the bnb quarterly projection model

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The BNB QuarterlyProjection Model

Emilia Penkova and Svilen Pachedzhiev



The BNB Quarterly Projection Model

Twinning Project “Adjustment of the Bulgarian National

Bank to operate as a full-fledged member of theEuropean System of Central Banks and the Euro-system”

Component 2: Research and preparation for monetary policy operations in line with ECB best practices



Introduction

The theoretical background – Neo-Classical Synthesis .The long-run equilibrium is determined by supply side factors(Neo-Classical theory) and short-run fluctuations are demand

driven (Keynesian theory).

Backward looking -expectations are reflected via laggedvariables , which is considered adequate for the purpose of generating short- to medium-term forecasts.

Behavioral equations – error correction form ( EngleGranger two step procedure has been employed).



The purpose of the BNBQM istwofold:

First, to produce macroeconomic forecasts for theBulgarian economy.

Second, to assess the effects of economicshocks on the Bulgarian economy in simulatedscenario analyses.



Outline of Presentation

Theoretical background

Structure of the model and estimated equations

Simulations

Concluding remarks and extensions of research



Supply side of the Economy

The standard theory of monopolistic competition isapplied.

Profits of an individual firm are determined byreturns from sale with costs of labour and capitalsubtracted.

The production process is represented by a CobbDouglas function.




iiiii cK wLY P Y −−=∏ )(

σ

)(i

i

P

P Y Y =

α ρ α −

=1)( i

t ii Le AK Y




where Π(Y i) are profits of the firm, Li is the labour force used bythe firm, K i is the capital stock of the firm, α’s are the incomeshares; ρ is the exogenous growth rate of technologicalprogress, σ is the elasticity of the demand for goods producedby the firm i to their relative price; w is the nominal wage level,c is the nominal cost of capital with

where r is the real rate of interest, δ is the physical

depreciation rate of capital, P I is price of investment goods, P i is the price of goods produced by the firm, P is the price of generic goods, Y i is the output of the firm i , Y is the aggregatesupply of generic goods.

)( δ += r P c I



Supply side of the EconomyFirst order conditions are:

0)1

())((1)

1(

11

1

=−−

=∂

∏∂ −−−

−

c K Le A PY K ii

t

i

σ

σ α

σ

σ α

σ

σ α ρ σ

0)1

)(1()(1)

1)(1(

1)1(

1

=−−

−=∂∏∂ −

−−

−−

w Le A K P Y Li

t

ii

σ

σ α α

σ

σ α

σ

σ α ρ σ




Using the assumption of symmetric equilibrium ( P i =P , Y i =Y , Li =L,K i =K ), we receive:

α ρ α −

=1

)( Le AK Y t

0)1

()( 1)1( =−−

=

∂

∏∂ −− c

K

L PAe

Ki

t

σ

σ α

α α ρ

0)1

)(1()()1( =−−

−=∂

∏∂ − w L

K PAe

Li

t

σ

σ α

α α ρ




The aggregate output and the long-run demand for capital andlabour are given by:

α ρ α −

=1)( Le AK Y t

P

c

Y K

σ

σ α )1( −=

P

w

Y L

σ

σ α )1)(1( −−=



Structure of the model andestimated equations

The simulation and projection features of the BNB QuarterlyProjection Model are driven by twenty behavioural equationsand additional forty three identities . Around one hundred andsixty variables enter the model.

The model is in Eviews 5.1 (a program file which imports the data,estimates equations, solves the model and produces forecastsoutput).

The model is structured into five blocks : production function andfactor demand equations, aggregate demand, prices and wages,monetary, and fiscal sector.



Model linkages



Error correction form

Most of the dynamic equations take the following general form:

where log(y t-1 )-log(y* t-1 ) is the error correction term;

γ(.) and σ(.) – are polynomials ;l - the lag operator

t t t

t t

y y yl yl

ε µ σ γ +−−

−∆=∆

−− ))*log()(log()log()()log()(

11



Potential output

R_YP_R = Potential output, prices of 2005

R_TFP_TD = Total factor productivity, trend (2005=100)L_EMPL_TD = Employment, trendR_K_R = Capital stock, prices of 2005

4.0

6.0

_ _ *

* _ _ * _ _ _ _ R K R

TD EMPL LTDTFP R RYP R =



Potential output

Total factor productivity is estimated as a residual fromthe production function for the estimated period thenusing Hodrick-Prescott filter we receive the trend.

The potential employment is received from a labour forceforecast and estimated NAIRU.

