We explore a part of the transmission mechanism in a sample of 16 countries that includes advanced, emerging market, and low-income countries, generally finding “well-behaved” yield curves and a functioning monetary transmission mechanism. By “well-behaved” we mean that policy or short-term interbank interest rates are transmitted seamlessly to market-determined, longer-term bond rates in all countries, with no arbitrage. The nominal interest rate part of the transmission mechanism appears to be functional and largely identical in all sample countries, including low-income ones, suggesting that the role traditionally ascribed to secondary markets can be fulfilled by primary markets.
After the financial crises of the 1990s and 2000s, many emerging market and low-income country central banks began reviewing their monetary frameworks to make policy more forward-looking, in order to promote macroeconomic stability, growth, and financial development. At the same time, these central banks felt uncertain about how monetary policy would transmit to longer term rates, and eventually, to output and prices. The task of identifying the transmission mechanism has been challenging in the environment of short, noisy time series plagued by policy-driven breaks and supply shocks. In generally, there is little agreement on the efficiency of monetary transmission in low-income and emerging market countries.1
Some economists claimed that the transmission mechanism in these countries is weak, relying on reduced-form analysis capturing the transmission channels in a VAR model (Mishra, Montiel and Spilimbergo, 2012 or Davoodi, Dixit, and Pinter, 2013). Berg and others (2013) argued that analyses based on such empirical models – requiring long time series without policy breaks – are unlikely to ever provide “statistically significant” results in low-income countries and used instead the “narrative approach” of Romer and Romer (1994) to identify textbook effects of transmission mechanism to output and prices.2
Our approach is less ambitious in the sense that we focus only on the first part of the monetary transmission mechanism. Monetary policy actions are expected to move the short-term market interest rates. While many central banks use a short-term rate as the policy instrument, other central banks change short-term (money market) rates indirectly by setting money growth targets and managing liquidity in line with these targets. According to the Keynesian interest rate channel (Hicks, 1937, Mishkin, 1995), a policy-induced increase in the short-term nominal interest rate leads to an increase in longer-term nominal interest rates as investors arbitrage away differences in risk-adjusted expected returns on debt instruments of various maturities (Figure 1).3 Under sticky prices, the movements in nominal interest rates then translate into movements in real interest rates and the agents find that their real cost of borrowing has increased over all horizons as a result of the initial short-term rate hike.
Figure 1:The Interest Rate Transmission Mechanism
In this paper we explore the first leg of the interest rate transmission mechanism: from the short-term rate or policy rate to the long-term bond rates. The three latent factors commonly used to describe the dynamics of the yield curve – the level, slope, and curvature – should explain most of the yield curve variability. Furthermore, in a well-behaved yield curve the level shift factor would dominate the slope and curvature factors, ensuring high correlation between the short and long rate moves. In other words, policy hikes/cuts would result in vertical shifts of the yield curve, minimizing arbitrage opportunities. To this end, we rely on two complementary empirical techniques to identify the yield curve latent factors and use them as a robustness check. First, the principal component analysis, PCA, initially applied by Litterman and Scheinkman or LS (1991).4 Second, we corroborate the PCA results by explicitly estimating the three latent factors using the Diebold and Li or DL (2006) methodology. We then inspect whether these two sets of estimated factors are correlated and whether they co-move with monetary policy and interbank rates.
Why do we stop at the long-term bond rates and do not continue to nominal lending rates? Unfortunately, the relevant lending rate series are available only for some industrial countries, while a few emerging market and low-income countries began to collect such series recently.
In the remained of the paper we proceed as follows. First, we outline the modeling techniques to derive the three factors. Second, we describe our sample and discuss the various empirical tradeoffs. Third, we present our results and sketch policy implications. The final section concludes.
2 The Methodology
We apply the LS and DL methodologies to detrended short and long yields to identify the latent factors that govern the movements in the yield curves, following the Diebold, Rudebusch, and Aruoba (2006) approach to explore the first leg of the transmission mechanism (Appendix A). LS finds these factors with the help of the sample covariance matrix of the data, sequentially identifying mutually uncorrelated principal components (PCs). DL employs the Nelson and Siegel dynamic representation of the yield curve, defining a state space model of the yield curve, and applying the Kalman filter to identify the three latent factors, the level, slope, and curvature, labeled β1, β2, and β3. DL is free of the PCA restriction of zero correlation of the factors.5 Furthermore, while the principal component analysis is designed for stationary data, DL is free of this restriction as well. We assess the interest rate channel as follows. First, we compute the share of the variability in the interest rates explained by the latent factors using the LS and DL methodologies.
