Simulations of inflation expectations and oil prices

I have run some Monte Carlo simulations of hypothetical oil prices implied by long-term inflation expectations. Based on the Hotelling model of a nonrenewable resource, modified to account for inflation expectations, described here, inflation expectations are assumed to contemplate only the next 50 years, with a 1%/year discount rate. Oil in each year is assumed to be 1% less valuable to producers than in the preceeding year due to considerations of producer's time preferences, substitution, and less than perfectly secure property rights. Based on a random walk of inflation expectations (in some cases biased upward to show what happens in an era of increasing inflation expectations, in some cases downward to show happier times of declining inflation expectations), this simulation computes the net present value of the sale of a barrel of oil in 50 years based on the expected inflation over those years minus the discount rate of 1%. Note that these are not predictions I believe will happen, they are all explanations of what has happened or scenarios of what might happen.

The most startling and important thing you'll notice in these charts is that oil prices are an exponential function of long-run inflation expectations. Put another way, oil prices swing at a rate that is an exponential function of changes in these inflation expectations. The reason is quite straightforward -- inflation, like an interest rate, compounds. With inflation the value of oil in the ground nominally grows in value at the rate of inflation, discounted (in this model at 1%) for the factors indicated above. Thus in this model when inflation expectations are 1% or below, oil trades simply based on supply/demand fundamentals and expectations about these fundamentals, which in this model are assumed constant. Note that we assumd the discount rate (based on time preferences, substitability, property rights security, etc.) should be higher than 1%, that would only shift the exponential curve to the right, it wouldn't change its shape.

Precious metals generally move in the same way as oil in response to changing inflation expectations, but minerals that can be more readily substituted for than oil will probably not as quickly move to extreme prices. So this model and these simulations are just as useful for precious metals as they are for oil, and are somewhat less useful but still explain most of the price movements of most other minerals.

Here is a scenario similar to what we've recently experienced, with a possible further spike due to a small further increase in long-term inflation expectations, with such expectations then subsiding back to near today's value. The simulation starts out with inflations expectations at 1% (assumed to correspond to $10/barrel oil), then the expectations move to as high as 7.5%, which gives us $330/barrel oil:




Here is a more extreme scenario of what might occur during a possible U.S. federal default discussed in my previous post. At these extremes, prices of coal, natural gas, ethanol, and other near-substitutes for oil have to keep up with oil, and even the capital costs of more indirect substitutes (e.g. nuclear and alternative electricity) have to lose some of their stickiness and keep up more with oil, otherwise oil will be substituted for and prices won't reach these extremes. My model does not properly account for increased substitability as oil prices increase, which is correct over the long run (inflation eventually reaches all goods and services) but incorrect over the shorter run (because oil prices are much less sticky than most other energy prices). As a result these models probably overstate oil prices at the higher inflation expectation values. Precious metals don't have the same problem, so hedging against the most extreme possibilities is better done with precious metals than with oil or other commodities.




Let's finish with a cheerier scenario, where oil prices start at $130/barrel (roughly what they recently have been) and then inflation expectations subside. I consider this scenario and the first scenario about equally likely, and both of these more probable than the extreme second scenario:

Too big to fail

Besides the extraordinary rises in commodity prices and near-tripling of the U.S. federal government's default risk, another important factor for those interested the world's economy to keep in mind is that foreign governments have been bailing out the U.S. federal government by buying more of its Treasury bonds. Much of the increase in inflation expectations, and now in overt default expectations, reflected in commodity prices probably comes from the possibility that this ongoing foreign bailout of the U.S. may at some point stop and reverse. If foreign central banks and sovereign funds suddendly dumped their Treasuries -- which paying a negative real interest rate and exposing one to dollar risk are after all a rather bad investment -- either the Federal Reserve would have to madly "print" trillions of dollars to buy up these Treasuries, causing oil prices to skyrocket still further and retail gasoline prices to quite possibly jump each week by dollars per gallon, until American cars, trucks, and airplanes would be useless, or the federal government, facing extraordinary costs of funding its deficits, would have to overtly default. The problem the Federal Reserve faces is that with modern digital markets any inflationary behavior on its part is reflected in oil prices as soon as any big money learns about said behavior, and is thus usually reflected at the retail gas pump within a week. I wrote in the above-linked post about sovereign debt risk of "covert default" through inflation, but that is an obsolete phrase -- you can go down to the local gas station and see these de facto federal defaults in progress. If foreign governments thought the Federal Reserve was going to hyperinflate, that would probably cause them to dump the Treasuries in a kind of self-fulfilling prophecy. It would be a run on the federal government itself, the biggest run on a bank the world has ever seen. This is not a probable risk, but it has now become a quite signficant risk.