NAIRU is assumed to be at around 7.7% level (slightlydecreasing over the forecasting period) and is estimatedusing Elmeskov (1993) approach.



Employment

Log(L_EMPL_STAR) = 3.278 + 0.600*log(R_Y_R) -(5.607) (-)

- 0.400 *log(L_W/I_HICP_P) (-)

Dlog(L_EMPL)= -0.089 - 0.296*(log(L_EMPL (-1)) – (18.365) (5.138)

- log(L_EMPL_STAR(-1)))+ 0.001* Dlog(L_EMPL(-1)) (0.002)

L_EMPL = Employment (employees + self employed)R_Y_R = GDP, prices of 2005L_W = Nominal wage bill per worker I_HICP_P = Harmonised index of consumer prices, 2005 = 100



Employment

Employment

3000310032003300340035003600370038003900

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

TRUE

FORECAS



Gross fixed capital formationLog(R_KF_R_STAR)= 1.942+ 0.700*log(R_Y_R)- (4.338) (-)- 0.108*M_LTIR_N - 0.007*I_I_P

(9.451) (2.516)

Dlog(R_KF_R) = 0.242 -0.003*(log(R_KF_R(-1))-(6.285) (-)

- log(R_KF_R_STAR(-1))) - 0.363*Dlog(R_KF_R(-1)) (2.135)

R_KF_R = Gross fixed capital formation, 2005 pricesR_Y_R = GDP, 2005 pricesI_I_P = Inflation, in percentagesM_LTIR_N =Nominal long-term interest rate, in percentages



Gross fixed capital formationGross fixed capital formati

1500

2000

2500

3000

3500

4000

4500

2 0 0

5 Q 1

2 0 0

5 Q 2

2 0 0

5 Q 3

2 0 0

5 Q 4

2 0 0

6 Q 1

2 0 0

6 Q 2

2 0 0

6 Q 3

2 0 0

6 Q 4

TRUEFORECAST



Private consumptionLog(R_C_R_STAR) = 2.365 + 0.800*log(R_DI_N/I_HICP_P) +

(21.979) (-)

+ 0.300*log(R_K_R) (-)

Dlog(R_C_R) = 0.077 - 0.483*(log(R_C_R(-1)) – (3.743) (2.200)

- log(R_C_R_STAR(-1))) -0.343*Dlog(R_C_R(-1)) (2.074)

R_C_R = Private consumption, prices of 2005R_DI_N = Disposable income (wages and salaries+ pensions and social benefits +imputed rent +compensation of employees(BOP) + current transfers (BOP))I_HICP_P = Harmonised index of consumer prices, 2005 = 100R_K_R = Capital stock, prices of 2005



Private consumption

Private consumptio

6500.00000

7000.00000

7500.00000

8000.00000

8500.00000

9000.00000

9500.00000

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

TRUE

FORECAST



ExportsLog(E_EX_R_STAR) = 6.108 + log(A_WTV_R)- (2.024) (-) - 0.451*log(E_EX_P/(A_MEPAE_P*E_ER_PI)) (4.758)

Dlog(E_EX_R) = -0.265 -0.206*(log(E_EX_R(-1))-(8.268) (1.448)

-log(E_EX_R_STAR(-1))) + 0.020*Dlog(E_EX_R(-1))(0.151)

E_EX_R = Exports, prices of 2005A_WTV_R = Volume of world trade (weighted average), 2005 = 100E_EX_P = Export deflator, 2005 = 100A_MEPAE_P = Manufacturing export price for advanced economies, 2005=100E_ER_PI = Exchange rate BGUSD, 2005=100



Exports

Exports

4000

5000

6000

70008000

9000

10000

11000

2 0 0

5 Q 1

2 0 0

5 Q 2

2 0 0

5 Q 3

2 0 0

5 Q 4

2 0 0

6 Q 1

2 0 0

6 Q 2

2 0 0

6 Q 3

2 0 0

6 Q 4

TRUE

FORECAS



ImportsLog(E_MP_R_STAR) = -2.473 + log(R_DD_R) – (13.023) (-)

- 0.305*log(E_MP_P/R_GDP_P) (3.821)

Dlog(E_MP_R) = 0.072 – 0.052*(log(E_MP_R(-1)) – (4.811) (0.645)

-log((E_MP_R_STAR(-1)))

E_MP_R = Imports, prices of 2005R_DD_R = Real domestic demand, prices of 2005 (private consumption expenditure +government consumption expenditure + gross fixed capital formation)E_MP_P = Import deflator, 2005 = 100R_GDP_P= GDP deflator, 2005 = 100



