Forecasting UK Industrial Production over the Business Cycle

Transcription

1 Forecasing UK Indusrial Producion over he Business Cycle Paul W. Simpson* Denise R. Osborn Marianne Sensier *Deparmen for Educaion and Employmen, Sheffield Cenre for Growh and Business Cycle Research School of Economic Sudies Universiy of Mancheser, Mancheser, M3 9PL, UK web address: hp:// Phone: , Fax: h January 2000 Absrac This paper examines he informaion available hrough leading indicaors for modelling and forecasing he UK quarerly index of producion. Boh linear and non-linear specificaions are examined, wih he laer being of he Markov-swiching ype as used in many recen business cycle applicaions. The Markov-swiching models perform relaively poorly in forecasing he 990s producion recession, bu a hree indicaor linear specificaion does well. The leading indicaor variables in his laer model include a shor-erm ineres rae, he sock marke dividend yield and he opimism balance from he quarerly CBI survey. JEL classificaion: C22, C32, E27, E32, E44. Keywords: Financial variables, business cycles, leading indicaors, Markov-swiching models, forecas performance.

2 INTRODUCTION This paper examines he exen o which leading indicaors improve forecas accuracy for quarerly real UK indusrial producion over he business cycle. In paricular, we focus on forecass for he 990s. This period is of paricular ineres because, afer a period of subsanial expansion during he laer half of he 980s, he UK economy saw he occurrence of a deep recession which, alhough laer aribued o endogenous facors, was widely unprediced a he ime (Dow, 998, p32). Thus, we are ineresed in wheher here were signs ha UK indusrial producion would go ino recession and wheher he lengh and deph of ha recession were signalled by he informaion hen available. Alhough we have he benefi of hindsigh in carrying ou such an analysis, i is neverheless he case ha lessons need o be learn from such episodes if hey are o be avoided in he fuure. Business cycles are a key feaure of our analysis. I has ofen been observed ha he business cycle is asymmeric in he sense he economy behaves differenly during expansions and recessions. A wide variey of linear and non-linear ime-series echniques have been employed o model business cycle feaures, bu a major heoreical limiaion of linear business cycle models is ha hey are generally incompaible wih cyclical asymmeries. In consequence, much recen ineres has focused on non-linear business cycle models. Perhaps surprisingly, however, Hess and Iwaa (997) produce evidence ha (in a univariae conex) non-linear models are in pracice no beer a reproducing he business cycle feaures of US oupu han a simple linear ime series model. Furher, he forecasing record of non-linear models for macroeconomic variables is mixed (Ramsey, 996). Therefore, in he curren paper, we adop boh linear and non-linear approaches o evaluae he forecasing role of leading indicaor variables. Several non-linear business cycle mehods have been employed in he lieraure o capure observed business cycle asymmeries. These include hreshold models (Tiao and Tsay, 994), smooh ransiion auoregressive models (Teräsvira and Anderson, 992, Osborn and Öcal, 998) and Markov-swiching regime models (Hamilon, 989, Filardo, 994). Of hese, we adop he Markov-swiching approach because i can focus on he phase of he business cycle. Indeed, in applying a wo regime Markov-swiching model o pos-war US quarerly real gross naional produc growh, Hamilon obained regimes which correspond closely wih he US business cycle expansion and recession phases as daed by he widely-respeced Naional Bureau of Economic Research. Despie he recen ineres in modelling he business cycle, he vas bulk of he ime series lieraure on his opic uses univariae models. However, in order o forecas business cycle movemens, i may be anicipaed ha leading economic indicaors should convey

3 useful informaion abou oupu, wheher gross domesic produc or indusrial producion. Filardo (994) developed he Markov-swiching model o allow leading indicaors o play a role hrough ime-varying ransiion probabiliies (TVTP), where he probabiliy of a change in regime varies wih movemens in leading indicaor variables. In applying his TVTP Markov-swiching model o he monhly US index of producion (IOP) using various leading indicaor series, he found evidence in suppor of business cycle asymmeries and he TVTP specificaion. Neverheless, he did no aemp o evaluae he role of he leading indicaors hrough a forecas evaluaion exercise. As noed above, our ineres is in evaluaing he role of leading indicaors for forecasing. In common wih mos leading applicaions, including he leading indicaor sysem for he UK formerly produced by Office for Naional Saisics (Moore, 993), he informaion conex of he indicaors is evaluaed in a reduced form conex which is free from any specific model specificaion suggesed by economic heory. Neverheless, we consider boh linear and non-linear specificaions, and also univariae models as sandards of comparison for he models employing leading indicaor variables. In our complemenary paper, Simpson, Osborn and Sensier (999), we focus on UK gross domesic produc (GDP) and find evidence ha he Markov-swiching models and he use of leading indicaors (especially ineres raes) deliver improved forecas accuracy. Here we examine forecass of indusrial producion. This variable exhibis more marked pos-war cyclical movemens han GDP, because i excludes he service secor which experienced almos unbroken pos-war growh in he UK unil he end of he 980s. In common wih our GDP paper, he leading indicaors we consider are housing sars, he Confederaion of Briish Indusry (CBI) opimism balance and a number of financial variables. The srucure of he paper is as follows: he Mehodology Secion discusses he empirical models, including he procedures used o derive he paricular specificaions adoped. The Daa Secion describes he daa employed in he analysis. Subsanive resuls are presened in he following wo secions, he firs (Seleced Models) discusses he esimaion resuls for boh he linear and Markov-swiching models, while he second (Forecas Resuls) compares heir forecasing performance. Finally, some conclusions are presened. 2

