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...

Under general conditions, it has been proved that free trade improves the welfare of open economies. However, the conditions to attain the free trade equilibrium are non trivial: when the productive process is planned, industries do not know the price that will prevail, while the production is...

This paper proposes a moment-matching method for approximating vector autoregressions by finite-state Markov chains. The Markov chain is constructed by targeting the conditional moments of the underlying continuous process. The proposed method is more robust to the number of discrete values and...

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...

This paper investigates extensions of the method of endogenous gridpoints (ENDGM) introduced by Carroll (2006) to higher dimensions with more than one continuous endogenous state variable. We compare three different categories of algorithms: (i) the conventional method with exogenous grids...

Food commodity prices fluctuations have important impacts on poverty and food insecurity across the world. Conventional models have not provided a complete picture of recent price spikes in agricultural commodity markets, while there is an urgent need for appropriate policy responses. Perhaps...

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...

We present a dynamic extension of the classic static model of Bertrand price competition that allows competing duopolists to undertake cost-reducing investments in an attempt to “leapfrog” their rival to attain low-cost leadership—at least temporarily. We show that leapfrogging occurs in...

The Portuguese economy has benefited from large amounts of European structural funds since the mid-eighties. At the same time, interest rates have decreased substantially, mainly due to a credibility phenomenon. The effects of those funds and the reduction of financial costs can be considered as...