AN ASSESSMENT OF THE STANDARD NEW KEYNESIAN MODEL …

Revue Économie, Gestion et Société N°14 décembre 2017

http://revues.imist.ma/?journal=REGS ISSN: 2458-6250

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AN ASSESSMENT OF THE STANDARD NEW KEYNESIAN MODEL

APPLIED TO MOROCCO: A BAYESIAN ESTIMATION

Par

Faical LAKHCHEN

Ph.D, Faculty of law, Economics and Social Sciences of Agadir Ibn Zohr

University.

&

Hassan HACHIMI ALAOUI

Professor, Faculty of law, Economics and Social Sciences of Agadir Ibn

Zohr University.

Abstract

In this paper, we criticize the use of the standard New Keynesian model in analyzing the

Moroccan economy. By showing that, in addition to the well-known structural short comings

of the model, it also fails to replicate the characteristics of the interest rate observed in data in

the case of the Moroccan economy. In order to improve the performance of the model in

replicating the characteristics of the interest rate, we moved from the standard model and we

estimated two other variants. We found that the Taylor rule, as it stands in the standard model,

doesn’t capture, wholly, the way that the monetary policy is conducted in Morocco. And a

version of the Taylor rule that reacts also to the deviations of inflation and output from their

values lagged by one period, improve the fit between the model and the data.

Key words: Standard New Keynesian model, Bayesian Estimation, persistence, interest rate,

Taylor rule, replication.

Résumé

Dans ce papier, nous critiquons l’utilisation du modèle nouveau keynésien standard dans

l’analyse de l’économie marocaine. En montrant que, en plus des défauts structuraux connus

du modèle, ce dernier échoue aussi à répliquer les caractéristiques du taux d’intérêt observées

sur les données dans le cas du Maroc. Afin d’améliorer la performance du modèle, dans la



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réplication des données, deux autres variantes du modèle sont estimées. Les résultats montrent

que la règle de Taylor, telle qu’elle est représentée dans le modèle standard, ne capte pas,

entièrement, la conduite de la politique monétaire au Maroc. Cependant, le modèle contenant

une règle de Taylor qui, en plus, répond aux déviations de l’inflation et de la production de

leurs valeurs retardées d’une période réplique mieux les données.

Mots clés : modèle nouveau keynésien standard, estimation keyésienne, persistance, taux

d’intérêt, la règle de Taylor, réplication.



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1-Introduction

New Keynesian models with imperfect competition are the cornerstone of modern monetary

theory(Wickens, 2012, p. 362). After the period of RBC (Real business-cycle) models,

initiated by Kydland and Prescott (1982) andLong Jr and Plosser (1983), a new kind of

models, called New Keynesian, were born by adding Keynesian theorizing features, as

monopolistic competition, to the RBC framework1(Clarida, et al., 1999). This modification

was necessary because the limit surrounding RBC models was their incapability to explain

some monetary aspects of the economy observed in the data. In the other hand, the New

Keynesian models did a better job than their predecessors in the matter. Furthermore, one

direct implication of adopting a New Keynesian framework is the non-neutrality of money,

and hence the comeback of the monetary policy to the forefront of macroeconomic research.

In this work, we estimate the standard New Keynesian DSGE model, in its compact form, as

inBennouna, et al. (2016) with a slight difference concerning the specification of the monetary

policy shock process. A principal references of this model areGalí (2008)and Walsh (2010).

The model is made up of three equations: IS dynamic equation, the New Keynesian Phillips

curve and the simple Taylor rule equation. As will be shown, the two first equations are

micro-founded and then respect the “Lucas critique”(Lucas, 1976).

Bayesian techniques are used to estimate the model. The advantage in using such techniques

lies in the possibility to use prior distributions so as to help the identification of parameters. In

the present work, our principal source of priors is Ait Lahcen (2014). The later has estimated

an open economy New Keynesian DSGE model with informal sector using Moroccan data.

Our First aim is to investigate if the standard New Keynesian model can replicate the business

cycles characteristics observed in the Moroccan data, so as to answer to the question: Is the

standard New Keynesian model a useful tool in analyzing the Moroccan economy?

