Proceedings of the IE 2013 International Conferencewww.conferenceie.ase.ro

A GREY APPROACH TO OPEN ECONOMIES REPRESENTATIVEAGENT MODELS: EMPIRICAL STUDY FOR ROMANIA

Ana Michaela ANDREI (1 )

aaeconomy@gmail.comAdrian BĂDESCU (1 )

adi_bad@yahoo.comIrina GEORGESCU (1 )

irina.georgescu@csie.ase.ro(1 ) Bucharest University of Economic Studies, DICE, Romania

Abstract. The model discussed in this paper is an open economies representativeagent model with finite time horizon, mono-factorial production function, andlogarithmic utility function. We have used as a basis the models developed byObstfeld, Rogoff and Honkapohja. Because the problems with the data of capitalstock, we used the GM(1,1) algorithm in order to adjust statistical data andconsequently we computed the grey production function, that was the basis of theempirical study we made for Romania. We made also forecasts for the mainmacroeconomic indicators: real GDP, consumption, government expenditures.

Keywords: Current account, grey production function, representative agent model.JEL classification: C53, C61, E27

1. Introduction

Representative agent models gained enormous popularity duringthe reign of the New Classical macroeconomists, such as Lucasand Sargent, starting back at the beginning of the 1970s.Representative agent models are for researchers a way torepresent the macroeconomic behaviour by means ofmicrofoundations, i.e. individual optimization as the basisfor aggregate behaviour. This approach was verycontroversial, beginning from the infeasibility of exact

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aggregation and the possible Pareto inconsistency of therepresentative agent [1]. Hansen and Sargent [2] give a rationale for using such models,that consists in the substitution of the estimation of theparameters of decision rules, with the estimation of theparameters of the objective functions of the agents and of therandom processes they faced historically.Analyzing the literature in this field, Hartley [3] drew theconclusion that the representative agent models are not properfor studying aggregate behavior. Despite many controversies[4], [5], the field is still of interest for many researchers[6], [7], [8].We chose this type of model for the reason of simplicity ofthe empirical application, for the possibility it offers tocalculate many macroeconomic aggregates and to forecast themas well. The paper is organized as follows: section 2 introduces the

small open economies representative agent model, section 3

deals with solving the model with logarithmic utility function

and with Cobb-Douglas production function, section 4

introduces empirical study and finally, section 5 deals with

highlighting the main conclusions.

1. 2. 2. Small open economies-representative agent model

The model [9], [10] assumes perfect competition and the finite time horizon. It includes two representative agents: the consumer and the firm.The consumer’s problem is to maximize the utility function under the budget constraint:

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maxUt=∑

s=t

T+tβs−tu (Cs)

(1+r )Bt+∑s=t

T+t(1

1+r )s−t (Ys−Gs)=∑s=t

T+t(1

1+r )s−t (Cs+Is)+(1

1+r )TBt+T+1. (1) The first order optimum condition (Euler equation) will be:u' (CS )=(1+r )βu' (Cs+1) , s=t, (t+1), (t+2), (2)The firm will maximize its profit. max (AsF(Ks)−rKs) (3) The first order condition for the firm will be:AsF' (Ks)=r . (4) The equation above is the well known optimum condition for thefirm, that is: the marginal productivity equals the marginal cost of the capital.

From (5) one can obtain Ks=F'

−1( rAs) (5) The value of Ks so calculated, could be introduced in production function F (Ks ) and in the investment functionIt=Kt+1−Kt , in order to calculate the corresponding values at the time s:Ys=(1+g)sA0F'

−1(r / (1+g)sA0) (6) Is=F'

−1 (r / (1+g) (s+1 )A0)−F'−1(r / (1+g )sA0) (7)In particular, for the Cobb-Douglas production function and for the logarithmic function, the main indicators have the form [11]:

Ks=( rαAs )

1α−1=( r

α (1+g)sA0 )1

α−1

s=1,2,… (8)

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Ys=( rα

α−1

[αα

α−1 (1+g )s

α−1A0

1α−1

) s=1,2,…

(9)Cs+1=(1+r)βCs (10)

