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Electronic copy available at: http://ssrn.com/abstract=2078920
1
Predicting power of Yield Curve – A study of Indian sovereign yield spread
Golaka C Nath
Saurabh Pratap Singh Manoj Dalvi
Abstract
In recent years, there has been renewed interest in the yield curve as a predictor of future economic activity. In this paper, we re-examine the evidence for this predictor for the Indian market. The paper tries to indicate how the yield curve spread in a government securities market may be used to indicate the future economic activity in an economy like India. The slope of the yield curve has often been considered as a leading economic indicator. The study suggests that the yield curve spread measured by the difference in the spot rates of 10-year and 3 months have predictive power to estimate the economic activity in terms of Index of Industrial production. Using the yield curve data from 1997-2011, the study has found that the yield curve spread can be used to estimate future economic activity.
Key words: Predicting power of Yield Curve, Indian Yield Curve, Inflation expectation, Recession, Industrial Production, IIP, Yield Spread, Probit Model, Logit Model Corresponding author: [email protected] JEL Classification: C22, E37, E43
Electronic copy available at: http://ssrn.com/abstract=2078920
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1. Introduction
The pricing of fixed income instruments – both sovereign and corporate – is centered
around the yield curve. The yield curve is used not only by market participants but also by
the policy makers to figure out the scope of recession in particular and the shape of the
economy in general. Market participants take positions in the market assuming that a
unique interest rate is mapped to a specific maturity of a debt paper in a particular class
and combining all the possible maturities against their corresponding yields in the same
class results in a continuous curve that can be constructed that can describe the spot
interest rate for each maturity. This is commonly called term structure of interest rates and
very widely followed by all. As bonds of all maturities do not either exist or traded, it is a
common practice to use various methods like bootstrapping or well accepted term
structure models like Nelson, and Siegel, Nelson, Siegel and Svensson, Splines, etc. to
construct a reasonably correct yield curve to represent the state of interest rate in the
economy. Sovereign Bond yields are the building blocks of the term structure theories. It is
extremely important to have a well-developed sovereign bond market so that a reasonably
good sovereign yield curve can be constructed to helps banks to value their portfolio of
sovereign bonds. The term structure of interest rates has important place in the financial
market as all financial instruments are priced off the sovereign yield curve topping up with
appropriate credit spread for the class. The spot yield curves can be used to construct the
forward interest rates for various terms and these forward rates given expectation of the
market participants about the future. Hence these indications are used by central banks in
framing the monetary policy.
Simply put, a forward rate is an interest rate which starts on a future date for a particular
term and ends at a date beyond that. Typically, market participants use implied forward
rates estimated from the spot yield curve. This clearly implies that the spot curve’s shape
most likely reflects market participants’ expectation of future interest rates. This is the logic
of using spot rate to estimate the implied forwards. The information content and predictive
Electronic copy available at: http://ssrn.com/abstract=2078920
3
power of a spot curve is based on the above premise. Forward rates indicate market
participants’ of expected future inflation levels. Monetary authorities like central banks
have a preference to look up forward rates for policy analysis. The forward curve can be
split into short term and long-term segments in a more straightforward manner than the
spot curve as the spot represent the expected average of forward rates.
Because of the central role it plays in pricing debt instruments, the spot curve need to be
estimated with great deal of accuracy without which the valuation models will suffer from
mispricing leading to unstable book values for banks as well for the policy makers. Invariably
researchers use the government debt market as the basis for modelling the term structure.
This is because the government market is the most liquid debt market in any country, and
also because (in a developed economy) government securities are default-free, so that
government borrowing rates are considered risk-free.
The motivation for studying the yield spread is of manifold. First, policy makers often need
to make decisions today, based on expectations regarding future economic conditions.
Although policymakers rely on a range of data and methods in forecasting possible future
scenarios, movements in the yield curve have in the past proved useful, and could still
represent a useful additional tool. Second, variations in the correlations between asset
prices and economic activity might explain the workings of the macro-economy. Short term
interest rate is typically lower in an economic downturn because decreased economic
activity decreases private sector demand for credit; at the same time the monetary
authority is likely to have decreased the policy rate in response to the slowdown. Further,
the monetary authorities raise rates that precipitate the subsequent slowdown.
The purpose of this paper is to indicate how the yield curve spread in a government
securities market may be used to indicate the future economic activity in an economy. The
paper has been organized into sections to focus on some of the central aspects of the study.
Section II describes the justification for using the spot yield curve as vehicle for deriving
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forward rates, allowing us to conclude that a spot curve has predictive content. Section III
uses some historical examples of where curves predicted future short-rates, while section IV
demonstrates the predictive power of the yield curve, section V explains the linkage of
economic activity with spread, section VI demonstrates the Probit/Logit models using the
spread to figure out recession, and section VII gives the concluding remarks.
