Interplay Between Business Cycles

The preceding section verified the existence of the Juglar and Kunznets cycles, with also some weaker evidence of the existence of the Kitchin cycle. In this section, we will apply the CF filter to portray the path of economic development by means of interplay between business cycles. The cyclical components of the fifteen countries aggregate GDP by filtering is displayed in Figure 1.9. A more recent decomposition of industrial production is displayed in Figure 1.10.

Figure 1.9 CF-filter decomposition of World GDP cycles, 1870-2008, yearly data

-8.00E-02 -6.00E-02 -4.00E-02 -2.00E-02 0.00E+00 2.00E-02 4.00E-02 6.00E-02 8.00E-02

1870 1875 1880 1885 1890 1895 1900 1905 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

3-5 7-11 15-25 40-60

Figure 1.10 CF-filter decomposition of World IP cycles, Q1/1961-Q1/2009, quarterly data

-0.05 -0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04 0.05

Q1 1961 Q3 1962 Q1 1964 Q3 1965 Q1 1967 Q3 1968 Q1 1970 Q3 1971 Q1 1973 Q3 1974 Q1 1976 Q3 1977 Q1 1979 Q3 1980 Q1 1982 Q3 1983 Q1 1985 Q3 1986 Q1 1988 Q3 1989 Q1 1991 Q3 1992 Q1 1994 Q3 1995 Q1 1997 Q3 1998 Q1 2000 Q3 2001 Q1 2003 Q3 2004 Q1 2006 Q3 2007 Q1 2009

3-5 7-11

How did the Kitchin, Juglar and Kuznets cycles fluctuated over the last fifty years?

Columns labeled R in Appendix 1.1 shows the peaks and troughs of business cycles in terms of business cycle reference dates recognized by the OECD. While the columns labeled Ki, Ju, Ku are the business cycle turning points of the Kitchin, Juglar and Kuznets cycles under the recognition of CF filter. Generally, the reference dates was always deemed as Kitchin cycles in literature. In Table 1.9, we compared the reference dates by the OECD and the turning points of our Kitchin cycles, and we found that within one year before and after OECD reference dates of peak and trough, 73.9% we can find a corresponding Kitchen cycle turning point. As for each of the countries discussed in this section, they are still highly in parallel between reference dates by OECD and our Kitchin cycles. However, the turning points of Kitchin cycles do not always have corresponding reference dates recognized by OECD. For example, in most of the 15 countries, there were a contraction phase of the Kitchin cycle in the period 2004~2005, but it has been recognized by the OECD as business cycle turning points in only a few countries. The reason for this was due to the interplay between shorter- and longer-term cycles.

Table 1.9 Matching the OECD business cycle reference dates and Kitchin cycle turning points

0^a 1^a 2^a 3^a 4^a U^b R^b

Austria 5 7 0 3 2 6 73.9%

Belgium 3 8 5 2 1 4 82.6%

Denmark 1 5 5 2 2 1 93.8%

Finland 5 11 2 1 3 1 95.7%

France 3 7 4 3 4 4 84.0%

Germany 5 5 6 4 2 1 95.7%

Italy 4 4 4 5 1 5 78.3%

Japan 3 9 4 1 0 4 81.0%

Nederland 2 8 5 6 2 0 100.0%

Norway 2 2 3 2 0 14 39.1%

Spain 4 5 4 2 1 7 69.6%

Sweden 3 6 5 2 2 4 81.8%

Switzerland 8 7 5 0 2 3 88.0%

UK 2 10 4 1 1 3 85.7%

USA 3 10 1 3 2 3 85.7%

Advanced countries

3 12 2 0 0 6 73.9%

a

0 denotes the turning points of business cycles dates of OECD and Kitchin cycle coincede, while 1, 2, 3, 4 denotes the two turning points are 1, 2, 3, and 4, quarters apart in time.

b

U denotes the number of turning points of OECD cycles dates that cannot be matched by Kitchin cycle turning points.

In the remainder of this subsection, we will discuss the effects of interaction between these cycles. For the convenience of discussion, we only discuss the incidents of joint upturns and downturns of all Kitchin, Juglar and Kuznets cycles and set aside the cases where one of the three cycles is in the downturn (or upturn) phase and the other two are in the other phase. The following are the brief summaries of the conclusions of Table 1.10.

