A Common-feature approach for testing present-value restrictions with financial data

It is well known that cointegration between the level of two variables (labeled Yt and yt in this paper) is a necessary condition to assess the empirical validity of a present-value model (PV and PVM, respectively, hereafter) linking them. The work on cointegration has been so prevalent that it is often overlooked that another necessary condition for the PVM to hold is that the forecast error entailed by the model is orthogonal to the past. The basis of this result is the use of rational expectations in forecasting future values of variables in the PVM. If this condition fails, the present-value equation will not be valid, since it will contain an additional term capturing the (non-zero) conditional expected value of future error terms. Our article has a few novel contributions, but two stand out. First, in testing for PVMs, we advise to split the restrictions implied by PV relationships into orthogonality conditions (or reduced rank restrictions) before additional tests on the value of parameters. We show that PV relationships entail a weak-form common feature relationship as in Hecq, Palm, and Urbain (2006) and in Athanasopoulos, Guillén, Issler and Vahid (2011) and also a polynomial serial-correlation common feature relationship as in Cubadda and Hecq (2001), which represent restrictions on dynamic models which allow several tests for the existence of PV relationships to be used. Because these relationships occur mostly with nancial data, we propose tests based on generalized method of moment (GMM) estimates, where it is straightforward to propose robust tests in the presence of heteroskedasticity. We also propose a robust Wald test developed to investigate the presence of reduced rank models. Their performance is evaluated in a Monte-Carlo exercise. Second, in the context of asset pricing, we propose applying a permanent-transitory (PT) decomposition based on Beveridge and Nelson (1981), which focus on extracting the long-run component of asset prices, a key concept in modern nancial theory as discussed in Alvarez and Jermann (2005), Hansen and Scheinkman (2009), and Nieuwerburgh, Lustig, Verdelhan (2010). Here again we can exploit the results developed in the common cycle literature to easily extract permament and transitory components under both long and also short-run restrictions. The techniques discussed herein are applied to long span annual data on long- and short-term interest rates and on price and dividend for the U.S. economy. In both applications we do not reject the existence of a common cyclical feature vector linking these two series. Extracting the long-run component shows the usefulness of our approach and highlights the presence of asset-pricing bubbles.

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.

Testing covariance stationarity

In this paper, we show that the widely used stationarity tests such as the KPSS test has power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) In the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) In the presence a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) The proposed test has the same size as traditional stationarity tests under the null hypothesis of covariance stationarity. An application to daily observations of return on US Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in sub-samples.

Testing for super-exogeneity in the presence of common deterministic shifts

This paper introduces the concept of common deterministic shifts (CDS). This concept is simple, intuitive and relates to the common structure of shifts or policy interventions. We propose a Reduced Rank technique to investigate the presence of CDS. The proposed testing procedure has standard asymptotics and good small-sample properties. We further link the concept of CDS to that of superexogeneity. It is shown that CDS tests can be constructed which allow to test for super-exogeneity. The Monte Carlo evidence indicates that the CDS test for super-exogeneity dominates testing procedures proposed in the literature.

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.

Análise do comportamento das expectativas de inflação no Brasil sob uma regra de aprendizado

Os estudos sobre as expectativas de inflação no Brasil rejeitam a hipótese de racionalidade. Essa rejeição se dá por meio de testes estatísticos que identificam a existência de um viés sistemático quando comparamos a expectativa de inflação e a inflação realizada. Atualizamos alguns destes testes com o tamanho de amostra disponível atualmente. No presente trabalho, realizamos um experimento de Monte Carlo que simula o comportamento da inflação e da sua expectativa em um modelo DSGE. Esse modelo inclui uma regra monetária sujeita a choques transitórios e permanentes (que representam uma mudança de regime). A partir das séries simuladas com esses modelos, realizamos testes estatísticos para verificar se os resultados são semelhantes aos observados na prática. O exercício de simulação realizado não foi capaz de gerar séries com essas mesmas características, não trazendo evidência que esse mecanismo de aprendizado possa explicar o viés encontrado nas expectativas de inflação.

Cherry picking with synthetic controls

The synthetic control (SC) method has been recently proposed as an alternative method to estimate treatment e ects in comparative case studies. Abadie et al. [2010] and Abadie et al. [2015] argue that one of the advantages of the SC method is that it imposes a data-driven process to select the comparison units, providing more transparency and less discretionary power to the researcher. However, an important limitation of the SC method is that it does not provide clear guidance on the choice of predictor variables used to estimate the SC weights. We show that such lack of speci c guidances provides signi cant opportunities for the researcher to search for speci cations with statistically signi cant results, undermining one of the main advantages of the method. Considering six alternative speci cations commonly used in SC applications, we calculate in Monte Carlo simulations the probability of nding a statistically signi cant result at 5% in at least one speci cation. We nd that this probability can be as high as 13% (23% for a 10% signi cance test) when there are 12 pre-intervention periods and decay slowly with the number of pre-intervention periods. With 230 pre-intervention periods, this probability is still around 10% (18% for a 10% signi cance test). We show that the speci cation that uses the average pre-treatment outcome values to estimate the weights performed particularly bad in our simulations. However, the speci cation-searching problem remains relevant even when we do not consider this speci cation. We also show that this speci cation-searching problem is relevant in simulations with real datasets looking at placebo interventions in the Current Population Survey (CPS). In order to mitigate this problem, we propose a criterion to select among SC di erent speci cations based on the prediction error of each speci cations in placebo estimations

