Estimating the output gap in a changing economy.

• Author: Kara, Hakan

Univariate filters used in output gap estimation are subject to criticism as being purely statistical and having no economic content. The information content of the output gap measures estimated by standard multivariate filtering techniques, on the other hand, can be distorted because of the possibly unrealistic restriction that system parameters stay constant over time. In this study, we seek to address these shortcomings by proposing an output gap estimation method that takes into account changing economic relations. We employ a nonlinear time series framework along with the extended Kalman filter, in which economic content is used by inflation and output gap dynamics and the parameters are allowed to be time varying. We use the Turkish economy as a laboratory to show that our method provides useful results, both in terms of the properties of output gap estimates and for the assessment of change in macroeconomic dynamics.

JEL Classification: C32, C63, E30

1. Introduction

   The emergence of price stability as the overriding goal of monetary policy in recent decades has led central banks to use all available information in the economy to foresee the future course of price dynamics. One important variable that is closely monitored by the central banks in this context has been the output gap--output in excess of its "neutral" or "potential" level. A positive output gap, for example, is often perceived as a signal of "excess demand," which might require tightening to prevent the economy from overheating.

   Output gap, by definition, cannot be directly observed and thus has to be estimated. However, the information content of conventional output gap measures might be limited. (1) Not surprisingly, studies on developing proper alternative techniques have intensified in recent years, especially after the shortcomings of the Hodrick--Prescott (HP) filter--the most commonly used methodology--were realized. (2) In this context, multivariate filtering techniques utilizing information from macroeconomic relationships have been proposed as alternatives. (3)

   One appropriate estimation technique in such a setting is the Kalman filter, which is a recursive algorithm for optimally forecasting the unobserved component given the observed variables and the imposed economic structure. However, existent multivariate techniques often impose strong restrictions in defining the relationships between key macroeconomic variables. For example, in these settings, the relationships that govern the dynamics of the economy stay intact over the sample period. This restriction might not hold for a constantly changing economy--at least for economies experiencing massive structural changes, as emerging markets do. Adopting different monetary policy regimes and experiencing frequent fiscal and financial restructuring periods affect the behavior of economic agents over time, changing the reduced-form relations between macroeconomic variables in these countries. (4) Therefore, although standard multivariate filters address and hence improve upon--the criticism regarding both the HP filter and other univariate statistical procedures, there may be room for improvement if one can relax the typical restriction that system parameters stay constant over time. This is the main motivation of our paper.

   In this study, we present a multivariate unobserved components model to estimate both the output gap and the time-varying system parameters. We use the Turkish economy as a laboratory to demonstrate this technique. As mentioned above, the estimation of output gap by this method allows us to address changing relationships in the economy, leaving room for assessing the effect of different policy regimes on the relationship between key macroeconomic variables such as inflation, interest rates, exchange rates, and output gap.

   When the state variables (including output gap, potential output, or both) and the system parameters are to be estimated simultaneously in a time-varying fashion, the model takes a nonlinear characteristic, and the standard Kalman filter (SKF) needs to be modified. In this case, the extended Kalman filter (EKF) emerges as an estimation procedure. Such a methodology has been previously used in Ozbek and Ozlale (2005) in a simple parametric form of output. However, their study does not allow the exogenous variables to be incorporated into both the state and the measurement equation. Nor do they present a structural background, which would be necessary to interpret the time-varying effects of the relevant macroeconomic variables on the estimated output gap.

   We believe that the findings in this paper will serve as a reference in two distinct ways. The major departure of this study from the existing literature of unobserved component methodology of output gap estimates is the joint estimation of unobserved variables and time-varying parameters in a simultaneous system. As a by-product, this methodology permits us to interpret the resulting output gap series and its time-varying relationship with other variables, allowing us to conduct an ex post evaluation of the changing economic structure across different policy regimes.

   The rest of the paper is organized as follows. In the next section, we present and discuss the model along with a state space representation. The estimation methodology is also introduced in this section. In section 3, we apply the methodology to Turkish data and present both the estimated output gap series and the estimated time varying parameters, interpreting them in view of developments in the Turkish economy in the last decade. A model sensitivity analysis is performed in section 4, where we analyze whether the results remain robust to different specifications about inflation and the output gap dynamics. This section also contrasts the estimated gap series with the ones obtained from the HP filter and the standard Kalman filter procedure. Finally, section 5 concludes the paper.

