Vysoká škola ekonomická v Praze Národohospodá ř ská fakulta
Exploring the relationship between the oil prices and inflation
bakalá ř ská práce
Autor: Michal Borák
Vedoucí práce: Ing. Miroslav Kollár, M.A.
prosinec 2007
Prohlašuji na svou čest, že jsem bakalářskou práci vypracoval samostatně a s použitím uvedené literatury.
Michal Borák
V Praze, dne 30.12.2007
Abstrakt
Tato práce se zabývá zkoumáním vztahu mezi cenami ropy a inflací v USA. Analýza časových řad zahrnuje období 1971 – 2007 a jako veličiny užívá index spotřebitelských cen a různé míry cen ropy. Ve své analytické části zahrnuje 12 zpoždění inflace. V práci jsou taktéž uvedeny výsledky nejznámějších světových prací týkajících se tohoto tématu. Ve druhé části tato práce zkoumá prosakování světových cen ropy do maloobchodních cen benzínu v České republice a dále se zabývá, jak byl tento vztah ovlivněn měnovým kurzem CZK / USD.
Klí č ová slova
cena ropy, inflace
Abstract
This paper considers the relationship between the oil prices and inflation in the USA.
Analysis of the time series evaluates the period between 1971 and 2007 using the Consumer Price Index and different measures of the oil prices. The research includes 12 lags of inflation in its analytical part. It also covers the results and opinions of influential papers about this topic. In the second part the work identifies how the oil prices were reflected in the retail gasoline prices in the Czech Republic and especially how this reflection was affected by the CZK / USD exchange rate.
Keywords
price of crude oil, inflation
JEL Classification
E310, L650
Content
Introduction ... 4
1. The oil price – inflation relationship... 5
1.1 The brief historical facts about oil shocks ... 5
1.2 Some unavoidable information at the beginning ... 7
1.2.1 Oil and inflation measures used... 7
1.2.2 A method of analysis ... 9
1.3 Results ... 15
1.3.1 Non-lagged correlations ... 15
1.3.2 Correlations using lags ... 17
1.3.3 Correlations using the core CPI... 20
1.4 Other works on this topic... 23
1.4.1 Some more evidences accusing monetary policy ... 24
2. Gasoline prices and USD / CZK exchange rate ... 26
3. Conclusion ... 29
Literature ... 31
List of tables and figures ... 32
Introduction
The main objective of this work is to consider the relationship between the oil prices and inflation. This is a highly popular topic because of the continuously rising oil prices that will shortly reach the level of $100 per barrel. Thanks to mass media we are forced to believe that the products we use every day are more expensive due to these rising oil prices. Therefore I decided to explore this statement.
To find that relationship I use only the statistical models and apply them on US inflation. The USA was chosen because of enough information for inflation. Also due to a very high per capita consumption of oil the influence of the oil prices on US inflation should be higher than in other countries. The most widely used measure of inflation is the Consumer Price Index which I also use in my analysis. I use both the all-items CPI and the CPI that excludes food and energy.
In the second part of the work I will briefly identify how the oil prices were reflected in the retail gasoline prices in the Czech Republic and especially how this reflection was affected by the CZK / USD exchange rate.
1. The oil price – inflation relationship
1.1 The brief historical facts about oil shocks
At the beginning I would like to provide some historical facts about the oil prices and the major oil crisis. Until the first oil shock in 1973, the oil prices were very stable at about
$2 – 3. This stable development was mainly due to a regulation of prices which was applied continuously from the end of the WWII to the end of the 1970s (Hevler, pg. 2). There was a stronger price increase in 1956 during the Suez crises when the oil prices jumped by 13%.
As mentioned, the first major oil shock occurred by the end of 1973 when OPEC placed an embargo on oil exports to countries that were supporting Israel in Israeli-Arab war, especially the USA and the Netherlands. World oil supplies were reduced by 8% causing a sudden jump in world oil prices. In response the oil prices were quadrupled to nearly $12 per barrel by 1974.
Just a few years later, world was struck by another oil shock as a reaction to Iranian revolution. The revolution shattered the Iranian oil production causing almost 9% losses to world production. The OPEC countries increased their production to moderate the effect of this oil shock. Nonetheless, the price of crude oil rose by almost 100% to $39.50 per barrel creating a new record that was not broken till 2006. Inflation adjusted prices got over $100 per barrel, the price that has not been reached so far.
In the middle of the 1980s, oil prices were significantly reduced for the first time after the oil shocks. However, from this moment oil prices are highly volatile. Iraqi’s invasion to Kuwait and the following outage of oil supplies from these two countries in 1990 was responsible for a $20/barrel jump (about 80%) as world oil supply loss reached 9%. This oil shock was shorter than the two previous oil crisis as OAPEC (the Organization of Arab Petroleum Exporting countries) increased their oil output to stabilize the oil market.
A bigger oil price rise also occurred in 1999 and 2000 when OPEC started to limit its production in order to increase the oil prices. The price of oil rose by 200% in two years.
Since then OPEC monitored the prices carefully and reduced its production immediately after the prices dropped below $22 per barrel (Hevler, pg. 3).
Lastly, rising demand for oil especially in emerging markets as well as Iraqi war caused another increase in oil prices in the last four years. Although this oil price hike was not sudden, it reached the all-time record of $99.29 per barrel in November 2007. It is highly probable that shortly we will see the oil prices breaking the $100 level.
