The relation between U.S. money growth and inflation: evidence from a band pass filter. Abstract

Transcription

1 The relaion beween U.S. money growh and inflaion: evidence from a band pass filer Gary Shelley Dep. of Economics Finance; Eas Tennessee Sae Universiy Frederick Wallace Dep. of Managemen Markeing; Prairie View AMUniversiy Absrac Chrisiano and Fizgerald () found a significan, posiive correlaion beween M money growh and CPI inflaion in all examined frequency bands for he U.S. prior o 9. However, for pos 9 daa, hey found a posiive correlaion only in he frequency band corresponding o cycles of years. Using heir filer, we verify his resul and exend he pre 9 sample o include he moneary base and inflaion calculaed from he GDP deflaor. In addiion, we exend heir pos 9 analysis o include growh in he moneary base, M, and M. A srongly posiive correlaion beween pos 9 money growh and inflaion exis only for he broad money aggregaes and wihin he year frequency band. Ciaion: Shelley, Gary and Frederick Wallace, () "The relaion beween U.S. money growh and inflaion: evidence from a band pass filer." Economics Bullein, Vol., No. 8 pp. Submied: March,. Acceped: Sepember,. URL: hp:// EA.pdf

2 . Moivaion and Mehodology As a pracical applicaion of heir band pass filer, Chrisiano and Fizgerald (), examined cycles in Unied Saes M money growh and CPI inflaion ha fall ino frequency bands corresponding o -8 years (business cycle frequencies), 8- years (long run frequencies), and - years (very long run frequencies). Using annual daa for he period from 9 hrough 9, hey find ha he correlaions beween componens of money growh and inflaion are significanly posiive and ha he correlaion increases as one moves from he business cycle o lower frequency bands. However, he resuls are markedly differen when hey examine daa from 9 hrough 997. For his daa sample, hey find ha he correlaions beween filered money growh and CPI inflaion are negaive in boh he business cycle and he long run frequency bands. A significan, posiive correlaion beween money growh and inflaion is found only for he very long run frequency band. The Chrisiano and Fizgerald resuls sugges ha a significan change has occurred in he relaionship beween money growh and inflaion. Their finding implies ha Milon Friedman s (98) famous saemen ha inflaion is always and everywhere a moneary phenomenon now may be valid only in he very long run. Given he poenial imporance (and possibly conroversial naure) of heir resuls, we seek o verify heir findings for he U.S. using a slighly differen daa se, and hen exend heir analysis by including oher money aggregaes and inflaion as measured by he GDP deflaor. The Chrisiano and Fizgerald band pass filer (hereafer denoed as he CF filer) provides a mehod for examining cyclical componens of a ime series ha move in differen frequency bands. For example, suppose one wans o sudy he cycles in an economic ime series, {x }, ha correspond o business cycle frequencies of -8 years. There exiss an orhogonal decomposiion: x = y + ~ x, () where he y componen has power only in he business cycle frequencies and he x~ componen has no power wihin hese frequencies. The y series hen is he cyclical componen of x of ineres. Chrisiano and Fizgerald show ha he y componen can be esimaed in he frequency domain by minimizing he condiional expeced mean squared error: Min : E[( y yˆ ) { x }]. () The CF filer is referred o as a band pass filer because he x~ componen is allowed o pass hrough he filer leaving only an esimae, ŷ, of he componen ha has power wihin he frequency band of ineres. In his paper, if x is a money growh (or inflaion) series, hen we will refer o he esimaed ŷ series as filered money growh (or filered inflaion). The CF filer is no limied o exracing he componen of a series corresponding o he business cycle frequencies, alhough i handles his ask quie well. The filer is paricularly useful for examining he longer erm, or lower frequency, componens of an economic series. Analysis of he long run componens of an economic series is no possible using he earlier Hodrick-Presco (997), or HP, filer. The HP filer is bes inerpreed as a high-pass filer isolaing frequencies of 8 years and higher in economic daa and is no inended for frequencies Long run and very long run are used in his paper o characerize hese frequency bands. This erminology was no used in he CF paper. Programs for esimaing he filered series using a variey of saisical sofware are available a he homepages of boh Chrisiano and Fizgerald.