2. The Model

   The general form of the model, in which the time-varying parameters and the gap series are estimated, is shown in Equations 1-5.

   Inflation Output Gap Dynamics

   [[pi].sub.t] = [[alpha].sub.1,t], [[pi].sub.t-1] + [[alpha].sub.2,t] [[pi].sub.t-2] + [[alpha].sub.3,t] [gap.sub.t-1] + [[alpha].sub.4,t] [reer.sub.t] + [v.sub.t] (1)

   Actual Output Decomposition

   [y.sub.t] = [y.sup.*.sub.t] + [gap.sub.t] (2)

   Potential Output Equation

   [y.sup.*.sub.t] [y.sup.*.sub.t-1] + [[mu].sub.t-1] + [[eta].sub.t] (3)

   Potential Output Growth Rate Equation

   [[mu].sub.t] = (1 - [[rho].sub.t]) [[mu].sub.0] + [[rho].sub.t] [[mu].sub.t-1] + [[epsilon].sub.t] (4)

   Output Gap Dynamics

   [gap.sub.t] = [[gamma].sub.1,t] [gap.sub.t-1] + [[gamma].sub.2,t]] [r.sub.t] + [[gamma].sub.3,t] [DI.sub.t] + [[gamma].sub.4,t] [reer.sub.t] + [[zeta].sub.t]

   where [[pi].sub.t], is the inflation rate defined as the logarithmic difference of the quarterly seasonally adjusted consumer price index (CPI), [gap.sub.t], is the unobserved output gap, [reer.sub.1], is the logarithmic difference of the real effective exchange rate (positive means appreciation), [y.sub.t] is the logarithmic seasonally adjusted real gross domestic product, [y.sup.*.sub.t] is the unobserved potential output, [[mu].sub.t] is the potential output growth rate, [r.sub.t] is the ex post real interest rate on the basis of government securities, and [DI.sub.t] is the demand index, which is constructed from the Business Tendency Survey of the Central Bank of the Republic of Turkey. The derivation of the demand index along with other data descriptions is presented in Appendix A. Finally, [v.sub.t], [[eta].sub.t], [[epsilon].sub.t] and [[zeta].sub.t] represent shocks to the system, which are assumed to be independent and identically distributed with zero mean and constant variances.

   It is important to point out that the parameters of the system are time varying. Therefore, one has to make a time series specification for the evolution of these parameters. Following the fairly standard procedure in the literature, we have assumed that each time-varying parameter follows a random walk. Thus, the system includes nine more equations, in which each time-varying parameter follows a random walk process.

   Equation 1 is a fairly standard reduced-form Phillips curve specification including lagged inflation terms, lagged output gap, and the change in the real effective exchange rate. Accordingly, persistence in inflation is reflected in inertial terms up to two lags. Output gap is assumed to affect inflation with a lag since it takes time for the pressure on production costs to be revealed and for prices to be adjusted in response to a demand shock. Changes in the real effective exchange rate capture the effects of the exchange rate dynamics on inflation through both the "cost of production channel" and the prices of imported final goods. (5)

   Equation 2 is the identity defining output as the sum of the potential output (trend component) and the output gap (transitory component). Equation 3 defines potential output as a random walk with a drift model, implying that shocks to trend output are permanent. Moreover, the drift term, trend growth, is allowed to vary over time, and the persistence can be shaped with respect to different values of [rho]. Needless to say, trend growth may change over time along with productivity, labor force, or technology developments. Moreover, in a recent study, Aguiar and Gopinath (2004) state that emerging markets are subject to extremely volatile shocks to the stochastic trend and provide evidence that emerging market business cycles are driven by shocks to the trend growth rate, which could result from extreme and relatively frequent changes in economic policies. Taking these factors into account, potential growth rate is modeled as time-variant. In this respect, Equation 4 defines potential growth as a first-order autoregressive process with a long-run average growth rate of and the autoregressive...