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QUEST_Serbia

DSGE Model

with

Practical Guide

Miroljub Labus

2014

QUEST_Serbia DSGE Model 2

Table of Contents

1 Introduction ..................................................................................................................................... 5

2 Production and Output Gap ............................................................................................................. 7

3 Profit Maximization ...................................................................................................................... 11

4 Technology Progress ..................................................................................................................... 14

5 Household Behavior ...................................................................................................................... 15

5.1 Consumption .............................................................................................................. 16

5.2 Equilibrium condition and consumption ................................................................... 20

5.3 Investments ................................................................................................................ 21

6 Wages ............................................................................................................................................ 27

7 Domestic and Foreign Markets ..................................................................................................... 30

8 Economic Policies ......................................................................................................................... 35

8.1 Monetary Policy ........................................................................................................ 36

8.2 Fiscal Policy .............................................................................................................. 39

9 The Rest of the World ................................................................................................................... 43

10 Steady State ............................................................................................................................... 44

11 Steady state solution .................................................................................................................. 48

12 Results of the steady state solution ............................................................................................ 57

13 Prior distribution and posterior estimation ................................................................................ 62

14 Replicates of time series ............................................................................................................ 67

15 Impulse Response Functions ..................................................................................................... 70

16 Decomposition of IRFs ............................................................................................................. 72

17 Sensitivity Analysis ................................................................................................................... 74

18 Identification Analysis .............................................................................................................. 78

References ............................................................................................................................................. 81

Annex I: List of Variables ..................................................................................................................... 82

Endogenous variables ........................................................................................................... 82


Permanent stochastic shocks ................................................................................................ 85

Annex II: List of Parameters and Temporary Shocks ........................................................................... 86

List of Figures

Figure 1: Basic Structure of the Model ................................................................................................... 6

Figure 2: Model’s Replicates of Price Time Series ............................................................................... 33

Figure 3: Model’s Replicates of Growth Rates' Time Series ................................................................ 34

Figure 4: IRFs to a Monetary Shock of One Standard Deviation ......................................................... 37

Figure 5: Trend Time Preference Rates ................................................................................................. 45

Figure 6: Trends of Quarterly Inflation Rates in Serbia and the Euro Zone ......................................... 46

Figure 7: Trend of Trade Deficit in Serbia ............................................................................................ 47

Figure 8: Trends of Quarterly GDP Growth Rates in Serbia and the EU.............................................. 47

Figure 9: Priors and Posteriors .............................................................................................................. 66

Figure 10: Consumption and government block of variables ................................................................ 68

Figure 11: Foreign trade block of variables .......................................................................................... 68

Figure 12: Investment and labor block of variables .............................................................................. 69

Figure 13: Output and price block of variables ..................................................................................... 69

Figure 14: Wage and ROW block of variables ..................................................................................... 70

Figure 15: IRF of the GDP growth rate to a monetary shock of one standard deviation ...................... 71

Figure 16: Decomposition of the IRF of GDP growth to a monetary shock for the most influential

eight variables........................................................................................................................................ 73

Figure 17: Histogram of the MC sample of the reduced form coefficient driving the relationship

between GDP growth rate and the real exchange rate versus monetary shock ..................................... 75

Figure 18: Histograms of the MC sample of the reduced form coefficients that effect the .................. 76

relationship between GDP growth rate and nominal interest rate, inflation and real exchange rate,

respectively ............................................................................................................................................ 76

Figure 19: Sensitivity indices of the key parameters driving the reduced form coefficient effects on

relationship between endegeous variables vs. stochastic shocks .......................................................... 76

Figure 20: Non-parametric curves of the key parameters driving the GDP growth response to a

monetary shock...................................................................................................................................... 77

Figure 21: Dynare identification strength of the QUEST_Serbia model .............................................. 79

List of Boxes

Box 1: The Model Script Rules ............................................................................................................... 7


Box 2: Production Function Script .......................................................................................................... 9

Box 3: Output Gap Script ...................................................................................................................... 10

Box 4: Labor Script ............................................................................................................................... 13

Box 5: Capacity Utilization Script ........................................................................................................ 14

Box 6: Technology Progress Script ....................................................................................................... 15

Box 7: Utility Script .............................................................................................................................. 19

Box 8: Equilibrium Script ..................................................................................................................... 20

Box 9: Capital Script ............................................................................................................................. 26

Box 10: Real Money Balances Script .................................................................................................... 26

Box 11: Wage Script ............................................................................................................................. 29

Box 12: Prices Script ............................................................................................................................. 32

Box 13: Foreign Trade Script ................................................................................................................ 35

Box 14: Inflation Targeting Script ........................................................................................................ 38

Box 15: Fiscal Policy Script .................................................................................................................. 42

Box 16: The ROW Script ...................................................................................................................... 44

Box 17: Steady State ............................................................................................................................. 48

Box 18: Printed output for the basic identification check ..................................................................... 79

List of Tables

Table 1: Two types of households ......................................................................................................... 16

Table 2: Calibrated parameters and steady state variables .................................................................... 55

Table 3: Steady state solution for variables ........................................................................................... 57

Table 4: Priors and Posteriors ............................................................................................................... 63

Table 5: Posterior estimation of temporary shocks ............................................................................... 67


1 Introduction

Our model is called the QUEST_SERBIA DSGE model, it refers to the economy of Serbia.

The model is based on the European Commission’s QUEST III model. QUEST III is a global

macroeconomic model developed for macroeconomic policy analysis and research. Since it

belongs to the class of new-Keynesian DSGE models, QUEST III has rigorous

microeconomic foundations derived from utility and profit optimization and it includes

frictions in goods, labour and capital markets. In their economic paper, Ratto et al. [2009]

provide a detailed exposition of the QUEST III model’s core version, using the euro area data

from Q1Y1978 to Q4Y2007, as well as Bayesian techniques to estimate most of the model’s

coefficients. We strongly recommend this paper to all those readers that might be interested in

the topic. Roeger and in't Veld [2009], Roeger and in't Veld [2010], in't Veld et al. [2011],

and Vogel [2011] describe extended versions of the model.

With empirically plausible estimation and calibration, the Serbian model is able to fit the main

features of the macroeconomic time series in Serbia between Q1Y2003 and Q3Y2013. Figure

1 illustrates the basic structure of the model1. The QUEST_SERBIA model does not

distinguish tradable from non-tradable production sectors due to the lack of appropriate data,

and it adopts hypotheses that tradables and non-tradables are treated as perfect substitutes in

consumption and investment demand.

Profit-maximizing monopolistically competitive firms produce output, using Cobb Douglas

technology with private and government capital, corrected for the capacity utilization rate,

and the labor input augmented by technological progress. The production function is defined

in terms of growth rates instead of being formulated through the factors linked to the

production levels. Goods and labor markets are subject to nominal and real rigidities, while, at

the same time, goods and capital markets are internationally integrated. Capital is perfectly

mobile, so that uncovered interest parity (UIP) holds.

Households make decisions on savings, consumption, and labor supply. There are two

different types of households: financially unconstrained (Ricardian) households that can

optimize through an intertemporal budget constraint, and liquidity-constrained households,

which do not have access to financial markets and constantly consume their entire disposable

income. Ricardian households maximize expected utility over an infinite period of time

subject to the budget constraint, which combines consumption and investment expenditures,

and financial investments in real money balances, domestic and foreign bonds, on one hand,

and labor and capital income, including labor and capital adjustment costs, on the other.

Within a process of collective bargaining, the trade union acts as an agent for households and

maximizes a joint utility function of the Ricardian and liquidity constrained households. The

wage rule is set in a sophisticated way, and includes both the marginal utility of leisure and

the marginal utility of consumption (the ratio of which defines the reservation wage rate), real

1The figure is adapted for the Serbian case from Vogel [2011, p.5].

2 This equation is obtained by inserting Equation 17 into Equation 12, see Box 9.


wages of both types of households, wage adjustment costs, real wage rigidity and a mark-up

over the marginal product of labor.

Figure 1: Basic Structure of the Model

The government is faced with intertemporal budget constraints. On the expenditure side, the

model recognizes three types of public spending: government consumption, government

investment and transfer payments (that are further subdivided into unemployment benefits and

pension transfers). On the revenue side, the model distinguishes consumption tax from taxes

on factor incomes. Tax revenues are linked to their corresponding tax bases, via linear tax

rates, and are sensitive to business cycle fluctuations. There is a debt rule which imposes the

adjustment of taxes and expenditure to a predetermined debt target.

To summarize, households, firms and the government make decisions which are consistent

with their intertemporal budget constraints and first-order conditions of their optimal

behavior. Additionally, there are rigidities in product and factor markets, and decision makers,

regardless of how rational they might be, are subject to uncertainties and exogenous stochastic

shocks. When the properties of the model are explained, special attention is paid in order to

demonstrate how it works, in practice, in the context of the Serbian economy. We will,

therefore, combine the analytic method with a programmatic approach. Ratto et al. [2009]

used the first approach in the original paper. In this paper, we will focus on practical

guidelines, which will be written in corresponding boxes. The model is written in Dynare

codes [Adjemian et al., 2013] and solved using MATLAB software. Finally, we will explain

specifics of the Serbian economy and adjustments of the corresponding model.


2 Production and Output Gap

It is assumed that firms are divided into those that produce intermediate goods and firms that

produce investment goods:

• There are 1,2,...,n firms that produce intermediate goods and sell them at a

monopolistically competitive market,

• Each firm makes j = 1,2,...,m different varieties of intermediate goods,

• Varieties are imperfect substitutes that are aggregated into a composite intermediate

good by CES aggregation function with the elasticity of substitution ( ),

• Domestic firms sell these goods to households, to firms that produce investment

goods, to the government and to exporting firms,

• Firms that produce investment goods buy intermediate goods and combine them with

imported goods in order to supply a perfectly competitive market with final

investment goods,

• The elasticity of substitution between domestic and imported goods is ( ).

In a general setting, Cobb-Douglas production function is defined at levels with embodied

capital and labor technological progress as:

(

)

(

)

Box 1: The Model Script Rules

The model has 111 equations, partly behavioral equations and partly definitional and permanent shocks equations,

Equations in the paper are labeled according to the order in which they are declared in the model file,

The algebraic version of equations is presented in the text, while their Dynare’s script counterparts are in the boxes,

Endogenous variables are written in capital letters and have no prefix, Endogenous variables in logarithms have the first letter “L”, Exponential values of variables are placed between brackets of the sign “exp(.)”, Endogenous variables in terms of growth rates have the first letter “G”, Temporary shocks are exogenous variables that are also written in capital letters

but have prefix “EPS_”, Parameters (calibrated or estimated) are written in small letters, Steady state values of endogenous variables are written in small letters with zero

“0” as the last character, Permanent shocks have prefix “ZEPS_”, Leads and lags of endogenous variables have brackets (+1) and (-1) at the end.


Where ( (

) (

) represent firms’ output, capital and labor inputs, and (

) ( ) are

embodied capital and labor technological progress, represented by respective stochastic

shocks or stochastic processes independent from capital accumulation and employment

dynamics. This general C-D production form is slightly modified in the model, so that it takes

into account existence of two types of capital, private capital ( ) and government capital

(

) that is accumulated through government’s investment process, and capacity utilization

rate. Additionally, total work force ( ) is divided into productive labor (

) and

overhead labor (

). Hence, C-D production function at the firm level has the following

form:

(

)

(

)

where ( is the capacity utilization rate, and stochastic shock (

) represents

unembodied technological progress.

In order to avoid the problem of non-stationarity, all level variables in the model are defined

as shares in GDP or growth rates. If capital and labor are aggregated across all firms, the C-D

function has the following form:

(20) ( (

[

( ( ]

(

where ( , ( , (

and( stand for the growth rates of GDP, private capital, labor and

government capital, while ( ) and (

) represent the rates of capacity utilization and

labor augmented technological progress.

The growth rate of capacity utilization is represented through a permanent technology shock

which has the form of a random walk process with a drift:

(81)

The growth rate of labor augmented technology progress is subject to a stochastic shock ( )

and is given by:

(50)

The total factor productivity or Solow residual is driven by the labour market shock and

represented as:

(79) (

Finally, overhead labor follows a first-order autoregressive process which oscillates around its

long-run value ( ) and is subject to a stochastic shock ( ):

(51) ( )


Box 2: Production Function Script

COBB-DOUGLAS PRODUCTION FUNCTION // EQUATION 20

GY = (1-alphae)*(GK+GUCAP) + alphae*(GLFP + GL*(1+LOL)) + GKG*(1-alphage);

EVOLUTION OF LABOR

// EQUATION 51

LOL-lol = rholol*(E_LOL(-1)-lol)+eps_lol;

TOTAL FACTOR PRODUCTIVITY

// EQUATION 79 GTFPUCAP = (1-ALPHAE)*GUCAP+ALPHAE*GTFP;

LABOUR PRODUCTIVITY PROCESS // EQUATION 50

(GLFP -GLFP0) = eps_Y;

CAPITAL PRODUCTIVITY PROCESS // EQUATION 81

GUCAP = log(UCAP)-log(UCAP(-1));

Output gap needs to be defined as well. The common approach in modeling output gaps

within a DSGE framework is based on Hodrick-Prescott filter. It takes empirical time-series

of output, and, initially, it estimates its trend-cycle component. After that, it calculates the

difference between the original data and the trend-cycle in order to get the cycle component.

The trend-cycle component is taken as a proxy for the potential level of output. Therefore, the

cycle component represents the corresponding output gap. Finally, this method estimates

regression coefficients of an auto-regressive equation based on the obtained data of the cycle

component. Using this information, the corresponding auto-regressive process of output gap

is included in a DSGE model as a separate equation.

In this model the output gap is obtained in a different way. A production function approach is

used to define the output gap as deviation of capital and labor utilization from their long run

trends:

(27) (

)

(

)

where ( ) and ( ) are the period’s levels of capacity utilization and employment,

respectively; while ( ) and (

) are the long-run trends in capacity utilization and

employment evolution, respectively. They are modeled as moving average figures in auto-

regressive processes:


Box 3: Output Gap Script

OUTPUT GAP // EQUATION 27

LYGAP = (1-alphae)*(log(UCAP)-log(UCAP0))+alphae*(LL-LL0);

EVOLUTION OF LABOR // EQUATION 28

LL0 = rhol0*LL0(-1) + (1-rhol0)*LL;

EVOLUTION OF CAPACITY UTILIZATION // EQUATION 29

UCAP0 = rhoucap0*UCAP0(-1) + (1-rhoucap0)*UCAP;

POTENTIAL OUTPUT // EQUATION 83

GY - GYPOT = LYGAP-LYGAP(-1);

(29)

(

)

and

(28)

(

)

The long-run variables move very in response to respective actual variables. Coefficient alpha

( ) is the elasticity of output with respect to labor.

Additionally, the output growth rate is affected by the changing conditions of business cycle.

The GDP growth rate represents a sum of the potential output and the change in output gaps:

(83)

( (

where (

) is the potential output. The potential output is a solution of the model and is not

approximated by a separate dynamic equation. This fact, once again, illustrates the alternative

method of defining output gap compared to traditional use of Hodrick-Prescott filter.


3 Profit Maximization

It is assumed that each firm has the goal to maximize the present discounted value of its

profit, defined as the difference between total revenue and total costs. Total cost is composed

of labor and capital rental costs plus adjustment costs due to rigidities in the labor and product

markets, as well as capacity utilization decisions.

Price rigidities are modeled as adjustment cost due to a convex functional form:

The cost of labor adjustment is represented by the following form:

While the cost of capacity utilization adjustment is:

Hence, each firm faces the following optimization problem:

The present discounted

value of profit of the j firm

[(

(

] Total revenue

(

Labor costs

(

Capital rental costs

{

[

(

)

]

[

(

]}

Adjustment costs of labor

{

[

(

]

[

(

]} Adjustment costs of prices

[ (

)

(

)

]

[ (

)

(

)

]

Costs associated with the

utilization of capital

Subject to

𝑗 ( 𝑡𝑗) =

𝑡𝐼𝑗

𝑡

[ 1( 𝑡𝑗

1) + 2

2( 𝑡

𝑗 1)

2]

𝑗 ( 𝑡𝑗) =

2 ∆ 𝑡

𝑗 2

𝑡 1𝑗

𝑗 ( 𝑡𝑗) = 𝑡 [ 𝑡

𝑗 𝑡

+

2(∆ 𝑡

𝑗)

2]


(1 + 𝑡

𝑡

𝑡 𝑡

= 𝜂𝑡

𝑡𝑗

(1 + 𝑙𝑜𝑙𝑡 ) 𝑡

𝑡

∆ 𝑡𝑗

+1

1 + 𝑟𝑡

𝑡+1

𝑡+1 𝑡+1

(1 + 𝑡 ∆ 𝑡+1𝑗

𝜂 {

(

(

(

}

The demand function for

firm j

Derived demand for labor input is obtained as the first-order condition with respect to labor:

or re-arranged:

Intermediate-good firms are able to charge a mark-up (𝜂 ) over the market price:

𝜂

Its optimal level is obtained as the first-order condition of profit maximization with respect to

the firm’s output:

since the firm’s output is by definition:

(

(

Taking into account the mark-up definition, derived demand for labor by each firm is:

(11)

or

where mark-up is(𝜂 , cost of labor adjustment( ) , elasticity of labor with respect to

output(α), logarithm of non-productive labor share in the total work (𝑙𝑜𝑙 , discount factor

(

), deviation of the growth rate around the steady-state growth ( ) , expected wage

share in nominal GDP (

), expected change of the supply of labor (∆ )and labor

stochastic shock( ).

If the aggregate output is:

𝜕 𝑟𝑡𝑗

𝜕 𝑡𝑗

= 𝑡

𝑗

𝑡

𝑡

𝑗

𝑡𝑗

𝐻 ,𝑡𝑗

𝑡

𝑡

1

𝑡

𝑡 [ 𝑡 + ( 𝑡

𝑗 𝑡 1

𝑗)] 𝑡

1

𝑡+1

𝑡+1 ( 𝑡+1𝑗

𝑡𝑗) = 0

𝑡

𝑡

= 𝑡

𝑗

𝑡

𝑡

𝑗

𝑡𝑗

𝐻 ,𝑡𝑗

𝑡

𝑡

𝑡

𝑡

𝑡

∆ 𝑡𝑗

+ 𝑡

1

1 + 𝑟𝑡

𝑡+1

𝑡+1

∆ 𝑡+1𝑗

𝜕𝑃𝑟𝑡𝑗

𝜕𝑌𝑡𝑗

=𝑃𝑡

𝑗

𝑃𝑡

− 𝜂𝑡 = 0

(1 + 𝑡

𝑡 𝑡𝑗

𝑡 𝑡

= 𝜂𝑡 (1 + 𝑙𝑜𝑙𝑡 ) 𝑡 𝑡

𝑗

𝑡

∆ 𝑡𝑗

+1

1 + 𝑟𝑡

𝑡+1 𝑡

𝑗

𝑡+1 𝑡+1

(1 + 𝑡 ∆ 𝑡+1𝑗


1 + 𝜀𝑡𝐿

𝑊𝑡

𝑃𝑡𝑌𝑡= 𝜂𝑡

𝛼

𝐿𝑡

1 + 𝑙𝑜𝑙𝑡 −𝑊𝑡

𝑃𝑡𝑌𝑡𝛾𝐿∆𝐿𝑡 +

1

1 + 𝑟𝑡

𝑊𝑡+1

𝑃𝑡+1𝑌𝑡+1(1 + 𝑔𝑡+1 − 𝑔)𝛾𝐿∆𝐿𝑡+1

Then, the economy-wide derived demand for labor is:

The derived optimal demand for capital is obtained as the first-order condition of the profit

optimization problem with respect to the capital input:

or

Value of the marginal product of capital equals the rental price of capital. This relation

depends on elasticity of capital with respect to output (1-α), rental rate of capital ( ), mark-up

(𝜂

) and relative price of investment goods (

). The total amount of capital is:

∫ 𝑗

.