2. Yield Curve Concepts
The term structure of spot rates depict a very consistent bundle of discount rates for all
sovereign bonds through bonds observed prices are not consistent with the discount rates
due to many idiosyncratic factors pertaining to a bond. Many bonds depict observed prices
which are either rich or cheap to the curve due to bond specific reasons like liquidity, on-
the-run, off-the-run, coupon, outstanding issues, auction factors, etc. The spot rate is the
discount rate if a single future cash flow such as a T-bill. A multi period spot rate may be
bifurcated into a product of one year forward rates. Hence, a given term structure of spot
rates implies a specific term structure of forward rates – if the 1-year and 2-year spot rates
are given to us, we can easily figure out the annualized forward rate between 1 and 2 year.
To generalize, we can put the same as
Any forward rate can be blocked today by simply buying x-period bullet cash flow at price
⁄ and shorting ⁄ units of bullet of y-year at price
⁄ . The spot rate can also be construed as a special case of forward rate
with x=0 and hence .
Consistent with this approach, a market participant can take the observed prices (yields) of
the bonds traded in the market and construct an average representative sovereign YTM
curve using boot strapping. Using the said prices or yields, we can use various techniques
and models to estimate a term structure of spot rates from where we can construct the no-
arbitrage implied one-year forward rate streams for the market. Alternatively, we can think
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the sovereign YTM curve as Par curve in the sense if the YTM curve is perfect representation
of all information, and if Government decides to issue bonds across all maturities starting
with one year and ending with the last point of the curve with an in between gap of 1 year,
it will issue bonds at Par (100) with coupon equating with the yield. If Par curve would have
been available in the market, then it would have been the best possible scenario but due to
many idiosyncratic factors, we very rarely observe Par curves in emerging market like India.
Typically spot curve lies above the Par curve and forward is on top of spot. Order can be
reversed when the spot curve is inverted. Intuitively, characterization of one curve is
applicable to other curves. One year forward rates measure the marginal compensation for
extending the maturity of an investment by one year whereas the spot is an average reward
for the period. Hence spot rates are geometric average of one or more forward rates.
Similarly, Par rate is average of one or more spot rates. The forward rates can be seen as
break-even rates.
The spot and implied forward rate relationship can be best explained with an example.
Suppose, we have 1-year spot rate at 7.5% and 2-year spot rate at 8.0%. The implied
forward starting 1-year from now and ending 2-years from now (1-year from 1-year from
now) is 8.50%. That implies, an investor investing in a zero (FV=100) for 2 years will have a
value of 92.1639 at the beginning of second years. Using the spot rate, the present value of
the zero paper is 85.7339. Hence, the return for next year is ⁄ .
Tenor Spot Forward Value
1 7.50% 7.50%
2 8.00% 8.50%
Value at beginning of Second Year (F) 92.1639 Pf
Value at end of Today using spot rate for 2 years (S) 85.7339 Ps2
Return over next year 7.50% =Pf/Ps2
The above example gives the break-even level of one year future spot rate or the one year
forward rate starting one year from now and ending two years from now as 8.50%. One
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year rate has to increase by 100bps before the two-year zero underperforms the one year
zero over the next year. If one year rate increases by less than 100bps, the capital loss of
the two year zero will not fully compensate its initial yield advantage over the one year
spot. Implied forwards are also used to estimate level of flattening needed by a trader to
break even in a position.
The shape of the curve represents market expectation of future rate changes. A steeply
upward curve indicates near term tightening by the central bank or rising inflation. When
the market participants expect an upward change in the bond yield, the current term
structure becomes upward sloping so that any long term bonds’ yield advantage and
expected capital loss due to expected increase in yields exactly offsets each other. Similarly,
expectations of yield declines and capital gains will lower current long term bond yields
below the short term rates, making the term structure inverted. The market’s expectation
regarding the future level of rates influence the steepness of today’s yield curve, the
markets’ expectations regarding the future steepness of the yield curve influence the
curvature of today’s yield curve.
The spread (difference between short and long term yields) gives expectation about the
future interest rates movements. This can be used by the policy makers as an important
tool to frame policies to share the future of the economy by taking corrective measures.
Among economists, there is a strong interest in looking at the ability of financial variables
like bond yields to predict real economic variables, such as future economic growth (Estrella
and Mishkin 1995).
A number of financial variables could conceivably have predictive power, but one in
particular, the yield spread, has been shown in previous research to be a good indicator of
future economic activity. The yield spread is the difference between two different interest
rates – usually the rate of a long term bond minus the rate on a short term bond.
