The Effect of the Monetary Expansion of QE1
on Inflation Expectations in the United States
Michiel Dotinga Master Thesis Finance Rijksuniversiteit Groningen Supervisor: Dr. Bernard Boonstra
April 25, 2012
Abstract
This paper studies the effects of the monetary expansion of Quantita-tive Easing 1 (QE1) on inflation expectations in the United States. The Mankiw Reis model predicts a 1.0-2.6 percentage points (pp) increase in two year inflation expectations. Five year inflation expectations are predicted to increase by 1.1-1.5 pp. The model predictions are not con-firmed by data of the Survey of Professional Forecasters, which show a decrease in inflation expectations of approximately 0.5 pp for both time frames.
JEL Codes: E31, E51, E52
Contents
1 Introduction 3 2 Literature review 5 2.1 Quantitative Easing . . . 5 2.2 Expectations . . . 7 2.2.1 Adaptive expectations . . . 8 2.2.2 Rational expectations . . . 10 2.3 Model assumptions . . . 12 2.4 Model selection . . . 143 The Mankiw Reis model 15 3.1 The sticky information model . . . 15
3.1.1 The interpretation of λ and α . . . 18
3.1.2 What happens after monetary expansion? . . . 19
3.1.3 Expectations on future inflation . . . 20
3.2 Estimation of the parameters . . . 21
3.2.1 Source data . . . 21
3.2.2 The persistency of the shock in money growth (ρ) . . 23
3.2.3 The dispersion coefficient (λ) . . . 23
3.2.4 The competition coefficient (α) . . . 26
3.2.5 The monetary shock of QE1 (t) . . . 28
4 Mankiw Reis model predictions versus actual inflation ex-pectations 30 4.1 Model predictions . . . 30
4.2 Survey data and BEIRs . . . 31
5 Conclusion and discussion 34
1
Introduction
Since 2008, the United States of America (US) struggles through a severe fi-nancial and economic crisis. Consumer and producer confidence plummeted as companies and consumers were unable to repay debts and banks’ reserves eroded. Interbank trust disappeared and liquidity on the (inter)national markets dropped to record depths.
The Federal Reserve (FED) implemented monetary expansion to restore confidence and to spur economic activity.1 The FED decreased the interest rate and increased the money supply. On November 25th 2008, the FED announced that it would buy mortgage backed securities, which were practi-cally worthless, for $500 billion from financial institutions. In addition, they would buy $100 billion in government sponsored enterprises (GSE). This monetary expansion was later referred to as Quantitative Easing 1 (QE1).
QE1 is a policy induced monetary expansion increasing overall money supply significantly. QE1 has a shock effect due to its relative (increasing M2 over 7.4%) and absolute magnitude. The monetary shock in Q4 2008 was the third largest monetary expansion since 1959. QE1 may affect future price levels and the expectations of agents on inflation. The research question of this thesis is as follows:
“What is the effect of the monetary expansion of QE1 on two and five year inflation expectations in the United States?”
The research question consists of two subquestions:
1. “What effect would be expected using a macroeconomic model?” 2. “How does the outcome of the model compare to data on inflation
There are many papers written on the effect of monetary policy on in-flation. This paper, however, provides an insight on the effects of monetary policy on inflation expectations.
There are three reasons why this approach is chosen. Firstly, investment and financing decisions are based on expectations, not actual inflation. For instance, debt to equity ratios may be increased if higher inflation is ex-pected. Secondly, higher inflation expectations increase the required returns on bonds and therefore government financing. Finally, analysis of inflation expectations can provide information to policy makers for future decision making.
The research question is investigated by using the Mankiw and Reis [2002] model. The parameters of the model are estimated using historical data and we compare the results to relevant literature. The focus of this paper is on the effects of QE1 via M2. We use the unexpected M2 growth in Q4 2008 and Q1 2009 as a proxy for the effects of QE1.
2
Literature review
The literature review comprises the following building blocks for our re-search:
1. Quantitative Easing 2. Expectations 3. Model assumptions 4. Model selection
These building blocks provide the foundation to answer our research ques-tion: “What is the effect of the monetary expansion of QE1 on two and five year inflation expectations in the United States?”.
In Section 2.1, the phenomenon of QE1 is explained. In Sections 2.2-2.4, we discuss the process to find a suitable model to evaluate the effects of QE1. Expectations are reviewed in depth, as these are an ingredient of paramount importance for macroeconomic models (Shiller [1978]). Subse-quently, we discuss slow moving variables, the need for a microfoundation and persistency. In the final part, we conclude on our model selection.
2.1 Quantitative Easing
can be seen as monetary policy of the last resort.
On November 25th 2008, the FED announced that it would buy prac-tically worthless Mortgage Backed Securities (MBS) from the financial in-stitutions for $500 billion cash.2 Thereby, the solvability and liquidity of
the financial institutions was strengthened. Also, the FED communicated that it would buy $100 billion in Government Sponsored Enterprises (GSE). We focus on the effects of the implementation in the period from November 2008 until March 2009. Note that, in March 2009 the Federal Open Mar-ket Commission (FOMC) announced that it would increase the purchases of MBS, GSE and government bonds up to $1.75 trillion.3 At the end of 2009 the FED had $919 billion of MBS and GSE on the asset side of the Federal Reserve’s balance sheet, over 40% of total assets.4 At the beginning of 2008 this was $0.
