Diese Arbeit behandelt die Instrumentalvariablenregression im Kontext der Stichprobenwiederholung. Es wird ein Rahmen geschaffen, der das Ziel der Inferenz identifiziert. Diese Abhandlung versucht die Instrumentalvariablenregression von einer neuen Perspektive aus zu motivieren. Dabei wird angenommen, dass das Ziel der Schätzung von zwei Faktoren gebildet wird, einer Umgebung und einer zu einem internen Model spezifischen Struktur. Neben diesem Rahmen entwickelt die Arbeit eine Methode der Stichprobenwiederholung, die geeignet für das Testen einer linearen Hypothese bezüglich der Schätzung des Ziels ist. Die betreffende technische Umgebung und das Verfahren werden im Zusammenhang in der Einleitung und im Hauptteil der folgenden Arbeit erklärt. Insbesondere, aufbauend auf der Arbeit von Spokoiny, Zhilova 2015, rechtfertigt und wendet diese Arbeit ein numerisches ’multiplier-bootstrap’ Verfahren an, um nicht asymptotische Konfidenzintervalle für den Hypothesentest zu konstruieren. Das Verfahren und das zugrunde liegende statistische Werkzeug wurden so gewählt und angepasst, um ein im Model auftretendes und von asymptotischer Analysis übersehenes Problem zu erklären, das formal als Schwachheit der Instrumentalvariablen bekannt ist. Das angesprochene Problem wird jedoch durch den endlichen Stichprobenansatz von Spokoiny 2014 adressiert. / Instrumental variables regression in the context of a re-sampling is considered. In the work a framework is built to identify an inferred target function. It attempts to approach an idea of a non-parametric regression and motivate instrumental variables regression from a new perspective. The framework assumes a target of estimation to be formed by two factors - an environment and an internal, model specific structure. Aside from the framework, the work develops a re-sampling method suited to test linear hypothesis on the target. Particular technical environment and procedure are given and explained in the introduction and in the body of the work. Specifically, following the work of Spokoiny, Zhilova 2015, the writing justifies and applies numerically 'multiplier bootstrap' procedure to construct confidence intervals for the testing problem. The procedure and underlying statistical toolbox were chosen to account for an issue appearing in the model and overlooked by asymptotic analysis, that is weakness of instrumental variables. The issue, however, is addressed by design of the finite sample approach by Spokoiny 2014.

Submitted by Lucas Pimentel Vilela (lucaspimentelvilela@gmail.com) on 2017-05-04T01:19:37Z No. of bitstreams: 1 Hypothesis Testing in Econometric Models - Vilela 2017.pdf: 2079231 bytes, checksum: d0387462f36ab4ab7e5d33163bb68416 (MD5) / Approved for entry into archive by Maria Almeida (maria.socorro@fgv.br) on 2017-05-15T19:31:43Z (GMT) No. of bitstreams: 1 Hypothesis Testing in Econometric Models - Vilela 2017.pdf: 2079231 bytes, checksum: d0387462f36ab4ab7e5d33163bb68416 (MD5) / Made available in DSpace on 2017-05-15T19:32:18Z (GMT). No. of bitstreams: 1 Hypothesis Testing in Econometric Models - Vilela 2017.pdf: 2079231 bytes, checksum: d0387462f36ab4ab7e5d33163bb68416 (MD5) Previous issue date: 2015-12-11 / This thesis contains three chapters. The first chapter considers tests of the parameter of an endogenous variable in an instrumental variables regression model. The focus is on one-sided conditional t-tests. Theoretical and numerical work shows that the conditional 2SLS and Fuller t-tests perform well even when instruments are weakly correlated with the endogenous variable. When the population F-statistic is as small as two, the power is reasonably close to the power envelopes for similar and non-similar tests which are invariant to rotation transformations of the instruments. This finding is surprising considering the poor performance of two-sided conditional t-tests found in Andrews, Moreira, and Stock (2007). These tests have bad power because the conditional null distributions of t-statistics are asymmetric when instruments are weak. Taking this asymmetry into account, we propose two-sided tests based on t-statistics. These novel tests are approximately unbiased and can perform as well as the conditional likelihood ratio (CLR) test. The second and third chapters are interested in maxmin and minimax regret tests for broader hypothesis testing problems. In the second chapter, we present maxmin and minimax regret tests satisfying more general restrictions than the alpha-level and