Multilevel approach to the analysis of housing submarkets

ABSTRACT There is a vast literature that seeks to define and identify spatial submarkets in metropolitan housing systems. These tend to use one of three methods to delineate submarkets: a priori geographies, ad hoc subdivision and data-driven approaches to grouping units. Recently, analysts have increasingly used multilevel modelling strategies to analyse spatial segmentation in the housing market. Despite the increasing prevalence of multilevel approaches, there is no existing systematic analysis of which of these three main approaches to submarket definition has the greatest effectiveness when employed in a multilevel modelling framework. This paper addresses the gap in the literature by comparing the utility of these main approaches to submarket definition. It develops and evaluates three separate, distinct multilevel models of submarkets to a data set comprising 2175 transactions in the Istanbul housing market of Turkey, an emergent market context. The results show that multilevel models with a priori submarket dummy variable can predict price more accurately than the models with ad hoc subdivision or data-driven stratified submarkets. Similarly, test results indicate that multilevel models with neighbourhood submarket dummy variables (a priori) perform better than other models. These test results show that granular definition of submarkets tend to perform better in terms of predictive accuracy than less spatially granular models. The paper also suggests that real estate agents’ views of submarket structures might be particularly useful as inputs into micro-modelling processes in contexts where datasets are thin.

INTRODUCTION
A substantial literature argues that house price models should accommodate housing submarkets for conceptual and technical reasons (see Watkins, 2012, for a review). From a conceptual perspective, it is argued that submarkets are a function of the multiple equilibrium (or, in some cases, disequilibrium) nature of the market (Goodman & Thibodeau, 1998;Maclennan et al., 1987;Watkins, 2001). In practical terms, it has been shown that submarkets must be taken into account to avoid aggregation bias (Straszheim, 1975) and enhance the predictive performance of house price models (Leishman et al., 2013). The vast majority of papers that take account of submarkets do so by either incorporating them within hedonic models (Fletcher et al., 2000) or by estimating submarket-specific hedonic models (Watkins, 2001). Importantly, however, an increasingly voluminous series of studies have begun to advocate the inclusion of submarkets within a multilevel modelling framework (see Goodman & Thibodeau, 1998, for an early example; also Orford, 2002;Leishman, 2009;Keskin, 2010). Significantly, Leishman et al. (2013) conducted an experiment that compares the performance of different approaches to modelling submarkets and demonstrates that multilevel techniques can improve model accuracy. These findings emerged from a systematic comparison of different approaches. Specifically, they evaluated the use of a simple hedonic augmented with dummy variables to capture submarket effects, a system of submarket specific hedonic equations, and a multilevel model specification with submarket levels included by comparing the likelihood of predicting prices within 10% of the actual price, and the average size of the standard errors of the model estimates to assess the utility of the modelling approaches.
An immense number of studies illustrate alternative partitioning methods for submarkets in hedonic modelling analysis. The last three decades have seen a growing body of research on the submarket delineation that employ multilevel models as an important strand of this literature. These multilevel studies have also been used to test the performance of alternative submarket definitions. Unlike the broader literature, however, there is a lack of research comparing the effectiveness of methods of allocating dwellings with submarkets or of their performance when used in multilevel modelling of housing prices. This study attempts to fill this gap by testing different submarket delineation approaches in a multilevel modelling framework as part of a systematic comparison of different modelling procedures.
The empirical analysis focuses on the Istanbul housing market of Turkey. In doing so, the analysis throws up a challenge common to many studies conducted in emergent property market contexts in that the datasets are thin in terms of both the number of observations and the number of hedonic variables for which data exist. In this context, although there are already several studies examining submarket identification and delineation as a prior stage in hedonic house price modelling procedures, this paper seeks to be distinctive in two ways. First, by comparing different methods of identifying submarket units for analysis, the paper offers a systematic review of which submarket description performs best when used in a multilevel modelling setting. Such comparisons of multilevel models are rare in the literature. Second, with the emergent market data limitations in mind, the use of real estate experts' views as one means of identifying submarket units as a prior step to modelling is explored (see also Palm, 1978;Watkins, 2001). This is of interest because it offers a shortcut to identifying submarkets where datadriven approaches are limited due to the paucity of market information. This has arguably been one of the constraints on the greater use of multilevel approaches in transitional and emergent market contexts.
Thus, this paper seeks to empirically explore the utility of the multilevel modelling framework further by looking at how it works when used with the three major approaches to submarket delineation. Furthermore, by using the Istanbul housing market as a case study in which to undertake the predictive performance of the multilevel modelling, the paper is also able to offer comments on the relative merits of the use of experts' views as part of the analytical process where data limitations exist.
The remainder of this paper is organized as follows. The next section reviews the concept of housing market segmentation and explores how it leads to the formation of housing submarkets. It focuses on the delineation of submarkets and also provides a brief review of studies that accommodate submarkets in multilevel models of metropolitan house prices. The paper then summarizes the research design. It introduces the case study area, provides an overview of the data, and explains the rationale for using multilevel models and the method used to estimate the models. The paper then sets out the results and compares the model performance when each of the three main approaches to submarket delineation are used. The final section summarizes the findings and offers some concluding remarks.

HOUSING SEGMENTATION AND FORM OF SUBMARKETS
Since housing is a multifunctional composite concept, all kinds of investments, actions, interventions and policies about housing affect the built environment as well as the socio-economic environment. This differentiation has an impact on both supply and demand side of the market, which also leads to segmentation in the housing market. Housing submarketsarising from housing market segmentationare crucial to understanding the operation and structure of the housing system, which is mainly shaped by the interaction of demand and supply dynamics (Maclennan & Tu, 1987).
The housing market activity involves the exchange of dwellings (or housing units) rights between buyers and sellers. This process determines the individual price of housing unit as well as the quantity that will be exchanged and the market level price structure. It is therefore important to understand the factors that influence and underpin demand and supply. The demand side of the housing market is composed of diverse consumer groups that vary based on their socio-economic background, household composition, cultural background, lifestyle preferences and tastes. On the other hand, the supply side can be viewed as consisting of products groups constituting of clusters of similar dwellings with variation between groups reflecting differences in dwelling size, type, quality of construction and location. All these variances, as well as heterogeneous demand, and differentiated supply interaction create complexity in the market structure, which also underpins spatial price differentiation.
In this context, Jones and Watkins (2009) point out that, in theoretical terms, submarket existence can be shown to be consistent with both disequilibrium and multiple equilibria processes. In the former case, a mismatch between demand and supply leads to disequilibrium, which is one of the aforementioned explanations of housing market segmentation. Disequilibrium can result from heterogeneous factors including financial conditions, individuals' preferences, information search costs, as well as from exogenous shocks such as pandemics or wars that change the dynamics of the market processes towards disequilibrium.
According to another explanation for the existence of submarketsmultiple equilibriaeach segment has its own equilibrium price; therefore, within each segment there is an equilibrium that is determined by the balance between supply and demand forces (Goodman, 1981). This assumption dominates most of the housing market studies since they acknowledge the existence of housing price differences among submarkets. Thus, most of the studies in the housing market literature assume that a housing market consists of a set of linked submarkets that exhibit supply and demand imbalances, resulting in spatial differences within the market (Watkins, 1998;Orford, 2000). This raises the question of whether a single/overall market analysisin other words fitting a general modelcould be sufficiently reliable in modelling.
In this study, a multiple equilibrium perspective is adopted. It is accepted that the existence of price differentials among market segments is based on the assumption of equilibrium within submarkets. The equilibrium of housing demand and supply in a submarket is achieved by changes to the housing stock and/or the turnover rate in the existing stock. The equilibrium house price will be determined by the sum of the value of individual physical attributes, local amenities and neighbourhood quality typical within the prevalent product group in the market segment.

