An estimated small open economy model with frictional unemployment Julien Albertini

∗

¨ nes¸ Kamber‡ Gu Michael Kirker

‡

Abstract This paper investigates labor market dynamics in New Zealand by estimating a structural small open economy model enriched with search and matching frictions in the labor market. We show that the model fits reasonably well the business cycle features of key macroeconomic variables. We then extend our analysis to understand the driving forces behind labor market variables. Our findings suggest that the bulk of variation in labor market variables is solely explained by disturbances pertaining to the labor market. Keywords: Search and matching frictions, small open economy models, inflation dynamics, unemployment

JEL Classification: H29; J23; J38; J41; J64

∗

EPEE et TEPA (FR CARS no 3126), University of Every, Bd. Fran¸cois Mitterand, 91025 Cedex, France. Reserve Bank of New Zealand, 2 the Terrace, Wellington, New Zealand. E-mail addresses: [email protected] (J. Albertini), [email protected] (G. Kamber), [email protected] (M. Kirker). ‡

1

1

Introduction

This paper investigates labor market dynamics in an estimated structural small open economy model. The starting point of the analysis is to incorporate search and matching frictions in the labor market into an otherwise standard microfounded general equilibrium model. We then estimate the model on New Zealand data using Bayesian estimation techniques. The methodology we adopt allows us to evaluate the ability of the model to match business cycle properties of key macroeconomic and labor market variables in New Zealand. Based on the theoretical framework developed by Gali and Monacelli (2005) and Monacelli (2005), dynamic stochastic general equilibrium (DSGE) models with staggered price setting have become the workhorses for analyzing business cycle fluctuations and monetary policy design in small open economies. For example, using such models, Lubik and Schorfheide (2007) investigate whether small open economy central banks respond to exchange rate movements, Justiniano and Preston (2010a) and Kam et al. (2009) consider the design of optimal policy for inflation targeting small open economies. There is also extensive literature that evaluates the fit of these models, including, Adolfson et al. (2007,2008) for Sweden, Justiniano and Preston (2010b) for Canada and Matheson (2010) for Australia, Canada and New Zealand. A number of works have applied this framework to the New Zealand economy. Liu (2006) builds and estimates a small open economy DSGE model to investigate the propagation mechanism of various shocks. Lees et al. (2007) examine the forecasting performance of these models. Kirker (2008) estimates the natural real rate of interest, inflation target, potential output, and neutral real exchange rate using a DSGE model with time-varying parameters. Furthermore, in the light of the empirical performance of DSGE models, the Reserve Bank of New Zealand has adopted a large scale multi-sector DSGE model, KITT, as its core forecasting model.1 None of the aforementioned models, however, incorporate features to explicitly analyze flows in the labor market. They are therefore silent with regards to unemployment fluctuations both over the business cycle and in response to monetary policy shocks. Our paper aims to fill this gap and is related to Campolmi and Faia (2009) and Hairault (2002), who examine labor market frictions in open economy models. However Campolmi and Faia (2009) focus on the labor market institutions in the Euro Area and Hairault (2002) examines the transmission of productivity shocks in a two country real business cycle model. Our contribution is to develop a small open economy model with sticky prices in which the central bank follows an independent 1

See Lees (2009) and Benes et al. (2009) for more details.

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monetary policy rule. The literature that explicitly introduces labor market flows into closed economy business cycle models has been vast. Seminal papers such as Merz (1995), Andolfatto (1996) and Den Haan et al. (2000) have introduced the concept of equilibrium unemployment in real business cycle models in a tractable way. By allowing the coexistence of workers searching for jobs and firms looking for employees, this setup allows us to explore labor market flows in conjunction with other macroeconomic aggregates over the business cycle. Recently, several works have focused on the implications of implicitly taking into account labor market frictions when it comes to inflation dynamics and monetary policy. This body of research incorporates search and matching frictions into otherwise standard New Keynesian business cycle models. Hence, these models explicitly link labor market frictions to inflation dynamics. Relevant papers include among others: Walsh (2005), Krause and Lubik (2007), Krause et al. (2008), Gertler et al. (2008), Christoffel and Kuester (2008), Tigari (2009) and Christoffel and Linzert (2010). This paper contributes to this literature by analyzing the role of labor market frictions for inflation dynamics and monetary policy in a small open economy. Our main findings are as follows. The estimated model describes well the second moments of the key macroeconomic and labor market variables in New Zealand for reasonable parameter values. It also predicts an appealing monetary transmission mechanism by providing the dynamic response of labor market variables, such as the unemployment and vacancy rates, alongside usual macroeconomic aggregates. However, the model implies that the bulk of the variation in unemployment and vacancies is solely due to shocks pertaining to the labor market and that there is a strong disconnect between the labor market and the rest of the economy. The rest of the paper is organized as follows. Section 2 details the model. Section 3 presents the data and the estimation method. Section 4 discusses our estimation results. In section 5, we investigate the driving forces of unemployment and vacancies. Section 6 concludes.

2

The economic environment and the model

We build a small open economy DSGE model based on Monacelli (2005), Gali and Monacelli (2005), and Justiniano and Preston (2010b). We include a non-Walrasian labor market with matching frictions and hiring costs in the spirit of Mortensen and Pissarides (1994, 1999). We focus on the flow of workers between employment and unemployment. Time is discrete, and our

3

economy is populated by homogeneous workers and firms. Domestic producing firms are large and employ many workers as their only input. Labor may be adjusted at the extensive margin (employment) as well as the intensive margin (hours). Wages and hours are both the outcome of a bilateral Nash bargaining process between the large firm and each worker. Firms face nominal wage rigidities. We separate hiring and pricing decisions by assuming that domestic retailers set home prices and face quadratic adjustment cost as in Rotemberg (1998). The import sector buy domestic goods from the rest of the world and set imported good prices under quadratic adjustment cost.

2.1

The labor market

The search process and recruiting activity are costly and time-consuming for both, firms and workers. A job may either be filled and productive, or unfilled and unproductive. To fill their vacant jobs, firms publish adverts and screen workers, incurring hiring expenditures. Workers are identical, they may either be employed or unemployed. The number of matches Mt is given by the following Cobb-Douglas matching function:

Mt = Xt Stmν Vt1−ν with ν ∈]0, 1[, Xt > 0

(1)

where Vt denote the mass of vacancies, and Stm represents the mass of searching workers. The labor force L is assumed to be constant over time. Assuming, L = 1 allows to treat aggregate labor market variables in number and rate without distinction. The matching function (1), satisfies the usual assumptions, it is increasing, concave and homogenous of degree one. Xt is matching efficiency shock. ν stands for the elasticity of the matching function with respect to the number of job seekers. A vacancy is filled with probability qtm = Mt /Vt and a job seeker finds a job with probability ftm = Mt /Stm .

