Modelling the Australasian financial cycle: A Markov-Regime Switching Approach

de Wet, Milan C. Article Modelling the Australasian financial cycle: A Markov- Regime Switching Approach International Journal of Business and Economic Sciences Applied Research (IJBESAR) Provided in Cooperation with: International Hellenic University (IHU), Kavala Suggested Citation: de Wet, Milan C. (2021) : Modelling the Australasian financial cycle: A Markov- Regime Switching Approach, International Journal of Business and Economic Sciences Applied Research (IJBESAR), ISSN 2408-0101, International Hellenic University (IHU), Kavala, Vol. 14, Iss. 1, pp. 69-79, https://doi.org/10.25103/ijbesar.141.06 This Version is available at: https://hdl.handle.net/10419/242246 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc/4.0/ †Corresponding Author: Milan Christian de Wet Email: [email protected] DOI: 10.25103/ijbesar.141.06 International Journal of Business and Economic Sciences Applied Research IJBESAR ijbesar.ihu.gr Modelling the Australasian Financial Cycle: A Markov-Regime Switching Approach Milan Christian de Wet University of Johannesburg ARTICLE INFO ABSTRACT Article History Received 24 May 2021 Accepted 15 July 2021 Purpose: The importance of the financial cycle has become a central point of consideration for policymakers since the 2007-08 financial crisis. This study aimed to construct and characterize the aggregate Australasian financial cycle. Design/methodology/approach: To construct the aggregate cycle, a dynamic factor model is employed, based on credit aggregates and aggregate property prices in Australia and New Zealand. To extract the aggregate Australasian financial cycle, the Christiano-Fitzgerald bandpass filter is implemented. Also, a Markov-Regime Switching Autoregressive model is employed to model, characterize and identify asymmetries in the aggregate Australasian financial cycle. Findings: The results indicate that Australian credit conditions are the prominent underlying driver of the aggregate Australasian financial cycle. The aggregate Australasian financial cycle exhibits a typical duration of 45 quarters, with expansions typically lasting 25 quarters and contractions lasting 20 quarters. Australasian financial cycles thus typically last longer than business cycles. The results also provide evidence that contractions in the aggregate Australasian financial cycle are typically shorter but harsher and more volatile than cyclical expansions, and that a level of linear persistence exists in the cycle. Research limitations/implications: A limitation of this study is that full data sets for all the variables that constitute the aggregate Australasian financial cycle is only available from 1978Q1. Therefore, the time horizon of the study starts at this point. However, given the long typical long duration of financial cycles, it would be ideal to have a time horizon of about 100 years. The implications of asymmetry in the aggregate cycle have several policy implications. Asymmetries might necessitate different policy strategies, as well as influence the timing of implementing policies during different financial cycle phases. The durational asymmetry in the aggregate financial cycle, whereby expansions in the aggregate financial cycle are typically longer than contractions, indicates that the employment of restrictive monetary and macroprudential policies should be implemented for longer periods than accommodative policies. Also, given that contractions in the aggregate financial cycle are steeper than expansions, policy response should be quicker and should be stronger with accommodative monetary policies once the aggregate financial cycle is in a contraction phase, relative to restrictive monetary policies during an expansion phase. Originality/value:The construction of a single aggregate measure that encapsulates the cyclical behaviour of a range of financial variables aids as a solution to simplify the study of aggregate financial cycles. In this light, this study contributes to the body of empirical literature on Australasian economic cycles by providing a single aggregate Australasian financial cycle measure that encapsulates the cyclical behaviour of several financial variables from two of the biggest economies in this region. This will provide policymakers with a single measure to consider the cyclical state of financial aggregates in Australasia. This study further contributes