# Mark W. Watson's research while affiliated with Princeton University and other places

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## Publications (134)

We propose a method for constructing confidence intervals that account for many forms of spatial correlation. The interval has the familiar `estimator plus and minus a standard error times a critical value' form, but we propose new methods for constructing the standard error and the critical value. The standard error is constructed using population...

We investigate the flattening Phillips relation by making two departures from standard specifications. First, we measure slack using real activity variables that are bandpass filtered or year‐over‐year changes in activity (these are similar), instead of gaps. Second, we study the components of inflation instead of the standard aggregates. We find t...

We develop a Bayesian latent factor model of the joint long-run evolution of GDP per capita for 113 countries over the 118 years from 1900 to 2017. We find considerable heterogeneity in rates of convergence, including rates for some countries that are so slow that they might not converge (or diverge) in century-long samples, and a sparse correlatio...

This paper studies Structural Vector Autoregressions in which a structural shock of interest (e.g., an oil supply shock) is identified using an external instrument. The external instrument is taken to be correlated with the target shock (the instrument is relevant) and to be uncorrelated with other shocks of the model (the instrument is exogenous)....

The classic papers by Newey and West (1987) and Andrews (1991) spurred a large body of work on how to improve heteroscedasticity- and autocorrelation-robust (HAR) inference in time series regression. This literature finds that using a larger-than-usual truncation parameter to estimate the long-run variance, combined with Kiefer-Vogelsang (2002, 200...

External sources of as‐if randomness — that is, external instruments — can be used to identify the dynamic causal effects of macroeconomic shocks. One method is a one‐step instrumental variables regression (local projections – IV); a more efficient two‐step method involves a vector autoregression. We show that, under a restrictive instrument validi...

This review tells the story of the past 20 years of time series econometrics through ten pictures. These pictures illustrate six broad areas of progress in time series econometrics: estimation of dynamic causal effects; estimation of dynamic structural models with optimizing agents (specifically, dynamic stochastic equilibrium models); methods for...

U.S. output has expanded only slowly since the recession trough in 2009, even though the unemployment rate has essentially returned to a precrisis, normal level. We use a growth-accounting decomposition to explore explanations for the output shortfall, giving full treatment to cyclical effects that, given the depth of the recession, should have imp...

The US economy has performed better when the president of the United States is a Democrat rather than a Republican, almost regardless of how one measures performance. For many measures, including real GDP growth (our focus), the performance gap is large and significant. This paper asks why. The answer is not found in technical time series matters n...

This paper examines empirically whether the measurement of trend inflation can be improved by using disaggregated data on sectoral inflation to construct indexes akin to core inflation but with a time-varying distributed lags of weights, where the sectoral weight depends on the timevarying volatility and persistence of the sectoral inflation series...

This paper considers nonstandard hypothesis testing problems that involve a nuisance parameter. We establish an upper bound on the weighted average power of all valid tests, and develop a numerical algorithm that determines a feasible test with power close to the bound. The approach is illustrated in six applications: inference about a linear regre...

The rate of inflation fell far less over the period 2007-2013 than in the period 1979-1985 despite similar large increases in the unemployment rate. This paper asks why. Possible explanations include a change in the persistence of inflation, changes in NAIRU, and other shocks. A change in the persistence of inflation, with inflation more anchored i...

This paper considers the estimation of approximate dynamic factor models when there is temporal instability in the factor loadings. We characterize the type and magnitude of instabilities under which the principal components estimator of the factors is consistent and find that these instabilities can be larger than earlier theoretical calculations...

Long-run forecasts of economic variables play an important role in policy, planning, and portfolio decisions. We consider
forecasts of the long-horizon average of a scalar variable, typically the growth rate of an economic variable. The main contribution
is the construction of prediction sets with asymptotic coverage over a wide range of data gener...

We study two decompositions of inflation, , motivated by a New Keynesian Pricing Equation. The first uses four components: lagged , expected future , real unit labor cost ( ), and a residual. The second uses two components: fundamental inflation (discounted expected future ) and a residual. We find large low-frequency differences between actual and...

This paper provides a simple shrinkage representation that describes the operational characteristics of various forecasting methods designed for a large number of orthogonal predictors (such as principal components). These methods include pretest methods, Bayesian model averaging, empirical Bayes, and bagging. We compare empirically forecasts from...