ImportsImports

6000

7000

8000

9000

10000

11000

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

TRUE

FORECAST



GDP deflator Log (R_GDP_P_STAR) = -0.011 + log(L_ULC)

(0.482) (-)

Dlog(R_GDP_P)=0.017-0.030*(log(R_GDP_P(-1))-

(2.202) (1.002)log(R_GDP_P_STAR(-1)))-0.071*dlog(R_GDP_P(- (0.397)

-1))+0.100*R_YG_R (-)

R_GDP_P = GDP deflator, 2005=100L_ULC = Unit labour cost, 2005=100R_YG_R = Output gap (% potential GDP)



GDP deflator GDP deflato

0.99

1

1.01

1.02

1.03

1.04

1.05

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

TRUEFORECAST



HICP without administered pricesLog(I_HICPEXA_P_STAR) = 0.007 + 0.488*log(R_GDP_P) +

(0. 588) (4.155) +0.512*log(E_MP_P) (-)Dlog(I_HICPEXA_P) = 0.029 - 0.381*(log(I_HICPEXA_P(-1))

(5.701) (3.891)-log(I_HICPEXA_P_STAR(-1))) +

+0.220*Dlog(I_HICPEXA_P(-1))(1.526)

I_HICPEXA_P = Harmonized Index of Consumer Prices without administered prices, 2005= 100L_ULC = Unit labour cost, 2005=100E_MP_P = Import deflator, 2005 = 100



HICP without administered prices

HIC P without administe re d p

0.98

1

1.02

1.04

1.061.08

1 .1

1.12

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

T R U E

FORECAS



Export deflator Log(E_EX_P_STAR) = -2.313 + 0.592*log(R_GDP_P) +

(5.052) (3.376)

+ 0.408*log(A_MEPAE_P*E_ER_PI) (-)

Dlog(E_EX_P) = 0.010 – 0.853*(log(E_EX_P(-1))- (2.110) (4.548)

- log(E_EX_P_STAR(-1))) -0.071*Dlog(E_EX_P(-1))- (0.697)- 0.058*Dlog(E_EX_P(-2)) +0.381*Dlog(E_EX_P(-3))- (0.580) (3.798)- 0.264*Dlog(E_EX_P(-4)))

(2.590)E_EX_P = Export deflator, 2005 = 100A_MEPAE_P = Manufacturing export price for advanced economies, 2005=100R_GDP_P = GDP deflator, 2005 = 100E_ER_PI = Exchange rate BGUSD, 2005=100



Export deflator

Export deflato

1

1.02

1.04

1.061.08

1.1

1.12

1.14

1.16

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

TRUE

FORECAS



Import deflator Log(E_MP_P_STAR)=-2.284 + 0.360*log(A_EU15MP_P*E_ER_PI)

(2.810) (4.710)

+ 0.640*log(R_GDP_P) (-)Dlog(E_MP_P) = 0.025 -0.116*(log(E_MP_P(-1)) –

(2.400) (0.827)

-log(E_MP_P_STAR(-1)))- 0.381*Dlog(E_MP_P(-1)) (2.530)

E_MP_P = Import deflator, 2005 = 100A_EU15MP_P = EU 15 Import deflator, 2005 = 100E_ER_PI = Exchange rate BGUSD, 2005=100R_GDP_P = GDP deflator, 2005 = 100



Import deflator

Import deflator

1.04

1.05

1.06

1.07

1.08

1.09

1.1

1.11

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

TRUE

FORECAST



WagesLog(L_W_STAR) = -5.822+ log(L_LPR) – 0.001*L_UR +

(3.087) (-) (0.712)

+ log(I_HICP_P) (-)

Dlog(L_W) = 0.131 -0.207*(log(L_W(-1)) – (10.598) (1.138)

- log(L_W_STAR(-1))) - 0.352*Dlog(L_W(-1)) (1.739)

L_W = Nominal wage bill per worker L_LPR = Labour productivity: GDP in prices of 2005/Number of employeesL_UR = Unemployment, in percentagesI_HICP_P = Harmonised index of consumer prices



Wages

Nominal wage bill per work

200

250

300

350

400

450

500

Q 1 ' 0 5

Q 2 ' 0 5

Q 3 ' 0 5

Q 4 ' 0 5

Q 1 ' 0 6

Q 2 ' 0 6

Q 3 ' 0 6

Q 4 ' 0 6

TRUEFORECAST



Fiscal sector

Government expenditures and government revenuesare modelled separately:

The government expenditures are disaggregated into fiveparts: government consumption, government investment,government transfers, government interest payments andother expenditure.

