E-book Review: Measuring Economic Slack

Transcription

1 BIS Working Papers No 451 Measuring Economic Slack: A Forecas-Based Approach wih Applicaions o Economies in Asia and he Pacific by James Morley Moneary and Economic Deparmen June 2014 JEL classificaion: E32; E37 Keywords: oupu gap; model averaging; business cycle asymmery; convex Phillips Curve

2 BIS Working Papers are wrien by members of he Moneary and Economic Deparmen of he Bank for Inernaional Selemens, and from ime o ime by oher economiss, and are published by he Bank. The papers are on subjecs of opical ineres and are echnical in characer. The views expressed in hem are hose of heir auhors and no necessarily he views of he BIS. This publicaion is available on he BIS websie ( Bank for Inernaional Selemens All righs reserved. Brief excerps may be reproduced or ranslaed provided he source is saed. ISSN (prin) ISSN (online) ISBN (prin) ISBN (online)

3 Measuring Economic Slack: A Forecas-Based Approach wih Applicaions o Economies in Asia and he Pacific James Morley * Universiy of New Souh Wales Absrac The presence of economic slack direcly implies ha an economy can grow quickly wihou any necessary offseing slow growh or rerenchmen in he fuure. Based on his link beween economic slack and fuure economic growh, I argue for a forecasbased esimae of he oupu gap as a measure of economic slack. This approach has he advanage of being robus o differen assumpions abou he underlying srucure of he economy and allows for empirical analysis of a Phillips Curve relaionship beween he oupu gap and inflaion. I apply his approach o invesigae economic slack and is relaionship wih inflaion for seleced economies in Asia and he Pacific, aking ino accoun srucural breaks in long-run growh and uncerainy abou he appropriae forecasing model. The esimaed oupu gap is highly asymmeric for mos he economies and implies a convex Phillips Curve in many of he cases. JEL Codes: E32; E37 Keywords: oupu gap; model averaging; business cycle asymmery; convex Phillips Curve * james.morley@unsw.edu.au. I hank Jun Il Kim, Aaron Mehrora, Tim Robinson, and James Yeman for insighful discussions and feedback. I also hank conference and seminar paricipans a he People s Bank of China-BIS Conference on Globalisaion and Inflaion Dynamics in Asia and he Pacific, he Coninuing Educaion in Macroeconomerics workshop a he Universiy of New Souh Wales, he Sydney Macroeconomics Reading Group, and he Universiy of Technology Sydney for helpful quesions and commens. Lillie Lam provided excellen assisance wih he daa. The usual disclaimers apply.

4 1. Inroducion Orphanides (2002) argues ha high inflaion in he 1970s was due o mismeasuremen of economic slack, no a failure of moneary policy o follow bes pracices. He uses daa available a he ime o show ha US moneary policy responses o inflaion and economic slack were sysemaic, forward-looking, and much he same as hey have been in laer decades when inflaion has been low and sable. Wha we now hink of as he policy misakes of he 1970s were only revealed wih he hindsigh of daa revisions, especially in erms of measures of economic slack. A worrisome implicaion of Orphanides s (2002) argumen is ha modern bes pracices for moneary policy provide no assurance ha he misakes of he 1970s will no be repeaed, a leas no as long as measures of economic slack are subjec o considerable uncerainy. Unforunaely, even ignoring he real-ime daa issues ha are he focus of Orphanides (2002), bu beyond he scope of his paper, accurae measuremen economic slack remains a significan challenge for a variey of reasons. Firs and foremos, here is no consensus abou he policy-relevan measure of economic slack. Even seling on he oupu gap (i.e., he difference beween acual and poenial real GDP for an economy), here remains a quesion of how o define poenial. Based on he idea ha economic slack implies a possibiliy for an economy o grow quickly wihou any necessary offseing slow growh or rerenchmen in he fuure, I argue for a forecas-based esimae of he oupu gap as he appropriae measure of economic slack. Specifically, if he opimal forecas of fuure oupu growh is above/below average, hen oupu is esimaed o be below/above poenial. This approach implicily defines poenial as he sochasic rend of oupu and has is origins in he influenial sudy by Beveridge and Nelson (1981, BN hereafer), wih his paricular inerpreaion of he BN decomposiion discussed in Morley (2011). 1 1 The forecas-based approach is relaed o, bu differen han he producion funcion approach employed by he Congressional Budge Office and oher agencies for which he oupu gap capures he deviaion of economic aciviy from a level of poenial defined by full-employmen of resources in a posulaed aggregae producion funcion. Wih his producion funcion approach, underuilized resources imply he possibiliy for he economy o grow quickly wihou necessary offseing slow growh in he fuure. So he forecas-based definiion of poenial aken in his paper is sill relevan. Bu he producion funcion approach requires a good measure of capial, as well as full-employmen levels of resources, while he forecas-based approach only requires a measure of overall economic 1

5 Second, even given a forecas-based approach o esimaing he oupu gap, here remains a quesion of how o consruc he opimal forecas of fuure oupu growh. BN consider low-order ARMA models, which sugges small oupu gaps, ofen wih counerinuiive sign (e.g., he esimaed gap is ofen posiive during recessions). Moivaed by he forecasing lieraure and recen sudies on esimaing he oupu gap by Garra, Michell, and Vahey (2011) and Morley and Piger (2012), I consider model-averaged forecass insead of relying on one paricular ime series model or class of models. Imporanly, I follow Morley and Piger (2012) by including nonlinear ime series models in he se of models under consideraion. Noably, his approach does no necessarily resul in oupu gap esimaes of counerinuiive sign as long as he model-averaged forecass imply negaive serial correlaion in economic growh a longer horizons. Third, a forecas-based oupu gap may no correspond o he heory-based measure implied by a srucural model of he economy e.g., he deviaion from a flexibleprice equilibrium in a New Keynesian DSGE model. However, Kiley (2013) argues ha a forecas-based rend may be a beer arge for policy han he flexible-price equilibrium in he medium-scale New Keynesian DSGE model used by he Board of Governors of he Federal Reserve Sysem in heir analysis of he US economy. His argumen hinges in par on some paricular feaures of he model ha he considers, including he exisence of financial fricions. Bu his main poin is ha he flexibleprice equilibrium converges o he sochasic rend of oupu, so a forecas-based oupu gap provides useful informaion abou curren and fuure heory-based gaps. Given lags in he implemenaion and ransmission of moneary policy, informaion abou fuure heory-based gaps is highly relevan for curren policy decisions. Meanwhile, as noed by Kiley (2013) and many ohers, DSGE models imply reducedform VAR, VECM, or VARMA models. Thus, forecas-based oupu gap esimaes provide robus measures of economic slack across a wide range of differen economic assumpions used o idenify a srucural model, a leas as long as he reduced-form model or models used o calculae he opimal forecas capure he dynamics in he daa (his poin relaes back o Sims, 1980). aciviy and forecasing models. Thus, he forecas-based approach is more readily applicable when a significan fracion of producion is driven by inangible capial and/or here are large social and demographic changes make full-employmen of labour paricularly difficul o measure, boh of which are relevan concerns for he fas-growing and quickly-evolving Asian economies ha I consider in my empirical analysis. 2