by establishing cyclical durations and identifying asymmetries in the cycle. Such an analysis aid in gaining a deeper understanding of the aggregate Australasian financial cycle and provide a means to improve the accuracy of predicting future movements in the financial cycle. This, in turn, could aid policymakers to manage fluctuations in the aggregate financial cycle and thereby reduce the potentially adverse effect of financial cycle fluctuations. JEL Classifications G32, L25, L30, O34 Keywords: Financial cycle, dynamic factor model, Markov- Switching, cyclical extraction, cyclical asymmetries DOI: 10.25103/ijbesar.141.06 70 ©International Hellenic University 1. Introduction Financial conditions are playing an increasingly important role in the economy, as a result, financial instability and aggregate financial cyclicality have emerged as a key economic concept since the 2007/08 financial crisis. However, before the 2007/08 financial crisis, policymakers and researchers largely neglected to consider the role of financial cyclicality on the economy, considering the role played by the business cycle far more important. Therefore, knowledge and understanding of business cycles are far more extensive than on financial cycles, resulting in several knowledge gaps. Ng (2011) and Borio (2014) propose a definition for aggregate financial cycles, suggesting that they are self-reinforcing, reflecting the ebb and flow of aggregate value, risk sentiment and funding availabilities, often driven by changes in credit levels and asset prices. This, in turn, typically result in periods of financial expansion, followed by financial contraction. This necessitates the need to correctly identify the current financial cycle regime, in order to identify prevailing financial market risks such as excessive leverage induced asset price appreciations. As argued by Strohsal, Proaño and Wolters (2019), our understanding of the nature of the financial cycle provides the ability to anticipate future cyclical movements in this cycle and can help predict crises. Since the financial crisis, characterising aggregate financial cycles have become a key focus of central banks and economic cycle research, in order to improve the understanding of such cycles (Strohsal et al., 2019). Timely and effective policy implementation, with the aim to manage destructive financial cycles, rely on the accurate modelling and identification of the cycle. A number of methods have been implemented in this regard, Pontines (2017), de Wet and Botha (2019) and Strohsal et al. (2019) utilise a spectral density analysis, Claessens, Kose and Terrones (2012) and Drehmann, Borio and Tsatsaronis (2012) implement a turning-point analysis and Aikman, Haldane and Nelson (2015) use Frequency-based band-pass filters. In this regard, empirical literature largely focuses on identifying the properties of financial cycles. The main findings are that financial cycles typically exhibits longer durations and larger amplitudes than the business cycle (Borio, 2014; Aikman et al., 2015 and Strohsal et al., 2019). Strohsal et al. (2019) argue that the relatively longer duration reflects the unsustainable build-up of macro-financial instabilities over an extended period of time, which then ends in a severe financial contraction with potentially disruptive economic implications. This emphasises the importance to effectively manage the financial cycle by means of timely and effective policies. Despite the growing body of literature on financial cycles, financial cycles are far less researched and understood than the traditional business cycle, leaving a number of research gaps. Two research gaps will be considered in this study. Firstly, financial cycle research focuses largely on the financial cycle of the United States of America, the United Kingdom and the European Union. Such results can not necessarily be generalised and applied to other financial cycles, requiring research to extend to the financial cycle on a broader range of economies (Pontines, 2017). Secondly, existing research does not formally consider cyclical asymmetries in financial cycles. Cyclical asymmetries prove to exist in business cycles, with several policy implications, rendering this a key topic in business cycle research. Financial cycles could exhibit similar cyclical asymmetries, necessitating research in this regard. The main aim of this study was to construct, model and