The second aim is to move from the standard representation of the model, in order to improve

the fit between the model and the data. This will be done by first, adding habit formation in

consumption (Fuhrer, 2000) to the model and second, by trying a different Taylor monetary

policy rule than the simple one, proposed byClarida, et al. (2000)and used in the standard

model, that sets the nominal interest rate in reaction to the output and inflation gaps only2.

Finally, to conduct the Bayesian estimation we use Dynare, a software for solving and

simulating DSGE models (Adjemian, et al., 2011). And three quarterly time series spanning

the period 1991Q1 to 2014Q4: real gross domestic product, consumer price index and the

nominal interest rate3. The data are taken from the International monetary fund database.

1A dynamics to chastic general equilibrium framework (DSGE).

2 Here we use the term Taylor rule to specify the monetary rule that reacts to the level of inflation and output in

general, and not to the specific case when the weight given respectively to the inflation and output gaps is 1.5

and 0.5 as stated in the original paper by John B Taylor, "Discretion versus policy rules in practice" (paper

presented at the Carnegie-Rochester conference series on public policy, 1993).. 3The series are transformed using HP filter to match the model.



4 4

2-The theoretical model

The economy is made up of a continuum of households represented by a unit interval and

indexed by 𝑗 ∈ 0,1 and a continuum of intermediate goods firms represented also by a unit

interval and indexed by𝑖 ∈ 0,1 . The nominal interest rate is fixed by the monetary

authorities following a simple Taylor rule. The final good that will be consumed by

households is produced by the final goods firm using the intermediate goods. To integrate the

price rigidity in the model the intermediate goods firms are considered to evolve in a

monopolistic-competition market.

2-1-Households

The representative Household 𝑗maximize a lifetime expected utility function of the form:

max𝑬t 𝛽𝑠𝑈 𝐶𝑡+𝑠 𝑗

1−𝜍

1 − 𝜍− 𝜒

𝐻𝑡+𝑠 𝑗 1+𝜑

1 + 𝜑

+∞

𝒔=𝟎

0 < 𝛽 < 1 , 𝜒 > 0

Subject to the following budget constraint:

𝑃𝑡𝐶𝑡(𝑗) + 𝑒𝜍𝜖 𝑡𝐷𝐵𝑡(𝑗) = 𝑅𝑡−1𝐵(𝑗)𝑡−1 + 𝑊𝑡𝐻𝑡(𝑗)

𝛽 is the subjective discount factor, 𝜒 a preference parameter, 𝜍 is the inverse of the

intertemporal elasticity of substitution, 𝜑 is the inverse of the Frisch’s elasticity and 𝜖𝑡𝐷is a

demand shock that follows an AR(1) process 𝜀𝑡𝐷 = 𝜌𝐷𝜀𝑡−1

𝐷 + 𝜂𝑡𝐷 with 𝜂𝑡

𝐷~𝒩(0,𝜍𝐷2).

𝑃𝑡 is the price of the final good,𝐶𝑡 is consumption,𝐵𝑡is the quantity of bonds purchased, 𝑅𝑡 is

the nominal interest rate,𝑊𝑡 is the nominal wage and𝐻𝑡 represents laborsupply.

Household j maximizes its utility function by choosing 𝐶𝑡 , 𝐻𝑡 and 𝐵𝑡 ,and yields the ordinary

optimality conditions:

The consumption Euler equation

𝑬𝑡

𝐶𝑡+1 𝑗

𝐶𝑡 𝑗

𝜍

=𝛽

𝑒𝜍𝜀 𝑡𝐷 𝑬𝑡

𝑅𝑡𝜋𝑡+1

(1)

And, the optimal condition setting the marginal rate of substitution between labor and

consumption equal to the real wage.

𝜒𝐶𝑡 𝑗

𝜍𝐻𝑡 𝑗 𝜑 =

𝑊𝑡

𝑃𝑡 (2)

By dropping the index, and log-linearizing (1) under the market clearing condition in the good

market, one gets the following IS dynamic equation4:

𝑦 𝑡 = 𝑬𝒕𝑦 𝑡+1 −

1

𝜍 𝑟 𝑡 − 𝑬𝒕𝜋𝑡+1 + 𝜀𝑡

𝐷 (3)

2-2-The Final Goods Firm

The final good is produced using inputs of the intermediate goods, following the production

function5:

4Variables with hatdenote the log-deviation from the steady state

5 Such production function is called: Dixit-Stiglitz CES aggregatorAvinash K Dixit and Joseph E Stiglitz,

"Monopolistic competition and optimum product diversity," The American Economic Review 67, no. 3 (1977)..

