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.

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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