Since Halloween, financial markets seem to be getting spooked again.

Larry Kudlow writes:

Until recently, I thought the Fed could stand pat at their December 11th meeting. However, I have completely changed my mind in light of the continuing credit market turbulence.

Kudlow notes that the spread between 30-day asset-backed commercial paper and U.S. Treasuries, which spiked up dramatically after August’s liquidity events but subsequently eased back down, climbed back up during November to the neighborhood of its previous high.

The same is true of the spread between the London interbank offered rate and Treasuries.

One of the features of the initial financial turmoil on which I commented last August is that it seemed to be confined specifically to the financing of problematic securities, but was not showing up as a broader risk premium in something like the spread between Baa-rated corporate bonds and 10-year Treasuries. But the latter spread has made a significant move up over the last month, and now stands 80 basis points higher than in July.

A sharp upward move in the Baa-Treasury spread is often associated with the early stages of an economic downturn, as the following longer-term perspective using monthly data illustrates:

For what it’s worth, bettors at Intrade also seem to believe that the risk of a U.S. recession during 2008 has crept up since mid-October.

Cross-posted from Econbrowser.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

Fret as we all might, the U.S. economy just keeps on growing.

The Bureau of Economic Analysis reported today that U.S. real GDP grew at a 3.9% annual rate in the third quarter. Housing remains in very bad shape, and subtracted a full percent from that total, just as it’s been doing for the last year and a half. But solid growth in nonresidential fixed investment was almost enough by itself to make up for the weakness in housing, and given the strength in exports and consumption spending, we came out with an above-average growth rate under pretty tough circumstances.

The new GDP numbers are sufficient to silent the alarm signal from our recession probability index, which previously had been climbing as a result of anemic growth rates at the end of last year and start of 2007. The index stood at 26.2% for 2007:Q1, but is now back down to 9.5% for 2007:Q2. This index is not a forecast of what may come next, but rather is an assessment of where the economy was as of the second quarter of this year. The index reports the state of the economy with a one quarter lag in order to allow for data revisions and to wait for confirmation from subsequent data before making a recession call.

The above is cross-posted at Econbrowser.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

I recently completed a new research paper studying how interest rates of different maturities change with market expectations of what the Fed is going to do next.

Settlement on a fed funds futures contract is based on the average effective fed funds rate over each of the calendar days of a specified month. If a month contains N calendar days and r_t denotes the effective fed funds rate on date t, settlement of the contract is based on the value of

(r₁ + r₂ + … + r_N)/N.

My latest research paper uses just the spot-month contract, whose payoff is based on what the current month’s average fed funds rate turns out to be. Suppose that the Fed raises the target by 50 basis points on the 16th day of a month containing N = 30 calendar days. If the target change doesn’t alter the fed funds rate for days 1 through 15, it would only raise the average effective rate over the month by 25 basis points, since half the observations that go into the average would be at the lower rate. If market participants had previously been assuming there would be no change at all, and then learned on some day t early in the month that the change was coming on the 16th, we would see the fed funds futures rate move on day t by 25 basis points, even though the market knows a 50-point hike is coming, as a consequence of the averaging. If we wanted to infer the change in the market’s expectation of the fed funds target from the change in the spot-month contract, we would need to multiply the observed spot-month contract change by 2. In general, for a month in which the target change, if it occurs, will come on day n of the month, a paper by Oberlin Professor Ken Kuttner published in the Journal of Monetary Economics in 2001 used such reasoning to propose that the change in the market’s expectation of the target might be measured by

(DF)(N)/(N – n + 1).

where DF is the observed change in the spot-month contract.

There are a couple of concerns that Kuttner and others have raised about this expression, however. For one thing, it does not take into account the fact that the effective fed funds rate (on which the futures contract payoff is based) is not exactly the same as the target rate itself. There are often quite significant deviations towards the end of the month, and the formula above would severely amplify this end-of-month measurement error. Furthermore, although there are some months when everybody knows exactly when the change, if there is to be one, is going to occur, there are also other months where we really don’t know, and some times when a target change did occur but was not announced, and the market did not immediately realize it. We speculated here at Econbrowser as to whether this could have happened this August, and a paper by Poole, Rasche, and Thornton discusses a number of other historical episodes.

My latest paper generalizes Kuttner’s formula in three directions. First, I explicitly model deviations between the effective rate and the target, and show how to modify the formula to take into account this measurement error. Second, I take the view that markets may be gradually learning about the target change well before it actually occurs. And third, I ask what the data would look like if the econometrician does not assume to know the exact date on which the target was changed.