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3. Literature Review
Researchers, market participants as well as policy makers have long been searching for a
way to forecast accurately the turning points of recessions. Since the 1990s, many leading
indicators have been created to identify possible onset of recession. Kessel (1965) examined
the predictive ability of the yield curve. In an extensive survey of leading indicators, Stock
and Watson, in their1989 article, include the yield spread as a component of their leading
indicators index. They included two yield spreads in their proposed Index of Leading
Indicators – the spread between the return on 6- month commercial paper and the 6-month
Treasury bill, and the spread between the return on the 10-year Treasury and the 1-year
Treasury. In four early essays, Evans (1987), Laurent (1988, 1989) and Keen (1989) offer the
yield curve’s movements as a simple method for predicting real output. Bernanke and
Blinder (1992) employ a non-linear model that demonstrates the yield spread better
predicts real output than other monetary aggregates.
Haubrich and Dombrosky (1996), Ahrens (1999) and Phillips (1998/1999) compare the yield
curve with other leading indicators and find the yield curve to be better. Haubrich and
Dombrosky (1996), by using a linear model, find the yield spread to be a good predictor.
Ahrens (1999) and Phillips (1998/1999) use regime-switching models and find the yield
spread to be the most reliable and with the longest lead. In addition, Ahrens (1999) finds
the predictive ability of the yield spread has remained strong across the entire period of
M1:1959-M5:1995, in contrast to Bernanke and Blinder (1992) and Haubrich and
Dombrosky (1996).The above articles all caution that, while the yield spread has been a
helpful guide for monetary policy, it should not be used in isolation. Berk (1998) presents
the survey of papers examining the relationship between the yield curve and real output.
Estrella and Hardouvelis (1991) explored the usefulness of the term structure in predicting
performance farther out. Using as their measure of spread the difference between the 10-
year treasury rate and the 3-month T-Bill rate, they find that the spread has a strong
predictive power for real growth for horizons up to four years.
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The results of Estrella and Hardouvelis (1991) were confirmed by Plosser and Rouwenhorst
(1994. In 1995, Estrella and Mishkin tried to predict the occurrence of recession, a binary
dependent variable. While other studies has performed linear regressions, Estrella and
Mishkin used a probit model to see if a number of financial variables were useful in
predicting whether or not the economy would be in recession. Of the variables they
examined, the ones which performed best were the yield spread and the quarterly average
change in the NYSE. Between these two, the performance of the NYSE was particularly
strong over short time intervals of one and two quarters ahead, while the yield spread was
the most accurate indicator between three and six quarters ahead.
In addition to looking at a probit model to predict recession as opposed to a model which
predicts level of future growth, Estrella and Mishkin also looked at the out-of-sample
performance of their indicators. Of all the variables, they found that the most accurate
predictor out-of-sample was a composite of the NYSE and yield spread, with this composite
deriving much of its short term power from the NYSE and its longer term power from the
yield spread. Estrella and Mishkin show that, among financial variables and existing indexes
of leading indicators, the simple yield spread is the best predictor of a recession four to six
quarters in the future.
Estrella and Hardouvelis (1991) had shown that the relationship between real growth and
the yield spread was not necessarily policy invariant – changing monetary policy regimes
could cause the relationship to change. They also point out that the relationship may not
be stable over time. In order to address these issues, Estrella, Rodrigues, and Schich (2000)
explored the issue of stability of the relationship between the slope of the yield curve and
real output.
Feroli (2004) finds that the yield spread is related to the output gap, but that the
relationship is a function both of how strongly the monetary authority targets the output
gap and of how strongly the monetary authority insists on smoothing interest rate
9
movements. He also notes a break in the predictive power of the yield curve, contrary to
the work of Estrella, Rodrigues, and Schich (2000), with the start of the Volcker monetary
policy regime in 1979.
Wright (2006) argues that adding the short term rate strengthens the in-sample forecasting
results when using a probit model to predict recessions. Kucko and Chinn (2010) tested the
predictive power of the yield curve for both US and European countries across time. They
have found that the predictive power of the yield curve has deteriorated in recent times.
Kanagasabapathy and Goyal (2002) studied the predictive power of yield spread for Indian
economy and found that the index of industrial production (as a proxy for economic
activity) is positively correlated to yield spread. They found that the probability of slowdown
increases when the yield spread falls. However, their study covered a small period (April
1996 to July 2001). During the period, the bond market liquidity was very low and they have
used the monthly average secondary market yield to maturity on 10-year Gilts.