6 Fourh, a key quesion in measuring slack is wheher o impose a specific relaionship beween slack and inflaion in esimaion (for example, Kuner, 1994, imposes a linear relaionship, while King and Morley, 2007, es for a relaionship). Relaed, here is a quesion of wheher measuremen should be based on mulivariae informaion (for argumens in favour, see Evans and Reichlin, 1994, and Basisha and Sarz, 2008). I migh seem ha he obvious answer o boh quesions is yes. Bu if he deeper goal in measuring slack is o es hypoheses abou is relaionship wih inflaion or wih oher macroeconomic variables, i can be problemaic o assume he answer by imposing a lo of srucure on he mulivariae relaionships in he firs place. 2 Thus, I consider univariae models of real GDP o esimae oupu gaps and hen es heir relaionship wih inflaion and across economies. Wih his background in mind, I invesigae economic slack and he Phillips Curve for seleced economies in Asia and he Pacific using model-averaged forecas-based esimaes of he oupu gap. To address various daa issues for hese economies, my analysis akes ino accoun srucural breaks in long-run growh and allows he incorporaion of prior beliefs in esimaion of model parameers. I find ha differen forecasing models produce very differen esimaes of he oupu gap for all of he economies. In mos cases, he model-averaged oupu gaps are highly asymmeric and closely relaed o he narrower measures of slack given by he unemploymen rae and capaciy uilizaion, similar o wha was found in Morley and Piger (2012) for US daa. Consisen wih he noion of an oupu gap as a measure slack, he model-averaged oupu gaps have srong negaive forecasing relaionships wih fuure oupu growh. The resuls for a Phillips Curve relaionship wih inflaion are more mixed. Bu here is an apparen convex relaionship in a number of cases, clearly arguing agains he imposiion of a linear relaionship when esimaing oupu gaps. Finally, I find noable dynamic linkages beween he model-averaged oupu gaps across many economies in Asia and he Pacific based on pairwise Granger Causaliy ess. 2 As an example of why assuming a fixed relaionship wih inflaion is problemaic, consider Sock and Wason (2009). Their analysis suggess ha inflaion is difficul o forecas using sandard measures of economic slack, excep when he esimaed oupu gap (or unemploymen gap) is large in magniude. This direcly suggess possible mismeasuremen and/or a nonlinear Phillips Curve relaionship (see Dupasquier and Rickes, 1998, and Meier, 2010). 3

7 The res of his paper is organized as follows. Secion 2 discusses he daa, including he possible presence of srucural breaks in long-run oupu growh for each economy. Secion 3 moivaes he model-averaging approach by demonsraing he sensiiviy of he resuls o he ime series model under consideraion. Secion 4 presens deails of he mehods employed in he empirical analysis. Secion 5 repors he resuls for he benchmark US case and for a selecion of economies in Asia and he Pacific. Secion 6 concludes. Technical deails are relegaed o an appendix. 2. Daa I consider macroeconomic daa for he Unied Saes (US) and 12 economies in Asia and he Pacific: Ausralia (AU), New Zealand (NZ), Japan (JP), Hong Kong (HK), Korea (KR), Singapore (SG), China (CN), India (IN), Indonesia (ID), Malaysia (MY), Philippines (PH), and Thailand (TH). Daa series for real GDP, he price level, he unemploymen rae, and capaciy uilizaion were sourced by he BIS from IMF IFS, CEIC, Daasream, and he relevan naional daa sources. For quarerly real GDP, I use he available seasonally-adjused series for he Unied Saes, Ausralia, New Zealand, Japan, Korea, Singapore, and Thailand. In he cases of Hong Kong, China, India, Indonesia, Malaysia, and he Philippines, I apply X12 procedures o he non-seasonally-adjused series, as hese were available for he longes possible sample periods. I hen consruc quarerly growh raes by aking firs differences of 100 imes he naural logs of he seasonally-adjused levels. The available sample periods for quarerly growh raes of real GDP are lised in Table 1. For he price level, I use he core PCE deflaor for he Unied Saes, core CPI for Japan and Indonesia, and headline CPI for he remaining economies. These choices were deermined by a general preference for core measures, bu only when hey are available for a relaively long sample period in comparison o real GDP. I calculae inflaion as he year-on-year percenage change in he price level and hen consruc 4- quarer-ahead changes in inflaion. The relevan sample periods based on common availabiliy of boh real GDP and price level daa are lised in Table 3 below. Unemploymen rae daa are available for all economies excep India and Indonesia, wih relevan sample periods based on common availabiliy wih real GDP lised in Table 4 below. Capaciy uilizaion is available for all economies excep Hong Kong, 4

