Term structure of interest rate and macro economy: an empirical study on selected emerging countries sovereign bond Open Access

The term structure of interest (also known as yield curve) of sovereign bonds stands as a key macroeconomic indicator. Prior to the COVID-19 pandemic, the yield curve in most countries was in a normal curve. However, the spread between long-term and short-term government borrowing rates has narrowed, not only in developed countries but also in emerging countries. To tackle soaring inflation, most central banks raise their interest rates, causing a high cost of funds. The inverted yield curve, historically, has been used to predict the onset of recession in an economy. It's widely recognized that the term structure of sovereign bond is used as a pricing benchmark for bank loans and many corporate debt market instruments (Elton et al., 2014). Furthermore, its role in asset pricing, portfolio management, capital valuation, and monetary policy can't be understated (Diebold and Rudebusch, 2013). During economic expansions (in a new normal period of COVID-19), the yield curve steepens as governments use low-interest rates to encourage spending and boost economic activity. However, more recently, the two-year yield rose above the 10-year yield, causing investors to worry about the economic slowdown. Therefore, an adequate understanding of term structure behavior is critical for a well-functioning macroeconomy.

Amid these global shifts, what remains underexplored is the term structure's behavior and persistence, particularly in emerging economies. Here lies the novelty of this study: embarking on an empirical exploration of the persistence of slope and curvature in selected emerging countries. Taking cues from prior macro-finance studies (Gadanecz et al., 2018; Byrne et al., 2019; Cepni et al., 2021), the approach uniquely sidesteps the “No Arbitrage” assumption, which, although theoretically sound, conflicts with the preferred habitat theorem (Vayanos and Vila, 2021). In addition, this study uses observable features of term structure, slope, and curvature instead of estimated latent variables. Estimating latent factors requires a complete dataset of yield across tenors, which might not be the case for emerging markets. Moreover, as noted by Cepni et al. (2021), the extracted latent factors might not be smooth, which hampers its use for subsequent analysis. Instead of delving into latent variables, this study focuses on observable features, thereby offering a more practical and straightforward interpretation, addressing a significant gap in the yield curve modeling literature.

This study focuses on observable proxies of the term structure, emphasizing the slope and curvature derived from government securities. Generally, the slope is obtained by comparing yields of long-term and short-term papers, while the curvature captures the non-linearity between these rates over different periods. These measures, informed by Gürkaynak and Wright (2012), are pivotal as they help avoid potential distortions inherent in extremely long tenors. This study also incorporates essential macroeconomic variables, such as expected short-term interest rates, foreign exchange movements, and prevailing fiscal conditions.

The main novelty of this study is twofold. First, this study model term structure features (level, slope and curvature) as endogenous to macroeconomic variables which is more appropriate (see the literature section as background). Second, the study uses a recent innovative econometric method: Mean Group Instrumental Variable (MGIV) to address this endogeneity issue. Mean Group instrumental variable (MGIV) developed by Norkutė et al. (2021) and Cui et al. (2020), brought fresh and promising treatment to the endogeneity issue. Specifically, MGIV has a better estimation fit for panel data with a large time unit-T (Long panel data). Better estimation fit is obtained due to the improvement of estimate consistency and efficiency by exploiting the common factor and unobserved heterogeneity inherent in this type of data structure (Chudik and Pesaran, 2015; Juodis and Sarafidis, 2018). The method extracts common factors as a set of instruments, uses them for consistent estimates of endogenous variables, and handles heterogeneity in cross-section dependency to gain efficiency.

The empirical framework is applied to an expansive monthly panel dataset spanning 9 emerging countries from January 2010 to October 2021 (1,278 observations). This study finds a highly significant persistence of slope and curvature. The level of short-term yield is positively associated with flattening the term structure, indicating a (future) yield reversal mechanism. Inflation and exchange rate change have a significant positive correlation with the steepening of term structure. Moreover, this study unearth intriguing associations between short-term yield levels, inflation, exchange rate changes, and term structure movements, providing fresh insights that can reshape the understanding of post-pandemic economic dynamics in emerging markets.

The term structure of interest rates, encompassing features like slope and curvature, has been a cornerstone of financial research for decades. Early theoretical development covers, among other expectation hypotheses, preferred habitat theorem and liquidity preference (Malkiel, 2015). Diebold and Rudebusch (2013) emphasize the importance of slope and curvature in assessing the yield curve. Yet, while such foundational works provide a solid background, there remain gaps empirically.