1.2 Some unavoidable information at the beginning 1.2.1 Oil and inflation measures used
For the purpose of measuring the oil price – inflation relationship I chose the US Consumer Price Index as a measure of price level in the USA. In my analysis I use the two different CPI indexes: the all-items CPI and the core CPI (the Consumer Price Index that excludes food and energy). Both of them are the non-seasonal adjusted indexes for all urban consumers. These are the most popular price indexes used to measure the price level in the USA. Food and energy are highly volatile commodities, the core CPI is therefore more stable (see Figure 1) and the final results will be slightly different when using this inflation measure.
I can now expect without any further analysis that there will be at least a small relationship between the oil prices and the all-items CPI due to a direct share of oil in the CPI basket.
Figure 1: Year-on-year changes in the Consumer Price Index
Year-on-year changes in the Consumer Price Index
0 2 4 6 8 10 12 14 16
1971 1975 1980 1985 1990 1995 2000 2005
Year
% change
all-items CPI core CPI
Source: Federal Reserve Bank of Saint Louis
Concerning the oil prices, there is a problem to find a relevant appropriate measure.
The most widely used and interpreted price of West Texas Intermediate, which is used as the underlying commodity for crude oil at NYMEX, goes as far as 1982. This is unsatisfactory for my purpose as it does not include the major oil crisis in the 1970s and only partially intercept the oil crisis in the early 1980s. Therefore, I am using the Refiner Acquisition Cost of Imported Crude Oil as an oil measure, instead. It is the cost of crude oil including transportation and other fees paid by the refiner. This type of measure is widely used by the
U.S. Energy Information Administration as it goes as far as 1974. It includes the second oil crisis in the early 1980s, however, it only partially covers the first oil crisis in 1973. To bridge over this period I am using the Official Price of Saudi Light for the first five years of the examined period, starting in 1970. The Refiner Acquisition Cost of Imported Crude Oil is usually about $4 lower than the price of West Texas Intermediate. The biggest negative of this type of oil measure is that it covers only the imported oil to the USA. As showed in the figure below, the Refiner Acquisition Cost of Imported Crude Oil copies very similarly the price of West Texas Intermediate and I believe it can be used for the goal of this work and the results will not be significantly deformed. To summarize, for the period of 1970 – 1974 I will use the Official Price of Saudi Light and for the rest of the years I will use the Refiner Acquisition Cost of Imported Crude Oil, thereinafter I will only refer to the oil price measure or to the oil price time series.
Figure 2: Different oil prices used in this work: Official Price of Saudi Light, Refiner Acquisition Cost of Imported Crude Oil and NYMEX light sweet crude oil.
Different oil prices
0 10 20 30 40 50 60 70 80 90
1975 1980 1985 1990 1995 2000 2005
oil price in US $
Saudi light
Refiner acquisition cost NYMEX crude oil
Source: EIA
For both the oil and inflation measure I am not using the absolute values but a calculated year-on-year changes. I start my analysis in 1971.1 The oil and the CPI data are in monthly periodicity and they are calculated as an average of daily values in a particular month. As was said above, there is a lack of availability of relevant data prior to 1970 and also due to the stable oil prices for the first 25 years after the WWII I decided to start my analysis in 1971 just before the first oil shock.
1 Year 1970 is used to calculate the year-on-year changes only. All the values I calculated myself using the absolute data.
1.2.2 A method of analysis
In order to find the connection between the price of oil and inflation I decided to use the Pearson correlation coefficient using the following formula:
2 2
y x xy
xy s s
r = s (1)
where rxy is the Pearson correlation coefficient, sxy is the covariance, sx and sy are the standard deviations and x and y are two time series with the same length. The Pearson coefficient measures the strength and direction of a relationship between two variables (time series). It can gain any value from the interval <-1; +1>. A coefficient equals to +1 means that there is a positive linear relationship between these time series, while a value of -1 indicates a negative relationship between the studied time series. A correlation coefficient equals to 0 indicates that there is no linear relationship at all. Very rarely, the Pearson correlation coefficient gains a value of 0, -1 or +1. More likely it will gain a value between these numbers. A coefficient closer to -1 or +1 shows stronger negative or positive relationship, while a coefficient close to 0 means that there is only weak linear relationship. (Hindls, Hronová, Seger, 2006, pg. 206)
When measuring a correlation of time series there is a problem that there might be a third unseen variable (factor) that affects both time series causing that they run in the same direction. This may lead us to a conclusion that there is a big correlation between two time series although there is no reason for such result. For example, we can find that there is a very strong relationship between the car accidents and divorces. In case that both time series run in the same direction, we find the Pearson correlation coefficient close to 1 although there is no reason to find any connection between these two totally different occurrences. This type of correlation is called the spurious correlation. (Hindls, Kaňoková, Novák, 1995, pg. 99)
A spurious correlation occurs when autocorrelation is present, i.e. a correlation between particular observations of a time series, most likely between two neighboring observations (Hindls, Hronová, Seger, 2006, pg. 320). The autocorrelation deforms the overall Pearson coefficient and deteriorates the results. Table 1 shows the Pearson correlation coefficients between the oil prices and inflation using the equation (1). I also included twelve lags of inflation (one lag means one month move in inflation). As we can see, there is a
moderate relationship between the oil prices and inflation and the biggest relationship occurred in the third lag meaning that the biggest influence of oil prices on inflation was in its third month. However, in Table 1 I do not take any autocorrelation into account and therefore a spurious correlation might be included in the bellow listed correlation coefficients.
