tag:blogger.com,1999:blog-17908317.post1616803017597945662..comments2023-12-08T00:56:25.716-08:00Comments on Unenumerated: Inflation expectations, gold, and oilNick Szabohttp://www.blogger.com/profile/16820399856274245684noreply@blogger.comBlogger9125tag:blogger.com,1999:blog-17908317.post-8230551001038364192008-08-13T19:57:00.000-07:002008-08-13T19:57:00.000-07:00Paul, you're mostly talking above my head there, b...Paul, you're mostly talking above my head there, but I'd love to learn more about these statistical methods. Friendly references? <BR/><BR/>Fred and Paul, I have read that differencing tends to exaggerate noise and lead to invalid rejection of true relationships, and that one has to guard against that as well as the accumulation of errors which the differencing method eliminates. I'm guessing this is what Paul is addressing with his sophisticated proposals.<BR/><BR/>Fred, what do you think about a correlation for a series that ends up roughly at the level where it started? The series I have in mind are implied inflation expectations derived from the monthly dollar gold and oil prices from January 1974 to June 2008. In other words, take the gold and oil prices, deflate them for the already occurred CPI, deflate oil for the 0.9% average secular fundamental rise wrt gold described above, and derive the rate of long-term price rises for gold and oil respectively implied if gold and oil represent the net present value given that price (assuming a certain price of gold and oil reflect expectations of zero price rise -- OK to do because correlation is concerned with the relative not the absolute). The result is a large positive correlation, 0.76, strongly suggesting that the long-term trends in oil and gold prices each reflect a common estimate of future inflation -- gold and oil fundamentals are very different and so cannot lead to such strong correlation. This compared to two random walks with no long-term tendency to rise, which on average have no correlation.<BR/><BR/>If you look at the graph (see the update above) of the implied inflation you see that the gold-implied inflation starts at 5.1% in 1974 and ends at 5.2% today, and the oil-implied inflation also starts at about 5% in 1974 and ends at about 5.5% today, with fluctuations for both as high as 7% and as low as 2.5%.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-17265912074011105122008-08-12T20:30:00.000-07:002008-08-12T20:30:00.000-07:00fred:stripping the levels from the trends tends to...fred:<BR/><BR/>stripping the levels from the trends tends to detract from their original relationship.<BR/><BR/>it is better to see if the variables are co-integrated, and then use an ECM model that adjusts for the short run deviations from the long run equilibrium.<BR/><BR/>ultimately all regressions suffer from the probalistic issue of spurious regression. we need to both show that the probability of the assumed DGP generating the series' to be high and that if the assumed DGP is actually not the one we've assumed, then that the probability of these series' happening should be concurrently low.<BR/><BR/>-paulAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-46767846693240526282008-08-12T19:30:00.000-07:002008-08-12T19:30:00.000-07:00fred, you're right, thanks for the correction and ...fred, you're right, thanks for the correction and for the clear specification. For the weekly changes I get .25, which is considered to be at the high end of small positive correlations, vs. the .93 for the overall 8-year price movement.<BR/><BR/>Interestingly as the time periods grow longer the correlation tends to grow. For 20 week deltas (that is the week t price - the week t-20 price, repeated every week) the correlation is 0.34. For the 40 week deltas the correlation is 0.64. (This is admittedly on data that has been adjusted to reflect a secular fundamental 0.9%/year inflation in the gold price of oil as described above, but I doubt this makes a huge difference at 40 weeks).<BR/><BR/>I tentatively conclude from this that non-monetary (probably fundamental) factors tend to outweigh monetary factors for shorter term price movements, but over longer periods (roughly 40 weeks or more) monetary factors tend to outweigh other kinds.<BR/><BR/>BTW your statement "Show me any two series that increase over time and I'll show you a correlation greater than 0.9" is a bit exagerated. I've just done some experiments with random walks based on the same function, x1 = x0 + rand()/100 + rand()/120, that is more likely to increase than decrease at each step (and I threw out sample sets that didn't end up increasing overall, which usually had negative correlations). Here are the correlations coefficients I got for the pairs of such series that both increased: .64, .81, .75, .91, .74. .87, .81, .72, .76, .91, .83. So .93 is at the outer range rather than near the mean of what one would expect from pairs of increasing random walks. Besides which, one also has to explain why both gold and oil are both increasing over the long term in the first place, and again the answer is monetary.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-51433463758000339842008-08-12T17:35:00.000-07:002008-08-12T17:35:00.000-07:00Here's a relevant comment I just made on another b...Here's a relevant comment I just made on another blog:<BR/><BR/>BTW, the current Russia/Georgia conflict is a good illustration of the dual influence of monetary and fundamental factors on oil prices, and how the monetary factors can outweigh even the most important and surprising fundamental factors. Many commentators seem puzzled that the dollar price of oil is dropping while Russia threatens vital oil and gas pipelines in Georgia. The conundrum is resolved by observing that since the invasion the price of oil in gold has in fact increased significantly. The drop in dollars per barrel of oil has been accompanied by an even greater percentage drop in dollars per ounce of gold.