PROJECTING ECONOMIC ACTIVITY AT THE STATE

Transcription

1 FORECASTING STATE LEVEL ECONOMIC ACTIVITY: AN ERROR CORRECTION MODEL WITH EXOGENOUS NATIONAL STRUCTURAL FORECAST COMPONENTS Michael Hicks, Ball Sae Universiy* INTRODUCTION PROJECTING ECONOMIC ACTIVITY AT THE STATE and subsae level is an area of considerable ineres o policymakers. The use of economic forecass for budge preparaion, economic developmen, and workforce invesmen planning effors consiue jus a few of he applicaions of formal economic modeling in regions. While many sae governmens mainain economic forecasing capaciy, few subsae regions ouside very large meropolian areas reain a forecasing capaciy. Furher, here are a number of saes where he forecasing of economic aciviy is ousourced from he execuive branch o universiies and privae secor forecasing firms. The U.S. Deparmen of Labor also provides some limied labor marke forecass hrough sae agencies as a par of he Labor Marke Informaion programs. 1 Despie he abundance of forecasing ools ha have been developed over he pas wo decades, significan demand for low cos, sae, and subsae economic forecass remains srong. This paper develops a mehod for projecing sae and subsae economic aciviy by combining large-scale srucural models wih low cos, flexible bu accurae vecor error correcion models. The emphasis of his work is in he pracical naure of he forecasing model. I proceed wih an explanaion of he modeling process, wih a brief descripion of he naional forecas model I employ. I hen ouline he error correcion model (ECM) wih exogenous variables, is srucure, and economeric consideraions. I conclude wih several forecas performance merics and a summary of he paper. THE NATIONAL MODEL Several high-qualiy naional forecass currenly exis. These include he well-known commercial models offered by Global Insigh and Sandard * I would like o hank paricipans of he 62 nd annual conference of he Associaion of Universiy Business and Economic Research, session on Forecas Model Performance, especially Gary Horvah, Marin Shields and David Keyser. and Poor s, as well as academic models such as he well respeced FAIRMODEL produced by Yale Universiy s professor Ray Fair. I employ he FAIRMODEL for my esimaes. Researchers in saes or regions wih access o commercial models, or locally produced models may op o use hese models. The procedures I describe here are largely invarian o he choice of exogenous variables employed in he ECM model of saes and regions. The FAIRMODEL is a solid choice as a naional forecas model for sae and local predicions for hree reasons. Firs, i is provided as a free model. The ease of downloading and applicaion is superb. Second, i enjoys a long hisory of accurae naional forecass. I has been widely used in research and forecasing seings, and remains he mos respeced privae forecas model. Finally, he model permis significan flexibiliy in assumpions. For example, here are five moneary policy assumpions which may be employed in he forecas. 2 The FAIRMODEL hen seems a logical approach under a common cos funcion crierion for predicion models. This is paricularly rue where he forecas for sae and local public policy acs as an economic baseline raher han as a budgeary ool. The model resuls I display in a laer secion sugges i also performs well on oher crierion as well. The FAIRMODEL employs a 30-equaion sochasic represenaion of he U.S. economy which is frequenly recalibraed. The model uses a 2SLS esimaion procedure, wih over 100 ideniies, and hus a significan choice in poenial variables for use a he sae and local area. The model has provided 98 separae forecass since is incepion, wih a mean absolue error of 1.07 percen across all prediced variables. The mos recen published forecas error for gross domesic produc (GDP) growh is displayed in Table 1. THE VECM MODEL The choice of a vecor error correcion model (VECM) for sae level forecass provides a 223

2 NATIONAL TAX ASSOCIATION PROCEEDINGS Table 1 Forecas Performance of FAIRMODEL, U.S. GDP Growh 2006:Q2 2006:Q3 2006:Q4 2007:Q1 2007:Q2 2007:Q3 2007:Q4 2008:Q1 2008:Q2 2008:Q3 Acual :Q :Q :Q :Q :Q :Q :Q :Q Source: Fair (2008, Table 4). relaively sraighforward plaform. Suppose he following vecor auoregression represenaion: Y = ΦY + e, where he lagged endogenous variables include an as ye unspecified number of lags, which are referred o predeermined variables. Obaining firs differences of his represenaion provides us wih: Y Y = Φ (Y Y )e, in which he as ye undeermined number of lags are of he firs differences of he endogenous variables. This model is now inegraed by an order, or I(1). This sep is necessary o laer consruc he error correcion model, bu a common approach a his juncure is o es hese series for non-saionariy. If he imes series are no saionary wih I(1), he series will require subsequen differencing o consruc a saionary ime series from which o forecas. 3 While i is no uncommon for ime series o require higher order inegraion prior o obaining a uni roo, he ypes of series employed in sae and local forecas models will ypically be I(1). 4 We seek for our forecas a coinegraing equaion(s) for he variables Y in he VAR represenaion above. A coinegraing equaion is a linear combinaion of wo or more equaions which may consis of a consan, rend, and error componen. Before describing in some echnical deail he coinegraing equaion, i is helpful o review he economic explanaion for he equaion and is use. The presence of nonsaionary variables imposes a real consrain on he forecaser. The absence of a uni roo suggess ha resuls from a direc modeling effor will yield a spurious regression. Differencing hese variables o I(1) or greaer, while providing a series ha is saionary (possesses a uni roo) will resul in significan losses in economic informaion. This is paricularly rue regarding a long-erm equilibrium condiion beween he variables of ineres (say inpus and oupus). The relaionship may be reesablished hrough he use of anoher equaion ha oulines equilibrium relaionships beween he ime series. This equilibrium equaion can include a sochasic elemen. For a forecaser, his offers an especially useful represenaion, since i offers boh a racable economeric model and an aracive economic explanaion based on economic heory. Wha remains is in evaluaing and esing he number and ype of coinegraing relaionships. If here are z equaions in he VAR represenaion, and he coinegraing rank of he VAR is p, here are up o z-p linear combinaions of he variables, which are referred o as coinegraing equaions. Also, p z-1. A shorcu o esimaing he coinegraing rank is possible hrough simple hypohesis es of z-1 coinegraing equaions. Coinegraing equaions which do no exhibi significance in a sandard -es should be discarded. This should be cauioned agains in some seings, bu in sae or local forecass of economic aciviy, he poenial error would seem miniscule relaive o he cos. The specificaion choice for a coinegraing equaion includes a consan, rend, and exogenous 224