In the case of QE1, MBS and GSE were bought with newly created money. Dellas [2011] defines the increase in the size of the balance sheet as the total quantity of money created. Dellas shows that the balance sheet of the central bank more than doubled in 2009.
Krishnamurthy and Vissing-Jorgensen [2011] distinguishes different chan-nels through which QE affects the economy: liquidity, safety premium, pre-payment, default risk, inflation expectations and inflation. They argue that to the extent that QE is expansionary, it will increase inflation expectations. Girardin and Moussa [2011] find that QE increases prices. We recognize that the effect of QE1 has more channels than M2 growth. However, our focus is on the effects of QE1 via M2. M2 is the money stock including cash, cash equivalents and other deposits with a maximum maturity of two years. We
2
Press release of the FED on November 25 2008.
3
Press release of the FED on March 18 2009.
4
use the unexpected M2 growth in Q4 2008 and Q1 2009 as a proxy for the effects of QE1.
Before QE1, the financial institutions provided loans and invested in counterparties who (partly) became unable to repay their debts. The money has not disappeared but went to other allocations in the economy. The bad and doubtful debts deteriorated the balance sheets of the financial institu-tions, reducing the ability to lend to new clients.
Figure 1: Quantitative Easing
The figure above illustrates the implementation of QE1 by the FED. The FED increased their balance sheet by buying the practically worthless MBS (and by buying the GSE) from the financial institutions. The FED now owned the MBS and thus participated in lending to consumers. The financial institutions have cash, instead of outstanding mortgages after QE1, which gives them an opportunity to lend again. The impact of QE1 on money supply was not (completely) neutralized by other actions of the FED. QE1 thus increases the money supply.
2.2 Expectations
ex-jor macroeconomic models one is impressed that most of the essential be-havioral relations are based on assumptions about how expectations are formed”(Shiller [1978] p.2). Therefore, it is important to thoroughly inves-tigate expectations.
Three views (or hypotheses) on expectations are recognized by Heijdra [2009]. The perfect foresight hypothesis (PFH) assumes a perfect ability to foresee the economic future. This is not a realistic assumption as the realized outcome should always equal the expected outcome. The second hypothesis, developed around 1930, is the adaptive expectations hypothesis (AEH). The AEH is the result of the first attempt to model expectations by “guessing the manner in which individuals form their expectations in practice and try to find some quantitative representation of this behavior”(Shiller [1978] p.2). The third hypothesis is rational expectations. Muth [1961] defines rational expectations as informed predictions of future events. All economic players (agents) know how the real economic model works and what the initial values of the variables are. Hence, expectations are essentially the same as the predictions of the relevant economic theory, according to Muth.
Adaptive and rational expectations are further discussed below.
2.2.1 Adaptive expectations
Fisher [1930] introduced the adaptive expectations. The AEH resulted from the first attempts to model a quantitative representation of immeasurable expected inflation. The AEH assumes that expected inflation is based on past inflation (on a linear basis).5 Prices adjust slowly to a new level after
a shock.
A second method of adaptive expectations is based on exponentially weighted past observations. Exponentially weighted past expectations,
de-5Adaptive expectations mechanism:
scribed by Muth [1960], is used in different studies such as the consumption function by Friedman [1957] and demand for cash balances during hyper-inflations by Cagan [1957]. Exponentially weighted forecasts are different from the original adaptive forecasts as they put more weight on the most recent observations.6 Prices adjust more quickly after a shock than with
using ordinary linear adaptive expectations.
Under adaptive expectations, monetary policy influences real economic variables. A monetary expansion increases money in circulation while prices are still based on the previous period, resulting in a temporary increase in real output. This gives the central bank incentive to increase the money supply in order to increase output.7
The AEH has shortcomings. Firstly, the formula for expected inflation is only based on past inflation and does not (instantly) allow for exogenous changes, e.g. a supply shock. This is shown by the Cobweb model used by Kalecki [1937], Buchanan [1939] and Kaldor [1940]. In this model, farmers of corn set prices by using previous prices. A one time shock due to bad harvest leads to continuous (increasing or decreasing) mispricing in the market due to adaptive expectations.
Secondly, Lucas [1976] argues that macroeconomic analysis using the conventional AEH cannot give reliable results as the change in agents’ ex-pectations after policy implementation is not taken into account. The im-plementation alters the decisions of agents, which alters the structure of the
6
Exponentially adaptive expectations mechanism: pet = β ∞ X i=1 (1 − β)i−1pt−i 7
economic model. Lucas also states that under adaptive expectations, a small standard error in the short term forecasts results in an infinite variance in the long run. Therefore, adaptive expectation models have no forecasting ability according to Lucas. Previous analysis such as the paper written by Phelps [1967], which studied the optimal fiscal control of aggregate demand, was criticized by Lucas [1976]. Phelps [1967] used adaptive expectations for inflation resulting in a fiscal control which could be undermined by the Lucas critique.
As models based on AEH are subject to the Lucas critique, AEH is not used in our analysis.
2.2.2 Rational expectations
In order to deal with the inability to incorporate changes in expectations and to create a more logical way of forming expectations, rational expectations were introduced.
Grunberg and Modigliani [1954] investigate the validity of the hypothesis that “in reacting to the published prediction of a future event, individuals influence the course of events and thereby falsify the prediction”. Further-more, they investigate how expectations can be forecast. Grunberg and Modigliani conclude that it is possible to correctly forecast public expecta-tions by using “private expectaexpecta-tions”. The key assumption of the model is that the agents have a complete predictive model and know the initial values of the variables.
stay on in year t = 1. Hence, rational expectations provide a better way to analyze markets than adaptive expectations, as mispricing is now prevented.
