Bulletin of Monetary Economics and Banking, Vol. 22, No. 4 (2019), pp. 507  528
DO MONETARY AGGREGATES BELONG IN A MONETARY
MODEL? EVIDENCE FROM THE UK
Mehmet Ezer
Department of Economics, Business, and Accounting,
ABSTRACT
Conventional monetary models focus on interest rates and omit monetary aggregates from policy discussions. This paper examines whether augmenting the measure of monetary policy with monetary aggregates helps determine more robust links between policy and economic fluctuations. After constructing the Divisia money index for the UK, I employ structural vector autoregression to identify two different UK monetary policy regimes. Inclusion of this (correct) measure of money and disentangling the money supply from demand resolve the price and liquidity puzzles. The results point to the informational content embedded in monetary aggregates, suggesting they should be taken into account in evaluations of monetary policy.
Keywords: Time series models; Monetary policy; Central bank policies.
JEL Classifications: C21; E52; E58.
Article history: 

Received 
: October 02, 2019 
Revised 
: December 26, 2019 
Accepted 
: January 7, 2020 
Available online : January 10, 2020
https://doi.org/10.21098/bemp.v22i4.1184
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I. INTRODUCTION
Monetary policy is one of the most important tools economic policymakers use while attempting to shape the economy. Therefore, it is crucial to successfully gauge its stance and understand the mechanisms through which it affects the variables in the economy.
Friedman and Schwartz (1963) document evidence that shows not only that money stock is procyclical, but also its movements lead the movements of output, suggesting a causal relation between these two variables. Later studies, however, show a weakening correlation structure between money stock and output. Combined with the expanding real business cycle literature, which attributes fluctuations in the economy to real variables, this weakening correlation structure has diminished interest in analyzing the behavior of money stock. New Keynesian models that were developed later1 study monetary policy and its effects by focusing on the role of interest rates, particularly the
Money stock could be an alternative or complementary measure to short term nominal interest rates in understanding the stance and role of monetary policy. However, the challenge is to disentangle the money demand from the money supply, since they together determine the level of the money stock. As the proponents of real business cycle theory observe, the money stock itself could be affected by movements in output, creating reverse causality where the business cycle drives the money stock, rather than vice versa.4
In a recent study, Belongia and Ireland (2016) show that monetary aggregates have the ability to explain aggregate fluctuations in the US economy, but only when properly measured. “Proper measurement” requires the use of Divisia aggregates instead of money. The authors first show that the correlation structure suggested by Friedman and Schwartz (1963) is still used. By utilizing a structural vector autoregression (SVAR) model, Belongia and Ireland (2016) draw tight links between monetary policy and economic fluctuations. The user cost (price dual) series of their preferred money stock measure, Divisia aggregates, enables them to disentangle the behavior of money demand from that of the money supply. Their analysis quantifies the contribution of monetary policy to instability in the US economy between 1967 and 2013 and suggests that monetary aggregates should be taken into account while evaluating the stance of monetary policy.
Three questions naturally arise: is there a discrepancy between the simple sum and Divisia quantities for other economies? Is there further evidence that the monetary aggregates should be taken into account to understand the stance of the monetary policy? Can augmenting the measure of monetary policy with monetary aggregates help to draw more robust links between monetary policy and economic fluctuations?
1Woodford (2003) provides examples of such models.
2See Estrella and Mishkin (1997) and Stock and Watson (1999), for example.
3Mishkin (2007) summarizes the channels through which monetary policy affects output.
4See King and Plosser (1984) and Plosser (1989).
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Following Barnett’s (1980) critique, many monetary authorities started calculating Divisia indexes, as well as
We first construct the
The remainder of this paper is organized as follows. Section II reviews the literature. Section III explains how the Divisia index is constructed and compares it with a
II. LITERATURE REVIEW
Interest in analyzing the behavior of money stock diminished in the 1980s and 1990s. Seminal studies by Bernanke and Blinder (1992), Estrella and Mishkin (1997), and Stock and Watson (1999) attribute a less significant role to money stock. Bernanke and Blinder (1992) argue that the interest rate on federal funds is a good indicator of monetary policy actions and is therefore informative about the future movements of real macroeconomic variables. The role of money is minimized once the federal funds rate is introduced into the empirical framework. Estrella and Mishkin (1997) suggest that monetary aggregates can play a role as information variables, indicators of policy actions, and instruments in a policy rule. However, these roles would require a stable relation between the aggregates and the final policy targets. By studying US data from 1979 to 1995, the authors show that such a relation did not exist in that period. Stock and Watson (1999) study inflation forecasts and suggest no gains from including the money supply in their analysis. These studies suggest that focusing on the federal funds rate suffices to study monetary policy.
