Monetary Policy The Taylor Rule

1 The Taylor Rule and Its Variants History of the Taylor Rule • Taylor (1993)* proposes a “feedback” monetary policy rule, where changes in policy instruments (e.g., the interest rate, the monetary base, the money supply) responds to changes in the price level or real income. • He argues that using rules to to control inflation is more effective than discretionary policy • Although different studies have shown different responsiveness of the instruments, there has been some indication of the functional forms and the signs of the coefficients. • Under discretion policy, the settings of the instruments are determined from scratch each period -- which may result in time-inconsistency problem. *Taylor, J.B., 1993. Discretion Versus Policy Rules in Practice. Carnegie-Rochester Conference Series on Public Policy 39, 195-214. 2 Discretion v. Rules • A policy rule is referred to as the “optimal,” the “rules,” or the “precommitted” solution, to a dynamic optimisation problem. • Discretionary policy is referred to as the “inconsistent,” the “cheating,” or the “shortsighted” solution. • The difference and the advantage of rules over discretion are like those of a cooperative over a noncooperative solution in game theory. Taylor Rule: Functional Form • Taylor (1993) claims that policy rules that seem to work well focus on the price level and real output directly. • Rules that focus on exchange rate or the money supply do not deliver as good a performance, which is measure by the variances of output and price. • Taylor (1993) finds that placing a positive weight on both the price level and real output is the interest-rate rule is preferable in most of his samples. • He proposes a simple feedback rule where the weights placed on the output gap and the inflation are both 0.5. i = ! + 0.5 !y + 0.5 ! " 2( ) + 2 3 Taylor Rule: Functional Form where i is the federal funds rate, π is the rate of inflation over the previous four quarters, is the percentage deviation of real GDP from a target. That is, i = ! + 0.5 !y + 0.5 ! " 2( ) + 2 !y !y = 100 y ! y*( ) y * where y is real GDP, and y * is trend real GDP (equals 2.2 percent per year from 1984/01 to 1992/03) Taylor Rule: Functional Form • The Taylor rule has the feature that the federal funds rate rises if – Inflation increases above a target of 2 percent or if – Real GDP rises above trend GDP • Note that if both the inflation rate and the real GDP are on target, the federal funds rate would equal 4 percent, or 2 percent in real terms. • Using the data from 1987 to 1992, the Taylor rule replicates the actual path of the federal funds rate remarkably well. 4 Actual v. Fitted The Output Gap 5 Inflation The Taylor Property • Since the publication of Taylor (1993) paper, there have been a large number of scholarly papers published using the Taylor rule. • The most common functional form employed has the following form • In this form, the estimated values of β and γ are 1.5 and 0.5 respectively • Notice that β = 1.5 implies that the federal funds rate rises by 1.5 percent in respond to a one percent increase in the rate of inflation. • This means that the real interest rate rises by 0.5 percent, causing a contractionary impact on the economy i t = ! + "# t + $ !y t where i t is the interest rate at time t, ! t is the rate of inflation at time t, and !y t is the output gap at time t 6 The Taylor Rule with Interest Rate Smoothing • The original Taylor rule proposed by Taylor (1993) does not take into account the gradual adjustment behaviour of interest rate. • Most of the interest rates, administered by major central banks, change gradually by a small amount in each period — usually by 25 basis points. • By including a lagged value of the interest rate on the right-hand side of the Taylor rule equation, we also mitigate the auto-correlation problem of the functional form. • Clarida et al (1998)* estimates the “augmented” Taylor rule for the G3 and the E3 countries • In their specification of the Taylor rule, the interest rates respond to inflation expectation, reflecting the real-world conduct of monetary policy. Clarida, R., Gali, J., Gertler, M., 1998. Monetary Policy Rules in Practice: Some International Evidence. European