Definition of housing submarkets
Many studies in the housing literature have suggested that the housing market system is best analysed as a collection of 'functionally independent geographic submarkets differentiated by the characteristics of their housing units and/or the locations of the submarkets' (Rothenberg et al., 1991, p. 63). Although there is a consensus on the theoretical existence of submarkets, there is insufficient agreement on how to delineate the submarkets in practice. As Watkins (2001) states, there is no single definition of housing submarket, and the precise definition of submarkets has always been contested.
For many scholars, Grigsby's approach on substitutability is considered the basis of submarket definition. Grigsby (1963) explains substitutability in terms of optimization of preferences within a price limitation. Substitutability requires home buyers to be indifferent between the entire bundle of structural, locational and neighbourhood quality attributes that characterize the competing housing units (Watkins, 2001). It has been revealed in many housing studies that both spatial and structural features are significant in leading to the emergence of housing submarkets and shaping their structure (Adair et al., 1996;Maclennan & Tu, 1996;Watkins, 2001;Kauko, 2002;Bourassa et al., 2007). As Evans (1995, pp. 6-7; added emphasis) pointed out: the buyer is purchasing a property which is a bundle of characteristics. So, in the case of a house, the purchaser buys a location relative, say, to shops and workplaces, fertility in the sense of the quality of environment, also a house where attributes of the housesuch as central heating, number of bathrooms, size and number of roomscannot be detached and sold separately.
Since submarkets are formed by a complex bundle of structural and spatial attributes, analysis through segments/submarkets can provide a better understanding of housing market dynamics than might be possible from an analysis at the aggregate level. Therefore, delineating submarkets and understanding their dynamics is a critical step in analysing housing markets.
Delineating submarkets in practice Three main approaches are used in the housing market literature to delineate submarkets: a priori geographies, ad hoc subdivision groupings and data-driven classifications. The first approach, which is often labelled a priori submarket delineation, typically uses predefined geographical areas or spatial contiguous boundaries such as administrative, postcode areas, census divisions and school catchment areas. This approach, based on predefined administrative spatial areas, has been widely used by scholars such as Maclennan et al. (1987), Adair et al. (1996), Goodman and Thibodeau (1998), Jones (2002), and Goodman and Thibodeau (2003) in housing market studies. This classification is simple to use and technically accessible, yet it cannot fully capture the dynamics of housing submarket due to its fixed structure.
The second approach is based on the ad hoc allocation of spatial boundaries by market experts such as real estate agents and valuers. Palm (1978) argued that submarkets that are defined by real estate agencies showed better performance than those determined by data or a priori classification. Similarly, Michaels and Smith (1990) used an expert-defined submarket model that yielded the best performance in housing price estimation when compared with alternative a priori submarket constructions. Bourassa et al. (2003) compared a set of submarkets based on geographical areas defined by real estate agents and appraisers with a set of statistically generated submarkets. They also found out that price predictions are more accurate when based on the housing segmentation defined by real estate appraisers than when based on statistical techniques. However, the use of this approach to establish submarket classifications has criticized for its lack of rigour (Costello et al., 2019).
The third common method is a data-driven approach that uses statistical techniques to delineate submarkets. Based on a given set of variables that capture structural and spatial characteristics, the data-driven techniques assign housing units into groups that are statistically shown to be relatively homogeneous within themselves and heterogeneous when compared with each other. As noted above, the nature of housing segmentation particularly depends on homogeneity within submarkets, while heterogeneity between submarkets is also expected. In this context, maximization of cluster homogeneity is the key principle used to operationalize Grigsby's notion of substitutability. Several studies use statistical methods when defining submarkets, such as cluster analysis (Bourassa et al., 1999), principal component analysis (Watkins, 1998;Bourassa et al., 1999Bourassa et al., , 2003 and, less commonly, factor analysis or neural network analysis (Kauko, 2003).
The improvements in quantitative research methods and increased availability of large micro-datasets (with geocodes, characteristics and price information) have contributed to conceptual and methodological debate about housing market analysis (Watkins, 2012). The increased accessibility to the more detailed and granular data enables one to delineate submarkets by using different methods that allows to collaborate with hard and soft boundaries. There are some studies using absolute location -{x, y} coordinatesto capture the impact of local and non-local externalities on properties (Pavlov, 2000;Clapp and Wang, 2006;Fik et al., 2003). By doing so, researchers could overcome with the obstacles of using a priori defined submarkets with hard boundaries which could 'mask significant value discontinuities' (Fik et al., 2003, p. 625). As an example, Bayer et al. (2007) applied a boundary discontinuity design (BDD) to address the endogeneity of school and neighbourhood characteristics in a heterogenous residential choice model. They identified elementary school attendance zone boundaries by implementing BDD and assigned each block to one of the school zones. Therefore, by combining a priori and data-driven approach, the study made a significant contribution in defining submarket boundaries and analysing the fixed effects of the submarkets whilst taking endogeneity into account.
Elsewhere in the literature, new modes of technology in online housing services and changes in search behaviour have been recognized by housing market studies (Dunning et al., 2019). Advances in collection of data and accessibility have opened up some innovative approaches to delineating the housing submarkets. One such pioneering study by Rae (2015) investigated the performance of 'user-generated search areas' as a form of submarkets and his findings show that this approach could contribute to the analysis of housing markets by providing a deeper, alternative understanding of how housing submarkets are formed and evolve. The influence of broader conceptual and methodological developments has started to become evident in housing submarket studies (see below).

Assessing submarket variation in multilevel models
To have a better understanding of the operation and structure of housing market through models, the conceptualization of submarkets is a fundamental step in the analysis. A number of studies have investigated the dynamics of the housing market by incorporating submarkets into multilevel models over the last three decades. The nature of the data used in housing studies that have a hierarchical structure with levels such as the housing unit is located in a neighbourhood/district/local authority/region. Multilevel models enable the analysis of the housing market at several levels simultaneously, rather than at single level of the data individually. This method is equipped to analyse multiple levels of data and is able to capture relationships between the independent and dependent variables that can vary between places (spatial units). Several housing market studies apply multilevel model specifically to explore spatial dependencies in both micro-(individual) and macro-levels (contextual level).
In one of the earliest housing market studies to employ multilevel models, Jones and Bullen (1993) employed an a priori approach to segmentation to investigate empirically the determinants of housing prices. They used a two-level approach: individual level (housing unit) and submarket level (local authority areas). The individual-level, property characteristics of housing units are examined within the submarket levels which were based on local authority areas in Southern England and London boroughs between 1980 and 1987. The study makes an innovative methodological contribution since it recognizes the distinction between compositional and contextual effects and provides an improvement in the empirical examination of housing prices by being sensitive to drivers that vary across both space and time. Bullen et al. (1997) built on this innovation when they investigated the variations in residential prices in England and Wales by using travel time-to-work areas (TTWAs)as determined by the Office for Statistics (ONS) derived from census dataas an alternative form of a priori definition of submarkets. Results from fitting a multilevel model with the TTWA-driven submarkets indicates that complex heterogeneity can be addressed better at both housing unit and submarket levels. Multilevel modelling appeared in this study to help overcome the problems arising from heterogeneity and spatial autocorrelation and thus offer what is arguably a better contextualized methodology. Orford (2000Orford ( , 2002 used a multilevel approach that allowed the compositional effects of the housing stock and the contextual effects of a priori determined submarkets in Cardiff, Wales. Both structural and locational attributes were taken into account and analysed at submarkets level, where the segments were based upon the 26 community units used by the city council for administrative purposes, and also at street level. The multilevel model allowed the impact of submarkets on price differentials to be clearly displayed in 'an holistic view of the housing market, one that is more comparable to conceptual than the standard single-level specification' (Orford, 2000(Orford, , p. 1670. It was also emphasized that a clear theoretical understanding is needed about how spatiality enters in the analytical process (Orford, 2002) Leishman et al. (2013) focused on spatially segmented submarkets based on real estate agents' definitions and postcode areas to compare different modelling strategies for Perth, Western Australia. They estimated a series of submarket-specific hedonic models and multilevel models with different spatial levels and compared their performance. The study found that more granular submarket specification (based on postcodes) increased analytical efficiency and decreased the occurrence of spatial autocorrelation. Keskin et al. (2017) adopted a priori definition of submarkets and used administrative neighbourhood boundaries in their study of changes in the pattern of housing prices in Istanbul, followed by earthquake activity in the wider region. The results revealed discrete spatial impacts on housing prices and showed that the impact of earthquake varied widely at the neighbourhood level. These findings were consistent with Leishman et al.'s (2013) argument that the more granular structure of submarkets tends to be more effective when it comes to the accurate prediction and measurement of house prices and modelling their spatial distribution.
Most recently, Alas (2020) explored the spatial of housing prices by implementing a further variant on the a priori approach to the definition of submarkets. The models were constructed by using submarkets based on administrative district boundaries, neighbourhood boundaries and street level in Istanbul. The study concluded that multilevel models based on smaller geographical spatial units are capable of increasing predictive efficiency in assessing housing price differences.
Most of these previous studies have adopted a two-level approach by using submarkets as a nested (second/contextual) level. They also usually compared the performance or multilevel model against hedonic model. Some of the studies tested the effectiveness of models employing a priori and ad hoc approach in submarket description. This study extends this literature by testing more approaches in submarket delineation, namely ad hoc, a priori and data-driven methods.