4 METHODOLOGY Linear Models: specificaion, esimaion and diagnosic ess A linear auoregressive (AR) model for he growh rae of IOP ( y ) is: y = α + φ( L) y + e () where α is he inercep, φ(l) = φ L +φ 2 L φ r L r is an AR polynomial in he lag operaor L and where e are NID[0, σ 2 ]. Also, linear single leading indicaor models are fied, where he linear univariae AR model () is augmened wih lags of he leading indicaor series (x ), so ha, y = α + φ( L) y + β ( L) x + e (2) where β(l) = β L+β 2 L β K L K. Search algorihms were employed o derive he linear univariae AR and single leading indicaor models; deails of hese can be found in Simpson e al. (999). Suffice o say here ha auoregressive orders up o 4 are considered in (), while he maximum leading indicaor lag considered in (2) is 8. The principal lag selecion crierion is he minimisaion of he Schwarz (978) informaion crierion (SIC). The opimal auoregressive lag from () is assumed o apply also in (2). In pracice, our procedure allows inermediae leading indicaor lags o be deleed, so ha no all lags o K necessarily appear in he final specificaion. The empirical resuls provide he esimaed parameer values and heir sandard errors, ogeher wih he values of SIC and he Akaike (973) informaion crierion (AIC) for each linear specificaion. The probabiliy values are provided for a number of diagnosic ess, namely he Breusch (978) Lagrange Muliplier (LM) es for AR(4) residual auocorrelaion (χ 2 AR[4]), he Engle (982) LM es for ARCH() (χ 2 HET[]) and Ramsey (974) RESET es. Muliple indicaor linear models are also esimaed. These are developed from he single indicaor specificaion preferred by SIC, in order o invesigae wheher oher leading indicaors hen provide addiional informaion o improve on he single indicaor forecass. Markov Regime Swiching Models The Hamilon (989) wo-regime Markov-swiching model wih AR dynamics of order r may be wrien as: { y µ 0 S } e y µ + (3) = 0 + µ S + φ( L) µ 3

5 where S {0,}, φ(l)=φ L +φ 2 L φ r L r is a polynomial in he lag operaor L and e are iid N[0, σ 2 ]. In his specificaion he inercep (µ 0 or µ 0 +µ ) of he sochasic process for y is a funcion of a binary regime variable, S, which represens he business cycle regime in operaion a dae. For example, imposing he resricion µ >0 idenifies regime as a higher growh regime han regime 0. These regimes are frequenly associaed wih expansions and recessions respecively. Hamilon assumed he binary regime variable, S, o follow a firsorder Markov process, wih ransiion probabiliy marix defined in he following way: P = p p p p The individual regime ransiion probabiliies are defined as: p p p p (4) [ S - ], [ 0 S - ], [ S - ] [ S - 0 ]. = Pr ob S = = = Pr ob S = = = Pr ob S = 0 = 0, = Pr ob S = = where p 0 = (-p ) and p 0 = (-p 00 ). Thus, he probabiliies of remaining in regime and regime 0 are p and p 00 respecively, while p 0 and p 0 represen he probabiliies of swiching from regime o regime 0 and regime 0 o regime respecively. Hamilon developed an algorihm for he join esimaion of he parameers of boh he swiching regression model (3) and he Markov process for he regime (4). His algorihm also generaes probabiliy esimaes for he laen regime variable (S ). Two ypes of probabiliy esimaes can be calculaed, namely he smoohed probabiliies for a specific period which use all informaion o he end of he sample period T ( T) and he filer probabiliies which are based only on observaions o period. While he former are useful for ex-pos analysis of business cycle regimes, i is he laer which are of primary ineres in forecasing. Filardo assumed he same form of swiching regression model as Hamilon (989), bu exended he Markov chain componen by allowing he ransiion probabiliies o flucuae over ime wih movemens in an indicaor variable, x. He uses a single indicaor TVTP specificaion of he logisic form: p p 00 = Prob = Prob [ S = S =, x ] K [ S = 0 S = 0, x ] K 0 = + exp = + exp { ( β + β x )} 0 K { ( β + β x )} 00 0 K 0, (5) 4

6 where β 0 and β 00 give rise o consan ransiion probabiliies for regime and regime 0 respecively when β = β 0 = 0, while β and β 0 are he regime and regime 0 coefficiens on he (respecive) lagged value of he leading indicaor. Thus, he probabiliy of remaining in a regime is condiional on he lagged value of he leading indicaor, x -j, as well as he lagged regime, S -. In Simpson e al. (999) we also apply an exponenial form for he TVTP in he conex of UK GDP. However, when his exponenial funcion was applied o IOP here were many esimaion problems so hose resuls are no repored. The logisic TVTP also produced beer forecass for IOP han he exponenial specificaion. In he empirical analysis he one-sep ahead forecass produced by he models are examined. The Markov-swiching model s one-sep ahead forecass are calculaed as: yˆ + = { ( ) ˆ [ ( )] ˆ... µ ˆ S + + φ y µ ˆ S φ r [ y r+ µ ˆ( S r + )]} s + = 0s = 0 s r = 0 Pr[ S + (6) + = s +, S = s,..., S -r+ = s r+ Y, X ; θˆ] where Pr[ S,,...,, ; ˆ + = s+ S = s S-r+ = s r+ Y X θ ] is he one-sep ahead prediced probabiliy disribuion of saes condiional on Y and X which denoe he se of informaion available on he dependen variable and he leading indicaor respecively hrough o dae. This is also condiional on he vecor of esimaed parameers for he model, denoed by θˆ. An algorihm (deailed in Simpson e al., 999) is employed o selec he Hamilon fixed ransiion probabiliy (FTP) and he single indicaor TVTP models. Essenially, SIC is used o selec he auoregressive lag r of he FTP model. This value is hen assumed o apply for he TVTP specificaion. The TVTP leading indicaor lags of K and K 0 are specified by searching over all combinaions wihin ± 2 quarers around he lags seleced in he linear specificaion (2). Alhough esimaion over he full sample period caused few difficulies, he numerical algorihm someimes broke down during he re-esimaion process used o generae value forecass and he esimaion did no converge for a number of differen saring parameer values. Given ha one of he main aims of his paper is o assess predicive abiliy, hen when he model is no robus o recursive re-esimaion, he specificaion is hrown ou and he nex bes model seleced. The empirical resuls provide he values of AIC and SIC for each Markov-swiching specificaion, ogeher wih he probabiliy values for he Filardo Likelihood-Raio es for Specifically, exponenial TVTP models were esimaed using he reasury bill yield and he dividend yield as leading indicaors, over a range of lags K 0 and K. Generally, hese models were no robus o parameer grid search and ofen boundary values resuled for he ransiion probabiliies. 5

