Stylized facts and regime changes: Are prices procyclical?

JOURNALOF

Monetary ELSEVIER

Journal of Monetary Economics 36 (1995) 497 526

ECONOMICS

Stylized facts and regime changes: Are prices procyclical? M o r t e n O. R a v n *'a'b, M a r t i n Sola c'd ~Department of Economics, University of Southampton, Southampton S017 I BJ, U K bCenter Jk~r Non-Linear Economic Modellin 9, University of Aarhus, DK-8000 Aarhus C, Denmark CBirkbeck College, London WC1E 7HX, UK dCenter fi~r Economic Forecasting, London Business School, London N W I 4SA, UK (Received May 1994; final version received October 1995)

Abstract We investigate empirically the stability of the correlation between o u t p u t growth a n d inflation using a technique t h a t allows for changes in regime. We look at recent quarterly d a t a for the G 4 a n d at historical data for the U.S. a n d U.K. We find evidence of changes b o t h in m e a n s a n d variances in b o t h sources of data. In the quarterly data we find that the covariance between o u t p u t g r o w t h a n d inflation is typically negative. In the historical data we find, as suggested in previous studies, that inflation was procyclical especially in the inter-war years, but has been countercyclical in the post-war period. K e y words: G r o w t h a n d inflation; Regime switching; Countercyclical prices J E L class{fication: C22; E31

1. Introduction In this paper we examine empirically the relationship between nominal prices and output. We look at two sets of data, the first consisting of quarterly

*Corresponding author. We thank the editor and a referee for very conslructive comments. We are grateful to Dave Backus for provision of data. The paper was initiated while the first author was a Jean Monnet fellow at the European University Institute. We would like to thank seminar participants at the University of Aarhus, Michael Beeby, John Driffill, Anthony Garratt, Jan Podivinsky, Ron Smith, Howard Wall, and, especially, Allan Timmerman for comments. We also thank Louise Crone for research assistance. We take responsibility for any remaining errors. 0304-3932/95/$09.50 (C: 1995 Elsevier Science B.V. All rights reserved SSDI 0 3 0 4 - 3 9 3 2 ( 9 5 ) 0 1 231-C

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M.O. Ravn, M. Sola / Journal of Monetary Economics 36 (1995) 497-526

post-war data for the G4 and the other consisting of annual historical data for the U.K. and the U.S. covering the period 1870 1994. Our interest in the relationship between prices and output stems from the recent resurgence of research into the stylized facts of macroeconomic fluctuations, research pointing towards some new, and maybe surprising, findings. One of the most controversial of these is the result that prices do not seem to behave in a consistently procyclical manner. Instead prices seem most of the time to be countercyclical. This paper considers whether the relationship between the prices and output is stable over time or whether it is subject to important changes. Early students of the U.S. business cycle, such as Kuznets (1930), Mills (1927), and Burns and Mitchell (1946), found that nominal prices usually behave procyclically, a finding later included in the famous Phillips curve relationship (Phillips, 1958), though this was originally formulated as an association between inflation and unemployment. This relationship, later changed into an association between output and prices, was for many years seen as a necessary ingredient of any serious model of macroeconomic fluctuations. New research has challenged the presumption that prices are procyclical. Friedman and Schwartz (1982), in their study of monetary relationships in the U.K. and the U.S., found that the price level has behaved countercyclically in the post-war period for both of these countries. Similarly, Meltzer (1986), using a multi-stage Kalman filter, records (Table 4, p. 178) that shocks to output are negatively correlated with shocks to prices in Canada, the U.K., the U.S., and Germany. Kydland and Prescott (1990) document that the U.S. price level (regardless of whether defined as the output deflator or as the CPI) has behaved consistently countercyclically in the post-Korean War period. Authors such as Blackburn and Ravn (1992), Brandner and Neusser (1992), Correia, Neves, and Rebelo (1991), and Kim et al. (1992) report similar results for the U.K., Austria, Germany, Portugal, and New Zealand. Backus and Kehoe (1992) study historical data for ten OECD economies. For both the U.S. and the U.K. they find procyclical prices in the period before World War I (WWI) and countercyclical prices in the post-WWII period. In the interwar period (1920-1939) they find that inflation was procyclical (countercyclical) in the U.S. (the U.K.). Another result from their analysis is that other moments of the data including means and variances have changed over time as well. The inter-war period stands out as having low mean growth but high variability of output growth. Inflation was moderate in both countries prior to WWI, negative in the inter-war period, and high in the post-WWII period. Hence, the evidence seems to suggest that the properties of inflation and output growth have changed over time. Smith (1992) provides a sensitivity analysis of Backus and Kehoe's (1992) results and his findings seem in general to underline their results. Cooley and Ohanian (1991) analyze the U.S. data at a detailed level using several sources of data and various empirical techniques. In annual historical data for the period 1870 1975 they find inflation and output growth to be