Table 1: The results for the Pearson correlation coefficient using lags of inflation Lags Correlation coeff.
0 0.4694
1 0.4892
2 0.4971
3 0.4999
4 0.4993
5 0.4973
6 0.4858
7 0.4740
8 0.4577
9 0.4365
10 0.4157
11 0.3894
12 0.3554
Source: My own calculations
To test whether there is any autocorrelation and a spurious correlation in the above coefficients I will use two different tests – the coefficient of autocorrelation (2) and the Durbin-Watson test (3). I use only the first order autocorrelation (correlation between the two immediate neighboring observations) as I suppose the highest correlation will be between the neighboring values.2 The Durbin-Watson test is primarily used to test the presence of autocorrelation in the residuals but for my purpose it can also be used to test autocorrelation in a whole time series. Both equations can be found in basic textbooks for statistics, e.g.
Hindls, Hronová, Seger, 2006 (pg. 320 and 334).
∑ ∑ ∑ ∑
∑ ∑ ∑
−
=
−
=
−
= +
+
−
=
−
=
−
= +
+
−
=
− −
−
− −
−
− −
− −
= −
1
1
1
1
1 2
1 1 1
1 2
1 1
1
1
1 1 1
1
1 1
1 1 1
1 1
1 1
1
1 1 1
1 1
1
n
t
n
t
n
t t t
n
t t t
n
t
n
t t t
n
t t t
n y n y
n y n y
n y y n y
n y
r (2)
2 The Table 2 shows a very high first order autocorrelation therefore I do not expect the second, third, etc. order autocorrelation to be higher.
( )
∑
∑
=
= − −
= n
t t n
t
t t
y y y DW
1 2 2
2 1
(3)
where r1 is the coefficient of the 1st order autocorrelation, n is the number of observations in a particular time series, yt, yt-1 and yt+1 are the values of particular observations and DW is the Durbin-Watson statistic. The following Table 2 includes results of the coefficient of autocorrelation and the Durbin-Watson test for both the oil and the CPI time series. Both statistics shows a very strong autocorrelation (observations in the CPI time series are almost perfectly correlated) implying that the correlations in Table 1 are spurious.
Therefore these results are not persuasive and the actual correlation will be probably smaller.
Table 2: The coefficient of autocorrelation and the Durbin-Watson statistic for the oil price time series and the all-items CPI time series
Coefficient of autocorrelation
Durbin-Watson statistic
Oil series 0.9497 0.090717
CPI series 0.9921 0.004668
Source: My own calculations
Because of existing autocorrelation in both time series I cannot proceed directly to measuring the relationship between these time series but the autocorrelation needs to be cleared away, first. To clear away the autocorrelation the systematic pattern has to be eliminated. Each time series consist of a systematic pattern and random noise (random component) that is difficult to identify. The systematic pattern usually contains two components: trend and seasonality. In order to find a relationship between time series where autocorrelations occurs, the random component must be isolated from the systematic pattern.
In correlation I will then use this random component.
For the purpose of eliminating the systematic pattern I assume that both the oil and the inflation time series are of additive type and they consist of trend and the random noise only:
t t
t T
y = +ε (4)
where yt is a time series, Tt is the trend pattern (component) and εt is the random component. I will abstract from any seasonal or other components. With these premises I will
need to eliminate the trend pattern Tt only. Please note that it is impossible to find the exact values of the random components. Therefore in correlation I will use estimates of the random components:
e t t
y y T
e = − (5)
where ey is an estimated value of a random component and Tte
are estimated values of a trend component. A relationship between the oil prices and inflation will be then equal to the correlation of residuals of these two time series.
As mentioned above, I will need to eliminate the trend pattern, first. This can be done by describing a time series using linear, quadratic, exponential or other regression functions and then removing this function (i.e. trend pattern) from a given time series. The problem is that both used time series include period almost 40 years long with many up- and downturns (see the Figures 1 and 2) and therefore they cannot be described using a simple regression function without deteriorating the final Pearson correlations. For this reason I decided to divide both time series into smaller parts that can be described easier. These parts have to be short enough, so they can be described correctly using the mentioned regression functions and at the same time long enough in order to provide enough observations so the results will not be deformed. After experimenting with different lengths of periods, the three-year periods proved the best results. Longer periods contain too many peaks and troughs and therefore it is difficult to describe and remove a trend component. This will lead to unexpectedly high autocorrelations. On the other side too short periods provide just a few observations and there is a bigger chance that the final results will be distorted. A three-year period provides 36 observations that are rather easy to smooth, however, it still contains several up- and downturns and cannot be described using a simple linear or exponential function. For my purpose I use a sixth order polynomial regression:
6 6 5 5 4 4 3 3 2 2 1
0 t t t t t t
Tt =β +β +β +β +β +β +β (6)
where Tt is a trend component, β0, β1, β2, β3, β4, β5 and β6 are unknown parameters and t is the time variable. To find appropriate regression function and to minimize the residuals I use the method of least squares (for more information, e.g. Hindls, Hronová, Seger, 2006, pg.
257). A relationship between the oil prices and inflation will be then equal to the correlation
of residuals of these two time series. As mentioned above, I divided the both time series into these parts: 1971 – 1973, 1974 – 1976, 1977 – 1979, 1980 – 1982, 1983 – 1985, 1986 – 1988, 1989 – 1990, 1991 – 1992, 1993 – 1995, 1996 – 1998, 1999 – 2001, 2002 – 2004 and 2005 – 2007. There are 11 three-year periods and 2 two-year periods. For the years 1989 through 1992 the three-year periods did not provide satisfactory results (correlations between residuals was too high) therefore I shortened the period to two years. The qualities of the residuals were tested by the coefficient of autocorrelation (2) using residuals et instead of yt.
