Improved instrumental variables estimation of simultaneous equations under conditionally heteroskedastic disturbances

In this paper we develop estimation techniques and a specification test for the validity of instrumental variables allowing for conditionally heteroskedastic disturbances. We propose modified two‐stage least squares (2SLS) and modified 3SLS procedures where the conditional heteroskedasticity is taken into account, which are natural extensions of the traditional 2SLS and 3SLS estimators and which achieve a lower variance. We recommend the use of these modified 2SLS and 3SLS procedures in practice instead of alternative estimators like limited‐information maximum likelihood/full‐information maximum likelihood, where the non‐existence of moments leads to extreme values, and also for ease of computation. It is shown theoretically and with simulation that in some cases 2SLS, 3SLS and our modified 2SLS and 3SLS procedures can have very severe biases (including the weak instruments case), and we present bias correction procedures to apply in practice along the lines of Flores‐Lagunes ( 2007 ). Our new estimation procedures can also be used to extend the test for weak instruments of Stock and Yogo ( 2005 ) and to allow for conditional heteroskedasticity. Finally, we show the usefulness of our estimation procedures with an application to the demand and supply of fish. Copyright © 2010 John Wiley & Sons, Ltd.     

Full-versus limited-information estimation of a rational-expectations model: Some numerical comparisons

This paper compares numerically the asymptotic distributions of parameter estimates and test statistics associated with two estimation techniques: (a) a limited-information one, which uses instrumental variables to estimate a single equation [Hansen and Singleton (1982)], and (b) a full-information one, which uses a procedure asymptotically equivalent to maximum likelihood to simultaneously estimate multiple equations [Hansen and Sargent (1980)]. The paper compares the two with respect to both (1) asymptotic efficiency under the null hypothesis of no misspecification, and (2) asymptotic bias and power in the presence of certain local alternatives. It is found that (1) full-information standard errors are only moderately smaller than limited-information standard errors, and (2) when the model is misspecified, full-information tests tend to be more powerful, and its parameter estimates tend to be more biased. This suggests that at least in the model considered here, the gains from the use of the less robust and computationally more complex full-information technique are not particularly large.     

GMM and 2SLS estimation of mixed regressive,spatial autoregressive models

The GMM method and the classical 2SLS method are considered for the estimation of mixed regressive, spatial autoregressive models. These methods have computational advantage over the conventional maximum likelihood method. The proposed GMM estimators are shown to be consistent and asymptotically normal. Within certain classes of GMM estimators, best ones are derived. The proposed GMM estimators improve upon the 2SLS estimators and are applicable even if all regressors are irrelevant. A best GMM estimator may have the same limiting distribution as the ML estimator (with normal disturbances).     

Codependence in cointegrated autoregressive models

This paper investigates codependent cycles, i.e., transitory components that react to common stimuli in a similar, although not necessarily synchronous fashion. Unlike previous studies, the methodology of this paper allows FIML estimation of the restricted VAR/VECM and therefore the extraction of the unobserved codependent cyclical components via a Beveridge‐Nelson decomposition. It is further shown that the number and order of cofeature combinations that yield the scalar component models associated with codependence is limited by the dimension of a finite‐order VAR system. Monte Carlo simulations indicate that LR tests based on FIML estimates have higher power than alternative GMM and canonical correlations tests, while maintaining good size properties. An empirical application investigates the presence of codependence in UK consumption data. Copyright © 2007 John Wiley & Sons, Ltd.     

K-matrix-class estimators and the full-information maximum-likelihood estimator as a special case

This article presents a unified treatment of simultaneous system estimation. A general class of full-information estimators is proposed, called K-matrix-class (KMC). It is shown that the K-matrix-class includes both full-information maximum-likelihood and three-stage least- squares estimators as special cases and that the k-class can be regarded as a subclass of the K-matrix-class. Conditions under which KMC estimators are consistent (similar to those of the k-class estimators) are given. Furthermore, as a full information-generalization of the double k-class estimators, the double K-matrix-class estimators (DKMC) are proposed.     

Some sampling properties of minimum expected loss (MELO) estimators of structural coefficients

Some sampling properties of Zellner's (1978) MELO estimates of structural coefficients of linear simultaneous equation models are examined by a series of sampling experiments. The MELO estimates appear to have more pronounced biases in estimating structural coefficients than the 2SLS estimates. However, MELO is found to outperform 2SLS according to several criteria, including MSE and MAE in a wide range of situations generated by varying structural coefficients, the variance-covariance matrix of structural disturbances, and the sample size. The magnitude of absolute sampling errors, the estimation of the variance of structural disturbances, and the large-sample standard errors are also compared among OLS, 2SLS, and MELO.     

