Eviews example3

Example #3: Estimation and Simulation of Small Macro Models - Evaluating Monetary Policy Rules

Attached files for download:

• Excel data file USqdata.xls
• Eviews program file Example3.prg
• Alternative EViews program file Example3_ev4.prg

This example looks at the estimation and simulation of small macroeconomic models. The specific application is the evaluation of monetary policy rules.

The EViews program was created for EViews 2.0.

1. Save the Excel 5.0/95 spreadsheet file USqdata.xls (save to floppy disk a:). Note: Do not left-click on the link, but right-click on the link (some browsers will otherwise immediately start the EViews, Excel, Word, or other progams)! 'Save the link' with the name USqdata.xls.
2. Save the EViews program file Example3.prg (save to floppy disk a:)
   1. (Alternatively, save the EViews 4 version of the program written by Kenneth Leong.)
3. Start EViews
4. Execute File Open Type=program .prg Drive= a: File Name=example3.prg. Click OK.
5. Run the program file example3.prg (execute Run Example3).
6. Let us see what the program has done.
   1. (a) The program loads the data from the Excel spreadsheet file USqdata.xls. This file contains basic quarterly time series for United States Gross Domestic Product in constant 1996 prices (real GDP), GDP Implicit Price Deflator (base 1996=100), real GDP potential or trend, and federal funds rate. (Data sources are provided in the Excel datasheet.)
   2. (b) Always start with a closer examination of the data you have been given. The programming lines generate a number of graphs. You can look at them by using the command Show <object name>. Carefully look for any irregularities in the data (typing errors, breaks, statistical characteristics: mean, variance, trends). Note: You can do this interactively in EViews. However, the purpose of this example is to show you the programming features of EViews.
   3. (c) Next the program will perform a number of data transformations. Taking logarithms and generating first-differences. These transformations are necessary to perform statistical analysis.
   4. (d) The program estimates and saves the results of 2 behavioral equations which make up a small macroeconomic model of the US economy. These equations describe inflation and output. Look at the results (use the Show <object name> command) and compare the estimates with the original results published in the associated journal articles.
   5. (e) The EViews model is built by 'appending' behavioral equations and a number of technical or definition equations. A policy rule for the policy variable is also included. Finally, the model is simulated in a historical simulation and stochastic simulations. Results are presented in a number of graphs, series and tables.

Rudebusch and Svensson (1999) estimated a small macroeconometric model of the US economy to evaluate a number of monetary policy rules.This model consists of 2 core equations. It is basically a dynamic old-fashioned Keynesian model. The inflation equation represents an accelerationist form of the Phillips curve, in which a) shocks in output cause permanent changes in inflation and b) monetary policy affects inflation only through its effect on the output gap. The output gap equation represents the view that monetary policy shocks temporarily affect output through changes in the real short-term interest rate.

(Some writers have, inappropriately, started the convention to refer to this model as the Rudebusch-Svensson model.)

Rudebusch and Svensson (2000) report the following estimates for the 2 equations.

The sample period is 1961:1 to 1996:4, coefficient standard errors given in parentheses, estimation method is OLS. The restriction that the sum of the lag coefficients of inflation equals one is imposed on the estimation. All variables were de-meaned prior to estimation, so no constants appear in the equations and the constant equilibrium level of the real interest rate is set equal to zero.

Variables definitions: infl is quarterly inflation in the GDP price index in percent at annual rate (i.e. 400*(ln P_t- ln P_t-1)), inflbar is the 4-quarter average of inflation (i.e. 1/4 SUM_{j=0 to 3} infl_t-j), i is the quarterly average federal funds rate in percent per year, ibar is the 4-quarter average federal funds rate (i.e. 1/4 SUM_{j=0 to 3} i_t-j), ygap is the relative gap between actual real GDP and potential GDP in percent (i.e. 100*(ln Q_t- ln Q*_t)), rbar is the constant average real interest rate derived from ibar - inflbar, the residuals eps and mu will be interpretated as economic shocks.

The EViews program estimates the 2 core equations and builds the model by adding the required add-on factors and technical or definition equations. A specific monetary policy rule is also added to the model. In this case a basic Taylor-rule for setting the short-term interest rate.

Taylor rules. Interest rate rules are usually some variant of the original rule from Taylor (1993). In general, this rule sets

i_t = rbar_t + infl_t + 0.5*(infl_t - infl*) + 0.5*ygap_t

where infl* is the inflation target (for example 2%) and rbar is the equilibrium real interest rate (usually set at some average of historical observations). Variants of this rule differ in the weights for inflation and output gap, forward-looking or lagged variables, and additional variables such as the lagged the interest rate to introduce smoothing objectives. Taylor (1999) provides a summary of recent research on monetary policy rules with interest rates.

Historical simulation. In a historical or counterfactual simulation the change in policy (i.e. a new policy rule) is confronted with the estimates of shocks that actually occurred in some historical time period. We can determine, if the model is correct, whether the alternative policy would have performed better or worse than the actual historical policy. A problem concerns robustness and recommendations for future policy. Historical results may depend on chance occurrances in the shocks, which may not be representative of future shocks.

Stochastic simulation. Stochastic simulations attempt to address the problem of robustness. New time series of shocks are generated, using assumptions about the distribution of the shocks (for example, a normal distribution with variance derived from estimated historical shocks). The performance of the new policy is examined for 'different economies'.

Policy performance. The performance of the policy rule is evaluated on the means and standard deviations of inflation, output gap, and the interest rate produced by the simulations. One might also use some form of utility or loss function to explicitly account for the possible tradeoffs between the different means and variances.

Note: The empirical estimates presented here are used only to introduce programming in EViews and to introduce econometric analysis on a simple level. The tests and results should not be taken at face value, i.e. as being the final results or as examples of 'best practice' on this specific topic. There exist many variants of the basic type of model used here, and there exist many models with fundamentally different behavioral equations.

References

McCallum, B.T., 'Issues in the design of monetary policy,' in J.B. Taylor, M. Woodford (eds.) Handbook of Macroeconomics. North Holland, 1999: . (NBER Working paper #6016 April 1997)

Rudebusch, G.D. and L.E.O. Svensson, 'Policy rules for inflation targeting,' in J.B. Taylor (ed.) Monetary Policy Rules. Chicago Univ. Press, 1999: . (NBER Working paper #6512 April 1998)

Rudebusch, G.D. and L.E.O. Svensson, 'Eurosystem Monetary Targeting: Lessons from U.S. data,' May 2000.

Taylor, J.B., 'The robustness and efficiency of monetary policy rules as guidelines for interest rate setting by the European central bank,' Journal of Monetary Economics, vol.43 (3) June 1999: 655-79.