3 falling ino oher bands. In addiion, adjusmens for handling annual, quarerly, and monhly daa are quie simple wih he CF filer, ye are problemaic for he HP filer. Finally, Chrisiano and Fizgerald find ha heir filer dominaes he Baxer-King (999) version of a band pass filer (referred o as he BK filer) in erms of heir opimaliy crierion, paricularly when examining bands of lower frequency han he business cycle. One reason for is dominance is ha he CF filer uses all observaions of a series while he BK filer does no. The CF filer hus provides a useful framework for sudy of he long run relaionships beween economic series.. Daa and Resuls We firs seek o verify Chrisiano and Fizgerald s finding ha here is a posiive correlaion beween M money growh and CPI inflaion for pre-9 U.S. daa. We exend heir examinaion of he pre-9 era by also looking a growh in narrow money as measured by he moneary base (MB) and by examining inflaion measured by growh in he GDP deflaor. Annual CPI daa are obained from he Bureau of Labor Saisics web sie. Annual MB and M are he money series used by Coe and Nason () in heir es for he long run neuraliy of money. The GDP deflaor was obained from Johnson and Williamson (). In all cases, growh raes refer o he log-differenced series. Using daa from 9 hrough 9, we separae he growh raes of narrow money (MB), broad money (M), and he wo price indexes ino he hree ses of frequency bands used by Chrisiano and Fizgerald. Resuls from he CF band pass filer using he 9-9 annual money and CPI inflaion daa are presened in Panel. Resuls using M as he money measure are shown in he column of graphs on he lef, while resuls using he moneary base are displayed in he column of graphs o he righ. In each case, he op row of graphs shows he business cycle componen of each series. The middle row of graphs displays he long run componens, while he boom row shows he very long run componens. Resuls using he percenage change in he GDP deflaor as he measure of inflaion are presened in he same manner in Panel. In boh panels, money growh and inflaion appear o move ogeher in all frequency bands, wih he co-movemen especially sriking for he 8- year (long run) and - year (very long run) frequency bands. This observaion is confirmed by he conemporaneous correlaions beween filered money growh and inflaion in each frequency band provided in Table I. Each correlaion is posiive and mos are larger han.. Furher he correlaions of M growh and inflaion move closer o uniy as he frequency diminishes. The correlaion beween growh in he moneary base and inflaion is somewha sronger a he long run frequency han a he very long run frequency, alhough he differences in he correlaions are no large. These resuls suppor he finding of Chrisiano and Fizgerald for he pre-9 period. We nex examine money growh and inflaion for he period 99-. We exend he analysis of Chrisiano and Fizgerald by including hree addiional money measures, he moneary base (MB), M, and M. Again inflaion is measured as log differenced growh raes in boh he CPI and he GDP deflaor. For his analysis, monhly money growh is mached wih he monhly growh rae of he CPI. Similarly, we mach quarerly money growh wih quarerly growh in he GDP Deflaor. Daa series are from he Federal Reserve Bank of S. Louis. The filered, monhly narrow money growh and CPI inflaion series are presened in Panel. Resuls for MB are presened in he lef column of graphs, and resuls for M are presened in he righ column of graphs. Filered broad money growh and CPI inflaion are presened in Panel, wih resuls using M growh displayed on he lef hand side of he page and resuls using M We are graeful o Coe and Nason for providing heir daa series.

4 displayed on he righ. In each panel, he business cycle componens, long run componens, and very long run componens are presened in each successive row of graphs. Inspecion of Panels and reveals no apparen posiive co-movemen beween filered CPI inflaion and money growh (eiher narrow or broad) in he -8 year or 8- year frequency bands. Thus, he moneyinflaion relaionship a -8 and 8- year frequencies differs sharply wih ha observed for he 9-9 period. No only do he resuls differ from he earlier period, bu here are negaive correlaions beween he business cycle and long run componens of money growh and inflaion as displayed in Table II. A business cycle frequencies, for example, M growh and inflaion as measured by he CPI have a correlaion of -.8 for he 99- period compared wih a correlaion of. for hese wo variables prior o 9. The very long run ( o year) posiive relaion beween money growh and inflaion sill appears o hold in his sample for MB, M, and M; bu, ineresingly, no for M The filered quarerly money growh and GDP deflaor inflaion series are presened in Panels and, wih he graphs arranged in he same manner as in he wo preceding panels. Similar o our findings for he monhly series, here is no apparen posiive co-movemen beween money growh and inflaion in eiher he -8 or 8- year frequency bands. In his case he only srongly posiive relaion beween he ploed filered series is for broad money growh and inflaion in he - year frequency band. As before, hese observaions are confirmed by he correlaions beween he filered series (presened in Table III). All bu one of he correlaions beween money growh and inflaion in he -8 and 8- year frequencies are negaive for he 99- period, and he single posiive correlaion is small. A srong, posiive correlaion beween money growh and inflaion is found only for M and M and only in he very long run, - year, frequency band. Surprisingly, he srong correlaion (.8) beween base money growh and CPI inflaion weakens considerably (.) when he deflaor is used o measure inflaion.. Conclusions We have verified Chrisiano and Fizgerald s resul ha a srong posiive correlaion beween M growh and CPI inflaion exised prior o 9 in all examined frequency bands. This resul is robus for a narrow money measure and for inflaion measured by he GDP implici price deflaor. Their finding ha he posiive relaion beween M growh and CPI inflaion in he -8 and 8- year frequency bands disappears afer 9 in he US is also confirmed. Exending he sudy o include he MB, M, and M money aggregaes and he GDP deflaor as a price index, we find ha he posiive relaion beween money growh and inflaion of he earlier period no longer holds in he business cycle and long run frequency bands for hese addiional series during 99-. Resuls sugges ha a srong, posiive correlaion beween money growh and inflaion sill exiss only for broadly defined money (M and M) and only for he very long run frequency band of - years. Two quesions are raised by his sudy. Firs, is he apparen breakdown in he relaion beween money growh and inflaion limied o he Unied Saes? Second, if inflaion is no longer linked o money growh a he business cycle and long run frequencies, hen wha are he causes of cyclical and long run inflaion since 9?