Studies show that the quantity of money contains valuable information; however, obtaining this information requires differentiating the money supply
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and the money demand, which is not a straightforward task. Hendrickson (2017) argues that deviations between money demand and money supply are an important source of economic fluctuations. Moreover, the author shows that shocks to the monetary base play a significantly more important role than money demand shocks in terms of generating instability. Belongia and Ireland (2019) identify a stable money demand function from 1967 through 2019 by using Divisia aggregates, which suggests that an aggregate quantity of money can play a role in monetary policy when properly measured.
There is a rapidly growing literature focusing on the “right way” of measuring the amount of money, since the “wrong measurement” leads to qualitatively misleading results. Belongia (1996) highlights the importance of choosing the right monetary index. The author replicates five studies analyzing the effects of money on aggregate activity and shows that, in four of the five cases, the qualitative inference in the original study is reversed when the
When the right measures of money stock are employed, the quantity of money is shown to have important macroeconomic properties. Dery and Serletis (2019) examine the cyclical behavior of Divisia money index and find support for a monetary effect on the business cycle. Their findings highlight the importance of using broad Divisia monetary aggregates. Belongia and Ireland (2015) show that Divisiameasuresofmoneyhelpinforecastingthemovementsofkeymacroeconomic variables. Furthermore, the statistical fit of SVAR improves significantly when these measures of money are included to identify monetary policy shocks. The results of Belongia and Ireland challenge the adequacy of conventional models, which focus solely on interest rates. Darvas (2015) creates a new data set based on euro area Divisia monetary aggregates. By estimating the responses to money and interest rate shocks in the euro area using SVAR, Darvas provides supporting evidence regarding the usefulness of Divisia monetary aggregates in assessing the impacts of monetary policy. Keating et al. (2019) propose abandoning the federal funds rate as the policy indicator and using, instead, broad Divisia monetary aggregates. This approach results in monetary policy effects that are qualitatively similar to those of the case in which the federal funds rate is the policy indicator; furthermore, it allows for the measurement of the effects of monetary policy, even if the federal funds rate hits a zero lower bound.
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In light of these studies, we construct a Divisia money index for the UK and conduct SVAR analysis to estimate the monetary policy rules and money demand equations. We determine which type of monetary policy rule better fits the data. Our analysis suggests the use of the interest
III. CONSTRUCTION OF THE DIVISIA INDEX
Conventional
The UK money stock is split between three sectors: household, private nonfinancial corporate, and other financial corporate. Following Hancock (2005), who shows that financial corporations’ Divisia data have high variance and that their volatility could be telling us little about
Monetary data for the UK must be adjusted for breaks that arise when building societies change classifications to become banks. Hancock (2005) explains that leaving data unadjusted would lead to reports of large flows out of building societies and into banks. As Bissoondeeal et al. (2010) point out,
The variable Mi,t denotes the unadjusted amounts outstanding (unadjusted level) of the ith monetary asset for period t, ∆Mi,t is the difference between successive amounts outstanding, and ∆Mi,tBA denotes the
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The Bank of England uses the following formula to compute its Divisia index,
Dt :
which means that the growth rate of the Divisia index weights the component growth rates by their average shares. Using the fact that the average shares sum to one, the above equation is rearranged to obtain the following iterative formula to compute the level of the Divisia index:
The Bank of England’s household and private nonfinancial corporate sector Divisia index includes the following components as of January 2008:
•Notes and coins
•
•
•
•
•
The Bank of England’s household sector data also include
savings accounts and individual savings accounts, introduced in 1991 and 1999, respectively. These assets are not incorporated into the index under construction, since they are primarily a form of savings for households, as Hancock (2005) explains.
The components constituting the Divisia index change over time. Interest bearing deposits of the private nonfinancial corporate sector at building societies are introduced to the index in July 1996.
While calculating the user costs of the components of the Divisia index, we use the quoted interest rates of assets until 1999, and the effective rates that year onward.5 As for the benchmark rate, we follow Bissoondeeal et al. (2010) and adopt an envelope approach similar to that used by the Bank of England. A total of 250 basis points are added to the
5See the explanatory notes for sectoral deposits and Divisia money at the Bank of England’s website (http://www. bankofengland.co.uk/statistics/Pages/iadb/notesiadb/divisia.aspx).
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Figure 1 plots the
Figure 1.
Divisia and
This graph shows the
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Simple Sum 

