The government revenues consist of five components:revenues from personal income tax, social securitycontribution, revenues from corporate income tax,revenues from indirect taxes and other revenue items.



Personal income taxes

G_PIT = G_PIT_TR*R_CE_N

G_PIT = Personal income taxes (million leva)G_PIT_TR =Personal income effective tax rateR_CE_N = Compensation of employees (million leva)



Social security contribution

G_SSC=G_SSC_TR*R_CE_N

G_SSC = Social security contribution (incl. employers’ and employees’contribution in million leva)

G_SSC_TR = Social security effective tax rateR_CE_N = Compensation of employees (million leva)



Indirect taxes

G_IND=G_IND_TR*R_C_N

G_IND = Indirect taxes (incl. VAT, customs revenue, excise duties)G_IND_TR = Indirect effective tax rateR_C_N = Private consumption, in current prices



Corporate income tax

G_CIT = G_CIT_TR*R_GOS_N

G_CIT = Corporate income tax

G_CIT_TR = Corporate income effective tax rateR_GOS_N = Gross operating surplus and mixed income



Simulations

To illustrate the simulation properties of the BNBQM, we assessthe response of the model’s main variables to the followingstandard shocks:

an increase in government consumption by 1% of GDP

an increase in volume of world trade by 1%

a depreciation of the lev against the US dollar by 1%

an increase in the price of oil by 10%

an increase in EURIBOR by 100 basis points



Simulation of an increase in government consumption by 1%of GDP (Q1’2002 – Q4’2008)Levels, percentage deviations from baseline

Year 1 Year 2 Year 3 Year 4 Year 5 Year 7

HICP 0.031 0.162 0.319 0.476 0.607 0.666ULC -0.506 0.040 0.316 0.538 0.670 0.709Comp. per employee 0.385 0.794 0.917 0.933 0.840 0.450Productivity 0.896 0.753 0.599 0.393 0.168 -0.256

GDP 1.012 1.058 0.973 1.053 0.498 -0.119

Private consumption 0.060 0.333 0.517 0.575 0.534 0.257Investment 0.003 0.009 0.014 0.017 0.020 0.020Exports -0.009 -0.086 -0.198 -0.300 -0.387 -0.427Imports 0.042 0.196 0.386 0.595 0.781 1.099



Simulation of an increase in world demand by 1% (Q1’2002 – Q4’2008)Levels, percentage deviations from baseline

Year 1 Year 2 Year 3 Year 4 Year 5 Year7HICP 0.005 0.071 0.204 0.379 0.564 0.807ULC -0.255 -0.205 0.077 0.366 0.551 0.788Comp. per employee 0.101 0.554 0.884 1.076 1.144 1.010Productivity 0.357 0.760 0.807 0.708 0.589 0.220

GDP 0.395 0.971 1.175 1.173 1.100 0.545Private consumption 0.007 0.158 0.397 0.576 0.662 0.571

Investment 0.001 0.005 0.011 0.016 0.021 0.027Exports 0.725 1.546 1.583 1.497 1.426 1.320Imports 0.001 0.029 0.106 0.235 0.390 0.728



An increase in world demandThis simulation is particularly important because of the openness of the Bulgarian economy. The external demand shock leads to astronger domestic demand. The external shock directly drives upthe volume of exports by 1.55% (second year), which in turn also increases imports.

Employment and nominal wages increase which leads to higher private consumption (0.57%-seventh year).

Higher aggregate demand widens the output gap that pushes upthe aggregate price level.



Simulation of a depreciation of the lev against the US dollarby 1%(Q1’2002 – Q4’2008)Levels, percentage deviations from baseline

Year 1 Year 2 Year 3 Year 4 Year 5 Year 7HICP 0.008 0.065 0.129 0.190 0.250 0.310Import deflator 0.067 0.190 0.279 0.337 0.390 0.005Export deflator 0.336 0.565 0.493 0.511 0.572 0.006ULC -0.067 -0.009 0.056 0.137 0.203 0.003Comp. per employee 0.032 0.145 0.236 0.328 0.387 0.004Productivity 0.099 0.154 0.180 0.191 0.184 0.001

GDP 0.110 0.205 0.266 0.308 0.325 0.288Private consumption 0.003 0.044 0.090 0.118 0.133 0.011Investment 0.000 0.001 0.002 0.003 0.004 0.001Exports 0.198 0.289 0.294 0.308 0.295 0.002Imports -0.003 -0.028 -0.066 -0.098 -0.110 -0.098



An exchange rate shockThe decrease in the value of the lev against the US dollar has animmediate impact on both the import and export deflators – they bothincrease .