7 ime-variaion (L-R), along wih LM ess agains AR(4) (χ 2 AR[4]) and ARCH() (χ 2 HET[]) disurbances. As discussed under he resuls below, some wo indicaor TVTP models were also esimaed using lags derived from he seleced single indicaor specificaions. All models, including he linear ones, were esimaed in GAUSS using he non-linear BFGS opimisaion algorihm. DATA One hundred imes he logarihmic firs-difference of he seasonally adjused index of producion (IOP) is employed as he dependen variable, y. This is shown in Figure over he sample period of 955q2 o 998q. Figure : IOP Growh Percenage Growh Rae 7.5 Prod Prod_adj Year The IOP series appears o be quie noisy, even hough i is seasonally adjused and in quarerly form, wih here being a number of exreme observaions or ouliers in he series. The ouliers are idenified on he basis of ± 3 sandard deviaions from he mean value of IOP growh. An iniial invesigaion revealed ha hese irregular observaions had an adverse effec on he performance of he models. For example, boh linear and non-linear models exhibied significan ARCH effecs. In he case of he Markov-swiching models hey also appeared o be causing esimaion difficulies and someimes boundary values for he ransiion probabiliies, wih oulier observaions being classified as a separae regime 2. The 2 The inclusion of dummy variables in he swiching regression model in order o ry and capure hese ouliers did no appear o solve hese difficulies. 6

8 observaions idenified as ouliers relae o 972q2 and 974q-2. The decline in 972q2 appears o be due o a coal miner s srike and ha in 974q-2 appears o be he resul of he hree day working week (see he Naional Insiue Economic Review s Calendar of Economic Evens). Since hese exreme observaions do no appear o be associaed wih genuine regime-shifs, hey are removed by linear inerpolaion of he levels series (afer aking logarihms). In general, removing hese ouliers led o beer residual diagnosics for boh he linear and non-linear Markov-swiching models and improved esimaion sabiliy in he case of he TVTP specificaions. The adjused series (as a growh rae) is ploed in Figure, ogeher wih he unadjused series (doed line). Examining Figure, i can be seen ha here are hree major recessions (as described in Dow, 998) in IOP, wih he mos recen corresponding o he conracion. I is also eviden ha he downurn is less pronounced in erms of quarerly declines han he earlier conracions in IOP. For he leading indicaor series, we considered he componens of he composie longer leading indicaor formerly produced by Office for Naional Saisics 3. Aris e al. (995) found his composie indicaor o provide useful predicive informaion for he UK business cycle. However, of he componens, only he prime bank bills ineres rae (IR), housing sars (HS) and CBI change in opimism (CBIO) are available for a long hisorical period, so hese are he only componens of his index used in he presen sudy. In addiion, following he sylised facs analysis of Andreou e al. (999) we also analyse he performance of a number of financial variables in he UK for heir leading properies. These are he FT acuaries all share sock price index (SP), he dividend yield of his index (DY), M0 narrow money aggregae, he 3-monh reasury bill yield (TBY), a long rae (LR, daed as he 20 year yield on Briish governmen securiies) and he erm srucure (TS = LR TBY). These same leading indicaors are also analysed in our companion paper ha models GDP (Simpson e al., 999). For more deailed daa descripions including sample period, source and graphs see he Appendix. The indicaors SP, DY, HS and M0 are ransformed logarihmically prior o heir use in he analysis. Mos analysis is based on firs differences of he leading indicaors. All, wih he excepion of CBIO and TS, are judged o be inegraed o order one by convenional Dickey Fuller uni roo ess. The variables CBIO and TS are saionary according o he Dickey-Fuller ess, bu we invesigae he performance of he levels and firs differences of hese. 3 The Office for Naional Saisics ceased producing hese indicaors in

9 Prior o parameer esimaion, each leading indicaor is ransformed o have a zero mean and sandard deviaion of uniy over he sample period for which i is used. The longes sample period employed for he esimaion and specificaion of he models for IOP is 957q o 998q (afer allowing for differences and lagging of he daa). For specific sample periods available for each leading indicaor variable see he Appendix. The predicive performance of he models is hen examined over he period 990q o 998q, which is referred o as he forecas period. THE SELECTED MODELS In his secion, we deail he model specificaion and provide an overall view of he models whose forecas performance we laer examine. Seleced Lag Lenghs for Linear and TVTP Models The lag lenghs seleced for he univariae linear AR model and he Hamilon FTP model for IOP boh involve a single lag of he dependen variable, so ha r =. Table repors he seleced lags for each disinc leading indicaor in he single indicaor linear and TVTP * logisic specificaions. For he TVTP model, K is he lag chosen for expansion regimes and * K 0 for conracions. Table : Leading Indicaor Lags for IOP Variable Linear TVTP K * * K * K 0 M IR SP HS DY 3 3 TBY 5, LR Level TS Difference TS Level CBIO n/a n/a Difference CBIO I migh be noed ha, alhough he procedure allows for muliple lags in he linear specificaion, in pracice muliple lags are seleced only for he reasury bill yield. No lag 8

