AN ASSESSMENT OF THE STANDARD NEW KEYNESIAN MODEL ...

33 downloads 0 Views 633KB Size Report
Ph.D, Faculty of law, Economics and Social Sciences of Agadir Ibn Zohr ... an open economy New Keynesian DSGE model with informal sector using Moroccan ...
Revue Économie, Gestion et Société

N°14 décembre 2017

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 http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

1

Revue Économie, Gestion et Société

N°14 décembre 2017

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.

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

2

Revue Économie, Gestion et Société

N°14 décembre 2017

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.

1

A dynamics to chastic general equilibrium framework (DSGE). 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).. 3 The series are transformed using HP filter to match the model. 2

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

3

Revue Économie, Gestion et Société

N°14 décembre 2017

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: +∞

𝐶𝑡+𝑠 𝑗 1−𝜍 𝐻𝑡+𝑠 𝑗 1+𝜑 𝛽 𝑈 −𝜒 0 < 𝛽 < 1,𝜒 > 0 1−𝜍 1+𝜑 𝑠

max 𝑬t 𝒔=𝟎

Subject to the following budget constraint: 𝐷

𝑃𝑡 𝐶𝑡 (𝑗) + 𝑒 𝜍𝜖 𝑡 𝐵𝑡 (𝑗) = 𝑅𝑡−1 𝐵(𝑗)𝑡−1 + 𝑊𝑡 𝐻𝑡 (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 𝜖𝑡𝐷 is a 𝐷 demand shock that follows an AR(1) process 𝜀𝑡𝐷 = 𝜌𝐷 𝜀𝑡−1 + 𝜂𝑡𝐷 with 𝜂𝑡𝐷 ~𝒩(0, 𝜍𝐷2 ). 𝑃𝑡 is the price of the final good,𝐶𝑡 is consumption,𝐵𝑡 is 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 𝜍

𝐶𝑡+1 𝑗 𝛽 𝑅𝑡 𝑬𝑡 = 𝑬𝑡 𝐷 𝐶𝑡 𝑗 𝜋𝑡+1 𝑒 𝜍𝜀 𝑡 And, the optimal condition setting the marginal rate of substitution between labor and consumption equal to the real wage.

(1)

𝑊𝑡 (2) 𝑃𝑡 By dropping the index, and log-linearizing (1) under the market clearing condition in the good market, one gets the following IS dynamic equation4: 𝜒𝐶𝑡 𝑗 𝜍 𝐻𝑡 𝑗

𝑦𝑡 = 𝑬𝒕 𝑦𝑡+1 −

𝜑

=

1 𝑟𝑡 − 𝑬𝒕 𝜋𝑡+1 + 𝜀𝑡𝐷 𝜍

(3)

2-2-The Final Goods Firm The final good is produced using inputs of the intermediate goods, following the production function5:

4

Variables with hatdenote the log-deviation from the steady state 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

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

4

Revue Économie, Gestion et Société 1

𝑌𝑡 =

N°14 décembre 2017 𝜖−1 𝜖

𝑌𝑡 𝑖

𝜖 𝜖−1

𝑑𝑖

(4)

𝑓𝑜𝑟 𝜖 > 1

0

So that 𝜖is the elasticity of substitution between the different intermediate goods. The final goods firm maximize its profit: 1

max 𝑃𝑟𝑜𝑓𝑖𝑡𝑡 = 𝑃𝑡 𝑌𝑡 𝑖

𝑌𝑡 𝑖

𝜖−1 𝜖

𝜖 𝜖−1

𝑑𝑖

1



0

𝑃𝑡 𝑖 𝑌𝑡 𝑖 𝑑𝑖 0

Solving the maximization problem yields the demand for good 𝑖: −𝜖

𝑃𝑡 𝑖 𝑌𝑡 𝑖 = 𝑌𝑡 𝑃𝑡 And, the price of the final good, under the zero profit: 1 1−𝜖

1

𝑃𝑡 =

𝑃𝑡 (𝑖)

1−𝜖

(5)

(6)

𝑑𝑖

0

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: min 𝐻𝑡 (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. −𝜖

𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜

𝑃𝑡 𝑖 𝑌𝑡 𝑖 ≥ 𝑌𝑡 𝑃𝑡 𝑌𝑡 𝑖 = 𝐻𝑡 (𝑖)1−𝛼

Solving the minimization problem yields the condition settingthe real marginal cost equal to real wage. 𝑊𝑡 (7) 𝑃𝑡 Second. The intermediate firm, when it’s not constraint, maximize its profit subject to (5) and following the Calvo’s rule8(Calvo, 1983) 𝐶𝑀𝑡 𝑖 =