2.2

The sequence of events

As Hall (2005) points out, fluctuations in labor market flows are mainly driven by job creation. So we abstract from job destruction decisions by assuming that, in each period, a fixed part of existing jobs are exogenously destroyed at rate ρx . Employment in period t has two components: new and old workers. New employment relationship are formed through the matching process in period t. New matches start working

4

within the same period. The number of job seekers is given by: Stm = 1 − (1 − ρx )Nt−1

(2)

This definition has two major consequences. First it allows workers losing their job in t to have a probability of being employed in the same period. Second it allows to make a distinction between job seekers and unemployed workers Ut = (1−Nt ). The last ones receive unemployment benefits. The employment law of motion is given by: Nt = (1 − ρx )Nt−1 + Mt

2.3

(3)

The representative household

All households receive an equal fraction of both domestic and retail firm profits in the domestic economy. The expected intertemporal utility of the large family writes:   ∞ X t ¯ max E0 β εc,t log(Ct − χCt−1 ) − Nt V (ht ) ΩH t

(4)

t=0

where β ∈]0, 1[ is the discount factor. χC¯t−1 is an external habit taken as exogenous by the household and χ is the deep-habit parameter. Indeed, the household is too small relative to the size of the economy to make a material impact on aggregate variables. Nt the aggregate employment over each firm and V (.) is the disutility of work which takes the following form: V (ht ) = κh

h h1+φ t 1 + φh

(5)

where ht denotes hours of work. φh is the inverse of the Frisch elasticity of labor supply. εc,t corresponds to a preference shock and κh to work disutility parameter. Ct is a composite consumption index of domestic and imported bundles of goods such that:  η  η−1 η−1 η−1 1 1 η η Ct = (1 − α) η CH,t + α η CF,t

(6)

where CH,t and CF,t are Dixit-Stiglitz aggregates of the available domestic and foreign produced goods. They are given by:  Z 1  −1 −1 CH,t = CH,t (i)  di

Z and

CF,t =

1

CF,t (i)

−1 

  −1 di

(7)

0

0

where α corresponds to the balance trade steady state share of foreign goods in the domestic consumption bundle. η > 0 denotes the elasticity of substitution between domestic and foreign goods and  > 1 the elasticity of substitution between the differentiated goods. Optimal allocation of expenditures between domestic and foreign bundles writes: 5

 CHt = (1 − α)

PH,t Pt

−η

 Ct

and

CFt = α

PF,t Pt

−η Ct

Optimal allocation between differentiated goods involves the following demand functions:     PF,t (i) − PH,t (i) − CH,t and CFt (i) = CF,t CHt (i) = PH,t PF,t

(8)

(9)

and Pt is a composite price index of domestic and imported bundles of goods such that: h i 1 1−η 1−η 1−η Pt = (1 − α)PH,t + αPF,t

(10)

It corresponds to the domestic CPI. PH,t and PF,t denotes the domestic goods prices and the domestic currency price of imported goods respectively. ∞ The representative household chose a set of processes ΩH t = {Ct , Bt , Dt , Nt , }t=0 taken as

given the set of processes {Pt , Wt , it , i∗t ftm }∞ t=0 and the initial wealth D0 and B0 so as to maximize (4) subject to:

1) the budget constraint, Pt Ct + Dt + et Bt = Dt−1 (1 + it−1 ) + et Bt−1 (1 + i∗t−1 )φt (At ) + Wt Nt ht + (1 − Nt )bt Pt + ΠH,t + Πt,t + Tt

(11)

2) the law of motion of employment (3) Nt = (1 − ρx )Nt−1 + ftm Stm

(12)

Dt is the household’s holding of one period domestic bonds at date t and Bt is the household’s holdings of one period foreign bonds. The corresponding foreign and domestic interest rates are it and i∗t respectively. et denotes the nominal exchange rate. Wt is the nominal wage level. ΠH,t and ΠF,t represent profits from holding shares in domestic and imported goods firms. b is the real amount of unemployment benefits an unemployed worker receives and Tt is a lump-sum tax. As in Benigno (2001), Kollmann (2002), Schmitt-Grohe and Uribe (2003) we introduce a debt elastic interest rate premium to close the model. It is governed by the function φt which takes the following form:

where

φt = exp(−φAt ) et−1 Bt−1 At = Y Pt−1 6

(13)

is the real quantity of outstanding foreign debt expressed in terms of domestic currency as a fraction of steady state output. The optimality conditions of the household’s problem can be written as follow: λt = εc,t (Ct − χCt−1 )−1

(14)

λt /Pt = Et [(1 + it )βλt+1 /Pt+1 ]

(15)

λt et /Pt = Et [(1 + i∗t )βφt+1 λt+1 et+1 /Pt+1 ]   Wt ht m ϕt = λt − b − εc,t V (ht ) + βEt (1 − ρx )(1 − ft+1 )ϕt+1 Pt

(16) (17)

where λt and ϕt are the Lagrange multipliers on the budget constraint and the employment law of motion respectively. (14) defines the standard Euler equation. (15) and (16) express the portfolio allocation of domestic and foreign bonds. (17) is the marginal expected value of an employed worker i.e. the expected value of employment minus the expected value of unemployment. Combining the two first-order conditions on domestic and foreign bond holdings results in the standard uncovered interest rate parity condition: et+1 it 1 = ∗ et it φt+1

2.4 2.4.1

(18)

Domestic producers Domestic intermediate sector

Domestic intermediate good producer operate in a perfectly competitive market using labor as their only input. The production of domestic intermediate firm is given by: YI,t = Zt (Nt ht )ζ

(19)

where Zt is a technology shock. The optimization problem of the intermediate firm consist of m ∞ choosing a set of processes ΩPt = {Vt , Nt }∞ t=0 taken as given the set of processes {PH,t , Wt , qt , ht }t=0 .

The domestic intermediate good producer maximizes the following intertemporal function:   ∞ X λt Wt max E0 βt mct YI,t − ht Nt − Γ(Vt ) − Υ(Wt )Nt λ0 PH,t ΩP t t=0

subject to the production function (19) and the evolution of employment, Nt = (1 − ρx )Nt−1 + qtm Vt and assuming the wage cost function takes the following form:  2 ψW Wt Υ(Wt ) = − 1 ht Y¯I,t w W 2 π ˜t−1 t−1 7

(20)

(21)

where mct is the relative price of intermediate good sector in terms of domestic price level and coincides with the marginal cost of domestic retail firm. YH,t is the intermediate good and PH,t is the domestic goods price. ζ corresponds to the employment share of production in the domestic good. Hiring is costly and incurs a cost Γ(Vt ) per vacancy posted. The intermediate goods-producing firm faces a quadratic wage adjustment cost which is proportional to the size of its workforce. πtw = Wt /Wt−1 represents the wage inflation and π ˜tw = πtw,γw π w,1−γw . γW governs the degree of backward-looking wage setting and π w is the steady state wage inflation. The optimality conditions of the above problem are:

Γ0 (Vt ) qtm YI,t Wt λt+1 = mct ζ − ht − Υ(Wt ) + β(1 − ρx )Et µt+1 Nt PH,t λt

µt =

(22)

µt

(23)

where µt is the Lagrange-multiplier associated to the employment constraint. It gives the expected marginal value of a job for the firm. Combining the two first-order conditions gives the job creation condition:

YI,t λt+1 Γ0 (Vt+1 ) Γ0 (Vt ) Wt x = mc ζ h − Υ(W ) + β(1 − ρ )E − t t t t m qtm Nt PH,t λt qt+1

(24)

It shows that the expected gain from hiring a new worker is equal to the expected cost of search (which is the marginal cost of a vacancy Γ0 (Vt ) times the average duration of a vacancy 1/qtm ). For the wage derivation we can also rewrite the job creation condition in terms of the real wage defined as the nominal wage divided by the consumer price level.