HICP increases by 0.25% in the fifth year. Compensation per employeeadjusts and income increases which drives the consumption up.

Because of the relative increase in foreign prices, imports decrease and exports increase slightly. The reaction of real GDP to an

exchange rate shock achieves its maximum in the fifth year (0.32%).



Simulation of an increase in the price of oil by 10%(Q1’2002 – Q4’2008)Levels, percentage deviations from baseline

Year 1 Year 2 Year 3 Year 4 Year 5 Year7HICP 0.016 0.110 0.177 0.227 0.296 0.413Import deflator 0.160 0.468 0.656 0.851 1.052 1.299Export deflator 0.481 0.814 0.618 0.886 1.031 1.103ULC 0.032 0.110 0.084 0.117 0.185 0.204Comp. per employee -0.005 -0.055 -0.048 0.028 0.088 0.352Productivity -0.037 -0.164 -0.132 -0.089 -0.097 0.148

GDP -0.041 -0.194 -0.186 -0.140 -0.146 0.220Priv. consumption 0.000 -0.012 -0.067 -0.125 -0.171 -0.231Investment 0.000 -0.001 -0.003 -0.004 -0.005 -0.006Exports -0.081 -0.394 -0.413 -0.432 -0.593 -0.621Imports -0.005 -0.057 -0.154 -0.280 -0.424 -0.774



An oil price shockAn oil price shock leads to increasing domestic prices through directchannels - rising import prices. The response grows gradually andachieves its maximum - 0.41% for HICP in the seventh year.

The rise in prices causes a reduction in the demand for domestic andforeign goods and the consequent fall in household consumption,imports and exports . As a result, GDP and real disposable income arebelow baseline till year six.

Higher oil price has a negative impact on output and domesticdemand (private consumption declines by 0.17% and GDP falls by0.15% in the fifth year).

Reduced economic activity leads to a lower demand for imports , realexports are also decreasing due to an increase in domestic prices.

Simulation of an increase in EURIBOR by 100 basis points



y p(Q1’2002 – Q4’2003) Levels, percentage deviations from baseline

Year 1 Year 2 Year 3 Year 4 Year 5 Year7HICP -0.001 -0.007 -0.017 -0.021 -0.015 0.015ULC 0.026 0.011 -0.049 -0.054 -0.031 -0.010Comp. per employee -0.010 - 0.051 -0.054 -0.001 0.041 0.082Productivity -0.086 -0.195 -0.156 -0.052 0.037 0.220

GDP -0.096 -0.269 -0.291 -0.182 -0.059 0.239Private consumption -0.066 -0.182 -0.243 -0.289 -0.342 -0.359Investment -0.283 -0.933 -1.256 -1.118 -1.038 -0.890Exports 0.000 0.000 0.001 0.001 0.000 0.001Imports -0.006 -0.071 -0.214 -0.396 -0.571 -0.865



Interest rate shockBecause of the fixed exchange rate regime the exchange rate does notreact to domestic interest rate changes. The main effect is throughinvestment- raising costs of capital and reducing output . Investmentdecreases by 1.12% and GDP is reduced by 0.18% in the fourth year.

The effect on domestic prices is negative due to a weaker domesticdemand.

Due to lower internal aggregate demand, employment and wages fall .

C l di k d



Concluding remarks andextensions

A first step towards building a structuralmacroeconomic model.

This practical work gives valuable information for thefuture development of the model which needs to becontinuously developed and could be improved in anumber of respects:

Availability of new data will require re-estimation and re-calibration of the model;



Concluding remarks andextensions

Developing a long-run baseline that reflects a fully theory-consistent long-run steady state;

To consider policy rules in the simulations;

Developing a more detailed representation of the tradeblock by including services on the one hand and differentregions on the other hand;

An extension of forward-looking behaviour. Expectationsshould be incorporated, particularly to allow for a specificrole in price and wage formation.



Baseline (work in progress)Real exports to GDP

35

40

45

50

55

60

65

70

2000 2025 2050 2075 2100 2125 2150 2175 2200



Baseline (work in progress)Real imports to GDP

30

40

50

60

70

80

90

100

2000 2025 2050 2075 2100 2125 2150 2175 2200



Baseline (work in progress)Real private consumption to GDP

45

50

55

60

65

70

75

80

2000 2025 2050 2075 2100 2125 2150 2175 2200



Baseline (work in progress)Real capital formation to GDP

5

10

15

20

25

30

35

2000 2025 2050 2075 2100 2125 2150 2175 2200

the bnb quarterly projection model

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