If the factors explain most of the variability in the actual data across all maturities, we would conclude that the shape of the yield curve and its dynamics are nonstochastic (Appendix [B]). Furthermore, a dominant level shift factor would imply that policy rate moves result in a vertical shift of the yield curve. Second, we inspect correlation among the policy-driven short-term rates and the factors, in particular, the level. We expect to find a positive correlation between the policy rate and the first factor as changes in the former shift the yield curve. Furthermore, assuming that inflation expectations are anchored and long rates reflect country fundamentals, we expect to find a negative correlation between the policy rate and the second factor. In other words, a tighter monetary policy flattens the yield curve and vice versa.
Extending yield curve analysis to emerging market and low-income countries proved to be challenging. Data are available for only a handful of countries, securities are rarely traded on secondary markets, and primary issue data are often with gaps. Periods of disinflation (or increasing inflation) have left the series with unit roots, removal of which is not trivial. To rectify this problem, we detrend interest rates and bond yields using the HP-based trend of policy rates. Hence, all interest rates and yields are expressed as term premiums. Furthermore, central banks that follow monetary targets or inflation targeters in low-income countries tend provide liquidity to the banking sector at rates that differ from their declared policy rates.
3.1 Sample countries
We explore the working of the interest rate channel in a sample of 16 countries, that is further divided into emerging market countries, EMC, low-income countries, LIC, and advanced countries, AC (Table 1).6 The seven EMCs are Egypt (EGY), Georgia (GEO), Indonesia (IDN), Malaysia (MYS), Morocco (MAR), South Africa (ZAF), and Turkey (TUR). The six LICs are Ghana (GHA), Kenya (KEN), Nigeria (NGA), Rwanda (RWA), Tanzania (TZA), and Uganda (UGA). The control group of three ACs comprises the Czech Republic (CZE), Israel (ISR), and Sweden (SWE), all countries practicing inflation forecast targeting (IT) as defined by Svensson (1997). According to the IMF (2012) de facto classification five out of 13 countries in the EMC/LIC group are also IT, however, most of them fail one or more of the Six Principles of Inflation Targeting (Freeman and Laxton, 2009). The sample is macro-economically diverse: average inflation ranged from 1.4 percent in Sweden to almost 15 percent in Ghana, with inflation being higher and more volatile in the EMC/LIC group. The average ex post short-term real interest rate was mostly positive, with a few negative-rate outliers among African countries. The poorest sample country is Uganda and the richest is Sweden. With the exception of Sweden and South Africa, the interest rate series start in the 2000s (Table 2).
|Czech Republic (CZE)||Inflation targeting||2.4||3.4||25,389|
|Egypt, Arab. Rep. (EGY)||Multiple objectives||8.0||7.0||5,893|
|Georgia (GEO)||Inflation targeting||5.3||10.4||4,932|
|Ghana (GHA)||Inflation targeting||14.8||11.6||2,679|
|Indonesia (IDN)||Inflation targeting||7.5||8.5||4,149|
|Israel (ISR)||Inflation targeting||2.0||4.1||30,535|
|Kenya (KEN)||Monetary aggregate targeting||9.6||13.9||1,582|
|Morocco (MAR)||Monetary aggregate targeting||1.6||6.3||4,554|
|Malaysia (MYS)||Multiple objectives||2.2||4.4||14,699|