M.O. Ravn, M. Sola /Journal of Monetary Economics 36 (1995) 497-526

499

positively associated prior to WWII. In the post-WWII period they find moderately countercyclical movements in inflation but more pronounced countercyclicality between output growth and inflation lagged two periods. They also find, as Backus and Kehoe, that the period including the inter-war years is the period in which inflation was most procyclical. Their conclusion after looking at many different sources of data and using various techniques is that US prices if anything - behave countercyclically. The counterview that prices are countercyclical has itself been challenged. Mankiw (1989) states that prices, or inflation rates, generally behave procyclically, and that a small number of real shocks biases the empirical results. Wolf (1991) analyzed the robustness of the findings of Kydland and Prescott (1990) using a rolling correlation technique. He reports that U.S. prices only became countercyclical in the 1970's and returned to being mildly procyclical in the 1980's. It is this view, that the relationship changes over time, that we look at. We look at the development of the joint distribution of prices and output over time employing the changes-in-regime approach of Hamilton (1988, 1989) and an extension provided by Phillips (1991). We model output and prices as being generated by Markov chains with changing means. This formulation is based on the observation that if the series do have changes in their means, these will appear as changes in the variance covariance matrix if not controlled for. Accordingly, one should allow the series in question to exhibit mean changes before it can be decided whether changes have occurred in variances and/or covariances. If a few major real shocks bias an overall positive relationship between prices and output, we should be able to single out these limited time periods. In our general framework we model the unconditional means of the two series as being generated by a four-state Markov process, where the state variables that dictate the switching between regimes for each variable may be correlated. An alternative specification is that the switching in prices and output are generated by independent processes. When testing the independent specification against the general model it turns out that this cannot be rejected for any country. We also investigate whether there is leading or lagging behaviour in the system, i.e., whether shocks to output lead shocks to prices or vice versa. Both specifications are rejected for all countries and both sets of data. Our results indicate that the finding of countercyclical prices is not an artifact of a few major real shocks. We do find that moments have changed over time both in the annual historical data and in the post-war quarterly data. In these data, however, we find that for most of the time the correlation between prices and output is negative. For the U.K. and Germany we consistently estimate a negative correlation between output and prices; for the U.S. we find inflation to be mildly countercyclical over most of the sample with the exception of the 1970's where there are instances of both more negative correlations and of procyclical prices; for Japan we find that in the period 1955 1970 there are instances of both procyclical prices and countercyclical prices, but from then on

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M.O. Ravn, M. Sola / Journal of Monetary Economics 36 (1995) 497-526

prices are countercyclical. For the historical data our findings can be summarized as follows. In the U.K. the period after 1938 is a period of eountercyclical prices. Prices were also countercyclical in a shorter period from 1915 to 1924. The early part of the sample, 1874 to WWI, was the period where procyclicality was most predominant, but the later part of the inter-war period (1925-1937) also had procyclical prices. The U.S. results are slightly different. Again the post-war period is a long period of countercyclical prices, but to a lesser degree than in the U.K. We also find an extended period from 1888 to the early 1920's where inflation was countercyclical. A period from 1926-1945 stands out as having very procyclical prices as does a shorter period in the nineteenth century (1880-1887). Hence, the conclusions seem to be that prices have been countercyclical in the post-war period in all countries that we look at regardless of the sampling frequency. Prior to this there were instances of procyclical prices. But the results do not suggest that countercyclicality is a finding caused by the existence of a few major real shocks as has been suggested elsewhere. The remainder of the paper is organized as follows. In Section 2 the data are presented. In Section 3 the empirical technique is described and some estimation issues are discussed. The results are contained in Section 4, while Section 5 summarizes and concludes.

2. A preliminary analysis We will look at two different sets of data, quarterly post-WWII data for the G4, and historical annual data for the U.S. and the U.K. The quarterly data cover the period 1955-94 for Japan and the U.K., 1957-94 for U.S., and 1960-94 for Germany. All series refer to quarterly seasonally adjusted data and were obtained from the IMF's IFS data tape. Gross Domestic Product at constant prices and the implicit G D P deflator are the output and price series used. We use an updated version of the data used by Backus and Kehoe (1992) for the historical data. The data cover the period 1870-1994. The U.S. data for the period 1870-1983 used by Backus and Kehoe (1992) were obtained from Balke and G o r d o n (1986). These data were linked with the IFS data to extend the sample period to 1994. The data for the U.K. were obtained from Feinstein (1972) for the period 1870 1947 and were extended by Backus and Kehoe (1992) using IFS data to cover the period 1948-1986. We extend this sample period with IFS data to cover the full period of 1870-1994. For our methodology to be appropriate we need data that are integrated of order zero. We detrend the data by taking first differences of the logarithms of the series. Accordingly, we investigate the relationship between the inflation rates and the output growth rates. The series are plotted in Fig. la (the quarterly data) and Fig. lb (historical data), and Table la and Table lb give some basic information about the series.

M.O. Ravn, M. Sola / Journal of Monetary Economics 36 (1995) 497 526 Percent 7-

Japan

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......................................

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Fig. la. Output growth and inflation

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Quarterly data.

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501

502

~LO. Ravn, M. Sola/ Journal of Monetary Economics 36 (1995) 497-526 Percent

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Germany I

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.

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1975 Date

1980

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Fig. l a (continued)

Note from Table la that in the quarterly G4 data the contemporaneous correlation between output and prices is negative for Germany, the U.S., and the U.K. The Japanese data indicate that the overall correlation is positive. There is no apparent systematic pattern across countries in the dynamic relationship between these two series since the series seem contemporaneous in the U.K., and prices seem to lead (lag) output in the U.S. (Germany and Japan). Furthermore, the series appear to have substantial changes over time in terms of variances and means. Dividing the sample period into three subperiods, the first going up to 1974, the second covering 1974 83, and the last covering 1983-94, this observation is convincingly supported by the data. All four countries experienced a decline of around 50 percent in the rate of output growth between the first two periods, and an increase from the middle subperiod to the last subperiod. The rates of inflation also changed but the cross-country picture is less clear. While the U.K. and the U.S. saw inflation more than doubling between the first two periods, Japan and Germany were almost unaffected. All four countries did, however, experience a marked fall in inflation from the second to the third subperiod. Note also the low variability of inflation and output growth in the 1980's compared to earlier periods. The negative correlation between output and prices, however, seems to be quite robust and it appears that prices in Japan are countercyclical in the last part of the sample. From Table lb (the historical data) we see that inflation is basically not correlated with contemporaneous output growth in the U.S. for the full sample but might be procyclical with a one-year lag. In the U.K. inflation is countercyclical, but it is difficult to determine whether it leads or lags the cycle (in the latter case, inflation appears procyclical). We also divide this sample into subperiods, the first covering the pre-World War I (WWI) gold standard (1870-1914), the

M.O. Ravn, M. Sola / Journal of Monetary Economics 36 (1995) ~97 526 Percent 25-

503

United States

2015 108 0 -5 -10 -15

i lnflation -20 -25 1871

1900

Percent 25

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Date

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Date

Fig. lb. Output growthand inflation Historicaldata.

