Crude Oil Price and Aggregate Economic Activity: Asymmetric or
Symmetric Relationship: Evidence from Canada’s Economy
Asgar Khademvatani1
Department of Economics
The University of Calgary
Calgary, Alberta, Canada, T2N 1N4
Phone: (403)210-2574
Email: akhademv@ucalgary.ca
Abstract:
We represent an alternative time series technique to examine alternative asymmetry
hypothesis based on the reliable vector Error Correction Model (ECM). We add up
negative and/or positive and negative changes of crude oil prices in bivariate and
multivariate ECM techniques among GDP, crude oil price, short-term interest rate, and
aggregate implicit price deflator. This paper unlike the literature considers unit root and
structural break tests for deciding whether co-integration and ECM techniques or VARs
technique and innovation accounting tools would be used to explain the interaction of
economic activities, oil price shocks, and other key economic variables. We apply this
alternative method to Canada’s economy using quarterly data over the period (19842002). Our results suggest the long-term equilibrium relationship among GDP, the crude
oil price, and other key economic variables. In contrast with the most literature, the
results show that there is a significant portion of the symmetric and reversible response of
Canada’s economy to the crude oil price changes in both bivariate and multivariate
context over the study period. We find that this symmetric response is due to the
symmetric relationship of the crude oil price with the short-term interest rate and the
aggregate price index in Canada’s economy.
Keywords: Error correction models, Asymmetry, Symmetry, Crude oil price,
Co-integration, Unit root, structural break, Aggregate economic activity.
1
Corresponding Author is a Ph.D. candidate at Department of Economics, university of Calgary, Canada.
1. Introduction
A considerable body of economic research suggests that oil prices fluctuations
have figured prominently in national economic activity since World War II. In fact, rising
oil prices preceded nine out of the ten post-World War II recessions (Hilsenrath and
Walker, 2004). But an acceleration of U.S. economic activity did not seem to follow the
oil price declines that occurred from the early 1980s to the late 1990s. In addition, rising
oil prices seemed to have less of an effect on economic activity over the past fifteen years
than they did in the 35 years following World War II.
By exploring the factors influencing the transmission of oil shocks into an
economy, researchers have argued that fluctuations of oil prices are linked empirically to
macroeconomic performance. This theoretical relationship between macroeconomics and
oil price movements has been widely applied and tested using various econometric
techniques, dealing largely with the economies of the United States and other OECD
countries (e.g., Hamilton, 1983, 1988, 1996, 2000; Tatom, 1988; Mork, 1989; Mork et
al., 1994; Kim and Loungani, 1992; Lee et al., 1995; Hooker, 1996, 1999; Ferderer, 1996;
Bernanke et al., 1997; and Brown and Yücel, 2002; Baharuddin, 2004). Nonetheless, the
analysis of the impacts of oil price fluctuations on macroeconomy has been complicated
by other key events and changing economic environment during the period in which the
price fluctuations occurred (Jones and Leiby, 1996).
Beyond establishing a relationship between oil price movements and aggregate
economic activity, research on the economic response to oil price shocks has gone in
several directions. A number of studies have investigated why rising oil prices appear to
retard aggregate economic activity by more than falling oil prices which stimulate it.
Other studies have investigated the channels through which oil price shocks are
transmitted to economic activity including monetary policy, the adjustment costs, and so
on. Also, several studies have examined the possibility of weakening relationship
between oil price fluctuations and aggregate economic activity. So, oil price shocks have
preceded all but one post-war recession (e.g., Hamilton, 1983), even though a robust
economic recovery did not follow the 1986 oil price collapse. Since, Canada has a plenty
amounts of productive capacity of crude oil specifically oil sands, the importance of
2
investigation of volatility of oil prices on Canada’s economy is very interesting subject
matter. The main point is that Canadian economy in some provinces such as Alberta,
British Columbia, and Saskatchewan depends on oil price fluctuations and crude oil is as
vital primary energy in supply-side of Canada’s economy. So, explaining symmetric or
asymmetric relationship of the oil price changes and aggregate economic activities could
be a controversial debate. Moreover, there are many experimental working papers about
the asymmetric or symmetric relationships between energy prices and aggregate
economic activities in the United States with similar economic structure while the works
of this type have rarely been done about Canada’s economy (e.g., Mork et al., 1994). In
addition, doing some practices of applying main context of time series techniques about
is another objective of this working paper. Since, the late 1980’s a number of studies
(e.g., Nathan, et al., 2002; Davis & Haltiwanger, 2001; Hamilton & Herrera, 1998; Mark,
1989), that investigated and confirmed an asymmetric relationship between oil prices and
aggregate economic activity in the United States economy, except (e.g., Huntington,
1998) that studied about some possible sources of this asymmetric relationship and
attributed some of the asymmetry to the relationship between crude oil and petroleum
products prices but does not preclude other sources. Through these studies, some causes
of the asymmetric relationship have been addressed by some possible channels.
For instance, one possible channel is the Adjustment Costs of shifting among
economic sectors in response to changing oil prices (e.g., Hamilton, 1983). Falling oil
prices stimulate economic activity, and rising oil prices decreases economic activity; but
the cost of adjusting to changing oil prices has negative effects on economic activities.
By considering these elements, rising oil prices could have two negative effects on
economic activities including direct effect of rising oil prices, and side-effect of the
adjustment costs. However, falling oil prices could represent two opposite effects such a
negative adjustment cost’s effect, and a positive effect of falling oil prices that tend to be
offsetting. Empirical work done by( e.g., Davis & Haltiwanger, 2001; Hamilton&
Herrera, 1999; Lee et al., 1995; Davis, 1987; Loungani, 1986), support but do not directly
test Hamilton’s explanation. As other source, Monetary Policy may account for the
asymmetric response of aggregate economic activity to oil price changes. Bohi (1989)
and Bernake et al., (1997) argue that concretionary monetary policy
declining of
3
aggregate economic activities following an oil price increase, but does not explore the
asymmetry issue explicitly. Tatom (1988, 1993) argues that the apparent asymmetric
response of U.S. economic activity to oil price shocks disappears when the stance of
monetary policy or changes in the misery index (which combines unemployment and
inflation rates) are taken into account. As another factor, Uncertainty and Financial
Stress offered by Ferderer (1996) who argues that changing oil prices could amplify the
negative effects of rising oil prices and offset to some degree the positive effects of
falling oil prices. These effects might be evident in the asymmetric response of interest
rates to oil price shocks.
The economy’s short run response to energy price shocks is considerably more
complicated than simple shifts along an aggregate production function for the nation. The
mechanism for explaining oil price shocks in most large-scale macro econometrics
models (as explained in Hickman (1987)) is essentially the aggregate supply and demand
models. It can be found in many text books (e.g., Dornbusch & Fischer, 1994; Hall &
Taylor, 1993) which emphasize the real balance effect through the interaction of the
goods and money markets.
This framework relies mostly on upward shifts in the
aggregate price level that reduces real monetary balances rather than relative price
adjustment. Shifts in short-run aggregate supply and demand curves of goods and money
push interest rates and prices upward while retarding economic growth. Energy price
shocks in such a framework can have large macroeconomic effects and these effects do
not need to be reversible with energy price decreases, if wages and other prices in the
economy are downward sticky.
Most researchers focus exclusively on the relationships between crude oil prices
and aggregate economic output. However, oil price shocks have also had significant
effects on wages, interest rates and prices throughout the explained framework. As a first
minor contribution, this paper represents the relationship between crude oil shocks and
economic activities within the context of the broader impact of oil prices on the aggregate
price level and short-term interest rate. Also recent empirical studies to explain the
economy’s response to oil price shocks have directly used vector autoregressive (VARss)
or near VARs techniques, without consideration of the order of integration of the
series(e.g., Balke, et al. 2002; Mork et al., 1994). Unlike the recent studies, as a second
4
minor contribution, this paper considers unit Root and structural break tests for deciding
whether bivariate and multivariate co-integration and error correction model(ECM) or
vector autoregressive (VARs) techniques and innovation accounting are appropriate tools
to explain the interaction of economic activities, oil prices shocks and other key
economic variables. The remainder of the paper proceeds as follows. Section 2 discusses
some basic theory and evidence on asymmetry in the economic literature. Section 3
explains methodological issues and data used in the empirical analysis. Section 4 reports
on the empirical results. Section 5 concludes the paper.
2. Asymmetry: The Basic Theory and Evidence of the Literature
The oil price shock of 1973 and the subsequent recession, gave rise to a plethora
of studies analysing the effects of oil price increases on the economy. The 1973 recession
was (at the time) the longest of the post-World –War-II recessions, and it gave new
gravity to the oil-macroeconomy relationship. The early studies about can be referred to
(e.g, pierce &Enzler, 1974; Rasche & Tatom, 1977; Mork &Hall, 1980; Darby, 1982;
Gisser & Goodwin, 1986; and the Energy Modeling Forum-7 study documented in
Hickman et al. 1987). They confirmed the inverse relationship between oil prices and
aggregate economic activity for the United States. Darby (1982); Burbidge &Harrison
(1984); Bruno & Sachs (1982, 1985); and Mork et al., 1994 documented similar oil-price
–economy relationships for countries other than the United States. In an extensive survey
of the empirical literature, Jones and Leiby (1996) found that the estimated oil price
elasticity of GNP in the early studies ranged from -0.02 to -0.08, with the estimates
consistently clustered around -0.05. During the 1980s and 1990s, it became increasingly
apparent that the U.S economic activity responded asymmetrically to oil price shocks.