|Nigeria (NGA)||Monetary aggregate targeting||11.7||15.5||2,293|
|Rwanda (RWA)||Monetary aggregate targeting||6.9||9.0||1,200|
|South Africa (ZAF)||Inflation targeting||5.7||3.9||10,105|
|Sweden (SWE)||Inflation targeting||1.4||2.9||37,498|
|Turkey (TUR)||Inflation targeting||14.6||10.3||13,110|
|Tanzania (TZA)||Monetary aggregate targeting||7.6||8.5||1,384|
|Uganda (UGA)||Monetary aggregate targeting||7.3||10.7||1,275|
|Country||Sample period||Yield type||Maturities|
|Czech Republic (CZE)||2000M4:2015M1||Yields at issue, primary market (pm), Bloomberg generic for the long tenors||3M, 6M, 1Y, 2Y, 5Y, 10Y|
|Egypt, Arab.||2006M7:2014M12||T-bills – yields at||3M, 6M, 1Y, 2Y, 3Y, 5Y,|
|Rep. (EGY)||issue, T-bonds – Bloomberg generic||7Y, 10Y|
|Georgia (GEO)||2010M9:2014M11||Yields at issue, pm||1Y, 2Y, 5Y, 10Y|
|Ghana (GHA)||2007M1:2014M9||Yields at issue, pm||3M, 6M, 1Y, 2Y, 3Y|
|Indonesia (IDN)||2005M7:2015M1||Bloomberg generic||1Y, 2Y, 5Y, 10Y, 15Y|
|Israel (ISR)||2005M1:2015M1||Bloomberg generic||2Y, 3Y, 5Y, 10Y|
|Kenya (KEN)||2007M1:2014M9||Yields at issue, pm||3M, 6M, 5Y, 10Y, 15Y|
|Morocco (MAR)||2007M1:2015M1||Yields at issue, pm||3M, 1Y, 2Y, 5Y, 10Y, 15Y|
|Malaysia (MYS)||2005M1:2014M12||Yields at issue, pm||3M, 6M, 1Y, 2Y, 3Y, 4Y, 5Y, 10Y, 15Y|
|Nigeria (NGA)||2006M9:2014M10||Yields at issue and yield to maturity, pm and secondary markets||3M, 6M, 1Y, 3Y, 5Y, 10Y|
|Rwanda (RWA)||2008M1:2014M10||Yields at issue, pm||3M, 6M, 1Y, 3Y|
|South Africa (ZAF)||1999M12:2014M3||Bloomberg generic||2Y, 3Y, 5Y, 7Y, 10Y, 15Y|
|Sweden (SWE)||1994M6:2014M12||Bloomberg generic||3M, 6M, 1Y, 2Y, 3Y, 5Y, 10Y|
|Turkey (TUR)||2007M6:2015M1||Bloomberg generic||3M, 6M, 1Y, 2Y, 5Y, 10Y|
|Tanzania (TZA)||2003M1:2014M10||Yields at issue, pm||3M, 6M, 1Y, 2Y, 5Y, 7Y, 10Y|
|Uganda (UGA)||2005M1:2014M12||Yields at issue, pm||3M, 6M, 1Y, 2Y, 3Y, 5Y|
3.2 Central bank and interbank rates and yields
All sample countries have treasury bills and bonds of various maturities, interbank money market rates and most have also a central bank interest rate. The latter rate is used differently across the sample, however. While all advanced and some emerging market countries use the central bank rate as a target rate for liquidity operations, most LICs countries occasionally provide liquidity at rates different from their central bank rates (Berg and others, 2013). As a result, the ACs and some EMCs exhibit average spreads between the central bank and interbank interest rates to the tune of tens of basis points, whereas in LICs the spreads are in hundreds of basis points (Figure 2 and also Table 8 in Appendix C). Hence, we use the rate only if the bank has used it consistently as a policy instrument and the interbank rates have been close to the central bank rate. Such conditions are satisfied only among the more advanced IT countries (the Czech Republic, Israel, and Sweden). Hence, we define the monetary policy stance either as the central bank rate or as the shortest maturity, typically overnight, interbank rate.
Figure 2:Spreads Between the Interbank and Policy Rates
Source: Authors’ calculations.
Notes: Sample correlation coefficients of the latent factors: the first, second, and third factors are labeled as the level, slope, and curvature. Statistically significant coefficients – at the 95 percent confidence interval – are highlighted in gray. A correlation coefficient larger than 0.4 is considered as indicating strong correlation (Doucouliagos, 2011).
