I’ve recently completed writing a research paper titled Daily Monetary Policy Shocks and the Delayed Response of New Home Sales. The paper develops some new measures of the delay between changes in Fed policy and the impact on the economy. In this, the second of three posts on the paper, I describe the paper’s findings about how the Federal Reserve affects mortgage lending rates.

In my first post on this paper, I related the theory and evidence supporting the view that fed funds futures prices approximately follow a martingale, meaning that daily changes are very difficult to predict. According to this view, the futures prices incorporate the market’s best prediction of where the fed funds rate will be over the next few months.

A related theory argues that daily changes in a very long-term interest rate, such as the 30-year fixed mortgage rate, would also be very difficult to predict. I don’t have data on daily mortgage rates, but found broad support for this view from the weekly Freddie Mac series ([1], [2]). Regressing the change in this mortgage rate on its own weekly lags, I did find statistically significant coefficients at lags 1 and 3, though the coefficients are less than 0.1 and imply very limited predictability, while longer term trends are not apparent.

OLS regression coefficients (standard errors in parentheses) for regressions of weekly changes in mortgage rates on interest spreads or economic indicators available 3 days prior to the preceding week. * denotes statistically significant at 5% level, ** at 1% level.

Explanatory variable
xd-1
10-year minus 5-year Treasury spread	0.005 (0.009)
5-year minus 2-year Treasury spread	-0.004 (0.006)
2-year minus 1-year Treasury spread	-0.016 (0.012)
1-year minus 6-month Treasury spread	-0.018 (0.019)
Baa minus 10-year Treasury spread	0.001 (0.006)
12-month job growth (revised data)	0.26 (0.25)
12-month job growth (real-time data)	0.21 (0.27)

I also tried predicting weekly mortgage changes on the basis of various interest rate spreads as they were available at the beginning of the preceding week. The table above shows that none of these, nor previous employment growth, would help you to forecast where mortgage rates will go next week.

This suggests that weekly changes in mortgage rates are primarily driven by some kind of new information that is arriving during the week. But what is the nature of that new information? One interesting candidate is the news that arrives each day about what the Fed is likely to do over the next few months, as summarized by that day’s change in near-term fed funds futures prices.

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). Although in principle there is separate information in each of these numbers, as a practical matter they contain much in common– the correlation between f_2d and f_3d, for example, is 0.90. For purposes of interpreting regression coefficients (which give answers to questions like, if x changes with z held fixed, what happens to y), I found it useful to summarize these effects in terms of the level of the near-horizon term structure of fed funds futures (measured by f_2d), the slope (measured by f_3d – f_2d), and the curvature (f_3d – 2f_2d + f_1d), which are relatively uncorrelated with each other.

I then regressed each week’s mortgage rate change on a constant, changes in mortgage rates over the last three weeks, and changes in the level, slope and curvature for each of the 13 most recent days, starting from the day on which the mortgage data were released (Thursdays under the current system, Fridays prior to 2004). The resulting coefficients, along with 95% confidence intervals, are summarized in the graphs below.

Coefficients relating weekly change in mortgage rates to changes in level, slope and curvature of near-term fed funds futures for 13 most recent days counting backward from the release date

The first striking thing about this figure is that none of the coefficients on days 1, 2, or 3 (corresponding to Thursday, Wednesday, and Tuesday, respectively, in the current reporting system) are statistically significant. Although the mortgage rates are released on Thursday, Freddie Mac tells me they actually stop collecting numbers on Wednesday, and most of their data come in on Monday and Tuesday. Furthermore, I’m guessing that many of the numbers reported on Tuesday are actually set on Monday. It would be physically impossible for a Monday mortgage rate to reflect information that nobody would have, and, according to the evidence I discussed previously, nobody could predict, until Tuesday, Wednesday, or Thursday. That view is clearly supported by these estimates.

The martingale theory of mortgage rates further implies that any information available prior to the preceding Monday should already have been incorporated into last week’s mortgage rates, so that the coefficients on lags 9, 10, 11, 12, and 13 should all be zero. Again this hypothesis is accepted on the basis of these data.

If there is a single effect that any given day’s change in the fed funds level has on that day’s mortgage rate, it would show up in the same coefficient being found in a regression of the weekly change in the mortgage rate on each of the intervening daily changes in the level for days 4, 5, 6, 7, and 8. Under this interpretation, the above regression provides 5 independent estimates of this single magnitude. Again the hypothesis that these 5 coefficients are the same is accepted. That common value is about 0.5, meaning that if there is an unanticipated 10-basis-point increase in the level of the near-horizon term structure of fed funds rates, long-term mortgage rates will rise by about 5 basis points. Likewise we accept the hypothesis that the slope coefficient is the same on all 5 relevant days. This coefficient is estimated to be 1.3, meaning that if the Fed unexpectedly enters a tightening mode, so that it is now expected to raise the rate 10 basis points per month for each of the next few months, mortgage rates would increase by 13 basis points.

Changes in the curvature appear to have no implications for mortgage rates.

I arrived at very similar estimates of these magnitudes in a number of different ways. One strategy was to use only those changes in the level or slope that occurred on days that
Fed researchers Refet Gurkaynak, Brian Sack, and Eric Swanson associated with major announcements of changes in monetary policy. I also found the same estimates emerging as one aggregates the data into weeks or months.

As an illustration of what these relations imply, consider the behavior of interest rates over this last summer. At the beginning of July, traders were anticipating a hike from the then-prevailing 5.25% up to 5.5% by the fall. Over the next two months, the market changed this assessment, becoming persuaded (correctly, as it turned out) by the end of August that no rate changes would be forthcoming. Over this period, the level of the near-horizon fed funds term structure declined by 14 basis points, which would lead us to anticipate a 7 basis point decline in mortgage rates. The slope fell by 4 basis points, which would cause a further 5.2 basis-point drop in mortgage rates. Putting these two together, one would have anticipated a 12.2 basis-point decline in mortgage rates during July and August. In the event, mortgage rates declined by 32 basis points. In other words, about a third of the decline can be attributed to the market’s changing assessment about what the Fed was going to do over the very near term.

Changing assessments about more intermediate-term Fed policy were surely also important, though the methodology described here does not give us a direct measure of that component.

The overall view supported by this research is that mortgage rates already incorporate an anticipation of what the Fed is going to do next. The only way the Fed can change mortgage rates is by doing something other than what the market previously anticipated. However, if the Fed can credibly signal a change in its near-term intentions, that information will translate immediately into a change in interest rates, and need not wait until the Fed actually acts.

Although the mortgage rate itself appears to respond in an immediate, anticipatory way to Fed policy, the effects of a change in the mortgage rate will then take a considerable amount of time before they affect the economy. I will take up this issue in my next post on this topic.

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