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1 :: : 3 ( ) : 1985, :,,,, ARCH, :,,,, ( inflation uncertainty) Friedman, (1977,467 ), (ex ante), :,,,, ;,,,, (ex post),,, Okun (1971) Friedman (1977),(Ball and Cecchetti,1990) 3, 60 转载

2 2005 8,,, (Okun,1971 ;Logue and Willett,1976 ; Foster,1978) (), Wachtel (1977),Carlson (1977) Fisher (1981) Taylor (1981) OECD,, Engle (1983) Engle, ARCH (unanticipated inflation) , ARCH Engle (Holland,1984 ;Cosimano and Jansen,1988 ;Jansen,1989) ARCH,:ARCH (variability) (uncertainty),( Fisher,1981) Taylor (1981),,, CPI,,(Markov regimes switching model) (AR ARCH ),, (i1i1d1) :,,,, :, () , ,20 80, (CPI), Foster (1978),,, 61

3 :: 2001,2001, CPI, CPI , (), CPI, , %( %), 1988,, , , %,,, (,1996) 1996,1 0, CPI 7 %, CPI () 1, : (6 72 ),; 1123 % 0122 %(1101 %), (0132 %) 95 % 1 ( ) CPI Jarque2Bera,,, ,12 ( ) 013,, ADF 2001, t = 2001 t t 2001 t, 2000, %, % ; % %, % 25 % 28 % ,M % Brandt Zhu(2000,2001),50000 (permute), 95 % [ ,01201 ],95 % [ ,01251 ] 62

4 2005 8, 4 48 ( ), , 019 %(11135 %) ;,1 %,, %, % , Π3,,, : ; ;,2000 ADF :,,1, 1995,, :,,, ;, 1 1, (break points),,adf ( Perron, 1990),,, 1 85 :1 03 :12 85 :1 89 :12 90 :1 94 :12 95 :1 99 :12 00 :1 03 :12 85 :1 94 :12 95 :1 03 : Jarque2Bera [0. 29 ] [0. 58 ] Q (5) [0. 64 ] ADF : , Q (5) 5 0 Ljung2Box Q ADF, ADF 10 % ,5 %, [ ] p, %5 % 63

5 ::, : 2 s t ) = ( < 1 + < 2 s t ) [ t ( s t - 1 ) ] + ( < 3 + < 4 s t ) [ t - 2 t - ( 1 + t = ( s t ) t, t : N (0,1). - ( s t - 2 ) ] + t, s t 0 1, s t,: pr[ s t = 0 s t - 1 = 0 ] = p 00, pr[ s t = 1 s t - 1 = 0 ] = p 01, p 00 + p 01 = 1, pr[ s t = 1 s t - 1 = 1 ] = p 11, pr[ s t = 0 s t - 1 = 1 ] = p 10, p 11 + p 10 = 1. (1), 1, ( 2 > 0) ; t, (1) , 2 0, (1),,, AR AR ( < 1 + < 3 ),( < 1 + < 2 + < 3 + < 4 ) Perron (1990), (DGP) (1) (2), ( 2 = 0),AR,1,1 (1985 : :12),,AR,,s 3 t (2), s 3 t s 3 t t : s 3 t = 1 if s t - 2 = 0, s t - 1 = 0, s t = 0 ; s 3 t = 2 if s t - 2 = 1, s t - 1 = 0, s t = 0 ; s 3 t = 3 if s t - 2 = 0, s t - 1 = 1, s t = 0 ; s 3 t = 4 if s t - 2 = 1, s t - 1 = 1, s t = 0 ; s 3 t = 5 if s t - 2 = 0, s t - 1 = 0, s t = 1 ; s 3 t = 6 if s t - 2 = 0, s t - 1 = 1, s t = 1 ; s 3 t = 7 if s t - 2 = 1, s t - 1 = 0, s t = 1 ; s 3 t = 8 if s t - 2 = 1, s t - 1 = 1, s t = 1.,P(1), = 1 : f ( t s 3 t = 1, t - 1 ; ) = 1 exp - [ ( t - 1 ) - < 1 ( t ) - < 3 ( t - 2 (1) (2) - 1 ) ] 2 t = ( t, t - 1,, 0 ),= ( 1, 2, 1, 2, < 1,, < 4, p 00, p 11 ), s 3 t = 2,,8 t = (1,0,0,,0) s 3 t = 1 (0,1,0,,0) s 3 t = 2 (0,0,0,,1) s 3 t = 8, t = f ( t s 3 t f ( t s 3 t f ( t s 3 t = 1, t - 1 ; ) = 2, t - 1 ; ) = 8, t - 1 ; ) (8 1) ^ tπt t s 3 t, j pr( s 3 t = j t ;) t 64

