Appendix 1

Memorandum

Working Group on Economic Indicators

In view of the changing dimensions of the Indian Economy with increasing openness and market orientation, it has been decided to set up a Working Group on "Economic Indicators" to suggest suitable approaches for research on relevant economic indicators.

2. The Terms of Reference of the Working Group are:

1. To suggest methodology for studying business cycles in the Indian context;
2. To suggest methodology for working out composite leading, coincident and lagging indicator;
3. To suggest ways for improving information base relevant for leading indicators of economic activity, including appropriate surveys on inventories at the level of manufacturers and distributors;
4. To examine the feasibility of studies on capacity utilisation in major industries;
5. To consider any other related matter/s.

The constitution of the Working Group would be as follows:

Dr. R.B.Barman	Convenor
Executive Director
Reserve Bank of India
Prof. Dilip Nachane	Member
Department of Economics,
University of Mumbai,
Vidyanagari Marg,
Mumbai – 400 098.
Prof. M.J.Manohar Rao	Member
Professor & Director,
Department of Economics,
University of Mumbai,
Vidyanagari Marg,
Mumbai – 400 098.
Dr. S.L.Shetty	Member
Director,
EPW Research Foundation,
Mumbai – 400 101.
Dr. Saumitra Chaudhary	Member
Economic Advisor & Research Co-ordinator
ICRA Limited
New Delhi – 110 001.
Dr. Ila Patnaik	Member
National Council of Applied Economic Research
11, Indraprastha Estate,
New Delhi – 110 002.

3. The Working Group may, if necessary, invite other persons for specific deliberations. The Bank will reimburse expenses on travel, transport and incidentals for non-official members for attending the meetings of the Working Group.

4. The Working Group could draw resource persons from the Department of Economic Analysis and Policy (DEAP), Department of Statistical Analysis and Computer Services (DESACS) and Monetary Policy Department (MPD).

5. The Working Group may submit its Report within four months from its first meeting*.

6. DESACS would provide secretarial assistance to the Working Group.

Sd/-
(Y.V.Reddy)
Deputy Governor

October 10, 2001

---

* The term of the Working Group was subsequently extended up to end-June 2002.

Appendix 2

Compilation of a Composite Leading Indicator for India:
An Illustrative Exercise

1. The official estimates of quarterly GDP in India are available since April-June 1996. As the exploratory exercise require larger time horizon for tracking the cyclical movements, it was decided to use the Index of Industrial Production (IIP) as an alternative choice though it represents only 24% share in GDP. However, the services sector account for nearly half of the GDP and their cyclical pattern is not likely to be different from that of Industry, as demand for services are likely to be synchronous with the industrial production. Research work on the interlinkages of these three sectors has also found that changes in the industrial sector have greater influences on the services sector.

2. Sometimes, changes in certain economic variables may superficially precede changes in other economic variables and the leading series may produce false signals of future changes or may produce contradicting signals. According to Zarnowitz (1992) "To increase the chances of getting true signals and reduce those of getting false ones, it is advisable to rely on a reasonably diversified group of leading series with demonstrated predictive potential." In addition, practical problems like measurement errors in preliminary data used for giving forecasts and occasional presence of high noise in individual variables, also argue in favour of using a composite index of leading indicators rather than relying on a single leading indicator. An attempt has been made to construct a composite leading indicator for IIP to predict six-month ahead movement of IIP.

3. Traditionally, seasonal adjustment was developed as a tool for analysing seasonal economic time series in the absence of suitable statistical and economic models for such series. In recent years, as new modelling procedures have become available, the reasons for seasonal adjustment have become debatable. The seasonal adjustment procedures (e.g., X-11 or its other variants) start by decomposing the series into trend, cycle, seasonal and irregular component with the underlying assumption that these three components are orthogonal and the components are fixed (non-stochastic). However studies by Miron (1996) and Franses (1996) show that both the assumptions, in general, do not conform to reality. The seasonal fluctuations in many quarterly or monthly observed macroeconomic time series do not appear to be constant over time. Sometimes changes in seasonality are so pervasive that there is evidence for seasonal unit roots in several economic variables [Hylleberg, Engle, Granger and Yoo (1990)]. On the other hand, for several macroeconomic series it appears that the seasonal fluctuations and non-seasonal fluctuations are not independent, in the sense that one may observe different seasonal fluctuations in business cycle expansion periods from those in recession periods. Miron (1996) shows that seasonal and business cycle fluctuations are driven by similar economic propagation mechanisms and also show that seasonal fluctuations raise many of the same questions for welfare and policy analysis as do business cycle fluctuation. This interdependency of the components violates the key assumption of seasonal adjustment methods that one can identify independent seasonal and non-seasonal components. Moreover, when seasonally adjusted data are used, Ghysels (1990) and Ghysels and Perron (1993) show that there are many well-known undesirable effects produced by seasonal adjustment filters. The adjusted series are smoothed series. The smoothing most likely induces higher persistence in the series and higher first order autocorrelation. Lead-lag relationships are disturbed because adjustment filters (including X-11-ARIMA) are generally two sided. The finding of Ghysels and Perron (1993) shows that consistency of the OLS estimates is not preserved with lagged dependent variables, when all variables are seasonally adjusted. In the light of these controversies, unadjusted data series has been used.