3. Grey one factor Cobb-Douglas production function

We start from the well known CD production function model, considering only stock of capital (K) as production factor:Y=AeγtKα (11)where the parameters stand for the usual interpretation.The multivariate least squares estimates could be employed toapproximate the parameters:A, γ, α .The macroeconomic time series often are confronted with highfluctuations that lead to estimation errors: negative valuesof the estimated coefficients, or values that exceed theeconomic explicable values of the parameters.In order to elude this inconvenient aspect, we can use GM(1,1)simulated data as original data for the parameter estimates,then, to a certain degree, we can eliminate some of the randomfluctuations , producing more reasonable values of parameterestimates and obtain a model that can accurately reflect therelationship between the production output and labor andcapital inputs and the progress of the technology.If we denote by Y, K the vectors of GM(1,1) simulated data ofY,K then, the function:Y=Aeγ tKα is the grey one factor Cobb-Douglas productionfunction model., that possesses a deep intensity of grey,embodies non-uniqueness principle of the solution and theabsoluteness principle of greyness. After the data series was approximated using GM(1,1) method,we estimated the coefficients of the Cobb-Douglas greyproduction function: Y=Aeγ tKα ,

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using the log-linear form of the production function and OLSmethod.

4. GM(1,1) grey model

GM(1,1) type of grey model is the most widely used in theliterature [12], pronounced as ‘‘grey model first order onevariable’’. The GM(1,1) model constructing process isdescribed below. If we consider the actual time sequence X

(0)

:

X(0)=(x(0 )(1),x(0)(2),...x(0 )(n)), n≥4,x(0 )(i)≥0 (12)

Applying the accumulated generating operation (AGO), we obtainthe sequence X

(1)

:

X(1)=(x(1 )(1),x(1)(2),...x(1 )(n)) , x(1)(k )=∑

j=1

kx(0)(j), k=1,2,...,n

(13)

Then we generate the mean sequence Z(1)

,Z(1)(z2

(1),z3(1),...zk

(1)), k=2,3,... ,

defined as:

z(1)(k)=λx(1 )(k)+(1−λ)x(1)(k−1), k=2,3,...n , generally λ=0,5 . (14)

The adjusted GM(1,1) data sequence is:

x(1)(k )=(x1(0 )−

ba

)(1−ea )(e−a(k−1 )), k=2,3,...,

(15)Where the parameters a (developing coefficient) and b (grey input coefficient), could be calculated as:

[a ¿ ] ¿¿

¿¿

yT=(x(0)(2),...,x(0)(n))T;B=¿ [−z(1)(2)...−z(1)(n) ¿ ] ¿¿

¿¿ (16)

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3. 5.Empirical study

Using quarterly data for real GDP and the gross capital formation between 2000.1 and 2012.4, we determined the grey data series, following GM(1,1) grey algorithm. Then we estimated the parameters of the CD production function, obtaining the grey production function:

Ycalc=101,0552(1,02579)t( Kgrey)0,39677 (17)

In order to apply the model and to compute the macroeconomicindicators, we used the average world interest rate r is 0.034(HomeFinance.nl, 2013).We consider that the consumer discount factor b is 0.968,computed according to the hypothesis that the discount factoris the inverse of the expected inflation index, consideringadaptive expectations.First, we computed the GDP data series using estimatedparameters and compared them with the actual data series(figure 1), then we made a 5-year prediction based on thismodel.

Figure 1: Actual, computed and predicted (2013-2018) grey realGDP

The same procedure we used for the computation and the prediction of the macroeconomic aggregates of consumption and government expenditures (figure 2).

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The growth rate of the government spending was the object ofour various simulations [11]. The rate d=0.0193 which weconsidered in the model is the largest that can ensure thedecrease of the burden of the debt in the total GDP, at thesame time ensuring an accomplishment, in a certain proportion,of social objectives and investment objectives of thegovernment. The exogenous government expenditures equation is:Gt=(1+δ)tG0=1.019

t×21384,9636×109 Considering the initial value G0 =21384,9636´ 109 (NationalInstitute of Statistics, 2013).It can be seen that the consumption growth rate is positive,as resulted from the international interest rate and discountfactor.

