Peter J. Stemp

Assessing two common approaches for solving models with saddle-path instabilities

This paper presents an approach for assessing the time taken by the well known reverse-shooting and forward-shooting algorithms to solve large-scale macroeconomic models characterized by saddle-path instability. We focus on a range of investment models with multi-dimensional specifications of the capital stock. Each algorithm presents a complicated exercise with a potentially unstable ordinary differential equation to be solved over a wide parameter space and involving a difficult search. Our results provide insights into how the complexity of the solutions to a broad range of macroeconomic models increases with the dimensionality of the models. We describe how econometric techniques could be used to summarize the likely success of competing algorithms when confronted with models exhibiting a range of properties.

Exploiting Model Structure to Solve the Dynamics of a Macro Model

This paper considers alternative numerical approaches to solvingthe time-path of a nonlinear representative agent model.

Calculating Short-Run Adjustments: Sensitivity to Non-Linearities in a Representative Agent Framework

Two common properties of macroeconomic models are non-linearities and dynamics characterised by a non-zero number of unstable eigenvalues. Under these circumstances, a common approach is to make analysis more tractable by linearising the model in the neighbourhood of an appropriate steady-state. The linearised model is then employed to calculate short-run adjustments following exogenous shocks. This can lead to different results than would be derived from the correct (non-linear) model. This paper investigates the magnitude of errors that come about as a consequence of using a linear approximation to a well-known representative agent model. This is achieved by taking a calibrated version of the Matsuyama (1987) model of a small open economy.

Fiscal Policy, Monetary Policy and the Exchange Rate

Domestic fiscal and monetary policy settings can influence the strength of the Australia dollar in a number of different ways.

The government's time discount rate: Choices and consequences in a dynamic framework

This paper considers a closed macroeconomy where the monetary authority pursues an inflation target and policy outcomes are the consequence of a Nash game between fiscal and monetary authorities. The specification of the macroeconomic framework is characterized by nonlinearities which lead to multiple equilibria with differing stability properties. Employing a calibrated model and simulations derived using the Mathematica package, the stability properties of the economy and the likely choice of equilibrium are examined. Within this framework, the dynamic consequences of different time discount rates for the fiscal authority are investigated, both in a world of certainty and also in a world of uncertainty. It is shown that, in a world of certainty, it will be optimal to choose the fiscal authoritys time discount rate equal to the market rate of interest. However, depending on the degree of uncertainty in evaluating the time discount rates of consumers and of the fiscal authority, it may be appropriate to bias the fiscal authoritys discount rate above or below the expected interest rate.

Solving the dynamics of a representative agent macro-economic model

This paper describes two alternative approaches (modified reverse shooting and forward shooting) for solving the time-path of a representative agent model following an exogenous shock. In particular, reverse shooting is demonstrably better for solving part of the model but must be modified before it can be used to solve the full model with the least computational effort. On the other hand, an unmodified form of forward shooting can be used to solve both part and full model.

Non-Linearities and Dynamics in a Neoclassical Model of Investment

In this paper, we investigate the magnitude of errors that come about as a consequence of using a linear approximation to a well-known optimising model. We do this by taking a calibrated version of the neoclassical adjustment-cost model of investment due to Hayashi (1982).

Achieving the Best Fiscal Outcome: What Does the Government Need to Know?

This paper examines the operation of fiscal policy under incomplete information when the central bank sets the stance of monetary policy so as to achieve a zero inflation target. The fiscal authority is assumed to aim to achieve a target level for output and a zero level of public debt. The best fiscal policy setting arises under full information and is one where output atains its full employment level and public debt is driven to zero. Deviations from full infomration can lead to a considerable divergence from the best fiscal setting involving substantial levels of public sector indebtedness. The result ssuggest that a government shoudl invest avilable resources determining what outcomes are achievable and what outcomes are not. Then it should focus all its energies on trying to deliver achievable outcomes. The benefits from such a strategy can be substantial.

The Choice of Fiscal Policy Settings under Alternative Inflation Targets

Abstract This paper considers an open-loop Nash game between independent monetary and fiscal authorities. The monetary authority is concerned solely with achieving a desired rate of inflation. The fiscal authority has multiple objectives defined by specific preference parameters. A dynamic game theory approach is used to analyse the impact of different inflation targets on the long-term level of public debt, on the level of government expenditure, and on the dynamic path of the economy.