This paper examines the macroeconomic dynamics of the 2007-09 recession in the United States and the subsequent slow recovery. Using a dynamic factor model with 200 variables, we reach three main conclusions. First, although many of the events of the 2007-2009 collapse were unprecedented, their net effect was to produce macro shocks that were large...

This paper examines the macroeconomic dynamics of the 2007–09 recession in the United States and the subsequent slow recovery. Using a dynamic factor model with 200 variables, we reach three main conclusions. First, although many of the events of the 2007–09 collapse were unprecedented, their net effect was to produce macro shocks that were larger...

We examine whether the U.S. rate of price inflation has become harder to forecast and, to the extent that it has, what changes in the inflation process have made it so. The main finding is that the univariate inflation process is well described by an unobserved component trend-cycle model with stochastic volatility or, equivalently, an integrated m...

Dating business cycles entails ascertaining economy-wide turning points. Broadly speaking, there are two approaches in the literature. The first approach, which dates to Burns and Mitchell (1946), is to identify turning points individually in a large number of series, then to look for a common date that could be called an aggregate turning point. T...

In the United States, the rate of price inflation falls in recessions. Turning this observation into a useful inflation forecasting equation is difficult because of multiple sources of time variation in the inflation process, including changes in Fed policy and credibility. We propose a tightly parameterized model in which the deviation of inflatio...

This paper uses a dynamic factor model for the quarterly changes in consumption goods' prices in the United States since 1959 to separate them into three independent components: idiosyncratic relative-price changes, a low-dimensional index of aggregate relative-price changes, and an index of equiproportional changes in all inflation rates that we l...

This paper explores the link between financial conditions and economic activity. We first review existing measures, including both single indicators and composite financial conditions indexes (FCIs). We then build a new FCI that features three key innovations. First, besides interest rates and asset prices, it includes a broad range of quantitative...

Robert Engle received the Nobel Prize for Economics in 2003 for his work in time series econometrics. This book contains 16 original research contributions by some of the leading academic researchers in the fields of time series econometrics, forecasting, volatility modelling, financial econometrics and urban economics, along with historical perspe...

Cointegration means that two or more time series share common stochastic trends. Thus, while each series exhibits smooth or trending behaviour, a linear combination of the series exhibits no trend. For example, short-term and long-term interest rates are highly serially correlated (so they are smooth and in this sense exhibit a stochastic trend), b...

Standard inference in cointegrating models is fragile because it relies on an assumption of an I(1) model for the common stochastic trends, which may not accurately describe the data's persistence. This paper considers low-frequency tests about cointegrating vectors under a range of restrictions on the common stochastic trends. We quantify how much...

Using factor methods, we decompose industrial production (IP) into components arising from aggregate and sector-specific shocks. An approximate factor model finds that nearly all of IP variability is associated with common factors. We then use a multisector growth model to adjust for the effects of input-output linkages in the factor analysis. Thus...

We develop a framework to assess how successfully standard time series models explain low-frequency variability of a data series. The low-frequency information is extracted by computing a finite number of weighted averages of the original data, where the weights are low-frequency trigonometric series. The properties of these weighted averages are t...

The conventional heteroskedasticity-robust (HR) variance matrix estimator for cross-sectional regression (with or without a degrees-of-freedom adjustment), applied to the fixed-effects estimator for panel data with serially uncorrelated errors, is inconsistent if the number of time periods T is fixed (and greater than 2) as the number of entities n...

This paper surveys the literature since 1993 on pseudo out-of-sample evaluation of inflation forecasts in the United States and conducts an extensive empirical analysis that recapitulates and clarifies this literature using a consistent data set and methodology. The literature review and empirical results are gloomy and indicate that Phillips curve...

Industrial production is both highly variable and correlated across sectors. This correlation arises in part from common or aggregate shocks and from sector-specific shocks that propagate across sectors via input-output linkages or other complementarities in production. Using factor analytic methods, we ask i) how much of the variability in sectora...

This paper uses a dynamic factor model for the quarterly changes in consumption goods’ prices to separate them into three components: idiosyncratic relative-price changes, aggregate relative-price changes, and changes in the unit of account. The model identifies a measure of “pure” inflation: the common component in goods’ inflation rates that has...

