A federal funds rate equation.

Mehra, Yash P.

I. INTRODUCTION

This paper estimates a monetary policy reaction function that explains the behavior of the federal funds rate during the period 1979 to 1992. This funds-rate equation consists of two pans: a long-run part and a short-run part. The long-run part, which assumes that the funds rate moves one-for-one with the inflation rate and that the real funds rate is mean stationary, determines the long-run, equilibrium component of the funds rate. In the short run, however, the funds rate differs from its long-run equilibrium value. The short-run part has the feature that the funds rate rises if real GDP is above potential GDP, if inflation rises, or if the long-term bond rate rises.

The funds rate equation is estimated with and without a money variable. Money growth, when included in the equation, is highly significant, indicating that money also influenced policy. The results also indicate, however, that in recent years the Fed has discounted the leading indicator properties of money.

The plan of this paper is as follows. Section II discusses the premises that underlie the federal funds-rate equation estimated here. Section III presents empirical results, and section IV contains conclusions and summarizes the findings.

II. THE MODEL AND THE METHOD

A Discussion of the Determinants of the Federal Funds Rate

The federal funds-rate equation studied here has a long-run part and a short-run part. Equation (1) specifies the long-run economic determinants of the funds rate:

(1) [Mathematical Expression Omitted]

where FR is the funds rate; [rr.sup.*] is the economy's underlying equilibrium real rate; and [p.sup.*] is the long-term expected inflation rate. The equilibrium real rate [rr.sup.*] can be viewed as the rate which equates the flows of desired saving and investment in the economy. Equation (1) says that the nominal federal funds rate depends upon the economy's underlying real rate and expected inflation. This relationship, which holds in the long run, hypothesizes that the Fed lets the funds rate move with the real rate plus the long-term inflation rate expected by the public. Failure to hold this equality in the long run results in monetary accelerations and rising inflation or monetary deceleration and deflation.

In the short run, however, the funds rate can differ from the long-run equilibrium value determined in (1) for a number of reasons. Both the real rate and long-term expected inflation are unobservable variables. The Fed has to track them in the short run, which it may do by focusing on the behavior of observables such as actual money, real growth, inflation etc. More importantly, the Fed may have some short-run objectives pertaining to real growth and inflation, resulting in funds-rate policy actions different from those dictated by (1).

How will one then specify a short-run federal funds-rate equation? Most studies of the policy reaction function summarized in Khoury [1990] indicate that the Fed "leans against the wind" - tightening or easing money growth in response to increases or decreases in inflation, labor market tightness and income. This aspect of Fed behavior is generally captured by including the unemployment rate and/or increases in income in the reaction function. I hypothesize instead that the Fed reacts to deviations of actual GDP over potential GDP rather than to changes in GDP. This specification reflects the assumption that the Fed's lean-against-the-wind procedures for adjusting the funds-rate target are gradual and display considerable short-run persistence. For example, during cyclical expansions the Fed generally ratchets up its funds-rate target gradually and only after growth in GDP is well established.(1) This means during expansions the funds rate does not always move up as soon as real growth becomes positive, thereby weakening the empirical link between movements in the funds rate and changes in GDP. Furthermore, the Fed may begin to worry about the inflation implications of real growth when real GDP is above potential.(2) These considerations suggest that in the short run the funds rate may be correlated more with deviations in output as measured from some potential than with changes in real output.(3) Hence, this paper follows Taylor [1993] and investigates a funds-rate equation that focuses directly on real output and inflation as in (2):

(2) [Mathematical Expression Omitted]

where y is real GDP, [y.sup.*] is potential GDP, [FR.sup.*] is the long-run equilibrium funds rate and [[Epsilon].sub.t] is a random disturbance term. Equation (2) implies that in the short run the Fed targets real GDP and changes in inflation. The Fed raises the funds rate if real GDP rises above potential GDP, or if expected inflation accelerates. The parameters [d.sub.2] and [d.sub.3] measure the vigor with which monetary policy "leans against the wind": the larger are [d.sub.2] and [d.sub.3], the more vigorously the Fed moves the funds rate in response to deviations of output from potential and accelerations in expected inflation.