10 specificaion is included in Table for a TVTP specificaion using he level of CBIO because no saisfacory model could be found. Esimaion and Diagnosic Tes Resuls Firs of all we briefly examine he linear model esimaion and diagnosic es resuls presened in Table 2. The LM residual diagnosics for he linear univariae AR() specificaion do no show srong evidence of model mis-specificaion, alhough here is a hin of heeroscedasiciy and/or non-lineariy in ha he χ 2 HET[] and RESET p-values are around 0.. When he leading indicaors are inroduced, only he models involving M0 and housing sars are no chosen by SIC over he simple univariae AR() specificaion. On he basis of SIC (or AIC), he dividend yield (DY) is he bes leading indicaor. Also, he difference of he erm srucure is preferred over is level, bu for CBIO he level is preferred. RESET indicaes ha he specificaions wih a greaer RESET saisic p-value han he linear AR() model are perhaps capuring more of he non-lineariies in indusrial producion. Noice he very high RESET p-value for he level of CBI opimism balance (CBIO), suggesing no nonlineariies are presen in his specificaion. A variaion on he linear indicaor model was ried by adding furher indicaors. As he DY linear model has he lowes SIC hen each variable 4 was added in urn o his model creaing a linear model wih wo leading indicaors. Noe ha he variables were incorporaed a he lags seleced in he individual indicaor analysis. From Table 3 i may be seen ha he specificaion involving DY and TBY (wih only lag 5 and no 7, which becomes insignifican) is he bes wo-indicaor model according o SIC, and his is preferred over he model involving only DY. The second bes model, involving DY and CBIO, is also seleced over he DY specificaion. Since, compared wih he single indicaor models, adding eiher TBY or CBIO o DY leads o a preferred specificaion, a hree-indicaor wih hese variables is also presened in Table 3. Again he second lag of TBY appears o be redundan and he model wih one lag of each variable is he bes of hose considered according o SIC. Had model choice been based on AIC, hen his would again be he seleced linear specificaion. The hree-indicaor model in he final column of Table 3 implies a srong role for each in modelling indusrial producion. As anicipaed, increases in shor-erm ineres raes (measured as he reasury bill yield) imply declines in indusrial producion, wih increases in 4 M0 was no considered here due o is poor performance in he single indicaor invesigaion. IR was also no examined because i is similar o TBY and TBY has a lower SIC han IR. Similarly, for TS and CBIO, he difference and he level respecively are used since hese are he preferred specificaions for hese variables in Table. 9

11 he dividend yield having a similar effec; he lags on hese are 5 and 3 quarers respecively. The CBI measure of opimism has a posiive sign a a lag of one quarer. However, one ineresing inerpreaion of he resuls for his model is ha, a leas in relaion o movemens in indusrial producion, he opimism measure does no incorporae fully all known informaion since longer lags of financial variables reain imporan roles. I is also worhy of noe ha, alhough all our models mainain he auoregressive erm, his coefficien is no significan a he 5 percen level for he models including he CBIO level and his lack of significance is even more noable in he wo and hree-indicaor models including his variable. Thus, hese laer models appear o explain he univariae dynamics of IOP. The sign and significance of he inerceps for he Hamilon FTP model in Table 4 indicae classical business cycle behaviour. The daa can be classified ino posiive and negaive growh rae regimes, wih an inercep of.67 per quarer in regime (expansion) and -2.4 in regime 0 (conracion). These values indicae an asymmery, wih he implied rae of growh in conracions being on average subsanially greaer in absolue value han in expansions. The ransiion probabiliy esimaes also indicae an asymmery in he persisence of expansion and conracion regimes. The values for he consan expansion-o-expansion and recession-o-recession ransiion probabiliies imply ha on average he economy is more likely o remain in an expansion han in a recession phase of he cycle. Thus, he FTP model esimaes show conracions o be sharper and shorer han expansions. Similar asymmeries have been repored o be a feaure of monhly UK IOP by Aris e al. (997). The LM ess for firs-order heeroscedasiciy and fourh-order serial correlaion give no sign of model misspecificaion. Noe ha he model selecion crieria AIC and SIC canno be compared wih he linear AR specificaion as an indicaion of regime swiching non-lineariy because of he non-sandard esing condiions ha are involved (see Hamilon and Perez-Quiros, 996). The TVTP resuls for he single indicaor and wo cases wih wo indicaors are also shown in Table 4. The esimaes of he regime dependen inerceps associaed wih he TVTP logisic esimaions are saisically significan and again indicae classical business cycle behaviour in IOP. According o SIC, he difference of he erm srucure (TS) provides he bes single indicaor specificaion in his conex and has a lower SIC han he Hamilon FTP model. Alhough all he oher models have higher SIC han he FTP model, here is sill a fair amoun of suppor for ime-variaion. In paricular, AIC favours he TVTP specificaion for mos variables, while he Filardo Likelihood Raio (L-R) es for he null hypohesis of consan ransiion probabiliies produces probabiliy value of around 5% or less for a number of leading indicaors, providing addiional evidence in favour of ime variaion. The residual diagnosic ess are generally saisfacory. 0

