The Information Content of Surprise Changes in the Fed Funds Futures Rate: Are They Monetary Shocks?

The Information Content of Surprise Changes in the Fed Funds Futures Rate: Are They Monetary Shocks? Wei Li January 20, 2014 Abstract Surprise changes in the Fed funds futures rate due to policy actions are widely used to gauge monetary shocks in the literature. This paper documents that the surprise changes exhibit the price puzzle usually found in monetary VAR models. A decomposition shows that the surprise changes are not clean monetary shocks, but rather contaminated by (1) information shocks due to an information gap between the Fed and the market on the current state of the economy, and (2) revisions in risk premia. The contamination is substantial. Up to 30% of variations in the surprise changes can be explained by information differences between the Fed and the market. Controlling for information differences largely alleviates the price puzzle. The contamination is also harmful. An example shows that the contamination may mislead our understanding of the response of market interest rates to monetary policy. 1 Introduction Surprise changes in the federal funds futures rate in response to the Fed s announcements of the target funds rate (henceforth, futures rate surprises) have been widely used in the literature to measure monetary shocks. Futures rate surprises are usually constructed as changes in current-month or one-month-ahead federal funds futures rate in a short time window around FOMC announcements of the target funds rate. Kuttner (2001) first constructs futures rate surprises and uses them to identify responses of market interest rates to monetary policy. Faust, Swanson and Wright (2004) use futures rate surprises to help identify monetary VAR models. Bernanke and Kuttner (2005) Wei Li, Erasmus University Rotterdam and Tinbergen Institute, H08-32, Burg. Ouldlaan 50, 3062 PA, Rotterdam, The Netherlands. Tel: +31 1040 88926. Email: w.li@ese.eur.nl. I thank Casper de Vries for his very valuable guidance. I am very grateful to Justinas Brazys and Clara Vega for sharing data with me. I thank participants at Tinbergen Institute, RES Postgraduate Meeting, and T2M Conference for helpful comments and suggestions. 1

use them to study the impact of monetary policy on equity returns. It seems that futures rate surprises have become a standard market-based measure of monetary policy shocks. 1 Though many papers use them, surprisingly few study their properties, in particular, whether they are a good measure of monetary shocks. 2 This paper studies the information content of futures rate surprises. It begins by documenting that responses of inflation and its forecasts to a positive futures rate surprise are substantial and significantly positive. The pattern is robust across a variety of specifications. The positive response contradicts predictions of typical monetary economic models, which usually predict that a tightening monetary policy lowers inflation and inflation expectations. The futures rate surprise thus exhibits the price puzzle usually found in parsimonious monetary VAR models. For this reason, it may be that futures rate surprises are not a clean measure of monetary shocks, just like monetary shocks identified by VAR models. So, what are contained in futures rate surprises? To answer this question, I follow Kuttner (2001) and express the futures rate in terms of the target funds rate and risk premia. Different from Kuttner (2001) however, I show that futures rate surprises are monetary shocks compounded with (1) information shocks, which are market s unanticipated policy changes due to information difference between the market and the Fed, and (2) revisions in risk premia upon the observation of the Fed s actions. I quantify the contamination. To this end, I first regress futures rate surprises on the Fed s information set proxied by Greenbook forecasts for current-quarter growth rate and inflation. Futures rate surprises are found not orthogonal to the Fed s information set. About 15% of the surprises can be accounted for as the Fed s reaction to the state of the economy. To further show information differences between the Fed and the market matter, I regress futures rate surprises on differences between the Fed s and the market s forecasts for current-quarter growth rate and inflation. It turns out that information differences matter, both statistically and economically. Forecast differences between the Fed and the market account for up to 30% of variations in futures rate surprises. This paper further studies the sources of contamination. To empirically disentangle information 1 Futures rate surprises are also employed to measure monetary shocks in the following researches. Faust, Rogers, Swanson and Wright (2003) use futures rate surprises to identity effects of monetary shocks on exchange rates; Gürkaynak, Sack and Swanson (2005b) study responses of long-term interest rates to monetary shocks. Barakchian and Crowe (2013) estimate the impact of monetary shocks on output; Gorodnichenko and Weber (2013) study responses of return volatilities to monetary shocks of firms with different levels of price stickiness. 2 There are a few exceptions. Faust, Swanson and Wright (2004) document that futures rate surprises do not contain the Fed s private information on macroeconomic indicators of the last month (or quarter) that are released after the futures rate surprises. Piazzesi and Swanson (2008) argue that, as a measure of monetary shocks, futures rate surprises are free of contamination of risk premia. 2

shocks and revisions in risk premia, I use two survey data to measure market s expected target funds rate that is not adjusted for risk premia. I find evidence for both information shocks and revisions in risk premia. Specifically, information shocks are tested by the fact that information difference between the Fed and the market predicts survey forecast errors in the target funds rate. Revisions in risk premia are tested indirectly as difference between futures rate surprises and survey forecast errors in the target funds rate. I find revisions in risk premia are substantial and explained by information difference between the Fed and the market. Having documented that futures rate surprises are contaminated monetary shocks, it is thus natural to ask whether the contamination is responsible for the price puzzle? To answer this question, I clean futures rate surprises by removing from them information shocks identified by forecast differences in current-quarter growth rate and inflation. This simple cleaning largely alleviates the price puzzle. In the best case, responses of inflation and its forecasts to the cleaned futures rate surprises become insignificant. The price puzzle implies that the contamination can substantially alter the impact of monetary shocks on macroeconomic variables. It is also interesting to ask whether the contamination affects our understanding of the impact of monetary policy on the financial market. To this end, I reconsider Kuttner s (2001) seminal work on monetary policy surprises and market interest rates. I find that yields on Treasuries with maturities longer than one year do not respond to monetary shocks at all, if monetary shocks are measured by a subsample of futures rate surprises that are clearly contaminated. This contradicts sharply with Kuttner (2001), who shows that yields on Treasuries at all maturities respond significantly to monetary shocks measured by futures rate surprises. The contradiction indicates measuring monetary shocks from futures rate surprises may mislead our understanding on responses of market interest rates to monetary policy. The remainder of the paper is organized as follows. Section 2 documents irregular responses of inflation and its forecasts to futures rate surprises, and discusses implications of the irregularities. Section 3 decomposes futures rate surprises using the expectations hypothesis and shows that futures rate surprises are monetary shocks contaminated by information shocks and risk premium revisions. Section 4 assess the magnitude of the contamination. Section 5 empirically investigates information shocks and risk premium revisions. Inflation responses to cleaned monetary shocks are shown in Section 6. Section 7 revisits Kuttner s (2001) study of monetary policy surprises and market interest rates. Section 8 concludes the paper. 3