While the Fed is free to pursue its short-run objectives, its short-run behavior is assumed to be constrained by the long-run relation postulated in (1). Thus, equation (2) also assumes that the Fed raises the funds rate if the actual funds rate is below its long-run equilibrium value. The parameter [d.sub.1] measures the vigor with which the Fed keeps the actual level of the funds rate in line with its long-run equilibrium value. If this parameter is unity, then the funds-rate equation given in (2) can be expressed as in (3).

(3) [Mathematical Expression Omitted].

As can be seen, the actual funds rate differs from its long-run equilibrium value only to the extent that the Fed pursues some short-run objectives. If the Fed achieves such objectives (y = [y.sup.*], [Mathematical Expression Omitted]), the proper funds rate equals the real rate plus the long-term inflation rate expected by the public.

Data, Definition of Variables, and Empirical Specifications of the Funds Rate Equation. The empirical work uses quarterly data over 1954:Q3 to 1992:Q4. The long-run part of the funds-rate equation estimated here is given in (4):

(4) [FR.sub.t] = a + b[p.sub.t] + [U.sub.t]

where FR is the actual, nominal federal funds rate (average for the quarter), p is the actual, annualized quarterly inflation rate measured by the behavior of the implicit GDP deflator, and U is a stationary random disturbance. Specification (4) thus assumes that actual inflation is a good proxy for long-term, expected inflation and that the random disturbance term is stationary. The parameter b measures the long-run response of the funds rate to inflation. If this parameter is unity, then the real federal funds rate ([FR.sub.t] - [p.sub.t] [equivalent to] a + [U.sub.t]) is mean stationary. Under these assumptions, the long-run equilibrium nominal funds rate equation may be expressed as follows:

[Mathematical Expression Omitted]

where [Mathematical Expression Omitted] is the mean real funds rate.

The short-run funds-rate equation given in (3) requires proxies for the equilibrium funds rate ([FR.sup.*]), the long-term expected inflation rate ([p.sup.*]), and potential GDP ([y.sup.*]). The empirical work here calculates the equilibrium funds rate ([FR.sup.*]) from equation (4). As indicated above, actual inflation (p) is used as a proxy for long-term expected inflation ([p.sup.*]).

The variable (y - [y.sup.*]/[y.sup.*]) requires an empirical proxy for the Fed's estimate of potential GDP, defined as the level of output that the Fed perceives to be consistent with noninflationary pressures in the economy. Here I proceed under the hypothesis that the Fed's estimate of potential GDP is given by the trend level of GDP and that trend growth had been constant. I approximate it by fitting a linear trend to real GDP over 1954:Q3 to 1992:Q4. I do however examine the sensitivity of results to some alternative hypotheses about the Fed's estimate of potential GDP. It is widely believed that the labor productivity slowdown of the 1970s reduced potential GDP and hence may have contributed to the decline in the trend growth rate of real GDP observed since then. Hence, following Perron [1989] I alternatively estimate the trend level of GDP allowing a break in its trend growth rate beginning with the period of exogenous oil price shocks. Others have estimated potential GDP using Okun's law in which estimates of potential output require estimates of the natural unemployment rate. One such procedure, given in Braun [1990], generates estimates of potential GDP in which the trend growth rate of real GDP declines in several steps during the sample period. I also examine results using one such series on potential GDP.

Goodfriend [1993] has convincingly argued that in order to establish and maintain credibility the Fed has reacted to the information the long-term bond rate contains about long-term, expected inflation. The empirical work here captures this reaction by including in equation (3) an additional variable measured as the ten-year bond rate (R10) minus the actual inflation rate (p).(4) This variable provides information about long-term expected inflation that is not in the actual inflation rate. Hence, the short-run funds-rate equation estimated is of the form

(5) [Mathematical Expression Omitted]

where all variables are as defined before. Lagged values of changes in the funds rate included in (5) capture short-run dynamics of the funds rate behavior. If the Fed does not smooth interest rates and adjusts its funds-rate target rapidly in response to the short- and long-run economic variables discussed above, then changes in the funds rate are likely to be serially uncorrelated. Furthermore, the Fed is assumed to react to known information, so that only lagged values of inflation and real output are included in the funds-rate equation, except for the long-term bond rate that enters contemporaneously.

