A Rational Expectations Model for Simulation and Policy...

A Rational Expectations Model for Simulation andPolicy Evaluation of the Spanish Economy

Direcci�on General de Presupuestos, Ministerio de Econom��a yHacienda

May 2007

MEH REMS May 2007 1 / 24

Introduction

A Rational Expectations Model for simulation and policy evaluationof the Spanish economy (REMS).

REMS is not used for forecasting but to analyse the e�ects of policyshocks.

Dynamic general equilibrium model with a strong microfoundedsystem of equations.

A small open economy model.


Introduction

Non-walrasian goods and labour markets.

Nominal rigidities and involuntary unemployment due to searchine�ciencies.

In the short run REMS is in uenced by the New Keynesianmodellization strategy.

The demand side is represented by an expectational IS curve.

Phillips curve is derived under the assumption of monopolisticcompetition.

ECB monetary policy: interest rule.

Supply-side and stabilization policies do play a role in a�ecting theeconomy in the long and short run, respectively.


Outline

Main characteristics of the model

BDREMS

Calibration and estimation

Simulations

Structural reforms


The model

Dynamic general equilibrium model.

The behavioural equations result from intertemporal optimization byperfect foresight economic agents.

Small open economy.

Agents:

1 Households: consumption, investment, labour supply.2 Firms: capital, employment (hours), energy, vacancies.3 Goverment: taxes, public expenditures, debt.4 Monetary authority: ECB.5 Rest of the world.


Households

Optimization problem

maxct;nt;jt;kt;bt;bwt ;mt

Et

1Xt=0

�t

"ln (ct) + nt�1�1

(1�l1t)1��1�� +

(1� nt�1)�2(1�l2)1��1�� + �m ln (mt)

#

subject to�rt(1� �kt ) + �kt �

�kt�1 + wt

�1� � lt

�(nt�1l1t + rrt (1� nt�1) l2)

+ (gst � trht) + mt�1�t

+ (1 + rnt )bt�1�t+ ernt (1 + r

nwt�1)

bwt�1�t

= (1 + � ct)ctP ctPt+ jt

�1 + �

2

�jtkt�1

��+ A N

�mt + bt +

ernt bwt

�bt

� A Nkt = jt + (1� �)kt�1

Nnt = (1� �)nt�1 + �wt (1� nt�1)

In equilibrium �wt (1� nt�1) = �1v�2t [(1� nt�1) l2]1��2 :


Pricing behaviour: the New Phillips curve

Intermediate good �rms operate in a monopolistically competitiveenvironment.

Following Calvo (1983), each period a measure 1� � of �rms set theirprices, ePit, to maximize the present value of future pro�ts.The aggregate price index at t is

Pt =h� (�Pt�1)

1�" + (1� �) eP 1�"t

i 11�"

As it is standard in the literature, we obtain an expression foraggregate in ation

�t = �Et�t+1 + �cmct


Production and factor demands

Technology

yit =

�hak��it�1 + (1� a)e

��it

i� 1�

�1��(nit�1li1t)

�

Cost minimization problem

minkt;nt;vt;et

Et

1Xt=0

�t�1t+1�1t

rtkt�1 + wt (1 + � sc)nt�1l1t + �vvt+

P etPtet (1 + �

e)

!

subject to

yt =

�hak��it�1 + (1� a)e

��it

i� 1�

�1��(nit�1l1it)

� � �

Nnt = (1� �)nt�1 + �ft vt


Wage and hours setting

The search process in the labour market takes time and is resourceconsuming.

Search models thus use a wage and hours determination schemesuitable for a bilateral monopoly framework.

We assume a Nash bargaining scheme. The solution is given by

(1 + � sct )wtl1t =�wh

1� (1� �w) rrt l2l1ti ��mct yt

nt�1+

�vvt(1� nt�1)

�+

(1� �w)h1� (1� �w) rrt l2l1t

i P ct ct (1 + � ct)Pt (1� �wt )

"�2 [1� l2]1�� 1 [1� l1t]1��

(1� �)

#

�2mctyt

nt�1l1t=P ct ct (1 + �

ct)

Pt (1� �wt )�1(1� l1t)��


Government

Government expenditure is �nanced through direct and indirect taxes:

tt = (�l+ � sc)wt(nt�1lt)+ �

k (rt � �) kt�1+ � cP ctPtct+ � e

P etPtet+ trht

Total receipts and outlays are made consistent through thegovernment's intertemporal budget constraint

A N (bt +mt) = gt+gut(1�nt�1)+gst� tt+(1 + rnt )

�tbt�1+

mt�1�t

To enforce the government's intertemporal budget constraint, thefollowing �scal policy reaction function is imposed

trht = trht�1 + 1

"btgdpt

��

b

gdp

�#+ 2

�btgdpt

� bt�1gdpt�1

�


Monetary policy

In REMS, monetary authorities -represented by the European CentralBank (ECB)- conduct monetary policy by targeting short-term interestrates according to the following interest rate policy reaction function

rnt = rnt�1 + �

�PtP �

� 1�

where rnt is the euro-area nominal short-term interest rate, Pt is theactual price level, P � is an exogenously speci�ed "target path" for theprice level, � captures the ECB's aversion to price deviations from itstarget level and is calibrated to re ect the weight of the Spanisheconomy in the euro area.