2 Irregularities: Responses of Inflation to Futures Rate Surprises To be a measure of monetary shocks, futures rate surprises need to behave like monetary shocks. In particular, positive surprises should have negative effects on inflation. I investigate responses of actual inflation and inflation forecasts to futures rate surprises. The data are quarterly, from 1990Q1 to 2007Q4. Quarterly futures rate surprises are surprise changes in the current-month federal funds futures rate associated with middle-quarter FOMC actions. 3 Futures rate surprises are obtained from Gürkaynak, Sack and Swanson (2005a). 2.1 Responses of Actual Inflation to Futures Rate Surprises I study the impact of the futures rate surprises by estimating a model as π t = α 0 + K b i π t i + i=1 J c j f t j + ε t, (1) where π t is an inflation measure, f t is the futures rate surprise. As in Romer and Romer (2004), who use this model to study inflation and output responses to their monetary shock estimate, lags of π t are included to capture the normal dynamics of inflation, and lags of f t are included to capture the direct impact of futures rate surprises on inflation. 4 j=1 In the baseline model, π t is measured by CPI inflation, and eight lags of inflation and the futures rate surprise are included. I summarize the results by examining the response of the level of log price index to a one-time realization of futures rate surprise of one percentage point. The estimated response of the log price index after one quarter is c 1. The estimated response after two quarters is c 1 + c 2 + b 1 c 1 ; and so on. 5 Figure 1 plots the response together with its bootstraped 68% and 95% confidence intervals. It is shown that the response of CPI to a positive surprise is positive, substantial and significantly different from zero. A positive, one-percent futures rate surprise raises CPI by 9.30% in 4 years. The irregular response of inflation to futures rate surprises is robust to different measures of inflation. Core CPI and core PCE index increase by 12.75% and 6.33%, respectively in 4 3 In one quarter, there are usually two futures rate surprises associated with scheduled FOMC actions, and occasionally some surprises associated with FOMC intermeeting actions. For example, the first quarter of 2001 saw three surprises on January 3, January 31, and March 20, respectively. The first surprise is due to an intermeeting action, and the last two are associated with scheduled FOMC actions. I measure the futures rate surprise in 2001Q1 as the one on January 31, which is in the middle of the quarter. 4 The contemporaneous futures rate surprises is not included by assuming monetary shocks do not affect inflation within the quarter. Allowing for contemporaneous response have little effect on the main results. 5 Note that the response of inflation one quarter after the impact is c 1, and the response two quarters after the impact is c 2 + b 1c 1. The response of log price level equals to cumulated inflation response. Thus, the response of log price index after two quarters is c 1 + c 2 + b 1c 1. 4

years in response to a positive, one-percent futures rate surprise. PCE index and GDP implicit deflator respond positively and significantly on impact to a positive futures rate surprise, though the responses become insignificant after one year. 2.2 Responses of Inflation Forecasts to Futures Rate Surprises To investigate the response of inflation forecasts to futures rate surprises, I estimate a model similar to (1), K J π t+1 t = α 0 + b i π t+1 i t i + c j f t j + ε t, (2) i=1 j=1 where π t+1 t is the one-quarter-ahead CPI inflation forecast from the Survey of Professional Forecasters. Again, eight lags of π t+1 t and f t are included. The results are summarized by responses of implied forecasts for log CPI index to a onepercent futures rate surprise. Figure 2 plots the response together with its bootstraped 68% and 95% confidence intervals. It seems that forecasters expect a 11.34% increase in CPI in 4 years in response to a positive, one-percent futures rate surprise. The positive response is robust to different measures of inflation forecasts. One-quarter-ahead GDP deflator forecasts increase by 9.31% in 4 years. The result is also robust to different forecasting horizons. For instance, four-quarter-ahead forecasts for CPI and GDP deflator both see a significant and substantial increase following a positive futures rate surprise. 2.3 Robustness To check the robustness of the irregularities documented above to different quarterly measures of futures rate surprises, I sum up all futures rate surprises in one quarter (including surprises associated with FOMC intermeeting actions) and estimate (1) and (2) using the sum as a quarterly measure of the futures rate surprise. Responses of CPI inflation and SPF forecasts to the futures rate surprise are again positive, substantial and significant, though weaker than the baseline model. CPI rises 6.05% and CPI forecasts rise 5.49% in 4 years. The positive response becomes stronger when inflation is measured by GDP deflator and its SPF forecasting counterpart. The irregularity is also robust to the sum excluding surprises associated with FOMC intermeeting actions: CPI increases by 9.58% in 4 years, though the response only becomes significant after 7 quarters. The response of CPI forecasts from SPF has a similar pattern. I also estimate (1) using monthly data from January 1990 to December 2007. For the months having no FOMC actions, futures rate surprises are set to zero. Twelve lags of inflation and futures rate surprises are included. The positive response of CPI inflation to a positive futures 5

