Dynamic Simultaneous Equation Model Research Articles

State Space Methods inRATS

This paper uses several examples to show how the econometrics program <b>RATS</b> can be used to analyze state space models. It demonstrates Kalman filtering and smoothing, estimation of hyperparameters, unconditional and conditional simulation. It also provides a more complicated example where a dynamic simultaneous equations model is transformed into a proper state space representation and its unknown parameters are estimated.

Who’s Cueing Whom?

The 2005 French and Dutch referendum campaigns were characterized by an alleged disconnect between pro-European political elites and Eurosceptic masses. Past evidence regarding elite-mass linkages in the context of European integration has been conflicting. Whereas some scholars argue that political elites respond to the changing preferences of their electorates, others suggest that party elites cue the mass public through a process of information and persuasion. We contend that these conflicting results stem from the reciprocal nature of elite-mass linkages and estimate a series of dynamic simultaneous equations models to account for this reverse causation. Using Euro-barometer and expert survey data from 1984-2002, we find evidence of a dual-process model, whereby party elites both respond to and shape the views of their supporters. We also find that the strength of these results is contingent on several factors, including the type of electoral system, intra-party dissent and voter characteristics.

An Empirical Investigation of Signaling in the Motion Picture Industry

The contribution of this research lies in the use of real-world data to test several hypotheses about the role of two signals—sequels and advertising expenditures—in the motion picture industry. The authors analyze the data with a dynamic simultaneous-equations model of the drivers and the interrelationships of the behaviors of movie audiences, studios, and exhibitors. Specifically, the authors test for the attenuating role of third-party information sources, such as critics' review consensus and cumulative word of mouth, on the strength of the two aforementioned signals. The authors find evidence of such an effect both at the release phase across movies and over the postrelease phase for any movie. Notably, they hypothesize and show that sequels and advertising expenditures have a positive interaction effect on box office revenues. This is an important finding because though most firms use multiple signals for their products, empirical work on the interaction of two or more signals is rare. This study offers several new and interesting empirical insights into the market dynamics of the motion picture industry.

Real Interest Rate Parity: Long-Run and Short-Run Analysis Using Wavelets

In this article, long-run and short-run relationships among real interest rates in G-7 countries are empirically analyzed. The evidence suggests the existence of long-run relationships among these real interest rates. However, the long-run relationship is not an equality relationship. Short-run relationships are estimated using dynamic simultaneous equation models. They reveal that the real interest rates of non-U.S. G-7 countries react and adjust to long-run disequilibrium conditions. A more detailed analysis based on wavelet transform indicates the existence of both short-run and long-run relationships; however, strict interest rate parity does not seem to hold true.

Early development of econometric software at the University of Auckland

Over the period 1964-1970, graduate students of Rex Bergstrom at the University of Auckland in New Zealand developed econometric computer programs to conduct estimation and inference for dynamic linear models, dynamic simultaneous equation models and systems of linear stochastic differential equations. Linear and nonlinear multiple equation regression programs were written in Fortran; and simulation experiments and empirical applications were performed on two small IBM mainframe computers.

A Temporal Dynamic Model of Spousal Family Purchase-Decision Behavior

The authors examine family purchase-decision dynamics to shed light on enhancing marketing communication effectiveness. In particular, the authors are interested in understanding the temporal nature of spousal behavioral interaction in family decision making to help marketers target communication messages, shape brand choice, and guide personal selling activities. The authors calibrate a dynamic simultaneous equations model to investigate spousal family purchase-decision behavior: What are spousal behavioral interactions in a discrete purchase decision, and what are the temporal aspects of spousal decision behavior across decisions? The results indicate that spouses tend both not to reciprocate coercion in a discrete decision and to adjust influence strategies over time. The authors also investigate the effectiveness of influence strategies and spousal satisfaction with decisions and their impacts on spousal subsequent decision behaviors from a postdecision perspective as a mechanism to explain why spouses revise decision behaviors across purchase decisions. The authors discuss marketing implications of their findings and present ideas about how to use these findings creatively to target advertising and sales messages to influential spouses in specific decision contexts.