These modifications imply a certain pattern for the volatility of daily changes in the spot-month futures contract over the days of the month. The volatility generally should decline during the month, as uncertainty becomes resolved as to what this month’s target is going to be, but then increases again a bit at the end of the month due to the greater volatility of deviations of the target from the actual on those days:

On the basis of the observed volatility of fed funds futures and the effective fed funds rate, the framework then implies a generalization of the Kuttner weights one should use to multiply an observed change in the spot-month futures contract to infer the change in the market’s expectation of the target. The relation is not monotonic. The ideal weight initially increases as one gets farther into the month, for the same reason as the original Kuttner formula. But it then starts the decrease in the last third of the month, because it is more likely that spot-month changes on those days are driven by noise in the effective fed funds rate rather than news about the target itself.

The model then implies a prediction as to what sort of response one should see of an interest rate such as the 1-year Treasury yield to a given change in the spot-month contract. Since it is the target itself, and not deviations between the effective rate and the target, that will matter for longer term yields, the coefficient from a regression of the change in yield on the spot-month change should show exactly the same calendar pattern as the figure above. The following figure reproduces the predicted pattern (the smooth red line), as well as the actual estimated coefficients when days of the month are grouped into octiles based on calendar date. The prediction seems to fit the facts reasonably well.

One thing we obtain from such calculations is an estimated average extent to which interest rates of various maturities respond to news about what the Fed is gong to select for the target for the current month. I found that a 10-basis-point increase in the expected target was on average associated with a 6- or 7-basis-point increase in Treasury yields at horizons up to 3 years, and a 4-basis-point increase even for a 10-year horizon. Although the methods and data sets are rather different from those of earlier researchers, these estimates are very similar to those obtained by earlier researchers. The consistent finding in this literature has been that changes in Fed policy have surprisingly long-lived consequences.

Cross-posted from EconBrowser.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

Despite what you may have read elsewhere, the probability of a fed funds rate cut has increased significantly over the last few weeks.

Felix Salmon and Barry Ritholtz seemed to find more merit in this analysis from WSJ Real Time Economics than I did.

Since the stock market began to sink a week ago, the federal funds rate for next January, as implied by futures markets, has plummeted to 5% from 5.2%. As a result, the implied odds of a quarter-point rate cut from the current 5.25% are said to have risen from 20% to 100%.

Well, nobody in their right mind would ever describe the odds as 100%, but let us not get diverted.

Lou Crandall, chief economist at Wrightson Associates, says while such action is commonly attributed to increased expectations of a Federal Reserve rate cut, that would be a mistake. The real reason, he said, is that investors are fleeing risk and seeking safety in Treasury bonds and bills and other high-quality paper, sending their prices up and yields down. As a result, the entire yield curve has shifted down. To maintain parity with that lower yield curve, the implied federal funds rate also has to drop, he says.

Mr. Crandall says, “99% of the universe, including a lot of people in those trades, don’t do it because they think the Fed will ease but because that’s the way the yield curve is shaped.”

But wait a minute: isn’t that a violation of efficient markets? If fed funds futures were out of line with a realistic expectation of Fed action, couldn’t smart people take positions in the mispriced futures and make a bundle six months later when it turns out the Fed didn’t cut rates? And shouldn’t such arbitrage push expectations of the Fed and pricing of futures back into line?

No, says Mr. Crandall, for two reasons. First, the Fed has gotten more predictable but gives no guarantees on where rates will go, so there is no assured profit on such a trade (so it wouldn’t really be arbitrage). Second, “The amount of money backing people who have opinions about where the Fed will be in six or nine months is dwarfed by the amount of real money being invested in short-term credit markets.” Nervous investors are willing to accept a lower yield than what might ordinarily be justified based on the economics in exchange “for safety. Market participants know that perfectly well. That’s why it’s called a flight to quality.”

The first odd thing about this statement is that it seems to suggest that there are two competing theories of how fed funds contracts get priced. The first theory evidently claims that the contracts reflect investors’ expectations of Fed actions, and a second, supposedly contradictory theory claims that the contracts just follow the Treasury yield curve, as if we have to choose whether the fed funds futures contracts are priced in a way that is consistent with expectations of what the Fed is going to do or if instead they are priced in a way that is consistent with the yield curve.

But of course the answer is that they are priced in a way that is consistent with both. These and every other financial market are responding to exactly the same news that we’ve been discussing here, and drawing the same conclusions as we have. The latest economic news points to a considerably higher likelihood of economic softness, a situation in which the Fed will want to lower the funds rate and short-term interest rates will come down. That scenario is priced in the fed funds futures, in the term structure of Treasuries, in the stock market, in foreign exchange, and what not. Here’s what’s been happening over the last few weeks to the price of the November fed funds futures contract, the simple-minded interpretation of which (and the one that I favor) is that the expected fed funds rate for November has now fallen to 5%.