4. It has been attempted to analyse growth rate cycles as opposed to study the classical business cycle. Since business cycle is more often studied with GDP as the reference series, it requires expansion in aggregate GDP at the time of boom and contraction (absolute declines) at the time of recession. However, IIP being an index generally does not decline in absolute sense, which, in turn, necessitates the analysis of cycles in growth rates rather than cycles in the level. By calculating growth rates, the problems involved in removing trend (band pass etc) do not arise, as generally growth rates are stationary. As quarterly or monthly growth rates are more erratic in nature, the present work has been confined to the annual (point-to-point) growth rates.

Selection of Leading Indicators

5. At the outset, 43 indicators have been chosen based on economic considerations. The list of variables has been given in Appendix 2.1. The entire data set, ranging from April 1992 to January 2002, has been divided into two subsets, viz., estimation set and validation set. The estimation set has been taken from April 1992 to October 1999 and validation set has been considered from November 1999 to January 2001 having 15 observations.

6. From this set of 43 indicators, finally only six Indicators have been selected based on cross correlation (up to lag 12) with the Index of Industrial Production. Cross Correlation, which essentially is simple product moment correlation between the indicator and the target series for various leads, projects the quality of the indicators as potential leading Indicators. Appendix 2.2 provides such cross correlation table for all these 43 indicators. However, since signs of some cross correlations do not conform to economic rationale, on the basis of the proper sign of the cross correlation, finally, 6 leading indicators (for lead period of at least six months) have been considered for the construction of composite index. Significance of cross-correlations has been evaluated adopting 0.1568 (=1.645/, where n, the no. of observations=110) as the critical value. Appendix 2.3 provides all these six indicators along with their cross correlation with the target series IIP. The Group, however, recognises that this is an illustrative exercise and it may be possible to have additional indicators.

7. In common belief, M1 and Non-food credit should not be considered simultaneously. However, since the inclusion of these two series does not pose any serious multicollinearity problem, both these series have been taken into account together. It may be noted here that initially Net Foreign Exchange Assets with RBI (NFC) was considered. However, as far as Methods 2 and 3 (described later) are concerned, the inclusion of NFC, which turns out to be statistically insignificant, does not improve the forecast performance. Moreover, it creates serious multicollinearity problem in Method 2. Silver price has not been considered due to confusion over the proper sign.

8. To get a better feel of the appropriateness of such selection, graphs of growth rates have been provided in Appendix 2.4. There are six plots, each plot providing visual inspection of the lead lag relationship with the IIP growth rats.

The Composite Leading Indicator

9. Out of the several variables possessing information about the future movement of industry growth, no single series can be said to definitely precede the expansionary and contractionary phases of business cycles/ growth cycle. Therefore, " to increase the chances of getting true signal and to reduce those of getting false ones, it is advisable to rely on a reasonably diversified group of leading indicators with demonstrated predictive potential" [Zarnowitz (1992)]. Moreover, the effect of outlier, high noise in some variables, etc., can be eliminated by taking combinations of several variables. It is, thus, perceived that an index composed of several of these leading series, selected from a variety of economic processes, may provide a better indication of future activity than any one particular series. Moreover, such composite leading indicator approach has the appeal of dimension reduction, and hence simplifies the underlying modelling strategy. Econometric models, e.g., Vector Autoregressive (VAR) considering all the leading variables may require estimating a large number of parameters, which in practice, may not be feasible.

10. The selected series are combined into one single Index, which is called the composite leading Indicator. Usually a weighted sum of the series is used for the purpose. Sometimes, the aggregation of important Economic Indicators (EI) are done by constructing a ‘diffusion Index’, which measures the proportion of indicators of economic activity in the overall economy that are experiencing expansion over a given span of time.

11. Another popular method of summarizing the information content of various Indicators is to apply ‘Principal Component’ Analysis (PCA). PCA is, however, a purely statistical procedure that yields one or more linear combinations of the series that explain major parts of the variations. Though PCA has a solid statistical background, the interpretations of the weights are often not very clear (Bikker and Kennedy, 1999, Samanta 2000). An alternative method is based on rigorous econometric modelling. A possible approach (Simone 2001) is "general to specific" modelling approach using distributed lags of several variables.

12. Three different methodologies have been considered for constructing the composite index. These are

Method 1: Taking simple average of the indicators so chosen,

Method 2: Regression based composite Index, with regression parameters as the weights for the composite index and where the regression analysis has been done with respect to the original growth series and not the standardised series and

Method 3: PCA based Composite Index. A detailed discussion of the three methods is presented in Appendix 2.5.

