## Adding market expectations to our models

Scott Sumner’s blog taught us to look at market prices as functions of of underlying market forecasts, with NGDP expectations playing a leading roll. If you watch markets closely, you’ll soon see that there are different types of “days” on the markets. Some days are really obvious revisions to the U.S. (and world) NGDP forecast. If—in USD terms—the yen rises while the euro, GBP, S&P 500, longer term yields and commodity prices fall, then we have an obvious case of lower NGDP expectations. If yields drift a bit lower while stocks drift a bit higher and the various commodity contracts—say WTI, Brent and copper—take rather small steps in opposite directions, then the market has little new to say about future NGDP on that day.

I think I’m closing in on a way to capture the market’s underlying NGDP forecast.

Here is what I propose, as a start:

Take daily time series data, closing prices, on 5-year U.S. government bonds, 5 year TIPS spreads, the broad trade-weighted dollar index, the S&P500, WTI front month contract prices and LME front month copper prices.

We should all agree that an ‘exogenous’ change in the market NGDP forecast, will yield a change in all of these market prices. Say, something like the Fed cutting rates more or less than expected, ditto QE. If you don’t believe that, then either you are allowing your ego-investment in decades of New Keynesian thinking to cloud your judgement, or you haven’t read Nunes and Cole’s new book. (I haven’t either, but I *will* and can only assume the content would lead one to this understanding)

So my idea is to take the first principal component of these time series, and treat it as in some way proportional to future NGDP. Lars did something similar a few months back. The resulting component wouldn’t be interpretable as an NGDP forecast, but we could aggregate it to quarterly frequency and use it to drive an NGDP forecast equation. We would need many equations actually, to find the “NGDP expectations curve” (which would be like this inflation curve) and in turn find the expected NGDP path. I deliberately included only 5 year bond yields, to weight the factor on 5 year NGDP expectations, though maybe 2 or 3 year rates would be better.

Here is a graph of the proposed shadow forecast.

And here is a graph of the same series, from 2007 to December 2012.

I’ve pondered just what this component might mean, and so far my best verbal description, is that the component is directly proportional to the expected present value of all income earned in the next five years. Exactly what geographical entities the series applies to are not clear, though it is surely dominated by the U.S.

I’ve played around with forecasting NGDP from this series. So far it is a respectable indicator of contemporaneous NGDP (when I convert the series to quarterly frequency) as well as NGDP up to 3 quarters ahead, after which it loses performance quickly, which is not surprising given how NGDP expectations have been buffeted in recent years. I don’t think those results are worth showing yet, but am confident there is a lot to be done with this, one way or another. My goal is to eventually build a website which somehow maps market prices to expected NGDP, in real time. It should be possible for a bank or forecasting firm to build a comprehensive line forecast products based on market data, which would allow clients real time forecast updates and perhaps finally give us an intellectually honest forecast methodology.

Regardless of how NGDP expectations are ultimately found (Scott has a link to an Evan Soltas article on another approach), we need a good estimate. *If* Market Monetarism is the best family of macroeconomic models for our age, then it follows that the best macro*econometric* models will probably be built around market NGDP expectations in one way or another.

JP, this is really interesting. I think that you are on to something here.

JP, that´s a great line of research. Keep me posted on developments and results.

Thanks guys, will do. BTW Marcus, looking forward to reading your new book!