III. EMPIRICAL RESULTS

A Short-run Funds Rate Equation

Empirical work pertaining to the long-run funds-rate equation indicates that there exists a cointegrating relationship between the funds rate and the inflation rate and that the Fed adjusts the funds rate one-for-one with inflation in the long run. Hence the real funds rate is mean stationary. It also appears that the long-run equation may have shifted once during the sample period and the date of shift is close to the fourth quarter of 1979, when the Fed changed its monetary policy operating procedures.(5) Hence the short-run funds-rate equation (5) is estimated including post-1979 slope dummies. Since the bond rate enters contemporaneously in (5), the equation is also estimated using instrumental variables.

Table I presents ordinary least squares (OLS) and instrumental variables (IV) estimates of the short-run funds-rate equation (5) over 1955:Q4 to 1992:Q4.(6) Since the OLS estimates are similar to the IV estimates, the discussion hereafter focuses on the OLS estimates. (All standard errors have been corrected for the possible heteroscedascity of the regression error.) The coefficients that appear on various economic variables are strikingly different over the pre- and post-1979 sample periods. In particular, the estimates indicate that for the sample period 1955:Q4 to 1979:Q3 the funds-rate equation is

[Delta][FR.sub.t] = -.07 [(FR - [FR.sup.*]).sub.t-1] + .04 [(lny - [lny.sup.*]).sub.t-1]

+ .57 [Delta][FR.sub.t-1] - .38[Delta][FR.sub.t-2].

For the period 1979:Q4 to 1992:Q4 the funds-rate equation is

[Delta][FR.sub.t] = -.35 [(FR - [FR.sup.*]).sub.t-1]

+ .26[(lny - [lny.sup.*]).sub.t-1] + .30 [Delta][p.sub.t-2]

+ .23 [(R10 - p).sub.t] + .10 [Delta][FR.sub.t-1]

- .38 [Delta][FR.sub.t-2].

Thus, during the sample period 1979:Q4 to 1992:Q4 the funds rate moved strongly in response to the discrepancy between the actual funds rate and its long-run equilibrium value, cyclical expansions in real GDP, accelerations in actual inflation, and the long-term bond rate.

The responses of the funds rate to the above mentioned economic variables are either weak or nonexistent before 1979. In particular, the funds-rate equation presented above indicates that during the pre-1979 sample period the funds rate responded weakly to discrepancies between the actual funds rate and its long-run equilibrium value and responded not at all to accelerations in actual inflation. The coefficient that appears on the cyclical expansion variable in the funds-rate equation is small, though statistically significant. One possible explanation of these results is that the Fed may have focused during this subperiod on some other indirect measures of real growth and/or inflation. McNees [1992] has in fact presented evidence that the Fed paid considerable attention to money growth between 1970 and 1992. To test robustness, the funds-rate equation here is also estimated including money. Following McNees [1992], money is defined by M2 over 1982:Q4 to 1992:Q4 and by M1 over the period before, and slope coefficients on money growth are assumed to be different during the subperiods 1955:Q4 to 1979:Q3, 1979:Q4 to 1982:Q3, and 1982:Q4 to 1992:Q4.

The funds-rate equation estimated including money is also presented in Table I. As can be seen, money growth is highly significant. Including money in the reaction function reduces somewhat the magnitudes of coefficients that appear on inflation and real output, including the bond rate. Nevertheless, direct measures of inflation and real output remain significant in the reaction function that spans 1979:Q4 to 1992:Q4.

[TABULAR DATA FOR TABLE I OMITTED]

Examining the Predictive Ability of the Federal Funds-Rate Equation over 1979 to 1992. This section examines whether funds-rate equations reported in Table I are consistent with the actual path of the federal funds rate during the period 1979:Q1 to 1992:Q4.(7) The equations given in Table I are re-estimated by OLS over 1955:Q4 to 1986:Q4 and then dynamically simulated over 1979:Q1 to 1992:Q4.(8)

Predicted values of the funds rate generated using the funds-rate equation without money are reported in column (2) of Table II and those generated using the equation with money are in column (5). As can be seen, the funds-rate equation with money tracks the actual path of the funds rate somewhat better than does the one without money. Both the mean error and the root mean squared error decline when money is included in the funds-rate equation (see Table II). The reason is that the funds-rate equation with money explains the actual path of the funds rate during the early part of the 1980s much better than does the one without money. Including money in the funds-rate equation reduces substantially the size of the prediction error that occurs over the subperiod 1979 to 1982 (compare columns (2) and (5), Table II).