A ridge-like method for simultaneous estimation of simultaneous equations

In the context of full information estimation in a linear simultaneous equations model, this paper considers a ridge-like modification of the 3SLS estimator. The proposed method is particularly desirable where the square matrix of the 3SLS normal equationsis singular (or near-singular) leading to non-existence (or poor performance) of the estimator. Furthermore, the type of solution suggested here does seem to result in the existence of the finite sample moments of the estimator even when the degrees of over identification are as low as zero (just identified models). This paper considers only a simple scalar form of the ‘ridge-matrix” with a relatively simple choice of the modifying scalar that preserves the asymptotic properties of the 3SLS estimator. A value of this scalar is derived which minimizes an appropriatequadratic risk criterion. The approximate quadratic risk function is based upon the asymptotic approximation of the relevant moments in the manner of Nagar (1959). A range of risk reducing values of the ‘ridge-scalar” is also given.     

Estimation of models with grouped and ungrouped data by means of “2SLS”

This paper deals with a special case of estimation with grouped data, where the dependent variable is only available for groups, whereas the endogenous regressor(s) is available at the individual level. By estimating the first stage using the available individual data, and then estimating the second stage at the aggregate level, it might be possible to gain efficiency relative to the OLS and 2SLS estimators that use only grouped data. We term this the mixed-2SLS estimator (M2SLS). The M2SLS estimator is consistent and asymptotically normal. We also provide a test of efficiency of M2SLS relative to OLS and “2SLS” estimators.     

Information and computation in simultaneous equations estimation

The complexity and size of simultaneous equations systems necessitates great care with computations for parameter estimation. In three-stage least-squares (3SLS) large matrix inversions are required, and because of the sensitivity of many economic systems to key parameters, accuracy in estimation is important. There are many numerical techniques available which yield accurate solutions to systems of equations. We make use of Householder transformations and recursive triangulation solutions in presenting numerical algorithms for the computation of 3SLS and k-class estimates. Another numerical technique, the singular value decomposition is valuable in providing additional information in k-class estimation. The values of k for which this estimator does not exist are accurately derived, their use being demonstrated by an example.     

Estimating an economic model of crime using panel data from North Carolina

This paper replicates the Cornwell and Trumbull ( 1994 ) estimation of a crime model using panel data on 90 counties in North Carolina over the period 1981–1987. While the Between and Within estimates are replicated, the fixed effects 2SLS as well as the 2SLS estimates are not. In fact, the fixed effects 2SLS estimates turn out to be insignificant for all important deterrent variables as well as legal opportunity variables. We argue that the usual Hausman test, based on the difference between fixed effects and random effects, may lead to misleading inference when endogenous variables of the conventional simultaneous equation type are among the regressors. We estimate the model using random effects 2SLS and perform a Hausman test based on the difference between fixed effects 2SLS and random effects 2SLS. We cannot reject the consistency of the random effects 2SLS estimator and this estimator yields plausible and significant estimates of the crime model. This result should be tempered by the legitimacy of the chosen instruments. Copyright © 2006 John Wiley & Sons, Ltd.     

Institutional perspective of financial sector development: A multidimensional assessment

Financial sector development is a multidimensional process that plays a vital role in the economic growth and development of a country. This study investigates the effect of institutional quality on multidimensional financial sector development, and its dimensions, such as, depth, access, and efficiency. We used a panel dataset of 85 emerging and developing economies from 1996 to 2018 for analysis. Our findings based on 2SLS estimation demonstrate that institutional quality has a significant positive effect on the progress of the financial sector, especially its depth, access, and efficiency. The breakdown analysis shows that most of the key components (control of corruption, government effectiveness, regulatory quality, rule of law, and voice and accountability) of institutional quality enhance the financial sector development. Our empirical results are robust across alternative measures of institutional quality, split-sample analysis, alternative instrument, and estimator. This paper also offers useful policy implications to the stakeholders in emerging and developing economies.     

Robust normal reference bandwidth for kernel density estimation

Bandwidth selection is the main problem of kernel density estimation, the most popular method of density estimation. The classical normal reference bandwidth usually oversmoothes the density estimate. The existing hi-tech bandwidths have computational problems (even may not exist) and are not robust against outliers in the sample. A highly robust normal reference bandwidth is proposed, which adapts to different types of densities.     

Inference regarding multiple structural changes in linear models with endogenous regressors

This paper considers the linear model with endogenous regressors and multiple changes in the parameters at unknown times. It is shown that minimization of a Generalized Method of Moments criterion yields inconsistent estimators of the break fractions, but minimization of the Two Stage Least Squares (2SLS) criterion yields consistent estimators of these parameters. We develop a methodology for estimation and inference of the parameters of the model based on 2SLS. The analysis covers the cases where the reduced form is either stable or unstable. The methodology is illustrated via an application to the New Keynesian Phillips Curve for the US.     

