1. what are the fistylized factsflabout money and economic...
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Monetary Policy, 15/2 2016
Henrik JensenDepartment of EconomicsUniversity of Copenhagen
1. What are the �stylized facts�about money and economic aggregates?
Does money matter for output and prices?
Are the responses to money shocks di¤erent in the short and long run?
Empirical problems/issues
Literature: Walsh (2010, Chapter 1)
2. Plan for next lectures
c 2016 Henrik Jensen. This document may be reproduced for educational and research purposes, as long as the copies contain this notice and are retained for personaluse or distributed free.
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What are the �stylized facts�about moneyand economic aggregates?
Long run correlations
� Most estimates show correlations between growth in monetary aggregates and in�ation close to one
�Hence, a reasonable characterization is that long-run changes in money growth are re�ected inequivalent changes in in�ation rates
�Causality?
� Long-run e¤ects on output are less robust
�Some �nd positive correlations between money growth and output
�Some �nd no correlation between in�ation and output
�Some �nd negative correlation between in�ation and output
�Results hinge on which countries are used; e.g., some �nd negative in�ation e¤ects in high in�ationcountries and zero or slightly positive e¤ects for low-in�ation countries
�Results may fail when nominal interest rates are at their lower bound
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� Despite more uncertainty about the relationship between of monetary aggregates and real economicactivity the John B. Taylor quote represents the consensus view in the economics profession:
�about which there is now little disagreement, ... that there is no long-run trade-o¤ between the rate ofin�ation and the rate of unemployment�
� I.e., the long-run Phillips curve is approximately vertical
� Nobel prizes to Milton Friedman (1976), Robert E. Lucas (1995), Edmund Phelps (2006) all supportthe �mainstream�property of the view
� In�ation and nominal interest rates in the long run?
�Fisher equation: it = rt+ Et�t+1
�In steady state, iss = rss + �ss
�Higher long-run in�ation should raise long-run interest rates (roughly con�rmed by empiricalanalyses)
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Short-run correlations
� Assessing the short-run e¤ects of monetary policy on real activity: much more controversial
� Aim is to analyze whether monetary aggregates are correlated with real activity at business cyclefrequencies
�One usually uses de-trended data; i.e., data exhibiting deviation from an underlying, hypotheticaltrend value which would prevail in absence of any shocks or frictions in the economy
�Issue is then whether above average monetary aggregates are associated with above or belowaverage economic activity
� Figure 1.1 in Walsh shows dynamic correlations for three monetary aggregates (M0, M1, M2) andGDP (US data for 1967�2008)
�In particular M2 exhibits a pattern: It is positively correlated with GDP at lags and negativelycorrelated at leads
�I.e., if M2 is above average, it is associated with above-average GDP ahead in time; money leadsoutput
� Figure 1.2 shows the same �gures for 1984�2008: Very di¤erent picture: Only M1 leads output; M2lags output; M0 is negatively correlated at lags)
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� Figure 1.3 shows dynamic correlations for three interest rates, prices (US data for 1967�2008)
�In particular, all interest rates exhibit a pattern: They are negatively correlated with GDP atlags and positively correlated at leads
�I.e., if the Federal Funds rate is above average, it is associated with below-average GDP ahead intime; interest rate leads output
�Prices are negatively correlated with GDP at lags (and contemporaneously) and positively cor-related at (long) leads
� Figure 1.4 shows the same �gures for 1984�2008: Less �lead e¤ect�of interest rates
� Upshot: Money measures are correlated with GDP, but in varying degrees for di¤erent periods anddi¤erent measures
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� And again, simple correlations tell little about causality
� E.g., Friedman and Schwartz� classic 1964 study, which concluded that money movements causeoutput movements after long (and variable) time, has been questioned
� The positive correlations may as well re�ect that money adjust endogenously to real output move-ments (�reverse causality�) (King and Plosser, 1984)
�The endogeneity of money is predominant for broader measures of money (such as M1 and M2),and in cases where the central bank uses the nominal interest rate as an instrument
�Indeed, some �nd that the positive correlation is only prevalent for broad monetary aggregates(�inside money�), as it re�ects the banking and �nancial system�s endogenous response to changesin economic activity.