next the inter-war period, then the post-Word War II (WWlI) period up to 1973, and finally the period 1974-1994. Over time means, variances, and correlations have changed. The pre-WWI period is mainly associated with low mean inflation and high growth (high growth relates primarily to the U.S.). The inter-war period (1920 1939) was a period of low growth and deflation in both countries. The variabilities of both output growth and inflation were, however, very high in both countries. During this period the U.S. data imply pronounced procyclically inflation rates. The post-WWII period up to 1973 was a period in which growth rates were high in both countries, and in this period inflation seems countercyclical in both countries. The period after 1973 is associated with lower growth and higher inflation than the earlier post-war period, but inflation rates remain

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M.O. Ravn, 5,L Sola / Journal of Monetary Economics 36 (1995) 497 526

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countercyclical. Hence, we find, as Backus and Kehoe (1992) and Cooley and Ohanian (1991), that moments change over time and that countercyclical inflation may be primarily a post-WWII phenomenon. Note also that the dynamic relationships between the series seem to change over time. Our interest is in the co-movements of the series, which do not necessarily change even in the face of changes in the marginal distribution of the individual series. A simple way to check whether the co-movements have changed over time is to compute rolling correlations between the two series as in Wolf (1991). Fig. 2a illustrates five-year rolling correlations for the post-war quarterly data for the four countries (the x-axis gives the central observation of a 21-quarter period

correlation

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M.O. Ravn, M. Sole/Journal of Monetary Economics 36 (1995) 497-526

Historical Data

Co,re~et~on 0.9 0.8 0.70.6 0.5 0.4 0.3 0.2" 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.9 -1 1879

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Fig. 2b. Rollingcorrelation- Historical data. in which the correlation is computed). From these plots it appears that the co-movements between output and inflation have indeed changed particularly for the U.S. and Japan. Fig. 2b illustrates 16-year rolling correlations for the historical data. These indicate that the correlation between inflation and output growth has changed a number of times during the sample period. There are periods of countercyclical prices and periods of procyclical prices in both countries. The problem with this technique is that one is imposing a continuing change in regime over the sample period by treating every five (16) successive years' observations separately. Such an assumption does not seem very realistic, and the information may be obscured if regimes have, in fact, not changed. This motivates our alternative technique outlined in the next section.

M.O. Ravn, M. Sola / J o u r n a l o f M o n e t a ~

E c o n o m i c s 36 (1995) 4 9 ~ 5 2 6

509

3. Stochastic representation Discrete state switching models have been used widely (e.g., Hamilton, 1988, 1989, 1990; Phillips, 1991; Sola and Driffill, 1994) to characterize dramatic movements in time series due for example to changes in macroeconomic policies or to take account of shocks. Our concern is to investigate the co-movements between prices and output. If these series have shifts in their unconditional means that are not taken into account, such changes will appear as changes in the variance-covariance matrix. We will try to avoid this problem by modelling the data as having state-dependent means. In particular, we will use a discretestate-space framework in which there are four possible states of nature made up of combinations of either series having 'high' of 'low' means. We are going to follow Phillips' (1991) application of Hamilton (1988). Phillips models a bivariate relationship a being generated by two independent M a r k o v processes. We make two changes. First, we will only be concerned with the joint distribution of the series instead of fitting autoregressive processes. Second, as in Hamilton (1990), the variance-covariance matrices will be allowed to change between the regimes. We will therefore explicitly model the changes in the means of the series and then analyze the variance-covariance matrices to obtain an estimate of the covariance in the different regimes. Consider a vector xt = [p,, y~]' (p denotes the rate of inflation and y the rate of output growth) which is generated by a vector stochastic process given by X t = ]Is, ~- 0 s Ut,

(1)

]ist = ] i 1 S l t + [12S2t -t- f l 3 S 3 t + tL, s4t,

(2)

where sit= 1

= 0

if the state is i at time t, otherwise.

Accordingly, the means of the series are modelled as

]i =

]As = 1

LYhJ

LYhJ ]is = 3

LYl J

Yl

'

where the indices h and I refer to 'high' and 'low'. The four-state M a r k o v process can be generated by assuming that each series, Pt and Yt, follows a two-state M a r k o v process. Define xt = [p,, y,]' with a state-dependent mean, ]i.,, given by ]is =

o + ills,

,, ,

where sl can take the values 0 or 1, and si' can take the values 0 or l, where s't and sy are independent of ut. We will make the following three distributional

510

M.O. Ravn, A'L Sola / Journal o f Monetary Economics 36 (1995) 497-526

assumptions: (1) u, ~ N(0, S),

(2) xtl(st = s) ~ N(/~s, X,) for s = 1,2,3,4,

(3) Z, = O'~NOs.

F o r each state there is an associated v a r i a n c e - c o v a r i a n c e matrix,

=(4/,i ..,(sq \~,..(s)

a~(s)J'

where the regime is indexed by st, and the states are modelled as the o u t c o m e of an unobserved discrete-time, discrete-four-state first-order M a r k o v process independent of ut-i for all i ¢ 0. In the general case the transition matrix will be given by a 4 x 4 matrix, A, with elements ~ij where rc/j = P(st = i[ st_ 1 = j), i,j = 1, 2, 3,4. It is imposed that each column of the transition matrix sums to unity and that all elements are nonnegative. U n d e r this scenario we have r tt allowed for a correlation between st and &. We can impose a n u m b e r of different restrictions on the transition matrix in order to test various alternative hypotheses. If we assume that inflation and o u t p u t g r o w t h each follows an independent regime-shifting process, the transition matrix will be given by I]indep :

rephrcy,,

(1 -- ~p,)Tcy,~

ZCp,,(1 - ~y,)

(1 - yVp,)(1 - ~:y,)~

(1 -- 7rph)rcyh

r~p,~r~

(1 -- rCph)(1 -- try,)

~p,(1 -- ~,,)

rrph(1 -- gy~)

(1 -- rcp,)(1 -- =yh)

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(1 -- ~p,)rty,

(1 -- 7rp~)(1 -- gy~)

~p,(1 -- rty.)