The slope measures the first derivative of yield against tenor, i.e. the distance of short-term yield versus long-term yield. The curvature is the second derivative; it measures how the slope changes, i.e. whether the yield curve is flattening or sharpening as it goes from the short to the long end. A more recent approach is macro-finance, which links the yield curve micro-underpinning with a standard macro model (Gürkaynak and Wright, 2012; Cochrane, 2017). Despite having a long and extensive investigation, term structure behavior remains elusive (Crump et al., 2018).

The expectation hypothesis posits that the term structure of interest is the average of expected short-term interest rates. Therefore, assuming no arbitrage, a permanent shift in short-term interest rate will alter the yield in various term structure tenors, resulting in changes in slope and curvature. Short-term interest rates can negatively affect the slope via the mean reversal mechanism (the current rate is too high from the perceived normal). The existence of this process has been modeled by Ross (2015) and Martin and Ross (2019) into the recovery theorem have extended this view, but empirical findings remain inconsistent. This gap, notably the transmission of short-term rates on the yield curve, has been a contentious topic.

The preferred habitat theorem asserts that each tenor has its clientele investors. Therefore, a shock to a tenor does not necessarily transmit to other tenors, i.e. changing the slope or curvature of the yield curve (Vayanos and Vila, 2021). While some scholars (Adrian et al., 2013; Abrahams et al., 2016) found negative correlations, others (Coroneo et al., 2016) and Gadanecz et al. (2018) discovered positive ones, as an evidence of increased term premium. Tillmann (2020) found the transmission conditional on monetary policy uncertainty, while Cepni et al. (2021) found no empirical support.

Liquidity preference theory (Keynes, 1936) asserts that investors prefer to place their money in short-term instruments for ease of transaction and precautionary reasons. Therefore, they must be compensated to put their money into long-term ones. There are other Keynesian channels, namely investors' psychology and uncertainty, from which short-term interest rates affect the slope and curvature; in this regard, liquidity preference is mixed up with the expectation hypothesis (Akram, 2021). Ornelas and de Almeida Silva (2015), in a study of Brazil's sovereign bond, managed to disentangle the significant liquidity preference effect from the expectation hypothesis. Akram and Das (2019) found empirical support for liquidity preference in the India Government Bond market. Although that research offers some insights, comprehensive empirical evidence across varied economies remains scant.

Furthermore, while canonical theories assert the persistence of slope and curvature (Diebold and Rudebusch, 2013). The persistency of slope and curvature is attributed to serial correlation and non-stationary characteristics (Krippner, 2015). Empirical support for this conjecture has been documented by Härdle and Majer (2016), Levant and Ma (2017), and Cepni et al. (2021). Empirical validation, especially for emerging economies, is limited, revealing another gap in existing knowledge.

The term structure's form (slope and curvature) contains information on macroeconomic risks (Christensen, 2018). This hypothesis is a foundation for the macro-finance term structure model-MTSM (Rudebusch and Wu, 2008; Gürkaryanak and Wright, 2012). Nevertheless, this hypothesis has been challenged by studies of Joslin et al. (2013, 2014), Coroneo et al. (2016). Recently Bauer and Rudebusch (2020) empirically showed the existence of macro risk that is unspanned by the yield curve. However, those studies highlight that much remains undiscovered about how these macroeconomic risks are reflected in yield curves, especially in emerging markets. Combining both views, this study concludes that term structure is at least partially endogenous to macroeconomic variables. Another channel of endogeneity of term structure to macro-economic risks could be attributed to cross-country co-movement due to policy effect spillover and risk compensation (Jotikasthira et al., 2015; Sowmya et al., 2016).

Breach et al. (2020), in a study of US sovereign bonds, found that for data before 2008, inflation changed short-term interest rate expectations and positively correlated with slope as a proxy of increased term premium. Currency depreciation can increase the perception of sovereign risk and cause investors to demand higher yields for holding local currency bonds (Gadanecz et al., 2018; Cuchiero et al., 2016). Afonso and Martins (2012), in a study of the US and German sovereign bonds, found that shock in fiscal conditions was initially associated with a negative shift in slope and curvature that eventually died out (hence no effect in the long run). However, there is limited understanding of their long-term impact and interrelation.