The ongoing foreign bailout of the U.S. government by massive purchases of Treasury debt helps explain two things: (1) why U.S. Treasuries and bank rates related to them don't seem to be reflecting inflation expectations (i.e. why they are paying negative real interest rates compared to the expected inflation suggested by commodity prices) -- their price is being held artificially low, not just by Federal Reserve net purchases but by foreign central bank net and sovereign fund purchases as well. Add to this the natural reduction in their interest rate due to the credit crunch causing a flight for safety (in a credit cruch people are willing to pay even negative real interest rates for a relatively safe investment). The foreign bailout also explains (2) why commodity prices have raced so far ahead of PPI and CPI inflation. Commodity prices may reflect, not so much increases in the dollar supply beyond dollar demand that have already happened, nor even expectations of a steady future consumer inflation that will happen eventually, nor an iminent severe consumer inflation is sure to happen soon, but expectations of a severe consumer inflation that mostly hasn't happened yet and may not happen, and of a possible Zimbabwe/Weimar-style hyperinflation that probably won't happen. But the increase in the probability of severe inflation combined with a great increase in the formerly extremely small (and still small, but not extremely so) probabilities of the more extreme hyperinflation still averages out to rather high inflation expectations.

Why are central bankers bailing out the U.S. federal government and its dollar rather than acting like rational profit maximizers? Central bankers and government treasury officials are very political animals, and they fear the disaster they believe would ensue should the "full faith and credit of the United States [federal government]" fail. It is the most unthinkable economic event for the entity with the most collosal budget, and the dominant threatener and wielder of military force in the world, to go under. The U.S. federal government has now deemed Bear Stearns, Fannie Mae, and Freddie Mac "too big to fail" and has bailed them out. That federal government itself is the ultimate entity that is "too big to fail", and thus foreign governments and central bankers are bailing it out, and will probably (but hardly surely) continue to do.

Extrapolating from oil prices rises (i.e. assuming the entire oil price rise has been due to monetary factors rather than to consumption, production cost, or non-monetary political fundamentals) using the net present value formula over 50 years, I estimate that long-run dollar inflation expectations have risen about 5%/year from 1998, when there the Asian crisis caused a flight to the dollar and many people thought deflation was the bigger worry, to today. This might for example reflect an increase in expectations from 0% to 5%/year, or 1% to 6%/year, etc. -- I don't have a way to estimate the absolute value. Gold price rises over the last decade give a slightly smaller rise in inflation expectations, of about 4%/year. Note that this doesn't mean 5% or 6%/year CPI or PPI inflation over the next 50 years is inevitable -- increased expectations reflect a range of probabilities, especially very heightened increases in probability estimates of extreme (>10%/year) and hyper (>100%/year) inflation in the dollar. It's also still significantly possible that the ultimate lagging indicator, "core inflation", will stay in the 2-3%/year range and the whole storm will blow over.

Besides the great rise in commodity prices, in particular the most "money-like" commodities oil and precious metals, the foreign bailout of the U.S. federal government is another reason to believe that all major currencies are falling against a hypothetical stable standard of value, not just the dollar. As foreign central banks buy more U.S. Treasuries they take on more of the risk associated with the dollar, so we should expect the floating currencies these central banks issue to move more in correlation with each other. Indeed, the dollar has held its own against the euro and against on average other major currencies since February as foreign central bank purchases of Treasuries have accelerated.

People interested in my writings about money might also want to check out my classic essay on monetary origins, "Shelling Out: The Origins of Money", my classic essay on micropayments, and my overview of the monetary reasons for the broad-based commodity price increases over the last decade and in particular over the last five years.

So much for the "risk-free investment"

Last week the default risk on U.S. Treasury bonds doubled. This week it has increased still more. This risk is measured by credit default swaps (CDS's), which insure investors against bond defaults. Of course this risk, contrary to a very stupid but very popular myth among U.S. economists, has never has been zero: there is no such thing as a "risk-free" investment. Anybody with a modicum of knowledge of economic history knows (in other words, alas, very few people know) that over historical timeframes government defaults on their debt, both overt and covert (through inflation), are common. Indeed over >20 year timeframes even stocks are less risky than government bonds, but for shorter timeframes bonds are, in nominal terms at least, normally far less volatile than stocks. Reuters observed,

The cost to insure Treasury debt with credit default swaps jumped to 16.5 basis points, or $16,500 per year for five years to insure $10 million in debt, from 8 basis points on Thursday, an analyst said....Debt protection costs on U.S. government debt are now higher than those for Germany, which trades at 9.5 basis points, and are trading at similar levels as Japan and the United Kingdom, which are around 16.5 basis points, the analyst said.