YI,t Wt x λt+1 Γ0 (Vt+1 ) Γ0 (Vt ) x = mc ζ − a − Υ(W ) + β(1 − ρ )E t t t t m qtm Nt Pt λt qt+1

(25)

where we define the fraction axt =

Pt PH,t

(26)

which will be related to the terms of trade below. 2.4.2

Wage and hours setting mechanism

We now turn to the wage and hours setting structure. At equilibrium, filled jobs generate a return (the marginal value of the job µt plus the corresponding employed worker value ϕt ) 8

greater than the values of a vacant job and of an unemployed worker. The net gain issued from a filled job is the total surplus of the match: St =

ϕt + µt λt

(27)

Nominal wages and hours are determined through an individual Nash bargaining process between each worker and his employer who share the total surplus of the match. Each participant threat point corresponds to the value of the alternative option, which is the value of being unemployed or the value of a vacant job for a firm. The outcome of the bargaining process is given by the solution of the following maximization problem:  1−ξt ϕt max µξt t Wt ,ht λt

(28)

where ξt ∈]0, 1[ and 1 − ξ denote the stochastic firms and workers bargaining power respectively. We assume that bargaining power is not constant over time and follow a stochastic process. The optimality conditions of the above problems are given by: ∂µt ∂Wt ∂µt ξt ϕt ∂ht

ξt ϕt

∂ϕt ∂Wt ∂ϕt = −(1 − ξt )µt ∂ht = −(1 − ξt )µt

(29) (30)

where ∂ϕt ∂Wt ∂µt ∂Wt ∂ϕt ∂ht ∂µt ∂ht

λ t ht Pt  w   w  πw πt ht ht YI,t πtw λt+1 ht+1 Yi,t+1 πt+1 t+1 − ψw = − − 1 + βEt ψw −1 w w PH,t Wt π ˜t−1 π ˜t−1 λt Wt π ˜t+1 π ˜t Wt = λt − V 0 (ht )εc,t Pt YI,t Wt = ζ 2 mct − Nt ht PH,t =

We can rewrite the wage level and individual hours as: ϕt ∂µt Pt = −(1 − ξ)µt ht λt ∂Wt     YI,t Wt Wt 2 0 ξϕt ζ mct − = −(1 − ξ)µt λt − V (ht )εc,t Nt ht PH,t Pt ξ

(31) (32)

Equation (31) is the wage setting equation. The wage level is a weighted sum of the worker’s outside option and its contribution to the product. Equation (32) determine the hours worked level. The disutility induced by working one additional hour is equal to its marginal productivity. Using the above optimality condition and the definition of ϕt and µt provided by (17) and 9

(24) one can get the real wage equation and the hours of work condition.

Flexible economy

Let discuss how the different price evaluations of wage affect the bargaining. To make the analysis tractable we discuss the case where wages are perfectly flexible (ψw = 0). The real wage and the hours of work can be written as:    axt+1 YI,t λt+1 x x + β(1 − ρ )Et µt+1 1 − (1 − ft ) x wt ht = ξat ζ Nt λt at   V (ht ) +(1 − ξ) b + λt 0 YI,t V (ht ) = axt ζ 2 λt ht Nt As in Campolmi and Faia (2009), the terms of trade now enter in the wage equation. The reason is that firms evaluate wage in terms of domestic prices while workers evaluate wage in terms of aggregate prices. We can show2 that the log-linear form of this ratio can be expressed as: a ˆxt = αˆ st This implies that an expected depreciation of the terms of trade (an increase in sˆt )) has a positive impact on the negotiated wage. This reflects the fact that a drop of domestic prices with respect to imported prices makes the workers’ purchasing power lower since they consume a composite of domestic and foreign goods. Workers demand a higher wage to compensate for this effect. As a result, the terms of trade effect act as a variation of bargaining power of workers. The extent to which terms of trade affects the real wage depends on the probability of workers finding a job, which is summarized by the coefficient (1 − ft ) . 2.4.3

Domestic retail firms

There is a continuum of monopolistically competitive retailers who combine the differentiated goods to the final good and sell it to the representative household. They buy intermediate good from the intermediate good producing firms and set a domestic retail price in a monopolistic ∞ ∞ environment choosing the process ΩR t = {PH,t (i)}t=0 taken as given the set of processes {Pt }t=0 ) 2

Details are given in the section market clearing.

10

facing a quadratic price adjustment cost (Rotemberg-style). The optimization problem of the retailers is: max E0 ΩR t

∞ X t=0

β

t λt



λ0

PH,t (i) ψH YH,t (i) − mct YH,t (i) − PH,t 2



PH,t (i) −1 π ˜t−1 PH,t−1 (i)

2

 YH,t

(33)

Subject to,  YH,t (i) =

PF,t (i) PF,t

− YH,t

(34)

The optimality condition of this problem with respect to PH,t (i) gives the standard New Keynesian Phillips Curve (NKPC):       πH,t (i) πH,t (i) PH,t (i) 1− PH,t (i) 1− H −1 = (1 − ) + t mct ψH π ˜H,t−1 π ˜H,t−1 PH,t PH,t   πH,t+1 (i) πH,t+1 (i) YH,t+1 λt+1 + βEt ψH −1 λt π ˜H,t π ˜H,t YH,t

(35)

1−γH γH . πH where inflation is defined as gross inflation πH,t = PH,t /PH,t−1 and where π ˜H,t−1 = πH,t−1

γH governs the degree of backward-looking price setting and πH is the steady state inflation.

2.5

Import sector

In the small open economy, there are a continuum of firms importing differentiated goods in a monopolistically competitive environment. They set the price of imported goods and face quadratic price adjustment cost. Firms maximize the expected present value of their profits ∞ and chooses the set of processes ΩFt = {PF,t (i)}∞ t=0 taken as given the set of processes {PF,t }t=0 .