The seeming breakdown in the relationship between oil and the economy led
researchers to explore different oil price specifications in an attempt to re-establish the
oil-output relationship. Mork (1989) did not find a significant relationship between oil
and GDP, and then he separated out oil price changes into negative and positive changes,
and re-established a significant relationship between oil price and GDP. Mory (1993)
followed Mork and separated the oil price into negative and positive changes and found
that the positive oil price shocks Granger-caused key macroeconomic variables, but the
5
negative shocks did not. Mork, et al. (1994) found an asymmetric relationship between
oil price and aggregate economic activity for seven industrialized countries. Lee, et al.
(1995) also found asymmetry between the effects of negative and positive oil price
shocks, which they attributed to, in part, to price uncertainty. Ferderer (1996) found that
increases of oil prices explained more than twice the variation of industrial production
growth than did decreases. Hamilton (1996 & 1999) proposed his own renowned “net oil
price”, and found a statistically significant and stable negative relationship between oil
price output.
Davis & Haltiwanger (1998) constructed another oil price series that
combines asymmetry and persistence.
Several different channels have been proposed to account for the inverse
relationship between oil price movements and aggregate economic activity. The most
basic one is the classic supply side-effect in which rising oil prices are indicative of the
reduced availability of an essential input (energy) to production. Other explanations could
be including, income transfers from the oil importing nations to the oil exporting nations,
a real balance effect, and monetary policy. Of these explanations, the classic supply-side
effect clearly explains why rising oil prices slow GDP growth down and stimulate
inflation2. Classic supply-side effects cannot explain asymmetry. Accordingly, in the
literature, a number of studies emphasize other channels through which oil prices may
affect economic activities. For example, monetary policy, adjustment costs, and
asymmetry in petroleum product price changes have been offered as possible
explanations for the asymmetry. These channels might be used as some explanations for
the asymmetry between oil price and economic activity. In the following, these possible
causes of the asymmetric relationship between oil price and economic activity are
brought in more details.
2.1. Monetary Policy and Asymmetry
Although the role of monetary policy was prominent in early explanations of how
oil price shocks affect real economic activity, it was gradually supplanted by real
business cycle theory. Nonetheless, an apparent breakdown in the relationship between
oil and the economy during the 1980s and 1990s led researchers to question the pure
supply shock models and to probe additional channels through which oil could affect the
2
See Macroeconomics texts (e.g., Dornbusch & Fischer, 1994; Hall & Taylor, 1993).
6
economy. Induced change in monetary policy was one such channel. Monetary policy is a
possible explanation for the asymmetric response of the economy to oil price shocks. If
wages are nominally sticky downward but not upward, monetary policy can have
asymmetric effects. When oil prices rise, wages that are sticky downward will aggravate
GDP losses if the monetary authority fails to hold nominal GDP constant through
unexpected inflation. When oil prices fall, however, real wages must rise to clear the
markets. Because nominal wages can adjust upward freely, a monetary policy that fails to
hold nominal GDP constant through the unexpected deflation need not be simulative.
Tatom (1988, 1993) and Bernanke, et al. (1997) provide some evidence that
monetary policy is a contributing factor to asymmetry. Tatom finds that the apparent
asymmetric response of U.S. economic activity to oil price shocks disappears when the
stance of monetary policy or changes in the misery index (which combines
unemployment and inflation rates) are taken into account. In contrast, Ferderer (1996)
shows that monetary policy cannot account for the asymmetry in his model. Bake,
Brown, and Yucel (1999, 2002) also show that the Federal Reserve’s response to oil price
shocks is not the cause of asymmetry. They find that the asymmetry does not go awayand is in fact enhanced-when the either the federal-funds rate is held constant or
expectations of the federal-funds rate are held constant.
In a more recent effort, Hamilton and Herrera (2000, 2004) revisit the Bernanke
et al. (1997) analysis and conclude that the potential for monetary policy to avert
concretionary consequences is not as great as suggested in the Bernanke et al. analysis.
By using longer lag lengths than Bernanke et al., Hamilton and Herrera show that oil
price shocks have a substantially larger direct effect on the real economy. Moreover, with
longer lag lengths, even when the federal funds rate is kept constant (Bernanke et al.`s
measure of neutral monetary policy), an oil price shock still yields a sizable reduction in
output, implying that monetary policy has little effect in easing the real consequences of
an oil price shock. Hence, monetary policy does not appear to be the sole cause of the
asymmetry on the real side.
2.2. Adjustment Costs and other Responses
Adjustment costs could lead to an asymmetric response to changing oil prices, as
first argued by Hamilton (1988). Rising oil price retards economic activity directly, and
7
falling oil price stimulates it so, but the costs of adjusting to changing oil prices also
retard economic activity. Falling oil prices would present both negative and positive
effects, which would tend to be offsetting. Adjustment costs could arise either from
sectoral imbalances, coordination problems between firms, or because the energy-tooutput ratio is embedded in the capital stock. Lilien (1982) and Hamilton (1988) examine
how changes in oil prices create sectoral imbalances by changing the equilibrium
relationship between the sectors. Huntington (2000) examines how coordination
problems associated with changing oil prices might affect economic activity. Atkeson and
Kehoe (1999) examine how putty-clay technology (that is, technology in which the
energy-to-output, capital-to-output, and labour-to-output ratios can be varied over the
long run but cannot be changed in the short run because they are embedded in the capital
stocks) affect on the economic response to changing oil prices. As explained by Ferderer
(1996), uncertainty about future oil prices can also adversely affect economic activity by
reducing investment demand. Another source can contribute is uncertainty effects on
investment or the investment-uncertainty hypothesis have their underpinning in what has
become known as “irreversible investment” theory (Pindyck, 1991; Pindyck &
Rotemberg, 1984). Bernanke (1983) demonstrates that firms will find it increasingly
desirable to postpone irreversible investment decisions when they are more uncertain
about future oil prices. The asymmetry caused by this hypothsis is known as “the bad
news principle” (Bernanke, 1983, pp. 90-93).
Although asymmetry is now fairly well accepted, relatively few studies have
attempted to determine empirically through what channels (other than monetary policy)
oil price shocks might yield an asymmetric response in aggregate economic activity.
Work by Loungani (1986); Davis (1987); Lee, et al. (1996); Davis, et al. (1997); and
Davis & Haltiwanger (1998) support but do not directly test Hamilton`s adjustment cost
explanation. Balke, Brown and Yucel (1999, 2002) find significant asymmetric output
and interest rate responses to oil price shocks, with transmission through market interest
rate. They find strong asymmetry in the output response and, in particular, a strikingly
similar negative response of output to both positive and negative oil price changes in the
short run, which are similar to Mork (1994) and Davis and Haltiwanger (1998). Such
findings are consistent with the explanation that oil price shocks necessitate costly
8
adjustment (either inter-sectoral or intra-sectoral as emphasized by Davis and
Haltiwanger), or sticky downward wages and/or prices (as emphasized by Mork).
2.3. Petroleum Product Prices
Petroleum product prices may also contribute to an asymmetric relationship
between crude oil prices and economic activity. Public scrutiny of gasoline markets has
led to the view that petroleum product prices respond asymmetrically to crude oil prices.
Research provides econometric support for public claims that gasoline prices rise more
quickly when crude oil prices are rising than they fall when crude oil prices are falling.
Bacon (1991) finds asymmetry for the U.K. gasoline market. Karrenbock (1991);
Borenstein, et al. (1997); and Balke, et al. (1998) all find some evidence for asymmetric
response in U.S. gasoline markets. Huntington (1998) translated the findings of
asymmetry in petroleum product prices into a possible explanation for the asymmetric
relationship between crude oil prices and aggregate economic activity. He finds that the
economy responds symmetrically to changes in petroleum product prices, but that
petroleum product prices themselves respond asymmetrically to crude oil prices. The
result is an asymmetric relationship between crude oil prices and aggregate economic
activity. Huntington also finds that inflation responds symmetrically to crude oil prices.
No follow-up studies have examined Huntington’s findings.
2.4. Asymmetry and Transmission Mechanisms
The most recent line of research on macroeconomic transmission mechanisms of
oil price shocks is being developed in the literature on real business cycle models (e.g.,
Brown et al., 2002; Mork et al., 1994; Kim & Loungani, 1992). These models first
developed in the early 1970s, just prior to the first oil price shock of that decade. It was
some times before oil price shocks were suspected to be the sort of recurrent, anticipated
shock that this class of models employs to obtain exogenous supply-side disturbances to
macroeconomic equilibrium. David Lilien`s (1982) dispersion hypothesis has been a
central focus of this research applied to oil price shocks. The dispersion hypothesis posits
that a considerable amount of unemployment can be accounted for by sectoral shifts in
demand, which require time for reallocation of labour. This mechanism involves
exogenous allocative disturbances causing reallocation of specialized labour and capital.