|Shortest Maturity||Longest Maturity||Slope (Long–Short Maturities)|
|Country||Policy rate and liquidity operations||Root mean square difference (basis points)||Range|
|Czech Republic||Liquidity operations conducted at the central rate – 2W repo rate.||14||2002M1–2015M1|
|(CZE)||The interbank rate (1D PRIBOR) close to the central bank rate.|
|Egypt, Arab. Rep. (EGY)||A corridor with overnight deposit and lending facility since June 2005 and the repo rate in the center of the corridor since March 2013. However, the overnight interbank rate close to the overnight deposit rate.||33||2005M6–2014M11|
|Georgia (GEO)||The refinancing rate introduced as a central bank rate in 2008. The overnight interbank rate close to the refinancing rate since the second half of 2010.||134||2008M2–2014M12|
|Ghana (GHA)||Liquidity operations and the central bank rate were periodically disconnected. As a result, the interbank rate differed from the central bank rate.||266||2004M2–2014M9|
|Indonesia (IDN)||The interbank JIBOR rate deviates from the central bank rate – the interbank rate.||183||2005M7–2015M1|
|Israel (ISR)||Bank of Israel interest rate is used for with liquidity operations and is closely followed by the interbank rate.||20||2001M1–2014M12|
|Kenya (KEN)||The central bank rate was used since July 2006, but it remained disconnected from liquidity operations. As a result, the interbank rate significantly deviates from the central bank rate.||401||2006M7–2015M1|
|Morocco (MAR)||The interbank rate deviates from the central bank rate.||47||2002M1–2015M1|
|Malaysia (MYS)||The interbank rate managed closed to the overnight policy rate.||20||2004M4–2014M1|
|Nigeria (NGA)||The interbank rate deviates from the central bank rate substantially.||323||2006M12–2014M10|
|Rwanda (RWA)||The repo rate and the interbank rate differ.||164||2008M1–2014M10|
|South Africa (ZAF)||The repo rate is the central bank rate and it is closely followed by the interbank rate.||104||1997M1–2014M5|
|Sweden (SWE)||The repo rate is the central bank rate and is closely followed by the interbank rate.||12||1998M6–2015M1|
|Turkey (TUR)||The interbank rate stays close to the overnight deposit rate and is disconnected from the repo rate.||213||2010M5–2014M11|
|Tanzania (TZA)||No official central bank rate. The overnight interbank rate frequently out of sync with the repo rate.||385||2002M4–2014M9|
|Uganda (UGA)||The central bank rate used since July 2011. Liquidity operations are conducted to the 7D interbank rate close to the central bank rate.||161||2011M7–2014M12|
The monetary policy rate should ultimately affect lending rates, however, this nexus is difficult to demonstrate empirically as the published lending rates in the EMC/LIC group are riddled with problems. First, some countries report as lending rates the so-called prime rate at which little or no retail lending is done. Second, the published data sometimes contain an average rate for all immature loans with a given maturity.7 Only ACs and some EMCs (Morocco) collect and publish usable series on current-period lending rates, classified by sector, firm size, and maturity, although some LICs (Uganda) start collecting such data. Even for those countries, however, the series are difficult to collect.
Finally, the EMC/LIC lending rates contain sizable credit and inflation premiums. Regarding the former, in Ghana the spread between the prime lending rate and the three-month interbank rate averaged about 2,000 basis points between 2004 and 2013, while in the Czech Republic the spread was only 200-300 basis points. The lending rates reflect the functioning of the domestic asset recovery system: in countries with poor creditor protection lenders charge higher loan-to-deposit spreads than in countries with good protection, to build a buffer against nonperforming loans. Regarding the latter, the inflation premium tends to be sizable in countries with high and volatile inflation, dampening the pass-through from the policy-induced changes in the (nominal) policy rate to the lending rate tends.
We therefore assess transmission mechanism using yield curves that are based on government security market rates, following past literature (Litterman and Scheinkman, 1991; Diebold, Rudebusch, and Aruoba, 2006; Aguiar, Martins, and Soares, 2012). The monthly yields on generic bonds, obtained from the Bloomberg and public databases (Table 2), have drawbacks, however.8 First, the time series for the EMCs and LICs are short, typically covering only the 2000s. Second, we frequently find only yields at issue on the primary market as the secondary markets are either non-existent or illiquid. The primary market yields are often subject to non-market forces as short maturities are used by the central bank for managing market liquidity and demand for the longer tenors is affected by regulatory measures targeting the capital and liquidity ratios of various financial institutions. Third, the primary market data have missing observations as not all maturities are auctioned at each point in time and we thus intrapolate the missing monthly observations using the Hodrick-Prescott filter with λ=14,400.
The empirical work is further complicated by secular moves in inflation and the corresponding increases/declines in nominal interest rates. Such an underlying trend in inflation is likely to bias upward the importance of the level factor. The stationarity assessment is complicated by the fact that individual yields cannot be detrended separately, as the underlying inflation trend should be common across all maturities. To this end, we detrend all yields using the trend of country’s monetary policy rate (Hodrick-Prescott filter with λ=14,400), that is, all yields are expressed as term premiums. Still, even after such detrending we cannot reject nonstationarity in one fifth of all yields (Egypt, Georgia, Israel, Morocco, Turkey, Tanzania, and South Africa, Appendix B.). This finding is hardly surprising as our detrended yields are measures of term premiums and these are generally nonstationary (Figure 3).9
Figure 3:Average Term Premiums: Countries Grouped by Their Monetary Policy Regimes
Source: Authors’ calculations.