Various studies are carried out to test the theory of rational expecta-tions. For instance, Mishkin [1981] studies whether market forecasts on the bonds market, and thus on inflation and interest rates, are rational. Mishkin concludes that market forecasts of the bond market are rational for all sam-ple periods between 1954-1976, except one.
Rational expectations are however not undisputed. Simon [1955] argues that concept of the “economic man”, a rational man who has the knowledge and skills to attain the highest attainable point on his preference curve, is unrealistic. Simon finds that observed behavior is different than what would be expected of rational agents. The concept of Simon is called “bounded rationality”.
DeCanio [1979] argues that rational expectations theory may not always be applicable because of the cost of getting information required for achiev-ing rational expectations. If these costs are higher than the benefits, rational producers might not be able to drive out irrational producers. This would make rational expectations irrelevant in the context of income-maximizing agents. Grossman and Stiglitz [1980] argue that it is not possible for markets to be informationally inefficient, countering the argument of DeCanio [1979].
Rational expectations do not suffer from the Lucas critique and can be used to analyze the effects of monetary policy. Therefore, we also select a model based on rational expectations. Sargent [1976], Sargent and Wallace [1976], Barro [1976], Barro [1978], Taylor [1975] and Lucas [1970] use ratio-nal expectations to aratio-nalyze the effects of macroeconomic policy.
depend on the economic school of thought used. New classical economists argue that monetary policy will have no effect on output and hence are less relevant for this study.8 New Keynesian models, such as Taylor [1975] and Fischer [1977], are based on rational expectations and include a slow-moving variable. New Keynesian models show real effects of monetary policy on output.
2.3 Model assumptions
The goal of QE according to the FED is to spur economic activity. Therefore, the FED will follow an economic school whereby monetary policy has a real effect on output. We also use a model in which monetary policy has real effects on output. Therefore, we will use a New Keynesian model based on rational expectations, including a slow moving variable and showing a real effect of monetary policy on output.
Taylor [1975] introduces a New Keynesian economic model in which mon-etary policy has impact during a transition period. Taylor concludes that monetary policy can influence real economic variables during this period. Eventually, inflation will be in rational expectations equilibrium. However, in the transition period inflation behaves in line with adaptive expectations theory.
Fischer [1977] introduces a similar model which uses contracts set in nominal terms for multiple periods, such that wages cannot change unre-stricted. This results in a slower price adjustment system. The central bank can thus steer output with monetary policy in the short run.
8Sargent and Wallace [1976] find that it is not possible to use monetary or fiscal policy
Two other popular New Keynesian models are the sticky price and the sticky information model. The sticky price model assumes that prices change slowly after a monetary shock. The sticky information model was introduced by Mankiw and Reis [2002]. The assumption of this model is that in each period a part of the firms gets new information on macroeconomic condi-tions while another part does not.
The model needs to have a microfoundation (Barro [1993]), to assure that the behavior of individual agents underpins the macroeconomic theory. Both the sticky price and the sticky information model have a microfoun-dation. Blinder [1995] recognizes implicit contracts, cost-based pricing and coordination failure as the most important microfoundations for the sticky price model. Reis [2006] describes inattentiveness, because of the cost of acquiring, absorbing and processing information, as the microfoundation for the sticky information model. Reis finds that “the model of inattentiveness fits post-war US inflation data remarkably well”.
Another feature of the selected model is to incorporate the persistency of inflation, the prolonged reaction to shocks hitting the economy (see Fried-man [1968], Christiano et Al. [1999], Christiano et Al. [2005] and Pivetta and Reis [2007]). Both the sticky information and the sticky price model show persistency of inflation.
Furthermore, the model has to deal with the fact that inflation has a delayed maximum reaction of inflation to the shock (see Nelson [1998], Batini and Nelson [2001] and Smets and Wouters [2003]). The sticky price model has the maximum price reaction directly after implementation of the shock. The sticky information model has the ability to incorporate the delayed maximum reaction to a monetary expansion. Hence, the sticky information model is preferred.
be used. Klenow and Willis [2007] show that empirical price changes in the US reacts to old information, just as the sticky price model predicts. The results of Carrillo [2010] suggest that sticky information may replace sticky prices as the explanation of price setting behavior.
2.4 Model selection
In the previous sections, we have reviewed various building blocks to arrive at a suitable model to estimate the effects of QE1 on inflation expectations. After our analysis of expectations, we conclude that our model should be based on rational expectations, as adaptive expectations are subject to the Lucas critique. Of the economic schools based on rational expectations only New Keynesian models, using a slow moving variable, show real effects on output after a monetary shock.
The New Keynesian sticky price and sticky information models are put forward as potential candidates. Both models have a microfoundation and incorporate inflation persistency. However, only the sticky information model generates a delayed maximum effect of inflation to a monetary shock. This results in selecting the sticky information model.
3
The Mankiw Reis model
To measure the effects of QE1, inflation expectations have to be modeled. To do this the Mankiw and Reis [2002] (MR) model is used. This section is structured as follows. In Section 3.1, the MR model is discussed from a theoretical point. The model is introduced and the parameters of the model are discussed. Also, the rationale behind the model is explained. Finally, assumptions on inflation expectations are discussed. In Section 3.2, the parameters are estimated.
