In this paper we examine, by Monte Carlo simulation, size and power of the Johansens trace test when the error covariance matrix is nonstationary, and we also investigate the properties of three different bootstrap cointegration tests. Earlier studies indicate that the Johansen trace test is not robust in presence of heteroscedasticity, and tests based on resampling methods have been proposed to solve the problem. The tests that are evaluated is the Johansen trace test, nonparametric bootstrap test and two different types of wild bootstrap tests. The wild bootstrap test is a resampling method that attempts to mimic the GARCH model by multiplying each residual by a stochastic variable with an expected value of zero and unit variance. The wild bootstrap tests proved to be superior to the other tests, but not as good as earlier indicated. The more the error terms differs from white noise, the worse these tests are doing. Although the wild bootstrap tests did not do a very bad job, the focus of further investigation should be to derive tests that does an even better job than the wild bootstrap tests examined here.

This thesis involves three essays that explore the theory and application of econometric analysis to labour market interventions. One essay is methodological, and two essays are applications. The first essay contributes to the literature on inference with data sets containing within-cluster correlation. The essay highlights a problem with current practices when the number of clusters is 11 or fewer. Current practices can result in p-values that are not point identified but are instead p-value intervals. The chapter provides Monte Carlo evidence to support a proposed solution to this problem. The second essay analyzes a labour market intervention within Canada--the Youth Hires program--which aimed to reduce youth unemployment. We find evidence that the program was able to increase employment among the targeted group. However, the impacts are only present for males, and we find evidence of displacement effects amongst the non-targeted group. The third essay examines a set of Graduate Retention Programs that several Canadian provinces offer. These programs are aimed at mitigating future skill shortages. Once the solution proposed in the first essay is applied, I find little evidence of the effectiveness of these programs in attracting or retaining recent graduates. / Thesis (Ph.D, Economics) -- Queen's University, 2013-07-05 15:56:33.805

Práce se vìnuje studiu variant metody bootstrap vhodných pro vy¹etøování vlastností autoregresních procesù s náhodnými koe cienty. Ètenáø je nejprve se- známen s pùvodní metodou bootstrap navr¾enou pro nezávislé stejnì rozdìlené náhodné velièiny a se základními variantami této metody bì¾nì pou¾ívanými pro analýzu èasových øad. Poté je pøedstaven autoregresní proces s náhodnými koe - cienty øádu p (RCA(p)). Jsou popsány základní vlastnosti tohoto procesu a blí¾e prozkoumány vlastnosti procesu RCA(1). V dal¹í èásti jsou uvedeny varianty me- tody bootstrap, které jsou v pøípadì procesu RCA(1) konzistentní, a pro metodu wild bootstrap je odvozena konzistence pro proces RCA(2). V poslední kapitole jsou na simulovaných datech ovìøeny vlastnosti popsaných metod. 1

This paper examines whether the CPI and real GDP for the US exhibit nonlinear reversion to trend as recently concluded by Beechey and Österholm [Beechey, M. and Österholm, P., 2008. Revisiting the uncertain unit root in GDP and CPI: testing for nonlinear trend reversion. Economics Letters 100, 221-223]. The wild bootstrap is used to correct for non-normality and heteroscedasticity in a nonlinear unit root test. The use of 'wild bootstrapped' critical values affects test conclusions in some cases. Results also are sensitive to the sample period examined.