The speed of reallocation may be determined by the particular type of disturbance (Davis,
9
1987). The dispersion hypothesis modifies the conventional macroeconomic model
specification that both the magnitude and direction of oil price shocks are important.
Under the dispersion hypothesis, the direction of change is not important: both positive
and negative changes increase the amount of labour reallocation required (Loungani,
1986, P.539). Mork, et al., (1994) estimated regressions of GDP on contemporaneous and
lagged oil prices as well as multivariate regressions which included also the inflation rate
(measured by the GDP deflator), short-run interest rates, the unemployment rate, and the
growth rate of industrial production for the entire OECD as a proxy for exogenous export
demand. The oil price-effects were stronger and more frequently statistically significant
in the multivariate analyses than in the bivariate. All countries except Norway
experienced negative relationships between oil price increases and GDP growth. In the
multivariate estimation, the U.S., Canada (both at the 2%level), Japan (at 3%), and
Germany (at 10%) demonstrated significant evidence of asymmetry. The studies by
Smyth (1993) and Jackson & Smyth (1986) suggest that some unknown biases maybe
introduced by such a procedure (separating negative and positive oil prices shocks),
particularly in longer time series that contain several price cycles.
A further business-cycle study on the subject of asymmetry and transmission
mechanisms is the recent real business cycle model simulated by Kim & Loungani
(1992). Their purpose is to distinguish the controversial role of stochastic shocks to
technology from other real shocks. They specify an energy price shock as such an
alternative and study what proportion of the variance in the volatility of output over the
business cycle can be accounted for the energy price shock and the others. Their results
tend to reinforce suspicious which have emerged in the past decade regarding the
importance of the allocative effects of oil price shocks in the labour market. Karras
(1993) estimated a structural VARs of real GNP, the real federal deficit, the GDP
deflator, the M2 money supply, the U.S dollar-SDR exchange rate, and the price of oil
over the period 1973:I-1989:IV. Karras`s approach to identifying shocks relies on the
error structure of the data series, and oil price shocks so defined account for small amount
of variation in GNP; more direct methods of inferring the volatility of oil prices attribute
a more prominent role to oil price shocks. Taking the asymmetry of the economic
response to the 1986 oil price collapse as one of its departure points, Bohi`s (1989)
10
monograph, and his article(1991) distilling that longer work, involve efforts to identify
microeconomics mechanisms by which energy price shocks might propagate their effects
throughout the economy. Bohi addresses the composition of demand as a possible route
of effect of energy price shocks, but again maintains his pure price-theoretic focus rather
than incorporating business –cycle considerations. As in his analysis of the labour
market, he estimates zero-order correlation coefficients between energy intensity and
changes in industry output price indexes, between intermediate input cost shares and
changes in output price indexes, and between energy intensity and changes in inventories.
In Bohi`s analysis of the labour market and demand decomposition, no formal models are
constructed to guide expectations regarding statistical results or to facilitate interpretation
of the results obtained. So, in the absence of formal modelling of business cycle
transmission mechanisms, the simplicity of statistical methods employed, and the
imprecision of implied hypothesis, the information content of Bohi`s results is unclear.
Composition of demand as a transmission has been investigated by Beresnahan & Ramey
(1992, pp.24-27), who have found that when oil prices increase, plants that produce small
cars operate at capacity and plants that produce large cars are idle.
Addressing the issue of asymmetry has led to a more general search for
transmission mechanisms by which oil price shocks may be propagated into economywide recessions. The empirically compelling shock that initiates the dispersion
hypothesis` employment mechanism is oil price shocks. There is evidence at both the
plant and aggregate levels that oil price shocks may operate through demand composition
effects. Nonetheless, in the search for particular types of shocks that, via various
transmission mechanisms, initiate business cycle in general, oil price shocks have not
been shown to be principal causes of business cycles.
As a group, these theories began to provide a conceptual basis for the apparent
asymmetry of the oil-macroeconomic relationship. Research on asymmetry of
macroeconomic responses to oil price shocks evolved into separate strands of research on
particular transmission mechanisms. Each posed specific transmission mechanisms that
might be observable at the level of the industry or firm.
11
3. The Methodology and dataset used in the Study
This paper unlike the literature considers unit root and structural break tests for
deciding whether co-integration and ECM techniques or VARs technique and innovation
accounting tools would be used to explain the interaction of economic activities, oil price
shocks, and other key economic variables. A narrow body of research (e.g., Hamilton,
1983; Gisser &Goodwin, 1986; Mork, 1989; Hooker, 1996a) contributed to demonstrate
possibility of changing the causal fundamental relationship between oil shocks and
economic activity over time. To do so, they used structural break tests to examine
whether there are changes in the causal factors linking oil and the economic activity. The
interaction of oil price shocks and economic activity has been studied and applied for
U.S. and other nations by using various econometrics’ techniques, mostly relying on
common VARs or recursive near VARs techniques (e.g., Baharuddin, 2004; Balke et al.
2002, 1999; Huntington, 1998; Bernanke et al. (1997); Ferderer, 1996; Mork et al. 1994;
Mory, 1993; Dotsey &Reid, 1992; Bohi, 1991, 1989; Mork, 1989; Burbidge &Harrison,
1984; Hamilton, 1983, and so forth). This paper examines an alternative asymmetry
hypothesis within a bivariate and multivariate context of co-integration and errorcorrection model (ECM) for Canada’s economic activities. In addition, we show whether
symmetry or asymmetry is transmitted by market interest rates and the aggregate implicit
price deflator to GDP.
This purpose is done in three steps. The first step is verifying the order of
integration of variables, through standard tests for the presence of unit root based on the
work done by Dicky & Fuller (1979, 1981) [ADF] and Kwiatkowski et al. (1992)
i
[KPSS] . Also, we are testing for the existence of structural breaks by using Perron
(1997) tests. Essentially, taking traditional VAR techniques or (ECM) error- correction
model (just the same as a near VAR model) is not valid without implementing these
standard testsii. So, the second step involves testing for co-integration using the Engle –
Granger (1987), and the error- correction method. Engle and Granger’s (1987) method is
a residual- based co- integration test, which has been criticized by Kremers et al. (1992)
that it has reduced power because it imposes the “ common factor restriction”. For this
reason an unrestricted error- correction model is employed to test directly for cointegration among variables. Engle and Granger (1987) show that, in the presence of co12
integration, there is always a corresponding error- correction representation, which
implies that changes in the dependent variables are a function of the first- lagged level of
the co-integration vector, as well as changes in other explanatory variables. In other
words, an error-correction model (ECM) is simply a VARs with the lagged co-integrating
vector added. The aggregate case of this model is as follows;
n
m
i =1
j =1
∆Yt = α1 + γ 2ε1t −1 + ∑ δ i ∆Yt −i + ∑ γ j ∆X t − j + µ1t
n
m
i =1
j =1
∆X t = α1 + γ 2ε 2t −1 + ∑ δ i ∆X t −i + ∑ γ j ∆Yt − j + µ 2t
Where; ∆Yt-i and ∆Xt-j are the lagged value as Integrated of degree zero I (0), if we
suppose the I (1) variables Xt and Yt are co-integrated and εit-1 is the lagged cointegrating vector. The coefficient on the co -integrating vector can be interpreted as the
amount of adjustment in each period towards the long-run equilibrium.
The analysis is consisted of estimating OLS equations that explain aggregate
output, price levels and the short-run interest rate as a function of the lagged crude oil
prices and other key variables including of the lagged values of themselves, also crude oil
prices as s function of the lagged of all specified key variables.
The present empirical analysis has been carried out by using Quarterly dataset of
nominal gross domestic product (NGDP), the average unit value-cost of imported crude
oil (NOIL) to Canada, a short - run interest rate (SIR) [Three months t-bill], the aggregate
implicit price deflator (IMP-1997=100), and the commodity price index (CPI) for the
period 1984-2002 for Canada ‘s economy. Some variables values are missing for the year
2002. So, the year 2002 dropped out for all specified variables. Since the short- run
interest rate and price level are nominal variables, GDP and the cost of imported crude oil
are measured as nominal values. In this paper the cost of imported crude oil is used as a
proxy for crude oil prices. All of the variables except crude oil prices have been obtained
through time series data produced by Statistic Canada (CANSIM II). The cost of
imported crude oil was obtained from the International Energy Agency (IEA) quarterly
document entitled “Energy Prices and Indexes”. Finally, to include the direct effects of
13
imported oil to Canada, Heckman et al, (1987, pp 24-9) used the aggregate implicit price
deflator instead of the personal consumption deflator. In order to account for monetary
policy that targets interest rate (money supply), so the short – run interest rate and the
implicit price deflator were added to variables.
The third step is related to implementing an asymmetry test and identifying
whether symmetrical or asymmetrical relationship does exist between oil price shocks
and economic activity through bivariate and multivariate examinations of asymmetry.