8 Singapore, China, and India, wih relevan sample periods based on common availabiliy wih real GDP lised in Table 5 below. In addiion o sample periods for real GDP growh daa, Table 1 repors esimaed srucural break daes for long-run growh raes i.e., expeced growh in he absence of shocks. Perron and Wada (2009) argue ha i is crucial o accoun for a srucural break in he long-run growh rae of US real GDP when measuring economic slack for he US economy. They impose a break dae of 1973Q1 based on he noion of a produciviy growh slowdown a ha ime. However, applying Bai and Perron s (1998, 2003) sequenial esing procedure for srucural breaks in he mean growh rae of US real GDP does no deec a break in he early 1970s. 3 Insead, I find he esimaed break dae is 2002Q2. This break is significan a he 1% level and corresponds o a reducion in he mean growh rae. I discuss he consequences of imposing his break dae when measuring economic slack for he US economy below. For he oher economies, i would seem exremely imporan o accoun for srucural breaks in long-run expeced growh, especially since many of hese economies are likely on a ransiion pah in erms of long-run growh in he absence of shocks. However, here is only mixed evidence of srucural breaks in real GDP growh raes, perhaps due o relaively shor sample periods in many of he cases. Considering significance a leas a a 10% level, I find no breaks for Ausralia, New Zealand, Singapore, China, and Thailand, one break for Hong Kong, Korea, India, Malaysia, and he Philippines, and wo breaks for Japan and Indonesia. The esimaed break daes and he corresponding sequence of mean growh regimes are repored in Table 1. 4 To accoun for srucural breaks in subsequen analysis, he oupu growh series 3 Following much of he applied lieraure, I consider rimming of 15% of he sample from is end poins and beween breaks for admissible break daes. 4 The regression model for esing srucural breaks includes only a consan. The evidence for srucural breaks is generally weaker when allowing for serial correlaion. However, I find ha i is more problemaic o underesimae han o overesimae he number of srucural breaks when esimaing forecas-based oupu gaps. Specifically, forecas-based oupu gaps can display permanen movemens ha proxy for large srucural breaks in growh raes when hese are no direcly accouned for in he daa, while accouning for smaller or possibly misspecified srucural breaks ends o have lile impac on forecas-based oupu gaps. 5

9 are mean-adjused based on he esimaed average growh rae in each regime unil here is no remaining evidence for addiional breaks Moivaion To moivae he model-averaging approach o measuring economic slack presened in he nex secion, I begin by considering forecas-based esimaes of he oupu gap based on wo models: an AR(1) model and Harvey and Jaeger s (1993) unobserved componens (UC) model ha corresponds o he Hodrick-Presco (HP) filer wih a smoohing parameer of 1,600 (denoed UC-HP hereafer). The AR(1) model is esimaed for quarerly real GDP growh and he oupu gap is esimaed using he BN decomposiion for an AR(1) model (see Morley, 2002, for deails of his calculaion). The UC-HP model is esimaed for 100 imes he naural logs of quarerly real GDP and he oupu gap is esimaed using he Kalman filer. Alhough i is specified in erms of log levels, he UC-HP model provides an implici forecas of fuure oupu growh, wih he Kalman filer calculaing he long-horizon condiional forecas of fuure oupu a each poin of ime. Figure 1 plos he esimaed oupu gaps based on he AR(1) and UC-HP models for US real GDP. As discussed in Morley and Piger (2012), hese esimaes are very differen from each oher, wih he oupu gap based on he AR(1) model being of small ampliude and posiive during NBER-daed recessions, while he oupu gap based on he UC-HP being of much larger ampliude and negaive during NBERdaed recessions. I is worh noing ha, in he case of hese wo models a leas, oupu gap esimaes for each model are virually idenical wheher or no he srucural break in 2002Q2 is aken ino accoun. I migh seem obvious from visual inspecion ha he UC-HP oupu gap is preferable, especially given is more inuiive relaionship wih recessions. Bu, alas, here is an inconvenien realiy ha he AR(1) model fis he daa much beer han he UC-HP 5 This approach explains why here are wo breaks wihin 15% of he sample of each oher for Indonesia. The firs break of 1996Q4 was found based on he original daa and he second break of 1998Q4 was found based on he adjused daa based on he firs break. These breaks correspond o he Asian financial crisis ha hi Indonesia paricularly hard and culminaed in Presiden Suharo s resignaion in Failure o accoun for boh breaks leads o esimaes of he oupu gap wih clear permanen movemens corresponding o he crisis. 6

10 model by any sandard meric used for model comparison, including AIC and SIC, a resul ha was highlighed in Morley and Piger (2012). 6 Furhermore, as poined ou by Nelson (2008), he noion of an oupu gap as a measure economic slack direcly implies ha i should have a negaive forecasing relaionship wih fuure oupu growh. Specifically, when he economy is above rend and he oupu gap is posiive, fuure growh should be below average as he economy reurns o rend and vice versa. Moivaed by he analysis in Nelson (2008), I calculae he correlaion beween a given esimae of he oupu gap and he subsequen 4- quarer oupu growh. 7 Table 2 repors hese correlaions and, consisen wih he findings in Nelson (2008), he correlaion for he US oupu gap based on he AR(1) model is negaive, while he correlaion for he UC-HP model is posiive. This resul direcly suggess ha he oupu gap based on he AR(1) model provides a more accurae measure of economic slack han he UC-HP model, even if is relaionship wih recessions seems counerinuiive. Figure 2 plos he esimaed oupu gaps based on he AR(1) and UC-HP models for real GDP daa from various economies in Asia and he Pacific. The figure makes i clear ha he very differen implicaions of he wo models for he oupu gap are no jus a quirk of he US daa. As in Figure 1, he oupu gap based on he AR(1) model is always smaller in ampliude han he oupu gap based on he UC-HP model and ofen of he opposie sign. The correlaion resuls for hese oher economies in Table 2 6 I follow he approach in Morley and Piger (2012) o ensure he adjused sample periods are equivalen for all models under consideraion. For he linear and nonlinear AR models discussed below, his involves backcasing sufficien observaions based on he long-run growh rae o condiion on in esimaion. For he UC models discussed below, i involves placing a highly diffuse prior on he iniial level of he sochasic rend and evaluaing he likelihood for he same observaions as for he models of growh raes. See Morley and Piger (2012) for deails. 7 Nelson (2008) considers regressions ha capure he correlaion beween a given esimae of he oupu gap and 1-quarer-ahead US oupu growh. My resuls for he US daa are qualiaively similar o his even hough I consider 4-quarer-ahead oupu growh, which arguably provides a beer sense of forecasing abiliy a a policy-relevan horizon. Also, Nelson (2008) conducs a pseudo ou-of-sample forecasing analysis by esimaing models and oupu gaps using daa only up o when he forecas is made (i is a pseudo ou-of-sample forecas because he daa are revised, alhough Orphanides and van Norden, 2002, find ha using revised or real-ime daa maers much less han incorporaing fuure daa in esimaion of he oupu gap a any poin in ime). However, even hough I use he whole sample o esimae models, I am implicily using daa only up o when he forecas is made o esimae oupu gaps. This is sraighforward for he Harvey and Jaeger (1993) UC-HP model, which direcly allows for filered inferences, as opposed o he radiional HP filer, which is a wo-sided filer, explaining why Nelson (2008) considers he ou-of-sample forecasing analysis when evaluaing he forecasing properies he oupu gap based on he radiional HP filer. 7