3.1 The sticky information model
Mankiw and Reis [2002] introduce the rationally orientated sticky infor-mation model. The sticky inforinfor-mation model is similar to the sticky price model. The difference is that not prices but information is sticky. Prices can be altered freely whereby price setting may still be based on old information. This is because information on macroeconomic conditions slowly becomes public. Each period, part of the agents gets to know new information, while another part does not. A part of the population updates their expected prices to new optimal expected prices, while another part uses outdated price plans. Let us discuss the model.
The model, which is in log levels, is set up as shown below. A firm’s optimal price (p∗t) is given by
p∗t = pt+ αyt (1)
The optimal price is based on the aggregate price level (pt) and the level
of the economy (yt). If the economy is booming, a firm’s optimal price
A firm sets its price according to the price plan (xjt) made j periods ago. The expected price in period t, set according to the price plan made at time t − j, is an average of all possible future prices
xjt = Et−jp∗t =
Z
ϕ(pt|pt−j)ptdpt (2)
ϕ is the subjective probability distribution. The expected price is equal to the rational price given the information available to the firm.
The aggregate price level in the economy is given by a weighted average of all prices9 pt= λ ∞ X j=0 (1 − λ)jxjt (3)
Note the similarity with the exponentially weighted adaptive expectations model in the literature review. The most recently made price plans have the highest weight. Combining (1),(2) and (3) leads to the following price level equation. The current price depends on the expected price levels and output of the past
pt= λ ∞
X
j=0
(1 − λ)jEt−j(pt+ αyt) (4)
with λ being the sticky information coefficient. A larger λ implies a larger group being updated in each period. λ can be seen as the dispersion coef-ficient of information. The larger λ, the faster the dispersion of a decision is.
Inflation is given by the following equation10
πt= αλ 1 − λyt+ λ ∞ X j=0 (1 − λ)jEt−1−j(πt+ α∆yt) (5)
The aggregate demand is given by the quantity theory of money in log levels, where log velocity is assumed constant at zero
m = p + y (6)
Combining (1) and (6) gives the following equation for the desired nom-inal price of a firm
p∗t = (1 − α)pt+ αmt (7)
This is again the best response function of a firm. α is the relative impor-tance of the overall price level and money in circulation. If 1 > α > 0, a firm that has received new information will not only look at the money in circulation but also take into account the prices of the competition. α can thus be seen as the importance of competition relative to macroeconomic variables. Therefore, we call α the competition coefficient.
The MR model assumes that money (mt) grows as shown below
∆mt= ρ∆mt−1+ t (8)
If there is a shock to the money supply, it is persistent if ρ > 0. ρ thus represents the persistency of the shock in money growth. The effect of the shock on money growth decreases each period returning to equilibrium in the economic system. The multiplier of the monetary expansion is given by 1/(1-ρ). ρ is estimated by the first order autocorrelation of money supply, on which we will elaborate later.
t represents a monetary shock. t is important as it is later used to
implement the exogenous shock of QE1 in our model. Equation (8) can also be seen as the reaction to unexpected money growth. This is the case if all firms are aware that there is a standard money increase, which they immediately incorporate in their prices.
Figure 2: Inflation after monetary expansion
We estimate λ, α and ρ in Section 3.2. In the next subsections λ and α are further defined.
3.1.1 The interpretation of λ and α
The dispersion coefficient (λ) is the driver of this model. Mankiw and Reis state that each period a fraction λ of the firms gets new information on the economy. In this paper, which investigates monetary policy, we define λ as dispersion of the information on decisions made by the central bank among the agents. If the central bank implements a monetary expansion (such as QE1) the information on the implementation disperses slowly through the economy. Well informed agents such as traders and investors quickly use the new information in their pricing. Less informed agents react slower. The decision thus disperses slowly among the agents. Another way of looking at λ is as a variable of tension between the possibilities of monetary policy.
ways. A firm sets the optimal price level in each period to obtain maximum profits with the information that has reached the firm. In order to do so, the reaction function takes into account competition effects (the general price level) and monetary effects. A high α puts high weight on monetary effects, while an α close to zero puts high weight on the prices of the competition.
3.1.2 What happens after monetary expansion?
Before the monetary expansion, all firms are assumed to be informed. The individual price level of all firms is thus equal to the average price. Then in period t = γ an expansionary monetary shock occurs, as is shown in Figure 3. tjumps and this increases mtin the first period with the size of the shock
and in the following periods with ρt−γt. The optimal price (p∗t) of all firms
changes. The price plans made in t = γ change as well. However, after the shock agents have different information on macroeconomic variables. The new information is dispersed to λ part of the population in the first period, as shown by equation 3.
Figure 3: The effect of a monetary shock
The increase in money in circulation due to the shock increases demand, as prices are not inflated to the new level yet. Therefore, real output will temporary increase. In the following periods the fraction of up to date price plans increases while the shock is still increasing mt. As time progresses,
end, inflation and the output gap asymptotically approach zero. Prices are on the new level and all firms are fully informed again.
3.1.3 Expectations on future inflation
In this section the effects of monetary policy on expectations of future in-flation in the MR model are described. The relevant case to estimate the effect of a monetary shock, is a stable situation with a monetary expansion at t = 0. Before the shock, all firms are up to date. After the shock, the relation between πte and mt is given by11
πet = ΛX αζt 1 − (1 − α)ζt mt− αζt−1 1 − (1 − α)ζt−1 mt−1 (9) with ζt= (1 − (1 − λ)t+1−γ) (10)
t − γ is the number of periods between time t and the monetary expansion (γ). ΛX is explained below.
