Stylized facts of business cycles in a transition economy in time and frequency

Economic Modelling 29 (2012) 2163–2173

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Stylized facts of business cycles in a transition economy in time and frequency☆ Petre Caraiani Researcher at the Institute for Economic Forecasting, Romanian Academy, Romania

a r t i c l e

i n f o

Article history: Accepted 17 June 2012 JEL Classification: E32 Keywords: Business cycles Filters Wavelets

a b s t r a c t We discuss the properties of business cycles in Romania between 1991 and 2011 using a wavelets based method. We compare it with the standard approaches in literature. We analyze the relationship between output and key macroeconomic variables in time and frequency. While in terms of comovement the results are mostly in line with previous findings, there is a better picture of the time varying features as well as the influence of recessions on the nature of the relationships. The approach applied here can also isolate the influence of specific events, like the accession to the European Union. © 2012 Elsevier B.V. All rights reserved.

1. Introduction Comparing the theoretical predictions of a model with the actual patterns remains one of the standard approaches in macroeconomics for testing a model. The methodology proposed by the Real Business Cycle school (RBC, hereafter) which consists in comparing the theoretical predictions of the model with respect to the second order moments of the variables with those from real data continues to represent a viable approach even for today much more complex dynamic stochastic general equilibrium models (DSGE hereafter). This topic remains in focus even today, see some very recent studies, Tawadros (2011) or Kollintzas et al. (2011). While many of the studies were carried for the case of G7 economies, see Kydland and Prescott (1990), Hodrick and Prescott (1997), Fiorito and Kollintzas (1994), Chadha and Prasad (1994), the emergent countries received less attention. This lack of studies is even more obvious for the former transition economies from Central and Eastern Europe, although some research has been taken recently, see Benczúr and Rátfai (2010). While in the first year during the transition such a deficiency was understandable, this major topic remains basically understudied for this particular area. At the same time there is however a wider interest in the synchronization between new member states and Euro Area, see Dumitru and Dumitru (2010) for a recent example. In this paper we contribute to the literature by discussing the stylized facts of business cycles in Romanian economy. We also contribute through the use of wavelets which will allow an analysis in both time and frequency. As expected, the literature on business cycles

☆ Many thanks to Prof. S. Hall as well as to an anonymous referee for his very useful comments. E-mail address: [email protected]. 0264-9993/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.econmod.2012.06.014

using wavelets is small, particularly for these economies, but some research has been carried for transition economies using the continuous wavelet transform, see Jagric and Ovin (2004). The paper is organized as follows. The second chapter discusses the standard approach to the analysis of business cycles as well as a proposed methodology to analyze business cycles properties using wavelets. We apply the wavelet approach on Romanian data on selected macroeconomic variables and discuss the results with respects to literature. The last section concludes and draws some possible developments of this paper. 2. The methodology 2.1. Traditional business cycles analysis We detail hereafter the main methods used in the business cycles analysis. We start by detailing the Kydland–Prescott approach that is quintessentially linked with the Real Business Cycles school. We also have two different methodologies that address some of the shortcomings in the standard approach, one based on the state space methodology and a second one that uses the Markov Switching model. 2.1.1. The Kydland–Prescott approach The standard approach in business cycles analysis originates from the work by Kydland and Prescott (1990). This approach is based on the definition of business cycles as proposed by Lucas (1977), cycles being defined as deviations of the output from its trend. One of the key ingredients of the approach is to isolate the cycles in output and other key macroeconomic variables. Originally, one of the most used approaches was to apply the Hodrick Prescott filter

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(a) Industrial Production 40 20

0 -20

-40 1991

1993

1995

1997

1999

2001

2003

2005

2007

2009

2001

2003

2005

2007

2009

(b) Wavelet Power Sectrum Period (years)

1

2

4

8 1991

1993

1995

1997

1999

Time Fig. 1. Industrial production: a) cycles; b) wavelet power spectrum.

(HP, hereafter) due to Hodrick and Prescott (1997). However this filter suffers from several shortcomings, see Cogley and Nason (1995) or Harvey and Jaeger (1993).

