Electronic copy available at: http://ssrn.com/abstract=2078920

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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: gcnath@hotmail.com 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

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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

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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.

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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).

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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

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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%