The Co-movement of Inflation and the Real Growth of Output *

Transcription

1 THE JOURNAL OF THE KOREAN ECONOMY, Vol. 7, No. 2 (Winer 26), The Co-movemen of Inflaion and he Real Growh of Oupu * Jae Ho Yoon ** In order o find ou wheher here really are co-movemens beween inflaion and he real growh of oupu for he pos-wwii period, his paper adops FIML Markov-Swiching Model o solve he equaion of Phillips Curve and he equaion of Okun s Law ogeher. The findings of his paper are as follows: inflaion is procyclical in movemen wih he real growh of oupu during he Korean War and he wo Oil Shock periods; and here is relaively lile evidence of co-movemen beween inflaion and real growh of oupu wih he excepions of he Korean War and he wo Oil Shock periods. JEL Classificaion: C3, C32 Keywords: FIML Markov-Swiching model, Hamilon Filer, Phillips Curve, Okun s Law, co-movemen, Korean War, Oil Shock, inflaion, real growh of GDP * Receiverd Augus, 26. Acceped Ocober, 26. This paper was presened a he Join Conference of AKES, KDI, KU, KIF and RCIE on Korea and World Economy V: Korea and he FTA, July 7-8, 26, Korea Universiy, Seoul, Korea. The auhor would like o hank So-Young In, Young-Wook Han, Sung-Tai Kim and seminar paricipans for heir valuable commens. ** POSCO Research Insiue, 47, Samsung-dong, Gangnam-gu, Seoul , Korea, Tel: , Fax: , jhyoon@posri.re.kr

2 24 Jae Ho Yoon. INTRODUCTION The relaionship beween inflaion and he real growh of oupu has been assumed o be posiive and sable. Mills (946), Michell (95), Kuznes (93) found a srong bu no perfec conformiy in he movemens of prices and oupu boh for shor erm conracion and longer erm cycles. For he pos-wwii period Lucas (972) observed ha inflaion and unemploymen rae are negaively correlaed, hus indicaing a sable Phillips Curve. However, Cooley and Ohanian (99) argued ha wih he excepions of he wo world wars, paricularly during he period of he Grea Depression ( ) and par of he lae 9h cenury, here was relaively lile evidence of procyclical prices over he las cenury and a half including he pos-wwii period. Cooley and Ohanian s (99) findings are quie differen from Mankiw (989) who claimed ha in he absence of idenifiable real shocks such as OPEC oil price changes, inflaion ends o rise during booms and fall during recessions. Cooley and Ohanian s findings are also differen from Den Haan (2) who found ha he co-movemen beween oupu and prices is posiive in he shor run and negaive in he long run using a VAR model. Thus he purpose of his paper is o find ou wheher here really are co-movemens beween inflaion and real growh of oupu for he pos- WWII period. To esablish he relaionship beween inflaion and he real growh of oupu, we adop FIML Markov-Swiching Model suggesed by Yoon (24) and Spagnolo, Psaradakis, and Sola (25) o solve he equaion of Phillips Curve and he equaion of Okun s Law ogeher. The equaion of Phillips Curve provides an empirical evaluaion of he relaionship beween inflaion and unemploymen rae. The equaion of Okun s Law, which is defined as a relaionship beween changes in he unemploymen rae and real growh of oupu, provide he relaionship beween inflaion and he real growh of oupu. ) ) Please refer pp. 8-9 in he exbook of Macroeconomics (5h ediion) by Dornbusch and Fisher (99).

3 The Co-movemen of Inflaion and he Real Growh of Oupu 25 The meri of he FIML Markov-Swiching Model is ha we can deal wih he problem of simulaneous equaions based on he Hamilon filer (989). So, we can easily find co-movemens periods of inflaion and he real growh of oupu. The findings of his paper are as follows: inflaion is procyclical in movemen wih he real growh of oupu during he Korean War and he wo Oil Shock periods for he pos-wwii period; and here was relaively lile evidence of co-movemen beween inflaion and he real growh of oupu wih he excepions of he Korean War and he wo Oil Shock periods. The paper has been divided in 4 secions. Secion 2 presens FIML Markov-Swiching Model. Secion 3 summarizes he empirical resuls. Secion 4 concludes his paper. 2. FIML MARKOV-SWITCHING MODEL In order o ge he consisen esimaion of he parameers of he Markovswiching model in he simulaneous equaions, we consider he following FIML Markov-Swiching Model. where YBs + ZΓ s = U, U ~ i. i. d. N(, Σ I ), () S S S T Y Y2 L Y M y Y2 Y22 L Y2 M y2 Y = =, M M O M M Y Y L Y y T T2 TM T