Harvey and Jaeger (1993) criticized the HP filter because it would produce spurious cycles as well as distortioned cyclical components. Cogley and Nason (1995) produced further evidence on the limits of

(a) Wavelet Coherency (IP,CPI) 1

Period

2

4

8 1991

1993

1995

1997

1999

2001

2003

(b) 1~4 years frequency band pi/2

pi/2

0

0

-pi/2

-pi/2

Difference Phase

pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

2007

2009

(c) 4~8 years frequency band

pi

-pi

2005

-pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 2. CPI: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

P. Caraiani / Economic Modelling 29 (2012) 2163–2173

where ηt is a white noise disturbance component and βt is the slope which is given by:

the HP filter, showing that when this filter is applied on processes that are integrated, it might lead to cycles that are not actually present in data. The HP filter remains however a standard tools in business cycles analysis. Some of the research also considered the setting of the key parameter lambda. Ravn and Uhlig (2002) showed that lambda should be corrected for the number of observations, suggesting a value of 129,600 for monthly data which is what we will use in this study. For thorough presentations of the standard methodology in business cycles analysis we direct the readers to the reference papers, see Kydland and Prescott (1990), or Hodrick and Prescott (1997).

βt ¼ βt−1 þ ζ t



ψt ¼ ρ cos λc ψt−1 þ ρ sin λc ψt−1 þ κ t 



ð4Þ 

ψt ¼ −ρ sin λc ψt−1 þ ρ cos λc ψt−1 þ κ t

ð5Þ

with ρ a damping factor for which 0≤ρ≤1, λc is the frequency of the cycles in radians while κt and κt*are normally distributed with N(0, σκ2). The two main advantages of this approach are that it takes into account the stochastic feature of economic time series as well as the seasonal and irregular components. This approach has also been demonstrated in Harvey and Jaeger (1993) as being a generalization of the HP filter.

ð1Þ

where t=1,…,T, yt is the observed series, μt is the trend, ψt is the cycle and εt the irregular component. The trend is modeled as a local linear trend given by: μ t ¼ μ t−1 þ βt−1 þ ηt

ð3Þ

ζt being a white noise disturbance. Furthermore, in Eqs. (1) to (3), each of the disturbances, namely the irregular disturbance εt, the level disturbance ηt, as well as the slope disturbance ζt, are mutually independent as well as normally and independently distributed N(0, σi2) where the index i refers to each of the three mentioned disturbances. The stochastic cycle component is modeled as follows:

2.1.2. The state space based approach That the state space approach can constitute a reliable framework for deriving the business cycles stylized facts has been demonstrated in a consistent way by Harvey and Jaeger (1993). We detail here the standard approach following Harvey (1989) as well as Harvey and Jaeger (1993). As advocated by them, a relevant model for this topic would comprise a trend component and a cycle component as explained below: yt ¼ μ t þ ψt þ εt

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2.1.3. The Markov Switching based approach Although known and applied for considerable time in economics following the seminal contribution by Hamilton (1989), the use of the regime switching models to derive the business cycles components

ð2Þ

(a) Wavelet Coherency (IP,Inflation) 1

Period

2

4

8 1991

1993

1995

1997

1999

2001

2003

Phase Difference

(b) 1~4 years frequency band pi

pi/2

pi/2

0

0

-pi/2

-pi/2

1993 1995 1997 1999 2001 2003 2005 2007 2009

2007

2009

(c) 4~8 years frequency band

pi

-pi

2005

-pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 3. Inflation: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

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(a) Wavelet Coherency (IP, Nominal Wages) 1

Period

2

4

8 1991

1993

1995

1997

1999

2001

2003

Phase Difference

(b) 1~4 years frequency band

2007

2009

(c) 4~8 years frequency band

pi

pi

pi/2

pi/2

0

0

-pi/2

-pi/2

-pi

2005

-pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 4. Nominal wages: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

has received less attention. The framework proposed by Hamilton (1989) proved itself capable of capturing well some of business cycles features but in its initial form was limited with respect to characterizing the whole set of stylize facts. One of the extensions that addressed these shortcomings is due to Krolzig and Toro (2004) who extended the baseline model to the multivariate setting. In the initial specification a univariate framework was chosen: Δyt −μ ðst Þ ¼ α 1 ðΔyt−1 −μ ðst−1 ÞÞ þ … þ α 4 ðΔyt−4 −μ ðst−4 ÞÞ þ ut

ð6Þ

Where the mean μ1 is positive in the first regime that corresponds to the expansion phase of the business cycle while μ2 is negative in the contraction period. The disturbance term is normally distributed. The multivariate extension proposed by Krolzig and Toro is given below: Δyt ¼ ν ðst Þ þ A1 Δyt−1 þ ut