11 are a bi more mixed, bu he correlaion wih fuure oupu growh is sill negaive for 9 ou of 12 economies for he AR(1) model oupu gap, while i is negaive for only 5 ou of 12 economies for he UC-HP model oupu gap. Finally, any formal model comparison, including based on AIC or SIC, srongly favours he AR(1) model in every case. More favourable o he UC-HP model is he forecasing relaionship beween he compeing model-based oupu gaps and fuure inflaion. Table 3 repors correlaions beween oupu gap esimaes and subsequen 4-quarer changes in inflaion. Consisen wih mos concepions of he Phillips curve, he correlaion is always posiive for he UC-HP model oupu gap. By conras, i is negaive for 9 ou of 13 economies, including he Unied Saes, when considering he AR(1) model oupu gap. Taken ogeher, he resuls in Tables 2 and 3 sugges ha neiher forecas-based esimae of he oupu gap provides a paricularly accurae measure of economic slack. Pu anoher way, here is considerable uncerainy abou he appropriae ime series model for real GDP when rying o measure economic slack. The AR(1) model fis he daa beer and is corresponding oupu gap generally provides a beer forecas of fuure real GDP growh. Bu he UC-HP model oupu gap is more consisen wih widely-held beliefs abou he relaionship beween economic slack and recessions, as well as generally providing a beer forecas of fuure changes in inflaion. These resuls moivae wo key aspecs of he mehods oulined in he nex secion. Firs, drawing from an insigh going back a leas o Baes and Granger (1969) ha combined forecass can ouperform even he bes individual forecas, I follow Morley and Piger (2012) and consruc a model-averaged esimae of he oupu gap, averaging over a range of linear and nonlinear forecasing models. Second, he disconnec beween cerain aspecs of an esimaed gap (e.g., he sign of he AR(1) model oupu gap during recessions) and widely-held beliefs direcly suggess he poenial usefulness of incorporaing informaive priors in esimaion when hese beliefs are held for valid reasons. Thus, I ake a Bayesian approach o esimaion ha allows me o incorporae prior beliefs wihou sricly imposing such beliefs in case hey are srongly a odds wih he daa. 8

12 To be more concree abou his laer issue, an obvious example of a widely-held belief in his conex is he sandard idea ha rends are smooh. Indeed, he UC-HP model imposes his as a dogmaic prior, while he esimaed oupu gaps for AR(1) model sugges oherwise. In principle, hen, one could incorporae he idea of smooh rends ino an informaive (bu no dogmaic) prior, as in Harvey, Trimbur, and van Dijk (2007). Specifically, one could esimae he signal-o-noise raio for he UC-HP model insead of imposing i, bu consider an informaive prior on his parameer ha suggess he rend is relaively smooh. Likewise, one could consider an informaive prior on he auoregressive coefficien in he AR(1) model ha implies negaive serial correlaion in oupu growh. However, despie giving he example of a smoohness prior on he rend, I should emphasize ha, in pracice, I do no acually impose such a prior in my analysis. As will be seen below, imposing such a prior is no necessary o esimae oupu gaps ha are negaive in recessions. Meanwhile, such a prior is srongly a odds wih he daa. Nelson and Plosser (1982) noed his wihin he conex of he signal-o-noise raio for he radiional HP filer. Perron and Wada (2009) have recenly suggesed ha a smooh rend for US real GDP can be reconciled wih parameer esimaes as long as he ime series model used o esimae he oupu gap allows for a srucural break in long-run growh corresponding o he produciviy growh slowdown in Ye, Morley and Piger (2012) and Morley, Panovska, and Sinclair (2013) find srong evidence for a relaively volaile sochasic rend in US real GDP even when allowing for he produciviy growh slowdown. Thus, a smoohness prior seems unwarraned. 4. Mehods As menioned above, my analysis closely follows he approach o esimaing a modelaveraged oupu gap (MAOG) developed in Morley and Piger (2012) for US real GDP. However, I consider a few modificaions ha make he approach more easily applicable o daa from oher economies. I ouline he approach, including he modificaions, in his secion. The full deails of he approach are in he original sudy and are also se ou in he appendix. Morley and Piger (2012) consider only univariae models of real GDP. However, his includes he AR(1) and UC-HP models discussed in he previous secion. Therefore, 9