RESEARCH DESIGN
The focus of this paper is to investigate the performance of different submarket delineations in modelling the dynamics of a local housing market. The empirical analysis underlying it uses multilevel modelling in order to examine the performance of different types of submarket delineation. To compare the efficacy of the different approaches in submarket definition, three separate multilevel models are analysed on the basis of a priori, expert-based (ad hoc) and datadriven submarket allocation.

Multilevel modelling in housing studies
The multilevel model approach has been adopted in housing studies in the last three decades with increasing attention since it has the capacity to analyse individual-level characteristics embedded in different spatial levels. This method provides an analysis of the data with a hierarchical structure by using combinations of individual-and group-level independent variables for finding the impact of contextual effects.
As reviewed in the previous section, multilevel modelling is widely applied in housing market studies due to the technical advantages that help to overcome the limitations of the conventional models. Hedonic modelling, a conventional model widely used in housing market studies, is based on fixed effects of the independent variables, whereas multilevel models focus on both fixed effects and random effects of the group level. Furthermore, it is assumed that the effects of housing unit attributes are the same across submarkets in hedonic models; for example, the effect of age of the building is the same within the market regardless of the submarkets/neighbourhood. In comparison multilevel modelling enables the relationship to vary spatially.
Although hedonic modelling is a useful tool for understanding housing markets, technical constraints such as spatial autocorrelation, spatial heterogeneity, ecological fallacy and atomic fallacy led commentators to observe robustness problems in modelling (Malpezzi, 2003). Creating a dummy variable for submarkets is a commonly suggested method to overcome these problems. However, the degrees of freedom (DoF), which is needed to analyse cross-level interaction, is still problematic since DoF is calculated based on individual data rather than group data. Multilevel models overcome these spatial heterogeneity-related problems by testing the individual-level attributes on the housing prices within different clusters such as neighbourhoods or submarkets. Thus, by using multilevel models, it is possible to overcome the atomic fallacy problem that emerges from the generalization of housing unit-level data to submarket-level data and also to overcome the ecological fallacy problem arising due to the practice of generalizing submarket characteristics information to the housing unit level. As a substitute to fitting a general model that assumes that the relationship between the independent and dependent variables is constant everywhere, multilevel models allow this relationship to vary spatially within the study area (Owen et al., 2016). These cross-level interactions help to explain the impact of housing unit variables on housing prices according to the different contexts in submarket levels. Thus, in other words, multilevel modelling enables one to distinguish the impact of housing unit-level variables and geographical/group-level (such as neighbourhood, submarket, district and region) indicators. It then becomes possible to estimate the random part and the proportion of the variance at different levels. This method answers the question of 'how big is the random part?' occurring due to the variance (1) between-group levels (such as neighbourhoods) and (2) within-group level but between housing units.
The two-level multilevel model involves of individual housing units, i, nested in area j (hereby submarket j). Leishman et al. (2013) express this as: where P i represents the price of the ith dwelling in the jth spatial area; Y i are physical and neighbourhood housing attributes for the ith dwelling; h 0j is the random intercept for the jth spatial area; h kj are random slope parameters for the k attributes, specific to the jth spatial area; and e ij is an error term or residual.
In parallel with the widespread use of the multilevel approach, some methodological studies have criticized the technical handicaps of this method, especially on the identification of group level. If the geographical presumptions associated with multilevel modelling are unreliable, then this approach cannot provide solid foundations for a methodology that aims to identify contextual effects and differences (Owen et al., 2016). The spatial design of the group level incorporated into multilevel models is crucial since using the same data will generate different results depending on the method of aggregating individual units into spatial units (Gehlke & Biehl, 1934, cited in Owen et al., 2016.
This brings the question: What is the best fit for a group level? To include submarketsas group levelthat are based on different approaches in multilevel models is a way to assess the performance of multilevel modelling. But how could we define the best fit for determining the group level? As reviewed in the previous section, the main approaches in the housing market literature to delineating submarkets are a priori classification, ad hoc and data-driven stratification. This study compares the utility of these three main approaches to group level definition as a prior step to modelling house prices. In this respect, the spatial determinants of housing prices can be analysed via multilevel models, which are based on different submarket descriptions.

Case study and data
The analysis in this paper used data from the Istanbul housing market. Istanbul has experienced a very rapid urbanization and has become one of the most populous cities globally. By 2018, the population of Istanbul reached 15.1 million, an increase from 7.3 million in 1990 (TUIK, 2021a). Having doubled in population over the last three decades, Istanbul has also undergone a polycentric development due to globalization. With 31% of the country's gross domestic product (GDP) held by the city, it has become a financial and trade centre (TUIK, 2021b). The major changes in the service sector and the expansion of transportation infrastructure played essential roles in the multicentre development of Istanbul (Arslanlı, 2020). Moreover, with the approval of the urban regeneration legislation in 2004, many areas in Istanbul have been designated transformative zones (Kuyucu, 2020) in order to improve the quality of housing stock due to earthquake risk. Decentralization of central business districts (CBDs) and industrial areas and the change in the accessibility pattern and urban transformation within the city has led to variation in housing prices (Koramaz & Dokmeci, 2012). The combined effects of these processes have produced an urban structure with high levels of spatial disaggregation and significant socio-economic segmentation (Kısar Koramaz, 2014).
The housing stock in Istanbul can be categorized under three broad groups: 'urban housing, suburban housing and residences' (Ozus et al., 2007, p. 346). Urban housing areas are located in the historic districts, usually in planned inner-city areas, yet not with enough infrastructure such as green areas and recreational areas. The higher land prices in urban areas have prompted developers to construct suburban housing projects in peripheral areas that were dominated with squatter settlements. These peripheral areas have become an attractive alternative to urban housing not only due to the escalation of land prices in the inner city but also as a means of meeting demand from middle-to-high-income groups who want to live in those areas where the risk of earthquake is relatively smaller (Onder et al., 2004;Keskin et al., 2017). A variety of factors, including urban transformation initiatives and modifications to plans to reflect changing market conditions, have contributed to an increase in property prices in these suburban housing areas (Ozkan & Turk, 2016). Presently, most of the existing housing stock consists of multi-family apartment buildings and residential projects located primarily in the suburbs. The other main source of change to the stock takes the form of residential developments located within the inner-city area, usually on brownfield locations. These are targeted at a specific demographic group that prefers urban living but is also motivated by a preference for convenience-based living and 'premier' locations (for details, see Ozus et al., 2007).
Taken together, these ongoing changes in the urban transformation process mean that Istanbul's housing market has a dynamic structure with clear differentiation in terms of product group locations and consumer group preferences for different localities. As such, the city provides an ideal case study location for multilevel analysis of the housing system and its submarket structure.
Data set Different data sources have been used to compile the database for the analysis in this study. The primary dataset comprises 2175 single-family house transactions sold in November 2006 and April 2007. These were obtained from two major real estates' websites. This dataset compiles housing unit transactions and characteristics from 283 neighbourhoods in 32 districts. Additionally, the second dataset consists of socio-economic characteristics, neighborhood quality characteristics, and location characteristics gathered from a survey that was conducted by the Istanbul Greater Municipality in 2006. This dataset (secondary data) provides information about the socio-economic structure of the neighbourhoods and the satisfaction of the inhabitants of the city. In addition to the socio-economic and neighbourhood quality characteristics, an important locational characteristicearthquake risk datais obtained from the JICA (2002) report on disaster prevention/mitigation plan in Istanbul. This is matched to the geocoded dwellings in the core dataset. As a whole, the data used in the study can be categorized into four groups of variables: housing unit characteristics; socio-economic characteristics, neighbourhood quality characteristics and location characteristics (Table 1). It should be noted that the number of variables available in this study is thin relative to other studies of this sort. This is a common challenge in studies of emergent markets and, even after multicollinearity issues are taken into account, the number of variables available is still comparable with those used in the baseline hedonic models in several key submarket studies (e.g., Fletcher et al., 2000;Watkins, 2001). In order to delineate the submarkets in Istanbul, three main approaches explained in the previous section are applied: . A priori (administrative neighborhood boundary) submarket delineation: the administrative neighborhood boundaries are used as the basis for our a priori submarket delineation criterion. When this research was conducted, there were 946 neighbourhoods in Istanbul. However, as many of them do not contain market housing, the data are drawn from 283 neighbourhoods. . Ad hoc (expert based) submarket delineation: 10 semi-structured interviews were held with real estate experts, and they were asked to draw the submarkets on the map that displayed all the administrative boundaries of neighbourhoods in Istanbul. The submarkets are shaped by overlapped boundaries and five submarkets were delineated by consensus from the experts. . Data-driven (cluster analysis) submarket delineation: hierarchical cluster analysis is applied to derive submarket clusters. A total of 12 submarkets are designed by taking into characteristics such as housing prices, floor area, age of the building and number of rooms, income of households, living period of inhabitants in Istanbul, neighbourhood quality, and satisfaction from the public transportation facilities. In line with previous studies, the risk of an earthquake is also treated as an input for the cluster analysis (Onder et al., 2004;Naoi et al., 2009).