In order to evaluate further the role of money in the funds-rate equation, Table II presents dynamic simulations of the funds rate over the shorter sample period 1987:Q1 to 1992:Q4 examined by Taylor [1992]. Predicted [TABULAR DATA FOR TABLE II OMITTED] values given in column (3) are from the funds-rate equation without money and those in column (4) from the one with money.(9) As can be seen, during this period the funds-rate equation without money tracks better the actual path of the funds rate than does the one with money. Both the mean error and the root mean squared error rise when money is included in the funds-rate equation.

One explanation of the results presented above is that the Fed may have discounted in recent years the leading indicator properties of money as measured by M2. The evidence reported in Carlson and Parrott [1991] and Mehra [1992] indicates that the relationship between M2 demand and its traditional determinants (such as income, prices and interest rates) has deteriorated in recent years. Hence, the reaction function that focuses directly on prices and real output (including the bond rate) can describe actual policy in recent years much better than the one that also includes money, a finding that is similar in spirit to that of Taylor [1992].

Figure 1 highlights the role of the bond rate in predicting the behavior of the funds rate during the period 1979 to 1992. The upper panel in this figure graphs the funds rate predicted with and without the bond rate in the funds-rate equation.(10) Actual values of the funds rate are also charted there. The lower panel graphs changes in the funds rate that are predicted by the bond rate against changes in the bond rate. This figure suggests two observations. First, the bond rate is quantitatively important in predicting the funds rate over 1979 to 1992. The funds-rate equation without the bond rate seriously underpredicts the level of the funds rate (see the upper panel). Second, movements in the funds rate accounted for by movements in the bonds rate are significant in 1981, 1983-1984, and 1987. These periods coincide with what Goodfriend [1993] calls periods of inflation scare.

Sensitivity Analysis. The funds-rate equations reported in Table I are estimated under some key assumptions about the Fed's behavior. I now examine how sensitive results are to some changes in those assumptions.

The Fed's lean-against-the-wind strategy is captured here by assuming that the Fed reacts to discrepancies between actual GDP and the trend level of real GDP as opposed to changes in the unemployment rate or income. In order to examine robustness with respect to the exclusion of these variables the short-run equations were re-estimated including these additional economic variables and then simulated over 1979 to 1992 as in Table II. These additional economic variables appear with coefficients that are correctly signed and statistically significant. Thus, the funds rate rises when the unemployment rate falls or real growth increases. However, these additional economic variables do not help in improving the out-of-sample forecast performance of the equation.(11) This result indicates that the Fed's reaction to cyclical expansions is better captured by the specification chosen here.(12)

Another key assumption made here is that the Fed's estimate of potential GDP is given by the trend level of GDP and that the latter can be approximated by the constant trend growth rate of real GDP. I now examine results under the alternative assumption that the trend growth of GDP may have declined following the oil price shocks of the 1970s. Following Perron [1989] I allowed a break in the trend rate of GDP beginning in 1973. The funds rate equations were re-estimated using this new measure of the trend level of GDP and then dynamically simulated over 1979 to 1992 as in Table II. The short-run equations based on this measure of trend GDP are similar to those reported in Table I and do somewhat better in predicting the actual behavior of the funds rate over 1979 to 1992 (the root mean squared errors are somewhat lower than those reported in Table II). Finally, I also estimated equations using the trend level of GDP generated by the method of Braun [1990].(13) The results using this measure of trend GDP are mixed. While this measure worsens the out-of-sample performance of short-run equations reported in Table I, that is not the case with the short-run equations estimated over 1970 to 1992 (see below).

The short-run equations in Table I are estimated over the period that includes the late-1950s and 1960s. During most of the 1950s and 1960s the Fed's attention was focused more on free reserves and money market rates in general than on the federal funds rate. To test robustness, the funds-rate equation is also estimated excluding the 1950s and 1960s. Table III presents such equations estimated over 1970:Q4 to 1992:Q4. The long-run part of the funds rate is still measured as the inflation rate plus the mean real funds rate, the latter now approximated by its sample mean over 1970:Q1 to 1992:Q4. Furthermore, the equations are reported with and without allowing breaks in trend growth of real GDP and include money growth. As can be seen, these equations yield conclusions that are broadly similar to those generated by equations estimated over 1954:Q3 to 1992:Q4. In particular, the equations indicate that during the sample period 1979:Q4 to 1992:Q4 the funds rate responded strongly to cyclical expansions in real GDP, accelerations in actual inflation, and increases in the long-term bond rate and the long-run equilibrium funds rate.(14) Furthermore, parameter estimates are robust with respect to how the trend component of GDP is measured.(15) Figure 2 compares the dynamic forecasts of the funds rate generated using these two alternative measures of trend GDP (Table III). As can be seen, both these equations do well in predicting the actual path of the funds rate over 1979 to 1992.