characterise the aggregate Australasian financial cycle. The multiple dimensional aspects of financial cycles in an economy make the study and analysis of Aggregate financial cycles complex. This, in turn, complexifies policy making related to aggregate financial cycles. The construction of a single aggregate measure that encapsulates the cyclical behaviour of a range of financial variables aids as a solution to simplify the study of aggregate financial cycles. In this light, this study contributes to the body of empirical literature on Australasian economic cycles by providing a single aggregate Australasian financial cycle measure that encapsulates the cyclical behaviour of a number of financial variables from two of the biggest economies in this region. This will provide policymakers with a single measure to consider the cyclical state of financial aggregates in Australasia. This study further contributes by modelling the aggregate Australasian financial cycle with a non-linear Markov-regime switching model and thereby establishing cyclical durations, identifying asymmetries in the cycle and identifying whether cyclical persistence exists in the cycle. Such an analysis aid in gaining a deeper understanding of the aggregate Australasian financial cycle and provide a means to improve the accuracy of predicting future movements in the financial cycle. This, in turn, could aid policymakers to manage fluctuations in the aggregate financial cycle and thereby reduce the potentially adverse effect of financial cycle fluctuations. Additionally, such information can aid in the decision-making process of economic participants, such as asset managers, risk managers and business managers, who are exposed to Australasian financial cycle fluctuations. 2. Review of Literature Provided the definition by Ng (2011) and Borio (2014), a single variable can not sufficiently be utilised to reflect aggregate financial cycle conditions. Thus, in literature, an aggregate financial cycle measure typically comprises of several variables, see for example, Claessens, et al. (2012), Borio (2014), Aikman et al. (2015), Schüler, Hiebert and Peltonen (2015), Farrell and Kemp (2020), Menden and Proano (2017) and Strohsal et al. (2019). The debate is around which variables to include in an aggregate financial cycle measure. A number of researchers, such as Claessens, et al. (2012), Borio (2014), Aikman et al. (2015), Pontines (2017) and Farrell and Kemp (2020), indicate that aggregate financial cycles are effectively proxied by property prices and credit aggregates. Property prices reflect information about the interplay between perceived value and risk sentiment in the economy. On the other hand, credit aggregates reflect funding availabilities and often prove to be at the core of DOI: 10.25103/ijbesar.141.06 71 financial crises (Aikman et al., 2013 and Schüler et al., 2015). As argued by Aikman et al. (2013), credit expansions often result in asset price inflation and multiple expansions, whereby increases in asset prices, i.e. aggregate equity prices, diverge from their underlying fundamentals. In tandem, Farrell and Kemp (2020) write that credit aggregates and property prices create a mutually reinforcing feedback effect, whereby an expansion in credit typically result in higher property prices, and higher property prices offer higher collateral levels, which in turn typically stimulate a further credit expansion. Historically, this feedback process has resulted in some of the most serious financial buildups and financial instabilities. In addition, evidence indicates that property price booms and credit expansions often precedes financial crises (Pontines, 2017). Therefore, jointly these two variables proxies aggregate financial cyclicality. Aggregate equity prices are often considered as a third variable to capture perceived value and risk sentiment. However, Claessens, et al. (2012) and Drehmann et al. (2012) provide evidence that equity prices can distort the financial cycle due to their short term volatility characteristics. Therefore, this study will construct the aggregate Australasian financial cycle by means of credit aggregates and property prices. Given that an aggregate financial cycle typically comprises of more than one variable, it's necessary to aggregate these variables into a single cyclical measure. To this end, dimension reduction techniques are the most common aggregation technique implemented