Modifying from Gadanecz et al. (2018), Bauer and Rudebusch (2020) and Cepni et al. (2021), this study proposes two regression models using a similar set of explanatory variables: lag of dependent variable, level of Yield, Interest Expectation, Foreign Exchange Changes, and Fiscal Condition. These models are given by Equations (1) and (2),

The previous section has pointed out the endogeneity nature of SLOPE, CURV, YIELD, Int_EXP, FX_C, and FIS_COND; hence, it must resort to instrumental variables for consistent estimation. Finding correct instruments can be daunting; however, recent breakthrough papers by Cui et al. (2020) and Norkutė et al. (2021) convincingly proposed that factors derived from model variables can be reliable instruments. This study adopts in this paper the operational version developed by Kripfganz and Sarafidis (2021), called the Mean Group Instrumental Variable-MGIV estimator.

Equations (1) and (2) are estimated using a sample panel dataset. The dataset based on monthly frequency comprises 9 (nine) emerging countries: Brazil, China, India, Indonesia, Malaysia, Russia, South Africa, Thailand, and Turkey from January 2010 to October 2021 (1,278 country monthly observations).

The complete list of variables, instruments, their measurement (proxies) and sign hypothesis are described in Table 1. This table presents the definition and calculation of all variables/proxies used in the study. All yield variables are of generic form. It is the average level of all similar-class sovereign bonds with the closest maturity in each tenor.

It can be noted that this study uses growth and VIXl as “external” instruments inspired by studies by Ozturk (2020) and Cepni et al. (2021). Yield-related data (level, slope, and curvature), foreign exchange, and VIX are obtained from Bloomberg; inflation and growth are obtained from CEIC. Fiscal condition (Fiscal Balance and Government Debt) data are obtained from the International Monetary Fund (IMF) Fiscal Monitor dataset. This data is of annual frequency, which then converted to monthly frequency using linear interpolation with a sum that matches the last criteria. This study uses expected short-term interest, foreign exchange changes, and fiscal conditions for the variables of interest.

In this study, the term structure of interest rates, represented by the yield curve, plays a pivotal role. Specifically, this study focuses on three crucial points or tenors on the yield curve: the 1 Year, 5 Year, and 10 Year yields. These tenors are instrumental in understanding the shape and dynamics of the curve.

Slope of the Yield Curve: The slope provides insight into the difference in yields between short-term and long-term bonds. This study calculates the slope using the formula: Slope = Yield of 10 Year Tenor −Yield of 1 Year Tenor. This calculation gives a measure of the steepness of the yield curve. A positive slope typically indicates that long-term bonds have a higher yield than short-term ones, which is the usual scenario in a growing economy.

Curvature of the Yield Curve: Beyond just the slope, the curvature provides a deeper understanding of how yields evolve over intermediate tenors. It is determined using the formula: Curvature = (Yield of 10 Year Tenor − Yield of 5 Year Tenor) − (Yield of 5 Year Tenor − Yield of 1 Year Tenor); Curvature = (Yield of 10 Year Tenor − Yield of 5 Year Tenor) − (Yield of 5 Year Tenor−Yield of 1 Year Tenor). By capturing how the middle tenor (5 Year) behaves relative to the short (1 Year) and long (10 Year) tenors, the curvature helps in discerning potential inflection points in the yield curve. Based on the guidance from Gürkaynak and Wright (2012), this study opted for the 10 Year yield as the representative long-end of the yield curve. This decision was influenced by the need to sidestep potential perverse downsloping features that might be observed from even longer tenors, a phenomenon attributed to the Jensen Inequality.

The analytical steps can be described as follows. First, we perform descriptive statistics that will give us the data profile and provide early warning of possible obstacles to subsequent analytics. Second, we conduct several preliminary analytics: panel Granger causality and unit root tests. The Granger causality test would serve as a confirmation of the endogeneity structure in the model. Since Granger Causality requires that variables be stationary, a unit root test must be performed first. There are two types of unit root test considering our long panel data. The first is standard unit root test and second is unit root test that accounts for structural breaks.

For standard type unit root test applied on panel variables (Y1, Y5, Y10, SLOPE, CURV, FX_C, GROWTH, INF, CBRATE, FIS_BAL, GOV_DEBT); Pesaran (2007, 2015a, b) proposed the Cross-Sectional Im, Pesaran and Shin (CIPS). According to Pesaran (2015a, b); CIPS is the most appropriate unit root test since long panel data is susceptible to cross section dependence (as verified by Table 4 below). While Augmented Dickey-Fuller (ADF) is applied on time series variables: VIXl. ADF is the most widely used unit root test due to its reliability (Lütkepohl, 2005; Enders, 2014). The null hypothesis of non-Stationary is used for all unit root tests with maximum lag set by following formula: max lag = floor $(T)1/3$ as proposed by Chudik and Pesaran (2015). For unit root test that accounts for possible structural breaks (unknown date assumed) we employ method proposed by Karavias and Tzavalis (2014) for panel variables and Zivot and Andrews (1992) for time series variable.