MODEL RESULTS
As noted, this study uses three different techniques that are most common in the literature. In this section, the results of three multilevel models of housing price based on the different submarket formulations are presented. First, the results of the intra-class correlation (ICC) values of different submarket delineation are discussed (Table 2). These are used to fit variance component models of housing prices without the explanatory variables for three nested levels: expert, cluster analysis and neighbourhood. According to the ICC analysis, around 27% of the variance in housing price differences is due to differences across both ad hoc (expert defined) and data-driven submarkets, with the remaining 73% attributable to housing unit level. Unlike the experts-defined or data-driven categorizations, 49% of the variance in housing price is related to housing unit characteristics in the a priori submarket categorization, whereas 51% of the variance comes from submarket (neighbourhood) level.  Table 3 displays the results of the model based on the a priori submarket classification and gives the results for the factors that determine the housing prices. This model has the most granular structure with 283 administratively determined neighbourhoods. Floor area of the housing unit, with a positive relationship with price, has the greatest impact on the housing prices. Floor area is followed in terms of scale of influence by average living period in Istanbul, income of the inhabitants living in the neighbourhood, housing unit being located in a vertical/horizontal gated community, and then low storey, respectively, again with a positive impact on the housing prices. Lastly, in addition to those explanatory variables and in line with other studies of Istanbul prices, earthquake risk has a positive significant factor in housing prices. Table 4 presents the ad hoc (experts' defined) submarket model results. Similar to model 1 (a priori based on neighbourhood boundaries) (Table 3), this implies that floor area, living period in Istanbul, being located in a gated community, income and being located in a low-storey building have a statistically significant positive impact on housing prices have a statistically significant positive effect on housing prices. Table 5 displays the results of the model based on the data-driven submarket structure and summarizes the results for the factors that are affecting the housing prices. Floor area of the housing unit, with a positive relation with price, has the greatest impact on the housing prices. In terms of scale of impact, floor area is followed by inhabitants' average living period in Istanbul  and income of the inhabitants living in the neighbourhood, respectively, which again have a positive impact on the housing prices. Aside from those explanatory variables, housing units located in vertical and horizontal gated communities and in low-storey buildings are significant positive factors affecting housing prices. Unlike the expert-based model, the earthquake risk does have an impact on the housing prices. In this case, as might be expected on the basis of prior knowledge, it is negatively related with housing prices. The variables included in Tables 3-5 are selected on the basis of their significance level. Pand Z-values are not presented, but they are available from the author upon request. Each specification also generated random effect estimates. As they are not used in the testing regime, they are not reported here, but again they are available from the author upon request.

Overview of the results
Prediction accuracy (PA) and root mean square error (RMSE) tests have been adopted in large number of studies where they are comparing the performance of different submarket delineations. These tests assess the accuracy in terms of the proportion of estimated prices that fall within a narrow tolerable range of the actual price. Examples of such tests can be seen in Watkins (2001), Bourassa et al. (2003), Goodman and Thibodeau (2003), Keskin et al. (2017) as well as a review of around 30 cases in Watkins (2012). Leishman et al. (2013) compared the performance of the submarkets, delineated by real estate professionals, with a priori delineated postcodes. Building on this approach, PA and RMSE tests are applied on models ( Table 6) that are derived from real estate experts' opinion, a priori administrative neighbourhood boundaries as well as data-driven delineated submarkets.
As can be seen from Table 5, the predictive performance for a priori submarket delineation, which consists of smaller spatial units, exceed all other submarket approaches examined in this  study. It is also evident that the spatial pattern of prediction errors is less concentrated. The results show that multilevel models with granular submarket delineation at group level have the capacity to improve predictive power and reduce spatial dependence. According to the test results, the model with a priori submarkets has the strongest predictive performance with more than 39% of cases within 20% accuracy and 21% within 10% accuracy. This is followed by data-driven, with 38% of cases within 20% accuracy and ad hoc (experts' opinion) submarket with 35% of cases within 20% accuracy. Furthermore, the RMSE test results show consistency with PA results since the difference between actual price and estimated values are least in a priori model which is followed again with data-driven and ad hoc submarket models.

CONCLUSIONS
Numerous previous market studies have argued that the complexity and dynamics of the housing system can be analysed more effectively and accurately by taking account of its segmented spatial structure. This implication of this assertion is that submarkets should be accommodated in modelling procedures and that the data used should ideally have a hierarchical and/or nested composition. Despite general agreement on this broad point, there remains a lack of consensus about how best to determine submarket delineations in practice, and the matter has become the subject of several recent empirical investigations. The literature is also unclear on what form econometric models should take to best undertake such an investigation. The methods used range from simple hedonic regressions that include submarket dummies, systems of submarket specific regressions equations, and the use of neural networks and cellular automata approaches. Several recent studies have also stimulated a resurgence in interest in the use of multilevel modelling. The rationale behind employing multilevel model is that the technique allows readily for the examination of within and between submarket variability. Despite advocacy for greater use of multilevel models, there are two constraints on their use. First, it is not clear from the literature how analysts should identify submarket units for inclusion in models. Can these be captured by including spatial administrative boundaries at different levels, or does prior work need to be done to identify functional submarkets? Second, do multilevel methods have utility in study areas, such in emergent market contexts, where datasets might be thin.
This paper attempts to contribute to the multilevel modelling strand of the submarket literature by addressing both of these issues. It addressed the former issue by using multilevel methods to compare the performance of some of the different submarket descriptions used in the literature. The empirical analysis presented here is based on an experiment that tests different approaches to variants of the three most common approaches used to construct housing submarkets: an a priori classification which is based on the use of administrative neighbourhood boundaries; a set of partitions based on experts' views of submarket composition; and a data-driven approach which groups dwellings based on cluster analysis. The study employs data from the Istanbul housing market. Of course, the use of expert opinion in this way has been advocated as a means of addressing data limitations (Watkins, 2001) and helps us explore the second constraint.
Since most house price applications such as tax assessment, valuation and marketing require high levels of model accuracy, this experiment focuses on predictive accuracy as the basis from which to determine which submarket definition performs best in these models. Based on their precision, the performance of these models is compared in terms of the proportion of predicted prices falling within 10% and 20% range of the actual price. The a priori (administrative neighbourhood boundaries) formulation generated the greatest proportion of estimates within 10% and 20% of actual price with 39% and 21%, respectively, in these intervals. Furthermore, the RMSE test results (which provide an alternative assessment of accuracy) indicate that the a priori classification has the smallest difference between actual and predicted standard error values. In other words, the categorization based on administrative neighbourhood boundaries has the largest reduction in terms of error. These test results show, as with previous studies in this field, that the most granular definition of submarkets deliver a better performance than those that use larger spatial units. Interestingly, in the context of markets where data constraints persist, the analysis suggests that real estate experts' views of submarket structures might be particularly useful as inputs into micro-modelling processes in contexts where datasets are thin.