4. Yield Curve Data
The spot rate for Indian sovereign curve has been obtained using Nelson-Siegel functional
form. The historical spot rate data period is from Jul1997 to Aug 2011 (about 14 years). Data
sources are CCIL and NSE. The short term rate has been tracking the long term rates in India
for a very long time. Looking at a plot of the rate on the 10-year treasury against the rate on
the 3-month T-Bill, we see that the long rate has not been tracking the short rate recently
nearly as closely as it has historically. We can see from the graph that, during the most
recent period of releasing excess liquidity (and artificially bringing down the rates to low
level) and tightening due to increase in inflationary pressure, the 10-year rate did not track
the short rate up. The 10-year rate appears to be to be varying less in general since about
April’09. If the relationship between the 3-month rate and the 10-year rate has changed,
then the fundamental information carried in the spread might have changed only recently.
-------Insert Figure 2 about here -----
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The descriptive statistics of the spread data is given in Table-1. We have computed both
median and mean spread as well as slope and results show that average spread has the
lower standard deviation than the slope. Further, the median spread and slope are very
close to the mean spread and slope respectively. Hence we have used the mean spread in
our analysis.
------------ Insert Table 1 about here ---------- -----------------Insert Figure 3 about here -------------- --------------Insert Figure – 4 about here ----------------
In so far as the relation between yield curve and economic fundamentals are concerned,
one can have a rough idea using the famous IS-Curve framework. This equation defines the
equilibrium in Goods market and can be written as:
Here, Y= Income of Economy, C= consumption level which is a function of Income; I=
Investment in goods market which is a function of Interest rate and Income level; G=
Government expenditure; and NX=Net export which is a function of exchange rate,
domestic income and foreign income. Investment is the only term which is directly linked to
Interest rates so we have focused our study on relation between interest rates and
Investments. Going further, Investment is defined as:
Where = Autonomous investment and b=Interest rate sensitivity of investment. As seen
from the equation, Investment is inversely proportional to interest rates because when
interest rates go up it becomes costly for the firms to borrow for either capacity
enhancement or running day-to-day operation. As we know, short term bond rates (91-days
T-Bills, for instance) are more responsive to change in policy rates than long term bonds
(10-years) therefore with every single rise in policy rates by RBI, T-Bills rates go up but 10
Years-Bond rates may change marginally. This results in fall in the value of yield spread. It’s
very simple to comprehend therefore that yield spread bears positive relation with
Investment. It means, if yield spread is going down (Short-term rates are going high) then
Investment goes down because of the increase in cost of borrowing and vice-versa.
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In the figure, we can see that from March 2010, the Short term rates are constantly
increasing while the long term rates are more or less same. This has put pressure on the
Yield Spread which has reached to level of 0.14% in August 2011 (It was negative on Sep 22,
2011; Y.S. =-0.12%). The typical interpretation for negative yield spread ( is that in
the short end of the curve, we are expecting interest rates to go high to restrict the growth
and inflation. In the long end of the curve, we expect rates to fall because, investor
anticipates low inflation due to decrease in investment and consumption (Recession), so
inflation risk in long term drops and therefore, the long term rates.
5. Yield Spread and Index of Industrial Production:
Index of Industrial Production (IIP) tells us about the growth of various sectors of economy.
It’s normally categorized into two ways- one separates it into “Mining, Electricity,
Manufacturing and General” and other into “Basic Goods, Capital Goods, Intermediate
Goods and Consumer goods-Used based IIP”. The data is available on the official website of
RBI. The base used is 1993-94=100 instead of 2004-05=100 because in later base, we do not
have data prior to 2005-06 for obvious reasons. The data given on the website is monthly
basis and it’s converted to quarterly basis by simply taking arithmetic average of 3-months
data. The same is done for calculating “Average quarterly Yield Spread”. Monthly IIP is
equal to:
The respective weights are: =0.3557, =0.0926, =.2651, =.2866 (Summation=1.00) Based on the above calculation, we have plotted the graph of IIP-Quarterly from March
1997 to Jun-2011.This graph has some seasonal attributes, as can be seen by IIP coming
down on regular frequency. Usually, in every Quarter-1 of a financial year there is a drop in
IIP figure compared to the Quarter-4 of last financial Year. Besides, the volatility of the IIP
has increased in the recent past because of the unstable economic factors.
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----------------Insert Figure – 5 about here --------------------------- Though, there are statistically advanced and sophisticated methods available to deal with
seasonality but with a very simple and easy-to-apply approach we can deal with seasonality:
[
]
Where = Growth Rate of IIP on quarterly basis, t= Recent Quarter, t-4= same quarter in last
financial year. This equation enables us to calculate the growth rate of say, Apr-Jun 2005
quarter on the basis of Apr-Jun 2004. This gives us the annual growth rate; we can divide it
by 4 to get quarterly growth rates.