So far this week it has increased to 22 basis points for five years of default insurance. Bloomberg observes the probable cause of this increased risk:

Treasury Secretary Henry Paulson said July 13 the U.S. would seek authority from Congress to buy unlimited equity in so-called government-sponsored enterprises Fannie Mae and Freddie Mac and to extend them as much credit as needed. The move effectively put the weight of the treasury behind the companies, which own or guarantee almost half of the $12 trillion in U.S. home loans outstanding. The Federal Reserve also agreed to lend directly to Fannie Mae and Freddie Mac.

In other words, not only is the Federal Reserve now playing John Law by printing dollars to buy bad real estate investments, but now the federal government has declared its willingness to get in on the act in an even bigger way.

Note that default risks measured by CDS's do not include the risks of what are effectively ongoing de facto mini-defaults on all dollar-denominated debt due to inflation, risks that have been rising substantially over the past ten years, as reflected by the prices of the main insurance against inflation risk, commodities.

In the U.S. there have been a number of de facto inflationary defaults on U.S. federal debt -- the Revolutionary War (Continentals), Civil War (Greenbacks), Great Depression (resetting the gold conversion rate). The largest de facto default occured in the 1970s (float and inflation) and we are in the midst of one currently (float and inflation) that may turn out to be even larger. But the only overt default on "national" governmental debt in our 232-year history was that of the Confederate States of America in the throes of losing its war against the (rest of the) U.S.

Compared to the 1970s, oil is responding faster and more completely to Fed inflation, and oil remains a crucial part of our industries. As a result, the havoc caused by high oil prices may put a stronger limit this time on how quickly the Fed shredder can dispose of the real value of U.S. paper. If the degree covert default is thus limited, but the risk of default increases, the risk of overt default rises. The market last week seemed to be saying that the Fed may be starting to approach some such limit, perhaps a political limit due to hysteria over gas and food prices, on its practical ability to inflate the U.S. currency. In other words, markets may be saying the Fed cannot necessary resort to a Weimar- or Zimbabwe-style hyperinflation -- that if federal financing gets to that extreme U.S. politicians may choose to overtly default instead.

The city of Vacaville, California recently overtly defaulted on its debt, as have a number of other municipalities in the U.S. Worldwide overt defaults on government debt during the second half of the 20th century usually occured in Third and Second World governments (e.g. Russia in the 1990s), but there were a large number of overt government defaults in governments of all sorts early in the Great Depression (indeed these were a leading cause of that economic disaster), and in prior centuries government defaults wherever governments borrowed money, including leading nations in Western Europe, were common. Mature democracies with central banks that can engage in covert defaults (inflation) have had a far lower rate of overt defaults than other forms of government or democracies without central banks.

That the risk of overt default has now substantially increased means that investors are are recognizing that the unprecedented revenue-generating combination created in 1913 -- IRS (which has been able to reliably collect $trillions per year) and the Federal Reserve (which has been reliably able to enage in covert gradual defaults by printing money to buy $trillions worth of Treasury debt per year) -- is not indestructible. U.S. Treasuries, like every other investment, have never been risk-free and they've just gotten quite a bit riskier. Nevertheless compared to historical averages for governments, the risk of overt default by that powerhouse 1913 duo is pretty low. With very high probability they will keep paying interest and principal on their debt while me and my fellow U.S. taxpayers will keep having to shell out substantial sums to the IRS every year, and see our dollars frittered away every year, that this dynamic duo may continue to uphold "the good faith and credit of the United States" while the discreditable activities, often done in rather poor faith, of the federal government in "redistributing" wealth, attacking foreign countries in very expensive ways, promising vast pensions that it cannot pay, promising health care that it cannot fund, and forcing private businesses to do bizarre things (like take on vast amounts of moral hazard by lending into "underserved communities", and to actually fund those government medical mandates) continues.