Driving green bond market through energy prices, gold prices and green energy stocks: evidence from a non-linear approach

Abstract One of the most controversial concerns among the researchers is the expansion of the green bond markets, so as to reduce environmental pollution. The present study estimates the factors that help drive the global green bond markets, such as energy prices, gold prices, and green energy stocks. The study has applied Quantile Autoregressive Lagged Approach (QARDL) and Quantile Granger Causality test to estimate the causal relationship among the variables for January 2010 and June 2021. The QARDL findings reveal that for all the quantiles, the error correction term is statistically significant with the predicted negative sign. This confirms the existence of a strong long-run equilibrium relationship between the relevant variables and the green bonds market on a global level. The findings revealed that gold and energy prices have a lower effect on the green bonds market on every quantile, and also from the low to medium quantiles, respectively. While at the same time, the green energy stocks have an increasing effect on the green bonds market at higher quantiles. The results of the causal examination using Granger-causality in quantiles show a bi-directional causal relationship between the green bonds, energy prices, gold prices, and green energy stocks in the world economy.

Introduction
A climate change adaptation or a minimal carbon economy is one of the key goals of environmentalists and government agencies around the world . In this regard, several efforts have already been made to attain this goal, and green projects financing, including mutual funds and investments based on sustainability (Capelli et al., 2021;Ferrat et al., 2022), green investments, and divestment from fossil fuels, are among some of the initiatives that have already been introduced to encourage the transition towards green economies . In addition to this, Green bonds (GB) are among the most popular techniques to support green environment projects. A green bond is a unique financial product that is defined as a 'the use proceeds' criterion that requires the funds generated through its issuance to contribute towards climate change remediation, conservation of the natural resource, biodiversity enhancement or conservation, pollution control and prevention, and so on (C.-W. . GBs are essentially unique, sustainability-oriented, fixed-income financial instruments that allow issuers to grow funds that are exclusively dedicated to environmentally beneficial initiatives, in line with a climate-resilient economy (Yan et al., 2022;Yu et al., 2022). Green bonds, more specifically, offer significant environmental benefits due to their green character, such as being energy-efficient, low on carbon, and climatefriendly (Park et al., 2020;Rizvi et al., 2021;Sartzetakis, 2021). This subject belongs to the developing body of knowledge in the field of energy finance, which includes sustainable finance and green finance (Guo et al., 2022;. This structure enables the local and global environmental organisations to increase funds by selling fixed income securities, which are then used to fund sustainable and environmentally beneficial projects (Chien et al., 2022;. In the long run, financing through a substantial bond market that can provide capital may thus be appropriate, and also, green bonds are a reliable source of long-term income for investors. Green bonds can essentially be studied by focussing on the general qualities of the bonds, and the bond market's relationship with the stock market has long been a source of study interest among researchers. In this regard, The bond's volatility spill-over mechanism is passed on to other traditional assets, which play a significant role in portfolio composition and risk management Ielasi et al., 2018). Because green bonds are a type of bond, understanding how they are interconnected to other assets can help international investors to better structure their relevant portfolios (Hung, 2021;Lobato et al., 2021;C.-W. Su et al., 2020).
The World Bank and the Swedish bank (SEB) issued the first GB in the year 2008, which has since then experienced an expansion of its international market from 11$in the year 2013 and 36$billion in the year 2014, to $167 billion in the year 2018 (Maltais & Nykvist, 2020). Green bond markets have grown in popularity in the recent years across the globe in order to provide an opportunity for sustainable and long-term infrastructure financing. According to Flammer (2020), this quick development is referred to as the global financial market's 'green bond boom.' According to multilateral development banks (European Investment Bank and World Bank), the issuance of GB has punctually been extended to all investors, e.g., institutional investors, commercial banks, municipalities, and a few of the largest organisations of the world . There has been an augmented and rapid round investments of about more than ten folds in the last five years in these new and expeditiously growing fixed-income instruments, and these are projected to reach an astonishing one trillion US dollars because of the increase in the demand for green bonds .
As per the climate bonds initiative database, the GB issuance has a stunning yearly growth of more than 113 percent, as it increased from one to more than two thousand from the years pertaining to 2007 to 2017. In the year 2017, China, France, and the United States accounted for 56 percent of the total issuance of global green bonds. According to this database, developing nations, on the other hand, have been left out of this rising source of climate capital that they require to carry out their climate change mitigation and adaptation plans . Therefore, only a limited number of governments and investors from these economies have issued GBs thus far. Nonetheless, an increasing number of them are gradually focussing on this market, which is influenced by various factors (Banga, 2019;Nawaz et al., 2021). East Asia & Pacific has the largest GB market among other geographical regions, and South Asia has had the second-largest green bond market expansion from the year 2012 to 2018, at 7.7 billion US dollars, as cited in Anh Tu et al. (2020). To validate this, Table 1 shows the issuance of green bonds in various regions of the world, over a time period stretching from 2012 to 2018.
Despite the fast expansion of the GB market, it has had a significant impact on the debt financing expenditures and the financial conditions (Deschryver & De Mariz, 2020;Flammer, 2020;Kaiser & Welters, 2019;Karim et al., 2022;Lobato et al., 2021). The GB market expansion in various countries is a contentious topic among the top academics. Several researchers such as (Partridge & Medda, 2020;Shair et al., 2021;Voica et al., 2015), have suggested that investors and government bodies are the main players of the GB market, and that they determine the growth level of the GB market. whereas some researchers have also suggested that there is a plethora of factors that tend to have an impact on the development of the GB market (Broadstock & Cheng, 2019;Ehlers & Packer, 2017;Flammer, 2020;Reboredo & Ugolini, 2020;Sun et al., 2021;Zerbib, 2019). (Broadstock & Cheng, 2019;Ehlers & Packer, 2017;Flammer, 2020;Reboredo & Ugolini, 2020;Sun et al., 2021;Zerbib, 2019), for instance, describe the impact of capital markets and macroeconomic determinants on the GB market. Furthermore, some studies, such as, (Bhattacharya et al., 2015;Della Croce & Yermo, 2013), claim that investment facilities can successfully promote the growth of the GB market. As a result, it has been obvious that the GB market's growth depends on a number of interconnected elements, making its development multi-dimensional in nature (Anh Tu et al., 2020;Chien et al., 2022).
Despite the fast expansion of the GB market, it has had a significant impact on debt financing expenditures and financial condition (Curley, 2014;Deschryver & De Mariz, 2020;Flammer, 2020;Tang & Zhang, 2020). GB market expansion in countries is a contentious topic among academics. Several researchers, like (Partridge & Medda, 2020;Shair et al., 2021;Voica et al., 2015), suggest that investors and government bodies are the main players of the GB market and that they determine the growth level of the GB market, whereas some researchers suggest that various factors have an impact on the development of the GB market (Broadstock & Cheng, 2019;Ehlers & Packer, 2017;Flammer, 2020;Reboredo & Ugolini, 2020;Sun et al., 2021;Zerbib, 2019). (Broadstock & Cheng, 2019;Ehlers & Packer, 2017;Flammer, 2020;Reboredo & Ugolini, 2020;Sun et al., 2021;Zerbib, 2019) for example, describe the impact of capital markets and macroeconomic determinants on the GB market. Furthermore, some studies, e.g., (Bhattacharya et al., 2015;Della Croce & Yermo, 2013), claim that investment facilities can promote the growth of the GB market. As a result, it is obvious that the GB market's growth depends on a number of interconnected elements, making its development multi-dimensional (Anh Tu et al., 2020;Chien et al., 2022). The significance of the expansion of the GB market and the presence of many influencing variables on this expansion necessitates a thorough examination of prioritising the influencing elements (Anh Tu et al., 2020). However, the relationship of oil price and green bond dynamics receives little attention in the studies. The awareness of their interactions is necessary for the investors since it can help them reap the benefits of a diverse portfolio and illustrate how oil market volatility affects green bond pricing (Lee et al., 2021). Inflationary pressures are created in global markets as oil prices rise. Higher price inflation has a major impact on the cash flow discount rate, resulting in lower stock values (Kocaarslan & Soytas, 2019). There is also a scarcity of empirical evidence connecting green bonds to the commodity market (Kanamura, 2020;Reboredo & Ugolini, 2020). However, whereas previous research has focussed on the connection between GB and energy commodities, there is little knowledge about the dynamic causality of GB to diverse types of commodities. The study of Dutta et al. (2021) and Brooks and Prokopczuk (2013) justify the use of different commodities, as they claim there is a lot of variation in the behaviour of individual commodities Zhuang et al., 2021).
The main goal of our study is to estimate the association between GB and specific commodities. Since the focus of previous empirical research has been on examining the relationship between GB and the general index of energy commodity, e.g., (Reboredo, 2018;Reboredo & Ugolini, 2020), we add to the existing body of literature by focussing on three groups of commodity: green energy stocks, energy price (oil price) and gold price. Our empirical research, as expected, reveals a significant variance in the behaviour of the GB market corresponding to these commodities, explaining why these commodities have different features (Chong & Miffre, 2009;Erb & Harvey, 2006). Second, because economic variables have non-linear patterns due to their underlying scattered features, we believe that green bonds are non-linearly related to gold prices, energy prices, and green energy stocks. Hence, we contribute to the empirical literature by presenting a non-linear econometric model as the optimum framework to explain the relationships in the study, as existing research that uses a linear approach may result in erroneous conclusions. In this vein, this study investigates this link using a comprehensive and appropriate econometric methodology, i.e., QARDL (Quantile Autoregressive Distributed Lag Model). This technique aims to simultaneously find long-run and short-run relationships in green energy bonds while accounting for any potential asymmetric and nonlinear associations in green energy stocks, oil price, and gold price . Additionally, this econometric methodology enables an in-depth exploration of variance in the quantile of GB by establishing linkage with gold prices, energy prices, and green energy stocks.
The remainder of the study is ordered as follows: Section 2 gives a review of the existing literature. The data and econometric methodology is provided in Section 3. Empirical findings and their discussion are given in section 4. Our study concludes in Section 5.