The asymmetry question has influenced much of the post-1989 research, to the extent that
it has become nearly standard to specify positive and negative oil price changes as
separate variables. Nearly all of the empirical analyses after Mork’s (1989) study, which
separated oil price movements into separate variables, have found asymmetric aggregate
GNP responses to oil price changes(e.g., Balke et al., 2002, 1999; Huntington, 1998;
Mory, 1993; Dotsey &Reid, 1992; Mork, 1989).
According to works done by (Balke et al., 2002, 1999 and Huntington, 1998), at
this study, testing for the symmetry null hypothesis is consisted of adding a separate
variable for crude oil price decreases that equalled the price change if negative and zero if
positive.(net oil price specification , first defined by Hamilton (1996, 1999), and used by
(e.g., Huntington, 1998; Balke et al. 1999, 2002). If this coefficient is significant;
symmetry can be rejected. We also estimate an equation with separate variables for price
increases and decreases, used by (e.g., Huntington 1998), While these two methods are
equivalent to each other, the coefficients in this second method are easier to be
interpreted; particularly when the relationships involves lagged values.
4. Empirical Results
4.1. Conventional unit Root Tests
As a starting point, Tables 1 and 2 present results of applying two standard
unit root tests including of the Augmented Dickey- Fuller (ADF) test and the
Kwitkowski, Philips, Shin, and Schimt (KPSS) test to all key economic variables
consisted of the Nominal Gross Domestic Product (NGDP), the nominal cost of
imported crude oil (NOIL), the short-run interest rate (SIR), the aggregate implicit
price deflator (IMP), and the commodity price index (CPI).
14
In Table 1, we present three versions of the ADF test, which differ by the
inclusion of a constant or trend in the regression equation by practising such as: no
constant and no trend, τ ; constant, no trend, τ c ; constant and trend, τ t . The null
hypothesis is that the series are integrated of the first-order, I (1). The ADF statistics
suggest that the all variables except the commodity price index are integrated of
order one, I (1), whereas the first differences are integrated of order zero, I (0).
Therefore, there is no evidence the fail to reject of the null hypothesis that the time
series contain an autoregressive unit root.
In Table 2, we present two versions of the KPSS test. The null hypothesis is
that the series are integrated of the zero-order, I (0) around level (ηµ ), or I (0) around
trend ( ητ ). These results are reported for only one lag-truncation parameters. Once
again, most of the results are consistent with a unit root, i.e. there are no enough
evidence the fail to reject the null hypothesis of I (0). The exception is the
commodity price index. The KPSS statistic do not reject the null hypothesis of I (0)
for the first differences of the series at different levels of significance. Therefore, the
combined results from both standard unit root tests (ADF, KPSS) suggest that all the
series except the commodity price index, appear to be I (1) processes.
4.2. The structural Break Alternative 3
In this section, we use the methodology developed by Perron (1997) of
endogenously determined breaks, as indicated in Table 3. That is, we undertake
estimation without assuming any prior knowledge of any potential break dates. The
model is estimated over all possible break dates in the data set, and the break date is
chosen to maximize the probability of rejection of the unit root hypothesis. We
estimate three models. Model (I) allows only a change in the intercept. A Test is
performed using the t-statistics for the null hypothesis that ρ =1(an unit root) in the
regression
3
This methodology is similar to that suggested by Zivot and Andrews (1992.) For details see
Perron,”Further evidence on breaking trend functions in macroeconomic variables”, journal of
Econometrics, 80(1997), page 361.
15
p
yt = α 0 + α1 DU t + dDTBt + β t + ρ yt −1 + ∑θ i ∆yt −i + et
(I)
i =1
Where
DU t = 1(t > Tb ) and
DTBt = 1(t = Tb + 1); Tb
is the endogenously
determined time of the break. The methodology searches over all possible breaks
points and chooses the break point based on the value of the t-statistic.
Under model (II), both a change in the intercept and the slope are allowed.
p
yt = α 0 + α1 DU t + dDTBt + β t + γ DTt + ρ yt −1 + ∑θ i ∆yt −i + et
(II)
i =1
Where DTt = t (t > Tb ) , and
Under model (III), only a change in the slope is allowed.
p
yt = α 0 + α1 DU t + β t + γ DTt + ρ yt −1 + ∑θ i ∆yt −i + et
(III)
i =1
The results of applying this procedure are presented in Table 3. As we see, at
the 1% and 5% significance levels, all of the models fail to reject the null hypothesis
underlying unit root for all series except the commodity price index. So we can say,
these results are not consistent with the hypothesis that the series are best
characterised as stationary around a breaking mean and/or trend function. In other
words, there is structural break in the endogenously given break dates except for the
commodity price index. So these results confirm the pervious results of standard unit
root tests.
4.3. Conventional Bivariate and Multivariate Co- integration Tests
Since, gross domestic product (NGPD), the proxy for average crude oil prices
and the other key economic variables are integrated of the same order, it is
appropriate to look for the relationship between the aggregate economic activity and
the crude oil price, the short-run interest rate, the aggregate implicit price deflator in
bivariate and multivariate models .The commodity price index is taken a way since
it is integrated of order zero, I (0). The Table 4 summarizes the results of cointegration analysis using the augmented Engle – Granger method.
16
In Table 4, we present a two versions of the Engle –Granger tests, which
differ by the inclusion of a constant or trend in the regression equation including of:
only a constant, no trend, τ cτ ; and constant and trend, τ cτ . The null hypothesis is no
co-integration among variables in the involved models. The results of the bivariate
regression model of aggregate economic activity on the crude oil price shows that the
hypothesis of no co-integration can be rejected in the both versions of Engle –
Granger method. Also, the tests, in regression model of the crude oil price on
aggregate economic activity, indicate evidence of co-integration in a both versions
The Engle-Granger tests in the Bivariate regression model of the implicit price index
and short-run interest rate on the crude oil price and vice-versa (i.e., in the regression
models of the crude oil price on aggregate implicit price index and interest rate)
suggest the null hypothesis of no co-integration could be rejected in both kind of
regression models.
As we can see, the Engle –Granger tests on the bivariate models imply there
is no evidence of weak exogeneity between the proxy for crude oil price and each of
the mentioned key economic variables in Canada‘ s economy. Since the effect of the
changes of crude oil price could be addressed by the changes in the aggregate price
level and monetary policy tools (e.g., changing the interest rate) into the aggregate
economic activities, the Bivariate co-integration tests are undertaken between the
crude oil price and these key economic variables. So, in order to account for
influences by these price and financial variables into
the relationship of gross
domestic product –crude oil price, changes in the price level and monetary policy,
and the aggregate implicit price level and short-run interest rate variables were added
to the bivariate models for doing Multivariate co-integration tests. These tests are
done in the three models as follow in the following.
(a) The regression model of GDP on the crude oil price, the interest rate and
the implicit price index; (b) The model of regression GDP on the crude oil price and
the short-run interest rate; and (c) The regression model of GDP on the implicit price
index and interest rate. Since the movement trend of the crude oil price and the
aggregate implicit price index are similar to each other, by assuming as substitute to
each other, these models are selected for multivariate co-integration tests. The results
17
suggest that we cannot fail to reject the null hypothesis of no co-integration in these
multivariate models in two versions of Engle-Granger test. On the basis of results,
we can support the proposition that a long –run relationship exists among the
aggregate economic activities, the average unit value of cost of imported crude oil,
the short-run interest rate and the aggregate implicit price deflator in Canada’s
economy over the period under examination (1984-2002).
4.4. The Error – Correction Models (ECM)
As we stated in the previous section, most of the economic literature has used a
simple short-run dynamic VARs or near VARs Models for performing an asymmetry test
of a changing crude oil price mostly for US. Economy. They used either ordinary least
square (OLS) as an efficient estimation of the VARs Model with similar structure for
each of the equations, or the SURE Method for estimating equations of a near -VARs
Model with a different structure for each of the equations in the model.
In some of these studies4, an arbitrary Choleski decomposition provides an extra
equation necessary for identification of the structural model. Also, innovation techniques,
like Impulse Response functions and variance decomposition, have been used to obtain
information concerning the interactions among the variables5.
But, in other studies6 asymmetry tests have been undertaken by adding up
negative changing crude oil prices and / or entering the both of negative and positive
changing crude oil prices in the aggregate economic activity model.
As discussed by scholars after 1990, (e.g,Hamilton, 1996; Mork; 1994, Ferderer,
1996, and so on), the oil price-economic activity relationship is sensitive to oil price
specification by including oil price variation of 1980s, 1990s and later. In better sense, no
significance relationship does exist between oil-economy by using only alone crude oil
price changing variable. So, all studies after 1990 turned to include a separate negative
and positive oil price changes variables or/and adding up a” net oil price” variable as an
4
“Oil price shocks and US economy: where does the asymmetry originate”, the Energy Journal, 2002, by
N.S.Balke, S. P.A.Brown and Mine.k.Yucel.
5
6
Applied Econometrics Time-Series, Iowa State University, 1992, by Walter Enders.
Crude oil prices and US economic performance, the Energy Journal, 1998. by Hillard G. Huntington.
18
alternative oil price specification thought models, as we discussed in the third section.