4 26 Jae Ho Yoon β, S β2, S2 L β MSM, β2, S β22, S2 L β2 MSM, Bs =, M M O M βm, S βm2, S2 L βmm, SM Z Z2 L Z K z Z2 Z22 L Z2K z2 Z = =, M M O M M Z Z L Z z T T2 TK T γ, S γ2, S2 L γ MSM, γ2, S γ22, S2 L γ2 MSM, Γ s =, M M O M γk, S γk2, S2 L γkm, SM u, S u2, S2 L u MSM, u2, S u22, S2 L u2 MSM, US = = ( us us 2 L usm ), M M O M ut, S ut2, S2 L utm, SM

5 The Co-movemen of Inflaion and he Real Growh of Oupu 27 us us2 EU ( SUS ) = E ( us us 2 L usm ) M u SM σss, IT σss, 2IT L σssm, I T σs2, SIT σs2, S2IT L σs2, SMIT = =Σ M M O M σsm, S IT σsm, S 2 IT σsm, SM I L T I S T. Y is he T by M marix of joinly dependen variables, B S is an M by M marix and nonsingular. Z is he T by K marix of predeermined variables, Γ S is K by M marix and rank (Z) = K. U s is T by M marix of he srucural disurbances of he sysem. Thus, he model has M equaions and T observaions. The srucural errors are assumed as a nonsingular M-variae normal (Gaussian) disribuion. σ is he covariance of he error erms. is an M by M marix and posiive definie and no resricions are placed on i. I is assumed ha all equaions saisfy he rank condiion for idenificaion. Also if lagged endogenous variables are included as predeermined variables, he sysem is assumed o be sable. An orhogonaliy assumpion, E( Z U S ) =, beween he predeermined variables and srucural errors is required and, we assume he presence of conemporaneous correlaion bu no ineremporal correlaion in (). If we assume ha he single Markov-swiching variable S has an N-sae, firs-order Markov process, hen we can wrie he ransiion probabiliy marix in he following way Σ S

6 28 Jae Ho Yoon p p2 L p N p2 p22 L p2 N p =, M M O M pn pn2 p L NN where p = Pr( S = j S = i) wih ij N p = for all i. j= To include differen firs order Markov-swiching variables S, S 2, S 3,, in he proposed model, we assume ha he dynamics of an unobserved wosae, firs order Markov-swiching variables, S, S 2, S 3, are independen and can be represened by a single Markov-swiching variable, S. For example, if our model involves only wo unobserved wo-sae firs order Markov-swiching variables such as S and S 2. The dynamics of Markov-swiching variables can be represened by a single Markovswiching variable S in he following manner ij S = if S = and S 2 =, S = 2 if S = and S 2 =, S = 3 if S = and S 2 =, S = 4 if S = and S 2 =, wih pij = Pr( S = j S = i), 4 p j= ij =. To derive he FIML Markov-Swiching Model in he simulaneous equaions, we can obain Pr( S = j ψ ) by applying a Hamilon filer (989) as follows

7 The Co-movemen of Inflaion and he Real Growh of Oupu 29 Sep : A he beginning of he h ieraion, Pr( S = i ψ ), i=,, L, N is given. And, we calculae N Pr( S = j ψ ) = Pr( S = i, S = j ψ ) i= N = Pr( S = j S = i)pr( S = i ψ ), i= where Pr( S = j S = i), i=,, L, N, j =,, L, N are he ransiion probabiliies. Sep 2: Consider he join condiional densiy of y and unobserved variable, which is he produc of he condiional and marginal densiies: S = j f( y, S = j ψ ) = f( y S = j, ψ )Pr( S = j ψ ), from which he marginal densiy of y is obained by N f( y ψ ) = f( y, S = j ψ ) j= N = f( y S = j, ψ )Pr( S = j ψ ), j= where he condiional densiy f( y S =, jψ ) is obained from (2)

8 22 Jae Ho Yoon M /2 /2 ( =, ψ ) (2 π) de( S) = Σ de( ) f y S j Bs + Γ Σ + Γ 2 - exp ( ybs z s) S( ybs z s), (2) where Σ S = ( YBs + ZΓ s )'( YBs + ZΓ s ), y is he h row of he Y marix. T z is he h row of he Z marix. Bs and Γ s is obained from (). Sep 3: Once y is observed a he end of ime, we updae he probabiliy erms Pr( S = j ψ ) = Pr( S = j ψ, y ) = = f( S = j, y ψ ) f( y ψ ) f y S j ψ S j ψ f( y ψ ) ( =, )Pr( = ). As a byproduc of he above filer in Sep 2, we obain he log likelihood funcion T ln L= ln f( y ψ ), = which can be maximized in respec o he parameers of he model. 3. EMPIRICAL RESULTS Le s consider he Phillips Curve. An OLS regression for =949 o 24 using annual daa for inflaion ( π ) and unemploymen rae u in year is given by equaion (3)