rate surprise persists. CPI rises 13.96% in four years following a one-percent, positive surprise. Including 24 lags of inflation and futures rate surprises in (1) does not change the irregularity. 6 The positive response of CPI becomes insignificant when intermeeting observations are excluded from the monthly data. However, the response of core CPI becomes significantly positive and very strong. Core CPI increases by 39.45% in four years. A longer sample that ends at December 2009 implies similar irregularities: CPI responds positively, though not significantly, to a positive surprise, and more problematically, core CPI responds positively and significantly. 2.4 Discussion The positive response contradicts predictions of new-keynesian models. In a typical new-keynesian model, a positive monetary shock lowers inflation and inflation expectations. 7 If futures rate surprises, as argued in the literature, are not contaminated, inflation responses should be negative. Therefore, the positive responses of inflation and inflation forecasts put doubts on the monetary shock interpretation of futures rate surprises. Admittedly, it is not uncommon to empirically find positive responses of inflation to a contractionary monetary shock. For instance, VAR models usually encounter the price puzzle, a positive response of inflation to a positive monetary shock. However, the price puzzle is not an intrinsic property of monetary shocks, but rather an indication of contamination in the estimated monetary shocks. The price puzzle arises from information limitation in a parsimonious VAR model, such that the interest rate equation in the VAR model omits variables, for example inflation expectations, that raise inflation (Sims, 1992; Romer and Romer, 2004). Monetary shocks, measured by residuals from the estimated interest rate equation, pick up information of the omitted variables and serve as a proxy for them. Since the omitted variables, such as inflation expectations, can positively drive inflation dynamics, it is thus possible to see a positive response of inflation to monetary shocks that are contaminated by omitted variables. It is also not really surprising to find irregular inflation responses to market-based measures of monetary shocks. 8 Cochrane and Piazzesi (2002) have documented similar irregularities. Similar 6 The response of industrial production to the futures rate surprise in monthly data is also problematic. Industrial production responds positively, though not significantly, to a positive futures rate surprise. It contradicts the prediction of standard new-keynesian models that a tightening monetary policy lowers industrial production. 7 There are a few theoretical exceptions. First, if a new-keynesian model is indeterminate, it is possible to generate a positive response of prices to a contractionary monetary policy (Lubik and Schorfheide, 2004; Castelnuovo and Surico, 2010). However, the literature tends to show that the US economy was in a determinant state for the sample period considered here (Lubik and Schorfheide, 2004; Mavroeidis, 2010). Second, if the cost channel of monetary policy transmission is sufficiently important, a tightening monetary policy may push up prices (Barth and Ramey, 2001; Chowdhury, Hoffmann and Schabert, 2006). 8 Barakchian and Crowe (2013) also find a price puzzle using their monetary shocks constructed as the first 6

to the practice of measuring monetary shocks from futures rate surprises, Cochrane and Piazzesi (2002) construct monetary shocks as changes in the one-month Eurodollar rate surrounding target changes. They argue that their monetary shocks are free of the omitted-variable problem, the timevarying parameter problem and the orthogonalization problem that usually afflict policy-rule-based or VAR-based monetary shocks. Despite these argued advantages, their monetary shocks find no evidence that a tightening shock reduces inflation or output. They comment the irregular responses this way: As often happens, the purer the shock, the more unusual the response. Moreover, they doubt that the Fed s information advantage is responsible to the unusual responses. In contrast to Cochrane and Piazzesi (2002), this paper shows that market-based monetary shocks are not necessarily pure, and furthermore the Fed s information advantage on the near-term economic state accounts for a large part of the irregular responses. 3 The Information Content of Futures Rate Surprises The irregularities discussed in previous section may suggest that futures rate surprises are not a clean measure of monetary shocks. It is thus worthwhile to study their information content. This section first discusses properties of monetary shocks. It then demonstrates how futures rate surprises are related to monetary shocks, and why the monetary-shock interpretation of futures rate surprises is probably incorrect. 3.1 Monetary Shocks I follow Christiano, Eichenbaum and Evans (1999) and Romer and Romer (2004) to define monetary shocks as the component of monetary policy unexplained by the central bank s reaction to the state of the economy. Suppose the central bank s policy stance is well gauged by its target interest rate. Monetary shocks are defined as residuals of a target rate equation, r t = f(ω t ) + s t, (3) where r t is the Fed s target funds rate, f(ω t ) is the systematic component of the target rate determined by a reaction function modeled implicitly on the Fed s information set Ω t ; and s t is a monetary shock, orthogonal to Ω t. Note that the orthogonality condition is not an identification assumption, but rather directly implied by the definition that monetary shocks are unexplained by the Fed s reaction to the economic conditions. 9 principal component of surprise changes in futures contracts for current month and up to 5 months ahead. construction, their monetary shocks are strongly correlated with futures rate surprises considered in this paper. 9 In VAR models that use data of monthly or lower frequency, the orthogonality condition that variables in Ω t do not respond to s t is indeed a controversial identification assumption (Christiano, Eichenbaum and Evans, 1999). By 7

3.2 Futures Rate Surprises Federal funds futures contracts settle on the average of the federal funds effective rate in the delivery month. For instance, the settlement price of the current-month federal funds futures is based on the average of current month s federal funds effective rate. 10 Suppose the market expects the Fed to change the target rate on day t of month m. Shortly prior to the announcement of the new target rate, the current-month futures rate fm,t can be interpreted as the conditional expectation of the average funds rate in month m, plus a risk premium term, fm,t = 1 t 1 r i + 1 n n i=1 n Et r j + ωt, j=t where r i is the effective overnight funds rate on day i of month m, n is the number of days in the month, E t r j is the expected funds rate on day j conditional on the information set prior to the announcement, and ω t is the risk premium prior to the announcement. Writing the effective funds rate as the sum of the target rate and a targeting error, r i = r i + η i, futures rate fm,t can be expressed as, fm,t = 1 t 1 ( r i + η i ) + 1 n n i=1 n Et ( r j + η j ) + ωt, (4) j=t where r i is the target funds rate of day i, and η i is the targeting error of that day. Different from Kuttner (2001), this paper allows risk premia to respond to the Fed s announcements. The reason is that market participants economic prospects are different from the Fed s. They thus may infer the Fed s economic prospects from its actions. So, when market participants observe r t, they may update their information set and adjust risk premia accordingly. Risk premia after the announcement, denoted by ω + t, can be different from that before the announcement, ω t. The futures rate shortly after the announcement, denoted by f m,t +, is thus given by f m,t + = 1 t 1 ( r i + η i ) + 1 n n i=1 n E t + ( r j + η j ) + ω t +, (5) j=t where E + t η j is the expected targeting error after observing the new target rate. Assume that the market expects no further changes in the target rate in the month. 11 That is E t r j = E t r t and The reason is that in monthly or lower-frequency data, a monetary shock in one particular period has time to affect contemporaneous macroeconomic variables. Fortunately, event studies like this paper do not involve the controversy. The information used by the Fed for making policy decision is predetermined before the realization of the shock. Thus contemporaneous response of the information set to the monetary shocks is impossible. 10 The average is based on calendar days of the month with rates on nonbusiness days carried over from the last business day. 11 As pointed out by Kuttner (2001), this assumption is not entirely justified. There are four months in the period 8

