An Estimated Dynamic Stochastic General Equilibrium Model for Armenian Economy

ISSN 1561-2422 An Estimated Dynamic Stochastic General Equilibrium Model for Armenian Economy Gayane Barseghyan Working paper No 13/11E This project...
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ISSN 1561-2422

An Estimated Dynamic Stochastic General Equilibrium Model for Armenian Economy Gayane Barseghyan Working paper No 13/11E

This project (No 11-5052) was supported by the Economics Education and Research Consortium and funded by GDN. All opinions expressed here are those of the authors and not those of the EERC, GDN and Government of Sweden Research dissemination by the EERC may include views on policy, but the EERC itself takes no institutional policy positions

An Estimated Dynamic Stochastic General Equilibrium Model for Armenian Economy∗ Gayane V. Barseghyan† September, 2013

Abstract The paper develops and estimates a microfounded small open economy new Keynesian dynamic stochastic general equilibrium (DSGE) model for Armenian economy. To capture empirical persistence in Armenian macroeconomic data the model features number of frictions. Estimation of structural parameters of the DSGE model is performed on Armenian quarterly data from 2000 to 2012, using Bayesian full-system estimation techniques. The estimation shows that the model is able to replicate Armenian quarterly data. Moreover, the paper finds that the estimated model provides competing out-of-sample forecast compared with VAR and random walk models. Keywords: New-Keynesian economics, small open economy DSGE models, nominal rigidities, Bayesian Approach JEL Classifications: E12, E27, E43, E52



The paper reflects the views of the author and not necessarily those of any other institution. Central Bank of Armenia, Yerevan State University; E-mail: [email protected]. I would like to thank expert panel, especially Oleksiy Kryvtsov and Oleksandr Shepotylo, for helpful comments. I also thank Ashot Mkrtchyan for insightful discussions of the results. †

2

Contents 1 Introduction

4

2 Review of the Literature

5

3 The 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9

Model Economy Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . Households . . . . . . . . . . . . . . . . . . . . . . . . . Labor Market Participation Decision and Unemployment Import Goods Retailers . . . . . . . . . . . . . . . . . . . Real Exchange Rate, Law of One Price Gap and the Rest Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . Closing the Model: International Risk Sharing Condition The Linearized Model . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . of the World . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Armenian Data and Recent Economic Events

7 8 11 16 17 18 19 20 20 21 25

5 Estimation of the model for Armenian Economy 30 5.1 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 5.2 Priors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 5.3 Estimation Results and Evaluation . . . . . . . . . . . . . . . . . . . 33 6 Variance Decomposition

39

7 Forecast performance: comparison with alternative models

42

8 Conclusion

46

3

1

Introduction

This paper develops and estimates a microfounded small open economy new Keynesian dynamic stochastic general equilibrium (DSGE) model for Armenian economy. The model features number of frictions and rigidities that are shown in the literature to be necessary to take the model to the data. The developed model economy is populated by number of agents. There is continuum of infinitely-lived households, who consume differentiated goods, both imported and domestically produced. Household members supply differentiated labor services in monopolistically competitive labor markets and at every point in time they make decision on participating in the labor market. As a consequence of disproportion between the labor force and aggregate labor hiring by the firms, the model economy faces unemployment. Since the household members are assumed to supply differentiated labor services, they have monopolistic power over the wages they set. At the same time it is assumed, that household members are not able to readjust their wage contracts at each time. It is assumed that whenever they do not have an opportunity to reset wage contract optimally, they just make partial indexation of wages to previous period wage inflation. This makes the model more able to capture persistence in the data. There is continuum of infinitely-lived firms, who act in monopolistically competitive markets and produce differentiated goods, using constant returns to scale production technology with only input of labor. Good markets are monopolistically competitive and prices are assumed to be sticky, this is an evidence well supported by the data. The price contracts are staggered a la Calvo, with partial indexation to previous period domestic price inflation. Note that there is no capital in the model. This is an assumption that would make a model more realistic. Nevertheless, the estimation shows that the prices and wages are quite sticky, implying very sticky marginal costs, the fact of key importance for this type of model to fit the data and in this sense, the absence of capital at some extent may not have serious consequences on the ability of the model to fit the data. There is continuum of retailers in the model economy importing differentiated goods for which law of one price does not hold. The import prices are also assumed to be sticky, with partial indexation to the previous period import inflation. The central monetary authority conducts monetary policy, setting interest rates according to an ad-hoc imposed simple interest rate rule. The presented model then is estimated based on Bayesian estimation techniques, using eleven Armenian macroeconomic variables. The estimation yields plausible estimates for the structural parameters of the model. Thus, there is considerable degree of domestic and import price stickiness in the Armenian economy. The stickiness of wage contacts is estimated to be smaller. The estimation shows that current consumption responds to interest rates with 0.38 coefficient. The monetary 4

policy is estimated to have considerable degree of interest rate smoothing. There is significant degree of habit persistence in the economy. The model is able to fit the observed variables quite well. Moreover, comparison of in-sample fit of the developed model with that of the existing DSGE model of Armenian economy (Mkrtchyan, Dabla-Norris, Stepanyan(2009)) yields singnificantly lower RMSEs for the former. Model-based potential levels of some variables are calculated, that is GDP, nominal interest rates and unemployment rate. These levels of variables are formed in the economy without wage and price stickiness and distortive markup shocks, the shocks are only coming from technologies and preferences. The paper studies also relative contribution of different structural shocks in the variation of the macroeconomic variables. Specifically, the markup shocks are found to be the most important determinants for the corresponding inflation processes. The predictive performance of the estimated DSGE model is evaluated comparing with those of random walk and vector autoregression. This exercise shows that overall the DSGE model does a better job in forecasting than the considered models. The remainder of the paper is organized as follows. Section 2 makes short review of the related literature. Section 3 develops and presents the model economy. Section 4 presents Armenian data and briefly discusses recent economic events. Section 5 estimates the structural parameters of the model using Bayesian estimation technique. Section 6 preforms forecast error variance decomposition. Section 7 evaluates the estimated DSGE model forecast performance. Section 8 concludes.

2

Review of the Literature

The term DSGE was originally used by Kydland and Prescott (1982) in their seminal contribution on Real Business Cycle (RBC) model. The typical RBC model is based on neoclassical framework with micro-founded optimization behavior of economic agents under flexible prices. Then RBC models were criticised, as they were not able to reproduce stylized facts. Though RBC models had strong impact on academic economics, they had a limited impact on central banks and other policy making institutions. In a typical RBC model with completely flexible prices monetary policy has no impact on real variables, since any change of nominal interest rate is accompanied with such an adjustment of prices that real interest rates remain unchanged. Later Keynesian short-run macroeconomic features were included into DSGE models. Combining micro-foundations of both households and firms optimization problems coming from RBC approach with nominal and real rigidities, has provided plausible short-run dynamic macroeconomic fluctuations and has made macroeconomic models more realistic. The paper that first introduced this framework was 5

Rotemberg and Woodford (1997). After a vast literature has been dedicated to find out whether DSGE models are able to fit the data as well as traditional macroeconometric models do and whether they are useful as policy tool. In particular, Christiano, Eichenbaum, Evans (2005) show, that a model with nominal rigidities is able to account for the effect of monetary policy shock. Moreover, Smets and Wouters (2003) show that a New Keynesian model could track and forecast time series as well as, if not better than, a vector autoregression estimated with Bayesian techniques (Tovar (2008)). Now there is a large literature that tries to improve DSGE models incorporating new assumptions. This paper takes into account some of recent developments and also those that are somewhat standard in DSGE modeling. The paper follows Abel (1990) in the introduction of habit formation in utility function in the way of being external to households consumption decisions. Domestic prices are assumed to be sticky: price decision is modelled as an indexation variant of the mechanism spelled out in Calvo (1983). The paper introduces staggered wage contracts following Erceg, Henderson, Levin (2000). In addition it assumes that there is also some degree of wage indexation. Smets and Wouters (2003, 2007), Christiano, Eichenbaum, Evans (2005) assume that the indexation is performed over previous period price inflation, in contrast, here it is assumed to be performed over wage inflation. This approach is also implemented in Zoltan and Vilagi (2008) model. The paper assumes presence of unemployment following Gali (2011), that suggests a new way of embedding unemployment into DSGE model. This approach was then implemented in Gali, Smets and Wouters (2011) and allowed to identify separately wage markup and labor supply shocks, overcoming the critique of new keynesian models, raised by Chari, Kehoe, McGrattan (2008). Since Armenian economy is a small open economy, this paper constructs small open economy model and it is done, following Gali and Monacelli (2003) that develops a DSGE model with Calvo (1983) type price stickiness without capital. The small open economy model is closed assuming complete asset markets, as is suggested by Schmitt, Grohe and Uribe (2003). The assumption of incomplete pass-through of exchange rate to import prices, common to many economies and especially to emerging market economies, is made following Monacelli (2005). As there is an aim to take the model to the data, additional assumption of import price indexation to past period import inflation is made. Monacelli (2005) does not have such an assumption. It is also assumed that import price contracts are staggered a la Calvo (1983). The simultaneous presence of staggered contracts in domestic prices, import prices and wages entails endogenous trade-off between inflation and output gap stabilization. The issues separately are discussed in Erceg, Henderson and Levin (2000) and Monacelli (2005). Barseghyan (2013) shows that simultaneous presence of both incomplete pass-through and staggered wage contracts has a crucial impact on op6

timal monetary policy conduct and provides rationale for CPI inflation targeting. Developments of theoretical framework of DSGE models are also accompanied with advances in econometric estimation methodology of these models. Now Bayesian techniques are one of the most successful tools to estimate and quantitatively evaluate DSGE models (Fernandez-Villaverde and Rubio-Ramirez (2004), An and Schorfheide (2007), Smets and Wouters (2003, 2007)). To estimate the developed DSGE model this paper implements the Metropolis-Hastings algorithm, discussed in Landon-Lane (1998), Otrok (2001). Many central banks develop their own DSGE models to forecast macroeconomic time series or to analyze monetary policy. There is an existing DSGE model for Armenian economy too (Mkrtchyan, Dabla-Norris, Stepanyan (2009)). The model developed and presented in this paper differs from that in a number of directions. First, it has a richer theoretical framework and is strongly micro-founded. Second, here the model parameters are estimated based on Bayesian methodology, using a much longer data sample. Third, this paper addresses an issue concerning the forecast ability of the DSGE model and compares forecast performance of the developed model with traditionally used simple forecasting models. Eventually, the paper shows that the new model developed here provides superior in-sample fit, along with being more realistic and capturing more aspects of the actual economy. Section 4 provides Armenian data description and makes evident that key assumptions made in the model are well supported by the data.

3

The Model Economy

We consider a small open economy, populated by (i) continuum of infinitely-lived firms, who act in monopolistically competitive markets and produce differentiated goods, using constant returns to scale production technology with only input of labor, (ii) continuum of infinitely-lived households, who consume differentiated (domestic and imported) goods and supply differentiated labor services in monopolistically competitive labor markets, (iii) central monetary authority, that conducts monetary policy, setting interest rates according to an ad-hoc imposed simple interest rate rule. As considered economy is small, foreign sector is modeled as exogenous. The model incorporates external habit formation in consumption decisions (Abel (1990)), law of one price gap (Monacelli 2003), Calvo-type price (both for domestically produced and imported goods) and wage rigidities (Erceg, Henderson, Levin (2000)) with partial indexation to previous period price and wage inflation. We next detail the agents objectives and constraints, presenting the settings and necessary conditions (FOCs) of optimizing problems.