All yield-curve calculations are performed with monthly data and correlations presented in the paper are sample Pearson product-moment correlation coefficients. For robustness checks we also calculate population correlations, computed from a first-order VAR model. These results are are not materially different from the sample correlations and are available on demand.10
4 Results and Policy Implications
A well-functioning transmission mechanism seamlessly transmits monetary policy innovations to longer-term rates.11 We find evidence of such well-behaved yield curves in our sample countries, basing this conclusion on the latent factors explaining most of the variability across all maturities. Furthermore, the factors are correlated with policy interest rates. Regarding robustness, first, we check the explanatory power of the LS and DL estimates of latent factors and compare the two techniques. Second, we discuss the links between the monetary policy rates and the first two factors. All checks suggest that our results are methodology invariant.
4.1 The LS and DL Estimates of the Latent Factors
The LS and DL estimates of the latent factors are highly correlated in most of the sample countries despite the different identifying restrictions and we thus consider these estimates to be robust (Table 3). By extension, as the DL-based factors have clear structural interpretation as the level, slope, and curvature, the LS-based estimates can be labeled in the same way.
Jointly the three factors explain more than 95 percent of the interest rate variability in all countries, with an exception of Nigeria, and the first two factors account for most of yield variability (Figure 4). Assessing the average explanatory power of the level and slope factors jointly across different maturities does not suggest any material differences – the two factors explain on average 95 percent of the yield variance. The first latent factor, the level, is a crucial indicator of transmission as it measures the vertical shifts of the yield curve and it clearly dominates in most countries.12 High contribution of this factor implies that the yields are correlated across maturities and, hence, innovations are quickly propagated. Of course, interest rate innovations may be propagated also through changes in the slope of the yield curve, especially if inflation expectations are anchored. To this end, we find that Sweden and South Africa, both inflation targeting countries, exhibit comparatively low contribution of the level factor. The contribution of noise and stochastic (unexplained) parts of yield curve variability is estimated to be fairly small. From this perspective, we find yield curves to be (i) well behaved in both developed and low income countries and (ii) difficult to differentiate the ACs from EMCs and LICs, that is, regime invariant. In other words, our sample countries behave very much in line with the theory of term structure of interest rates, with relatively small shocks to the term structure (see Appendix A for Monte Carlo simulations).
Figure 4:Interest Rate Variability Explained by Three Factors Using the LS and DL Methodologies
Source: Authors’ calculations.
We find two major differences between the advanced IT countries and the rest of the sample. First, the contribution of the level factor declines at the 5-year and 10-year maturity in all three advanced countries, that is, the common innovations do not transmit to the longest maturities (see full dark blue line in Figure 5). This finding indicates that the long maturities in AC inflation targeters are anchored by a credible inflation target and do not need to react to policy shocks. Central banks in the rest of the sample lack such a credible anchor and the contribution of the level factor remains high at longer maturities. In other words, while in the ACs the yield curves move vertically and become flatter (pivot) at longer maturities after a policy shock, in the rest of the sample we observe mostly the vertical shift.
Figure 5:LS Variability Attributed to the Level and Slope: Countries Grouped by Their Monetary Policy Regimes
Source: Authors’ calculations.
Second, the contribution of the level factor is small at short tenors in the sample of monetary targeters and EMC/LIC inflation targeters – the 3-month, 6-month, and 12-month interbank rates do not move with the rest of the yield curve (see light blue line with triangle markers in Figure 5). Our interpretation is that the central banks in these countries do not have complete control over the short end of the yield curve and the level factor explains thus relatively little of the variability of short tenors. The lack of control can be attributed, first, to monetary targets that determine the short-term rates residually and, second, to the earlier discussed unwillingness of some central banks to synchronize their policy rates with rates at which liquidity operations are executed.
Grouping countries into AC, EM, and LI suggests only small differences in explained variability (Figure 6). The first two factors explain on average 96 percent of yield variance in ACs and EMCs, declining to 92 percent in LICs. Breaking down the sample by maturity points again to the credibility issue in the EMCs and LICs as long-term yields do not appear to be anchored by the inflation targets. We take these results as suggesting that advanced IT countries are more likely to have well-behaved yield curves than less developed countries, irrespective of their income level. The summary differences are fairly small and fail to make a strong case for developed secondary financial markets in order to obtain a meaningful yield curve, presumably because commercial banks are the main buyers and sellers of central bank and government paper in EMCs and LICs.
Figure 6:LS Variability Attributed to the Level and Slope: Countries Grouped by the Level of Economic Development
Source: Authors’ calculations.