12 The signs of he parameers across he various TVTP logisic specificaions appear o be generally economically sensible. Wih he single excepion of he specificaion using he level of he erm srucure, he sign of he esimae of β is he same as he sign of he slope coefficien in he corresponding linear model. Thus, during expansions, movemens in he leading indicaor have a similar inerpreaion in erms of direcion of change of IOP as in he linear case. For his inerpreaion o carry over o conracions, he sign of he esimae of β 0 should be opposie o ha of he linear model, and his is he case, excep for DY and (he firs difference of) CBIO. Their size and significance also sugges ha a number of variables provide differen amouns of informaion abou expansions and conracions. The mean of he expansion-o-expansion ransiion probabiliy (denoed by p and obained by seing he condiioning informaion o zero) is approximaely he same as ha of he FTP specificaion for all variables. On he oher hand, he mean of he recession-o-recession probabiliy someimes differs subsanially from ha of FTP. For example, he prime bank bills ineres rae (IR), his is.933 compared wih.706 for FTP. Thus, when no informaion is provided by IR (x = 0) here is on average a 93% chance of remaining in a recession regime. This probabiliy declines wih decreases in he ineres rae, and IOP is more likely o exi recession for larger ineres rae decreases. Two-indicaor TVTP models were also considered. Boh such models shown in Table 4 use IR as he leading indicaor during conracions (regime 0), since in erms boh of he magniude and significance of is esimaed slope coefficien β 0 his variable apparenly provides mos leading indicaor informaion in his regime. During expansions (regime ), he difference of TS and also housing sars (HS) are considered, he former having he larges and mos significan slope coefficien in ha regime wih he laer also having a highly significan coefficien. Due o esimaion difficulies encounered when he logisic TVTP specificaion involves a single slope coefficien wihin a regime, no aemp is made o add an addiional leading indicaor in he logisic funcion of (5). Neiher wo-indicaor TVTP specificaion is very successful. In boh cases, IR is insignifican in he recession probabiliies. Also, boh SIC and AIC sill poin o he singleindicaor difference TS model as he preferred TVTP specificaion. A few oher specificaions were also ried, bu yielded no improvemens on hose repored. Regime Classificaions As menioned in he Inroducion, one aracion of he use of Markov-swiching models in he analysis of business cycles is ha hey are capable of providing explici informaion abou he

13 regime. We illusrae he regime classificaion performance of our Markov-swiching models in Figure 2, where we show he filer probabiliies of regime 0 (recession) generaed from he FTP and he TVTP logisic models for each indicaor series, where he TS model uses he differences. These probabiliies are generaed from he esimaed models and employ all sample daa. The shaded areas in his figure (DRec) represen recessionary regimes for UK IOP as daed by Aris e al. (997). Hence, he shading provides some benchmark for he performance of he models of Table 4 in erms of capuring hisorical recessions. A few poins abou Figure 2 are worh noing. Firsly, alhough Aris e al. dae recessions around 967 and 97, neiher is well deeced by he models since he recession probabiliies generally do no exceed.5 during hese periods (apar from TBY briefly). This is paricularly rue for he laer recession. However, all Markov-swiching models capure he major recessions of he mid-970s and he early 980s. Many also provide some evidence of a mid-980s recession in IOP. However, he majoriy of models produce only a weak signal of a recession during Only he TVTP specificaion for prime bank ineres raes (IR) seem o provide a srong indicaion of a conracion during he 990s. The FTP model iself provides very lile evidence of his las recession. Essenially, he reason appears o be ha he wo-regime Markov-swiching models of Table 4 associae recession wih very srong quarerly declines in indusrial producion. Alhough he 990s recession evidenced a susained period of producion declines, i did no conain any single quarer wih a decline of he magniude seen in each of he hree previous IOP recessions (mid-970, early 980s and mid-980s). Indeed, if we accep he judgemen of Aris e al. (997) ha an indusrial producion recession occurred in he UK around 97, i is also clear from Figure ha his recession does no conain a quarer of large enough decline. This may also explain he failure of he Markov-swiching models o deec his earlier recession. In summary, he linear models esimaion and es resuls imply ha DY is he mos useful single indicaor variable for IOP. A combinaion of hree indicaors (DY, TBY and CBIO) achieves he lowes SIC of all linear models considered. The resuls of he Markovswiching esimaions lend suppor for classical cycles and cyclical asymmeries in IOP. The findings show suppor for ime-variaion beween business cycle phases. In paricular, ou of he indicaors considered he difference of he ineres rae erm srucure appears o perform well a fiing IOP growh. Overall, he univariae Hamilon model appears o require srong evidence of recession in he form of a sharp decline in order o provide reliable regime classificaion for indusrial producion. However, prime bank bills ineres raes appear o be useful in helping o classify he 990s recession. We anicipae ha his las finding will be refleced in improved value forecass over his period, which are deal wih in he nex secion. 2

14 Table 2: Linear Models for IOP wih one Leading Indicaor Leading Indicaors AR()* M0 IR SP HS DY TBY LR Level TS Diff TS Level CBIO Diff CBIO α.298 (.8).233 (.46).322 (.6).278 (.9).307 (.6).284 (.22).320 (.20).34 (.5).37 (.22).296 (.2).40 (.20).323 (.9) σ.403 (.069).45 (.092).358 (.07).334 (.075).385 (.07).329 (.076).325 (.074).357 (.07).37 (.074).362 (.073).342 (.07).368 (.072) φ.329 (.074).35 (.089).278 (.072).290 (.083).30 (.079).275 (.075).298 (.074).295 (.072).305 (.087).347 (.079).53 (.06).36 (.079) β (.28) (.097).486 (.5).227 (.07) (.04) -.38 (.03) (.098).304 (.9).33 (.08).542 (.45).374 (.08) β (.03) L T (θ) AIC SIC χ 2 AR[4] χ 2 HET[] RESET Noes : α is he inercep, σ is he sandard error of he regression and φ is he coefficien on he lag of producion. β i represens he coefficien on he i-h regressor (no he coefficien on he i-h lag, see Table for he appropriae lag). Sandard errors are given inside parenheses. L T (θ) is he sample condiional log-likelihood value (excluding he consan 2π erm). *Esimaed over he sample period saring in 960q2. 3