In related financial news, what I've been predicting for a long time would happen is starting to happen: the U.S. dollar inflation indices PPI and CPI, despite being under-reported compared to prior decades (due to a radical revision of the formulae), are starting to rise to 1970s rates of increase. Sticky prices in manufactured goods and services, as well as wages (the stickiest prices of all), are playing a very long-term game of catch-up to commodity prices, and especially to gold and oil, which are leading indicators of inflation. I continue to predict 5%-15%/year increases in the CPI and PPI, and probable "stagflation" (inflation plus recession, which according to Keynesians is not supposed to happen), until such time as they catch up to the commodity price increases. Commodity prices themselves, despite their stratospheric levels, may continue to increase as the Federal Reserve tries to deal with large government deficits and the fallout from the awful moral hazard in our housing markets, a moral hazard in no small part due to previous inflationary policy by the Fed itself combined with the outrageous pressures from U.S. politicians to relax lending standards in order to get people to buy houses in "under-served communities" and naive "real estate always goes up" bubble behavior on the part of the real estate industry and house buyers. The Fed-and-IRS-backed political franchises Freddie Mac and Fannie Mae have been moral hazard disasters waiting to happen. Inflation is still by far the largest problem these federal activities are causing; the doubling of the overt default risk is just an interesting related blip. My recommendation: keep only spending money, not savings or long-term investments, in dollars or dollar-denominated debt, and keep trying to unstick your own wages by frequently asking your boss for a big raise.

On the increase in Treasury default risk H/T to Alex Tabarrok.

Hampton Sides sheds light on Mancur Olson and Ronald Coase

Hampton Sides' book Blood and Thunder is a detailed and colorful account of the Western frontier in the United States around the mid-19th century, mostly from the Mexican War to the Civil War. It is half biography of the trapper, guide, and soldier Kit Carson, who participated in a wide variety of interesting and important events, and half general history, mostly of what is now the Southwestern U.S. and much of that in New Mexico, where Navajo, Apache, Pueblo, Mexicans, and Americans collided. There is also some coverage of the prior history and prehistory of the Mexicans and "Indian" (aboriginal American) tribes in the area. Sides seems to have no theoretical axe to grind, and indeed doesn't try to explain events in terms of political or economic theories, but rather simply relates a large number of incidents in unabashed detail, letting readers draw whatever theories, if any, the reader might wish to draw. Nevertheless Sides' account of the old U.S. frontier does shed quite a bit of light on a number of theoretical topics I have discussed here.

Most of the book involves interactions between Indian tribes, often nomadic, and agricultural-based Mexican and Anglo-Saxon cultures. The Navajo, for example, were nomadic herders that also profited from stealing, usually livestock, from nearby Pueblo, Mexican, and later United States ranches. In his account of prehistory Sides relates how, a few hundred years before Columbus, the spectacular pueblos (apartment buildings) of the Anasazi farm-based civilization in the Chaco Canyon were abandoned just as the Navajo were migrating into Anasazi territory from the north. Sides invokes as the main reason the popular ecological theory: that the Anasazi declined due to depleting nearby resources such as soils and forests, and suggests the Navajo as a contributing reason.

I think this gets it backwards. The Navajo entry at the same time the Anasazi's pueblos were abandoned is no coincidence, it is the main cause. Faced by a militarily superior group of roving bandits, the Anasazi's agricultural property was no longer secure. The Anasazi, ruled by stationary bandits, were conquered by the Navajo, nomadic herders and hunters. Further evidence that Mancur Olson's bandit theory, rather than ecological theory, explains the abandonment of their civilization in the Chaco Canyon is that the Anasazi culture didn't disappear, it declined and moved. Their descendants are the Pueblo Indians, and they dispersed to build a pueblos at the fringes of the Navajo territory. ("Anasazi", incidentally, is a Navajo term meaning "ancestors of our enemies"). Accelerated depletion of resources is a symptom of insecure property rights: where property is insecure people act (with respect to natural resources rather than with respect to fellow humans) as roving bandits, whereas secure property owners extract their resources like stationary bandits, i.e. at a much lower and far more sustainable rate.

Per Olson the Navajo, being roving bandits (with respect to both people and fixed resources) would have had a far higher Laffer maximum extortion rate and thus were not able to accumulate wealth to support a level of civilization nearly as high as the Anasazi under stationary bandits had supported. The Pueblo Indians and later the Mexicans who bordered the Navajos and other roving bandit cultures were able to support agriculture, but were far poorer than other most other fully agricultural regions of the time due to the costs of Navajo and Apache raids. The fall of the Anasazi was hardly the first time roving bandits had conquered stationary bandits causing a massive decline in wealth and civilization: it is a common pattern throughout history.

