Optimal control in nonlinear models: a generalised Gauss-Newton algorithm with analytic derivatives

In this paper we propose an algorithm for the solution of optimal control problems with nonlinear models based on a generalised Gauss- Newton algorithm but making use of analytic model derivatives. The method is implemented in WinSolve, a general nonlinear model solu- tion program.

Terminal conditions in forward-looking economic models

In this paper we show how the popular L-B-J algorithm for solving forward-looking economic models using Newton methods can be gen- eralised to allow for a block of terminal equations for variables that appear with a lead. The e¤ect of choosing di¤erent types of termi- nal condition is explored in a simple stochastic growth model using WinSolve, a general nonlinear model solution package.

Linear-quadratic approximation, external habit and targeting rules

We examine the linear-quadratic (LQ) approximation of non-linear stochastic dynamic optimization problems in macroeconomics, in particular for monetary policy. We make four main contributions: first, we draw attention to a general Hamiltonian framework for LQ approximation due to Magill (1977). We show that the procedure for the ‘large distortions’ case of Benigno and Woodford (2003, 2005) is equivalent to the Hamiltonian approach, but the latter is far easier to implement. Second, we apply the Hamiltonian approach to a Dynamic Stochastic General Equilibrium model with external habit in consumption. Third, we introduce the concept of target-implementability which fits in with the general notion of targeting rules proposed by Svensson (2003, 2005). We derive sufficient conditions for the LQ approximation to have this property in the vicinity of a zero-inflation steady state. Finally, we extend the Hamiltonian approach to a non-cooperative equilibrium in a two-country model. JEL Classification: E52, E37, E58dynamic stochastic general equilibrium models, Linear-quadratic approximation, utility-based loss function

Linear-Quadratic Approximation, Efficiency and Target-Implementability

We examine linear-quadratic (LQ) approximation of stochastic dynamic optimization problems in macroeconomics (and elsewhere), in particular in policy analysis using Dynamic Stochastic General Equilibrium (DSGE) models. We first define the problem that is solved by a social planner, given that the objective of the latter is to maximize average welfare; this yields the efficient solution. We then comment on the LQ approximation when a tax or subsidy can be imposed such that the zero-inflation competitive steady state output level is equal to the efficient level. We then examine the correct procedure for replacing a stochastic non-linear dynamic optimization problem with a linear-quadratic approximation. We show that a procedure proposed by Benigno and Woodford (2004) for large underlying distortions in the economy can be more easily implemented through a second-order approximation of the Hamiltonian used to compute the ex ante optimal policy with commitment (the Ramsey problem). We then define the notion of Target-Implementability, which is also a sufficient condition for a particular steady-state maximum of the Ramsey problem, and explain the usefulness of this in the context of stabilization policyLinear-quadratic approximation, dynamic stochastic general equilibrium models, utility-based loss function

Monetary Policy Coordination Revisited in a Two-Bloc DSGE Model

We reassess the gains from monetary policy coordination within the confines of the canonical NOEM in the light of three issues. First, the literature uses a number of cooperative and non-cooperative equilibrium concepts that do not always clearly distinguish commitment and discretionary outcomes, and in some cases adopts inappropriate concepts. Second, our analysis is welfare based. Moreover, as with much of this literature, we adopt a linear-quadratic approximation of the actual non-linear non-quadratic stochastic optimization problem facing the monetary policymakers. Our second objective then is to re-assess welfare gains using an accurate approximation for such a problem, a feature that for the most part is lacking in previous studies. Finally, we examine the issue where the monetary authority is restricted to rules that are operational in two senses: first, the zero lower bound constraint is imposed on the optimal rule and second, we study simple Taylor-type commitment rules that unlike fully optimal rules are easily monitored by the public.monetary rules, open economy, coordination games, commitment, discretion, zero bound constraint

Causality between Energy Consumption and GDP: Evidence from 30 OECD and 78 Non-OECD Countries

Energy arguably plays a vital role in economic development. Hence many studies have attempted to test for causality between energy and economic growth; however, no consensus has emerged. This paper, therefore, tests for causality between energy and GDP using a consistent data set and methodology for 30 OECD and 78 non-OECD countries. Causality from aggregate energy consumption to GDP and GDP to energy consumption is found to be more prevalent in the developed OECD countries compared to the developing non-OECD countries; implying that a policy to reduce energy consumption aimed at reducing emissions is likely to have greater impact on the GDP of the developed rather than the developing world.Energy; GDP; Development; Causality; Modelling

Growth and Welfare Effects of East-West European Migration

Using a calibrated two-bloc endogenous growth model of the European economy, we assess the growth and welfare impact of East-West European migration of different skill compositions. The East has a lower total factor productivity and a lower endowment of skilled labour. Migration can induce two growth-enhancing effects: an efficiency effect from the more e±cient use of labour in the West and a sectoral reallocation effect from a fall in the Western skilled-unskilled wage rates. Despite growth gains there are both winners (migrants, the representative Western non-migrant household) and losers (the representative Eastern household remaining). Remittances can see the latter group joining the winners.migration, endogenous growth, welfare, immigration surplus, emigration

Risk Management in Action. Robust monetary policy rules under structured uncertainty.

Recent interest in ‘Risk Management’ has highlighted the relevance of Bayesian analysis for robust monetary- policy making. This paper sets out a comprehensive methodology for designing policy rules inspired by such considerations. We design rules that are robust with respect to model uncertainty facing both the policy-maker and private sector. We apply our methodology to three simple interest-rate rules: inflation-forecast- based (IFB) rules with a discrete forward horizon, one targeting a discounted sum of forward inflation, and a current wage inflation rule. We use an estimated DSGE model of the euro area and estimated measures of structured exogenous and parameter uncertainty for the exercise. We find that IFB rules with a long horizon perform poorly with or without robust design. Our discounted future targeting rule performs much better, indicating that policy can be highly forward-looking without compromising stabilization. The wage inflation rule dominates whether it is designed to have good robust properties or not. JEL Classification: E52, E37, E58Interest-rate rules, Robustness, structured uncertainty