13. After the construction of the composite index next task is to evaluate the performance of its out-of-sample forecasts. Performance mainly refers to the closeness of the predicted with the actuals. To test the forecasting accuracy of the composite indicator, we can use the usual distance measures like Root Mean Square Percentage Errors (RMSPE), Mean Absolute Error (MAE), Mean Square Error (MSE) and Mean Absolute Percentage Errors (MAPE) can be used. However, for our analysis we confine to MSE and MAE as performance criteria.

14. The forecast performance of the different methods is presented in Table 2.6A of Appendix 2.6. They indicate that Method 2 is relatively superior as compared to the other two methods with respect to both point wise forecast performance and direction. Here, it needs to be mentioned that for both the methods if the insignificant variables are excluded, forecast performances relatively worsens. Table 2.6B provides a comparative analysis of various method-based forecasts with the actuals. One important observation, which needs to be emphasised, is that both money supply and non-food credit have significant positive effect on industrial output.

15. As in the context of monthly series, the same set of six indicators, viz., Narrow Money (M1), Non-food-credit (NFC), WPI-Raw materials (WPIIR) Production of Aluminium (Alu), Rails good traffic Originated (Gtr) and Production of Coal (Prod. Coal) have been considered in an empirical exercise based on quarterly data. Data period is from April 1993 to December 2000, whereas monthly series data were considered from April 1993 to January 2001.

16. The OLS results using quarterly data are summarized in Table 2.7A, which shows that only non-food credit is the significant variable. However, the other variables have not been dropped as forecast performances became relatively worse and DW statistic deteriorated when they are not included in the equation.

17. Comparing the results, it is observed that the in-sample performances of the quarterly data based results are better than the monthly data based results. Table 2.7C summarises the forecast (out of sample) performances of both quarterly as well as monthly series based forecasts. Forecasts are for two quarters (six months) ahead. The criteria used are mean square error (MSE) and Mean absolute error (MAE) and per cent of correct direction.

Appendix 2.1: Initially-selected 43 Indicators based on Economic Considerations

Variable Name	Unit
Broad Money (M3)	In Rs.Crores
Narrow Money (M1)	In Rs.Crores
Reserve Money (RM)	In Rs.Crores
Currency with public (CWP)	In Rs.Crores
Aggregate Deposit (AD)	In Rs.Crores
Non-food credit (NFC)	In Rs.Crores
Bank credit (BC)	In Rs.Crores
Investment Deposit Ratio (IDR)	Per cent
Net foreign exchange asset with RBI (NFE)	In Rs.Crores
Call money rate (CMR)	% Per annum
Real Bank Rate (BR) **	% Per annum
Real Prime lending Rate (PLR) **	% Per annum
Exchange rate (Dollar Vs. Rs.) (ER)
REER
US$ vs. Yen Exchange rate (ERY)
US$ vs. Pound Exchange rate (ERP)
Export	In US $
Import	In US $
Stock of Foodgrains with Government (FCI)*	In Million Tonnes
SENSEX	Index
Gold Price (Mumbai)(GP)	Rs per 10 grams
Silver Price (Mumbai) (SP)	Rs. Per Kilogram
International Oil price (Dubai) (IOP)	In US$ per Barrel
Dow-Jones Stock Price Index (DW)	Index
Registered Unemployment* (UMP)	Thousand Number
WPI All Commodities (WPI)	Index (1993-94=100)
WPI Manufactured Products (WPIMP)	Index (1993-94=100)
WPI Food Article (WPIFA)	Index (1993-94=100)
WPI Industrial Raw Material (WPIIR)	Index (1993-94=100)
CPIIW	Index (1982=100)
No. of Commercial Vehicle production* (CVP)	Thousand Number
Production of Steel* (steel)	Thousand Number
Production of Cement* (Cement)	Thousand Number
Production of Aluminium* (Alu)	Tonnes
Electricity-Total (Elec)*	Mn. Kwh
Hydro-Electricity (Hyelec)*	Mn. Kwh
Thermal Electricity (Thelec)*	Mn. Kwh
Railway Goods Traffic Originating* (Gtr)	Crores Tonnes
Railway Gross Earnings*	Rs. Crores
Tourists *	Number
Production of Coal*	Lakhs tonnes
Sale of Coal*

Note: All data except those marked with * are from April 1982 to October 2001 and data corresponding to (*) is from April 1992 to January 2001.