The optimization problem is as follow:  2   ∞ X PF,t (i) ψF t λt PF,t (i) ∗ max E0 YF,t (i) − − 1 YF,t − et PF,t (i)YF,t β λ0 PF,t 2 π ˜F,t−1 PF,t−1 (i) ΩF t

(36)

t=0

Subject to,  YF,t (i) =

PF,t (i) PF,t

−Ft YF,t

(37)

As previously, inflation is defined as gross inflation πF,t = PF,t /PF,t−1 . ψF is an adjustment γF cost parameter and π ˜F,t−1 = πF,t−1 πF1−γF and γF governs the degree of backward-looking price

setting. The optimality condition of the above problem is:     F   F πF,t (i) πF,t (i) PF,t (i) 1−t PF,t (i) 1−t ψF −1 = (1 − Ft ) + t mcFt π ˜F,t−1 π ˜F,t−1 PF,t PF,t   πF,t+1 (i) πF,t+1 (i) YF,t+1 λt+1 + βEt ψF −1 λt π ˜F,t π ˜F,t YF,t

(38)

∗ (i) is the marginal cost of providing the foreign good. Once more, we can where mcFt = et PF,t

drop (i) subscript by symmetry. 11

2.6

The monetary authorities

We assume that central bank adjust the nominal interest rate to deviations of inflation, output and the exchange rate from their steady state values. The monetary authorities chooses the short-run interest rate i according to a Taylor type rule:       1−ρR    1 Et πt+1 ρπ Yt ρY Yt ρ∆Y e t ρe ρR it = it−1 exp(εm t ) β π Y Yt−1 et−1

2.7

(39)

Market clearing and international risk-sharing

The real exchange rate is defined as qt = et Pt∗ /Pt . When the law of one price doesn’t hold, we have et Pt∗ /PF,t 6= 1. In the domestic and foreign economies, goods market clearing involves: ∗ YH,t = CH,t + CH,t

and Yt∗ = Ct∗

(40)

The model is closed assuming foreign demand for the domestically produced good is specified as: ∗ CH,t

=

∗ PH,t

P∗

Yt∗

(41)

The unemployment insurance and government spending are financed by the lump-sum tax. As in Monacelli (2005) the “law of one price gap” is defined as ΨF,t = et

Pt∗ PF,t

(42)

and the term of trade in difference as: st =

πF,t πH,t

(43)

The term of trade and the real exchange rate are related according to the following relation qt = et

Pt∗ ≡ ΨF,t s1−α t Pt

(44)

The domestic CPI and home goods prices are related by the following condition: πt =

πH,t (st /st−1 )α

(45)

Finally, using the definition of the real exchange rate, the uncovered interest-rate parity condition (18) can be written in the following manner: Et

∗ it πt+1 qt+1 = Et φt+1 qt πt+1 i∗t

(46)

The foreign sector is assumed to be exogenous to the small open economy. We assume that the foreign economy variables, πt∗ , Yt∗ and ı∗t follow independent autoregressive processes. 12

3

Data and Estimation

3.1

Data

Our estimation uses quarterly data for New Zealand from the period 1994Q3 to 2010Q1 and covers most of the inflation targeting era. The beginning of our sample is dictated by the availability of the vacancy data in New Zealand. Output per capita (Yˆt ) is defined as the seasonally adjusted gross domestic product (GDP) divided by the active labor market population (the sum of official employment and official unemployment measures). Inflation (ˆ πt ) is defined as the quarterly percent change in the New Zealand CPI. The nominal interest rate (ˆit ) is defined as the 90-day bank bill yield. The real exchange rate (ˆ qt ) is defined to be the real effective exchange rate. Unemployment (ˆ ut ) is measures by the official seasonally adjusted Household Labour Force Survey (HLFS) unemployment ˆ t ) is defined as the seasonally adjusted HLFS hours worked divided rate. Hours per worker (h by the official seasonally adjusted HLFS employment rate. The real wage (w ˆt ) is defined as the seasonally adjusted Quarterly Employment Survey (QES) measure of average hourly earnings (ordinary time in the private sector) divided by the CPI. Vacancies (ˆ vt ) are measured by aggregating the monthly Job Ad Series from the Department of Labour, and normalizing by the active labor market population. For the foreign economy variables we use the composite measures published by the Reserve Bank of New Zealand. Foreign output (Yt∗ ) is defined as an export weighted measure of the GDP of 16 of New Zealand’s largest trading partners.3 Foreign inflation (πt∗ ) is an import weighted measure of the CPI inflation rates in the same 16 countries. The foreign nominal interest rate (i∗t ) is defined as an 80-20 weighted measure of the United States 90-day bank bill yield and the Australian 90-day bank bill yield. All data are detrended using Hodrick-Prescott filters with a smoothing parameter (lambda) of 1600 apart from domestic and foreign inflation rates and interest rates which are detrended using the sample mean.

3.2

Estimation method

We estimate model parameters and shocks using Bayesian techniques.4 Posterior density are evaluated using a random-walk Metropolis-Hastings algorithm for which we generate 4000000 draws and we target an acceptance ratio of 0.3. We log-linearize the model around the de3

This GDP-16 measure covers around 80 percent of New Zealand’s merchandise trade by value. See An and Schorfheide (2007) and Lubik and Schorfheide (2005) for a detailed analysis of Bayesian estimation of DSGE models for small open economies 4

13

terministic steady state and apply the Kalman-filter to evaluate the likelihood function. We combine the likelihood function with the prior distribution of the model parameters to get the posterior distribution. We calibrate seven parameters in the model to avoid identification problems. We set the discount factor (β)to 0.99, which gives an annual steady state interest rate close to 4%. The share of foreign goods in the domestic consumption bundle (α) is equal to 0.3 to match the share of imports in New Zealand. The elasticity of the production function with respect to the labor input (ζ) is set to 2/3. The level of unemployment benefits is set to match the average replacement ratio of about 0.5. We set the exogenous job separation rate (ρx ) to match the evidence reported in Bell and Silverstone (2010). They calculate that, over the period 19862010, the average probability of an employed worker to become unemployed or “out of the labor force” is 0.06. In addition, we calibrate the steady state values of the match efficiency X to reproduce the average unemployment rate of 0.12 which is larger than the rate observed in the data (about 0.065) to account for workers not in the labor force but searching for a job. κv is set in such a way the steady state total cost of vacancies is about 1% of output. We normalize the job filling rate (q m ) to 0.71 to get a steady state job finding rate similar to the average observed in the data (taking into account the “out of the labor force” pool) which is 0.31 (Bell and Silverstone(2010)). We adopt relatively loose priors for the rest of the model parameters (see table 1) and assume a Beta-distribution for share parameters defined on unit interval and Gamma-distribution for positive-valued parameters. In line with Krause, Lubik and Lopez-Salido (2008), we choose loose priors for the inverse of the Frisch elasticity of labor supply and the habit persistence which are centered on the means of 1 and 0.5 respectively. We assume the mean of the prior of the elasticity of substitution between domestic and foreign goods to be equal to 1. The prior mean of domestic and import price adjustment costs (ψH and ψF ) as well as the wage adjustment cost ψw are all set to 50. Similarly, the prior for home and foreign price indexation parameters (γH and γF respectively) and the wage indexation parameter are set to 0.75. Because we do not have any information on the firm bargaining power and the elasticity of the matching function, we follow the common approach and set both equal to 0.5 (see Petrongolo and Pissarides (2001)). The mean prior of the parameter governing the convexity or the concavity of the vacancy adjustment cost function (κv ) is set to 1 i.e. the function is initially linear. We set the response of the monetary authority to inflation prior to 2 while the response to variation of output, output