in financial cycle literature. Such techniques include principal component analysis (PCA) and dynamic factor modelling (DFM), see for example; Stock and Watson (2011), Stock and Watson (2011), Farrell and Kemp (2020), Adarov (2018) and Strohsal et al. (2019). A DFM model will be implemented in this study, given the ability of the DFM to incorporate lag dynamics between variables. The body of literature on financial cycles largely focus on the properties of financial cycles. Ng (2011), Claessens, et al. (2012), Borio (2014), Aikman et al. (2015), Pontines (2017) and Farrell and Kemp (2020) consider the properties of credit, property and equity cycles, providing evidence that credit cycles and property price cycles tend to be significantly more severe and longer than the traditional business cycle. Furthermore, Claessens, et al. (2012) provide evidence that booms are driven by credit expansions typically result in relatively deeper contractions and slower recoveries. Schularick and Taylor (2012) and Jorda, Schularick and Taylor (2016) provide similar evidence. An important consideration in economic cycle literature is economic cycle asymmetries. In this regard, research primarily focuses on business cycles where a number of researchers, such as Goodwin (1993), Layton and Katsuura (2001), Chauvet and Hamilton (2006), Tastan and Yildirim (2008), Narayan and Pop (2009) and Breitung and Eickmeier (2015), provide evidence that business cycles often exhibit asymmetries. Empirical evidence primarily indicates that cyclical contractions are typically shorter but more volatile and steeper than expanding cycles (McQueen and Thorley, 1993; Tastan and Yildirim, 2008 and Breitung and Eickmeier, 2015). Furthermore, evidence indicates that cyclical troughs are deeper than cyclical peaks (Tastan and Yildirim, 2008 and Breitung and Eickmeier, 2015). Financial cycles might exhibit similar asymmetries, which could have both policy and modelling implications. Yet, very limited to no research has been done on financial cycle asymmetries. The identification of such asymmetries could enhance the understanding of financial cycles and thereby make a significant policy contribution as well as enhance the modelling process of financial cycles. For example, symmetric policies measures across the financial cycle might render subpar results given cyclical asymmetries. Thus, as argued by Tastan and Yildirim (2008), the presence of cyclical asymmetries could require different policy measures and magnitudes, as well as timing adjustments during different cyclical regimes (Tastan and Yildirim, 2008). Furthermore, by definition, linear modelling procedures are unable to identify cyclical asymmetries and are therefore unable to account for such asymmetries. Therefore, modelling financial cycles with linear models might provide sub-par results (Bouali, Nasr, and Trabelsi, 2016). Hence the argument by researchers, such as Tastan and Yildirim (2008), Sarbijan (2014) and Bouali et al. (2016), to employ non-linear methods to model cycles. The Markov regime-switching model, proposed by Hamilton (1989), is widely implemented in this regard, see, for example, Simpson, Osborn and Senier (2001), Moolman (2004), Tastan and Yildirim (2008) and Bouali et al. (2016). There are four common types of asymmetries identified in cyclical research namely: asymmetry in the steepness; asymmetry in the deepness; asymmetry in the sharpness; and asymmetry in the duration of a given cyclical measure (Tastan and Yildirim, 2008). This will further be discussed in the methodology section. The body of literature on the business cycle of Australia and New Zealand are rich. See for example Layton (1997), Crosby (2002) and Cashin and Ouliaris (2004) on the Australian business cycle and Kim, Buckle, and Hall (1994 and 1995), Hall and McDermott (2009), Chetwin (2012) and Hall, Thomson and McKelvie (2017) on the New Zealand business cycle. However, financial cycles of these countries are far less researched. To the best of my knowledge, the only published work in this regard is the work by Davies and Gai (2020) who identified the characteristics of the New Zealand financial cycle by means of a Spectral density analysis. The findings by Davies and Gai (2020) indicate that the. New Zealand financial cycle has a duration of approximately 8 years. The paper by Davies and Gai (2020) focus only on the financial cycle of New Zealand, and does not consider any cyclical asymmetries, nor does the paper estimate the financial cycle with a model that allows for a formal hypothesis testing procedure. This study aims to extend the knowledge on Australasian financial cycles. 