---------------Insert Figure 6 about here -----------------------
Now, in Figure 6 we have plotted Yield spread and IIP growth rate together. It’s quite
interesting to see that the graphs of IIP and Yield spread move almost together and in the
same direction. It proves the point we made during our discussion in previous sections that
Yield spread and IIP Growth rate are positively correlated with each other. The reasoning
for the same has already been discussed. One more important observation could be the
time-lag which is followed by IIP Growth rate. The rates change at present affects the
borrowing today which is used for future production and expansion plans. Therefore, if we
face rate hikes today then it’s going to affect investment and production with a significant
time lag.
6. Statistical Relation between Yield Spread and IIP:
Based on the Reasoning, data and graph we have seen, we can safely assume that there is a
relation between Yield Spread and IIP Growth rate. We would try to find this relation using
“Simple Bivariate Regression model”
Where, =IIP Growth rate of quarter ‘i’; =Intercept; =Slope of linear curve; and =Yield
spread of qtr ‘j’. i=j+k, (k=0, 1, 2, 3, 4,.., n) depending on its statistical significance.
13
We have run regression analysis for different forecast horizon to get the best possible fit for
our model. The summary of the analysis is given below in Table - 2;
-----------------------Insert Table – 2 about here ------------- Necessary adjustment has been done in the lag structure for correcting standard error for
the first order auto-correlation by including the autoregressive term as per the Chrochane-
Orcutt procedure. We have values of correlation coefficient, Alpha, Beta, R-Square and
Standard Error for different forecasting horizons (k=0, 1, 2, 3, 4) along with DW statistics.
We have stopped the process at k=3 because the value of R-square is close to zero. The best
possible forecasting horizon is k=1 with highest correlation coefficient (0.4027), highest R-
square (0.07). However, the values for k=2 is also closer to the values we obtained with k=1.
Therefore, we can use any of these forecasting horizons to forecast/predict the future IIP
Growth rate.
For instance, let’s assume that the yield spread of June 2009 quarter is equal to 4.19% and if
we use k=1, then the IIP Growth rate of Sep 2009 (over Sep 2008 on quarterly basis) should
be equal to= 1.35% + 0.1737*4.19% =2.08% (Real figure is 2.07%).
This relation (k=1, 2) can also be verified by looking carefully the graph of IIP Growth rate
and Yield spread. It’s easy to find that IIP Growth rate is lagging behind by one to two
quarters only. The difference between predicted value and actual (using k=1) is presented in
the graph below against the backdrop of normal distribution.
----------------------Insert Figure 7 about here ----------------------- 7. Probability of Recession:
As discussed in the previous sections, the main concern of all financial pundits is to predict
the state of economy for say 1-4 quarters ahead and plan accordingly. But this job is not
really easy. Even the yield spread predicts the economic indicators like IIP growth rates with
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average level of accuracy. The maximum explanation of IIP variance is 30% (value of R-
Square for k=1) which leaves the remaining 70% to other variables. But we would attempt
to figure out the possible percentage figure for recession in coming quarters using Yield
spread. The nature of outcome is Binary (Either recession or not) so we will use two
different models (see for reference:
http://irving.vassar.edu/faculty/wl/Econ210/LPMf02.pdf) suitable to deal with binary
outcomes, to calculate probabilities of recession for given forecast horizons.
a. Probit Model:
All variables stand for their standard notation. Last term is the error term.
{
( )
( )
Here, ( ) is cumulative distribution function of . In Probit Model, we assume that
the error term follows standard normal distribution;
This implies that ( )= Normsdist (
Probability of recession= Normsdist (
b. Logit Model:
All variables stand for their standard notation. Last term is the error term.
{
( )
( )
Here, ( ) is cumulative distribution function of we assume that the error term
does not follow Standard Normal Distribution but follows Logistic distribution. The
Probability density function (PDF) for logistic distribution is
And, the cumulative distribution function (CDF) is given by:
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( ) ( )
( )
------------------Table – 3 about here ----------------------- Using the above two equations, we have calculated Probability of recession for k=1 and k=2. The yield spread of quarter ending Jun 2011 is 0.81% which shows that the probability of
recession (or simply, negative growth rate of IIP) in Quarter ending Sep 2011 and Quarter
ending Dec-2011 is about 6.80% (according to Probit Model) and about 18.4% (according to
Logit Model). When we extend the data, the average yield of quarter ending Sep-2011(most
recent one) is around 0.20-0.30% and this gives the probability of recession in next 1-2
quarters, roughly equal to 8.04% (Probit model) and about 19.75% (Logit Model) which is
little high.
8. In-Sample & Out-of-Sample Analysis:
In-Sample analysis uses full sample in fitting the models of interest. It considers all the data
points available to build the model. However, Out-of-Sample fit is obtained from sequence
of recursive or rolling regression. Many academicians support “out-of-sample” fit simply
because they think that “in-sample” model has weaker predictive power and it often comes
up with spurious results (Campbell and Thompson (2004)). Granger (1990,p3) writes that
“one of the main worries of the present methods of model formulation is that the
specification search procedure produces model that fit the data spuriously well and also
makes standard techniques of inference unreliable”. However, we also have some
academicians who would prefer to use “in-sample” over “out-sample”- e.g. Inoue and Kilian
(2002).