Therefore, the analogous techniques (i.e., adding up negative changing crude oil price
and / or entering both negative and positive changing crude oil price) are used to perform
the asymmetry test in this paper. By the way, there are the other methods in the economic
literature that has been used to carry out asymmetry tests of changing energy price.
As shown, in the bivariate and multivariate co-integration tests there are evidence
of co-integration among involved variables, and so as we know a principal feature of cointegrated variables is that their time paths are influenced by some extent of deviations or
errors from a long run equilibrium path. Hence, after all, if the system is to return to a
long run equilibrium path, by taking the movements of at least some of the variables most
respond to the magnitude of the this equilibrium. So the short-run dynamic model (simple
VARs) must be affected by a proxy variable, the lagged co-integrated vector, considering
deviation or error from the long run relationship. On the whole, unlike the literature
particularly related to Canada’s economy, we apply Error-Correction Model. Therefore
according the stance of given reported co-integration tests, bivariate and multivariate
error correction models (ECM) have been undertaken to demonstrate the adjusting
process.
The results of the estimated ECM models have been reported in Tables 5 to10.
The coefficients of the lagged co-integrated vector are the speed of adjustment
coefficients, so one or both of these coefficients should be significantly different from
zero, otherwise a long run relationship does not appear and the model is not one of error
correction or co-integration. In these tables, only coefficients with t-statistics greater than
one have been reported, and all of the variables are in first differences. Also, all of the
estimated ECM results have been given in terms of drift and trend in the original cointegrated models.
In Tables 5, 6 and 7, we present some bivariate ECM models done
between
aggregate economic activity and the crude oil price, the implicit price deflator and the
crude oil price, and the short-run interest rate and the crude oil price, respectively, so as
done reversely as well. The results based on ECM models with trend are more reliable
than models with drift. Also, at least one of the coefficients of long run equilibrium term
in two -ways models is significantly different from zero, so we can say; there are the long
19
run equilibrium relationships between nominal GDP and the crude oil price, the
aggregate implicit price deflator and the crude oil price, and the short-run interest rate
and the crude oil price. According the Schwartz –Bayesian criteria (SBC), the best model
has been selected with 4 lags and no significant coefficients have not been brought in the
results .It seems the entering more key economic variables into the bivariate long run
equilibrium models would be useful to examine the effect of other key variables.
To illustrate, multivariate error correction models have been estimated and
reported in Tables 8, 9, and 10. Since, the multivariate co-integration tests show evidence
of co-integration among involved variables, so ECM models have been selected for
estimating the long run equilibrium relationship of these variables. In Table 8, we present
the long run equilibrium relationship among nominal GDP and the crude oil price, the
implicit price deflator and the short – run interest rate. The coefficient of the speed of
adjustment term (first lagged co-integrating vector) is not significantly different from
zero, in both models with drift and trend. But, in some of the estimated ECM models, i.e.,
in the regression of the implicit price index on the other variables, these coefficients are
not necessarily different from zero (that is not been reported here). Therefore, we cannot
say there is not the long run equilibrium relationship among these four key economic
variables. Also according SBC criteria, model with four lags is the best model that the
coefficients with a t-statistics more than one have been reported. Since, the movement
trends of crude oil price and the aggregate implicit price index are similar to each other,
in Table 9; we present the error correction model of the regression of nominal gross
domestic product on the crude oil price and the short – run interest rate. As we see, the
ECM model with trend statistically has the most significant coefficient of the error
correction term. So we can say, there would be a long run equilibrium relationship among
economic activity with the crude oil price and the short-run interest rate, as a
representative of monetary policy. Also, in Table10, are presented the error correction
model of the regression of GDP on the short-run interest rate and the aggregate implicit
price deflator with drift and trend separately. It seems this ECM model indicates a
reliable long run equilibrium relationship among these variables.
20
4.5. Bivariate and Multivariate Asymmetry Tests
Thus far, we showed that an error correction model could be used for
studying the relationships amongst aggregate economic activity, the average unit
value of cost of imported crude oil and other key economic variables in Canadian
Economy. Some of the previous studies (e.g., Balke et al., 2002; Huntington, 1998)
used directly efficient OLS estimation of short-run dynamic VARs models to allow
asymmetry tests according to the aforementioned techniques (adding up negative
changes of crude oil price and /or taking positive and negative changes of crude oil
price in the estimated output equation of VARs model) without assessing cointegration tests and the long run relationships of the involved variables. In this
paper, we used an efficient OLS estimation of error correction models as bivariate
and multivariate to do asymmetry test with adding up negative changes of crude oil
price and /or taking positive and negative changes of crude oil price in the estimated
output equation of ECM model. These results have been shown throughout Tables 5
to 9. These tests are done to assess the symmetry relationship between crude oil price
changes and GDP.
Table 5 shows the asymmetry test only in the regression model of GDP on
the crude oil price with drift and trend in the both equivalent techniques. As we see,
there is no evidence for rejecting the null hypothesis of a symmetrical relationship.
The changing crude oil price has effects on aggregate economic activity via changes
in the aggregate price level and interest rate as a symbol of monetary policy. This
could make happen under affecting of dictated policy by government after oil price
shocks for adjusting effects of the crude oil price shocks on the aggregate economic
activity or natural aggregate supply and demand effects. So, in Tables 6 and 7 we are
doing the source asymmetry tests with drift and trend under ECM models. The
results indicate that there is not any reason for rejecting the symmetry null hypothesis
with some techniques for the short-run interest rate. While, there is an evidence of an
asymmetry between oil price and implicit price deflator. That means, the symmetric
relationship between changing crude oil price and the aggregate economic activity is
due to symmetric relationship of oil price changes with the changing short-run
interest rate not by aggregate implicit price index. The important point is that the
21
results are volatile in terms of used techniques, and type of considered financial and
price level variables, not so reliable.
The multivariate asymmetry tests have been reported in Tables 8 and 9 with
drift and trend by using the equivalent oil price changes techniques. In Table 8, we
present asymmetry tests in the multivariate regression model of GDP regressed on
the crude oil price, the implicit price deflator and the short-run interest rate. In Table
9, this test is reported for the multivariate model among GDP and the crude oil price,
and the short-run interest rate. All of the results indicate in some cases fail to reject
the null hypothesis of a symmetric relationship between aggregate economic
activities and changing of the crude oil price. Therefore, according to the results in
Tables 8 and 9 (which are potentially more reliable than the bivariate asymmetry
tests, because the some of the important key economic variables such as the
aggregate price level and the interest rate are in the aggregate economic activity
model), we can say that the imported crude oil price shocks to Canada (as reliable
proxy of the crude oil price) has a symmetric effects on aggregate economic activity
and this effect can be routed by the monetary policy tools and changes in the price
level. We still see the volatility of the results with respect to different asymmetry test
methods, the type of taken financial and price level proxies, nature of structural
models.
This result contradicts most of the studies in economic literature about the
effect of crude oil price shocks on mostly about the United States economy. But, by
some extent verify some of concluded results by Mork et al., (1994) specifically the
asymmetry test for Canada, and US. More precisely saying, while potentially an
asymmetry test underlying the multivariate context could be more reliable than that
by a bivariate one, but based on reported results and validity of results, we can say,
we can draw and verify moderately symmetry result between oil price and Canada’s
economic activity more based on bivariate context than a more unstable resulting of a
multivariate context.
22
5. Concluding Remarks
The purpose of this paper was to examine the asymmetry between crude oil
price shocks and aggregate economic activities in the frame work of developed
various recently time-series techniques in the bivariate and the multivariate context
for Canada’s economy and finding out some of its affecting factors over period 1984
to 2002. In doing so, time series techniques such as Unit-Root testing, a structural
break test, bivariate and multivariate co-integration and procedures in vector ErrorCorrection Models were presented. This analysis can support several conclusions as
follows:
1-The all of the key economic variables including; the aggregate economic
activities (NGDP), the average unit value of cost of imported crude oil (NOIL), the
aggregate implicit price deflator (IMP), the short-run interest rate (SIR), and the
commodity price index (CPI) are integrated of order one, I(1). In the other words,
these variables have a unit root.
2- The conventional structural alternative break test by Perron (1997)
suggests no evidence of structural breaks, based on the endogenously taken break
dates. This confirmed the results of unit root tests.
3- The conventional Bivariate and Multivariate co-integration tests by Engle
and Granger support that there is a co-integration between nominal GDP and the
crude oil price. Moreover results shows a co-integration of nominal GDP with the
crude oil price, the aggregate implicit price deflator and the short-run interest rate in
the frame work of different multivariate models. Also, evidence of co-integration is
seen between the crude oil price and the implicit price index as well between the
short-run interest rate and the crude oil price. On the other hand, there is an evidence
of weak exogeneity between GDP and the crude oil price and, between each of the
other key economic variables and the crude oil price.