6 ^ t t = ^ t +1 t ^ 1 (^ t t - 1 t t t - 1 t ) (3) = P ^ t t (4),1 1 (8 1), Hamilton (1994,pp ) T f ( t t - 1 ; () l ( 8 ) = t = 1 T ) = t = 1 f ( t, s 3 t 8 = t = 1 = 1 (^ f ( t s 3 t t t - 1 t ) logf ( t t - 1 ; ) (5) = i t - 1 ; ) = i, t - 1 ; ) pr( s 3 t = i t - 1 ; ) (1) 2, AR(2) AR(4) AR(4) : t - 1 = < 1 ( t ) + < 2 ( t ) + < 3 ( t ) 2 + < 4 ( t ) + 1 w t, w t N (0,1) (6) (,1985 : :12) AR(2) AR(4) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) < ( ) ( ) ( ) < ( ) ( ) ( ) < ( ) ( ) < ( ) ( ) : (), %5 % p 00 + p 01 = p 11 + p 10 = 1, p 00 = exp ( 1 )Π[1 + exp ( 1 ) ], p 11 = exp ( 2 )Π[1 + exp ( 2 ) ], p 01 = 1Π[1 + exp ( 1 ) ], p 10 = 1Π[ 1 + exp ( 2 ) ] 1 2 p 00 = , p 11 = OLS, 1,, AR (4) AR (2), % ; 65

7 :: 0155 %, % 01624( = ) 01811( = ),,,1 (6), %01336 %,01745 %( = % %) %( = % %) 215, 3 ( 1),, (1), AR(2), (F t ) ( Hansen,1992) (LR) (Hamilton and Susmel,1994) LR, LR (1) ,AR (2) , [ = - 2 ( ) ],, (1) t t T,( s t = 0 s t = 1),(3) ^ pr( s 3 t t t + 1 = i t - 1 ; ) f ( i s 3 t = pr( t, s 3 t t s t pr( t, s 3 t 8 i = 1 f ( t, s 3 t = i t - 1 ; ) t i t s t = i, t - 1 ; ) = i t - 1 ; ), i = 1,2,L,8. = i t - 1 ; ) = pr( s 3 t = i t, t - 1 ; ) = pr( s 3 t = i t ; ), i = 1,2,,8. (7) t (filter probabilities), t s t = 0 s t = 1 : pr( s t pr( s t = 0 t ; = 1 t ; 4 ) = i = 1 pr( s 3 t 8 ) = i = 5 pr( s 3 t = i t ; ) ; = i t ;., Kim(1993) (smoothed inferences), T : ^ t T = ^ t t {P [^ t +1 T ( ) ^ t +1 t ]} (9) (8) Hamilton(1989) GNP (+ d s t, s t = 0 1) AR(4) Hansen(1992) d 2 (1) t, 2 (3) Hamilton (1989) AR(4) d, p 00 p 11 66

8 ( ) ^ T T (3) t = T (3) (4) (9) (8) (9),2,( s t = 0) ( s t = 1), 0192,1 [ = 1Π(1-0192) = 12 ] ; 0180,5 [ = 1Π(1-018) = 5 ] s t = 0, , (stop2go),,,, ( ) 2 ( s t = 0 s t = 1),,,,,,1985 ( ), ; ,1988 s t = 1,, 1992,,1993 3, s t = 1 () (1),, t,, t t - 1, : var ( t t - 1 ) = E{var ( t t - 1, s 3 t ) t - 1 } + var{ E( t t - 1, s 3 t ) t - 1 } (10) s 3 t, s 3 t,,, ( ) ( ) %, 017 % 67