15 DY DY, SP DY, HS DY, TBY Table 3: Linear Models for IOP wih more han one Leading Indicaor DY, TBY Leading Indicaors DY, LR DY, TS DY, CBIO DY, CBIO, TBY () (2) () α (.22) (.24) (.2) (.7) (.7) (.2) (.9) (.9) (.5) σ (.076) (.090) (.077) (.075) (.075) (.076) (.077) (.076) (.078) φ (.075) (.090) (.082) (.072) (.072) (.075) (.085) (.04) (.04) β (.04) (.33) (.04) (.09) (.04) (.36) (.02) (.00) (.06) β (.46) (.5) (.05) (.04) (.37) (.8) (.43) (.42) β (.09) (.02) β (.09) DY, CBIO, TBY L T (θ) AIC SIC χ 2 AR[4] χ 2 HET[] RESET Noes : β represens he coefficien of DY a lag 3, β 2 represens he coefficien of he second variable wih lag lengh given in Table, β 3 represens he coefficien of he second lag of TBY when ha is included or he lag of he hird variable and β 4 represens he coefficien of he second lag of TBY. Sandard errors are given inside parenheses. All models are esimaed over he sample saring in 966q2. (2).35 (.5).228 (.075). (.00) -.4 (.00).406 (.38) (.0) -- 4

16 Table 4: FTP and TVTP Models for IOP FTP* M0 IR SP HS DY TBY LR Level TS Diff TS Diff TS, IR HS, IR CBIO µ 0 +µ.670 (.29).700 (.58).720 (.4).674 (.63).656 (.2).625 (.46).686 (.65).68 (.34).698 (.39).683 (.36).676 (.33).685 (.37).654 (.26) µ (.53) (.507) -.67 (.62) (.630) (.56) (.543) (.782) (.57) (.523) (.50) (.56) (.553) (.682) φ.206 (.066).207 (.086).92 (.064).23 (.073).62 (.07).275 (.077).202 (.068).205 (.066).254 (.066).242 (.065).23 (.07).244 (.065).68 (.070) σ.232 (.060).22 (.069).258 (.064).24 (.067).236 (.059).80 (.070).29 (.07).230 (.059).225 (.060).238 (.054).267 (.058).239 (.055).244 (.059) β (.454) (.660) (.378) (.703) 4.53 (.77) (.830) (.693) (.27) (.46) (.978) (.989) (.848) (.79) β (.67) -.95 (.89).78 (.58).300 (.40) (.532) (.838) (.853) (.9) (.447).69 (.488) (.435).26 (.427) β (.437).392 (.839) (.74).849 (.065).562 (.76) (.875).252 (.894).38 (.62).009 (.578).245 (.094) (.880).08 (.884).659 (.736) β (.84) (.899) (.9) -.0 (.84) (.975) (.0).89 (.646) (.593) (.22).26 (.965).393 (.93).347 (.088) p p L T (θ) AIC SIC L-R χ 2 AR[4] χ 2 HET[] Noes: β i and β 0i (i 0) correspond o he i-h regime and regime 0 TVTP leading indicaor coefficiens respecively (no he i-h lag, see Table for he appropriae lag). Sandard errors are given inside parenheses. L T (θ) is he sample condiional log-likelihood value (excluding he consan 2π erm). * Esimaed over he sample period saring in 960q2. TVTP 5

17 Figure 2: FTP and TVTPs Recession Probabiliies FTP DRec SP DRec M0 DRec HS DRec IR DRec DY DRec TBY DRec CBIO DRec LR DRec TS_IR DRec TS DRec HS_IR DRec

18 Table 5: Linear and Non-linear Models Forecas Resuls Linear Leading Indicaor AR()** M0 IR SP HS DY TBY LR Level TS Diff TS Level CBIO Diff CBIO MSFE Direcion-of-Change*: Toal 26/33 28/33 25/33 24/33 26/33 24/33 26/33 24/33 26/33 27/33 26/33 23/33 y 0 23/23 23/23 22/23 20/23 22/23 20/23 22/23 22/23 2/23 22/23 2/23 9/23 y<0 3/0 5/0 3/0 4/0 4/0 4/0 4/0 2/0 5/0 5/0 5/0 4/0 FTP** M0 IR SP HS DY TBY LR Level TS Diff TS Diff CBIO MSFE Direcion-of-Change*: Toal 24/33 23/33 26/33 26/33 25/33 25/33 26/33 26/33 23/33 23/33 23/33 y 0 23/23 23/23 23/23 22/23 22/23 23/23 23/23 22/23 23/23 23/23 23/23 y<0 /0 0/0 3/0 4/0 3/0 2/0 3/0 4/0 0/0 0/0 0/0 DY, CBIO DY, TBY () DY, TBY (2) TVTP More han one Leading Indicaor Linear Leading Indicaor DY, SP DY, HS DY, LR DY, TS DY, CBIO, TBY () DY, CBIO, TBY (2) MSFE Direcion-of-Change*: Toal 28/33 29/33 27/33 25/33 25/33 24/33 24/33 29/33 29/33 24/33 24/33 y 0 23/23 22/23 2/23 20/23 2/23 20/23 8/23 23/23 23/23 23/23 23/23 y<0 5/0 7/0 6/0 5/0 4/0 4/0 6/0 6/0 6/0 /0 /0 Noes: *The firs value gives he number of correc forecass and he second value gives he number of observaions. **Esimaed over he sample period saring in 960q2. TS, IR TVTP HS, IR 7