(1 -- gp,.)rcy,

~p,rty,

)

'

(5) where, e.g., rtph = P(s't = 1 Is't- 1 = 1) is the probability of remaining in a state with high mean of inflation at time t, and the other transition probabilities are defined similarly. This model is clearly a restricted version of the general model which allows for correlation between the states, and we can test the plausibility of the restricted version by using a likelihood ratio test that (under the null hypothesis) is distributed as a X2(8). We will also be interested in testing whether one of the variables leads or lags the other variable, which is equivalent to prices (output) always being in the state that o u t p u t (prices) was one period ago. It should be clear that rejection of this hypothesis does not imply that one series does not lead the other series. We simply test whether the unobserved state variables can be modelled such that one state variable in period t is in the state that the other state variable was in the previous period. The appropriateness of this specification can be tested [using L R tests distributed as ;~2(10)] by checking if we can reduce the transition

511

M.O. Ravn, M. Sola / Journal of Monetary Economics 36 t1995) 49~526

matrices to

II ply

(1--Ttp~) 0 0

ilYtp =

0

0 0 (1--~r~,)

0

1 0

~p,

'

0

0 0

(1--Tzr,) 0 0

/

0

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0 1

~)'l

/

(6) where 17pty (IP qv) indicates 'prices lead o u t p u t ' ('output leads prices').

3. I. Why correct for a changing mean? 1 it is useful to show why it m a y be i m p o r t a n t to model the m e a n correctly when looking at the c o - m o v e m e n t s of the series. We will show that both the unconditional and the conditional covariance will be biased if a changing mean is not corrected for. First, assume that the states can be observed and let i indicate the states defined above. In that case the covariance between p, and y, is given by

covi(Pt, Y~) = E(PtYt) - (~o + ~lS'tl (flo +/31si'),

i = 1, 2, 3,4,

where cov(pt, y,) denotes E[(pt - ~o - ~lS't)(y, - flo -/31si')] s',, s'/]. N o w assume that % ~ (~o, ~o + ~l) and T v e (rio,/3o +/31) where ~p is the unconditional mean of Pt and T r is the unconditional m e a n of Yt when we do not allow for different regimes. Then, not allowing for changes in regime when changes do take place will generate a positive bias in the unconditional covariance in state 1 and a negative bias in state 4. In states 2 and 3 the sign of the bias will depend on the relative sizes of ~0, ~1,/3o,/31. W h e n the states are unobserved, we need only multiply by the (unconditional) probabilities of the states, 7ri = P(s = it. If one did not allow for regime changes, then the covariance is given by E(pt, Y t ) - TrT~,. One can now show lhat a positive bias in the covariance will be induced whenever tPpttly < 9~¢0(/30 ~- /31(gl "1- TO21) -IF !Z1(/30(IZ'l q- 7~3) ~- /317~1).

Therefore, the unconditional covariance will in general be biased when a changing m e a n is not corrected for. An alternative measure, that is highly informative, is the conditional covariance where the covariance is evaluated as the sum over the four possible states of the covariance in each state times the

tWe are grateful to Allan Timmerman for discussions of this section.

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M.O. Ravn, M. Sola / Journal of Monetary Economics 36 (1995) 497-526

probability of the state. This yields a time-varying measure of the conditional covariance taking the different regimes into account.

4. Empirical results In this section we apply the techniques outlined above to the two different sets of data on output growth rates and inflation rates. First, we investigate which of the specifications of the Markov structure appears appropriate. The following table gives the results of likelihood ratio tests of the restrictions implied by either of the alternative hypotheses (independent Markov chains, prices leading output, and output leading prices) when tested against the general specification. From the table, it is clear that the specifications 'prices leading output' and 'output leading prices' can be soundly rejected for all countries and for both sets of data. However, there is strong evidence in favour of the alternative specification in which the (unobserved) states are generated by independent Markov chains. There is no way that one can reject the restrictions implied by this alternative specification, especially for the U.S. and the U.K., independently of whether one inspects the results for the quarterly post-war data or the annual historical data. The evidence is less strong for Japan and Germany, but one would accept the alternative at conventional levels of significance. Therefore, we will be using the results of this alternative specification. It should be absolutely clear that this does n o t imply that the series themselves are independent or that they cannot change regime simultaneously; it simply means that the unobserved states that generate the changes in means can be modelled as independent Markov chains. Table 2 LR tests of the specification of the Markov-switching model Alternative hypothesis

Country

Independent states

Output leads prices

Prices leads output

LR

Prob(%)

LR

Prob(%)

LR

Prob(%)

14.42 13.50 6.11 2.92

7.15 9.58 63.54 93.94

35.82 21.41 32.66 32.31

0.01 !.84 0.03 0.04

48.10 25.44 26.00 33.75

0.00 0.46 0.37 0.02

4.86 7.40

77.20 49.46

43.27 75.12

0.00 0.00

44.80 73.34

0.00 0.00

A. Quarterly data Japan Germany U.S. U.K. B. Historical data U.S. U.K.

M.O. Ravn, M. Sola / Journal of Moneta~ Economics 36 (1995) 497 526

513

Table 3 Results for means in the preferred specifications

Japan

Germany

United States

United Kingdom

A. Quarterly rates Mean of output growth in state 1 Difference of mean output growth rate Mean of inflation in slate 1 Difference of mean inflation rate Eog-likelihood

1.935 (11.650)

0.616 (5.6111

0.990 q l 1.778)

0.637 (2.816)

1.028 ( - 5.363)

0.539 (1.675)

0.958 6.514)

- 0.060 ( - 0.2391

1.723 (14.649)

0.779 (15.364)

1.193 t21.2331

1.142 (13.321)

- 1.331 ( - 10.262)

0.609 (5.323)

137.925

0.803 i21.04)

- 117.448

2.395

1.892 (9.942) - 202.054

B. Historical data Mean of output growth in state 1 Difference of mean output growth rate Mean of inflation in state 1 Difference of mean inflation rate Log-likelihood

-

(

3.657 (7.852}

2.409 (7.552)

2.124 0.841)

- 0.839 ( - 0.720)

2.907 (7.938)

4.637 (12.7831

4.375 7.050t

5.(14I ( - 7.095)

- 478.138

389.815

Moments computed for log first differences multiplied b y 100. Numbers in parentheses a r e t-statistics.