+∞

max 𝑬𝒕 ∗ 𝑃𝑡 𝑖

Solving for

𝛽𝜃

𝜏

𝑃𝑡∗ 𝑖 − 𝑒 𝜅

−1 𝜀 𝑆 𝑡

𝑃𝑡+𝑠 𝐶𝑀𝑡+𝑠 𝑖 𝑌𝑡+𝑠 𝑖

𝒔=𝟎

𝑃𝑡∗ (𝑖)yields:

6

In the standard New Keynesian model, we often exclude the capital factor. The 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). 7

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

5

Revue Économie, Gestion et Société

N°14 décembre 2017

𝜖 𝑬 +∞ 𝛽𝜃 𝑠 𝑃𝑡+𝑠 𝐶𝑀𝑡+𝑠 𝑖 𝑌𝑡+𝑠 𝑖 𝜅 −1 𝜀 𝑡𝑆 𝒕 𝒔=𝟎 (8) = 𝑒 𝑠 𝜖−1 𝑬𝒕 +∞ 𝒔=𝟎 𝛽𝜃 𝑌𝑡+𝑠 𝑖 𝜖 is the gross markup and the term𝜀𝑡𝑆 represents a supply shock thatfollows an AR(1) 𝜖−1 𝑆 process 𝜀𝑡𝑆 = 𝜌 𝑆 𝜀𝑡−1 + 𝜂𝑡𝑆 with 𝜂𝑡𝑆 ~𝒩(0, 𝜍𝑆2 ). 𝑃𝑡∗ (𝑖)

Log-linearizing (8) gives: +∞

𝑝∗ 𝑡 = (1 − 𝛽𝜃)𝑬𝒕

𝛽𝜃

𝜏

𝑝𝑡+𝑠 + 𝑐𝑚𝑡+𝑠 𝑖 + 𝜅 −1 𝜀𝑡𝑆

(9)

𝒔=𝟎

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

𝑝𝑡 = 𝜃𝑝𝑡−1 + (1 − 𝜃)(1 − 𝛽𝜃)𝑬𝒕

𝛽𝜃

𝑠

𝑝𝑡 + 𝑐𝑚𝑡 𝑖 + 𝜅 −1 𝜀𝑡𝑆

𝒔=𝟎

To eliminate the infinite sum, we multiply each side, of the equation above, by (1 − 𝛽𝜃𝐿−1 ). With L is the lag operator9. +∞

𝑝𝑡 − 𝑝𝑡+1 𝛽𝜃 = 𝜃𝑝𝑡−1 − 𝛽𝜃𝜃𝑝𝑡 + 1 − 𝜃 1 − 𝛽𝜃 𝑬𝒕

𝑠

𝑆 𝑝𝑡+𝑠 + 𝑐𝑚𝑡+𝑠 + 𝜅 −1 𝜀𝑡+𝑠

𝒔=𝟎

+∞

− 1 − 𝜃 1 − 𝛽𝜃 𝛽𝜃𝑬𝒕

𝛽𝜃

𝛽𝜃

𝑠

𝑆 𝑝𝑡+𝑠+1 + 𝑐𝑚𝑡+𝑠+1 + 𝜅 −1 𝜀𝑡+𝑠+1

𝒔=𝟎

With a bit of algebra 𝑝𝑡 − 𝑝𝑡+1 𝛽𝜃 = 𝜃𝑝𝑡−1 − 𝛽𝜃𝜃𝑝𝑡

+∞

+ 1 − 𝜃 1 − 𝛽𝜃 𝑬𝒕

𝛽𝜃

𝑠

𝑆 𝑝𝑡+𝑠 + 𝑐𝑚𝑡+𝑠 + 𝜅 −1 𝜀𝑡+𝑠 − 𝛽𝜃(𝑝𝑡+𝑠+1

𝒔=𝟎

𝑆 + 𝑐𝑚𝑡+𝑠+1 + 𝜅 −1 𝜀𝑡+𝑠+1 )

Eliminating the terms in t+1 gives: 𝑝𝑡 − 𝑝𝑡+1 𝛽𝜃 = 𝜃𝑝𝑡−1 − 𝛽𝜃𝜃𝑝𝑡 + 1 − 𝜃 1 − 𝛽𝜃 (𝑝𝑡 + 𝑐𝑚𝑡+ + 𝜅 −1 𝜀𝑡𝑆 ) With further simplifications: 𝜋𝑡 = 𝛽𝑬𝒕 𝜋𝑡+1 + 𝜅𝑐𝑚𝑡 + 𝜀𝑡𝑆 With 𝜋𝑡 = (𝑝𝑡 − 𝑝𝑡−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 = 𝛽𝐸𝑡 𝜋𝑡+1 +