1978 
1980 
1982 
1984 
1986 
1988 
1990 
1992 
1994 
1996 
1998 
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2002 
2004 
2006 
2008 
2010 
2012 
Figure 2.
Differences in
Aggregates, in Percentage Points
This graph shows the differences in
Divisa  Simple Sum
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1978 
1980 
1982 
1984 
1986 
1988 
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1992 
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1996 
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2004 
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2010 
2012 
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IV. MODEL AND METHODOLOGY
Following Belongia and Ireland (2016), a vector autoregression (VAR) model is used to describe the behavior of six variables: the output Yt, measured by the real GDP; the price level Pt, measured by the GDP deflator; money Mt, measured by the Divisia index; the
(1)
we can build a structural model of the form
(2)
where A is a 6×6 matrix of coefficients with ones along the diagonal; μ is a 6×1 vector of constant terms; each Φj, j=1,2,…,q, is a 6×6 matrix of slope coefficients; Σ is a 6×6 matrix with the standard deviations of the structural disturbances along its diagonal, and zero elsewhere; and εt is a 6×1 vector of serially and mutually uncorrelated structural disturbances, normally distributed, with zero means, and
(3)
The reduced form associated with Equations (2) and (3) is
(4)
where the constant term
(5)
The structural and
such that
(6)
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Since the covariance matrix Ω for the
(7)
where aij denotes the coefficient from row i and column j of A and σ44 is the fourth element along the diagonal of Σ. The terms involving the constant μ and lagged values
(8)
which can be interpreted as a money demand equation, linking the money demand to the price level, the output, commodity prices, and the
We use a second, alternative identification scheme in which the money stock plays a larger role in the making and transmission of monetary policy. In this scheme, A is allowed to take the nontriangular form
(9)
In this alternative identification, the first two rows are similar to the triangular identification in which the aggregate price level and output respond to the other shocks hitting the economy with a lag of one period. Row three of Equation (9) indicate that the commodity prices are assumed to react immediately to every shock to the economy.
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In particular, the monetary system is modeled by the last three rows of Equation (9). The monetary policy rule described by the fourth row is similar to the rules employed by Sims (1986) and Leeper and Roush (2003):
(10)
This monetary policy rule associates a monetary policy shock with simultaneous movements in the interest rate and the nominal money supply. For a positive σ45 coefficient, such a rule associates monetary policy tightening with an immediate increase in interest rates and a decrease in the money stock.
This policy rule can be expanded so that it includes prices and output, which would mean that the interest rate immediately responds to changes not only in the money supply, but also in the price level and output, as follows:
(11)
The fifth row in Equation (9) suggests a money demand equation of the form
(12)
which links the real value of the Divisia index to the output and the user cost as the associated price.
The behavior of private financial institutions can be characterized by the sixth row of Equation (9):
(13)
which suggests that both the official bank rate and the quantity of real monetary services created are passed along to user costs.
We employ the maximum likelihood method to estimate the described SVAR model as outlined by Hamilton (1994) and Lutkepohl (2006). Fully efficient estimates of the
By maximizing the following concentrated
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This approach can be employed to estimate both the overidentified case suggested by Equation (9) and the triangular model identified just now (although, in the latter case, the usual approach of Cholesky decomposition for would yield the same result).
V. SVAR RESULTS
Below is a timeline for the official monetary policy regimes pursued by the Bank of England and recessions that took place in the UK:
•July 1976 to April 1979: monetary targeting (M3)
•May 1979 to February 1987: monetary targeting
•1980Q1 to 1981Q1: recession
•March 1987 to September 1990: informal linking of the pound to the Deutsche mark
•1990Q3 to 1991Q3: recession
•October 1990 to September 1992: membership in the exchange rate mechanism
•October 1992 to April 1997: inflation targeting prior to the operational independence of the Bank of England
•2008Q2 to 2009Q2: recession
Running the SVAR analysis for different samples and factoring in the above
developments show that the UK data can be split into two samples: an early sample that spans 1978Q3 to 1990Q1 and a recent sample that spans 1993:Q1 to 2011:Q3. We exclude the period in between, since the data are too noisy due to the UK’s exchange rate mechanism membership in that period. Similarly, the period after 2011Q3 is not included, because it was a tumultuous time during which unconventional monetary policy tools, such as quantitative easing, were applied.
The estimated monetary policy, money demand, and monetary system equations are provided in Tables 1 to 4. Tables 1 and 2 provide the regression results for the early sample, with the data as logarithmic levels and growth rates, respectively. Tables 3 and 4 do the same for the recent sample. We use a likelihood ratio test to see whether the inclusion of monetary aggregates in the monetary policy rule improves the fit.6 The restriction of excluding the monetary aggregates from the monetary policy rule given by Equation (11) is rejected at the 99% confidence level for all the samples. The constraint of excluding prices and the output from Equation (11), however, does not decrease the model’s fit by much. These results point to a monetary policy rule that includes the monetary aggregates.
6The test is conducted by multiplying the difference of the maximized likelihood values with 2, and then comparing it with the critical
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Table 1.
Maximum Likelihood Estimates from SVARs Data in Log Levels, Early Sample:
1978:3  1990:1
This table presents SVAR analysis results for four different specifications of the monetary policy rule. Standard deviations are in parentheses.
Model 