4.2 The Short-term Rates and Factors
We proceed to explore how well are policy rate hikes/cuts reflected in the longer-term rates by examining, first, the correlations between the actual interest rates and the estimated latent factors and, second, the shape of the PCA loadings. While neither technique proves causality from to policy to long-term rates, the alternative of the policy rate passively reflecting long-term bond rate movements is inconsistent with the forward-looking behavior of the sample central banks. Diebold, Rudebusch, and Aruoba (2006) argued that these correlations are unlikely to be driven by a third variable. Our results strongly suggest that changes on the short end of the yield curve have a powerful impact on long-term yields.
First, we show how the monetary policy rates interacts with the yield curves. All correlations between the monetary policy rates and the shortest available maturity yield are positive (Table 4, first column). In particular, the correlations are high among the IT countries.13 Furthermore, monetary policy rates are positively correlated with the level factors identified using LS in most of countries, however, for a few IT countries we found negative correlations using the DL methodology (Table 4, second column). We also find the expected negative correlation coefficients between the policy rates and the slope in all countries, except in Nigeria. Of course, not all correlations between the policy rates and the later factors have to be statistically significant – in some countries policy moves are reflected mostly in vertical shifts of the yield curve, while in others the yield curve pivots (for example in multiple objective countries).
Second, we assess the loading factors. In all sample countries, the level loadings are essentially constant at about 0.4-0.6, suggesting that all observed maturities enter the first factor with similar weights (the full blue line labeled PC1 in Figure 7 and 8). The only exceptions are Rwanda, where the loadings level off at the 1-year maturity, and Malaysia, where the loading is close to zero for short maturities up 2 years. The estimated second and third latent factors also have the expected properties (see the green and red lines, respectively). The loadings of the second principal component are either downward or upward sloping across maturities, proxying the slope of the yield curve and the factor is correlated with the empirical measures of the slope.14 The loadings of the third principal component approximate the convex/concave curvature of the yield curve.
Figure 7:Principal Component Loadings
Source: Authors’ calculations.
Figure 8:Principal Component Loadings
Source: Authors’ calculations.
Turning to individual countries, the first factor is positively correlated both with the empirical short and long-term yields in all 16 countries (Appendix D). As before, we find no material differences among the sample countries, either for short or long tenors, interpreting these findings as supporting our hypothesis that the interest rate transmission mechanism is present in all sample countries.
Policy-induced interest rate moves are correlated with the vertical shifts of the yield curve, however, such moves may affect also the slope of the yield curve. As expected, the first and second latent factors are positively correlated and most of these correlations are statistically significant. In other words, monetary tightening/loosening pivot the yield curve, in addition to the level shift (see the first column in Table 5).15 As before, we fail to observe any systematic differences between the advanced and low income countries. In contrast, the correlations between the first and third and between the second and third latent factors are small and change signs.
4.3 Policy Implications
Our sample findings have useful policy implications and we summarize them into five sets. First, we find a strong co-movement between the policy rate and bond yields, suggesting well-behaved yield curves without arbitrage opportunities. Such a yield curve is a necessary, if not sufficient, condition for monetary transmission. Second, for countries that use their policy rate as a monetary policy instrument, we find a strong link between such a rate and short-term interbank or treasury bill rates. Third, we find a number of intuitive results linked to the credibility of the policy regime and the level of development. Only in advanced countries – all practicing inflation forecast targeting – inflation expectations are anchored and the long rates thus react less to the first (level) factor than in the other countries. Conversely, the level shift matters equally for all maturities in the EMC/LIC sample. Furthermore, monetary targeters and EMC/LIC inflation targeters have incomplete control over the short end of the yield curve and the level factor explains less of the variability of short tenors as compared to AC inflation targeters.
Fourth, transmission gains from deeper secondary markets in ACs appear surprisingly small. Or to put it differently, deep secondary markets do not seem to be absolutely necessary for a well-behaved yield curve, presumably on the account of commercial banks being the main buyers and sellers across all maturities. Finally, the link between short rates and lending rates in EMCs and LICs remains a topic for future research as series on meaningful loan rates are unavailable but for a few advanced countries. Such rates would allow extending the transmission mechanism for the “lending nexus”.
