Realidad problemática

To evaluate the credibility of our results, we conduct a series of placebo tests. First, we test to see if the treatment effect, i.e. the difference between real and synthetic per capita GDP, is similar in magnitude and direction when applied to the countries in our donor pool. As is evident in the left panel of Figure 12, Norway (blue line) outperforms all donor countries over the entire period,

Figure 12: In-space placebo test

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with a positive treatment effect throughout.⁵⁸ This is also shown in the right-hand panel, where countries are ranked based on the ratio between post- and pre-treatment root mean squared prediction error (RMSPE).⁵⁹ A higher RMSPE-ratio indicates a better fit in the pre-treatment period, and a larger post-treatment difference. Norway has the highest RMSPE-ratio (21.6), almost double that of second-ranked Belgium (12).

As discussed in part 5.6 Inference in synthetic control, the treatment effect should not be substantially different if we move it in time to a period either before or after the discovery of oil.

We control this by replicating the same procedure as our initial synthetic control, but setting the treatment period to a period before the oil discovery: 1964q4. Iteratively, we repeat the

58 Japan, Switzerland and New Zealand were not included in the plot, due to poor performance in the pre-treatment period.

59 RMSPE measures a lack of fit between real and synthetic GDP per capita. Pre-treatment RMSPE for Norway is defined as:

𝑅𝑅𝑅𝑅𝑅𝑅𝑃𝑃𝑅𝑅 = �1

𝑇𝑇0� �𝑌𝑌1𝑡𝑡− � 𝑤𝑤_𝑗𝑗^∗𝑌𝑌𝑗𝑗𝑡𝑡 𝐽𝐽+1 𝑗𝑗=2

�

𝑇𝑇0 2

𝑡𝑡=1

�

12

RMSPE is calculated analogously for post-treatment periods, and other countries.

Figure 13:

In-time Placebo

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procedure, moving the treatment period one quarter for each iteration. This allows us to compare the treatment effects to see if the results are really driven by the discovery of oil, rather than a lack of fit. In Figure 13, the blue line is that for a treatment period in 1972q1 as before, and the grey lines indicate treatment effects for each of the 60 quarters between 1964q4 and 1979q4. As we allow the pre-treatment period to be extended, the weights assigned to countries and variables change somewhat – although they do not alter the treatment effect substantially. We see that the full distribution of treatment periods show a positive treatment effect for the same time periods, with both the recession of the early 1990s and the peak-oil era clearly visible for all iterations. As the blue line lies comfortably near the centre of the distribution, we are assured that our synthetic control estimate is not owed to the relatively few pre-treatment observations at our disposal, but rather an effect of Norway growing substantially different from its peers throughout the post-treatment periods. Naturally, the distribution spreads out towards the end, as the synthetic control grows more sensitive to slight alterations between country-weights through time.

We also control for whether the results of the synthetic control is owed to a particular country performing significantly worse through the post-treatment period by conducting a leave-one-out cross-validation. We re-run the model, each time leaving out one of the 10 donor countries. The right-hand panel of Figure 14 shows that the initial control is not very sensitive to omitting individual countries from the donor pool. Notably, the banking crisis of the 1990s is significantly reduced in magnitude when either Finland or Sweden is omitted. Still, the synthetic control proves robust. Note that the growth rate of the synthetic control after 2010 is positive in two of the placebo scenarios, contrary to the zero-growth for Synthetic Norway. As Finland and Belgium, the two largest weights, have negative and zero growth rates after 2010, respectively, we must be careful not to emphasise the results after this period.

Although the placebo tests consistently indicate that there has been a detachment in GDP per capita growth between Norway and comparable OECD countries since the 1970s, we cannot exclude the possibility that this effect is owed to other factors in the Norwegian economy than having a petroleum sector. Fortunately, oil and gas resources were also discovered in the British sector of the North Sea only a few years after Norway, making it an ideal country for comparison.

Although Britain’s oil reserves and petroleum sector are of modest size compared to Norway’s, if we are able to identify a positive treatment effect for the United Kingdom, it would strongly

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indicate that oil and gas resources is the explanation for Norway’s deviation from synthetic trend.

We also control for Australia as the treated unit, for the same reasons as for the United Kingdom.

Figure 15 shows these results: Clearly, there is a positive, albeit delayed, positive treatment effect in the United Kingdom. As their oil and gas reserves were discovered only in 1975, this is in accordance with the effect we find for Norway. As for Australia, the mining boom of the late 1990s is clearly visible in the data, showing a rising treatment effect at the end of the series.

These are clear indications that the positive treatment effect for Norway can be owed to the petroleum resource boom.

Figure 14:

Leave-one-out cross validation

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