Comunidades zooplanctônicas como bioindicadoras da qualidade da água de quatro reservatórios da região semi-árida do Rio Grande do Norte

The response of zooplankton assemblages to variations in the water quality of four man-made lakes, caused by eutrophication and siltation, was investigated by means of canonical correspondence analysis. Monte Carlo simulations using the CCA eingenvalues as test statistics revealed that changes in zooplankton species composition along the environmental gradients of trophic state and abiogenic turbidity were highly significant. The species Brachionus calyciflorus, Thermocyclops sp. and Argyrodiaptomus sp. were good indicators of eutrophic conditions while the species Brachionus dolabratus, Keratella tropica and Hexarthra sp. were good indicators of high turbidity due to suspended sediments. The rotifer genus Brachionus was the most species-rich taxon, comprising five species which were associated with different environmental conditions. Therefore, we tested whether this genus alone could potentially be a better biological indicator of these environmental gradients than the entire zooplankton assemblages or any other random set of five species. The ordination results show that the five Brachionus species alone did not explain better the observed pattern of environmental variation than most random sets of five species. Therefore, this genus could not be selected as a target taxon for more intensive environmental monitoring as has been previously suggested by Attayde and Bozelli (1998). Overall, our results show that changes in the water quality of man-made lakes in a tropical semi-arid region have significant effects on the structure of zooplankton assemblages that can potentially affect the functioning of these ecosystems

Análise de agrupamentos dos dados de DFA oriundos de perfis elétricos de indução de poços de petróleo

The main objective of this study is to apply recently developed methods of physical-statistic to time series analysis, particularly in electrical induction s profiles of oil wells data, to study the petrophysical similarity of those wells in a spatial distribution. For this, we used the DFA method in order to know if we can or not use this technique to characterize spatially the fields. After obtain the DFA values for all wells, we applied clustering analysis. To do these tests we used the non-hierarchical method called K-means. Usually based on the Euclidean distance, the K-means consists in dividing the elements of a data matrix N in k groups, so that the similarities among elements belonging to different groups are the smallest possible. In order to test if a dataset generated by the K-means method or randomly generated datasets form spatial patterns, we created the parameter Ω (index of neighborhood). High values of Ω reveals more aggregated data and low values of Ω show scattered data or data without spatial correlation. Thus we concluded that data from the DFA of 54 wells are grouped and can be used to characterize spatial fields. Applying contour level technique we confirm the results obtained by the K-means, confirming that DFA is effective to perform spatial analysis

ALGORITHM FOR PROBABILISTIC ANALYSIS of DISTRIBUTION SYSTEMS WITH DISTRIBUTED GENERATION

In this paper an efficient algorithm for probabilistic analysis of unbalanced three-phase weakly-meshed distribution systems is presented. This algorithm uses the technique of Two-Point Estimate Method for calculating the probabilistic behavior of the system random variables. Additionally, the deterministic analysis of the state variables is performed by means of a Compensation-Based Radial Load Flow (CBRLF). Such load flow efficiently exploits the topological characteristics of the network. To deal with distributed generation, a strategy to incorporate a simplified model of a generator in the CBRLF is proposed. Thus, depending on the type of control and generator operation conditions, the node with distributed generation can be modeled either as a PV or PQ node. To validate the efficiency of the proposed algorithm, the IEEE 37 bus test system is used. The probabilistic results are compared with those obtained using the Monte Carlo method.

Propriedades críticas do processo epidêmico difusivo com interação de Lévy

The diffusive epidemic process (PED) is a nonequilibrium stochastic model which, exhibits a phase trnasition to an absorbing state. In the model, healthy (A) and sick (B) individuals diffuse on a lattice with diffusion constants DA and DB, respectively. According to a Wilson renormalization calculation, the system presents a first-order phase transition, for the case DA > DB. Several researches performed simulation works for test this is conjecture, but it was not possible to observe this first-order phase transition. The explanation given was that we needed to perform simulation to higher dimensions. In this work had the motivation to investigate the critical behavior of a diffusive epidemic propagation with Lévy interaction(PEDL), in one-dimension. The Lévy distribution has the interaction of diffusion of all sizes taking the one-dimensional system for a higher-dimensional. We try to explain this is controversy that remains unresolved, for the case DA > DB. For this work, we use the Monte Carlo Method with resuscitation. This is method is to add a sick individual in the system when the order parameter (sick density) go to zero. We apply a finite size scalling for estimates the critical point and the exponent critical =, e z, for the case DA > DB

Tests of proportional hazards and proportional odds models for grouped survival data

In this paper, we derive score test statistics to discriminate between proportional hazards and proportional odds models for grouped survival data. These models are embedded within a power family transformation in order to obtain the score tests. In simple cases, some small-sample results are obtained for the score statistics using Monte Carlo simulations. Score statistics have distributions well approximated by the chi-squared distribution. Real examples illustrate the proposed tests.

Commissioning and performance of the CMS silicon strip tracker with cosmic ray muons

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)