** Real interest rates are computed as nominal interest rates less WPI - All Commodities based inflation rate in this exercise

Appendix 2.2: Cross-Correlation in Growth Rates with IIP-lags

Variable \ Lag

1

2

3

4

5

6

7

8

9

10

11

12

Broad Money (M3)

0.08

0.07

0.05

0.08

0.09

0.11

0.1

0.1

0.1

0.12

0.16 *

0.18 *

Narrow Money (M1)

0.32 *

0.28 *

0.23 *

0.27 *

0.23 *

0.21 *

0.19 *

0.13

0.13

0.09

0.07

0.05

Reserve Money (RM)

0.18*

0.14

0.02

-0.05

-0.07

-0.15

-0.18 *

-0.22 *

-0.28 *

-0.27 *

-0.29 *

-0.33 *

Currency with public (CWP)

0.45 *

0.39 *

0.33 *

0.30 *

0.24 *

0.19 *

0.12

0.03

-0.02

-0.07

-0.05

-0.03

Aggregate Deposit (AD)

0.08

0.11

0.15

0.18 *

0.20 *

0.23 *

0.24 *

0.26 *

0.29 *

0.30 *

0.33 *

0.32 *

Non-food credit (NFC)

0.39 *

0.43 *

0.45 *

0.46 *

0.44 *

0.44 *

0.42 *

0.40 *

0.39 *

0.35 *

0.33 *

0.29 *

Bank credit (BC)

0.32 *

0.36 *

0.37 *

0.38 *

0.36 *

0.35 *

0.33 *

0.31 *

0.29 *

0.26 *

0.25 *

0.22 *

Investment Deposit Ratio (IDR)

-0.18 *

-0.20 *

-0.19 *

-0.2 *

-0.22 *

-0.18 *

-0.21 *

-0.21 *

-0.21 *

-0.20 *

-0.23 *

-0.22 *

Net foreign exchange asset with RBI (NFE)

0.39 *

0.43 *

0.45 *

0.46 *

0.44 *

0.44 *

0.42 *

0.4 *

0.39 *

0.35 *

0.33 *

0.29 *

Exchange rate (Dollar Vs.Rs.) (ER)

-0.01

-0.02

-0.01

0.02

0.06

0.08

0.03

-0.01

-0.03

-0.06

-0.1

-0.1

REER

-0.05

-0.12

-0.19 *

-0.18 *

-0.26 *

-0.22 *

-0.19 *

-0.22 *

-0.20 *

-0.17 *

-0.15

-0.11

US$ vs. Yen Exchange rate (ERY)

0.09

0.08

0.13

0.18 *

0.22 *

0.26 *

0.24 *

0.21 *

0.17 *

0.17 *

0.20 *

0.21 *

US$ vs. Pound Exchange rate (ERP)

0.09

0.20 *

0.29 *

0.36 *

0.43 *

0.47 *

0.50 *

0.52 *

0.54 *

0.57 *

0.57 *

0.54 *

Export

0.24 *

0.28 *

0.20 *

0.09

0.09

-0.01

0.04

-0.06

-0.09

-0.12

-0.18 *

-0.19 *

Import

0.27 *

0.26 *

0.20 *

0.14

0.07

0.02

0.08

0.04

0.01

-0.08

-0.16 *

-0.19 *

Stock of Foodgrains with Government (FCI)

-0.13

-0.18 *

-0.21 *

-0.26 *

-0.27 *

-0.31 *

-0.34 *

-0.35 *

-0.37 *

-0.36 *

-0.38 *

-0.37 *

SENSEX

0.04

0.05

0.05

0.02

0

-0.01

-0.05

-0.06

-0.07

-0.13

-0.18 *

-0.24 *

Gold Price (Mumbai) (GP)

0.19 *

0.19 *

0.16 *

0.15

0.19 *

0.15

0.11

0.07

0.03

-0.07

-0.12

-0.18 *

Silver Price (Mumbai) (SP)

0.42 *

0.47 *

0.47 *

0.43 *

0.47 *

0.39 *

0.35 *

0.28 *

0.19 *

0.04

-0.14

-0.25 *

International Oil price (Dubai) (IOP)

0.15

0.19 *

0.24 *

0.25 *

0.29 *

0.27 *

0.29 *

0.29 *

0.27 *

0.28 *

0.25 *

0.21 *

Dow-Jones Stock Price Index (DW)

0.36 *

0.29 *

0.25 *

0.25 *

0.19 *

0.18 *

0.11

0.1

0.07

0.06

0.02

0.05

Registered Unemployment (UMP)

-0.02

0.03

0.08

0.11

0.13

0.2

0.21 *

0.19 *

0.22 *

0.24 *

0.27 *

0.29 *

Note : * denotes significance of correlation coefficient at 5 % level of significance

(Contd.)

Appendix 2.2: Cross-Correlation in Growth Rates with IIP-lags (Concl.)