Coefficients 
Other 



Estimates 









Panel A. Triangular Identification 








L=2856.2 
Monetary Policy 
R = 0.11P  0.19Y  0.00CP 

σ = 0.0070 


(0.26) 
(0.27) 
(0.03) 

(0.0004) 

Money Demand 
M = 0.42P + 0.48Y + 0.05R + 0.02CP 
σ = 0.0077 


(0.26) 
(0.28) 
(0.15) 
(0.04) 
(0.0005) 


Panel B. Interest 








L=2852.2 
Monetary Policy 
R = 2.19M 




σ = 0.0143 

(1.64) 




(0.0036) 
Money Demand 
M  P = 0.88Y  11.97U 

σ = 0.0873 


(1.75) 
(20.43) 

(0.0708) 

Monetary System 
U = 0.64R + 

σ = 0.0145 


(0.07) 
(0.06) 


(0.0040) 






Panel C. Taylor Rule with Money 








L=2853.7 
Monetary Policy 
R =  0.83P  1.23Y + 2.46M 

σ = 0.0157 


(1.25) 
(1.37) 
(2.54) 

(0.0044) 

Money Demand 
M  P = 0.92Y  15.88U 

σ = 0.0776 


(2.17) 
(48.91) 

(0.0577) 

Monetary System 
U = 0.64R + 

σ = 0.0147 


(0.08) 
(0.06) 


(0.0041) 






Panel D. Taylor Rule without Money 








L=2823.9 
Monetary Policy 
R = 0.11P  0.18Y 


σ = 0.0070 


(0.25) 
(0.26) 


(0.0004) 

Money Demand 
M  P = 0.75Y  0.01U 

σ = 0.0100 


(0.25) 
(0.34) 

(0.0007) 

Monetary System 
U = 0.46R + 

σ = 0.0050 


(0.05) 
(0.05) 


(0.0005) 
Do Monetary Aggregates Belong in a Monetary Model? Evidence From The UK 
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Table 2.
Maximum Likelihood Estimates from SVARs Data in Growth Rates, Early Sample:
1978:3  1990:1
This table presents SVAR analysis results for four different specifications of the monetary policy rule. Standard deviations are in parentheses.
Model 


Coefficients 
Other 



Estimates 









Panel A. Triangular Identification 








L=1193.2 
Monetary Policy 
R = 0.19P  0.05Y + 0.00CP 

σ = 0.0089 


(0.18) 
(0.18) 
(0.03) 

(0.0008) 

Money Demand 
M = 0.15P + 0.14Y  0.08R  0.01CP 
σ = 0.0075 


(0.19) 
(0.18) 
(0.16) 
(0.03) 
(0.0007) 