This paper presents and describes a newly available data set on monthly building permits for U.S. states from 1969-2007. These data are used to estimate regions of common housing construction activity. Building permits exhibit substantial comovement across states, and these comovements are modeled as being associated with a national factor, a regio...

This paper estimates a common component in many price series that has an equiproportional effect on all prices. Changes in this component can be interpreted as changes in the value of the numeraire since, by definition, they leave all relative prices unchanged. The first aim of the paper is to measure these changes. The paper provides a framework f...

The dynamics of a linear (or linearized) dynamic stochastic economic model can be expressed in terms of matrices (A, B, C, D) that define a state space system for a vector of observables. An associated state space system (A,ˆB,C,ˆD) determines a vector autoregression for those same observables. We present a simple condition for checking when these...

We examine whether the U.S. rate of price inflation has become harder to forecast and, to the extent that it has, what changes in the inflation process have made it so. The main finding is that the univariate inflation process is well described by an unobserved component trend-cycle model with stochastic volatility or, equivalently, an integrated m...

Bai and Ng proposed a consistent estimator for the number of static factors in a large N and T approximate factor model. This article shows how the Bai-Ng estimator can be modified to consistently estimate the number of dynamic factors in a restricted dynamic factor model. The modification is straightforward: The standard Bai-Ng estimator is applie...

The paper examines consolidation episodes in the EU since 1970 with a view to shedding light on the factors that determine the success or failure of fiscal adjustment. Compared to the existing literature on successful fiscal consolidations we add a number of new dimensions. Two deserve particular attention. Firstly, we explore a broader set of pote...

Historically, time series forecasts of economic variables have used only a handful of predictor variables, while forecasts based on a large number of predictors have been the province of judgmental forecasts and large structural econometric models. The past decade, however, has seen considerable progress in the development of time series forecastin...

“Iterated” multiperiod-ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas “direct” forecasts are made using a horizon-specific estimated model, where the dependent variable is the multiperiod ahead value being forecasted. Which approach is better is an empirical matter: i...

We analyze the effects of neutral and investment-specific technology shocks on hours and output. Long cycles in hours are removed in a variety of ways. Hours robustly fall in response to neutral shocks and robustly increase in response to investment-specific shocks. The percentage of the variance of hours (output) explained by neutral shocks is sma...

This paper considers VAR models incorporating many time series that interact through a few dynamic factors. Several econometric issues are addressed including estimation of the number of dynamic factors and tests for the factor restrictions imposed on the VAR. Structural VAR identification based on timing restrictions, long run restrictions, and re...

This paper provides a simple shrinkage representation that describes the operational characteristics of various forecasting methods that are applicable when there are a large number of orthogonal predictors (such as principal components). These methods include pretest methods, Bayesian model averaging, empirical Bayes, and bagging. We then compare...

‘Iterated’ multiperiod ahead time series forecasts are made using a one-period ahead model, iterated forward for the desired number of periods, whereas ‘direct’ forecasts are made using a horizon-specific estimated model, where the dependent variable is the multi-period ahead value being forecasted. Which approach is better is an empirical matter:...

This paper uses forecast combination methods to forecast output growth in a seven-country quarterly economic data set covering 1959-1999, with up to 73 predictors per country. Although the forecasts based on individual predictors are unstable over time and across countries, and on average perform worse than an autoregressive benchmark, the combinat...

REPLY Oil Shocks and Aggregate Macroeconomic Behavior: The Role of Monetary Policy A Reply by Ben S. Bernanke, Mark Gertler, and Mark W. Watson JEL codes: E32, E50 Keywords: oil shocks, monetary policy. Hamilton and Herrera (HH) have provided an interesting comment on our 1997 paper (Bernanke, Gertler, and Watson 1997 [BGW]). We take the opportunit...

The volatility of economic activity in most G7 economies has moderated over the past forty years. Also, despite large increases in trade and openness, G7 business cycles have not become more synchronized. After documenting these twin facts, we interpret G7 output data using a structural VAR that separately identifies common international shocks, th...

Are asset prices useful predictors of inflation and real output growth? After reviewing the large literature on this topic, we undertake an empirical analysis of quarterly data for seven OECD countries spanning 1959-99. The literature review and the empirical analysis yield the same conclusions. Some asset prices predict inflation or output growth...

