Monte Carlo studies on the effectiveness of the bootstrap bias reduction method on 2SLS estimates

If first moments exist, two stage least squares estimators are consistent although biased. In this paper several bias correction methods are compared including bootstrap two stage least squares, Nagar's k-class and jackknife estimators for both parametric and non-parametric cases. Monte Carlo experiments on several models investigate the non-large sample properties of these estimators. The results strongly favor the bootstrap procedure judged by the amount of bias reduction and comparative variances.     

A medium-N approach to macroeconomic forecasting

This paper considers methods for forecasting macroeconomic time series in a framework where the number of predictors, N, is too large to apply traditional regression models but not sufficiently large to resort to statistical inference based on double asymptotics. Our interest is motivated by a body of empirical research suggesting that popular data-rich prediction methods perform best when N ranges from 20 to 40. In order to accomplish our goal, we resort to partial least squares and principal component regression to consistently estimate a stable dynamic regression model with many predictors as only the number of observations, T, diverges. We show both by simulations and empirical applications that the considered methods, especially partial least squares, compare well to models that are widely used in macroeconomic forecasting.     

A note on the computation of inequality constrained least squares estimates

We derive the implications of the Kuhn-Tucker conditions for the inequality constrained least squares problem. A novel implication is that if each imposed constraint fails if individually relaxed, at least one will fail if any number are relaxed jointly.     

Some remarks on the undersized sample problem in econometrics

This paper discusses three approaches to the problem of undersized samples: the estimable function, the generalized inverse and the principal component method. It turns out that the k-class estimation methods amount to ordinary least squares if use is made of estimable function or generalized inverses. The generalized inverse approach is a special case of the estimable function approach and of the principal component solution.     

The information matrix test: Simplified calculation via a score test interpretation

In Chesher (1982) I show that the Information Matrix test introduced by White (1982) is a score test for parameter constancy. In this letter I show that this result leads to a simple computational procedure for calculating the Information Matrix test. The procedure involves computing, for a sample of n observations, n times the R² from the least squares regression of a column of ones on a matrix whose elements are functions of 1st and 2nd derivatives of the log density function.     

A more general class of biased estimators of the co-efficients in linear regression

In a recent paper, Ullah and Ullah (1978) proposed a class of biased estimators, namely double k-class (k₁, k₂) for the coefficients in a linear regression model. Even though, this set of estimators contains James and Stein (1961) as a special case, in its present form, it does not contain the ridge type estimators. The aim of this note is to extend Ullah and Ullah set of estimators and then establish a relationship with the various operational ridge estimators. The conditions under which the extended set of estimators dominates the ordinary least squares estimator are analyzed.     

Forecasting Inflation Using Constant Gain Least Squares

This paper assesses the usefulness of constant gain least squares when forecasting inflation. An out‐of‐sample forecast exercise is conducted, in which univariate autoregressive models for inflation in Australia, Sweden, the United Kingdom and the United States are used. The results suggest that it is possible to improve the forecast accuracy by employing constant gain least squares instead of ordinary least squares. In particular, when using a gain of 0.05, constant gain least squares generally outperforms the corresponding autoregressive model estimated with ordinary least squares. In fact, at longer forecast horizons, the root mean square forecast error is reliably lowered for all four countries and for all lag lengths considered in the study.     

Lessons from the experience of OECD nations on macroeconomic growth and economic freedom, 2004–2008

This study empirically investigates the impact on per capita real economic growth of each of the ten measures of economic freedom computed annually by the Heritage Foundation. Within the context of the Random Effects Model, panel least squares estimations using a 5-year panel (2004 through 2008) dataset for the OECD nations as a group reveal that the percentage growth rate in the purchasing-power-parity adjusted per capita real GDP for OECD nations was, at the 5?% statistical significance level or better, an increasing function of at least seven of the ten economic freedom measures. The results underscore the critical role that economic freedom plays in a nation??s economic growth and prosperity and the importance of pursuing policies that are consistent with increasing economic freedom.     

The exact estimation of logit models by non-linear least squares

The purpose of this paper is to examine the relationship between least squares and maximum likelihood estimation, where the likelihood function is the product of two explicit functions. We illustrate the correspondence for the particular case of the logit model, and show that this can be estimated by commonly accessible non-linear least squares estimation packages. Unlike the conventional non-linear least squares approach the estimates obtained following the proposed method are maximum likelihood for all sample sizes.     

A New Economy Forecasting Method Based on Data Barycentre Forecasting Method

A new and useful method of technology economics, parameter estimation method, was presented in light of the stability of gravity center of object in this paper. This method could deal with the fitting and forecasting of economy volume and could greatly decrease the errors of the fitting and forecasting results. Moreover, the strict hypothetical conditions in least squares method were not necessary in the method presented in this paper, which overcame the shortcomings of least squares method and expanded the application of data barycentre method. Application to the steel consumption volume forecasting was presented in this paper. It was shown that the result of fitting and forecasting was satisfactory. From the comparison between data barycentre forecasting method and least squares method, we could conclude that the fitting and forecasting results using data barycentre method were more stable than those of using least squares regression forecasting method, and the computation of data barycentre forecasting method was simpler than that of least squares method. As a result, the data barycentre method was convenient to use in technical economy.     

Macroeconomic environment,country risk and stock market performance: Evidence for Brazil

The paper aims at providing empirical evidence about (i) the influence of macroeconomic variables and economic policies on country risk and (ii) the influence of macroeconomic variables and country risk on the main Brazilian index of the stock market (Ibovespa). The study analyzes the role that macroeconomic fundamentals plays, but also the role that the credibility of the regime of inflation targeting and the reputation of the central bank play in lessening country risk and in the improvement of the stock market performance. The empirical evidence was obtained through the application of ordinary least squares (OLS), generalized method of moments (GMM) and GMM systems. The results found suggest that monetary policy and public debt management, as well as credibility and reputation affect country risk and the performance of the Brazilian stock market.     