14

growth and nominal exchange rate are set to 0.25. Monetary policy parameters are assumed to be normally distributed. We assume that all the exogenous disturbances follow independent AR(1) processes. The prior means for the persistence of shocks persistence are set to 0.5. Finally, the standard deviation of shocks follow an Inverse Gamma distribution with prior mean 0.01.

4

Estimation results

4.1

Parameter estimates

Table 1 reports posterior means of estimated parameters and the 90% confidence intervals. The inverse of the labor supply elasticity is estimated to be between 1.08 and 1.29 with a posterior mean of 1.19. The estimated elasticity of substitution between domestic and foreign goods is quite low (0.51) but consistent with the results of Justiniano and Preston (2010a). The posterior mean of the habit persistence is 0.29 and contrast the values obtained in closed economy models. However Krause, Lubik and Salido (2008) estimate low values of habit formation parameter in a closed economy model with search and matching frictions. Additionally, Justiniano and Preston (2010a) report low values of this parameter when they estimate a small open economy model for Australia, Canada and New Zealand. The estimated indexation to past inflation in price and wage setting are similar and concentrated around 0.6. However, the model implies that nominal rigidities are more important in the goods market than in the labor market. In particular, the price adjustment cost parameter in the import sector is higher than in the domestic retail sector, possibly in order to capture the low pass through from the exchange rate movements to domestic prices. The search and matching frictions in the labor market seems to limit the need for nominal rigidities, since the model doesn’t rely on high degrees of nominal rigidities to capture wage dynamics. The parameters of the interest rate rule we obtain are close to the ones found by Justiniano and Preston (2010a) although their sample period begin in 1988Q3 while we only consider the inflation targeting era. We estimate the coefficient determining the response to inflation to be 2.14. Both output gap and output growth enter the monetary policy rule with positive coefficients. The response of nominal exchange rate growth is very weak (0.08) but significantly positive and broadly consistent with Lubik and Schorfheide (2007)5 who show that Australia and New Zealand do not respond to exchange rate movements. Lastly, interest rate setting 5

Whose estimated coefficient on the interest rate rule is 0.04

15

exhibits a substantial smoothing with posterior mean of the interest rate smoothing parameter estimated to be 0.8. Estimated parameters of the labor market reveal that the model doesn’t seem to differ from the prior value. The estimated confidence band are quite large suggesting this parameter is not clearly pinned down from the data. The estimated elasticity of the matching function with respect to unemployment is equal to 0.71 which is similar to the one obtained by Shimer (2005) on US data. The posterior mean of the firm bargaining power (0.51) is very close to its prior. According to the confidence interval there is little evidence the Hosios condition (1990) (ν = 1 − ξ) is satisfied, involving inefficiencies in the labor market. Finally, we estimate the vacancy posting adjustment cost parameter to be 5.86 well above the prior mean. This suggests that the vacancy adjustment cost function is clearly convex. The implied value support Yashiv (2006) against Rotemberg (2008) and highlights the costly process of adjusting the level of vacancies over the cycle. As for the shock processes, the UIP, preference and vacancy posting shocks are estimated to be highly persistent while all the other domestic shocks have an AR(1) coefficient below the prior mean of 0.5. In terms of volatilities, the estimated values for monetary policy, technology and UIP shocks seem plausible. The domestic cost-push shock and shocks pertaining to the labor market are the most volatile disturbances.

4.2

Moments

In this section, we evaluate the model’s performance to match the cyclical properties of New Zealand data. In doing so, we take into account the parameter and shock uncertainty. Figures 1, 2 and 3 present cyclical properties of the data and those implied by the estimated model. In each graph the line is the second order moment of the data while the shaded area represents the density of the corresponding moment generated by drawing from the posterior distribution of the parameters and shocks.

6

Figure 1 presents the standard deviation of output and for other variables their relative standard deviations with respect to output. The model matches well the volatility of output, interest rate and inflation. Although the model implies a lower volatility of exchange rate compared to the data, it still able to generate a considerably more volatile real exchange rate than output. 6

Specifically, we calculate the model based moments by simulating 2000 artificial data series of equal length to our sample.

16

We now turn to the performance of the model in terms of replicating the volatilities of the labor market variables. First, the model is able to generate highly volatile unemployment and vacancies dynamics. However, the volatilities in the data still lie on the upper bound of the model implied values. For the real wage, the model overestimate its volatility. As it will become clearer below, the main failure of the model is with regards to the dynamics of individual hours. The model implied volatility of individual hours is higher than output while in the data individual hours is much less volatile than output. Figure 2 presents the correlation of the selected macroeconomic aggregates with output as well as the correlation between unemployment and vacancies. The models does well again for interest rate, inflation, and exchange rate. However, the model underestimate the strong countercyclicality of unemployment and the strong procyclicality of vacancies. In a related note, the model implied correlation between unemployment and vacancies is not as negative as in the data. In other words, the model based slope of the Beveridge curve is higher in the data. The model also seem to generate a slightly procyclical real wages compared to acyclical wage dynamics in the data. Again, the model implies a much stronger procyclicality of hours. Figure 3 shows the model and data based persistence of the selected variables. We define persistence as the first order autocorrelation of each variable. The model does well for most of the variables that we consider by replicating the high observed persistence in the data. Nevertheless, the model overestimates the persistence in inflation, real wages and individual hours. In particular, the persistence of inflation and individual hours very low in the data, a feature the model is not able to replicate. Overall the model seems to do a reasonably good job in describing the second-order properties of the New Zealand data. Nonetheless, the model moments pertaining to labor market variables don’t appear to be as close to the data as other macroeconomic aggregates.