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Missing data is a common issue in data analysis. Numerous techniques have been proposed to deal with the missing data problem. Imputation is the most popular strategy for handling the missing data. Imputation for data analysis is the process to replace the missing values with any plausible values. Two most frequent imputation techniques cited in literature are the single imputation and the multiple imputation. The multiple imputation, also known as the golden imputation technique, has been proposed by Rubin in 1987 to address the missing data. However, the inconsistency is the major problem in the multiple imputation technique. The single imputation is less popular in missing data research due to bias and less variability issues. One of the solutions to improve the single imputation technique in the basic regression model: the main motivation is that, the residual is added to improve the bias and variability. The residual is drawn by normal distribution assumption with a mean of 0, and the variance is equal to the residual variance. Although new methods in the single imputation technique, such as stochastic regression model, and hot deck imputation, might be able to improve the variability and bias issues, the single imputation techniques suffer with the uncertainty that may underestimate the R-square or standard error in the analysis results. The research reported in this thesis provides two imputation solutions for the single imputation technique. In the first imputation procedure, the wild bootstrap is proposed to improve the uncertainty for the residual variance in the regression model. In the second solution, the predictive mean matching (PMM) is enhanced, where the regression model is taking the main role to generate the recipient values while the observations in the donors are taken from the observed values. Then the missing values are imputed by randomly drawing one of the observations in the donor pool. The size of the donor pool is significant to determine the quality of the imputed values. The fixed size of donor is used to be employed in many existing research works with PMM imputation technique, but might not be appropriate in certain circumstance such as when the data distribution has high density region. Instead of using the fixed size of donor pool, the proposed method applies the radius-based solution to determine the size of donor pool. Both proposed imputation procedures will be combined with the Gaussian mixture model framework to preserve the original data distribution. The results reported in the thesis from the experiments on benchmark and artificial data sets confirm improvement for further data analysis. The proposed approaches are therefore worthwhile to be considered for further investigation and experiments.

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Bootstrapping is a resampling technique which treats the original data set as a population and draws samples from it with replacement. This technique is widely used, especially, in mathematically intractable problems. In this study, it is used to obtain the empirical distributions of the parameters to determine whether they are statistically significant or not in a special case of nonparametric regression, Conic Multivariate Adaptive Regression Splines (CMARS). Here, the CMARS method, which uses conic quadratic optimization, is a modified version of a well-known nonparametric regression model, Multivariate Adaptive Regression Splines (MARS). Although performing better with respect to several criteria, the CMARS model is more complex than that of MARS. To overcome this problem, and to improve the CMARS performance further, three different bootstrapping regression methods, namely, Random-X, Fixed-X and Wild Bootstrap are applied on four data sets with different size and scale. Then, the performances of the models are compared using various criteria including accuracy, precision, complexity, stability, robustness and efficiency. Random-X yields more precise, accurate and less complex models particularly for medium size and medium scale data even though it is the least efficient method.

Dans cette thèse, nous étudions des tests du type : (H0) : E [U | X] = 0 p.s. contre (H1) : P {E [U | X] = 0} < 1 où U est le résidu de la modélisation d'une variable Y en fonction de X. Dans ce cadre et pour plusieurs cas particuliers – significativité de variables, régression quantile, données fonctionnelles, modèle single-index –, nous proposons une statistique de test permettant d'obtenir des valeurs critiques issues d'une loi asymptotique pivotale. Dans chaque cas, nous donnons également une méthode de bootstrap appropriée pour les échantillons de petite taille. Nous montrons la consistance envers des alternatives locales – ou à la Pitman – des tests proposés, lorsque ce type d'alternative ne tend pas trop vite vers l'hypothèse nulle. À chaque fois, nous vérifions à partir de simulations sous l'hypothèse nulle et sous une séquence d'hypothèses alternatives que les résultats théoriques sont en accord avec la pratique. / In this thesis, we study test statistics of the form : (H0) : E [U | X] = 0 p.s. contre (H1) : P {E [U | X] = 0} < 1 where U is the residual of some Y modeling with respect to covariates X. In this setup and for several particular cases – significance, quantile regression, functional data, single-index model –, we introduce test statistics that have pivotal asymptotic critical values. For each case, we also give a suitable bootstrap procedure for small samples. We prove the consistency against local – or Pitman – alternatives for the proposed test statistics, when such an alternative does not get close to the null hypothesis too fast. Simulation studies are used to check the effectiveness of the theoretical results in applications.

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