Here I provide an example of how the correlation is measured for better imagination. I take the first three-year period (1971 – 1973), describe both the oil price and the inflation time series using the polynomial regression (6) and the method of least squares. In this case the following equations come out:
6 9 5
6 4
3 2
, 5.5521 0.3622t 0.0477t 0.0042t 0.0002t 2.3725 10 t 6.8453 10 t
TteCPI = − + − + − ∗ − + ∗ −
6 6 5
4 3
2
, 7.7448 11.1911t 1.1817t 0.0164t 0.0034t 0.0002t 2.5394 10 t
Tteoil =− + − + + − + ∗ −
The first equation describes the CPI time series for the years 1971 – 1973 and the second equation describes the oil price time series for the same time period. Using the above trend equations and the equation (5) I will calculate the residuals (there will be one residual for each observation, making the total of 36 residuals for each time series). The relationship between the oil price measure and the CPI in this given period is then measured by the Pearson correlation coefficient (1) using the calculated residuals. In this particular period the Pearson coefficient is -0.1694 while the coefficient before removing the autocorrelation was 0.5525. This number indicates that this correlation was spurious. Just for illustration I plotted graphs (Figure 3) showing the values of the CPI and the oil prices between 1971 and 1973 (in red) and the above mentioned polynomial regression for this data (in black). The residuals are the difference between the measured values and the specific trend pattern, i.e. the difference between the red curve and black curve. This way I will correlate all the other periods. These results are not taking any lags into account. I will focus on them later.
Figure 3: The all-items CPI and the oil price measure between 1971 and 1973 and the sixth order polynomial regression
The inflation measure 1971 - 1973
0 2 4 6 8 10
III.71 VI.7 IX.71 XII.7 III.72 VI.7 IX.72 XII.7 III.73 VI.7 IX.73 XII.7
% change
The oil price measure 1971 - 1973
0 20 40 60 80 100 120 140
III.71 VI.7 IX.71 XII.7 III.72 VI.7 IX.72 XII.7 III.73 VI.7 IX.73 XII.7
% change
Source: Myself
Note: The oil price time series is in red, the sixth polynomial regression is in black color
1.3 Results
The method of my research is set, I can now proceed to the main point of my work, i.e.
calculating the correlations. First, I will issue the correlations using the non-lagged and lagged all-items CPI and then the correlations using core inflation.
1.3.1 Non-lagged correlations
Here I posted the first results using the method described in the previous chapter. The Table 3 shows the Pearson correlation coefficient of the oil price time series and the overall CPI time series without any lags as these will be discussed in the next chapter. The third column shows the correlation coefficient of the residuals, i.e. after eliminating a systematic component. For better imagination I also listed the Pearson correlation coefficients calculated directly from the inflation and the oil price time series that is before removing a trend component (the second column). I wanted to highlight that the relationship between the non- adjusted (that is with the systematic component) time series is spurious, in some periods very high.
Table 3: The Pearson correlation coefficients of the oil price time series and the non-lagged all-items CPI time series
Pearson correlation coefficients Period before removing a trend
pattern
after removing a trend pattern
1971-1973 0.5525 -0.1694
1974-1976 0.5973 -0.2043
1977-1979 0.8335 0.2323
1980-1982 0.9188 0.2440
1983-1985 0.7685 0.3784
1986-1988 0.6995 0.5094
1989-1990 0.6722 0.4851
1991-1992 0.4787 0.3177
1993-1995 0.3891 0.0928
1996-1998 0.9652 0.3683
1999-2001 0.3306 0.2355
2002-2004 0.7409 0.3237
2005-2007 0.7087 0.2975
Source: My own calculations
From the Table 3 is evident that the correlation coefficient barely reached the value of 0.5 indicating that the oil price – inflation relationship was rather weak than strong. From 13 periods only one exceeded this value. The highest correlation occurred between 1986 and 1990 averaging almost 0.5. It is worth noting that the first two values were in negative relationship implying that when the price of oil increased, the CPI actually decreased.
However, these negative correlations were reached when lags of inflation were not applied and it is probable that there will be a positive relationship when calculating with lags. The average correlation during the whole period is 0.2333 (I used weighted average because not all the periods are of the same length). Not surprisingly, the correlations before removing a trend pattern are much higher than those after removing this trend, averaging 0.6659. This is due to mentioned spurious correlation. The highest difference between the spurious and actual correlation occurred in 1980 – 1982 with the difference of 0.6748.
To show the quality of the results the Table 4 provides the coefficients of autocorrelation. The average coefficient is 0.2138 for the CPI time series and 0.21423 for the oil price time series. These are quite small values but in some periods (especially 1983 – 1985 and 1989 – 1990) the autocorrelation coefficient is too high and there is still a slight possibility of a spurious relationship.