13 as is eviden from Figures 1 and 2, he univariae models capure a range of possibiliies abou he naure of he oupu gap. Also, as menioned in he inroducion, univariae analysis allows us o es mulivariae relaionships raher han assume he answer a priori. The benefis of his approach for he relaionship wih inflaion in paricular will become eviden when he resuls are presened below. All of he models allow for a sochasic rend in real GDP, which is moivaed by sandard uni roo and saionariy ess, even when allowing for srucural breaks in long-run growh. This is imporan because many off-he-shelf mehods such as linear derending, radiional HP filering, and Bandpass filering produce large spurious cycles when applied o ime series wih sochasic rends (see Nelson and Kang, 1981, Cogley and Nason, 1995, and Murray, 2003). By conras, as long as he models under consideraion avoid massive overfiing of he daa, he forecas-based approach will no produce large spurious cycles. Following Morley and Piger (2012), I consider linear AR(p) models of orders p = 1, 2, 4, 8, and 12 wih Gaussian errors or Suden errors, he linear UC-HP model due o Harvey and Jaeger (1993), he linear UC0 and UCUR models wih AR(2) cycles from Morley, Nelson, and Zivo (2003), he nonlinear bounceback (BB) models from Kim, Morley, and Piger (2005) wih BBU, BBV, and BBD specificaions and AR(0) or AR(2) dynamics, he nonlinear UC0-FP model wih an AR(2) cycle from Kim and Nelson (1999), and he nonlinear UCUR-FP model wih an AR(2) cycle from Sinclair (2010). 8 Again, see he appendix and he original sudies for more deails of hese models. The firs major modificaion from Morley and Piger (2012), menioned above, is ha models are esimaed using Bayesian mehods insead of maximum likelihood esimaion (MLE). This allows incorporaion of informaive priors in he esimaion. Mos of my priors are no paricularly srong, wih esimaes based on he poserior 8 As a minor modificaion o Morley and Piger (2012), I drop he linear AR(0) models and nonlinear Markov-swiching model from Hamilon (1989) wih AR(0) and AR(2) dynamics. In he former case, he oupu gap is always zero by consrucion, so is inclusion merely serves o shrink he modelaveraged oupu gaps owards zero. In he laer case, he oupu gap is linear by consrucion, so is inclusion as a nonlinear model pus addiional prior weigh on a linear oupu gap. As demonsraed below, dropping hese models has very lile pracical impac on he model-averaged esimae of he oupu gap for US real GDP. 10

14 mode virually idenical o MLE for many of he models. 9 However, for economies wih relaively shor samples for real GDP or oher quirks in he daa such as large ouliers, here is some endency for MLE of he UC models and he nonlinear models o overfi he daa. By incorporaing more informaive priors abou he persisence of he auoregressive dynamics or he persisence of Markov-swiching regimes based on US esimaes from Morley and Piger (2012), I am able o avoid problems associaed wih shor samples and ouliers, while obviaing he need o underake a long, proraced search for he bes model specificaions for each economy. 10 The full deails of he priors are presened in he appendix. The second major modificaion from Morley and Piger (2012) is ha I consider equalweighs on he models when consrucing MAOGs raher han weighs based on Bayesian model averaging (BMA). Alhough a number of models receive nonrivial weigh based on he SIC approximaion of BMA when considering he US daa in Morley and Piger (2012), his is no always he case for oher economies. For example, a simple AR(0) model would receive all weigh for Ausralian real GDP based on SIC if i were included in he model se. Bu such a model implies he oupu gap is always exacly zero by consrucion (no jus zero on average), which clearly runs conrary o widely and srongly held beliefs and, as will be seen below, would produce inferior forecass of fuure oupu growh and changes in inflaion in comparison o he Ausralian MAOG. The problem of BMA puing oo much weigh (from a forecasing perspecive) on one model has been highlighed recenly by Geweke and Amisano (2011). They find ha linear pooling of models produces beer densiy forecass han BMA and discuss he calculaion of opimal weighs for linear pooling of models. However, as long as he model se is relaively diverse, applying equal weighs o models works almos as well as opimal weighs and is much easier o implemen. Thus, I ake his simple approach of using equal weighs for he reasonably diverse se of linear and nonlinear 9 The AR(1) and UC-HP models discussed in previous secion were esimaed using he poserior mode. Bu he esimaed oupu gaps for hese models are indisinguishable from hose based on MLE. For example, for he US daa, he correlaion beween he Bayesian and MLE oupu gaps is > in boh cases. 10 In principle, his seup would also make i possible o apply he approach oulined in his paper even given severe daa limiaions (e.g., very small samples) or a desire o impose igher priors based on srongly held beliefs. 11

15 models discussed above. 11 Again, see he appendix for more deails of he model averaging. 5. Resuls Before proceeding o he resuls for he Asian and Pacific economies, I firs consider resuls he Unied Saes as a benchmark case in order o provide perspecive on he impac of he modificaions o Morley and Piger (2012) described in he previous secion, as well as providing conex for he oher resuls. To begin, I compare he updaed MAOG based on he US real GDP daa described in Secion 2, equal weighs, and Bayesian esimaion o he original MAOG repored in Morley and Piger (2012) based on a shorer sample period, a differen vinage of daa, BMA weighs, and MLE. For compleeness, I also consider he updaed MAOG based on he Morley and Piger (2012) vinage of daa, equal weighs, and Bayesian esimaion. Figure 3 plos hese hree MOAGs ogeher. The mos noiceable hing is heir similariy, wih he major finding in Morley and Piger (2012) of a highly asymmeric shape holding for he updaed MAOGs. The correlaion beween he updaed MAOGs and he original MAOG is abou The mos noable difference is in erms of he behaviour of he oupu gap around he 2001 recession. However, as he updaed MAOG based on he vinage sample reveals, his difference is largely due o daa revisions, no o modificaions in he approach. The impac of incorporaing prior informaion abou parameers may be obscured in Figure 3 given ha he priors were calibraed based on he esimaes for US daa in Morley and Piger (2012). However, i is imporan o emphasize ha he asymmeric shape of he oupu gap is in no way driven by he priors on he nonlinear models. The priors favour Markov-swiching in he mean growh rae corresponding o business cycle phases along he lines of Hamilon (1989). Bu here is no prior ha shocks have more emporary effecs in recessions han in expansions. Figure 4 makes his clear by applying he modified approach o daa simulaed from a simple random walk wih 11 In pracice, I place equal weighs on linear and nonlinear classes of models and divide hose equal weighs up evenly amongs he models wihin he classes. Because he nonlinear models include linear dynamics in heir parameer space, here is sill more prior weigh on linear han nonlinear dynamics, alhough his is addressed somewha by he somewha informaive priors for parameers in he nonlinear models. 12