4-In this paper we showed that there are a long-run equilibrium relationships
between nominal GDP and the crude oil price, the aggregate implicit price deflator
and the crude oil price, and the short-run interest rate and the crude oil price in the
framework of bivariate error correction models. Also, we see similar long-term and
equilibrium relationships among nominal aggregate economic activity and the other
23
mentioned key economic variables in different multivariate ECM models. By the
way, the control on instruments of money markets (i.e., interest rate) and the
aggregate price level can be seen a long-run equilibrium adjustment in affecting of
oil price shocks on GDP under the framework of reliable ECM models. In other
words the control on instruments of money markets (i.e., interest rate) and the
aggregate price level gives a long-run equilibrium adjustment in effecting of oil price
shocks on GDP under the framework of reliable ECM models.
5-The asymmetry test for crude oil price changes in both equivalent technique
(adding up negative changes of crude oil price and/or adding the positive and
negative changes in the crude oil price) are applied to explain effect of changes in the
crude oil price on the aggregate economic activity by Error-Correction model
techniques in both Bivariate and Multivariate models. In contrast with a majority of
economic literature, except work done by Mork et al., 1994, the results show a
significant portion of the symmetry in the Canada’s economy response to the crude
oil price changes in bivariate model in both equivalent techniques. Also, this
symmetry economy’s response is obtained in the multivariable model with adding up
the interest rate and the aggregate price level or only the interest rate by some extent,
but by having result volatility and not so much reliable. While, we can not reject an
asymmetry response of Canada’s economy to oil price shocks. More monetary
policy tool (i.e., interest rates) and less implicit price deflator are taken to be by some
degrees as some sources of symmetry response of Canada’s economy to the crude oil
price shocks. So, as source of this symmetric response, we performed the equivalent
asymmetry tests under the framework of bivariate model as the regression of the
aggregate implicit price deflator and the interest rate on the crude oil price. The
results indicate there is a symmetry relationship between the changes of crude oil
price and the short-run interest rate and a volatile symmetry for the implicit price
deflator as some possible sources of Canada economy’s response to the oil price
changes. In other words, the mentioned symmetry response of aggregate economic
activity has been originated from changes of the short run interest rate by monetary
policy of the government or by natural reaction based on aggregate classic demand
and supply, and unstably in the aggregate level of price index. Therefore, it seems
24
some financial monetary policy tools (e.g., interest rates) and the implicit price
deflator to be as some sources of routing response of Canada’s economy to the crude
oil price shocks.
6. Despite of given moderate result, we can not deny taken result might be as
an artefact of used data series, estimation techniques, and or applied method to
perform the asymmetry test. As an extension of this work, and since drawn results
based on multivariate models are volatile, we need to implement the asymmetry
study by a more reliable and dynamic technique such as non-linear impulse response
function analysis.
In addition, through these models, as a future works, the effects of changing
energy price on aggregate economic activity could be addressed via such indirect
effects as redistribution of the real income between energy-exporting and energyimporting countries (Terms-of-trade), changes in the aggregate demand of a given
country’s trading partners (Foreign demand), uncertainty in both house- hold and
businesses, the impact on the production costs of non- energy producers and the real
income of households, and short and long-term effects on energy supply productions,
and so forth. Further more is that this work can extended by using other routs as
possible symmetry or asymmetry other channels like financial variable such as
money supply, and employment or unemployment rate.
25
Table 1
Augmented Dickey-Fuller Tests
τ
τc
k
Variable
NOIL
-.5
0
NGDP
2.2
SIR
-3.08
τt
K
Conclusion:
The variable is:
K
3
-3.18
3
I (1)
6 -.73
4
-2.37
4
I (1)
-1.29
1
-2.09
0
-3.35
0
I (1)
IMP
1.95
4 -1.71
4
-1.94
4
I (1)
CPI
-.31
0
3
-4.16
3
I (0)
-3.9
Notes:
1) This table reports the ADF tests, for testing the unit root null hypothesis in the relevant
variables. All of the variables are in nominal values. The τ,
τ
c and
τt
statistics are
described in the text. The k is the optimal number of lags that has been selected using the
Schwartz-Bayesian criteria (SBC).
τ τ
2) At the 1% significance level, the critical value for the ,
c and
τt
statistics are -
2.6, -3.51, and -3.18 respectively. Also, the critical values at the 5% significance level for
the
τ, τ
c and
τt
statistics are -1.95, -2.89 and -3.45 respectively. These critical
values are reported from Hamilton (1994).
26
Table 2
KPSS Tests for (I=1)*
ηµ
Lags
NOIL
NGDP
SIR
IMP
CPI
0
.84
6.7
4.49
6.76
1.16
1
.45
3.46
2.41
3.46
.61
2
.33
2.36
1.67
2.35
.43
3
.26
1,81
1.29
1.79
.35
4
.23
1.47
1.06
1.46
.3.
0
.72
.63
.41
1.37
.16
1
.39
.28
.39
.24
.73
.08
.32
.17
.51
.06
.23
.2
.26
.14
.39
.05
.21
.11
.31
.04
I (1)
I (1)
I (1)
I (1)
I (0)
2
ητ
3
4
Conclusion:
The variable
is:
Notes:
1) ηµ and
ητ
are the KPSS statistics for testing the null hypothesis that these series are I
(0), when the residual are computed from a regression equation, with only an intercept
and with a time trend, respectively. The critical values for
ηµ and ητ at 5% significant
levels are .463 and .146 and at 1% level of significance are .739 and .216 respectively.
Also, at 10% Significance level for η µ and ητ are .347 and .119 respectively.
2) KPSS statistics are reported only for (I=1) lag – truncation parameters.
27
Table3
Unit roots under structural Break
Perron methodology of endogenously determined Breaks
Model 1: change in the intercept
Tb
k
( tα =1)
NOIL
1998:04
3
-4.46
NGDP
1998:03
4
-5.99
SIR
1995:01
12
-4.07
IMP
1988:04
12
-3.26
CPI
1990:02
7
-6.04
Variables
Model 2: change in the intercept and in the slope
NOIL
1985:03
3
-4.42
NGDP
1994:03
4
-5.14
SIR
1995:01
12
-4.47
IMP
1992:01
8
-4.88
CPI
1990:02
7
-6.46
Model 3: change in the slope
NOIL
2000:03
3
-4.2
NGDP
1999:04
4
-4.39
SIR
1988:02
4
-2.64
IMP
1991:01
5
-4.56
CPI
1984:01
7
-5.21
Notes:
1) The critical values at 10% significance level for model 1, model 2, model 3 are -4.92, -5.29, and -4.48
respectively; at 5% significance level are -5.23, -5.59, and -4.83 respectively. Also, the critical values at 1
% significance level for 3 mentioned models are -5.92, -6.32, and -5.45 respectively.
2) This table reports the Perron structural test with unit root null hypothesis. The critical values are taken
from “Further evidence on breaking trend functions in macroeconomics variables”, journal of
Econometrics, 80(1997) by P. Perron.
28
Table 4
Bivariate and Multivariate Co-integration Tests
NGDP=f
NOIL=f
SIR=f
NOIL=f
IMP=f
NOIL=f
(NOIL)
(NGDP)
(NOIL)
(SIR)
(NOIL)
(NIMP)
NGDP
NOIL
SIR
NOIL
IMP
NOIL
Dependent
Dependent
Dependent
Dependent
Dependent
Dependent
variable
variable
variable
variable
variable
variable
2
3
1
3
4
3
-74.67
-42.55
-24.06
106.51
-235.53
-38.79
K2
4
3
1
3
4
3
τ ct
-35.42
-34.2
-24.06
-40.20
-43.21
-44.09
Bivariate
Model
K1
τ
c
NGDP=f (NOIL, P, SIR)
NGDP=f (MP, SIR)
NGDP=f (OIL, SIR)
Multivariate
NGDP
NGDP
NGDP
Model
Dependent variable
Dependent variable
Dependent variable
K1
4
4
0
-30.34
-36.1
-33.31
K2
4
4
4
τ ct
-10.17
-15.56
-12.92
τ
c
Notes:
1) This table shows the co-integration on bivariate and multivariate model with the null
hypothesis no co-integration among variables in the involves models, k1, k2, are the best
lags that have been selected by SBC criteria and τ c , τ ct are statistics that have been
described in the text.
2) The critical values at 5% significance level for models with intercept and time trend
are -3.34 and -3.78 respectively. These critical values are taken from “Estimation and
inference in Econometrics “, by Russell .D and J. G.Mackinnon, (1993).
