Did Large-Scale Asset Purchases Work ? ∗ Adina Popescu† Version last updated on 1 May 2015
∗ †
Acknowledgements. Economist, International Monetary Fund. Email:
[email protected]. Comments welcome!
2 Contents
Page
I.
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
II.
Data and Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . A. Non-Standard Monetary Policy Measures During the Financial Crisis B. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C. Construction of the Announcement Shock Series . . . . . . . . . . . D. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
III. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A. How Asset Purchases Affect the Real Economy: Channels . . . . B. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. Responses of Real Activity, Income, Consumption and Sales 2. Responses of Labor Market Variables . . . . . . . . . . . . . 3. Response of Housing Markets . . . . . . . . . . . . . . . . . 4. Responses of Monetary and Credit Aggregates . . . . . . . . 5. Responses of Prices . . . . . . . . . . . . . . . . . . . . . . 6. Summary of LSAPs Effects . . . . . . . . . . . . . . . . . . C. Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . D. Comparison with Other Studies . . . . . . . . . . . . . . . . . . IV.
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Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 Appendices .1. Chronology of Key Announcements about Changes in Asset Purchases .2. Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3. Estimation Methodology . . . . . . . . . . . . . . . . . . . . . . . . . .3.1.Two-step Estimation Through Principal Components . . . . . . . .3.2.One-step (Joint) Estimation Through Maximum Likelihoood . . .
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55 56 57 57 60
Tables 1. 2. 3. Box
Peak Effects on Key Variables: Baseline Specification, All Shocks . . . . . . . . . 50 Peak Effects on Key Variables: Robustness . . . . . . . . . . . . . . . . . . . . . . 51 Data: Definitions, Sources and Transformations . . . . . . . . . . . . . . . . . . . 65
3 Extraordinary times call for extraordinary measures.1
Abstract This paper analyzes the effects of the Federal Reserve’s Large-Scale Asset Purchase (LSAP) programs on a large set of macroeconomic variables (based on the updated Stock and Watson (2002) dataset), over a sample covering the entire duration of quantitative easing policies. We find that these unconventional policies have significantly stimulated the real economy, boosting output, income, consumption, industrial activity, investment and confidence. They also spurred a recovery in the labor and housing markets. At the same time, in spite of the increase in money and credit aggregates, there has been little positive impact on inflation or wages. Our results are robust to analyzing LSAP announcements versus actual asset purchases. The estimates suggest that both the portfolio rebalancing and the signaling channels have been of considerable importance for the transmission of asset purchases to the broader economy.
1 Ben
Bernanke, then Federal Reserve’s chairman, on February 18, 2009, in a speech to the National Press Club Luncheon.
4 I. I NTRODUCTION
In the midst of the Great Recession in 2008, the United States faced a precipitous decline in activity, with output plummeting at an annual rate of 8.9 percent in the fourth quarter of 2008 and ongoing tensions in financial markets, which peaked after Lehman Brothers’ collapse in September 2008. Some commentators were warning against the risk of a second Great Depression. In this context, at the end of 2008 the Federal Reserve Board cut the target federal funds rate essentially to the zero lower bound (ZILB) and embarked on unconventional monetary policies of unprecedented size and scope. The weak economic recovery which followed, together with the generalized slack, in particular in labor markets, prompted the Federal Reserve to continue expanding its balance sheet via Large-Scale Asset Purchase (LSAP) operations for another 6 years. While the effects of these exceptionally accomodative monetary conditions continue to work their way through the economy, there seems to be growing consensus at the end of 2014 that the US economy has "turned the corner". This paper addresses the question: how much of the recovery was due to the central bank’s extraordinary measures ?2 By now, it has been well documented that the Federal Reserve‘s quantitative easing (QE) policies have significantly affected long-term yields of government bonds and other financial assets. However, substantial more uncertainty remains about the effects of these policies and the effectiveness of LSAPs to boost the broader economy. Theoretical and empirical work has tended to focus on the effects on a few key variables, such as GDP and inflation. Also, until recently, reseachers have not been able to look at a sample containing the entire history of asset purchases. This paper aims to fill some of these gaps in the literature. To the best of our knowledge, this is the first paper to analyze the effects of the entirety of the Federal Reserve’s QE programs during the ZILB period, when the central bank’s balance sheet has effectively been the main monetary policy instrument. We take a relatively well-know large dataset of macroeconomic variables (based on Stock and Watson (2005)) and estimate the effects of asset purchases using a factor augmented vector autogressive model (FAVAR) a la Bernanke, Eliasz, and Boivin (2005) (henceforth BBE). Unlike previous studies which focused on a parcimonious set of variables (often using the cross-country dimension in order to alleviate the problem 2 The
Federal Reserve has relied on two types of unconventional monetary policies: forward guidance and largescale asset purchases (LSAPs). The latter are the focus of the current paper. For some papers on the effects of forward-guidance, see e.g. Hattori, Schrimpf, and Sushko (2013).
5 stemming from insufficiently long datasets), this paper makes use of factor models as well as Bayesian shrinkage in order to provide a comprehensive assessment of the impact of asset purchases on a far wider set of macroeconomic variables than done before. Our answer to the question posed in the first paragraph is that the recovery in the real economy seems to owe quite a lot to the Federal Reserve’s exceptional policies. Overall, the Large-Scale Asset Purchases have significantly boosted real GDP (at the peak by about 0.5%1%). Measures of cyclical conditions and capacity utilization are also consistent with an upswing. In particular, various indicators of industrial activity and investment rebounded strongly across most sectors as a result of QE and confidence in the manufacturing sector was boosted. Probably most important given the Federal Reserve’s dual mandate, we document that the measures contributed to a robust recovery in labor markets. The unemployment rate declined by around 1%, accompanied by an increase in employment which was broad-based across sectors. As far as the housing market is concerned, a key driver of real activity in the U.S., we document that the Federal Reserve’s actions had significant stimulative effects also in this area. However, we also find that the recovery driven by increased monetary and credit expansion was not accompanied by a similar increase in prices and wages. Contrary to some fears, we find that the LSAPs did little to stoke inflation, which remained rather subdued (and in some sectors prices have even declined). As mentioned before, this paper adds to the growing literature on the effects of unconventional monetary policy. A significant part of the literature has focused on the impact of quantitative easing policies on financial variables like the shape of the yield curve and other asset prices 3 . These papers generally find that LSAP programs have indeed been effective in reducing long-term rates and boosting various asset prices. Fewer papers have examined the effects of unconventional monetary policy on the wider macro-economy. Chen, Curdia, and Ferrero (2012) simulate the impact of the US Federal 3 See,
e.g. Gagnon and others (2010), Doh (2010), Fuster and Willen (2010), Neely (2015), Krishnamurthy and Vissing-Jorgensen (2011), Hancock and Passmore (2011), Hancock and Passmore (2012), Swanson, Reichlin, and Wright (2011), Joyce and others (2011), Hamilton and Wu (2012), D’Amico and others (2012), Stroebel and Taylor (2012), Rosa (2012), D’Amico and others (2012), Glick and Leduc (2013), Fratzscher, Duca, and Straub (2013), Swanson, Reichlin, and Wright (2011), Rogers, Scotti, and Wright (2014), Hattori, Schrimpf, and Sushko (2013), Gilchrist and Zakrajsek (2013), etc.
6 Reserve second Large-Scale Asset Purchase program (LSAP II) in a DSGE model enriched with a preferred habitat framework and estimated on US data. They conclude that the effects of LSAP programs on macroeconomic variables, such as GDP and inflation, are likely to be moderate. The empirical literature has so far used several approaches to quantify the impact of unconventional monetary policy on financial and macroeconomic variables. One leading methodology has been using event studies (dummy variables) to capture the announcement affects of policies (see Krishnamurthy and Vissing-Jorgensen (2011), Gagnon and others (2010), Swanson, Reichlin, and Wright (2011), and Glick and Leduc (2013), etc.) Another strand of the literature employs (Bayesian) VARs and FAVARs identified through a mix of timing and sign restrictions (see Baumeister and Benati (2012),Gambacorta, Hofmann, and Peersman (2014), Weale and Wieladek (2014), etc.) Using a sample of eight advanced economies, the US and/or the UK, these papers find that asset purchase shocks tend to result in a rise in output and a less conclusive increase in consumer prices. This paper is also related to Wu and Xia (2014), who employ a similarly large dataset in a FAVAR to estimate the macroeconomic effects during the the ZILB period of a "shadow" interest rate, which they derive from an term structure model. They also find that unconventional monetary policy has been stimulative for the real economy. However, their shorter crisis sample size prevents them from drawing strong conclusions about more than a handful of the variables. Compared to the existing literature, this paper differs by combining a large data methodology (a FAVAR a la BBE) with a structural indentification of the asset purchase shocks based on aggregates in the Federal Reserve’s balance sheet. To alleviate the concern that asset purchase increases may have been anticipated, we also construct several announcements series and assess the robustness of our results. We find that the qualitative conclusions do not change. However, the effects of the implementation of LSAPs, i.e. the actual balance sheet increases, are larger than those of the announcements, suggesting that portfolio rebalancing effects are important, in addition to signalling effects. The remainder of the paper is organized as follows. Part two presents a narative of the key events related to LSAP operations. It describes the data and the construction of the announcements series. Section III presents the results. First, we discuss the channels of transmission of QE. Then, after a brief methodological review (most details are relegated to an appendix), the main results in the form of impulse responses are presented in a comparison across
7 shocks. After a discussion on robustness checks and a comparison with previous studies, we conclude.
II. DATA AND M ETHODOLOGY
A. Non-Standard Monetary Policy Measures During the Financial Crisis One can distinguish two main phases in the Federal Reserve’s response to the 2008 crisis 4 , which had significant effects on its balance sheet (see Figure 1). In the first period, the Federal Reserve expanded its balance sheet through what can be mostly considered reversible and/or short-term operations. In particular, it extended loans aggressively through a variety of new facilities such as the Term Auction Facility (TAF), foreign currency swaps with other central banks, and the Commercial Paper Funding Facility (CPFF), etc. 5 In the second phase, the Federal Reserve engaged in what has been called quantitative easing (QE), de facto outright purchases of assets (treasuries, mortgage-backed securites and agency debt). The Federal Reserve carried out three rounds of large-scale asset purchases during the Great Recession. 6 The first round of large scale asset purchases (LSAPs), dubbed QE1, was announced in November 25, 2008, when the Federal Reserve communicated plans to purchase purchase USD $100 billion in government-sponsored enterprise (GSE) debt and $500 billion in mortgagebacked securities (MBS) issued by the GSEs. On March 18, 2009, this was followed by an announcement for additional purchases of $100 billion in GSE debt, $750 billion in MBS, and $300 billion in long-term Treasury securities. The stated goal of the operations was to “reduce the cost and increase the availability of credit for the purchase of houses, which in turn should support housing markets and foster improved conditions in financial markets more generally.“ 7 Altogether these purchases roughly doubled the size of the US monetary base and substantially increased bank excess reserves. 4 See
e.g. Chairman Ben S. Bernanke’s testimony “Federal Reserve’s exit strategy“ before the Committee on Financial Services, U.S. House of Representatives, Washington, D.C., on February 10, 2010. 5 Most
of these operations, including those which were first unsterilized, like the CPFF, have since been fully or largely unwound. Christensen, Lopez, and Rudebusch (2009), McAndrews, Sarkar, and Wang (2008), Taylor and Williams (2009), Adrian, Kimbrough, and Marchioni (2011) and Duygan-Bump and others (2013) provide empirical assessments of the effective of these measures. 6 In
the subsequent narative we largely follow Fawley and Neely (2013).