The optimal capacity utilization is:

If we re-arrange this first order condition, we get:

𝑡 = 𝑡𝑗

1

𝑜

𝜕 𝑟𝑡𝑗

𝜕 𝑡𝑗

= (1 𝑡

𝑗

𝑡

𝑡𝑗

𝑡𝑗 𝑡

𝑗

𝑡𝐼𝑗

𝑡

[ 1 + 2( 𝑡𝑗

1)] = 0

𝜕𝑃𝑟𝑡𝑗

𝜕𝐾𝑡𝑗

=𝑃𝑡

𝑗

𝑃𝑡

𝑌𝑡𝑗

𝐾𝑡𝑗 1 − 𝛼 − 𝑖𝑡

𝑘𝑃𝑡

𝐼𝑗

𝑃𝑡= 0

𝜂𝑡

𝑌𝑡𝑗

𝐾𝑡𝑗 1 − 𝛼 = 𝑖𝑡

𝑘𝑃𝑡

𝐼𝑗

𝑃𝑡

Box 4: Labor Script

LABOR DEMAND EQUATION // EQUATION 11

(1+ZEPS_W)/(exp(LYWR)) = ETA*alphae/exp(LL)*(1+LOL) - 1/(exp(LYWR))*gamle*(LL-LL(-1)) +

1/(exp(LYWR(+1)))*(1+GY(+1)-GY0)*gamle/(1+R)*(LL(+1)-LL);

OUTPUT TO REAL WAGE GROWTH EQUATION // EQUATION 82

GWRY= -LYWR+LYWR(-1);

OUTPUT TO REAL WAGE EQUATION // EQUATION 92

-WPHI + GY + PHI = LYWR - LYWR(-1);


1 − 𝛼 ∙ 𝜂𝑡 ∙ 𝑌𝐾𝑃𝑃𝐼𝑡 = 𝑈𝐶𝐴𝑃𝑡𝑗 𝛾1

𝑢𝑐𝑎𝑝+ 𝛾2

𝑢𝑐𝑎𝑝 𝑈𝐶𝐴𝑃𝑡

𝑗− 1

or

(14)

where the value of output-capital ratio is:

𝐼

The marginal product of capital services is equal to the marginal cost of increasing capacity.

By definition, the growth rate of output-capital ratio can be defined by using growth rates of

GDP and capital ( ), respectively, and GDP deflator rate and investment-good inflation

rate ( ):

(76) (

(

) (

)

The aggregate price mark-up will be explained in section 7 which deals with equilibrium

conditions in domestic and foreign markets.

4 Technology Progress

Technology progress is materialized in the investment-good sector of a two-stage production

system. At the first level of production, investment-good firms combine domestic

intermediate goods with corresponding imported goods into a CES aggregate input (𝐼

).

At the second level of production, firms in the investment-good sector employ a linear

technology to transform the aggregate intermediate input into the final output of investment

goods. The linear production function is subject to the technology shock ( ):

(1 𝑡

𝑗

𝑡

𝑡𝑗

𝑡𝑗 𝑡

𝑗=

𝑡𝐼𝑗

𝑡

[ 1 + 2( 𝑡𝑗

1)]

Box 5: Capacity Utilization Script

UTILIZATION OF CAPACITY EQUATION // EQUATION 14

(ETA*(1-alphae)*(exp(LYKPPI) ) ) = (a1e+2*a2e*(UCAP-ucap0))*UCAP;

GROWTH RATE OF CAPACITY UTILIZATION

// EQUATION 76 (GY - GK + PHIPI) = LYKPPI - LYKPPI(-1);


𝐼 𝐼

The technology shock in investment-good sector is a permanent shock which smoothly

evolves over time and is subject to temporary shocks:

(62)

The weight coefficients ( ), (

),( ) and (

) have descending values and add-up to less

than one indicating that the process of inertia does not exclusively command the technology

progress. The temporary shock ( ) is a stochastic variable with zero mean value and variance

( ). The investment goods shock plays an important role in the model. With technical

improvements, prices of investment goods should decline with respect to prices of

consumption goods and reveal a progress in technology. Hence, relative prices depend on the

state of technology:

Relative prices of consumption and investment goods reveal technological progress in the

economy:

(52)

5 Household Behavior

The household sector is divided into two parts: (i) Liquidity non-constrained households (i.e.

Ricardian households) and (k) Liquidity constrained households (i.e. Subsistence or Non-

Ricardian households), as illustrated in Table 1. Labor income of Non-Ricardian households

provides only for their consumption without any surplus for savings and investments. They

neither possess shares of firms, nor do they receive dividends or trade in bonds and equities.

On the other side, Ricardian households earn income from labor and ownership as well as

from proceeds of financial investments. As rational market agents, two types of households

face different maximization problems that should be solved, which underline their different

Box 6: Technology Progress Script

TECHNOLOGY PROGRESS // EQUTION 52

PHIPI = gpcpi0 + ZEPS_PPI;

EVOLUTION OF TECHNOLOGY PROGRESS // EQUTION 62

ZEPS_PPI = rhoppi1*ZEPS_PPI(-1)+rhoppi2*ZEPS_PPI(-2) +rhoppi3*ZEPS_PPI(-3)+rhoppi4*ZEPS_PPI(-4)+eps_PPI;


behavior patterns. More precisely, Ricardian households optimize over present consumption

and uncertain future consumption (investments), while Non-Ricardian households do not

optimize and consume their entire labor income at each date. Households’ utility functions are

specific for each case, but, for the sake of simplicity, the allocation of labor skills across

households is identical. Reservation wages and consumption functions are also household

specific. Unfortunately, statistical database does not support this important difference between

households. Any household-specific variables are therefore non-observable variables, and are

the results of the model’s solution or its simulation.

Table 1: Two types of households

Earning side

Types of

house-

holds

Spending side

Labor

income

Income

from

financial

investment

Rental and

profit

earnings

Consump-

tion Savings

Financial

investments

Yes No No

Liquidity

constrained

households

Yes No No

Yes Yes Yes

Liquidity

non-

constrained

households

Yes Yes

Domestic

and foreign

bonds, cash

balances,

physical

capital

5.1 Consumption

Let us start with presenting the optimization problem of the Ricardian households. Parameter

slc represents the share of liquidity-constrained households in the total number of households,

while (1-slc) is the remaining share of Ricardian households in the total population. The

model assumes that there is a continuum of households in the finite interval [0,1], and

Ricardian households populate a part of it, indexed as i ϵ[0,1-slc].On the revenue side,

Ricardian households earn labor income (

), dividends from firm’s profit ( 𝑟 ) and factor

income from renting physical capital to firms (

). They pay taxes on labor income

(𝑡 ), social security contributions (𝑡 ), taxes on rental income (𝑡

), value-added

tax (𝑡 ), and lump-sum taxes (𝑡 ). Disposable income is a difference between total

personal income and levied taxes. This income is used for buying consumers’ goods ( ),

investing in additional capital goods ( ), holding cash balances (

), and investing in

domestic bonds ( ) or in foreign bonds (

). Domestic bonds are risk-free, while foreign

bonds are risky due to high foreign indebtedness. This triggers a premium (risk) that will be

charged on foreign bonds. Returns on equity assets are also uncertain and subject to a

premium ( 𝑟 for corresponding equity risk.


It is obvious that a Ricardian household has a wide range of options. It has to make rational

decisions on the following set of variables { }. Hence, the optimization

problem reads as follows:

{

}

∑ (

)

Expected utility

j=i,k

∑

{

Subject to expected

constraints

( 𝑡

Consumption

𝐼

Investment

+

Real money balance

( ( 𝑡

Real domestic bonds

( ( 𝑡

( 𝑟 (

Real foreign bonds

( 𝑡

( 𝑟

𝑡

Real net capital income

before depreciation

{( 𝑡

∆

}

Real labor income

corrected for cost of

adjustments

{

[

[

(

)]

(∆

)

]}

Real cost of investment

adjustments

∑ 𝑟

} Profit and lump-sum tax

∑

{

(

}

Accumulation f capital

This problem shall be split into several separate blocks and we will demonstrate how the

blocks are solved. Let us start with the optimal level of consumption of Ricardian households.

The maximization problem has the form:

for which the Lagrangian function is given by:

{ 𝑡 ,} 0 ∑ 𝑡 ( 𝑡

, 1 𝑡 )

∞

𝑡=0

0 ∑ 𝑡 𝑡

∞

𝑡=0

(1 + 𝑡 𝑉 ) 𝑡

𝑐

𝑡 𝑡


Its first-order condition is:

or alternatively:

Lagrange multiplier ( ), (

) is the (inverse of) relative price of consumption goods in terms

of GDP deflator, and (

) it is, also, the first-order derivative of the utility function.

Furthermore, we need to specify a utility function of the Ricardian households and take its

derivative with respect to consumption.

It is common to assume a specific form of the utility function that embodies separate effects

of consumption (as indicator of utility) and labor (as indicator of dis-utility) on household’s

utility. However, in this model a non-separable utility function is used in the form as follows:

With ( ) and ( ) are denoted habits in consumption and employment, levels of

consumption and labor are ( ) and (

), while stochastic shocks to consumption and labor

are ( ) and (

). Its first-order derivate with respect to consumption is:

If we divide it with output level in order to get utility share in output, we will end up with this

expression:

(1)

[

(

)]

[ (

)

]

This formula relies on the following approximation:

(

)

[

(

)]

ℒ𝑡 = ( 𝑡

, 1 𝑡 ) 𝑡 (

(1 + 𝑡 𝑉 𝑡

𝑡 𝑡

)

+ 𝑡 ( 𝑡+1 , 1 𝑡+1

) 𝑡+1 𝑡 ((1 + 𝑡 𝑉 ) 𝑡+1

𝑡+1 𝑡+1

)

𝜕ℒ𝑡

𝜕 𝑡

= ′ , 𝑡

(1 + 𝑡 𝑉 𝑡

𝑡= 0

𝜆𝑡 =1

1 + 𝑡𝑎𝑥𝑉𝐴𝑇∙𝑃𝑡

𝑃𝑡𝐶 ∙ 𝑈 𝑡

𝐶,𝑖

𝑡 ( 𝑡

, 1 𝑡 ) =

𝑡

{( 𝑡 𝑡 1

) [1 𝑡 ( 𝑡

𝑡 1 )

𝜅]}

1 1

1

𝑈 𝑡𝐶,𝑖 =

𝜕𝑈𝑡𝑖 𝐶𝑡

𝑖 , 1 − 𝐿𝑡𝑖

𝜕𝐶𝑡𝑖

= 𝑒𝜀𝑡𝐶 𝐶𝑡

𝑖 − ℎ𝐶𝐶𝑡−1𝑖

−𝜌 1 − 𝑒𝜀𝑡

𝐿𝜔 𝐿𝑡

𝑖 − ℎ𝐿𝐿𝑡−1𝑖

𝜅

1−𝜌


that the steady state output growth (g) mimics nominal GDP growth, and the consumption

level of one period before may be written as the current consumption divided by (

), where ( ) is the current growth rate of Ricardian households’ consumption. It is

important to notice that temporary shocks are replaced with permanent shocks ( ) and (

),

which follow random walk processes with a drift.

For Non-Ricardian households, there are no habits in consumption or any uncertainties related

to it. Therefore, we have two constraints for this type of households:

Accordingly, the utility share in nominal GDP for Non-Ricardian households is given by:

(2)

[

]

[ (

)

]

ℎ𝐶 = 0 , 𝜁𝑡𝐶 = 1

Box 7: Utility Script

UTILITY OF RICARDIAN HOUSEHOLDS // EQUATION 1

exp(LUCYN) = exp(ZEPS_C)*(exp(LCNLCSN)*(1-habe/(1+GCNLC-gy0)))^(-sigc)* (1-omege*exp(ZEPS_L)*(exp(LL)-hable*exp(LL(-1)))^kappae)^(1-sigc);

UTILITY OF LIQUIDITY-CONSTRAINED HOUSEHOLDS

// EQUATION 2 exp(LUCLCYN) = exp(LCLCSN)^(-sigc)*

(1-omege*exp(ZEPS_L)*(exp(LL)-hable*exp(LL(-1)))^kappae)^(1-sigc);

LEISURE OF RICARDIAN HOUSEHOLDS // EQUATION 3

VL = exp(ZEPS_C)*(exp(LCNLCSN)*(1-habe/(1+GCNLC-gy0)))^(1-sigc) *(1-omege*exp(ZEPS_L)*(exp(LL)-hable*exp(LL(-1)))^kappae)^(-sigc)

*kappae*omege*(exp(LL)-hable*exp(LL(-1)))^(kappae-1)*exp(ZEPS_L);

LEISURE OF LIQUIDITY-CONSTRAINED HOUSEHOLDS // EQUATION 4

VLLC = exp(LCLCSN)^(1-sigc) *(1-omege*exp(ZEPS_L)*(exp(LL)-hable*exp(LL(-1)))^kappae)^(-sigc)

*kappae*omege*(exp(LL)-HABLE*exp(LL(-1)))^(kappae-1)*exp(ZEPS_L)

LIQUIDITY CONSTRAINED CONSUMPTION // EQUATION 7

(1+tvat)*exp(LCLCSN) = ((1-TW-ssc)*WS + TRW*WS - TAXYN );

WEIGHTED CONSUMPTION // EQUATION 9

exp(LCSN)=slc*exp(LCLCSN)+(1-slc)*exp(LCNLCSN);


(1 + 𝑡𝑎𝑥𝑉𝐴𝑇) ∙Pt

c ∙Ctk

Pt ∙Yt= 1 − TAXt

W − 𝑡𝑎𝑥𝑠𝑠𝑐 + TRANtW ∙ (

W t ∙Lt

Pt ∙Yt) −

TAX tLS

Pt ∙Yt

Box 8: Equilibrium Script

EQUILIBRIUM // EQUATION 32

1 = exp(LCSN)+exp(LISN)+exp(LIGSN)+exp(LGSN)+TBYN - tbtar;

Additionally, Non-Ricardian households do not optimize, and their consumption function is

structured in a different manner. It depends on the disposable income and relative consumers’

prices:

(7)

where (𝑡 ) is VAT tax, (𝑡 ) is the social security contribution rate, ( ) and

( ) represents wage tax revenue and transfer payments that depends on the cyclical

movements of the economy, and ( ) is lump-sum tax related, inter alias, to the level of

public debt.

5.2 Equilibrium condition and consumption

So far, we have been exploring optimal behavior of Ricardian households, we have also set-

up marginal utility functions for both types of households, and indicated how distinct the

consumption pattern of Non-Ricardian households is. However, the equation for Ricardian

households’ consumption is still missing. It is important to notice that such an equation does

not exist in the model! The consumption of Ricardian households is implicitly defined by the

first-order condition (FOC) of the utility function and the general equilibrium condition.

The FOC, with respect to Ricardian consumption, is defined above. The general equilibrium

condition is written bellow and specifies that all final demand components of GDP must add

up to GDP:

(32)

𝐼

𝐼

Nominal value of private and public consumption (

), private and public

investment expenditures ( 𝐼

𝐼 ) plus trade balance in terms of domestic currency

( ) must add up to nominal GDP ( ). If this identity is divided by the nominal GDP,

the equilibrium condition in terms of shares states that all these shares must add up to one (1)

as it is written above.

General equilibrium models can be closed in two different ways, i.e. that the number of

independent equations is equal to the number of endogenous variables. The first option is that

the model is supply-driven, in which case a component of final demand must adjust itself to a

level that guarantees existence of equilibrium for the whole system of equations. The second


option is that the model is demand-driven, when components of final demand determine the

level of GDP, which is in turn adjusted to ensure the general equilibrium. QUEST_SERBIA

DSGE model is a supply-driven model. Consequently, a component of the final demand must

be adjusted to the general equilibrium condition. It can be either consumption or investment,

and, in the case of Ricardian households, it is consumption. Therefore, if we write a separate

equation for this consumption, the whole system will be over-determined, and there will be no

solution.

In the stated equilibrium equation, the total consumption is present, not its components. It is

obtained as weighted average of both types of households’ consumption shares:

𝑙𝑐

( 𝑙𝑐

where (slc) is the share of liquidity constrained consumption in the total consumption. Of

course, this equation is presented differently in the model’s script. Since level variables are in

logarithm values, the above defined equation is written as an exponential equation with

logarithm of variables as its exponents:

(9)

(

) 𝑙𝑐

(

( 𝑙𝑐 (

5.3 Investments

Ricardian households can decide to reduce their potential consumption, save a part of the

disposable income, and invest the savings in money balances, domestic and foreign bonds or

buy physical assets and rent them to production firms. First, let us rewrite the part of the

households’ optimization problem related to investments in domestic bonds:

{ } ∑ (

)

∑

( ( 𝑡

Bonds are denoted with ( ), interest rate with ( ) and tax on interest income with (𝑡

).

Discount future utility is maximized due to the constraint of discounted future income from

domestic bonds. Discount factor is ( ). Bonds have maturity of just one period t, and will be

repurchased in the period t+1.

The Lagrangian function is given by:

Its FOC with respect to domestic bonds is:

ℒ𝑡 = ( 𝑡

, 1 𝑡 ) 𝑡 (

𝑡

𝑡

(1 + (1 𝑡 𝑡𝑟) 𝑡 1) 𝑡 1

𝑡)

+ 𝑡 ( 𝑡+1 , 1 𝑡+1

) 𝑡+1 𝑡 ( 𝑡+1

𝑡+1

(1 + (1 𝑡 𝑡+1𝑟 ) 𝑡) 𝑡

𝑡+1)


Since 𝑡 , we obtain the expression for the discounting factor:

that is related to the rate of time preferences and optimality condition for investing in

domestic bonds.

Households’ optimization problem related to investing in foreign bonds can be defined in a

similar way:

{

} ∑ (

)

∑

{

( ( 𝑡

( 𝑟 (

}

Where nominal exchange rate is ( ), foreign bonds (

), (𝑟 ( ) represents unspecified

risk function, and (

) is a stochastic shock that captures uncertainties in investing in foreign

bonds.

The Lagrangian function and the FOC for this optimization problem are, respectively, given

by:

ℒ (

) {

[( ( 𝑡

] [( 𝑟 (

]

}

(

) {

[( (

][( (

]

}

𝜕ℒ

𝜕

{ [( ( 𝑡

] [( 𝑟 (

] }

The latter function has not been used to modeling foreign bonds market. Instead, a pragmatic

specification is adopted in the sense that foreign bonds are used to finance trade deficit and

cost of servicing foreign debt.