Table 1.10 Average duration of expansion and contraction during long cycle upturn and downturn (quarters)

Upturn Downturn

Expansion Contraction Expansion Contraction

OECD 16.0 7.3 3.0 8.6

Austria 11.0 4.0 7.0 10.0

Belgium 12.0 6.0 5.0 4.5

Denmark 11.0 7.0 4.0 13.0

Finland 8.0 5.0 NA 6.0

France 7.0 7.5 5.0 11.5

Germany 10.7 5.0 6.0 8.5

Italy 8.0 6.5 5.0 14.0 Japan 19.7 NA NA 8.5

Netherlands 11.7 10.0 9.0 9.7

Norway 12.0 6.0 NA 6.5

Spain 11.8 7.0 4.0 9.3 Sweden 9.3 10.0 NA 14.0

Switzerland 11.5 4.0 6.0 8.0

UK 10.7 4.5 7.0 13.3 USA 13.7 8.0 7.3 6.4

Average 11.5 6.5 5.7 9.5

(1) Generally, when the Juglar and Kuznets cycles are in their upturn phase based on our identification, the upturn of the reference cycle defined by OECD countries always lasts longer. This can be seen in last row in Table 1.10: expansions during the simultaneous upturn of Juglar and Kuznets cycles last for an average of 11.5 quarters, is longer than the average expansion of 5.7 quarters when Juglar and Kuznets cycles are in simultaneous downturn. Besides, during these circumstances, expansion periods are longer than the contraction periods, which are 11.5 quarters and 6.5 quarters, respectively.

Below we shall take the aggregate OECD and the US as examples. The durations of expansions that started at Q4/86 and Q4/01 of OECD were 14 and 25 quarters, and they all lie in simultaneous upturn of Juglar and Kuznets cycles. In the US, there were also

longer expansions when Juglar and Kuznets cycles are in their upturn phases, especially the expansion starting Q4/01, the expansion of US lasted 25 quarters. In addition to the US, Germany and Japan both experienced the longest expansion of the postwar era as recognized by the OECD in the first decade of the 21^st century at the time with simultaneous upturns of Juglar and Kuznets cycles. It should be noted that, the contraction phase of Kitchin cycle did occur during 2004~2005, as shown in Appendix 1.1. However, literature has deemed slowdowns in that time as “mid-cycle pause”, which may strongly suggest that even with a Kitchin downturn, if the longer cycles are in the stronger parts of their upturn, the Kitchen downturn could be completely mitigated.

(2) In the simultaneous downturn of Juglar and Kuznets cycles, the duration of expansion is shorter and there could easily be two contractions within a brief time span.

The average period of contractions with simultaneous downturns of Juglar and Kuznets cycles is 9.5 quarters, which is longer than the average of 5.7 quarters of expansion periods when Juglar and Kuznets cycles are in simultaneous downturns. Besides, it is also longer than the average contraction period with simultaneous upturns of Juglar and Kuznets cycles which is 6.5 quarters. Take the OECD aggregate as example, during the period of Q1/64 thru Q3/67, the expansion that started at Q3/65 only lasted 3 quarters and it was sandwiched by two contractions during a span of merely less than four years.

With regard to contractions that started at Q4/79 and Q2/90, they lasted 13 quarters each and were the lengthier recessions in the post war era. Noteworthy, there were also double dips in the recession periods Q1/91~Q3/96 of Austria, Q1/80~Q2/83 of Belgium, Q2/89~Q2/93 of Spain, and Q1/79~Q4/82 of the US, and they were at a time when downturns of Juglar and Kuznets cycles coincide. In addition to the current financial

in Q2/64~Q4/67 and Q4/00~Q3/03 of Austria, Q4/88~Q2/91 and Q4/00~Q4/04 of Denmark, Q4/91~Q1/95 of Finland, Q4/00~Q2/03 of France, Q1/80~Q4/82 of Germany, Q4/89~Q3/93 of Italy, Q1/91~Q4/93 of Japan, Q1/80~Q1/83 of the Netherlands, Q2/98~Q1/02 of Spain, Q2/74~Q1/78 of Sweden and Q4/88~Q2/92 of UK. Consistent to our thesis results, they all occurred at times when the Juglar and Kuznets cycles were both in downturn.

In summary, the durations of upturns and downturns in the reference cycle of OECD were affected by the direct impact of medium- and longer-term waves. The observations presented above provide clear evidence for the existence of both medium- and longer-term cycles in the post war economy in the scope of the countries discussed in this section.