The discussion though is not about the preference but the results we get from these two
models and their plausible inferences. One of the parameter which is very crucial in
evaluating these models is “Root Mean Square of Error”- (see Haubrich and Dombrosky).
16
This is nothing but the standard deviation of actual values and the values we have
calculated based on our model.
RMSE of Out-of-Sample:
Before, calculating RMSE of Out-of-Sample model, we need to discuss the process through
which we get the values of intercept and slope of this model. Hansen and Timmermann
(2011) discusses at length about how to split the given sample between “Estimation
sample” and “Evaluation sample”. Normally, we do not have any given set of formula
available to do so but we try to minimize the value of “p” of slope for different split points
and the minimum one is selected for modeling. In our case, we have about 48 data points
(small data sets are often not reliable) and we tried to split the sample for estimation and
evaluation purpose by regressing it for different split points. Hansen mentions in his paper
that the value of “p” is close to zero at the upper part of the sample size. Our result
confirms his point.
----------------------Insert Table 4 about here ---------------- Note: λ=24 is the optimal split point for the data and k=1 and k=2 are almost equally accurate
Then variance of the estimated value over real one is calculated. RMSE is calculated by the given formula:
√
∑
Value of RMSE (which is nothing but standard error) for “In-the-sample” can be taken
directly from the regression statistics table for k=1 and k=2.
RMSE (K=1) RMSE (K=2)
In-Sample 0.00718 0.00735
Out-Sample 0.00734 0.00764
It simply states that value of Root Mean Standard error (RMSE) for In-sample and Out-sample is
almost equal for k=1 and k=2. This model confirms that k=1 is slightly a better fit compared to k=2. It
also confirms that “In-sample” model offers a good explanation for variability in growth rate of IIP
17
and the results have been authenticated by the nearly equal value of RMSE of “Out-of-sample”
model. We can also conclude that “In-sample” regression analysis performs slightly better than
“out-of-sample” (Haubrich and Dombrosky).
9. Conclusion:
This paper has explored the importance of the yield spread in forecasting future industrial
production growth in India. Overall, when using the data series from 1997 to 2011, in‐
sample results suggest the yield spread is indeed important and has significant predictive
power when forecasting industrial production growth over a one‐year time horizon. The
data suggest the yield curve possess good deal forecasting power for Indian economy.
References Bonser‐Neal, Catherine and Timothy R. Morley. 1997. “Does the Yield Spread Predict Real Economic Activity? A Multicountry Analysis,” Federal Reserve Bank of Kansas City Economic Review 82(3), pp. 37‐53. Chen, Nai‐Fu. 1991. “Financial Investment Opportunities and the Macroeconomy,” Journal of Finance 46(2), pp. 529‐54. Council of Economic Advisors. 2009. The Economic Reoprt of the President Washington, DC: Government Printing Office. Davis, E. Philip and Gabriel Fagan. 1997. “Are Financial Spreads Useful Indicators of Future Inflation and Output Growth in EU Countries?” Journal of Applied Econometrics 12, pp. 701‐14. Davis, E. Philip and S.G.B. Henry. 1994. “ The Use of Financial Spreads as Indicator Variables: Evidence for the United Kingdom and Germany,” IMF Staff Papers 41, pp. 517‐25. Dotsey, Michael. 1998. “The Predictive Content of the Interest Rate Term Spread for future Economic Growth,” Fed. Reserve Bank Richmond Economic Quarterly 84:3, pp. 31‐51. Estrella, Arturo and Gikas Hardouvelis. 1991. “The Term Structure as a Predictor of Real Economic Activity,” Journal of Finance 46(2), pp.555‐76 Estrella, Arturo and Frederic S. Mishkin. 1997. “The Predictive Power of the Term Structure of Interest Rates in Europe and the United States: Implications for the European Central Bank,” European Economic Review 41, pp. 1375‐401.