A second idea in the statement quoted above is the suggestion that one needs to add a significant risk premium to that fed funds futures calculation in order to arrive at the objective expectation of what the fed funds rate will be. It is true that risk premia play a role in the Treasury term structure, and fed funds futures should incorporate that same risk premia. A recent paper by Monika Piazzesi and Eric Swanson finds some indication that risk premia may play a role in longer-horizon fed funds contracts. But evidence for significant risk premia operating in very short-horizon fed funds contracts is much harder to find, as indeed theory predicts it would be. In recent years the Fed’s actions have become much easier to predict. As the accuracy of your forecast improves and the time horizon for your forecast gets smaller, the risk premium necessarily shrinks, and the risk premium on something you know with certainty has to be exactly zero. Perhaps Crandall is right that risk premia could be playing some role in the January fed funds futures contracts. But I find this story much less plausible for October or November contracts, and, as the figure demonstrates, movement in these was quite dramatic this week.

My guess is that we will indeed see a cut in the fed funds rate by the October 30/31 meeting, if not sooner.

The above article is cross-posted from Econbrowser.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

The Bureau of Economic Analysis reported today that U.S. real GDP grew at an annual rate of 1.3% in the first quarter of 2007, moving our recession probability index up to 16.9%. This post provides some background on how that index is constructed and what the latest move up might signify.

What sort of GDP growth do we typically see during a recession? It is easy enough to answer this question just by selecting those postwar quarters that the National Bureau of Economic Research (NBER) has determined were characterized by economic recession and summarizing the probability distribution of those quarters. A plot of this density, estimated using nonparametric kernel methods, is provided in the following figure; (figures here are similar to those in a paper I wrote with UC Riverside Professor Marcelle Chauvet, which appeared last year in Nonlinear Time Series Analysis of Business Cycles). The horizontal axis on this figure corresponds to a possible rate of GDP growth (quoted at an annual rate) for a given quarter, while the height of the curve on the vertical axis corresponds to the probability of observing GDP growth of that magnitude when the economy is in a recession. You can see from the graph that the quarters in which the NBER says that the U.S. was in a recession are often, though far from always, characterized by negative real GDP growth. Of the 45 quarters in which the NBER says the U.S. was in recession, 19 were actually characterized by at least some growth of real GDP.

One can also calculate, as in the blue curve below, the corresponding characterization of expansion quarters. Again, these usually show positive GDP growth, though 10 of the postwar quarters that are characterized by NBER as part of an expansion exhibited negative real GDP growth.

The observed data on GDP growth can be thought of as a mixture of these two distributions. Historically, about 20% of the postwar U.S. quarters are characterized as recession and 80% as expansion. If one multiplies the recession density in the first figure by 0.2, one arrives at the red curve in the figure below. Multiplying the expansion density (second figure above) by 0.8, one arrives at the blue curve in the figure below. If the two products (red and blue curves) are added together, the result is the overall density for GDP growth coming from the combined contribution of expansion and recession observations. This mixture is represented by the yellow curve in the figure below.

It is clear that if in a particular quarter one observes a very low value of GDP growth such as -6%, that suggests very strongly that the economy was in recession that quarter, because for such a value of GDP growth, the recession distribution (red curve)is the most important part of the mixture distribution (yellow curve). Likewise, a very high value such as +6% almost surely came from the contribution of expansions to the distribution. Intuitively, one would think that the ratio of the height of the recession contribution (the red curve) to the height of the mixture distribution (the yellow curve) corresponds to the probability that a quarter with that value of GDP growth would have been characterized by the NBER as being in a recession. Actually, this is not just intuitively sensible, it in fact turns out to be an exact application of Bayes’ Law. The height of the red curve measures the joint probability of observing GDP growth of a certain magnitude and the occurrence of a recession, whereas the height of the yellow curve measures the unconditional probability of observing the indicated level of GDP growth. The ratio between the two is therefore the conditional probability of a recession given an observed value of GDP growth. This ratio is plotted as the red curve in the figure below.