This paper compares several time series methods for short-run forecasting of Euro-wide inflation and real activity using data from 1982 to 1997. Forecasts are constructed from univariate autoregressions, vector autoregressions, single equation models that include Euro-wide and US aggregates, and large-model methods in which forecasts are based on e...

This article considers forecasting a single time series when there are many predictors (N) and time series observations (T). When the data follow an approximate factor model, the predictors can be summarized by a small number of indexes, which we estimate using principal components. Feasible forecasts are shown to be asymptotically efficient in the...

From 1960-1983, the standard deviation of annual growth rates in real GDP in the United States was 2.7%. From 1984-2001, the corresponding standard deviation was 1.6%. This paper investigates this large drop in the cyclical volatility OF real economic.activity. The paper has two objectives. The first is to provide a comprehensive characterization o...

This article studies forecasting a macroeconomic time series variable using a large number of predictors. The predictors are summarized using a small number of indexes constructed by principal component analysis. An approximate dynamic factor model serves as the statistical framework for the estimation of the indexes and construction of the forecas...

This paper critically reviews the use of vector autoregressions (VARs) for four tasks: data description, forecasting, structural inference, and policy analysis. The paper begins with a review of VAR analysis, highlighting the differences between reduced-form VARs, recursive VARs and structural VARs. A three variable VAR that includes the unemployme...

Using quarterly macro data and annual state panel data, we examine various explanations of the low rate of price inflation, strong real wage growth, and low rate of unemployment in the U.S. economy during the late 1990s. Many of these explanations imply shifts in the coefficients of price and wage Phillips curves. We find, however, that once one ac...

Using quarterly macro data and annual state panel data, we examine various explanations of the low rate of price inflation, strong real wage growth, and low rate of unemployment in the U.S. economy during the late 1990s. Many of these explanations imply shifts in the coefficients of price and wage Phillips curves. We find, however, that once one ac...

We consider both frequentist and empirical Bayes forecasts of a single time series using a linear model with T observations and K orthonormal predictors. The frequentist formulation considers estimators that are equivariant under permutations (reorderings) of the regressors. The empirical Bayes formulation (both parametric and nonparametric) treats...

This paper first reviews the large literature on the prediction of real economic activity and inflation using asset prices. We then undertake our own assessment of the practical value of the information in asset prices for short- to medium-term economic forecasting using data from seven developed economies,. This analysis of the literature and the...

This chapter examines the empirical relationship in the postwar United States between the aggregate business cycle and various aspects of the macroeconomy, such as production, interest rates, prices, productivity, sectoral employment, investment, income, and consumption. This is done by examining the strength of the relationship between the aggrega...

A panel of ex-ante forecasts of a single time series is modeled as a dynamic factor model, where the conditional expectation is the single unobserved factor. When applied to out-of-sample forecasting, this leads to combination forecasts that are based on methods other than OLS. These methods perform well in a Monte Carlo experiment. These methods a...

The variability of changes in long-term interest rates increased dramatically in the 1980s and 1990s. Can such increased variability be accounted for by changes in the behavior of short-term interest rates? While changes in short-term interest rates have become less variable, they have become more persistent. This latter development can explain the...

This paper investigates forecasts of U.S. inflation at the 12-month horizon. The starting point is the conventional unemployment rate Phillips curve, which is examined in a simulated out of sample forecasting framework. Inflation forecasts produced by the Phillips curve generally have been more accurate than forecasts based on other macroeconomic v...

This paper investigates forecasts of US in#ation at the 12-month horizon. The starting point is the conventional unemployment rate Phillips curve, which is examined in a simulated out-of-sample forecasting framework. In#ation forecasts produced by the Phillips curve generally have been more accurate than forecasts based on other macroeco-nomic vari...

This paper considers forecasting a single time series using more predictors than there are time series observations. The approach is to construct a relatively few indexes, akin to diffusion indexes, which are weighted averages of the predictors, using an approximate dynamic factor model. Estimation is discussed for balanced and unbalanced panels. T...

A forecasting comparison is undertaken in which 49 univariate forecasting methods, plus various forecast pooling procedures, are used to forecast 215 U.S. monthly macroeconomic time series at three forecasting horizons over the period 1959 - 1996. All forecasts simulate real time implementation, that is, they are fully recursive. The forecasting me...