CES stands for Constant elasticity of substitution



5 5

𝑌𝑡 = 𝑌𝑡 𝑖 𝜖−1

𝜖 𝑑𝑖1

0

𝜖

𝜖−1

𝑓𝑜𝑟 𝜖 > 1 (4)

So that 𝜖is the elasticity of substitution between the different intermediate goods.

The final goods firm maximize its profit:

max𝑌𝑡 𝑖

𝑃𝑟𝑜𝑓𝑖𝑡𝑡 = 𝑃𝑡 𝑌𝑡 𝑖 𝜖−1

𝜖 𝑑𝑖1

0

𝜖

𝜖−1

− 𝑃𝑡 𝑖 1

0

𝑌𝑡 𝑖 𝑑𝑖

Solving the maximization problem yields the demand for good 𝑖:

𝑌𝑡 𝑖 =

𝑃𝑡 𝑖

𝑃𝑡

−𝜖

𝑌𝑡 (5)

And, the price of the final good, under the zero profit:

𝑃𝑡 = 𝑃𝑡(𝑖) 1−𝜖

1

0

𝑑𝑖

1

1−𝜖

(6)

2-3-The Intermediate Goods Firms

The intermediate good firm solvesa two-stages problem. First, the intermediate goods firm

chooses its inputs in order to minimize the following cost function6:

min𝐻𝑡 𝑖

𝐻𝑡(𝑖)𝑊𝑡

𝑃𝑡

Subject to the demand for its output by the final goods firm(5)and to its Cobb-Douglas

production function7.

𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑌𝑡 𝑖 ≥

𝑃𝑡 𝑖

𝑃𝑡

−𝜖

𝑌𝑡

𝑌𝑡 𝑖 = 𝐻𝑡(𝑖)1−𝛼

Solving the minimization problem yields the condition settingthe real marginal cost equal to

real wage.

𝐶𝑀𝑡 𝑖 =

𝑊𝑡

𝑃𝑡 (7)

Second. The intermediate firm, when it’s not constraint, maximize its profit subject to (5) and

following the Calvo’s rule8(Calvo, 1983)

max𝑃𝑡∗ 𝑖

𝑬𝒕 𝛽𝜃 𝜏 𝑃𝑡∗ 𝑖 − 𝑒𝜅

−1𝜀𝑡𝑆𝑃𝑡+𝑠𝐶𝑀𝑡+𝑠 𝑖 𝑌𝑡+𝑠 𝑖

+∞

𝒔=𝟎

Solving for 𝑃𝑡∗(𝑖)yields:

6 In the standard New Keynesian model, we often exclude the capital factor.

7The 𝛼 is equal to 0.

8 Every period only a fraction 1 − 𝜃 of firms, that are randomly chosen, can choose their prices optimally, and

the other fraction 𝜃 set their prices according to the following rule: 𝑃𝑡 𝑖 = 𝑃𝑡−1(𝑖).



6 6

𝑃𝑡∗(𝑖) =

𝜖

𝜖 − 1𝑒𝜅

−1𝜀𝑡𝑆 𝑬𝒕 𝛽𝜃 𝑠+∞

𝒔=𝟎 𝑃𝑡+𝑠𝐶𝑀𝑡+𝑠 𝑖 𝑌𝑡+𝑠 𝑖

𝑬𝒕 𝛽𝜃 𝑠𝑌𝑡+𝑠 𝑖 +∞𝒔=𝟎

(8)

𝜖

𝜖−1 is the gross markup and the term𝜀𝑡

𝑆 represents a supply shock thatfollows an AR(1)

process 𝜀𝑡𝑆 = 𝜌𝑆𝜀𝑡−1

𝑆 + 𝜂𝑡𝑆with 𝜂𝑡

𝑆~𝒩(0,𝜍𝑆2).