Since the switching element in our analysis relates to the means of the series, the four states relate to the combinations of 'high' and "low" means of the two series. These states are estimated as the mean in one state plus the difference of the means in the two states. Table 3 gives the results for the means estimated in the specification with independent states. Our primary interest in this table is to check whether either series has experienced changes in its mean. A test of whether these two means are different is to check the significance of the t-ratio of the parameter 'difference of mean'. First, we will inspect the results for the post-war quarterly data for the G4. Output growth and inflation rates have both experienced changes in their unconditional means over time, though the evidence is less clear for the output growth series for the U.K. (the absolute value of the change in the mean is quite small and the t-statistic is insignificant). The reason for this is clear from

514

M.O. Ravn, M. Sola / Journal of Monetary Economics 36 (1995) 497-526

Fig. 1; for the U.K. there is no clear evidence of changes in the mean of output growth. Notice, however, that the changes in the variance of output growth still occur over the sample period, a feature we are still able to model. A case where the difference between the two means is large is the rate of growth for the U.S., where the mean in the 'low' state is close to zero, while in the 'high' state it is almost 1 percent per quarter. These differences are even more evident as far as the rates of inflation are concerned. For all countries in the sample we estimate that the rate of inflation in the 'high' state is around twice as high as the rate of inflation in the 'low' state. The most extreme case is Japan where inflation in the 'high' state is close to 4 times inflation in the 'low' state. From the results for the historical data, it is clear that there have been significant changes in the mean inflation rates over time. Our estimates imply that there is a high-inflation regime in both countries in which the inflation rate is positive (around 3 percent in the U.S. and round 4.6 percent in the U.K.). In the low-inflation regime, the estimates imply deflation rates of around 1.5 percent in the U.S. and 0.4 percent in the U.K. Relative to the results of the quarterly data, these results are explained by the fact that both countries experienced falling prices, or very stable prices, in the inter-war period as well as during the Classic Gold Standard. Hence, in historical perspective, the post-war period qualifies as a period with relative high inflation. The evidence of changes in the mean growth rate of output in either country is less clear since the t-statistics on the change in the mean growth rate are not particularly significant. But, again there have important changes in the variance of output growth and we will be able to model these changes. The point estimates imply that the U.S. has a high-growth regime with a mean output growth rate of just above 3.5 percent annually and a low-growth regime in which the growth rate is close to 1.5 percent. The U.K. growth rate in the high-growth regime is, not surprisingly, estimated to be lower with a point estimate of 2.4 percent, but the growth rate in the low-growth regime is close to the U.S. estimate being 1.6 percent. Fig. 3 plots the estimated probabilities of output growth and inflation being high for the four countries included in the post-war dataset and for the two countries in the historical dataset. Table 4 lists the periods where (1) the probability of either regime is bigger than 80 percent and (2) the regime lasts for at least for four periods (i.e., one year for the quarterly data and four years for the historical data). From the table (and Fig. 3) we can see that in general the filter allocates substantial time spells to each of the regimes. The only exception is the lowgrowth regime for the U.S. in the quarterly data which is singled out as the dominating regime for a period of a year between 1979.2 1980.1.2 An interesting 2Because of the definition of a 'dominating regime" this does not imply that the probability of low growth in the U.S. is zero over the rest of the sample period. The regime occurs, but dominates less, in periods around 1961, 1970, 1974/75, 1979/80, and 1991.

M. O. Ravn, M. Sola / Journal of Monetary Economics 36 (1995) 497 526

Japan Independent Specification

Probability 1"9 t 1.2

High Growth 0.9

~

0.8

~

!

!

o.61ii

!

o.6ili

i

! i

0.7

t

ii

ii...............::.,.;..L......':."~--:,,~ .........

.........................................................

o ....... !- ................. i........... i........... 1965 1970 1960

Date

1976

1~60

1965

1990

United Kingdom

Probabilit 1.3

Independent

Specification

1.2 1.1

High Growth ";~

"'½]i } ..... High Inflation

0.9

!:~ii

0.8 0.7 0.60.50.4

jl

0.3 0.2 0.1

0 ,;,,,":,,~,;~7,.,,,',;r,-,n,,;7,,7,~;f't~rrm~ 1970 1975 1955 1960 1965 Date

United

Probability 1.3

1980

1965

1990

States

Independent Specification

1.2 1.1 1

High Growth

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 ~igh Inflation

0.1 0 1957 1960

1965

1970

F i g . 3a. E s t i m a t e d

1975 Date

probabilities

1980

1985

Quarterly

1990 data.

515

516

M.O. Ravn, M Sola / Journal of Monetary Economics 36 (1995) 497-526

Germany Independent Specification

ProbabiIity 1.3 1.1 ]

,

i;"'i ~"i

0.9 i~

High

Inflation

0.8

0.81i 0.71 ~i 0.5

i

0,4 0.3

i i

0.2 0.1

i }

............!~',: 1960 1965

0

1970

1975 Date

1980

1985

1990

Fig. 3a (continued)

set of observations from the quarterly data concerns the experience of the four economies in the early 1970's. The high inflation of the 1970's is normally attributed to the first oil price shock of October 1973 when crude oil prices rose by 70 percent. There is though some evidence that this may not be the only explanation. The high-inflation regime in Japan starts, at the latest, in the second quarter of 1973, whilst for the U.K. the low-inflation regime is predicted to end by the last quarter of 1970, with high inflation taking over by the fourth quarter of 1974. For the United States, low inflation ends in the first quarter of 1973 with high inflation taking over in the third quarter. These observations may imply that the exchange rate uncertainty associated with the Smithsonian agreement (established on December 18th, 1971) and the loss of credibility of the central banks' commitment to fixed exchange rates affected worldwide inflation rates. It is also noticeable that for the U.K. our estimates imply a period of low growth around 1971.3 1973.1. From the annual data we see that, in historical perspective, the post-WWII period has for both the U.S. and the U.K. been a period of high inflation. Low inflation in the U.S. seems associated with the period from 1927-1945 and the initial years of the gold standard (1873 1898). For the U.K., the low inflationary experience of the inter-war period is estimated starting in 1926 and ending in 1936, but the periods 1875 1899 and 1902-1911 are also estimated to have low inflation. Output growth is less divided into a pre-WWII and a post-WWII phenomena, but for both countries it is the case that there was an extended period in the 1950's and the 1960's in which output growth was relatively high. Table 5 lists the variance covariance matrices associated with each of the possible regimes.