Households’ optimization problem related to capital provides the solution for relative

investment goods prices. The optimization set-up is as follows:

{ } ∑ (

)

𝜕ℒ𝑡

𝜕 𝑡

= 𝑡

𝑡+ 𝑡+1 𝑡 (

1

𝑡+1

(1 + (1 𝑡 𝑡+1𝑟 𝑡 ) = 0

𝛽 = 𝐸𝑡

𝜆𝑡

𝜆𝑡+1∙

1

1 + 𝑖𝑡∙𝑃𝑡+1

𝑃𝑡


∑ ( 𝑡

( 𝑟

𝑡

∑

{

( }

It has two constraints. The first one discounts the ith

household’s future net rental income from

capital over the infinite time period. Capital is labeled as ( ), uniform depreciation rate is

( ), prices of investment goods and GDP composite goods are ( and ), rental on capital

and tax on capital income are ( and𝑡

), and risk premium for investing in real assets

( 𝑟 ). This constrain is written in real terms, i.e. the net rental income is divided by the

GDP deflator. The second constrain refers to the accumulation process. Physical capital, at the

end of the period (t), is equal to the non-depreciated capital stock accrued up to the end of the

previous period (t-1) plus physical investments during this period ( ). This discount stream of

capital goods is accumulated over the infinite period of time.

The corresponding Lagrangian function is given by:

ℒ (

)

( 𝑡

( 𝑟

𝑡

{

( }

(

)

( 𝑡

( 𝑟

𝑡

{

( }

The FOC with respect to capital, after slight rearrangements, is:

( 𝑡 (

𝑟 𝑡

(

It postulates the relationship between Lagrangian coefficients and the relative price of

investment goods, which indicates the path of embodying technological progress.

A part of the households’ optimization problem is linked to investments. We distinguish

between real investment expenditures (𝐼 ) and physical investments (

). The real investment

expenditures with respect to capital are subject to convex adjustment costs. They are given by:

𝐼

[

(

)]

(∆

)

The complete optimization problem of households with respect to investment expenditures

reads as follows:


With corresponding Lagrangian function:

The FOC with respect to investment expenditures is:

or slightly rearranged

If we define

, and recall that discount factor beta is (

), then

the optimal level of physical investments is given by:

or

(

∆

)

∆

Investments depend on variable Qt that is called Tobin’s Qt. Tobin's Qt is the ratio between

the market value and replacement value of the same physical asset. The above equation is

rewritten in terms of growth rates as2:

(12)

( (

(

2 This equation is obtained by inserting Equation 17 into Equation 12, see Box 9.

𝑡 0 ∑ 𝑡 ( 𝑡 , 1 𝑡

) 𝑜𝑟 = 𝑗, ,∞𝑡=0

0 ∑ 𝑡 𝑡∞𝑡=0

𝑡 1𝐼

𝑡[ 𝑡

(1 +

2 (

𝑡

𝑡 1 )) +

𝐼

2(∆ 𝑡

)2]

0 ∑ 𝑡 𝑡∞𝑡=0 { 𝑡

𝑡 (1 ) 𝑡 1

}

ℒ𝑡 = ( 𝑡

, 1 𝑡 )

𝑡 𝑡 1

𝐼

𝑡[ 𝑡

(1 +

2 (

𝑡

𝑡 1 )) +

𝐼

2(∆ 𝑡

)2]

𝑡 { 𝑡 𝑡

(1 ) 𝑡 1 }

+ 𝑡 ( 𝑡+1 , 1 𝑡+1

)

𝑡 𝑡+1 𝑡

𝐼

𝑡+1[ 𝑡+1

(1 +

2 (

𝑡+1

𝑡 )) +

𝐼

2(∆ 𝑡+1

)2]

𝑡 𝑡+1 { 𝑡+1 𝑡+1

(1 ) 𝑡 }

𝜕ℒ𝑡

𝜕 𝑡 = 𝑡

𝑡 1𝐼

𝑡{1 +

𝑡

𝑡 1 + 𝐼∆ 𝑡

} + 𝑡 𝑡+1 𝑡

𝐼

𝑡+1 𝐼∆ 𝑡+1

+ 𝑡 = 0

1 + ( 𝑡

𝑡 1 + 𝐼∆ 𝑡

) 𝑡 𝑡+1

𝑡

𝑡

𝑡+1

𝑡𝐼

𝑡 1𝐼 𝐼∆ 𝑡+1

𝑡

𝑡

𝑡

𝑡 1𝐼 = 0

𝛾𝐾𝐽𝑡𝑖

𝐾𝑡−1𝑖 + 𝛾𝐼∆𝐽𝑡

𝑖 − 𝐸𝑡1

1+𝑖𝑡

𝑃𝑡𝐼

𝑃𝑡−1𝐼 𝛾𝐼∆𝐽𝑡+1

𝑖 = 𝑄𝑡 − 1


So far, Tobin’s has generally been defined in terms of relative prices of investment goods

and Lagrangian multipliers. However, this is not sufficient in order to proceed. Therefore,

Tobin’s is, separately, specified as the net present discounted value of return on capital,

corrected for capacity utilization rate and expected relative inflation of investment goods:

(13)

( 𝑡 𝑡

) (

{[ 𝑟𝑡 𝑟

𝑡

𝑡

𝑟

( 𝑡

( 𝑡 𝐼 𝐼 ] } [

( 𝑡

( 𝑡 ] ( 𝑡 𝑡

)

Finally, households may decide to hold real money balances instead of investing or

consuming their disposable income. The optimization problem, with respect to holding real

money balances, is given by:

∑ (

) 𝑜𝑟 𝑗

∑ {

}

The corresponding Lagrangian function is:

ℒ (

) {

} (

) {

}

with the first-order conditions:

𝜕ℒ

𝜕

This equation provides a general definition of the discount factor beta:

Since money does not yield any interest income, this discount factor is the same as in the case

of households’ investing in domestic bonds at the interest rate equal zero (it=0).

The model provides the amount of money consistent with general equilibrium solutions for

output and prices. Therefore, the share of money in nominal GDP depends on the interest rate

( ) and income elasticity of money ( ):

(16)

(


Box 9: Capital Script

TOBIN'S Q //EQUATION 12

gamie*(exp(LIK)-(deltae +gpop0+gy0+gpcpi0)) + gami2e*(GI-gy0-gpcpi0) - gami2e/(1+INOM)*(GI(+1)-gy0-gpcpi0) = Q - 1;

RETURN ON CAPITAL

// EQUATION 13 ETA*(1-tp)*(1-alphae)*(exp(LYKPPI)) =

Q-(1-R-deltae-rpremk-ZEPS_RPREMK-PHIPI(+1)+gpcpi0)*Q(1) + (a1e*(UCAP-ucap0)+a2e*(UCAP-ucap0)^2)*(1-tp) ;

CAPITAL GROWTH RATE

// EQUATION 17 GK-(gy0+gpcpi0) = exp(LIK) -(deltae +gpop0+gy0+gpcpi0);

PUBLIC CAPITAL GROWTH RATE // EQUATION 18

E_GKG-(gy0+gpcpi0)= exp(E_LIKG)-(deltage+gpop0+gy0+gpcpi0);

INVESTMENT SHARE

// EQUATION 19 LISN = -LYKPPI+LIK+GY0+GPCPI0-GK;

DEFINITIONS

// EQUATION 73 GI - GK(-1) = LIK - LIK(-1);

// EQUATION 74

GIG-GKG(-1) = LIKG-LIKG(-1);

Box 10: Real Money Balances Script

REAL MONEY BALANCES DEMAND //EQUATION 16

MRY = (1+INOM)^(-zete);


6 Wages

The wage rate is defined as a real wage rate (

) in terms of price of consumption goods (

),

and the nominal wage rate is ( ). The wage rate is the same across all households, assuming

that types of labor are equally distributed between them. There is another working assumption

that a trade union maximizes a joint utility function for each type of labor. Wages are, more or

less, rigid and consist of two parts. One part draws on the inherited wage rate from the

previous period, while the other part represents adjustments in the labor market:

(

Coefficient ( ) displays rigidity in the labor market as a process of inertia of real wages,

while the remaining part in the equation ( shows how real wages adapt to the

changing market conditions.

The key part of the wage adjustment process is the reservation wage. This is a level of wage

rate bellow which no one is ready to accept any jobs. By definition, the reservation wage is

the ratio between marginal dis-utility of labor (i.e. marginal utility of leisure) and marginal

utility of consumption for both types of households:

( 𝑙𝑐 𝑙𝑐

( 𝑙𝑐 𝑙𝑐

Total labor force is normalized to one (1), participation rate is (L), and (1-L) define leisure

time. Ricardian and Non-Ricardian households are indexed with (i,k), ( ) is dis-utility of

labor by ith

household and jth

type of labor, while ( ) is the corresponding utility of

consumption. If the reservation wage is equal to the actual wage, households will not supply

additional unit labor since they are indifferent between such increase in labor supply and

spending the additional income on consumption without any change in labor supply. As a

rule, the reservation wage rate deviates from the actual wage rate.

The reservation wage should be also corrected for taxes. The model assumes that the marginal

utility of leisure is taxed with a VAT rate, while the marginal utility of consumption is

defined before the wage tax. The tax factor that multiplies the reservation wage is:

𝑡

𝑡

The labor market is not a perfectly competitive market. The trade union has the market power

to enforce the wage markup ( ). The model assumes that the wage markup fluctuates around

the inverse of the elasticity of substitution between different types of labor (

). This

fluctuation depends on two factors: wage adjustment costs and the indexation formula. Only a

fraction (1-sfw) of workers are in the position to index the growth rate of wages ( ) to the

inflation in the previous period ( ). The indexation formula therefore has the following

specific form:

( ( (

(


where beta is a common discounting factor for expected wage inflation. If we combine the

long-term level of wage markup and its short-term deviations around it, we get the following

expression for the evolution of the wage markup:

(

( ( (

Let us recall from the households’ optimization problem that coefficient ( ) is the wage

adjustment cost. Now, we are ready to write, in full detail, the equation for the real wage rate

that puts together all elements of its definition:

This wage equation is rather complex. The Dynare script of the model and its algebraic

version is written in Box 11. We will, somehow, get more economic insights from it if this

equation is re-written in the following way:

(10)

( )

( )

(

(

(

( (

[(

(

]

[

(

]

Nominal GDP per wage unit is equal to net wage multiplied by the wage markup and divided

by the product of the reservation wage and the inherited wage rate from the previous period

corrected for the corresponding wage rigidity.

As already stated, the reservation wage is the ratio between marginal dis-utility of labor and

marginal utility of consumption for both types of households. Marginal utility functions were

described in the section 5.1which deals with household consumption. However, marginal dis-

utility functions remain undescribed. With respect to dis-utility of labor, the first-order

conditions for both types of households are given by:

or

𝜕𝑉𝑡𝑖 𝐶𝑡

𝑖 ,1−𝐿𝑡𝑖

𝜕𝐿𝑡𝑖 = 𝑒𝜀𝑡

𝐶 𝐶𝑡


−𝜌 1 − 𝑒𝜀𝑡

𝐿𝜔 𝐿𝑡


𝜅 −𝜌

𝑘 ∙ 𝑒𝜀𝑡𝐿𝜔 𝐿𝑡

𝑖 − ℎ𝐿𝐿𝑡−1

𝑖 𝜅−1

𝐶𝑡𝑖 − ℎ𝐶𝐶𝑡−1

𝑖

𝜕𝑉𝑡𝑖 𝐶𝑡

𝑖 ,1−𝐿𝑡𝑖

𝜕𝐿𝑡𝑖 = 𝑒𝜀𝑡

𝐶 𝐶𝑡


1−𝜌 1 − 𝑒𝜀𝑡

𝐿𝜔 𝐿𝑡


𝜅 −𝜌

𝑘 ∙ 𝑒𝜀𝑡𝐿𝜔 𝐿𝑡

𝑖 − ℎ𝐿𝐿𝑡−1

𝑖 𝜅−1

𝑊𝑡

𝑃𝑡𝑐 𝛾𝑊𝑅

𝑊𝑡

𝑃𝑡 𝑐

𝛾𝑊

𝜂𝑡𝑊

( 𝑡𝑎𝑥𝑡𝑉𝐴𝑇

( 𝑡𝑎𝑥𝑡𝑊

(( 𝑠𝑙𝑐 𝑈 𝐿 𝑡

𝑖 𝑠𝑙𝑐𝑈 𝐿 𝑡𝑘

(( 𝑠𝑙𝑐 𝑈𝑐 𝑡𝑖 𝑠𝑙𝑐𝑈𝑐 𝑡

𝑘

Sluggish

adjustment

Mark up Reservation wage

Taxes


Box 11: Wage Script

WAGE EQUATION //EQUATION 10

(1+tvat)*{[(1-slc)*VL+slc*VLLC ]/[(1-slc)*exp(LUCYN)+slc*exp(LUCLCYN)]}^(1-wrlag)*{[(1-TW-ssc)/(1+tvat)]*[(thetae-1)/thetae]/exp(LYWR(-1))/(1+GY-gy0)}^wrlag = [(thetae-1)/thetae/exp(LYWR)*(1-TW-ssc)]+ gamwe/thetae/exp(LYWR)*(1-TW-ssc)*

[(WPHI-gp0-gy0)-(1-sfwe)*(PHI(-1)-gp0)] - betae* gamwe/thetae/exp(LYWR)*[(WPHI(1)-gp0-gy0)-(1-sfwe)*(PHI-gp0)]

The algebraic counterpart of the model’s script is:

( 𝑡𝑎𝑥𝑡𝑉𝐴𝑇 [

( 𝑠𝑙𝑐 𝑈 𝐿 𝑡𝑖 𝑠𝑙𝑐𝑈 𝐿 𝑡

𝑘

( 𝑠𝑙𝑐 𝑈𝑐 𝑡𝑖 𝑠𝑙𝑐𝑈𝑐 𝑡

𝑘 ] 𝛾𝑊𝑅

[ 𝑡𝑎𝑥𝑡

𝑊 𝑡𝑎𝑥𝑆𝑆𝐶

( 𝑡𝑎𝑥𝑉𝐴𝑇) 𝜃

𝜃

( 𝑔𝑡 𝑔 𝑊𝑡

𝑃𝑡 𝑌𝑡 ]𝛾𝑊𝑅

𝜃

𝜃

𝑊𝑡

𝑃𝑡𝑌𝑡( 𝑡𝑎𝑥𝑡

𝑊 𝑡𝑎𝑥𝑆𝑆𝐶 𝛾𝑊

𝜃

𝑊𝑡

𝑃𝑡𝑌𝑡( 𝑡𝑎𝑥𝑡

𝑊 𝑡𝑎𝑥𝑆𝑆𝐶 𝑤𝑡𝜋 𝜋 𝑔 ( 𝑠𝑓𝑤 𝜋𝑡

𝜋 𝛽𝛾𝑊

𝜃

𝑊𝑡

𝑃𝑡𝑌𝑡 (𝑤𝑡

𝜋 𝜋 𝑔 ( 𝑠𝑓𝑤 (𝜋𝑡 𝜋

WAGE SHARE IN GDP // EQUATION 8

WS = exp(LL-LYWR);

To avoid the problem of non-stationarity, we need to point out that these variables are in

terms of their shares in GDP. Hence, Ricardian households’ disutility share in GDP is given

by:

(3)

𝑉

[

(

)]

[ (

)

]

(

)

Non-Ricardian households’ leisure share in GDP is given by:

(4) 𝑉

[

]

[ (

)

]

(

)

The corresponding model script is put in Box 7 in section 5.1. This completes our

presentation on the wage setting in the model.


7 Domestic and Foreign Markets

As it was already mentioned in section 4, technology plays the key role in domestic goods

market as a driving force for reduction of production costs in the sector that manufactures

investment goods. Relative price of investment goods is expressed in terms of consumers’

goods price and the state of technology, which follows random walk with a drift:

or

(

Domestic and foreign goods are present side by side in the domestic market and represent

substitute for each other. They create a composite commodity aggregated on the least cost

principle and corresponding elasticity of substitution. The price of such a composite

commodity is simply called domestic price ( ) and it is obtained as a CES aggregation of

prices from domestically produced consumption goods ( ) and imported goods (

):

(24) [ ( (

)

]

Share of exported goods in GDP is ( ), while the remaining share of imported goods is (1-

). In fact, ( ) is utility based consumer price deflator. Elasticity of substitution between

domestic and foreign goods is ( ).

Sellers charge a markup in the market for composite commodity. It is a function of the

elasticity of demand ( ) and changes in inflation discounted by the interest rate:

𝜕 𝑟

𝜕

[

𝑟

] 𝜂

The average of markup is equal to the inverse of the price elasticity of demand, i.e. the period

markups fluctuate around it. For the purposes of pragmatic modeling, an indexation process is

added up in the model assuming that only a fraction (1-sfp) of firms index price increase to

inflation in the previous period. Also, markup fluctuates over time due to random shocks that

are modelled as permanent shocks following random walk with a drift:

If we combine optimal firms’ behavior, uncertainties due to stochastic shocks and indexation

of prices to the previous inflation, we get the following expressed for the composite price

markup:


(15) 𝜂 ( ) ( ( (

It should be noted that markup also takes into account the long-run steady state rate of

inflation ( ).

On the export side, exporters purchase domestically produced goods and sell them in the

foreign markets. It is assumed that exporters have some market power in export markets and

charge a markup (𝜂 ) over domestic prices. Hence, export prices (

) are given by:

( 𝜂

Export price markup fluctuates over time due to random shocks, price adjustment costs and

some backward indexation of prices. Shocks are modelled as permanent shocks that follow

random walk with a drift:

(56)

Price adjustment costs are ( ), while a fraction of exporters ( ) is indexing changes

of prices to past inflation:

(

where ( ), (

) and ( ) are contemporary, past and expected inflation rates of export

prices. Assuming that the indexation formula refers to the steady state inflation rate ( ), the

model writes the export price as a relative price ratio of export price level to domestic

composite price deflator:

(31)

{

(

(

}

On the import side, importers also act as monopolistic competitors and charge a markup (𝜂 )

over foreign prices ( ):

( 𝜂

where ( ) import price is defined in terms of domestic currency by the means of nominal

exchange rate ( ). Since Serbia is a small country, the nominal exchange rate is defined in an

inverse manner as the amount of dinars relative to one unit of euro (RSD/EUR).