4.3

Impulse response analysis

In this section, we characterize the transmission of monetary policy in New Zealand by presenting the impulse responses implied by the model to a monetary policy shock. We pay a particular attention to the dynamics of the labor market variables by presenting in figure 4 the dynamic response of additional labor market variables. We compute the impulse responses at the posterior mode as well as the 90% posterior probability intervals around the impulse responses. The monetary policy shock is scaled to

17

generate a 1% increase in the annual interest rate. A first inspection of the impulse responses suggests that the response of all the variables we consider is statistically significant. Following the increase in the interest rate, as prices are sticky, the real interest rate increases which yields a contractionary impact in the model economy. Output drops by a little more than 1%. The response of inflation (expressed in annual terms) is gradual over time after dropping 1.5% on impact. As a result of higher real interest rates, the exchange rate appreciates persistently. Now we turn to the dynamic response of labor market variables. Following the contractionary monetary policy, the marginal value of a job decreases for firms which makes them to lower their vacancy posting and cut the hours of work. This increases the number of unemployed workers and the number of job seekers. The two latter variables’ responses display hump shaped patterns. Unemployment rate increases by around 1.2% initially and the impact of monetary policy shock on unemployment lasts almost for two years. The higher number of job seekers and lower number of vacancies imply that the labor market tightness and the job finding rate are below their steady states. These in turn put a downward pressure on the negotiated wage. The wage inflation drops by 0.5% on impact. The real wage drops initially and increases later since the decline in the inflation rate after the monetary policy shock lasts longer than the decline in the wage inflation. Overall, the monetary policy shocks seems to create statistically significant and quantitatively important fluctuations in the labor market variables.

5

Dynamics of Unemployment and Vacancies

In the previous section, we have shown that our model provides a fairly good description of macroeconomic and labor market variables in New Zealand. In this section, our objective is to use our structural model to investigate which shocks are the driver of unemployment and vacancies in New Zealand. To do so, we analyze the variance decomposition of unemployment and vacancies. Figures 5 and 6 presents variance decomposition of vacancies and unemployment. The model is driven by eleven structural shocks. Three of these shocks are directly related to the labor market of the model: Matching efficiency shock, bargaining power shock and vacancy posting cost shock. In figures 5 and 6, while we detail the contribution of labor market shocks to the fluctuations in unemployment and vacancies, we group together the contribution of all the other shocks. Inspecting figures 5 and 6 makes clear that the bulk of variation in both series

18

are due to the disturbances pertaining to the labor market. In particular, most of the variation in unemployment is due to shocks to matching efficiency (which is in line with the results of Krause et al.(2008) in a closed economy model), while most of the variation in vacancies is due to shocks to vacancy posting cost. All the other shocks, foreign, domestic or policy, play only a marginal role in explaining cyclical variations in these two key labor market variables. The model is thus unable to generate an internal propagation mechanism from shocks affecting the rest of the economy to the labor market variables. As an another way to put forward the disconnect between labor market part and the rest of the model, figure 7 presents the variance decomposition of output. In accordance with our argument, shocks the labor market variables contribute marginally to the fluctuations in output. This result is consistent with Christoffel and al. (2009) who use a model with a shock on the separation rate instead of on the matching function. They find that the contribution of vacancy shocks to unemployment and vacancies fluctuations is important but that the latter shock does not affect output fluctuations. In addition, they find that the contribution of bargaining shock to the labor market variables is relatively small. Reallocation shocks, modeled as exogenous movements in the matching efficiency, play a central role in our model since they essentially drive unemployment fluctuations. However, such a shock tend to produce a weak negative correlation between unemployment and vacancies compare to the one observed. As mentioned in Lubik (2009) these shocks act as a residual and capture what the matching function is not able to explain. Therefore, considering a small open economy with search and matching frictions doesn’t change the disconnect between the labor market and the rest of the model.

6

Conclusion

In this paper, focusing on New Zealand, we have developed and estimated a structural small open economy model enriched with search and matching frictions in the labor market. The methodology we adopt allows us to evaluate the ability of the model to match business cycle properties of key macroeconomic and labor market variables in New Zealand. We show that the model match the data well with reasonable parameter values. Impulse response functions analysis highlight an appealing monetary transmission mechanism. However, the model implies that the bulk of the variation in unemployment and vacancies is solely due to shocks pertaining to the labor market and that there is a strong disconnect between the labor market and the

19

rest of the economy. This last result naturally raise the question whether the model lacks of propagation mechanisms or if exogenous disturbances in the matching function are a plausible explanation. Since the latter captures what the matching function is not able to explain, it’s legitimate to question the ability of the matching function to reproduce the Beveridge curve and, at the same time, investigate further the role of this shock. It would be interesting to investigate these two aspect for further research. Many alternative specifications of the standard search and matching models can be considered (in line with Christoffel and al. (2009)) endogenous job destructions, alternative wage setting mechanisms (such as right-to-manage bargaining) and heterogeneity among the job seekers by modeling labor market participation. Finally, our model based monetary policy transmission mechanism implies strong movements in labor market variables in New Zealand. However, the empirical evidence using structural econometric models is scarce on the subject when it comes to small open economies. Future empirical research, in the line of Ravn and Simonelli (2008) and Kamber and Millard (2010), that identify the impact of monetary policy shocks on labor market variables would help improve the modeling of labor market frictions in small open economies.

20

References Adolfson, M., Laseen, S., Linde, J. and Villani, M. (2007): “Evaluating an estimated new Keynesian small open economy model,” Journal of Economic Dynamics and Control,vol. 32(8), 2690-2721, August Adolfson, M., Laseen, S., Linde, J. and Villani, M. (2007): “Bayesian estimation of an open economy DSGE model with incomplete pass-through,” Journal of International Economics, vol. 72(2), 481-511, July An, S. and Schorfheide, F. (2007): “Bayesian Analysis of DSGE Models,” Econometric Reviews,, 26(2-4), 113-172 Andolfatto, D. (1996): “Business cycles and labor market search,” The American Economic Review, Vol. 86(1), 112-132. Bell, W. and Silverstone, B. (2010): “Labour Market Flows in New Zealand: Some Questions and Some Answers,” mimeo. Bene, J., Binning, A., Fukac, M., Lees, K. and Matheson, T. (2009): “K.I.T.T.: Kiwi Inflation Targeting Technology,” http://www.rbnz.govt.nz/research/kitt/. Campolmi, A. and Faia, E. (2009): “Labor market institutions and inflation volatility in the Euro area,” Journal of Economic Dynamics and Control, Forthcomming. Christoffel, K. and Kuester, K. (2008): “Resuscitating the wage channel in models with unemployment fluctuations,” Journal of Monetary Economics, 55(5), 865-887. Christoffel, K., Kuester, K. and Linzert, T. (2009): “The role of labor markets for Euro area monetary policy,” European Economic Review, 53, 908-936. Christoffel, K. and Linzert, T. (2010): “The role of wage rigidity and labor market rigidities for inflation persistence,” Journal of Money, Credit, and Banking, 42(7), 1435-1446. Den Haan, W., G. Ramey, and J. Watson (2000): “Job Destruction and Propagation of Shocks,” American Economic Review, 90(3), 482-498. Fujita, S. and Ramey, G. (2007): “Job matching and propagation,” Journal of Economic Dynamics and Control, vol. 31(11), pages 3671-3698. Gali ,J. and Monacelli, T. (2005): “Monetary Policy and Exchange Rate Volatility in a Small Open Economy,” Review of Economic Studies, vol. 72(3), pages 707-734. Gertler, M., Sala, L. and Trigari, A. (2008): “An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining,” Journal of Money, Credit and Banking, vol. 40(8), pages 1713-1764. Hairault J-O. (2002): “Labor-Market Search and International Business Cycles,” Review of Eco-