� E.g., increased (succesful) lending activity by banks in anticipation of an upcoming boom,increases broad monetary aggregates, even though the ensuing boom in not caused by money
� Lots of econometric work has therefore been conducted to assess the e¤ects of money on output
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� Early famous econometric studies regressed (often nominal) output on money and other variables
�Friedman and Meiselman (1963) found statistically signi�cant coe¢ cients on money
� Such �St. Louis�regressions were in�uential, but . . . the issue of endogeneity pops up:
�If money is endogenous, the regressions are misspeci�ed
�Also, at the extreme, if monetary policy is successful in stabilizing output, then money and outputwould be uncorrelated, and a St. Louis regression would show that money had no e¤ect on output� even though it had!
� Sims (1972) introduced Granger causality analysis, and found that money Granger-caused output
�That is, lagged values of money have predictive power for output (while the opposite is not true)
� Findings less robust when other variables, e.g., interest rates, are included in empirical analysis(indicating that how one measures monetary policy matters)
� We now look at another, deeper, problem using St. Louis regressions . . .
. . .and look at recent methods of assessing the real e¤ects of money in the short run
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Empirical problems/issues
Problems with using simple regressions for policy evaluation: The Lucas critique
� Estimated relationship between log output, yt, and log nominal money, mt:
yt = a0mt + c1zt + c2zt�1 + ut (1.3 simpli�ed)
(Simpli�ed version of (1.3) with: a1 = 0.)
� Assume zt and ut are zero in expectations and unknown when mt is set.The best output-stabilizing money-supply rule:
mt = �c2a0zt�1 + vt
= �2zt�1 + vt; �2 � �c2a0< 0
(1.4 simpli�ed)
vt is a �control error�� an unanticipated, unsystematic part of monetary policy
� Resulting output if (1.3) is true: yt = a0vt + c1zt + ut. Hence, the systematic monetary policyresponse towards zt�1 works!
�No theory needed in order to stabilize output!
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� This can be dangerous in design of the policy rule (Sargent): Suppose the true model for output is:
yt = d0vt + d1zt + d2zt�1 + ut (1.5 simpli�ed)
I.e., only unanticipated monetary policy
vt � mt � Et�1mt
has real e¤ects. Many theoretical models have this feature
� With the policy rule, we have vt = mt � �2zt�1, so:
yt = d0 [mt � �2zt�1] + d1zt + d2zt�1 + ut= d0mt + d1zt + [d2 � d0�2] zt�1 + ut
(1.6 simpli�ed)
� This is observationally equivalent to (1.3):
yt = a0mt + c1zt + c2zt�1 + ut (1.3 simpli�ed)
� Even if only unsystematic monetary policy matters� (1.5) is true� a simple estimation can give thefalse impression that systematic monetary policy matters, i.e., false belief that (1.3) is true
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� Things are worse than just that: The estimated coe¢ cients depend on policy parameters!
(Here: coe¢ cient �d2 � d0�2�depends on �2)�Hence, a systematic change in policy (here, a change in �2) will change the estimated coe¢ cients
�Simple estimated relationships will �break down�when the policy rule changes
=> One cannot evaluate the implications of a policy change using the estimated relationships
� Estimated coe¢ cients are obtained from under a policy regime of the past!
�An example of Lucas�(1976) famous and in�uential critique of policy evaluation
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� �Proof�: Assume one believes in (1.3) based on an empirical investigation, and one wants to assessoutput e¤ects less policy response towards zt�1:
mt = (�2 + ") zt�1 + vt; " > 0
� Resulting output when one believes in the estimation, (1.3):
yt = a0 [(�2 + ") zt�1 + vt] + c1zt + c2zt�1 + ut
= a0
���c2a0+ "
�zt�1 + vt
�+ c1zt + c2zt�1 + ut
= a0vt + c1zt + a0"zt�1 + ut
One will conclude that zt�1 now a¤ects yt by a0"
� But if (1.5) is the true model, changes in policy rule have no output e¤ect, and the conclusion is false!
�Even thoughmt systematically responds less towards zt�1 � allowing a greater impact on outputof size d0" = a0" � this will be perfectly neutralized by the decrease in the coe¢ cient on zt�1:d2 � d0 (�2 + "); it falls by d0"
�No output e¤ects of a systematic change in the policy rule
�By de�nition, vt = mt � Et�1mt: Systematic changes in mt, change Et�1mt accordingly!