IDENTIFICATION AND DICHOTOMIZATION OF LONG- AND SHORT-RUN RELATIONS OF COINTEGRATED VECTOR AUTOREGRESSIVE MODELS

We show that the usual rank condition is necessary and sufficient to identify a vector autoregressive process whether the variables are I(0) or I(d) for d = 1,2,.... We then use this rank condition to demonstrate the interdependence between the identification of short-run and long-run relations of cointegrated process. We find that both the short-run and long-run relations can be identified without the existence of prior information to identify either relation. But if there exists a set of prior restrictions to identify the short-run relation, then this same set of restrictions is sufficient to identify the corresponding long-run relation. On the other hand, it is in general not possible to identify the long-run relations without information on the complete structure. The relationship between the identification of a vector autoregressive process and a Cowles Commission dynamic simultaneous equations model is also clarified.

Demand for international telephone services between US and Africa

Abstract This paper uses a two-equation dynamic simultaneous equation model that accounts for call externality and arbitrage, and a dynamic panel estimator to investigate the demand for international telephone calls between the US and African countries. Using panel data from 45 African countries over the 1992–1996 period, we find that the demand for telephone calls from African countries to the US is price elastic while the demand for telephone calls from the US to African countries is price inelastic. We find telephone calls originating from African countries to the US are complementary to calls from the US to African countries while calls originating in the US to African countries are substitutes for calls to the US that originate in African countries, and calls between the two sets of countries exhibit reciprocal and arbitrage effects. We also find that the demand for telephone calls between the US and African countries show strong dynamic effects. Finally, we find that telephone demand between African countries and the US responds positively to income and trade. Our results have interesting research and policy implications.

Cointegration and Dynamic Simultaneous Equations Model

We demonstrate that despite variables that are integrated, the fundamental issues on structural equation modeling raised by the Cowles Commission remain valid and standard estimation and testing procedures can still be applied. A basic framework linking the multiple time series model and the dynamic simultaneous equation model is provided and implications under the long-run cointegrating relations are discussed. Conditions for identifying both the short-run dynamics and long-run equilibrium conditions are given. Limiting properties of the least squares and simultaneous equation estimators under cointegration are derived. Implications for hypothesis testing are also discussed.

The firm's leverage-cash flow relationship

Two separate strands of the literature on capital structure under asymmetric information consider the relationship between a firm's financial leverage and cash flow. Signalling theory suggests a positive relationship, while pecking order behavior implies a negative relationship. These contrasting theoretical implications appear contradictory. However, both are supported in different bodies of empirical literature. Leverage-changing event studies tend to support a positive relationship while cross-sectional studies typically reveal a negative relationship. This paper proposes that the appropriate pecking order relationship is contemporaneous — between current leverage and current cash flow, while the relevant signalling relationship is intertemporal-between current leverage and future cash flow. A dynamic simultaneous equations model is built which allows the firm's leverage, cash flow, and risk to interact jointly in the same period, as well as across time. Empirical results reveal that, in the same time period, leverage and cash flow tend to be negatively related, while across time leverage is positively related to future cash flow. Thus the apparent contradictions in the theoretical and empirical literature may be reconciled by considering both the contemporaneous and dynamic aspects of the firm's leverage/cash flow relationship.

Asymptotically Optimal Tests Using Limited Information and Testing for Exogeneity

By appropriately partitioning the joint hypothesis of weak exogeneity and the maintained overidentifying restrictions in the linear dynamic simultaneous equations model and showing that the component subhypotheses are separable, asymptotically optimal tests for the weak exogeneity hypothesis may be constructed using limited information statistics. A necessary and sufficient condition for the separability of parametric hypotheses of the mixed implicit function and constraint equation type is derived which generalizes conditions previously obtained in the literature. Consequently, limited and full information procedures for testing the weak exogeneity hypothesis are asymptotically equivalent. The impact of these results for testing strong exogeneity in the linear dynamic simultaneous equations model is also explored.