We proceed in this way to avoid the problem of price levelindeterminacy that a�ects rational expectations models.


The external sector

SOE: all goods (both consumption and investment) are tradables.Aggregate consumption (and aggregate investment) is a compositebasket (CES) of home and foreign produced goods:

ct =

�(1� !c)

1�c c

�c�1�cht + !c

1�c (cft)

�c�1�c

� �c�c�1

The consumer price index is:

P ct =�(1� !c)P 1��ct + !cP

m1��ct

� 11��c

Domestic demand of home and foreign consumption goods (demandfor investment goods is similar):

cht = (1� !c)�PtP ct

��cct

cft = !c

�PmtP ct

��cct


Aggregate imports in our model is the sum of consumption andinvestment of foreign goods:

imt = cft + ift

Exports are given by (some degree of pricing to market is assumed):

ext = sx�PFM ter

nt

Pt

�(1�ptm)�xywt

Net foreign assets accumulation is given by:

A Nernt bwt

�bt=(1 + rnwt )

1 + �ternt�1b

wt�1 +

P xtPtext �

PmtPt

imt


Data base and baseline

We have assembled a quartely data base for the Spanish economy(REMSDB).

Main source: INE quarterly national accounts (QNA) and StabilityProgramme.

SEC95 and seasonally adjusted variables 1980-2006 and 2006-10.

Government accounts (all levels): quadratic interpolation of IGAEannual data.

Capital stock: from BDMORES (5% annual depreciation rate).

Energy.

Labour market:1 Employed workers from QNA and hours from EPA, adjusted bydi�erent employment status. From 1980 to 1987, rates of growth fromLabour Cost Index.

2 Vacancies: we use the method proposed by Antolin (1994) and correctfor ruptures.

3 Matchings: we correct for contract changes in the same job andtemporary contracts.


Implementation

The model is programmed in Matlab with two objectives:transparency and easy use.

Simulations are performed in �ve steps:

1 Estimation.2 Data loading.3 Residuals calculation.4 Baseline simulation.5 Policy simulation.


Estimation

The parameters of the model are obtained using a hybrid method ofestimation and calibration.

Unobserved variables together with some parameter values arecalibrated.

Setting a set of parameters, some others have been estimated byGMM.


Data loading

The whole set of parameters are loaded and the baseline data isconstructed.

The baseline for all the variables in the model includes:

1 Core data from the BD-REMS.2 Predictions (2010:4).3 Interpolation to a steady state (2060:4).


Residuals and baseline simulation

The dynamic model and the baseline are used to iteratively computethe residuals for each equation.

The solution of the model, once the residuals are included asexogenous variables, gives the constructed baseline (baseline solution).

Thus, the baseline solution is a solution of the dynamic model thatcorresponds exactly to the actual data and forecasts in a situationwithout shocks.


Policy simulation

Given the computed residuals for the baseline scenario and the desiredpolicy experiments, solve for the transitional dynamics with Dynare

Results are compared with the baseline simulation.

Example:

1 Fiscal reform: Decrease in the e�ective labour (-0.20 percentagepoints) and capital tax rates (-0.65).


Fiscal reform e�ects (annual data)

Percentage deviationrespect to the baseline2008 2009 2010

Consumption 0.362 0.418 0.475Investment 0.711 0.756 0.850GDP 0.498 0.516 0.560Tax revenues -0.584 -0.422 -0.290Hours worked 0.748 0.652 0.643Employment rate 0.128 0.185 0.207Real wage -0.529 -0.482 -0.469


Fiscal reform e�ects (long run e�ects)

Percentage deviation

Consumption 0.55Investment 1.25GDP 0.75Tax revenues 0.24Hours worked 0.24Employment rate 0.10Real wage 0.07


Modelling Structural Reforms

Labour market reforms:

1 Change in the e�ciency of the matching process.2 Change in the cost of vacancies.3 Change in the job destruction rate.



Goods market reforms:

1 Change in the mark-up.2 Change in the energy intensity use.

Tax reforms:

1 Labour taxes.2 Capital taxes.3 Social security taxes.4 Consumption taxes.5 Energy taxes.



Extensions to our model:

1 Infrastructures, technological capital (R&D) and human capital.2 RoT consumers: liquidity restrictions.3 Training and �ring costs.


Date post:	17-Oct-2019
Category:	Documents
Upload:	others
View:	6 times
Download:	0 times

A Rational Expectations Model for Simulation and Policy...

Documents