3 variables. Suppose wo variables share a common rend and inercep hen: y y + e z z + e. Then he coinegraing relaionship can be consruced as: z w + e y + Πe, where Π is referred o as he coinegraing vecor. The single equaion exrac of he error correcion model akes he form: Δy Δ Π Π e, which is he I(1) VAR represenaion wih he coinegraing equaion for variable z represened by he coinegraing relaionship and he VAR consruc. The inclusion of exogenous variables ino his relaionship does no aler he esimaion process unless hey comprise a componen of he coinegraing equaion. In pracice I have no observed exogenous variables as par of he coinegraing equaion in regional forecasing models. Touched briefly on, bu lef unanswered as ye is he deerminaion of he opimal lag lengh selecion for Φ(ΔY ). The mos common approach is o employ an informaion crierion selecion process. The Akaike Informaion Crierion or Schwarz- Bayesian mehods are commonly employed. 5 Tesing various lag lenghs and choosing ha which minimizes he informaion crierion is he usual echnique. This leaves us wih a single represenaive model. The model we consruc employs quarerly sae daa from 1990 hrough he second quarer The series we forecas are real personal income, earnings a place of work, and earnings in he manufacuring, wholesale, reail, consrucion, finance, informaion, and healh care secors. We employ naional GDP as he exogenous variable, using hisory and forecass from he FAIRMOD- EL s 2 nd quarer 2008 forecas. All variables were differenced and we were unable o rejec a uni roo a he 1 percen level for he I(1) series using he augmened Dickey-Fuller es. We assumed iniially eigh coinegraing equaions, bu rejeced wo, leaving us wih eigh coinegraing vecors. We included boh an inercep and rend, bu no exogenous variables in he coinegraing equaion. The opimal lag lenghs were generaed for he enire VECM by minimizing he Akaike Informaion Crierion. In Table 2 hese diagnosics offer mixed resuls for his model, bu are srikingly similar o resuls obained in oher similar modeling effors employing ECM wih exogenous variables. Imporanly, sample model performance does no include he sandard for forecasing models. Raher, sample predicive abiliy should have he objecive of forecasing. To evaluae his, we now urn our aenion o model performance on earlier esimaes of his ype of model. MODEL PERFORMANCE I have prepared four separae forecass of sae level economic aciviy using his approach wo in Wes Virginia, and wo in Indiana. The Wes Virginia models are derived from he Wes Virginia Economeric Model (Hicks and Simpson, 1999) and consis of a draf wih es diagnosics and a populaion forecas model. The ou-of-sample performance of each are repored in Table 3. Table 2 Seleced Model Diagnosics PI Earnings Manufac Whole Reail Finance Inform Consr Healh Log likelihood Akaike AIC Schwarz SC Mean dependen S.D. dependen saisic on Exogenous variable (U.S. GDP)