Such an inference strategy seems quite reasonable and robust, but unfortunately it is not particularly useful– for most of the values one would be interested in, the implication from Bayes’ Law is that it’s hard to say from just one quarter’s value for GDP growth what is going on. However, there is a second feature of recessions that is extremely useful to exploit– if the economy was in an expansion last quarter, there is a 95% chance it will continue to be in expansion this quarter, whereas if it was in a recession last quarter, there is a 75% chance the recession will persist this quarter. Thus suppose for example that we had observed -10% GDP growth last quarter, which would have convinced us that the economy was almost surely in a recession last quarter. Before we saw this quarter’s GDP number, we would have thought in that case that there’s a 0.75 probability of the recession continuing into the current quarter. In this situation, to use Bayes’ Law to form an inference about the current quarter given both the current and previous quarters’ GDP, we would weight the mixtures not by 0.2 and 0.8 (the unconditional probabilities of this quarter being in recession and expansion, respectively), but rather by magnitudes closer to 0.75 and 0.25 (the probabilities of being in recession this period conditional on being in recession the previous period). The ratio of the height of the resulting new red curve to the resulting new yellow curve could then be used to calculate the conditional probability of a recession in quarter t based on observations of the values of GDP for both quarters t and t – 1. Starting from a position of complete ignorance at the start of the sample, we could apply this method sequentially to each observation to form a guess about whether the economy was in a recession at each date given not just that quarter’s GDP growth, but all the data observed up to that point.

Once can also use the same principle, which again is nothing more than Bayes’ Law, working backwards in time– if this quarter we see GDP growth of -6%, that means we’re very likely in a recession this quarter, and given the persistence of recessions, that raises the likelihood that a recession actually began the period before. The farther back one looks in time, the better inference one can arrive at. Seeing this quarter’s GDP numbers helps me make a much better guess about whether the economy might have been in recession the previous quarter. We then work through the data iteratively in both directions– start with a state of complete ignorance about the sample, work through each date to form an inference about the current quarter given all the data up to that date, and then use the final value to work backwards to form an inference about each quarter based on GDP for the entire sample.

All this has been described here as if we took the properties of recessions and expansions as determined by the NBER as given. However, another thing one can do with this approach is to calculate the probability law for observed GDP growth itself, not conditioning at all on the NBER dates. Once we’ve done that calculation, we could infer the parameters such as how long recessions usually last and how severe they are in terms of GDP growth directly from GDP data alone, using the principle of maximum likelihood estimation. It is interesting that when we do this, we arrive at estimates of the parameters that are in fact very similar to the ones obtained using the NBER dates directly.

What’s the point of this, if all we do is use GDP to deduce what the NBER is eventually going to tell us anyway? The issue is that the NBER typically does not make its announcements until long after the fact. For example, the most recent release from the NBER Business Cycle Dating Committee was announced to the public in July 2003. Unfortunately, what the NBER announced in July 2003 was that the recession had actually ended in November 2001– they are telling us the situation 1-1/2 years after it has happened.

Waiting so long to make an announcement certainly has some benefits, allowing time for data to be revised and accumulating enough ex-post data to make the inference sufficiently accurate. However, my research with the algorithm sketched above suggests that it really performs quite satisfactorily if we just wait for one quarter’s worth of additional data. Thus, for example, with the advance 2007:Q1 GDP data just released, we form an inference about whether a recession might have started in 2006:Q4. The graph below shows how well this one-quarter-delayed inference would have performed historically. Shaded areas denote the dates of NBER recessions, which were not used in any way in constructing the index. Note moreover that this series is entirely real-time in construction– the value for any date is always based solely on information as it was reported in the advance GDP estimates available one quarter after the indicated date.

Although the sluggish GDP growth rates of the past year have produced quite an obvious move up the recession probability index, it is still far from the point at which we would conclude that a recession has likely started. At Econbrowser we will be following the procedure recommended in the research paper mentioned above– we will not declare that a recession has begun until the probability rises above 2/3. Once it begins, we will not declare it over until the probability falls back below 1/3.

So yes, the ongoing sluggish GDP growth has come to a point where we would worry about it, but no, it’s not at the point yet where we would say that a recession has likely begun.

[James Hamilton is professor of economics at the University of California, San Diego. The above is cross-posted from Econbrowser].

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

I have been suggesting that the best statistical approach, when confronted with conflicting signals such as the employment estimates from the BLS payroll survey, the separate BLS household survey, or the huge database from the private company Automatic Data Processing, is not to selectively throw some of the data out but rather to combine the different measures. Judging from some of the comments this suggestion has received at Econbrowser, Calculated Risk and Outside the Beltway, I thought it might be useful to say a little more about the benefits of combining forecasts.

Suppose we have available two polls that have surveyed voters for a particular election. The first surveyed 1,000 voters, and found that 52% of those surveyed favored candidate Jones, with a margin of error of plus or minus 3.2%. [By the way, in case you've forgotten your Stat 101, those margins of error for purposes of evaluating the null hypothesis of no difference between the candidates can be approximated as (1/N)^0.5, or 0.032 when N = 1,000]. The second poll surveyed 500 voters, of whom 54% favored candidate Jones, with the margin of error for the second poll of plus or minus 4.5%. Would you (a) throw out the second poll, because it’s less reliable than the first, and (b) then conclude that the evidence for Candidate Jones is unpersuasive, because the null hypothesis of no difference between the candidates is within the first poll’s margin of error?