7 See
the 11/25/2008 FOMC press release (Table A1).
8 The second round QE2 was launched in an environment of sluggish real activity and consumer price index inflation falling toward 1 percent, while financial market disorder had substantially receded and the European sovereign debt crisis was gaining momentum. On August 10, 2010, the Fed announced that it would maintain the size of its balance sheet by reinvesting the principal payments on LSAP assets into Treasuries. The FOMC also began to signal that it was considering further asset purchases: In a speech on August 27, 2010, Chairman Bernanke suggested that the Fed could purchase more assets, should conditions warrant. The FOMC announced on November 3, 2010, that it would purchase an additional $600 billion in U.S. Treasuries to “promote a stronger pace of economic recovery and to help ensure that inflation, over time, is at levels consistent with its mandate.“ 8 It is important to note that unlike QE1, which represented a large surprise (Neely (2012), for example, reports that 10-year constant maturity Treasury yields fell by a cumulative 94 basis points), financial markets widely expected the November 2010 asset purchase announcement. However, it is important to note that there was substantial uncertainty as to the amount of the operation. In a Reuters poll conducted October 5, 2010, 16 of 16 primary dealers expected the Fed to ease monetary policy and 14 of 15 respondents expected the announcement to be made at the November 3 FOMC meeting, but the projected size of the quantitative easing ranged from $500 billion to $1.5 trillion. 9 Operation Twist 1 was launched in an environment of renewed fears of recession in the U.S. and a spike in financial stress indices, on September 21, 2011. Officially termed the Maturity Extension Program and Reinvestment Policy and nicknamed after a similar, though smaller scale, operation in the early 1960s, Operation Twist 1 committed the Federal Reserve to sell $400 billion in short-term assets while purchasing $400 billion in long-term assets. This was intended to reduce long-term interest rates relative to short-term interest rates, thus “twisting“ the yield curve. Operation Twist did not entail any expanssion of the monetary base because the long-term asset purchases were to be funded by short-term asset sales rather than money creation. Operation Twist 2 was launched on June 20, 2012, also in the context of deteriorating U.S. real activity and weakness in the labor market. Final purchases under the Maturity Extension Program had originally been scheduled for the end of June. The Fed announced that it would extend its Maturity Extension Program that committed the Fed to buy long Treasuries and sell 8 See
the 11/3/2010 FOMC statement (Table A1).
9 These
anticipation effects probably account for the fact that 10-year yields cumulatively actually rose slightly around the set of important QE2 announcements (Neely (2012)).
9 an equivalent quantity of short Treasuries through the end of the year at the same pace and the additional purchases (and sales) were expected to total $267 billion. Following Operation Twist, labor-market data continued to exhibit signs of a weaker-thandesired recovery. To engender a stronger labor market, the FOMC began a third round of large-scale asset purchases (QE3) on September 13, 2012. The announcement came after significant ancitipation (including a comment by Chairman Bernanke at his annual Jackson Hole speech, that “the stagnation of the labor market in particular is a grave concern“ and that “the Federal Reserve will provide additional policy accommodation as needed.“ 10 QE3 marked a departure from previous operations in that the Fed committed to a pace of purchases rather than a total quantity. Initially, this entailed additional purchases of $40 billion MBS per month, together with continuing the program to extend the average maturity of its holdings of securities announced in June (that is, continuing Operation Twist 2 and adding long-term securities at a pace of $45 bn per month). 11 However, after Operation Twist ended in December 2012, on December 12, 2012, the FOMC announced that long-term Treasury purchases would continue at the pace of $45 billion per month, but such purchases would no longer be sterilized through the sale of short-term Treasuries. Hence, the entire operation would contributed to expanding the monetary base. Together with continuing agency mortgage-backed securities purchases at a pace of $40 billion per month, the Federal Reserve would from then onwards expand its balance sheet at a rate of $85 billion monthly. In an innovation compared to previous rounds of LSAPs, the QE3 program was designed to be state-contingent and open-ended, meaning economic conditions rather than a static end date would determine when the program concluded: “a highly accommodative stance of monetary policy will remain appropriate for a considerable time after the asset purchase program ends and the economic recovery strengthens. In particular, the Committee decided to keep the target range for the federal funds rate at 0 to 1/4 percent and currently anticipates that this exceptionally low range for the federal funds rate will be appropriate at least as long as the unemployment rate remains above 6-1/2 percent, inflation between one and two years ahead is projected to be no more than a half percentage point above the Committee‘s 2
10 See
Bernanke (2012).
11 See
the 9/13/2012 FOMC statement (Table A1).
10 percent longer-run goal, and longer-term inflation expectations continue to be well anchored.“ 12
The last phase (dubbed "Tapering") in the Federal Reserve’s LSAP’s programs was commenced in the December 18, 2013 meeting, when, in response to an improvement in economic activity and labor market conditions, the FOMC decided to reduce its monthly asset purchase for the first time, dropping the total purchases to $75 billion from $85 billion beginning in January. While maintaining its threshold-based guidance, the Federal Reserve created expectations of continuing to taper at a similar pace, while refraining from a firm commitment: “ If incoming information broadly supports the Committee’s expectation of ongoing improvement in labor market conditions and inflation moving back toward its longer-run objective, the Committee will likely reduce the pace of asset purchases in further measured steps at future meetings. However, asset purchases are not on a preset course, and the Committee’s decisions about their pace will remain contingent on the Committee’s outlook for the labor market and inflation as well as its assessment of the likely efficacity and costs of such purchases.“ 13 A similar pace of tapering (by $10 billion) was maintained for each of the subsequent FOMC meetings (January, March, April, June, July, September, October) leading to a conclusion to asset purchase programs in October 2014. At this point, the Federal Reserve’s balance sheet had expanded to close to $4.5 trillion, more than double the slightly over $2 trillion balance sheet at the commencement of the LSAP operations. To put this figure into perspective, it amounted to close to 30 percent of current yearly GDP.
B. Data This paper evaluates the effects of unconventional monetary policy measured by the expansion of the Federal Reserve’s balance sheet. Looking at quantities allows one to asses the "bang for the buck" of these operations and the importance of channels like portfolio rebalancing. An important empirical choice relates to which balance sheet aggregate to use for the estimation. Previous literature has employed various measures of balance sheet expansion. Some papers have used total central bank assets, thus combining all types of central bank policies (see 12 See
the 12/11/2012 FOMC Press Release.
13 See
the 12/18/2013 FOMC Press Release.
11 e.g. Gambacorta, Hofmann, and Peersman (2014)), while others have been more specific, analyzing the impact of securities purchases of treasuries and mortgage-backed securities (see, e.g. (Weale and Wieladek (2014)). This paper’s preferred balance sheet measure are "securities held outright", which includes all asset holdings (treasuries, federal agency and mortgage-backed securities) from the consolidated statement of all Federal Reserve Banks (form H.4.1. Table 8). We find this metric more relevant since, compared to total assets, it abstracts from the impact of temporary operations undertaken by the Federal Reserve (like the Term Auction Facility), which in the first part of our sample were being wound down (for a graphical comparison of these series see Figure 2). However, for robustness purposes and in order to enable comparison with earlier research, we estimate also the impact of total asset purchases. The macro dataset consists in a balanced panel of one hundred time series based on a relatively well-studied dataset (see, e.g. Stock and Watson (2005) and BBE, among many others and Table 3 for a complete description). One key difference from the above-mentioned papers is that we abstract from all the financial variables (bond yields, stock market variables, exchange rates) as they are not the focus of this paper (and they have been analyzed in numerous other papers). The frequency of the data is monthly and it covers the period 2008:10 to 2014:11. We thus capture the entire LSAP operations period, which commenced with the first QE1 announcement on November 25, 2008 and ended with Tapering in October 2014. In the robustness section we discuss some effects of chosing an alternative starting date for the estimation.
C. Construction of the Announcement Shock Series This paper uses balance sheet stock variables to identify unconventional monetary policy shocks. This strategy faces the potential criticism that these measures were in general announced ahead of their actual implementation and thus were to a large extent anticipated. It is therefore important to assess whether taking into account the impact of the announcements would significantly alter our results. This is particularly important when shocks are identified in a VAR framework using timing restrictions. This section describes in detail how we construct our "announcements" variables. We focus our attention on the announcements which contained an explicit quantitative target, since an analysis of the broader implications of forward guidance is outside the scope of this paper. Appendix .1 provides the list of the announcements that we have taken into account. Weale
12 and Wieladek (2014) pursue a similar approach, however, their estimation does not cover QE3 or the Taper period. We construct several "announcements" series to incorporate various assumptions about timing of the impact of each operation (see Figure 3). First, let’s note that one can distinguish between three types of communications undertaken by the Federal Reserve to announce balance sheet operations. First, the FOMC has issued statements containing precise quantitative targets with a specified time-horizon: QE1, QE2 and Tapering fall in this category (with some possible different interpretation for Tapering). Second, the Federal Reserve announced operations implying maturity extension, such as the two Operations Twist. Third, it has announced open-ended purchases, with a monthly target but an unspecified duration, such as QE3. In the case of Tapering, the Federal Reserve retained considerable discretion as to the continuation of the reduction in asset purchases from one operation to the other, so to some extent this operation can also be also considered as having unspecified duration. The first announcements series we construct (abbreviated ANN1) assumes that the entire impact of each operation takes place on the day when the announcement was made. Such series would capture well the announcement shock if the following assumptions held: the announcement itself was not anticipated, it would be fully credible and agents would immediately incorporate it into their decision-making. From the perspective of the channels of transmission of quantitative easing, this series captures best the signalling effect. More precisely, ANN1 accounts for the full impact of QE1 and QE2 on the days they were announced. QE1 consisted of two announcements: on November 25, 2008 and March 18, 2010, for totals of USD 600 billion and respectively USD 1.25 trillion of assets. QE2 involved one announcement for USD 600 billion on Novermber 3rd, 2010. The two Operations Twist have no effects, as they simply represented an asset substitution in order to extend the maturity of the balance sheet without any net asset purchases. Accounting for QE3 is more difficult since its duration was less certain. The September 13, 2012 announcement of purchases of USD40 billion per month of MBS can be reasonably interpreted as having an expected duration of at least until the end of the year. However, the December 12, 2012 announcement contained no such guidance on duration, so one needs to make some assumptions in order to quantify its effect. We assume that QE3 operations were assumed to continue for one year following the December 13, 2012 announcement, at the rate of USD85 billion per month. The one year duration is correct ex-post (Tapering was announced in December 2013) as well as in line with reasonable expectations at the time of the announcement (the September 13, 2012 FOMC press release contained the following time
13 specific guidance: "... the Committee ... currently anticipates that exceptionally low levels for the federal funds rate are likely to be warranted at least through mid-2015"14 ). In the case of Tapering, as before, we assume that the entire effect of the operation would be internalized by agents on the date of the FOMC statement (December 18, 2013). The quantitative impact of the operation can be easily computed as the aggregation of the operations, which were pre-announced to decrease asset purchases at a rate of USD10 billion at each of the ensuing FOMC meetings and were expected to end in October 2014. Let’s note that compared to earlier papers, we have the advantage of being able to include the entire Tapering period in our estimation. For robustness purposes, we experiment with several alternative definitions of the announcements shock. The second series (called ANN2) is similar to ANN1 except the way it takes into account QE3 and the Tapering period. For these two operations with uncertain duration and monthly targets, we assume that the shock in each month is equal to the announced quantities for each month. For example, for QE3 during 2014, this would amount to USD85 billion per month. This definition of the shock assumes that, since the Federal Reserve did not commit to a certain duration of QE3 or Tapering, agents would every month update their information set with the information of whether the operation is continued and the size of the purchases. This would be a valid representation of the shock if there would be some uncertainty as to the exact timing or magnitude of the central bank operation, which arguably characterized QE3 and the Tapering periods. Thus ANN2 series differs from ANN1 in that after December 2012 it has a gradual and staggered increase. A third announcements series (ANN3) is produced when we assume that QE3 had unknown duration (thus its impact is modelled as incremental from month to month), while the effect of Tapering is assumed to be in one operation (based on the interpretation that the Federal Reserve gave sufficient information so that market particiants would correctly anticipate its duration as well-defined). This series thus would be a mix of the two previous ones, exhibiting a slight difference towards the end. So far we have refrained from modelling Operation Twist, as it did not involved an increase in purchases but rather a maturity swap. In order to take into account the maturity transformation aspect, we experiment with an additional annoucements series called ANN4. Essentially, ANN4 captures all announcements of long-term securities purchases, including Treasuries, MBS and Agency securities. Both QE3 and Tapering are assumed to be incorporated into the 14 Assuming
that QE3 would entend to a one year and a half period did not materially change the results.