Literature review
GBs and various relevant energy and financial asset categories are the subjects of the research's new and fast-increasing strand. Although there are several research studies on the interaction between GBs and assets and energy asset markets, empirical investigations evaluating the non-linear associations between GBs and commodities and energy markets are still limited as per the available literature Mohsin et al., 2021). For instance, Reboredo (2018) used bivariate copula models to investigate the interrelated movement of the international GB market with a collection of conventional energy and financial markets, and the author argued that GB was closely associated with corporate bonds of treasury and grade investment, but only marginally to energy and stock commodity market (Reboredo, 2018). Using the technique of wavelet coherence and rolling window wavelet correlation, Nguyen et al. (2021) studied the connections between GBs and some other asset categories across time and across investment horizons, including common and clean energy equities, conventional bonds, and commodities . Across nearly all time frames and frequencies, they found strong comovement between GB and regular bonds and, to a lesser degree, between GBs and substitute stocks of energy. However, green bonds were observed to have a weak correlation with common stocks and commodities and confirmed that green bonds are safe havens . Similarly, by employing the Diebold Yilmaz technique and the connectedness model of Barun ık and K rehl ık (2018), and Le et al. (2021) estimated the frequency and time volatility connectedness across cryptocurrencies, fintech stocks, GBs, and other conventional assets, including gold, USA dollar, general stocks, VIX volatility index and crude oil . The results indicated that volatility is predominantly transmitted across various markets in the short run, and GBs tend to be net recipients of shocks in volatility (Le et al., 2021).
In the framework of the fourth industrial revolution, (Huynh, 2020) investigated tail dependency and volatility interconnectivity along with a range of conventional and new asset categories, such as stocks of robotics firms and artificial intelligence, overall stocks, GBs, crude oil, gold, Bitcoin, and the VIX index. Copula functions and Barun ık and K rehl ık (2018) connectedness technique was used for this purpose. The research showed that portfolios including these asset types had a high degree of heavy tail reliance, meaning a higher likelihood of great joint losses in times of economic and financial chaos. In addition, short-run volatility transmission was larger than long-run volatility transmission, and bitcoin and gold were essential hedging assets . According to Le et al. (2021), bitcoin and gold substantially impacted green bonds and NASDAQ AI (Le et al., 2021). While Liu et al. (2021) proposed a positive and significant normal and tail dependency between clean energy and GB markets, they also proposed a positive dynamic normal and tail dependency between GBs and other conventional financial markets (Liu et al., 2021). Dutta et al. (2021) applied GARCH Based Quantile Regression on daily data, and their findings showed that risk was considerably transmitted from silver, gold, and crude oil markets to multiple green stock indices in India. During the bearish stock market period, the influence of commodities market influence transmission was stronger than during bullish stock market periods, implying that green stock indices are more likely to get instability from precious metal and energy markets (Dutta et al., 2021). Azhgaliyeva et al. (2021) made an examination of the oil price shocks affect on the issuance of green bonds in private using the multilevel longitudinal random intercept and random coefficient models. Their empirical analysis found that oil supply shocks had positive effects on green bond issuance in contrast to the general market. It was also observed that the issue of sovereign GBs in the public market tended to encourage the issuing of GBs in the private market (Azhgaliyeva et al., 2021).
Applying the spill-over frameworks proposed by Diebold and Yılmaz (2014) and Barun ık and K rehl ık (2018),  explored the asymmetrical connectedness between GBs and commodities in the temporal and frequency domains. The findings showed asymmetric spill-overs between assets over time and across frequency cycles. Although spill-over was higher for commodities in the same class, silver and gold had the strongest links to green bonds across all time periods. On the other hand, crude oil had a strong long-term correlation with green bonds . In another study by them using the Cross-Quantilogram approach, they tried to document asymmetric association between GBs and metals, agriculture, and energy. They discovered the greatest hedging advantage of GBs against variations of natural gas, various agricultural products, and industrial metals, as indicated by the non-correlation or negative association with the commodities in moments of higher volatility . (Kanamura, 2020) investigated the greenness of green bonds and their performance with regard to energy, concluding that energy and environmental values were positively related. As a result, it was suggested that greenness was factored into the Bloomberg Barclays MSCI and S and P green bond indexes (Kanamura, 2020).
Applying structural VAR models (Reboredo & Ugolini, 2020) evidenced that GBs had a weak relationship with energy possessions and equities, implying diversification benefits. Moreover, it was found that GBs were little affected by equity and energy markets return spill-overs (Reboredo & Ugolini, 2020). Under exceptional and market situations applying Quantile VAR, Saeed et al. (2020) examined return spill-overs between GBs, renewable energy equities, and different unclean energy assets, e.g., oil and gas businesses and crude oil stocks. Spill-overs were found strong, particularly in the upper and lower quantiles (Saeed et al., 2020). Bachelet et al. (2019) found that GBs had higher liquidity than GBs issued by institutional issuers, whereas GB produced by the private issuers had higher liquidity and variability than institutional bonds. Financial market unpredictability, oil prices, uncertainty in economic policies, and negative and positive news stories all influence the relationship between the two markets (Bachelet et al., 2019).
These studies are significant since they look into the properties of green bonds, including their performance and the relationship between GBs and other markets. Studies found it crucial to demonstrate the interconnectedness between the GBs market and other markets at various frequency intervals, while some studies preferred frequency and time-based techniques that can reveal the directional connectedness of diverse frequency horizons and time. Tail dependency and connectedness appear to be more of focus in some studies. It is revealed in the existing literature that prior studies had not mutually estimated the long-run and short-run causality between the oil prices, gold prices, green energy stocks, and green bonds. To fill in this research gap, we applied the QARDL methodology. As mentioned in the introduction part, this methodology can also solve some of the challenges that other non-linear approaches experience.

Data and methodology
The effect of gold prices, oil prices, and green energy stocks on the green bonds market has been examined in this study from 01 Jan 2010 to 30 June 2021 for Turkey. For this purpose, we use green bond markets (GB), gold Price (GP), oil price (EP), and green energy stocks (CLEAN). THE S&P GB index (SPGB) is considered the principal variable in this study sourced from Bloomberg. Other variables included in the study are the WilderHill clean energy index (WCEI), gold price, and oil price, all sourced from Bloomberg. The WilderHill clean energy index consists of the USA's publically traded company stocks occupied in developing clean energy and energy conservation business. The S&P Green Bond Index comprises 5 series: S&P GB Index, the S&P 500 Composite Index, S&P Clean Energy Index, the S&P GSCI Commodity Index, and Barclays Bloomberg Global Treasury Index (BCONV). The GBs market is represented by S&P GB Index (SPGRNB). The range of our daily data is from 01/01/2010 to 30/06/2021. The sample period start date is determined based on the S&P GB index data.
Following the line of the study of Reboredo and Ugolini (2020), Dutta et al. (2021), Kanamura (2020), , and Azhgaliyeva et al. (2021), the econometric model of the study is specified as follows: Where GB is the green bond market, GP is gold price, EP is the oil price, and CLEAN is the green energy stocks measured as clean energy stocks and e t is the error term.