Table 4: The coefficients of autocorrelation for the non-lagged all-items CPI and the oil price time series Coefficients of autocorrelation
Period
the CPI time series the oil price time series
1971-1973 0.1225 -0.0076
1974-1976 0.1031 0.2014
1977-1979 0.1894 0.1107
1980-1982 0.2340 0.3137
1983-1985 0.3474 0.2893
1986-1988 0.2674 0.2732
1989-1990 0.3174 0.1691
1991-1992 0.1461 0.1984
1993-1995 0.2194 0.2486
1996-1998 0.2409 0.3001
1999-2001 0.0157 0.2009
2002-2004 0.3671 0.2705
2005-2007 0.2407 0.2135
Source: My own calculations
3 Both are weighted averages.
Once again all the results in this chapter are based on the non-lagged inflation. I do not expect that inflation reacts on changing oil prices straightaway but there is at least a small lag.
This possibility is described in the next chapter.
1.3.2 Correlations using lags
This chapter provides more important results as here I consider the relationship between the oil prices and inflation when the series do not start at the same time. To figure out this dependence, I will move the inflation series forward by one time unit (month). For example, the oil price series will start in January 1971, while inflation in February 1971 and ends in January 1974. This way both time series will have the same number of observations – 36. I will use the same procedure to find the correlation between both time series as I used for the non-lagged correlation. I will include the total of 12 lags of inflation gaining 12 different correlation coefficients for each three- or two-year period of the oil price series.
Table 5 shows the results for the Pearson correlation coefficient when lags of inflation are involved. I used 12 lags of inflation as I suppose that inflation does not react on a change in the oil prices later than in the first year after this change. Table 5 shows the results for all 12 lags and all the periods. The highest correlations in a particular period are marked in red.
There some periods (1983 – 1985, 1989 – 1990 and 2005 - 2007) when a correlation was higher when not using lags than correlations calculated with lags. The correlation coefficients in these periods are not marked in red.
As expected, in most cases there is a bigger relationship between the lagged CPI and the oil prices than between the same but non-lagged time series. The overall Pearson correlation coefficient is 0.42584 compare to 0.2333 when the lags of inflation were not included. The highest inflation occurred mostly in the first lag or without any lag. This means that in most cases inflation reacted on the changing oil prices within a month after a change appeared. However, there is quite a big variance in these values. Some of the highest correlations occurred in the 11th lag. To summarize Table 5, the value of 0.4258 indicates a moderate relationship between the prices of oil and inflation.
4 Again, I used the weighted average because of different lengths of periods.
Table 5: The Pearson correlation coefficient with 12 lags of inflation using the core CPI Lags of inflation
Period
1 2 3 4 5 6
1971-1973 -0.1710 0.0168 0.2688 0.3292 -0.1212 -0.2637 1974-1976 0.0451 0.1817 0.2645 0.3890 0.1826 -0.0671 1977-1979 0.2382 -0.0125 -0.1626 -0.2685 -0.1684 0.0356 1980-1982 -0.1533 -0.5420 -0.6599 -0.5003 -0.1277 0.3010 1983-1985 -0.1354 -0.6242 -0.6984 -0.3760 -0.0374 0.3850 1986-1988 0.5393 0.1774 -0.2565 -0.3796 -0.3715 -0.3950 1989-1990 0.4212 0.0063 -0.2681 -0.4027 -0.6129 -0.3269 1991-1992 0.3568 0.1923 -0.1999 -0.0586 0.0058 -0.3111 1993-1995 0.3720 0.3870 0.1740 -0.1498 -0.2323 -0.3192 1996-1998 0.4143 0.4268 -0.0844 -0.5005 -0.6632 -0.5082 1999-2001 0.2800 0.0582 0.2114 0.0976 -0.0720 0.0276 2002-2004 0.3645 0.2990 -0.2309 -0.4898 -0.2396 0.1282 2005-2007 0.2449 0.1991 -0.0325 -0.3171 -0.3624 0.0123
7 8 9 10 11 12
1971-1973 -0.1051 0.2623 -0.1245 -0.0868 0.2604 0.0190 1974-1976 -0.0839 -0.1189 0.0040 0.3798 0.3123 0.0089 1977-1979 0.1342 0.2694 0.3447 0.3564 -0.0709 -0.6057 1980-1982 0.3327 0.3555 0.3140 0.2883 -0.1419 -0.6658 1983-1985 0.3771 0.3723 0.0150 -0.3857 -0.5484 -0.3633 1986-1988 -0.1762 0.1003 0.1568 0.1856 0.1197 -0.0619 1989-1990 0.1480 0.4366 0.4584 0.4328 -0.0842 -0.5326 1991-1992 -0.2643 -0.0915 -0.2114 -0.0003 0.2719 -0.0106 1993-1995 -0.3259 -0.2053 0.0560 0.3438 0.3210 -0.0334 1996-1998 -0.0575 0.2847 0.4343 0.4592 0.4907 0.2063 1999-2001 0.0816 -0.2128 -0.4078 -0.0096 0.3102 -0.0464 2002-2004 0.2210 0.0195 -0.0373 0.2128 0.3356 -0.0801 2005-2007 0.1156 -0.3742 -0.4485 0.1797 0.2876 0.2616 Source: My own calculations
Note: The highest correlations in each period are marked in red. The periods where the highest correlation occurred in non-lagged inflation are not marked in red.