16 drif. 12 For his daa, he rue oupu gap is always zero. The esimaed MAOG is no always zero, bu, unlike wha would be he case for he HP filer given a random walk, he spurious cycle is quie small in magniude relaive o he US MAOG and, imporanly, i flucuaes symmerically around zero. Thus, any finding of asymmery for he MAOGs reflecs he daa, no he incorporaion of prior informaion in esimaing model parameers. 13 One possibly surprising resul for he updaed US MAOG displayed in Figures 3 and 4 is ha i implies lile remaining economic slack for he US economy a he end of he sample in 2012Q3. This resul urns ou o be sensiive o allowing for a srucural break in long-run growh in 2002Q2. Figure 5 plos he updaed US MAOG agains a version under he assumpion of no srucural break. Assuming no change in he longrun growh, he US economy appears o sill be below rend a he end of he sample. Given uncerainy abou he srucural break, i migh make sense o average across hese wo scenarios, which would sill imply he economy remains below rend a he end of he sample, alhough no by as much as in he no break case. Bu is i compleely oulandish o infer ha he US economy is close o rend by he end of he sample? This would clearly imply ha recessions can permanenly shif he rend pah of oupu downwards, which is he implicaion of many forecasing models for US real GDP, including low-order AR(p) models, Hamilon s (1989) Markovswiching model, and, o some exen, he bounceback models of Kim, Morley, and Piger (2005). Figure 6 plos he esimaed rend in US real GDP based on he modelaveraged oupu gap. A permanen negaive effec of he Grea Recession of he rend pah is quie eviden for his esimae of rend and is much larger han for previous recessions. One way o judge he plausibiliy of he US economy being a rend a he end of he sample is o compare he US MAOG o oher narrower measures of slack. Figure 7 plos he US MAOG agains he US unemploymen rae and US capaciy uilizaion. Similar o he findings in Morley and Piger (2012), here is a clear relaionship 12 The drif and sandard deviaion of shocks are boh se o 1, which is a surprisingly reasonable calibraion for 100 imes he naural logs of quarerly US real GDP. 13 Indeed, model averaging would end o undersae asymmery if i were presen in he daa generaing process (e.g., suppose Kim and Nelson s, 1999, UC0-FP model was he rue model) by shrinking he mean of he esimaed MAOG owards zero given ha he mean of he esimaed oupu gap is zero by consrucion for all of he linear models under consideraion. 13

17 beween he MAOG and hese variables. Meanwhile, in erms of he quesion of wheher here remains a lo of slack in he US economy a he end of he sample, hough, he unemploymen rae provides a differen answer han capaciy uilizaion. The unemploymen rae has no reurned o is pre-recession levels, consisen wih he MAOG in he no break case, while capaciy uilizaion has essenially reurned o is pre-recession level, consisen wih he MAOG allowing for a srucural break. The hisorical persisence of he unemploymen rae suggess ha i can ofen remain elevaed long afer he MAOG has reurned o zero, while he relaionship wih capaciy uilizaion is a bi igher in erms of iming (alhough correlaions wih he MAOG are similar in magniude for he wo series, wih a correlaion of for he unemploymen rae and 0.59 for capaciy uilizaion). Thus, hese resuls are mildly supporive of he MAOG allowing for a srucural break. More supporive of relaively lile remaining slack a he end of he sample is he simple fac ha he MAOG in he no break case would imply relaively fas growh and downward pressure on inflaion in he period immediaely afer he Grea Recession. In paricular, reurning o Tables 2 and 3, he US MAOG has a reasonably srong negaive correlaion of wih fuure oupu growh and posiive correlaion of 0.51 wih fuure changes in inflaion. These resuls are much sronger han hose for he oupu gaps based on he AR(1) and UC-HP models and suppor he MAOG as a highly relevan measure of economic slack. Bu, given lacklusre growh and sable inflaion afer he Grea Recession, hese resuls also suppor he MAOG allowing for a srucural break and he idea ha he US economy is acually close o rend a he end of he sample, noing ha he rend pah is lower han before he recession, as suggesed in Figure 6. Having demonsraed how he modified approach works in he benchmark US case, I now apply he approach o real GDP daa for 12 economies in Asia and he Pacific. Figure 8 plos MAOGs for he various economies. In mos of he cases, he MAOGs are highly asymmeric, similar o he US resuls. Specifically, he oupu gaps for Ausralia, Japan, Hong Kong, Korea, Singapore, China, India, Malaysia, and Thailand ake on much larger negaive values han posiive ones. The excepions are New Zealand, Indonesia, and he Philippines, all of which have more symmeric flucuaions of relaively small ampliude. The implicaion for hese economies is ha 14

18 more of he flucuaions in real GDP have permanen effecs, including during recessions. 14 How plausible are he MAOGs as measures of economic slack? As wih he US benchmark, I compare he MAOGs o oher narrower measures of slack when available for a given economy. Table 4 repors he correlaion of each MAOG wih he corresponding unemploymen rae for all bu India and Indonesia. For comparison, I also repor correlaions for oupu gaps based on AR(1) and UC-HP models. Corresponding o an Okun s Law relaionship, he MAOG has he mos negaive correlaion wih he unemploymen rae in 8 ou of 11 cases (including he US benchmark), wih many of he correlaions being quie large in magniude. In he remaining cases, he correlaions are small for all esimaes of he oupu gap. Table 5 repors he corresponding correlaions wih capaciy uilizaion for all bu Hong Kong, Singapore, China, and India. The MAOG has he mos posiive correlaion wih capaciy uilizaion in 6 ou of 9 cases (including he US benchmark) and has very high correlaions in wo of he oher cases. Surprisingly, he correlaion is negaive for he Philippines. Bu his is rue for all hree esimaes of he oupu gap, perhaps raising doubs abou capaciy uilizaion as a good measure of slack in his case, especially given ha he UC-HP oupu gap and he MAOG have he expeced negaive correlaions wih he unemploymen rae. Overall, he srong coherence wih oher measures of slack lends credence o he MAOGs. The coherence is paricularly noable given ha he MAOGs are esimaed using only univariae models of real GDP. A he same ime, he MAOGs provide a broad measure of slack even when unemploymen rae or capaciy uilizaion daa are no available or are heavily influenced by long-run srucural facors. Revisiing Table 2, he MAOGs provide a sronger signal abou fuure economic growh han he wo oher oupu gap esimaes in 11 ou of 13 cases (including he US benchmark), wih reasonably large negaive correlaions in all bu one case. This 14 I should be noed ha for all of he economies, regardless of wheher or no here is asymmery in he esimaed oupu gap, he sochasic rend appears o be reasonably volaile. The esimaed sandard deviaion of permanen shocks is paricularly large, abou wice ha of he Unied Saes, for Hong Kong, Korea, Singapore, India, Indonesia, Malaysia, Philippines, and Thailand. This resul is consisen wih Aguiar and Gopinah (2007), who find ha emerging economies are subjec o exremely volaile shocks o rend oupu. 15