Variable/ Lag	1	2	3	4	5	6	7	8	9	10	11	12
WPI-All Commodities (WPI)	-0.03	-0.01	0.05	0.08	0.1	0.15	0.18 *	0.22 *	0.25 *	0.26 *	0.24 *	0.22 *
CPIIW	-0.15	-0.15	-0.14	-0.14	-0.15	-0.1	-0.1	-0.09	-0.09	-0.08	-0.1	-0.12
WPI Manufactured Product (WPIMP)	-0.14	-0.18 *	-0.23 *	-0.28 *	-0.32 *	-0.32 *	-0.35 *	-0.37 *	-0.38 *	-0.39 *	-0.40 *	-0.41 *
WPI Food Article (WPIFA)	-0.17 *	-0.14	-0.04	0.01	0.07	0.14	0.19 *	0.27 *	0.33 *	0.39 *	0.38 *	0.37 *
WPI Industrial Raw Material (WPIIR)	-0.16 *	-0.19 *	-0.18 *	-0.17 *	-0.18 *	-0.17 *	-0.17 *	-0.18 *	-0.18 *	-0.20 *	-0.22 *	-0.21 *
No. of Commercial Vehicle production (CVP)	0.16 *	0.16 *	0.17 *	0.13	0.15	0.06	0.14	0.06	0.07	0.07	0.01	-0.02
Production of Steel (steel)	0.20 *	0.13	0.05	0	-0.06	-0.08	-0.14	-0.15	-0.18 *	-0.19 *	-0.16 *	-0.12
Production of Cement (Cement)	0.24 *	0.13	0.19 *	0.12	0.17 *	0.07	0.12	-0.01	-0.09	-0.14	-0.19 *	-0.08
Production of Aluminium (Alu)	0.21 *	0.18 *	0.13	0.21 *	0.25 *	0.21 *	0.15	0.13	0.18 *	0.17 *	0.21 *	0.09
Electricity-Total (Elec)*	0.22 *	0.14	0.04	-0.03	-0.03	-0.13	-0.01	-0.09	-0.1	-0.16 *	-0.28 *	-0.22 *
Hydro-Electricity (Hyelec)	-0.26 *	-0.27 *	-0.32 *	-0.33 *	-0.28 *	-0.21 *	-0.05	-0.08	-0.04	-0.1	-0.08	-0.05
Thermal Electricity (Thelec)	0.41 *	0.34 *	0.28 *	0.22 *	0.18 *	0.03	0.03	-0.02	-0.06	-0.08	-0.22 *	-0.17 *
Railway Goods Traffic Originating* (Gtr)	0.36 *	0.42 *	0.29 *	0.31 *	0.24 *	0.20 *	0.16 *	0.14	0.07	0	-0.03	0.01
Railway Gross Earnings	0.15	0.03	0.02	-0.05	-0.05	-0.04	-0.11	-0.13	-0.16 *	-0.19 *	-0.19 *	-0.06
Tourists	0.16 *	0.16 *	0.17 *	0.13	0.15	0.06	0.14	0.06	0.07	0.07	0.01	-0.02
Production of Coal	0.27 *	0.32 *	0.25 *	0.32 *	0.25 *	0.33 *	0.34 *	0.32 *	0.32 *	0.18 *	0.15	0.1
Sale of Coal	-0.20 *	-0.13	-0.12	-0.17 *	-0.11	-0.15	-0.06	-0.08	0	-0.01	0.01	0
Call money rate (CMR)	0.33 *	0.43 *	0.35 *	0.36 *	0.32 *	0.34 *	0.30 *	0.17 *	0.14	0.09	0.05	-0.01
Real Bank Rate (BR)	0.22 *	0.23 *	0.22 *	0.22 *	0.24 *	0.20 *	0.22 *	0.21 *	0.21 *	0.21 *	0.21 *	0.22 *
Real Prime lending Rate (PLR)	0.32 *	0.33 *	0.33 *	0.32 *	0.33 *	0.28 *	0.28 *	0.26 *	0.26 *	0.24 *	0.24 *	0.25 *

Note : * denotes significance of correlation coefficient at 5 % level of significance

Appendix 2.3: Finally Selected Indicators for Construction of

Composite Index of Leading Indicators

Variable	Lead period (in months) for Composite Index
M1	6 (0.21)
Non food credit	6 (0.44)
WPI-Raw materials	11 (-0.17)
Prod. Of Aluminium	6 (0.21)
Rails good traffic originated	6 (0.20)
Prod. Of Coal	6 (0.33)

Note: Cross correlations are given in parenthesis (). The sign of the correlation indicates the nature of relationship with IIP.

Appendix 2.4

 

(Figures 1 - 6 are on the same time point, e.g.,IIP_t vs. M_1t, whereas

Figures 7 - 12 are on the lead-lag, e.g., IIP_t vs M_1(t-6))

 

Appendix 2.5: Methodologies for Construction of Composite Indicator

Method 1

Let and be two leading indicators with lead period and , respectively. Then the composite leading index for the target series for the time period is . This combination is formed with respect to the standardised series. This technique gives unequal weight inversely proportional to the standard deviation of the corresponding series. However, forecasts are given for the original growth series using inverse transformation.