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3.1

Firms

Economy is populated by a continuum of domestic firms, indexed by i ∈ [0, 1], each of which produces differentiated good with the following technology: Yt (i) = At Nt (i)

(1)

where Yt (i) is the output of good i, At denotes exogenous technology parameter, common to all firms, Nt (i) is an index of labor input, used by firm i, and has the Dixit-Stiglitz (1977) form: 1

Z Nt (i) ≡

Nt (i, j)

εw,t −1 εw,t

 ε εw,t−1 w,t

dj

(2)

0

where Nt (i, j) denotes the quantity of type j labor employed by firm i in period t. Parameter εw,t > 1 represents the elasticity of substitution among labor varieties, indexed by j ∈ [0, 1] (Erceg, Henderson, Levin (2000)). Following Smets and Wouters (2003), we assume that εw,t changes due to exogenous markup shock (defined in Section 3.2). In the absence of markup shock εw,t = εw = const. Let Wt (j) denote the nominal wage for type j labor, which is set by the worker (see Section 3.2), and is taken as given by the firms. For any given level of wage (Wt (j), the cost minimization by each firm i yields the following demand schedule for each labor type j: −εw,t  Wt (j) Nt (i) (3) Nt (i, j) = Wt for any i, j[0, 1], where Wt is the aggregate wage index1 and is given as follows: Z Wt ≡

 1−ε1

1 1−εw,t

Wt (j)

w,t

dj

(4)

0

Optimal allocation of costs among labor varieties according to (3) yields minimum cost of firm i, given as follows:  −εw,t Z 1 Z 1 Wt (j) Wt (j)Nt (i, j)dj = Wt (j) Nt (i)dj = Wt Nt (i) (5) Wt 0 0 The standard static first-order condition for cost minimization associated with hiring labor input implies that the firm’s real marginal cost is given by 2 : 1

Aggregate wage index is the shadow price of labor input. This can easily be shown solving cost minimization problem subject to given labor input, where the corresponding Lagrange multiplier will be the aggregate wage index. t (i) 2 The firm’s real total cost is WPt N , where PH,t is an aggregate domestic price index. H,t

8

mct (i) =

Wt PH,t At

(6)

which depends on wage index, domestic prices and technology, and therefore is the same for all firms (mct (i) = mct ). Firm’s profits (ΠH,t ) are given by: ΠH,t (i) = PH,t (i)Yt (i) − M Ct (i)Yt (i)

(7)

where M Ct (i) = mct (i)PH,t is the nominal marginal cost. So, firms operate within a monopolistic competition: there is a continuum of firms, producing differentiated goods that buyers view as imperfect substitutes for one another (εt > 1 captures degree of substitution, see section 3.2). Due to differentiated nature of goods, each firm has pricing power in the market for its particular product variant and has some decision power over the price it charges, being explicitly a price setter. In this market structure firms maximize their profits with respect to their price facing demand with constant elasticity and subject to barriers to price adjustment. The price setting decision is modeled as an indexation variant of the mechanism opt spelled out in Calvo (1983). Prices are changed and set optimally, P˜H,t (i), when “price-change signal” is received. In each period a firm receives a “price-change signal” with a constant and exogenously given probability (1 − θH ). The probability, that in any given period a firm will be able to reset its price, is independent across firms and time. Firms that do not receive the “signal”, update their previous period price by partially indexating it to the previous period domestic good inflation rate: PH,t (i) = PH,t−1 (i)(1 + π ˆH,t−1 )γH P

(8)

−P

H,t−2 denotes domestic good inflation and 0 ≤ γH ≤ 1 is the where π ˆH,t−1 ≡ H,t−1 PH,t−2 degree of price indexation. In special cases, when γH = 0, there is no indexation and the prices that cannot be re-optimised remain constant and when γH = 1, there is perfect indexation to past period price inflation. opt Let P˜H,t (i) denote the optimal price, set by a firm, which at time t receives a opt “price-change signal”. The firm chooses P˜H,t (i) to maximize 3 :

max Et

opt P˜H,t (i)

∞ X

k

(θH ) Qt,t+k

h

H ˜ opt PH,t (i) Xt+k

i

− M Ct+k Y˜t+k (i)

(9)

k=0

subject to 3

Here and hereafter the variables that are affected by domestic price optimization decision will be denoted by ∼ subscript.

9

Y˜t+k (i) =



PH,t+k (i) PH,t+k

−εt+k

∗ CH,t+k + CH,t+k + Gt+k opt H P˜H,t+k (i) = X P˜ (i) t+k

( H = Xt+k



H,t

1,

if k = 0

(1 + π ˆH,t )γH (1 + π ˆH,t+1 )γH ...(1 + π ˆH,t+k−1 )γH =



PH,t+k−1 PH,t−1

γH

, if k ≥ 1

where P˜H,t+k (i) is the price of a firm, in period t + k, which received “signal” and optimized the price at time t but never again in the future and Y˜t+k (i) is the corresponding production of that firm. opt Note that P˜H,t (i) influences firm i’s profits only as long as it cannot reoptimize k its price. The probability that this happens for k periods ahead is θH , in which H ˜ opt k ˜ case PH,t+k (i) = Xt+k PH,t (i). The presence of θH in (9) has the effect of isolating opt future realizations of idiosyncratic uncertainty in which P˜H,t (i) continues to affect the firms profits. Since firms are owned by households, they maximize expected profits using ε (Ct+k −hCt+k−1 )−σ Pt Pt = β k c,t+k , which stochastic discount factor Qt,t+k = β k ΛΛt+k εc,t (Ct −hCt−1 )−σ Pt+k t Pt+k is a pricing kernel for nominal returns used by the shareholders-households4 . It includes time discount factor, β, and the marginal utility of an extra unit of wealth. The first-order condition associated with the problem above (9) is given by: Et

∞ X

h i opt H (θH )k Qt,t+k Y˜t+k (i) P˜H,t (i)Xt+k − Mt mct+k PH,t+k = 0

(10)

k=0 t where Mt = εtε−1 . So, the optimized price set by domestic firm i, at time t, is a function of expected future marginal costs. The price is a mark-up over these marginal costs. Let 1 + πH ,t ≡ Mt , πH ,t ∈ (0, ∞) and

ln πH ,t = (1 − ρπH ) ln πH + ρπH ln πH ,t−1 + ηtπH where ηtπH is the domestic price markup shock. When prices are perfectly flexible (θH → 0), the profit maximizing price in opt every period t is a simple markup over marginal cost of production5 , P˜H,t (i) = Mt M Ct . For the specific case εt ≡ ε = const the mark-up is time-invariant and constant, regardless of any shocks hitting the economy. When prices are sticky and the economy is hitted by the shocks, the mark-up is not equal to Mt and is variable over time. 4

Λt is the Lagrange multiplier on the budget constraint of the household decision problem, e.g. marginal utility of consumption. 5 The εt > 1 restriction is required in the monopolistically competitive environment in order to produce positive marginal profits (in this case also positive total profits due to assumption of zero fixed costs).

10

Note that all firms, who get ”price-change signal” at time t, face the same probopt opt lem (9) and behave symmetrically, choosing the same price, P˜H,t (i) = P˜H,t , therefore Y˜t (i) = Y˜t . That is, in the symmetric equilibrium, firm index i can be dropped. The definition of domestic price index, defined in the next section, implies that the law of motion of the aggregate price index is given by: h

γH 1−εt

PH,t = θH (PH,t−1 (1 + π ˆH,t−1 ) )

3.2

opt + (1 − θH )(P˜H,t (i))1−εt

1 i 1−ε

t

(11)

Households

The representative household consists of a continuum of members, indexed by a pair (j, s) ∈ [0, 1] × [0, 1]. The dimension j ∈ [0, 1] represents the type of labor in which a given household member is specialized. Supplying labor of type j household member experiences disutility of work given by χt sϕ , otherwise it is equal to 0 (when unemployed). χt > 0 is exogenous preference shifter (hereinafter referred to as “labor supply shock”). The period t utility of the household member who consumes and currently is employed is given by: (Ct (j, s) − Ht )1−σ − χt sϕ (12) εc,t 1−σ where 0 ≤ β ≤ 1 is the discount factor and the restriction on its value will assure convergence of discounted lifetime utility. σ > 0 is the coefficient of relative risk aversion, 0 < ϕ < ∞ is the inverse of the elasticity of labor supply with respect to the real wage. εc,t is consumption preferences shock that follows: ln εc,t = ρc ln εc,t−1 + ηtc ,

ηtc ∼ N (0, σC )

The instantaneous utility function of (j, s) individual (12) depends positively on the consumption of goods Ct (j, s), relative to an external habit variable Ht . Following Abel (1990) habit formation is assumed to be exogenous and external to households decisions (depends on aggregate consumption): Ht = hCt−1 , where 0 ≤ h ≤ 1 is the degree of habit persistence. If the household member is not employed, there is no disutility of work, and period utility function depends only on consumption stream. Full consumption risk sharing among household members is assumed as in Merz (1995), following Gali (2011), Gali, Smets and Wouters (2011), so that Ct (j, s) = Ct for any (j, s) ∈ [0, 1] × [0, 1].

11

Thus, period utility of the household is an integral over the utilities of its members: Z 1 Z Nt (j) Z 1 (Ct − Ht )1−σ (Nt (j))1+ϕ (Ct − Ht )1−σ ϕ s dsdj = εc,t εc,t − χt − χt dj 1−σ 1−σ 1+ϕ 0 0 0 (13) where Nt (j) is the employment rate of type j worker, employed in period t. Household maximizes an expected lifetime utility function given by: E0

∞ X

β

t=0

t



(Ct − Ht )1−σ εc,t − χt 1−σ

Z 0

1

(Nt (j))1+ϕ dj 1+ϕ

 (14)

As we consider small open economy, household has an opportunity to consume both domestically produced and imported goods. Composite consumption index is given by the following function: η  η−1  η−1 η−1 1 1 η η Ct ≡ (1 − γ) η CH,t + γ η CF,t

(15)

where CH,t and CF,t are indices of consumption of domestic goods and imported goods, respectively, consumed by household. Parameter γ ∈ [0, 1] is an index of openness. Parameter η > 0 measures the substitutability between domestic and foreign goods, from the viewpoint of the domestic consumer. Consumption indices, CH,t and CF,t , are given by the following CES functions: Z CH,t ≡

1

εt −1 εt

CH,t (i)di

t  ε ε−1

Z

t

,

CF,t ≡

1

εt −1 εt

CF,t (i)di

t  ε ε−1 t

(16)

0

0

where CH,t (i) and CF,t (i) denote consumption of domestic and imported goods of variety i by household, and εt > 1 is the elasticity of substitution between these varieties. The optimal allocation (minimization) of expenditures within each category of goods yields the following demand functions:  −εt  −εt PH,t (i) PF,t (i) CH,t (i) = CH,t , CF,t (i) = CF,t (17) PH,t PF,t 1 1 R  1−ε R  1−ε 1 1−εt 1 1−εt t t is the domestic price index and PF,t ≡ 0 PF,t (i)di where PH,t ≡ 0 PH,t (i)di is a price index for imported goods (shadow prices of corresponding consumption indices). Then, one can show, that the minimum costs to purchase domestically produced and imported goods, are: 12

Z

1

1

Z PH,t (i)CH,t (i)di = PH,t CH,t ,

PF,t (i)CF,t (i)di = PF,t CF,t

0

(18)

0

Analogously, the optimal allocation of expenditures between domestic and imported goods is given by:  −η  −η PH,t PF,t CH,t = (1 − γ) Ct , CF,t = γ Ct (19) Pt Pt   1 1−η 1−η 1−η is the overall price index (consumer price where Pt ≡ (1 − γ)PH,t + γPF,t index (CPI)). Accordingly, minimum value of total consumption expenditures by domestic household is given as follows: PH,t CH,t + PF,t CF,t = Pt Ct