Figure 2: Actual, computed and predicted (2013-2018) grey consumption and government expenditures.As far as the investments are concerned, the model reveals a rather extensive investment process in Romania between 2004-2005, emphasizing a continuous change of branch structure of investments.After 2008-2009, there was a severe economic crisis inRomania, marked by a decrease in real GDP and, in the secondhalf of 2010 the resumption of economic growth took place.Starting with 2013-2014, the estimated average annual growthrate of 4,12%, will mark a sustained economic growth inRomania, with a predominantly intensive character.

6. Conclusions

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In our empirical works [11] we applied the model using a twofactor production function as in [10]. The results were notsatisfactory, taking into account that the estimates werebased on data up to the year 2004, because of the decreasingtendency of the total population due both to the decreasingbirth rate and increasing migration for work.From 2004 until now, the two phenomena have been worsening so,it is no longer justified using the two factor productionfunction (capital stock and employment), since the marginalproductivity of labor comes out negative, which affects theexistence and uniqueness of firm’s optimum solution. One mean to prevent this shortcoming should be to use humancapital stock instead of employment, and that will be one ofour future concerns.Another major problem of using the production function formodeling Romanian economy is the lack of an adequate dataseries for the capital stock. We used for estimation as datafor capital stock, quarterly indexes of tangible fixed assets,GM(1,1) adjusted.Except for the initial values of macroeconomic indicators andthe estimated parameters, the predictions depend on thepolitical decision parameter government expenditures growthrate δ , and the discount factor β , calculated as inverse ofexpected inflation index. While δ was set so as to achieve the political objectives ofthe government, β has been established considering theadaptive inflationary expectations.

References[1] M. Grabner, Agents and the microfoundations of macroeconomics, 2002, Available:http://www.econ.ucdavis.edu/graduate/mgrabner/research/microfoundations.pdf[2] L. P. Hansen and T. Sargent, „Formulating and estimatingdynamic linear rational expectations models,” Journal ofEconomic Dynamics and Control, vol. 2, pp. 7-46, 1980.[3] J. E. Hartley, The Representative Agent in Macroeconomics. New York.Routledge, 1997.

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[4] S. An, C. Yongsung and Kim Sun-Bin, „Can a Representative-Agent Model Represent a Heterogeneous Agent Economy,” EconomicJournal: Macroeconomics: vol. 1, no. 2, pp. 29-54 , 2009.[5] N. G. Mankiw, J.J Rotemberg and L. H. Summers,„Intertemporal Substitution in Macroeconomics,” QuarterlyJournal of Economics, vol. 100, no. 1, pp. 225-251, 2005.[6] D. Backus, M. Chernov abd S. Zin, Sources of entropy inrepresentative agent models, 2012, Available:http://pages.stern.nyu.edu/~dbackus/BCZ/ms/BCZ_entropy_latest.pdf[7] A. Maussner, CoRRAM: Computing recursive representativeagent models, 2009, Available:http://dge.repec.org/codes/maussner/CoRRAM.rar[8] A. I. Telyukova, „Computing Representative Agent Models: ValueFunction Methods,” UCSD ECON 216 Computational Methods inMacroeconomics, 2013.[9] M. Obsfeld and K.S. Rogoff, Foundations of InternationalMacroeconomics. MIT Press, Massachusetts, 1996.[10] S. Honkapohja, Open Economies and International FinancialMarkets, FPPE/KAVA, 2001.[11] A. Andrei, S. Stancu, I. Georgescu and A. M. Constantin,„Open economies representative agent models: empiricalapplication for Romania,” in Proc. of 2013 AASRI InternationalConference on Social Sciences (AASRI ICSS 2013), 15-16November 2013, Singapore, pp. 159-164.[12] D. Julong, „Introduction to Grey System Theory, ” The Journal of Grey System, vol.1, pp.1- 2, 1989.

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