29
Table 5
The Estimated Bivariate Error-Correction Models for GDP with crude oil prices (1984-2001)
Equation with drift
DNGDP
DNOIL
Constant
Resids (t-1)
939.1
-.154
(1.17)
(-2.16)
-1.924
-.245
(-1.8)
(-3.14)
DNGDP (t-1)
-
DNGDP (t-2)
-.151
(-1.57)
-
DNGDP (t-3)
-
DNGDP (t-4)
.855
(8.726)
DNOIL (t-1)
-
DNOIL (t-2)
103.56
(1.97)
DNOIL (t-3)
DNOIL (t-4)
-
-
.00022
-.34
-.184
.274
(1.72)
(2.67)
(-1.38)
(2.1)
-
-
-
Equation with trend
DNGDP
DNOIL
-.141
-
(-2.61)
-.261
-
(-3.07)
-
-
-
.908
(9.8)
.00019
.352
(1.49)
(2.74)
-
-90.9
-92.23
(-1.99)
(-2.12)
.276
(2.1)
-
Estimated equation for Asymmetric test for GDP with adding up negative changes in crude oil prices (1984-2001)
Equation with drift
DNGDP
Equation with trend
DNGDP
Constant
1080.8
(1.058)
Resides (t-1)
DNGDP (t-1)
-
-
-.158
-
(-2.66)
-
DNGDP (t-2)
-.1729
(-1.69)
-
DNGDP (t-3)
-
-
DNGDP (t-4)
.844
(8.16)
.918
(9.29)
NNOIL (t-1)
-
-
NNOIL (t-2)
NNOIL (t-3)
260.46
-231.25
(1.48)
(-1.3)
-
-268.23
(-1.61)
NNOIL (t-4)
-
-
Estimated equation for Asymmetric test for GDP with positive and negative changes in crude oil prices (1984-2001)
Equation with drift
DNGDP
Equation with trend
DNGDP
Constant
1080.8
(-1.05)
-
Resides (t-1)
DNGDP (t-1)
-
-
-.158
(-2.66)
-
DNGDP (t-2)
-.172
(-1.69)
-
DNGDP (t-3)
-
-
DNGDP (t-4)
.844
(8.16)
.918
(9.299)
NNOIL (t-1)
NNOIL (t-2)
-
-
-
-
NNOIL (t-3)
-374
(-1.19)
-404.96
(-1.37)
NNOIL (t-4)
-
-
Notes: The all of t-statistics have been reported in the parenthesis. The null hypothesis is a symmetrical relationship between crude oil
prices and GDP, and all of the variables are in the first difference.
30
Table 6
The Estimated Bivariate Error-Correction Models for IMP with crude oil prices (1984-2001)
Equation with drift
DIMP
DNOIL
Constant
Resids (t-1)
.004
-.015
(3.97)
(-1.3)
DIMP (t-1)
DIMP (t-2)
DIMP (t-3)
-
-
-
-.178
-.221
52.7
70.93
(-2.08)
(-3.12)
(2.06)
(1.98)
.0078
-.09
-.149
-.395
(5.35)
(-1.59)
(-1.29)
(-3.4)
-1.05
-.027
73.08
88.56
(-1.96)
(-3.62)
(1.5)
(1.96)
DIMP (t-4)
DNOIL (t-1)
DNOIL (t-2)
-
-
-
-
-
-
-
DNOIL (t-3)
DNOIL (t-4)
-
-
.367
-.171
300
(2.9)
(-1.42)
(2.34)
-
Equation with trend
DIMP
DNOIL
.0006
-
(2.11)
-
.383
-.15
.328
(3.09)
(-1.27)
(2.6)
DNOIL (t-2)
NNOIL (t-1)
-
Estimated equation for source Asymmetric test for IMP with adding up negative changes in crude oil prices (1984-2001)
Constant
Resids (t-1)
DIMP (t-1)
DIMP (t-2)
.006
-.0226
-.204
-.495
(3.46)
(-1.98)
(-1.82)
(-4.16)
Equation with trend
.0027
-.127
DIMP
(1.51)
(-2.16)
-
-
Equation with drift
DIMP
DIMP (t-3)
DIMP (t-4)
DNOIL (t-1)
-
-
(1.99)
-
-
.001
-
.0011
-
(2.15)
-.0016
(-1.81)
-.002
(-2.44)
NNOIL (t-2)
-
-
Estimated equation for source Asymmetric test for IMP with positive and negative changes in crude oil prices (1984-2001)
Constant
Resids (t-1)
DIMP (t-1)
DIMP (t-2)
.0006
-.022
.204
-.459
(3.46)
(-1.98)
(-1.82)
(-4.16)
Equation with trend
.0012
-.124
DIMP
(4.1)
(-2.14)
-
-
Equation with drift
DIMP
DIMP (t-3)
DIMP (t-4)
-
-
-
-
NNOIL (t-1)
-.00057
(-1.11)
-
NNOIL (t-2)
-
-
PNOIL (t-1)
.00106
(1.99)
-
PNOIL (t-2)
-
-
Note: The all of t-statistics have been reported in the parenthesis, the null hypothesis is symmetry relationship between crude oil prices
and GDP, and all of the variables are in the first difference.
31
Table 7
The Estimated Bivariate Error-Correction Models for SIR with crude oil prices (1984-2001)
Equation with drift
Constant
DSIR
-
DNOIL
-
Resids (t-1)
DSIR (t-1)
-.1
-.31
(-1.57)
(-2.317)
-.164
(-2.28)
-
DSIR (t-2)
DSIR (t-3)
-
-
-
-
-
-
DSIR (t-4)
.3
(2.43)
-
DNOIL (t-1)
DNOIL (t-2)
.456
.199
DNOIL (t-4)
-
-
-
-
-
(2.13)
(1.6)
DNOIL (t-3)
Equation with trend
DSIR
DNOIL
-.234
-.206
(-2.24)
(-1.41)
-1.05
-.027
73.08
88.56
(-1.96)
(-3.62)
(1.5)
(1.96)
-
-
.346
.414
-.211
.335
(2.75)
(3.29)
(-1.73)
(2.75)
.383
-.15
.328
(3.09)
(-1.27)
(2.6)
DNOIL (t-2)
NNOIL (t-1)
-
-
Estimated equation for source Asymmetric test for IMP with adding up negative changes in crude oil prices (1984-2001)
Equation with drift
DSIR
Constant
Resids (t-1)
DSIR (t-1)
.006
-.0829
-.298
(1.95)
(-1.34)
(-2.44)
Equation with trend
.0027
-.280
-.274
DSIR
(1.51)
(-3.28)
(-2.17)
DSIR (t-2)
DSIR (t-3)
-
-
-
-
DSIR (t-4)
DNOIL (t-1)
.3
-
.563
(2.43)
-
(2.16)
.365
-
(3.2)
-
NNOIL (t-2)
-.263
(-1.87)
-.326
-.211
(-1.78)
(-1.65)
PNOIL (t-1)
PNOIL (t-2)
Estimated equation for source Asymmetric test for IMP with positive and negative changes in crude oil prices (1984-2001)
Equation with drift
DSIR
Constant
Resids (t-1)
DSIR (t-1)
.0006
-.829
-.298
(1.65)
(-1.34)
(-2.44)
Equation with trend
.0012
-.28
-.186
DSIR
(1.86)
(-3.28)
(-1.99)
DSIR (t-2)
DSIR (t-3)
DSIR (t-4)
-
-
-
-
-
`
NNOIL (t-1)
NNOIL (t-2)
-.00057
-.456
(-1.11)
(-2.16)
-
-.315
(-2.03)
-
-
.533
(1.93)
.452
(1.73)
Note: The all of t-statistics have been reported in the parenthesis, the null hypothesis is symmetry relationship between crude oil prices
and GDP, and all of the variables are in the first difference.
32
Table 8
The Multivariate Error-Correction Models for GDP with IMP, SIR and NOIL (1984-2001)
Equation with drift
DNGDP
Constant
Resids (t-1)
DNGDP (t-2)
DNGDP (t-4)
DSIR (t-3)
DSIR (t-4)
DIMP (t-2)
DIMP (t-3)
DNOIL (t-1)
DNOIL (t-2)
2830.2
.083
-.193
.734
-362.02
-413.03
-81296
-78017
105.2
202.5
(2.23)
(1.6)
(-1.42)
(5.05)
(-2.22)
(-1.95)
(-1q.5)
(-1.41)
(1.87)
(1.98)
-
-
-
-
-
-
NNOIL (t-2)
DNOIL (t-3)
Equation with trend
DNGDP
-
-.173
(-1.08)
-
.918
(6.76)
Estimated GDP equation for Asymmetric test with adding up negative changes in crude oil prices (1984-2001)
Equation with drift
DNGDP
Equation with trend
DNGDP
Constant
Resids (t-1)
DNGDP (t-2)
DNGDP (t-4)
DSIR (t-1)
DSIR (t-4)
DIMP (t-2)
DIMP (t-3)
3371.5
.102
-.253
.685
333.3
-478.2
-99946
-60841
500.3
310.46
(2.2)
(1.78)
(-1.69)
(4.29)
(1.89)
(-2.23)
(-1.74)
(-1.02)
(1.42)
(1.96)
-
-
-
-
-
-.168
(-1.02)
-
.912
(6.43)
-481.4
(-2.38)
-
Estimated GDP equation for Asymmetric test with positive and negative changes in crude oil prices (1984-2001)
Equation with drift
DNGDP
Equation with trend
DNGDP
Constant
Resids (t-1)
DNGDP (t-2)
DNGDP (t-4)
DSIR (t-4)
DIMP (t-2)
NNOIL (t-2)
PNOIL (t-3)
3377
-102
-.253
.685
-478
-99946.3
496.48
310.6
(2.2)
(1.78)
(-1.69)
(4.29)
(-2.02)
(-1.74)
(2.35)
(1.48)
-
-
-
-.158
(-2.66)
-
.912
(6.43)
-316.9
(-1.55)
-
-
-
-.168
(-1.02)
-
Notes: The all of t-statistics have been reported in the parenthesis, the null hypothesis is symmetry relationship between crude oil
prices and GDP, and all of the variables are in the first difference.