(Incidentally, the Laffer maximum for banditry from a sedentary neighbor, where there are a few but not many competing bandits, is probably somewhere in between the maxima for fully roving and fully stationary bandits: Sides recounts how the Navajo would not steal every animal from their Pueblo or Mexican neighbors during raids, but made sure to leave them enough breeding stock to rebuild their herds).

There are a large number of people who, following David Friedman, use the Coase Theorem as if it applied to the coercive bargaining that occurs in an anarchy. Sides' relentless accounts of attacks and reprisals put a lie to this Coaseian analysis of anarchy. The Navajo came as close, perhaps, to anarchy has any recorded culture has ever come. They had, for example, no sovereign leaders with which to make binding treaties. When American generals tried to make treaties with individuals they thought were Navajo chiefs, they would find that said "chiefs" could not actually enforce treaty terms, at least not beyond their own small band. Thus promises, for example, by Navajo "chiefs" to stop animal-stealing raids turned out to be unenforceable, because these "chiefs" could not actually punish young men in the many other Navajo bands for their raiding. (Even with sovereign governments there is still a tension between limiting the scope of sovereign power, e.g. by a doctrine of enumerated powers or by federalism, and giving the federal government complete "freedom of treaty", i.e. the ability to enter treaties on any subject, or at least in suppression of any kind of coercion, that they can actually enforce against their citizens and residents).

Coercion in all the forms one can imagine, and many that one would rather not try to imagine, was endemic to life among the native American tribes and to relations between those tribes and encroaching civilizations of the Mexicans and later Americans. Raids involving theft (especially of livestock), looting, kidnapping, rape, murder, war, massacre, torture, extortion, mutilation of the living and the dead, and many other, shall we say, non-Coaseian interactions were a normal part of the external relationships between the Indian tribes and between the encroaching civilizations and those tribes. "Counting coup", that is keeping track of wrongs that needed to be avenged, was standard among the Indian cultures and became standard among people like Kit Carson who dealt with them. Another interesting phenomenon is that the tit-for-tat cycle of violence between tribes was often based on group blame: rather than solving the (usually insurmountable) problem of identifying and punishing the particular perpetrators, missions of vengeance would usually target relatives, fellow tribe members, or even broader groups that happened to be convenient. Sometimes Indians aggrieved by a white attack would even take revenge on whites generally, for example the next group of white emigrants to come down the Santa Fe Trail, and this far too often happened in the reverse direction as well. Sometimes individual blame morphed into group blame when a tribe to which an alleged perpetrator was thought to belong failed to arrest and surrender the accused. This circumstance was especially used by American armies to justify invasion, massacre, and ethnic cleansing of tribes that refused to surrender or punish (often because they had no sovereign power to capture or punish) their thieves, kidnappers, and murderers. The role such group blame plays in contemporary politics is left as an exercise for the reader.

Mancur Olson's explanations fit Sides' detailed accounts of life in an anarchy far better than the the Coaseians'. The trajectories of the Anasazi, Navajo, Pueblo, Mexicans, and Americans are classic cases of interactions between stationary and roving bandits. The Laffer maximum extortion of the stationary bandit is far lower than the combined Laffer maxima of the roving bandits. Most kinds of farms can operate economically only if those stealing from the farm are stationary rather than roving.

Finally, Sides gives a sad account of the utopian social engineering that led to America's Indian reservation system. Bosque Redondo (the Round Forest) is a tragic example of this: an idealistic general of New England upbringing, a forerunner is spirit at least of the Bellamies, rounded up the Navajos, marched them off to a promising-looking but empty stretch of the Pecos River and tried to teach them sedentary agriculture. The general's overall reason for for conducting this experiment was not inaccurate: in Olson's terms, the Navajo would give up their roving banditry only if converted into (or put under the thumb of) stationary bandits. But just as the Navajos did not learn to live like Anasazi, but instead displaced the Anasazi culture with their own, so they could not readily learn to live like Mexicans or Americans, or even like Pueblo Indians. For example, for religious reasons they stubbornly refused to live in pueblos (apartment buildings) and these had to be abandoned. Worse, the project had most of the trappings of utopia we would later see in the Soviet Union: forced concentration and mass movement of peoples, communal farms, and military-style central planning. The communal property and military command structure under which the Navajo were subjected utterly failed to replicate the property rights and other crucial aspects of legal systems under which Mexicans and Americans had successfully conducted their agriculture. The Bosque Redondo experiment was a miserable and deadly failure. Stationary bandits can also destroy rather than allow the building of civilization if their policies are sufficiently pathological.