There are two cases which can be distinguished with respect to inflation expectations. The first case assumes aggregate expectations which take into account expectations of all firms, while in the second case only informed firms are considered. In the first case, ΛX is the percentage informed firms
at the time the expectations are made. For instance, if expectations are formed in period 3, 58% of the firms are informed. The other part of the population (1 − ΛX) expects inflation to be zero. Before period 3, expected
inflation is equal to inflation as this has already taken place. The result is shown in Figure 10a below on the left.
11
Figure 4: Expected inflation in period 3 after monetary shock
(a) Based on all firms (b) Based on informed firms
The second case only includes informed firms. Carroll [2003] argues the first group to be informed is based on the information provided by pro-fessionals. We follow this approach in Section 3.2.3. If the data used to measure inflation expectations are only based on professionals, this would result in Figure 10b above (with λX = 1). To measure real inflation
fore-casts, Break-Even Interest Rates (BEIRs)12 and data of the Survey of Pro-fessional Forecasters are used. Both data sources are based on proPro-fessionals. Therefore, the second case is used for further analysis.
3.2 Estimation of the parameters
In order to estimate the effects of QE1 with the MR model, it is necessary to determine the values for ρ, λ and α. The estimations will be indicated as ˆρ, ˆλ and ˆα. In Section 3.2.1, the source data for determining ρ and λ are discussed. In Section 3.2.2, ˆρ is calibrated. In Section 3.2.3, ˆλ is estimated. In Section 3.2.4, ˆα is determined. Finally, Section 3.2.5 determines the monetary shock of QE1 ( ˆt).
3.2.1 Source data
In this section the source data of ρ and λ are reviewed.
ρ represents the persistency of the shock in money growth. Quarterly US Federal Reserve data on M2 from 1959 until 2007 are used to estimate ρ. M2 is the money stock including cash, cash equivalents and other deposits with a maximum maturity of two years.13 We use the logarithm of M2 as this indicated by the MR model.
λ represent the dispersion coefficient. λ is estimated using the method of Carroll [2003]. Carroll distinguishes an uninformed and an informed group with regards to inflation expectations. The data to proxy the uninformed group is of the University of Michigan’s Survey Research Center. The proxy for the inflation expectations of the informed group is of the Survey of Profes-sional Forecasters (SPF) of the Federal Reserve. All the data on estimating λ are quarterly one year mean inflation expectations from 1983 until 2007.
Table 1: Descriptive statistics
Variable Mean Std. Dev. # of observations
∆ log M2 0.017 0.010 194
Inflation expectations Michigan 3.95 0.74 100
Inflation expectations SPF 3.34 0.96 100
We want to compare the modeled inflation expectations with actual in-flation expectations. Actual two and five year expectations are measured by the Survey of Professional Forecasters (SPF) and Break-Even Interest Rates (BEIRs). It is therefore important to adapt the modeled inflation expecta-tions to the actual expectaexpecta-tions. Five year forecasts measure the average annual expected inflation both using the SPF and BEIRs. Two year fore-casts differ between the SPF and BEIRs. The SPF measures the expected inflation in two years time, while BEIRs represent the average over the two
13
years. Therefore, we model two year inflation expectations separately.
3.2.2 The persistency of the shock in money growth (ρ)
To calibrate ˆρ, we follow the approach of Mankiw and Reis [2002]. The growth in mt is a first order autoregressive process: ∆mt = ρ∆mt−1+ t.
We generate the log of M2 and calculate the money growth. This variable is stationary. Then, we estimate the first (order) autocorrelation of quarterly M2 growth.
Estimation over the period 1959-2007 results in a ˆρ of 0.37. For the period 1979-2007, ˆρ is 0.29. This is lower than the estimation for the pe-riod 1959-2007. For the pepe-riod 1999-2007 autocorrelation is negative, but insignificant.
Table 2: First-order autocorrelation M2 growth
Period ρˆ # of observations
1959-2007 0.37*** (0.07) 196
1979-2007 0.29** (0.09) 116
1999-20007 -0.14 (0.17) 36
*, ** and *** indicate, respectively, statistical significant at 10, 5 and 1 percent levels. The residuals are not autocorrelated and are normally distributed. The estimation is corrected for heteroskedasticity using White.
When we test for first and second order autocorrelation combined, the result for second autocorrelation is insignificant. The first order autocorrela-tion is thus a better measure. ρ is set at 0.37, as this stems from the largest sample and is significant at a 1% level. This means that the persistency of a monetary shock equals 0.37 per quarter year.