4.5.2. Experience in the Great Depression and the most Recent Global Recession

Before the World War II, due to the lack of officially recognized business cycle reference dates, as was available in discussions of the above subsection, we cannot discuss the issue in the same manner. However, there was a well known worldwide recession that is similar to the recent global financial crisis that can be used to discuss the interplay between business cycles, the Great Depression of 1930. Table 1.11 shows the nearest turning points of the three cycles before the start of the Great Depression of the 1930s. When the turning point before the outbreak of Great Depression is a peak, it means that the Great Depression occurred in the contraction phase of the corresponding cycle. Otherwise, it means that the Great Depression occurred in the expansion phase of the corresponding cycle

Table 1.11 Nearest turning points of each cycles before the Great Depression of 1930

Kitchin Cycle Juglar Cycle Kuznets Cycle Austria Peak (1930) Trough (1926) Peak (1925) Belgium Trough (1928) Peak (1930) Peak (1929) Denmark Peak (1930) Trough (1922) Peak (1922) Finland Peak (1929) Peak (1929) Peak (1928) France Peak (1929) Peak (1930) Trough (1922) Germany Trough (1927) Peak (1928) Peak (1923) Italy Peak (1928) Trough (1929) Trough (1927) Japan Peak (1929) Trough (1929) Trough (1930) Nederland Peak (1929) Peak (1930) Trough (1921) Norway Peak (1930) Trough (1925) Peak (1924) Spain Trough (1927) Trough (1929) Peak (1929) Sweden Peak (1930) Peak (1929) Peak (1929) Switzerland Peak (1929) Peak (1929) Peak (1917)

UK Peak (1930) Trough (1930) Peak (1917)

USA Peak (1930) Peak (1928) Peak (1925)

Advanced countries Peak (1928) Peak (1925) Peak (1922)

a

Turning point dates are in the parentheses.

From Table 1.11, 13 out of 15 countries we discussed in this section were already in the contraction phase of the Kuznets cycle before the start of the Great Depression.

Meanwhile, 8 countries were also in the contraction phase of the Juglar cycle and 12 countries were in the contraction phase of the Kitchin cycle. Due to the coincidence of Kitchin, Juglar and Kuznets cycle downturns across a majority of countries at the time, the severity of the recession is not surprising in the view of interplay between business cycles.

As for the current financial crisis, Table 1.12 is the nearest turning points before the start of this current recession. The aggregate OECD has passed the peak of the Kuznets cycle in 2006, and the peaks of Kitchin and Juglar in 2007. Therefore, when this worldwide recession started, it was in the downturn phases of all Kitchin, Juglar and Kuznets cycles. As previously discussed, there were only 7 incidents of simultaneous downturns of all Kitchin, Juglar and Kuznets, where 6 of them experienced severe recessions, with the current financial crisis one of them. In respect to country specific

data, 14, 8 and 13 countries of the 15 have passed the Kitchin, Juglar and Kuznets cycle peaks before 2008, respectively, the outbreak year of the recent crisis, which mirrors the Great Recession of 1930. The quarterly data also confirmed such observation.

Table 1.12 Nearest turning points before the 2008 World Recession

Kitchin Cycle Juglar Cycle Kuznets Cycle Austria Peak (2007) Advanced countries Peak (2007)

Peak (Q4/2007)

Peak (2007) Peak (Q1/2007)

Peak (2006)

a

Turning point dates are in the parentheses.

What are the implications when the economy in the joint downturns of Kitchin, Juglar and Kuznets cycles? From the discussions above, the implications are:

(1) The recession is probably longer than average.

(2) Recessions could be double-dipped even though recoveries have begun.

Thus, even when it seems to be signs of recovery in the second half of 2009, from the discussion of this section, the path to full recovery is likely to be long, hard and uncertain.

4.6. Concluding Remarks

In concluding this section, we would like to re-emphasis the observations in this section:

business cycles are not of the short-term type alone. The exercise in this section illustrates the importance of considering shorter- and longer-term cycles together, while interplay is essential to a comprehensive understanding of the process of the world economy.

Appendix 1.1

Table A.1.1 Reference business cycle date of 15 OECD countries

OECD Austria Belgium Denmark

Table A.1.1. (cont.)

Table A.1.1. (cont.)

Table A.1.1. (cont.)

Chapter 2.

Measuring CPI’s Reliability: the Stochastic Approach to Index Numbers Revisited

In this chapter, we shall discuss the measurement of the reliability of CPI. Here we will try to construct a new regression model that can measure the reliability of CPI, which model is an extension of the stochastic approach to index numbers. We allow for the mechanism of systematic change in relative prices in the literature of stochastic approach to index numbers to vary with time. Therefore, our model includes inflation rate and phases of business cycle dummies to allow for time varying. Such an extension can answer the Keynes’s critic on stochastic approach to index numbers. Moreover, we used US and Australian data, and compared the results from our setting with those from the traditional setting, and further confirmed that our setting was more appropriate than the convention.

