Estimation Of Simultaneous Equation Models Research Articles

Estimation of simultaneous equation models by backpropagation method using stochastic gradient descent

Simultaneous equation model (SEM) is an econometric technique traditionally used in economics but with many applications in other sciences. This model allows the bidirectional relationship between variables and a simultaneous relationship between the equation set. There are many estimators used for solving an SEM. Two-steps least squares (2SLS), three-steps least squares (3SLS), indirect least squares (ILS), etc. are some of the most used of them. These estimators let us obtain a value of the coefficient of an SEM showing the relationship between the variables. There are different works to study and compare the estimators of an SEM comparing the error in the prediction of the data, the computational cost, etc. Some of these works study the estimators from different paradigms such as classical statistics, Bayesian statistics, non-linear regression models, etc. This work proposes to assume an SEM as a particular case of an artificial neural networks (ANN), considering the neurons of the ANN as the variables of the SEM and the weight of the connections of the neurons the coefficients of the SEM. Thus, backpropagation method using stochastic gradient descent (SGD) is proposed and studied as a new method to obtain the coefficient of an SEM.

Bayesian Estimation of Simultaneous Equation Models with Outliers and Multicollinearity Problem

Bayesian Estimation of Simultaneous Equation Models with Outliers and Multicollinearity Problem

Board structure in emerging markets: A simultaneous equation modeling

This paper unravels the board structure of 42,146 firms in China and 21 European emerging markets and empirically examines its determinants. Structural estimation of simultaneous equation models that endogenize board size, outside board chairmanship, and board independence produced evidence supporting our predictions about potential factors that determine these three variables, which are based on previous studies of developed economies. However, we found striking differences in the combination of factors that strongly affect board structure between China and European emerging markets and between public and private companies. Furthermore, the empirical results in this paper suggest that the close interdependence among board components requires analytical consideration.

Nonparametric regression with nonparametrically generated covariates

We analyze the statistical properties of nonparametric regression estimators using covariates which are not directly observable, but have be estimated from data in a preliminary step. These so-called generated covariates appear in numerous applications, including two-stage nonparametric regression, estimation of simultaneous equation models or censored regression models. Yet so far there seems to be no general theory for their impact on the final estimator's statistical properties. Our paper provides such results. We derive a stochastic expansion that characterizes the influence of the generation step on the final estimator, and use it to derive rates of consistency and asymptotic distributions accounting for the presence of generated covariates.

Estimation of simultaneous equation models with latent dependent variables: a Monte Carlo evaluation

Three methods can be used to estimate simultaneous equation models with latent dependent variables: two-stage, minimum distance (MD) and full-information maximum likelihood. Theoretically all the three methods provide asymptotically consistent estimates, but the performance of these estimators in finite samples cannot be determined in theory. This letter evaluates the performance of these estimators in finite samples using Monte Carlo simulation. The results show that the MD estimator performs very poorly; overall the full information maximum likelihood estimator performs better than the other two estimators.

The canonical least squares estimation of large-scale simultaneous-equations models

The equation-by-equation ordinary least squares (OLS) estimation of simultaneous-equations models (SEMs) is known to be biased and even inconsistent. In addition, OLS is not normalization invariant. Yet, the OLS method is still widely used, especially for large-scale SEMs with many exogenous variables, because two-stage least squares, limited information maximum likelihood, and other related methods are not applicable. A canonical least squares (CANLS) method is developed here to overcome the normalization bias and to alleviate the simultaneity bias. The CANLS method contrasts one set of endogenous variables with the other set of exogenous variables in a structural equation through canonical correlation analysis. A linear combination of endogenous variables is then determined by the first canonical variable, which is subsequently regressed on the individual exogenous variables of the structural equation. The new method is shown to be more accurate than OLS through a series of Monte Carlo experiments.