The non-monotonicity of the bias and mean squared error of the two stage least squares estimators of exogenous variable coefficients

Owen (1976) [Owen, A.D., 1976. A proof that both the bias and mean squared error of the two stage least squares estimator are monotonically non-increasing functions of sample size. Econometrica 44, 409–411.] has shown that in a two equation static simultaneous equation model both the bias and mean squared error of the two stage least squares estimator of the endogenous variable coefficient are monotonically non-increasing functions of the sample size. This paper shows that neither property carries over to the exogenous variable coefficient estimator.     

The Relationship between Multiple Choice and Essay Response Questions in Assessing Economics Understanding

Efficiency considerations have led to increased use of multiple-choice questions to assess economics understanding at the secondary and tertiary levels throughout Australia. A multiple-choice test would suffice if multiple-choice and essay questions measure the same dimensions of knowledge, as suggested by least squares estimation of the relationship between these two forms of testing. We show a simultaneous equation bias inherent in least squares estimation of the relationship between these two forms. A two-stage least squares estimation reveals no relationship, implying that these testing forms measure different dimensions of knowledge. Thus, a single form of testing economics knowledge must be avoided.     

Estimation of Structural Nonlinear Errors‐in‐Varibles Models by Simulated Least‐Squares Method

This article proposes a simulation approach to obtain least‐squares or generalized least‐squares estimators of structural nonlinear errors‐in‐variables models. The proposed estimators are computationally attractive because they do not need numerical integration nor huge numbers of simulations per observable. In addition, the asymptotic covariance matrix of the estimator has a simple decomposition that may be used to guide selection of appropriate simulation sizes. The method is also useful for models with missing data or imperfect surrogate covariates, where application of conventional least‐squares and maximum‐likelihood methods is restricted by numerical multidimensional integrations.     

A simultaneous equations model of the educational process

This paper models the educational process as a system of six simultaneous equations. The endogenous variables include a student's achievement, motivation, expectations, efficacy, and perceived parents' and teachers' expectations. The model also includes forty-eight individual, home, peer, teacher, and school exogenous variables. Using a sample of over sixteen thousand twelfth grade students from the Equality of Educational Opportunity survey, we estimate the model by two-stage least squares and present the reduced form and structural form equations. We find that many educational outputs jointly determine one another. Also, the results suggest that school and teacher variables have important effects on educational outcomes.     

Small sample properties of Canonical Cointegrating Regressions

Monte Carlo simulations are performed to examine small sample properties of Canonical Cointegrating Regressions (CCR). The first data generation process is designed to generate both cointegrated and non-cointegrated systems with normal disturbances. If the near-observational equivalence of the stationary and the integrated processes is not significant, both powers and empirical sizes of CCR tests are acceptable. The second data generation process is based on the error correction model. Cointegrated systems with various fat-tailed disturbances are generated and analyzed. The empirical sizes of CCR tests with studentt disturbances and GARCH disturbances are found to be reasonable under certain restrictions. The last data generation process is a generalized least squares (GLS) process that incorporates heteroskedasticity into the error correction model. Again, the empirical sizes of CCR tests are reasonable.     

Extreme bound analysis for residential load curve models

Using the theory ofLindley andSmith andSmith a hierarchical load curve model is applied to 16 households in a Southern Californian electricity demand study. Using the global sensitivity concept ofLearner [1982] we carry out an extreme bound analysis for the first stage load curve coefficients. The following three models are employed: Model 1, a quadratic load curve model without economic variables. Model 2, a quadratic load curve with four economic variables. Model 3, a cubic load curve with four economic variables. The posterior mean of these models are given by matrix weighted averages of the ordinary least squares (OLS) estimate of the first stage parameters and the GLS-estimates of the second stage parameters. The set of all estimates are given by a natural extreme bound analysis and the restricted bound analysis based on bounds for the second stage covariance matrix \(\hat \sum \) .     

Improving forecast accuracy of financial vulnerability: PLS factor model approach

We present a factor augmented forecasting model for assessing the financial vulnerability in Korea. Dynamic factor models often extract latent common factors from a large panel of time series data via the method of the principal components (PC). Instead, we employ the partial least squares (PLS) method that estimates target specific common factors, utilizing covariances between predictors and the target variable. Applying PLS to 198 monthly frequency macroeconomic time series variables and the Bank of Korea's Financial Stress Index (KFSTI), our PLS factor augmented forecasting models consistently outperformed the random walk benchmark model in out-of-sample prediction exercises in all forecast horizons we considered. Our models also outperformed the autoregressive benchmark model in short-term forecast horizons. We expect our models would provide useful early warning signs of the emergence of systemic risks in Korea's financial markets.     

Alternate estimation criteria and measures of forecast accuracy

The purpose of this paper is to investigate and illustrate the effect that alternate estimation criteria have on measured forecast accuracy. In most instances forecast evaluation criteria (error measures) differ from the model estimation criterion, the latter most often being the traditional least squares. The results suggest that forecast accuracy may be improved when criteria other than least squares are used for model estimation purposes.     

Estimating the statistical cost curve: an application of the stochastic frontier technique

Estimates of the statistical cost curve are usually derived using the least squares technique, with the implication that the deviations from the fitted relationship are normally distributed. However, a theoretical restriction on the distribution of the disturbances implies that the least squares technique is inappropriate. An alternative specification and estimation technique are considered and applied in a study of the operating costs of British crematoria.