Import prices also depend on random shocks, price adjustment costs, some backward

indexation of prices and the exchange rate, since foreign prices are expressed in terms of

foreign currency. Shocks are modelled as permanent shocks that follow random walk with a

drift:

(56)


Box 12: Prices Script

PRICE MARKUP //EQUTION 15

ETA = 1 - (taue+ZEPS_ETA) - gampe*(betae*(sfpe*PHI(1)+(1-sfpe)*PHI(-1)-gp0)-(PHI-gp0));

RELATIVE CONSUMERS PRICE

EQUTION 24 exp(LPCP) = (se +(1-se)*(exp(LPMP))^(1-sigime))^(1/(1-sigime));

RELATIVE EXPORT PRICE

// EQUTION 31 exp(LPXP) = (1 + ZEPS_ETAX + gampxe*( betae*(sfpxe*PHIX(1) +

(1-sfpxe)*PHIX(-1)-gp0)-PHIX+gp0));

RELATIVE IMPORT PRICE // EQUTION 25

exp(LPMP) = (1 + ZEPS_ETAM + gampme*( betae*(sfpme*PHIM(1) + (1-sfpme)*PHIM(-1)-gp0) -PHIM+gp0))*exp(LER);

MARKUP SHOCK ON RELATIVE EXPORT PRICE

// EQUTION 56 ZEPS_ETAX = rhoetax*ZEPS_ETAX(-1)+eps_ETAX;

MARKUP SHOCK ON RELATIVE IMPORT PRICE

// EQUTION 55 ZEPS_ETAM = rhoetam*ZEPS_ETAM(-1)+eps_ETAM;

Price adjustment costs are ( ), while a fraction of importers ( ) is indexing changes

of prices to past inflation:

(

where ( ), (

) and ( ) are contemporary, past and expected inflation rates of import

prices. The real exchange rate (

) is what affects the foreign trade, not a nominal exchange

rate. Relative price ratio of import price to domestic composite price deflator is therefore

given by:

(25)

{

(

(

}

(

)

The markup on the composite good price is declared in the model as a separate endogenous

variable. The model always provides a solution for it. However, markups on export and


import goods are implicitly defined in the equations for relative export and import prices. As

for them, the model only provides solutions for their stochastic shocks, not for them per se.

Figure 2 illustrates how the model is able to replicate empirical time series relating to the key

inflation rates. Dotted lines show the estimated price series, while solid lines show the

original price series. In the case of consumers’ inflation there are some differences, while in

other cases two series are almost overlapping. This outcome includes the GDP deflator

inflation.

Figure 2: Model’s Replicates of Price Time Series

So far we have explained how domestic, export and import prices are articulated in the model.

We now proceed to determine underlying export and import functions. The aggregate import

depends on several factors including (i) the share of imported goods in the bundle of

composite commodity ( ), (ii) relative consumer and import prices (

), (iii) the lag

structure in relative prices ( ), which shows the impact of inertia on relative prices, (iv)

elasticity of substitution between bundles of domestic and foreign goods ( ), and (v) the

total demand of all agents for domestically produced consumption and investment goods

( 𝐼 𝐼

, private and public respectively:

( [

(

]

( 𝐼 𝐼

or in terms of GDP share:

(34)

( [ (

) ( (

)]

(

)

Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

0.045

Consumers inflation

Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

-0.02

0

0.02

0.04

0.06

0.08

Export price inflation

Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

-0.02

0

0.02

0.04

0.06

0.08

Import price inflation

Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

-0.01

0

0.01

0.02

0.03

0.04

0.05

Inflation


Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

-0.04

-0.02

0

0.02

0.04

0.06

Consumption growth rate

Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Export growth rate

Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

-0.35

-0.3

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Import growth rate

Q1-05 Q1-07 Q1-09 Q1-11 Q1-13

-0.04

-0.02

0

0.02

0.04

0.06

Output growth rate

(

)

The last term is modified by the targeted trade balance ( ) reflecting fundamental dis-

equilibrium in the foreign trade that Serbia can hardly overcome in the long run. This means

that whatever the relative prices are, the economy will keep running a trade deficit in the

steady state. The only doubt is how high this deficit is prevailing over the long run.

The export function is treated symmetrically and is given by the following equation:

(35)

[

(

]

(

)

Inertia in the evolution of the real exchange rate is ( ). Export depends on the ratio

between foreign and domestic output (

) corrected for the share of internal trade. Elasticity

of substitution between bundles of exported and foreign goods is ( ).

The trade balance is defined in terms of its shares in nominal GDP:

(35)

Export and import functions separately do not encompass stochastic shocks, but the trade

balance as the difference between export and import is subject to a permanent shock ( ):

(57)

Figure 3: Model’s Replicates of Growth Rates' Time Series


Figure 3 shows the model’s replicates of growth rates that correspond to the price series

plotted in Figure 2. Output and consumption growth rates are quite well simulated, while

export and import growth rates reveal some misalignments. This is something that we had to

expect if we recall structural breaks in foreign trend series in the period of the Global

recession.

8 Economic Policies

The model has been primarily created in order to evaluate fiscal policy measures in a general

equilibrium setup, but it can trace effects of monetary measures as well. The Central Bank

pursues monetary policy, while the Ministry of Finance does fiscal policy. Monetary and

fiscal measures may be dissonant since the Central Bank is institutionally independent from

the Government and may not necessarily share its priorities. If this happens, the model is able

to unveil effects of non-synchronized policy measures and help to improve the decision

making process. The Central Bank has the goal to keep inflation as low as possible. On the

other hand, the Government is to provide favorable business climate for growth and

employment. In a business cycle framework these goals may, from time to time, contradict to

each other. In any case, the model assumes that the Government sets the long-tern priorities

and adopts fiscal measures which will support their realization. First, we will explain how

monetary policy functions, and then turn to fiscal policy.

Box 13: Foreign Trade Script

IMPORT SHARE IN GDP // EQUATION 34

exp(LIMYN) = (1-se)*(exp(rhopcpm*(LPCP(-1)-LPMP(-1))+ (1-rhopcpm)*(LPCP-LPMP)))^sigime*exp(LPMP-LPCP)*(exp(LCSN)

+exp(LISN)+exp(LIGSN)+exp(LGSN))-tbtar;

EXPORT SHARE IN GDP // EQUATION 35

exp(LEXYN) = se*exp(rhopwpx*(LER(-1)* se)+ (1-rhopwpx)*(LER* se))^sigexe*exp(LYWY) ;

TRADE BALANCE

// EQUATION 33 TBYN = exp(LEXYN)-exp(LIMYN) + ZEPS_EX ;

TRADE BALANCE SHOCK

// EQUATION 57 ZEPS_EX = rhoexe*ZEPS_EX(-1)+eps_EX;


8.1 Monetary Policy

Monetary policy is thought-out as a rule based policy following a well-known Taylor rule.

The Central Bank adjusts its policy interest rate (repo rate) in order to achieve inflation target

rate ( 𝑡𝑡 𝑟 𝑡

) over the mid-term. If expected inflation rate ( ) is above the target, the

Central Bank will increase the policy rate, causing the real interest rate to increase and reduce

final demand. This will ease the pressure on price increase and help to bring expected

inflation in line with the target. Coefficient ( ) represent the Central Bank’s averseness

against inflation.

The Central Bank also monitors the output gap3. If the output gap is positive, indicating

heating of the economy and pressuring prices up, it will also increase the repo rate. The model

simulates this policy by using logarithms of the output gap. If the output gap, as a deviation

over the long-run trend, was positive in the previous period ( its logarithmic value is also

positive and a penalty coefficient ( ) will be applied to increase the interest rate. Also, if the

rate of change of the output gap increases ( ), the same penalty coefficient will be used:

(30) ( ) [(

) 𝑡

𝑡 𝑟 𝑡 (

𝑡𝑡 𝑟 𝑡

)

(

]

The nominal interest rate also depends on the real interest rate. However, the part of the

Taylor rules ((

) 𝑡

𝑡 𝑟 𝑡) takes care of the steady state real interest rate, but not of the

period real interest rate. The rationality behind this is that the nominal interest rate oscillates

around the long run real interest rate if expected inflation coincides with the target inflation

rate, what should happen in the steady state. The period real interest rate (𝑟 ), known as the

Fisher’s real interest rate, will be defined below. And finally, interest rate evolution should be

smooth in order to be able to reflect monetary realism in which there aren't any extreme

jumps or drops in the repo rate. Coefficient of inertia ( ) does the task of smoothing the

interest rate response to the inflation and output gap. Finally, the whole process is subject to

stochastic shocks ( ).

Figure 4 shows impulse response functions that reveal a traditional response of inflation and

output growth to an increase in the policy interest rate. For effectiveness of the monetary

policy, it is absolutely important that increase in the interest rate is sufficiently high to be able

to generate adequate rise in the real interest rate and contraction of the output. The real

exchange rate appreciates as well. This effect is implied in the uncovered interest rate parity

setup:

(36)

𝑟

3 We have defined the output gap in section 2.


2 4 6 8 10 12 14 16 18 20-6

-5

-4

-3

-2

-1

0

1

2

3

4x 10

-4 GDP growth rate

2 4 6 8 10 12 14 16 18 20-3

-2.5

-2

-1.5

-1

-0.5

0

0.5x 10

-4 Overall inflation rate

2 4 6 8 10 12 14 16 18 20-6

-5

-4

-3

-2

-1

0

1x 10

-3 Real exchange rate

2 4 6 8 10 12 14 16 18 20-2

0

2

4

6

8

10

12

14

16x 10

-4 Real interest rate

Figure 4: IRFs to a Monetary Shock of One Standard Deviation

The parameter ( ) represents disparity between inverse domestic and foreign time

preference rates:

The domestic nominal interest rate is adjusted for the real rates disparity. Alternatively, the

expected change in the nominal exchange rate depends on the differential between domestic

and foreign interest rates reduced for the real interest rates gap:

𝑟

It is subject to stochastic shock (

) and two additional factors. The one factor refers to

the share of stock of the sovereign debt in GDP (

). If this share increases (

(

), the country’s borrowing risk rises, and the interest rate has to go up.

Parameter (𝑟 ) captures this risk premium.

The stock of sovereign debt accumulates over time on two accounts. Firstly, it depends on the

real interest costs of financing the previous level of sovereign debt. Secondly, it increases if

the country runs trade deficit. We get the net foreign liabilities ( ) by adding up amounts

of these two components. The evolution of net foreign liabilities with respect to nominal GDP

is given by:

(37)

(


The other factor is the country specific characteristic of the institutional setup. The domestic

rate of time preference is permanently lower than the foreign rate of time preference. For

some reasons, residents of the country value present consumption over future consumption

much higher than foreigners. Therefore, the domestic real interest rate is permanently higher

than the foreign real interest rate. Free movement of capital across borders is not able to fix

these differences and to equalize real interest rates. This gap is captured by parameter ( ).

The uncovered interest rate parity rule assumes free movement of (short-term) capital across

the borders. It is also assumed that all other interest rates follow the path of the policy interest

rate. Hence, curing inflation by using the policy interest rate might be costly in terms of

forgiven output and an increase in the trade deficit due to real appreciation of the exchange

rate. This is a typical trade-off between inflation and growth.

The real interest rate (𝑟 ) is defined in terms of expected inflation:

(21) 𝑟

Box 14: Inflation Targeting Script

TAYLOR RULE // EQUATION 30

INOM = ilage*INOM(-1)+(1-ilage)*((1/betae-1) + zphit + tinfe*(PHIC-zphit) + tye1*LYGAP(-1) ) + tye2*(LYGAP-LYGAP(-1)) + ZEPS_M;

UNCOVERED INTEREST RATE PARITY

// EQUATION 36 INOM = INOMW + GE(+1) + E_ZEPS_RPREME +

time_pref_diff + rpreme*(BWRY-BWRY(-1));

NET FOREIGN LIABILITY // EQUTION 37

BWRY = (1+INOM-PHI(+1)-GY-GPOP0)*BWRY(-1) + TBYN - tbtar;

UTILITY-BASED TIME PREFERENCE RATE //EQUATION 5

1/BETAE-1 = GUC(1) + INOM - PHIC(1);

DEFINITION OF THE UTILITY GROWTH RATE //EQUATION 6

LUCYN-LUCYN(-1) = GUC + SIGC*(GY-GY0 - PHIC + PHI);

FISHER’S EQUATION OF REAL INTEREST RATE // EQUATION 21

R = INOM(1)-PHI(1);

EXCHANGE RATE CHANGE // EQUATION 23

GE + PHIW-PHI = LER-LER(-1) ;


and it is related to the rate of time preference and expected change in the consumers’ utility

(

):

(5)

The model also assumes that the purchasing power parity (PPP) rule prevails in the steady

state. By definition, the rate of change of nominal exchange rate is:

(23)

(

) (

)

The following PPP condition holds in the steady state:

(

)

Let us notify that the exchange rate policy is not discretionary based, and there are therefore

no specific measures that the Central Bank may launch in the case of a need (like

interventions in the foreign exchange market in the country). The exchange rate policy is a

passive policy under control by the inflation targeting policy measures.

8.2 Fiscal Policy

Fiscal policy is not only rules based, and in some cases it is discretionary. Fiscal policy

mostly responds to an output gap indicator of the business cycle, but not all the time. To

explain this, let us start with the expenditure side. Government expenditures are government

spending on consumer goods, government investments and transfer payments:

𝐼

Government consumption is directly exposed to changing business cycle conditions. This is

modeled by its temporary deviations around the long run growth rates:

(39)

(

) [ (

) (

)

]

[ ( )

(

)]

or

∆

∆

∆

∆


where (

) is the deviation of the government consumption growth rate around

the steady state GDP growth rate; (

) is the target share of government consumption in

GDP. Parameter ( ) indicates the level of inertia in the reaction process, while parameter

( ) captures delay with which the fiscal response to an output gap takes place. The

remaining parameter ( ) measures the speed of adjustment of temporary deviations to the

target share of government consumption in GDP. Finally, the whole process is subject to

permanent stochastic shocks ( ).

The response of government investments to changing business conditions is formulated in a

symmetric way:

(40)

( )

[ (

) (

)

]

[ ( ) (

)]

or

∆ ∆

∆

∆

where (

) is deviation of the government investment growth rate

around the steady state GDP growth rate corrected for the embodied technological progress;

(

) is the target share of government investment in GDP. It is assumed no inertia in this

process, while parameters ( ), and (

) capture some delays in adjustment to the policy

target and frictions in responding to the output gap.

The transfer payment system may act as an automatic stabilizer in a business cycle by

coupling the income for unemployed people and for pensioners with the actual realization of

wage payments in the economy. This role of transfer system is not yet fully incorporated in

the model. For now, we assume that the Government regards the share of transfer payments in

GDP as a decision variable, and on top of that, it provides income for unemployed people:

(42)

(

)

(

The target share of transfer payments in GDP is ((

)

), the target labour participation

rate is ( ), while parameter (b) measures the generosity of the social safety nets. The whole

process is subject to a stochastic shock ( ).

Let us now turn to the revenue side. Government revenue ( 𝑉 ) is collected from taxes on

labour income (including social security contributions), consumption, and profit, as well as

from lump-sum taxes:

𝑉 (𝑡

𝑡 𝑡 𝑡

𝑡


Social security contributions, value-added tax and tax on profit are linear and their average

rates are fixed independently of business cycle conditions (𝑡 ,𝑡 ,𝑡 ). The labour

income tax is progressive and its first-order Taylor expansion around zero output gap is:

(44) 𝑡

Parameter ( ) captures the degree of progressivity of the labor income tax. Let us recall

that this tax serves as an automatic stabilizer during business fluctuations.

Finally, a lump-sum tax is included in order to facilitate the Government to control public

debt. The Government sets the target share of public debt in GDP ( ). If the realized

share of public debt in GDP in the previous period is higher than the target debt-to-GDP ratio,

the Government will apply addition tax rate ( ). Also, the Government monitors the trend of

debt-to-GDP ratio. If this ratio is increasing, meaning that the rate of its change is positive

(∆ (

)), the Government will charge addition taxes by the rate ( ):

(43) ∆𝑡 (

) ∆ (

)

The burden of the lump-sum tax falls on consumers and their disposable income.

The lump-sum tax points out the existence of the public debt. It has two parts. The first part in

equation (38) refers to costs of servicing the debt that is already incurred, while the second

part adds up to the stock of public debt and is due to fiscal deficit.


Box 15: Fiscal Policy Script

PUBLIC CONSUMPTION GROWTH RATE // EQUATION 39

GG-gy0 = gslag*(GG(-1)-GY0) + gvecm*(LGSN(-1)-log(gsn)) + g1e*(LYGAP-LYGAP(-1)) + ZEPS_G

PUBLIC INVESTMENT GROWTH RATE

// EQUATION 40 GIG-gy0-gpcpi0 = (GIG(-1)-gy0-gpcpi0)+ igvecm*(LIGSN(-1)-log(igsn))

+ ig1e*(LYGAP-LYGAP(-1)) + ZEPS_IG

RELATIVE GROWTH OF PUBLIC INVESTMENTS // EQUATION 41

GIG-GI = LIGSN-LISN-LIGSN(-1)+LISN(-1);

TRANSFER PAYMENTS RELATED TO WAGE BILL // EQUATION 42

TRW = trsn + tr1e*(1-exp(LL)-(1-L0)) + ZEPS_TR;

LUMP-SUMM TAXES SHARE IN GDP NOMINAL // EQUATION 43

TAXYN -TAXYN(-1) = bgadj1*(exp(LBGYN(-1))-bgtar) +bgadj2*(exp(LBGYN)-exp(LBGYN(-1)));

TAXES ON WAGES

// EQUATION 44 TW=tw0*(1+tw1*LYGAP);

SOVEREIGN DEBT TO GDP RATIO // EQUATION 38

exp(LBGYN) = (1+INOM-gp0-GY-gpop0)*exp(LBGYN(-1))+exp(LGSN) + exp(LIGSN) + E_TRW*exp(LL-LYWR)

-(TW+ssc)*WS -tp*(1-WS) -tvat*exp(LCSN) - TAXYN + EPS_BG ;

DEFIN ITIONS:

RATIO OF TRANSFER PAYMENTS TO GDP // EQUATION 45

TRYN = TRW*exp(LL-LYWR) ;

RATIO OF NET TRANSFER PAYMENTS TO GDP // EQUATION 46

TRTAXYN = TRW*exp(LL-LYWR) - TAXYN;

NET WAGE SHARE TO GDP // EQUATION 47

WSW = (1-TW-ssc)*WS;

.


Public debt is a policy variable, and is subject to decision making process. The model is still

not open to financial sector and the only way to manage the public debt is by fiscal and

monetary policy measures. A fact that is usually neglected in Serbia is that the monetary

policy influences the public debt as well. It is clear from the above equation that monetary

policy may manage the real interest rate and consequently the cost of servicing it. On the

other hand, the Taylor rule reveals that dynamics of public debt has a feedback effect on the

level of the interest rate. Hence, coordination between monetary and fiscal policy is a must,

and the model may provide useful information on that account

9 The Rest of the World

Serbia is a small open economy that highly depends on business cycle conditions in the rest of

the world (ROW). The European economy is the ROW economy for Serbia. More precisely, it

is the Euro Zone for which we take data from the ECB web site. We use a simple unrestricted

VAR model with one period lag to model the Euro Zone economy independently from all

other variables in the model. As it is well known, the VAR approach is treating every

endogenous variable in the model as a function of the lagged values of all of the endogenous

variables in the model. It is able to trace the dynamic impact of random disturbances on the

system of variables. Variables for the Euro Zone are interest rate ( ), inflation (

) and

GDP growth rate ( ). It is also included a link between the EU output and the Serbian

output (

). The coefficient of interest (𝑟 ) is set exogenously, and at a very low level

indicating almost irrelevant influence of the Serbian economy on the EU economy. On the

other hand, the EU economy substantially influences the Serbian economy through the

channel of export. The EU provides foreign demand for domestically produced commodities.