This paper examines the empirical relationship in the postwar United States between the aggregate business cycle and various aspects of the macroeconomy, such as production, interest rates, prices, productivity, sectoral employment, investment, income, and consumption. This is done by examining the strength of the relationship between the aggregate...

Many linear macroeconomic models can be cast in the first-order form, AE t y t+1 = By t +CE t x t ; if the matrix A is permitted to be singular. For this singular linear dierence system under rational expectations, we show there is a unique stable solution under two requirements: (i) the determinental polynomial jAz Bj is not zero for some value of...

A first-order linear difference system under rational expectations is, AEy t+1 jI t = By t +C(F)Ex t jI t ; where y t is a vector of endogenous variables; x t is a vector of exogenous variables; Ey t+1 jI t is the expectation of y t+1 given date t information; and C(F)Ex t jI t = C 0 x t + C 1 Ex t+1 jI t + ::: + C n Ex t+n jI t . Many economic mod...

This article considers inference about the variance of coefficients in time-varying parameter models with stationary regressors. The Gaussian maximum likelihood estimator (MLE) has a large point mass at 0. We thus develop asymptotically median unbiased estimators and asymptotically valid confidence intervals by inverting quantile functions of regre...

This paper examines the precision of conventional estimates of the NAIRU and the role of the NAIRU and unemployment in forecasting inflation. The authors find that, although there is a clear empirical Phillips relation, the NAIRU is imprecisely estimated, forecasts of inflation are insensitive to the NAIRU, and there are other leading indicators of...

Macroeconomic shocks such as wil price increases induce a systematic (endogenous) response of monetary policy. We develop a VAR-based technique for decomposing the total economic effects of a given exogenous shock into the portion attributable directly to the shock and the part arising from the policy response to the shock.

Propositions about long run neutrality are at the heart of most macroeconomic models. Yet, since the 1970's when Lucas and Sargent presented powerful critiques of traditional neutrality tests, empirical researchers have made little progress on testing these propositions. In this paper we show that. in spite of the Lucas-Sargent critique. long run n...

This paper studies the problems of estimation and inference in the linear trend model y<sub>t</sub> = α + βt + u<sub>t</sub>, where u<sub>t</sub> follows an autoregressive process with largest root ρ and β is the parameter of interest. We contrast asymptotic results for the cases |ρ| < 1 and ρ = 1 and argue that the most useful asymptotic approxima...

This paper investigates the precision of conventional and unconventional estimates of the natural rate of unemployment (the 'NAIRU'). The main finding is that the NAIRU is imprecisely estimated: a typical 95% confidence interval for the NAIRU in 1990 is 5.1% to 7.7%. This imprecision obtains whether the natural rate is modeled as a constant, as a s...

An experiment is performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability. Formal tests for instability and out-of-sample forecasts from sixteen different models are computed using a samp...

Many economic models imply that ratios, simple differences, or “spreads” of variables are I(0). In these models, cointegrating vectors are composed of 1's, 0's, and —1's and contain no unknown parameters. In this paper, we develop tests for cointegration that can be applied when some of the cointegrating vectors are prespecified under the null or u...

The inability of forecasters to predict accurately the 1990-1991 recession emphasizes the need for better ways for charting the course of the economy. In this volume, leading economists examine forecasting techniques developed over the past ten years, compare their performance to traditional econometric models, and discuss new methods for forecasti...

The asymptotic distributions of cointegration tests are approximated using the Gamma distribution. The tests considered are for the I(1), the conditional I(1), as well as the I(2) model. Formulae for the parameters of the Gamma distributions are derived from response surfaces. The resulting approximation is flexible, easy to implement and more accu...

This paper surveys three topics: vector autoregressive (VAR) models with integrated regressors, cointegration, and structural VAR modeling. The paper begins by developing methods to study potential "unit root" problems in multivariate models, and then presents a simple set of rules designed to help applied researchers conduct inference in VARs. A l...

Average postwar expansions are twice as long as prewar expansions and contractions are one-half as long. This paper investigates three possible explanations. The first explanation is that shocks to the economy have been smaller in the postwar period. The second explanation is that the composition of output has shifted from very cyclical sectors to...