Method 2

Here the focus is on the fitted regression line. The linear regression, which looks like:

is estimated by ordinary Least Square (OLS) method. The estimated OLS equation is as follows:

The OLS results are summarized in Table 2.5A, which shows that intercept, WPI for Industrial Raw Material (WPIIR), Production of Aluminium (Alu), Railway Goods Traffic Originating (Gtr) and Production of Coal (Coal) are insignificant. However, these variables have not been dropped as forecast performances became worse and DW statistic deteriorated after dropping them. Results of OLS after dropping these insignificant variables are presented in Table 2.5B.

 

Table 2.5 A: OLS Results Corresponding to the IIP equation

Coefficients and Different Test Statistics*	Different Explanatory Variables
	Intercept	M1	NFC	WPIIR	Alu	Gtr	Coal
Coefficient	-1.58	0.30	0.27	0.04	0.005	-0.08	-0.06
t-statistics	-0.82 (1.65)	2.44 (1.65)	3.57 (1.65)	0.58 (1.65)	0.17 (1.65)	-0.69 (1.65)	0.75 (1.65)
Hansen’s test (l)	0.14 (0.47)	0.16 (0.47)	0.21 (0.47)	0.25 (0.47)	0.26 (0.47)	0.60 (0.47)	0.27 (0.47)
Model criteria	R2=0.38; R2 (adjusted)=0.33; DW= 0.90; F= 7.397
Hansen’s test (l) for variance	0.73 (0.47)
Hansen’s Joint test (Lc)	3.79 (2.11)
Condition Number (test for Multicollinearity)	16.94 (20-above) signal for danger due to multicollinearity

Note: 5% critical values are given in brackets

Table 2.5 B: OLS Results for Significant Variables

Coefficients and Different Test Statistics*	Different Explanatory Variables
	Intercept	M1	NFC
Coefficient	-2.00	0.34	0.25
t-statistics	-1.49 (1.65)	4.73 (1.65)	4.26 (1.65)
Hansen’s test (l)	0.12 (0.47)	0.18 (0.47)	0.18 (0.47)
Model criteria	R2=0.35; R2 (adjusted)=0.33; DW= 0.87; F= 20.63
Hansen’s test (l) for variance	0.85 (0.47)
Hansen’s Joint test (Lc)	1.94 (1.24)
Condition Number (test for Multicollinearity)	8.49 (20-above) signal for danger due to multicollinearity

Note: 5% critical values are given in brackets

 

Durbin-Watson (DW) test statistic suggests that residuals are positively autocorrelated. This essentially implies that there is scope to improve the model and there is leftover information in the data. Several other specifications with other variables like prime lending rate, WPI-All commodities, CPIIW, production of cement, steel etc., were attempted without any improvement to DW statistic. In order to resolve the problem of DW, several lags of IIP were incorporated. Lag 1 has turned out significant and consequently DW has improved substantially. However, this specification involving autoregressive-distributed lag / transfer function model was ignored since the main purpose is to generate forecast for at least six-months ahead.

From Table 2.5A, it is evident that Hansen’s ‘l’ (individual-parameter stability test) criteria evidenced parameter instability in variance and also in slope coefficient of ‘Gtr’. Parameter instability in variance suggests there is scope for improvement of the model. The overall test or the joint test statistics i.e., ‘L_c^’ criteria is 3.78 (5% critical value is 2.11) which also implies that the distributional parameters are time dependent. As the parameters are not stable, at the time of forecasting, for every new observation, the model has been re-estimated.

 

Method 3

Typically, the form of principal components based on indicators X_l(t)’s, l=1,2,…,k is as below;

P_j(t) = a_j1 X₁(t) + a_j2 X₂(t) + ….. + a_jp X_p(t); j =1,2, ….k,

where P_j(t) is the j-th principal component and a_jl,s l=1,2,…,k are the coefficient, known as factor loadings, of l-th indicator in j-th principal component. In practice first (or at least first few) principal component(s) normally captures sufficient information to represent the multivariate data. Suppose k leading indicators are selected to form the composite index. Let l_j, j=1,2,…,k; be the lead period of j^th indicator/series X_j(t), which is suitably transformed. Thus to assess the prospect of the target series (IIP) at time point t, one has to combine X_j(t-l_j), j=1,2, …,k values. Therefore, principal components (PCs) may be derived based on past information on X_j(t-l_j)’s. Composite index can be constructed by following two possible approaches; first by regressing target series on a few PCs and second, by regressing target series on summation of first few PCs. In both the approaches, one needs to choose first few PCs. The PCs can be chosen based on either of the two criteria. One is based on the cumulative contribution of chosen PCs to the total data variation where the number of PCs chosen is decided by some cut-off for the cumulative contribution. The other criterion is based on the out-of-sample forecast performance of the PCs. As the primary interest here is forecasting of the targeted series, the second criterion is adopted for selection of PCs. Based on this criterion, all the six PCs are chosen for further computation of the composite index. The cumulative contribution of various principal components (PC) is given below.