Panel B. Interest 


Monetary Policy 
R = 3.70M 




L=1191.3 

(3.58) 




(0.0113) 
Money Demand 
M  P = 2.24Y  23.62U 

σ = 0.0409 


(4.40) 
(48.31) 

(0.0264) 

Monetary System 
U = 0.66R + 

σ = 0.0099 


(0.08) 
(0.06) 


(0.0027) 


Panel C. Taylor Rule with Money 








L=1193.2 
Monetary Policy 
R =  0.40P  0.61Y + 4.02M 

σ = 0.0206 


(1.07) 
(1.12) 
(4.69) 

(0.0085) 

Money Demand 
M  P = 2.49Y  26.97U 

σ = 0.0420 


(5.84) 
(70.49) 

(0.0248) 

Monetary System 
U = 0.68R + 

σ = 0.0099 


(0.08) 
(0.06) 


(0.0027) 






Panel D. Taylor Rule without Money 








L=1172.9 
Monetary Policy 
R = 0.19P  0.05Y 


σ = 0.0089 


(0.18) 
(0.18) 


(0.0008) 

Money Demand 
M  P = 0.48Y  0.60U 

σ = 0.0102 


(0.22) 
(0.48) 

(0.0010) 

Monetary System 
U = 0.43R + 

σ = 0.0050 


(0.05) 
(0.05) 


(0.0006) 
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Table 3
Maximum Likelihood Estimates from SVARs Data in Log Levels, Recent Sample:
1993:1  2011:3
This table presents SVAR analysis results for the recent sample for four different specifications of the monetary policy rule. Standard deviations are in parentheses.
Model 


Coefficients 
Other 



Estimates 









Panel A. Triangular Identification 








L=1027.5 
Monetary Policy 
R = 0.10P + 0.03Y + 0.02CP 

σ = 0.0020 


(0.07) 
(0.10) 
(0.01) 

(0.0002) 

Money Demand 
M = 0.38P  0.24Y  0.27R + 0.03CP 
σ = 0.0050 


(0.19) 
(0.26) 
(0.29) 
(0.02) 
(0.0005) 


Panel B. Interest 








L=1021.7 
Monetary Policy 
R = 0.62M 




σ = 0.0074 

(0.30) 




(0.0079) 
Money Demand 
M  P =  0.21Y  12.81U 

σ = 0.0171 


(0.63) 
(5.78) 

(0.0084) 

Monetary System 
U = 0.51R + 

σ = 0.0083 


(0.06) 
(0.02) 


(0.0052) 


Panel C. Taylor Rule with Money 








L=1022.5 
Monetary Policy 
R =  0.33P + 0.31Y + 1.19M 

σ = 0.0426 


(0.51) 
(0.45) 
(1.23) 

(0.3015) 

Money Demand 
M  P =  0.27Y  21.12U 

σ = 0.0148 


(0.97) 
(18.57) 

(0.0066) 

Monetary System 
U = 0.55R + 

σ = 0.0086 


(0.07) 
(0.03) 


(0.0053) 


Panel D. Taylor Rule without Money 








L=1019.1 
Monetary Policy 
R = 0.10P + 0.04Y 


σ = 0.0020 


(0.08) 
(0.10) 


(0.0002) 

Money Demand 
M  P =  0.13Y  1.10U 

σ = 0.0055 


(0.25) 
(0.34) 

(0.0006) 

Monetary System 
U = 0.32R + 

σ = 0.0023 


(0.04) 
(0.02) 


(0.0005) 
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Table 4.
Maximum Likelihood Estimates from SVARs Data in Growth Rates, Recent
Sample: 1993:1  2011:3
This table presents SVAR analysis results for the recent sample for four different specifications of the monetary policy rule. Standard deviations are in parentheses.
Model 


Coefficients 
Other 



Estimates 









Panel A. Triangular Identification 








L=897.3 
Monetary Policy 
R = 0.07P + 0.04Y + 0.02CP 

σ = 0.0015 


(0.07) 
(0.09) 
(0.01) 

(0.0002) 

Money Demand 
M = 0.37P  0.14Y  0.35R + 0.04CP 
σ = 0.0045 


(0.18) 
(0.22) 
(0.29) 
(0.02) 
(0.0005) 