9 :: t, (1) 2 = 0,(10) 0, t, t,,t, var{ E( t t - 1, s 3 t ) t - 1 } > 0, ARCH ( Engle,1983),,, ARCH, t - 1 t : E{var ( t t - 1, s 3 t var{ E( t t - 1, s 3 t = ) t - 1 } ) t - 1 } = 8 i = 1 var ( t t - 1 ) pr( s 3 t = i t - 1 ) = ^ 2 1 pr( s t = 0 t - 1 ) + ( ^ 1 + ^ 2 ) 2 pr( s t = 1 t - 1 ) [ E( t t - 1, s 3 t = i) - E( t t - 1, s 3 t = j) ] 2 pr( s 3 t = i t - 1 ) pr( s 3 t i j = j t - 1 ) 4 Markov t - 1 t, var ( t t - 1 ), var{ E( t t - 1, s 3 t ) t - 1 }, E{var ( t t - 1, s 3 t ) t - 1 }, E{var ( t t - 1, s 3 t ) t - 1 }var{ E( t t - 1, s 3 t ) t - 1 } ( ), 012 %,,,,:, (10) :, ;,,,, ;,(Ball and Cecchetti,1990),,,90,,,,,,, ;,,, 1988,,,, 68

10 t - 1,(1) (4),(one2step ahead forecast) : e t = E( t t - 1 ; ) = E{ ( s t ) + ( < 1 + < 2 s t ) [ t ( s t - 1 ) ] + ( < 3 + < 4 s t ) [ t ( s t - 2 ) ] t - 1 ;}. (11) ,01538 % % ( e t = t - e t ) %,,,( 1 AR(1) ) : t = a + b e t + t (12) t a = 0, b = 1, (12) ( ) : t = (01060) e t R 2 = ; D2W = (01018) a = 0, b = 1 F 0120 (p 0181) t F 3 t e t AR(1) ( ) ( ) (0. 066) : 1,AR(1) (), 33 5 % e t e t e t,, : e 2 t = t w t (13) = 01294,t 3153 t (13) t = 69

11 :: 01431( t 5135), ARCH, ARCH 1985 : :12, (,p, %5 % ) : t = ( ) 2 t = ( ) t - 1 ( ) v 2 t - 1 ( ) t - 2 ( ) + v t, v 2 t - 2 ; ( ) ARCH(1) = [0. 75 ], 1 = , Q (5) = 4. 54[0. 47 ]. (14) (14) v t ARCH(1) ARCH LM ARCH,5 Lung2Box Q AR(2) 5 (14) t,, t ARCH,6,: E( 2 t T ) = ^ 2 1 pr( s t = 0 T ) + ( ^ 1 + ^ 2 ) 2 pr( s t = 1 T ) (15),,ARCH ARCH 1 2, ARCH (1) (6) (14), AR ARCH (standardized residuals) (6) w t (1Π 1 ), 5 ARCH ARCH ( 5),(15) AR ARCH,, AR ARCH (AR ARCH ), Jarque2Bera,,Jarque2Bera p 0146,, ARCH ARCH, ARCH AR,AR ARCH,Markov

12 AR ARCH AR(4) ARCH Jarque2Bera [ ] [ ] [ ] Q (5) [ ] [ ] [ ] Q 2 (5) [ ] [ ] [ ] ARCH(1) [ ] [ ] [ ] : 1, Q (5) 5 0 Ljung2Box Q [ ] p 2 1 Q 2 (5) 1 Ljung2Box Q,ARCH(1) 1 ARCH LM : : ;,,,,,,ARCH,,,,,,, ARCH,,, (Ball,1992 ;Devereux,1989),,1996 :: , Ball,Laurence and Stephen G. Cecchetti,1990.Inflation and Uncertainty at Short and Long Horizons. Brookings Papers on Economic Activity 1, Brandt Loren and Xiaodong Zhu,2000,Redistribution in a Decentralized Economy : Growth and Inflation in China under Reform,Journal of Political Economy 108, Brandt Loren and Xiaodong Zhu,2001,Soft Budget Constraints and Inflationary Cycles, Journal of Development Economics 64,