14 agents’ information set gradually (i.e. as in ANN 2). Thus, Operation Twist 1 accounts for a shock of USD400 billion and Operation Twist 2 for a further USD267 billion of long-term securities at the time of their respective announcements.
D. Methodology The recent econometric literature has made substantial progress in developing methods to reduce the curse of dimensionality problem inherent in large VARs, thus allowing the exploitation of more comprehensive sets of information than before 15 . Such approaches, in which a wide set of variables examined by central banks is taken into account, have been shown to improve the estimation of monetary policy VARs along various dimensions, for example by improving forecasting performance and eliminating issues like the price puzzle. One of the most widely used methods to address the issue of the curse of dimensionality has been to employ dynamic factor models 16 . These are based on the premise that there exists a small number of unobserved common dynamic factors that explain most of the observed comovements of macro-economic time series. The desire to be able to conduct structural analysis has motivated research into how to integrate factor methods into VARs. BBE propose a "Factor Augmented" VAR (FAVAR) model, where factors from a large cross-section of economic indicators are included as extra endogenous variables in a VAR. They find that the FAVAR provides a good description of the monetary transmission mechanism. This paper employs a FAVAR model to estimate the effects of asset purchases in the ZLB regime. Let’s start by assuming that a large number of “informational“ time series, denoted Xt can be summarized by a small number of unobservable factors Ft and a vector Yt of observable economic variables:
Xt = ΛF Ft + ΛY Yt + εt
(1)
where ΛF is a N × K matrix of factor loadings, ΛY is a N × M matrix of loadings of the other observable macroeconomic variables and εt is a N × 1 vector of error terms with mean zero, 15 See,
e.g. Stock and Watson (2002a), Stock and Watson (2002b), Giannone, Reichlin, and Sala (2004), Bernanke, Eliasz, and Boivin (2005), Forni and others (2008), Banbura, Giannone, and Reichlin (2010).
16 See.e.g.
Forni and others (2008), Stock and Watson (2002a), Stock and Watson (2002b), etc.
15 either normal and serially uncorrelated or weakly correlated, depending on whether the estimation is by maximum likelihood or principal components, as described below. As far as dimensionality is concerned, if K × 1 is the size of Ft , N × 1 is the size of Xt and M × 1 the dimension of Yt , then K + M N, that is, the rich information contained in the large set of economic variables Xt should be meaningfully summarized by a low-dimensional vector of factors and the policy variable. In our application, Yt will contain only the policy variable the asset purchases/announcements - thus M will be equal to 1. We further assume that the joint dynamics of the factors and the observable variable can be described by a VAR(p) model:
Ft Yt
! = Φ1
Ft−1 Yt−1
! + ... + Φ p
Ft−p Yt−p
! + vt
(2)
where the error term vt is assumed to have mean 0 and covariance matrix Q. Estimation of the model (1) and (2) can be done in two ways: a two-step principal components approach (PC) or a single-step Bayesian likelihood approach (see Appendix .3 for a detailed exposition). The first estimation procedure follows Stock and Watson (2002b). In the first step, principal components are used to extract the common factors. Next, the FAVAR equation is estimated by Bayesian methods, replacing Ft by the estimated factors. As the two-step approach implies the presence of generated regressors, confidence intervals for the impulse responses are obtained through bootstrapping. This method has the advantage of being computationally simple. It also imposes few distributional assumptions and allows for some degree of cross-correlation in the idiosyncratic error term εt . The second approach assumes independent normal errors and estimates (1) and (2) jointly by maximum likelihood. However, for highly dimensional problems like this one, such an approach is computationally not feasible. Instead, as in BBE we consider joint estimation by likelihood-based Gibbs sampling. As BBE comment in their paper, each of the methods has its advantages and there is no clear ex-ante preferred approach. As the first approach is semi-parametric while the second one is fully parametric, they will produce different biases and variances. We experiment with several prior specifications (full prior specifications and the estimation algorithms are explained in Appendix .3). In the baseline estimation reported below, we have
16 imposed a relatively uninformative independent Normal-Wishart prior on the parameters of the FAVAR equation (2) and a uninformative Normal-Gamma prior in the factor equation when using the one-step procedure (1). Experimentation with several alternative priors did not change our results qualitatively (see the robustness section). The correct specification of the number of factors is critical for the empirical validity of the factor model as well as for properly capturing the effects of the quantitative easing shock. Our choice on the number of factors is guided both by the original paper of BBE as well as the literature on the determination of the number of factors. BBE employ 3 and respectively 5 factors finding comparable results, however, the model with 5 factors tends to alleviate some puzzling results, at least in the two-step approach (such as for example the liquidity puzzle). We also consider the Bai and Ng (2002) criteria, which all suggest a relatively small number of factors. The preferred criteria for this type of models IC p1 and IC p2 both find 4 factors while the PC p1 and PC p2 identify respectively 6 and 5 common factors17 . We have experimented with 3 to 7 factors, however, this is subject to some constraints, due to the rapid loss of degrees of freedom. Although this paper does benefit from more data than previous papers, our sample size is relatively short with a total of T = 73 observations in the baseline specification. This imposes limits on the number of factors and lags that can be included while still producing meaningful estimates. While one could expand the size of the sample for example by adding the data from the onset of the financial crisis, we prefer not to, since this would contaminate our findings as a result of the temporary measures that the Federal Reserve has taken, which also had balance sheet effects 18 . Closely related papers have dealt with this issue in the following way. Wu and Xia (2014) estimate a FAVAR(1) with 3 factors for the duration of the ZILB period (with 46 observations). Weale and Wieladek (2014) use use Bayesian methods for a 5 variable VAR and assume 2 lags (with 51 observations). We find that it is possible to estimate the FAVAR as long as we p(K + M) + 1 < T /3, which is essentially fitting up to T /3 parameters per equation. With 3 factors, we are able to run the model with 6 lags, while with 5 factors, we can go up to 4 lags. These results are obtained still in the context of using relatively uninformative priors. We have also experimented imposing tighter priors, which make it possible to estimate the model based on more than 5 factors, 17 Bai
and Ng (2002) note that the IC p criteria tend to underparametrize for small samples, while the PC p tend to overparametrize. They define small samples as when min(N, T ) < 60. The length of our sample is slighly larger than 60.
18 For
example, the Federal Reserve’s temporary lending of securities is reflected in the balance sheet
17 however, we find these experiments do not affect our main conclusions (see robustness section for more details). The reported results are based on 5 factors and 4 lags (standard residuals checks show little evidence of autocorrelation). As it is typical in this literature, we find that the first 5 components explain slightly over 50% of the dynamics of the series. The observed macroeconomic variables load on the factors as can be seen in Figure 5. While one may associate these factors to underlying unobservables like real activity, inflation, housing markets, etc, a clear identification of the factors is not possible. The advantage of the FAVAR method, however, is that this is not necessary, since impulse response functions can be constructed for any variables in the information set using the loadings. We identify the asset purchase shock through timing assumptions. The recursive strategy is borrowed from the identification of conventional monetary policy shocks, where it is quite standard. However, contemporaneous zero restrictions have been applied to identify exogenous innovations to the central bank balance sheet in Gambacorta, Hofmann, and Peersman (2014) and Weale and Wieladek (2014) 19 . Essentially, we order the policy variable (asset purchase or announcements) last, which is consistent with the assumption that the latent factors do not respond to the monetary policy innovation during the month. The restrictions are credible as we have only "slow-moving" variables in our dataset, thus the factors themselves can be regarded as "slow-moving" relative to monetary policy.
III. R ESULTS
A. How Asset Purchases Affect the Real Economy: Channels Before analyzing the empirical results, it seems useful to review the main transmission channels proposed in the literature. These channels operate largely simultaneously, often reinforcing each other and thus are not always easy to disentagle empirically (see also Figure 4). The first main channel is through portfolio rebalancing effects. The general idea is that central bank purchases of particular assets crowd out private investors, who then rebalance their portfolios towards other financial assets, leading to a chain of price effects. For example, central bank purchases of government bonds increase monetary deposits for the sellers of 19 The
large number of variables does not allow us to use another structural identification or sign restrictions, as it is difficult to find enough restrictions to be supported by theory.
18 these bonds. However, these agents are unlikely to want to hold low yielding excess money balances so they would bid up the price of other bonds and potentially of other assets. The breadth of this process is likely to depend on the degree of market segmentation. In theory, the process should continue to the point where on aggregate, in the economy, the prices of assets have been bid up and their yields lowered to the point that they equal the opportunity costs of holding the excess monetary liquidy, so that agents are indifferent between holding the overall supplies of assets and money. In practice, asset purchases would start by affecting the yields (and risk premia) of the purchased assets, like government bonds and then spillover to additional price effects on a broader range of assets (this would depend on the degree of market segmentation and investor preferred-habitat behaviour). Related to portfolio rebalancing, the finance literature has emphasized two subchannels in fixed income markets. First, the scarcity channel is a mechanism by which Fed purchases of assets with a specific maturity lead to higher prices (and lower yields) of securities with similar maturities. Second, the duration channel is a mechanism by which the removal, by means of Fed purchases, of aggregate duration from the outstanding stock of Treasury debt reduces term premiums on securities across maturities (see, e.g. Vayanos and Vila (2009) for a model, and Krishnamurthy and Vissing-Jorgensen (2011) for some evidence). From a macroeconomic perspective, the consequence of these channels, namely a reduction in yields and risk premia for various financial assets, should translate in lower borrowing costs for households and corporations, and thus should stimulate borrowing, consumption and investment. Also as a consequence of asset price increases, one should observe positive wealth effects on asset holders, with further expansionary effects (including positive financial accelerator effects). The improvement in the aggregate economy should further reduce default risk (for both corporations and households), which would further encourage activity (this has been dubbed the default risk channel by some authors, see Krishnamurthy and VissingJorgensen (2011)). The second main channel of transmission of LSAPs is the signalling channel. This channel may work through the "commitment to keep rates low" (see, e.g. Krishnamurthy and VissingJorgensen (2011)). In other words, the quantitative easing measures tend to signal that the central bank is committed to maintaining accomodative policies for some time, either by balance sheet expansion and/or by maintaining interest rates lower than, for example, what a Taylor rule may call for, after the economy recovers (see, e.g. Eggertsson and Woodford (2003)). Asset purchases (in particular of long-term assets) serve as a credible commitment device since the central bank takes a substantial risk on its balance sheet, as higher rates im-
19 ply potentially significant losses (see e.g. James and others (2003)). In this context, QE may help anchor expectations on the shape of the yield curve, through the expectations hypothesis. These effects may not only stimulate aggregate demand, but also have implications for inflation expectations (see the inflation channel in Krishnamurthy and Vissing-Jorgensen (2011)). Finally, there may be a more generalized impact on expectations, for example consumer or business confidence, through the perceived desire of the central bank to stimulate activity.
