## Rate Expectations Versus Rates

Within modern mainstream Dynamic Stochastic General Equilibrium (DSGE) models, the level of interest rates is not supposed to be the variable of interest, rather it is expected path of rates. This leads to some fairly complex mathematics, as we are now defining interest rate policy as a "reaction function," and not just a time series of interest rates.

Although I have my doubts about DSGE macro, I do not object to the importance of interest rate expectations as a concept. This is because long-term government bond yields reflect the expected path of interest rates. Roughly speaking, a bond yield is equal to the expected average of the policy rate over the lifetime of the bond, plus a "small" risk premium (term premium). All of the mathematical difficulties of DSGE models become understandable if we realise we are interested in the entire term structure of interest rates, and not just a single point of the yield curve.

## Which Point To Use?

If we want to do econometric analysis to determine the effect of interest rates on the economy (without just assuming we have the model dynamics), we need to do something like run regressions on an interest rate time series versus other economic time series. Unfortunately, it is unclear what point to pick.Pretty well any borrower has the option of locking in a fixed rate of interest for multiple years, or else borrowing at a floating rate. Which rates appear most attractive at any given point in time depends upon the psychology of borrowers. Given the fragmentation of the lending markets, we only have a limited idea of the mix of borrowing maturities. As a result, we do not have an idea what points on the curve matter most for borrowing decisions at any given time.

For central bankers, they administer the overnight rate, and it is natural for them to pick that point to run their statistical analysis. "If we move the administered rate by 100 basis points in this direction, what happens?" However, the relationship between the policy rate and points further on the curve is vague.

If we are at very short maturities, it does not make too much of a difference what point you choose. As the chart of the 2-year Treasury yield and the overnight policy rate (Fed Funds) shows, the two rates are fairly close together most of the time. If the Fed hikes rates by 400 basis points, the 2-year yield will rise 300-400 basis points. That is pretty close to a 1:1 relationship, at least when we compare the error to the other sources of error in any estimates we are trying to make.

This breaks down even when we go out to the 5-year point of the curve. If we look at the interest rate cycle of the mid-2000s, the slope from the overnight rate to the 5-year yield went from +300 basis points to about -100 basis points. Although the time series for the 5-year yield and the overnight rate are correlated, the magnitudes of the change in yields are quite different. This means that it is very unclear what the sensitivity of other variables towards interest rates will be.

This relationship between the overnight rate and the 5-year yield is what you would expect to happen if the bond markets are efficient; they will price in yield reversion at both extremes of the cycle. (Many observers, including those at the Fed, were mystified by this "conundrum," which tells us how well the Fed understands their own models.)

Making the situation even more complicated is the fact that only the Federal Government borrows at the "risk free" rate; other entities are borrowing at a spread over the Treasury curve. The variability of these spreads further muddies the relationship between the policy rate and the interest rates faced by private sector borrowers.

## Interest Income

Mainstream analysis is almost entirely focused on the rate of interest (the price of borrowing money), and not the income flows associated with borrowing. Post-Keynesian analysis (in particular, Modern Monetary Theory) puts much more emphasis on the income flows from debt. Changing interest rates will change the income flows within the economy.If you want to pursue this angle, you will need to dig into the interest income flows within the flow of funds. The rate of interest has only a slow lagged effect on these flows, as a great deal of borrowing is done a fixed rate of interest, and the interest rate paid has been already locked in. For example, if you are looking at government interest expense, it will only move slowly as the average maturity of most developed government bond markets is at least 5 years or so. So long as the Treasury Bill segment of the curve can be locked down near the policy rate, the average interest cost on the portfolio of government debt will only move slowly, with a reversion time comparable to the average maturity of the debt.

## Concluding Remarks

Although some analysts can generate very precise sounding predictions about the effect of Fed rate hikes on other economic variables, the reality is that even if we had good models of the economy, the sensitivity of other variables towards the overnight rate would be hard to pin down. Unless the Fed hikes rates by several hundred basis points (which admittedly was the norm for previous cycles), the flattening of the yield curve would reduce the effect of hikes on effective interest costs.(c) Brian Romanchuk 2015

I think the interest income aspect is important, particularly in the UK, for the distributional effects within the private sector. Most UK mortgages are floating rate, so a rise in rates immediately reduces income for borrowers. This matters because those households that have high debt service to income ratios seem to have higher marginal propensities to consume, so they respond by cutting their spending by much more than the lucky recipients of higher interest increase theirs. I suspect this has a much more noticeable impact than the inter-temporal substitution effect supposed by DSGE models.

ReplyDeleteDon't think that's the case any more. 80% of new business in the mortgage market is Fixed Rate, and has been for quite some time now.

DeleteTrue, the effects vary by country. The yield curve historically was flat in the UK, and mortgages were floating. (Even the "fixed" mortgages often only had a short term when I looked at it,) The US is at the other extreme of mortgage finance, with 30-year fixed terms being common. (Since a mortgage pays down principal, the effective maturity is shorter, comparable to a 7- to 10-year bond.)

DeleteThanks for the link, Neil. That's higher than I would have guessed, but that's a new business figure. The outstandings for fixed will be lower because many of those fixed deals are for short periods, which then flip into floating. I was under the impression that it was still the case that the majority of outstanding loans were floating (which is what matters here). Any idea whether that is correct?

DeleteActually, I just found that info in the data in your link. The latest figures for fixed loans are between 40 - 45% of outstandings.

Delete