We find a well-behaved yield curve of bond yields in advanced, emerging, and low-income countries, indicating a working interest rate transmission channel in all of our sample countries. The three latent factors – the level, slope, and curvature – explain the bulk of interest rate moves, and the vertical shift dominates. The link from policy/interbank rates to bond yields appears to be robust across estimation techniques and largely unaffected by the monetary policy regime or the stage of economic development. We find no evidence that well-developed secondary markets supercharge the transmission mechanism as commercial banks do most of the trading of government paper in low-income countries. Furthermore, we find only weak evidence that the transmission mechanism operates more smoothly in more developed countries practicing inflation targeting than in less developed countries. These results are broadly invariant to the methodologies used and they are also remarkably consistent across the sample countries, despite short samples, gaps in longer maturities, monetary policy regimes, and so on.
The findings of this paper have a strong policy implication – the presence of the first leg of the monetary transmission is broadly independent of the level of financial sophistication. To the extent that advanced inflation targeting countries appear to have marginally better-behaved yield curves than countries that follow other objectives, the functioning of the transmission mechanism seems partly a matter of domestic choice and credibility thereof. These results are relevant as the sample central banks continue to gauge their ability to steer the economy with indirect instruments. The overall message is clear – the central bank actions do matter even in low income countries.
The paper replicates the LS principal component analysis and DL methodology to capture the dynamics of the sample-country yield curves. Both approaches characterize the movements of the yield curves by identifying three latent factors labeled as the level, slope, and curvature. We briefly describe both methodologies and list the relevant references.
Principal Component Analysis
Principal component analysis (PCA) is a well established method for reducing data dimensionality. It transforms the multiple observed series into a set of uncorrelated principal components. As the interest rate series are correlated, one should be able to capture their variability with fewer principal components than what was the count of the observed series.
Let us assume that the data are collected in an X(m × n) matrix, where the n columns are the observations and the m rows are the variables (yields). PCA finds a transformation matrix W(m × m) such that it projects X into principal components PC(m × n):
choosing W such that the rows of PC are uncorrelated with each other and hold the same information as the original matrix X. The rows of PC are ordered in a descending order according to their importance as there are a total of m principal components. It can be shown that in order to fulfill the objectives above, the rows of W are the eigenvectors of the covariance matrix, X XT, and W is called the matrix of factor loadings.
We follow Litterman and Scheinkman (1991) who applied PCA to observed yields. The data are normalized by dividing each maturity yield by its sample standard deviation, interpolating missing data with the Hodrick-Prescott filter. Principal components are ordered in a descending order by the total variance explained and the first, second, and third principal components are labeled as the level, slope and curvature factors of the yield curve.
The Diebold and Li Framework
Diebold and Li (2006) suggested a modification to the Nelson and Siegel exponential component framework to fit yield curves. The DL framework uses three time-varying parameters, which can be interpreted also as the level, slope, and curvature. These unobserved parameters are identified based on the data and mean square error optimization, after imposing simple structural restrictions. The state-space representation along with Kalman filtration allow for missing observations.
In our version the yield curve follows:
where yt(τ) is the yield at time t of a bond with maturity τ. β1t, β2t, and β3t are the time-varying parameters (or factors) and λ are country-specific parameters driving the exponential decay rate. Following Diebold and Li (2006), we set λ based on countries’ average maturity of government paper. DL show that the parameter β1 can be interpreted as a level shift, as it increases all maturity yields equally. The parameter β2 is closely related to the slope of the yield curve. The loading on this parameter,
In order to identify unobserved time-varying parameters, we transformed the model to a state-space form following Diebold, Rudebusch, and Aruoba (2006). The transition equations driving the dynamics of yields are:
The factors, βi’s, are assumed to be random-walk processes:
where ε and η are white noise shocks with zero means and covariance matrices Q and H:
The measurement equations then link the observed yields with state variables assuming no measurement errors:
We match the state-space model with the data using the Kalman filter. For each country we estimate matrices Q and H using the Bayesian estimation techniques with inverse gamma distribution of priors.
We simplify the original DL framework in three aspects, without loosing any of its structural advantages. First, we reduce the number of estimated parameters by filtering the noise in the data via the error terms, ε’s, rather than by treating measurement errors explicitly. Second, we impose the random walk processes for the latent factors. Third, we do not allow for cross-factor dynamics and correlations. The last two simplification follow Diebold, Rude-busch, and Aruoba (2006) who found factors to be highly persistent with insignificant cross-factor dynamics.
