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Empirical Economics

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04-01-2016

Measuring the US NAIRU as a step function

Authors: Hiroshi Yamada, Gawon Yoon

Published in: Empirical Economics | Issue 4/2016

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Abstract

This paper reestimates the time-varying nonaccelerating inflation rate of unemployment (NAIRU) in the US. By assuming the NAIRU is a step function, not a smooth function, we show that a simple empirical model provides evidence supporting the consensus among macroeconomists that the US NAIRU was constant at about 6.0 % from the 1980s to the mid-1990s and then fell sharply below 6.0 % in the late 1990s.

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See, for example, Ball and Mankiw (2002) and references therein. See also the Congressional Budget Office’s (CBO) website, which provides historical estimates for the US NAIRU.

$U^{*}$ in the quotation denotes the NAIRU.

The HP filter is a low-pass filter that extracts the low-frequency component of data. This is to minimize

$$\begin{aligned} \sum _{t=1}^{T}\left( y_{t}-z_{t}\right) ^{2}+\psi \sum _{t=3}^{T}\left( \Delta ^{2} z_{t}\right) ^{2} \end{aligned}$$

with respect to $z_{1},z_{2},\ldots ,z_{T}$, where $\psi >0$ is a tuning parameter. Note that the HP filter is a penalized least squares method.

Specifically, letting $\hat{\varvec{\beta }}=[\hat{\mu }_{1},\hat{\mu }_{2},\ldots ,\hat{\mu }_{m+1},\hat{a}]'$ and $\varvec{w}_{t}'=[d_{1,t},d_{2,t},\ldots ,d_{m+1,t},-U_{t}]$, $ \hat{\varvec{\beta }}=(\sum _{t=1}^{T}\varvec{w}_{t}\varvec{w}_{t}')^{-1}\sum _{t=1}^{T}\varvec{w}_{t}(\Delta \Pi _{t}), $ where, for $i=1,2,\ldots ,m+1$, $d_{i,t}=1$ if $T_{i-1}\le t\le T_{i}-1$ and $d_{i,t}=0$ otherwise.

Harchaoui and Lévy-Leduc (2010) proposed detecting multiple change points so that the following objective function is minimized:

$$\begin{aligned} \sum _{t=1}^{T}(y_{t}-z_{t})^{2}+\lambda \sum _{t=2}^{T}|\Delta z_{t}| \end{aligned}$$

with respect to $z_{1},z_{2},\ldots ,z_{T}$, where $\lambda >0$ is a tuning parameter. Tibshirani and Taylor (2011) referred to this penalized regression as the 1d fused lasso and Kim et al. (2009) proposed a filter class that includes this penalized regression as a special case. This penalized regression is known as total variation denoising in signal processing. This filter is closely related to the exponential smoothing (ES) filter. The ES filter minimizes

$$\begin{aligned} \sum _{t=1}^{T}(y_{t}-z_{t})^{2}+\lambda \sum _{t=2}^{T} (\Delta z_{t})^2 \end{aligned}$$

with respect to $z_{1},z_{2},\ldots ,z_{T}$, where $\lambda >0$ is a tuning parameter. See King and Rebelo (1993).

Hobijn and Şahin (2013) note that “since the summer of 2009 the vacancy rate has trended upward while the unemployment rate has only come down slightly”.

The minimization given in (7) was accomplished by utilizing CVX, which is a MATLAB-based modeling system for convex optimization (Grant and Boyd 2013). Other than the CVX, we may use the genlasso package in R (Tibshirani and Taylor 2011).

Bai J, Perron P (1998) Estimating and testing linear models with multiple structural changes. Econometrica 66:47–78CrossRef

Bai J, Perron P (2003) Computation and analysis of multiple structural change models. J Appl Econ 18:1–22CrossRef

Ball L (2009) Hysteresis in unemployment. In: Fuhrer J, Kodrzycki YK, Little JS, Olivei GP (eds) Understanding inflation and the implications for monetary policy: a Phillips curve retrospective. MIT Press, Cambridge, pp 361–381CrossRef

Ball L, Mankiw G (2002) The NAIRU in theory and practice. J Econ Perspect 16:115–136CrossRef

Gordon RJ (1997) The time-varying NAIRU and its implications for economic policy. J Econ Perspect 11:11–32CrossRef

Grant M, Boyd S (2013) CVX: Matlab software for disciplined convex programming, version 2.0 beta. http://cvxr.com/cvx

Harchaoui Z, Lévy-Leduc C (2010) Multiple change-point estimation with a total variation penalty. J Am Stat Assoc 105:1480–1493CrossRef

Hobijn B, Şahin A (2013) Beveridge curve shifts across countries since the Great Recession. IMF Econ Rev 51:566–600CrossRef

Hodrick RJ, Prescott EC (1997) Postwar US business cycles: an empirical investigation. J Money Credit Bank 29:1–16CrossRef

Kim S, Koh K, Boyd S, Gorinevsky D (2009) $\ell _{1}$ trend filtering. SIAM Rev 51:339–360CrossRef

King RG, Rebelo ST (1993) Low frequency filtering and real business cycles. J Econ Dyn Control 17:207–231CrossRef

Staiger D, Stock JH, Watson M (1997a) How precise are estimates of the natural rate of unemployment? In: Romer C, Romer D (eds) Reducing inflation: motivation and strategy. University of Chicago Press, Chicago, pp 195–242

Staiger D, Stock JH, Watson M (1997b) The NAIRU, unemployment and monetary policy. J Econ Perspect 11:33–49CrossRef

Stiglitz J (1997) Reflections on the natural rate hypothesis. J Econ Perspect 11:3–10CrossRef

Tibshirani R (1996) Regression shrinkage and selection via lasso. J R Stat Soc B 58:267–288

Tibshirani RJ, Taylor J (2011) The solution path of the generalized lasso. Ann Stat 39:1335–1371CrossRef

Title: Measuring the US NAIRU as a step function
Authors: Hiroshi Yamada
Gawon Yoon
Publication date: 04-01-2016
Publisher: Springer Berlin Heidelberg
Published in: Empirical Economics / Issue 4/2016
Print ISSN: 0377-7332
Electronic ISSN: 1435-8921
DOI: https://doi.org/10.1007/s00181-015-1048-2

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