If the banks have some control over the endogenous money supply, then they partly determine the market rates of interest in the borrowing and saving process on various terms through a mark-up on the ‘bank’ rate set by the Central Bank. The link between the rates implies that they could well be formed by the term structure through either the expectations theory or an imperfect configuration of it, with an empirical illustration.
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The analysis addresses the expectations theory of the term structure of interest rates. The hypothesis crucially depends on the measurement of expectations and the monetary transmission that exists via short-term rates of interest. The novel idea embodied in the econometric analysis here is the conversion of the Livingston Survey of half-yearly observations into monthly data on the forward-looking rates of interest on the three-month Treasury bill. The empirical results show a clear ‘one-to-one’ relationship between the six- and three-month rates of interest on Treasury bills within USA by way of the VAR methodology of estimation.
Macroeconomics essentially assumes one interest rate, when in fact there are many existing in the practice of finance for many reasons. The term structure of interest rates, however, recognises a common link between them all in the form of expectations of the future, whether long or short, which determines the holding of various financial assets of maturity as well as influencing the determination of aggregate demand and supply within the real economy. The term structure , therefore, is important for Central Bank ’s policymakers. If these monetary instruments affect short-term rates of interest in the first instance, which leads to the determination of long-term rates of interest, which drives capital and consumption expenditure, then analysing the term structure is crucial for understanding the transmission mechanism of monetary policy (Fender 2012). 1
Nevertheless, it is also relevant for many households in terms of the portfolio choice of assets. Suppose a family requires expenditure on private school fees in ten years’ time and decides to save now. There are a number of options. They could save by investing into a ten-year bond. Alternatively, they could purchase a short-term bill and then take the earnings into another bond each time it matures, until the ten years are up.
Clearly, the important components determining the choice will be the expected return (or cost) and the risk involved, embodied in the term structure . Therefore, the analysis must consider the various theoretical models put forward in the literature to explain the relationship between interest rates on bonds (or bills) of differing maturity, although the hypothesis can applied to other assets as diverse as housing and the mortgage rate.
The foremost theory of the term structure of interest rates is the so-called expectations hypothesis, which focuses on the rôle of expectations of future short-term interest rates in the determination of prices and yields on longer-term bills (or bonds ). There a number of ways in which the theory in the literature differs in terms of the length of the bills (or bonds ) included in the analysis. The discussion will employ a simple version of the theory and adopt this within the empirical framework using the VAR methodology with its associated tools of analysis.
The expectations hypothesis indicates that there is generally a systematic relationship between the yields and the term to maturity as when plotted, leading to a smooth curve known as the time-yield amongst homogenous categories of assets. A subset of assets such as government bonds or Treasury bills will have default risk that is close to the of value zero. The major factor of influence over this relationship is the expectations of future interest rates, where future changes affect the current structure . If the yield curve is stable, then lenders and borrowers are in equilibrium at the current pattern of interest rates. The rewards from longer-term loan must therefore equal the average of the series of shorter-term advances. This is how the future enters the analysis.
Suppose the choice of loans is either in the form of six- or three-month bond (or bill). This means lenders can lend for six months or on two conservative occasions with a three-month bill. Thus, the long-term is for the six-month period and expressed in the form of
$$i_>,t>> = \frac + \hat_ >>,$$where \(i_>\) is the long-run interest rate and equal to the average of the current and the expected three-month rate of interest , where the future plays a vital rôle via the expectations relating to the course of the short-run rate of interest . The link between yields (the rates) on various assets differentiated by their term to maturity is essentially the term structure of interest rates. The hypothesis clearly assumes a transmission mechanism for monetary policy .The opposite theory is that financial assets are separate and there is no link between them, unlike the expectations speculation. This is the so-called segmented hypothesis. The term structure becomes represented by different markets. The demand and supply for a particular bond determine the interest rate and the expected return do not influence any other interest-bearing assets. These markets are segmented and do not act as substitutes one another. This is the reverse of the expectations theory , where bonds (or bills) of differing maturities are substitutes and influence each other.
The reason for the adoption of this assumption is because investors’ preference is to invest in one particular level of maturity. This is because they desire to hold for a specific period with a certain return and risk . Some investors have a short-holding period to minimise the interest-risk . In other words, the rise in interest rates on different bonds cannot affect each other and their maturity.
The bridge between the two extreme theories is the preferred habitat speculation proposed by Hicks (1946), suggesting that the term structure expresses the interest rate on the six-month bond as equal to the average of the three-month rate, as in the case of the expectations model, but plus a risk premium which is determined by demand and supply conditions. According to this theory, bonds (or bills) of different maturities are imperfect substitutes, because savers have preferences for particular periods, that is the preferred habitat . Savers prefer bonds of a particular maturity, but are willing to consider other assets if the somewhat expected return is high. If the preferred habitat is short-term over long-term bonds , investors are only willing to hold long-term bonds if liquidity premiums are paid, which alters (6.13) as follows:
$$i_>,t>> = \frac <<\left(Moreover, which theory is correct could well be a statistical matter, although there is a considerable body of empirical work on the term structure of interest rates. Useful summaries are provided by Shiller (1990) and Cuthbertson and Nitzsche (2004). The key studies in the field of study are Campbell and Shiller (1987) for an application to USA data and Cuthbertson (1996) for the UK economy. The overall assessment of the empirical work on this topic is inconclusive. The major difficulty, however, in testing these theories is the measurement of expectations . The next section of the discussion considers the measurement of the expectations by the Livingston Survey, which becomes a crucial component of the empirical study.
