Optimal Monetary Policy with Asymmetric Targets

We investigate the derivation of optimal interest rate rules in a simple stochastic framework. The monetary authority chooses to minimise an asymmetric loss function made up of the sum of squared components, where the monetary authority places positive weight on squared negative (positive) deviations of output (inflation) and zero weight on squared positive (negative) deviations. Recent approaches to monetary policy under asymmetric preferences have emphasised the adoption of a linear exponential (linex) preference structure. This paper presents a new and different analytic methodology that is based on the explicit calculation of semi-variances. This approach can be used to derive precise coefficients of the optimal interest rate rules. We derive optimal interest rate rules based on two different informational assumptions. In the first case, which we call a fixed interest rate rule, the monetary authority knows only the structure of the economy and the variance of sectoral shocks so that interest rates must take a constant value. In the second case, which we call a flexible interest rate rule, the monetary also has access to additional information in that it can observe the contemporaneous inflation rate. In this second case, we restrict our analysis to the class of linear interest rate rules. The more standard approach in the literature derives optimal monetary policy rules using symmetric loss functions, where monetary policy is designed to minimise the sum of squared components. We also compare optimal interest rate rules under both symmetric and asymmetric loss functions.Monetary Economics; Interest Rate Rule; Inflation Target; Output Target; Asymmetric Loss Function; One-sided Target; Linex Preferences; Semi-Variance; Symmetric Loss Function.

Optimal Monetary Policy in an Open Economy

This paper analyzes the optimal intertemporal tradeoff between inflation and output in an open economy under perfect foresight. The announcement of the optimal plan may, or may not, generate an initial jump in the exchange rate. That depends upon the real adjustment costs, which such unanticipated changes impose on the economy. In the case that such jumps occur, the question of time consistency of the optimal policy arises. A time consistent solution is obtained provided: (i) the policy maker is not too myopic; (ii) the adjustment costs associated with the jump in the exchange rate are of an appropriate form. The optimal monetary rule is derived and properties of this rule, as well as the overall optimal adjustment of the economy are discussed.

Reverse-Shooting versus Forward-Shooting over a Range of Dimensionalities

This paper investigates the properties of dynamic solutions that have been derived using the well-known reverse-shooting and forwardshooting algorithms. Given an arbitrary large-scale model about which we have limited information, how successful are the algorithms likely to be in solving this model? We address this question using a range of investment models, both linear and non-linear. By extending the investment models to allow for multi-dimensional specifications of the capital stock, we are able to examine the computational efficiency of the competing algorithms as the dimensionality of the capital stock is allowed to increase. Our approach provides insights into how the complexity of the solutions to a broad range of macroeconomic models increases with the dimensionality of the models.Macroeconomics; Reverse-shooting; Forward-shooting; Saddlepath instability; Computational techniques; Investment models.

Solving Macroeconomic Models with "Off-the-Shelf" Software: An Example of Potential Pitfalls

When working with large-scale models or numerous small models, there can be a temptation to rely on default settings in proprietary software to derive solutions to the model. In this paper we show that, for the solution of non-linear dynamic models, this approach can be inappropriate. Alternative linear and non-linear specifications of a particular model are examined. One version of the model, expressed in levels, is highly non-linear. A second version of the model, expressed in logarithms, is linear. The dynamic solution of each model version has a combination of stable and unstable eigenvalues so that any dynamic solution requires the calculation of appropriate “jumps” in endogenous variables. We can derive a closed-form solution of the model, which we use as our "true" benchmark, for comparison with computational solutions of both linear and non-linear models. Our approach is to compare the "goodness of fit" of reverse-shooting solutions for both the linear and non-linear model, by comparing the computational solutions with the benchmark solution. Under the basic solution method with default settings, we show that there is significant difference between the computational solution for the non-linear model and the benchmark closed-form solution. We show that this result can be substantially improved using modifications to the solver and to parameter settings.Solving non-linear models, reverse-shooting, computational economics, computer software

REVERSE SHOOTING IN A MULTI-DIMENSIONAL SETTING

This paper investigates the properties of dynamic solutions that have been derived using the well-known reverse-shooting algorithm. Given an arbitrary large-scale model about which we have limited information, how successful is the algorithm likely to be in solving this model? We address this question using a range of investment models, both linear and non-linear. By extending the investment models to allow for multidimensional specifications of the capital stock, we are able to examine the computational efficiency of the reverse shooting algorithm as the dimensionality of the capital stock is allowed to increase. Our approach provides insights into how the complexity of the solutions to a broad range of macroeconomic models increases with the dimensionality of the models.Macroeconomics; Reverse shooting; Saddlepath instability; Computational techniques; Investment models

Airborne gravimetry from a small twin engine aircraft over the Long Island Sound

In January 1990, a test of the feasibility of airborne gravimetry from a small geophysical survey aircraft, a Cessna 404, was conducted over the Long Island Sound using a Bell Aerospace BGM-3 sea gravity meter. Gravity has been measured from large aircraft and specially modified de Havilland Twin Otters but never from small, standard survey aircraft. The gravity field of the Long Island Sound is dominated by an asymmetric positive 30 mGal anomaly which is well constrained by both marine and land gravity measurements. Using a Trimble 4000 GPS receiver to record the aircraft's horizontal position and radar altimeter elevations to recover the vertical accelerations, gravity anomalies along a total of 65 km were successfully measured. The root mean square (rms) difference between the airborne results and marine measurements within 2 km of the flight path was 2.6 mGal for 15 measured values. The anomalies recovered from airborne gravimetry can also be compared with the gridded regional free air gravity field calculated using all available marine and land gravity measurements. The rms difference between 458 airborne gravity measurements and the regional gravity field is 2.7 mGal. This preliminary experiment demonstrates that gravity anomalies, with wavelengths as short as 5 km, can be measured from small aircraft with accuracies of 2.7 mGal or better. The gravity measurements could be improved by higher quality vertical and horizontal positioning and tuning the gravimeter's stabilized platform for aircraft use

Unemployment, inflation and some relevant policy issues

This thesis is an attempt to consider in some detail a few of the important theoretical and policy issues associated with unemployment and inflation, using a fairly standard framework which many economists would accept as plausible. Part 1 is concerned with "The Role of Expectations and Deficit Financing." Here we introduce the rational expectations approach to economic modeling and also show how the short-run responses of endogenous variables can be calculated. We do this in conjunction with an examination of the stability properties associated with alternative forms of deficit financing. In Parts 2 and 3 of the thesis we use the techniques developed in Part 1 to examine some policy issues more closely. Frequently, a government policy maker may want to lower both inflation and unemployment in a manner which is as painless as possible. One solution to the policy maker's problem is presented in Part 2, entitled "Optimal Stabilization Policies Under Perfect Foresight." Here we formalize the policy maker's objective and discuss what policy instruments can be used to achieve that objective. We also spend some time discussing whether it is desirable for prices to jump and if this is the case what is the magnitude of the appropriate jump. Time consistency of the optimal solution is also considered. "Some Relevant Policy Issues" are discussed in Part 3. When unemployment becomes high, two issues that are frequently raised concern "easy" methods for lowering unemployment and ways of relieving the hardship of the unemployed. One method of lowering unemployment is by lowering the length of the standard working week and hence lowering the aggregate supply of labor. A way of making life more acceptable to those who are unemployed is by paying higher unemployment benefits to those without work. Both these "solutions" are examined in Part 3. An important part of this thesis is the way in which the issues mentioned above have been analysed within a consistent framework of models. This framework provides a common thread which, along with the common theme of the issues discussed, unifies the thesis into a coherent whole