Log-linearizing (8) gives:

𝑝 ∗𝑡

= (1 − 𝛽𝜃)𝑬𝒕 𝛽𝜃 𝜏+∞

𝒔=𝟎

𝑝 𝑡+𝑠 + 𝑐𝑚 𝑡+𝑠 𝑖 + 𝜅−1𝜀𝑡𝑆 (9)

Combining (9) with the Calvo Rule 𝑝 𝑡 = 𝜃𝑝𝑡−1 + (1 − 𝜃)𝑝𝑡 ∗yields

𝑝 𝑡 = 𝜃𝑝𝑡−1 + (1 − 𝜃)(1 − 𝛽𝜃)𝑬𝒕 𝛽𝜃 𝑠+∞

𝒔=𝟎

𝑝 𝑡 + 𝑐𝑚 𝑡 𝑖 + 𝜅−1𝜀𝑡𝑆

To eliminate the infinite sum, we multiply each side, of the equation above, by (1 − 𝛽𝜃𝐿−1).

With L is the lag operator9.

𝑝 𝑡 − 𝑝 𝑡+1𝛽𝜃 = 𝜃𝑝 𝑡−1 − 𝛽𝜃𝜃𝑝 𝑡 + 1 − 𝜃 1 − 𝛽𝜃 𝑬𝒕 𝛽𝜃 𝑠+∞

𝒔=𝟎

𝑝 𝑡+𝑠 + 𝑐𝑚 𝑡+𝑠 + 𝜅−1𝜀𝑡+𝑠𝑆

− 1 − 𝜃 1 − 𝛽𝜃 𝛽𝜃𝑬𝒕 𝛽𝜃 𝑠+∞

𝒔=𝟎

𝑝 𝑡+𝑠+1 + 𝑐𝑚 𝑡+𝑠+1 + 𝜅−1𝜀𝑡+𝑠+1𝑆

With a bit of algebra

𝑝 𝑡 − 𝑝 𝑡+1𝛽𝜃 = 𝜃𝑝 𝑡−1 − 𝛽𝜃𝜃𝑝 𝑡

+ 1 − 𝜃 1 − 𝛽𝜃 𝑬𝒕 𝛽𝜃 𝑠+∞

𝒔=𝟎

𝑝 𝑡+𝑠 + 𝑐𝑚 𝑡+𝑠 + 𝜅−1𝜀𝑡+𝑠𝑆 − 𝛽𝜃(𝑝 𝑡+𝑠+1

+ 𝑐𝑚 𝑡+𝑠+1 + 𝜅−1𝜀𝑡+𝑠+1𝑆 )

Eliminating the terms in t+1 gives:

𝑝 𝑡 − 𝑝 𝑡+1𝛽𝜃 = 𝜃𝑝 𝑡−1 − 𝛽𝜃𝜃𝑝 𝑡 + 1 − 𝜃 1 − 𝛽𝜃 (𝑝 𝑡 + 𝑐𝑚 𝑡+ + 𝜅−1𝜀𝑡𝑆)

With further simplifications:

𝜋 𝑡 = 𝛽𝑬𝒕𝜋𝑡+1 + 𝜅𝑐𝑚 𝑡 + 𝜀𝑡𝑆

With 𝜋 𝑡 = (𝑝 𝑡 − 𝑝 𝑡−1) 𝑎𝑛𝑑 𝜅 = 1−𝜃 1−𝛽𝜃

𝜃

Log-linearizing and combining (2) and (7) with the equation above gives the New Keynesian

Phillips curve:

𝜋 = 𝛽𝐸𝑡𝜋 𝑡+1 +

1 − 𝜃 1 − 𝜃𝛽

𝜃 𝜍 + 𝜑 𝑦 𝑡 + 𝜀𝑡

𝑠 (10)

9For example: 𝑥𝐿𝑛 = 𝑥𝑡−𝑛



7 7

2-4-Monetary Authority

We assume that the monetary authority conducts the monetary policy by targeting the nominal

interest rate according to the following simple Taylor rule(Clarida, et al., 2000):

𝑅𝑡

𝑅 =

𝑅𝑡−1

𝑅 𝜌

𝜋𝑡𝜋 𝜙𝜋

𝑌𝑡

𝑌 𝜙𝑦

1−𝜌

𝑒𝜀𝑡𝑅 (11)

After log-linearizing(11)we get:

𝑟 𝑡 = 𝜌𝑟 𝑡−1 + 1 − 𝜌 𝜙𝜋𝜋 𝑡 + 𝜙𝑦𝑦 𝑡 + 𝜀𝑡𝑅 (12)

𝜌 is the interest rate smoothing, 𝜙𝜋and 𝜙𝑦are respectively the weight that the monetary

authority attaches to the inflation gap and to the output gap.𝜀𝑡𝑅 represents the monetary policy

shock. The later doesn’t follow an autoregressive process as the supply and demand shocks, in

this matter we follow Ait Lahcen (2014), and we specify 𝜀𝑡𝑅=𝜂𝑡

𝑅 with 𝜂𝑡𝑅~𝒩(0,𝜍𝑅

2). Even if

Ait Lahcen (2014)didn’t justify this choice in his master thesis, one can consider that the

persistence is already captured by the parameter of persistence 𝜌 in the Taylor rule equation.