If that’s the conclusion you reach, you’re really not making proper use of the data in hand. You should instead be reasoning that, between the two polls, we have in fact surveyed 1,500 voters, of whom a total of 520 + 270 = 790 or 52.7% favor Jones. In a poll of 1,500 people, the margin of error would be plus or minus 2.6%. So, even though neither poll alone is entirely convincing, the two taken together make a pretty good case that Jones is in the lead.

In the above example, it’s pretty obvious how to combine the two polls, just by counting the raw number of people covered by each poll and then combining the two as if it were one big sample. But this example illustrates a statistical procedure that works in more general settings as well. We have two different estimates, 0.52 and 0.54, of the same object. We know that the variance of the first estimate is (0.5)²/1000, while the variance of the second estimate is (0.5)²/500 [again, does that sound familiar from Stat 101?]. If we followed the general principle of taking a weighted average of the two, with weights inversely proportional to the variances, that would mean in this case calculating [(1000)(0.52) + (500)(0.54)]/(1000 + 500) = 0.527, which amounts to combining the two estimates in exactly the way that common sense requires for the two-poll example. That principle, of taking a weighted average of different estimates, with weights inversely proportional to the sampling variance of each, turns out to be a good way not just to combine two polls but also to combine independent estimates that may have come from a wide range of different statistical problems.

But what if the second poll not only covered fewer people, but is also less reliable because it is a week older? One way to think about the issue in that case is to notice that the second poll’s estimate differs from the true population proportion because of the contribution of two terms. The first is the sampling error in the original poll (correctly measured by the (0.5)²/500 formula), and the second is the change in that population proportion over the last week. If we knew the variance governing how much public preferences are likely to change within a week, we would just add this to the sampling variance to get the total variance associated with the second estimate, and use this total variance rather than (0.5)²/500 to figure out how strongly to downweight the earlier poll. The earlier poll would then get much less weight than the newer one, but you’d still be better off making some use of the data rather than throwing it out altogether.

And what if you believe that one of the polls is systematically biased, but you’re not sure by how much? Many statisticians in that case might give you the OK to go ahead and ignore the second poll. On the other hand, there are many of us who would still want to make some use of that data, accepting some bias in the estimate in order to achieve a smaller mean squared error. In doing so, we acknowledge that we may make a systematic error in inference that you will avoid, but we will nevertheless be closer to the truth most of the time than you will if there are substantial benefits to bringing in extra data.
Examples where such an approach is quite well-established are estimating a spectrum (where we use the value of the periodogram at nearby frequencies, even though we know it would be a biased estimate of the spectrum at the point of interest) and nonparametric regression (where we use the value when x takes on values other than the one we’re interested in, even though again our assumption is doing so necessarily introduces some bias to the final estimate).

Robert Clemen, in a paper in the International Journal of Forecasting in 1989 surveyed over 200 different academic studies, and concluded:

Consider what we have learned about the combination of forecasts over the past twenty years…. The results have been virtually unanimous: combining multiple forecasts leads to increased forecast accuracy. This has been the result whether the forecasts are judgmental or statistical, econometric or extrapolation. Furthermore, in many cases one can make dramatic performance improvements by simply averaging the forecasts.

If I ask you what you think U.S. employment growth was in December, and your answer is the December BLS payroll number, one could say you have decided that the optimal weights to use for “combining” the payroll, household survey, and ADP estimates are 1.0, 0.0, and 0.0 respectively. But there’s an awful lot of statistical theory and practical experience to suggest those aren’t the best possible weights.

Or to put it another way, even though the payroll numbers were encouraging, the fact that ADP estimates that the U.S. lost 40,000 jobs in December should surely make you a little less confident about the robustness of employment growth than you otherwise would have been.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

In talking about the Fed’s likely next move, it’s useful first to review how we got to where we currently are. The Fed now clearly understands that it overdid the stimulus in 2002-2004, and brought us uncomfortably close to a resurgence of inflation as a result. The high inflation rates for the headline CPI during 2005 might be dismissed as a temporary influence of energy prices. But the upward drift by the start of 2006 of other measures, such as the core CPI (measured by removing energy and food prices from the total) or the median CPI (measured by the price change of the expenditure-weighted median item purchased by consumers), were not so easily ignored. Here’s how Fed Chair Ben Bernanke described his concerns last June:

core inflation measured over the past three to six months has reached a level that, if sustained, would be at or above the upper end of the range that many economists, including myself, would consider consistent with price stability and the promotion of maximum long-run growth. For example, at annual rates, core inflation as measured by the consumer price index excluding food and energy prices was 3.2 percent over the past three months and 2.8 percent over the past six months. For core inflation based on the price index for personal consumption expenditures, the corresponding three-month and six-month figures are 3.0 percent and 2.3 percent. These are unwelcome developments.