(20)

In each period t, the household’s budget constraint is given by: Z 1 Z 1 Wt (j)Nt (j)dj+Tt +Divt (PH,t (i)CH,t (i) + PF,t (i)CF,t (i)) di+Et (Qt,t+1 Dt+1 ) = Dt + 0

0

Taking into account (18) and (20) relations, the budget constraint can be rewritten as: Z 1

Wt (j)Nt (j)dj + Tt + Divt

Pt Ct + Et (Qt,t+1 Dt+1 ) = Dt +

(21)

0

where Dt+1 is the nominal pay-off in period t + 1 of the portfolio held at the end of period t, Qt,t+1 is the stochastic discount factor for one-period ahead nominal pay-offs relevant to the domestic household. Tt denotes lump-sum transfers/taxes. Divt denotes the dividends received by the household in period t. All the firms in the economy are owned by the households and it is assumed that dividends are distributed equally among them. Next we derive optimal condition associated with consumption and asset holding. Then we turn to optimal wage setting by the household member, who receives “wage-change signal” and also present the rule according to which other household members, who are not able to optimize their wages, update their existing wages. In every period t household maximizes utility functional (14) with respect to its choice of consumption, and its holdings of contingent claims (asset holding) subject to the demand for its labor (24) and its intertemporal budget constraint (21). The first-order conditions for consumption and holdings of state-contingent claims imply the “consumption Euler equation”:   εc,t+1 (Ct+1 − hCt )−σ Pt =1 (22) (1 + it )Et β εc,t (Ct − hCt−1 )−σ Pt+1 13

where 1 + it = Et (Q1t,t+1 ) and it is domestic risk-free interest rate. Now we turn to the problem of setting utility maximizing wages for the labor services by household members. The wage setting decision is modeled as an indexation variant of the mechanism spelled out in Calvo (1983). Household member supplying a given type of labor optimizes nominal wages whenever he receives a “wage-change signal”, which occurs randomly at a constant and exogenously given probability, (1 − θw ). Household members, who do not receive the “wage-change signal”, update their previous period wage by partially indexating it to the previous period wage inflation rate, formally, following an indexation rule of the form: γ  Wt−1 w γw Wt (j) = Wt−1 (j)(1 + π ˆw,t−1 ) = Wt−1 (j) (23) Wt−2 where 0 ≤ γw ≤ 1 is the degree of wage indexation. In special cases, when γw = 0, there is no indexation and the wages that cannot be re-optimised remain constant and when γw = 1, there is perfect indexation to past period wage inflation. In contrast to Smets and Wouters (2003) the wage indexation is assumed to be performed over the previous period wage inflation, rather than to the previous period inflation. In any period t a household member, who does not get “wage-change signal”, sets its wage according to the indexation rule (23) and the labor supply is simply determined by labor demand equation, formally given by (24)6 : −εw,t  Wt (j) Nt (24) Nt (j) = Wt A household member, who receives a “wage-change signal” in period t and is able ˜ topt (j), taking into account to reset its wage contract, sets a new nominal wage7 , W the probability that it will not be re-optimized in the near future. The household member chooses wages in order to maximize the family’s welfare criterion. Thus, the household member maximizes household utility (as opposed to their individual utility) (14) with respect to the wage rate subject to budget constraint (22), demand for its labor (24) and indexation rule (23), formally: # " Z 1 ˜ ∞ 1+ϕ 1−σ X ( N (j)) (C − H ) t+k t+k t+k − χt+k dj max Et (βθw )k εc,t+k opt ˜ 1 − σ 1 + ϕ Wt (j) 0 k=0

(25)

subject to −εw,t R1 R1 Total demand of type j labor is given by: Nt (j) ≡ 0 Nt (i, j)di = 0 WWt (j) Nt (i)di = t  −εw,t Wt (j) Nt Wt 7 Here and after the variables which values depend on the wage optimization decision will be denoted by ∼ subscript. 6

14

R1 ˜ t+k (j)N ˜t+k (j)dj + Tt+k + Divt+k Pt+k Ct+k + Et (Qt+k,t+1+k Dt+1+k ) = Dt+k + 0 W ˜ −εw,t+k ˜t+k (j) = Wt+k (j) N Nt+k Wt+k

˜ t+k (j) = X w W ˜ opt W t+k t (j) ( w = Xt+k

1,

if k = 0

ˆw,t+k−1 )γw = ˆw,t+1 )γw ...(1 + π (1 + π ˆw,t )γw (1 + π



Wt+k−1 Wt−1

γw

, if k ≥ 1

˜ t+k (j) = X w W ˜ opt where W t+k t (j) is the wage rate of the household member j in period t + k, who received “wage-change signal” at time t and never again in the future ˜t+k (j) is the corresponding labor supply of that household. and N The first-order condition associated with the above problem (25) is given by: # " ∞ X ˜ topt (j) W w ˜t+k (j) − Mw,t Mg RS t+k (j) = 0 (26) Xt+k Et (βθw )k (Ct+k − Ht+k )−σ N P t+k k=0

εw,t ˜t+k (j))ϕ ε−1 (Ct+k − where Mw,t ≡ εw,t > 1 is the frictionless wage markup, Mg RS t+k (j) ≡ χt+k (N c,t+k −1 σ Ht+k ) is the household-relevant marginal rate of substitution (MRS) between consumption and employment in period t + k for type j worker, when that household member never adjusted wages in (t, t + k) time interval. Let 1 + πw ,t ≡ Mw,t , πw ,t ∈ (0, ∞) and

ln πw ,t = (1 − ρπw ) ln πw + ρπw ln πw ,t−1 + ηtπw where ηtπw is the wage markup shock. In the limiting case, in which all household members are able to optimize their wages every period (θw → 0), equation (26) reduces to the following condition: Wt Pt

=

Wtopt (j) Pt

= Mw,t M RSt ,

In the absence of nominal rigidities in every period t real wage equals marginal rate of substitution multiplied by the (flexible wage) wage markup. Under flexible wages, given that εw,t does not vary exogenously, the mark-up is time-invariant and constant regardless of shocks hitting the economy. When wages are rigid, the mark-up becomes variable over time. All optimizing household members, facing the same conditions and an identi˜ topt (j) = W ˜ topt , hence N ˜t (j) = cal problem, behave symmetrically and therefore W ˜t , Ct (j) = Ct , Dt (j) = Dt . Household members, who do not optimize their wages, N might have different wages and consequently different labor supplies, but consumption and asset holding is the same due to full risk sharing among household members. Given the relation (4), the law of motion of the aggregate wage index is given by: h i 1 ˜ topt (j))1−εw,t 1−εw,t Wt = θw (Wt−1 (1 + π ˜w,t−1 )γw )1−εw,t + (1 − θw )(W (27) 15

3.3

Labor Market Participation Decision and Unemployment

Unemployment is introduced in the model according to Gali (2011), Gali, Smets and Wouters (2011). Recall that Wt (j) is the nominal wage of labor type j. The household member specialized in labor service j and being employed at time t experiences disutility of work given by χt sϕ . Given the household welfare criterion and current labor market condition (Wt (j)), the individual will decide to participate in the labor market if and only if: Wt (j) σ (28) χt sϕ ε−1 c,t (Ct − hCt−1 ) ≤ Pt where Ct is the consumption of each household member, common to all of them due to assumption of full consumption risk sharing among all household members. The household participates in the labor market unless the subjective value of laborconsumption alternative exceeds the market value. If the marginal supplier of labor j is denoted by Lt (j), then (28) reduces to: σ χt Lt (j)ϕ ε−1 c,t (Ct − hCt−1 ) =

Wt (j) Pt

(29)

in terms of deviations from steady state the following relation is obtained: σ(ˆ ct − hˆ ct−1 ) + ϕˆlt 1−h

wˆt − pˆt = χˆt − εˆc,t +

(30)

R1 where lt ≡ 0 lt (j)dj is aggregate participation or labor force. Unemployment rate is defined as: uˆt = ˆlt − n ˆt

(31)

This is the definition of Gali (2011), from which unemployment can be interpreted as involuntary. Thus ut involves all individuals (31), who find it optimal to participate in the labor market (30), given the labor market conditions (are in ˆlt ), but currently are unemployed (are not in n ˆ t ). Given the definition of unemployment rate, it is easy to show that average wage markup is proportional to unemployment rate8 : µ ˆw,t = ϕˆ ut µ ˆw,t = w ˆt − pˆt − mrs d t = ϕˆlt − εˆc,t + χ ˆt + ϕ(ˆlt − n ˆ t ) = ϕˆ ut 8

σ(ˆ ct −hˆ ct−1 ) 1−h

16

(32) −χ ˆt + εˆc,t − ϕˆ nt −

σ(ˆ ct −hˆ ct−1 ) 1−h

=

3.4

Import Goods Retailers

Following Monacelli (2005), domestic market is assumed to be populated by local retailers i ∈ [0, 1], who import differentiated goods for which the law of one price holds “at the dock”. A local retailer, importing good i, purchases that good at the ∗ world-market price et PF,t (i) and sells it at domestic currency denominated PF,t (i) ∗ price, where et is the level of the nominal exchange rate and PF,t (i) is the price of good i denominated in foreign currency. Due to large number (continuum) of retailers and differentiated nature of imported goods, each retailer has some market power in the market and is a price setter. The price, set by a retailer, maximizes expected profits subject to demand schedule and barriers to price adjustment. The price setting decision is modeled analogous to the ones already discussed, that is, as an indexation variant of the mechanism spelled out in Calvo (1983). opt Therefore, prices are changed and set optimally, P˜F,t (i), when “price-change signal” is received. In each period a retailer receives a “price-change signal” with a constant and exogenously given probability (1−θF ). The probability, that in any given period a retailer will be able to reset its price, is independent across retailers and time. Retailers that do not receive the “signal”, update their previous period price by partially indexating it to the previous period imported good inflation rate: PF,t (i) = PF,t−1 (i)(1 + π ˆF,t−1 )γF P

(33)

−P

F,t−2 imported good inflation and 0 ≤ γF ≤ 1 is the degree where π ˆF,t−1 ≡ F,t−1 PF,t−2 of price indexation. In special cases, when γF = 0, there is no indexation and the prices that cannot be re-optimised remain constant and when γF = 1, there is perfect indexation to past period import price inflation. Like the local producers, the retailer i faces a downward sloping demand for opt i-th good and at time t, receiving “price-change signal”, chooses a price P˜F,t (i), expressed in units of domestic currency, to maximize:

max Et opt

P˜F,t (i)

∞ X

h i ∗ (θF )k Qt,t+k P˜F,t+k (i) − et+k PF,t+k (i) C˜F,t+k (i)

(34)

k=0

subject to −εt+k ˜ P (i) CF,t+k C˜F,t+k (i) = PF,t+k F,t+k P˜F,t+k (i) = X F P˜ opt (i) t+k

( F Xt+k =

F,t

1,

if k = 0

(1 + π ˆF,t )γF (1 + π ˆF,t+1 )γF ...(1 + π ˆF,t+k−1 )γF = 17



PF,t+k−1 PF,t−1

γF

, if k ≥ 1

F ˜ opt where P˜F,t+k (i) = Xt+k PF,t (i) is the price of a retailer, in period t+k, which received “signal” and optimized the price at time t but never again in the future and C˜F,t+k (i) is the corresponding import of that retailer (exactly equal to its demand). The problem is identical to the one, already solved for domestic producers. θFk opt is the probability that the price P˜F,t (i) set for good i at time t still holds k periods ahead, and Qt,t+k is a relevant stochastic discount factor, as for the case of local producers. The first-order condition for the presented problem is:

Et

∞ h i X F ˜ opt ∗ (θF )k Qt,t+k C˜F,t+k (i) Xt+k PF,t (i) − Mt et+k PF,t+k (i) = 0

(35)

k=0 t . where Mt ≡ εtε−1 Let 1 + πF ,t ≡ Mt , πF ,t ∈ (0, ∞) and

ln πF ,t = (1 − ρπF ) ln πF + ρπF ln πF ,t−1 + ηtπF where ηtπF is the import price markup shock. In the limiting case of no price rigidities (θF → 0), the previous condition collapses to the well-known result of monopolistic competition, that is: P˜ opt (i) = Mt et P ∗ (i). F,t

F,t

Prices are set above the marginal cost and Mt is the frictionless markup in the absence of constraints on the frequency of price adjustment. When there is no ε t exogenous markup shock, then Mt ≡ εtε−1 = ε−1 = const. When prices are rigid (θF 6= 0), markup becomes variable over time. Note that all firms, who are able to set a price at time t optimally, face the same opt problem and behave symmetrically, choosing the same price, P˜F,t (i). The definition of import price index implies that the law of motion of aggregate price index is given as follows: h

γF 1−εt

PF,t = θF (PF,t−1 (1 + π ˆF,t−1 ) )

3.5

opt + (1 − θF )(P˜F,t (i))1−εt

1 i 1−ε

t

(36)

Real Exchange Rate, Law of One Price Gap and the Rest of the World

It is assumed that economy exports domestically produced good, foreign demand for which is given by the following expression9 :  −εt  −εt  −η PH,t (i) PH,t (i) PH,t ∗ ∗ CH,t (i) = CH,t = γ Ct∗ (37) PH,t PH,t et Pt∗ 9

The relation is obtained solving the expenditure minimizing problem symmetric to the one described for domestic household in Section 3.2.

18

where γ corresponds to the share of domestic goods in consumption basket of foreign agents and η is price elasticity of foreign demand. The real exchange rate with the rest of the world is defined as the ratio of the two countries CPIs, both expressed in terms of domestic currency, formally: Qt ≡

et Pt∗ Pt

(38)

Law-of-one price gap (l.o.p gap henceforth) is defined as a deviation of the world price from the domestic currency price of import10 : ΨF,t ≡

et Pt∗ PF,t

(39)

The size of the small open economy is negligible relative to the rest of the world, which allows to treat the rest of the world as an approximately closed economy (Gali, Monacelli (2002), Monacelli (2005)), whose equilibrium in the limit is taken as exogenous. Therefore, foreign variables are assumed to follow first order autoregressive AR(1) processes11 : ∗ yˆt∗ = ρy∗ yˆt−1 + εy∗ ,t (40) ∗ π ˆt∗ = ρπ∗ π ˆt−1 + επ∗ ,t

(41)

which are ˆt∗ denote foreign GDP and inflation rate, respectively, where yˆt∗ and π ∗ ∗ with the log-deviations from corresponding steady-states. εyt , επt are exogenous stochastic shocks.

3.6

Monetary Policy

The central bank conducts monetary policy according to a monetary policy rule. Monetary policy is modeled as a Taylor-type rule of the following form:  ρ "  φy  φ∆e #1−ρi 1 + it−1 i Y 1 + it e t t φπ εit (42) (1 + π ˆ ) e = t f 1 + ¯i 1 + ¯i et−1 Yt where ρi , φy , φ∆e > 0 and φπ > 1. it denotes the short-term nominal interest rate, which is the policy instrument of the monetary authority, πt is CPI inflation and et is the depreciation rate of the nominal exchange rate, and Yt is the aggregate et−1 output. Ytf is the natural level of output that prevails in the flexible wage and price economy in the absence of markup shocks (Smets and Wouters(2007)). εit stands 10

Goods produced in the small economy represent a negligible fraction of foreign economy’s ∗ et PF,t e P∗ ∗ consumption basket, hence Pt∗ ≈ PF,t and we have PtF,tt instead of PF,t . 11 Variables representing foreign economy are denoted by stars.

19

for an exogenous monetary policy shock. It is assumed that central bank performs nominal interest rate smoothing policy and 0 < ρi < 1 governs monetary policy inertia.

3.7

Equilibrium

The i-th good market clears if production equals its demand by domestic and foreign households and by the government. Thus, formally equilibrium condition in i-th good market is given by: ∗ Yt (i) = CH,t (i) + CH,t (i) + Gt (i)

(43)

Using corresponding demand functions one can get: Yt (i) =



Taking into account, that Yt ≡

PH,t (i) PH,t

 R1 0

−εt

Yt

εt −1 εt

∗ [CH,t + CH,t + Gt ]

 ε ε−1 t di

t

, PH,t ≡

R

1 0

1−εt PH,t (i)di

1  1−ε

t

, the

following is obtained: ∗ Yt = CH,t + CH,t + Gt

(44)

or, in terms of deviations from steady state: yˆt =

3.8

C∗ G CH cˆH,t + H cˆ∗H,t + gˆt Y Y Y

(45)

Closing the Model: International Risk Sharing Condition

It is assumed that agents have access to complete array of state-contingent claims, traded internationally. In the rest of the world, agents have access to the same array of financial assets as in the domestic economy. Consequently, one first-order condition of the foreign household is an equation similar to Eq. (22). Letting starred letters denote foreign variables or functions and assuming that domestic and foreign households have the same preferences and share the same discount factor, we arrive at the following first-order condition for the foreign household:  −ξt+1 ∗  e (Ct+1 − hCt∗ )−σ et Pt∗ =1 (46) (1 + it )Et β −ξt ∗ ∗ ∗ e (Ct − hCt−1 )−σ et+1 Pt+1 where ξt is the preference shock to foreign representative household. Instantaneous ∗ )1−σ e−ξt (Ct∗ −hCt−1 utility function of foreign representative household is given by: . 1−σ 20

Note, that following Mkrtchyan, Dabla-Norris, Stepanyan (2009), preference shock is interpreted as remittances sent to domestic economy, which is, in fact, a negative shock from the perspective of foreign reprenstative household. Combining the domestic and foreign “consumption Euler” equations - Eqs. (22) and (46) - yields:  Et

εc,t (Ct − hCt−1 )−σ et Pt∗ ∗ )−σ Pt e−ξt (Ct∗ − hCt−1



 = Et

∗ εc,t+1 (Ct+1 − hCt )−σ et+1 Pt+1 ∗ − hCt∗ )−σ Pt+1 e−ξt+1 (Ct+1

 (47)

This means that the domestic marginal utility of consumption is proportional to its foreign counterpart. Formally, 1

ξt

1

∗ σ Ct − hCt−1 = ϑ(Ct∗ − hCt−1 )Qtσ e σ εc,t

(48)

where ϑ is a constant parameter determining differences in wealth across countries (Schmitt-Grohe, Uribe (2003)) and depends on initial conditions regarding relative net asset positions. Without loss of generality it is assumed that ϑ = 1 (Gali and Monacelli (2005)). So, equilibrium condition, derived above and called international risk sharing condition, states, that under complete asset markets marginal utility of consumption of domestic household is proportional to foreign counterpart, that is, UC0 t = α(U ∗ )0Ct∗ , where U denotes the period utility function and stars are used to denote foreign variables. Foreign consumption, Ct∗ = Yt∗ , is determined exogenously by stationary AR(1) process (Section 3.5), therefore, stationarity of Ct∗ implies stationarity of Ct and assures stationarity of the model in the equilibrium dynamics (Schmitt-Grohe, Uribe (2003)).

3.9

The Linearized Model

The model equations are linearised around the non-stochastic steady state and are summarised below12 . The “hat” above a variable denotes its log deviation from corresponding steady state, that is: xˆt = ln XXt ≈ XtX−X . The consumption Euler equation is given by: cˆt =

h 1 1−h ˆ cˆt−1 + Et cˆt+1 − (it − Et π ˆt+1 ) + εˆc,t 1+h 1+h σ(1 + h)

(49)

This equation is derived, assuming external habit formation in consumption decisions. From (49) one can see that consumption in the current period depends both 12

The full system of equations (including the ones describing flexible wage and price economy) is available upon request.

21

on past and expected future consumption, this allows to keep the volatility of consumption in line with what is observed in the data. For the special case of no habit formation (49) reduces to traditional consumption Euler equation, where elasticity of consumption with respect to real interest rate depends only on σ, in contrast to (49), where that elasticity also depends on degree of habit persistence: other things being equal, the higher is habit persistence, the lower is the impact of ex ante real interest rate on consumption and the higher is the impact of previous period consumption. εˆc,t is consumption preferences shock: εˆc,t = ρc εˆc,t−1 + ηtc ,

ηtc ∼ N (0, σc )

Under the assumption of partial indexation the domestic inflation equation is given by: γH 1 β (1 − θH )(1 − βθH ) Et π ˆH,t+1 + π ˆH,t−1 + mc c t + ˆπH ,t 1 + βγH 1 + βγH 1 + βγH θH (50) This is a hybrid new- Keynesian Phillips curve, which reduces to the traditional one, when there is no price indexation γH = 0. In (50) inflation depends on both past and expected future inflation and current marginal cost, which is a function of real wages and the productivity. The higher is the degree of indexation; the lower is the impact of current marginal cost on current inflation and the more backward-looking is inflation process. ˆπH ,t is domestic price markup shock: π ˆH,t =

ˆπH ,t = ρπH ˆπH ,t−1 + ηtπH ,

ηtπH ∼ N (0, σH )

In the model economy real marginal costs are given by: mc ct = ω ˆt +

γ ˆ γ qˆt − ψF,t − a ˆt 1−γ 1−γ

(51)

where ω ˆ t is the deviation of actual real wage from its steady state level and ψˆF,t is l.o.p gap. Similarly, under partial indexation of import prices, the import inflation equation is given by: β γF 1 (1 − θF )(1 − βθF ) b Et π ˆF,t+1 + π ˆF,t−1 + ψF,t + ˆπF ,t 1 + βγF 1 + βγF 1 + βγF θF (52) Import inflation depends on past, expected future inflation and current period l.o.p gap. Backward-looking component in the import inflation equation is the result of partial indexation. The higher is the degree of indexation; the lower is the impact of current l.o.p gap on current inflation and the more backward-looking is import π ˆF,t =

22

inflation process. When there is no partial indexation, (52) reduces to forward looking new-Keynesian Phillips curve (Monacelli (2005)). ˆπF ,t is import price markup shock: ˆπF ,t = ρπF ˆπF ,t−1 + ηtπF ,

ηtπF ∼ N (0, σF )

Law of one price gap is given by ψˆF,t = eˆt + pˆ∗t − pˆF,t relation, where eˆt + pˆ∗t is the domestic currency denominated price paid by retailers in the world market and pˆF,t is the price at which retailer sells imported goods in the domestic economy. Increase of eˆt + pˆ∗t component (either as a result of domestic currency depreciation or foreign price shock) increases real marginal costs, ψˆF,t , and according to (52) increases imported goods inflation. Under partial indexation of nominal wages, wage inflation equation is given as follows: (1 − βθw )(1 − θw ) γw 1 β (ϕˆ ut − ˆπw ,t ) Et π ˆw,t+1 + π ˆw,t−1 − 1 + βγw 1 + βγw 1 + βγw θw (1 + εw ϕ) (53) The wage inflation depends on past, expected future wage inflation and current period unemployment rate. Backward looking component is a result of partial indexation of nominal wages. When γw = 0, wage inflation does not depend on the lagged inflation rate and (53) reduces to purely forward looking equation. The higher is the degree of wage indexation, the lower is the impact of current unemployment rate on the wage inflation and the more backward looking is wage inflation process. The wage inflation equation depends only on wage markup shock as it is opposed to the model without unemployment, where would also be labor supply shock (shock to labor preferences). Introduction of unemployment allows separately identify those shocks and overcome the critiques of new keynesian models raised by Chari, Kehoe, McGrattan(2008). For further and detailed discussion of the issue one is referred to Gali, Smets and Wouters (2011). ˆπw ,t is the wage markup shock: π ˆw,t =