2.2. Analyzing business cycles properties using wavelet coherence The wavelets are a technique imported from signal processing which allows us to represent time series in both frequency and time. Using wavelets we can decompose any time series into its frequencies. In this paper we follow the developments by Aguiar-Conraria and Soares (2011a,b) who proposed the use of the wavelet coherence to study the relationship between two variables. Following Aguiar-Conraria and Soares (2011a,b) we present in a short manner the main ingredients of this approach. While most of the research with wavelets applied in economies, see Gallegati and Gallegati (2007) and Gallegati (2008), used the discrete wavelet transform, Aguiar-Conraria and Soares (2011a,b) based their approach on the continuous wavelet transform. Two key concepts in the wavelet analysis are those of mother and father wavelets. The father and mother wavelets have the following properties: The father wavelet integrates to one, namely it is characterized by the following relationship:

ð7Þ ∫ϕðt Þdt ¼ 1

Here ut|st ~N(0, Σ(st)), Δyt is a vector of growth rates, ν(st) are regime-conditional mean growth rates. More recent research, see Morley and Piger (2008), showed how to generalize the decomposition method proposed by Beveridge and Nelson (1981), using a regime switching forecasting model.

The mother wavelet has the property of integrating to zero:

∫ψðt Þdt ¼ 0

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Following Aguiar-Conraria and Soares (2011c), one can derive from a mother wavelet ψ a family of “daughters” through two operations, scaling and translation:

We define the following quantities, the wavelet power spectrum of x(t) given by:

  1 t−τ ψτ;s ðt Þ ¼ pffiffiffiffiffi ψ s jsj

ðWPSÞx ¼ W xx ¼ jW x j

2

ð10Þ

the wavelet power spectrum of y(t) as:

with the parameter s representing the scaling parameter that controls the length of the wavelet, while τ is a location or translation parameter indicating where the wavelet is centered. For a certain wavelet function ψ, the continuous wavelet transform of a time series xðt Þ∈L2 ðRÞ can be written as:   ∞ 1 t−τ dt W τ;s ¼ ∫ xðt Þ pffiffi ψ  s s −∞

ð8Þ

where * implies the use of complex conjugation, while Wτ,sis a daughter wavelet. Starting from the continuous wavelet transform, one can derive the wavelet power spectrum of a series. As one usually works in economics with discrete time series, considering the discrete time series xn, as is the usual case in economic applications, having N observation, n=0, …,N−1, with a uniform time step δt, the wavelet power spectrum is obtained by discretizing the integral from Eq. (8):   −1 δt NX δt s  W m ðsÞ ¼ pffiffi xn ψ ðn−mÞ s s n¼0

 2   ðWPSÞy ¼ W yy ¼ W y 

ð11Þ

and the cross wavelet power spectrum for the two series x(t) and y(t) defined by:     ðCWPSÞxy ¼ W xy ¼ W xy 

ð12Þ

We use the wavelet power spectrum to describe the variance of a univariate time series, while the cross wavelet power spectrum describes the covariance between two time series in time and frequency. Finally, the wavelet coherence can be computed as the ratio of cross-spectrum to the product of the spectrum of the series.

Rxy

     S W xy  ¼

   1   2 2 SjW x j2 SW y 

ð13Þ

ð9Þ With S representing a smoothing operator along both time and scale and 0≤Rxy ≤1.

where m=0, …,N−1,

(a) Wavelet Coherency (IP, Real Wages) 1

Period

2

4

8

1991

1993

1995

1997

1999

2001

2003

Phase Difference

(b) 1~4 years frequency band pi

pi/2

pi/2

0

0

-pi/2

-pi/2

1993 1995 1997 1999 2001 2003 2005 2007 2009

2007

2009

(c) 4~8 years frequency band

pi

-pi

2005

-pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 5. Real wages: a) wavelet coherence with industrial production (IP); b) phase difference between the two series.

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Similarly to the use of cross-correlations from standard business cycles analysis, one can depict whether a time series is synchronous with, leading, or lagging behind another time series by using the so called phase difference between two time series. This phase difference is given by:

ϕx;y

− Comovement with output, given by the correlation between output and a certain variable; − Phase shifting with respect to business cycles, detected through cross-correlations. The wavelets coherence allows us to characterize the business cycles based on the same key features:

o1 0 n I W xy −1 @ n oA ¼ tan R W xy

ð14Þ

where ϕx,y ∈[−π, π]. Following Aguiar-Conraria et al. (2012), we can read the results following a few rules that allow an economic interpretation of the phase difference. The two series are positively correlated when the

phase difference is in the interval − π2 ; π2 . When the phase difference



is within −π; − π2 or π2 ; π , the two variables are in an anti-phase re

lationship (they are negatively correlated). For ϕx;y ∈ − π2 ; 0 or π



ϕx;y ∈ 2 ; π , y leads x. For ϕx;y ∈ −π; − π2 or ϕx;y ∈ 0; π2 , the variable x is leading. 2.3. A comparison between the two approaches The traditional approach to deriving the stylized facts of business cycles relies in characterizing the business cycles with respect to several key features: − Volatility of the variables, usually characterized through standard deviation;