The QARDL model
To estimate the non-linear relation between the green bonds market, oil prices, gold prices, and green energy stocks, the latest QARDL methodology introduced by Cho et al. (2015) has been applied in this study. Specifically, the QARDL methodology allows examining the long-run quantile equilibrium effect of the gold price, oil price, and green energy stocks on green bond markets in the world. Additionally, this econometric methodology enables an in-depth exploration of variance in the quantile of GB by establishing linkage with gold prices, energy prices, and green energy stocks. Wald test is applied to further check the measures of parameter dependability in each quantile for the long-run and short-run equilibrium both. At first, the conventional linear ARDL model is described as follows: Where e t is the error term which is represented by the lowest field generated by {GB t , GP t , EP t , CLEAN t , G t-1 , where p, q, r, and s show the lag order selected through SIC (Schwarz Information Criterion), in addition, GB t , GP t , EP t , CLEAN t , refer to the natural log of green bonds market, gold price, oil price, and green energy stocks respectively, the following framework of the QARDL approach is suggested by the rewriting of eq (i) to a quantile context: where e (s) ¼ GB t -Q GBt ( s etÀ1 Þ and 0 <s < 1 is the quantile (Troster, 2018). To execute data analysis, the successive pair of quantiles s are used that belong to {0.05, 0.10, 0.20, 0.30 … 0.90 and 0.95}. Moreover, the comprehensive QARDL model is given in eq (ii).
Furthermore, the preceding eq (iii) can be updated to get the following error correction model for the QARDL framework measurement: The D technique is utilised to estimate the combined short-run effect of the previous GB market on the current GB market, which is evaluated by b Ã ¼ P pÀ1 i¼1 b 1 : A similar process is used to assess the residual increasing short-run influence of prior and current on the current level of the gold price, oil price, and green energy stocks on the green bonds market. last, in eq (iii), the coefficient of the speed of adjustment must be significantly negative (Cho et al., 2015).
Finally, the Wald test is applied (with specific null and alternative hypotheses for short-run and long-run parameters), which follows the Chi-Squared distribution asymptomatically for the statistical investigation of the short run and the long-run asymmetric and non-linear effects of green energy stock, gold price, oil price on GB markets in the short run and long run both. Small numbers of motivating facts emerge after the prior equations (Cho et al., 2015). The long-run and short-run values may be quantile-based at first, implying that the QARDL method coefficients may differ on every quantile, indicating that these coefficients could be modified at any time. The Wald test can also be used to check the limits of the short and longterm coefficients within and between quantiles (Cho et al., 2015). Wald Test is used to examine the null and alternative hypotheses for the parameters of short-run and long-run such as ; Ã , x Ã , b Ã and q Ã given below: Where F and f are h Ã ps and h Ã l, referred to as pre-defined matrices. S and s are h Ã s and h Ã l, the pre-specified matrices with h being the restriction number. i denotes EP, GP, and CLEAN, respectively. Wald test is specifically applied to investigate the nonlinearities on the adjustment speed parameter and integrating parameter of the long run (He et al., 2021). Four tests are run for every group and every parameter.

Quantile granger causality test
The literature has indeed investigated whether a variable is a predecessor to some other variable by using Granger's (1969) causality analysis approach. The Granger causality test, in general, implies that the present value of the explained variable is affected by its own value and the lagged values of the explanatory variables. Many novel causality tests were created after (Granger, 1969) using diverse methodologies. We use the quantile granger causality approach that (Troster, 2018) introduced recently to investigate the quantile causal of GB markets with the gold price, energy price, and green energy stocks in the current study. Granger (1969) states that a variable (X i ) does not granger cause another variable (Y i ) if the prior Xi does not help in the estimation of Yi, resulting in the previous Yi. an explained vector is supposed (N i¼ N i y , N i x ) ' 2 R e , s ¼ o þ q, where N i x is the earlier indication group of X i N ix : ¼ (Xi-1, … ., Xi-q)' 2 R q. Furthermore, the H0 of granger non causality from one variable X i to other variable Y i is described in the current study as follows: Where provisional distribution purpose of Y i is F y (.j N i Y , N i X ) provided that (N i Y , N i X ) . The DT check is applied by the classification of the QAR method m (Á) for whole p 2 & C [0,1], which is based on the H0 of no granger causality relationship as below.
We estimate the coefficients [o(p) ¼ (k 1 (p) k 2 (p)] and l t through maximum likelihood in equal quantile points, and À X À1 Y (.) is the reverse of a usual fundamental distribution function. Our study evaluates the QAR approach in eq (vi) to confirm causality between the components with lagged to alternative factors. Lastly, the QAR(1) equation with the help of eq (vi) is given below:

Results and discussion
Now we proceed to the interpretation and discussion of the empirical analysis. First, it is necessary to provide descriptive statistics and check the series' stationarity features before proceeding to QARDL analysis. Table 2 provides the results of the descriptive statistics of our selected variables, i.e., GB, EP, GP, and CLEAN. It is indicated from the results that the average gold price (GP) is the highest among all the variables in Turkey. At the same time, oil price (EP) has the highest variability about the mean among all the variables. 'Jarque-Bera normality test' developed by Jarque and Bera (1980), is performed to test data abnormality. The null hypothesis of this test states the normality of data, and the alternative hypothesis states the reverse. The H0 of normal distribution of the Jarque-Bera test is rejected for every series understudy at a 1% level of significance. Thus, the application of quantile estimation techniques is considered necessary and suitable for our study following Godil et al. (2021), Godil et al. (2020), Chang et al. (2020), and Suki et al. (2020).
Since the series are not normally distributed, the unit root in quantile test techniques is followed instead of conventional unit root test techniques (such as Phillips & Perron and Augmented Dickey-Fuller test for unit root, etc.) to get robust inference and unbiased results. The unit root test results of our variables of the study at quantiles are reported in Table 3. It is evidenced from the results that all the variables are nonstationary at the level and become stationary by taking the first difference. So a unique integration order is found between the variables in this analysis.
The estimation findings of the QARDL model are given in Table 4. The quantiles ranging from 0.05-0.30 are classified as the bearish market situation, 0.40 À 0.60 are considered the normal market situation, and from 0.70 À 0.95 are considered the bullish market situation. The findings reveal that the coefficient for adjustment speed (q Ã ) is significant and negative at every quantile, demonstrating that the green bond markets, gold price, oil price, and green energy markets have reverted to long-run equilibrium. More specifically, the adjustment speed has the highest value in the last quantile. The symbol b's in Table 3 shows the long-run relationships of independent variables (GP, EP, CLEAN) with the dependent variable (GB).
The coefficient of GP is negative, which shows that a downward trended longterm relation of GP and GB exists at all quantiles, while the level of significance of GP is progressively increasing as we move towards higher quantiles. Although in the upper quantiles, the long-run relationship of EP with GB is statistically insignificant, the results indicate the significant negative impact of EP on GB up to a mediumrange of quantiles, i.e., (0.05-0.50). In another way, increasing oil prices will decrease the investment in GB in the long run during bearish and normal market conditions.
In contrast, the empirical findings reveal that the long-run coefficient of green energy stock (CLEAN) positively affects GB. However, the magnitude of impact and level of significance of green energy stocks are different at different quantiles. Over the range of quantiles 0.05-0.20 indicating bearish market conditions, the impact of green energy stock is insignificant, whereas in bullish market conditions, i.e., at the quantiles of 0.30-0.95, its impact is significant and positive.
In the short-run dynamics scenario, the findings reveal that earlier values of GB have a positive and significant effect on the present value of GB at all quantiles. The contemporary variations in GP are found to impact GB positively at the lower range of quantiles (0.05-0.20) only. Similarly, the results from the short-run scenario indicate that present GB variations are negatively and significantly affected by present changes in EP over the quantile range (0.05-0.60). Contrarily, the past and current changes of green energy stock positively and significantly impact GB's past and current changes at all quantiles except (0.05-0.10). Thus, the overall QARDL model concludes that GP and EP have a significantly positive impact from lower to medium quantiles both in the long and short run, while green energy stock is found to have a significant and positive impact from medium to upper quantiles both in the short run and long run.
To observe the parameter constancy (linearity) of the estimated parameters, the Wald test is applied, and its results are given in Table 5.
As per the estimation, the test's null hypothesis (H0) of the symmetric and linear relationship between the variables is not accepted at a 1% significance level. Thus it can be inferred that the parameters are asymmetric and non-linear in various quantiles in the long run globally. In the same way, the null hypothesis which considers the linearity of short term increasing impact of the previous values of GB over the estimated quantiles. In addition, the test results indicate that green energy stock has a non-linear asymmetric effect on GB as the H0 of parameter linearity is rejected overall quantiles. Contrarily, GP and EP have a symmetric and linear impact on GB in the short run.  The results of the Granger causality test are provided in Table 6. A bidirectional causal association is found among all the considered variables overall quantiles, i.e. (0.05-0.95). The findings indicate that contemporary and earlier realisations of GP, EP, and CLEAN are better predictors of GB and vice versa.