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Estrella, Arturo; Antheony P. Rodrigues and Sebastian Schich. 2003. “How Stable is the Predictive power of the Yield Curve? Evidence from Germany and the United States,” Review of Economics and Statistics 85:3. Groen, Jan J.J. and George Kapetanios. 2009. “Model Selection Criteria for Factor‐Augmented Regressions,” Staff Report no. 363 (Federal Reserve Bank of New York, February). Hamilton, James D., and Dong Heon Kim. 2002. “A Reexamination of the Predictability of Economic Activity Using the Yield Spread,” Journal of Money, Credit and Banking 34(2), pp. 340‐360. Harvey, Cam 340‐360 pbell R. 1988. “The Real Term Structure and Consumption Growth,” J. Financial Economics 22, pp. 305‐333 Harvey, Campbell R. 1989. “Forecasts of Economic Growth from the Bond and Stock Markets,” Financial Analyst Journal 45(5), pp. 38‐45 Harvey, Campbell R. 1991. “The Term Structure and World Economic Growth,” Journal of Fixed Income (June), pp 7‐19. Haurbrich, Joseph G. and Ann M. Dombrosky. 1996. “Predicting Real Growth Using the Yield Curve,” Federal Reserve Bank of Cleveland Economic Review 32(1), pp. 26‐34. Koenig, Evan, Sheila Dolmas, and Jeremy Piger. 2003. “The Use and Abuse of ‘Real‐Time’ Data in Economic Forecasting,” Review of Economics and Statistics 85. Kozicki, Sharon. 1997. “Predicting Real Growth and Inflation with the Yield Spread,” Federal Reserve Bank Kansas City Economic Review 82, pp. 39‐57. Moneta, Fabio. 2003. “Does the Yield Spread Predict Recessions in the Euro Area?” European Central Bank Working Paper Series 294. Plosser, Charles I. and K. Geert Rouwenhorst. 1994. “International Term Structures and Real Economic Growth,” Journal of Monetary Economics 33, pp. 133‐56. Rudebusch, Glenn, Eric T. Swanson and Tao Wu. 2006. “The Bond Yield “Conundrum” from a Macro‐Finance Perspective,” Federal Reserve Bank of San Francisco Working Paper No. 2006‐16. Sarno, Lucio and Giorgio Valente (2009), “Exchange Rates and Fundamentals: Footloose or Evolving Relationship?," Journal of the European Economic Association 7(4), pp 786‐830.
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Smets, Frank and Kostas Tsatsaronis. 1997. “Why Does the Yield Curve Predicte Economic Activity? Dissecting the Evidence for Germany and the United States,” BIS Working Paper 49. Stock, James and Mark Watson. 1989. “New Indexes of Coincedent and Leading Economic Indicators,” NBER Macroeconomics Annual Vol. 4 pp. 351‐394. Stock, James and Mark Watson. 2005. “Implications of Dynamic Factor Models for VAR Analysis,” NBER Working Paper No. 11467 (July). Stock, James and Mark Watson. 2003. “Forecasting Output and Inflation: The Role of Asset Prices,” Journal of Economic Literature Vol. XLI pp. 788‐829. Warnock, Frank and Veronica Cacdac Warnock. 2006. “International Capital Flows and U.S. Interest Rates,” NBER Working Paper No. 12560. Wright, Jonathan. 2006. “The Yield Curve and Predicting Recessions,” Finance and Economic Discussion Series No. 2006‐07, Federal Reserve Board, 2006. Wu, Tao. 2008. “Accounting for the Bond‐Yield Conundrum,” Economic Letter 3(2) (Dallas: Federal Reserve Bank of Dallas, February).
20
Figure – 1:
Figure – 2:
Figure-3:
7.00%
7.50%
8.00%
8.50%
9.00%
9.50%
10.00%
10.50%
11.00%
11.50%
12.00%
1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0
Par Spot Forward
2.5
4.5
6.5
8.5
10.5
12.5
14.5
Jan
-97
Au