The VAR model has the following form:

(22) ( 𝑟 𝑟

𝑟 ( 𝑟 (

(26) 𝑟 (

𝑟 ( 𝑟 (

(48)

𝑟 (

𝑟 ( 𝑟 (

𝑟 ( (

) (

))

After all, VAR coefficients are estimated in a separate file, they are included in the model file

in the corresponding equations as calibrated parameters.


10 Steady State

QUEST_SERBIA follows the main lines of modeling provided in the QUEST III model.

However, it is not a copy-paste version of the original for a good reason. Serbia is a small

open economy which reacts differently to external shocks. Frictions in the adjustment process

are due to the institutional setup and unfinished transition to a market economy. Contrary to

this, the EU economy is a large open economy with full mobility of capital, goods and

financial assets that adjusts more-or-less smoothly to the changing conditions in the

international market. Differences in the size and adjustment costs are taken into account in

defining steady state properties of the Serbian economy.

On the other hand, data set underlying the QUEST III model is much richer than our data set.

The European Commission originally estimated the model using quarterly data for the period

from Q1Y1978 to Q4Y2007, which implies 149 data points. In our case, due to data

constraints, we use only 43 data points and estimate the model from Q1Y2003 to Q3Y2013. It

is interesting to note that the first release of quarterly GDP data disaggregated by final use

was in April 2013 (a year before the date of this paper).

Finally, parameters in the model are modified to fit the macroeconomic properties of the

Serbian economy. In few cases, we have initially relied on similar parameter values as in the

QUEST III. Since these parameters are overridden by the Bayesian estimation based on

Serbian empirical framework, a possible bias is afterwards substantially reduced, if not

completely eliminated. In most cases, however, we use separate small econometric models

with Serbian data to estimate parameters at hands. The steady state parameters are partly

based on the econometrics and partly on the theory. In the following part, we will underline

four fundamental specifics of the QUEST_SERBIA model relating to the model’s steady state

properties.

Box 16: The ROW Script

FOREIGN INTEREST RATE // EQUATION 22

INOMW = (1-rii)*EX_INOMW + rii*INOMW(-1) + rip*(PHIW(-1)-gpw0) + rix*(GYW(-1)-gyw0) + EPS_INOMW;

THE ROW INFLATION

// EQUATION 26 PHIW-gpw0 = rpi*(INOMW(-1) - EX_INOMW)

+ rpp*(E_PHIW(-1)-gpw0) + rpx*(E_GYW(-1)-gyw0) + EPS_PW;

THE ROW GROWTH RATE // EQUATION 48

GYW-gyw0 = rxi*(INOMW(-1) - EX_INOMW) + rxp*(PHIW(-1)-gpw0) + rxx*(GYW(-1)-gyw0) + rxy*(LYWY(-1)-lywy0)+ EPS_YW ;


There is no mobility of financial capital across borders without frictions, and households that

save income and invest in domestic and foreign bonds face no pressure to adjust their

intertemporal preferences. Therefore, the real interest rate in Serbia is permanently above the

EU real interest rate. Additionally, the real interest rate convergence between two real interest

rates cannot be detected over past ten years. This means that the rate of time preference in

Serbia is permanently lower than in the EU. In terms of utility, domestic households value

present income over future income much more than their counterparts in the EU. This is given

by:

𝑟 𝑟

and

𝑟 𝑟

where ( ) is the difference in inverse rates of time preferences or the difference in

domestic and foreign real interest rates that are determined by corresponding time preference

rates. Quite differently, the QUEST III assumes that steady state domestic and foreign rates of

time preference are equal. That implies:

We cannot employ the same assumption in this model, because there is a permanent gap

between domestic and foreign rates of time preference. These rates are plotted in Figure 5 as

Hodrick-Prescott trends for the period Q1Y2003-Q3Y2013. We see no tendency that the

Serbian time preference series was converging to the EU counterpart. The gap between them

was narrowing between 2006 and 2009, but afterwards it was increasing. The model’s

consequence is that the uncovered interest rate parity rule has to be modified to accommodate

time preference differences (see Equation 36).

0.980

0.984

0.988

0.992

0.996

1.000

03 04 05 06 07 08 09 10 11 12 13

EU

Serbia

Figure 5: Trend Time Preference Rates


There is also no perfect mobility of goods and services across borders. Due to transaction

costs and markups, domestic inflation is permanently higher than foreign inflation. In the

steady state these differences are bound to vanish if the purchasing power parity holds.

However, this does not hold in Serbia and the QUEST_SERBIA has to respect this fact. Even

in the steady state, the rate of inflation in Serbia is higher than in the EU. The QUEST III, on

the other side, assumes zero difference between these two rates ( ):

Trends of quarterly inflation rates in Serbia and the Euro Zone are plotted in Figure 6. Over

the past ten years there were no significant convergence episodes between these two inflation

rates. Significant part of prices in Serbia is under administrative control. These prices are

related to services that state-owned enterprises (SOE) provide to the public. SOEs are

notoriously overstaffed and inefficient. Until a comprehensive reform of the state sector is

undertaken, it would be hard to expect a lower inflation pressure. This is rationality behind

our assumption that in the long run Serbian inflation must be higher than in the ROW.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

03 04 05 06 07 08 09 10 11 12 13

EU

Serbia

Perc

en

t

Figure 6: Trends of Quarterly Inflation Rates in Serbia and the Euro Zone

The QUEST III states the trade balance is zero in Europe in the long run. The Serbian case is

quite the opposite; it is hard to assume that the Serbian economy will balance exports and

imports over next ten years. The steady state value of the trade balance will stay negative. The

only doubt is how negative it will be.

Figure 7 shows Hodrick-Prescott trend component of the trade balance as a share in GDP in

Serbia in the period between Q1Y2003 and Q3Y2013. The trade balance was improving in

the second part of the observed period, and especially in 2013. However, it is still deeply

below 10% of GDP. Equation 32 (in Box 8) and Equation 34 (in Box 13) are effected by the

presence of the permanent trade deficit.

Finally, the Serbian economy grew faster than the average EU economy from the beginning of

the period under study until the emerging of the Global recession. This was an indicator that

smaller and underdeveloped economies must grow faster than mature developed economies in

order to catch up with them. This is the core of the theory of growth convergence. However,


Serbian economy was badly affected by the Global recession. Since then, its growth rates are

lower than comparative growth rates in the EU. This is revealed in Figure 8.

-23

-22

-21

-20

-19

-18

-17

-16

03 04 05 06 07 08 09 10 11 12 13

Perc

en

t o

f G

DP

Average

Figure 7: Trend of Trade Deficit in Serbia

This fact shows some consequences in our modeling. The QUEST_III model assumes that

steady state growth rates of Europe and the ROW are equal to each other:

This assumption does not hold for Serbia. We need to employ a different assumption that

steady state growth rates may not converge to each other over the long-run:

(49) (

-0.4

0.0

0.4

0.8

1.2

1.6

2.0

03 04 05 06 07 08 09 10 11 12 13

Qu

art

erl

y g

row

th r

ate

s

EU

Serbia

Figure 8: Trends of Quarterly GDP Growth Rates in Serbia and the EU


The model is a forward looking DSGE model. One needs to envisage future changes in the

development of Serbia and to incorporate adequate modifications in the model structure.

Depending on this judgment, the value of convergence parameter will be chosen. It will affect

relationship between domestic and foreign outputs in the model (see Equation 47 in Box 17).

Apart from the modeling side, this one of the key decision variables and the Government has

to set it when adopting the mid-term policy priorities and policy measures.

11 Steady state solution

The information set behind a steady state solution of the model is hierarchical. It starts with

the rest of the world long run restrictions imposed upon the domestic economy, and ends up

with growth rates, nominal shares, and parameters derived from the specifics of the model.

There are, in the middle, restrictions due to policy priorities, the theoretical foundation,

empirical evidences and modelers’ perception of the actual economy.

Let us start with the rest of the world restrictions. This model is based on intertemporal

choices of households, who discount their utility over time with respect to consumption and

leisure, and derive from these decisions individual consumption and investment functions that

are afterwards aggregated into corresponding macroeconomic functions. Discounting utility

does not only describe how households actually make intertemporal choices, but provides the

key input for macroeconomic modeling and public policy. On this account, the rate of time

preference gets the instrumental role in defining domestic and foreign interest rates. Present

goods are more valuable than future goods. Preferences for future goods are lower than

preferences for present goods. The rate of time preference must be lower than one (β < 1).

Central banks can manipulate with nominal interest rates through open market operations and

the policy interest rate, but have not direct command over the real interest rate. Recall

equation (5) from our model to demonstrate this important fact:

(5)

Box 17: Steady State

CONVERGENCE

// EQUTION 49 LYWY-LYWY(-1)= convergence *GYW -GY;

// STEADY STATE EQUATION

PERMANENT INFLATION DIFFERENCE

gp0 = price_diff + gpw0;


The real interest rate ( ) depends not only on expected inflation, but also on expected

change of utility and the time preference rate ( ). The rate of time preference is outside of

reach of the monetary authorities and is subjectively determined by the actions of millions of

households.

In the steady state equation (5) is modified to the following expression:

(5ꞌ)

since there is no change in utility in the long run, and ( ) and ( ) are steady state nominal

interest rate and inflation in our model, respectively. However, people in the EU have higher

time preferences ( ) than people in Serbia, even if they face the similar long run restriction:

(5ꞌꞌ)

The value for ( ) is given to the EU monetary authority, while the long run rate of inflation

( is set as its long run policy priority. We take both of them from the QUEST III model.

Then, the steady state nominal interest rate ( ) is directly obtained from equation (5ꞌꞌ).

Altogether, their values are:

We assume that these values are known to the Serbian authorities, which put them as

exogenous variables into the QUEST_Serbia model. This is not all, since one more exogenous

variable should be given to the model. The variable in question is the long run GDP quarterly

growth rate in the EU:

[ ] = [0.0046]

The vector [ ] is on the top position in the information set that we need in order

to define the steady state of the model. The next level of information deals with the policy

priorities. The Serbian authorities have to set in advance where the economy will be in the

long run compared to the EU economy as the benchmark. They have to decide on three key

parameters: (i) the convergence rate, (ii) the time preference difference, and (iii) the inflation

differential, which are given by:

(

Based on this policy decision we adopt the following vector of steady state variables:


The third level of information set is based on the assumptions related to technology, and the

population growth:

The relative inflation in the investment goods sector is equal to the long run technology

progress ( ). This means that technology ceases to improve in the long run. On the

other hand, population is Serbia keeps to decline even in the long run by the quarterly

exponential rate of -0.000901.

The next level of information reveals the remaining policy choices. They refer to various

targets as the public debt to GDP ratio, the trade balance to GDP ratio, and the transfer

payments to GDP ratio:

𝑡 𝑡𝑟

We now move to other steady state variables that are derived from the higher level in the

hierarchy of steady state variables. Growth rates of all GDP components are determined by

the real GDP growth rate:

[

]

The steady state growth rate of investment includes the technology progress:

The steady state growth rates of capital, and public capital and public investment refer to the

steady state growth rate of investment:

[

]

The remaining steady state growth rates are set to zero:

[ ]

Also, related per capita growth rates are calculated by adding the population growth rate to

the original growth rate. For instance, the per capital consumption growth rate is given by:

All of the per capita growth rates are reported in Table 1.

The steady state inflation rate of the GDP deflator defines the steady state of all other inflation

rates in the model:

Nominal wage inflation rate is given by:


The technology growth is determined by the Cobb-Douglas function, which steady state

version is given by:

(20ꞌ) ( ( ( (

Its solution is:

(20ꞌ)

Equation (37) defines the nominal net foreign liability share in GDP. Its steady state version is

given by:

(37ꞌ)

(

This implies a steady state level for the nominal trade balance share:

(37ꞌꞌ)

(

This share is equal to the target steady state level of trade balance:

if (

). The QUEST III model assumes a zero level of the steady state trade balance, but

it also leads to the same steady state share of NFL in GDP. Hence, the existence of a

permanent trade deficit does not make here a difference.

The next three steady state conditions are related to relative price ratios of import, export and

consumer price levels to the GDP deflator level. The relative import price equation (25) has

the following steady state version, if we recall that , and in the

steady state:

(25ꞌ)

( ( (

)

The steady state real exchange rate (

) is given by:


(25ꞌꞌ)

The relative export price equation (31) has the following steady state version, if we recall that

holds in the steady state:

(31ꞌ)

( (

with a solution

(31ꞌꞌ)

Finally, the relative consumer price ratio is given by the steady state version of equation (24):

(24ꞌ)

[ ( (

)

]

The steady state import share in GDP is derived from the steady state version of equation (34)

as:

(34ꞌ)

( (

)

(

)

The steady state export share in GDP is a residual determined by steady state conditions for

import and trade balance:

(35ꞌ)

The QUEST III model has differently determined the steady state conditions for export and

import shares in GDP. Firstly, from equation (34) and (35) it is derived corresponding steady

state shares for import and export in GDP under assumption that the relative foreign to

domestic output is normalized to one (

). Secondly, in the uncovered interest rate parity

equation (36) it is assumed that the domestic rate of time preference is equal to the one of the

rest of the world ( ), and that the domestic nominal interest rate is also equal to the


rest of the world’s nominal interest rate ( ) in the steady state. Put together these

assumptions lead to determination of the trade balance share in GDP at zero level in the

steady state.

We use Tobin’s Q to derive a steady state share of nominal capital in the GDP. Tobin’s Q

equation (13) has the steady state version according to the following formula:

(13ꞌ) ( 𝑡 (

𝐼 ( 𝑟 𝑟

In the steady state mark-up is ( ) from equation (15), and ( ) by the assumption,

which put together transform equation (13ꞌ) into the following steady state condition (13ꞌꞌ) for

the nominal capital share in GDP:

(13ꞌꞌ)

( ( 𝑡 ) (

(

𝑟 )

From this condition, the steady state nominal share of investment in GDP is derived in a

straightforward way:

𝐼

𝐼

The steady state capital accumulation implies that rental rates for private and government

capital are set equal to the corresponding depreciation rates:

and

The wage share is given by:

(

where parameter ( ) is set to match the average wage share in GDP. The QUEST III model

sets alpha value at the level to match the wage share at the end of the sample. This approach

would be appropriate for Serbia if the wage share was a stationary series. However, due to the

Global recession, the wage share in Serbia has an inverse U shape with the peak in Q4Y2007.

Since then, the wage share was constantly decreasing with a cyclical pattern. We expect the

wage share to stabilize in years to come at a historic average figure. Also, a part of the wage

bill was hidden in the net mixed income of the entrepreneurial sector due to a specific tax

system in Serbia. We have added all the entrepreneurial net income to the wage bill. This has

lifted up the value of parameter alpha.

The steady state of employment rate is set at 0.65 as it has been adopted by the QUEST III

model. The model can easily accept a higher rate of employment, but it is not realistic to

expect such a scenario. In any case, whatever is the steady state employment rate, this rate

sets restriction on parameter omega ( ), which is the key parameter in the wage equation

(10):

𝜅 ( (


where the auxiliary parameter (A) is:

𝑡 𝑡

𝑡

( 𝑙𝑐

( 𝑙𝑐

( 𝑙𝑐

( 𝑙𝑐

This relation relies on the steady state solutions for related equations (1)-(4), (7), (9) and (32):

(1ꞌ)

[

( ]

(

(2ꞌ)

[

]

(

(3ꞌ) 𝑉

[

( ]

( (

(4ꞌ) 𝑉

[

]

( (

(7ꞌ)

( 𝑡 𝑡

𝑡

(9ꞌ)

( 𝑙𝑐

𝑙𝑐

(32ꞌ)

𝐼

𝐼

These equations take the following tax rates:

𝑡 𝑡 𝑡 𝑡 𝑡

The remaining tax rate is a lump-sum tax. Its steady state rate is a residual derived from

equation (38). It depends, among other factors, on the target level of debt to GDP ratio

(

𝑡 𝑟 𝑡). This level is legally set in Serbia to 45 percent at the annual level, but it is beyond

the reach in practice. More realistic (not without some degree of hopefulness) is 60 percent.

(38ꞌ)

(𝑟

(𝑡

𝑡

𝑡 (

) 𝑡


Policy priorities are revealed by the following target shares:

[(

)

(𝐼

)

]

Finally, the steady state capacity utilization rate is set to one:

We present in Table 2 the complete list of values assigned to calibrated parameters, and the

expected levels of steady state variables that we discussed above.

Table 2: Calibrated parameters and steady state variables

Declared

symbols

Algebraic

symbol Parameters Value

alphae α Elasticity of output with respect to labour 0.7263

alphage αG Share of private capital 0.9

betae β Rate of time preference 0,986

bgadj1 τB Public debt penalty parameter 0.000004

bgadj2 τDEF

Fiscal correction parameter 0.04

bgtar Target public debt to GDP ratio 0.60

deltae δ Depreciation rate 0.025

deltage δ G Public capital depreciation rate 0.0125

e_ex_inomw Steady state foreign nominal interest rate 0.0090

e_ex_r r Real interest rate consistent with the time

preference rate 0.0142

e_ex_rw 𝑟 Foreign real interest rate consistent with the time

preference rate 0.0040

gp0 π Steady state quarterly inflation rate 0.0096

gpcpi0 Steady state rate of technology progress 0

gpop0 λpop

Steady state population growth rate -9.0100e-04

gpw0 πW

Steady state quarterly foreign inflation rate 0.0050

gsn (

)

Target share of government consumption in GDP 0.2067

glfp0 Steady state rate of labour augmented technology

progress 0.0060


gy0 g Steady state GDP growth rate 0.0069

gyw0 gW

Steady state foreign GDP growth rate 0.0046

ilage Inertia in the evolution of nominal interest rate 0.85

igsn (𝐼

)

Target share of government investment in GDP 0.0250

l0 L Participation rate 0.65

ler0 𝑙 (

Logarithm of the PPP real exchange rate 0

lol LH Logarithm of steady state overhead labour 0

lywy0 𝑙 (

)

Logarithm of steady state foreign to domestic

output 0

omege ω

Derived parameter from utility and leisure

functions as well as wage equation, which

supports the steady state labour participation rate

1.5220

rhoppi1 The first lag of technology progress weights 0.2480

rhoppi2 The second lag of technology progress weights 0.1374

rhoppi3 The third lag of technology progress weights 0.1048

rhoppi4 The fourth lag of technology progress weights 0.0928

rhoexe Inertia in evolution of the export permanent shock 0.9750

rholol Inertia in the evolution of overhead labour 0.99

rii 𝑟 Foreign interest lagged parameter in VAR model

of foreign interest 0.9266

rip 𝑟 Foreign price lagged parameter in VAR model of

foreign interest 0.3285

rix 𝑟 Foreign output lagged parameter in VAR model of

foreign interest 0.3513

rpi 𝑟 Foreign interest lagged parameter in VAR model

of foreign prices -0.0138

rpp 𝑟 Foreign price lagged parameter in VAR model of

foreign prices 0.5784

rpx 𝑟 Foreign output lagged parameter in VAR model of

foreign prices 0.0979

rxi 𝑟 Foreign interest lagged parameter in VAR model

of foreign output -0.0171

rxp 𝑟 Foreign price lagged parameter in VAR model of

foreign output -0.5284

rxx 𝑟 Foreign output lagged parameter in VAR model of

foreign output 0.7828

rxy 𝑟 Domestic output lagged parameter in VAR model

-0.0000001


of foreign output

ssc τ SSC

Social security contribution 0.15

taue τ Tax on markup 0.10

tp τ pf

Tax on profit 0.15

thetae θ Elasticity of substitution between various variety

of labour 1,60

tinfe ϕπ Parameter of Central Bank’s aversion on inflation 5.00

trsn TRAN Steady state unemployment and pensions

compensation rate to wage bill 0.2384

tvat τ VAT

Value-added tax 0.1136

tw0 Linear tax rate on wages 0.0730

tw1 Progressive tax rate on wages 0.80

ucap0 gUCAP

Steady state rate of capacity utilization 1

zete μ Interest semi-elasticity od demand for real money

balances 0.4

12 Results of the steady state solution

Results of the steady state solution, based on calibrated parameters and steady state levels of

endogenous variables, are presented in Table 3. To get these results, we need to write two

separate MATLAB files. In the first one all parameters are declared and the corresponding

values should be assigned to them. The second file is more important. In this file all steady

state relations between endogenous variables must be explicitly written. Most of them were

indicated above as equations with a prime sign. We should note that endogenous variables

must have the steady state counterparts assigned to them either by a simple link to one

previously declared variable or by a derived expression. Writing such a file is probably the

most challenging task in practical DSGE modeling.