3.2.3 The dispersion coefficient (λ)
estimate the value for λ we follow the approach of Carroll [2003]. Carroll assumes that expected inflation of consumers consists of an informed group (ˆλ), “who reads the newspaper”, and an uninformed group. Carroll assumes that inflation expectations are stationary. Carroll states: “mean measured inflation for the next year (Mt[πt,t+4]) should be a weighted average
be-tween the current newspaper forecast (Nt[πt,t+4]) and last period’s mean
measured inflation expectations (Mt−1[πt−1,t+3])”. The process of inflation
expectations can be written as:
Mt[πt,t+4] = ˆλNt[πt,t+4] + (1 − ˆλ)Mt−1[πt−1,t+3] (11)
The equation is estimated by using data on the mean inflation expecta-tions of the University of Michigan’s Survey Research Center and data of the Survey of Professional Forecasters (SPF) as a proxy for the informed group. The equation is estimated over the period 1983Q4 and 2007Q4. The period 1981Q3 to 1982Q3 are excluded as these were outliers in the SPF forecast. The equation is estimated as follows
Mt[πt,t+4] = γ0+ γ1Nt[πt,t+4] + γ2Mt−1[πt−1,t+3] (12)
The results of the estimation are given in the table below. Table 3: Estimating λ
Eqn γ0 γ1 γ2 Adj R2 StdErr
Constant Informed Uninformed
(SPF) (Michigan)
(a): 3.95 (0.15)*** 0.00 0.74
(b): 0.22 (0.07)*** 0.81 (0.06)*** 0.65 0.44
(c): 0.88 (0.23)*** 0.25 (0.07)*** 0.56 (0.08)*** 0.70 0.41
Equation (a) represents a model in which the Michigan index of inflation expectations is equal to a constant (γ0). Equation (a) has an adjusted R2
of zero (by definition) and a standard error of 0.74. Equation (b) estimates the process of inflation expectations without a constant. This results in the equation below
Mt[πt,t+4] = γ1Nt[πt,t+4] + γ2Mt−1[πt−1,t+3] (13)
If the equation above is compared to equation (11) this leads to the fol-lowing restriction γ1 + γ2 = 1. γ1 is equal to 0.22 and γ2 is equal to 0.81,
totaling 1.03. This suggest that the restriction holds true. Also, γ1 is close
to the results of other research, which is discussed below.
Finally, equation (c) shows that if a constant is included in the equation regression, the constant turns out to be significant. However, the standard error only declines from 0.44 to 0.41. Hence, the fit of the equation only in-creases marginally. A constant term is, however, an unrealistic assumption as it would imply that if inflation goes to zero indefinitely, the survey will still show an expectation equal to the constant.
The results of our empirical test are similar to the results of Carroll [2003], which could be expected as it is the same estimation over a longer time range. Carroll estimates λ close to 0.27. Also, if we estimate λ for different periods, such as 1990-2007 and 1995-2007 we get similar results (0.29 and 0.24).
between 0.20 and 0.30 in France, Germany and the United Kingdom. D¨opke et Al. [2008a] use the same approach as Carroll [2003] in Europe, which re-sults in a λ between 0.17 and 0.25.
Our research and the research of D¨opke et Al. [2008a] provides addi-tional evidence (next to Carroll [2003]) that the first group to be informed have equal ideas as the professional (reported by the SPF). This strengthens the case to set λX = 1.
In conclusion, based on our analysis and other research, λ is set at 0.22 for our model. From an economic perspective, this means that each period 22% of the agents is updated.
3.2.4 The competition coefficient (α)
If α < 1 firms take into account the general price level next to macroeco-nomic conditions. Firms who have the knowledge of macroecomacroeco-nomic condi-tions wait until this information is dispersed to other firms. From a profit maximizing view this is a reasonable assumption. If the informed firm in-creases its price immediately, they will be out priced by competition. If the firm does not adapt slowly to the monetary expansion, its price will be too low, reducing profitability. As the firms continuously have the possibility to adjust their prices, they set their individual prices close to the price level.
To find an assumption on α, literature is reviewed. Based on the lit-erature, a sensitivity analysis of inflation expectations with respect to α is made.
Literature on α
Bre-demeier and Goecke [2011] finds α = 0.11 in the United Kingdom. For the US α is estimated at 0.25, which is higher than the baseline scenario of Mankiw and Reis [2002]. Woodford [2003] argues that α should be between 0.10 and 0.15 taking into account both macro and microeconomic evidence.
The literature suggest an α between 0.10 and 0.25. It is important to see how the results of the MR model are influenced by α. As stated before, there are two measures of two year inflation expectations. The sensitivity of two and five year inflation with respect to α after a 1% monetary shock is shown below. The sensitivity analysis is based on our estimations of ρ and λ.
Figure 5: Sensitivity of 2 and 5 year inflation expectations to α
Expected inflation for two year BEIRs increase 0.36-0.54 percentage points14
(pp), for two year SPF forecasts the increase is 0.41-0.47 pp. For the five year inflation expectations the increase is constant at 0.31 pp. When estimating the effects of QE1, the same range of α is used. The agents take the general price level into account when setting their prices.
14
The assumptions on the parameters are shown in the table below. We use these values to predict the shock of QE1 on inflation expectations.
Table 4: Model inputs
Parameter ρ λ α ΛX
Value 0.43 0.22 0.1-0.25 1
In the next section, we explain how the monetary shock of QE1 is mea-sured.
3.2.5 The monetary shock of QE1 (t)
As stated, we proxy the monetary expansion due to QE1 by using the un-expected money growth. Historical M2 data in the US are used to quantify the unexpected money growth due to QE1. The average quarter on quarter (QoQ) growth between Q1 1995 and Q3 2008 was 1.5%. The growth of M2 has been relatively stable over different periods as is shown by the table below.
Table 5: Quarter on Quarter M2 growth
Period 1995-2008Q2 1995-2000 2001-2005 2005-2008Q2
Avg. growth 1.5% 1.4% 1.5% 1.4%
M2 growth in Q1 2009 was 3.5%, implying 2.0% unexpected money growth.