− The volatility of a time series can be detected through the wavelet power spectrum; − The comovement can be analyzed using the wavelet coherence; − We can analyze the phase shifting by means of phase difference of two series. As we can see, by means of wavelet coherence we can derive the key properties of business cycles as we can do with the standard methodology. Moreover, as argued by Aguiar-Conraria and Soares (2011a, p. 489), the wavelets are a natural approach to business cycles analysis since they provide an estimator of the spectrum in time. With respect to comovement, one should notice that recent research, see Rua (2010) or Aguiar-Conraria and Soares (2011d), has shown how to derive a corresponding correlation measure in the time-frequency space based on the phase difference between two time series. The advantage of the wavelet approach to other standard approaches has been already demonstrated for the case of modeling political cycles, see Aguiar-Conraria et al. (2012) who showed how using wavelets one can reveal both the time dimension as well as

(a) Wavelet Coherency (IP,M2) 1

Period

2

4

8

1993

1995

1997

1999

2001

2003

Phase Difference

(b) 1~4 years frequency band pi

pi/2

pi/2

0

0

-pi/2

-pi/2

1993 1995 1997 1999 2001 2003 2005 2007 2009

2007

2009

(c) 4~8 years frequency band

pi

-pi

2005

-pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 6. Real money supply: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

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the frequency dimension of the cycles combining thus the relative advantages of the ARMA and spectral decompositions. Applying this technique to the electoral cycles in US they have revealed some patterns that were harder to uncover based on traditional approaches. The application of the wavelets in the analysis of the business cycles has also revealed a few new results that enhance our understanding of them. Aguiar-Conraria and Soares (2011c) found evidence that the Great Moderation has started much earlier than generally thought, the decline of volatility at business cycles frequencies beginning with 1960. Aguiar-Conraria and Soares (2011a) found for Euro Area that the proximity of the cycle is strongly correlated with the geographical proximity, while the new member states do not have a strong synchronicity with the Euro Area business cycles. 3. Stylized facts of Romanian business cycles We choose monthly data from Romanian economy thus ensuring a maximal sample. Other papers in literature also approached the business cycles using monthly data and the industrial production as a proxy for economic activity, see Stock and Watson (1998). Benczúr and Rátfai (2010) used in their study quarterly data for selected CEE economies that included Romania. In their paper the sample for Romania started with 1994. However, no official quarterly data are reported for Romania earlier than 1997. We preferred to use data at monthly frequency in order to obtain longer time series. The data range from January 1991 to December 2010 (except inflation rate,

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from 1992, and employment, from 1993) and include, besides industrial production, prices, exchange rates, wages, employment and unemployment, money and credit. For all series the cycles are derived after the variables are seasonally adjusted using Census X12 procedure, and filtered using the standard Hodrick Prescott filter with lambda set at the value proposed by Ravn and Uhlig (2002) for monthly data. All the computations for the wavelets were carried using wavelet toolbox ASToolbox by Luis Aguiar-Conraria and Maria Joana Soares.

3.1. Output volatility A common feature for all the transition economies was the initial drop in output that they experienced at the beginning of the economic transformation. Not only that its magnitude was high, but it also lasted for more than one year in some cases. For the case of Romania, the 1990's were characterized also a second recession between 1997 and 1999, although this time the magnitude of the recession was much lower. Fig. 1 shows both the dynamics of the cycles of industrial production in 1a, and the wavelet power spectrum in 1b. There is a clear drop in volatility after 2000. The wavelet power spectrum indicates an increased variance at business cycles frequencies which lasted until mid 2000s. There is also an increased volatility at lower scales at the beginning of the sample, which might correspond to the initial drop in production that was short lived.