An Econometric Analysis of Brand-Level Strategic Pricing Between Coca-Cola Company and PepsiCo.

We investigate market structure and strategic pricing for leading brands sold by Coca-Cola Company and PepsiCo. in the context of a flexible demand specification (i.e., nonlinear AIDS) and structural price equations. Our flexible and generalized approach does not rely upon the often used ad hoc linear approximations to demand and profit-maximizing first-order conditions, and the assumption of Nash-Bertrand competition. We estimate a conjectural variation model and test for different brand-level pure strategy games. This approach of modeling market competition using the nonlinear Full Information Maximum Likelihood (FIML) estimation method provides insights into the nature of imperfect competition and the extent of market power. We find no support for a Nash-Bertrand or Stackelberg Leadership equilibrium in the brand-level pricing game. Results also provide insights into the unique positioning of PepsiCo.'s Mountain Dew brand.     

On B-robust instrumental variable estimation of the linear model with panel data

The aim of this paper is to demonstrate how to acquire robust consistent estimates of the linear model when the fundamental orthogonality condition is not fulfilled. With this end in view, we develop two estimation procedures: Two stage generalized M (2SGM) and robust generalized method of moments (RGMM). Both estimators are B-robust, i.e. their associated influence function is bounded, consistent and asymptotic normally distributed. Our simulation results indicate that the relatively efficient RGMM estimator (in regressions with heteroskedastic and/or autocorrelated errors) provides accurate parameter estimates of a panel data model with all variables subject to measurement errors, even if a substantial portion of the data is contaminated with aberrant observations. The traditional estimation techniques such as 2SLS and GMM break down when outliers corrupt the data.     

Simultaneous determination of inventories and accounts receivable

The study presents a model based on 3375 observations from industrial firms in Pakistan, and the three‐stage least square (3SLS) technique has been applied for the estimation. The results indicate that the economic order quantity (EOQ) of inventories is not a constant magnitude; it is a variable closely associated with ‘time trend’. While the ‘buffer stock’ element can be estimated through the constant term of an equation. Receivables from customers show a negative correlation with liquid assets and the cost of production. Receivables are also shown to act as substitute for closing inventories. Copyright © 2005 John Wiley & Sons, Ltd.     

A profit-center game with incomplete information

Profit centers in a firm in multidivisional form agree in the ex ante stage upon a plan about their joint production and profit imputation. The plan is executed in the subsequent two periods of the interim stage: the setup period and the manufacturing period. In the setup period, each center has its private information, but a part of its information is revealed to the other centers through its action. Based on the information endogenously pooled this way, the centers take another round of actions in the manufacturing period. A core plan is defined as a Bayesian incentive-compatible plan of the grand coalition of profit centers, upon which no coalition can improve using its Bayesian incentive-compatible plan. A core plan is called full-information revealing if each center fully reveals its private information in the setup period. Three existence theorems for a full-information revealing core plan are established. The first two theorems impose alternative conditions on returns to scale: (1) the neoclassical convex technology, and (2) increasing returns to scale. In case (2), a stronger condition than Scarf's distributiveness is imposed on the total production set. The third theorem is based on a specific supplier-customer relationship among the divisions. Received: 13 October 1997 / Accepted: 26 July 1999     

Estimation of financial agent-based models with simulated maximum likelihood

This paper proposes a general computational framework for empirical estimation of financial agent-based models, for which criterion functions have unknown analytical form. For this purpose, we adapt a recently developed nonparametric simulated maximum likelihood estimation based on kernel methods. In combination with the model developed by Brock and Hommes (1998), which is one of the most widely analysed heterogeneous agent models in the literature, we extensively test the properties and behaviour of the estimation framework, as well as its ability to recover parameters consistently and efficiently using simulations. Key empirical findings indicate the statistical insignificance of the switching coefficient but markedly significant belief parameters that define heterogeneous trading regimes with a predominance of trend following over contrarian strategies. In addition, we document a slight proportional dominance of fundamentalists over trend-following chartists in major world markets.     

Tests with correct size when instruments can be arbitrarily weak

This paper applies classical exponential-family statistical theory to develop a unifying framework for testing structural parameters in the simultaneous equations model under the assumption of normal errors with known reduced-form variance matrix. The results can be divided into the limited-information and full-information categories. In the limited-information model, it is possible to characterize the entire class of similar tests in a model with only one endogenous explanatory variable. In the full-information framework, this paper proposes a family of similar tests for subsets of endogenous variables’ coefficients. For both limited- and full-information models, there exist power upper bounds for unbiased tests. When the model is just-identified, the Anderson–Rubin, score, and (pseudo) conditional likelihood ratio tests are optimal. When the model is over-identified, the (pseudo) conditional likelihood ratio test has power close to the power envelope when identification is strong.