One of the key red flags for the Fed was the growing spread that developed in May and June between the yields on nominal and inflation-adjusted 10-year Treasuries. At the end of April Bernanke was still taking some comfort in the fact that these remained below 2.5%:

The stability of core inflation is also enhanced by the fact that long-term inflation expectations–as measured by surveys and by comparing yields on nominal and indexed Treasury securities–appear to remain well-anchored.

But when this spread started to signal a long-run expected inflation rate of 2.7% in the weeks following those remarks from Bernanke, that in my mind was a key factor in persuading the Fed to continue hiking the funds rate all the way to 5.25% in June.

As the above graph shows, these long-run inflation expectations have since come back down, stabilizing around a much more desirable 2.3% level. Markets evidently have now have come to share the faith in Bernanke that I have had from the beginning. On the other hand, that faith is predicated on the belief that the Fed is willing to sacrifice some short-run GDP growth in order to keep inflation from returning, and those core inflation figures have been coming down rather stubbornly.

William Poole, President of the Federal Reserve Bank of St. Louis, stated in November that

“‘We need a policy that is disciplined enough to get the job done, but not more so,” Poole told reporters after a speech in Wilmington, Delaware. “If all the information taken together suggests that we are not making progress, then I will be among those who will push for a tighter policy.”

Poole said inflation expectations are “well controlled… The market does believe we’re serious” [about containing inflation]

He reiterated that he sees the outlook for the fed funds rate as “roughly symmetrical,” meaning the chances of an interest-rate cut and an increase are about equal. … ”I can imagine data coming in that would make me want to tighten policy, and I could imagine data coming in that would make me want to ease policy,” Poole said.

And just what might be the circumstances in which the Fed would choose yet another rate hike? I suppose that if those core inflation numbers and nominal-TIPS spreads again surged, the Fed might be forced to consider it. But I view that as rather unlikely at this point, and even if it happened, the Fed would have to be very reluctant to tighten any further. If we want to avoid a recession (which I’ve always believed that Bernanke very much does want to avoid), you really can’t go any farther than we already have, and indeed the verdict is still out on whether a recession is already in the cards based on what the Fed has done so far. Realistically, I think we can take the possibility of another rate hike off the table.

And what about a rate cut? If we do see widespread defaults sending housing into a freefall from here, then I certainly would expect the Fed to start cutting rates, though at that point it would be too late to do much good. But in my opinion, such a prospect, while a tangible possibility, is not the most likely outcome.

And what is the most likely outcome for housing? Even if home sales fall no further, the inventory of unsold homes will continue to be a drag on residential construction, meaning that below-average GDP growth and employment growth will likely continue for some time. Would that be enough to cause the Fed to ease on interest rates? My guess is that it would not. Precisely because a resurgence of those inflation fears would put the Fed in such a tight spot, the Fed may be quite willing to see the current slow growth continue for several more quarters as long as the trajectory appears to be holding stable rather than spiraling down.

And the data that came in during December seem largely consistent with the claim that things are not getting any worse. Certainly the stock market is not signaling any fear by investors that a recession is about to begin:

For the equities of homebuilders in particular, the Dow Jones Construction Index continues to reflect a market consensus that the worst is behind us:

Fed funds futures, which started out the month betting on a rate cut by the March meeting, had by the end of the month converged to a predicted fed funds rate for April that is not far from the current 5.25%:

That works for me as well. So here’s my call: no change in the fed funds rate until May.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

This seems like a good time to review some of the occasions over the last year when I’ve been brave (or foolish) enough to make a specific quantitative prediction.

December 8, 2005.

Only 17 more (oil) shopping days until December 31.

Let me for my part point out that there is an alternative to the positions of the fiercest bulls and bears, which is that oil may be priced correctly about where it is right now. The basic reality that drove prices so high this year was the need to reconcile booming world demand with limited short-run ability to increase production and also to establish a current price consistent with the future depletion concerns…. Sixty dollars a barrel seems to have accomplished its mission.

May 7, 2006.

Have oil prices peaked?

Since concerns about a further move up in price have been well represented, I thought there might be some value in trying to provide some balance by calling attention to a few of the possibilities on the downside.

May 17, 2006.