13 :: Carlson,John,1977,A Study of Price Forecasts. Annals of Economic and Social Measurement 6, Cosimano,Thomas F.,and Dennis W.Jansen,1988,Estimates of the Variance of U. S. Inflation Based upon the ARCH Model :Comment, Journal of Money, Credit and Banking 20, Devereux,M.,1989,A Positive Theory of Inflation and Inflation Variance. Economic Inquiry 27, Engle,Robert F.,1983,Estimates of the Variance of U. S. Inflation Based on the ARCH Model. Journal of Money, Credit and Banking 15, Fischer,Stanley,1981,Towards an Understanding of the Costs of Inflation. Carnegie2Rochester Conference Series on Public Policy 15,5 42. Foster,Edward,1978,The Variability of Inflation,Reviews of Economics and Statistics 60, Friedman,Milton,1977,Inflation and Unemployment,Journal of Political Economy 85, Hamilton,J. D.,1989,A New Approach to the Economic Analysis of Non2stationary Time Series and the Business Cycle. Econometirca 57, Hamilton,J. D.,1994, Time Series Analysis,Princeton University Press :New York. Hamilton James D.,Susmel,Raul,1994,Autoregressive Conditional Heteroskedasticity and Changes in Regime. Journal of Econometrics 64, Hansen,B. E.,1992,The Likelihood Ratio Test under Nonstandard Conditions : Testing the Markov Switching Model of GNP. Journal of Applied Econometrics 7,s61 s82. Holland,A. Steven,1984,Does Higher Inflation Lead to More Uncertain Inflation?Federal Reserve Bank of St.Louis. Review 66, Jansen W. Dennis,1989,Does Inflation Uncertainty Affect Output Growth? Further Evidence,Federal Reserve Bank of St.Louis, Review (71 JulyΠAugust) Kim Chang2jin,1993,Dynamic Linear Models with Markov2switching,Journal of Econometrics 60,1 22. Logue,Dennis E.,and Thomas D. Willett,1976,A Note on the Relation between the Rate and Variability of Inflation,Economica 43,151 Okun,Arthur M.,1971,The Mirage of Steady Inflation,Brookings Papers on Economic Activity 2, Perron,Pierre,1990,Testing for a Unit Root in a Time Series with a Changing Mean,Journal of Business and Economic Statistics 8,153 Taylor John,1981,On the Relation Between the Variability of Inflation and the Average Inflation Rate,Carnegie2Rochester Conference Series on Public Policy 15, Wachtel,Paul,1977,Survey Measures of Expected Inflation and Their Potential Usefulness,In Analysis of Inflation : , Edited by Popkin,Joel. Inflation Rates and Inflation Uncertainty : Regime Switching Analysis for China Monthly Data Zhao Liuyan,Wang Yiming and Cai Jing (School of Economics,Peking University) Abstract :This paper intends to discover the link between inflation and inflation uncertainty in China. Markov switching model is used to explain the changing time series behavior of inflation since January Through the model inflation uncertainty can be decomposed into two components : The uncertainty reflecting the variance of future shocks to the inflation process and the uncertainty about future changes in the inflation regime. We show that the two components increase simultaneously with the increase in inflation level,which implies that the costs of inflation are associated closely with those of inflation uncertainty. Switching model describe Chinaπs inflation behavior more appropriately than linear AR model or ARCH model. Estimates of inflation uncertainty that ignore the effects of regime switches may seriously bias the inflation forecast or the degree of uncertainty. Key Words : Inflation ; Inflation Uncertainty ;Markov Switching Model JEL Classification : E320,E410,C320 ( :) ( :) 72

Girton Roper (1977),,,,,, ( ),,,,,,, ( Exchange Market Pressure) 30 EMP, EMP EMP,Girton Roper (1977), ,,, Kim(1985) ,,, T

Girton Roper (1977),,,,,, ( ),,,,,,, ( Exchange Market Pressure) 30 EMP, EMP EMP,Girton Roper (1977), ,,, Kim(1985) ,,, T : : : 3 : 1994 1 2008 1,,,,,,, : 1994,,, 1994 1 1, 1 8172, 1997 7, 1 8130, 418 % 2005 7 21, 1 8111, 2 % 2005,,2007, 1 713046, 2006 619 %, 2005, 1313 %,2007, 0141 %, 310,,?,?,?, Girton Roper (1977) ( EMP),