3. Data Discussion As discussed previously, this article will consider property prices and credit aggregates as financial cycle constituents. The real long-series property price index from the Bank of International Settlements is used as a property price proxy for both Australia and New Zealand. Furthermore, total non-financial credit is used as a credit aggregate proxy for DOI: 10.25103/ijbesar.141.06 72 both Australia and New Zealand, also sourced from the Bank of International Settlements. The data frequency is quarterly and the timestamp range from 1978Q1 to 2018Q3. These measures will be aggregated into a single Australasian financial conditions index from which cycles will be extracted to represent the aggregate Australasian financial cycle. To ensure that there are no bias loadings due to non-stationarity, the variables subjected to the DFM will be tested for unit roots by means of an Augmented Dickey-Fuller unit root test and the series will be differenced where necessary to ensure that each variable is stationary when applying the DFM (Stock and Watson, 2011). Furthermore, variables modelled with the MS-AR model will also be tested for stationarity to ensure no spurious regression. Research has shown that the standard augmented Dickey-Fuller unit root test is often sub-par when working with a time series that exhibits cycles and regime-switching properties (Nelson, Piger and Zivot, 2000). Nelson et al. (2000) suggest using the Phillips-Perron unit root test or a breakpoint augmented Dickey-Fuller unit root test, which allows for endogenous probabilistic trend fluctuations in a series when testing a cyclical series for stationarity. Therefore, a Phillips-Perron unit root test and breakpoint augmented Dickey-Fuller unit root test will be used to test the level of integration of cyclical variables to be modelled with the MS-AR model. 4. Methodology This study will implement a dynamic factor model to aggregate the various variables into a single variable that will serve as an Australasian financial conditions index. A Christiano-Fitzgerald (CF) bandpass filter will then be implemented to extract cycles from the Australasian financial conditions index. The extracted cycle will then be modelled by means of a Markov-regime Switching autoregressive MS-AR model. Within the MS-AR model, Wald’s hypothesis testing process will be implemented to test for various cyclical asymmetries, as suggested by Clements and Krolzig (2003). 4.1 The dynamic factor model In accordance with the specification by Stock and Watson (2011), the static DFM model is specified as follows: Xt= λ(L)ft+ et (1) ft= δ(L)ft−1 +νt (2) Where there are N series, so Xt and et are (N x 1) vectors of the observable variables in the model and errors respectively. There are q dynamic factors, so ft and νt are (q x 1) vectors of dynamic factors and idiosyncratic disturbances, respectively. It is assumed that both et and νt are uncorrelated with the factors in the model at each lead and lag innovation. Furthermore, L is the lagged operator, and the lag polynomial matrices λ(L) and δ(L) are (N x q) and (q x q) lag polynomial matrices, respectively. A shortcoming of the static dynamic factor model is that ft are not directly estimated, limiting the practical usage of the results (Stock and Watson, 2011). Hence, in literature, the DFM is commonly estimated within a state-space and the Kalman filter is implemented to determine the Gaussian likelihood and identify the parameters by means of maximum likelihood (Stock and Watson, 2011). A state-space DFM model can be specified by adjusting the DFM specification in equations 1 and 2 as follow. Let p be the degree of the lag polynomial matrix λ(L), let Ft= (ft′,ft−1 ′,…,ft−p ′)′ denote an r x 1 vector, and let ᴧ = (λ0,λ1,…,λp), where λi is the N x q matrix of coefficients on the ith lag in λ(L). Also, let (L) be the matrix consisting of 1’s and 0’s, and the element of ǔ(L) such that the static model in equations 1 and 2 is rewritten in terms of Ft Xt= ᴧFt+et (3) ǔ(L)Ft= Gvt (4) Where G is a matrix of 1’s and 0’s selected so that equation 2 and 4 are equal. Furthermore, it is assumed that et follow the following process: di(L)et= ζit,i = 1,…,N. (5) With the assumption that