Andrew Binning

Underidentified SVAR Models: A Framework for Combining Short and Long-Run Restrictions with Sign-Restrictions

I describe a new method for imposing zero restrictions (both short and long-run) in combination with conventional sign-restrictions. In particular I extend the Rubio-Ramirez et al.(2010) algorithm for applying short and long-run restrictions for exactly identified models to models that are underidentified. In turn this can be thought of as a unifying framework for short-run, long-run and sign restrictions. I demonstrate my algorithm with two examples. In the first example I estimate a VAR model using the Smets & Wouters (2007) dataset and impose sign and zero restrictions based on the impulse responses from their DSGE model. In the second example I estimate a BVAR model using the Mountford & Uhlig (2009) data set and impose the same sign and zero restrictions they use to identify an anticipated government revenue shock.

Third-Order Approximation of Dynamic Models Without the Use of Tensors

I outline a new method for finding third-order accurate solutions to dynamic general equilibrium models. I extend the Gomme & Klein (2011) solution for second-order approximations without using tensors, to a third-order. In particular I derive a third-order matrix chain rule and use this to solve the third-order approximation. My solution method is easier to understand and code-up, and faster to implement in Matlab. I provide Matlab code and demonstrate my solution method with a simple RBC model. The resulting code is up to 80 times faster than Matlab code using tensor notation.

Solving second and third-order approximations to DSGE models: A recursive Sylvester equation solution

In this paper I derive the matrix chain rules for solving a second and a third-order approximation to a DSGE model that allow the use of a recursive Sylvester equation solution method. In particular I use the solution algorithms of Kamenik (2005) and Martin & Van Loan (2006) to solve the generalised Sylvester equations. Because I use matrix algebra instead of tensor notation to find the system of equations, I am able to provide standalone Matlab routines that make it feasible to solve a medium scale DSGE model in a competitive time. I also provide Fortran code and Matlab/Fortran mex files for my method.

Sigma point filters for dynamic nonlinear regime switching models

In this paper we take three well known Sigma Point Filters, namely the Unscented Kalman Filter, the Divided Difference Filter, and the Cubature Kalman Filter, and extend them to allow for a very general class of dynamic nonlinear regime switching models. Using both a Monte Carlo study and real data, we investigate the properties of our proposed filters by using a regime switching DSGE model solved using nonlinear methods. We find that the proposed filters perform well. They are both fast and reasonably accurate, and as a result they will provide practitioners with a convenient alternative to Sequential Monte Carlo methods. We also investigate the concept of observability and its implications in the context of the nonlinear filters developed and propose some heuristics. Finally, we provide in the RISE toolbox, the codes implementing these three novel filters.

Modelling Occasionally Binding Constraints Using Regime-Switching

Occasionally binding constraints are part of the economic landscape: for instance recent experience with the global financial crisis has highlighted the gravity of the lower bound constraint on interest rates; mortgagors are subject to more stringent borrowing conditions when credit growth has been excessive or there is a downturn in the economy. In this paper we take four common examples of occasionally binding constraints in economics and demonstrate how to use regime-switching to incorporate them into DSGE models. In particular we investigate the zero lower bound constraint on interest rates, occasionally binding collateral constraints, downward nominal wage rigidities and irreversible investment. We compare our approach against some well-known methods for solving occasionally-binding constraints. We demonstrate the versatility of our regime-switching approach by combining multiple occasionally binding constraints to a model solved using higher-order perturbation methods, a feat that is difficult to achieve using alternative methodologies.

Endogenous Growth Without Patents

This paper constructs an analytically tractable model of endogenous innovation with a special focus on the effects of barriers to entry, namely patents. Conventional models of endogenous growth rely on the existence and enforcement of intellectual property rights with patents. Those legal rights are seen as necessary evils, required to encourage innovation by ensuring successful innovators are rewarded with monopoly rents. This paper takes a different approach. By integrating Aghion, Harris, and Vickers (1997) and the Boldrin and Levine (2003) framework into a conventional vintage capital growth model such as Greenwood, et al (1997), the paper characterizes economic conditions under which patents may decrease the growth rate. The model is calibrated to the US economy to match its long run time series of GDP per hour. Simulations of that calibrated model provide important insights regarding growth-promoting policies. The model also provides an explicit numerical algorithm to measure cross-country differences in total factor productivity due to barriers to technology adoption.

A Migration Based Theory of the Exchange Rate and the New Zealand's Experience

Conventional exchange rate theory has proven unreliable in its attempts to explain the real exchange rate. In the March 2003 Reserve Bank Monetary Policy Statement two graphs appeared, one of total net migration and the other the nominal TWI exchange rate. Closer inspection revealed they were correlated. This paper aims to answer the question: can migration be used to predict the exchange rate? The hypothesis tested in this paper is that the heterogeneity in the market shares of aggregate demand and labor supply between the migrants and the native-born population constitute important determinants of the real exchange rate. In particular, the model provides an analytically tractable equation consistent with a general equilibrium theory of the exchange rate determination as a function of migration. It turns out that migration data is able to partially explain the movements in the real exchange rate. The correctly specified general equilibrium performs well in and out of the sample and gives valuable insight into the determination of the real exchange rate for New Zealand.