(a) Wavelet Coherency (IP,Credit) 1

Period

2

4

8 1991

1993

1995

1997

1999

2001

2003

Phase Difference

(b) 1~4 years frequency band

2007

2009

(c) 4~8 years frequency band

pi

pi

pi/2

pi/2

0

0

-pi/2

-pi/2

-pi 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

2005

-pi 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 7. Real non-governmental debt: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

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3.2. Prices We use two different measures of prices, as the literature appears to have shown different conclusions with respect to their cyclical behavior. We use both the consumer price index (CPI) as well as inflation rate. The CPI is taken with the fixed base in 1990. Inflation rate is computed at an annual level and its sample ranges from January 1992 to December 2010. In the initial studies, for example Keynes' “General Theory”, prices were viewed as flexible and pro-cyclical, a thing that was also confirmed by statistics. However in the RBC school, see for example the study by Kydland and Prescott (1990), prices are viewed as countercyclical, a thing supported by data in US in the post Korean war period. Other studies confirmed this finding, see Cooley and Ohanian (1991), Backus and Kehoe (1992). At the same time, inflation appears as pro-cyclical in most of the developed economies. Figs. 2 and 3 present the results of the wavelet coherence between the two measures of prices and industrial production. We found a strong relationship between output and prices taken either as CPI or as inflation rate for the whole sample at scales larger than 8 years. The relationship is even stronger up to 2003, while up to 2000 it also appears at business cycles frequencies, 4 to 8 years. We also find a stronger short term relationship after 2005–2007 for both variables, CPI and inflation. One possible explanation for the strong relationship between output and prices at longer horizons can be probably tied to the disinflationary trend. We can also suggest an explanation for the stronger relationship that emerges after 2005 at the shorter horizon of 2–4 years, as changes in inflation after this year are at higher frequencies and as the disinflationary efforts focused on short run movements in inflation.

Inflation is in anti-phase in the first ten years, maybe due to its very high volatility. After 2003, the inflation is in-phase (positively correlated) and is leading the output. After 1995, the prices are also in phases with the output.

3.3. The wages Two measures of monthly wages are used, the nominal average wage as well as the real average wage rate (the nominal wage deflated by CPI). The behavior of wages, especially of real wages has important implications for modeling. While in the RBC framework, real wages behave in a procyclical way, and they are expected to be procyclical in a strong manner, in the New Keynesian framework the wages are rather expected to behave in a countercyclical way. McDermott et al. (1999) in the study on the emerging economies business cycles also finds a procyclicity of the real wages in most of the countries included in the sample. However, under certain conditions, like models with countercyclical markups, see Rotemberg and Woodford (1991), real wages can become procyclical also in New Keynesian models. We find a strong relationship between wages, see Figs. 4 and 5, either nominal or real, and output especially during the first ten years of transition. We observe a quite strong relationship between real wages and output even after 2000 which may be attributed to the trend of growth of real wages that accompanied the economic growth period. There is also a powerful relationship at short to business cycles frequencies from 2005 for nominal wages and 2007 for real wages that can be attributed to the rapid growth of wages especially in the budgetary sector as well as the cut of public wages in 2010 due to the crisis.

(a) Wavelet Coherency (IP,Employment) 1

Period

2

4

8 1993

1995

1997

1999

2001

2003

Phase Difference

pi

pi/2

pi/2

0

0

-pi/2

-pi/2

1997

1999

2001

2003

2005

2007

2009

(c) 4~8 years frequency band

(b) 1~4 years frequency band pi

-pi 1993 1995

2005

2007

2009

-pi 1993 1995

1997

1999

2001 2003

2005

Fig. 8. Employment: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

2007

2009

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With respect to the phase difference we notice that most of the sample the series are in phase (pro-cyclical), except for nominal wages in the first part of transition, probably due to the initial shocks in economy (falling output). Nominal wages and production commove most of the time after 2000 at business cycle frequencies. In case of real wages, except between 1997 and 2003, when production is leading the output, for the other parts of the sample, the real wages are leading underlining the role of expectations in setting the wages.

3.4. Money and credit The relationship between money and output remains one of the key questions in macroeconomics. The New Keynesian school admits a role to the monetary side of the economy because the monetary shocks do influence the real activity due to the rigidities in the short run of the prices and wages. The New Keynesian school thus implies procyclical money in the short run, money having an important role in the business cycles. In the RBC school, as business cycles are led by technological shocks, theoretically money are neutral. However, some extensions of the baseline RBC model showed that it is possible to have procyclical money in a RBC model as rise in the productivity in the booms leads to a rise in the demand of transaction services, the result being that the banking sector responds by increasing the money supply, see King and Plosser (1984). For the credit, the literature showed that there is an obvious role for the credit in the business cycle, especially in an emerging economy, due to its underdeveloped financial markets, as underlined by McDermott et al. (1999).