E + t r j = r t for all j [t + 1, n]. Also assume the target rate change does not affect the expected targeting errors. That is E + t η j = E t η j for all j [t, n]. Futures rate surprise, f t, are defined as (Kuttner, 2001), where the multiplier from (4) and (5) that n n t+1 f t = n n t + 1 (f + m,t f m,t ), reflects the number of days affected by the target change. It follows f t = r t E t r t + n n t + 1 (ω+ t ωt ). (6) My interpretation of (6) differs from Kuttner s (2001) in two aspects. n n t+1 (ω+ t First, I do not treat ωt ) as negligible, as I do not rule out the possibility that market participants update their information set by inferring the Fed s economic prospects from its actions. Second, I do not interpret r t E t r t as monetary shocks as Kuttner (2001), Bernanke and Kuttner (2005) and Faust, Swanson and Wright (2004) do. 12 To see how futures rate surprises are related to monetary shocks, suppose market participants form their expectations on the new target rate and calculate risk premia using the following functional forms, E t r t = h(θ t ) and ω t = ω(θ t ), (7) where Θ t is the private sector s information set. Substituting (3)and (7) into (6) yields, f t = s t + f(ω t ) h(θ t ) + n n t + 1 (ω(θ+ t ) ω(θ t )), (8) where Θ t and Θ + t are market participants information set prior to and after the announcement, respectively. So, the futures rate surprise is a sum of three components, among which s t is the monetary shock, f(ω t ) h(θ t ) is an information shock due to information difference between n the market and the Fed, and finally n t+1 (ω(θ+ t ) ω(θ t )) is the revision in risk premia by the market upon the observation of the new target rate. The quality of futures rate surprises as a measure of monetary shocks depends on the magnitude of information shocks and revisions in risk premia relative to that of monetary shocks. Next section turns to investigate the empirical importance of information shocks and revisions in risk premia. from June 1989 to December 2007 that experienced two target rate changes (July 1989, December 1990, December 1991 and January 2001). Before 1994, the ex ante probability of having two changes in one month is even higher, since unscheduled FOMC actions were common then. 12 Actually, Kuttner (2001) and Bernanke and Kuttner (2005) only refer to r t E t r t as monetary policy surprises, not calling them monetary shocks explicitly. On the other hand, f t are called monetary shocks in Faust, Swanson and Wright (2004), Gürkaynak, Sack and Swanson (2007) and Piazzesi and Swanson (2008). Cochrane and Piazzesi (2002) also refer to surprises in Eurodollar rates constructed similarly to futures rate surprises as monetary shocks. 9

4 Contamination of Futures Rate Surprises 4.1 Orthogonality to the Fed s Information It follows from (3) that monetary shocks, s t, are orthogonal to the Fed s information set Ω t. Therefore, f t is orthogonal to Ω t under the monetary-shock interpretation of futures rate surprises. The empirical strategy to test the orthogonality is as follows. I use Greenbook forecasts prepared by the Fed s staff economists to proxy the Fed s information set, Ω t. Greenbook forecasts are usually made about one week before the corresponding FOMC meeting, which makes decision on the new target rate. In the baseline test, I assume the Fed s policy rule is linear, for instance a Taylor rule. Specifically, I regress futures rate surprises on two Taylor-rule variables, f t = α 0 + α 1 g t t + α 2 π t t + ɛ t, (9) where g t t and π t t are Greenbook forecasts for current-quarter growth rate of real GDP and GDP inflation. 13 The sample is from 1990Q1 to 2007Q4. Table 1 shows that orthogonality of futures rate surprises to the Fed s current-quarter growth and inflation forecasts is rejected at the 1% significance level. Individually, g t t and π t t both have significant, non-negligible explanatory powers to futures rate surprises. A one-percent increase in g t t leads to a surprise of 1.5 basis points. The figure for π t t is 1.1 basis points. Together, g t t and π t t account for 15% of variations in futures rate surprises. In summary, futures rate surprises are not purely the irregular component of the Fed s target rate, but related to the Fed s prospects on the current state of the economy. 4.2 The Magnitude of Contamination As suggested by (8), information shocks, f(ω t ) h(θ n t ), and revisions in risk premia, n t+1 (ω(θ+ t ) ω(θ t )), may contaminate monetary shocks, s t. As long as information shocks and revisions in risk premia are not negligible, futures rate surprises are at best contaminated monetary shocks. The empirical strategy to assess the magnitude of the contamination is as follows. I use Greenbook forecasts to proxy the Fed s information set, and use mean forecasts from the Survey of Professional Forecasters (SPF) to proxy the market s information set prior to announcements, Θ t.14 The market s updated information set, Θ + t, is not directly measurable. As suggested by Romer and Romer (2001), private forecasters tend to update their forecasts toward the Fed s following the Fed s announcements. I thus use the Fed s information set, Ω t, to proxy Θ + t. 13 The measure of GDP price index varies over time. It is the GNP implicit deflator prior to 1992Q1, and GDP implicit deflator between 1992Q1 and 1996Q1. After 1996Q2, it is measured by chain-weight price index for GDP. 14 Using median SPF forecasts instead of mean forecasts does not change conclusions of this paper. 10