Table 3: Steady state solution for variables

Declared variables Values Algebraic symbols or

expressions Description

BGYN 0.60

Share of government debt in

nominal GDP

BWRY 0 𝑙

Share of net foreign liability in

GDP

CLCSN 0.5960

Liquidity constrained

consumption share in nominal

GDP


DBGYN 0 𝑙 (

) 𝑙 (

)

Change in the share of

government debt in nominal

GDP, i.e. Fiscal deficit

ETA 0.90 𝜂 Price markup

LER 0 𝑙 (

Logarithm of the real exchange

rate

GC 0.0069 Growth rate of consumption

GCL 0.0060 Growth rate of aggregate

consumption per capita

GCLC 0.0069

Growth rate of consumption

liquidity constrained

households

GCNLC 0.0069

Growth rate of consumption

liquidity non-constrained

households

GE 0.0046 Nominal exchange rate growth

GEX 0.0069 Export growth rate

GEXL 0.0134 Export growth rate per capita

GG 0.0069

Growth rate of government

consumption

GGL 0.0060


consumption per capita

GI 0.0069 Growth rate of investments

GIG 0.0069


investments

GIL 0.0060 Growth rate of investments per

capita

GIM 0.0069 Import growth rate

GIML 0.0246 Import growth per capita

GK 0.0069 Capital growth rate

GKG 0.0069 Government capital growth rate

GL 0 Employment growth rate

GSN 0.2067

Share of government

consumption in nominal GDP

GTAX 0.0165 Lump sum tax growth

GLFP 0.0059 Labor factor productivity

growth


GTFPUCAP 0.0043 Total factor productivity

growth

GTR 0.0069 Transfer payments growth

GUC 0 Utility growth

GUCAP 0 Capacity utilization growth

GWRY 0 𝑙 (

) 𝑙 (

)

Growth rate of real GDP per

real wage rate

GY 0.0069 GDP growth rate

GYL 0.0060 GDP per capita growth rate

GYPOT 0.0069 Potential GDP growth rate

GYW 0.0046 Foreign GDP growth

INOM 0.0238 Domestic nominal interest rate

INOMW 0.0090 Foreign nominal interest rate

LBGYN -0.5108 𝑙 (

)

Logarithm of government debt

in nominal GDP

LCLCSN -0.51738

Logarithm of the share of

consumption liquidity

constrained households in

nominal GDP

LCNLCSN -0.5098

Logarithm of the share of

consumption liquidity non-

constrained households in

nominal GDP

LCSN -0.5135

Logarithm of aggregate


GDP

LEXYN -0.7717 (

Logarithm of export share in

nominal GDP

LGSN -1.5764

Logarithm of government


GDP

LIGSN -3.6888 𝐼

Logarithm of government

investment share in nominal

GDP

LIMYN -0.4907

Logarithm of import share in

nominal GDP

LIK -3.4730 𝑙 (𝐼

Logarithm of investment

expenditures to capital ratio


LIKG -3.9888 𝑙 (𝐼

Logarithm of investment to

capital ratio in the government

sector

LISN -1.7722 𝑙 ( 𝐼

Logarithm of investment share

in nominal GDP

LL -0.4307 𝑙 ( Logarithm of employment rate

LL0 -0.4307 𝑙 ( Logarithm of steady state

employment rate

LOL 0 ( Logarithm of labour overhead

LPCP 0 𝑙 (

Logarithm of consumption

price to GDP deflator ratio

LPMP 0 𝑙 (

Logarithm of import price to

GDP deflator ratio

LPXP 0 𝑙 (

Logarithm of export price to

GDP deflator ratio

LTRYN -1.8587 𝑙 (

Logarithm of transfer payments

to GDP ratio

LUCYN 5.2954 𝑙 (

Logarithm of liquidity non-

constrained consumption utility

in nominal GDP

LUCLCYN 1.5163 𝑙 (

Logarithm of liquidity

constrained consumption utility

in nominal GDP

LYGAP 0 𝑙 ( Logarithm of output gap

LYKPPI -1.7008 𝑙 (

Logarithm of nominal output to

nominal capital ratio

LYWR -0.0056 𝑙 (

Logarithm of real GDP to real

wage ratio

LYWY 0 𝑙 (

Logarithm of foreign to

domestic GDP ratio

MRY 1.0094 ln(

Logarithm of real money

balances share in GDP

PHI 0.0096 Overall inflation or the rate of

growth of GDP deflator

PHIC 0.0096 Consumption inflation

PHIPI 0 Investment inflation deflator

PHIM 0.0096 Import deflator inflation

PHIML 0.0056 Import deflator inflation

corrected for intra trade level


PHIW 0.0050 Foreign inflation

PHIX 0.0096 Export deflator inflation

PHIXL 0.0056 Export deflator inflation

corrected for intra trade level

Q 1 Tobin's Q

R 0.0141 𝑟 Real interest rate

TAXYN 0.1206

Nominal lump sum tax to GDP

ratio

TBYN -0.1500 𝑡

Target nominal trade balance to

GDP ratio

TRTAXYN 0.0351

Transfer payments net of lump

sum tax to GDP ratio

TRW 0.2384

Transfer payments to wage bill

share

TRYN 0.1558 𝑡𝑟

Transfer payments share in

GDP

TW 0.0730 𝑡 Tax on wages

UCAP 1 Capacity utilization

UCAP0 1 Steady state capacity utilization

evolution

VL 46.6276 𝑉 Value of leisure Ricardian

households

VLLC 7.0471 𝑉 Value of leisure of liquidity

constrained households

WPHI 0.0165 Nominal wage inflation

WRPHI 0.0069 Rate of growth of real wages

WS 0.6537

Gross wage share

WSW 0.5079 ( 𝑡 𝑡

Net (after taxes and

contributions) wage share in

GDP

ZPHIT 0.0096 Inflation target

LCY -0.5135 𝑙 (

Logarithm of real consumption

to real GDP ratio

LGY -1.5764 𝑙 (

Logarithm of real government

consumption to real GDP ratio

LWS -0.4251 𝑙 (

Logarithm of gross wage share

ZEPS_C 0 Utility of consumption shock


ZEPS_ETA 0 Price markup shock

ZEPS_ETAM 0 Import price markup shock

ZEPS_ETAX 0 Export price markup shock

ZEPS_EX 0 Trade balance shock

ZEPS_G 0 Government spending shock

ZEPS_IG 0 Government investment shock

ZEPS_L 0 Leisure shock

ZEPS_M 0 Monetary shock

ZEPS_PPI 0 Technology shock

ZEPS_RPREME 0 Interest parity risk premium

shock

ZEPS_RPREMK 0 Capital risk premium shock

E_ZEPS_TR 0 Transfers shock

E_ZEPS_W 0 Labour demand shock

EXYN 0.4622

Share of export in nominal

GDP

IMYN 0.6122

Share of import in nominal

GDP

EXCHR 1

Real exchange rate

PMP 1

Import price to GDP deflator

ratio

PXP 1

Export price to GDP deflator

ratio

CY 0.5983

Consumption share in GDP

13 Prior distribution and posterior estimation

The QUEST_Serbia follows the QUEST III model’s approach that structural coefficients are

estimated using the Bayesian technique. The model runs DYNARE toolbox that was

developed for MATLAB software. DYNARE is a software platform for handling a wide class

of economic models, in particular dynamic stochastic general equilibrium (DSGE) models

relying on the rational expectations hypothesis (Adjemian et al, 2011).

Structural coefficients in a DSGE model differ from calibrated coefficients in the following

way. As for calibrated coefficients, there is no uncertainty about their value. From the

modeling point of view, information on them is collected from the outside of the model and


afterwards inserted into the model as exogenously fixed quantity. This quantity usually relies

on econometrically estimated coefficients providing the adequate data set and econometric

models. Quite the opposite, the structural coefficients ( ) are treated as stochastic variables

due to uncertainty about their value. As for any stochastic variable, before the data are

approached, the modeler has to assign to them his or her subjective prior distribution π( ), 0

≤ ≤ 1 with the standard errors ( ). Bayesian inference centers on the posterior distribution,

π( ǀy), which is the distribution of the random variables , conditioned on having observed

the data y. As there are many structural parameters in the model, the posterior distribution is

the joint distribution of all the parameters, conditioned on the observed data. The observed

data in our case are quarterly data on the Serbian economy from Q1Y2003 to Q4Y2013. The

set of structural coefficients is listed in Table 4.

Table 4: Priors and Posteriors

Declared

symbols

Algebraic

symbol Parameters

Distri-

bution

Prior

mean

Prior

st.dev.

Poste-

rior

mean

Poste-

rior

st.dev.

a2e γ2UCAP

Cyclical rate of capacity

utilization beta 0.05 0.02 0.0573 0.024

g1e

Parameter of public

consumption adjustment to

output gap

beta 0 0.60 0.0411 0.060

gami2e γI Non-linear part in the

investment adjustment costs gamma 5 20.00 5.4373 1.000

gamie γK Linear part in the investment

adjustment costs gamma 7 10.00 7.1777 1.000

gamle γL Parameter for labour


gampe γP Parameter for price


gampme γPM

Parameter for import price


gampxe γPX

Parameter for export price


gamwe γW Elasticity of wage inflation gamma 2 20.00 0.921 1.000

gslag

Inertia in government

consumption beta 0 0.40 -0.0325 0.040

gvecm

Penalty parameter for

missing government

consumption target

beta -0.5 0.20 -0.5244 0.020

habe hC Habits in consumption beta 0.7 0.10 0.6996 0.010

hable hL Habits in leisure beta 0.8 0.10 0.806 0.010

igvecm

Penalty parameter for

missing government

investment target

beta -0.5 0.20 -0.498 0.020

ig1e Parameter of public beta 0 0.60 0.0273 0.050


investment adjustment to

output gap

kappae k Elasticity of labour supply gamma 1.25 0.50 1.2528 0.050

rhoce

Inertia in evolution of the

consumption permanent

shock

beta 0.5 0.08 0.4843 0.050

rhoeta


price markup permanent

shock

beta 0.5 0.20 0.0851 0.200

rhoetam


import price markup

permanent shock

beta 0.85 0.08 0.8788 0.050

rhoetax


export price markup

permanent shock

beta 0.85 0.08 0.8172 0.050

rhoge


government consumption

permanent shock

beta 0.5 0.20 0.6121 0.075

rhoig


government investment

permanent shock

beta 0.85 0.08 0.7667 0.075

rhol0

Inertia in the evolution of

steady state employment beta 0.95 0.02 0.9809 0.020

rhole Inertia in the permanent

employment shock beta 0.85 0.08 0.9655 0.075

rhopcpm γPCPM

Coefficient of inertia of the

ratio of domestic prices to

import prices

beta 0.5 0.20 0.4382 0.050

rhopwpx γPFPX

Coefficient of inertia of the

ratio of domestic prices to

export prices

beta 0.5 0.20 0.4879 0.050

rhorpe γrprem

Coefficient of inertia in the

permanent shock of the

country risk premium

beta 0.85 0.08 0.9872 0.075

rhorpk γrpremK

Coefficient of inertia in the

permanent shock of the

equity premium

beta 0.85 0.08 0.9498 0.075

rhoucap0

Drift parameter in AR(1)

process of capacity

utilization

beta 0.95 0.02 0.9322 0.020

rpreme 𝑟 Country risk premium beta 0.02 0.01 0.0357 0.008

rpremk 𝑟 Equity risk premium beta 0.02 0.01 0.03 0.008

se sM

Share of import goods in the

composite good basket beta 0.538 0.08 0.7189 0.080

sfpe sfp

Share of firms that adjust

prices to the expected

inflation

beta 0.3 0.20 0.3022 0.050


sfpme sfpM

Share of importers that adjust

import prices to the expected

inflation

beta 0.5 0.20 0.5641 0.050

sfpxe sfpX

Share of exporters that adjust

export prices to the expected

inflation

beta 0.5 0.20 0.6277 0.050

sfwe sfw

Share of employers that

adjust wages to the expected

inflation

beta 0.4 0.20 0.348 0.050

sigc σC

Elasticity of substitution

between consumption and

leisure

gamma 3 1.00 2.7892 0.500

sigexe σX


between domestic and

exported goods

gamma 1.25 0.50 1.4935 0.500

sigime σM


between domestic and

imported goods

gamma 2.25 0.50 1.1423 0.500

slc sls

Share of liquidity constrained

households in the total

number of households

beta 0.3 0.10 0.2299 0.050

tr1e b Cyclical unemployment and

pensions compensation rate beta 0.1 0.60 0.0743 0.050

rhotr γTRAN

Inertia in evolution of

permanent shock on transfer

payments

beta 0.85 0.08 0.9447 0.075

tye1 Interest rate reaction to

output gap beta 0.3 0.20 0.3486 0.075

tye2 Interest rate reaction to

output gap change beta 0.1 0.20 0.1393 0.075

wrlag γwr Rigidity of real wages beta 0.2 0.20 0.1765 0.075


Figure 9: Priors and Posteriors


Table 5: Posterior estimation of temporary shocks

14 Replicates of time series

The model estimates the expected value of variables given the information available at the

current date (Etyt). We compare empirical time series with the model’s updated time series.

Results are reported in Figures 10 to 14. This is a visual check of the goodness of fit of the

model. Estimated series are plotted as dotted lines, while original time series are plotted as

solid lines.

We are satisfied how the model replicates empirical time series. There are two cases,

however, for further consideration. One is related to foreign trade. The export and import

functions should be fine-tuned in order to better represent sudden changes in the international

trade as it was the break out of the Global recession. The other is related to transfer payments.

We have included in the transfer data all payments for social and unemployment benefits as

well as for pensions. It seems that this aggregate transfer payment was decoupled from the

wage bill in the middle of the period under consideration, and this has been never corrected up

to the end of the period. Benefit entitlements were created independently from the wage bill

Shocks Prior

mean Posterior mean

90% HPD*

interval

Prior

distribution

Posterior

deviation

eps_C 0.050 0.1522 0.1444 0.1604 gamma 0.030

eps_ETA 0.100 0.1084 0.0662 0.1542 gamma 0.060

eps_ETAM 0.020 0.0697 0.0664 0.0722 gamma 0.015

eps_ETAX 0.100 0.1388 0.124 0.1632 gamma 0.060

eps_EX 0.005 0.0191 0.0152 0.0229 gamma 0.030

eps_G 0.050 0.0416 0.037 0.046 gamma 0.030

eps_IG 0.050 0.0538 0.0529 0.055 gamma 0.030

eps_L 0.050 0.1152 0.1086 0.1221 gamma 0.030

eps_LOL 0.005 0.0125 0.0096 0.0163 gamma 0.003

eps_M 0.003 0.0139 0.0127 0.0154 gamma 0.002

eps_RPREME 0.005 0.0157 0.0141 0.0175 gamma 0.003

eps_RPREMK 0.005 0.0221 0.0193 0.0253 gamma 0.003

eps_TR 0.050 0.0119 0.0113 0.0133 gamma 0.030

eps_W 0.050 0.0593 0.0386 0.0804 gamma 0.030

eps_Y 0.050 0.0441 0.0331 0.056 gamma 0.030

eps_BG 0.050 0.0507 0.0412 0.0595 gamma 0.030

* HPD is Highest Posterior Density


development. This part of the exogenous transfer payment should be better modeled in the

future.

Q1-06 Q1-09 Q1-12

0.3

0.4

0.5

0.6

Public debt

Q1-06 Q1-09 Q1-12

0.01

0.02

0.03

0.04

Consumers inflation

Q1-06 Q1-09 Q1-12

0.76

0.78

0.8

0.82

0.84

0.86

0.88

Consumption

Q1-06 Q1-09 Q1-12

-0.04

-0.02

0

0.02

0.04

0.06

Consumption growth rate

Q1-06 Q1-09 Q1-12

-0.04

-0.02

0

0.02

0.04

0.06

Consumption per capita growth rate

Q1-06 Q1-09 Q1-12

-0.05

0

0.05

0.1

Exchange rate growth rate

Q1-06 Q1-09 Q1-12

0.18

0.19

0.2

0.21

Government consumption

Q1-06 Q1-09 Q1-12

-0.05

0

0.05

0.1

Government consumption growth rate

Q1-06 Q1-09 Q1-12

-0.05

0

0.05

0.1

Government consumption per capita growth rate

Q1-06 Q1-09 Q1-12

0.022

0.024

0.026

0.028

0.03

Government investment

Q1-06 Q1-09 Q1-12

-0.15

-0.1

-0.05

0

0.05

0.1

Government investment growth rate

Q1-06 Q1-09 Q1-12

-0.1

0

0.1

0.2

Export growth rate

Q1-06 Q1-09 Q1-12

-0.1

0

0.1

0.2

Export per capita growth rate

Q1-06 Q1-09 Q1-12

-0.02

0

0.02

0.04

0.06

0.08

Export price inflation

Q1-06 Q1-09 Q1-12

-0.02

0

0.02

0.04

0.06

0.08

Export price per capita inflation

Q1-06 Q1-09 Q1-12

-0.3

-0.2

-0.1

0

0.1

Import growth rate

Q1-06 Q1-09 Q1-12-0.4

-0.3

-0.2

-0.1

0

0.1

Import per capita growth rate

Q1-06 Q1-09 Q1-12

-0.02

0

0.02

0.04

0.06

0.08

Import price inflation

Figure 10: Consumption and government block of variables

Figure 11: Foreign trade block of variables


Q1-06 Q1-09 Q1-12

-0.02

0

0.02

0.04

0.06

0.08

Import price per capita inflation

Q1-06 Q1-09 Q1-12

-0.01

0

0.01

0.02

0.03

0.04

0.05

Inflation

Q1-06 Q1-09 Q1-12

0.025

0.03

0.035

0.04

0.045

0.05

Interest rate

Q1-06 Q1-09 Q1-12

0.16

0.18

0.2

0.22

0.24

0.26

Investment

Q1-06 Q1-09 Q1-12

-0.1

-0.05

0

0.05

0.1

Investment goods inflation

Q1-06 Q1-09 Q1-12

-0.2

-0.1

0

0.1

0.2

Investment growth rate

Q1-06 Q1-09 Q1-12

-0.2

-0.1

0

0.1

0.2

Investment per capita growth rate

Q1-06 Q1-09 Q1-12

0.68

0.69

0.7

0.71

0.72

0.73

Labor

Q1-06 Q1-09 Q1-12

-0.06

-0.04

-0.02

0

0.02

Labor growth rate

Q1-06 Q1-09 Q1-12-0.04

-0.02

0

0.02

0.04

0.06

Output growth rate

Q1-06 Q1-09 Q1-12

-0.04

-0.02

0

0.02

0.04

0.06

Output per capita growth rate

Q1-06 Q1-09 Q1-12

0.78

0.8

0.82

0.84

0.86

Real consumption share in GDP

Q1-06 Q1-09 Q1-12

0.19

0.2

0.21

0.22

Real government consumption share in GDP

Q1-06 Q1-09 Q1-12

0.9

0.95

1

1.05

1.1

Real wage share

Q1-06 Q1-09 Q1-12

0.92

0.94

0.96

0.98

1

Relative consumption prices

Q1-06 Q1-09 Q1-12

0.85

0.9

0.95

1

Relative export prices

Q1-06 Q1-09 Q1-12

0.85

0.9

0.95

1

Relative import prices

Q1-06 Q1-09 Q1-12

0.14

0.15

0.16

0.17

0.18

0.19

0.2

Transfer payments

Figure 12: Investment and labor block of variables

Figure 13: Output and price block of variables


15 Impulse Response Functions

The QUEST_Serbia can be represented in a generic DSGE form, i.e. in a structural form as

the following:

(1) (

where are endogenous variables, are stochastic shocks:

(

(

A reduced form of the model (1) provides the solution of the system of equations in terms of a

steady state ( ), reduced form coefficients ( ) and ( ), state variables ( ) and the period

shocks ( ):

(2)

with that is called variable gaps.