Table 6 shows the coefficients of autocorrelation for the values in Table 5. The values in red color are for the highest coefficients in Table 5. Autocorrelations for the oil price series are not listed because these are the same as those in Table 4 (I use lags for the CPI series and the oil price time series remains unchanged). The coefficients of autocorrelation are similar to the non-lagged time series (in Table 4) with an average of 0.1671. This indicates quite small autocorrelations (and small spurious correlations in Table 5) but there is a big variance in results, ranging from 0.0009 to 0.4294. The more important are the values in red as they show the credibility of the highest correlations coefficients. The values smaller than 0.1 indicate a very weak autocorrelation implying that there is almost no spurious relationship in corresponding values in Table 5. On the other side, there are some coefficients of a greater value (esp. periods 1977 – 1979 and 2002 – 2004) indicating that a pattern was not removed
satisfactorily and there is still (although weaker) spurious correlation between the oil price and the CPI time series. This is probably because of some other factor(s) that influence a particular time series and was not fully removed.
Table 6: The coefficients of autocorrelation for the lagged all-items CPI time series Coefficients of autocorrelation Period
1 2 3 4 5 6
1971-1973 0.1104 0.0973 0.1455 0.0990 0.0242 -0.0201 1974-1976 0.0600 0.1087 0.1072 0.1257 0.1816 0.2013 1977-1979 0.2034 0.1728 0.2184 0.2277 0.2714 0.1813 1980-1982 0.2313 0.2363 0.2367 0.2401 0.2421 0.2424 1983-1985 0.3113 0.2873 0.2627 0.2453 0.2262 0.2196 1986-1988 0.2780 0.2891 0.3084 0.3144 0.3115 0.3029 1989-1990 0.3131 0.3172 0.3210 0.3283 0.3240 0.3116 1991-1992 0.1355 -0.1544 -0.2126 -0.2305 -0.2286 -0.2183 1993-1995 0.2101 0.2046 0.2013 0.2007 0.1983 0.1886 1996-1998 0.2302 0.2221 0.2147 0.2093 0.1572 0.1582 1999-2001 0.0167 0.0173 0.0271 0.0392 0.0398 0.1451 2002-2004 0.3093 0.2509 0.2416 0.2397 0.2255 0.2388 2005-2007 0.2398 0.2415 0.2246 0.2197 0.2170 0.2051
7 8 9 10 11 12
1971-1973 0.0009 -0.0636 -0.1780 -0.2221 -0.2209 -0.2043 1974-1976 0.3535 0.3564 0.3521 0.3668 0.4146 0.4294 1977-1979 0.1092 0.0252 0.2700 0.2980 0.3147 0.3171 1980-1982 0.2385 0.2213 0.1877 0.1447 0.1318 0.1452 1983-1985 0.2172 0.2302 0.2727 0.2723 0.2681 0.2645 1986-1988 0.2830 0.2800 0.3076 0.1899 0.2320 0.2787 1989-1990 0.2909 0.2745 0.2578 0.2479 0.2396 0.2242 1991-1992 -0.2040 -0.1655 -0.1344 -0.3155 -0.1397 -0.1442 1993-1995 0.1839 0.1862 0.1897 0.1954 0.2139 0.2260 1996-1998 0.0957 0.0903 0.0578 0.0520 0.0565 0.0628 1999-2001 0.1882 0.1982 0.1402 0.0629 0.0262 0.0574 2002-2004 0.2517 0.2663 0.2683 0.2690 0.2781 0.2828 2005-2007 0.1682 0.1603 0.1641 0.1677 0.1697 0.1729 Source: My own calculations
Note: The values in red are the autocorrelations coefficients corresponding to the highest correlations in Table 5.
For better illustration Figure 3 shows the changes of the Pearson coefficient within the examined period. To plot this graph I used the highest correlations in each period. The correlation coefficient is oscillating between the values 0.3 and 0.4 most of the time.
Figure 3: The changes in the Pearson correlation coefficient in time
Changes in the Pearson correlation coefficient
0,0000 0,1000 0,2000 0,3000 0,4000 0,5000 0,6000
1971-1973 1974-1976
1977-1979 1980-1982
1983-1985 1986-1988
1989-1990 1991-1992
1993-1995 1996-1998
1999-2001 2002-2004
2005-2007 Pe riod
Pearson correlation coefficient
Source: Myself
1.3.3 Correlations using the core CPI
In the last part of my analysis I changed the measure in the inflation time series and used the core CPI (CPI less food and energy) instead of the all-items CPI. Energy has about 7% share in the all-items CPI basket (Hooker, 2002, pg. 3) and therefore it has a direct immediate influence on inflation measured by the all-items CPI. Therefore I expect that the relationship between inflation and the oil price measure will be higher when using the all-items CPI than when using the core CPI.
To find this relationship I used the same procedure as in the previous chapters. Table 7 shows these results. In this table I included both the non-lagged and lagged CPI. The results for non-lagged inflation are in the column 0. The highest correlations in each period are shown in red. The average correlation of the highest value is 0.28705. This is consistent with my assumption that the relationship will be weaker when using the core CPI. The values in Table 7 as well as the average value shows that the relationship between the core CPI and the oil price time series is rather weak. It is worth noting that there is much more values indicating negative relationship than in Table 5 which shows the results for the all-items CPI.
Also the values are less stable in each period.
5 Weighted average of the highest (red) values
The highest correlation occurred averagely in the 7th month compare to the 4th month when calculating with the all-items CPI. This conclusion is understandable as all-items inflation is affected mostly through direct share of oil in an inflation basket. This influence is immediate. On the other side, inflation which excludes energy is affected by other items in a particular basket that use oil as an input (e.g. higher prices of plastics). There is a certain lag between a change in the price of oil and a change in the prices of these items and therefore core inflation reacts later on changing oil prices.
