The effects of autocorrelation among errors on the consistency property of OLS variance estimator

In a linear regression model the ordinary least squares (OLS) variance estimator (S²) converges in probability to E(S²) even when the errors are autocorrelated. Of interest, however, is the rate of convergence. In this paper we shed some light on this question for the case of a linear trend model. In particular the relation between the rate of convergence and the correlation property of the errors is explored. It is shown that the retardation of the rate of convergence is not appreciable if the correlation is moderate, but it can be severe for extreme correlations.     

A simple ordered data estimator for inverse density weighted expectations

We consider estimation of means of functions that are scaled by an unknown density, or equivalently, integrals of conditional expectations. The “ordered data” estimator we provide is root n$n$ consistent, asymptotically normal, and is numerically extremely simple, involving little more than ordering the data and summing the results. No sample-size-dependent smoothing is required. A similarly simple estimator is provided for the limiting variance. The proofs include new limiting distribution results for functions of nearest-neighbor spacings. Potential applications include endogenous binary choice, willingness to pay, selection, and treatment models.     

Re-examining 50-year-old OLS estimates of the Klein–Goldberger model

This paper examines the ordinary least squares estimates of the Klein–Goldberger model by Fox ( Journal of Political Economy , 64 , 1956, 128). Because Klein and Goldberger published the data set with the model, it is possible to re-examine Fox's results years later, and investigate the accuracy with which these estimates were calculated. The examination reported in this paper was conducted by making independent estimates using three different modern econometric software packages. This examination reveals that the Fox estimates for a number of the equations of this model are replicable, to the two or three digits reported by Fox. Fox's results for other equations cannot be replicated. Not all the reasons for this lack of replicability can be determined, but in several cases the computational methods used by Fox and his assistants have been found to be faulty by modern computational standards.     

On the Lp error of the Grenander-type estimator in the Cox model

We consider the Cox regression model and study the asymptotic global behavior of the Grenander-type estimator for a monotone baseline hazard function. This model is not included in the general setting of Durot (2007). However, we show that a similar central limit theorem holds for L_p-error of the Grenander-type estimator. As an illustration of application of our main result, we propose a test procedure for a Weibull baseline distribution, based on the L_p-distance between the Grenander estimator and a parametric estimator of the baseline hazard. Simulation studies are performed to investigate the performance of this test.     

Another look at the naive estimator in a regression model

We consider the linear regression model where only a particular linear function of the dependent variables is observed, Stahlecker and Schmidt (1987) proposed a naive least squares (LS) estimator for regression coefficients in such a case. In this note we represent their estimator as a general ridge estimator. This observation leads to a view different from the previous work and provides an easy way of obtaining many important properties of the naive LS estimator. Our approach also gives some insight into the relationship between the naive LS estimator and the generalized least squares estimator.     

Heavy tails of OLS

Suppose the tails of the noise distribution in a regression exhibit power law behavior. Then the distribution of the OLS regression estimator inherits this tail behavior. This is relevant for regressions involving financial data. We derive explicit finite sample expressions for the tail probabilities of the distribution of the OLS estimator. These are useful for inference. Simulations for medium sized samples reveal considerable deviations of the coefficient estimates from their true values, in line with our theoretical formulas. The formulas provide a benchmark for judging the observed highly variable cross country estimates of the expectations coefficient in yield curve regressions.     

The modified second-round estimator in the general qualitative response model

This paper suggests a modification of the method of scoring in the general multivariate qualitative response model to attain simpler computation when there are many observations per cell. The paper shows that the proposed estimator is asymptotically efficient even in the cases when the generalized Berkson's estimator (see Amemiya, Journal of the American Statistical Association, June 1976) is not.     

The exact moments of the least squares estimator for the autoregressive model

Exact mean and variance of the least squares estimate of the stationary first-order autoregressive coefficient, i.e., β in y_t=α+βx_t+u_t are evaluated algebraically as well as numerically. It turns out that the least squares estimate is seriously biased for the sample of two-digits sizes typically dealt with in econometrics if the mean of the process is unknown, i.e., if the equation has a non-zero intercept (α≠0). Kendall's approximation to the mean and Barlett's approximation to the variance are shown to be fairly good. Also, our numerical results confirm Orcutt and Winokur's (Econometrica, Vol. 37) based on Monte Carlo experiments.     

Estimation of the monetary model of exchange-rate determination under rational expectations

This paper develops a sticky-price version of the monetary model of exchange-rate determination under rational expectations. The reduced-form difference equation for the exchange rate has two roots which lie on either side of unity. In the solution the stable root is solved backwards and the unstable forwards. The model is estimated by the full-information maximum-likelihood method on deutsche mark-dollar data. The results are supportive of the rational-expectations restrictions.     