M.O. Ravn, M. Sola / Journal o¢ Moneta O, Economics 36 (1995) 497 526

Jnited States

Probability

1 019 pJf~

0.8 0.7 0.6 0.5 0.4

517

1

iv !High Inflationi

High Growth !

0.3 0.2 0.1

1900

1871

1920

1940

1960

1980

1994

1980

1994

Date

United Kingdom

Probabilit

018

_ _

oi7i

!

0.6 }

High Growth

02 i

ii

oi,

ii] i'i

o 1871

2

: .,,-,,

1900

.......

1920

'

Date

1940

Fig. 3b. Estimated probabilities

1960

Historical data.

First, we comment on the association between the mean of inflation and its variance. In a classic study, Okun (1971) examined the relationship between the level of inflation and its variability. For data covering 17 O E C D countries he found that countries with high average inflation also had high variation in inflation. He also analyzed whether there was a typical association between output variability and inflation variability, but found no strong evidence of this. Okun's findings were re-examined and supported in a number of other studies (see, e.g., Gordon, 1971; Logue and Willet, 1976). 3 Taylor (1981) provides some 3Gordon (1971) showed that the correlation between mcan inflation and inflation variability is sensitive to the sample period. Logue and Willet (1976} found evidence of nonlinearities such that the correlation was stronger in high-inflation countries.

518

M.O. Ravn, M. Sola /Journal of Monetary Economics 36 (1995) 497-526

Table 4 Dating of regimes Regime

Japan

Germany

United States

United Kingdom

High growth

1955.3-1956.2 1957.2 1975.3

1960.2-1962.1 1962.3 1963.4

1961.3 1969.2 1972.3 1973.2 1974.3 1978.4 1980.2-1981.1 1983.2 1990.2 1992.1-1993.1 1993.3 1994.4

1958.2 1960.4 1961.2 1962.3 1963.2 1964.3 1974.2-1975.4

Low growth

1976.1-1994.3

1964.4 1969.3 1974.2-1986.4 1987.4 1994.4

1979.2 1980.1

1965.3-1967.3 1971.3 1973.1 1976.3 1990.4 1991.2-1994.4

High inflation

1956.3-1957.2 1959.3-1962.1 1970.2 1971.1 1973.2-1978.3

1960.2-1961.1 1968.2-1969.2 1973.4-1974.4

1973.3 1981.1

1973.4 1978.2 1980.1~1981.1

Low inflation

1966.4-1967.3 1979.1-1994.3

1963.1-1967.4 1975.2 1976.3 1977.1 1979.2 1979.4 1994.4

1957.2 1970.1 1970.3-1973.1 1982.3-1994.4

1956.1 1970.4 1981.2 1994.4

1872-1879 1889 1893 1902 1907 1953 1973 1984-1994

1872 1887 1949 1972 1983-1994

1916 1924 1931 1936 1941 1944 1946-1949 1978-1982

1892-1897 1915 1928 1944-1947 1973 1981

A. Quarterly data

B. Historical data High growth --.... Low growth

---

-

--High inflation

--

--

1902 1910 1915 1924 1946-1994

1915-1923 1939 1949 1951 1959 1961-1994

Low inflation

--

--

1872 1897 1927-1936 1938-1945

1874-1899 1902 1911 1926 1936

--

We attribute a regime to a given time period when the probability is above 0.8 and the duration of the regime is at least four periods.

M.O. Ravn, AlL Sola / Journal of Moneta~ Economics 36 (I 995) 497-526

519

Table 5 Variance covariance matrices of the preferred specification Regime

Japan

Germany

United States

United K i n g d o m

A. Quarterly data Low ,qrowth and low inflation w~r(3,)

0.517 (5.057)

I. 180 (6.537)

0.932 (5.658)

0.550 (7.7001

var(pt

0.188 (4.531)

0.256 (6.715)

0.315 (0.992)

0.577 (5.451 )

0.014 0.284)

-- 0.077 I -- 1.310)

0.033 (0.227)

coy( y. pt ( -

co r( y. p)

0.045

(

0.119 1.217)

0.146

0.065

0.21 I

Low growth and high inflation vat(y)

0.377 (4.263)

5.166 (2.323)

0.249 (1.544}

2.848 (3.332)

var(pl

0.302 (2.780)

1.185 (2.345)

0.066 (1.173)

0.914 (3.7961

- 2.377 2.277)

0.122 (1.297)

cov(), p) ( cor(y, p)

- 0.138 1.122)

(

0.408

(-

0.641 1.890)

0.961

0.950

0.398

High growth and low inflation var(y)

0.942 (2.676)

6.011 (7.868)

0.448 (5.737)

2.329 (4.541t

var(p}

2.123 (3.197)

0.240 (0.063)

0.120 (5.825)

1.783 (4.459)

cov(y, p)

0.675 (1.631)

cot(y, p)

0.477

(

- 0.155 0.84l)

(

0.011 0.354)

(

0.283 0.881)

0.129

0.046

0.139

High growth and high inflation vat(y)

3.090 (5.208)

2.510 (3.346)

t .818 (3.412)

4.816 (2.123)

var(p)

1.710 (5.641)

1.813 (3.339)

0.266 (3.467)

5.875 (2.185)

0.431 1.240)

- 0.347 ( - 0.770)

- 0.213 ( - 1.409)

cov(y, p) ( cot(y, p)

- 0.188

0.163

- 0.306

(

1.538 0.920) - 0.289

520

M.O. Ravn, M. Sola / Journal of Moneta~ Economics 36 (1995) 497-526

Table 5 (continued) Regime

Japan

Germany

United States

United K i n g d o m

B. Historical data Low growth and low inflation var(y)

64.41 (1.544)

9.20 (1.317)

var(p)

31.68 (1.787)

1.690 (1.511)

38.47 (1.409)

0.300 (0.321)

0.852

0.078

44.43 (15.82)

29.19 (33.76)

cov( y, p)

--

cor(y, p)

Low growth and high inflation var(y)

--

vat(p) cov(y, p)

67.48 (1.802) --

108.74 (11.64)

6.308 (-2.912)

- 9.180 (-4.516)

- 0.115

- 0.174

cot(y, p)

High growth and low inflation var(y)

31.62 (1.926)

2.934 (2.987)

var(p)

7.978 (3.564)

5.516 (0.95 I)

- 5.646 ( - 0.835)

2.532 (0.647)

cov(y, p) cor(y, p)

.