Table 7: The Pearson correlation coefficient with 12 lags of inflation using the core CPI Lags of inflation
Period
0 1 2 3 4 5 6
1971-1973 0.0120 0.0573 -0.1820 -0.2125 0.0352 0.0434 -0.1908 1974-1976 -0.2198 0.0260 0.0481 0.0742 0.1046 -0.0831 0.0435 1977-1979 0.1609 0.1557 0.0617 -0.1125 -0.3147 0.1878 0.0540 1980-1982 -0.1851 0.1772 0.2556 0.1363 0.1491 -0.1270 -0.2802 1983-1985 -0.2109 -0.1560 -0.1265 -0.1215 0.1086 0.0563 -0.0766 1986-1988 0.3383 0.1440 0.1206 0.1659 -0.0102 -0.1336 -0.1521 1989-1990 0.3052 0.1387 0.0126 0.0405 0.1331 0.1895 0.0359 1991-1992 -0.0756 -0.0678 0.0423 0.1417 0.1426 0.1753 0.0831 1993-1995 -0.0735 -0.0920 -0.0372 0.1208 -0.1499 0.2138 0.2083 1996-1998 -0.4556 -0.5498 -0.0858 0.1367 0.1729 0.1509 0.1229 1999-2001 -0.3215 -0.2541 0.2630 0.2838 0.2038 0.1698 0.0897 2002-2004 0.0454 -0.0354 0.0800 -0.2134 0.1992 0.4753 0.3402 2005-2007 -0.0929 -0.0752 0.1946 0.2185 0.3435 -0.0857 0.2109
7 8 9 10 11 12
1971-1973 -0.0351 0.1054 0.1270 0.1795 0.1480 0.1730 1974-1976 0.1241 0.2645 0.1302 -0.0185 -0.2393 -0.3095 1977-1979 0.1593 0.2297 0.2462 0.2155 0.1871 0.2295 1980-1982 -0.1138 -0.0820 0.0926 0.0563 -0.0047 -0.0900 1983-1985 0.2419 0.1080 -0.3307 -0.2068 0.1090 0.3811 1986-1988 0.1921 0.2252 0.1898 0.1285 0.0092 0.0783 1989-1990 -0.2617 -0.1904 0.1306 0.0965 0.0387 0.0383 1991-1992 -0.2815 -0.5647 -0.3531 0.0287 0.1340 0.1466 1993-1995 0.1889 0.1914 0.1724 -0.1543 -0.1735 -0.1316 1996-1998 0.0321 -0.0603 -0.0104 -0.2374 -0.1037 0.3591 1999-2001 0.0722 -0.0144 -0.2428 -0.3218 -0.0954 0.3291 2002-2004 0.1290 0.0113 -0.1343 -0.2786 -0.5455 -0.5175 2005-2007 -0.1503 0.1670 0.3676 -0.1852 -0.1108 0.2408 Source: My own calculations
Note: The highest correlations in each period are marked in red.
Similarly as in the previous chapter I posted below (Table 8) the coefficients of autocorrelation to show the quality of the results. I used the same oil prices time series therefore the coefficients of autocorrelation for this series is the same and the values are
shown in Table 4. Qualities of the Pearson correlation coefficients rise with the decreasing value of the coefficients of autocorrelation. The weighted average of the autocorrelation coefficients is 0.11946 indicating a very small spurious correlation that I was not able to eliminate. However, the results are of better quality (less deformed) than those calculated from the all-items CPI. The biggest autocorrelation occurred for the results in 1986 – 1988 period and thus the Pearson coefficient in this period is deformed the most. I assume that the correlation coefficients would be smaller after fully removing the autocorrelation.
Table 8: The coefficients of autocorrelation for the core CPI time series
Coefficients of autocorrelation Period
0 1 2 3 4 5 6
1971-1973 0.0061 0.0360 0.0448 0.0364 -0.0298 -0.0229 0.0196 1974-1976 0.0684 0.0829 0.1156 0.1081 0.0914 0.1444 0.1251 1977-1979 0.2191 0.2934 0.2131 0.2510 0.1845 0.2104 0.2281 1980-1982 0.1869 0.1700 0.2055 0.1961 0.1568 0.1750 0.1434 1983-1985 0.2393 0.2114 0.2249 0.2479 0.1839 0.2530 0.1772 1986-1988 0.2531 0.3058 0.3786 0.3761 0.3600 0.3677 0.3350 1989-1990 0.0858 0.0969 0.0823 0.0517 0.0723 0.0518 0.1362 1991-1992 -0.1281 -0.1251 -0.1554 -0.1233 -0.1269 -0.0980 -0.0075 1993-1995 0.2594 0.2284 0.2560 0.1902 0.1734 0.1784 0.1011 1996-1998 0.0613 0.0383 0.0341 0.0088 0.0142 0.0228 0.0319 1999-2001 0.2920 0.2322 0.2826 0.3426 0.3320 0.3753 0.2299 2002-2004 -0.0408 -0.0706 0.0330 0.0720 0.0430 0.1226 0.0964 2005-2007 0.1264 0.1752 0.1493 0.0982 0.0150 0.0708 0.0844
7 8 9 10 11 12
1971-1973 0.0234 0.0266 0.0497 0.0481 0.0311 0.0248 1974-1976 0.1616 0.1395 0.1168 0.1508 0.1942 0.1480 1977-1979 0.1202 0.0992 0.1311 0.1789 0.2576 0.2302 1980-1982 0.1908 0.2384 0.1859 0.1269 0.0922 0.0775 1983-1985 0.1444 0.1581 0.1699 0.1735 0.1658 0.1561 1986-1988 0.2405 0.2277 0.2014 0.1809 0.2598 0.1989 1989-1990 0.1421 0.0915 0.0727 0.0461 0.0545 0.0231 1991-1992 -0.0786 -0.0530 -0.0962 -0.0798 -0.0443 -0.0100 1993-1995 0.0251 0.1561 0.1270 0.0858 0.1107 0.1727 1996-1998 0.0753 0.1202 0.1713 0.2145 0.1878 0.1271 1999-2001 0.1947 0.1685 0.1616 0.0935 0.1401 0.1344 2002-2004 0.0840 0.0793 0.0642 0.1289 0.1177 0.1526 2005-2007 0.1018 0.1236 0.0260 0.0826 0.1399 0.0624 Source: My own calculations
Note: The values in red are the autocorrelations coefficients corresponding to the highest correlations in Table 7.