2SLS and OLS in a spatial autoregressive model with equal spatial weights

The paper considers a Cliff–Ord type spatial model with a spatially lagged dependent variable and a row normalized weighting matrix with equal weights. We show that the 2SLS and OLS estimators are inconsistent unless panel data are available. The weighting matrix in question is one which would naturally be considered if all units are neighbors to each other, and there is no other reasonable or observable measure of distance between them.     

基于修正OLS模型的湖南省城镇居民消费影响因素分析

文章对传统的OLS模型进行了改进,主要利用MATLAB作为统计分析软件对1990年至2013年湖南省城镇居民消费数据进行了分析,得出工资性收入是影响城镇居民消费的主要因素,最后提出改善湖南省城镇居民消费支出结构、扩大消费需求长效机制的对策。     

The finite-sample effects of VAR dimensions on OLS bias,OLS variance,and minimum MSE estimators

Vector autoregressions (VARs) are important tools in time series analysis. However, relatively little is known about the finite-sample behaviour of parameter estimators. We address this issue, by investigating ordinary least squares (OLS) estimators given a data generating process that is a purely nonstationary first-order VAR. Specifically, we use Monte Carlo simulation and numerical optimisation to derive response surfaces for OLS bias and variance, in terms of VAR dimensions, given correct specification and several types of over-parameterisation of the model: we include a constant, and a constant and trend, and introduce excess lags. We then examine the correction factors that are required for the least squares estimator to attain the minimum mean squared error (MSE). Our results improve and extend one of the main finite-sample multivariate analytical bias results of Abadir, Hadri and Tzavalis [Abadir, K.M., Hadri, K., Tzavalis, E., 1999. The influence of VAR dimensions on estimator biases. Econometrica 67, 163–181], generalise the univariate variance and MSE findings of Abadir [Abadir, K.M., 1995. Unbiased estimation as a solution to testing for random walks. Economics Letters 47, 263–268] to the multivariate setting, and complement various asymptotic studies.     

A comparison among partial adjustment,rational expectations and error correction estimates of the canadian demand for money

Starting from a dynamic optimization principle, the currently most popular approaches to modelling money demand functions are derived. The partial adjustment/adaptive expectations, rational expectations, and error correction mechanism formulations are then estimated using a common data set. The error correction mechanism equation is found to dominate the others either because their implicit restrictions are rejected (rational expectations) or by employing the encompassing principle (partial adjustment/adaptive expectations). Surprisingly all three forms have similar long-run solutions. Since the short-run dynamics differ substantially, the results have important implications for the conduct of monetary policy.     

A note on a Bayesian estimator in an autocorrelated error model

For a simple autocorrelated error model studied by Fomby and Guilkey (1978) we demonstrate that there is a Bayesian counterpart to the class of sampling theory pre-test estimators.     

A note on the efficiency of the cochrane-orcutt estimator of the ar(1) regression model

This paper shows that the Cochrane-Orcutt transformation which deletes the initial observation of the AR(1) regression model with known autocorrelation is strictly less efficient than a weighted generalized least squares estimator which gives the initial observation less weight than the true model requires, and may be more or less efficient than an estimator which gives the initial observation more weight than required. It also shows that the estimator based on the Cochrane-Orcutt transformation is strictly less efficient than one based on the Prais-Winsten transformation, if the AR(1) process has a finite past. These results give further support to the conclusion that, whenever possible, the estimator based on Prais-Winsten transformation should be used.     

Formation of expectations: A model in temporary general equilibrium theory

The paper studies, in a temporary general equilibrium framework, the way expectations of agents can be formed along time through some learning mechanism. One is then faced with a set of coupled equations from which the time evolution of both the state of the economy and the individual expectations have to be derived. Three main results are proven, for an open dense set of economies. First, there actually exists a recurrence which allows to determine, locally around some stationary temporary equilibrium, the time dependant dynamics for the states and the time dependant expectations. Next, sufficient first-order conditions are given for the dynamics and expectations to converge to some limits when time goes to infinity. Last, additional sufficient first-order conditions guarantee that the chosen stationary temporary equilibrium has definite stability properties for the time dependant dynamics.     

A comparison of the Box-Cox maximum likelihood estimator and the non-linear two-stage least squares estimator

This paper investigates the limiting behaviour of the ‘maximum likelihood estimator’(MLE) based on normality, as well as the nonlinear two-stage least squares estimator (NL2S), for the i.i.d. and regression models in which the Box-Cox transformation is applied to the dependent variable. Since the transformed variable cannot in general be normally distributed, the untransformed variable is assumed to have a two-parameter gamma distribution. Tables of probability limits and asymptotic variance demonstrate that, in this case, the inconsistency of the ‘normal MLE’ is often quite pronounced, while the NL2S is consistent and typically well behaved.     

On efficiency of the ratio estimator

Summary The exact mean square error for the ratio estimator of a finite population total based on simple random sampling without replacement is shown to have an expected value less than that of the variance of the ratio estimator based on Midzuno’s scheme, under a usual super-population model.