g-9
7
Mar
-98
Oct
-98
May
-99
De
c-9
9
Jul-
00
Feb
-01
Sep
-01
Ap
r-0
2
No
v-0
2
Jun
-03
Jan
-04
Au
g-0
4
Mar
-05
Oct
-05
May
-06
De
c-0
6
Jul-
07
Feb
-08
Sep
-08
Ap
r-0
9
No
v-0
9
Jun
-10
Jan
-11
Au
g-1
1
Axi
s Ti
tle
Interest Rate Movement - 3 Months Vs 10 Yr
91D Tbills 10YR YLD
21
Figure – 4:
Figure – 5:
-0.0075
0.0025
0.0125
0.0225
0.0325
0.0425
0.0525
Jan
-97
Jul-
97
Jan
-98
Jul-
98
Jan
-99
Jul-
99
Jan
-00
Jul-
00
Jan
-01
Jul-
01
Jan
-02
Jul-
02
Jan
-03
Jul-
03
Jan
-04
Jul-
04
Jan
-05
Jul-
05
Jan
-06
Jul-
06
Jan
-07
Jul-
07
Jan
-08
Jul-
08
Jan
-09
Jul-
09
Jan
-10
Jul-
10
Jan
-11
Jul-
11
spre
ad/s
lop
e (%
) Spread and Slope
avgsp avgslp medsp medslp
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
Jan
-97
Au
g-9
7
Mar
-98
Oct
-98
May
-99
De
c-9
9
Jul-
00
Feb
-01
Sep
-01
Ap
r-0
2
No
v-0
2
Jun
-03
Jan
-04
Au
g-0
4
Mar
-05
Oct
-05
May
-06
De
c-0
6
Jul-
07
Feb
-08
Sep
-08
Ap
r-0
9
No
v-0
9
Jun
-10
Jan
-11
Au
g-1
1
Movement of Rates and Spread
avgsp Y3M Y10
22
Figure – 6
Figure – 7:
125
175
225
275
325
375
425Ja
n-9
7
Jul-
97
Jan
-98
Jul-
98
Jan
-99
Jul-
99
Jan
-00
Jul-
00
Jan
-01
Jul-
01
Jan
-02
Jul-
02
Jan
-03
Jul-
03
Jan
-04
Jul-
04
Jan
-05
Jul-
05
Jan
-06
Jul-
06
Jan
-07
Jul-
07
Jan
-08
Jul-
08
Jan
-09
Jul-
09
Jan
-10
Jul-
10
Jan
-11
IIP
IIP
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
Mar
-97
Oct
-97
May
-98
De
c-9
8
Jul-
99
Feb
-00
Sep
-00
Ap
r-0
1
No
v-0
1
Jun
-02
Jan
-03
Au
g-0
3
Mar
-04
Oct
-04
May
-05
De
c-0
5
Jul-
06
Feb
-07
Sep
-07
Ap
r-0
8
No
v-0
8
Jun
-09
Jan
-10
Au
g-1
0
Mar
-11
Movement of Qtrly IIP growth vs Yld spread
IIPG Sprd
23
Table-1:
Parameters Mean Standard deviation
Average spread 1.6922 1.0279
Average slope 1.7356 1.0543
Median spread 1.6996 1.0273
Median slope 1.7432 1.0536
Figure – 2
Lags Alpha p-val SE beta SE p-val R2 DW Corr RMSE
Lag k= 0 0.015 0.0001
0.00231 0.076 0.089 0.4 0.014 1.73 0.295 0.00757
Lag K=1 0.0135 0.0001
0.00245 0.174 0.091 0.062 0.067 1.721 0.403 0.00718
Lag k=2 0.015 0.0001
0.00239 0.11 0.088 0.216 0.031 1.787 0.365 0.00735
Lag K=3 0.01605 0.0001
0.00234 0.07 0.085 0.412 0.014 1.935 0.192 0.00781
Table – 3:
-0.0225 -0.0175 -0.0125 -0.0075 -0.0025 0.0025 0.0075 0.0125 0.0175 0.0225 0.0275
0
5
10
15
20
25
30
35P
erc
ent
Error
Yield Spread Probit Model Logit Model
Lag -> k=1 k=2 k=3 k=1 k=2 k=3
1.67 5.05% 4.62% 4.26% 16.25% 15.67% 15.17%
1.21 5.94% 5.13% 4.56% 17.36% 16.35% 15.59%
0.81 6.80% 5.60% 4.84% 18.38% 16.95% 15.96%
0.46 7.64% 6.05% 5.09% 19.31% 17.50% 16.30%
0.30 8.04% 6.26% 5.21% 19.75% 17.76% 16.45%
24
Table-4:
λ=Split Point
Out-of-the Sample Analysis
Different λ Alpha p-value Beta p-value R-square
k=1,λ=12 0.634892 0.116329 0.411431 0.056433 0.317448
k=1,λ=20 0.36978 0.186514 0.523212 0.004012 0.376444
k=1,λ=24 0.531427 0.050367 0.454241 0.00813 0.277835
k=1,λ=36 1.540792 4.50E-06 0.000982 0.99569 8.71E-07
Different k Alpha p-value Beta p-value R-square
k=1,λ=24 0.531427 0.050367 0.454241 0.00813 0.277835
k=2,λ=24 0.489666 0.063197 0.486227 0.004188 0.316846
k=3,λ=24 0.842582 0.006867 0.258259 0.147069 0.093116
0.20 8.31% 6.40% 5.28% 20.02% 17.92% 16.55%
-0.17 9.33% 6.93% 5.57% 21.07% 18.52% 16.91%
-0.50 10.33% 7.42% 5.83% 22.04% 19.07% 17.24%
-0.82 11.36% 7.93% 6.10% 23.01% 19.62% 17.56%
-1.13 12.43% 8.44% 6.37% 23.98% 20.16% 17.88%
-1.46 13.65% 9.01% 6.66% 25.04% 20.75% 18.22%
-1.85 15.18% 9.73% 7.02% 26.33% 21.47% 18.63%
-2.40 17.54% 10.81% 7.56% 28.23% 22.50% 19.22%