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We discuss in this section the properties of real money supply (M2 deflated by CPI) and real credits (nongovernmental credits deflated by CPI). There is a strong relationship between money and business cycles at both high frequencies, see Fig. 6, business cycles frequencies, and low frequencies during first ten years of transition. The relationship maintains after 2001 only at low frequencies. We can observe a stronger relationship at high to business cycles frequencies starting with 2008. In terms of leading behavior, for most of the period, as one would expect, money led the production. During the last recession however, from 2008, production was leading. There are thus evidences that in the last economic crisis, the money became a factor that intensified the severity of the downturn. A similar behavior is found for credit for the whole sample. There is also a stronger relationship around 4 years frequency in the last part of the economic boom toward 2008. Credits led the production except the very last part of the sample. Both money and credit are pro-cyclical for the whole sample (Fig. 7).

3.5. Employment and unemployment For measuring the fluctuations in the labor market we have used two variables – the number of employed persons, in thousands persons, and the unemployment rate. For employment we found a strong relationship with production at business cycles frequencies. The relation is again stronger at the end of the sample in the crisis period, as employment varied due to the changing conditions in the economy. Employment leads production at business cycles frequencies for most of the time, but during the last crisis is production that leads, as both government and

(a) Wavelet Coherency (IP,Unemployment Rate) 1

Period

2

4

8 1991

1993

1995

1997

1999

2001

2003

Phase Difference

(b) 1~4 years frequency band pi

pi/2

pi/2

0

0

-pi/2

-pi/2

1993 1995 1997 1999 2001 2003 2005 2007 2009

2007

2009

(c) 4~8 years frequency band

pi

-pi

2005

-pi 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 9. Unemployment: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

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private firms reduced employment due to the worsening conditions in the real economy. For the case of unemployment we find a strong relationship with output during the first decade at all frequencies except the highest ones. Unemployment changed from almost zero to a double figure during a few years so that variations at most frequencies appear. There is also a strong relationship after 2007, as unemployment decreased until the end of the economic growth and then rapidly increased during the crisis. In terms of phase difference, the behavior is similar to that of employment. The employment behaves in a pro-cyclical manner at business cycles frequencies for the who sample while unemployment is counter-cyclical only at the beginning and end of the sample (Figs. 8 and 9).

3.6. The exchange rate We used both the nominal exchange rate against the dollar as well as the real exchange rate (the nominal one deflated by using the GDP deflator). There is a strong short term relationships at the beginning of transition probably marking the exchange rate depreciation in nominal terms and its appreciations in real terms (due to high inflation rates). For the whole period there is a strong relationship between nominal and real exchange rate at frequencies lower than business cycle. For most of the period, the nominal exchange rate lagged the dynamics in the business cycles, suggesting that the investors'

expectations regarding the production might have been a determinant of the nominal exchange rate dynamics. For both nominal and real exchange rates there is a stronger relationship around the four years frequency starting with 2005. This may be due again to the expectations regarding Romania's accession into EU. In terms of comovement, at business cycles frequencies, the real exchange rate is in-phase with the output, except the very end of the sample (Figs. 10 and 11).

4. Conclusion While the wavelet approach discussed here cannot account for all types stylized facts usually discussed in the literature, like for the relative standard deviation, nevertheless it can at least serve as a complementary tool in analyzing the properties of the business cycles. We found changing relationships between output and main macroeconomic variables, both in time, frequency and in intensity. The results here may be further tested with respect to statistical significance given the current debate in literature with respect to testing for significance the wavelet coherence, see Ge (2007) or Lachowicz (2009). The evidence found here can also be used to further refine the models applied for such economies. The use of models with regime switching or time varying coefficients is suggested for some of the variables.

(a) Wavelet Coherency (IP,Nominal Exchange rate) 1

Period

2

4

8 1991

1993

1995

1997

1999

2001

2003

(b) 1~4 years frequency band pi/2

pi/2

0

0

-pi/2

-pi/2

Phase Difference

pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

2007

2009

(c) 4~8 years frequency band

pi

-pi

2005

-pi

1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 10. Nominal exchange rate: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

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(a) Wavelet Coherency (IP,Real Exchange rate) 1

Period

2

4

8 1991

1993

1995

1997

1999

2001

2003

(b) 1~4 years frequency band pi

pi/2

pi/2

0

0

-pi/2

-pi/2

Phase Difference

2007

2009

(c) 4~8 years frequency band

pi

-pi 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

2005

-pi 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009

Fig. 11. Real exchange rate: a) wavelet coherence with industrial production (IP); b–c) phase difference between the two series.

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