Stagflation.

I’ll throw my hat in the ring by predicting another hike in the fed funds rate to 5.25% at the end of June.

August 4, 2006.

A pause it shall be.

The big question over the last month has been whether the Fed would opt for yet another hike at next Tuesday’s meeting…. the BLS release seems to have settled the argument, as least as far as the CBOT Fed watchers are concerned.

September 1, 2006.

Gasoline prices coming down.

U.S. gasoline prices have been dropping and will likely fall further….another 30-cent-per-gallon drop to $2.50 is quite reasonable to predict.

September 13, 2006.

Gasoline prices will fall even more.

a retail gasoline price below $2.20 a gallon appears to be quite reasonable to anticipate.

October 26, 2006.

More evidence that housing may be stabilizing.

Data on new home sales and inventories released today from the Census Bureau continue to support the view that the market downturn may have reached its bottom.

Ah, that last one will give us something fun to watch for in 2007, won’t it?

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

I’m just finishing writing a new research paper whose goal is to come up with a better measure and understanding of the lagged effect of monetary policy on the economy. One of my claims is that the public’s expectations of what the Fed is going to do next play a key role in that process. In this, the first of several posts based on that paper, I describe some of the properties I’ve found for fed funds futures prices as predictors of subsequent Fed policy changes.

The primary policy tool of the U.S. Federal Reserve is manipulation of the federal funds rate, an overnight interest rate on interbank loans that is quite sensitive to the total quantity of reserve deposits that are created by the Fed. The Chicago Board of Trade offers a futures contract whose payoff is based on the average value for the effective fed funds rate over all of the calendar days of a specified month.If this were a pure forward contract, no money would change hands until the first-of-month settlement day. The actual futures contracts are a little more complicated, since the exchange will require you to commit collateral to prove you can honor the contract, and these margin requirements will increase if the market moves against you. However, a recent paper by Monika Piazzesi and Eric Swanson demonstrates that the impact of these margin calculations on the value of the contracts should be quite small, and I will discuss here the simpler case of how to evaluate a pure forward contract.

Consider first how a contract that specified a 5.25% value for the current month’s fed funds rate would be valued at the start of the last day of the month (the day before settlement). If the actual rate turns out to be lower than 5.25%, the next day the seller of the contract will have to compensate the buyer for the difference (paying $41.67 per basis point in the standard contract). If you were the buyer of the contract, this would for you be a pure profit. The primary consideration that might prevent you from taking this bet is a concern that perhaps the rate would end up above 5.25%, in which case you’ll owe money. If speculators are risk neutral, the contract price will be bid up or down to the point at which its implied interest rate just equals traders’ expectations of what the settlement rate will turn out to be.

On the next-to-last day of the month, similar logic would again imply that the price reflects the market expectation at that time. New information could well come in after this, causing the price to move up or down before settlement. But if it were possible to anticipate, say, a price increase between the penultimate and last day of the month, there is a pure profit opportunity from buying on October 30 and selling on October 31. A statistical principle known as the Law of Iterated Expectations implies that the October 30 price should not only equal the expected settlement value, it should also equal the expected October 31 price. As time goes on and new information comes in, of course we know that the price is likely to change. But none of us can predict the direction. In other words, this simple theory suggests that the futures price should follow a martingale, in which the best forecast of where the price is going to be tomorrow is always just today’s price.In my statistical analysis I looked at daily changes in the interest rate implied by the current month’s fed funds contract (denoted f_1d), the following month’s contract (f_2d), and the month after that (f_3d); for example, for d = October 31 we could consider the change in the October contract (f_1d), the November contract (f_2d), or the December contract (f_3d). The graph below plots daily changes in the interest rate implied by the current month contract from October 1988 through June 2006.

On average, the values of f_1d, f_2d, and f_3d all turn out to be negative over this sample period, with t-statistics around -4. This represents strong evidence against the martingale hypothesis, and some researchers have interpreted this bias as evidence of some kind of average risk or hedging premium reflected in the futures prices.

However, if you look at the graph above, you will see that it is a pretty wild series. Forty-six percent of the observations are identically zero, while 25 observations exceed 5 standard deviations. The variance is considerably larger at the beginning of the sample or the start of a month, with the volatility appearing in clusters and particularly on days of major monetary policy announcements. If one models all these volatility dynamics and departures from a Gaussian distribution, the maximum likelihood estimate of the population mean of f_1d, f_2d, or f_3d all turn out to be positive rather than negative, and far from statistically significant. The sample median of all three series is also exactly zero. I therefore see the nonzero sample mean not as an indication of bias on the part of futures markets, but rather as reflecting the fact that there were a few big moves down in interest rates over this period

that caught traders by surprise.