B. Results In Figure 6 - Figure 24 we plot the impulse response functions of all variables to several measures of balance sheet expansion and announcements. Each row shows impulse responses based on a different definition of the shock. For example, our preferred measure of asset purchases, the increase in the portfolio of government and agency securities held outright (FRAGB) is presented on top. The response to increases in total assets (FRATO) and reserve balances of the banking system (FRBW) are plotted next. The following series represent various measures of announcements regarding LSAP operations, which were described in detail in a previous section. The shocks are calibrated to a 1 percent increase in the ratio of asset purchases to 2009:1 GDP. The shaded areas represent 90 percent confidence intervals.
1. Responses of Real Activity, Income, Consumption and Sales We first look at the impact of LSAPs on measures of real activity (see Figure 6). We find robust evidence of strong expansionary effects. Real GDP, as measured by Macroeconomic Advisers’ index, rises significantly regardless of the shock. The magnitude of the peak response ranges between approximately 0.5%-1%. The recovery seems to be quite persistent, as most of the responses are still positive 3 years after the shock. Business cycle conditions, as measured by the Arouba-Diebold-Scotti index, are found to increase very significantly and persistently, at the maximum by around 1%-2%. The PMI Composite Index for manufacturing very closely mirrors the improvement in business cyle. Capacity utilization also significantly increases for about one year after the shock. We find that industrial production is strongly boosted and the effects are both very significant and persistent (see Figure 7 and Figure 8). While there are differences by subsectors of industrial activity, we find the expansion to be quite generalized and quantitatively robust, with the
20 peak median responses in the range of 0.5%-1.5%. Final and intermediate goods, manufacturing and business equipment are the most buoyant while utilities and non-durable consumer goods are among the least. Figure 9 plots personal income - total and net - and it is apparent that both measures significantly increase after the asset purchase shocks by about 0.5%. As income growts, there is an almost one-to-one rise in personal consumption expenditures. We also find that manufacturing and trade sales are boosted significantly (which is in line with the results on industrial activity), while retail sales are less so. Figure 10 shows that the improvement in business confidence (as measured by the disaggregated PMIs) is both significant and persistent. Measures of new orders also increase (for durable and capital goods), as do inventories (see Figure 11). Together these are consistent with the rebound in overall industrial activity.
2. Responses of Labor Market Variables Turning on to the labor markets, we find strong evidence of significant improvements. The unemployment rate decreases by between 0.4%-2% at the maximum level reached after about half a year to one year (see Figure 12). The average duration of unemployment seems to decline strongly, while average weekly hours do not exhibit significant responses. Corroborating these findings, we further see that the number of the unemployed goes down, driven by both medium and long-term unemployment (all categories over 5 weeks unemployment exhibit significant declines, see Figure 13). The employment figures are also convincingly increasing across all sectors following the unconventional monetary stimulus (see Figure 14 to Figure 16). The key figure of nonfarm employees increases in the median by a maximum of 0.4%-2.5% and the response is highly significant for one to two years. In what seems to be a particularly robust result, we notice a similar dynamics and magnitudes in all the 12 sectors that are analyzed. These findings support the conclusion that the Federal Reserve’s balance sheet expansion significantly supported the recovery in the labor markets, thus achieving one of the main objectives of these policies. However, the dynamics of wages has remained subdued, as can be seen in Figure 17. Average hourly earnings in goods-producing industries, manufacturing or construction do not seem to increase or may have even declined following the Federal Reserve’s asset purchases.
21 3. Response of Housing Markets The financial crisis started in the housing market and lead to a collapse in the sector. The LSAPs were implemented to a large extent via purchases of agency mortgage-backed securities in order to provide direct support to this sector which is very critical to economic activity in the United States. Thus, it seems interesting to explore whether the Federal Reserve’s actions helped revive the housing market. We find that in general the evidence supports that claim (see Figure 18 and Figure 19). We find in most areas a significant positive impact of asset purchases on housing starts, which becomes significant about one to two years after the shock. We find that the responses to the asset purchase shocks are larger than to the announcements shocks. Looking at housing permits points to a similar positive picture, although again there is some variability across the regions. However, looking at the overall indicators, we interpret the evidence as pointing to a recovery in the housing sector as a result of the LSAP programs, which presumably contributed to the overall recovery.
4. Responses of Monetary and Credit Aggregates While the LSAP operations by their nature lead to an increase in base money, did this translate into an increase in the higher monetary aggregates and in credit to the economy ? We find significant evidence that the monetary aggregates M1 and M2 also expanded very significantly (Figure 20). Importantly, we find evidence that the quantitative easing did impact positively credit to the private sector. This is evidenced by the highly significant and persistent increases in both commercial and industrial loans by up to 4-7%. Figure 20 further documents that consumer credit also went up very strongly and significantly (up to around 5-8% in some specifications).
5. Responses of Prices Figure 21 - Figure 24 document the impact on prices. Producer prices seem to significantly decline, by up to 2-4%. Moving on to consumer prices, the behaviour of key figures like the headline CPI for urban consumers or the Federal Reserve’s preferred measure of inflationary pressures, the index for personal consumption expenditures (PCE) also suggests a strong and
22 persistent decline in inflation (at the peak, by about 1-3%, depending on the specification). Looking at various subindeces, it appears that with the exception of services prices which increased quite buoyantly, most categories of consumer goods exhibited a very subdued price dynamics or there is evidence of significant price declines. Overall these results suggest virtually negligible positive impact of QE on inflation up to this stage. On the contrary, we find deflationary effects, which is in line with accounts of considerable slack which has characterized this recovery.
6. Summary of LSAPs Effects Altogether, these findings paint of picture of asset purchases having a strong impact on real measures of activity, starting from industrial activity, manufacturing and moving on to housing markets - and as a result significantly reducing unemployment. The LSAPs have contributed to both a rebound in labor markets and in credit, so fears of a "jobless and creditless" recovery appear unfounded. Our results also reveal that LSAPs did not have a significant positive impact on nominal variables, like prices and wages, on the contrary, the effects so far has rather been deflationary. This would tend to indicate still large levels of slack in the economy and a weakness in private demand compared to a more buoyant supply side, in spite of unprecedented balance sheet expansion by the Federal Reserve. Regarding the transmission channels of quantitative easing measures, these results seem to suggest that both signalling and portfolio rebalancing effects play a role. The first channel is supported by findings of significant response to the announcements series shocks. However, we find the portfolio (scarcity) chanel also to be important, since the responses tend to be larger to the asset purchase shocks than to the announcements shocks, meaning that the full impact can be seen when the measures are actually implemented (see Table 1 20 ). In general, responses are qualitatively very similar across the various specification of the shocks, in spite of their significant differences, which increases the credibility of the results. Responses to total asset shocks (FRATO) and outright purchases (FRAGB) are very similar in shape and size, as are the announcement series (in particular ANN2 to ANN4). Let’s just note that our preferred asset purchases metric, outright purchases, tends to produce both the largest
20 The
table presents peak effects for some key variables. These are generally maximum effects, with the exception of variables which declined in response to the shocks, where we have considered the minimum. Note that prices fell in the latter category since in response to all shocks, they were found to be falling.
23 magnitudes and the most persistent responses, highlighting the importance of the specific balance sheet measure for the quantitative conclusions.
C. Robustness In terms of robustness exercises, several alternative specifications have been already mentioned and are reported here (see Table 2 for results on some key variables of interest). We have conducted experiments with various numbers of factors in the FAVAR equation (as well as various lags). Most of our specifications have involved between 3 to 5 factors, but we have run the estimation with up to 7 factors. While we find quantitative differences in the results, as well as different levels of significance, the shape of the estimated impulse responses are remarkably similar to the baseline and the maximum impacts are comparable. In terms of robustness to different priors, we have experimented with losening and tightening the priors, as well as with different priors. As BBE, we have also implemented a conjugate Normal-Wishart prior matching the variances of the modified Minnesota prior in the FAVAR equation. Here of course the possibilities are numerous and some results are more robust than others. However, we report for example the peak effects from using the Minnesota prior in the FAVAR equation, which are very close to those from the independent Normal InverseWishart. Most of our experiments with relatively diffuse priors look very similar, confirming the fact that the dataset is very informative and speaks for itself without a lot of ex-ante structure. As discussed in the methodological section, we have estimated the model also jointly via likelihood-based Gibbs sampling and found that these generally confirm the results from the two-step approach using principal components. However, in some cases the results did not turn out to be as significant as in the 2-step PC method (output, industrial production, housing markets, prices, etc.) Finally, we have carried out a robustness exercise to varying the starting date. One possibility is to start our sample at the beginning of 2009, to cover only the ZLB regime (as on December 16, 2008 the Federal Reserve lowered the federal funds rate to effectively zero). However, this sample would be missing the first QE1 announcement (which, according to various estimates, was the most impactful). Our results from using this shorter sample are not significantly different, suggesting that for most macro variables, the bulk of the impact came through the implementation of these measures.
24 D. Comparison with Other Studies We discuss in this section how our results compare with the most closely related studies. Wu and Xia (2014) use a similar methodology (FAVAR) based on broadly the same large dataset (97 macro variables) and a shorter estimation sample. They identify the effects of an unconventional monetary policy shock measured by the shadow interest rate constructed from a term structure model and similar to BBE, employ a recursive identification. In their results based on the crisis sample (2009:7-2013:5), they report 5 impulse responses. In response to a 25 basis points shock to monetary policy, they find a very small and insignificant response of industrial production (approximately 0.2%), a small and insignificant reduction in the CPI (of up to 0.2%), a significant increase in housing starts by about 3%, a decrease in the unemployment rate by about 0.23% and an increase in capacity utilization by about 0.6%. While they use a different monetary policy shock and a more "simple" FAVAR(1), their results are qualitatively quite comparable with this paper. Among the papers which identify the asset purchase shocks using central bank balance sheet variables, Gambacorta, Hofmann, and Peersman (2014) examine the macroeconomic impact of unconventional policies in 8 OECD countries using a small panel VAR (data from 2007:1 - 2011:6). Using a sign restrictions identification procedure, they find in their baseline specification that both output and inflation significantly increase in response to an asset purchase shock, modeled as an increase in total central bank assets. However, the response of inflation is not robust to the inclusion of government debt and a modification of the identification scheme. Baumeister and Benati (2012) and Kapetanios and others (2012) also use sign restrictions to identify a “pure“ spread shock, which compresses the spread between the long and the short rate, while leaving the short rate unchanged. Baumeister and Benati (2012) find that a spread shock had a significant impact on output growth, inflation and unemployment in the US and the UK. Without the large scale asset purchas program, the US economy would have been in deflation, with annualized inflation being as low as minus 1 percent in 2009Q2, annualized GDP would have contracted by 10% in the first quarter of 2009, and the unemployment rate would have reached 10.6% at the end of 2009. Kapetanios and others (2012) who study only the UK, find that QE had a peak effect on the level of real GDP of around 1 1/2% and of about 1 1/4% on annual CPI inflation. Similar to this paper, Weale and Wieladek (2014) use the expansion in central bank balance sheets to identify both asset purchase and announcement shocks. They find that QE may have
25 had a peak effect on the level of real GDP of around 1.5% and a peak effect on annual CPI inflation of about 1.25% (increase), on a sample from 2009:3 - 2013:5. Maybe with the exception of Weale and Wieladek (2014), it is not entirely straight-forward to compare quantitatively results in this paper with these earlier studies. However, in a broad sense it seems that this paper confirms the strong expansionary effects of QE on output, but if finds a negative impact on inflation. It is interesting that the only paper using a similar data-rich model (Wu and Xia (2014)) is able to document a decline in prices. Thus, it may be that this key result is due to a combination of the longer sample and the different, more comprehensive methodology. In addition, this paper documents more thoroughly than previous papers the transmission of asset purchase shocks to real and nominal variables, differentiated by announcement versus implementation, which adds to our understanding of these effects.