.

.

.

.

0.355

0.629

var(y)

8.393 (1.378)

2.542 (4.141)

var(p)

2.238 (0.671)

4.533 (4.714)

0.606 0.163)

- 1.433 ( - 2.213)

0.140

-- 0.422

High growth and high inflation

cov(y, p)

-(

cor(y, p)

--

var(y) denotes the variance of the o u t p u t growth rate. var(p) denotes the variance of the inflation rate. cov(y, p) (cot(y, p)) denotes the covariance (correlation) between the o u t p u t growth rate and the infaltion rate. N u m b e r s in parentheses are t-statistic.

M.O. Ravn, M. Sola / Journal of Moneta O, Economics 3c~ (1995) 497 526

521

time series evidence that a similar relationship holds over time. We can provide some additional information on this issue by combining the information of Table 5 with the estimated probabilities of each of the regimes. Since the quarterly data provides more information on this due to the fact that more countries are included, we will concentrate on these data. For Germany it is unambiguously the case that high inflation and high variability of inflation go hand in hand. Furthermore, from the estimated probabilities we get the result that the high-inflation period, which was also associated with high-inflation variability, covers mainly the period 1968 1974.4. A similar but slightly less clear result appears for the U.S. where most of the period 1973.3-1981.1 is associated with high variability of inflation and persistently high levels of inflation. To give some numbers, we estimate the level of inflation to be around 1.2 percent per quarter before and after this period but as high as 2 percent per quarter within this period. For the U.K. we estimate that inflation is high during a similar period extending from 1973 1981.1, whereas the variability of inflation is only abnormally high during a shorter period which starts in 1973.4 and ends in 1976.2. In the Japanese data high-inflation variability is estimated to be associated with high output growth, and there is therefore no strong evidence in favour of an association between the mean inflation rate and the variability of the inflation rate for this country. However, it is clear that the lowest inflation variability occurs in the regime that involves low growth and low inflation which dominates for a very long period (from 1976 to 1994). In summary, we find some evidence in favour of Okun's finding of a positive association between the mean inflation rate and its variability. It is noticeable that the difference between the estimated variances of the series in the four regimes are in some cases remarkable. As an example, note that while the variance of inflation for the quarterly U.K. data in the regime with high growth and high inflation is only slightly less than 6, the variance in the regime with low growth and low inflation is only 0.58. The changes in the variances estimated for the annual data are equally considerable. Our primary interest lies in the co-movement of the series summarized here by the covariance between the rate of output growth and inflation. In the quarterly data we find that the covariance between the two series is negative in all but three cases: (i) the regime with high growth and low inflation in Japan, a regime that dominated in the late 1950's and again in two periods during the 1960's: (ii) a regime with low inflation and high growth in the United States (which dominates for a few short spells during the sample); and (iiil a regime with low growth and high inflation in the United States. This latter regime occurs for a few quarters in the period 1974 1981. In most other periods and in all other regimes, the covariance between output growth and inflation is estimated to be negative for the four countries in the sample. The results for the annual historical data imply that the covariance between inflation and output growth is negative in five out of eight cases. For the U.S. we

522

M.O. Ravn, M. Sola /Journal of Monetary Economics 36 (1995) 497 526

find a negative covariance in all regimes except when inflation and output growth is low. In this regime the correlation between the two series is high and positive although the covariance is not significantly different from zero. This was the dominating regime primarily during the last part of the inter-war period and during WWII (1931-1944). In the other regimes the covariance between inflation and output growth is estimated to be negative but moderately so. For the U.K. there are two regimes in which the point estimate of the covariance between inflation and output growth is negative: (i) when growth and inflation both are high and (ii) when growth is low and inflation is high. These regimes correspond mainly to the period after 1949 and to a period from 1915-1923. Pronouncedly procyclical inflation is related to the regime where growth is high and inflation is low, a regime that mainly is associated with the early years of the gold standard (1875 1889). Notice, however, that the covariance is not significantly different from zero in this regime. The important question is what the estimated covariance matrices together with the estimated probabilities of each of the regimes imply for the correlation between output growth and inflation. In other words, are the negative correlations in Table 1 the result of a few major real shocks? An informative measure in this respect is the conditional correlation given by the sequences cor(pt, Yt)] f2t which we can compute as 4-

cor(pr, y,)l f2t = ~

¢r(st = i)c6r(p,, y,)g,

i=1

where Or(st = i) = P(s, = i[ f2~)(i = 1, 2, 3, 4) is the estimated probability that the state at time t is i, and c6r(pt, Y,)i is the estimated correlation between the inflation rate and the output growth rate in state i. Plots of these sequences of (time-varying) conditional correlations for the four countries are given in Fig. 4a (quarterly data) and Fig. 4b (historical data) and can be thought of as our equivalent to the rolling correlations (see Fig. 2) once the different regimes are taken into account. Fig. 4a, the post-war data for the G4, makes it clear that the negative correlation between output growth and inflation is not caused by a few major real shocks during this period. The implied conditional correlation for the U.K. is negative over the whole period. It is more pronouncedly negative during the period 1971.3 to 1981.1, but at no point does it become positive. Note that the period with the more negative correlation begins prior to the first oil price shock. For Germany we also find a negative correlation between output growth and inflation over the whole sample with only two short spells of a very negative correlation and a typical correlation in the neighbourhood of - 0.15. The two instances with a very negative conditional correlation occur first in the late 1960's and then around the first oil price shock (1974.2-1974.4). For the U.S. we estimate a very mild negative conditional correlation between output growth and inflation over most of the sample. The exceptions to this are the following. First, there is a rather long period of a more pronounced negative correlation

M.O. Ravn, M. Sola / Journal oJ'Monetao, Economics 3¢5 (1995)497 526

523

correlation

0.2 0.1 O

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

-0.1 ..............