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� This calls for use of models where coe¢ cients and stochastic processes are invariant to changes inpolicy regimes
� Labelled �structural models�in modern macroeconomics, as �structural parameters�are de�ned asparameters invariant to policy changes.
� Many probably follow (Hurwicz, 1962) in de�ning �structural�relative to the class of policy experi-ments one considers (Fernández-Villaverde et. al, 2015)
� Beware though. Still leaves plenty of room for subjectivism.
� The aim of microfounded theories on how money a¤ects the economy is indeed to develop structuraltheoretical models for monetary policy, so as to avoid the Lucas critique
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Using (S)VAR analysis for assessing policy e¤ects
� Structural Vector Autoregressive (SVAR) methods have been widely adopted to assess the impact ofmonetary policy
� One estimates a system like �ytxt
�= A (L)
�yt�1xt�1
�+
�uytuxt
�(1.8)
�yt is, e.g., output and xt is the policy variable (all variables are stationary/detrended)
�A (L) is a matrix polynomial in L (the lag operator) � so independent variables can go far backin time
�uyt and uxt are innovations to output and policy, de�ned as linear combinations of orthogonaloutput and policy shocks: �
uytuxt
�=
�eyt + �ext�eyt + ext
�=
�1 �
� 1
� �eytext
�(1.9)
� Main goal is to �nd the impact of a policy shock on output (and other variables in larger systems)
� I.e., how will a certain realization of ext� a structural/exogenous component of residuals� a¤ectoutput in the short, medium and long run?
�What is the impulse response pattern?
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� Problem: Estimation of (1.8) gives the parameters of A (L), and the residuals uyt and uxt� One cannot, however, as long as � 6= 0 and � 6= 0, say anything about the individual e¤ects of eytand ext:
�As � and � are unknown, knowledge about uyt = eyt + �ext and uxt = �eyt + ext makes inferenceabout eyt and ext impossible <=> The VAR model is not identi�ed
�One needs to place an a priori restriction on either � or �
� E.g., assign a particular value to �. Then one can estimate �, and infer the shocks eyt and ext:
�Use that
uxt = �eyt + ext
= � [uyt � �ext] + ext= �uyt + (1� ��) ext
�Estimate uxt on uyt, and obtain an estimate of �
�The residual from the estimation is (1� ��) ext from which ext can be inferred as both � and �are known (the shock eyt can then readily be inferred)
� One can then assess the impact of a shock ext as the system�ytxt
�= A (L)
�yt�1xt�1
�+
�1 �
� 1
� �eytext
�is identi�ed
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� How can one just assign a value to either � or �?
� By using �appropriate�identifying restrictions. NOTE: �Appropriate�leaves room for judgement. ..
� Example with simple version of the VAR:�ytxt
�=
�a1 a20 0
� �yt�1xt�1
�+
�1 �
� 1
� �eytext
�; 0 < a1 < 1
(1.10)
� Hence,
yt = a1yt�1 + a2xt�1 + eyt + �ext
xt = �eyt + ext
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� The impulse response pattern of output following a policy shock can now be assessed:
�Period t: �
�Period t + 1: a1� + a2
�Period t + 2: a1 (a1� + a2)
�Period t + 3: a21 (a1� + a2)
.....
� Possible identifying assumptions:
�� = 0. This is assuming that a policy shock has no contemporaneous e¤ect on output
�� = 0. This is assuming that the policy variable is exogenous to contemporaneous output shocks
�� + (a1� + a2) + a1 (a1� + a2) + a21 (a1� + a2) + :::: = 0:This is assuming that the cumulative e¤ect of the policy shock policy is zero. If yt is representingoutput growth, this corresponds to an assumption that policy is neutral on the output level in thelong run
� All involves a judgement about what is a reasonable identifying assumption
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� Other issuess with the VAR approach:
�What is the relevant monetary policy variable?
�A satisfactory VAR should include more variables than just output (This increases the numberof identifying restrictions: For n variables n(n� 1)=2 restictions.)