ζit is independent and indirectly distributed, N(0,σζi 2), i = 1, …,N and vt is independent and indirectly distributed, N(0,σvj 2), j = 1, …, q and {ζt} and {vt} are independent. Given these parameters, the Kalman filter can be used to compute the maximum likelihood and to estimate the filtered values of Ft and ft. The Kalman filter is a recursive process constructed on the error zt ∗ and factor matrix ft∗ over time. This is done by systematically updating the mean’s conditional distribution αt|Ft~Ɲ(at|t,Pt|t) and the conditional distribution of variances αt+1|Ft~Ɲ(at+1|t,Pt+1|t) depicted in the following process as shown in the paper by Katzfuss (2016): at|t = at|t−1 +Pt|t−1H′tFt −1vt, (6) Pt|t = Pt|t−1 +Pt|t−1H′tFt −1HtPt, (7) at+1|t = Ttat|t, (8) Pt+1|t = TtPt|tT′t+Rt∑R′tŋ . (9) Where Ht is a (N x k) probabilistic time-varying matrix, and Tt is a (k x k) probabilistic time-varying matrix, these are also known as transition matrices. The filtered estimate of αt is depicted in terms of at|t and at+1|t is the one period ahead forecast of αt. Pt|t shows the covariance matrix of each corresponding predicted value at|t. This recursive process will allow the coefficient estimations of Tt, Ht,∑є and ∑ŋ by means of the log-likelihood function inbuilt into the Kalman filter (Harvey, 1989). To ensure that there are no bias loadings due to non-stationarity, the variables DOI: 10.25103/ijbesar.141.06 73 subjected to the DFM will be differenced where necessary to ensure that each variable is stationary (Stock and Watson, 2011). Brooks (2019) suggests that only factors with eigenvalues larger than one are worthwhile considering. The reasoning behind this is that components with eigenvalues larger than one encapsulate information of more than one variable. Hence, only common factors larger than one will be considered As suggested by Chao and Wu (2017), the Eigenvalues and factor loadings will be used to determine the weights of each constituent towards the final Australasian financial conditions index. If there’s only one factor with an Eigenvalue larger than one, the weightings will be calculated as follows (Chao and Wu, 2017): WX= ( LX ∑Li>0.4)∗ 100 (10) Where LX represents the factor loading exhibited by variable Xi and ∑Li is the sum of the factor loadings of all the variables with an absolute loading value greater than 0.4. The Australasian financial conditions index will then be calculated as follows: Index AFCI = ∑Xi(WX) (11) Where Index AFCI is the Australasian financial conditions index. The Christiano Fitzgerald Band-pass filter will be implemented to extract cycles from the Australasian financial conditions index. 4.2 Christiano Fitzgerald Band-pass filter: The CF Band-pass filter are calculated as follows (Christiano and Fitzerald, 2003): 𝑐𝑡= 𝐵0𝑦𝑡+𝐵1𝑦𝑡+1+ ⋯+𝐵𝑇−1−𝑡𝑦𝑇−1 +𝐵 𝑇−𝑡𝑦𝑇+𝐵1𝑦𝑡−1…+𝐵𝑡−2𝑦2+𝐵 𝑡−1𝑦1 (12) where, 𝐵𝑗=sin(𝑗𝑏)−sin(𝑗𝑎) 𝜋𝑗 ,𝑗 ⪰ 1,𝑎𝑛𝑑𝐵0=𝑏−𝑎 𝜋,𝑎 = 2𝜋 𝑝𝑢,𝑏 = 2𝜋 𝑝𝑙, (13) 𝐵 𝑘= −1 2𝐵0−∑ 𝐵𝑗 𝑘−1 𝑗=1 (14) 𝑝𝑢 is the lower limit of the cyclical duration and 𝑝𝑙 depicts is the upper limit of the cyclical duration. The bandpass will range from two years to 32 years. Thus the CF filters will isolate and extract aggregate Australasian financial cycles with durations ranging from two years to 32 years. Two years is chosen as a lower band in case the aggregate Australasian financial cycle have similar durations than a typical business cycle, which typically range from two to eight years (Botha, 2006). On the other hand, empirical evidence shows that financial cycles can last up to 32 years, hence 32 years as an upper limit (Claessens et al., 2012). Cyclical movements with a duration lower than two years will be eliminated by the filters to eliminate any potential short-term noise. 4.3 Markov-regime switching autoregressive model In literature, MS-AR models are often categorised by means of their regime dependent parameters (Bouali et al., 2016 and Tastan and Yildrim, 2008). The base model assumes that the mean and the variance are non-regime dependent. Such a model in this study has the following specification (Kim, 1994 and Hamilton, 1989): 𝑦𝑡 = 𝛽𝑠1(𝑦𝑡−1 +𝑦𝑡−2 +⋯+𝑦𝑡−𝑘 + 𝑥𝑡)+ 𝛽𝑠2(𝑦𝑡−1 + 𝑦𝑡−2 +⋯+ 𝑦𝑡−𝑘 +𝑥𝑡)+𝜀𝑡 (15) Where 𝑠𝑡∈ {1,2} shows the regime state under consideration, 𝑘 shows the optimal lag length, 𝜀𝑡 is a non-state dependent error term, and 𝑥𝑡 is a vector of explanatory variables. To allow for a regime-switching mean, equation 15 can be restated as follows (Bouali et al., 2016 and