IV. C ONCLUSIONS
This paper undertakes the most comprehensive-to-date investigation of the effects of the Federal Reserve’s large asset purchase programs on a relatively well-known large macroeconomic dataset, for the entire period of balance sheet expansion, until the end of tapering. We find that these unconventional policies have significantly stimulated the real economy, boosting output, income, consumption, industrial activity, investment and confidence. They also spurred a recovery in the labor and housing markets. At the same time, in spite of the increase in money and credit aggregates, there has been little positive impact on inflation or wages. According to these findings, some fears of a "creditless and jobless recovery" or inflationary consequences of LSAPs have been so far unsubstantiated by the data. Moreover, our results are robust to analyzing LSAP announcements versus actual asset purchases. The estimates suggest that both the portfolio rebalancing and the signaling channels have been of considerable importance for the transmission of asset purchases to the broader economy. In the end, a word of warning regarding the intepretation of our results. While this research suggest overwhelmingly positive short and medium-run effects of quantitative easing policies on real variables (arguably one of the key objectives of policy-makers), it does not look into the effects of such measures on, for example, financial market variables (such as measures financial stability or risk-taking). Whether LSAPs affected incentives or even lead to reallocation (possibly missalocation) in the financial world, which may later on have a bearing on
26 real activity, are interesting enough topics that would warrant more investigation in future research.
27
Figure 1. Federal Reserve balances sheet asset composition, by type, 2007:1-2014:7. Source: The Federal Reserve.
Figure 2. Evolution of various measures of balance sheet expansion of Federal Reserve Banks, 2008:1-2014:11. Source: Consolidated Statement of Condition of All Federal Reserve Banks (H.4.1. Table 8)
28
Figure 3. The announcements series are constructed based on FOMC announcements, as described in detail in the paper. Briefly, ANN1 assumes that the full quantitative impact of each announcement is felt on the date of the announcement (in the case of QE3, which has no quantitative target, the assumption is that these operations would continue for 1 year). ANN2 assumes that the impact of QE3 and the Tapper is felt only gradually given the announced pace of these operations. ANN3 assumes that QE3 impacts only gradually at the monthly preannounced rate, while the effect of the Taper is immediate, since the Federal Reserve provided indication as to the cumulative impact of these operations. ANN4 takes into account all announcements of purchases of long-term securities, thus incoporating the Operation Twist 1 and 2 (assumed to have an immediate impact).
QE
Signalling channel
Portfolio rebalancing
Consumer/business confidence
Yield curve flattens and shifts down
Inflation expectations Inflation uncertainty
Expectations channel (yield curve)
Inflation channel
Yield curve flattens
Asset prices rise Risk premia fall
Confidence channel
Duration channel
Scarcity channel
Increase inflation
Stimulate activity
29
Figure 4. Transmission channels of quantitative easing policies (QE)
30
Loadings on macro factor 1
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Figure 5. Loadings of the standardized economic variables on the 5 macroeconomic factors. On the X-axis are the identification numbers for the economic variables as in Table 2.
31
Figure 6. Impulse response functions to various measures of asset purchase shocks. RGDP = Monthly Real GDP Index; ADSBCI = Aruoba-Diebold-Scotti Business Conditions Index; INDPRO = Industrial Production Index; NAPM = ISM Manufacturing: Production Index; TCU = Capacity Utilization: Total Industry. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
32
Figure 7. Impulse response functions to various measures of asset purchase shocks. IPFINAL = Industrial Production: Final Products (Market Group); IPCONGD = Industrial Production: Consumer Goods; IPDCONGD = Industrial Production: Durable Consumer Goods; IPNCONGD = Industrial Production: Nondurable Consumer Goods; IPBUSEQ = Industrial Production: Business Equipment. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
33
Figure 8. Impulse response functions to various measures of asset purchase shocks. IPMAT = Industrial Production: Materials; IPDMAT = Industrial Production: Durable Materials; IPNMAT = Industrial Production: Nondurable Materials; IPMANSICS = Industrial Production: Manufacturing (SIC); IPUTIL = Industrial Production: Electric and Gas Utilities. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets; FRBW = Reserve Balances. The announcement series ANN1-4, ANN MBS and ANN TRES are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
34
Figure 9. Impulse response functions to various measures of asset purchase shocks. RPI = Real Personal Income; W875RX1 = Real personal income excluding current transfer receipts; DPCERA3M086SBEA = Real personal consumption expenditures (chain-type quantity index); CMRMTSPL= Real Manufacturing and Trade Industries Sales; RSAFS = Retail and Food Services Sales. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
35
Figure 10. Impulse response functions to various measures of asset purchase shocks. NAPMI = ISM Manufacturing: Inventories Index; NAPMNOI = ISM Manufacturing: New Orders Index; NAPMSDI = ISM Manufacturing: Supplier Deliveries Index; NAPMII = ISM Manufacturing: Inventories Index; ACOGNO = Value of Manufacturers’ New Orders for Consumer Goods Industries. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
36
Figure 11. Impulse response functions to various measures of asset purchase shocks. UMDMNO = Value of Manufacturers’ New Orders for Durable Goods Industries; ANDENO = Value of Manufacturers’ New Orders for Capital Goods: Nondefense Capital Goods Industries; AMDMUO = Value of Manufacturers’ Unfilled Orders for Durable Goods Industries; BUSINV = Total Business Inventories; ISRATIO = Total Business: Inventories to Sales Ratio. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
37
Figure 12. Impulse response functions to various measures of asset purchase shocks. UNRATE = Civilian Unemployment Rate; UEMPMEAN = Average (Mean) Duration of Unemployment; CES0600000007 = Average Weekly Hours of Production and Nonsupervisory Employees: GoodsProducing; AWOTMAN = Average Weekly Overtime Hours of Production and Nonsupervisory Employees: Manufacturing; AWHMAN = Average Weekly Hours of Production and Nonsupervisory Employees: Manufacturing. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
38
Figure 13. Impulse response functions to various measures of asset purchase shocks. UEMPLT5 = Number of Civilians Unemployed - Less Than 5 Weeks; UEMP5TO14 = Number of Civilians Unemployed for 5 to 14 Weeks; UEMP15OV = Number of Civilians Unemployed for 15 Weeks & Over; UEMP15T26 = Number of Civilians Unemployed for 15 to 26 Weeks; UEMP27OV = Number of Civilians Unemployed for 27 Weeks and Over. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
39
Figure 14. Impulse response functions to various measures of asset purchase shocks. CLF16OV = Civilian Labor Force; CE16OV = Civilian Employment; PAYEMS = All Employees: Total nonfarm; USGOOD = All Employees: Goods-Producing Industries; CES1021000001 = All Employees: Mining and Logging: Mining. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
40
Figure 15. Impulse response functions to various measures of asset purchase shocks. USCONS = All Employees: Construction; MANEMP = All Employees: Manufacturing; DMANEMP = All Employees: Durable goods; NDMANEMP = All Employees: Nondurable goods; SRVPRD = All Employees: Service-Providing Industries. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
41
Figure 16. Impulse response functions to various measures of asset purchase shocks. USTPU = All Employees: Trade, Transportation & Utilities; USWTRADE = All Employees: Wholesale Trade; USTRADE = All Employees: Retail Trade; USFIRE = All Employees: Financial Activities; USGOVT = All Employees: Government. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
42
Figure 17. Impulse response functions to various measures of asset purchase shocks. ICSA = Initial Claims; NAPMEI = ISM Manufacturing: Employment Index; CES0600000008 = Average Hourly Earnings of Production and Nonsupervisory Employees: Goods-Producing; CES2000000008 = Average Hourly Earnings of Production and Nonsupervisory Employees: Construction; CES3000000008 = Average Hourly Earnings of Production and Nonsupervisory Employees: Manufacturing. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
43
Figure 18. Impulse response functions to various measures of asset purchase shocks. HOUST = Housing Starts: Total: New Privately Owned Housing Units Started; HOUSTNE = Housing Starts in Northeast Census Region; HOUSTMW = Housing Starts in Midwest Census Region; HOUSTS = Housing Starts in South Census Region; HOUSTW = Housing Starts in West Census Region. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
44
Figure 19. Impulse response functions to various measures of asset purchase shocks. PERMIT = New Private Housing Units Authorized by Building Permits; PERMITNE = New Private Housing Units Authorized by Building Permits in the Northeast Census Region; PERMITMW = New Private Housing Units Authorized by Building Permits in the Midwest Census Region; PERMITS = New Private Housing Units Authorized by Building Permits in the South Census Region; PERMITW = New Private Housing Units Authorized by Building Permits in the West Census Region. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
45
Figure 20. Impulse response functions to various measures of asset purchase shocks. M1SL = M1 Money Stock; M2SL = M2 Money Stock; BUSLOANS = Commercial and Industrial Loans, All Commercial Banks; FOTA = Break-Adjusted Consumer Credit Outstanding; NONREVSL = Total Nonrevolving Credit Owned and Securitized, Outstanding. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
46
Figure 21. Impulse response functions to various measures of asset purchase shocks. PPIFGS = Producer Price Index: Finished Goods; PPIFCG = Producer Price Index: Finished Consumer Goods; PPIITM = Producer Price Index: Intermediate Materials: Supplies & Components; PPICRM = Producer Price Index: Crude Materials for Further Processing; PPICMM = Producer Price Index: Commodities: Metals and metal products: Primary nonferrous metals. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
47
Figure 22. Impulse response functions to various measures of asset purchase shocks. CPIAUCSL = Consumer Price Index for All Urban Consumers: All Items; CPIAPPSL = Consumer Price Index for All Urban Consumers: Apparel; CPITRNSL = Consumer Price Index for All Urban Consumers: Transportation; CPIMEDSL = Consumer Price Index for All Urban Consumers: Medical Care; CUSR0000SAC = Consumer Price Index for All Urban Consumers: Commodities. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
48
Figure 23. Impulse response functions to various measures of asset purchase shocks. CUUR0000SAD = Consumer Price Index for All Urban Consumers: Durables; CUSR0000SAS = Consumer Price Index for All Urban Consumers: Services; CPIULFSL = Consumer Price Index for All Urban Consumers: All Items Less Food; CUUR0000SA0L2 = Consumer Price Index for All Urban Consumers: All items less shelter; CUSR0000SA0L5 = Consumer Price Index for All Urban Consumers: All items less medical care. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
49
Figure 24. Impulse response functions to various measures of asset purchase shocks. PCEPI = Personal Consumption Expenditures: Chain-type Price Index; DDURRG3M086SBEA = Personal consumption expenditures: Durable goods (chain-type price index); DNDGRG3M086SBEA = Personal consumption expenditures: Nondurable goods (chain-type price index); DSERRG3M086SBEA = Personal consumption expenditures: Services (chain-type price index); UMCSENT = University of Michigan: Consumer Sentiment. The mnemonics for the shocks stand for: FRAGB = Securities Held Outright; FRATO = Total Assets. The announcement series ANN1-4 are as described in the text. Median responses in black, surrounded by 90 percent confidence intervals.