The Taylor rule is used in many studies for its empirical fitting and also for its simplicity.

Nevertheless, it suffers from an important drawback. It has no micro-foundations.

2-5-Model Stability

The standard model, to be estimated, is made up of the equations (3)(10)(12) and of the AR(1)

shock processes. To check the stability of the model, first we write it in a state-space

representation.

𝐀

𝑟 𝑡𝑬𝒕𝑦 𝑡+1

𝑬𝒕𝜋 𝑡+1

= 𝐁

𝑟 𝑡−1

𝑦 𝑡𝜋 𝑡

+ 𝐆

𝜀𝑡𝑅

𝜀𝑡𝐷

𝜀𝑡𝑆

If A is invertible, which is verified here, one can write the system abovein the following form

𝑟 𝑡

𝑬𝒕𝑦 𝑡+1

𝑬𝒕𝜋𝑡+1

= 𝐖

𝑟 𝑡−1

𝑦 𝑡𝜋 𝑡

+ 𝐀−𝟏𝐆

𝜀𝑡𝑅

𝜀𝑡𝐷

𝜀𝑡𝑆

With 𝐖 = 𝐀−𝟏𝐁

𝑟 𝑡

𝑬𝒕𝑦 𝑡+1

𝑬𝒕𝜋𝑡+1

= 1𝜍𝛽

𝜍𝛽𝜌 𝛽𝜍 1 − 𝜌 𝜙𝑦 𝛽𝜍 1 − 𝜌 𝜙𝜋

𝛽𝜌 𝛽 + 𝛽 1 − 𝜌 𝜙𝑦 + 𝜅 𝛽 1 − 𝜌 𝜙𝜋 − 10 −𝜍𝜅 𝜍

𝑟 𝑡−1

𝑦 𝑡𝜋 𝑡

+ 𝐀−𝟏𝐆

𝜀𝑡𝑅

𝜀𝑡𝐷

𝜀𝑡𝑆

To guarantee the existence of a stable solution, the number of eigenvalues greater that one (in

absolute value) of the matrix 𝐖must be equal to the number of expectational variables. This

condition is known as the Blanchard- Kahn condition (Blanchard and Kahn, 1980). However,

when using Dynare to estimate the model, one cannot worry about the satisfaction of the

Blanchard-Kahn condition, because a warning will be displayed if the condition is not

satisfied.

3- Calibration, Estimation and prior specification

Except the two parameters 𝛽and 𝜑 that are calibrated, all the remaining parameters are

estimated. We choose the values 0.99 for 𝛽 and 1.5 for 𝜑.



8 8

In the existent literature of DSG Emodels applied to the Moroccan economy most of them are

entirely calibrated, that force us to use, as source of priors, onlyAit Lahcen (2014) and as well

as the well-known values used in the literature. But unlike Bennouna, et al. (2016) we choose

relatively some large standard deviations for the parameters estimated to let the Metropolis-

Hastings’s algorithm used in the Bayesian estimation to investigate a large domain.

The choice of Ait Lahcen (2014) as source of priors is also motivated by the fact that it takes

into account the informal sector that is one among other characteristics of the Moroccan

economy.

Following Ait Lahcen (2014) : The Calvo parameter 𝜃 is set to follow a beta distribution with

a mean of 0.75 and a standard deviation of 0.1. The monetary policy reaction to inflation 𝜙𝜋

and output 𝜙𝑦 in the Taylor rule are both set to follow a normal distribution with a mean of 2

and a standard deviation of 0.5. The persistence parameters 𝜌𝐷and 𝜌𝑆are set to follow a beta

distribution with a mean of 0.75 and a standard deviation of 0.1. The inverse of the

intertemporal elasticity of substitution 𝜍 is set to follow a normal distribution with a mean of

3 and a standard deviation of 0.1.

