Friday, July 19, 2013

Global Warming - The Supply Side matters

I recently read the paper "Public policies against global warming a supply side approach," by Hans-Werner Sinn, in which he coins the  term "green paradox" to denote the phenomenon that some policies proposed against global warming may have the perverse consequence of increasing CO2 emissions once we take into account the response by resource suppliers. I will show one example of how this might happen and talk about some implications for designing policies intended to decrease CO2 emissions.

In order to understand the core of Sinn's argument, we will abstract from various complications that might weaken or strengthen his result, but that do not change the fundamental point that perverse CO2 emission responses are at least possible, even if not likely. That is, we will assume that resource extraction technology and the total stock of extractible resources (e.g. oil reserves in the ground), as well as the interest rate, are given and constant.

In that case, we can think about the problem of a resource producer, e.g. a global oil company, in the following way: If the oil producer leaves the oil in the ground today and sells it tomorrow, she gains if the price of oil increases in the meantime, so that she can sell it at a higher price tomorrow. The return of that is ΔP, the change in the oil price per time unit. If she extracts the oil today, she would have extraction costs c, earn price P, and then be able to invest the net profit for a per-period return of i(P-c). Thus, in any given period, the oil producer will adjust the resource extraction path until 
 which implies
i=ΔP/(P-c)       (1)
To see that this is true, consider what happens when this equation does not hold: For example, if the current price level is such that the expected increase in price over time, and therefore the return to leaving the oil in the ground is lower than the returns i that can be had elsewhere, then the oil producer will try and sell more oil now, in order to invest his money at those relatively favorable interest rates. However, this will increase the current supply of oil, which in turn lowers the oil price. As the amount of oil in the ground is fixed this means that there will be less oil left to be extracted in the future, which raises the future price of oil. As the current price of oil goes down and the future price goes up, the expected increase in the oil price per period increases, which raises the return to leaving the oil in the ground (the RHS of equation (1) above). This will continue until equation (1) holds, because at that point there is no gain to be had from transforming oil int eh ground into money that can be invested or vice versa.

In order to give an example of what this dynamic might look like, I have built a small model of the optimal extraction path (see footnote 1 for further details): Let's assume that the market price of the resource, say "Oil," is negatively related to the amount that is extracted in a given time period, but that the total amount of oil in the ground is fixed and that all oil will be produced within 10 time periods, with zero extraction cost, for simplicity's sake. All prices are assumed to end up at 10 in the last period, which is a stand-in here for the price of the last drops of oil right before the exhaustion of the resource. Moreover, the opportunity cost of keeping oil in the ground is assumed to be 10%, which means that the optimal extraction path following equation (1) will adjust extraction so that the increase in the oil price per period is also 10%. That optimal extraction path is shown as the dark green line R1 in Figure 1 below and the price path that it determines is the light green line P1. Note that the oil producer produces more oil in the beginning and less later, which is why the price rises towards the later periods.

Now, let's ask ourselves what would happen if we threatened the oil producer with constant taxes on oil extraction profits? Because the exogenous interest rate still determines the optimal price path, and remains unchanged at 10%, the extraction path R1 that we initially determined is still optimal. In some sense, as the tax is constant over time, the oil producer has handed over a share of his lifetime oil extraction profits to the government, but the problem of maximizing the value of his remaining share is the same as that of optimizing his extraction path if there were no tax. That is, a constant tax rate on oil extraction profits would not change CO2 emissions at all in this very simplified model. While the setup here is certainly unrealistic, it is not necessarily more so than most of the discussion in the media of climate change policy. And it suggests that at least under some conditions, taking into account the supplier's incentives can undo the intuition that might equate a rise in tax on oil production with a decline in CO2 emissions.

Figure 1
However, some carbon policy proposals go farther than that: they propose raising carbon taxes over time. Now, let's assume that at least some of those tax increases would fall on the oil producer, and is explicitly taken out of his profits after she sells the oil at the market price  - you can also think about this as an increasing discount in the form of a rebate or voucher that the oil producer has to give his customers, who would be willing to buy the oil  at the market price otherwise. As a result, the optimal extraction path is now determined by
i=(ΔP/(P-c))-Δpi/pi,       (2)
where pi is the level of the tax rate and the additional term on the RHS expresses the fact that any increase in oil revenue that can be had by leaving the oil in the ground for another  time period will be mitigated by the increase in the share of profits that are taken away by the tax. Thus, if the interest rate on the LHS of equation (2) remains at 10%, but the tax rate grows by 15% every period, the price of oil would have to grow by 25% in order for the equation to hold. That is, the oil supplier will want the price path to be steeper to make it worthwhile for him to wait until she can sell his oil, if the future brings ever higher tax rates. Put differently, as later oil extraction will be less profitable due to rising taxes, she moves some of the extraction to earlier time periods to escape the higher future tax rates, and as a result current oil prices fall, while exhaustion price in period remains the same, steepening the price curve. This is shown in Figure 1 by the red extraction path R2 and the light blue price path P2, which result from using the same model as above, but replacing the required rate of price increase with 15%.