ˆπw ,t = ρπw ˆπw ,t−1 + ηtπw ,

ηtπw ∼ N (0, σw )

The unemployment rate is defined as a difference between labor supply and actual rate of employment: uˆt = ˆlt − (ˆ yt − a ˆt ) (54) The total labor supply is determined by: ω ˆ t = ϕˆlt +

σ (ˆ ct − hˆ ct−1 ) + χˆt − εˆc,t 1−h

(55)

As one can see, real wages have positive impact on labor supply, which reflects the substitutuion effect: the higher are the wages, the more the individuals are willing 23

to work today in favor of tomorrow’s consumption. The higher is marginal utility of consumption, the higher is total labor supply. The positive labor supply shock exogenously shifts labor supply preferences of individuals and as a consequence labor supply decreases. The international risk sharing condition is given by. qˆt =

σ ∗ (ˆ ct − hˆ ct−1 − (ˆ yt∗ − hˆ yt−1 )) − ξˆt + ˆq,t 1−h

(56)

from which real exchange rate, qˆt , is determined. ˆq,t is interpreted as real exchange rate shock and is assumed to follow: ˆq,t = ρq ˆq,t−1 + ηtq ,

ηtq ∼ N (0, σq )

The monetary policy reaction function is given by the following simple interest rate rule: ˆit = ρiˆit−1 + (1 − ρi )(φπ π ˆt + φy (ˆ yt − yˆtf ) + φ∆e ∆ˆ et ) + εi,t

(57)

The parameter ρi is the degree of nominal interest rate smoothing. The monetary authority responds to inflation, output gap and to the change of exchange rate. The monetary policy shock is given by εi,t , which follows: εˆi,t = ρi εˆi,t−1 + ηti ,

ηti ∼ N (0, σi )

The goods market-clearing/ equilibrium condition is given by :     ηγ η ηγ ηγ yˆt = α1 + α2 + α2 ψˆF,t +α1 cˆt +α2 yˆt∗ +(1−α1 −α2 )ˆ gt +ˆ εy,t qˆt − α1 1−γ 1−γ 1−γ 1−γ (58) ∗ CH CH where α1 ≡ Y is the steady state domestic consumption-output ratio, α2 ≡ Y is the steady-state foreign consumption of domestic goods (export) -output ratio. Eq. (58) determines the real GDP. εˆy,t is the shock to real GDP: εˆy,t = ρy εˆy,t−1 + ηty ,

ηty ∼ N (0, σy )

The law of one price gap is given by the following relation: ψˆF,t = ψˆF,t−1 + eˆt − eˆt−1 + π ˆt∗ − π ˆF,t

(59)

The nominal exchange rate is determined by: eˆt = eˆt−1 + qˆt − qˆt−1 − π ˆt∗ + π ˆt

(60)

CPI inflation is equal to weighted average of domestic and import inflations: π ˆt = γ π ˆF,t + (1 − γ)ˆ πH,t 24

(61)

The wages are determined by the following identity: ω ˆt = ω ˆ t−1 + π ˆw,t − π ˆt

(62)

The dynamics of foreign output and inflation is given by the following autoregressive processes: ∗ yˆt∗ = ρy∗ yˆt−1 + εy∗ ,t (63) ∗ π ˆt∗ = ρπ∗ π ˆt−1 + επ∗ ,t

(64)

The private remittances, government expenditures, productivity and the labor supply shock are described by the following AR(1) processes: ξˆt = ρξ ξˆt−1 + εξ,t

(65)

gˆt = ρg gˆt−1 + εg,t

(66)

a ˆ t = ρa a ˆt−1 + εa,t

(67)

χˆt = ρχ χˆt−1 + εχ,t

(68)

The system of linear rational expectation equations is solved using Dynare13 software. There are 33 endogenous variables (7 natural variables included) in the model, its stochastic behavior is given by exogenous 13 shocks.

4

Armenian Data and Recent Economic Events

This section provides description of Armenian quarterly data, which makes evident recent economic events and supports key assumptions made in the model. Until 1991 Armenia was a part of Soviet Union. After the restoration of the independence, Armenia has made a full switch to a market economy. This was performed by a number of economic reforms, specifically privatization, price liberalization and etc, causing drastic changes in the economy. Soon after due to implementation of appropriate fiscal and monetary policies the economy has started to recover, facing double digit economic growth and single-digit inflation. The source of economic growth was mainly the expansion of construction and service sectors. The average annual economic growth was in double-digit from 2002 to 2007 (13%), but then the picture has been somewhat changed due to impact of global economic slowdown, and as a result, the average economic growth from 2001 to 2012 was only 7.6%. 13

Dynare is a software platform for handling, in particular DSGE models and is freely available at www.dynare.org.

25

The Figure 1 depicts some of the seasonally adjusted quarterly Armenian macroeconomic variables, as well as their corresponding trends. The data sample spans from the first quarter of 2000 to the fourth quarter of 2012. As one can see, real GDP, real wages, remittances, government spending display increasing trend, but after 2008 that was somewhat reversed. In 2008 there was an impact of global financial and economic crisis on Armenian economy. This caused dramatic change of real GDP, specifically in the fourth quarter of 2008 and in the first quarter of 2009. Remittances have been one of the mechanisms through which the impact of global economic events have transmitted to the domestic economy, as Armenian economy heavily depends on remittances, sent by the Armenian diaspora14 . The remittances declined sharply in the fourth quarter of 2008 and had a negative impact on the economy. The domestic, import price and consumer price indices are computed with respect to the first quarter of 2000. As one can see, these indices have increasing trend over time. Note that import price index demonstrates relatively large fluctuations around the trend, than the domestic price index does, though the latter is more volatile. Nominal exchange rate has a decreasing trend, that is Armenian dram appreciates over time. Due to global financial crisis, in the first quarter of 2009 there was a sharp appreciation of Armenian dram, this was caused by the reduction in the supply of US dollars in the economy, as a result of the fall in both the remittances and the export revenues. There was also some speculative demand of US dollars, as a credible alternative to invest in during the crisis. Unemployment rate15 seems to decline over time. Note that again as a result of economic crisis there is a considerable increase of unemployment in the second quarter of 2009. At the begining of the sample nominal interest rate is quite high, after it declines and demonstrates decreasing trend. The nominal interest rate is the policy instrument of the Central Bank of Armenia (interest rate of repurchasing agreement, e.g. repo). In the very begining of 2006 the Central Bank officialy announced the switch 14

Armenia has a large diaspora (8 million by some estimates, exceeding the 3 million population of Armenia itself). The main reason that led to the settlement of Armenians in the world was Armenian Genocide in 1915. 15 Since 2008 the National Statistical Agency (NSA) has started to compute unemployment rate based on the labour force survey conducted within the framework of Households Integrated Living Conditions Survey. The alternative data is the officially registered unemployment rate, which, for instance, in 2011 was 6.2 %, but according to the survey data it was 18.4%. Moreover, since the February 2012 NSA stopped the calculation of this indicator by the administrative statistical records. The new data based on the survey is more reliable and is able to capture real state in the labor market more precisely, that is why will be used in the estimation part of the model. The series for the whole sample is provided and is used by the the Monetary Policy Department of the Central Bank of Armenia, after filling in the missing points from 2000 to 2008 by a particular model.

26

to inflation targeting monetary policy regime16 . Since the announcement of new regime the monetary policy have been conducted through the interest rates. Before that, the monetary policy had been conducted by targeting monetary aggregates. This policy turned out to be ineffective, as the relationship between inflation and monetary aggregates was no more stable. Thus during the estimation period the monetary policy regime has been changed, but because the conisdered sample is small, it is not divided into sub-samples in the estimation part of the model. Figure 1: Armenian macroeconomic variables and long-term trends 5

8

x 10

Consumption

GDP

5

10

x 10

Import Price Index 200

8

6

150

6 4

100

4

2 00:Q2

03:Q2

06:Q2

09:Q2

12:Q2

2 00:Q2

Domestic Price Index

03:Q2

06:Q2

09:Q2

12:Q2

50 00:Q2

Consumer Price Index 200

600

400

150

500

200

100

400

03:Q2

06:Q2

09:Q2

12:Q2

50 00:Q2

Nominal Interest Rate

4

30

10

20 10 0 00:Q2

03:Q2

06:Q2

09:Q2

12:Q2

x 10

03:Q2

06:Q2

09:Q2

12:Q2

300 00:Q2

Real Wage

09:Q2

12:Q2

03:Q2

06:Q2

09:Q2

12:Q2

Remittances 400

8

300

6

200

4

100

2 00:Q2

06:Q2

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600

0 00:Q2

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0 00:Q2

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time 4

10

x 10

Government Spending

Unemployment Rate 30

8

25

6 20

4 2 00:Q2

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time

09:Q2

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15 00:Q2

03:Q2

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time

Note: The variables are seasonally adjusted, using Census X12 method. The corresponding trends are computed with Hodrick-Prescott Filter. 16 Initially the inflation target was set at 3%, but from the perspective to gain credibility very soon in 2007 it was changed to 4% with ±1.5% confidence band and after has never been changed.

27

Figure 2 depicts percentage deviations of discussed macroeconomic variables from their trends. This is the data used in the model parameters estimation process as the observable variables. As one can see, consumption is quite volatile, real GDP displays a large deviation from its trend as a result of an increase of an economy followed by a sharp slowdown. CPI index inflation is the target variable of monetary policy and as one can see, it is in single-digit and shows the success of implemented policies. Figure 2: Deviations from long-term trends Consumption

Output

10 0 −10 −20 00:Q2

03:Q2

06:Q2

09:Q2

12:Q2

Import Inflation

20

10

10

5

0

0

−10

−5

−20 00:Q2

Domestic Inflation

03:Q2

06:Q2

09:Q2

12:Q2

−10 00:Q2

Overall Inflation

5

5

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0

03:Q2

06:Q2

09:Q2

12:Q2

Nominal Exchange Rate 20 10 0 −10

−5 00:Q2

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−5 00:Q2

Nominal Interest Rate 5 0

03:Q2

06:Q2

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−20 00:Q2

Real Wage

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06:Q2

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time Remittances

Government Spending

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40 20

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time

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03:Q2

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time

Note: The deviations are in perecntage, computed as a difference of natural logarithm of the seasonally adjusted variable from its trend, except for interest rates.

Figure 3 depicts comovements of some macroeconomic variables at business cycle frequencies. In the considered sample there is both negative and positive relashionship between remittances and real GDP17 . This means that there is both altrouistic 17

Correlation coefficient computed for the whole sample is 0.55.