19 Figure 3: One-Sep Ahead Forecass ACTUAL FTP AR - ACTUAL DYTBCBIO DY_TBY ACTUAL TSTVTP TS - ACTUAL HS_IR TS_IR

20 FORECAST RESULTS In his secion he one-sep ahead forecass for indusrial producion growh of he linear and non-linear Markov-swiching regime specificaions are examined. The forecas period covers he las hiry hree quarers of he sample, 990q o 998q, which includes he conracion. I should be noed ha his is no a genuine pos-sample experimen, as he forecas period is included in he period used for model specificaion. The one-sep ahead value forecass are generaed recursively. Specifically, he forecas of he firs observaion in he forecas period, y 90q, is derived using parameer esimaes obained using daa up o 989q4. Subsequen forecass are calculaed by re-esimaing each model wih he new daa poin and hen forecasing he nex observaion. Several recen empirical sudies have indicaed ha he forecas performance of nonlinear regime-shif models depends on he regime in which he forecas was made, (see for example, Pesaran and Poer, 997, Clemens and Smih, 999, and Öcal and Osborn, 997). In paricular, non-linear models have generally shown beer forecasing performance during recessions han linear specificaions. Furher, Dacco and Sachell (999) show ha a nonlinear model wih a good in-sample fi may be ou-performed when is forecass are compared using mean square forecas error o a random walk due o he effecs of misclassificaion errors. Thus, evaluaing forecas performance in erms of he direcion of change for he dependen variable may be more informaive abou he predicive performance of regime dependen business cycle models han he magniude of he forecas error capured by he sandard forecas accuracy measures such as mean square forecas error (MSFE). The forecass here are firs evaluaed according o wo crieria, namely he MSFE and he direcion-of-change. The direcion of change resuls repored are he proporion of periods where posiive and negaive growh are correcly indicaed by he model s forecas (Toal), along wih he corresponding resuls when periods of posiive (y 0) and negaive acual (y < 0) growh are considered separaely. Table 5 provides he resuls for all models included in Tables 2, 3 and 4. Graphs of he forecass for some models are shown in Figure 3. Table 5 indicaes ha he Hamilon FTP model has a poor forecas performance compared o he univariae AR() model over his period, as i no only exhibis a higher MSFE bu i correcly predics he direcion of change for jus one of he en observaions for which y < 0, whereas he AR() correcly predics hree such observaions. However, he firs graph in Figure 3 indicaes ha boh ses of forecass are poor a predicing he pah of acual IOP, especially during he recession. This reinforces he preceding discussion of classificaion performance, which noed ha he FTP model fails o deec any change in regime during he 990s. 9

21 In erms of he MSFE crierion and considering linear models, he use of single leading indicaors (specifically IR, SP, DY, TBY, LR, ogeher wih boh TS specificaions and he level of CBIO) lead o more accurae forecass compared wih he AR() model. The direcion-of-change forecas resuls are more complex, wih he univariae model being relaively good for he oal because i never incorrecly forecass a decline in IOP. The leading indicaor specificaions ofen have a rade-off relaive o he AR(), wih poorer direcion-of-change forecass for periods of acual growh bu beer forecass of acual declines. Overall, he level of he CBI opimism balance appears o be he bes single indicaor linear model in erms of forecas accuracy over his period, wih he lowes MSFE and relaively good direcion of change resuls, correcly predicing half of he falls in IOP. Noe ha he single indicaor forecass using he level of TS, shown in he boom lef-hand panel of Figure 3, forecass he deph of he recession very successfully. Neverheless, we should also bear in mind ha he preferred linear specificaion above was argued o be he hree-indicaor model wih a single lag of DY, CBIO (level) and TBY. I is impressive ha Table 5 shows his o also be he mos accurae specificaion in erms of MSFE in his forecasing conex. Furher, i yields he equal bes overall direcionof-change score, alhough i is marginally beaen by he firs wo-indicaor wih DY and TBY models for periods of decline alone. The forecass for he muliple indicaor models also appear o capure he deph of he recession as illusraed in Figure 3 (upper righ-hand panel) for models of DY wih TBY and hen combining DY, TBY and he level of CBIO. In comparison o hese linear leading indicaor models, he TVTP logisic ones produce disappoining IOP forecass over his period. This is rue even if he comparison is confined o single indicaor specificaions for he linear case. The TVTP models for IR, SP, HS, DY, TBY and LR have beer MSFE values han ha of he FTP model, and generally an improvemen of he direcion-of-change as well. However, hese non-linear models are almos always inferior in forecasing according o MSFE compared o he corresponding linear model, and (perhaps more surprisingly) his is ofen rue by direcion-of-change oo. The use of wo indicaors in he TVTP framework makes maers worse, wih heir poor performance in forecasing he recession shown by he lower righ-hand graph of Figure 3. In Table 5 and also in Figure 3 (see he illusraive comparison of forecass using he level of TS), here is lile evidence ha Markov-swiching models perform beer in forecasing he 990s recession for producion han linear specificaions. 20

22 CONCLUSIONS This paper se ou o examine he informaion available from leading indicaors in he conex of forecasing UK indusrial producion growh over he business cycle. The resuls obained from he seleced linear specificaion, which includes hree leading indicaors, is promising. This model no only suggess ha financial variables (shor-erm ineres raes and he dividend yield of he sock marke) can play an imporan role in forecasing he real economy, bu also ha business opimism may no fully ake accoun of he informaion in hese variables. A leas wih he benefi of hindsigh, we can conclude ha he 990s recession in UK indusrial producion could have been foreseen. Less posiive resuls are, however, obained abou he usefulness of non-linear Markov-swiching models in his conex. This is surprising in ha our companion paper (Simpson e al., 999) finds hese models o ouperform linear specificaions over a similar period when forecasing UK gross domesic produc. Alhough we can only speculae on he reasons for his, he source could lie in he naure of he 990s recession for indusrial producion compared wih earlier episodes. In paricular, as we have noed above, on he basis of he evidence presened in he wo-regime Markov-swiching model, i appears o associae one regime wih very sharp declines in indusrial producion, and he 990s recession never winessed such a decline in any one quarer. While his is also rue o some exen for GDP, he 990s recession in ha case is no as dissimilar o earlier ones as in he case of indusrial producion. In oher words, he roo cause could be regime classificaion errors, which Dacco and Sachell (999) show can lead o poor forecass for regime-swiching models. Alhough his suggess a possible explanaion, i does no immediaely poin o how hese models should be developed o recognise he recession suffered by UK indusrial producion during he early 990s. 2