The functional form of policy rules and risk premia are not known. I consider a special case, in which the Fed s and the market s rules are linear and identical. I also assume risk premia are linear in the market s information set. In this case, the magnitude of information shocks and risk premia can be tested by looking at the correlation between f t and the difference between the Fed s forecasts and the market s forecasts. Specifically, the magnitude of contamination is tested by estimating a model as f t = γ 0 + γ 1 g t t + γ 2 π t t + υ t, (10) where g t t and π t t are differences between Greenbook and SPF forecasts on current-quarter real GDP growth rate and GDP inflation, respectively. To match the frequency of SPF, which has four sets of forecasts every year, only four observations of the futures rate surprise in one year (and four sets of the corresponding Greenbook forecasts) are used. The futures rate surprises are selected to match the timing of SPF as close as possible. The timing mismatch between Greenbook and SPF forecasts is discussed in detail later. The sample covers the period from 1990Q1 to 2007Q4. The contamination is indeed substantial. Differences in forecasts for current-quarter real GDP growth rate and GDP inflation together account for 15% of variations in futures rate surprises. The effect of g t t on f t is strong and significant at the 5% significance level. ˆγ 1 is 3.8, which means that a standard deviations of g t t of 0.89 percentage point causes a surprise of 3.4 basis points. The effect of π t t is negative, relatively small, and insignificant. In summary, a substantial part of futures rate surprises are caused by information differences between the Fed and the market. Futures rate surprises are at best a contaminated estimate of monetary shocks. 4.3 Robustness A. Influential Observations Some observations may have undue influence on estimating (9) and (10). I detect potential influential observations using Cook s method. Taking (10) as an example, for each observation i a statistic, c i = (ˆγ(i)) ˆΣ 1 (ˆγ(i)) is calculated, where ˆγ(i) is the change in the vector of estimates, ˆγ, resulting from dropping the ith observation, and ˆΣ is the estimated covariance matrix for ˆγ. Observations with c i greater than 0.3 are treated as influential. Figure 3 shows the identified influential observations on a scatter plot of futures rate surprises against g t t. The scatter plot shows that influential observations usually lie far away from the center, and thus may have high leverage for the results. Nevertheless, it also makes clear that the explanatory power of g t t on futures rate surprises is a genuine pattern, not driven entirely by influential observations. To check the robustness of the results from the baseline regression, I remove from the sample all six identified influential observations. As shown in the right panel of Table 1, excluding influential 11

observations makes g t t and π t t jointly insignificant in explaining the futures rate surprise, though g t t is individually significant at the 5% significance level. However, g t t and π t t have even stronger explanatory powers to the futures rate surprise after removing influential observations. They jointly explain 20% of variations in the surprise. Therefore, the explanatory power of information difference is not driven by outliers. B. Forecast Timing The timing of SPF forecasts does not match that of futures rate surprises exactly. To study the timing issue, I use the deadline for forecasters submitting their projections to approximate the date of SPF forecasts, and compare it with the date of the futures rate surprise. For the sample from 1990Q3-2007Q4 (excluding 1996Q1), SPF forecasts in general were made several days later than futures rate surprises. 15 The fact that SPF deadlines fell behind the dates of futures rate surprises may cause endogeneity problem to the least-square estimation of (10). Two endogeneity issues can arise from the late SPF forecasts. First, before submitting their projections SPF forecasters may have updated their forecasts by incorporating the impact of monetary shocks, s t, on the economy. Second, SPF forecasters may try to update their forecasts by extracting information from f t. In each case, least-square estimates for γ s are biased for the effect of forecast difference on futures rate surprises. To overcome the endogeneity problem, I instrument g t t and π t t by Greenbook forecasts for g t t and π t t. Results from the instrumental variable estimation are presented in Panel C of Table 1. For the full sample, IV estimates indicate that a one-percent increase in forecast difference for g t t gives the market a surprise of 6.5 basis points. The figure is significant at the 1% significance level, and higher than the least-square estimate. The effect of π t t is positive, yet insignificant. Joint insignificance of g t t and π t t is rejected at the 10% significance level by the Wald test. The IV estimation is unlikely subject to the weak instrument problem. Cragg-Donald statistic is 21.59, much higher than Stock and Yogo s (2001) critical value 7.03, at which all Wald tests based on 2SLS estimates at a 5% level have the maximal size of 10%. 16 For the sample excluding influential observations, the IV estimation yields similar results. The IV estimate for γ 1 is significant at the 5% significance level, and higher than the least-square 15 On average SPF forecasts fell behind futures rate surprises for 4.43 days. The lag varies from 10 day to 20 days. SPF deadlines for 1990Q1 and 1990Q2 are not known. The 1996Q1 survey deadline was delayed because of the shut down of federal government, and thus the deadline lags the corresponding Greenbook for 36 days. Note that none of them is identified as influential in the baseline regression. 16 Note that Stock and Yogo s (2001) test for weak instruments based on Cragg-Donald statistics only applies to models with iid errors. Nevertheless, I still report the test for a check. 12

