Browsing by Author "Alastair Hall, Committee Chair"

Now showing 1 - 2 of 2

Second Order Approximations to GMM Statistics
(2006-05-08) Kyriakoulis, Konstantinos; Denis Pelletier, Committee Member; David Dickey, Committee Member; Atsushi Inoue, Committee Member; Alastair Hall, Committee Chair
This thesis uses second order approximations to study the finite sample behavior of statistics that are employed under the GMM setting. We present a Nagar (1959) approximation to the MSE of the IV estimates, when the disturbances are elliptically distributed. The accuracy of the approximation is illustrated through a comparison of the Nagar-type expansion with the exact finite sample MSE, that was derived in Knight (1985). The comparison suggests that second order approximations can be quite accurate, even when the sample size is 60 observations. This, alongside with the fact that exact results are more difficult to derive and harder to interpret, suggests that second-order approximations are powerful alternatives to the standard, first-order, asymptotic approximations. We proceed by analyzing the finite sample behavior of the LMstatistic, as it is employed under the GMM setting. This is achieved through a second order expansion, known as Edgeworth Expansion, of the distribution of the LM statistic. Our analysis suggests that the passage from the finite to the limiting distribution of the LM test is based on several measures, such as the variance-covariance matrix of the moments and its first derivative, the fourth product moment of the population moment condition, the covariance between the moments and their variance, the number of parameters, and the number of moments. We conclude with a simulation study that illustrates how these measures drive the passage from the finite sample to the asymptotic distribution.
Three Essays on Trend Analysis and Misspecification in Structural Econometric Models
(2003-09-02) Doorn, David John; David Flath, Committee Member; David Dickey, Committee Member; Alastair Hall, Committee Chair; John Seater, Committee Member
The purpose of this research has been to look into several econometric issues of concern to researchers doing applied work in macroeconomics. The first essay looks at Bureau of Economic Analysis data on inventories and sales of finished goods often used in studies of inventory behavior. Applying recently developed methods, the series are rigorously tested to determine their stationarity properties. Results indicate that neither first differencing nor linearly detrending the data is appropriate. For most series a trend function with one or more breaks offers a better fit and also generates stationarity. The results are used to determine the impact on estimation in a simple production-smoothing model of inventory behavior. The impact of different trend specifications on univariate forecasting of inventories is also considered. The second essay considers an alternative method of detrending time series data — the Hodrick-Prescott (HP) filter. Previous research has shown that HP filtering can have serious adverse consequences when used to analyze co-movements between data series at business cycle frequencies. Despite this, the filter has also been used to induce stationarity in a data series prior to estimation of structural econometric models. Little work has been done in analyzing the possible effects this may have on parameter estimates from such models. A simulation study is conducted to assess the impact of HP filtering on parameter estimation and a comparison is made to other detrending methods. It is shown that the HP filter induces bias in the parameter estimates and also increases the root mean squared error of the estimates from the simulations. In addition, there is some adverse impact on the size of certain test statistics. The final essay looks at the impact of misspecification on estimation results from a structural econometric model when using a Generalized Method of Moments estimator. Simulated data consistent with a particular specification of the model is used to estimate two misspecified versions. It is shown that misspecification causes the probability limit of the estimator to differ from the true value. It is further shown that a popular specification test performs poorly in detecting the misspecification. An alternative method of model selection is shown to perform far better. Finally, because the use of conventional asymptotic theory is not appropriate in misspecified models, a recently proposed alternative asymptotic theory is tested to determine whether there is improvement in the ability to perform inference on the parameters from misspecified models.