Panel B. Interest 








L=891.5 
Monetary Policy 
R = 0.68M 




σ = 0.0078 

(0.34) 




(0.0092) 
Money Demand 
M  P =  0.09Y  12.51U 

σ = 0.0331 


(0.53) 
(5.18) 

(0.0318) 

Monetary System 
U = 0.56R + 

σ = 0.0074 


(0.07) 
(0.02) 


(0.0035) 


Panel C. Taylor Rule with Money 








L=894.1 
Monetary Policy 
R =  0.54P + 0.28Y + 1.69M 

σ = 0.0037 


(0.95) 
(0.56) 
(2.42) 

(0.0018) 

Money Demand 
M  P =  0.19Y  22.30U 

σ = 0.0458 


(0.90) 
(20.38) 

(0.0569) 

Monetary System 
U = 0.60R + 

σ = 0.0071 


(0.07) 
(0.03) 


(0.0034) 






Panel D. Taylor Rule without Money 








L=882.2 
Monetary Policy 
R = 0.09P + 0.05Y 


σ = 0.0016 


(0.07) 
(0.09) 


(0.0002) 

Money Demand 
M  P = 0.04Y  1.18U 

σ = 0.0072 


(0.24) 
(0.95) 

(0.0016) 

Monetary System 
U = 0.34R + 

σ = 0.0025 


(0.04) 
(0.02) 


(0.0003) 
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The results in Tables 1 to 4 suggest that variables other than the money stock (i.e., the output and prices) do not enter the monetary policy equation significantly. Therefore, there is little support for a Taylor rule depiction of the UK’s monetary policy in either sample period. Instead, the interest
An important difference between the early and recent samples is the reaction of the interest rate to the stock of money, as can be seen from the monetary policy equations. The coefficient on the money stock is much larger in the early sample than in the recent sample. However, in terms of significance, the coefficient on the money stock in the monetary policy equation fares better after 1993.
Figures 3 and 4 illustrate the impulse responses in percentage points to one
Figure 3.
Early Sample Impulse Responses to
Monetary Policy Shock
This figure shows the responses of
1,5 

R: Triangular. Log Levels 


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Figure 3.
Early Sample Impulse Responses to
Monetary Policy Shock (Continued)
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Figure 4.
Recent Sample Impulse Responses to
Monetary Policy Shock
This figure shows the responses of
0,5 


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0,5 




0 





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R: 







































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10 
15 
20 
5 
10 
15 
20 
(b)
Do Monetary Aggregates Belong in a Monetary Model? Evidence From The UK 
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Figure 4.
Recent Sample Impulse Responses to
Monetary Policy Shock (Continued)
0,6
0,2
0
0,5
0

R : Triangular , Growth Rates 


2 

M : Triangular , Growth Rates 















1 








0 




5 
10 
15 
20 
5 
10 
15 
20 


Y : Triangular , Growth Rates 




P : Triangular , Growth Rates 






0,2 








0,1 








0 













5 
10 
15 
20 
5 
10 
15 
20 
(c) Triangular, growth rates
0,6
0,4
0,2
0
0,5
0
R :
5 
10 
15 
20 
R :
5 
10 
15 
20 



M : 


0,5 





0 















5 
10 
15 
20 




P : 


0,5 





0 





0 
5 
10 
15 
20 
(d)
Two established puzzles in the VAR literature need to be addressed. Following a positive shock to the interest rate, it is common to observe an increase in the price level (price puzzle) and an increase in the money stock (liquidity puzzle) in empirical models, which is inconsistent with the theory. The estimated monetary policy rules for both samples suggest that the incorporation of monetary aggregates into the monetary policy rule helps resolve both puzzles, and, following a monetary policy shock, price levels and monetary aggregates behave in line with what macroeconomic theory suggests.
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VI. CONCLUSION
It is very important to successfully gauge the stance of monetary policy and understand the mechanisms through which it affects the variables in the economy. To achieve these goals, we can use the money stock as an alternative or complementary measure to
The study starts with constructing the Divisia index for the UK for the period between 1978 and 2011. We use SVAR to estimate the monetary policy equation for the early and recent samples. The results show little support for a Taylor rule depiction of UK monetary policy and suggest the interest
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