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nomic Dynamics, vol. 5(3), pages 535-558, July Hagedorn, M. and Manovskii, I. (2008): “The Cyclical Behavior of Equilibrium Unemployment and Vacancies Revisited,” American Economic Review, vol. 98(4), pp 1692-1706 Hall, R. (2008): “Employment Fluctuations with Equilibrium Wage Stickiness,” American Economic Review, vol. 95(1), pp. 50-65. Justiniano, A. and Preston, P. (2010a): “Monetary Policy and Uncertainty in an Empirical Small Open Economy Model,” Journal of Applied Econometrics,, 25(1), Justiniano, A. and Preston, P. (2010b): “Can structural small open economy models account for the influence of foreign disturbances,” Journal of international economics, vol. 81(1), pp 61-74 Kam, T., Lees, K. and Liu, P. (2009): “Uncovering the Hit List for Small Inflation Targeters: A Bayesian Structural Analysis,” Journal of Money, Credit and Banking, vol. 41(4), pages 583-618, 06 Kamber, G. and Millard, S. (2010): “Using estimated models to assess nominal and real rigidities in the United Kingdom,” Bank of England working papers, 396. Kirker, M. (2008): “Does natural rate variation matter? Evidence from New Zealand,” Reserve Bank of New Zealand Discussion paper series, DP2008/17. Krause, M., and Lubik, T. (2007): “The (ir)relevance of real wage rigidity in the New Keynesian model with search frictions,” Journal of Monetary Economics, vol. 54 706-727. Krause, M., Lubik, T. and Lopez-Salido, D. (2008): “Do search frictions matter for inflation dynamics,” European Economic Review, vol. 52, 1464-1479. Krause, M., Lubik, T. and Lopez-Salido, D. (2008): “Inflation dynamics with search frictions: a structural econometric analysis,” Journal of Monetary Economics, vol. 55, no. 5, 892-916. Lees, K., Matheson, T. and Smith C. (2007): “Open economy DSGE-VAR forecasting and policy analysis - head to head with the RBNZ published forecasts,” Reserve Bank of New Zealand Discussion Paper Series, DP2007/01. Lees, K. (2006): “Introducing KITT: The Reserve Bank of New Zealand new DSGE model for forecasting and policy design,” RReserve Bank of New Zealand Bulletin, , vol. 72, 5-20. Liu, P. (2006): “A small New Keynesian model of the New Zealand economy,” Reserve Bank of New Zealand Discussion paper series, DP2006/03. Lubik, T. (2009): “Estimating a search and matching model of the aggregate labor market,” Economic Quaterly, vol. 95.2 101-120. Lubik, T. and Schorfheide, F. (2007): “Do central banks respond to exchange rate movements? A structural investigation,” Journal of Monetary Economics, vol. 54, no. 4, 1069-1089.

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Matheson, T. (2010): “Assessing the fit of small open economy DSGEs,” Journal of Macroeconomics,vol. 32(3), pages 906-920, September Monacelli, T. (2005): “ Monetary Policy in a Low Pass-Through Environment,” Journal of Money Credit and Banking, Vol. 37, N. 6. 1047-1066. Merz, M. (1995): “Search in the labor market and the real business cycle,” Journal of Monetary Economics, vol. 36, 269-300. Mortensen, D., and C. Pissarides (1994): “Job creation and job destruction in the theory of unemployment,” The review of economic studies, 61(3), 397- 415. Mortensen, D., and C. Pissarides (1999): “Job reallocation, employment fluctuations and unemployment,” Handbook of Macroeconomics, vol. 1, chap. 18, pp. 1171-1228. Elsevier Science, New York. Mortensen, D., and Nagypal E. (2007): “More on Unemployment and Vacancy Fluctuations,” Review of Economic Dynamics, 10 (3), pp. 327-347. Ravn, M., and Simonelli S. (2008): “Labor Market Dynamics and the Business Cycle: Structural Evidence for the United States,” candinavian Journal of Economics, vol. 109(4), pages 743-777, 03 Pissarides C. (2009): “The Unemployment Volatility Puzzle: Is Wage Stickiness the Answer?,” Econometrica, vol. 77, pp. 1339-1369 Rotemberg, J. (2008): “Cyclical wages in a search-and-bargaining model with large firms,” NBER Chapter, pp 65-114. Shimer, R. (2005): “The Cyclical Behavior of Equilibrium Unemployment and Vacancies,” American Economic Review, 95(1), 25-49. Thomas, C. and Zanetti, F. (2007): “Labor market reform and price stability: an application to the Euro Area,” Journal of Monetary Economics, vol 55(6) pp 885-899 Trigari, A. (2009): “Equilibrium unemployment, job flows, and inflation dynamics,” Journal of Money, Credit and Banking, 41(1) 1-33. Walsh, C. (2005): “Labor market search, sticky prices, and interest rate policies,” Review of Economic Dynamics, 8(4), 829-849. Yashiv, E. (2006): “Evaluating the performance of the search and matching model,” European Economic Review. Vol. 50, No. 4, pp. 906-936. Zanetti, F. (2007): “Labor market institutions and aggregate fluctuations in a search and matching model,” working paper 333, Bank of England.

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7

Tables

Structural parameters Habit persistence Inverse of Frisch elast. Elasticity of sub. between H & F Backward home price param. Backward foreign price param. Backward wage Price adj. cost home good Price adj. cost foreign good Wage adj. cost Interest rate smooth. Resp. inflation Resp. output gap Resp. ∆ output Resp. exch. rate Firm barg. power Elast. matching Hiring cost.

Prior density β(0.5, 0.1) Γ(1, 0.2) Γ(1, 0.2) β(0.75, 0.1) β(0.75, 0.1) β(0.75, 0.1) Γ(50, 15) Γ(50, 15) Γ(50, 15) β(0.75, 0.1) Γ(2, 0.25) N (0.25, 0.1) N (0.25, 0.1) N (0.25, 0.1) β(0.5, 0.2) β(0.5, 0.2) Γ(1, 0.5)

Symbol χ φh η γH γF γw ψH ψF ψw ρR ρπ ρY ρ∆Y ρe ξ ν e

Post. mod

CI

0.29 1.19 0.51 0.58 0.61 0.57 51.9 77.4 15.2 0.80 2.14 0.43 0.22 0.08 0.51 0.71 5.86

[0.2, 0.38] [1.08, 1.29] [0.44, 0.57] [0.39, 0.76] [0.43, 0.80] [0.36, 0.78] [34.4, 68.9] [48.5, 105.3] [9.79, 20.4] [0.74, 0.85] [1.73, 2.54] [0.29, 0.56] [0.06, 0.38] [0.01, 0.17] [0.29, 0.79] [0.59, 0.83] [4.58, 7.15]

Table 1: Estimation results - Structural parameters.