In June and December of each year, from 1946, the Livingston Survey asks a number of professional economists in academic, business, Government and finance sectors to forecast a number of key variables of the economy such as the rate on the three-month Treasury bill, although this particular dataset started in 1992. They provide, for example, forecasts for the end of the current month as well as six- and twelve-month-ahead, receiving, on average , fifty replies each time (Cronshore 1997).
Pesando (1975) suggested that the six-month-ahead forecasts were unbiased, whereas the twelve-month forecasts were biased. In fact, Carlson (1977) compared statistical forecasts with the Survey predictions and found that the latter performed better than the former despite a number of problems with the Survey. 2 Given the discussion within the literature, and the results of a statistical experimentation between the two Surveys, the empirical analysis adopted the six-month-ahead, mean statistics.
To create monthly forecast values of the rate of interest on the three-month Treasury bill over the next six months, an econometric model based on Ordinary Least Squares Method of Estimation was constructed from the half-yearly rates, 1992: H2 to 2012: H1. This allowed the empirical analysis to derive the missing, monthly expected values, from the actual average rates. The statistical model used in the process of conversion is as below:
$$\begin
where \(\Delta \hat_ = \hat_ - i_ , \,\hat_\) denotes the forecast values of rates of interest on the three-month Treasury bill over the next six months, \(t + 1\) , so that \(\Delta \hat_\) represents the change in predicted observations at time t, and finally, \(i_\) equals the actual rates of interest on three-month Treasury bills. The next stage in the analysis is to check the order of integration.
The data generated above, along with the rates of interest on the six-month Treasury bills, \(i_>,t>>\) , were subject to statistical tests to observe whether the endogenous variables are I(1) before including them into the cointegrating analysis. The statistical findings using the Dickey–Fuller tests for stationarity are showing in Table 6.2.
Table 6.2 Stationarity tests over sample period of 1992 M12–2012 M8 aIt is clear from Table 6.2 that all the data sets are stationary on first-difference, so that all variables included in the VAR are I(0). The next part of the process is to determine the order of the VAR .
In order to determine the lag structure , the empirical study ran an unrestricted VAR of a relatively high order of twelve with all the available data, including an intercept term with the variables of interest. This included a dummy variable, D, which takes on the values of minus one for 2007 M: 12 and 2008 M: 12, otherwise takes the value of zero elsewhere. The inclusion of the dummy variable captures the effect of the financial crisis that started to ‘bite’ in 2007, leading to observations that can be regarded as outliers in order to identify the long-term relationship. Since interest rates are not trended, the analysis did not include a trend in the VAR .
According to Table 6.3, both statistics, the Akaike Information Criterion (AIC) and Schwarz Bayesian Criterion (SBC), agree that order of VAR should be two for determining whether the cointegrating vector exists, which is the process in the next section of the analysis.
Table 6.3 Test statistics and choice criteria for selecting the order of the VAR modelTo identify and test the relationships in (6.14) and (6.15), the next stage in development of the modelling process is to determine the number of cointegrating vectors along with a constant term and the dummy variable by examining the sequence of log-likelihood statistics that exposes the rank of the long-run multiplier matrix, as shown in Table 6.4. As expected, the statistics provide support for the existence of one cointegrating vector amongst the variables of interest, presented in Table 6.5. The results and the LR statistics for the testing of two, over-identifying restrictions, \(\chi^ \left( 2 \right) = 1.4100\) , are included. At the 95% critical value, \(\chi^\) with two degrees of freedom, the restrictions are accepted. It should be noted that the constant term with \(\left( + \hat_ > \right)/2\) does not add any statistical significance to the cointegrating vector.
Table 6.4 Cointegration with restricted intercept and no trend, log ratio test (LR) based on maximal and trace eigenvalues of the stochastic matrix
Table 6.5 ML estimation of cointegrating vector with restricted intercept and no trendOverall, the weight of statistical evidence suggests that the pure expectations theory of the term structure of interest rates does exist and that future values of interest play vital rôle in linking short- and longer-run rates on Treasury bills between three and six months in US economy. This is tentative, empirical evidence, suggesting that monetary policy may have an important function in determining the future direction of financial assets and pending aggregate demand and supply within the product market. This is an essential element of monetary policy and leads to a ripple effect on interest rates over time and within the term structure of interest rates. The transmission mechanism of monetary policy on saving could well exist!