IV. CONCLUDING OBSERVATIONS

Previous work has found that the federal funds rate and the inflation rate are cointegrated during the sample period 1954:Q3 to 1992:Q4. These results indicate that the Fed adjusts the funds rate one-for-one with the actual inflation rate in the long run.(16) In the short run, however, the funds rate differs substantially from the value given by this cointegrating relationship. Furthermore, in the short run the funds rate has responded to some direct and indirect measures of inflation and real GDP, the two final goal variables the Fed cares about.

These short-run responses have not been stable over time. In particular, the evidence reported here indicates that the actual behavior of the funds rate during most of the 1980s is well predicted by a reaction function in which the funds rate rises if real GDP is above potential GDP, if actual inflation accelerates, or if the long-term bond rate and the equilibrium funds rate rise. Some of these short-run responses are found to be weak before 1979.

[TABULAR DATA FOR TABLE III OMITTED]

The results here, however, do not rule out the potential role of some other economic variables in the reaction function. In fact, I have considered several extensions. However, many of these expanded equations do not help in improving the out-of-sample forecasts of the funds rate over 1979 to 1992, with the possible exception of one which includes money. That result indicates that the funds-rate equation (with money) identifies the major determinants of the funds-rate during this subperiod.

The views expressed are those of the author and not necessarily those of the Richmond Fed or the Federal Reserve System. The author thanks Tim Cook, Marvin Goodfriend, Robert Hetzel, Bennett McCallum, and two anonymous referees for many useful comments.

1. Hetzel [1995] discusses this issue in great detail.

2. The idea that output in excess of potential output leads to rising inflation is an important component of inflation models built on the Phillips curve and monetarist traditions. Therefore, the behavior of actual GDP over potential GDP may be a significant factor in monetary policy deliberations as in Boschen and Mills [1990].

3. The output gap may in fact be a proxy for the unemployment rate because the former is related to the latter via Okun's [1970] law. Nevertheless, I do examine the robustness of the chosen specification with respect to the exclusion of the unemployment rate or changes in real GDP.

4. The empirical work uses the data on real GDP and the implicit GDP deflator that reflect latest revisions, assuming that data revisions are unlikely to alter the long-run secular nature of the series. The interest rate data are averages for the quarter. All the data are from Citibank's data base, except the series on potential GDP which is based on the method of Braun [1990].

5. This work is laid out in an appendix available from the author.

6. In instrumental variables regressions I use the lagged values of the economic variables included in the reaction functions as instruments. Thus, the instruments used in the reaction function (without money) are a constant, one-period lagged values of [(FR-[FR.sup.*]).sub.t] [(lny - [lny.sup.*]).sub.t], and [(R10 - p).sub.t], two-period lagged values of [Delta][p.sub.t], and two lagged values of [Delta][FR.sub.t]. The instruments for interactive-dummy variables enter similarly.

7. The federal funds-rate equation reported here is less successful in tracking the actual behavior of the funds rate during the pre-1979 period.

8. Simulations are partly within- and partly out-of-sample. The out-of-sample period 1987:Q1 to 1992:Q4 chosen here is the one studied by Taylor [1992] and happens to span most of Greenspan's term as Fed Chairman. These simulations thus implicitly assume that reaction functions display stable parameters over the period 1979:Q4 to 1992:Q4 that spans Volcker's and Greenspan's terms as Fed Chairman.

9. Predicted values use OLS regressions estimated over rolling horizons and are the dynamic, one-year-ahead sample forecasts conditional on actual values of other economic variables. The forecasts are generated as follows. The reaction functions are initially estimated over 1955:Q4 to 1986:Q4 and then dynamically simulated over 1987:Q1 to 1987:Q4. The end of the estimation period is then advanced four quarters, reaction functions re-estimated and forecasts prepared as above. This process is repeated until the end of the estimation period reaches 1991:Q4.