Generalized Predictive Tests and Structural Change Analysis in Econometrics

A generalized predictive testing procedure for structural stability in nonlinear dynamic simultaneous equations models is presented. It has several attractive features: (1) the tests are based on easy-to-compute predicted residuals; (2) the prediction subsample can be arbitrarily small; (3) only consistency is required and allowance is made for data-based model selection; (4) it is possible to analyze the timing and form of structural change equation by equation or globally, allowing an exploratory analysis of structural change conveniently summarized in a predictive analysis table; and (5) general forms of temporal dependence between model disturbances are allowed. Copyright 1994 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Asymptotic Distributions of Impulse Responses, Step Responses, and Variance Decompositions of Estimated Linear Dynamic Models

Formulas are derived for computing asymptotic covariance matrices of sets of impulse responses, step responses, or variance decompositions of estimated dynamic simultane- ous-equations models in vector autoregressive moving-average (VARMA) form. Com- puted covariances would be used to test linear restrictions on sets of impulse responses, step responses, or variance decompositions. The results unify and extend previous formulas to handle any model in VARMA form, provide accurate computations based on analytic derivatives, and provide insights into the structures of the asymptotic covariances. FOLLOWING THE LEAD OF SIMS (1980), impulse responses, step responses, and variance decompositions have become standard tools for examining the empiri- cal validity of economic theories or interpreting the forecasting and policy implications of estimated linear dynamic models. Runkle (1987) demonstrated the importance of accounting for sampling variability in these exercises. He computed confidence bounds for impulse responses and variance decomposi- tions derived from estimated vector autoregressive (VAR) models with sto- chastic simulations and asymptotic normal approximations. The two methods produced comparable results, but the simulations took about 160 times longer to compute than normal approximations based on numerical derivatives. Whereas Runkle only reported confidence bounds for individual impulse re- sponses and decomposed variances of VAR models, the present paper derives equations for computing full asymptotic covariance matrices of sets of impulse responses, step responses, or variance decompositions of estimated dynamic simultaneous-equations models in autoregressive moving-average form. The computed covariances may be used to jointly test multiple linear restrictions-or linear approximations of differentiable nonlinear restrictions-on sets of im- pulse responses, step responses, or variance decompositions of estimated mod- els. Because the derived computational equations are based on analytical derivatives, they have at least two advantages: they lead to more accurate and often faster computations than those based on numerical derivatives; they provide insight into the structures of asymptotic covariances of the estimated quantities. By allowing for various identifying restrictions, the paper extends and unifies results of Schmidt (1973), Evans and Wells (1986), and Liutkepohl (1988, 1989,

On Testing the Exogeneity Specification Underlying the Monetary Approach to Balance of Payments: The Indian Case

The Monetary Approach to Balance of Payments (MABP) has triggered off a controversy over fundamental proposition of exogeneity of price level, real income, interest rate, money multiplier and changes in domestic credit with respect to reserve flows. The present study investigates into the validity of the exogeneity assumptions under-lying the monetary model in three different ways. Firstly, a simultaneous estimation of the reserve flow and sterilization equations is made to confirm the absence of sterilization. Secondly, using three causality tests viz., the Granger, Sims and Multiple Rank F tests, bi-variate causality is examined. Finally, a multivariate systems test of causality within the framework of a Complete Dynamic Simultaneous Equation Model (CDSEM) is applied to test the joint exogeneity of the right hands side variables in the reserve flow equation. The findings of the study which are based on Indian annual data relating to the period 1950-90, by and large, do not support the exogeneity specification. While the causality tests collectively fail to provide any definite pattern of pair-wise causality, the OLS and 3SLS estimates of the reserve flow and sterilization equations, and Wald and likelihood ratio tests of the CDSEM, clearly reject the exogeneity assumptions.

Introduction to Multiple Time Series Analysis

This graduate-level textbook deals with analyzing and forecasting multiple time series. It considers a wide range of multiple time series models and methods. The models include vector autoregressive, vector autoregressive moving average, cointegrated and periodic processes as well as state space and dynamic simultaneous equations models. Least squares, maximum likelihood and Bayesian methods are considered for estimating these models. Different procedures for model selection or specification are treated and a range of tests and criteria for evaluating the adequacy of a chosen model are introduced. The choice of point and interval forecasts as well as innovation accounting are presented as tools for structural analysis within the multiple time series context.

