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A state space representation of a linearized DSGE model implies a VAR in terms of observable variables. The model is said be non-invertible if there exists no linear rotation of the VAR innovations which can recover the economic shocks. Non-invertibility arises when the observed variables fail to perfectly reveal the state variables of the model. The imperfect observation of the state drives a wedge between the VAR innovations and the deep shocks, potentially invalidating conclusions drawn from structural impulse response analysis in the VAR. The principal contribution of this chapter is to show that non-invertibility should not be thought of as an “either/or” proposition – even when a model has a non-invertibility, the wedge between VAR innovations and economic shocks may be small, and structural VARs may nonetheless perform reliably. As an increasingly popular example, so-called “news shocks” generate foresight about changes in future fundamentals – such as productivity, taxes, or government spending – and lead to an unassailable missing state variable problem and hence non-invertible VAR representations. Simulation evidence from a medium scale DSGE model augmented with news shocks about future productivity reveals that structural VAR methods often perform well in practice, in spite of a known non-invertibility. Impulse responses obtained from VARs closely correspond to the theoretical responses from the model, and the estimated VAR responses are successful in discriminating between alternative, nested specifications of the underlying DSGE model. Since the non-invertibility problem is, at its core, one of missing information, conditioning on more information, for example through factor augmented VARs, is shown to either ameliorate or eliminate invertibility problems altogether.

New approaches for non‐classical neural‐based computing are introduced. The developed approaches utilize new concepts in three‐dimensionality, invertibility and reversibility to perform the required neural computing. The various implementations of the new neural circuits using the introduced paradigms and architectures are presented, several applications are shown, and the extension for the utilization in neural‐systolic computing is also introduced.

The new neural paradigms utilize new findings in computational intelligence and advanced logic synthesis to perform the functionality of the basic neural network (NN). This includes the techniques of three‐dimensionality, invertibility and reversibility. The extension of implementation to neural‐systolic computing using the introduced reversible neural‐systolic architecture is also presented.

Novel NN paradigms are introduced in this paper. New 3D paradigm of NL circuits called three‐dimensional inverted neural logic (3DINL) circuits is introduced. The new 3D architecture inverts the inputs and weights in the standard neural architecture: inputs become bases on internal interconnects, and weights become leaves of the network. New reversible neural network (RevNN) architecture is also introduced, and a RevNN paradigm using supervised learning is presented. The applications of RevNN to multiple‐output feedforward discrete plant control and to reversible neural‐systolic computing are also shown. Reversible neural paradigm that includes reversible neural architecture utilizing the extended mapping technique with an application to the reversible solution of the maze problem using the reversible counterpropagation NN is introduced, and new neural paradigm of reversibility in both architecture and training using reversibility in independent component analysis is also presented.

Since the new 3D NNs can be useful as a possible optimal design choice for compacting a learning (trainable) circuit in 3D space, and because reversibility is essential in the minimal‐power computing as the reduction of power consumption is a main requirement for the circuit synthesis of several emerging technologies, the introduced methods for non‐classical neural computation are new and interesting for the design of several future technologies that require optimal design specifications such as three‐dimensionality, regularity, super‐high speed, minimum power consumption and minimum size such as in low‐power control, adiabatic signal processing, quantum computing, and nanotechnology.

This volume of Advances in Econometrics is devoted to dynamic stochastic general equilibrium (DSGE) models, which have gained popularity in both academic and policy circles as a theoretically and methodologically coherent way of analyzing a variety of issues in empirical macroeconomics. The volume is divided into two parts. The first part covers important topics in DSGE modeling and estimation practice, including the modeling and role of expectations, the study of alternative pricing models, the problem of non-invertibility in structural VARs, the possible weak identification in new open economy macro models, and the modeling of trend inflation. The second part is devoted to innovations in econometric methodology. The papers in this section advance new techniques for addressing key theoretical and inferential problems and include discussion and applications of Laplace-type, frequency domain, empirical likelihood, and method of moments estimators.

This chapter develops a set of two-step identification methods for social interactions models with unknown networks, and discusses how the proposed methods are connected to the identification methods for models with known networks. The first step uses linear regression to identify the reduced forms. The second step decomposes the reduced forms to identify the primitive parameters. The proposed methods use panel data to identify networks. Two cases are considered: the sample exogenous vectors span Rn (long panels), and the sample exogenous vectors span a proper subspace of Rⁿ (short panels). For the short panel case, in order to solve the sample covariance matrices’ non-invertibility problem, this chapter proposes to represent the sample vectors with respect to a basis of a lower-dimensional space so that we have fewer regression coefficients in the first step. This allows us to identify some reduced form submatrices, which provide equations for identifying the primitive parameters.

This article reviews the literature on the econometric relationship between DSGE and VAR models from the point of view of estimation and model validation. The mapping between DSGE and VAR models is broken down into three stages: (1) from DSGE to state-space model; (2) from state-space model to VAR( ∞ ); (3) from VAR( ∞ ) to finite-order VAR. The focus is on discussing what can go wrong at each step of this mapping and on critically highlighting the hidden assumptions. I also point out some open research questions and interesting new research directions in the literature on the econometrics of DSGE models. These include, in no particular order: understanding the effects of log-linearization on estimation and identification; dealing with multiplicity of equilibria; estimating nonlinear DSGE models; incorporating into DSGE models information from atheoretical models and from survey data; adopting flexible modeling approaches that combine the theoretical rigor of DSGE models and the econometric model’s ability to fit the data.

The purpose of this paper is to propose a new control strategy based on adaptive inverse control aiming at high performance control of permanent magnet synchronous motor (PMSM).

This scheme adopts the vector control with double closed-loop structure and introduces a multi-dimensional Taylor network (MTN) inverse control method into velocity-loop. First, the invertibility of PMSM’s mathematical model is proved. Second, a novel dynamic network (MTN) is presented, which has simple structure and faster computing speed. Besides, to realize the high-precision speed control, three MTNs are applied to achieve system modeling, inverse modeling and noise disturbance elimination which correspond to the function of the adaptive identifier, adaptive feed-forward controller and nonlinear adaptive filter, respectively.

This scheme is designed with the full consideration of the PMSM’s particularity. For the PMSM’s unknown dynamics and time-varying characteristics, the variable forgetting factor recursive least squares algorithm is adopted to improve identification ability, and the weight-elimination algorithm is used to remove redundant regression items in the MTN identifier and inverse controller. In addition, to reduce the influence arose from measurement noise and other stochastic factors, adaptive MTN filter is introduced to eliminate noise disturbance. The computational results show that the proposed scheme possesses excellent control performance and better robustness against the load disturbance.

The paper presents a new inverse control scheme with MTN which is practical and flexible, and the MTN-based control system is very promising for real-time applications.

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.

The purpose of this paper is to derive a robust nonlinear attitude control law intended for practical application.

The method of input/output feedback linearization is utilized for having a linear model and a recently developed almost disturbance decoupling (ADD) approach is adopted for designing a robust satellite attitude control (SAC) system. The kinematics of the satellite is modeled by modified Rodriguez parameters because of their continuous invertibility. The design is simulated on the model of a realistic satellite project (BILSAT‐I), which is developed by the Turkish Scientific and Technological Research Council.

The torque requirement of the operation does not exceed the maximum limit provided by the actuator. The square error levels are staying under the boundary of final global attractor, which is one of the important proofs for the successful operation of the generated ADD control law.

The ADD concept is investigated on SAC problem. By that way, simple control structures with known disturbance attenuation capability can be designed.