10. These predictions, which use the funds-rate equation without money reported in Table I, were generated as follows. The funds rate predicted including the bond rate is given by the dynamic simulations of the funds-rate equation in which the bond rate takes the historical values over the simulation period 1979:Q4 to 1992:Q4. The funds rate predicted without the bond rate is then given by the dynamic simulations in which the bond rate is held fixed at the 1979:Q4 value during the simulation period. The differences between these two sets of simulations give predictions of the funds rate that are due to the bond rate.

11. Both the mean error and the root mean squared error rise when the expanded funds-rate equations are dynamically simulated over 1979 to 1992.

12. I also examined the potential role of oil price shocks and exchange rate changes in the funds-rate equation. The main criterion used is whether these variables help improve the out-of-sample forecasts of the funds rate over 1979 to 1992. The possible impact of oil price shocks was examined by including oil price dummies. The impact of exchange rate changes was examined by including first differences of the relative price of imports (defined as the log ratio of the implicit price deflator for imports to the implicit GDP deflator). The oil price dummy was generally insignificant. The economic variables measuring changes in the relative price of imports were generally significant in the funds-rate equation. However, the expanded funds-rate equation did not aid in improving the out-of-sample forecasts of the funds rate over 1979 to 1992.

13. As indicated before, this procedure generates estimates of potential GDP in which trend growth declines from about 3.5% to about 2.5% in several steps over 1954:Q3 to 1992:Q4. In particular, trend growth is 3.5% over 1954 to 1965:Q2, 3.0% over 1965:Q3 to 1973:Q4, 2.6% over 1974:Q1 to 1990:Q2, and 2.4% over 1990:Q3 to 1992:Q4.

14. There are some differences. The funds-rate equations estimated over the shorter sample period 1970:Q4 to 1992:Q4 indicate rather strong responses of the funds rate to cyclical expansions and the bond rate even before 1979:Q4. In general, the funds rate equation estimated over 1970:Q1 to 1992:Q4 is more robust with respect to changes in specification than the one estimated over 1954:Q3 to 1992:Q4.

15. Additional variables such as the unemployment rate or changes in income do not aid in improving the out-of-sample forecasts of such equations over 1979 to 1992. To save space I do not report such results.

16. These results are available from the author in a separate appendix.

REFERENCES

Boschen, J., and L. Mills. "Monetary Policy with a New View of Potential GDP." Federal Reserve Bank of Philadelphia Business Review, August 1990, 3-10.

Braun, Steven N. "Estimation of Current-Quarter Gross National Product by Pooling Preliminary Labor-Market Data." Journal of Business and Economic Statistics, July 1990, 293-304.

Carlson, John B., and Sharon F. Parrott. "The Demand for M2, Opportunity Cost, and Financial Change." Federal Reserve Bank of Cleveland Economic Review, 27(Q2), 1991, 2-11.

Goodfriend, Marvin. "Interest Rate Policy and the Inflation Scare Problem 1979-1992." Federal Reserve Bank of Richmond Economic Quarterly, Winter 1993, 1-24.

Hetzel, Robert L. "Why the Price Level Wanders Aimlessly." Journal of Economics and Business, May 1995, 151-63.

Khoury, Salwa S. "The Federal Reserve Reaction Function: A Specification Search," in The Political Economy of American Monetary Policy, edited by Thomas Mayer. Cambridge: Cambridge University Press, 1990, 27-49.

McNees, Stephen K. "A Forward Looking Monetary Policy Reaction Function: Continuity and Change." New England Economic Review, November/December 1992, 3-13.

Mehra, Yash P. "Has M2 Demand Become Unstable?" Federal Reserve Bank of Richmond Economic Review, September/October 1992, 27-35.

Okun, A.M. The Political Economy of Prosperity. Washington, D.C.: The Brookings Institution, 1970.

Perron, Pierre. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis." Econometrica, November 1989, 1361-1401.

Taylor, John B. "Discretion versus Policy Rules in Practice." Carnegie-Rochester Conference Series on Public Policy, December 1993, 195-214.

Yash P. Mehra: Vice President and Economist, Federal Reserve Bank of Richmond, Phone 1-804-697-8247 Fax 1-804-697-8255, E-mail elypm01@frb.org