Table 6: Unexpected M2 growth Q4 2008 Q1 2009
M2 growth 3.8% 3.5%
Unexpected M2 growth 2.3% 2.0%
To analyze the effect of the monetary shock of QE1, we implement the unexpected growth in Q4 2008 and Q1 2009 in the model. The monetary shock of QE1 is implemented in the model via tin equation (8). The effect
4
Mankiw Reis model predictions versus actual
in-flation expectations
In this section the effect of the monetary shock of QE1 on inflation expecta-tions are estimated with the MR model. Secondly, the results are compared to data of the Survey of Professional Forecasters (SPF) and Break-Even Interest Rates (BEIRs).
4.1 Model predictions
To ensure robustness of the prediction, we use three different cases to esti-mate the effect of QE1. The base case reflects our estimations of λ and ρ. The high and low case are one standard deviation higher and lower than the base values, as shown in the table below.
Table 7: Different cases Low case Base case High case
ρ 0.30 0.37 0.44
λ 0.15 0.22 0.29
The table below show the increase in inflation expectations after the monetary expansion of QE1 using the MR model with 68% accuracy. The increase in inflation expectations is shown in percentage points (pp).
Table 8: Change in two and five year expected inflation due to QE1 2 year SPF 2 year BEIRs 5 year Base ∆ Expected inflation 1.8-1.9 pp 1.6-2.3 pp 1.3-1.4 pp
In the base case the shock leads to an increase of two year SPF inflation expectations of 1.8-1.9 percentage points, while two year BEIRs increase with 1.6-2.3 percentage points. Five year inflation expectations increase with 1.3-1.4 percentage points.
The implementation of the monetary shock of QE1 in the MR model results in the following hypotheses:
1. Two year inflation expectations measured according to the SPF in-crease with 1.0 to 2.6 percentage points
2. Two year inflation expectations measured according to BEIRs increase with 0.8 to 3.2 percentage points
3. Five year inflation expectations increase with 1.1 to 1.5 percentage points
In the next subsection actual survey data of the SPF and BEIRs are examined.
4.2 Survey data and BEIRs
In Figure 6, the two year forecast of the SPF is shown.15 As shown in the
graph, expected inflation is expected to rise with 1.0-2.6 percentage points according to the MR model. However, actual data shows a fall in inflation expectations after QE1.
15
Figure 6: Expected inflation in 2 years by SPF versus prediction by MR model
In Figure 7 the two year BEIRs is shown. As shown, BEIRs fall after QE1. However, BEIRs are deemed less representative as inflation expecta-tions than the SPF data.16
16Part of the fall in inflation expectations may be due to counter party risk as Lehman
Figure 7: Expected inflation in 2 years by BEIR versus prediction by MR model
Inflation expectations, as per the SPF and BEIRs, fall after QE1. For five year inflation expectations a similar pattern is shown.
5
Conclusion and discussion
This paper investigates the following research question: “What is the effect of the monetary expansion of QE1 on two and five year inflation expecta-tions in the United States?”
The research question consists of two subquestions:
1. “What effect would be expected using a macroeconomic model?”
2. “How does the outcome of the model compare to data on inflation expectations?”
Literature review provides the required guidance in search of a model. The Mankiw Reis (MR) model fulfils the criteria of being a New Keynesian model with a real effect on output after a monetary shock. Furthermore, the model has a microfoundation, incorporates the persistency of inflation and caters for a delayed maximum effect of monetary policy on inflation.
The parameters of the model are estimated using historical data and compared to the results of other relevant studies.
Subsequently the outcomes of the model with regards to inflation ex-pectations after the monetary expansion of QE1 are confronted with survey data of the Survey of Professional Forecasters (SPF) and Break-Even Inter-est Rates (BEIRs).
Prediction of the effects of the monetary expansion of QE1 by the MR model leads to the following hypotheses:
1. Two year inflation expectations measured according to the SPF in-crease with 1.0 to 2.6 percentage points
3. Five year inflation expectations increase with 1.1 to 1.5 percentage points
The Survey of Professional Forecasters show a decrease of approximately 0.5 percentage point in inflation expectations after QE1 for both time frames. The BEIRs decrease even to a greater extent. The hypotheses above are not confirmed by SPF and BEIRs data and thus rejected.
In conclusion, the comparison between the model predictions and the actual SPF and BEIRs data shows contradictory results. The MR model proofs unable to predict the inflation expectations after QE1 in the United States with 95% certainty. Hence, policy makers cannot use the MR model to estimate the reaction of investors on inflation expectations after monetary expansions.
Limitations
The first limitation is that α is not estimated. Although literature show similar values for α, it may be that another value of α is more appropriate. This could be subject for further studies.
The second limitation is that unexpected M2 growth in Q4 2008 and Q1 2009 does not account for all effects of QE1. The other channels recognized by Krishnamurthy and Vissing-Jorgensen [2011] could be explored in further studies.
The third limitation is that QE1 is only one event in which inflation expectations are studied. Other large monetary shocks can be studied in further research.
few articles could be found on QE1. Further research on QE1 may proof useful.
This study is limited to QE1. QE2 and QE3 can also be subject to review. One should however be aware that the money growth prior to QE1 was relatively stable. This is not the case for QE2 and QE3.