estimate. The IV estimate for γ 2 is small, insignificant, yet positive. Thus, the negative leastsquare estimate for γ 2 is probably a sign of the endogeneity problem. The joint insignificance is rejected at the 10% significance level. Again, the IV estimation seems to be free of the weak instrument problem. C. An Unrestricted Monetary Policy Rule In the baseline regression, I assume that the market uses a linear monetary policy rule that is identical to the Fed s. Therefore, f(ω t ) h(θ t ) reduces to a linear function of forecast differences between the Fed and the market on variables that enter the monetary policy rule. Here I relax the assumption on identical policy rules, though the assumption about linearity of the rules is maintained. That is to say, the monetary policy rule used by the market differs from the Fed s not only in measures of variables that enter the rules, but also in parameters of the rules. As in the baseline model, I assume revisions in risk premia are linear functions of forecast differences between the Fed and the market. Under the assumption of less restricted monetary policy rules, the magnitude of contamination can be tested by regressing the futures rate surprises on Greenbook and SPF forecasts in an unrestricted way, f t = α 0 + α 1 g t t + α 2 π t t + α 3 π SPF t t + υ t, (11) where πt t SPF is current-quarter GDP inflation forecast from SPF. For the concern of colinearity, I do not include the SPF forecast for current-quarter real GDP growth rate, which is strongly correlated with its Greenbook counterpart (the correlation is 0.95). Colinearity between πt t SPF and π t t does not seem to be a problem, as they have only a moderate correlation of 0.80. As discussed earlier, πt t SPF are usually made serval days later than, and thus likely endogenous to, f t. The endogeneity problem implies that least-square estimates for α s in (11) can not be interpreted as economic forecasts causing surprises of the futures rate, as I intend to. endogeneity problem, I instrument π SPF t t using its one-period lag, π SPF t 1 t 1 To circumvent the and one-period lag of one-quarter-ahead forecast, π SPF t t 1. Table 2 reports least-square and IV estimation results for (11). As expected, a larger share of variations in futures rate surprises is explained in the unrestricted model than the baseline model (10). R 2 from the least-square estimation is 0.30, indicating that a substantial part of the surprises is explained by the three explanatory variables. The explanatory variables are jointly significant at the 1% significance level. Individually, g t t and πt t SPF both are significant at the 1% level, and π t t is significant at the 10% level. IV estimation gives similar point estimates and standard errors. Validity of instruments can not be rejected by Hansen overidentification tests. Estimation results do 13

not change substantially when influential observations identified using Cook s method are deleted. Weak identification is unlikely to be an issue as the instruments are strongly correlated with π SPF t t. D. FOMC Meeting Frequency The baseline regression considers only four futures rate surprises in a year that have a close match to the timing of SPF forecasts. To see whether the baseline regression is subject to selection bias, it is worthwhile to consider the endogeneity problem for all futures rate surprises. In the period from 1990Q1 to 2007Q4, there are eight futures rate surprises in a year associated with scheduled FOMC meetings and accompanied by Greenbook forecasts. Beside scheduled surprises, there are also surprises associated with intermeeting actions on an irregular basis. These surprises have no corresponding Greenbook forecasts. I use the nearest previous Greenbook forecasts to proxy the Fed s economic prospects when intermeeting actions are taken. The effect of forecasts for current-quarter GDP growth rate on the surprise is significant at the 1% significance level, and quantitatively similar to that in the baseline regression. The effect of current-quarter inflation forecasts is much smaller compared to the baseline regression, and not significant. Nevertheless, exogeneity of the futures rate surprises to g t t and π t t is rejected at the 1% significance level. Together g t t and π t t account for 9% of variations in the futures rate surprises. 17 4.4 Discussion A. Reconciling the Findings with the Literature The finding of substantial contamination contradicts with Faust, Swanson and Wright (2004), who argue that futures rate surprises do not contain the Fed s private information. To support the argument, they investigate whether futures rate surprises add additional values to the private sector s estimates for macroeconomic indicators of the last month (or quarter) that are released after the corresponding futures rate surprises. The idea is that if futures rate surprises indeed reveal the Fed s private information, the private sector should improve its estimates for the macroeconomic indicators by incorporating information revealed by futures rate surprises. Faust, Swanson and Wright (2004) find that incorporating futures rate surprises does not improve the private sector s estimates, and thus conclude that futures rate surprises do not contain the Fed s private information. However, a proposition as futures rate surprises do not contain the Fed s private information can almost never be verified, as the Fed s information set is not well 17 For the reason that SPF has only four sets of forecasts each year, we do not have a good measure for forecast differences between the Fed and market for all policy actions. Therefore, I do not have a regression of futures rate surprises at all policy actions on forecast differences. 14

defined. On the contrary, the proposition is falsified as long as a single piece of evidence is found against it. Faust, Swanson and Wright s findings only verify that futures rate surprises do not reveal the Fed s backward-looking information, namely, estimates on macroeconomic indicators of the last month (or quarter). However, the findings of this paper show that futures rate surprises reveal the Fed s forward-looking information, namely, forecasts on current-quarter macroeconomic indicators. B. Longer Forecast Horizons Differences in the Fed s and the market s forecasts beyond the current quarter are found having no explanatory power for futures rate surprises. So, why only differences in current-quarter forecasts matter for the surprises? There are two interconnected reasons. First, the Fed s forecasts for current-quarter inflation and growth rate are superior to the private sector s. D Agostino and Whelan (2008) shows that to make optimal current-quarter forecasts, a forecaster accessible to both Greenbook and SPF forecasts should put a substantial weight on Greenbook forecasts but essentially no weight on SPF forecasts. The Fed s superior performance in current-quarter forecasts is well founded. As pointed out by Bernanke (2007), to forecast near-term (current or one-quarterahead) inflation the Fed s staff rely on a bottom-up approach that focuses on estimating and forecasting price behavior for individual components that make up the price index in question. The Fed s forecast superiority for current-quarter real GDP growth rate may come from the fact that the Fed collects data for compiling the industrial production index. The Fed s private data on industrial production probably help to forecast current-quarter GDP growth rate. The second reason is that forecastability of inflation and real growth rates beyond current quarter is very low for the sample from 1990Q1 to 2007Q4. D Agostino and Whelan (2008) show inflation and growth rates one- or more-quarter ahead become very difficult to forecast during the Great Moderation. They show that neither Greenbook nor SPF forecasts for inflation and real GDP growth rates beyond current quarter are useful to predict the actual data. If the market is aware of the the predictability limit, it should not try to infer from the futures rate surprises the Fed s forecasts beyond the current quarter, which are not more precise than the market s. Furthermore, if the Fed knows the predictability limit, it should not bases its policy actions on forecasts beyond current quarter. Thus, the difference between forecasts at horizons beyond current quarter is irrelevant to the futures rate surprises. 15