Let's note what this means: the policy of increasing carbon taxes over time, which is supposed to lead to lower carbon emissions than no taxes or constant taxes, in fact leads to more oil extraction in earlier periods, which means higher, not lower, carbon emissions than without the tax increases! Of course, this model abstracts from many things, among them the possibility of switching to new technologies, which is often one of the goals of carbon taxes. All I wanted to show here is that Sinn's paper suggests that including the suppliers' incentives in our CO2 emission policy analysis may lead to policies having the inverse of the intended effect in this simplified setting. As a result, when reading of any analysis of the impact of policy X on carbon emissions, it might be worthwhile checking whether the results take into account the incentives of resource producers, and, if not, take its policy recommendations with a grain of salt.

While Sinn's model assumes that the "resource suppliers" are a single entity that is free to alter its extraction path any time, the case of oil production would require us to model more complex market characteristics: most major oil producers are members of the OPEC cartel and therefore bound by production quotas that are intended to keep them from increasing their oil production unilaterally in a way that would lower the oil price received by all other producers. Then, the question becomes to what extent OPEC itself can be seen as an optimizing agent in Sinn's sense. On the other hand, there are other factors that might accelerate or decelerate oil production - some of which Sinn mentions: If a country faces an unstable political situation, the current government might not be able to profit from the national oil company's revenues after it loses power and therefore prefers earlier oil production to later oil production. Moreover, if a substantial share of the fiscal budget of a country comes from oil revenues, fiscal deficits may lead to an attempt to raise more revenues from oil production in the short run. In the end, the supply side response to expectations of the future profitability of oil extraction might be quite complicated, but that is no reason to ignore it.

FN 1:
1. The model used is the following: P=a-1.2*R,  where a is chosen to ensure that (aggregate resource extraction)=(resource stock in the ground)=50.
2. i1=10% for the first pair of lines and i2=25% for the second pair of lines.
3. Then, equation (1) determines the price path, with exhaustion price set exogenously at P(t=10)=10.

Thursday, July 4, 2013

Should companies be required to take out Building-Removal-Insurance?

Emily Badger at The Atlantic recently summarized a new proposal for dealing with the problem of how to pay for clearing away the abandoned buildings that stay behind when the corporations that built them are no more:
"You can't force companies that no longer exist to pay for dismantling these buildings. But what if the government required them – years earlier – to buy property insurance to do that? Think of it as life insurance for commercial sites. ...
...A similar solution already exists for landfills, mining sites and oil rigs. In some communities, companies must also put up bonds on new cell phone towers to ensure that they eventually come down (no one wants an abandoned cell phone tower to tip over). ...
...In short, force companies to financially plan for a property's end-game, and it could change how they think about every stage of the building's life."
 While this may sound like a good idea, I will argue that it neglects some important considerations, while raising some important questions regarding the purpose of public policy.

First, let's be clear on what this policy does: by requiring companies to take out insurance or put up a bond to pay for the removal of any structures that may remain after the company's demise, the policy would impose some of the cost of a company's failure that is currently borne by all local taxpayers in advance on any company that wants to build a factory, office building etc. In other words, it is a tax on companies that want to invest locally in a way that requires a building.

The main reason why this might be a good idea according to the paper by LaMore and LeBlanc is that empty buildings that might be left behind impose a negative externality on the community that has to remove them, and decrease the desirability of the surrounding neighborhoods.

However, does the fact that a negative externality exists always justify taxing that activity  - in this case building factories? Only, if the negative externality is not outweighed by the positive externalities of the activity. And in this case, the presumption should be that the positive externalities are large: not only may the investment of capital into factories and buildings increase the productivity of a firm's workers, but the establishment of local production facilities usually has a positive impact on the economic activity of surrounding areas as well. The best evidence for that is probably the fact that many cities have policies in place that subsidize companies that are willing to invest in building factories nearby.

As a result, we have to weigh any negative externalities of companies investing in new buildings against the positive externalities and only then can we know whether or not to encourage (subsidize) the activity or discourage (tax) it, but doing both in an offsetting way is certainly not advisable.

As the insurance payment for buildings would be higher in regions that are more likely to suffer from  economic problems and the resulting empty buildings, the intended policy would make it more expensive for companies to expand into exactly the struggling areas of the country that are most in need of investment, while encouraging them to crowd even more into metropolitan areas like New York City, where the resale of a company building is almost certain and the insurance premium accordingly low. Regional inequalities may be exacerbated as a result.

Last but not least, the administrative deadweight cost of having to evaluate, administer and enforce the insurance requirement for every privately built structure might be quite considerable - and the interest groups (e.g. insurance companies) that would thrive on an expansion of this policy would lobby strongly for these costs to ever increase.

Overall, I think it is unlikely that such a policy would be beneficial due to its negative impact of discouraging investment in less affluent regions of the country. After all, factories and other company structures are very different from "cell phone towers" and "oil rigs" where such insurance schemes may be appropriate: factories are embedded in economic communities, and, as nodes of local production networks, their investments and increases in productivity have positive externalities due to supporting "specialized providers of industry inputs, thick markets for specialized labor skills, and information spillovers" (Krugman, 2010).