By solving the model, Dynare retrieves reduced form coefficients ( ) and ( ). The solution

equations (2) are called decision or transition functions. The IRF of a variable ( ) responding

to a shock ( ) is obtained from the transition functions (2) in a consecutive way. At the first

Q1-06 Q1-09 Q1-12-0.1

-0.05

0

0.05

0.1

Transfer payments growth rate

Q1-06 Q1-09 Q1-12

0.21

0.22

0.23

0.24

0.25

0.26

Transfers to wages

Q1-06 Q1-09 Q1-12

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

Wage inflation

Q1-06 Q1-09 Q1-12

0.65

0.7

0.75

Wage share

Q1-06 Q1-09 Q1-12

-2

0

2

4

6

8

10

x 10-3 Foreign inflation

Q1-06 Q1-09 Q1-12

2

4

6

8

10

12

x 10-3 Foreign interest rate

Q1-06 Q1-09 Q1-12

-0.01

0

0.01

0.02

Foreign output growth rate

Q1-06 Q1-09 Q1-12

0.95

1

1.05

1.1

Foreign over domestic output

Q1-06 Q1-09 Q1-12

0.75

0.8

0.85

0.9

0.95

1

Real exchange rate

Figure 14: Wage and ROW block of variables


step in the period t=1, the steady state value for responding variable is included in calculation

and the initial value of the ith

shock is added up ( 𝑜 𝑡 )4

. The second step is

performed in the period t=2. The shock is set to zero ( ) and the value of ( ) is taken

from the previous step. Then the value for is obtained by applying equation (2). At the

third step, the second step calculation is repeated for a number of periods t=1,2,…,n (for

instance n=20 corresponds to a five year time horizon if time series have quarterly

frequencies).

IRFs are an important analytical tool used to reveal properties of a DSGE model. They outline

behaviour of endogenous variables subject to external shocks, conditioned on the model

specification. We will demonstrate usefulness of IRFs by applying this tool to analysing

monetary policy based on inflation targeting. As it is well known, the National Bank of

Serbia, as many other central banks, use open market operations and the policy of repo rate to

control money demand, inflation and inflationary expectations. The repo policy is based on a

simple Taylor rule, which takes into account only expected inflation. If expected inflation is

above the inflation target, the NBS will increase the repo rate. All other short term interest

rates on the money market and in the commercial banks’ sector adjust to its level within a

band. The long-term interest rate also adjust to this level with some lags. The current repo rate

is set at 9.5 %, while the current inflation rate is 2.5%. The mid-term target inflation rate is

4.5% with +/-2.5% band. The NBS does not care about effects of such a high interest rate on

the real sector performance. It cares only about a pass-through effect of the nominal exchange

rate on inflation. Therefore, it uses a rather high repo rate to prevent unexpected increases in

the nominal exchange rate that might put on threat price stabilization. However, the NBS has

never assessed how costly such a policy may be.

4 The quantity of a shock must be set by a modeler. Usually, it is set to one or a standard deviation of the variable

in question.

Figure 15: IRF of the GDP growth rate to a monetary shock of one

standard deviation

0 5 10 15 20-6

-4

-2

0

2

4x 10

-4 Output growth rate

0 5 10 15 20-6

-4

-2

0

2x 10

-3 Real exchange rate

0 5 10 15 20-1

0

1

2

3x 10

-3 Domestic interest rate

0 5 10 15 20-3

-2

-1

0

1

2x 10

-4 Inflation


We simulate impacts of a one standard deviation monetary shock, i.e. unexpected increase in

the repo rate of the magnitude corresponding to one standard deviation. Then, we track this

impact on output growth rate, interest rate, inflation and real exchange rate. Figure 15 shows

outcomes.

The graphs represent deviation of variables around their steady states. Due to interest rate

inertia, the QUEST_Serbia model simulates rather smooth and slow return of the repo rate to

its steady state5. Inflation rate will immediately fall down, due to revised inflationary

expectation, and will keep decreasing for some time. The effect of a one-off rise of the repo

rate will generate longer off-equilibrium adjustment in the good market than in the money

market. A high repo rate policy causes real depreciation of the exchange rate. The real

exchange rate falls sharply below the steady state, but rather quickly return to it (after five

periods, which coincides with the adjustment period of the repo rate). The pattern of output

growth is interesting one. An immediate effect of the output is that it shrinks due to a

reduction in the aggregate demand. However, the output growth resumed in the third period,

and after additional three periods it returns to the steady state. The overall effect on output is,

however, negative: a restrictive monetary policy is costly in terms of unrealized output. IRF

analysis persuasively supports this inference.

16 Decomposition of IRFs

In most cases results of an IRF analysis are self-evident and expected by theory and

experience. However, there are some exceptional cases which raise doubts and call for

additional clarification. One of these cases is the pattern of output growth adjustment to a

monetary shock indicated above. Why did not output also smoothly adjust to the steady state?

How is possible to have episodes of output growth? Are there other forces triggered by a

monetary shock, which drive output adjustment? Those are some questions that should be

answered.

In order to address these questions, we innovated IRF analysis. The idea is very simple. If

there is a procedure to decompose shocks contributions to the total variance of a variable, why

not realize the similar idea and decompose individual contributions of all endogenous

variables to the total IRF value. The size of IRF at each point of time is the general

equilibrium effect that a stochastic shock generate on an endogenous variable. Decomposition

of an IRF would trace partial equilibrium effects of all the other variables through time. We

did this exercise and report its results in Figure 16.

5 The repo rate represents all other interest rates in the system.


There are 43 variables that directly or indirectly influence IRF of the output growth to a

monetary shock (‘the IRF’ in the rest of this chapter). There is no sense to keep partial

equilibrium effects for all of them. We sort their overall effects for each of them by the sign

and the size, and extract the four most influential variables with positive effects on the IRF,

and four most influential variables with negative effects on the IRF. Their bar graphs are in

Figure 26. The line represents the overall IRF, while the dark brown bar stands for effects of

the excluded variables.

In the first period only output growth directly and negatively responded to the shock. All

other variables did not influence it, but were by themselves adjusted to the same shock. In the

second period they started to generate feedback effects on the output growth. Mostly these

effects were negative. Especially, appreciation of the real exchange rate strongly reduced the

output growth. The interest rate continued to penalize output growth, and kept this influence

for the next three period, albeit at a decreasing pace. In the fifth period its impact completely

died out, which makes sense because at that point the interest returned to the steady state. The

relative import prices also, due to an exchange rate appreciation, negatively influenced the

output growth. This effect was present in three consecutive periods. Finally, there was an

effect due to the business cycle. The monetary shock triggered the output gap which, in turn,

pull down the output growth. Unfavourable circumstances lasted for four periods and died

out at the same time as negative effects of the interest rate.

So much for the negative drivers of output growth. There are the positive drivers as well, but

initially their contributions were smaller compared to the negative ones. Among positive

drivers the most important was foreign demand, i.e. the relative foreign to domestic output. It

contributed almost all of the time to a positive side, but stronger in the initial five periods.

Surprisingly, a better utilisation of capacity assisted the output growth in the initial four

periods. The (probably) lower real wage cost all the time supported the output growth. But its

influence was rather modest one. The excluded factors played strong role in the first three

periods and substantially contributed to the output growth to recover in the third period. After

6 One needs a color print out to distinguish between different contributions.

Figure 16: Decomposition of the IRF of GDP growth to a monetary shock

for the most influential eight variables


that, the relative import prices changed the role and started to support the output growth.

Since the real appreciation of exchange rate ceased, the relative import prices supported the

output growth between the fifth and the twelfth period. On the other hand, all excluded factors

change their role and counterbalanced the output growth.

17 Sensitivity Analysis

A DSGE model (1) can we re-written as:

(3) (

This form emphasizes the role of structural parameters ( ) in solving the model. More

precisely, we are now interested in a relationship between the reduced form coefficients,

which solve the model, and the structural parameters that drive this solution. This relation can

be investigating with respect to different forms of the model ‘output’ (to use Ratto’s term).

One model ‘output’ Y(.) may be the IRF as indicated in equation (4):

(4) (

The other model ‘output’ may be the partial equilibrium effect of a predetermined variable on

another endogenous variable given by (5):

(5) (

To proceed on, we will specify equation (4) as to encompass IRF of the GDP growth rate to a

monetary shock ( ( )), and follow the sensitivity analysis developed by Ratto and the

Dynare team (Ratto, 2008, Ratto and Iskrov, 2011). The sensitivity analysis is based on the

estimation of a non-parametric regression model on the Monte Carlo sample used for

simulating IRF of the GDP growth rate to a monetary shock. The cornerstone of this analysis

is the mapping

(6) (

( ∑ (

where ( is the mean of Y, u is the residual of the non-parametric regression model,

and ( ( are the non-parametric regression terms for each model

parameter, i.e. the conditional expectation of Y, given .The ( terms provide the best

least-squares predictors of Y, based on univariate functions of single model parameters.


We draw 512 Monte Carlo samples of the structural coefficients from posterior ranges

obtained after estimating the QUEST_Serbia model using Serbian data for the period between

Q1Y2003 and Q4Y2013. Let us now consider a relation between the growth rate and the

monetary shock, which we already investigated above. Panel (a) in Figure 17 shows the

histogram of the posterior uncertainty distribution of the first period response of the GDP

growth rate to a monetary shock. The mode of the histogram is on the negative part. Under the

posterior assumptions, implied by the model structure and posterior distributions, the model puts a

very larger probability for a negative initial response of the growth to a stabilization monetary

policy.

We skip explanation of Panel (b) in Figure 17 for a moment, and turn to analyse the reduced

form coefficients effects on the relationship between GDP growth rate, on one hand, and

nominal interest rate, inflation and real exchange rate, on the other. For that purpose we

appropriately change Dynare script to adjust the equation (5). These relations are at the core

of the inflation targeting monetary policy. One should expect that an initial increase in the

interest rate drives down the GDP growth rate. Panel (a) in Figure 4 indeed reports a high

level of probability that this will happen. However, the National Bank of Serbia (NBS)

usually neglects this effect of the monetary policy and focus only on its anti-inflationary

effects. Therefore, the NBS is much more concerned with a negative effect of inflation on

growth. That concern is supported by Panel (b) in Figure 18, which shows the extremely high

probability that inflation negatively effects GDP growth. This is the main argument used by

the NBS to justify its restrictive monetary policy. Panel (c) in Figure 18 requires some

clarification before interpretation. The real exchange rate is set in a logarithmic value, and

defines in such a way that any increase of its value implies depreciation of the real exchange

rate ( ( ( ( ( ). Since the mode of the histogram is far away

on the negative side, there is a high probability that depreciation of the real exchange rate will

negatively impact the GDP growth rate.

Now, we will return to Panel (b) in Figure 18. The mode of the histogram is almost set at zero

point, and the shape of the histogram looks like a Gaussian. One can infer from it that there is

equal probability that a monetary shock either depreciate or appreciate the real exchange rate.

It is interesting to note that this conclusion is not fully supported by Figure 1 and IRFs

-5 -4 -3 -2 -1 0 1 20

10

20

30

40

50

60E_GY vs. E_EPS_M, log(-Y)

-4 -3 -2 -1 0 1 2 30

10

20

30

40

50

60

70E_LER vs. E_EPS_M, log(-Y)

Panel (a): GDP growth vs. monetary shock

Y=(gt vs. ui)

Panel (b): Real exchange rate vs. monetary

shock Y=(zt vs. ui)

Figure 17: Histogram of the MC sample of the reduced form coefficient

driving the relationship between GDP growth rate and the real exchange

rate versus monetary shock


reported there. The IRF of the real exchange rate to a monetary shock shows the strong

appreciation effect for initial four periods.

Sensitivity analysis can indicate which parameters are the most important for driving the

model ’output’. Let’s consider again IRFs as the model ‘output’, particularly the relationship

between the GDP growth rate and a monetary shock. Given the model structure, the model

‘output’ of Y depends on the values of , as indicated by equation (6). It is already

mentioned that the ( terms provide the best least-squares predictors of Y, based on

univariate functions of single model parameters. Using ANOVA technique, it is possible to

obtain variance for each of the k parameters, which facilitate measuring the importance of

parameter on the variation of Y. The total variance (𝑉( ) is a sum of the all partial variances

(𝑉( ). The ratio between a particular variance and the total variance is a natural measure of

its sensitivity index ( ). Dynare also includes covariance effects and normalize the partial

variances, and gets the final form of sensitivity indices as:

(𝜕

𝜕 )

𝑉(

𝑉(

These indices provide the percentage of the model ‘output’ variance which is explained by

each parameter.

We plot in Figure 19 sensitivity indices of the key parameters driving the reduced form

coefficient effects on the relationship between GDP growth rate versus a monetary shock

(Panel a) and between the real exchange rate and a monetary shock (panel b).

-6 -5 -4 -3 -2 -1 0 1 20

10

20

30

40

50

60E_GY vs. E_INOM, log(-Y)

-7 -6 -5 -4 -3 -2 -1 0 1 20

5

10

15

20

25

30

35

40

45

50E_GY vs. E_PHI, log(Y2)

-3.5 -3 -2.5 -2 -1.5 -1 -0.5 00

5

10

15

20

25

30

35

40

45E_GY vs. E_LER, log(Y)

Panel (a): GDP growth versus

interest rate Y=(gt vs. it-1)

Panel (b): GDP growth versus

inflation Y=(gt vs. πt-1)

Panel (c): GDP growth versus real

exchange rate, Y=(gt vs. zt-1)

Figure 18: Histograms of the MC sample of the reduced form coefficients that effect the

relationship between GDP growth rate and nominal interest rate, inflation and real exchange

rate, respectively

0

0.1

0.2

0.3

0.4

0.5

ILA

GE

SIG

EX

E

RH

OP

WP

X

GA

MP

E

TIN

FE

GA

ML

E

SE

A2

E

SIG

C

SF

PE

log E_GY vs. E_EPS_M

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

ILA

GE

TIN

FE

SIG

EX

E

GA

MP

E

SE

TY

E2

RH

OP

WP

X

GA

MP

ME

SIG

IME

A2

E

log E_LER vs. E_EPS_M

Panel (b): GDP growth vs. Monetary shock Panel (b): Real exchange rate vs. monetary shock

Figure 19: Sensitivity indices of the key parameters driving the reduced form coefficient

effects on relationship between endogenous variables vs. stochastic shocks


The interest rate inertia parameter (ILAGE) in the Taylor rule is a calibrated parameter. It is the

most important parameter in the process of obtaining IRF of the GDP growth rate to a

monetary shock. Since this parameter is calibrated, but not estimated parameter, this

information is of the utmost importance for proper modelling the Serbian economy. It

explains more than 40% of the all variance in that particular IRF. The next to it by importance

is the parameter which represents the elasticity of substitution between bundles of exported

and foreign goods (SIGEXE). It explains around 20% of the total variance. The parameter

which captures inertia in adjustment process of relative foreign-to-export prices (RHOPWPX)

explains 7% of the total variance, while the price adjustment cost parameter is at the fourth

place (GAMPE) with the explanatory power of 5.5%.

The inertia parameter in the Taylor rule is also the most important parameter which influences

IRS of the real exchange rate to a monetary shock. Is explains more than 60% of the total

variance in this relationship. The next two parameters have much lower influence. Each of

them separately explains 8% of the total variance. One is the target inflation rate (TINFE), and

the other is the elasticity of substitution between domestic and foreign goods.

Since the most important parameters are detected by the size of sensibility indices, we can

now plot the estimates of entire function ( for each parameter. In Figure 20 we show these

plots for the most important parameters driving the GDP growth response to a monetary shock

(red lines). Dotted (blue) lines show the width of the 90% confidence bands of the estimated non-

parametric curves. The values in the y axis show by how much a monetary shock can change the

value of the GDP growth rate (with respect to its posterior mean values) by varying each single

parameter.

All parameters, but three out of twelve, display a strong non-linear pattern. They either

increase or decrease approaching the upper bound of their posterior distribution. The two

most influential parameters – the inertia in the interest rate and the substitution between

0.4 0.5 0.6 0.7 0.8 0.9-1

-0.5

0

0.5

1

1.5

2

ILAGE, Si=0.42

2 4 6-1.5

-1

-0.5

0

0.5

SIGEXE, Si=0.22

0.3 0.4 0.5 0.6 0.7-0.6

-0.4

-0.2

0

0.2

0.4

RHOPWPX, Si=0.07

2 4 6 8 10 12 14-0.6

-0.4

-0.2

0

0.2

0.4

GAMPE, Si=0.06

3 4 5-0.4

-0.2

0

0.2

0.4

TINFE, Si=0.04

2 4 6 8 10 12 14-0.2

0

0.2

0.4

0.6

GAMLE, Si=0.03

0.2 0.4 0.6 0.8-0.4

-0.2

0

0.2

0.4

SE, Si=0.02

0.02 0.04 0.06 0.08-0.2

-0.1

0

0.1

0.2

A2E, Si=0.01

2 4 6-0.2

-0.1

0

0.1

0.2

0.3

SIGC, Si=0.01

0.1 0.2 0.3 0.4 0.5 0.6-0.2

-0.1

0

0.1

0.2

SFPE, Si=0.00

0.3 0.4 0.5 0.6 0.7-0.15

-0.1

-0.05

0

0.05

0.1

SFPME, Si=0.00

2 4 6 8 10 12 14-0.1

-0.05

0

0.05

0.1

0.15

GAMI2E, Si=0.00

Figure 20: Non-parametric curves of the key parameters driving the GDP growth

response to a monetary shock


bundles of exported and foreign goods – have negative impact on the GDP response to a

monetary shock at their low values. Before crossing the confidence bounds, they turn to the

positive side and monotonically increase since then at an increasing pace (ILAGE) or

decreasing pace (SIGEXE). Hence, the both parameters in the confidence interval and beyond

it have positive influence on the GDP response to a monetary shock as one should expect it.