5 The Sources of Contamination Having documented that the contamination is substantial, this section turns to study the sources of contamination: information shocks or revisions in risk premia? The Fed s private information is well documented in the literature. For instance, Romer and Romer (2001) show that the Fed has superior information to the market, and moreover, the market learns the Fed s information from its actions. Therefore, it is reasonable to expect information difference between the Fed and the market causing information shocks, f(ω t ) h(θ t ), as in (8). Time-varying risk premia that respond to economic fundamentals and monetary policy are well documented in the literature. Alvarez, Atkeson and Kehoe (2009) show that a model featured with time-varying risk premia that respond to monetary policy can explain the forward premium anomaly. Empirically, Piazzesi and Swanson (2008) document that risk premia associated Fed funds futures are substantial and predictable by macroeconomic variables. Ludvigson and Ng (2012) show that macroeconomic fundamentals have important forecasting power for excess bond returns. Bansal and Shaliastovich (2013) show that bond risk premia are closely related to uncertainty about expected inflation and growth. It thus seems natural to think that risk premia compensating investors holding a Fed funds futures contract respond to monetary shocks and the Fed s private information revealed by its policy actions. In other words, risk premia could change along with the Fed s policy action. Therefore, the assumption that ω(θ + t ) ω(θ t ) = 0 is a difficult case to make. 5.1 Information Shocks It follows from (3) that r t h(θ t ) = s t + f(ω t ) h(θ t ). This equation indicates that the difference between the target rate and the market s expected target rate measures the information shock up to a monetary shock, s t. Since s t is orthogonal to f(ω t ) and h(θ t ), I thus test the presence of information shocks by testing whether information difference between the Fed and the market explains the market s forecast errors in the target federal funds rate. I measure h(θ t ) using median forecasts from the Bloomberg survey on the target federal funds rate. I use survey forecasts to measure h(θ t ) for two reasons. First, it is usually found that few statistical models outperform median survey forecasts for macroeconomic variables. Second, compared to market expectations derived from asset prices, survey forecasts are physical expectations, not involving risk premia (see e.g., Cieslak and Povala, 2013 and references therein). The Bloomberg survey is conducted on the same days as FOMC scheduled announcements. The data are available since May 20, 1997. I complement the Bloomberg survey data with median forecasts 16

from the Money Market Services Survey, which conducts a Friday telephone survey of about 40 money managers and collects forecasts of the target funds rate to be released during the next week. 18 The Money Market Services Survey data are available since 1993. Figure 4 plots survey forecast errors from 1993 to 2007, together with superimposed futures rate surprises. In most cases, median survey forecasts get the target rate correctly. There are only eleven forecasts errors, five of which are positive. More interestingly, all forecast errors have a magnitude of 25 basis points. 19 I thus estimate an ordered logit model using forecasts on current-quarter GDP growth and inflation to explain the 25-, 0-, and 25-basis-point forecast errors on the target funds rate, 25, < I t < τ 1, r t h(θ t ) = 0, τ 1 < I t < τ 2, 25, τ 2 < I t <. where I t = β 1 g t t + β 2 π t t + ς t, and ς t has the logistic density, and τ 1 and τ 2 are two threshold values to be estimated. Results are reported in Table 3. For the full sample from 1993 to 2007, which have eight observations in one year, Greenbook forecasts g t t and π t t jointly have marginally significant explanatory power for survey forecast errors in the target funds rate. The p-value associated with Wald test is 0.07. The positive estimates for β 1 and β 2 (though not individually significant) imply that higher growth and inflation forecasts from Greenbook tend to cause a positive survey forecast error in the target funds rate. This is consistent with intuitions: when the Fed sees a strong economy it tends to set a high target rate so as to cause a 25-basis-point forecast error to private forecasters. The result is not robust, however. For the middle-quarter sample, which as explained in Section 4 is selected to match SPF forecasts, Greenbook forecasts g t t and π t t lose their explanatory power for the survey forecast errors in the target funds rate. Nevertheless, it is worthwhile to note that forecast differences between Greenbook and SPF, g t t and π t t, are jointly significant in explaining survey forecast errors in the target funds rate. 18 In a study on the response of exchange rates to macroeconomic announcements, Andersen, Bollerslev, Diebold and Vega (2003) construct monetary policy surprises as the difference between announced target rates and median forecasts from the Money Market Services Survey. 19 This is understandable since that it is well known to the market that the Fed changes the target funds rate with a 25-basis-point incremental. 17

5.2 Revisions in Risk Premia Since risk premia associated with the futures are not directly measurable, I test revisions in risk premia caused by Fed announcements in an indirect way. Specifically, I rewrite (8) as f t = r t h(θ t ) + φ(ω(θ+ t ) ω(θ t )). (12) This equation shows that the difference between f t and r t h(θ t ) are risk premium revisions. I again use median forecasts from Bloomberg survey and the money market services survey to measure h(θ t ). Figure 4 clearly shows that revisions in risk premium (measured as differences between f t and r t h(θ t )) are non-zero. They are actually the main variations in the futures rate surprises. In other words, the median market forecasts usually get the forthcoming target rate correctly, and therefore the Fed s announcements surprise the futures market only to the extent of revisions in risk premia. I further investigate whether information difference between the Fed and the market caused risk premium revisions, as suggested by (8). The empirical strategy is as follows. After controlling for r t h(θ t ), I regress futures rate surprises on Greenbook and SPF forecasts of current-quarter growth and inflation, f t = θ 0 + θ 1 ( r t h(θ t )) + θ 2g t t + θ 3 π t t + µ t. (13) Results are reported in Table 4. After controlling for r t h(θ t ), the explanatory power of Greenbook forecasts remains. Moreover, forecast differences between Greenbook and SPF continue to contribute to futures rate surprises. Indeed, information differences between the Fed and the market significantly explain revisions in risk premia. 6 Contamination and the Inflation Response Having shown that information shocks account for substantial variations in futures rate surprises, it is interesting to see whether they are responsible for the irregular inflation responses documented in Section 2. To this end, I clean the futures rate surprises by removing from them information shocks identified by (10) or (11). Note that because of the possible endogeneity of SPF forecasts discussed earlier, not all variations in right-hand-side variables of (10) and (11) are sources for the contamination. Part of the variations are due to endogenous responses of SPF forecasts to the Fed s policy actions. A conservative way to solve the problem is to treat variations in right-hand-side variables projected to the instrumental space as sources for the contamination. Specifically, clean 18

