For example, there's an issue of whether oil price shocks have a symmetric impact on GDP growth--that is, do we find that both oil price increases and oil price decreases affect real GDP growth, or is the relationship only significant with an increase in oil prices? Ni, Lee, and Ratti (1995) found that positive normalized shocks have a powerful effect on growth while negative normalized shocks do not. Their results, however, are based on the premise theat oil pirce change is likely to have greater impact on real GNP in an invironment where oil prices have been stable, than in an environment where oil price movement has been frequent and erratic. Then we also find on the other side of the spectrum woks such as Killian and Vigfusson (2009). Using an alternative approach, they find that impulse responses are actually of roughly the same magnitude in either direction of the oil price change. Their result is consistent with formal tests of symmetric responses.
We can do a simple test of the symmetry on our own with the use of STATA. All we need first is data, which I got from the excellent Economic Research Department of the Federal Reserve Bank of St. Louis. We just need quarterly data on real GDP, West Texas Intermediate (WTI) crude oil prices, and the producer price index (PPI). We calculate real crude oil prices by dividing WTI by PPI. We then take the natural log and then take a first difference of these two variables to approximate growth rates (DLRGDP and DLROIL). Finally, to test the symmetry, we create a series consisting of only the positive elements of the oil price changes with negative changes set to zero (DLROILP), and another series consisting of only the negative elements of the oil price changes with positive changes set to zero (DLROILN).
We use a bivariate VAR for our model with 4 quarterly lags. The exclusion tests then proceeds as follows: (1) we estimate the whole model--DLRGDP, DLROILP and DLROILN; (2) save the results in STATA; (3) we do a second estimation, this time excluding either DLROILP or DLROILN; (4) save the second results in STATA; and (5) run the F-test that the excluded lagged variables of DLROILP/DLROILN are indeed not significantly different from zero. The following commands in STATA are used
reg dlrgdp l.dlrgdp l2.dlrgdp l3.dlrgdp l4.dlrgdp l.dlroilp l2.dlroilp l3.dlroilp l4.dlroilp l.dlroiln l2.dlroiln l3.dlroiln l4.dlroiln
est store a
reg dlrgdp l.dlrgdp l2.dlrgdp l3.dlrgdp l4.dlrgdp l.dlroiln l2.dlroiln l3.dlroiln l4.dlroiln
est store b
ftest a b
a and b are arbitrary names I assign to the two estimations. The result of the F-test is as follows:
The exclusion test of real oil price increases is very signficant while that of real oil price decreases is not. These results confirm a positive effect of oil price increases on real GDP but not real oil price decreases. There is asymmetry in this case. Although I didn't present it here, the coefficients of the lagged variables of positive oil price shocks are all negative in the four quarters (significant in the second and fourth quarters), indicating that positive oil price shocks have negative effects on real GDP growth.
We could also check the symmetry of oil price shocks on overall price level. Data on CPI can also be obtained from the St. Louis Fed website. The hypothesis is that establishments are quick to increase the prices of the commodities they sell if they see that world oil price has increased. But if there was a decrease in world oil price, the adjustments in their prices is slow, if there will be changes at all. We can check this empirically by going through the same procedure above--this time having first difference in log CPI as the dependent variable (and using nominal oil prices instead of real oil prices). The results are:
Well, there's also asymmetry on the effects of oil price shocks on consumer price index. Increases in oil prices are significant, but decreases in oil prices are not. I also did not show it here, but the coefficients of the lagged variables of positive oil price shocks are positive (except for the fourth quarter). This indicates that increases in oil prices are associated with increases in overall consumer prices.