28

and investment motives to send remittances. Since there is no strong evidence to assume dominance of one of this motivations over the other, the paper simply assumes exogenous AR(1) process for remittances. In general remittances are correlated with foreign economic activity, which is also modeled as exogenous autoregressive process. Figure 3: Business cycle comovements 50

Remittances GDP

20

0

0

10

Real Wages Unemployment Rate

5

10

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0

−5

−50 00:Q2

03:Q2

06:Q2

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−10 00:Q2

Import Inflation Nominal Exchange Rate 10

20

03:Q2

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0

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50

03:Q2

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GDP Nominal Interest Rate

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There is an inverse relationship between real wages and unemployment rate, an empirical evidence supporting the New Keynesian wage Phillips curve. The correlation coefficient is equal to -0.4. Remittances flow into economy in the form of foreign currency and have an impact on nominal exchange rate. The correlation coefficient between these two time series over the whole sample is equal to -0.57. This fact is expressed in the model by inversely relating the real exchange rate with remittances through international risk sharing condition. The change of exchange rate is not fully reflected in the change of import inflation, supporting the model assumption of incomplete pass-through of exchange rate to import prices. The positive relationship between inflation and nominal interest rate is more evident from 2006, the date after which the Central Bank conducts inflation targeting monetary policy regime. The correlation coefficient between nominal interest rate and CPI inflation from 2006 to 2012 is 0.5. For the sample from 2000 to 2006 there is no significant correlation (-0.19). 29

Nominal interest rates and real GDP exhibit positive comovement, this evidence is reflected in the model by incorporating output (real GDP) gap in the monetary policy rule.

5

Estimation of the model for Armenian Economy

The estimation of the model is based on the quarterly data of Armenian economy from 2000 to 2012. All variables are in natural logarithms (except for interest rates) and with deviations from their dynamic trends (Figure 2). The variables are seasonally adjusted using Census X12 method and the corresponding trends are computed by Hodrick-Prescott (HP) filter (λ = 1600). The estimation is performed using Bayesian full system estimation techniques. In the estimation process additional information is incorporated as priors. The method can be studied for instance in An and Schorfeide (2007).

5.1

Calibration

As commonly done in the DSGE literature number of parameters are calibrated and are left constant in the estimation process. Incorporating fixed parameters in the estimation process can be viewed as imposing a very strict prior, which is consistent with Bayesian approach of estimation of DSGE model parameters. The calibrated parameters are of three types: (i) the parameters that can be directly computed using actual data (these parameters are crucial to determine the steady-state and to replicate the main steady-state key ratios of the Armenian economy); (ii) the parameters of autoregressive processes that can be estimated by AR(1) estimation procedure; (iii) the parameters for which there are reliable estimates from other sources (from the well-cited literature or other specific studies). Thus the ratio of domestic consumption to output is set to α1 = 0.7; export/output ratio is set to α2 = 0.15. The share of foreign goods in consumption basket is set to γ = 0.25. Note that γ also shows the degree of openness of the economy. These values represent the sample averages of corresponding ratios. The discount rate is set to β = 0.99, to produce a steady-state long-run real interest rate of about 4% per year. For autoregressive processes the following estimates are obtained: ∗ ∗ ξˆt = 0.6ξˆt−1 + εξ,t , yˆt∗ = 0.85ˆ yt−1 + εy∗ ,t , π ˆt∗ = 0.49ˆ πt−1 + επ∗ ,t , a ˆt = 0.6ˆ at−1 + εa,t , (0.11) (0.06) (0.13) (0.12) where the standard errors are shown in parentheses. The autoregressive coefficients, as well as the other calibrated parameters, are summarized in Table 1. 30

Table 1: Calibrated Parameters Parameter Symbol Value Discount factor β 0.99 Coefficients of AR(1) processes Productivity ρa 0.6 World output ρy∗ 0.85 World inflation ρπ∗ 0.49 Remittances ρξ 0.6 Government Spending ρg 0.44 Implied steady state relationships Consumption - output ratio α1 ≡ CH /Y 0.7 ∗ Export - output ratio α2 ≡ CH /Y 0.15 Government spending-output ration 1 − α1 − α2 ≡ G/Y 0.15 Share of foreign goods in consumption basket γ 0.25

5.2

Priors

For parameters bounded to be positive, the inverse gamma distribution is used. Parameters, which are bounded between zero and one, are assumed to follow a beta distribution. The coefficient of habit formation, h, is assumed to have mean value of 0.9 with standard deviation of 0.05. 0 ≤ h ≤ 1 is assumed to follow beta distribution. The inverse of the elasticity of labor supply with respect to real wages, ϕ, is assumed to follow gamma distribution with mean 1.0 and standard deviation of 0.3, which are conventional and common values in the literature. The inverse of the elasticity of intertemporal substitution (or more correctly coefficient of relative risk aversion, since there is also habit coefficient), σ, is assumed to have gamma distribution with mean of 1.7 and standard deviation of 0.2. The elasticity of substitution among different labor varieties, εw > 1, is assumed to follow gamma distribution with mean value 3.0 and standard deviation of 0.1. This represents the fact that in economy different labor types are described with low degree of substitution. The elasticity of substitution between domestic and foreign goods, η > 0, is assumed to follow gamma distribution with mean value of 0.73 and standard deviation of 0.2. Calvo and indexation parameters that underlie the wage and price-setting decisions are bounded between zero and one and therefore are assumed to follow beta distribution. The means for the priors of Calvo parameters are set at 0.8 for both wages and prices, so that the average contract duration is 5 quarters. The standard deviations are set at 0.15.

31

Table 2: Prior Distribution of the Model Parameters Parameter

h ϕ σ εw η θH θF θw γH γF γw φπ φy φ∆e ρi

Beta Gamma Gamma Gamma Gamma Beta Beta Beta Beta Beta Beta Gamma Gamma Gamma Beta

0.90 1.00 1.70 3.00 0.73 0.8 0.8 0.8 0.5 0.5 0.5 1.6 0.7 0.60 0.60

Std. Dev. 0.05 0.30 0.20 0.10 0.2 0.15 0.15 0.15 0.1 0.1 0.1 0.25 0.10 0.10 0.20

ρχ ρa ρπw ρπH ρπF ρc ρy ρq ρεi

Beta Beta Beta Beta Beta Beta Beta Beta Beta

0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50 0.50

0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20 0.20

σq σi σc σy σH σF σw σχ σy∗ σπ ∗ σξ σg σa

InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma InvGamma

0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01 0.01

2.00 2.00 2.00 2.00 2.00 2.00 0.02 2.00 2.00 2.00 2.00 2.00 2.00

Symbol Distribution Mean

Habit formation Inverse labor supply elasticity The inverse elasticity of intertemporal substitution Elasticity of substitution of labour services Elasticty of substitution of domestic and imported goods Probability of not adjusting prices, domestic goods Probability of not adjusting prices, imported goods Probability of not adjusting wages Degree of domestic price indexation Degree of import price indexation Degree of wage indexation Taylor rule: inflation Taylor rule: output Taylor rule: depreciation rate Taylor rule: smoothing Coefficients of AR(1) processes of the shocks Labor supply shock Productivity shock Wage markup shock Domestic price markup shock Import price markup shock Consumption preferences shock Real GDP shock Real exchange rate shock Monetary policy shock Standard deviations of shocks Real exchange rate shock Monetary policy shock Consumption preferences shock Real GDP shock Domestic price markup shock Import price markup shock Wage markup shock Labor supply shock World output shock World inflation shock Remittances shock Government spending shock Productivity shock

32

For price and wage indexation parameters prior means are set at 0.5 and standard deviations at 0.1. The coefficients of monetary policy rule are assumed to follow gamma distribution. Specifically, φπ , has a prior mean of 1.6 with standard deviation of 0.25; φy has a prior mean of 0.7 with a standard deviation of 0.1; and a reaction coefficient to exchange rate fluctuations, φ∆e , has a prior mean of 0.6 with a standard deviation of 0.1. The coefficient of interest rate smoothing, 0 ≤ ρi ≤ 1, is assumed to have a beta distribution with mean 0.6 and standard deviation equal to 0.2. The AR(1) coefficients of shocks are assumed to have a beta distribution with mean value 0.5 and standard deviation 0.2. The standard deviations of all shocks are assumed to follow inverse gamma distribution and the mean value for all shocks is set to 0.01, a low value which is assumed in the literature to ensure success of numerical optimization of the posterior kernel. The standard deviation is set at 2. Priors of the model parameters are summarized in Table 2.

5.3

Estimation Results and Evaluation

The results of estimated parameters are reported in Table 3, where one can find (i) the parameters modes and standard deviations, obtained by maximizing posterior kernel (Chris Sim’s csminwel) (ii) the mean and 10% and 90% percentiles of the posterior distribution computed with the Metropolis-Hastings algorithm based on 300 000 draws with 7 parallel chains. Estimation results are discussed below. The estimation shows that all the parameters are significantly different from zero. The prices for both domestically produced and imported goods turn out to be quite sticky. Estimation implies average duration of price contracts to be 3.6 years and 1.4 years for domestic and imported goods, respectively. Thus in Armenian economy import prices seem to be renegotiated more frequently, than those for domestic goods. For the Euro area Smets and Wouters (2003) estimate price stickiness to be 2.5 years. Calvo probability of wages to be unchanged is estimated 0.5. This implies average duration of wage contracts equal to 2 quarters. Though the priors for stickiness parameters have been set the same both for price and wage contracts, the estimation provides more rigid prices than wages. Estimation results for indexation parameters are γH = 0.46, γF = 0.53,γw = 0.44, hence the coefficients on previous period inflations in domestic inflation, import inflation and wage inflation equations are 0.32, 0.35 and 0.31, respectively. The most backward looking process turns out be import inflation. The inverse of labor supply elasticty is estimated to be 1.96. The estimated values of elasticity between different labor types is approximately 3, implying steady state wage markup to be 3/2. This means that average unemployment rate is 25% (32). 33

Table 3: Posterior Distributions of the Model Parameters Posterior Maximization Mode Std.dev. h 0.4886 0.0492 ϕ 1.7707 0.2899 σ 1.2997 0.1383 εw 2.9930 0.0999 η 0.6358 0.1715 θH 0.9611 0.0586 θF 0.8276 0.0506 θw 0.4809 0.0675 γH 0.4655 0.1059 γF 0.5109 0.0966 γw 0.4391 0.0954 φπ 1.3187 0.2025 φy 0.8016 0.0996 φ∆e 0.5054 0.0823 ρi 0.7215 0.0517 Coefficients of AR(1) processes of the shocks ρχ 0.4965 0.2757 ρπw 0.2268 0.1193 ρπH 0.3603 0.1487 ρπF 0.5968 0.1235 ρc 0.2762 0.1133 ρy 0.5467 0.1035 ρq 0.5042 0.2784 ρεi 0.3586 0.0965 Standard deviations of shocks σq 0.0046 0.0019 σi 1.3514 0.1478 σc 2.5235 0.3887 σy 3.8079 0.3733 σH 0.6611 0.1331 σF 0.5929 0.1214 σw 20.5776 8.2897 σχ 0.0046 0.0019 σy ∗ 6.5840 0.8625 σπ∗ 0.0046 0.0019 σξ 16.8422 1.6206 σg 7.4791 0.7197 σa 6.5133 0.7749 Parameter

34

Metropolis-Hastings sampling Mean 10% 90% 0.4882 0.4287 0.5475 1.9643 1.5648 2.4065 1.3254 1.1515 1.5088 2.9971 2.8704 3.1257 0.6748 0.4572 0.9108 0.9363 0.8807 0.9854 0.8256 0.7612 0.8911 0.5386 0.4351 0.6635 0.4596 0.3347 0.5854 0.5269 0.4089 0.6454 0.4422 0.3268 0.5599 1.3820 1.1247 1.6551 0.8009 0.6753 0.9317 0.5324 0.4259 0.6455 0.7155 0.6463 0.7796 0.5001 0.2470 0.3710 0.5768 0.2950 0.5470 0.5016 0.3640