Discussion
The findings of negative GP showing a downward trended long-term relation of GP and GB signifies that the green bond market faces more difficulty with the rise in gold prices. This is a fascinating finding, showing that gold's safe-haven attributes give investors diversification opportunities during all market conditions, particularly more significantly during bullish market situations. The finding seems intuitively reasonable because the goals of investing in gold and green bonds are so dissimilar. Gold investors are commonly referred to as 'gold bugs', who invest in gold as a safe haven. On the other hand, Green bond investors are drawn to the sector because it offers a combination of sustainability and fixed income. This finding adds this work to the domain of earlier research (Kocaarslan & Soytas, 2019) but contrasts with (Dutta et al., 2021), and therefore, it makes a significant contribution to the existing literature.
Considering the relationship between EP and GB, findings seems credible because high oil prices stifle investments in green bonds in the long run due to the increasing opportunity cost of energy market investment. On one hand, rising oil prices influence economic activities in a significantly negative way because of their negative impact on household income and the cost of production of the firms. Increases in production costs diminish profitability, which has a negative impact on future and present cash flows. A spike in oil prices, on the other hand, causes price inflation in worldwide markets. Augmented inflation pressure has a major impact on the cash flow discount rate, resulting in lower stock values (Kocaarslan & Soytas, 2019). This throws off the balance of the economy and, as a result, makes the investment climate worse. When looking at the economic process, in the long run, it is clear that a rise in oil prices negatively impacts green bond values, contrary to common assumptions. The finding of our study is in line with (Kanamura, 2020;Saeed et al., 2020;Kocaarslan & Soytas, 2019) but in contrast with (Dutta et al., 2021;Azhgaliyeva et al., 2021;Lee et al., 2021). Considering the relationship between CLEAN and GB, the findings are consistent with the findings of Liu et al. (2021) but in contrast to Nguyen et al. (2021) and Reboredo (2018), who found that green bond markets are weakly linked with clean energy markets. Thus it indicates that the green bond market and green energy stocks experience booms and bursts together, implying that an increase in green energy stock prices attract an inflow of capital and helps in the expansion of the scale of investment, which further leads to a rise in the more investment in green bonds (Liu et al., 2021). Lastly, the outcome of green energy stock and GB contrasts with the finding of Dutta et al. (2021), who observed the opposite phenomenon while studying green bonds and green stock indices relationship for India.

Conclusion and policy recommendations
Because of its significant role in funding environment-friendly projects by limiting the adverse consequences of climate change, the GB market has achieved significant development in terms of its benefits for stakeholders as well as for governments over the past decade. However, research about the interaction of this market with other environmental and financial aspects is still scarce. To fill in this gap, this study investigates the non-linear linkages between GB and environmental and financial variables such as oil prices, gold prices, and the green (clean) energy stocks over the period from 01-01-2010 to 30-06-2021. To achieve this purpose, Quantile Autoregressive Distributed Lagged (QARDL) approach developed by Cho et al. (2015) is applied in this study. The reason for selecting this analysis is its property to check the effect of a range of quantiles of oil price, gold price, and green energy stock green bond markets, thus providing a more comprehensive explanation of the dependence of green bond markets and oil price, gold price and green energy stocks harmonised to conventional techniques such as quantile regression or OLS. We also examined causality in quantiles, as described by Troster (2018), to see a causal relationship between gold, oil, green energy stock, green bond markets, and vice versa.
The QARDL results reveal that the error correction value is significant for all quantiles, with the predicted negative sign suggesting that there is a considerable reversion towards the long-run relationship between the associated variables and the GB market. Specifically, the findings suggested that gold prices decrease green bonds in the long run on every quantile. But, an increase in oil price decrease green bonds at lower to middle quantiles. It suggests that the increase in oil and gold prices causes a decline in green bond investments in the long run. As for green energy stocks, it is implied from the results that an increase in green energy stock brings a positive impact on green bond investment in the long run. Furthermore, the results of the short-term dynamic established an asymmetric impact of oil price, gold price, and green energy stocks on GBs in the short run. In addition, the outcomes of the causal relationship given by the granger causality test in quantiles reveal a bidirectional causality link between oil price, gold price, and green energy stocks on green bonds in Turkey.
The GB market has made significant progress, but there are still prospects for development and improvement. Our findings have several significant implications for shareholders and policymakers in this context. To achieve additional market expansion, particularly in the green energy sector, numerous stakeholders must work together. By implementing climate-related green bond standards and providing supportive policies to foster the clean energy industry's development, policymakers can help to increase the availability of GBs. To promote GBs, public financial institutions can demonstrate issuance and capacity growth. Institutional investors can contribute by matching the investment goals with sustainability concerns over the long run. Other parties, such as financial institutions, retail investors, and rating agencies, can help develop the GB market and accelerate the global energy transformation.
The finding of a positive relationship between GB and green energy stocks suggests that there is no hedging between long positions in GBs clean energy stocks because both assets have movement in the same direction at different market conditions. It is critical to consider systemic risks when developing the best portfolio investing plan, as these risks might reduce diversification returns. When constructing their investment portfolio strategies, investors should be aware of the non-linear causal positive relationship between GBs and green energy assets. Because asset correlation is the most critical aspect in developing a risk-diversifying portfolio, an increase in asset association can result in a considerable drop in the original portfolio's ability to spread risks. A considerable increase in the correlation between the GB and the green energy stock market, especially after a crisis, would greatly raise the total portfolio risk, necessitating a rapid portfolio solution adjustments of GBs and equivalent assets.
Green bonds are negatively linked to world gold prices, indicating that gold is safe for green bonds in harsh market situations. Gold prices are viewed as a more effective hedge for green bonds. Hedging indicates that while the price of an item rises, it lowers the hedge asset price. In general, a stock's price rises following a severe negative shock. The existence of a hedge, on the other hand, works against haven in the long run. Investors must comprehend and thoroughly evaluate the linkage dynamics between different financial stocks for optimum advantages from increased portfolio diversification obtained through investment selections. To improve their hedging performance, investors must be able to accurately foresee varying trends in these critical commodities. For better protection and hedging approaches and well-informed asset allocation considerations, they must be fully aware of the shifting dynamics in the links between the commodities and equities returns. Finally, oil price fluctuations signal a shift in macroeconomic conditions, necessitating government intervention to encourage more green investment at a time when oil prices are low. Following a drop in oil prices, while the green investment does provide favourable incentives, policymakers should rethink and reinterpret their strategy to promote the green bond investment. Government authorities should increase their subsidies for green bonds investment and launch huge public awareness campaigns regarding its beneficial impacts on environmental quality.

Limitations
Similar to other research studies, the current study also possesses certain limitations, which provide an avenue of exploration for future researchers. Firstly, the availability of the data is the prime limitation. Though for the application of the statistical technique, daily data was utilised. Nevertheless, the higher the data, the higher is the predictive ability. Secondly, the current study analyzes the data of Turkey only, whereas exploration of other countries could also expand the literature. Thirdly, the present study is a time series, and more contributions to the literature can be made through the studies following panel methodologies. Lastly, the application of QARDL only establishes the linkage with the quantiles of the dependent variable, whereas applying techniques that link the quantiles of the dependent variable with the quantiles of independent variables can lead to more insightful findings.

Disclosure statement
No potential conflict of interest was reported by the authors.

Funding
Achievements of scientific research and innovation team of 'digital economy serving port economy research' of Zhejiang Wanli University (Grant No. 202036