Economic Review 42, 1033-1067 The Taylor Rule with Interest Rate Smoothing • In their paper, the modification has been made assuming that within each operating period the central bank has a target for the nominal short-term interest rate that is based on the state of the economy. i t * = i + ! E " t+n |#t[ ]$ " *( ) + % E y t |# t[ ]$ yt * y t * & '( ) *+ where i is the long-run equilibrium nominal rate, ! t+n is the rate of annualised inflation n period ahead, E is the mathematical expectation operator and " t is the information available to the central bank at the time it sets the interest rate. 7 The Taylor Rule with Interest Rate Smoothing • Assuming further that the actual rate partially adjusts to the target • The reasons behind the gradualist approach are – Data uncertainty – Uncertainty about the effect of parameters* – Fear of reputation loss – Fear of disrupting financial market – Attempt to minimise output fluctuation i t = 1! "( )i t * + "i t!1 + vt where v t ~ i.i.d. is an exogenous random shock to the interest rate and the parameter ! " 0,1[ ] captures the degree of interest rate smoothing. Brainard, W.C., 1967. Uncertainty and the Effectiveness of Policy. The American Economic Review. Paper and Proceedings of the Seventy-ninth Annual Meeting of the American Economic Association 57, 2, 411-425. The Taylor Rule with Interest Rate Smoothing • Define • We then rewrite the equation as • Combining the equation shown above with the partial adjustment mechanism yields ! = i " #$ * and !y = y t " y t * y * i t * = ! + "E # t+n |$ t[ ] + % E !yt |$t[ ] i t = 1! "( ) # + $E % t+n |&t[ ] + ' E !yt |&[ ]( ) + "it!1 + vt 8 The Taylor Rule with Interest Rate Smoothing • Finally, to obtain the estimable equation, eliminate the unobserved forecast components from the expression by rearranging the policy rule in terms of realised variables as follows. where the residual i t = 1! "( )# + 1! "( )$% t+n + 1! "( )& !yt + "it!1 + 't ! t = " 1" #( ) $ % t+n " E % t+n |&t[ ]( ) + ' !yt " E !yt |&t[ ]( ){ } + vt is the linear combination of the forecast errors of inflation and output and the exogenous disturbance v t , E is the mathematical expectation operator, and ! t is the information available to the central bank at the time it sets the interest rate. The parameters ", #, $ , and % are to be estimated. The Taylor Rule for the Federal Reserve • As for the Federal Reserve, previous research has suggested that the second- order partial adjustment model fits the us data significantly better than the first-order model used for Germany and Japan. • Since foreign variables are not very helpful for predicting US inflation and output, the exchange rates and foreign interest rates were excluded from the instrument list. i t = 1! " 1 ! " 2( ) # + $% t+n + & !yt( ) + "1it!1 + "2it!2 + 't 9 Data • Clarida et al (1998) use the augmented Taylor rule to estimate the policy reaction function for 6 countries: – G3: The US, Germany, and Japan – E3: England, France, and Italy • Sample periods for each country are as follows: – The US: 1979/10 - 1994/12 – Germany: 1979/04 - 1993/12 – Japan: 1979/04 - 1994/12 – England: 1979/06 - 1990/10 – France: 1983/05 - 1989/12 – Italy: 1981/06 - 1989/12 Data • Variables used in each economy are as follows: – The interest rates used in each estimation are the central bank’s instrument. • Federal Funds rate for the Federal Reserve • The overnight call rate for the Bank of Japan • The ‘day-to-day’ rate for Germany – The Consumer Price Index (CPI) is used as a proxy to measure inflation. – The Index of Industrial Production (IP) is used to measure output. The output gap for each eonomy is obtained by detrending the log of the IP using linear-quadratic trend. • The model is estimated using GMM with the instrument set including 1-6, 9, 12 lagged values of the output gap, the inflation rate, the log difference of a world commodity price index, the interest rate, and the log difference of the local currency/USD real exchange rate. 10 Results • Results show that the estimated coefficients β for the G3 countries satisfy the Taylor property, while those for the E3 don’t. • Evidence explains why the E3 economies experienced high inflation during a good part of the 80’s.