50 Table 1. Peak Effects on Key Variables: Baseline Specification, All Shocks
RGDP ADSBCI NAPM TCU INDPRO RPI W875RX1 DPCERA3M086SBEA BUSINV ISRATIO UNRATEˆ CE16OV PAYEMS HOUST PERMIT M2SL BUSLOANS FOTA PPIFGSˆ CPIAUCSLˆ PCEPIˆ SEPUIˆ
FRAGB
FRATO
ANN1
ANN2
ANN3
ANN4
0.77* 2.2* 1.67* 0.72* 1.36* 0.73* 0.68* 1.53* 1.68* 2.2* -2.03* 0.33* 3.35* 0.76* 0.64* 1.74* 5.23* 6.02* -3.74* -3.11* -3.66* -7.25*
0.42* 1.33* 1.15* 0.49 0.92* 0.36* 0.44* 0.6* 1.07* 1.04* -1.08* 0.15* 1.72* 0.33* 0.23* 0.85* 2.18* 2.34* -1.38* -1.1* -1.32* -2.5*
0.57* 0.79* 0.43* 0.93* 1.07* 0.35* 0.31* 0.45* 0.02 0.21 -0.46* 0.35* 0.45* 0.53* 0.19 0.04 0.41* 0.55* -1.24* -1.44* -1.31* -0.99*
0.55* 1.55* 1.06* 0.72* 1.2* 0.65* 0.74* 0.93* 1.02* 1.04* -1.16* 0.17 1.84* 0.54* 0.41* 1.03* 2.47* 2.98* -1.81* -1.56* -1.74* -4.24*
0.44* 1.39* 1.1* 1.06* 1.35* 0.57* 0.7* 0.59* 0.84* 0.63* -0.98* 0.23 1.37* 0.57* 0.26* 0.53* 1.42* 1.5* -0.7* -0.62* -0.68* -1.75*
0.42* 1.18* 0.64* 0.58* 0.98* 0.58* 0.65* 0.63* 0.69* 0.75* -0.86* 0.15 1.31* 0.55* 0.49* 0.71* 1.59* 1.61* -0.9* -0.87* -0.9* -1.65*
Notes: Table shows the peak median effects (maximum or minimum for the variable marked with " ˆ ". Each column shows results from a different shock. The results are based on the baseline specification, using estimation through 2-step PC, 5 factors and 3 lags and the independent Normal-Inverse Wishart prior in the FAVAR equation. (*) represents significance at the 90 percent level. Mnemonics correspond to: RGDP = Monthly Real GDP Index ; ADSBCI = Aruoba-Diebold-Scotti Business Conditions Index; INDPRO = Industrial Production Index; NAPM = ISM Manufacturing: Production Index; TCU = Capacity Utilization: Total Industry; RPI = Real Personal Income; W875RX1 = Real personal income excluding current transfer receipts; DPCERA3M086SBEA = Real personal consumption expenditures (chain-type quantity index); BUSINV = Total Business Inventories; UNRATE = Civilian Unemployment Rate; CE16OV = Civilian Employment; PAYEMS = All Employees: Total nonfarm; HOUST = Housing Starts: Total: New Privately Owned Housing Units Started; PERMIT = New Private Housing Units Authorized by Building Permits; M2SL = M2 Money Stock; BUSLOANS = Commercial and Industrial Loans, All Commercial Banks; FOTA = Consumer Credit Outstanding; PPIFGS = Producer Price Index: Finished Goods; CPIAUCSL = Consumer Price Index for All Urban Consumers: All Items; PCEPI = Personal Consumption Expenditures: Chain-type Price Index; SEPUI = Economic Policy Uncertainty Index.
51 Table 2. Peak Effects on Key Variables: Robustness
RGDP ADSBCI NAPM TCU INDPRO RPI W875RX1 DPCERA3M086SBEA BUSINV ISRATIO UNRATEˆ CE16OV PAYEMS HOUST PERMIT M2SL BUSLOANS FOTA PPIFGSˆ CPIAUCSLˆ PCEPIˆ SEPUIˆ
Spec 1
Spec 2
Spec 3
Spec 4
Spec 5
0.77* 2.2* 1.67* 0.72* 1.36* 0.73* 0.68* 1.53* 1.68* 2.2* -2.03* 0.33* 3.35* 0.76* 0.64* 1.74* 5.23* 6.02* -3.74* -3.11* -3.66* -7.25*
0.44* 1.72* 1.3* 0.41* 0.95* 0.43* 0.51* 1.48* 1.31 4.13 -1.98* 0.07 3.82* 0.08 0.63* 3.01* 7.31* 8.18* -3.4* -2.79* -3.35* -7.2*
0.76* 2.41* 2.03* 1.56* 1.95* 0.68* 0.8* 1.25* 1.91* 1.86* -1.96* 0.3* 3.07* 0.8 0.49 1.43* 4.13* 4.56* -2.84* -2.37* -2.75* -4.81*
0.69 0.98* 0.44 -0.41 0.1 0.23* 0.24* 1.28 0.76* 3.35* -1.8* 0.02 3.15* 0.04 0.42 2.62* 6.43* 7.49* -2.65 -2.01 -2.61 -7.3*
0.82* 2.32* 1.17* 0.48 1.44* 0.97* 0.95* 1.87* 1.09* 2.12* -1.73* 0.25 3.22* 0.71* 0.73* 1.73* 4.87* 5.57* -3.59* -3.03* -3.66* -6.38*
Notes: Table shows the peak median effects (maximum or minimum for the variable marked with " ˆ "). Spec 1: estimation through 2-step PC, with 5 factors, 3 lags, Indep. NIW prior in the FAVAR Eq. Spec 2: estimation through 2-step PC, with 3 factors, 4 lags, Indep. NIW prior in the FAVAR Eq. Spec 3: estimation through 2-step PC, with 5 factors, 3 lags, Minnesota prior in the FAVAR Eq. Spec 4: estimation through 1-step ML, with 5 factors, 3 lags, Indep. NIW prior in the FAVAR Eq. Spec 5: estimation through 2-step PC, with 5 factors, 3 lags, Indep. NIW prior, start 2009:1. (*) represents significance at the 90 percent level. Mnemonics correspond to: RGDP = Monthly Real GDP Index ; ADSBCI = Aruoba-Diebold-Scotti Business Conditions Index; INDPRO = Industrial Production Index; NAPM = ISM Manufacturing: Production Index; TCU = Capacity Utilization: Total Industry; RPI = Real Personal Income; W875RX1 = Real personal income excluding current transfer receipts; DPCERA3M086SBEA = Real personal consumption expenditures (chain-type quantity index); BUSINV = Total Business Inventories; UNRATE = Civilian Unemployment Rate; CE16OV = Civilian Employment; PAYEMS = All Employees: Total nonfarm; HOUST = Housing Starts: Total: New Privately Owned Housing Units Started; PERMIT = New Private Housing Units Authorized by Building Permits; M2SL = M2 Money Stock; BUSLOANS = Commercial and Industrial Loans, All Commercial Banks; FOTA = Consumer Credit Outstanding; PPIFGS = Producer Price Index: Finished Goods; CPIAUCSL = Consumer Price Index for All Urban Consumers: All Items; PCEPI = Personal Consumption Expenditures: Chain-type Price Index; SEPUI = Economic Policy Uncertainty Index.
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54 McAndrews, James, Asani Sarkar, and Zhenyu Wang, 2008, “The effect of the Term Auction Facility on the London Inter-Bank Offered Rate,” Techn. rep. Neely, Christopher J, 2015, “Unconventional Monetary Policy Had Large International Effects,” Journal of Banking & Finance, Vol. 52, pp. 101–111. Rogers, John H., Chiara Scotti, and Jonathan H. Wright, 2014, “Evaluating Asset-Market Effects of Unconventional Monetary Policy: A Cross-Country Comparison,” International Finance Discussion Papers 1101, Board of Governors of the Federal Reserve System (U.S.). Rosa, Carlo, 2012, “How "Unconventional" Are Large-Scale Asset Purchases? The Impact of Monetary Policy on Asset Prices,” Techn. rep. Stock, J. H., and M. W. Watson, 2002a, “Forecasting Using Principal Components from a Large Number of Predictors,” Journal of the American Statistical Association, Vol. 97, pp. 147–162. ———, 2002b, “Macroeconomic Forecasting Using Diffusion Indexes,” Journal of Business and Economics Statistics, Vol. 20, pp. 147–162. ———, 2005, “An Empirical Comparison of Methods for Forecasting Using Many Predictors,” Internet. ˘ Zs ´ Stroebel, Johannes, and John B. Taylor, 2012, “Estimated Impact of the Federal ReserveâA Mortgage-Backed Securities Purchase Program,” International Journal of Central Banking, Vol. 8, No. 2, pp. 1–42. Swanson, Eric T, Lucrezia Reichlin, and Jonathan H Wright, 2011, “Let’s Twist Again: A High-Frequency Event-Study Analysis of Operation Twist and Its Implications for QE2 [with Comments and Discussion],” Brookings Papers on Economic Activity, pp. 151–207. Taylor, John B., and John C. Williams, 2009, “A Black Swan in the Money Market,” Proceedings, , No. Jan. Vayanos, Dimitri, and Jean-Luc Vila, 2009, “A Preferred-Habitat Model of the Term Structure of Interest Rates,” CEPR Discussion Papers 7547, C.E.P.R. Discussion Papers. Weale, Martin, and Tomasz Wieladek, 2014, “ What Are the Macroeconomic Effects of Asset Purchases?” External MPC Unit Discussion Paper 42, Bank of England. Wu, Jing Cynthia, and Fan Dora Xia, 2014, “Measuring the Macroeconomic Impact of Monetary Policy at the Zero Lower Bound,” NBER Working Papers 20117, National Bureau of Economic Research, Inc.
55 .1. Chronology of Key Announcements about Changes in Asset Purchases
QE1 - December 2008 to March 2010 11/25/2008
FOMC announces plans to purchase $100 bn of Agency debt and up to $500 bn in MBS.
3/18/2009
FOMC announces that it will purchase an additional $750 bn in MBS, up to an additional $100 bn of Agency debt, and up to $300 bn of long-term US Treasuries.
QE2 - November 2010 to June 2011 11/3/2010
FOMC announces plans to purchase $600 bn of long-term US Treasuries.
Operation Twist 1 - September 2011 to June 2012 09/21/2011
FOMC announces plans to purchase $400 bn of US Treasuries with maturities of 6 to 30 years and to sell an equal amount of US Treasuries with maturities of 3 years or less.
Operation Twist 2 - June 2012 to December 2012 06/20/2012
FOMC announces an extension to the Twist programme by adding $267 bn throughout 2012.
