methodology

# Annex – Is the oil price-GDP link broken?

Following the approach employed by Kilian (2009) and Kilian and Park (2009)[1], we use a structural VAR model based on monthly data. The structural VAR model that we employ is the most viable method to isolate the three shocks without making too restrictive assumptions regarding the dynamics of crude oil price. In fact, it allows us to obtain a vector of shocks composed by elements both serially and mutually uncorrelated, which enables us to understand the reasons for fluctuations in the price of oil over time. Moreover, the structural VAR approach makes it possible to analyse the relationship between the three types of shocks and macroeconomic variables of interest, such as the GDP; more common methods, which questionably assume that the oil price is exogenous, do not make it possible to perform accurate inference.

The set of variables used for the model is, where corresponds to the growth in crude oil production in logs, is the index of real economic activity and is the growth of the West Texas Intermediate (WTI) price of crude oil in dollars per barrel in logs.

We use lags for 24 periods in the VAR model, which has the following form:

The inverse of the matrix has a structure such that the reduced-form errors obtained from the estimation can be written as:

The model imposes the following exclusion restrictions:

- Innovations in real economic activity can affect aggregate demand for industrial commodities and oil demand, while leaving oil supply unaffected, since oil supply shocks are assumed to be induced by unpredictable changes in global oil production only;
- An innovation in the oil price has a delayed effect on real economic activity. The latter is affected with a delay of one month at least;
- The oil supply is not affected by changes in the real price of crude oil in less than one month.

Since we are interested in the cumulative effect of the three shocks over the period under analysis, we focus on the decomposition of oil prices into its three components. These are obtained by multiplying the structural shocks obtained from the estimation of the model above by their relative weights, also derived from the estimation process. A correct identification of the three components requires the use of a measure of real economic activity driving the demand for commodities in the global market. Hence, Kilian built an index based on dry bulk cargo freight rates, which increase when the global demand for commodities experiences an increase. This index, made available by Kilian[2], can be used to identify periods of high and low economic activity. In order to build it, he used monthly data for dry bulk cargo freight rates, detrended the time-series and then adjusted it for the US consumer price index.

For the oil price we used the series of West Texas Intermediate prices and data regarding World production of crude oil[3]. We use data for the period February 1994-February 2016. Since data regarding the Kilian index is only available until September 2015, we employed the monthly Baltic Dry Index[4], an economic indicator of the price of moving raw materials by sea provided by the Baltic Exchange, to estimate the missing values for our index. Finally, for what concerns data for crude oil production, we use the time series of total World production provided by the International Energy Agency.

In order to analyse the effect of oil supply, aggregate demand and oil demand shocks on the EU GDP we rely on the following specification, following Kilian (2009):

where j=1, 2, 3 indexes the three shocks, is the EU GDP in log differences, constitute the impulse response coefficient and is a potentially serially correlated error term. For what concerns, this variable corresponds to the estimated j shock averaged by quarter. In fact, because of the unavailability of monthly GDP data, we have aggregated the monthly oil price shocks obtained from the estimation of the structural VAR model by quarter. We used seasonally adjusted GDP quarterly data for the EU from 1995 to 2015, available on Eurostat. Since the oil price is expressed in US dollars, we used quarterly USD-EURO exchange rates from Federal Reserve Economic Data (FRED) for the conversion in dollars.

The supply side shocks identified by the model (Figure 2) indeed correspond to exogenous changes in production:

- 2002: Negative oil supply shock due to production quota cuts by OPEC (6 months) and the halt of the oil-for-food program for 1 month by Iran; these events also generated uncertainty about oil production, leading to a negative oil-demand shock
- 2006: Oil production in Iraq dropped by 1 million barrels per day, generating an oil-supply shock; positive oil-demand shock due to a major cut to oil demand in the developed countries (1
^{st}time in 20 years) - 2009: Negative supply shock because of the Libyan war
- 2010: Positive oil supply shock due to the approaching end of the war in Iraq; the country was finally able to regain the control of oil production.
- 2011: Negative supply shock because of the war in Libya
- 2012-2016: positive oil supply shock due to the shale oil revolution

__Chow test for the presence of structural breaks__

The aim of this subsection is to provide empirical evidence for the existence of a structural break in the time series under analysis, since our argument is that the mechanism of oil price formation has changed over time, being the change more abrupt in 2008. For our purpose we use a version of the Chow test for multivariate dynamic models also known as sample split test, as presented in Candelon and Lutkepohl (2001)[5]. Assuming the occurrence of a structural break in period *t*_{B} of the sample period *T*, the sample is split in two parts, with *T*_{1} and *T*_{2} being the time subsamples before and after the time break, respectively. The sample split statistic *λ*_{SS }is calculated as follows:

The statistic is distributed as a Chi-square with *k *degrees of freedom, *k* being the difference between the sum of the number of coefficients estimated in the two subsample periods and the number of coefficients in the full sample case, equal to 72 in our framework. Finally, corresponds to the determinant of the estimated errors covariance matrix, with its elements divided by the number of periods in the sample. The null hypothesis is that no structural break is observed. We run the test by considering *t*_{B} being equal to January 2007 and January 2008. We were unable to perform the test by considering January 2009 as the time break because of the sample dimension. As shown in the table below, we find that the null hypothesis is rejected in both cases, but the rejection occurs with a higher level of significance for January 2008. In fact is larger than only when we consider January 2008 as the time break.

t_{B} |
|||

January 2007 | 114.5425 | 102.816 | 114.835 |

January 2008 | 156.7767 | 102.816 | 114.835 |

Hence, the empirical evidence supports the argument that there is a structural break in the formation of the oil price, which is more evident is 2008.

[1] http://onlinelibrary.wiley.com/doi/10.1111/j.1468-2354.2009.00568.x/abstract

[2] http://www-personal.umich.edu/~lkilian/

[3] Data for crude oil prices and production has been taken on the Energy Information Administration website.

[4] http://www.bloomberg.com/quote/BDIY:IND

[5] https://core.ac.uk/download/files/153/6527110.pdf