The presence of endogeneity can lead to biased and inconsistent estimators. This is where the concept of instrumental variables (IV) comes. In the context of this study, where panel data is at play, traditional IV methods might not be sufficient due to the intricate structures, potential heterogeneity, and cross-sectional dependencies. This is where the Mean Group Instrumental Variable (MGIV) method, as advanced by Norkutė et al. (2021) and Cui et al. (2020), becomes particularly useful. The MGIV method not only provides a remedy for endogeneity but also accommodates unobserved heterogeneity and exploits common factors in panel data. By catering to the idiosyncrasies inherent in long panel data structures, such as the one this study employs, the MGIV offers a robust and consistent estimation strategy.

Third, this study estimates Equations (1) and (2) with 2 Stage Instrumental Variable (2SIV) and MGIV. This study follows closely empirical strategy proposed by Kripfganz and Sarafidis (2021). It has the following objective: 2SIV is used as a complement to MGIV to assess the adequacy of factors used as instruments inferred from overidentifying restriction test (Hansen statistic p-value) and endogenous variables variance explained. The estimation requires instruments in the form of factors extracted from variables in lagged form (at order 2–3). This study employs Principal Component Analysis (PCA) to extract the factors. PCA is applied to variables used in the study: dependent variable, independent variables, and instruments.

Specification of 2SIV requires information on cross-section dependence and slope heterogeneity. The existence of cross-section dependence (cross-section factor loading) will be verified by the ex-ante cross-section dependence test proposed by Pesaran (2015a, b). The slope of regressors (⁠$βi′$⁠) can be assumed to be heterogenous and are randomly distributed around a common mean. This assumption is subject to further test cross-section slope heterogeneity (Pesaran and Yamagata, 2008; Blomquist and Westerlund, 2013), operationalized by Bersvendsen and Ditzen (2021). If the null hypothesis of the homogenous slope can be rejected, then the mean Group type is appropriate. This study needs to use the pooled version (Pesaran, 2006) as the correct specification. Norkutė et al. (2021) show that 2SIV and MGIV are consistent and asymptotically normally distributed as long as N/T is kept around a finite constant.

This study does proper interpolation to fill missing values and winsorizing at 1 and 99 percentiles in data preparation. Table 2 shows the statistical profile of variables used in the study. The statistics calculated are mean, median, standard deviation, minimum, maximum, 1st percentile, 99th percentile, and number of observations. Overall, the variables are reasonably well-behaved. The mean SLOPE of sovereign bonds is 1.535% with a maximum of 8.022% and a minimum -of 7.96%; hence, there are occasions when term structure was inverted. The average of CURV is −0.864, indicating that the shape of the term structure is typically hump shape. Its minimum is −7.96, meaning there are occasions where the shape is parabolic (or triangle with a kink at 5%).

The macroeconomy indicator shows that economic management in sampled country and period is quite good. Average inflation is around 4.9%, with minimum and maximum at −3.4 and 25.24%, respectively. Monthly Exchange rate changes are about −2.29%–0.286%. Monthly growth ranges from −1% to +1% area. The fiscal condition perhaps should be noted since the maximum Government Debt ratio reached 99.8% of GDP while the fiscal deficit reached almost 14%.

As can be seen from Table 3; unit root condition on variables is quite varied. If we assume at least one structural break occur then following variables: Y1, Y5, Y10, SLOPE, CURV, GROWTH, INF, CBRATE, GROWTH and GOV_DEBT possess stationary processes; and FX_C is the only variable that is non stationary. The structural break assumption is quite supported by the data for some variables. On the other hand if we do not assume any structural break occur than the following variables: SLOPE, CURV, FX_C, GROWTH and INF exhibit stationarity while Y1, Y5, Y10 exhibit non stationary. Therefore, it is not ideal to use Granger Causality since it requires all variables to be stationary. Nevertheless, this study still uses Granger Causality and bear in mind the result of the unit root test.

Table 4 shows that all variables exhibit cross-section dependence. Hence there might be a common factor that influences the movement of variables. Furthermore, from Table 5; we can see that null hypothesis of slope homogeneity of all regression specifications used in the paper is decisively rejected by the data. The presence of both cross-section dependence and slope heterogeneity suggest that MGIV-type estimator is more appropriate for our model.