5 References Baxer, M., and R.G. King (999) Measuring Business Cycles: Approximae Band-Pass Filers for Economic Time Series Review of Economics and Saisics 8, 7-9. Bureau of Labor Saisics, websie a Chrisiano, L.J., and T.J. Fizgerald () The Band Pass Filer Inernaional Economic Review, -. Coe, P.J. and J.M. Nason () The Long-horizon Regression Approach o Moneary Neuraliy: How Should he Evidence be Inerpreed? Economics Leers 78, -. Federal Reserve Bank of S. Louis, websie a hp://research.slouisfed.org/fred/ Friedman, M. (98) Inflaion in Dollars and Deficis, Prenice Hall: Englewood Cliffs, NJ, 7-. Hodrick, R.J., and E.C. Presco (997) Poswar Business U.S. Cycles: An Empirical Invesigaion Journal of Money, Credi, and Banking 9, -. Johnson, L., and S.H. Williamson () "The Annual Real and Nominal GDP for he Unied Saes, Presen" Economic Hisory Services, websie a:

6 Panel Filered Annual Money Growh and 9-9 M and he CPI MB and he CPI 8 Filered M Growh and o 8 Year Frequencies 7. Filered MBGrowh and o 8 Year Frequencies M Growh MBGrowh Filered M Growh and 8 o Year Frequencies 8 7. Filered MB Growh and 8 o Year Frequencies M Growh MBGrowh Filered M Growh and o Year Frequencies. Filered MB Growh and o Year Frequencies M Growh MBGrowh

7 Panel Filered Annual Money Growh and GDP Deflaor Inflaion 9-9 M and he GDP Deflaor MB and he GDP Deflaor 8 Filered M Growh and GDP Deflaor Inflaion o 8 Year Frequencies 7. Filered MB Growh and GDP Deflaor Inflaion o 8 Year Frequencies M Growh GDPDeflaor Inf MBGrowh GDPDeflaor Inf Filered M Growh and GDP Deflaor Inflaion 8 o Year Frequencies 8 7. Filered MBGrowh and GDP Deflaor Inflaion 8 o Year Frequencies M Growh GDPDeflaor Inf MBGrowh GDPDeflaor Inf Filered M Growh and GDP Deflaor Inflaion o Year Frequencies. Filered MBGrowh and GDP Deflaor Inflaion o Year Frequencies M Growh GDPDeflaor Inf MBGrowh GDPDeflaor Inf

8 Table I Correlaions beween Filered Money Growh and Inflaion 9-9 Frequency M & CPI MB & CPI M & GDP Deflaor MB & GDP Deflaor -8 years years years

9 Panel Filered Monhly Narrow Money Growh and 99: - : MB and he CPI M and he CPI. Filered MB Growh and o 8 Year Frequences. 7. Filered M Growh and o 8 Year Frequences MB Growh M Growh -. Filered MB Growh and Filered M Growh and. 8 o Year Frequences.. 8 o Year Frequences MB Growh M Growh Filered MB Growh and o Year Frequences. Filered M Growh and o Year Frequences MB Growh M Growh

10 Panel Filered Monhly Broad Money Growh and 99: - : M and he CPI M and he CPI. Filered M Growh and o 8 Year Frequences. Filered M Growh and o 8 Year Frequences M Growh M Growh. -. Filered M Growh and 8 o Year Frequences.. Filered M Growh and 8 o Year Frequences M Growh M Growh Filered M Growh and Filered M Growh and o Year Frequences.. o Year Frequences M Growh M Growh

11 Table II Correlaions beween Filered Monhly Money Growh and Inflaion 99: - : Frequency MB & CPI M & CPI M & CPI M & CPI -8 years years years

12 Panel Filered Quarerly Narrow Money Growh and GDP Deflaor Inflaion 99: - : MB and he GDP Deflaor M and he GDP Deflaor Filered Percen Changes in MB and wh o 8 Year Frequences. Filered Percen Changes in M and wh o 8 Year Frequences MB Growh M Growh - - Filered Percen Changes in MB and wh 8 o Year Frequences Filered Percen Changes in M and wh 8 o Year Frequences MB Growh M Growh - -. Filered Percen Changes in MB and wh o Year Frequences. Filered Percen Changes in M and wh o Year Frequences MB Growh M Growh

13 Panel Filered Quarerly Broad Money Growh and GDP Deflaor Inflaion 99: - : M and he GDP Deflaor M and he GDP Deflaor Filered Percen Changes in M and wh o 8 Year Frequences. Filered Percen Changes in M and wh o 8 Year Frequences M Growh M Growh - - Filered Percen Changes in M and wh 8 o Year Frequences. Filered Percen Changes in M and wh 8 o Year Frequences M Growh M Growh - -. Filered Percen Changes in M and wh o Year Frequences. Filered Percen Changes in M and wh o Year Frequences M Growh M Growh

14 Table III Correlaions beween Filered Quarerly Money Growh and Inflaion 99: - : Frequency MB & Deflaor M & Deflaor M & Deflaor M & Deflaor -8 years years years