Estimating NGDP Expectations
Rather than revise my approach further, I’m going to post a working version of how I propose to estimate market NGDP expectations.
Here is what I have in mind
Take a vector
![I_t = [stocks_t,10yr.rate_t,WTI.oil.3mo_t,USD.Index_t,copper_t]^T](http://s0.wp.com/latex.php?latex=I_t+%3D+%5Bstocks_t%2C10yr.rate_t%2CWTI.oil.3mo_t%2CUSD.Index_t%2Ccopper_t%5D%5ET&bg=ffffff&fg=555555&s=0 "I_t = [stocks_t,10yr.rate_t,WTI.oil.3mo_t,USD.Index_t,copper_t]^T")
Representing the price of a set of assets. I propose that this set of assets is strongly correlated with the market’s implicit outlook on U.S. nominal GDP. This is not necessarily a perfect data set, we can imagine that events in East Asia or Europe could steer any single one of these prices for an extended period. Ideally, we’d also have an inflation indexed bond spread, though in this case, this would hinder the analysis as TIPS have only traded since 2003. We might also include a safe private sector bond index.
Take the first and second principal components of 
I’ve not labeled the graphs, the black line is the first PC, the red line is the second.
Next, model these components along with lagged nominal GDP in the vector ![N=[NGDP_{t-1},PC1_t,PC2_t]^T](http://s0.wp.com/latex.php?latex=N%3D%5BNGDP_%7Bt-1%7D%2CPC1_t%2CPC2_t%5D%5ET+&bg=ffffff&fg=555555&s=0 "N=[NGDP_{t-1},PC1_t,PC2_t]^T")
Call these models: 
Fit these models to data sequentially, covering period 1 (1989Q1) to as little as 40 (1998Q1) or as much as 97 (2012Q4).
At first, fit model to date index positions 1 to 40, forecast NGDP with this model for period 41 through 45 (remembering that NGDP is lagged one period relative to the market components). Save the percent change in NGDP for periods t+1 to t+5, in the 57×1 vector
Repeat this process over the dataset, in essence simulating the result a forecaster would have had in each quarter of the data set after position 40 (the amount of data needed to give the model a moderately good fit).
Here are the resulting 
That is run off quarterly averages. This looks about right to me, as far as the deviations from 5% approximating the effective stance of policy. Here is the system run at quasi daily frequency, the choppiness of NGDP data make this cumbersome.
You could think of lots of different ways to make the models somehow account for the fact that the principal components are probably distorted by international factors, or otherwise not reliably related to NGDP expectations.
I suggest setting up some sort of Bayesian model averaging or combination system, on a wide set of potential models. That, would be an undertaking.
On and BTW: Link to the quarterly NGDP expectations here.
Gold and Bitcoins?
So the story here is that gold investors have found a new ‘crank asset’ for their marginal savings ?
I say crank asset with the best of intentions.
Lady Thatcher is dead.
It is hard to overstate how important Thatcher was in turning back the worst elements of the Western mixed economy. She saved Britain from itself, at least for a time, and was right about the Euro. Rest in peace.
Why U.S. yields are low
A quick post, inspired by silly things I’ve seen in the financial media.
The U.S. 10-year yield is about 1.8%, down from just over 2% before Cyprus. Some people say Treasury prices are rising because the Fed is buying up so much of the debt stock, though Sumner reminds us that this is not so (the PPPS at the bottom).
Instead of falling because of QEIII, U.S. treasury yields are low (despite a firmer recovery) because of developments in Europe.
I think this plot says it all:
That is a correlation of -0.79, between U.S. bonds and the Spain-Germany spread. Correlation does lift the odds of causation, just not that much.
Think of U.S. bond prices as a function of 1. NGDP expectations and 2. a “haven fee” which goes up when EMU default risk rises. Before the QEIII framework was in place, we couldn’t be sure if Europe was mostly affecting U.S. yield through #1 or #2 , but it is plainly obvious to anyone who watches financial markets carefully that Europe is the driver. You’d have to come up with one hell of a just-so model to explain how quantitative easing is able to push down U.S. yields (which is supposedly bullish) while also seemingly exacerbating the Euro Zone mess. Why the negative correlation?
Since the Bernanke-Evans rule went into effect, Treasury yields have still moved opposite the Spain-Germany spread, but commodity prices, TIPS spreads and stocks all tell us that NGDP is set to grow around 4%. So I am fairly confident that most of recent weakness in yields springs from the “haven fee” effect.