1955

1960

1965

1970

1975

1980

..........

1985

............

1990

Date correlation 1.4-

Quarterly Data

1.2

1 0.80.6 0.4 0.2 0 -0.2 -0.4 -0.6 -]

-0.8 1

,.j

-1 1957 1960

1965

~

1970

1975

1980

1985

1990

Dote

Fig. 4a. Estimated conditional correlations Quarterlydata.

from 1974-1979. Then there are three instances of procyclical prices: the first is 1973/74, the second 1979/80, and the third covers two quarters in 1981. Results over the remainder of the sample imply that the correlation between growth and inflation is mildly negative. For Japan we find that inflation has been negatively correlated with output growth ever since the first oil price shock. Before 1973/74, there seems to be no typical relationship and there are periods both with procyclical prices as well as periods with countercyclical prices. The longest period with procyclical prices is the spell from 1965.4 to 1968.3 where output growth was high. Fig. 4b. which replicates the analysis for the historical data, gives a similar picture. From the annual data, we lind a quite stable and negative correlation between inflation and output growth in both countries during the post-WWll

524

M.O. Ravn, M, Sola / Journal of Moneta~ Economics 36 (1995) 497-526 Correlation 1 0.9 0.80.70.6 i.'.J 0.5 i 0.4-

i

Historical Data

i

~Jiite; ~'i!g dOm

United States

o.3 i 0,2 0.10 -0.1

i ! ~

I

-0.2-0.3-

/~J '

-0.4 -0.5 -

1871

-

1900

1920

Date

1940

~ ~,,'-." 7 ~.......i

1960

" ........ -.s

1980

1994

Fig. 4b. Estimated conditional correlations - Historical data. period. The correlation is more strongly negative for the U.K. and the regime starts earlier than in the U.S. In the U.K. inflation seems countercyclical basically from 1938 and onwards. Prior to this, the period 1874 to 1914 is mainly associated with procyclical inflation as is a shorter period from 1925 to 1937. In between these two periods, there is a period of moderately countercyclical inflation from 1915 to 1924. For the U.S. the result imply that strong procyclicality of inflation is a phenomenon mainly associated with the later part of the inter-war period and WWII (to be precise, the period 1926 1945). Before and after this interval, inflation seems generally to have behaved countercyclically with the exception of the period 1880 1887. Hence, for the U.S., the results imply that at the annual frequency a moderately negative association between contemporaneous inflation and output growth seems more the rule than the exception• The question that remains is whether our results are comparable to the others in the literature that have looked at the stability and time dependence of the relationship between prices and output from the perspective of rolling correlations (e.g., Wolf, 1991; Smith, 1992). Our technique differs from rolling correlations in that, while the latter implicitly assumes a continuous change in regime and treats observations within a given window as independent of observations outside the window, ours tests for any such changes and models them as discrete. We can compare the results of the measure computed when the regimes are taken into account with the rolling correlations computed for the same data set in Section 2. This comparison clearly indicates that the rolling correlations tend to exaggerate the movements in the correlation and may therefore not be very informative. By using rolling correlations one would conclude from the quarterly data that the correlation between inflation in the U.K. and the U.S. are quite unstable, whereas the conditional correlations imply a very stable correlation with the exception of the U.S. in the 1970's. A similar observation holds for

M.O. Ravn, M. Sola / Journal of Monetar), Economics 36 (1995) 49"7526

525

Germany. The only exception is Japan where the two measures give more or less the same answer for the period after 1971, though differing prior to this. Similarly, the rolling correlations computed for the annual data make it unclear whether inflation is procyclical or countercyclical, but lhe results we have found imply a more stable relationship especially during the post-WWII period. 5. Conclusion and summary

New research on business cycles has found that prices and output are in general negatively related over the business cycle, thereby rejecting a 'monetary myth'. Criticism of this new view has been that it is a few major real shocks which bias a typically positive correlation between prices and output so that the measured correlation is negative. Our paper has tried to investigate this issue. In particular, we assumed changes in the means of output and prices to be governed by a four-state Markov process. Using this technique, we found that changes in means and second moments have occurred during our sample periods and that the negative relationship between output and prices is not dictaled by a few major real shocks. Instead, we have found that the typical correlation in the post-WWll quarterly data is negative. A similar result holds for the historical annual data in which we find, as Backus and Kehoe (1992) and Cooley and Ohanian (1991t, that the typical covariance is negative and that, especially in the U.S., procyclical inflation is an inter-war phenomenon. In the U.K. procyclical inflation extends over a longer period, but countercyclical behaviour appears to start somewhal earlier than in the U.S., and the correlation is more pronouncedly negative than in the U.S. Our findings differ from previous results, particularly Wolf's (1991) study which finds that in the U.S. countercyclical prices are a post-1973 ito 19801 phenomenon with prices being procyclical before and after this period. While the detrending techniques used are different, our results still imply that rolling correlations may exaggerate movements in the correlation because of the implicit assumptions that are made when computing such a measure. We find a much more stable relationship. To conclude, one cannot easily dismiss the finding that prices are countercyclical with reference to a few major real shocks. References

Backus, David K. and Patrick J. Kehoe, 1992. International evidence on the historical properties of business cycles, American Economic Review 82, 864 888. Balke, Nathan and Robert Gordon, 1986, Appendix B: Historical data, in: R. Gordon, cd.. Tile American business cycle: Continuity and change (University of Chicago Press, Chicago, IL). Blackburn, Keith and Morten O. Ravn, 1992, Business cycles in the I_J.K.: Facts and ficlions, Economica 59, 383 401.

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