the power control over all alternative hypothesis constraints. More general restrictions enable us to eliminate trivial known tests and obtain tests with desirable properties, such as unbiasedness, local unbiasedness and similarity. In sequence, we prove that both tests always exist and under suficient assumptions, they are Bayes tests with priors that are solutions of an optimization problem, the dual problem. In the last part of the second chapter, we consider testing problems that are invariant to some group of transformations. Under the invariance of the hypothesis testing, the Hunt-Stein Theorem proves that the search for maxmin and minimax regret tests can be restricted to invariant tests. We prove that the Hunt-Stein Theorem still holds under the general constraints proposed. In the last chapter we develop a numerical method to implement maxmin and minimax regret tests proposed in the second chapter. The parametric space is discretized in order to obtain testing problems with a finite number of restrictions. We prove that, as the discretization turns finer, the maxmin and the minimax regret tests satisfying the finite number of restrictions have the same alternative power of the maxmin and minimax regret tests satisfying the general constraints. Hence, we can numerically implement tests for a finite number of restrictions as an approximation for the tests satisfying the general constraints. The results in the second and third chapters extend and complement the maxmin and minimax regret literature interested in characterizing and implementing both tests. / Esta tese contém três capítulos. O primeiro capítulo considera testes de hipóteses para o coeficiente de regressão da variável endógena em um modelo de variáveis instrumentais. O foco é em testes-t condicionais para hipóteses unilaterais. Trabalhos teóricos e numéricos mostram que os testes-t condicionais centrados nos estimadores de 2SLS e Fuller performam bem mesmo quando os instrumentos são fracamente correlacionados com a variável endógena. Quando a estatística F populacional é menor que dois, o poder é razoavelmente próximo do poder envoltório para testes que são invariantes a transformações que rotacionam os instrumentos (similares ou não similares). Este resultado é surpreendente considerando a baixa performance dos testes-t condicionais para hipóteses bilaterais apresentado em Andrews, Moreira, and Stock (2007). Estes testes possuem baixo poder porque as distribuições das estatísticas-t na hipótese nula são assimétricas quando os instrumentos são fracos. Explorando tal assimetria, nós propomos testes para hipóteses bilaterais baseados em estatísticas-t. Estes testes são aproximadamente não viesados e podem performar tão bem quanto o teste de razão de máxima verossimilhança condicional. No segundo e no terceiro capítulos, nosso interesse é em testes do tipo maxmin e minimax regret para testes de hipóteses mais gerais. No segundo capítulo, nós apresentamos testes maxmin e minimax regret que satisfazem restrições mais gerais que as restrições de tamanho e de controle sobre todo o poder na hipótese alternativa. Restrições mais gerais nos possibilitam eliminar testes triviais e obter testes com propriedades desejáveis, como por exemplo não viés, não viés local e similaridade. Na sequência, nós provamos que ambos os testes existem e, sob condições suficientes, eles são testes Bayesianos com priors que são solução de um problema de otimização, o problema dual. Na última parte do segundo capítulo, nós consideramos testes de hipóteses que são invariantes à algum grupo de transformações. Sob invariância, o Teorema de Hunt-Stein implica que a busca por testes maxmin e minimax regret pode ser restrita a testes invariantes. Nós provamos que o Teorema de Hunt-Stein continua válido sob as restrições gerais propostas. No último capítulo, nós desenvolvemos um procedimento numérico para implementar os testes maxmin e minimax regret propostos no segundo capítulo. O espaço paramétrico é discretizado com o objetivo de obter testes de hipóteses com um número finito de pontos. Nós provamos que, ao considerarmos partições mais finas, os testes maxmin e minimax regret que satisfazem um número finito de pontos possuem o mesmo poder na hipótese alternativa que os testes maxmin e minimax regret que satisfazem as restrições gerais. Portanto, nós podemos implementar numericamente os testes que satisfazem um número finito de pontos como aproximação aos testes que satisfazem as restrições gerais.