Following Smets and Wouters (2003) the shocks’ standard deviations 𝜍𝑅 , 𝜍𝑆 and 𝜍𝐷are set to

follow an inverse gamma distribution with a mean of 0.1, but based on the estimation of Ait

Lahcen (2014) we set a standard deviation of 0.01.

The persistence parameter𝜌 in the Taylor rule is set to follow a beta distribution with a mean

of 0.6 based on the results of Table 2,and a standard deviation of 0.1.

4-Results

The results of the estimation are shown in Table 1. The principal remarks are:

(1) The monetary authority responds to the fluctuations of inflation around its target more

aggressively than the fluctuations of output around its steady state. This result

highlights the priority given to price stability as the principal mission of BANK AL-

MAGHRIB10

.

(2) The Calvo parameter 𝜃is equal to 0.34what indicates that, in average, prices are

adjusted once every 1.5 quarters. Such result highlights the high flexibility of prices

that characterize the developing economies11

.

(3) The supply shocks, hitting the economy, last a longer period of time than the demand

and the monetary policy shocks.

Table 1: Results of the Bayesian estimation

Parameters PDF12

Prior Mean Posterior Mean Confidence Interval

L.B13

U. B14

𝜍 Normal 3 2.79 2.61 2.96

10

The central bank of the Kingdom of Morocco. 11

For further information about prices flexibility between developed and developing economies see, for

example,Peter J Klenow and Benjamin A Malin, "Microeconomic evidence on price-setting," (National Bureau

of Economic Research, 2010). 12

Probability Density function 13

Lower band 14

Upper band



9 9

𝜃 Beta 0.75 0.34 0.30 0.38

𝜙𝜋 Normal 2 4.78 4.40 5.18

𝜙𝑦 Normal 2 1.71 0.99 2.38

𝜌 Beta 0.6 0.21 0.12 0.30

𝜌𝑆 Beta 0.75 0.48 0.33 0.65

𝜌𝐷 Beta 0.75 0.36 0.20 0.53

𝜍𝐷 Inverse Gamma 0.1 0.066 0.059 0.072

𝜍 𝑆 Inverse Gamma 0.1 0.089 0.075 0.101

𝜍 𝑅 Inverse Gamma 0.1 0.068 0.061 0.075

To evaluate the performance of the model, we compare the unconditional moments of the

model, using smoothed variables generated by Dynare, with those of the data. This will allow

us to see if the model is a good representation of the Moroccan economy.

Table 2shows that the model does a great job in replicating the characteristics of output and

inflation but it fails in replicating the characteristics of the interest rate and more largely its

persistence. The latter is captured by the autocorrelation coefficient.

Table 2: Moments comparison (Standard model)

Variables Standard

deviation

Correlation

with Output

Autocorrelation

(order 1)

Data Model Data Model Data Model

Y 1.49 1.45 1 1 0.18 0.14

𝜋 0.27 0.27 0.04 0.02 0.50 0.48

𝑟 0.09 0.02 -0.26 -0.01 0.59 0.0009

We thought that by making the model more backward looking, it will handle the problem of

the low persistence of the interest rate. So, we estimated another version of the model with

habit formation15

. This implies that Household’s utility function is impacted by the gap

between today consumption and past consumption. In the estimation, we replace (3) in the

standard model by the following IS dynamic equation:

𝑦 𝑡 =

1

1 + ℎ𝑬 𝒕 𝑦 𝑡 +1 +

ℎ

1 + ℎ𝑦 𝑡 −1 −

1 − ℎ

(1 + ℎ)𝜍 𝑟 𝑡 − 𝑬 𝒕 𝜋 𝑡 +1 + 𝜀 𝑡

𝐷 (13)

Unfortunately, even though this modification, the results obtained are almost the same as in

the standard model.

However, when we replace, in the estimation, the simple Taylor rule (12) by the generalized

Taylor rules(14), close to the one used by Adjemian, et al. (2007), the fit between the model

and the data improve significantly. The results are shown in Table 3.

15

In this case, utility function takes the following form: (𝐶𝑡−ℎ𝐶𝑡−1)1−𝜍

1−𝜍− 𝜒

𝐻𝑡1+𝜑

1+𝜑with ℎ as the habit formation

parameter.