Table 2.5 C

Eigen values in ascending order	Cumulative contribution
195.6625	33.4459
165.7020	61.7704
103.1879	79.4090
69.2480	91.2460
32.6660	96.8298
18.5462	100.0000

 

Approach 1: In this approach, suppose two PCs are chosen then the composite index, say CI1(t), is calculated from the relationship

CI1(t) = a + b [ P₁(t) + P₂ (t) ]

where a and b are estimated from the following regression equation

Y(t) = a + b [ P₁(t) + P₂ (t) ] + e(t); e(t) being the residual series.

Approach 2: In this approach, the target series, Y(t) is regressed on the first three PCs so chosen and the estimated value of Y(t) is treated as the composite index. Thus the form of this composite index, denoted by CI2(t), looks like

CI2(t) = a + b₁P₁(t) + _b2 P₂(t)

where a, b_1, and _b2 are estimated coefficients in the regression equation

Y(t) = a + b₁P₁(t) + _b2 P₂(t) + e(t), e(t) being the residual series.

However, the second approach, which is more general, has been considered..

The following table, Table 2.5D summarises the OLS results corresponding to Approach 2. Only the first two PCs (PC1 and PC2) have been found as significant. However, as far as DW is concerned this PC based OLS suffers from same problems as seen in applying Method 2.

Table 2.5 D - OLS results based on Principal Components

Coefficients and Different Test Statistics*	Explanatory Variables
	Intercept	PC1	PC2	PC3	PC4	PC5	PC6
Coefficient	6.29	0.53	-1.21	0.55	-0.65	0.61	0.82
t-statistics	(17.97)	(2.12)	(-4.66)	(1.46)	(-1.59)	(1.09)	(1.05)
Hansen’s test (l)	0.144	0.4152	0.3119	1.0510	0.6670	0.0622	0.3609
Model criteria	R2=0.38; R2 (adjusted)=0.33; DW= 0.90; F= 7.397
Hansen’s test (l) for variance	0.73 (0.47)
Hansen’s Joint test (Lc)	3.79 (2.11)
Condition Number(test for Multicollinearity)	1.057 (20-above) signal for danger due to multicollinearity

Notes:

i. 5% critical values are given in brackets

ii. As expected (matter of tautology) that regression diagnostics of Table 2.5 A and Table 2.5 D are same. Similar fact also holds for forecasts (see Appendix 2.6 and 2.7). If insignificant PCs are dropped, the resulting OLS findings are summarised in Table 2.5 E.

Table 2.5 E: The OLS results based on significant PCs only.

Coefficients and Different Test Statistics*	Explanatory Variables
	Intercept	PC1	PC2
Coefficient	6.22	0.56	-1.24
t-statistics	(18.01)	(2.26)	(-4.82)
Hansen’s test (l)	0.1283	0.3985	0.5074
Model criteria	R2=0.31; R2 (adjusted)=0.29; DW= 0.86; F= 16.73
Hansen’s test (l) for variance	1.4286 (0.47)
Hansen’s Joint test (Lc)	2.31 (1.24)
Condition Number(test for Multicollinearity)	1.04 (20-above) signal for danger due to multicollinearity

Note: 5% critical values are given in brackets

Appendix 2.6: Forecast Performance of the Composite Indicator

Table 2.6 A

Forecast Performance Criteria	Various Methods
	Method 1	Method 2		Method 3
		All Variables	Only Significant indicators	All PCs	Only Significant PCs
MSE	6.3279	1.6235	2.4778	1.6235	2.5456
MAE	2.0594	1.0510	1.3826	1.0510	1.3847
Per cent of correct direction	47%	67 %	53%	67%	40%

Note: ,, and , are actuals and forecast, respectively, for the time point t, k=number of forecasts. In our case k=15.

 

Table 2.6 B - Actuals Vs Forecasts

Month	Actuals	Forecasts
		Method 1	Method 2		Method 3
			All variables	Only Significant Indicators	All PCs	Only Significant PCs
Nov 1999	8.0495	2.9849	6.7507	5.8235	6.7507	6.2931
Dec 1999	3.7538	5.8309	5.4847	5.5990	5.4847	6.9260
Jan 2000	7.7587	6.0065	6.3088	6.7125	6.3088	7.2273
Feb 2000	4.7688	5.5620	5.6278	6.0268	5.6278	6.4651
Mar 2000	7.8497	4.8864	6.4235	6.6062	6.4235	6.0957
Apr 2000	7.9279	4.6340	5.8523	6.1315	5.8523	5.5754
May 2000	6.2623	4.5482	5.9476	6.1062	5.9476	5.3177
Jun 2000	5.7894	5.7632	5.7449	6.7594	5.7449	5.8787
Jul 2000	5.7120	6.8534	6.0128	7.5925	6.0128	6.1123
Aug 2000	4.9110	6.4689	5.1118	6.8407	5.1118	5.6911
Sep 2000	4.8727	9.5251	5.4151	7.3504	5.4151	6.4994
Oct 2000	5.7047	4.9716	5.6072	5.2060	5.6072	4.0401
Nov 2000	6.5640	8.6179	5.0639	6.5056	5.0639	5.4703
Dec 2000	7.1708	7.0247	5.1647	6.2431	5.1647	5.1032
Jan 2001	3.5486	6.4697	5.4658	5.9732	5.4658	4.3898