Food for Thought
QE1 did not lead to continued high growth in M2. This is shown in Table 5, by the similar levels of M2 growth in various periods. Also, it is confirmed by Figure 8, which shows M2 between Q1 2000 and Q3 of 2010. As you can see M2 returns to the trend line quickly after QE1.
Figure 8: M2 including trend line
In the MR model this would mean that there was a negative shock (t) after
Q1 2009, or that the shock of QE1 was absorbed, never reaching the real economy.
all excess reserves to be excess reserves, but necessary reserves. Also, in the Emergency Economic Stabilization Act of 2008 the FED decided to pay interest on excess reserves. This made holding excess reserves more attractive. Furthermore, interbank trust was low resulting in a ‘flight to safety’.
Figure 9: Excess reserves
Required and excess reserves are no part of M2 and no driver of inflation. This is because required and excess reserves are not used for financing the real economy. Therefore, QE1 might not have resulted in a shock to the M2 growth after Q1 2009.
Figure 10: Excess reserves dampen effects
cen-tral bank absorbed the increase given by QE1. Figure 1 thus has to be reconsidered. Although the FED provided the financial institutions with a healthier balance sheet, this did not increase the money supply. The cash paid for the MBS was returned to the FED as excess reserves (see Figure 14). Therefore, the money of QE1 was extracted from the money supply.
If excess reserves are expected to decline in the future, this may increase M2 and inflation expectations. This could become reality when the market is less distorted and interbank trust increases again. The effect of QE1 could then again be analyzed.
Quantitative Easing in the European Union
In December 2011, the ECB gave out 489.2 billion in long-term refinanc-ing operations (LTRO) with three year maturity.17 Immediately, overnight deposits increased to record heights. Although it is too early to draw con-clusions, the similarity with this paper is striking. The expansion does not increase M2, but increases excess reserves. The ECB could have learned from the situation in the US, possibly resulting in a more efficient way to increase market liquidity. Please note the difference between LTRO which have to be paid back to the ECB, and QE1 which was an acquisition by the FED. The second difference is that this event has taken place in European Union, while QE1 was in the US. Further research could investigate the difference in the effects of these monetary policies.
6
Appendix
Appendix I
To proof that the equation below is true, please see the steps below
∞
X
j=0
(1 − λ)j = S = 1
λ (14)
S = (1 − λ)0+ (1 − λ)1+ (1 − λ)2+ ... + (1 − λ)n (15) S(1 − λ)1 = (1 − λ)1+ (1 − λ)2+ ... + (1 − λ)n+1 (16) If n ⇒ ∞ and (16) is deducted from (15) this results in
S − S(1 − λ) = (1 − λ)0 (17)
S − S + λS = 1 (18)
S = 1
λ (19)
Appendix II
To derive the formula for inflation the price level equation18 is rewritten as follows pt= λ(pt+ αyt) + λ ∞ X j=0 (1 − λ)j+1Et−1−j(pt+ αyt) (20)
The previous price level is written as
pt−1= λ ∞
X
j=0
(1 − λ)jEt−1−j(pt−1+ αyt−1) (21)
Subtracting equation (21) from equation (20) and rearranging yields
πt= λ(pt+αyt)+λ ∞ X j=0 (1−λ)jEt−1−j(πt+α∆yt)−λ2 ∞ X j=0 (1−λ)jEt−1−j(pt+αyt) (22) Now equation (20) is rewritten as
pt− αλ 1 − λ yt= λ ∞ X j=0 (1 − λ)jEt−1−j(pt+ αyt) (23)
Equation (23) replaces the last term in (22) delivering for inflation
Appendix III
To get to equation (9), the following steps are taken. Firstly, equation (4) and equation (6) are combined, resulting in the equation below
pt= λ ∞
X
j=0
(1 − λ)jEt−j((1 − α)pt+ αmt) (25)
Then the fact that all agents are informed is used. After the shock there is an informed group and a uninformed group. The group that is uninformed is equal to
(1 − λ)t+1−γ (26)
The informed group is
ζt= 1 − (1 − λ)t+1−γ (27)
Prices depend on the price of the informed group and the price of the uninformed group. The price of the uniformed group is based on previous information and thus equal to zero. This results in
pt= (1 − (1 − λ)t+1−γ)((1 − α)pt+ αmt) + 0 (28)
This is equal to
pt− ζt(1 − α)pt= ζtαmt (29)
This can be written as
pt(1 − ζt(1 − α)) = ζtαmt (30) Resulting in pt= ζtαmt 1 − ζt(1 − α) (31) Deducting pt−1 from ptand using ΛX for the relevant assumption on
expec-tations, results in the equation (9).
Data Sources
• The data on M2 is taken from the Board of Governors of the Federal Reserve System.
• The data to estimate λ is the mean response of the Survey of Profes-sional Forecasters and the University of Michigan Inflation Expecta-tions.
http://research.stlouisfed.org/fred2/series/MICH/downloaddata?cid=32455 • The data underlying Figure 6 is the mean response from the Survey of
Professional Forecasters. The data is taken from the Federal Reserve Bank of Philadelphia (www.philadelphiafed.org).
• The data underlying figure 7 are Break-Even Interest Rate for two years in advance. The data is taken from Bloomberg, ticker: USG-GBE02:Ind.
• The data underlying figure 9 are the Excess Reserves of Depository Institutions (EXCRESNS). The data is taken from the Economic Re-search department of the Federal Reserve Bank of St. Louis
(http://research.stlouisfed.org/fred2/series/EXCRESNS).
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