23 Daa Appendix Table A: Daa descripions wih source and sample period Variable Full Name Sample Source/ code SA or NSA* IOP Index of producion (990=00) 55q 98q2 ONS/ DVZI SA 57q 97q ONS/ DKDH SA IR 3 monh prime bank bills 97q2 98q3 Daasream/ SA (period average) UK3MTHINE 59q - 7q4 ONS/ DKDK SA CBIO** CBI Change in Opimism 72q 98q4 Daasream/ UKCBIOMB NSA HS Housing Sars 57q 98q ONS/ CTOZ SA SP DY FT acuaries all share index (0 April 962=00) FT acuaries all share index: dividend yield % 63q 98q3 ONS/ AJMA NSA 63q 98q3 ONS/ AJMD NSA TBY Treasury Bills 3 monh yield 60q2 98q3 ONS/ AJRP NSA LR Briish Governmen Securiies: long-daed (20 years): Par yield - % per annum 57q 98q3 ONS/ AJLX NSA TS Term Srucure 60q2 98q3 LR - TBY NSA M0 Noes and coins in circulaion plus sigh deposis 69q2 98q3 ONS/ AVAE SA * SA = Seasonally Adjused and NSA = No Seasonally Adjused. ** The CBI Indusrial Trend Survey was only conduced hree imes a year beween 959 and 97 and he ONS have inerpolaed hese values o give a quarerly series before seasonally adjusing i wih X-. Afer his he auhor uses a regression wih seasonal dummies o seasonally adjus he daa. 22

24 ACKNOWLEDGEMENTS Financial suppor from he UK Economic and Social Research Council under gran R is graefully acknowledged. We would like o hank seminar paricipans a he Bank of England and he Sockholm School of Economics for heir helpful commens. REFERENCES Akaike H Informaion Theory and an Exension of he Maximum Likelihood Principle. In 2nd Inernaional Symposium on Informaion Theory, Perov B and Csake F (eds.); Akademiai Kiado: Budapes. Andreou E, Osborn DR and Sensier M A Comparison of he Saisical Properies of Financial Variables in he USA, UK and Germany over he Business Cycle. School of Economic Sudies Discussion Paper Series, Universiy of Mancheser No Forhcoming in The Mancheser School. Aris, MJ, Bladen-Hovell RC, Osborn DR, Smih G and Zhang WD Turning poin predicion for he UK using CSO leading indicaors. Oxford Economic Papers 47: Aris MJ, Konolemis Z and Osborn DR Business Cycles for G7 and European Counries. Journal of Business 70: Breusch T Tesing for Auocorrelaion in Dynamic Linear Models. Ausralian Economic Papers 7: Clemens MP and Smih JP A Mone Carlo Sudy of he Forecasing Performance of Empirical SETAR Models. Journal of Applied Economerics 4: Dacco R. and Sachell S Why do Regime-swiching Models Forecas so Badly? Journal of Forecasing 8: -6. Dow C Major Recessions: Briain and he World, Oxford: Oxford Universiy Press. Driffill J and Sola M Inrinsic Bubbles and Regime Swiching. Journal of Moneary Economics 42: Engle RF A General Approach o Lagrange Muliplier Model Diagnosics. Journal of Economerics 20: Filardo AJ Business Cycle Phases and Their Transiional Dynamics. Journal of Business and Economic Saisics 2:

25 Hamilon JD A New Approach o he Economic Analysis of Nonsaionary Time Series and he Business Cycle. Economerica 57: Hamilon JD and Perez-Quiros G Wha Do he Leading Indicaors Lead? Journal of Business 69: Hess, GD and Iwaa S 997. Measuring and comparing business-cycle feaures. Journal of Business and Economic Saisics 5: Moore, B 993. A review of CSO cyclical indicaors. Economic Trends no. 477 (July): Öcal N and Osborn DR Business Cycle Nonlineariies in UK Consumpion and Producion. School of Economic Sudies Discussion Paper Series, Universiy of Mancheser No.970. Forhcoming in Journal of Applied Economerics. Osborn DR and Öcal N Leading Indicaors, Nonlinear Models and Forecass for UK Macroeconomic Variables. Universiy of Mancheser mimeo. Pesaran MH and Poer SM A Floor Ceiling Model of US Oupu. Journal of Economics Dynamics and Conrol 2: Ramsey JB Classical model selecion hrough specificaion error ess. In Froniers in Economerics, Chaper Zarembka P (ed.); Academic Press: New York. Ramsey JB If nonlinear models canno forecas, wha use are hey? Sudies in Nonlinear Dynamics and Economerics : Schwarz G Esimaing he Dimensions of a Model. Annals of Saisics 6: Simpson PW, Osborn DR and Sensier M Modelling Business Cycle Movemens in he UK Economy. School of Economic Sudies Discussion Paper Series, Universiy of Mancheser, No Teräsvira T and Anderson HM Characerising Nonlineariies in Business Cycles Using Smooh Transiion Auoregressive Models. Journal of Applied Economerics 7: S9- S36. Tiao GC and Tsay RS Some Advances in Non-Linear and Adapive Modelling in Time Series. Journal of Forecasing 3:

26 Auhors Biographies: Paul Simpson has recenly compleed a PhD in economerics a he Universiy of Mancheser. He is now working as a Saisician for he Deparmen for Educaion and Employmen in Sheffield. Denise Osborn is Professor of Economerics a he Universiy of Mancheser. Her primary ineress are he ime series analysis of macroeconomic ime series, wih recen work focusing on non-linear business cycle models and he role of financial variables. Marianne Sensier is a Research Associae a Universiy of Mancheser. Research ineress include business cycle asymmeries and financial economerics. 25