I also looked for whether changes could be predicted on the basis of lagged changes, by regressing f_id on a constant and five of its own lagged changes. OLS coefficient estimates along with their 95% confidence intervals are shown below.

The first lag is always highly statistically significant. Its value, however, is only around 0.15, which gives the regression an R² of less than 0.03 and essentially zero predictability looking more than one day ahead. It is quite likely that this very modest degree of predictability could be attributed to measurement error in resolving daily bid-ask factors rather than systematic errors or risk factors in futures markets.

The paper by Piazzesi and Swanson mentioned above documents some predictability using monthly data of longer-horizon fed funds futures prices based on a number of interest rate spreads. However, consistent with their findings, I find these spreads do not predict the daily movements in the prices associated with the near-term fed funds futures contracts that I am studying, as summarized in the table below:

I also replicate with these data Piazzesi and Swanson’s observation that employment growth helps predict futures prices, though again for my data the R² is only 2%, and the results I will describe in my next post turn out to be insensitive to whether one includes this conditioning variable. Overall, I conclude that although these data do not appear to follow an exact martingale, that is really an excellent approximation to their behavior.

A separate question from whether changes in futures prices are possible to predict is the question of how far in advance they give a useful estimate. One standard of comparison is the mean squared error, or the average squared difference between the implied futures forecast at a given date and what the actual fed funds rate turns out to be. A benchmark for comparison is the assumption that the fed funds rate itself follows a martingale, so that one’s forecast for the future value of the fed funds rate is always its current value. Such “no-change” forecasts have often proven to be very difficult to beat out-of-sample with financial data. The table below shows that, if you simply predicted that the fed funds rate isn’t going to change, you’d have a mean squared error of 389 basis points (that is, a standard deviation of about 20 basis points or 0.2%) predicting one month ahead and 2,522 basis points (50 basis-point standard deviation) predicting 3-months ahead. For comparison, the MSEs of the futures-derived forecasts are only a third as large.

Futures prices have become even better predictors over the last three years, with an incredible 97% improvement over the “no-change” forecast:

The moral is, if you think the fed funds rate is going to do something over the next few months that differs from what is predicted by the futures prices, then think again.

And what the futures prices say right now is, no change in December.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish

Something for everyone in this week’s data on housing from the Census Bureau. Pessimists will note the alarming 6% plunge during the month of September in seasonally adjusted new building permits. That one-month drop from the already low levels of August leaves them down 28% from September 2005. News this week of rising delinquencies and foreclosures provides more fuel for the pessimists’ fire.

Optimists, on the other hand, might see new evidence that the housing bottom has been reached in the encouraging move in the number of new housing units started. This was up 6% from August to September, though still down 18% year to year:

For those of us who were unsure before this week, we’re stuck in the same rut at the end of the week. The effect of this summer’s drop in mortgage rates should start to show up in next month’s home sales, and we’ll have to wait to see if that effect is sufficient to outweigh the possible dynamics from financial distress and rapidly changing expectations.

The optimists seem to be winning the argument as far as commodity markets are concerned. Commodity prices had been battered down as the dismal housing data came in during September. But over the last two weeks, copper, zinc, and aluminum have surged back up dramatically. It may be that the only way these prices will be kept in check is if GDP growth stays below 2% for the coming year.

And although the headline CPI showed a dramatic 0.5% drop within the month of September alone, Dave Altig is none too impressed, noting that more robust measures such as the median CPI are still up 3.5% year-to-year:

Mixed (as opposed to really bad) news for housing and “unwelcome” news on core inflation have eroded the likelihood that we will see the Fed cut interest rates by spring. Here’s the recent behavior of the March 2007 fed funds futures contract (subtract from 100 to get the implied interest rate):

At the start of this month, traders had been betting on a 5.0% rate (a cut of 25 basis points from the current value) by March. Those hopes have now evaporated, with the current consensus for a prediction of no change.

I’m wondering though whether “no change” might be the least likely outcome at this point. If we start to see some serious financial repercussions develop in housing, I’d look for a rate cut, and wouldn’t worry in that event about commodity prices, since I would expect to see commodities fall sharply on news of a big downturn in economic activity. On the other hand, if instead we have seen the bottom for housing and the core inflation numbers remain this high, I’d look for the Fed to tighten further.

Either way, you might want to exercise some caution before thinking you’ll pick up some homebuilder equities at these bargain prices.

Midas Oracle = About + Archives + Authors + Best + Contact + Information Technology + Links + Probabilistic Predictions + Post-Mortem Predictions + Prediction Exchanges + Prediction Software + Publish Your Post + How To Publish