Tastan and Yildrim, 2008): 𝑦𝑡 = 𝑐𝑡𝑠 +𝛽𝑠1(𝑦𝑡−1 +𝑦𝑡−2 +⋯+𝑦𝑡−𝑘 +𝑥𝑡)+𝛽𝑠2(𝑦𝑡−1 +𝑦𝑡−2 + ⋯+𝑦𝑡−𝑘 + 𝑥𝑡)+ 𝜀𝑡 (16) Where 𝐶𝑡𝑠 is a state-dependent intercept. Lastly, equation 15 can be restated to account for both a regime-switching mean and a regime-switching variance: 𝑦𝑡− 𝜇𝑠𝑡 = 𝑐𝑡𝑠 +𝛽𝑠1(𝑦𝑡−1+ 𝑦𝑡−2 +⋯+𝑦𝑡−𝑘 +𝑥𝑡− 𝜇𝑠𝑡−1)+𝛽𝑠2(𝑦𝑡−1 +𝑦𝑡−2 + ⋯+𝑦𝑡−𝑘 + 𝑥𝑡−𝜇𝑠𝑡−2)+ 𝜀𝑡 (17) Assuming that 𝑆𝑡 is a first-order Markov process, as done by Hamilton (1989), indicating that the current regime is a function of the previous regime 𝑆𝑡−1, then the transition probabilities of progressing from one regime to another regime can be stated as (Tastan and Yildrim, 2008): 𝑝𝑖𝑗 =𝑃𝑟(𝑆𝑡= 𝑗|𝑆𝑡−1 = 𝑖),∑ 𝑝𝑖𝑗 𝑛 𝑗=1 = 1,∀𝑖,𝑗 ∈ {1,2,…,𝑛) (18) 5. Results and findings The first section will consider the characteristics of the Australian and New Zealand credit and property cycle. These measures are then aggregated and discussed. Figure 1 depicts the Australian and New Zealand property and credit cycles. Figure 1: Australian and New Zealand property and credit cycles DOI: 10.25103/ijbesar.141.06 74 Source: Author’s construction Table 1 depicts the MS-AR results for the various cyclical aggregate Australasian financial cycle factors. The regimedependent means of both regimes, μs1and μs2, for all four cyclical measures are statistically significant at a 99% confidence level and have opposite signs. This indicates that the point estimates of the mean in each regime differ significantly from each other, supporting the assumption that each one of these cyclical measures is characterised by two distinct regimes (Li, Lin and Hsiu-Hua, 2005 and Layton and Katsuura, 2001). This provides justification for the implementation of non-linear techniques to estimate these cycles. Provided that μs1 > μs2, whereby μs1is positive and μs2 is negative, regime one can be interpreted as the growth or expanding regime of these cycles and regime two as the corrective or contracting regime (Tastan and Yildirim, 2008). Table 1: Estimation outputs for Australian and New Zealand credit and property cycles Variable Australian credit cycle Australian property cycle New Zealand credit cycle New Zealand property cycle 𝜇𝑠1 0.038*** 0.053*** 0.155*** 0.085*** 𝜇𝑠2 -0.049*** -0.070*** -0.222*** -0.077*** 𝛽1𝑠1𝑡−1AR(1) 1.006*** 1.495*** 1.633*** 1.531*** 𝛽2𝑠1AR(2) 0.746*** 1.174*** -0.979** 1.134*** 𝛽3𝑠1AR(3) -0.977** -1.177*** 𝛽1𝑠2AR(1) 1.538*** 0.865** 1.048** 2.038*** 𝛽2𝑠2AR(2) 0.965*** -0.642** 0.489** 0.748** 𝛽3𝑠2AR(3) -0.665** 0.977** -0.827** 𝜎𝑠1 -7.076*** -7.831*** -6.034*** -3.523*** 𝜎𝑠2 -7.455*** -8.198*** -6.919*** -2.764*** Transition Matrix Parameters P11-C 2.583*** 3.508*** 3.174*** 2.751*** P21-C -2.908*** -3.014*** -2.594*** -2.858*** Typical duration (in quarters) Regime 1 31.620 28.382 24.910 16.662 Regime 2 29.514 21.359 14.380 18.429 DOI: 10.25103/ijbesar.141.06 75 Full cyclical duration 60.710 49.740 39.290 35.091 Transition probabilities 𝑝11 0.930 0.971 0.959 0.939 𝑝12 0.070 0.029 0.042 0.060 𝑝22 0.948 0.953 0.930 0.946 𝑝21 0.052 0.047 0.070 0.054 **, and *** denote statistical significance at a 95%, and 99% confidence level, respectively, based on p-values. Source: Author’s calculation Furthermore, the variance parameters, σs1 and σs2 of all four cycles are statistically significant with varying magnitudes across regimes. In absolute terms, the variance parameters of the Australian and New Zealand credit cycle, as well as the Australian property cycle prove to be larger during a contraction relative to an expansion. Thus indicating that contractions in these cycles are more volatile than expansions. In contrast, the New Zealand property cycle proves to be more volatile during an expansion relative to a contraction given that σs1 < σs2 in absolute terms (Kuan, 2002). Statistically significant AR terms for all four cycles provide evidence that preceding periods in these cycle significantly affect the current state of these cycles. This is the case for both expanding and contracting regimes. Positive AR terms, particularly AR(1) terms, suggests that a level of linear presence exist in these cycles from one quarter to the next (Kuan, 2002). This corresponds to the transition probabilities, p11 and p22, which provide evidence that the conditional probability of remaining in either an expansion or contracting regime is larger than transitioning to another regime, reflected by p12 and p21. Furthermore, the results indicate that an expansion in the Australian