QE3 - December 2012 to December 2013 9/13/2012
FOMC announces that it will purchase MBS at a rate of $40 bn per month, while continuing to extend the average maturity of its holdings of US Treasuries as announced in June.
12/12/2012
FOMC announces that it will continue to purchase MBS at a pace of $40 bn per month and will also purchase long-term US Treasuries at a pace of $45 bn per month.
Tapering - December 2013 to October 2014 12/18/2013
FOMC announces it would be tapering back at a rate of $10 bn at each of the next meetings (2014: January, March, April, June, July, September, October)
56 .2. Data This appendix and Table 3 describe the dataset used in the estimation. The dataset contains the slowmoving variables from original Stock and Watson (2002b) dataset. We have excluded or replaced several series which have been discontinued or present gaps. While the original dataset was based on the Global Insights Basic Economics Database, we use the same series collected by the Federal Reserve’s FRED database, while a few additional series are from Haver Analytics. The sources and brief methodology for the additional series are described below. Macroeconomic Advisers’ index of Monthly GDP (MGDP) is a monthly indicator of real aggregate output. It is consistent with official GDP at quarterly frequency while displaying intra-quarter variation determined by the monthly source data. Aruoba-Diebold-Scotti Business Conditions Index is an index designed to track real business conditions at high frequency. The components of the index are weekly initial jobless claims, monthly payroll employment, industrial production, personal income less transfer payments, manufacturing and trade sales, and quarterly real GDP. The Economic Policy Uncertainty Index, developed by Scott Baker and Nicholas Bloom of Stanford University and Steven Davis of the University of Chicago, is a monthly index made up of three components which measure economic policy uncertainty. One component quantifies newspaper coverage of policy-related economic uncertainty. A second component reflects the number of federal tax code provisions set to expire in future years. The third component uses disagreement among economic forecasters as a proxy for uncertainty. The dispersion in three forecast variables, the consumer price index (CPI), purchase of goods and services by state and local governments, and purchases of goods and services by the federal government are used as proxies for uncertainty about monetary policy and about government purchases of goods and services at the federal level. If zi,t is the original untransformed series, the transformation codes are: 1) no transformation (levels): xi,t = zi,t 2) first difference: xi,t = zi,t − zi,t−1 3) second difference: xi,t = zi,t − zi,t−2 4) logarithm: xi,t = ln(zi,t ) 5) first difference of logarithm: xi,t = ln(zi,t ) − ln(zi,t−1 ) 6) second difference of logarithm: xi,t = ln(zi,t ) − ln(zi,t−2 )
57 Table 3 lists the mnemonics, short names, the transformations for each variable.
.3. Estimation Methodology One can re-write the factor/observation equation (1) in the following way:
Xt
!
Yt
=
Λ F ΛY 0
!
1
Ft Yt
! +
et
! (3)
0
where Yt is a M × 1 vector of observable economic variables, in whose dynamic properties we are primarily interested, Ft is a K × 1 vector of unobservable factors, X t is a N × 1 vector of observable economic variables from which we will extract the factors, Λ F is a N × K matrix of factor loadings, Λ Y is a N × M matrix of loadings of the other observable macroeconomic variables Yt and et ∼ N(0, Σ), 2 ) is a diagonal matrix. For our analysis Y will consist of one variable, i.e. a where Σ = diag(σ12 , ..., σM t
measure of balance sheet expansion or annoucement about such operations. We are further assuming the following VAR(p) representation for the state equation:
Ft Yt
! = Φ1
Ft−1 Yt−1
! + ... + Φ p
Ft−p Yt−p
! + ut = Φ(L)
Ft−1 Yt−1
! + ut
(4)
where ut is an error vector of size (K + M) × 1 which is independent of et , ut ∼ N(0, Σ f ) and Φ(L) is a conformable lag polynomial of finite order p. This is a state-space system, with (3) being the measurement or observation equation and (4) the transition or FAVAR equation. Two methodologies have been employed to estimate this state-space system: a two-step procedure based on principal components and joint estimation through maximum likelihood. This section explains both in detail, starting with the first one as it is the least computationally intensive. During each procedure we need to discuss two distinct identification choices: the identification of the factors and the identification of the structural shocks.
.3.1. Two-step Estimation Through Principal Components In the first step of this procedure, the common factors Fbt are obtained only using the observation equation (3) as the first K principal components of X t . The identification of the factors is standard.
58 One can either restrict the loadings or the factors to be orthogonal, both approaches deliver the same common component and the same factor space. We impose the factor restriction. In the second step, the FAVAR equation (4) is estimated by standard methods, with Ft replaced by Fbt . The identification of the structural monetary policy shock is done via recursive ordering, with Yt being placed last. As the factors have been extracted only "slow-moving" variables, it is defensible to assume that they should not respond contemporaneously to the monetary policy innovation. Further, taking a Bayesian perspective, we model the parameters θ = Σ f , vec(Φ) as random variables, where vec(Φ) is a column vector of the elements of the stacked matrix Φ of the parameters of the lag operator Φ(L). The parameters are sampled conditional on the PC estimates of the factors using the following prior and posterior distributions.
(.3.1.1) Priors in the FAVAR equation. A very general prior for this model is the independent Normal-Wishart prior. An advantage of using this prior is that it does not involve the restriction inherent in the natural conjugate prior which BBE use. More pecisely:
p(Φ, (Σ f )−1 ) = p(Φ)p((Σ f )−1 ) where:
Φ ∼ N(Φ,V Φ ) and: (Σ f )−1 ∼ W (S−1 , ν)
This specification allows the prior covariance matrix to be anything that the researcher chooses, rather than the restrictive Σ ⊗V from the natural conjugate prior. A relatively noninformative prior is obtained by setting:
Φ = 0n
V Φ = 10(nxn) where n = (K + 1)2 p is the total number of coefficients to be estimated (the size of the vector vec(Φ)), and
59
ν =0
S = 0(K+M)(K+M)
(.3.1.2) Posteriors in the FAVAR equation. Let’s denote the history from period 1 through e T = (X1 , X2 , ..., XT ) and respectively F eT = (F1 , F2 , ..., FT ). Using this prior, the posterior period T as: X does not have the convenient form of the natural conjugate prior (e.g. posterior means and variances do not have analytical forms). However, the conditional posterior distributions do have convenient forms:
e T, F eT ∼ N(Φ, ¯ V¯Φ ) Φ | Σf ,X
where:
V −1 Φ +
V¯Φ =
T
∑
!−1 F0t−1 (Σ f )−1 Ft−1 )
t=1
and
¯ = V¯Φ Φ
V¯Φ−1 Φ +
T
∑ Ft−1 (Σ
! f −1
) Ft
t=1
while at the same time: e T, F eT ∼ W (S¯−1 , ν) ¯ (Σ f )−1 | Φ, X
where:
ν¯ = T + ν
and T
S¯ = S + ∑ (Ft − Φ(L)Ft−1 )(Ft − Φ(L)Ft−1 )0 t=1
60 A Gibbs sampler which sequentially draws from the Normal and Wishart can be used to calculate posterior properties of any functions of the parameters and to do prediction. The advantages of this procedure are its simplicity and computational tractability, regardless of the dimension of the data. At the same time, the method is non-parametric and requires few distribution assumptions, while possibly allowing for a degree of cross-correlation in the idiosyncratic term et . Among the limitations are that principal components, by construction, provide static factors with normalized covariance I and which are subject to sampling error.
.3.2. One-step (Joint) Estimation Through Maximum Likelihoood In the joint estimation procedure the factors are identified using both equation (3) and (4). Thus, compared to the previous approach, one uses also the structure of the transition equation in the estimation bf. of the factors. Additionally this methodology provides us with dynamic factors with covariance Σ Also, having the full posterior of the factors eliminates any sampling uncertainty. In this method, ensuring unique identification requires that one identifies the factors Ft against possible rotations of the form Ft∗ = AFt − BYt , where A is a K × K nonsingular matrix and B is a K × M. As we prefer not to restrict the FAVAR equation we impose the restrictions in the observation equation (3), which implies that:
Xt = ΛF A−1 Ft∗ + (ΛY + ΛF A−1 B)Yt + et The unique identification of factors requires that:
ΛF = ΛF A−1
(5)
ΛY = ΛY + ΛF A−1 B
(6)
and
Conditions (5) and (6) are satisfied by setting the upper K × K block of ΛF to an identity matrix and the upper K × M block of ΛY to zero (sufficient conditions). Let’s note that that latter restriction imposes that Yt has no contemporaneous impact on the first K variables in Xt i.e. are “slow-moving’, which is satisfied here. To further simplify the exposition, let’s denote Xt =
Xt Yt
! , et =
et 0
! and Ft =
Ft Yt
! .
61 The state-space system then becomes:
Λ F ΛY
Xt = ΛFt + et
(7)
Ft = Φ(L)Ft−1 + ut
(8)
!
and Σ = cov(et e0t ) is the covariance matrix augmented with zeros in order to 0 1 conform with the VAR transformation. We have re-written the transition equation (8) as a first-order
with Λ =
Markov process, such that the order of Φ(L) equals 1, in order to be able to estimate the latent factors using the Kalman filter. Let’s denote the parameters to be estimated as θ = Λ F , ΛY , Σ, Σ f , vec(Φ) . Likelihood estimation is done through multi-move Gibbs sampling (Carter and Kohn (1994)) which proceeds by alternating sampling the parameters θ and the unobservable factors Ft . The steps of the methodology are described in detail below.
(.3.2.1) Choose starting values for the parameters θ 0 . While in principle any starting values could be used and one would need to experiment with various to ensure convergence, in practice, given the dimensionality of the problem, it is useful to start from some informed choices. A reasonable starting point is to use as initial values the parameter estimates from the estimation of (3) and (4) using principal components. In addition, one needs to impose the restrictions implied by (5) and (6) on the loadings matrices. We have checked the robustness of our results to alternative starting values generating similar empirical distributions.
e1 from the conditional distribution. Conditional on the (.3.2.2) Sample the latent factors F T parameters, the factors can be sampled using state-space methods, where the factors play the role of e T , one can sample the unobserved state variables. More, precisely, conditional on θ 0 and the history X e1 from the conditional density p(F eT | X e T , θ 0 ) using Carter and Kohn (1994). latent factors F T The conditional distribution of the whole history of factors can be expressed as the product of conditional distributions of factors at each date t as follows: T −1
eT | X e T , θ 0 ) = p(FT | X e T , θ 0 ) ∏ p(Ft | Ft+1 ,X e t, θ 0) p(F t=1
62 e t = (X1 , X2 , ..., Xt ) and we have made use of the fact that Ft is Markov, implying that we can where X e t , θ 0 ) = p(Ft | Ft+1 ,X e t , θ 0 ). simplify: p(Ft | Ft+1 ,Ft+2 , ..., FT , X As the state-space model (7) and (8) is linear and Gaussian, we have:
e T , θ ∼ N(FT/T , PT/T ) FT | X
(9)
e T , θ ∼ N(Ft/t,F , Ft/t,P ),t = T − 1, ..., 1 Ft | Ft+1 , X t+1 t+1
(10)
where:
e T, θ ) FT/T = E(FT | X
e T, θ ) PT/T = cov(FT | X
e t , θ ) = E(Ft | Ft+1 , Ft|t , θ ) Ft/t,Ft+1 = E(Ft | Ft+1 , X
e t , θ ) = cov(Ft | Ft+1 , Ft|t , θ ) Pt/t,Ft+1 = cov(Ft | Ft+1 , X The Kalman filter proceeds with starting values of zeros for the factors and the identity matrix for the covariance matrix (Hamilton, 1994) and calculates Ft/t and Pt/t , t = 1, 2, ..., T conditional on θ and e t . The last iteration yields FT/T and PT/T , which can be used to draw FT the data through period t, X using (9). With this information, one can move “backwards in time”, using the Kalman filter to obtain updated values of FT−1/T−1,Ft , PT−1/T−1,Ft , then drawing FT−1 using (10) and continuing in a similar manner to draw values for Ft , t = T − 2, T − 3, ..., 1. As the order p of Φ(L) exceeds one, then lags of the factors appear in the state vector Ft and Σ f is singular, as is Pt/t,Ft+1 for any t < T (the singularity of the covariance matrices follows from the fact that Ft and Ft+1 have common components). In this case, one cannot condition on the full factor Ft+1 when drawing Ft , but only on the first p elements of Ft+1 . Kim and Nelson (1999, p.194-6) show how to modify the Kalman filter algorithm in this case.