0.2296 0.1101 0.2007 0.4194 0.1562 0.4116 0.2322 0.2379

0.7690 0.3957 0.5530 0.7282 0.4384 0.6805 0.7707 0.4878

0.0087 1.4233 2.5729 3.9292 0.7029 0.6395 36.9413 0.0081 6.6830 0.0087 17.2568 7.6679 6.5368

0.0037 1.2293 2.0975 3.4443 0.5279 0.4811 16.4072 0.0036 5.6218 0.0037 15.2024 6.7465 5.5926

0.0158 1.6358 3.0847 4.4549 0.8836 0.8069 72.1434 0.0145 7.8400 0.0160 19.4661 8.6895 7.5802

The coefficient of relative risk aversion is estimated to be 1.33. The habit persistence parameter is 0.49. Thus, 1% change of interest rate has an impact on consumption equal to 0.38. The estimation shows that the interest rates respond to inflation with 1.38 coefficient. The respond coefficient to output gap and to the change of exchange rate are estimated 0.8 and 0.5, respectively. The interest rate smoothing coefficient is estimated at 0.7. For the comparison note that Gali, Smets and Wouters (2011) in the US economy find interest rate smoothing parameter equal to 0.83. Figure 4: Observed and model generated (filtered) data Consumption

GDP

10 0 −10 −20 00:Q2

03:Q2

06:Q2

09:Q2

12:Q2

Import Inflation

20

10

10

5

0

0

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03:Q2

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−5 00:Q2

03:Q2

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Government spending 40 20

Observed Data

0

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03:Q2

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35

09:Q2

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10

Remittances 50

−50 00:Q2

−40 00:Q2

Real Wages

10

−5 00:Q2

03:Q2

12:Q2

12:Q2

Estimated standard deviations of shocks show that most volatile shocks in the model are wage markup shock, remittances, government spending, productivity and foreign output shocks, then the real GDP and consumption preferences shocks. Figures 4 presents observed and model generated data. As one can see, the model provides close fit and therefore is able to replicate actual data. Specifically the model is able to reproduce dynamics of inflation measures and interest rates, which are, in fact, of key importance in the monetary policy conduct process. Figure 5 presents actual and natural levels of GDP, unemployment and interest rates. The natural level of a variable is defined as the level that would prevail in the flexible price and wage economy without distortive mark-up shocks (Smets and Wouters (2007)). The difference between the actual and natural levels is a consequence of stickiness of prices and wages in the economy and their interactions with different shocks. Figure 5: Observed and natural levels of the variables GDP

Unemployment rate

20 15 10

Interest rate

15

8

10

6 4

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−15 00:Q2

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Observed variable Natural level of the variable

The Table 4 reports in-sample RMSEs of the model developed in this paper (Model 1) and the model developed by Mkrtchyan et al. (2009) (Model 2). The RMSEs are calculated using the same observable variables and are based on the filtered variables of both models under the estimated parameters. Table 4: 2000:1-2012:4 in-sample RMSEs of two DSGE models y Model 1 3.01 Model 2 3.40

π

i

πH

πF

w

0.58 2.14

1.00 1.88

1.50 3.04

0.91 2.43

1.35 10.78

e

ξ

g

c

6.06 8.77 3.37 1.73 24.55 5.48 7.61 1.50

As one can see, the model developed in this paper has superior in-sample fit along with being more realistic and capturing more aspects of the actual economy. Nevertheless, Model 2 provides lower RMSE for the remittances, which is associated with a higher calibrated AR(1) coefficient of remittances in that model. 36

Figure 6: Estimated parameter distribution: priors and posteriors SE_eta_q

SE_eta_i

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Figures 6 presents prior and posterior distributions (grey and black lines) with the mode obtained from posterior kernel maximization. For the most of parameters the mode obtained from posterior maximization is close to the mode of posterior distribution or they coincide. The shape of posteriors for most of the parameters is close to normal. For several parameters prior and posterior distributions are distinct, that is observed data does provide additional information and obtained results are not only prior driven. Figure 7 plots the minus of the posterior density for values around the computed mode for each estimated parameter in turn, which as one can see, are at the bottom of the minus of the posterior distribution. Thus, diagnosis concerning numerical 37

maximization of posterior kernel shows that overall optimization procedure is able to precisely obtain robust maximum for posterior kernel and there are no problems with the optimizer. Figure 7: Posterior maximisation diagnosis SE_eta_q

SE_eta_i

1696

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38

Convergence of MH algorithm is obtained, as one can see from Figures 8 of multivariate MH diagnosis18 . The red and blue lines on the charts represent specific measures of the parameter vectors both within and between chains19 . Figure 8 shows that the convergence and relative stability in all measures of the parameter moments is obtained. Figure 9: Multivariate MH convergence diagnosis Interval 13 12 11 10 9

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6

Variance Decomposition

This section performs variance decomposition to evaluate the contribution of the structural shocks to the fluctuations of main endogenous variables. The forecast variance decomposition is based on the mean of the posterior distribution. The results for different forecast horizons are reported in Table 5. In the very short-run (within a quarter) the remittances shock account for 14% of the forecast error variance of consumption, but for longer horizons this contribution is reduced. On the contrary, the share of productivity shock becomes two times higher in all forecast horizons than it is for the very short run. The monetary policy shock accounts for about 15% of the variation in consumption. The next important shock that motivates for about 13% of the consumption variance is consumption preferences shock that directly affects consumption Euler equation. 18

The convergence of MH algorithm is also obtained for univariate diagnosis. For breviety they are not presented, but are available upon request 19 Three measures are reported: “interval”, being constructed from an 80% confidence interval around the parameter mean, “m2”, being a measure of the variance; “m3” based on third moments. The horizontal axis represents the number of Metropolis-Hastings iterations that have been undertaken, and the vertical axis the measure of the parameter moments, with the rest, corresponding to the measure at the initial value of the Metropolis-Hastings iterations.

39

The main driving forces of output variation are real GDP, productivity shock, consumption preferences and monetary policy shocks. In the very short run a significant fraction of the variance of output is explained by its own (real GDP) shock, but this effect somewhat reduces at longer time horizons. Note that for the US economy Smets and Wouters (2007) find that in the short run exogenous spending shock drives most variation in the output, but in the longer horizon the wage markup is the most important shock and dominates also productivity shock. Smets and Wouters (2003) for Euro area find the importance of labor supply shock in the variance of GDP. On the contrary, in Armenian economy labor supply and wage markup shocks are found to be not of crucial importance for output variance. Variations in inflation measures are mostly driven by their own shocks, e.g. markup shocks and this contribution is relatively stable over time. As described in Smets and Wouters (2003), the importance of markup shocks is explained by the fact that inflation process is very volatile and as prices are estimated to be very sticky, then it is necessary to have such shocks that are able to account for most variation in prices. The monetary policy shock has a limited impact on inflation measures, but the contribution at some extent builds up as the forecast horizon lengthens. The crucial shocks for nominal interest rates forecast variance are world output and remittances shocks that together account for more than 65% variation in interest rates. The contribution of consumption preferences is relatively stable over the forecast horizons. The real wage variations are mainly driven by domestic price markup and wage markup shocks, accounting for more than 70%. The monetary policy shock explains 9% of variation in real wages. Consumption preferences and productivity shocks are the crucial determinants of variation in unemployment rate and labor force. Remittances shock have significant impact (up to 20%) on the labor force in the very short run, but from medium to long run the impact is smaller, for about 10%. In the long run monetary policy shock explains for about 8% of labor force variance. Remittances and world output shocks together account for more than 75% of the variance of real exchange rate and law of one price gap.

40

Table 5: Variance Decomposition

t=1

t=4

t=20

t=100

Shock World output World inflation Remittances Government spending Productivity Labor supply Wage markup Domestic price markup Import price markup Consumption preferences Real GDP Real exchange rate Monetary policy World output World inflation Remittances Government spending Productivity Labor supply Wage markup Domestic price markup Import price markup Consumption preferences Real GDP Real exchange rate Monetary policy World output World inflation Remittances Government spending Productivity Labor supply Wage markup Domestic price markup Import price markup Consumption preferences Real GDP Real exchange rate Monetary policy World output World inflation Remittances Government spending Productivity Labor supply Wage markup Domestic price markup Import price markup Consumption preferences Real GDP Real exchange rate Monetary policy

C 8.6 0.0 14.2 0.1 12.5 0.0 0.0 0.5 0.8 51.0 2.1 0.0 10.4 5.4 0.0 10.2 0.3 25.6 0.0 0.1 2.8 4.1 31.0 4.5 0.0 16.1 6.4 0.0 9.3 0.3 26.3 0.0 0.3 3.1 6.1 28.0 4.8 0.0 15.5 6.4 0.0 9.3 0.3 26.3 0.0 0.3 3.1 6.1 28.0 4.8 0.0 15.5

Y 0.0 0.0 2.4 4.8 6.8 0.0 0.0 0.7 0.0 25.9 54.0 0.0 5.3 0.6 0.0 3.7 3.1 18.1 0.0 0.2 4.8 0.1 20.8 38.3 0.0 10.4 0.7 0.0 4.7 2.9 19.5 0.0 0.4 5.5 0.1 19.6 36.2 0.0 10.3 0.7 0.0 4.7 2.9 19.5 0.0 0.4 5.5 0.1 19.6 36.2 0.0 10.3

πF 21.6 0.0 23.7 0.0 1.1 0.0 0.1 1.4 49.2 1.3 0.2 0.0 1.3 25.2 0.0 24.9 0.0 1.2 0.0 0.4 5.3 40.4 0.7 0.3 0.0 1.7 23.5 0.0 23.3 0.0 1.2 0.0 0.8 7.8 41.1 0.6 0.3 0.0 1.5 23.6 0.0 23.3 0.0 1.2 0.0 0.8 7.7 41.0 0.6 0.3 0.0 1.5

41

πH 0.1 0.0 0.3 0.0 0.9 0.0 1.7 96.2 0.0 0.1 0.0 0.0 0.5 0.7 0.0 1.5 0.0 0.8 0.0 4.3 90.4 0.1 0.3 0.0 0.0 1.9 2.8 0.0 2.8 0.0 1.1 0.0 4.5 85.9 0.3 0.3 0.0 0.0 2.3 2.8 0.0 2.8 0.0 1.1 0.0 4.5 85.9 0.3 0.3 0.0 0.0 2.3

