OECD Economics Department Working Papers

Working papers from the Economics Department of the OECD that cover the full range of the Department’s work including the economic situation, policy analysis and projections; fiscal policy, public expenditure and taxation; and structural issues including ageing, growth and productivity, migration, environment, human capital, housing, trade and investment, labour markets, regulatory reform, competition, health, and other issues.

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Comparing Semi-Structural Methods to Estimate Unobserved Variables

The HPMV and Kalman Filters Approaches

Economists often seek to estimate unobserved variables, representing “equilibrium” or “expected” values of economic variables, as benchmarks against which observed, realised values of these variables may be evaluated. Such comparisons are often used as economic policy indicators, for example the output gap, as measured by the ratio of actual to potential GDP, is commonly used as a measure of excess demand in assessing inflation pressures. To estimate these unobserved variables, a popular approach is the so-called semi-structural approach which includes: the Hodrick Prescott multivariate filter (developed by Laxton and Tetlow, 1992) and the Kalman filter (see, among others Harvey, 1992 and Cuthberson et al., 1992). This paper shows that the two approaches are closely linked, and specifically, it explains how to reproduce theHodrick Prescott multivariate filter using the Kalman filter. Being able to do so has at least two possible advantages. First, while the traditional HPMV filter ...


Keywords: unobserved component models, Kalman filter, standard errors, NAIRU
JEL: C22: Mathematical and Quantitative Methods / Single Equation Models; Single Variables / Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; E24: Macroeconomics and Monetary Economics / Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy / Employment; Unemployment; Wages; Intergenerational Income Distribution; Aggregate Human Capital; Aggregate Labor Productivity; C32: Mathematical and Quantitative Methods / Multiple or Simultaneous Equation Models; Multiple Variables / Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models; C13: Mathematical and Quantitative Methods / Econometric and Statistical Methods and Methodology: General / Estimation: General; E31: Macroeconomics and Monetary Economics / Prices, Business Fluctuations, and Cycles / Price Level; Inflation; Deflation
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