Bondholder Wealth Effects in Mergers and Acquisitions: New Evidence from the 1980s and 1990s

We examine the wealth effects of mergers and acquisitions on target and acquiring firm bondholders for a sample of 940 offers involving 3,901 bonds during the period 1979-1997. We find strong evidence of a coinsurance effect for target bondholders, and we are able to trace target bondholder gains to a wealth-redistribution from target stockholders. During the announcement period, average acquirer excess bond returns are significantly negative while average target excess bond returns are significantly positive. For target bonds, the average excess return to below investment grade bonds is over 4%. Target bondholder returns are significantly larger when the merger reduces asset risk, when the target bond rating is below the acquirer bond rating, when the pre-merger leverage ratio of the target is greater than the pre-merger leverage ratio of the acquirer, and when the average target bond maturity is shorter than the average acquirer bond maturity. In addition, both target and acquirer excess bond returns are significantly smaller if the offer is hostile and are significantly larger in the 1990s, an era marked by increased bondholder event risk protection. Estimation of simultaneous equations models reveals that target stockholder dollar gains are significantly decreasing in target bondholder dollar gains, a result consistent with the view that target bondholder gains in takeovers come at the expense of target stockholders.

Estimation of simultaneous equation models with stochastic trend components

The estimation of a single equation within a system of simultaneous equations is considered. The equation is assumed to contain a stochastic trend component which implicitly makes allowance for factors, such as technical progress and tastes, which are difficult to measure. Various instrumental variable estimators and the limited information maximum likelihood estimator are compared on the basis of asymptotic results and small sample simulations.

Estimation of simultaneous equation models with stochastic trend components

The estimation of a single equation within a system of simultaneous equations is considered. The equation is assumed to contain a stochastic trend component which implicitly makes allowance for factors, such as technical progress and tastes, which are difficult to measure. Various instrumental variable estimators and the limited information maximum likelihood estimator are compared on the basis of asymptotic results and small sample simulations.

Bayesian specification analysis and estimation of simultaneous equation models using Monte Carlo methods

Bayesian procedures for specification analysis or diagnostic checking of modeling assumptions for structural equations of econometric models are developed and applied using Monte Carlo numerical methods. Checks on the validity of identifying restrictions, exogeneity assumptions and other specifying assumptions are performed using posterior distributions for discrepancy vectors and functions representing departures from specifying assumptions. Several mappings or functions of reduced form coefficients are defined and their posterior distributions are computed. A restricted reduced form approach is used to compute posterior distributions for structural parameters. These procedures are applied in analyses of two econometric models.

Recursive estimation of simultaneous equation models

A recursive instrumental variable estimator is derived. For simultaneous equation estimation, the choice of the instruments is discussed. A computationally simple and asymptotically efficient recursive estimator is proposed in this context.

Specification and Estimation of a Simultaneous-Equation Model with Limited Dependent Variables

Single equation models with limited dependent variables have received considerable attention in the econometrics literature, but little is known about the specification and estimation of simultaneous-equation models in which some or all endogenous variables are limited. The one relevant published paper by Amemiya [1974] considers a model in which all endogenous variables are truncated at zero, reveals certain necessary restrictions on the model, and suggests a method of estimation. But his model is not applicable to all situations and the merits of his estimation procedure are confined to consistency and tractability. Here we propose an alternative specification which may be more appropriate than Amemiya's for many problems and discuss a relatively simple limited-information estimation procedure.

Estimation of Simultaneous Equation Models with Measurement Error

Estimation of Simultaneous Equation Models with Measurement Error

Dummy Endogenous Variables in a Simultaneous Equation System

This paper considers the formulation and estimation of simultaneous equation models with both discrete and continuous endogenous variables. The statistical model proposed here is sufficiently rich to encompass the classical simultaneous equation model for continuous endogenous variables and more recent models for purely discrete endogenous variables as special cases of a more general model.