9

For example: 𝑥𝐿𝑛 = 𝑥𝑡−𝑛

1 − 𝜃 1 − 𝜃𝛽 𝜃

http://revues.imist.ma/?journal=REGS

𝜍 + 𝜑 𝑦𝑡 + 𝜀𝑡𝑠

(10)

ISSN: 2458-6250

6

Revue Économie, Gestion et Société

N°14 décembre 2017

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 𝑅𝑡−1 = 𝑅 𝑅 After log-linearizing(11)we get:

𝜌

𝜋𝑡 𝜋

𝜙𝜋

𝑌𝑡 𝑌

𝜙 𝑦 1−𝜌

𝑅

𝑒 𝜀𝑡

(11)

(12) 𝑟𝑡 = 𝜌𝑟𝑡−1 + 1 − 𝜌 𝜙 𝜋 𝜋𝑡 + 𝜙 𝑦 𝑦𝑡 + 𝜀𝑡𝑅 𝜌 is the interest rate smoothing, 𝜙 𝜋 and 𝜙 𝑦 are 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 =𝜂𝑡𝑅 with 𝜂𝑡𝑅 ~𝒩(0, 𝜍𝑅2 ). 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. 𝑟𝑡 𝐀 𝑬𝒕 𝑦𝑡+1 𝑬𝒕 𝜋𝑡+1

𝜀𝑡𝑅 𝑟𝑡−1 = 𝐁 𝑦𝑡 + 𝐆 𝜀𝑡𝐷 𝜋𝑡 𝜀𝑡𝑆

If A is invertible, which is verified here, one can write the system abovein the following form 𝜀𝑡𝑅 𝑟𝑡−1 𝑟𝑡 𝑬𝒕 𝑦𝑡+1 = 𝐖 𝑦𝑡 + 𝐀−𝟏 𝐆 𝜀𝑡𝐷 𝑬𝒕 𝜋𝑡+1 𝜋𝑡 𝜀𝑡𝑆 With 𝐖 = 𝐀−𝟏 𝐁 𝑟𝑡 𝜍𝛽𝜌 1 𝑬𝒕 𝑦𝑡+1 = 𝜍𝛽 𝛽𝜌 𝑬𝒕 𝜋𝑡+1 0

𝛽𝜍 1 − 𝜌 𝜙 𝑦 𝛽 + 𝛽 1 − 𝜌 𝜙𝑦 + 𝜅 −𝜍𝜅

𝛽𝜍 1 − 𝜌 𝜙 𝜋 𝛽 1 − 𝜌 𝜙𝜋 − 1 𝜍

𝜀𝑡𝑅 𝑟𝑡−1 𝑦𝑡 + 𝐀−𝟏 𝐆 𝜀𝑡𝐷 𝜋𝑡 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. http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

7

Revue Économie, Gestion et Société

N°14 décembre 2017

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 MetropolisHastings’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 𝜙 𝜋 and output 𝜙 𝑦 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 𝜌𝐷 and 𝜌 𝑆 are 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 𝜍𝐷 are 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 ALMAGHRIB10. (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

𝜍

Normal

3

2.79

Confidence Interval L.B13 U. B14 2.61 2.96

10

The central bank of the Kingdom of Morocco. 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 11

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

8

Revue Économie, Gestion et Société

Beta Normal Normal Beta Beta Beta Inverse Gamma Inverse Gamma Inverse Gamma

𝜃 𝜙𝜋 𝜙𝑦 𝜌 𝜌𝑆 𝜌𝐷 𝜍𝐷

𝜍𝑆 𝜍𝑅

N°14 décembre 2017

0.75 2 2 0.6 0.75 0.75 0.1 0.1 0.1

0.34 4.78 1.71 0.21 0.48 0.36 0.066 0.089 0.068

0.30 4.40 0.99 0.12 0.33 0.20 0.059 0.075 0.061

0.38 5.18 2.38 0.30 0.65 0.53 0.072 0.101 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 Y

𝜋 𝑟

Standard deviation Data Model 1.49 1.45 0.27 0.27 0.09 0.02

Correlation with Output Data Model 1 1 0.04 0.02 -0.26 -0.01

Autocorrelation (order 1) Data Model 0.18 0.14 0.50 0.48 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: 1 ℎ 1−ℎ (13) 𝑬 𝒕 𝑦 𝑡 +1 + 𝑦 𝑡 −1 − 𝑟 𝑡 − 𝑬 𝒕 𝜋 𝑡 +1 + 𝜀 𝐷𝑡 1+ℎ 1+ℎ (1 + ℎ)𝜍 Unfortunately, even though this modification, the results obtained are almost the same as in the standard model.