Funny isn’t it? The staunchly anti American “Europe” project is now indirectly subsidizing the U.S. Treasury.
PS: I’m not meaning to be a jingoistic Yank by pointing out that the U.S. Treasury is getting a subsidy from the European Commission. I’m just taking a swing at the EU, which has brought so much trouble to the continent.
Sumner on Econtalk
The latest Econtalk is with Scott Sumner. Can’t wait to listen. A great week for podcasts.
Pinker on London Real
Steven Pinker, who is maybe my favorite public intellectual, has new and worthwhile interview on the London Real podcast.
If you’re facing an hour and a half train or car trip or just need some conversational supplementation, I’d check this one out.
A look at the 1987 stock market crash
I liken the ’87 crash to that sequence in Pulp Fiction where John Travolta accidentally shoots the man sitting in the back of Samuel L. Jackson’s car. Stick with me. The mistaken shot is the stock market crash (or maybe the rally before the crash), and Travolta and Jackson are the financial market participants. The two frantically seek shelter in Quentin Tarantino’s house, uncertain of how the situation can be resolved. They call Ving Rhames (representing Alan Greenspan) in a panic. Greenspan calmly answers by sending Harvey Keitel (monetary easing) and all is well…at least for a while.
This (not safe for work) clip from the film is at least what came to my mind when a macro professor explained the ’87 crash to me some years ago. Everyone freaked, Greenspan said he was on the problem, cut rates, and “confidence” was maintained. When people speak of financial market confidence, they really mean the implicit NGDP forecast hidden in market prices.
In January I posted about a method I was toying with for estimating the market’s underlying NGDP forecast. I have some results, and will post something soon. But before that, I’d like to share some principal component graphs I’ve made along the way, which support the Mr.Wolf interpretation of October 1987. You can click the graphs below for a closer look.
To start, lets look at the first principal component from: the ten year Treasury yield and logs of the S&P 500, West Texas Intermediate month ahead futures, the major currencies, trade weighted dollar index, and three month copper futures. These are somewhat arbitrarily chosen, just what I was able to get back to ’86 without hassling my Datastream source too much. The component was calculated from mid 1986 to early 2013, though in this first graph I focus on the ’87 crash. If you are new to principal components, think of this series as a sort of multidimensional midpoint of the five series, the scale has no meaning.
I’ve proposed that principal components like this are proportional to expected NGDP in some way. In the next post we’ll see that lagged values of these components are strongly correlated with NGDP. If the component really is a proxy for NGDP expectations (the true stance of monetary policy in the Market Monetarist model), then it would seem that expected NGDP certainly dipped abruptly on Black Monday, but not catastrophically so. Put simply, the ’87 crash didn’t much shake NGDP expectations.
Now let’s look at the market prices themselves. I’ll show fewer days of trading in these plots, because it becomes too messy to get a clear read on October ’87 if I show as much as I did in the graph above. Also, note that the dates are in YYYY-MM-DD format for these plots.
If you read Sumner in 2010, you’ll quickly see the difference between ’87 and ’08/’09.
This graph of 20 day log differences shows us that oil traders were unimpressed with the stock market collapse. Oil prices didn’t fall until weeks later when stocks were rallying. Copper prices plunged on black Monday (that abrupt drop just before the 1987-10-26 date marker), but quickly rallied thereafter.
Next, the S&P 500 index along with the U.S. dollar index:
This is a fascinating graph. The dollar strengthened on Black Monday, but then quickly weakened as monetary policy eased. I had to double check the figures; I couldn’t believe the dollar fell 10% in a quarter, but it happened. This is the opposite of what we saw in late 2008 when the dollar soared.
The last constituent of the component is the five year yield:
The 5 year yield shot up before the crash, plunged back to August 1987 levels on Black Monday and then held steady for the rest of the year.
Lastly, here is a plot of the component in 2008-2009. This really needs to be mapped to an NGDP forecast to easily interpret (next post) but still gives a rough sense of how different the two market crashes were.
We already knew that market NGDP expectations held up in ’87 and plunged in 2008/2009. I view this more as a test of the principal component approach. This doesn’t mean the component is really mirroring NGDP expectations, but if I’d seen a sustained drop in the component after Black Monday, it would be back to the proverbial drawing board. Failure to reject is something.