Parameter capturing inertia in the relative foreign-to-export prices (RHOPWPX) has also a non-

linear pattern, but with a downward slope. It ends up in negative numbers at the upper bound

of posterior distribution range. This also makes sense: the slower export price adjustment the

lower GDP response to a monetary shock.

The pattern of the parameter reflecting price adjustment cost (GAMPE) has a rather

counterintuitive shape. It reveals a non-linear upward trend starting from a negative range and

approaching a positive definite level at the upper bound of posterior distribution. This implies

that a rising price adjustment cost shifts up the GDP response to a monetary shock.

18 Identification Analysis

Dynare provides tools to check the model assumptions concerning the value of parameters

declared within a probability distribution at the prior mean that initially seems plausible to the

modeler. The program performs the ex post identification check at a local point for the prior

parameters. In that sense, the program assists the modeler to verify intuition about the priors

and rigorously analysis the acceptance domain of the model within the prior space. In order to

perform such a check, Monte Carlo filtering method is used as developed by Ratto (2008).

This approach is based on generating a Monte Carlo sample of model parameters from their

prior distributions, taking into account the model structure. In general, there are not known

conditions for which unique solutions of a system of non-linear equations exist. Therefore,

Dynare mimics such a solution by computing transition or decision functions which have

linear form. This is the way how Dynare linearizes a non-linear DSGE model.

The reduced form coefficients from the transition functions mostly depend on prior

parameters, but some of them not. The later are excluded from farther consideration since we

are only interested in relationship between deep parameters and the reduced form coefficients.

Ratto and Iskrev (2011) called the vector which comprises these parameter as vector τ.

Another crucial vector is which contain the mean and the variance of data.

The vector τ is provided by Dynare as a solution of the model. The vector should be

simulated by MC process since we still neither take into account data nor do Bayesian

estimation of the model based on these data. What we do is a preliminary check of priors. In

order to overcome the absence of data, MC sampling is done. We did this with 1812 replicas

of length 300 periods (T=300). Based on this sampling, the theoretical mean and the variance

are obtained.

After this step, one needs to compute the Jacobian matrix of a continuous differentiable

function ( - which represents dependence of non-constant reduced form coefficients on

prior parameters – at a local point:

( 𝜕

𝜕


Then is locally identifiable if the Jacobian matrix J(q) has a full column rank at for

(Ratto and Iskrev, 2011, p.8). If a deep parameter does not affect the solution of the

model, the column of J(q) corresponding to will have a vector of zeros for any T, and

identification of the corresponding prior will fail. Dynare internally labels the Jacobian matrix

J(q) as J matrix and reports its rank.

There is one more condition for successful identification of priors. The point in the prior

space is locally identifiable only if the rank of the Jacobian matrix:

𝜕

𝜕

at is equal to k (k represents deep parameters). This matrix Dynare internally calls H

matrix.

We did a full identification analysis, but report here only the basic identification check of

deep parameters over the prior space. Dynare’s printed output of this analysis is written in

Box 1. All parameters are identified in the model (rank of H matrix) and all parameters are

identified by J moments (the first and the second theoretical moment). This means that the

prior space is well defined.

Box 18: Printed output for the basic identification check

Starting Dynare (version 4.4.2). Substitution of endo lags >= 2: added 3 auxiliary variables and equations. Found 114 equation(s). Evaluating expressions...done Computing static model derivatives: - order 1 - order 2 - derivatives of Jacobian/Hessian w.r. to parameters Computing dynamic model derivatives: - order 1 - order 2 - derivatives of Jacobian/Hessian w.r. to parameters ...

==== Identification analysis ==== Testing prior mean... Evaluating simulated moment uncertainty ... Doing 1812 replicas of length 300 periods... Simulated moment uncertainty ... done! All parameters are identified in the model (rank of H). All parameters are identified by J moments (rank of J).

Panel (a): Identification strength with moments information matrix

relative to prior mean, (log scale)

Panel (b): Sensitivity component with moments information matrix

related to prior mean, (log scale)

Figure 21: Dynare identification strength of the QUEST_Serbia model


Figure 21 plots Identification strength with moments information matrix scaled to the prior

mean (Panel a) and Sensitivity components with moments information matrix also scaled to

the prior mean (Panel b). It will be helpful to divide deep parameters into two groups by the

strength of identification: the strongly identified parameters and the weakly identified

parameters. All parameters that we considered in the example taking IRF of the GDP to a

monetary shock belong to the former group. The most important one is the inertia in the

interest rate movement from the Taylor rule (ILAGE). It is placed to the 9th

position from the

top one according to identification strength (out of 64 deep parameters). The first three of the

most strongly identified parameters are: the elasticity of substitution between bundles of

domestic and imported goods (SIGME), the share of bundle of imported goods in the

composite good basket (SE) and the elasticity of substitution between bundles of exported and

foreign goods (SIGEXE).


References

Adjemian Stéphane, Houtan Bastani, Michel Juillard, Frédéric Karamé, Ferhat

Mihoubi,George Perendia, Johannes Pfeifer, Marco Ratto and Sébastien Villemot

(2011),“Dynare: Reference Manual, Version 4,” Dynare Working Papers, 1, CEPREMAP.

Ratto, M. (2008): „Analysing DSGE models with global sensitivity analysis“, Computational

Economics 31, 115–139.

Ratto, M. And N. Iskrov (2011): „Identification analysis of DSGE models with DYNARE“,

https://www.ifk-cfs.de/fileadmin/downloads/.../RATTO_IdentifFinal.pdf .

Ratto, M., W. Roeger and J. in’t Veld (2009): "QUEST III: An Estimated Open-Economy

DSGE Model of the Euro Area with Fiscal and Monetary Policy", Economic Modeling, Vol.

26, No. 1, 222-233.

Roeger W. and J. in't Veld (2009): "Fiscal Policy with Credit Constrained Households",

European Economy Economic Paper 357.

Roeger W. and J. in't Veld (2010): "Fiscal Stimulus and Exit Strategies in the EU: A Model-

Based Analysis", European Economy Economic Paper 426.

in’t Veld, J., R. Raciborski, M. Ratto M., and W. Roeger (2011): “The Recent Boom-Bust

Cycle: The Relative Contribution of Capital Flows, Credit Supply and Asset Bubbles”,

European Economic Review 55 (3): 386–406.

Vogel L. (2011): „Structural reforms and external rebalancing in the euro area: a model-based

analysis“, European Economy Economic Paper 443.


Annex I: List of Variables

Declared

symbols

Algebraic

symbols

Algebraic expressions instead

of symbols Description of variables

Endogenous variables

BGYN

Share of government debt in nominal

GDP

BWRY

Share of net foreign liabilities in GDP

CLCSN

Liquidity constrained consumption share

in nominal GDP

DBGYN

𝑙 (

) 𝑙 (

) Change in the share of government debt in

nominal GDP, i.e. Fiscal deficit change

ETA 𝜂 Price markup

GC Growth rate of consumption

GCL

Growth rate of aggregate consumption per

capita

GCLC

Growth rate of consumption liquidity


GCNLC

Growth rate of consumption liquidity non-


GE Nominal exchange rate growth

GEX Export growth rate

GEXL

Export growth rate per capita

GG Growth rate of government consumption

GGL

Growth rate of government consumption

per capita

GI Growth rate of investments

GIG Growth rate of government investments

GIL

Growth rate of investments per capita

GIM Import growth rate

GIML

Import growth per capita

GK Capital growth rate

GKG

Government capital growth rate

GL Employment growth rate

GTAX

Lump sum tax growth

GLFP Labor factor productivity growth


GTFPUCAP Total factor productivity growth

GTR Transfer payments growth

GUC

Utility growth

GUCAP Capacity utilization growth

GWRY

𝑙 (

)

𝑙 (

)

Growth rate of real GDP per real wage

rate

GY GDP growth rate

GYL

GDP per capita growth rate

GYPOT

Potential GDP growth rate

GYW Foreign GDP growth

INOM Domestic nominal interest rate

INOMW Foreign nominal interest rate

LBGYN 𝑙 (

) Logarithm of government debt in nominal

GDP

LCLCSN

Logarithm of the share of consumption

liquidity constrained households in

nominal GDP

LCNLCSN

Logarithm of the share of consumption

liquidity non-constrained households in

nominal GDP

LCSN

Logarithm of aggregate consumption

share in nominal GDP

LCY

𝑙 (

Logarithm of real consumption to real

GDP ratio

LER 𝑙 (

Logarithm of the real exchange rate

LEXYN (

Logarithm of export share in nominal

GDP

LGY

𝑙 (

Logarithm of real government

consumption to real GDP ratio

LGSN 𝑙 (

Logarithm of government consumption


LIGSN 𝑙 (

𝐼

Logarithm of government investment


LIMYN 𝑙 (

Logarithm of import share in nominal

GDP

LIK 𝑙 (𝐼

Logarithm of investment expenditures to

capital ratio

LIKG 𝑙 (𝐼

Logarithm of investment to capital ratio in

the government sector


LISN

𝑙 (

𝐼

Logarithm of investment share in nominal

GDP

LL 𝑙 ( Logarithm of employment rate

LL0 𝑙 ( Logarithm of steady state employment

rate

LPCP

𝑙 (

Logarithm of consumption price to GDP

deflator ratio

LOL 𝑙 ( Logarithm of labour overhead

LPMP

𝑙 (

Logarithm of import price to GDP deflator

ratio

LPXP 𝑙 (

Logarithm of export price to GDP deflator

ratio

LTRYN 𝑙 (

Logarithm of transfer payments to GDP

ratio

LWS

𝑙 (

Logarithm of gross wage share

LUCYN 𝑙 (

Logarithm of liquidity non-constrained

consumption utility in nominal GDP

LUCLCYN 𝑙 (

Logarithm of liquidity constrained

consumption utility in nominal GDP

LYGAP 𝑙 ( Logarithm of output gap

LYKPPI 𝑙 (

Logarithm of nominal output to nominal

capital ratio

LYWR

𝑙 (

Logarithm of real GDP to real wage ratio

LYWY

𝑙 (

Logarithm of foreign to domestic GDP

ratio

MRY ln(

Logarithm of real money balances share in

GDP

PHI Overall inflation or the rate of growth of

GDP deflator

PHIC Consumption inflation

PHIPI Investment inflation deflator

PHIM Import deflator inflation

PHIML

Import deflator inflation corrected for

intra trade level

PHIW Foreign inflation

PHIX Export deflator inflation

PHIXL

Export deflator inflation corrected for

intra trade level

Q Tobin's Q


R 𝑟 Real interest rate

TAXYN 𝑡

Nominal lump sum tax to GDP ratio

TBYN

Nominal trade balance to GDP ratio

TRTAXYN

𝑡

Transfer payments net of lump sum tax to

GDP ratio

TRW

Transfer payments to wage bill share

TRYN

Transfer payments share in GDP

TW 𝑡 Tax on wages

UCAP Capacity utilization

UCAP0 Steady state capacity utilization evolution

VL 𝑉 Value of leisure Ricardian households

VLLC 𝑉

Value of leisure of liquidity constrained

households

WPHI Nominal wage inflation

WRPHI

Rate of growth of real wages

WS

Gross wage share

WSW

( 𝑡 𝑡

Net (of taxes and contributions) wage

share

ZPHIT

Inflation target

Permanent stochastic shocks

ZEPS_C Utility of consumption shock

ZEPS_ETA Price markup shock

ZEPS_ETAM

Import price markup shock

ZEPS_ETAX

Export price markup shock

ZEPS_EX Trade balance shock

ZEPS_G Government spending shock

ZEPS_IG Government investment shock

ZEPS_L Leisure shock

ZEPS_M Monetary shock

ZEPS_PPI Technology shock

ZEPS_RPREME

Interest parity risk premium shock

ZEPS_RPREMK

Capital risk premium shock

E_ZEPS_TR Transfers shock


E_ZEPS_W Labour demand shock

Annex II: List of Parameters and Temporary Shocks

Declared

symbols

Algebraic

symbol Parameter names

Parameters

a1e γ1UCAP

Capacity utilization rate

a2e γ2UCAP

Cyclical rate of capacity utilization

alphae α Elasticity of output with respect to labour

alphage αG Share of private capital

betae β Rate of time preference

bgadj1 τB Public debt penalty parameter

bgadj2 τDEF

Fiscal correction parameter

bgtar Target public debt to GDP ratio

convergence The growth rate differential between the EU and Serbia

deltae δ Depreciation rate

deltage δ G Public capital depreciation rate

e_ex_inomw Steady state foreign nominal interest rate

e_ex_r r Real interest rate consistent with the time preference rate

e_ex_rw 𝑟 Foreign real interest rate consistent with the time preference rate

g1e Parameter of public consumption adjustment to output gap

gami2e γI Non-linear part in the investment adjustment costs

gamie γK Linear part in the investment adjustment costs

gamle γL Parameter for labour adjustment costs

gampe γP Parameter for price adjustment costs

gampme γPM

Parameter for import price adjustment costs

gampxe γPX Parameter for export price adjustment costs

gamwe γW Elasticity of wage inflation

gp0 π Steady state quarterly inflation rate

gpcpi0 Steady state rate of technology progress

gpop0 λpop

Steady state population growth rate

gpw0 πW

Steady state quarterly foreign inflation rate

gslag Inertia in government consumption

gvecm Penalty parameter for missing government consumption target

gsn (

)

Target share of government consumption in GDP


glfp0 Steady state rate of labour augmented technology progress

gy0 g Steady state GDP growth rate

gyw0 gW

Steady state foreign GDP growth rate

habe hC Habits in consumption

hable hL Habits in leisure

igvecm Penalty parameter for missing government investment target

ilage Inertia in the evolution of nominal interest rate

ig1e Parameter of public investment adjustment to output gap

igsn (𝐼

)

Target share of government investment in GDP

kappae k Elasticity of labour supply

l0 L Participation rate

ler0 𝑙 (

Logarithm of the PPP real exchange rate

lol LH Logarithm of steady state overhead labour

lywy0 𝑙 (

) Logarithm of steady state foreign to domestic output

omege ω Derived parameter from utility and leisure functions which supports the

steady state labour participation rate

price_diff Inflation differential between the EU and Serbia

rhoce Inertia in evolution of the consumption permanent shock

rhoppi1 The first lag of technology progress weights

rhoppi2 The second lag of technology progress weights

rhoppi3 The third lag of technology progress weights

rhoppi4 The fourth lag of technology progress weights

rhoeta Inertia in evolution of the price markup permanent shock

rhoetam Inertia in evolution of the import price markup permanent shock

rhoetax Inertia in evolution of the export price markup permanent shock

rhoexe Inertia in evolution of the export permanent shock

rhoge Inertia in evolution of the government consumption permanent shock

rhoig Inertia in evolution of the government investment permanent shock

rhol0 Inertia in the evolution of steady state employment

rhole Inertia in the permanent employment shock

rholol Inertia in the evolution of overhead labour

rhopcpm γPCPM

Coefficient of inertia of the ratio of domestic prices to import prices

rhopwpx γPFPX

Coefficient of inertia of the ratio of domestic prices to export prices

rhorpe γrprem

Coefficient of inertia in the permanent shock of the country risk premium

rhorpk γrpremK

Coefficient of inertia in the permanent shock of the equity premium

rhoucap0 Drift parameter in AR(1) process of capacity utilization

rii 𝑟 Foreign interest lagged parameter in VAR model of foreign interest

rip 𝑟 Foreign price lagged parameter in VAR model of foreign interest

rix 𝑟 Foreign output lagged parameter in VAR model of foreign interest


rpi 𝑟 Foreign interest lagged parameter in VAR model of foreign prices

rpp 𝑟 Foreign price lagged parameter in VAR model of foreign prices

rpx 𝑟 Foreign output lagged parameter in VAR model of foreign prices

rxi 𝑟 Foreign interest lagged parameter in VAR model of foreign output

rxp 𝑟 Foreign price lagged parameter in VAR model of foreign output

rxx 𝑟 Foreign output lagged parameter in VAR model of foreign output

rxy 𝑟 Domestic output lagged parameter in VAR model of foreign output

rpreme 𝑟 Country risk premium

rpremk 𝑟 Equity risk premium

se sM

Share of import goods in the composite good basket

sfpe sfp Share of firms that adjust prices to the expected inflation

sfpme sfpM Share of importers that adjust import prices to the expected inflation

sfpxe sfpX Share of exporters that adjust export prices to the expected inflation

sfwe sfw Share of employers that adjust wages to the expected inflation

sigc σC Elasticity of substitution between consumption and leisure

sigexe σX Elasticity of substitution between domestic and exported goods

sigime σM

Elasticity of substitution between domestic and imported goods

slc sls Share of liquidity constrained households in the total number of

households

ssc taxSSC

Social security contribution

taue τ Tax on markup

time_pref Time preference difference between households in the EU and households

in Serbia

tp taxK Tax on profit

thetae θ Elasticity of substitution between various variety of labour

tinfe ϕπ Parameter of Central Bank’s aversion on inflation

tr1e b Cyclical unemployment and pensions compensation rate

trsn TRAN Steady state unemployment and pensions compensation rate

rhotr γTRAN

Inertia in evolution of permanent shock on transfer payments

tye1 Interest rate reaction to output gap

tye2 Interest rate reaction to output gap change

tvat taxVAT

Value-added tax

tw0 Liner tax rate on wages

tw1 Progressive tax rate on wages

ucap0 gUCAP

Steady state rate of capacity utilization

wrlag γwr Rigidity of real wages

zete μ Interest semi-elasticity od demand for real money balances

Temporary shocks


eps_C Utility stochastic shock

eps_ETA Price markup stochastic shock

eps_ETAM

Import price stochastic shock

eps_ETAX

Export price stochastic shock

eps_EX Export stochastic shock

eps_G Government consumption stochastic shock

eps_IG

Government investment stochastic shock

eps_INOMW

Foreign interest rate stochastic shock

eps_L Leisure stochastic shock

eps_LOL Labor overhead stochastic shock

eps_M Monetary stochastic shock

eps_PPI Technology stochastic shock

eps_PW

Foreign price stochastic shock

eps_RPREME

Foreign parity risk premium stochastic shock

eps_RPREMK

Equity premium stochastic shock

eps_TR Transfer payments stochastic shock

eps_W Wage stochastic shock

eps_Y Labor productivity stochastic shock

eps_YW

World productivity stochastic shock

eps_BG Public debt stochastic shock

eps_INOMW

Foreign interest rate stochastic shock

eps_PW

Foreign price stochastic shock

eps_YW

Foreign output stochastic shock

eps_PPI Technology stochastic shock

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