I. Introduction

Price indexes play a vital role in economic and business decision-making. The Consumer Price Index (CPI) is inarguably the most commonly cited and eye-catching among them. However, as Manchau (2007) pointed out recently, “… prices were rising everywhere, yet the price index gives the illusion of price stability,” which signaled the CPI growth rate has become less reliable now in its measure of inflation. Therefore, searching for a better means in gauging the reliability of the CPI is not only theoretically an attractive topic, but also essentially important. To this end, this chapter

focuses on providing a new regression specification that can better help detect whether or not the CPI can be depended upon.

Essentially, we seek to provide new insights to the following familiar problem in the stochastic approach to index numbers (Bowley; 1907, 1911, 1919, 1926, 1928;

Edgeworth, 1888; Jevons, 1863, 1865, 1869; Liang and Chen, 2000; Mills, 1927;

Selvanathan and Rao, 1994). Given the inflation rate of n goods in

t

=1, 2,...,

T

periods

11... _n1, 12... _n2,..., 1_T... _nT

Dp Dp Dp Dp Dp Dp , how should we use this information to measure

the general inflation rate, which represents the proportionate change in the general price level?

The conventional approach to this problem was proposed by Clements and Izan (1987) and Crompton (2000). The basic assumption of their regression models was that an individual commodity’s inflation rate at time t is driven by an unknown central tendency, along with a time-invariant individual price trend of each respective n commodity. Consequently, by applying the panel estimation technique to the n individual commodities’ inflation rate data during the time period T, they obtained the estimates of the two corresponding sets of parameters, i.e., their central tendencies and individual price trends, as well as their corresponding estimated standard errors. Based on the stochastic approach to index numbers, the central tendency estimates were utilized to calculate the general inflation rates of

t

=1, 2,...,

T

, while the corresponding estimated standard errors could represent the reliability of the estimated general inflation rates (Selvanathan and Rao, 1994).

Yet, the models proposed by Clements and Izan (1987) and Crompton (2000) were incomplete, since the aforementioned time-invariant assumption in fact contradicted

with Mill’s (1927) proposition that specific individual price trends would vary in different price levels and business cycle phases. In the absence of addressing these concerns, the estimated standard errors of the general inflation rate may correlate with the inflation rate levels (Chang and Cheng, 2000; Debelle and Lamount, 1997; Fielding and Mizen, 2000; Parsley, 1996; Vining and Elwertowsky, 1976) and business cycle phases (Reinsdorf, 1994). As a result, the estimators of the standard errors of the estimated inflation rates obtained from Clements and Izan (1987), as well as Crompton’s (2000) regression models, can be subjected to the biased statistical problem.

We thus propose a resolution by relaxing the time-invariant assumption of the individual price trend by adding two sets of dummy variables representing different inflation rate levels and business cycle phases. Based on this framework, we try to estimate the general inflation rates and their corresponding standard errors in avoiding the statistical problems caused by the model misspecification, due to the omitted variables. Through our new regression, the estimated inflation rates are still computed by an expenditure-share-weighted average of the n commodities, which means its corresponding standard errors can still be interpreted as a reliability measure of the CPI.

Using Australian and US data spanning between September 1990 to March 2009 and January 1990 to December 2008, respectively, and comparing with the results of Crompton (2000), our research shows that the estimated standard errors of the estimated inflation rates have a weaker correlation with the inflation rate levels and business cycle phases in our specification. This implies that Clements and Izans’ (1987) and Crompton (2000)’s models were indeed incomplete. Without the unrealistic time-invariant assumption imposed on the inflation rates of individual commodity groups, this study

takes a step further in addressing the “Keynes’ (1930) critic” regarding the stochastic approach to index numbers.

II. Brief Introduction of Stochastic Approach to Index Numbers

Traditional schools studying index numbers wish to provide a most ideal formula to calculate inflation and other purposes they were interested in. However, the stochastic approach to index numbers is a very dissimilar framework, as it considers the index number to be merely an estimate of the true figure, and therefore there is uncertainty as indexes are the results of estimation. Hence the stochastic approach to index numbers emphasizes statistical protocols and would yield the entire probability distribution of inflation estimates rather than just providing a single number representing the rate of inflation. This section reviews the key elements of the approach and then discusses dome of its previous developments.

There are two major schools in the index-number theory. The first is the test approach that is associated with Fisher (1927) in particular, where indexes are judged for their ability to satisfy certain criterions. The other is the economic theory of index numbers that is founded on utility theory. In addition to those two, the stochastic approach is a less popular methodology but has recently been attracting considerable attention, since this method may provide more information than the two conventional approaches.