Assessing Yield Curves Using LS and DL Methodologies
The LS and DL methodologies are commonly used to fit yield curves and we argue that they can be used to assess the transmission of short-term to long-term rates along the yield curves. We consider a yield curve to be “well behaved” if short-term interest rates transmit to long tenors in line with the expectation theory of term structure implying that a long-term yield adjusted for a term premium has to be equal to expected short-term yields compounded to the same maturity. As a result, there will be nonzero correlation between long-term and short-term yields. Lord and Pelsser (2005) derive sufficient conditions for a correlation matrix under which the level, slope, and curvature are jointly present. However, we use the LS and DL methodologies instead of correlation analysis, as these methodologies provide an easy decomposition into the level, slope, and curvature shifts. These shifts can be easily crosschecked with monetary policy actions.
One may wonder, however, whether the LS and DL methodologies are too general so that one always obtains the same type of latent factors. In order to demonstrate how the LS and DL methodologies can be used for assessing the yield curves, we generated artificial yield curve data using Monte Carlo simulations. The data were generated by a workhorse gap model similar to Berg, Karam, and Laxton (2006) augmented with the expectation theory of interest rates.16 Using the model, we generated yield samples and conducted our analysis. First, we generated artificial yields by assuming a common set of business cycle shocks (short-term demand, supply, exchange rate, and policy shocks; long-term inflation target and country risk premium shocks) without any shocks to term structure of interest rates. Second, we did the same exercise with the term structure shocks explaining about 25 percent and 50 percent of yield variability. Finally, we generate yields as white noise.
The results suggest that interest rate variability in our Monte Carlo simulations – for a plausible setup of term-structure shocks being equivalent to 25 to 50 percent of yield variability – is mostly explained by the first factor, much as in the actual sample (Figure 9).17 As expected, the contribution of the first factor declines with the magnitude of term-structure shocks. The first two factors explain more than 90 percent of observed interest rate variability in the case of the pure term structure (both LS and DL) and in the case of 25-50 percent noise contribution in addition to the term structure (LS), see the top three left-hand-side charts. The explained share, especially for the first factor, is somewhat lower for the DL methodology. In the extreme case of white noise data, the variability explained by any factor is very low (bottom row). Based on these results, we conclude that well-behaved yield curves are mirrored in LS and DL methodologies: first, level is the leading factor as measured by its explanatory power and, second, level and slope together explain most of the variability in the data.
Figure 9:Variability Explained Using LS and DL Methodologies (Monte Carlo Simulations)
Source: Authors’ calculations.
Most countries in our sample contain a trend in inflation, typically as a results of past disinflation and, hence, we find also a trend in the in central bank rate series. Therefore, the data have to be detrended, otherwise the presence of a unit root would affect the correlation matrixes. We detrend the data using trends in the domestic monetary policy rate (either the central bank rate or the interbank rate), in effect re-defining all series as term premiums. The trend of monetary policy rate is identified using the HP filter. The Augmented Dickey-Fuller tests show that we can reject the null hypothesis of stationary series for most but not all of the detrended yields (Table 6).
Latent factor correlations
The LS and DL estimates of factors are highly correlated in most sample countries despite different identification techniques. The first factor estimates are strongly correlated in all countries, except in Rwanda. The same holds for the second factor, except Israel, Nigeria, South Africa, and Turkey. The evidence is mixed for the third factor: the correlations are high mostly in low income countries which exhibit unit roots even after detrending (Egypt, Morocco, and Malaysia).
Factors and their empirical counterparts
In order to check robustness of the latent factors, we compared them with the commonly used empirical measures of level, slope, and curvature. The first factor is positively correlated both with the short and long-term yields in all 16 countries, suggesting that the first factor is a good proxy of the level shift and that it affects all maturities along the yield curve.
All sample countries have interbank money markets and most have also a policy interest rate. However, the latter instrument is used differently across the sample (Table 8). All advanced and some emerging market countries used the policy rate as a target rate for liquidity operations. As a result, these countries exhibit very high correlation between policy and interbank interest rates, see Table 8. For example, in the Czech Republic the one-day interbank rate has been on average higher by only 14 basis points than the policy rate of the Czech National Bank (the two-week repo rate). Only at the height of the 2008 financial crisis the spread temporarily widened to 100 basis points.
In contrast, most LICs countries periodically provided liquidity at rates different from their policy rates. For example, in Ghana the policy rate and the main liquidity instrument, approximated by the 30-day Bank of Ghana bill, stayed periodically far apart: while between mid-2005 and end-2007 liquidity was made available to commercial banks on average 270 basis points below the policy rate, during 2013 it was made available some 600 basis point above the policy rate. As the effective liquidity rate differed from the policy rate in these countries, correlation between policy and interbank rates was low.
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