�The data frequency will matter for the appropriateness of identifying restrictions
�Monetary policy is seen as a sequence of exogenous and random events; monetary policy�s en-dogenous nature is neglected:
� E.g., if monetary policy is a feedback rule, one could conclude that ext = 0, all t� I.e., conclude that monetary policy did not matter even though it may have played an impor-tant role for how the economy have adjusted to other shocks
�Di¤erent operating procedures and policy instruments across various time periods will make theresults sensitive to choice of period
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� Nevertheless, several VAR studies have some common �ndings:
�A contractionary monetary policy shock (an increase in the short interest rate), has a �hump-shaped�impact on output, and a negative e¤ect on output is most prominent after some time
�A �price puzzle�is often apparent: Prices increase after a contractionary policy shock; in contrastto common priors
� Possible explanation: The VAR ignores some of the monetary policymakers�information; e.g.,forecasts about rising in�ation due to factors the policymakers cannot o¤set, or maybe thepolicymaker reacts too late to raising prices
� Introducing forward-looking variables like asset prices in a VAR sometimes eliminates the pricepuzzle; they act as a proxy for the policymaker�s forecasts
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� A �representative� VAR analysis (with �� = 0� type identifying restriction(s) together with anassumption about a nominal interest-rate response function):
Source: Christiano, Eichenbaum and Evans (1999)
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Other approaches to address monetary policy and output
� Structural Econometric Models
�These are typically models with various estimated behavioral equations (consumption functions,labour supply schedules, etc.)
�Monetary policy is typically modelled as a feedback rule, making it possible to assess the impli-cations of various policy regimes
�Earlier models in 1960s and 1970s (like Danish �ADAM�and �SMEC�) were/are vulnerable tothe Lucas critique, and shocks are �reduced-form� shocks: residuals of regressions with littleinterpretation (the name �Structural models�is misleading modern terminology)
�Recent models used in central banks today have progressed� both small-scale and large scalemodels: Models are micro-founded and contains more interpretable shocks
� Real-life examples are estimated DSGE models used for business cycle analyses in Bank ofEngland, the ECB, Sveriges Riksbank, Norges Bank, Danmarks Nationalbank: Check theseinstitutions�webpages!
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� The �Narrative approach�(initiated by Friedman and Schwartz)
�Exogenous shifts in monetary policy are sought identi�ed by reading policy directives and minutesfrom FOMC meetings
�Romer and Romer (1989), e.g., identi�es six instances of clear contractionary shifts in monetarypolicy
� All of these are followed by recessions
�Supportive of the view that monetary policy matter for output in the short and medium run
�Romer and Romer (2004) extend this work, and extract time series for intended interest-ratepolicy, to distinguish this from the interest rate�s endogenous response to output movements(example: higher economic activity usually cause endogenous increase in interest rates)
� This distinction suggests that intended policy changes have stronger output e¤ects than thosefound in VARs (where identi�ed policy shocks are contaminated by endogenous movements)
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Summary
� In the long run:
�Monetary policy has predominantly e¤ects on prices, and not output
�Changes in money growth rates are re�ected in changes in in�ation rates, and nominal interestrates and very small e¤ects on output growth
� In the short run:
�The impact of monetary policy on real output is more controversial
�Many empirical problems arise when assessing the impact
�Some consensus have emerged: Monetary policy shocks produce a �hump-shaped� impact onoutput, and the maximum e¤ect is reached after some lag
�Monetary policy shocks a¤ect prices with an even longer lag
� Endogenous monetary policy responses, and their impact, are best understood within structuraleconometric models, which are not vulnerable to the Lucas critique
� So, we need theories to understand how monetary policy a¤ects the economy
� In terms of �policy shocks�and, in particular, in terms of assessing how endogenous responses to thestate of the economy a¤ect economic �uctuations
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Plan for next lectures
Thursday, February 18
1. Money in the utility function (start)
a. The basic money in the utility function model
b. Optimal behavior and steady-state equilibrium properties:Long-run superneutrality of money
Literature: Walsh (2010, Chapter 2, pp. 33�52)
Monday, February 22
1. Money in the utility function (continued)
a. Welfare costs of in�ation
b. Potential non-superneutrality of money
c. Dynamics and calibration
Literature: Walsh (2010, Chapter 2, pp. 52�86, so check the Appendix as well; i.e., get a grip on (orrelive the) the linearization technique)
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