tectum is a structure localized in the roof of the midbrain in vertebrates, and is taken to be highly conserved in evolution. The present article assessed three hypotheses concerning the evolution of lamination and citoarchitecture of the tectum of nontetrapod animals: 1) There is a significant degree of phylogenetic inertia in both traits studied (number of cellular layers and number of cell classes in tectum); 2) Both traits are positively correlated accross evolution after correction for phylogeny; and 3) Different developmental pathways should generate different patterns of lamination and cytoarchitecture.Methodology/Principal Findings: The hypotheses were tested using analytical-computational tools for phylogenetic hypothesis testing. Both traits presented a considerably large phylogenetic signal and were positively associated. However, no difference was found between two clades classified as per the general developmental pathways of their brains.Conclusions/Significance: The evidence amassed points to more variation in the tectum than would be expected by phylogeny in three species from the taxa analysed; this variation is not better explained by differences in the main course of development, as would be predicted by the developmental clade hypothesis. Those findings shed new light on the evolution of an functionally important structure in nontetrapods, the most basal radiations of vertebrates.

Proposição e validações de equações para estimativa da erosividade de dois municípios do estado de São Paulo

The equations and extrapolation use to localities whose characteristics of soil and climate, even if partial, distinguish the town to which they were generated, still permeate in studies to estimate the rainfall erosivity (EI 30). This work has objective to propose and validate mathematical equations to estimate the rainfall erosivity of two cities of Sao Paulo State's. The adjusted to estimate obtaining and validate data of equations of erosivity (EI 30) according to values of coefficient of rain (Rc) were obtained from pluviographic and pluviometric rainfall data, respectively, using of distinct historical rainfall series. Mutiple comparisions test and confidence intervals were performed to compare absolute average of EI 30, pluviometric data (Pp), and Rc. The correlation between EI 30 and Rc was verified by of Pearson correlation coefficient. Test of the hypothesis of equality between population variance was used to compare the equations. Pluviometrics data of historical series rainfall data different than those that the models were generated were used to validate and to assess the performance of the equations, proposed of this study and compare them with another equation already consolidated in literature. The results show that for the conditions under which the study was conducted, the simple linear equations, shown to be the most appropriate to estimate the rainfall erosivity these two cities. According to the test of the hypothesis of equality variances between populations, the equations adjusted for each city differ statistically so that the rainfall erosivity of each city must be estimated by their respective equation.