<BR/><BR/>Even though the Russia/Georgia conflict is a very important and surprising fundamental factor, and thus should and has had a significant upward effect on oil prices, it is outweighed in the dollar price of oil by changes in the dollar. Quite likely this was primarily due to a decrease in long-term inflation expectations for the dollar which led to an exponentially larger decrease in the dollar prices of gold and oil.<BR/><BR/>In this case, it happens that most of the changing expectations for the dollar did not also occur for the euro, and thus the dollar also strengthened against the euro as well as against gold and oil, but this is not always (and probably not even usually) the case -- monetary dominance of oil prices does not imply substantial correlations between dollar oil prices and the euro/dollar exchange rate, because many monetary factors influence both the dollar and the euro, which can both inflate or deflate together. But on occasion the change in expectations is largely unique to the Fed or to the ECB and in these cases one can see exchange rates of other currencies for the dollar or thhe euro move along with the dollar or euro prices of oil and gold, as we have seen so far this week.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-85502856564754757342008-08-12T17:07:00.000-07:002008-08-12T17:07:00.000-07:00Let G(t) be the price of gold in week t and let O(...Let G(t) be the price of gold in week t and let O(t) be the price of oil in week t. Correlation asks the question, "suppose I tell you that G(t) is above its mean by a certain amount, how much info does that give you about O(t)?" <BR/><BR/>Correlation equals one if knowing G(t) allows you to exactly predict O(t). Correlation equals zero if your best prediction of O(t) is the mean whether or not you know G(t). If both G(t) and O(t) increase over time, then their correlation will be large because they are both below their respective means in the first half of the sample and above their means in the second half of the sample. If you don't believe me, try it with two series that you know are unrelated but have strong upward trends.<BR/><BR/>For trending series, the correlation between weekly changes is much more informative. You should compute:<BR/><BR/>corr(G(t)-G(t-1),O(t)-O(t-1)).<BR/><BR/>In a program like Excel, you could have, say, column A containing the weekly CHANGE in oil prices (i.e, O(t)-O(t-1)) and column B containing the weekly CHANGE in gold prices. Suppose you have 420 data points in each column. You would then use the following Excel command:<BR/><BR/>correl(A1:A420,B1:B420)Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-53462745989604831282008-08-12T16:32:00.000-07:002008-08-12T16:32:00.000-07:00Fred, the correlation coefficient does measure th...Fred, the correlation coefficient does measure the similarity between changes, and it does give 0.93 for the week-to-week changes in oil and gold from 2000 to the middle of July 2008. What specific data and formula did you use to arrive at below 0.2? I'd like to try to reproduce it.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-76826021519795850412008-08-12T15:03:00.000-07:002008-08-12T15:03:00.000-07:00Show me any two series that increase over time and...Show me any two series that increase over time and I'll show you a correlation greater than 0.9. If you calculate the correlation between the weekly CHANGE in the oil price and the weekly CHANGE in the gold price, you'll get a correlation less than 0.2.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-80606179541084325052008-08-12T14:33:00.000-07:002008-08-12T14:33:00.000-07:00The implied inflation in 1980 does look very trust...The implied inflation in 1980 does look very trusting given the then contemporary inflation rate, but in retrospect gold investors weren't quite trusting enough. If you look at the nominal gold price (which hit $800 an ounce and later in the 1980s went down to $250) it looks like a bubble. Everybody underestimated Paul Volcker. <BR/><BR/>Also keep in mind that the dollar price of gold reflects inflation expectations in all dollar-linked currencies, not just in the dollar itself and certainly not just in the U.S, much less just among U.S. urban consumers. In that sense, my (not to mention others') use of CPU-I to estimate inflation is very misleading. The inflation expectations implied by the gold price is (perhaps for the first time -- does anybody know of an earlier attempts to derive this?) an intersubjective estimate of global dollar and dollar-linked currency inflation, i.e. one that takes into account every market participant's actual estimates of inflation based on their actual consumption expectations as reflected in market prices, rather than being based on formulas like CPI-U that attempt to mimick (without really knowing) the consumption expectations of consumers.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-17908317.post-48414711614375521492008-08-12T13:12:00.000-07:002008-08-12T13:12:00.000-07:00This is the best analysis of oil prices that I've ...This is the best analysis of oil prices that I've seen. 0.93 is a very close correlation between gold and oil, and visually it looks like there is a correlation dating back at least to the 1970s. When looked at this way, the behavior of gold investors looks surprisingly stable, eyeballing your graph expectations have not changed by more than 4% over 30 years, even when inflation was approaching 20% in 1980.Anonymousnoreply@blogger.com