10 10

𝑟 𝑡 = 𝜌 𝑟 𝑡 −1 + 1 − 𝜌 𝜙𝜋𝜋 𝑡 + 𝜙𝑦 𝑦 𝑡 + 𝜙∆𝑦 (𝑦 𝑡− 𝑦 𝑡 −1) + 𝜙∆𝜋 (𝜋 𝑡

− 𝜋 𝑡 −1) + 𝜀 𝑡𝑅

(14)

Table 3: Moments comparison (Model with equation(14))

Variables Standard

deviation

Correlation

with Output

Autocorrelation

(order 1)

Data Model Data Model Data Model

Y 1.49 1.45 1 1 0.18 0.15

𝜋 0.27 0.35 0.04 0,04 0.50 0.36

𝑟 0.09 0.09 -0.26 -0.25 0.59 0.57

The first remark is that the low persistence of interest rate disappears from the scene.This

improvement it also highlights the importance that the monetary authority accords to the

deviations of inflation and output from their level lagged by one period (a quarter), and that

the generalized Taylor rule describes better the behavior of the Moroccan monetary authority

than the simple Taylor rule..

Another way to evaluate the performance of the model is by looking at how the model

responds to shocks. This will be done by studying the Bayesian impulse-response functions.

The only remarks that can be drawn from Figure 1and Figure 2 below are: The Impulse-

response functions give results that are equivalent to those in the theory. And a result that

appears strange at first glance in Figure 2 is the reaction of the monetary authority to a

monetary policy shock. One can think that the monetary authority responds to the monetary

policy shock by increasing the nominal interest rate, which is contradictory! The fact is that

the monetary authority reacts to the monetary policy shock by lowering the nominal interest

rate, and it over compensates the initial increase of the interest rate, because of the strong

reaction due to the parameters in the Taylor rule.

Figure 1: Bayesian impulse-response functions



11 11

Figure 2: Bayesian impulse-response functions (Model with equation (14))

5-Conclusion

Despite its small structure, the standard New Keynesian model succeeds well in fitting the

data except for the interest rate, where the model replicates badly its characteristics. However,

it’s well-known in the literature that such a model cannot be used to draw policies from it.

And, in this paper, we didn’t focus on the structural shortcomings or on the theoretical

foundations of the standard New Keynesian model. the latter has been subject to several

critics, and one can refer, for example, to Mankiw and Reis (2002) for more in-depth

discussion of the limits of New Keynesian Phillips curve, or toWickens (2012, p. 366) who

demonstrates that the IS dynamic equation has no room for certain monetary policy channel

that links output and interest rate. Instead, in the case of the Moroccan economy, the low

persistence of the interest rate generated by the model, is a one more reason that cannot be

avoided.

The model is estimated using Bayesian techniques. Before the estimation, the model was

derived from a microeconomic level, by solving agents’ optimization problems, and log-

linearized around its steady state. The data were also transformed, using Hodrick-Prescott

filter, to match the model.

In order to improve the performance of the model in replicating the characteristics of the

interest rate, we moved from the standard model and we estimated two other variants. We

found that the Taylor rule, as it stands in the standard model, it doesn’t capture, wholly, the

way that the monetary policy is conducted in Morocco. And a version of the Taylor rule, that

reacts also to the deviations of inflation and output from their values lagged by one period, as

in Adjemian, et al. (2007), improve the fit between the model and the data.

Even tough, the second variant of the Taylor rule estimated gives good results, it’s obvious

that it lacks a very important variable in the case of the Moroccan economy, which is the

exchange rate. Indeed, the Moroccan monetary authority under the fixed exchange rate

regime, at least in the sample considered in the present paper, reacts also to the deviations of

the exchange rate from its target. Nonetheless, it is worth noting that the Moroccan monetary



12 12

authority still enjoys some autonomy on its monetary policy, allowed by the existence of

controls on capital flows in Morocco.

However, it’s hard from a small-scale model to capture the monetary policy rule that

describes well the behavior of the monetary authority. Because the model doesn’t take into

account several important things as: Openness of economy, financial market, capital and so

on. Be that as it may, the standard New Keynesian modelis still used but only for pedagogical

purposes thanks to its small simple structure, and also because it constitutes the canonical or

the baseline model for medium and large scale New Keynesian DSGE models.

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