When applied to the prices, the stochastic approach to index numbers treats the underlying rate of inflation as an unknown parameter to be estimated from the individual sub sector prices. That is, the individual sub sector prices are observed with

error and the issue of obtaining a general price index becomes a signal-extraction problem, which is how to obtain a single estimation from combining the noisy sub sector prices while minimizing the effects of measurement errors. Under certain circumstances, this approach results in familiar index-number formulas such as Divisia, Lasypeyres, etc. The stochastic approach to index numbers provides not only a point estimate of the rate of inflation, but also its variance, which source is the divergence of the individual sub sector prices from a common trend, that is, the aggregate structure of relative prices changes. Accordingly, the stochastic approach provides a more intuitively plausible result that, it is more difficult to obtain precise estimates of inflation when there are large changes in relative prices.

The stochastic approach to index numbers is also relevant to the conduct of monetary policy and inflation targeting in particular. Although, the present popular approach to monitor inflation for policy makers is to exclude volatile items from the price index, such as food and energy, and specify inflation targets with “core” or

“underlying” inflation. However, as the goods with high price volatility have increased in their significance on economic affairs, it is inappropriate to conduct monetary policy without considering these volatile items. Therefore, more and more central banks have adopted the inflation rate target zone⁹ that included volatile items. In fact, the soft target (inflation rate target zone) could be established on a more satisfactory statistical foundation by employing the stochastic approach to index numbers, as it gives specific guidance on the weighting scheme of the index; which is comprehensive as it deals with all items in the basket, rather than assigning zero to the weights of volatile items. For

9

The Reserve Bank of Australia currently has a “soft” inflation target of 2-3 percent on average over the

cycle. Current Fed chairman Bernanke (2002) had also asserted the preference of an inflation target zone.

example, when conducting a soft target, the stochastic approach to index numbers could be used to express the inflation target as X percent ± 1.96 standard errors.

The stochastic approach originated in the works of Jevons and Edgeworth. They assumed the data generating process to be

it t it

Dp

=

α μ

+

(1)

where

Dp is the inflation rate in each commodity group (sub sector) at time t;

_it

α

_t is the general inflation rate at time t and

μ

_it denotes the independent error term. Under these assumptions, the best linear unbiased estimator of

α

_t is

ˆ_t 1

Dp

_it

α

=

n

(2)

which is the simple unweighted average of the n prices. Also we have

1 2

From (3) and (4), we see that when there is substantial divergence in relative prices, the sampling variance of

α

_t will be higher. This fits with the common intuition of the public that the general price index is more imprecise when the relative prices of many items diverge significantly with the general price trend. However, this regression specification fell into obscurity, perhaps in part due to the criticism by Keynes (1930,

pp. 85-88)¹⁰, saying that it was too rigid as the approach made no allowance for sustained changes in relative prices.

Following the tradition of Jevons and Edgeworth, there are two major branches of research on index numbers. The first is the “new stochastic” approach to index numbers that rectifies the “Keynes Critic” (Keynes, 1930) by introducing commodity specified dummies to allow for systematic changes in relative prices (or, specified individual price trend) (Clements and Izan, 1987; Crompton, 2000; Selvanathan and Rao, 1994).

The second branch deals with the problem of how relative price variability of Jevons and Edgeworth’ method varies with different economic environments (Chang and Cheng, 2000; Debelle and Lamount, 1997; Fielding and Mizen, 2000; Parsley, 1996;

Reinsdorf , 1994; Vining and Elwertowsky, 1976).

Of the first branch, the specification of Clements and Izan (1987) is an extension Jevons and Edgeworth’s by adding a commodity dummy to (1):

it t i it

Dp

=

α β μ

+ + (5)

where

β

_i denotes the constant systematic change in the relative price of commodity i.

Conceptually, these systematic changes can be interpreted as the expectation of the deviation of the ith relative price trend from the general price trend¹¹.

10

“The hypothetical change in the price level, which would have occurred if there had been no changes in relative prices, is no longer relevant if relative prices have in fact changed -- for the change in relative prices has in itself affected the price level.

I conclude, therefore, that the unweighted (or rather he randomly weighted) index number of prices

-- Edgeworth’s ‘indefinite’ index number -- ...has no place whatever in a rightly conceived discussion of

the problems of price levels.”

Clearly, Clements and Izan (1987) made great progress in the stochastic approach

Clearly, Clements and Izan (1987) made great progress in the stochastic approach

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