The bias of the least squares estimator over interval constraints

We show that the interval constrained least squares estimator for a regression model is in general bias. The bias and some of its properties are given when the regression residuals are normally distributed.     

A comparison of bias approximations for the two-stage least squares (2SLS) estimator

We consider the bias of the two-stage least squares (2SLS) estimator in linear instrumental variable regression with only one endogenous regressor. By using asymptotic expansion techniques, we approximate the 2SLS coefficient estimation bias under various scenarios regarding the number and strength of instruments.     

On least squares estimation with a particular linear function of the dependent variable

We consider the standard linear regression model where the endogenous variable y is substituted by Ty, T being a symmetric, idempotent matrix. Comparing the mean square error (MSE) matrices we show that a ‘naive’ LS-procedure may work better than a competing estimator usually proposed in the literature and may even perform better than the LS-estimator based on untransformed data. We derive necessary and sufficient conditions for MSE-dominance and outline some ideas for testing.     

Finite sample bias of the least squares estimator in an AR(p) model: estimation,inference, simulation and examples

This paper shows that the first order bias of least squares estimators of the coefficients of an AR(p) model is important for ‘typical’ macroeconomic time series and proposes a simple to apply method of bias reduction. Biases in individual coefficients often cumulate in the sum with far-reaching consequences for the cumulative impulse response function. This function, being nonlinear in the underlying coefficients, is particularly sensitive to biases when, as is often the case, the shocks are long-lived. Simulations and examples demonstrate some of the magnitudes involved.     

Asymptotic distribution of least squares estimator and a test statistic in linear regression models

This paper presents a fairly general and sufficiently weak condition on the observation matrix for the asymptotic normality of the least squares estimator of coefficient vector in a linear regression model. The asymptotic distribution of a statistic for testing the nullity of coefficient vector is also considered.     

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.     

Initial beliefs and the global stability of least squares learning

This article provides an operational framework of global stability analysis when Ljung's (1977) ordinary differential equation (ODE) approach is applied to the recursive stochastic system. We first establish the notion of stable set under which sufficient conditions for the equivalence between them can be translated to restrictions on initial beliefs in agents' forecasts. The maximum ODE-stable set is simply the largest range of initial beliefs. We then demonstrate how to implement this operational framework for the analysis of stability beyond the local sense in some well-known models in the learning literature.     

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.     

Generalized least squares and maximum likelihood estimation of the logistic function for technology diffusion

Given a simple stochastic model of technology adoption, we derive a function for technological diffusion that is logistic in the deterministic part and has an error term based on the binomial distribution. We derive two estimators—a generalized least squares (GLS) estimator and a maximum likelihood (ML) estimator—which should be more efficient than the ordinary least squares (OLS) estimators typically used to estimate technological diffusion functions. We compare the two new estimators with OLS using Monte-Carlo techniques and find that under perfect specification, GLS and ML are equally efficient and both are more efficient than OLS. There was no evidence of bias in any of the estimators. We used the estimators on some example data and found evidence suggesting that under conditions of misspecification, the estimated variance-covariance of the ML estimator is badly biased. We verified the existence of the bias with a second Monte-Carlo experiment performed with a known misspecification. In the second experiment, GLS was the most efficient estimator, followed by ML, and OLS was least efficient. We conclude that the GLS estimator of choice.     

On the equivalence of indirect inference and bootstrap bias correction for linear IV estimators

This note shows that two ways of simulation based bias correction–indirect inference and bootstrap bias correction–are equivalent for two-stage-least-squares, as well as k$k$-class estimators for the standard linear model with endogenous regressors.     

On the inconsistency of certain axioms on solution concepts for non-cooperative games

The mutual compatibility of four recently discussed axioms on solution concepts for extensive form games is explored. Two subsets of the axioms are shown to be inconsistent. Our results underline the importance of the information lost in moving from the extensive form to the normal (or agent-normal) form of a game.     

On the asymptotic bias and mean squared error of an improved estimator for coefficients in linear regression

An estimator for regression coefficients of Kadiyala (1984) is considered. It is proved that the estimator is asymptotically unbiased. The asymptotic weak mean squared error of the estimator is also derived and it is proved that, under certain conditions, the estimator dominates a general class of estimators given by Vinod and Ullah (1981).     

A note on S in a spatially correlated error components regression model for panel data

The ordinary least squares based estimator of the disturbance variance in a panel regression model with spatially correlated error component is shown to be asymptotically unbiased and weakly consistent without any restrictions on the regressor matrix.     

The coefficient of the whole is an average of the coefficients of its parts: A special case of restricted least squares

This paper provides a consistent estimate of the bound of the marginal effect of an unobserved right-hand side variable on the dependent variable when only the sum of that variable with a positively correlated variable is available.     

Regression-based measure of urban sprawl for Italian municipalities using DMSP-OLS night-time light images and economic data

ABSTRACT

Night-time light can be used in order to evaluate the degree of urbanization and urban sprawl in a specific territory. In fact, at the local level, the lower the urban density, the higher the per-capita length of collector roads and the area covered by buildings and infrastructures. It follows that the lower the urban density, the higher the municipal luminosity. Urban sprawl is determinant in defining the mobility condition in a specific territory and the service and infrastructure needs. This paper uses regression analyses in order to estimate a ‘relative’ measure of urban sprawl that takes into account also demographic and economic characteristics. We apply this technique to a panel of Italian municipalities over the period 2004–2012 and compare the resulting measure to the ‘absolute’ measures provided by the Italian Institute for Environmental Protection and Research in order to evaluate the contribution of our measure to the knowledge of the sprawl phenomenon.     

Material efficiency and economic-environmental sustainability. Results of simulations for Germany with the model PANTA RHEI

Based on empirical evidence, the paper discusses the impact of a consulting and information program for the improvement of material productivity with regard to economic and environmental targets for Germany. The instrument used in the analysis is the integrated economic-environmental model PANTA RHEI, which is parameterized econometrically. The paper presents the model and shows in a baseline forecast that without policy changes, sustainability will be violated in both the economic and the environmental dimensions. This applies to the latter particularly with regard to land use and material consumption. The alternative simulation that introduces a consulting and information program for the improvement of material productivity yields a win-win result: growth rates of GDP and employment are rising, the public debt is reduced, and material consumption is much lower than in the baseline and remains at the actual level, which means that a decoupling of growth and material consumption is possible.     

An aspect of the wald test for linear restrictions in the seemingly unrelated regressions model

This paper shows that, in a SUR context, there is an exact relationship between the Wald statistic for testing linear restrictions and the ‘F statistic’ based upon an estimate of the covariance matrix that adjusts for degrees of freedom.     

我国军民融合产业对制造业运行的动态响应

基于db（n=5）小波函数,对我国证券市场军工航天板块收盘价与成交量自2005年6月以来的2 512个交易日进行时序模拟,通过对低频信号进行提取后认为,我国军工航天产业发展对宏观经济政策的依赖度较高,军民融合产业整体仍面临着深度发展的良好机遇。基于VAR模型,对我国制造业宏观经济运行指标进行了动态模拟、脉冲函数响应分析与方差分解。结果显示,制造业新产品订单指数可作为研究我国制造业经济运行的重要指标,经对数化后其每提升1个百分点或高端装备制造业指数每增长1个百分点,相应的军民融合产业指数分别提高2.86%和1.22%。为提升我国制造业尤其是高端装备制造业水平,应促进军民融合产业深度发展。