9 The Co-movemen of Inflaion and he Real Growh of Oupu 22 6 Figure Inflaion π and Unemploymen Rae u UNEMP INFLA 5 INFLA UNEMP π = u + π + e , (.2) (.22) (.) (3) where sandard errors of he parameers esimaes are repored in he parenheses. The OLS regression (3) reveals saisically insignifican evidence of an inflaion-unemploymen rade-off because he parameer of unemploymen rae u in he equaion (3) reveals saisically insignifican. Figure depics he relaionship beween inflaion π and unemploymen rae u. From he equaion (3) and figure, we can find ha he shor run Phillips Curve does no remain sable. These resuls sugges us o uilize a Markov-

10 222 Jae Ho Yoon Figure 2 Changes in he Unemploymen Rae and Real Growh of GDP DUNEMP RGDP 5 RGDP DUNEMP Swiching Model for he unsable Phillips Curve for he pos WWII period. To find ou he relaionship beween unemploymen and he real growh of oupu, he equaion of Okun s Law for =949 o 24 is given by equaion (4) Δ u = y + ν, (.3) (.3) (4)

11 The Co-movemen of Inflaion and he Real Growh of Oupu 223 where y, is he annual real growh of GDP, Δ u is changes in he unemploymen rae in year. The equaion of Okun s Law in (4) reveals saisically significan evidence beween changes in he unemploymen rae and real growh of GDP. From he equaion (4) and figure 2, we can find ha he sable Okun s Law for he pos-wwii period. For he esimaion of Phillips Curve and Okun s Law ogeher, he proposed FIML Markov-Swiching Model was applied, which adops a simple wo-sae Markov swiching parameers in he simulaneous equaions. π = α + β u + γπ + e S S S Δ u = φ + φ y + ν, 2, (5) u = u + + y + (6) φ φ2 ν, where αs = αs + α ( S ), βs = βs + β ( S ), Pr( S = S = ) = q, Pr( S = S = ) = p, p q es p =, ~... iid N(, Σ ) S IT. p q ν To solve he equaion (5) and (6) ogeher, we can rewrie i as follows γ es =, βs ν [ π u ] [ π y u ] φ [ α φ ] 2 S

12 224 Jae Ho Yoon es where ~... iid N(, ΣS IT ), ν Σ S = ( YBs+ ZΓ s )'( YBs+ ZΓ s ) = T σ S, S σ 2,2, αs = αs + α ( S ), βs = βs + β ( S ), Pr( S = S = ) = q, Pr( S = S = ) = p, p q p =. p q Table repors esimaion resuls using annual daa for The coefficien β =.95 in able is negaive during regime period. However, β =.9 is negaive, saisically insignifican during he regime period. Table Maximum Likelihood Esimaion of The Model: π = 8.58S + 2.( S) + {.95S.9( S)} u +.68π + es (3.37) (.) (.57) (.2) (.) u = u y + ν (.3) (.3) Pr( S ).96, Pr( = = ) =.85 = S = = S S (.4) (.4) Log Likelihood 65.2

13 The Co-movemen of Inflaion and he Real Growh of Oupu 225 Figure 3 Probabiliies of Regime Pr( S = S = ) = p for PROB_Phillips Curve From figure 3, he inferred probabiliies Pr( S = S = ) = p accord quie well wih he Korean War (95) and he wo Oil Shock periods ( , ). Alhough he resuls of β in able seems o be saisically meaningful during regime period using annual daa, we esimae he model again wih quarerly daa because quarerly daa has more precise informaion han annual daa. We can idenify regime swiching probabiliies more concisely wih quarerly daa, which may be missed by annual daa for he unsable Phillips Curve. We obained seasonally adjused quarerly daa of he unemploymen rae and he consumer price index for he U.S. from he Bureau of Labor Saisics, and seasonally adjused quarerly GDP percen change based on he chained 2 dollars from he Bureau of Economic Analysis. Inflaion raes are calculaed from he log differenced consumer price index. The sample period is from 949:I o 24:IV. Table 2 repors esimaion resuls using quarerly daa for 949:I-24:IV.