π 4.4 0.0 5.5 0.0 0.2 0.0 1.5 79.0 7.7 0.5 0.0 0.0 1.1 7.2 0.0 8.6 0.0 0.1 0.0 3.6 69.9 7.5 0.5 0.0 0.0 2.6 8.3 0.0 8.7 0.0 0.2 0.0 4.1 67.5 7.8 0.4 0.0 0.0 2.9 8.3 0.0 8.7 0.0 0.2 0.0 4.1 67.5 7.8 0.4 0.0 0.0 2.9

i 37.7 0.0 40.2 0.0 1.2 0.0 0.0 1.6 0.0 17.3 0.1 0.0 1.8 29.2 0.0 36.6 0.1 6.8 0.0 0.3 5.2 0.5 15.5 0.9 0.0 4.9 28.9 0.0 35.9 0.1 7.2 0.0 0.5 5.4 0.6 15.3 1.1 0.0 4.9 28.9 0.0 35.9 0.1 7.2 0.0 0.5 5.4 0.6 15.3 1.1 0.0 4.9

w 1.6 0.0 0.5 0.1 0.7 0.0 72.9 13.7 2.1 3.3 1.6 0.0 3.4 2.7 0.0 0.2 0.1 0.5 0.0 56.6 23.0 4.8 3.1 1.3 0.0 7.8 3.7 0.0 0.6 0.1 2.0 0.0 48.6 26.5 5.9 2.6 1.1 0.0 9.1 3.7 0.0 0.6 0.1 2.0 0.0 48.6 26.5 5.9 2.6 1.1 0.0 9.1

u 3.5 0.0 1.9 1.4 27.4 0.0 3.9 0.1 0.2 35.5 14.5 0.0 11.7 2.7 0.0 2.3 1.1 21.6 0.0 16.7 0.3 0.3 28.3 11.4 0.0 15.4 2.7 0.0 2.5 1.0 21.0 0.0 18.6 0.8 0.3 27.2 11.0 0.0 14.8 2.7 0.0 2.5 1.0 21.0 0.0 18.6 0.8 0.3 27.2 11.0 0.0 14.8

l 9.9 0.0 19.5 0.4 22.4 0.0 11.9 0.4 0.3 19.3 5.2 0.0 10.8 5.2 0.0 10.3 0.4 22.7 0.0 31.8 3.7 0.2 11.4 7.5 0.0 6.9 4.7 0.0 9.6 0.4 20.7 0.0 31.8 7.6 0.3 10.6 6.9 0.0 7.5 4.7 0.0 9.6 0.4 20.7 0.0 31.8 7.6 0.3 10.6 6.9 0.0 7.5

q 43.7 0.0 43.9 0.0 2.0 0.0 0.0 0.1 0.1 8.1 0.3 0.0 1.6 39.3 0.0 48.9 0.0 3.0 0.0 0.0 0.3 0.5 5.6 0.5 0.0 1.9 42.0 0.0 46.7 0.0 2.8 0.0 0.0 0.3 0.6 5.2 0.5 0.0 1.8 42.0 0.0 46.7 0.0 2.8 0.0 0.0 0.3 0.6 5.2 0.5 0.0 1.8

ψF 43.4 0.0 43.6 0.0 1.8 0.0 0.0 0.0 0.7 8.5 0.3 0.0 1.7 36.8 0.0 46.3 0.0 2.4 0.0 0.0 0.3 5.5 6.3 0.4 0.0 2.0 35.4 0.0 44.3 0.0 2.3 0.0 0.0 0.6 9.0 6.0 0.4 0.0 1.9 35.4 0.0 44.3 0.0 2.3 0.0 0.0 0.6 9.0 6.0 0.4 0.0 1.9

7

Forecast performance: comparison with alternative models

This section evaluates the ability of the DSGE model to forecast the observable variables out of the estimation sample, compared with those of alternative models, specifically with random walk forecast and VAR forecast. On this purpose the available sample on Armenian data is divided into two sub-samples from 2000:1 to 2009:4 and from 2010:1 to 2012:4. The models are estimated over the first subsample and then estimated models are used to forecast the variables in the second sub-sample. Note that, if VAR model is estimated on the same dataset as in Section 5, that contains 11 variables, then the degrees of freedom will be wasted due to available short sample. Taking into account this shortcoming, in this section DSGE and VAR models are estimated using only 5 Armenian macroeconomic variables, that are real GDP, nominal interest rate, CPI (overall) inflation, domestic inflaton and real wages. Table 6 reports likelihood ratio (LR), final prediction error (FPE), Akaike’s information criterion (AIC), Schwarz’s Bayesian information criterion (SBIC) and Hannan and Quinn information criterion (HQIC) for different lag orders of vector autoregression. These statistical criterias are computed for the sample period 2000:1-2009:4 using 5 endogenous variables without constant. Table 6: VAR Optimal Lag Length Selection Model VAR VAR VAR VAR

(1) (2) (3) (4)

LR

FPE

AIC

HQIC

SBIC

44.041 40.992 62.32*

322.4* 406.4 634.3 698.3

19.96* 20.1 20.4 20

20.3* 20.9 21.5 21.6

21* 22.3 23.7 24.4

* indicates lag order selected by the criterion The lag selection test suggests optimal lag order of one for VAR model. Therefore, the comparison with DSGE model, solution to which can be treated as VAR(1), is intuitevely more meaningful. The random walk forecast is an often used benchmark. In this scenario the last observations on each date are used as the forecasts for the next horizons, e.g. the best prediction of a variable for tomorrow is the current value. The estimated DSGE, VAR(1) and random walk models then are used to forecast the 5 data series20 in the second sub-sample from 2010:1 to 2012:4. To save computational time, in this exercise the fixed scheme of the forecast is used, e.g. the models are estimated once. For each variable there are twelve 1 quarter-ahead 20

The Armenian macroeconomic data is discussed in Section 4.

42

forecasts, eleven 2 quarter-ahead forecasts and eventually five 8 quarter-ahead forecasts to compare with the realized available values of variables. The forecast performance is evaluated based on the following metric: v u Th u 1 X t RM SExhM = (xt − xˆhM,t )2 (69) h T t=1 where x is the observable variable to be forecasted, xˆhM is the h period ahead forecast of the M model (made h-periods before in the past) and T h represents the total number of out-of-sample forecasts for a given method and forecasting horizon. The lower is the value of the forecast root-mean-squared error (RM SE), the better is the forecast provided by a particular model. For different forecast horizons absolute values of the forecast RMSEs of the variables under dfferent models are computed and reported in Table 7, from which one can conclude that overall the estimated DSGE model can successfully be used for forecasting key macroeconomic variables. Table 7: Out-of-sample (2010:1-2012:4) prediction performance: RMSE statistic for different forecast horizons

Domestic inflation DSGE VAR(1) Random Walk Nominal interest rate DSGE VAR(1) Random Walk Overall inflation DSGE VAR(1) Random Walk Real Wages DSGE VAR(1) Random Walk Real GDP DSGE VAR(1) Random Walk

1q

2q

3q

4q

5q

6q

7q

8q

0.75 1.71 2.08

1.63 1.86 2.78

1.85 1.73 2.76

1.68 1.63 2.93

1.63 1.62 3.08

1.42 1.43 2.59

1.38 1.38 2.93

1.35 1.40 3.13

0.25 0.80 0.46

0.35 1.00 0.77

0.46 0.96 0.81

0.64 0.80 0.88

0.70 0.68 1.10

0.72 0.63 1.23

0.61 0.41 1.03

0.54 0.22 0.89

0.73 1.43 1.42

1.48 1.98 2.23

1.97 2.25 2.85

2.15 2.30 3.38

2.19 2.35 3.84

1.77 1.94 3.79

1.47 1.51 3.54

1.61 1.53 2.85

1.03 1.21 1.54

1.43 1.88 2.67

2.45 2.51 3.51

2.27 2.94 4.18

2.25 3.20 4.66

2.35 3.03 4.57

2.51 2.81 4.51

2.26 3.02 4.67

1.00 2.71 3.15

2.95 3.37 4.10

3.73 3.68 3.98

2.40 3.04 4.19

2.12 2.91 5.33

2.59 2.74 5.99

2.91 2.70 6.61

2.81 2.29 7.84

43

Figure 10: Forecast Relative RMSEs

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Figure 10 for the five variables depicts the out-of-sample RMSEs of DSGE model forecasts relative to those of random walk and VAR(1) forecasts at different horizons. A value of relative RMSE below one indicates that DSGE model outperforms a model, being compared with. The figure visually shows the good performance of the DSGE model relative to both the VAR and random walk. Specifically, the DSGE model relative to random walk does considerably better in forecasting the variables at all forecast horizons. Moreover, this seems to improve as the forecast horizon lengthens. The DSGE model forecast of real wage outperforms one provided by VAR(1) at all considered forecast horizons. In forecasting real GDP, CPI inflation and domestic inflation DSGE model again does a better job relative to VAR(1) (for each of these variables there is only one observation that VAR(1) is able to forecast better). Next statistical difference between these forecasts is evaluated. Table 8: Diebold-Mariano statistic: DSGE model versus alternative models 1q Domestic Inflation VAR(1) Random Walk Nominal Interest Rate VAR(1) Random Walk Overall inflation VAR(1) Random Walk Real Wage VAR(1) Random Walk GDP VAR(1) Random Walk

2q

3q

4q

5q

6q

7q

8q

2.73*** 1.44 -1.18 2.5** 2.17** 1.89*

-0.66 -0.12 0.11 -0.05 2.1** 2.66*** 2** 3.82***

0.94 1.84*

2.54** 2.15** 1.72* 1.77*

0.7 1.15

-1.21 1.09

1.44 1.7*

-0.18 1.58

-0.55 1.51

-1.05 1.15

2.01** 2.02** 1.6 0.99 1.3 1.73* 0.41 1.75* 1.99** 3.16*** 2.96*** 2.35** 2.32** 2.43**

-1.15 2.17**

0.64 0.84 2.8*** 2.12**

0.08 1.09

2.15** 1.7**

1.87* 2.5**

-0.09 0.18

1.04 1.39

1.3 1.62

1.97** 1.26 0.69 2.05** 2.02** 1.85**

1.27 2.02 0.75 2.04** 2.42** 1.93*

-1.12 1.63

-2.15*** 1.76*

*** p < 0.01, ** p < 0.05, * p < 0.1 To compare forecast accuracy of the DSGE model versus alternative models, Diebold and Mariano (1995) statistic is computed and reported in Table 8. Note that if this statistic is positive, then the DSGE model provides better forecast, than the other model. The Table 8 shows that the equal forecast accuracy of DSGE and random walk models is rejected at statisticlly significant level for the most of the forecast horizons. Compared to VAR(1) model, DSGE model provides statistically significant forecast mainly at shorter forecast horizons. Above it has been shown that VAR(1) outperforms DSGE model in forecasting nominal interest rate starting 45

from six-quarter ahead forecast, but according to Diebold-Mariano statistic the only significant difference turns out to be associated with one-quarter and two-quarter ahead forecasts.

8

Conclusion

This paper has developed and estimated a New-Keynesian DSGE model for the Armenian economy. A brief survey on the main Armenian economic events has been provided. The model setup has been based on new Keynesian framework and to capture empirical persistence in Armenian macroeconomic data, number of frictions, real and nominal rigidities have been assumed. The model economy has been built, assuming monopolistic competition in goods and labor markets; habit formation to consumption decisions; unemployment in the labor market; sticky wages and prices; partial indexation of wages and prices; exchange rate incomplete pass-through and etc. The estimation has been performed on Armenian quarterly data from 2000 to 2012, using Bayesian full system estimation techniques. Generally the estimates of the parameters have been found to be in line with the relevant literature. Estimation have shown that domestic and import prices are quite sticky. The wages have been estimated to be relatively flexible. Both wage cantracts, domestic and import price contracts exhibit considerable degree of indexation to previous period values. Moreover, the most backward looking process has been found to be import inflation. Overall, the diagnostic measures of estimation quality have been satisfactory. The filtered data have provided quite close fit to observed data, indicating that the model is able to replicate Armenian key macroeconomic variables. Moreover, the model’s superior in-sample fit of observable variables in comparison with previous DSGE model on Armenian economy has been documented. Model-based natural levels of GDP, unemployment and interest rates have been calculated. The study of forecast error variance decomposition have made evident the importance of different structural shocks for driving variation in endogenous variables at different horizons. Considering two benchmark models, the forecast performance of the DSGE model has been evaluated. The exercise has shown that the DSGE model does a better job in out-of-sample forecating, compared with VAR and random walk models. The constructed and estimated DSGE model has been shown to be of value in capturing developments in the economy, as well as in forecasting of observable variables. Thus, the model can be used to guide decisions on necessary economic adjustments and policy responses, specifically in an inflation targeting framework. 46

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