Introduction to Multiple Time Series Analysis

This graduate-level textbook deals with analyzing and forecasting multiple time series. It considers a wide range of multiple time series models and methods. The models include vector autoregressive, vector autoregressive moving average, cointegrated and periodic processes as well as state space and dynamic simultaneous equations models. Least squares, maximum likelihood and Bayesian methods are considered for estimating these models. Different procedures for model selection or specification are treated and a range of tests and criteria for evaluating the adequacy of a chosen model are introduced. The choice of point and interval forecasts as well as innovation accounting are presented as tools for structural analysis within the multiple time series context.

Analysis and forecasting of income statement account balances: The dynamic interdependency and ARIMA approaches: Journal of Forecasting, 11 (4), 283–307 (June 1992)

This paper develops a dynamic simultaneous-equations model for analyzing and forecasting the account balances in the income statement of a firm. In the model, the income statement accounts play the role of the dependent variables that are jointly determined and explained by three types of exogenous variables: non-controllable, performance, and controllable. The model is estimated by the three-stage least-squares method using annual series of data for six firms during the period from 1936 or 1950 to 1981. The immediate, delayed, and cumulated impacts of an exogenous shock on the income accounts are analyzed and the implications for managerial decisions and strategies discussed. To run as a standard of comparison for the dynamic interdependency model, the Box-Jenkins approach is also used to develop an autoregressive integrated moving average (ARIMA) model for each of the accounts. Assessing the forecasting performance of the dynamic model against a naive model and the ARIMA and Elliott-Uphoff models for the 1982-4 period beyond the estimation period, we conclude that the dynamic model is a better representation of income statement accounts of the firm and increases forecasting accuracy.

A simulation study of structural estimators of dynamic simultaneous equations models with autoregressive disturbances

This is a Monte Carlo study of the small sample performances of the six Hatanaka's two-step structural estimators of dynamic simultaneous equations models with autoregressive disturbances. It is concluded that among the limited information methods HL1 performed relatively the best. Among the full information methods HF1 performed the best. The results of this study support that the full information methods are relatively more reliable than the limited information methods.

Analysis and forecasting of income statement account balances the dynamic interdependency and ARIMA approaches

AbstractThis paper develops a dynamic simultaneous‐equations model for analyzing and forecasting the account balances in the income statement of a firm. In the model, the income statement accounts play the role of the dependent variables that are jointly determined and explained by three types of exogenous variables: non‐controllable, performance, and controllable. The model is estimated by the three‐stage least‐squares method using annual series of data for six firms during the period from 1936 or 1950 to 1981. The immediate, delayed, and cumulated impacts of an exogenous shock on the income accounts are analyzed and the implications for managerial decisions and strategies discussed. To run as a standard of comparison for the dynamic interdependency model, the Box‐Jenkins approach is also used to develop an autoregressive integrated moving average (ARIMA) model for each of the accounts. Assessing the forecasting performance of the dynamic model against a naive model and the ARIMA and Elliott‐Uphoff models for the 1982‐4 period beyond the estimation period, we conclude that the dynamic model is a better representation of income statement accounts of the firm and increases forecasting accuracy.

Monte Carlo Methodology and the Finite Sample Properties of Instrumental Variables Statistics for Testing Nested and Non-Nested Hypotheses

Using Monte Carlo methodology, this paper investigates the effect of dynamics and simultaneity on the finite sample properties of instrumental variables statistics for testing nested and nonnested hypotheses. Simple numerical-analytical formulae (response surfaces) are obtained which closely approximate the statistics' unknown size and power functions for a dynamic simultaneous-equations model. The analysis illustrates the value and limitations of asymptotic theory in interpreting finite sample properties. Two practical results arise. The F form and the Wald statistic is favored over its chi-squared form, and large-sigma and small effective sample size strongly affect the test of over-identifying restrictions and the Cox-type test. Copyright 1991 by The Econometric Society.