19 resul provides he mos direc suppor of he MAOGs as measures of economic slack based on he definiion considered in his paper. I also confirms he possibiliy ha oupu growh can be somewha predicable even when sandard model comparison merics would selec a random walk model, as he SIC would in he case of Ausralia. Looking back a Table 3, he resuls for he MAOGs in erms of correlaion wih fuure changes in inflaion are more mixed. The MAOGs provide a sronger signal han he UC-HP model oupu gap in only 6 of he 13 cases (including he US benchmark). However, a correlaion coefficien may be oo simplisic as a measure of he relaionship beween he oupu gap and inflaion. Figure 9 displays a scaerplo of he US MAOG (x-axis) agains he subsequen 4-quarer change in US inflaion (yaxis) and here is a clear nonlinear, convex Phillips Curve relaionship beween he oupu gap and fuure changes in inflaion ha would only be parially capured by a correlaion coefficien. Figure 10 displays he corresponding scaerplos for he 12 economies in Asia and he Pacific. The same convex relaionship as for he US daa is eviden for Ausralia, Japan, Korea, and, o a lesser exen, India. These are all cases where he correlaion in Table 3 was larges for he MAOG and for which here were relaively long samples for he inflaion daa. For some of he oher cases, such as New Zealand, Malaysia, and Thailand, he Phillips Curve relaionships look more linear. Meanwhile, he resuls for Singapore, China, and Indonesia are more puzzling, alhough his could be due o a number of facors including he measures of inflaion, which may be heavily influenced by cos push facors or oher large evens during he paricular sample periods under consideraion. Bu a clear implicaion of Figures 9 and 10 is ha i is imporan no o impose a specificaion for he Phillips Curve relaionship a priori, as is done in some approaches o esimaing oupu gaps (e.g., Kuner, 1994). If he imposed relaionship is incorrecly specified, hen he resuling oupu gap esimae will be disored and canno be used o deermine a beer specificaion of a Phillips Curve relaionship. The convexiy of he Phillips Curve in some cases argues agains a linear specificaion. Also, here is some evidence ha he relaionship beween he oupu gap and inflaion has evolved over ime, wih many of he observaions of sable inflaion following large negaive oupu gaps corresponding o he recen Global 16

20 Financial Crisis. Consisen wih he Lucas s (1976) famous criique ha reducedform Phillips Curve relaionships should change wih policy regimes, his apparen breakdown in he previous paern near he end of he sample could be due o an anchoring of inflaion expecaions (see IMF, 2013) and argues srongly agains imposing a fixed relaionship wih inflaion when esimaing he oupu gap. Given general suppor for he MAOGs as measures of economic slack, especially in erms of he crucial definiional sense of forecasing fuure economic growh, he las quesion considered in his paper is wheher he MAOGs are relaed across economies. To answer his quesion, I conduc pairwise Granger Causaliy ess. Table 6 repors he resuls for hese ess. A he 10% level, he oupu gaps appear o be relaed across many of he economies, wih 46 rejecions of no Granger Causaliy. The paerns are generally sensible, alhough he 10% may include some rejecions of he null merely due o random sampling given ha a oal of 156 ess were conduced. However, he fac ha he number of rejecions holds up a 31 for he ess a he 5% level and 19 for ess a he 1% level suggess ha many of rejecions are simply because he null hypohesis is false. Noably, he Granger Causaliy ess using MAOGs provide more suppor for crosseconomy spillovers han when using oupu gap esimaes for he AR(1) and UC-HP models or he underlying real GDP growh rae daa. 15 This resul suppors he MAOGs as capuring an imporan economic phenomenon and, given a forecas-based approach o esimaing he oupu gap, suggess he poenial usefulness of incorporaing daa from oher economies in he region in he forecasing models for each economy. In erms of general paerns for cross-economy spillovers and focusing on he resuls a he 5% level, he oupu gaps for Singapore and Hong Kong appear o Granger-cause he larges number of oher economies, while he oupu gaps for Hong Kong and Malaysia are Granger-caused by he larges number of oher economies. 6. Conclusions There is much more uncerainy abou he degree of economic slack han is commonly acknowledged in academic and policy discussions, which ofen rea he oupu gap as 15 The respecive number of rejecions a he 10%, 5%, and 1% levels is 33, 21, and 11 for he AR(1) model oupu gap, 43, 30, and 14 for he UC-HP model oupu gap, and 39, 23, and 13 for he underlying real GDP growh rae daa. 17