24

Shocks Productivity persist. UIP persist. Preference persist. Cost-push persist. Monetary persist. Matching persist. Bargaining persist. Vacancy persist. Foreign output persist. Foreign inflation persist. Foreign interest r. persist. Productivity sd. UIP sd. Preference sd. Cost-push sd. Monetary sd. Matching sd. Bargaining sd. Vacancy sd. Foreign output sd. Foreign inflation sd. Foreign interest r. sd.

Symbol ρz ρs ρc ρH ρm ρX ρξ ρv ρY ∗ ρπ∗ ρ i∗ σz σs σc σH σm σX σξ σv σY ∗ σπ ∗ ρi∗

Prior density β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) β(0.5, 0.2) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, ) Γ−1 (0.01, )

Post. mean

CI

0.40 0.77 0.91 0.08 0.36 0.18 0.18 0.83 0.79 0.18 0.87 0.009 0.007 0.067 0.391 0.003 0.104 0.137 0.452 0.004 0.003 0.002

[0.24 ,0.57] [0.68 ,0.87] [0.85 ,0.98 [0.01 ,0.15] [0.22 ,0.50] [0.03 ,0.31] [0.04 ,0.32] [0.74, 0.91] [0.67 ,0.91] [0.04 ,0.30] [0.82 ,0.92] [0.007, 0.010] [0.004, 0.010] [0.031, 0.099] [0.268, 0.512] [0.002 ,0.003] [0.088 ,0.119] [0.055 ,0.215] [0.350 ,0.550] [0.003 ,0.004] [0.002 ,0.003] [0.001 ,0.002]

Table 2: Estimation results- Shocks.

25

8

Figures Figure 1: Standard deviations

Output

Interest rate

140

Inflation

4.5

0.35

3

0.3

2.5

0.25

2.5

2

0.2

2

1.5

0.15

1

0.1

0.5

0.05

4

120

Real exchange rate

3.5

3.5 100

3

80 60

1.5

40

1 20

0.5

0

0.01

0.02

0.03

0

0.2

Unemployment

0.4

0.6

0.8

0.2

0.4

Vacancies

0.25

0.6

0.8

1

0

0

5

Real wage

0.18

10

Individual hours

1.4

1.4

1.2

1.2

1

1

0.1

0.8

0.8

0.08

0.6

0.6

0.4

0.4

0.2

0.2

0.16 0.2

0.14 0.12

0.15

0.1

0.06 0.04

0.05

0.02 0

0

0

5

10

15

0

5

10

15

20

26

25

0

0

1

2

3

0

1

2

3

Figure 2: Correlation

Interest rate

Inflation

2

2

1.5

1.5

1

1

0.5

Real exchange rate

0.5

0 −0.5

0

0.5

0 −0.5

1

0

Vacancies

0.5

1

1.4

1.2

1.2

1

1

0.8

0.8

0.6

0.6

0.4

0.4

0.2

0.2

0

−1

−0.5

Real wage

1.6

Unemployment

1.4

0

0 −1

0.5

Individual hours

1.5

1.4

3 1

1

0.5

1.6

3.5

1.2

0

Unemployment and Vacancies 1.8

4

1.4

−0.5

1.2

2.5

1 0.8

2 0.8

0.6

1.5

0.5

0.4

1

0.2

0.5

0

−0.5

0

0.5

1

0

−0.5

0

0.5

27

1

0

0.6 0.4 0.2 0

0.5

1

0

−1

−0.5

0

0.5

Figure 3: Persistence

Output

Interest rate

Inflation

4.5

8

3.5

4

7

3

3.5

4 3.5

6

3

Real exchange rate 4.5

2.5

3

5 2

2.5

2.5

4 2

2

1.5 3

1.5

1

2

1

1 0.5

1

0.5 0

0.4

0.6

0.8

1

0

0.6

Unemployment

0.8

1

0

Vacancies

5

0.5 0

0.5

1

0

0.2

Real wage 6

3.5

3

5

3

2.5

0.4

0.6

0.8

1

Individual hours

3.5

4

3

1.5

2.5

4

2

2 3

1.5

2

1.5 2

1 1 0.5 0

0.2

0.4

0.6

0.8

1

0

1

1

0.2

0.4

0.6

0.8

28

1

0

0.5

0.6

0.8

1

0

0

0.5

1

29

15

20

20

0

0.9

1

1.1

1.2

1.3

5

10

15

20

−0.2

0

−1

−1.5

0.2

0.4

−0.5

0

Tightness

−0.4 15

15

20

−0.6 10

Wage inflation

10

Real exchange rate

10

0

0.5

1

−0.2

5

5

5

Output

−0.4

−0.2

0

−3

−2

−1

−1.5

−1

−0.5

0

5

5

5

5

15

10

Real wage

10

Job finding rate

10

15

15

15

Unemployment rate

10

Interest rate

20

20

20

20

−2

−1.5

−1

−0.5

0

−0.1

0

0.1

0.2

−1.5

−1

−0.5

0

−2

−1

0

Figure 4: Impulse responses to a monetary policy shock

5

5

5

5

10

Individual hours

10

Job seekers

10

Vacancies

10

Inflation

15

15

15

15

20

20

20

20

30

0.2

0.15

0.1

0.05

0.2

0.15

0.1

0.05

−0.15

−0.15

−0.2

−0.1

−0.1

exi echi eV Others −0.2 1996q3 1997q3 1998q3 1999q3 2000q3 2001q3 2002q3 2003q3 2004q3 2005q3 2006q3 2007q3 2008q3 2009q3

−0.05

−0.05

0

0.25

0.25

0

0.3

0.3

Figure 5: Variance decomposition: Unemployment

31

0.2

0.1

0.2

0.1

−0.1

−0.2

−0.3

−0.4

−0.5

−0.1

−0.2

−0.3

−0.4

exi echi eV Others −0.5 1996q3 1997q3 1998q3 1999q3 2000q3 2001q3 2002q3 2003q3 2004q3 2005q3 2006q3 2007q3 2008q3 2009q3

0

0.3

0.3

0

0.4

0.4

Figure 6: Variance decomposition: Vacancies

32

0.01

0.01

−0.01

−0.02

−0.03

−0.01

−0.02

exi echi eV Others −0.03 1996q3 1997q3 1998q3 1999q3 2000q3 2001q3 2002q3 2003q3 2004q3 2005q3 2006q3 2007q3 2008q3 2009q3

0

0.02

0.02

0

0.03

0.03

Figure 7: Variance decomposition: Output