>

Appendix 2.7: Results of Empirical Exercise using Quarterly Data

As in the case of monthly data, the following regression line has been estimated by Ordinary Least Square (OLS) method:

The estimated OLS equation is as follows:

Here it can be noted that the monthly series based equation was:

The OLS results corresponding to Monthly data are given in Table 2.7A.

Table 2.7 A: OLS Results corresponding to Regression based on Quarterly Data

Coefficients and Different Test Statistics	Explanatory Variables
	Intercept	M1	NFC	WPIIR	Alu	Gtr	Coal
Coefficient	2.63	0.02	0.26	0.18	0.06	-0.19	-0.22
t-statistics	0.55 (1.65)	0.33 (1.65)	1.84 (1.65)	1.27 (1.65)	0.6 (1.65)	-0.60 (1.65)	-0.85 (1.65)
Hansen’s test (l)	0.07 (0.47)	0.06 (0.47)	0.13 (0.47)	0.13 (0.47)	0.22 (0.47)	0.13 (0.47)	0.21 (0.47)
Model criteria	R2=0.66; R2 (adjusted)=0.48; DW= 1.58; F= 3.17
Hansen’s test (l) for variance	0.43 (0.47)
Hansen’s Joint test (Lc)	1.41 (2.11)
Condition Number (test for Multicollinearity)	19.34 (20 and above) signal for danger due to multicollinearity

* 5% critical values are given in brackets

 

Table 2.7 B: OLS Results corresponding to Regression based on Monthly data

Coefficients and Different Test Statistics*	Explanatory Variables
	Intercept	M1	NFC	WPIIR	Alu	Gtr	Coal
Coefficient	-1.58	0.30	0.27	0.04	0.005	-0.08	-0.06
t-statistics	-0.82 (1.65)	2.44 (1.65)	3.57 (1.65)	0.58 (1.65)	0.17 (1.65)	-0.69 (1.65)	0.75 (1.65)
Hansen’s test (l)	0.14 (0.47)	0.16 (0.47)	0.21 (0.47)	0.25 (0.47)	0.26 (0.47)	0.60 (0.47)	0.27 (0.47)
Model criteria	R2=0.38; R2 (adjusted)=0.33; DW= 0.90; F= 7.397
Hansen’s test (l) for variance	0.73 (0.47)
Hansen’s Joint test (Lc)	3.79 (2.11)
Condition Number (test for Multicollinearity)	16.94 (20 and above) signal for danger due to multicollinearity

* 5% critical values are given in brackets

Table 2.7 C: Comparison of Forecast Performances

	Quarterly data	Monthly data
MSE	1.98	1.62
MAE	1.09	1.05
Per cent of correct direction	54%	67 %

 

Appendix 3

Illustrative List of Cyclical Indicators

Leading Indicators

Average weekly hours, mfg. (hours)
Average weekly initial claims, unemploy. Insurance
Vacancies
Mfrs' new orders, consumer goods and materials (Amount)
New Orders (from Business Surveys)
Order Books (from Business Surverys)
Balance of new orders
New Company formation
New car registrations,
Vendor performance, slower deliveries diffusion index (pct.)
Mfrs' new orders, nondefense capital goods
Production bottlenecks (from Business Surveys)
Financial surplus / deficit of industrial and commercial companies
Building permits for new private housing units
Raw material prices
Index of Stock Prices
Production (from Business Surveys)
Money Supply
Deposit
Inverted yield curve,
Interest rate spread, 10-year Treasury bonds less federal funds
Short-term interest rate on prime bank bills (inverted),
Exports
Terms of Trade
Change in consumers' outstanding borrowing
Consumer expectations

Coincident Indicators

Real GDP
Real Non-Agricultural GDP
Employees on nonagricultural payrolls
Personal income less transfer payments
Index of industrial production
Manufacturing and trade sales

Lagging Indicators

Interest rate spread
Average duration of unemployment in weeks (weeks)
Ratio, Manufacturing and trade inventories to sales (chain 1996 $)
Change in labor cost per unit output, mfg. (6-m pct. AR)
Average prime rate charged by banks, NSA (pct.)
Commercial and industrial loans outstanding (mil. Chain 1996 $)
Ratio of consumer installment credit to personal income (pct.)
Change in CPI for services (6-m pct. AR)

 

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