21 if is direcly observed. Canova (1998) argues ha his uncerainy has huge implicaions in erms of sylized facs abou he business cycle used o moivae heoreical analysis. Also, as discussed in he inroducion, Orphanides (2002) argues ha his uncerainy is responsible for huge policy misakes in he pas, especially in erms of he high inflaion in he 1970s. In ligh of his uncerainy abou he degree of economic slack prevailing in an economy a any given poin of ime and is imporance for policy, I argue for a modelaveraged forecas-based esimae of he oupu gap. For mos economies, he modelaveraged esimae is closely relaed o he narrower measures of slack given by he unemploymen rae and capaciy uilizaion and, consisen wih he noion of an oupu gap as a measure economic slack, has a srong negaive forecasing relaionship wih fuure oupu growh. The model-averaged oupu gaps are also generally highly asymmeric, as was found for US real GDP in Morley and Piger (2012). Evidence for a Phillips Curve relaionship beween he model-averaged oupu gap and inflaion is more mixed. Bu he overall resuls argue agains imposing a linear relaionship in esimaing oupu gaps. Meanwhile, here are noable dynamic linkages beween he model-averaged oupu gaps across many economies in Asia and he Pacific based on pairwise Granger Causaliy ess. The esimaes of oupu gaps in his paper were deliberaely based on univariae models. Bu i would be ineresing o see he influence of mulivariae informaion on he esimaes. Also, furher analysis of he Phillips Curve relaionship ha allows differen specificaions and akes cos push facors and oher shocks ino accoun would be helpful o beer undersand wha drives inflaion for each economy. Finally, i is likely ha he correlaions beween oupu gaps across economies have changed over ime, which could be considered wih a facor model wih ime-varying loadings (e.g., Del Negro and Orok, 2008). Bu hese exensions are lef for fuure research. 18

22 Appendix Following Morley and Piger (2012), I define he oupu gap, c, as he deviaion of log real GDP, y, from is sochasic rend,, as implied by he following rend/cycle process: y c, (1) 1, (2) c j0, (3) j j where 0 1,, and, wih and following maringale difference sequences. The rend,, is he permanen componen of y in he sense ha he effecs of he realized rend innovaions,, on he level of he ime series are no expeced o be reversed. By conras, he cycle, c, which capures he oupu gap, is he ransiory componen of y in he sense ha he Wold coefficiens, j, are assumed o be absoluely summable such ha he realized cycle innovaions,, have finie memory. The parameer allows for non-zero drif in he rend, while he parameer allows for a non-zero mean in he cycle, alhough he mean of he cycle is no idenified from he behaviour of he ime series alone, as differen values for all imply he same reduced-form dynamics for assumpion being ha 0. y, wih he sandard idenificaion The opimal esimae (in a minimum mean-squared-error sense) of rend for a range of rend/cycle processes as in (1)-(3), including hose wih regime-swiching parameers, can be calculaed using he regime-dependen seady-sae (RDSS) approach developed in Morley and Piger (2008). The RDSS approach involves consrucing long-horizon forecass using a given ime series model o capure he dynamics of he process. Imporanly, he long-horizon forecass are condiional on sequences of regimes and hen marginalized over he disribuion of he unknown regimes. Specifically, he RDSS measure of rend is 19

23 ˆ RDSS p M S ˆ RDSS RDSS ˆ S, (4) S ~ M * j ~ M * S lim E y S i, S, j E y S i j j k ~ where S { S,..., S } is a vecor of relevan curren and pas regimes for m forecasing a ime series, k 1 M p is he probabiliy disribuion wih respec o he, (5) forecasing model, S is an unobserved sae variable ha akes on N discree values according o a fixed ransiion marix, and i is he normal regime in which he mean of he ransiory componen is assumed o be zero. The choice of normal regime i is necessary for idenificaion. Meanwhile, for a given forecasing model ~ p M S, can be wih Markov-swiching parameers, he probabiliy weighs in (4), obained from he filer given in Hamilon (1989). Noe ha he RDSS rend simplifies o he Beveridge and Nelson (1981) rend in he absence of regime swiching. In pracice, he correc model for he dynamics of he ime series process is unknown. Thus, following Morley and Piger (2012), I consider a range of models, as lised in he main ex. The linear and nonlinear AR(p) models are specified as follows: y e ( L) (6) S,..., S ), (7) ( m where (L) is p h order. I consider versions of he AR(p) models wih Gaussian errors 2 2 (i.e., e ~ N(0, ) ) or Suden errors (i.e., e ~ (,0, ) e ). 0,1 e S is a Markov sae variable wih fixed coninuaion probabiliies Pr[ S 0 S 1 0] p00 and Pr[ S 1 S p. In he linear case,, while here are hree differen 1 1] 11 specificaions of in he nonlinear case ha correspond o he BB models developed by Kim, Morley, and Piger (2005): 1. U -Shaped Recessions (BBU) 20

24 m 0 1S 1 j1 S, (8) j 2. V -Shaped Recessions (BBV) m 0 1S 1 S 1S j, (9) j 1 3. Recovery based on Deph (BBD) 0 1S j 1 m 1 y j S, (10) j where he sae S 1 is labeled as he low-growh regime by assuming 0. Following Kim, Morley, and Piger (2005), I assume m 6. See he original sudy for he full moivaion of hese specificaions. The linear and nonlinear UC models are based on (1)-(3), wih he following parameric specificaion of he ransiory componen in (3): 1 ( L), (11) c j where 0 for he linear UC0 and UCUR models and S for he nonlinear UC0-FP and UCUR-FP models, wih he sae S 1 labeled by assuming 0. The 2 2 shocks o he rend and cycle are Gaussian (i.e., ~ N(0, ), ~ N(0, ) for he UC0 and UC0-FP models and ~ N(0, ), for he UCUR and UCUR-FP models). Given an AR(2) cycle, he covariance for he UCUR and UCUR-FP models is idenified (see Morley, Nelson, and Zivo, 2003). As menioned in he main ex, Bayesian esimaes for hese models are based on he poserior mode. The priors for he various model parameers are se ou in Table A.1. Noe ha he prior for bounceback coefficien has zero mean, implying a prior mean of zero for he oupu gap. The prior for he mean of he ransiory shock for he UC- FP models has a negaive mean, bu his has very lile impac on he prior mean of he model-averaged oupu gap given he small weighs on any given model. The prior on he AR coefficiens clearly places hem in he saionary region. Finally, he prior 21