63 (.3.2.3) Sample the parameters θ 1 from the conditional distribution. Conditional on the eT and the data, draw a new set of values of the parameters θ , say θ 1 , from the consampled values of F e1 ,X e T , θ 0 ). With known factors, equations (7) and (8) amount to standard ditional distribution p(θ | F T
regression equations. We can split this into two substeps by equation.
(.3.2.3.1) Priors in the factor equation. In the measurement/factor equation, we use a prior of the Normal-Gamma form as BBE. More precisely, we sample the factor loadings matrix Λ from a Normal distribution:
Λ | σi2 ∼ N(0, σi2 M0−1 ) As the upper K × K block of Λ is the identity matrix, one needs to sample the rest N − K rows only. We also sample the elements of diagonal covariance matrix of the errors in the factor equation Σ from an inverse Gamma distribution: σi2 ∼ iG(α, β )
We use rather non-informative priors and set α and β as in BBE to have a proper but diffuse prior, respectively to the values 3 and 0.001 and M0 = I.
(.3.2.3.2) Posteriors in the factor equation. Standard Bayesian results (this is a conjugate prior) deliver posteriors of the form:
¯ i , σi2 M¯ −1 ) Λi ∼ N(Λ i
where: 0
e(i) F e(i) )Λi ¯ i = M¯ −1 (F Λ i T T and 0
e(i) F e(i) M¯ i = M0 + F T T while the posterior for the covariances is of the form:
64
e T, F eT ∼ iG(α¯i , T + β ) σi2 | X
where: 0
e(i) )−1 ]−1 Λ e(i) F ˆ 0i [M −1 + (F ˆi α¯i = α + eˆ0i eˆi + Λ 0 T T e(i) correspond to the regressors of the i-th ˆ and eˆ are the OLS estimates from equation (7) and F and Λ T equation.
(.3.2.3.3) Priors and posteriors in the FAVAR equation. Proceeding similarly as when using factors estimated through principal components, we impose the same independent Normal-Wishart prior.
es and θ s have converged, (.3.2.4) Iterate until convergence Iterate on the previous steps until F T es , θ s ), for s ≥ B, where B where s indexes the iteration. Inference is based on the joint distribution of (F T stands for the burn-in-draws and should be large enough to ensure the convergence of the algorithm. It has been shown (Geman and Geman (1994)) that as the number of iterations s→ ∞, the marginal and es and θ s converge to the true corresponding distribution joint distributions of the sampled values of F T
at an exponential rate. The Gibbs-sampling algorithm is guaranteed to closely approximate the shape of the likelihood, especially arond its peak, even for an irregular and complicated likehood like for this class of large models. We have used a Gibbs sampler with 10000 replications (with 2000 burn-in draws to minimize the effects of initial conditions). There seemed to be no problems achieving convergence and the use of 20,000 iterations do not change the results. The joint likelihood estimation can be cumbersome in large problems. Also, MCMC estimation of dynamic factors using the Kalman filter requires strong identification restrictions which may lead to factors with poor economic content. Whether this is advantageous is not entirely clear apriori and depends on the how well specified the model is, which may justify the additional computational costs.
65 Table 3. Data: Definitions, Sources and Transformations No.
Mnemonic
Name
Source
Transf.
FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED
5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 2
FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED
5 5 2 2 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 1 1 1 1
FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED
4 4 4 4 4 4 4 4 4 4
Income and Real Output 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
RPI W875RX1 DPCERA3M086SBEA CMRMTSPL RSAFS INDPRO IPFINAL IPCONGD IPDCONGD IPNCONGD IPBUSEQ IPMAT IPDMAT IPNMAT IPMANSICS IPUTIL NAPMPI TCU
20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46
CLF16OV CE16OV UNRATE UEMPMEAN UEMPLT5 UEMP5TO14 UEMP15OV UEMP15T26 UEMP27OV ICSA PAYEMS USGOOD CES1021000001 USCONS MANEMP DMANEMP NDMANEMP SRVPRD USTPU USWTRADE USTRADE USFIRE USGOVT CES0600000007 AWOTMAN AWHMAN NAPMEI
47 48 49 50 51 52 53 54 55 56
HOUST HOUSTNE HOUSTMW HOUSTS HOUSTW PERMIT PERMITNE PERMITMW PERMITS PERMITW
Real Personal Income Real Personal Income Excluding Current Transfer Receipts Real Personal Consumption Expenditures (chain-type quantity index) Real Manufacturing and Trade Industries Sales Retail and Food Services Sales Industrial Production Index Industrial Production: Final Products (Market Group) Industrial Production: Consumer Goods Industrial Production: Durable Consumer Goods Industrial Production: Nondurable Consumer Goods Industrial Production: Business Equipment Industrial Production: Materials Industrial Production: Durable Materials Industrial Production: Nondurable Materials Industrial Production: Manufacturing (SIC) Industrial Production: Electric and Gas Utilities c ISM Manufacturing: Inventories Index Capacity Utilization: Total Industry Employment and Hours Civilian Labor Force Civilian Employment Civilian Unemployment Rate Average (Mean) Duration of Unemployment Number of Civilians Unemployed - Less Than 5 Weeks Number of Civilians Unemployed for 5 to 14 Weeks Number of Civilians Unemployed for 15 Weeks & Over Number of Civilians Unemployed for 15 to 26 Weeks Number of Civilians Unemployed for 27 Weeks and Over Initial Claims All Employees: Total nonfarm All Employees: Goods-Producing Industries All Employees: Mining and Logging: Mining All Employees: Construction All Employees: Manufacturing All Employees: Durable goods All Employees: Nondurable goods All Employees: Service-Providing Industries All Employees: Trade, Transportation & Utilities All Employees: Wholesale Trade All Employees: Retail Trade All Employees: Financial Activities All Employees: Government Average Weekly Hours of Production and Nonsupervisory Employees: Goods-Producing Average Weekly Overtime Hours of Production and Nonsupervisory Employees: Manufacturing Average Weekly Hours of Production and Nonsupervisory Employees: Manufacturing c ISM Manufacturing: Employment Index Housing Starts and Permits Housing Starts: Total: New Privately Owned Housing Units Started Housing Starts in Northeast Census Region Housing Starts in Midwest Census Region Housing Starts in South Census Region Housing Starts in West Census Region New Private Housing Units Authorized by Building Permits New Private Housing Units Authorized by Building Permits in the Northeast Census Region New Private Housing Units Authorized by Building Permits in the Midwest Census Region New Private Housing Units Authorized by Building Permits in the South Census Region New Private Housing Units Authorized by Building Permits in the West Census Region
66 No.
Mnemonic
57 58 59 60 61 62 63 64 65 66
NAPM NAPMNOI NAPMSDI NAPMII ACOGNO UMDMNO ANDENO AMDMUO BUSINV ISRATIO
67 68 69 70 71
M1SL M2SL BUSLOANS FOTA NONREVSL
72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90
PPIFGS PPIFCG PPIITM PPICRM PPICMM CPIAUCSL CPIAPPSL CPITRNSL CPIMEDSL CUSR0000SAC CUUR0000SAD CUSR0000SAS CPIULFSL CUUR0000SA0L2 CUSR0000SA0L5 PCEPI DDURRG3M086SBEA DNDGRG3M086SBEA DSERRG3M086SBEA
91 92 93
CES0600000008 CES2000000008 CES3000000008
94 95 96
FRBW FRATO FRAGB
97 98 99 100 101
UMCSENT SEPUI ADSBCI RGDP USPHPIM
Name Inventories and Orders c ISM Manufacturing: PMI Composite Index c ISM Manufacturing: New Orders Index c ISM Manufacturing: Supplier Deliveries Index c ISM Manufacturing: Inventories Index Value of Manufacturers’ New Orders for Consumer Goods Industries Value of Manufacturers’ New Orders for Durable Goods Industries Value of Manufacturers’ New Orders for Capital Goods: Nondefense Capital Goods Industries Value of Manufacturers’ Unfilled Orders for Durable Goods Industries Total Business Inventories Total Business: Inventories to Sales Ratio Money and Credit Aggregates M1 Money Stock M2 Money Stock Commercial and Industrial Loans, All Commercial Banks Break-Adjusted Consumer Credit Outstanding (EOP, SA, Bil.$) Total Nonrevolving Credit Owned and Securitized, Outstanding Prices Producer Price Index: Finished Goods Producer Price Index: Finished Consumer Goods Producer Price Index: Intermediate Materials: Supplies & Components Producer Price Index: Crude Materials for Further Processing Producer Price Index: Commodities: Metals and metal products: Primary nonferrous metals Consumer Price Index for All Urban Consumers: All Items Consumer Price Index for All Urban Consumers: Apparel Consumer Price Index for All Urban Consumers: Transportation Consumer Price Index for All Urban Consumers: Medical Care Consumer Price Index for All Urban Consumers: Commodities Consumer Price Index for All Urban Consumers: Durables Consumer Price Index for All Urban Consumers: Services Consumer Price Index for All Urban Consumers: All Items Less Food Consumer Price Index for All Urban Consumers: All items less shelter Consumer Price Index for All Urban Consumers: All items less medical care Personal Consumption Expenditures: Chain-type Price Index Personal Consumption Expenditures: Durable goods (chain-type price index) Personal Consumption Expenditures: Nondurable goods (chain-type price index) Personal Consumption Expenditures: Services (chain-type price index) Wages Avg. Hourly Earnings of Production and Nonsupervisory Employees: Goods-Producing Avg. Hourly Earnings of Production and Nonsupervisory Employees: Construction Avg. Hourly Earnings of Production and Nonsupervisory Employees: Manufacturing Asset Purchases Reserve Balances With Federal Reserve Banks (EOP, Mil.$) All Fed Res Banks: Total Assets (EOP, Mil.$) All Fed Res Banks: U.S. Gvt. and Agency Sec. held Outright (EOP, Mil.$) Other c University of Michigan: Consumer Sentiment Economic Policy Uncertainty Index (1985-09=100) Aruoba-Diebold-Scotti Business Conditions Index Monthly Real GDP Index FHFA House Price Index: Purchase Only
Source
Transf.
FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED
1 1 1 1 5 5 5 5 5 2
FRED FRED FRED FRED FRED
6 6 6 6 6
FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED FRED
6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6
FRED FRED FRED
6 6 6
FRED FRED FRED
6 6 6
FRED Haver Haver Macroec. Advs. FRED
2 1 1 2 2