credit cycle typically lasts 31.2 quarters and a contraction lasts 29.51 quarters. Thus, a full cycle lasts an estimated 60.71 quarters. An expansion in the Australian property cycle typically lasts 28.38 quarters and a contraction lasts 21.36 quarters. Thus, a full cycle lasts an estimated 49.74 quarters. An expansion in the New Zealand credit cycle typically lasts 24.91 quarters and a contraction lasts 14.38 quarters. Thus, a full cycle lasts an estimated 39.29 quarters. An expansion in the New Zealand property cycle typically lasts 16.66 quarters and a contraction lasts 18.43 quarters. Thus, a full cycle lasts an estimated 35.09 quarters. The results indicate that, with the exception of the New Zealand property cycle, expansions typically last longer than contractions in these cycles. Furthermore, the Australian credit cycle proves to exhibit the longest cyclical durations, where a full cycle typically lasts 60.71 quarters, or 15 years and 2 months. This is longer than the typical business cycle, aligning with the findings by Claessens, et al. (2012), Borio (2014), Aikman et al. (2015), Pontines (2017) and Farrell and Kemp (2020). 5.1 The aggregate Australasian financial cycle Table 2 depicts the outputs rendered by the dynamic factor model. The results indicate that only the first factor has an Eigenvalue larger than 1, therefore, only the factor loadings onto factor one will be considered. The first factor captures about 69% of the variance between the various aggregate Australasian financial Measures. This is in line with the suggested appropriate level of 50% by Breitung and Eickmeier (2005), and the suggested level of 55% by Ng (2011). This provides evidence that there is a significant portion of the fluctuations between the various financial components that are systemic or syncretic. Thus, these variables can be well represented by a single measure, for example, an index. Table 2: Dynamic factor outputs Sour ce: Aut hor’ s calc ulati on Furt her more, the results indicate that the Australian credit measure has the largest factor loading and will constitute 30.81% towards the Australasian financial conditions index, which is the largest contribution towards this index. This is Eigenvalues of factors Factor one Factor two Variance explained by factor one 3.165 0.951 69.146% Factor loadings Variable Loading Weighting Australian credit measure 0.753 30.810% New Zealand credit measure 0.642 26.268% Australian property measure 0.575 23.527% New Zealand property measure 0.474 19.394% DOI: 10.25103/ijbesar.141.06 76 followed by the New Zealand credit measure which contributes 26.268% towards the index. Australian credit levels are thus the strongest underlying driver of the Australasian financial conditions index, and ultimately the strongest driver of the aggregate Australasian financial cycle. Figure 2 depicts the Australasian financial cycle. Figure 2: the Australasian financial cycle Source: Author’s construction Table 3 depicts the estimated MS-AR outputs for the Australasian financial cycle. The significant difference in the mean and variance across regimes justifies the use of a non-linear model. Similar to the other cyclical measures considered previously, given that μs1 > μs2, regime one represents a growth or expanding regime in the aggregate Australasian financial cycle and regime two represents a corrective or contracting regime (Tastan and Yildirim, 2008). The results also indicate that a contracting regime is slightly more volatile than an expanding regime, given that σs1 < σs2 in absolute terms. Therefore, similar to the research on business cycles, such as the findings by McQueen and Thorley (1993), Tastan and Yildirim (2008) and Breitung and Eickmeier (2015), contractions in the Australasian financial cycle prove to be more volatile than expansions. Table 3: MS-AR estimation output for the Australasian financial cycle Variable The aggregate Australasian financial cycle 𝜇𝑠1 0.019 𝜇𝑠2 -0.014 𝛽1𝑠1𝑡−1AR(1) 1.450 𝛽2𝑠1AR(2) 0.965 𝛽1𝑠2AR(1) 1.519 𝛽2𝑠2AR(2) 0.935 𝜎𝑠1 -4.022 𝜎𝑠2 -4.739 Transition Matrix Parameters P11-C 2.928 P21-C -2.709 Typical duration (in quarters) Regime 1 24.835 Regime 2 19.700 Full cyclical duration 44.535 Transition probabilities 𝑝11 0.949 𝑝12 0.041 𝑝22 0.938 𝑝21 0.073 Wald hypothesis testing asymmetry results Asymmetry Sign Null hypothesis P-value -3 -2 -1 0 1 2 3 1980 1985 1990 1995 2000 2005 2010 2015 Australasian financial cycle Magnitude Time