𝑦𝑡 =

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

𝐻𝑡 1+𝜑 with 1+𝜑

ℎ as the habit formation

parameter.

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

9

Revue Économie, Gestion et Société

N°14 décembre 2017

𝑟 𝑡 = 𝜌 𝑟 𝑡 −1 + 1 − 𝜌 𝜙 𝜋 𝜋 𝑡 + 𝜙 𝑦 𝑦 𝑡 + 𝜙 ∆𝑦 (𝑦 𝑡 − 𝑦 𝑡 −1 ) + 𝜙 ∆𝜋 (𝜋 𝑡 − 𝜋 𝑡 −1 ) + 𝜀 𝑅𝑡

(14)

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

𝜋 𝑟

Standard deviation Data Model 1.49 1.45 0.27 0.35 0.09 0.09

Correlation with Output Data Model 1 1 0.04 0,04 -0.26 -0.25

Autocorrelation (order 1) Data Model 0.18 0.15 0.50 0.36 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 Impulseresponse 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

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

10

Revue Économie, Gestion et Société

N°14 décembre 2017

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 loglinearized 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 http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

11

Revue Économie, Gestion et Société

N°14 décembre 2017

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.

References Adjemian, Stéphane, Houtan Bastani, Michel Juillard, Ferhat Mihoubi, George Perendia, Marco Ratto, and Sébastien Villemot. "Dynare: Reference Manual, Version 4." Citeseer, 2011. Adjemian, Stéphane, Matthieu Darracq Pariès, and Stéphane Moyen. "Optimal Monetary Policy in an Estimated Dsge for the Euro Area." ECB Working Paper, 2007. Ait Lahcen, Mohammed. "Dsge Models for Developing Economies: An Application to Morocco." University of Lausane, 2014. Bennouna, Hicham, Kamal Lahlou, and Anas Mossadak. "Analyse Des Canaux De Transmission De La Politique Monétaire Au Maroc." Bank Al-Maghrib, Département de la Recherche, 2016. Blanchard, Olivier Jean, and Charles M Kahn. "The Solution of Linear Difference Models under Rational Expectations." Econometrica: Journal of the Econometric Society (1980): 1305-11. Calvo, Guillermo A. "Staggered Prices in a Utility-Maximizing Framework." Journal of monetary Economics 12, no. 3 (1983): 383-98. Clarida, Richard, Jordi Gali, and Mark Gertler. "Monetary Policy Rules and Macroeconomic Stability: Evidence and Some Theory." The Quarterly journal of economics 115, no. 1 (2000): 147-80. ———. "The Science of Monetary Policy: A New Keynesian Perspective." National bureau of economic research, 1999. Dixit, Avinash K, and Joseph E Stiglitz. "Monopolistic Competition and Optimum Product Diversity." The American Economic Review 67, no. 3 (1977): 297-308. Fuhrer, Jeffrey C. "Habit Formation in Consumption and Its Implications for Monetary-Policy Models." American Economic Review (2000): 367-90. Galí, Jordi. "Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework". Princeton University Press, 2008. Klenow, Peter J, and Benjamin A Malin. "Microeconomic Evidence on Price-Setting." National Bureau of Economic Research, 2010. Kydland, Finn E, and Edward C Prescott. "Time to Build and Aggregate Fluctuations." Econometrica: Journal of the Econometric Society (1982): 1345-70. Long Jr, John B, and Charles I Plosser. "Real Business Cycles." Journal of political Economy 91, no. 1 (1983): 39-69. Lucas, Robert E. "Econometric Policy Evaluation: A Critique." Paper presented at the Carnegie-Rochester conference series on public policy, 1976.

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

12

Revue Économie, Gestion et Société

N°14 décembre 2017

Mankiw, N. Gregory, and Ricardo Reis. "Sticky Information Versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve." Quarterly Journal of Economics 117(4) (2002): 1295-328. Smets, Frank, and Raf Wouters. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area." Journal of the European economic association 1, no. 5 (2003): 1123-75. Taylor, John B. "Discretion Versus Policy Rules in Practice." Paper presented at the Carnegie-Rochester conference series on public policy, 1993. Walsh, Carl E. "Monetary Theory and Policy". 3rd ed. Cambridge, Mass.: MIT Press, 2010. Wickens, Michael. "Macroeconomic Theory: A Dynamic General Equilibrium Approach". Princeton University Press, 2012.

http://revues.imist.ma/?journal=REGS

ISSN: 2458-6250

13