The regression specification and instrument construction require at least a raw depiction of endogeneity. Table 6 reported panel VAR Granger Causality ^[1]; we can see that proposed order of variables endogeneity (from least to the most endogen): FX_C-GROWTH-Y1-CURV-SLOPE is well supported. For example, the null hypothesis of Y1 does not granger cause the Slope is rejected, while simultaneously, the reverse causality (Slope does not cause granger Yield) is not rejected.

Table 7 shows the result of PCA. Here we can see that three components can be extracted from the covariance matrix. This study uses an eigenvector score 0.2 to classify a variable into a particular factor with discretion. In this case, there is a variable, namely Slope, whose eigenvector score exceeds the threshold. If a variable can be classified into more than 1 component, this study classifies it based on the components with the highest score. This study has three alternative sets of factors to be used as Instruments.

• (1)

  Factor 1 (Y1, INF, CBRATE), Factor 2 (Slope, VIXl), Factor 3 (Growth, FX_C)

• (2)

  Factor 1 (Y1, INF, CBRATE), Factor 2 (Slope), Factor 3 (VIXl, FX_C, GROWTH).

• (3)

  Factor 1 (Y1, INF, CBRATE, SLOPE), Factor 2 (VIXl), Factor 3 (FX_C, GROWTH).

This study employs all three alternative sets as a means of robustness check.

The regression result for the dependent variable SLOPE is reported in Table 8. First, this study observes the persistency of slope as previously found by Härdle and Majer (2016), Levant and Ma (2017), and Cepni et al. (2021). It can be seen that estimates for short-term yield (Y1) are all negative and highly significant. This finding supports the mean reversal mechanism for future yields as stipulated by Ross (2015) and Martin and Ross (2019). It corroborates earlier studies by Adrian et al. (2013), Abrahams et al. (2016), and Shareef and Shijin (2016). As proxied by inflation, interest rate expectation has a positive and significant influence on the slope of yield. This finding corroborates earlier findings by Coroneo et al. (2016) and Gadanecz et al. (2018), Sowmya and Prasanna (2018), Bulíř and Vlček (2022).

Local currency depreciation is associated with an increase in the slope aligned with the risk premium hypothesis. These findings confirm similar findings by Gadanecz et al. (2018), Cuchiero et al. (2016), and Chernov et al. (2019). Factors used (and corresponding instruments) have performed exceptionally well, as shown by the magnitude of endogenous variable explained variance that accounts for more than 90%.

Persistence is also an empirical feature of curve regression (see Table 9). However, unlike slope regression, this study no longer observes a significant role of macroeconomic variables in shaping yield curvature. This finding hence contradicts earlier results by Cepni et al. (2021).

Finally, the previous findings generally hold when alternative proxies (robustness check) are performed. As seen in Table 10, a rise in short-term interest expectation still poses a positive relationship with the slope when replacing INF with CBRATE. The central bank rate is also a credible proxy for short-term rate change. This study also still finds an insignificant role in fiscal conditions when replacing Gov_Debt with FIS_BAL (See Table 11).

This research aims to see the relationship of key features: slope and curvature of sovereign bonds from selected emerging countries. Departing from conventional yield curve modeling, this study treats slope and curvature as observable features (calculated from the data). The slope and curvature then regress against macroeconomic variables established in the literature: short-term yield, short-term interest expectation, foreign exchange depreciation, and fiscal condition. This study addresses the endogeneity problem inherent in the model and data structure using a novel econometric: MGIV. The dataset comprises nine emerging countries from January 2010 to October 2021 (1,278 observations).

The study reveals several significant findings. First, this study found slope and curvature to be highly persistent phenomena. Second, short-term yield is found to exert a reversal mechanism. Third, the results support the expectation hypothesis and contradict the preferred habitat and liquidity preference hypothesis. Fourth, local currency depreciation is found to increase term premiums significantly. The result is robust against alternative proxies and specifications.

Nevertheless, this study noted that panel unit root test that yielded mixed order of integration in the variables should serve as a methodological note. The main econometric method: MGIV and its variants are all silent about the implications of mixed order of integration in the variables used. Mixed order of integration is not rare occurrence in empirical works. Hence future works could aim to address this issue.

The study highlights the importance of maintaining financial stability. The empirical findings show that the impact of financial stability variables could be spread across the curve, affecting a broad spectrum of financial activities that could disrupt economic performance.

This study has shown that yield curve modeling can be studied empirically. The model and estimation result can generate sensible and comparable results using a more (constrained) theoretical-based model. This provides a research avenue to an approach that is intriguingly still scarce. Furthermore, the method can be modified to resolve several outstanding questions like the preferred habitat empirics, the role of global uncertainties, and cross-country linkages between yield curves.