Five Debates over Macroeconomics Policy, Mankiw 5th ed., Ch. 23 Problem 4 Econom
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Question
Five Debates over Macroeconomics Policy, Mankiw 5th ed., Ch. 23 Problem 4Economist John Taylor has suggested that the Fed use the following rule for choosing its target for the federal funds interest rate (r):
r= 2% + p + 1/2 (y-y*) / y* + 1/2 (p - p*),
Where p is the average of the inflation rate over the past year, y is real GDP as recently measured, y* is an estimate of the natural rate of output, and p* is the Fed's goal for inflation.
a. Explain the logic that might lie behind this rule for setting interest rates. Would you support the Fed's use of this rule?
b. Some economists advocate such a rule for monetary policy but believe p and y should be the forecasts of future values of inflation and output. What are the advantages of using forecasts instead of actual values? What are the disadvantages?
Explanation / Answer
Economist John Taylor has suggested that the Fed use the following rule for choosing its target for the federal funds interest rate (r):
fft = 3 + 2 + ½(1) + ½(1)
fft = 3 + 2 + .5 + .5 = 5
If inflation started to heat up to 4 percent, the Fed should respond by raising the fed funds target to 6.5:
fft = 4 + 2 + ½(2) + ½(1) = 6.5
The Taylor Rule is a simple equation—fft = + ff*r + ½( gap) + ½(Y gap)—that allows central bankers to determine what their overnight interbank lending rate target ought to be given actual inflation, an inflation target, actual output, the economy’s potential output, and an estimate of the equilibrium real fed funds rate.
When the Fed has maintained the fed funds rate near that prescribed by the Taylor Rule, the economy has thrived; when it has not, the economy has been plagued by inflation (when the fed funds rate was set below the Taylor rate) or low output (when the fed funds rate was set above the Taylor rate). Personally I don’t recommend the Taylor Rule, here are my reasons. Foreign exchange rates can also flummox central bankers and their policies. Specifically, increasing (decreasing) interest rates will, ceteris paribus, cause a currency to appreciate (depreciate) in world currency markets. Why is that important? The value of a currency directly affects foreign trade. When a currency is strong relative to other currencies (when each unit of it can purchase many units of foreign currencies), imports will be stimulated because foreign goods will be cheap. Exports will be hurt, however, because domestic goods will look expensive to foreigners, who will have to give up many units of their local currency. Countries with economies heavily dependent on foreign trade must be extremely careful about the value of their currencies; almost every country is becoming more dependent on foreign trade, making exchange rate policy an increasingly important one for central banks worldwide to consider.
Forecasts are usually wrong! A good forecast is more than a single number it includes a mean value and standard deviation it also includes accuracy range (high and low). Aggregated forecasts are usually more accurate. Accuracy erodes as we go further into the future. Forecasts should not be used to the exclusion of known information.
The forecast error in period t, et, is the difference between the forecast for demand in period t and the actual value of demand in t. For a multiple step ahead forecast: et = Ft - t, t - Dt. For one step ahead forecast: et = Ft – DtTo evaluate Forecasting accuracy we develop a chart of Forecasting errors using:
MAD = (1/n) S | e i |
MSE = (1/n) S ei 2
We would find that the value
MSE0.5 = 1.25MAD = error
We can set up a “Control Chart” for tracking errors to study acceptability of our model of the forecast “Control” limits can be set at 3(error) or 3.75MADThis chart can be used to study bias (trends that deviate in only one direction for some time indicating lags) or very large errors (or growing) indicating a need to review the models. Forecast are helpful but not very reliable.
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