Corrigendum: "Identification and Estimation of Simultaneous Equation Models with Measurement Error,"

Corrigendum: "Identification and Estimation of Simultaneous Equation Models with Measurement Error,"

On the Use of Two-Stage Least Squares in Financial Models: A Comment

There appears to be growing interest in the development and estimation of simultaneous equation models for finance. Simkowitz and Jones [11] stimulated much of this concern in their observations on the need for these structures. Moreover, Simkowitz's application to the modeling of security returns with Logue [12] provides some support for these suggestions. Recently Lloyd [6] has argued that there may be significant problems in using two-stage least squares (hereafter 2SLS) with such models as a result of the potential for contemporaneous correlation in the structural errors across equations. The purpose of this note is to question several of Lloyd's conclusions and to provide some evidence that his findings may not be representative for the broad array of simultaneous models applicable to financial problems.

Identification and Estimation of Simultaneous Equation Models with Measurement Error

Identification and Estimation of Simultaneous Equation Models with Measurement Error

Efficient Estimation of Simultaneous Equations with Auto-Regressive Errors by Instrumental Variables

T HE purpose of this paper is to point out how the efficient instrumental-variables technique discussed by Brundy and Jorgenson (1971) can be modified to take into account auto-regressive properties of the error terms. The limited-information and full-information estimators proposed in this paper are consistent and have the same asymptotic distributions as the limited-information and full-information maximum likelihood estimators, respectively. The full-information estimation of simultaneous equations models with auto-regressive errors has been discussed by Sargan (1961), Hendry (1971), Chow and Fair (1973), and Dhrymes (1971). Sargan originally proposed the full-information maximum likelihood estimation of such models, and Hendry and Chow and Fair have recently developed computationally feasible methods for obtaining the maximum likelihood estimates. Hendry considered only the case of completely unrestricted auto-regressive coefficient matrices (i.e., no zero elements), whereas Chow and Fair considered the case of restricted auto-regressive coefficient matrices as well. Dhrymes has recently proposed the three-stage least squares estimator of simultaneous equations models with auto-regressive errors. Dhrymes also considered only the case of completely unrestricted auto-regressive coefficient matrices. The limited-information estimation of simultaneous equations models with auto-regressive errors has been discussed by Sargan (1961), Amemiya (1966), and Fair (1970), among others. Sargan proposed the limited-information maximum likelihood estimation of such models, and Amemiya and Fair considered various two-stage least souares estimators of such models. Most of the work on limited-information estimators has been concerned with the case of diagonal auto-regressive coefficient matrices. Brundy and Jorgenson's criticism of the twoand three-stage least squares estimators, namely, that the first stage involves estimating reduced form equations with a very large number of variables included in them, holds even more so for models with auto-regressive errors. For these models, the reduced form equations include not only all of the predetermined variables in the system but also all of the lagged endogenous and lagged predetermined variables. In fact, one of the main purposes of the work by Fair (1970) was to suggest ways in which the number of variables used in the first stage regressions of two-stage least squares might be decreased with perhaps small loss of asymptotic efficiency. The advantage of the instrumental-variables techniques proposed in the Brundy-Jorgenson paper and in this paper is that the first stage regressions need not be run.

Maximum Likelihood Estimation of Systems of Simultaneous Regression Equations with Errors Generated by a Vector Autoregressive Process

A MAJOR COMPLICATION AFFECTING the estimation of simultaneous equation models is the presence of autocorrelated error terms, especially so when some of the explanatory variables are lagged values of endogenous variables, since the. resultant estimates are then not consistent. Two general maximum likelihood solutions have been proposed, the former based on the assumption that the errors are generated by a vector autoregressive process (see Sargan [17]), while the second assumes the errors follow a vector moving-average scheme. (See Phillips [13]). Below we develop and apply the estimator suggested by Sargan, for systems of stochastic difference equations, when the errors are of a first-order autoregressive form. Consider a standard simultaneous equation model written as

The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Correlated Errors

In this paper various methods for the estimation of simultaneous equation models with lagged endogenous variables and first order serially correlated errors are discussed. The methods differ in the number of instrumental variables used. The asymptotic and small sample properties of the various methods are compared, and the variables which must be included as instruments to insure consistent estimates are derived. A suggestion on how to estimate the approximate covariance matrix of the estimators is made.