6In this average are included only those values that are written in red in Table 8. This average therefore shows the quality of the average of the Pearson correlation coefficient (in the above paragraph) which was calculated using the highest values.
1.4 Other works on this topic
In this chapter I would like to provide some opinions and results from different working papers on this topic. All the authors I have studied find a weak or moderate relationship between the prices of oil and inflation similarly to my results. But in addition they also find a structural breakpoint dividing this relationship into two parts. This structural breakpoint occurred in the early 1980s. The correlation was stronger prior to this year then afterwards. In my results I did not find such breakpoint as my result were quite similar and consistent through the whole examined period.
The first thing that has to come to mind when thinking of why the breakpoint occurred is the oil crisis in the 1970s. The OPEC restrictions caused the increase in the price of oil by 400% which was the most dramatic jump in the oil prices in history. Such an increase should have had the impact on the CPI. However, today many economists suggest that the changes in price indexes were much higher than the changes in the price of oil that caused them. This leads to the conclusion that oil shocks were not the only cause of high inflation in the post- war period. Despite of the evident disproportion and clearly visible structural break in the oil price – inflation relationship, it was not till the 1990s when economists start to investigate the hypothesis that monetary policy had substantial impact on the 1970s inflation jumps. Recent papers suggest that oil prices could have such a huge impact only if accommodated by monetary policy. If this hypothesis is true and we have a structural breakpoint in the relationship between oil prices and inflation, then there also ought to be a structural break in the Fed’s monetary policy at about the same time when the oil – inflation structural break appeared (Rogoff, 2006, pg. 14).
Stability of the Fed’s monetary policy was in detail examined in a paper by Clarida, Galí, Gertler (2000). They divided post-war monetary policy into two terms: the pre-Volcker period (period when Martin, Burns and Miller were in charge of the Federal Reserve System) and the Volcker-Greenspan period (when Volcker and Greenspan were chairmen of the Federal Resreve). Paul Volcker was appointed to his office in August 1979, just shortly before the breakpoint in the oil price – inflation relationship appeared. When Volcker was appointed US inflation was at record-high levels. Shortly, he changed the Fed’s policy as he changed its operating procedures from targeting a short-term interest rate to targeting nonborrowed reserves (Hadjimichalakis, 1984, pg. 37).
By comparing the before and after breakpoint periods Clarida, Galí, Gertler (2000, pg.
177) conclude that the Fed performed two different monetary policies. In the pre-Volcker era the Fed raised its nominal rates by less than an increase in expected inflation and anticipated inflation rose as a result. On the other hand, Volcker and Greenspan focused especially on reducing inflation. Before Volcker appointment, inflation ranged from 2 percent to as high as 11 percent during oil shocks. On the other side, in the Greenspan period it was only up to 4 percent. Average inflation after World War II reached 3.7 percent in the pre-Volcker period, however, the inflation average felt down to 2.4 percent afterwards. US inflation was also less volatile in recent 25 years than before the structural breakpoint appeared. The standard deviation dropped from 2.77 in the pre-Volcker period down to 1.00 after 1982.
Clarida, Galí, Gertler proved that there was a breakpoint in the Fed’s monetary policy sometime between 1979 and 1982. There is a severe downfall during these years, when inflation dropped from 11 percent down to 4 percent and remained bellow this level ever since. Clarida’s et al. structural break is consistent with Hooker’s and my structural breakpoint for oil price – inflation relationship.
1.4.1 Some more evidences accusing monetary policy
Influential paper issued by Bernanke, Gertler and Watson (1997) showed different reactions of the Fed to oil shocks over different periods. They brought impulse-response function based on a seven-variable vector autoregression. Figure 4 presents result of a respond of the federal funds rate to a 1 percent increase in the price of oil in three consecutive periods:
1966-75, 1976-85 and 1986-95. The graphs are constructed for 24 months. As we can see between 1966 and 1985 the Fed reacted to oil price increases by a tightening of policy as shown by rising federal rates. Very tight monetary policy occurred between 1976 and 1985 following by a 10-years-period when the Fed responded very mildly by easing rather than tightening of monetary policy. The latest period is dominated by an increase in oil prices which occurred in 1990 and to which the Fed reacted by easing of its policy. The primary goal of this figure is to show once again that the Fed reacted to oil shocks differently over time.
The three periods reveal the different Fed’s reaction to oil shock. However, the biggest negative of Figure 4 is that Bernanke at al. included the 1980-breakpoint in one of the periods