4 NATIONAL TAX ASSOCIATION PROCEEDINGS Table 3 The Wes Virginia Economeric Model, ou-of-sample performance Bea Tes Resuls: percenage error in ou-of-sample forecass of employmen levels Non- Farm Employmen Con Man Non- Durable Goods Durable Goods TCPU Wholesale Trade Reail Trade FIRE Unemploymen Rae 1998:1-0.54% -1.62% -3.06% -3.41% -2.54% -1.37% -1.23% -0.22% 0.51% 24% 1998:2 1.14% 3.99% 0.23% 0.67% -0.36% -0.23% 2.35% 0.26% -0.67% 26.84% 1998:3 0.82% -1.11% 0.64% 1.30% -0.32% 0.20% -0.07% 0.77% 0.12% -2.11% 1998:4-0.99% 0.52% -4.68% -5.82% -2.97% -1.34% -0.47% -0.83% -1.42% 38.52% 1999:1 0.19% -0.22% 0.21% 0.15% 0.29% -0.38% -0.48% 0.20% -3.23% 27.40% 1999:2 1.70% 6.77% -2.36% -3.33% -0.95% 2.56% 0.88% -0.19% 0.14% 25.20% 1999:3 1.92% -0.91% -0.17% -0.13% -0.23% 0.77% 0.54% 0.77% -0.10% 19.90% Average 0.61% 1.06% -1.31% -1.51% -1.01% 0.03% 0.22% 0.11% -0.67% 22.79% Table 4 Wes Virginia Economeric Model Populaion Forecas, % 1.17% 1.01% 0.83% 0.88% 0.76% Acual populaion forecas performance is available from his model, as he resul of a long-erm forecas performed in These resuls appear in Table 4. Our experience in Indiana includes he annual Indiana Labor Marke Forecas, which began in This forecas employs daa from he Quarerly Workforce Indicaors ino a ime-series model of employmen dynamics. The four quarers of experience we have esablished yield robus model performance resuls in wha are among he mos volaile economic variables o forecas. See Table 5. These resuls offer a much more hopeful prognosis of his approach. One addiional esimae is an ou-of-sample predicion of he Indiana model Table 5 Indiana Labor Marke Forecas Performance Employmen New Hires 2006:Q3-0.04% 3.52% 2006:Q4-0.11% 8.46% 2007:Q1-0.57% 1.34% 2007:Q2 0.36% 4.86% deailed in he secion above. This model performance was compared o he resuls of an official sae level forecas in Indiana. See Table 6. SUMMARY This paper oulines a racable, low-cos modeling hybrid for sae and local economic forecasing. The model relies on an exernal forecas o develop exogenous variables for an error correcion model. We hen deail he developmen of he ECM, diagnosics for model specificaion, and finally an example model of Indiana. We also include model performance for four of hese models (wo in Wes Virginia and wo in Indiana). We also compare hese o a Sae Budge Agency forecas in Indiana. The VECM models offered superb overall forecasing performance in a series of ou-ofsample forecas comparisons. In personal income esimaes, in Wes Virginia, over six quarers from he average error was percen. Populaion esimaes from 2001 hrough 2006 a he aggregae sae level yielded an average error of 0.98 percen. The model applied o he Sae of Indiana showed a 4-quarer error of.09 percen in employmen and only 4.55 percen in he highly 226

5 Table 6 ECM vs. Sae Budge Agency 2007:1 o 2008:2 ECM SBA GDP Acual Forecas MAD Forecas MAD 2007:Q % 13, % 2007:Q % 13, % 2007:Q % 13, % 2007:Q % 14, % 2008:Q % 14, % Average Error 0.62% Average Error 0.75% ECM SBA Personal Income Acual Forecas MAD Forecas MAD 2007:Q1 11,451,855 11,382, % 11, % 2007:Q2 11,568,700 11,543, % 11, % 2007:Q3 11,722,750 11,712, % 11, % 2007:Q4 11,867,043 11,854, % 11, % 2008:Q1 12,002,122 12,011, % 11, % Average Error -0.16% Average Error -1.26% volaile new hire series from he Quarerly Workforce Indicaors series. As a comparison of his model agains official sae forecass, he VECM error was only 82.7 percen of he official sae forecas, wih an aggregae error over six quarers of 0.62 percen for Sae GDP. Sae Personal Income was also forecas during he same period, wih an error only 12.7 percen of he official forecas. The resuls of hese models are promising for sae and local economic forecass. The echniques employed here are no new, bu heir applicaion o he very real problem of imely and accurae lowcos forecass for sae and local policymakers is rare. Noes 1 See for example he LMI daa a Indiana s Division of Workforce Developmen. 2 The complee reference is available a Fair (2004). The enire model in elecronic form, deailed appendices and daa, an analysis of model performance and oher reference maerial is available a hp://fairmodel.econ. yale.edu/. 3 The saionariy es mos commonly available in sofware packages is he Augmened Dickey-Fuller es. Some packages also include he Phillips-Peron es. See Greene (2003). 4 These variables are likely o include employmen, personal income, sae GDP, unemploymen raes and earnings by indusry. Many of hese will be saionary in levels, especially in slower growing regions. However he firs differencing of hese variables, while no necessary, is a commonly applied approach, and consisen wih he inen of he error correcion model. 5 Akaike (1974) and Schwarz (1978). References Akaike, Hirougu. A new look a he saisical model idenificaion. IEEE Transacions on Auomaic Conrol 19 (1974): Fair, Ray. Esimaing How he Macroeconomy Works. Cambridge, MA: Harvard Universiy Press, The Forecasing Record of he U.S. Model. New Haven, CT: Yale Universiy, Greene, William. Economeric Analysis, 5 rd ed. Upper Saddle River, NJ: Prenice Hall, Hicks, Michael and Marc Simpson. The Wes Virginia Economeric Model. Huningon, WV: Marshall Universiy, Schwarz, Gideon. Esimaing he Dimension of a Model. Annals of Saisics 6 (1978):