In 1958, A.W. Phillips discovered a strong negative correlation between inflation and unemployment in United Kingdom data. Continuing controversy surrounds the long-run trade-off suggested by a curve he drew through these observations.We conduct a wide-ranging investigation of the post-war U.S. Phillips correlations and Phillips curve. Many economi...

The primary aim of the paper is to place current methodological discussions in macroeconometric modeling contrasting the ‘theory first’ versus the ‘data first’ perspectives in the context of a broader methodological framework with a view to constructively appraise them. In particular, the paper focuses on Colander’s argument in his paper “Economist...

Efficient estimators of cointegrating vectors are presented for systems involving deterministic components and variables of differing, higher orders of integration. The estimators are computed using GLS or OLS, and Wald statistics constructed from these estimators have asymptotic x [superscript] 2 distributions. These and previously proposed estima...

This paper suggests a new procedure for evaluating the fit of a dynamic structural economic model. The procedure begins by augmenting the variables in the model with just enough stochastic error so that the model can exactly match the second moments of the actual data. Measures of fit for the model can then be constructed on the basis of the size o...

This paper examines the forecasting performance of various leading economic indicators and composite indexes since 1988. in particular during the onset of the 1990 recession. The primary focus is on an experimental recession index (tile "XRI"). a composite index which provides probabilistic forecasts of whether the U.S. economy will be in a recessi...

## Citations

... For instance, Cogley et al. (2010) rely on a multivariate time series models to analyze the money-inflation nexus. Similar econometric models have been employed to forecast inflation, treating the underlying inflation trend as an unobserved component (Stock and Watson, 1999, Chan et al., 2013, Stock and Watson, 2020; to decompose output into a long-term trend (potential or natural output) and the output gap (Planas et al., 2008, Jarociński andLenza, 2018); and as mentioned before, to infer the unobserved natural real interest rate (e.g., Del Negro et al., 2017). The paper is structured as follows. ...

... Population-weighting (rather than area-weighting) is more likely to capture the effects of climate onto socio-economic activity (see Tol, 2017). To project climate impacts to the end of the century, we construct a dataset of country-level changes in temperatures based on CMIP5 climate models (Taylor et al., 2012) and use long-term country-level forecasts of GDP per capita for our baseline (Müller et al., 2019). In the appendix, we also consider the impact of precipitation (see Figure C.10). ...

... These incorporate different identification strategies based either on timing (Kilian, 2008a(Kilian, ,b, 2009 or on sign restrictions Murphy, 2012, 2014;Lippi and Nobili, 2012;Baumeister and Peersman, 2013;Baumeister and Hamilton, 2019). Montiel Olea et al. (2020) and Känzig (2021) adopt an alternative approach that uses either proxy or external instrumental variable procedures within the SVAR model (proxy SVAR). These empirical studies (an exhaustive review on this literature is in Kilian and Zhou (2020b)) show that oil supply and demand shocks are hard to identify in practice. ...

... We should note that low (or even negative) TFP growth in services is not specific to Turkey. Other studies find similar findings for OECD countries and USA (see among others Kets and Lejour, 2003;Foerster et al., 2019). ...

... Newey-West standard errors are usually the go-to choice. Alternative procedures have been suggested (Müller, 2014), but in practice the choice is not trivial even though some guiding principles exist (Lazarus et al., 2018). ...

... As outlined by Stock and Watson (2018), the identification problem in the SVAR model involves determining how to shift from the moving-average representation (in terms of innovations) to the impulse response function (IRF), with respect to a unit increase in the structural shock of interest, which, in this study, occurs within US monetary policy. Previously, classical strategy imposed certain economic restrictions, such as short-term, long-term and sign restrictions, which imply the short-term and long-term or positive and negative relationship between economic variables and structural shocks. ...

... Another factor is the discrepancy in potential to actual labour force participation (and hence a lower amount of actual relative to potential hours worked), and partially also a lower realization of potential total factor productivity (cf. Shackleton, 2018, Figures 2, 5, 7;Fernald et al., 2017). Such an outcome is an inherent risk in the CBO's approach, because its measure of potential output only focusses on the supply-side components of economic growth, where the estimates of the (partially unobservable) potential input factors like services from fixed capital and labour (including the NAIRU) and, especially, estimates of total factor productivity are heavily prone to measurement errors (Arnold, 2009, p. 277). ...