33
Table 9
The Multivariate Error-Correction Models for GDP with NOIL and SIR (1984-2001)
Equation with drift
DNGDP
Constant
Resids (t-1)
1058.83
-.022
(1.18)
(-1.96)
DNGDP (t-1)
-
DNGDP (t-2)
DNGDP (t-4)
DSIR (t-1)
DNOIL (t-2)
-.145
.859
-398.28
135.5
(-1.46)
(8.09)
(-2.46)
(2.45)
.952
-352.36
(8.54)
(-2.032)
DNOIL (t-3)
DNOIL (t-4)
-
-
-
-
-113.32
122.8
(-1.72)
(2.35)
NNOIL (t-3)
-
-
-
-
-
-
NNOIL (t-3)
NNOIL (t-4)
PNOIL (t-3)
-
-
Equation with trend
DNGDP
-
-.195
.153
(-2.2)
(1.1)
-
-
-
Estimated GDP equation for Asymmetric test with adding up negative changes in crude oil prices (1984-2001)
Equation with drift
DNGDP
Equation with trend
DNGDP
Constant
3371.5
(2.2)
-
Resids (t-1)
DNGDP (t-1)
-
-
-.22
.188
(-2.28)
(1.27)
DNGDP (t-2)
DNGDP (t-4)
DSIR (t-1)
DNOIL (t-3)
-.166
.846
488.8
199.89
-421.9
(-1.61)
(7.71)
(2.65)
(2.02)
(-1.34)
-
-
-
.953
(8.17)
-413.06
(-2.33)
Estimated GDP equation for Asymmetric test with positive and negative changes in crude oil prices (1984-2001)
Equation with drift
DNGDP
Equation with trend
DNGDP
Constant
Resids (t-1)
3377
-.027
(2.2)
(-1.88)
-
DNGDP (t-1)
-
-.22
.188
(-2.28)
(1.27)
DNGDP (t-2)
DNGDP (t-4)
DSIR (t-1)
-.166
.846
-488.88
268.8
(-1.61)
(7.77)
(-2.65)
(2.51)
-
-
-
.953
(8.17)
NNOIL (t-2)
-291.8
(-2.63)
-
199.89
(1.02)
174.4
(-1.09)
Notes: The all of t-statistics have been reported in the parenthesis, the null hypothesis is symmetry relationship between crude oil
prices and GDP, and all of the variables are in the first difference.
34
Table 10
The Multivariate Error-Correction Models for GDP with SIR and IMP (1984-2001)
Equation with
drift
DNGDP
Constant
1244.2
(1.16)
DNGDP
Resids (t-1)
-
DNGDP (t-4)
.833
(6.51)
DIMP (t-1)
-
DIMP (t-2)
DIMP (t-3)
DSIR (t-1)
DSIR (t-2)
-68696.5
-85270.4
347.04
-390.03
(-1.3)
(-2.63)
(1.24)
(-2.29)
-474.4
-.34
.917
9605.4
.952
-352.36
(-1.7)
(-3.53)
(8.76)
(1.69)
(8.54)
(-2.032)
-
-113.32
(-1.72)
Notes: The all of t-statistics have been reported in the parenthesis, the all of t-statistics have been reported in the parenthesis.
35
References
Brown, Stephen P. A. & Yücel, M. K. (2002) Energy Prices and Aggregate Economic
Activity: An Interpretative Survey, Federal Reserve Bank of Dallas, Quarterly review of
Economics and Finance, Forthcoming, pp. 1-29.
Brown, Stephan P.A., Yücel, M. K. Thompson, J. (2002) Business Cycles: The Role of
Energy Prices, Federal Reserve bank of Dallas, Working Paper 0304, pp. 1-19.
Balke, N.S., Brown, Stephen P. A. & Yücel, M. K. (2002) Oil price shocks and the
U.S. economy: where does the asymmetry originate?, The Energy Journal, 23(3), pp. 27-52.
Brown, Stephen P. A. & Yücel, M. K. (1999) Oil Prices and U.S. Aggregate economic
Activity: A question of Neutrality, Economic and Financial Review, Federal Reserve Bank of
Dallas, Second Quarter, pp. 16-23.
Bernanke, B. S., Gertler, M. & Watson, M. (1997) Systematic Monetary Policy and the
Effects of Oil Price Shocks, Brookings Papers on Economic Activity, 1997:1, pp. 91- 142.
Bohi, D.R. (1989). On Macroeconomic Effects of Energy Price Shocks, Resources and Energy,
1991, 13, pp. 145-162.
Frederer, J.P. (1996) Oil Price Volatility and Macroeconomy: A solution to the
asymmetry Puzzle, Journal of Macroeconomics, 18(1), pp.1-26.
Gerald Stuber, (Summer 2001) The Changing Effects of Energy –Price Shocks on
Economic Activity and Inflation, The Bank of Canada Review.
Gisser, M. and T. H. Goodwin, (1986) Crude oil and the Macro economy: Tests of
some popular Nations, Journal of Money, Credit and Banking, 18, pp.95-103.
Hillard G.Huntington (1998) Crude Oil Prices and U.S. Economic Performance:
Where Does the Asymmetry Reside?, The Energy Journal, Vol 19, No.4, pp.107-132.
Hooker, Mark a. (1996) What Happened to the Oil price –Macro economy
relationship?, Journal of Monetary Economics, 38(2), pp.195-213.
Hamilton, James D, (1983) Oil and macro economy Since World War II, Journal of
Political Economy, 91(2), pp.228-248.
Jones, D. W. & Leiby, P. N. (1996) The Macroeconomic Impacts of Oil price Shocks:
A Review of Literature and Issues, Oak ridge national laboratory, Energy Division, Martin
Marietta Energy System, INC.
37
Lee, Kiseok, Shawn Ni, and Ronald A. Ratti (1996) Oil Shocks and the
macroeconomy: the Role of Price variability, The Energy Journal, 16(4) pp.39-56.
Mork, Knut Anton, Hans Terje Mysen, and oyestein Olsen (1994) Macroeconomic
Response to Oil Price Increases and Decreases in Seven OECD countries, The Energy Journal,
15(4), pp.19-35.
Mory, Javier F. (1993) Oil Price and economic Activity: Is the relationship
symmetric?, The Energy Journal, 14(4), pp.151-161.
Mork, K. A. (1989) Oil and the Macroeconomy when prices Go up and Down: an
Extension of Hamilton’s Results, Journal of Political Economy, 97, pp.740-744.
Natahan, S. B., Brown, Stephen P.A. & Yücel M. K. (2002) Oil Price Shocks and the
U.S. Economy: Where Does the Asymmetry Originate, The Energy Journal, Vol 23, No.3,
pp.27-52.
Papapetrou, E. (2001) Bivariate and multivariate of the inflation – productivity Granger
–temporal causal relationship: evidence from Greece, The Journal of Economic Studies,
Vol.28, NO.3, pp.213-226.
Russell .D and J.G. Mackinnon, (1993) Estimation and inference in Econometrics,
Oxford University Press.
Smyth, D. J.(1993) Energy Prices and the Aggregate Production Function, Energy
Economics, 15, pp.105-110.
Tatom, J. A. (1993) Are There Useful Lessons from the 1990-91 Oil Price Shock?, Energy
Journal, 14(4), pp. 129-150.
Tatom, J. A. (1988) Are the Macroeconomic Effects of Oil Price Changes Symmetric?,
in K.Brunner and A. H. Meltzer, eds., Stabilization Policies and Labor Markets,CarnegieRochester Conference Series in Public Policy, 28, pp. 324-368.
Walter Enders, (1992) Applied Econometric Time Series, John Wiley & Sons, INC.
38
Endnotes:
i
The KPSS procedure assumes that the univariate series can be decomposed into the sum of a deterministic trend.
Random walk and stationary I(0) disturbance and is based on a Lagrange multiplier score testing principle. This
test reverses the null and the alternative hypothesis .A finding favourable to a unit root in this case requires strong
evidence against the null hypothesis of stationary .The KPSS test is defined as :
2
η = T −2 ∑ St
S 2 (k )
Where
t
St = ∑ ei
(i=1, 2, 3… t)
i =1
And ei is the partial sum of the residual from regressing the series on an intercept and possibly a time
2
trend. S ( k ) is a consistent non-parametric estimate of the disturbance variance and T is the sample size
ii
The issue of whether the variables in the VAR model need to be stationary is controversial
debate. Sims (1980) and others, such as Doan (1992), recommended against differencing even if
the variables contain a unit root. They argue that the goal of VAR analysis is to determine the interrelationships
among variables, not the parameter estimates. The main argument against differencing is that it “throws away”
information concerning the co- movements in the data (such
as the possibility of co-integrating relationships). However, the majority view is that the form of
the variables in the VAR should mimic the true data -generating process. This is particularly true if the aim is to
estimate a structural model.
39