monetary shocks identified from (10), denoted by s DIFF t, are calculated as s DIFF t = f t (ˆγ 0 + ˆγ 1 P Z g t t + ˆγ 2 P Z π t t ), where ˆγ s are IV estimates for γ s in (10), and P Z is a projection matrix of instrumental variables Z, defined as P Z = Z(Z Z) 1 Z, where Z is a matrix with (1, g t, π t ) as its tth row. Similarly, clean monetary shocks identified from (11), denoted by s UR t, are calculated as s UR t = f t (ˆα 0 + ˆα 1 g t t + ˆα 2 π t t + ˆα 3 P W π SPF t t ), where ˆα s are IV estimates for α s in (11), and P W is a projection matrix of instrumental variables W, which has (1, πt 1 t 1 SPF, πspf t t 1 ) as its tth row. Having obtained clean monetary shocks, s DIFF t or s UR t, I estimate (1) and (2) replacing the original futures rate surprises, f t by the clean monetary shocks. Figure 5 presents responses of CPI inflation to the clean monetary shocks. To compare, the dashdot line replicates the central tendency response to f t as shown in Figure 1. central tendency of cumulative dynamic multipliers of s DIFF t responses of which one-standard-error bands do not include zero. Cleaning the contamination helps to alleviate the irregularities. The dashed line and the solid line show the and s UR t, respectively. Circles signify Compared to responses to the original futures rate surprises, inflation responses to s DIFF t are weaker, and only significant occasionally. Responses to s UR t become even weaker and essentially insignificant except the response two quarters after the impact. Similar changes emerged in responses of one-quarter-ahead CPI inflation forecasts from SPF to clean monetary shocks. Figure 6 shows central-tendency responses of the forecasts to the clean monetary shocks. To compare, the dashdot line replicates the centraltendency response to f t as shown in Figure 2. It seems that purifying the futures rate surprises according to (10) does not help much to decrease the positive response. However, purification according to (11) is effective. Responses to s UR t becomes insignificant six quarters after the impact, and the central tendency response after 16 quarters is reduced to 2.44% from 11.34% in the original response. In summary, the contamination indeed contributed to the irregularities. Nevertheless, central tendency responses to the clean monetary shocks are still positive and substantial. It may imply that purification according to (10) and (11) can not completely clean the contamination. 7 Monetary Policy Surprises and Interest Rates Having shown that futures rate surprises are not a clean measure of monetary shocks, a natural question to ask is whether the contamination affects our understanding of the impact of monetary 19

shocks on the financial market. To answer this question, this section reconsiders Kuttner s (2001) seminal work using futures rate surprises to study interest rate responses to monetary policy. The idea is to use futures rate surprises to disentangle anticipated and unanticipated changes in monetary policy, and use the later to identity responses of market interest rates to monetary policy. In particular, Kuttner (2001) uses futures rate surprises to gauge unanticipated changes in monetary policy, and do the following regression, y t = β 0 + β 1 f t + β 2 e t + η t, (14) where y t represents in turn daily changes in yields on 3-, 6- and 12-month Treasury bills, 2-, 5- and 10-year notes, and 30-year bonds; f t is the futures rate surprise, measuring unanticipated changes in the target funds rate; e t is the expected change in the target rate, calculated as the actual change minus f t. To be comparable, I use daily futures rate surprises constructed by Kuttner (2001) instead of surprises in a 30-min time window used in previous sections. Nevertheless, using the 30-min time window does not change the main findings in this section. Table 5 reports estimation results for three sets of sample. The full sample has all futures rate surprises associated with scheduled FOMC meetings during the period from 1990Q1 to 2007Q4. 20 The middle-quarter sample contains only futures rate surprises associated with middle-quarter FOMC meetings in the period. Futures rate surprises that are in the full sample but not in the middle-quarter sample are grouped in the end-quarter sample. There are two reasons for splitting the full sample into the middle-quarter and end-quarter samples. First, as discussed in previous sections, the middle-quarter sample is contaminated in the sense that futures rate surprises are not a good measure of monetary shocks. Second, some evidence shows that the end-quarter sample is less contaminated. 21 Results for the full sample are broadly consistent with Kuttner s (2001) findings: futures rate surprises have substantial effects on interest rates of a wide range of maturities; the longer is the maturity, the weaker the effect; expected changes in the target rate have negligible effects on market interest rates. However, results for the middle-quarter sample are in sharp contrast with the full sample. The futures rate surprises basically have no effect on yields on Treasury notes and bonds, which have maturities longer than one year. The contrast becomes even sharper if results from the middle-quarter sample are compared with that from the end-quarter sample, in which futures rate surprises have substantial and significant effects of Treasuries of all maturities from 3 months to 30 20 Using Kuttner s (2001) original sample, that is all futures rate surprises associated with scheduled FOMC meetings in the period from June 6, 1989 to February 2, 2000, does not change main findings of this section. 21 A clue is that end-quarter sample seems to be exogenous to Greenbook forecasts, while the middle-quarter sample does not. Because I do not have private forecasts corresponding to end-quarter futures rate surprises, studying exogeneity of the end-quarter sample to difference between private and Greenbook forecasts is currently not feasible. 20