14 226 Jae Ho Yoon Table 2 Maximum Likelihood Esimaion of he Model: 949:I-24:IV π =.689S +.34( S ) + {.42S.38( S )} u +.36π +.23π + e 2 S (.426) (.27) (.68) (.36) (.6) (.6) u = u y + ν (.27) (.5) Pr( S ).99, = S = = S S Pr( = = ) =.96 (.) (.3) Log Likelihood From able 2, he coefficien β =.42 is negaively, significan during he regime period which is affeced by shocks such as war or oil shocks. If he unemploymen rae increases % wih shock periods such as war or oil shocks, hen he inflaion is down.42%. From his resul, we can find ha here is an inflaion-unemploymen rade-off during he regime period. However, β =.38 is negaively and saisically insignifican during he regime period which has no such shocks such as war or oil shocks. Figure 4 show ha he inferred probabiliies Pr( S = S = ) = p accord quie well wih he Korean War (95:III-95:II) and he wo Oil Shock periods (974:I-975:IV, 978:II-984:III). From β =.42 in he able 2 and figure 4, we can conclude ha inflaion is procyclical in movemen wih he real growh of oupu during he Korean War(95:III-95:II) and wo Oil Shock periods(974:i-975:iv, 978:II-984:III). As he resuls of β in he able and able 2 are saisically insignifican, here was relaively lile evidence of co-movemen beween inflaion and he real growh of oupu wih he excepion of he Korean War and he wo Oil Shock periods.

15 The Co-movemen of Inflaion and he Real Growh of Oupu 227 Figure 4 Probabiliies of Regime Pr( S = S = ) = p for 949:I~24:IV PROB_Phillips Curve The findings of his paper are quie differen from Cooley and Ohanian s (99) who suggesed ha wih he excepions of he wo world wars, paricularly in he period of he Grea Depression ( ) and par of he lae 9h cenury, as hey found relaively lile evidence of procyclical prices over he las cenury and a half including he pos-wwii period. The findings of his paper are also differen from Den Haan (2) who suggesed ha he co-movemen beween oupu and prices is posiive in he shor run, when demand shocks dominae and negaive in he long run. 4. CONCLUSIONS As he equaions of he Phillips Curve wih Okun s Law was applied o he FIML Markov-Swiching Model for he pos-wwii period, The findings of his paper are as follows: inflaion is procyclical in movemen wih he real growh of oupu during he Korean War (95:III-95:II) and he wo Oil Shock periods (974:I-975:IV, 978:II-984:III) for he pos-wwii period; and here was relaively lile evidence of co-movemen beween inflaion

16 228 Jae Ho Yoon and he real growh of oupu wih he excepions of he Korean War and he wo Oil Shock periods. These resuls sugges anoher explanaion ha when here are exremely large shocks such as big wars or oil shocks, inflaion is procyclical in movemen wih he real growh of oupu, and he procyclical movemen occurs in conjuncion wih he big shocks, exiss no only pre-wwii period bu also pos-wwii period, which is he differen resul from Cooley and Ohanian s findings. REFERENCES Cooley, T. F. and L. E. Ohanian, The cyclical behavior of prices, Journal of Moneary Economics, 28, 99, pp Den Haan, W. J., The comovemen beween oupu and prices, Journal of Moneary Economics, 46, 2, pp Dornbusch, R. and S. Fisher, Macroeconomics, 5h ediion, Mcgraw-Hill, Inernaional Ediion, 99. Hamilon, J. D., A new approach o he economic analysis of nonsaionary ime series and he business cycle, Economerica, 57(2), 989, pp Kuznes, Simon, Secular movemens in producion and prices, NY: NBER, 93. Lee, J. W., S. D. Lee, and K. H. Kim, New approach o esimaion of he core inflaion, The Journal of Korean Economy, 4(2), Fall 23, pp Lucas, R. E., Economeric esing of he naural rae hypohesis, in Oo Ecksein, ed., The economerics of price deerminaion, Board Governor he Federal Reserve Sysem, 972. Mills, F. C., Prices quaniy ineracion in business cycles, NBER, NY, 946. Michell, W. C., Wha happens during business cycles, Houghon Mifflin Co., 95.

17 The Co-movemen of Inflaion and he Real Growh of Oupu 229 Mankiw, N. Gregory, Real business cycles: A new Keynesian perspecive, Economic Persepcive, 3, 989, pp Spagnolo, F., Z. Psaradakis, and M. Sola, Tesing he Unbiased Forward Exchange Rae Hypohesis Using. a Markov Swiching Model and Insrumenal Variables, Journal of Applied Economerics, 2(3), 25, pp Yoon, J. H., Simulaneous equaions in he markov-swiching model, POSCO Research Insiue working paper, 24.