Indian Auto

Published on December 2016 | Categories: Documents | Downloads: 74 | Comments: 0 | Views: 397
of 53
Download PDF   Embed   Report

Comments

Content

FIRST GLOBAL
www.first-global.us

India Research

FIRST GLO BAL

Sector: Indian Auto
The Regression Crystal Ball
What's in store for various auto segments (CVs, Passenger vehicles, 2-wheelers, 3-wheelers and tractors) Cars and 2-wheeler sales set to zoom in FY06…tough times ahead for Commercial Vehicles and Tractors
(See Pg. 3 for the FY06 estimates)

June 14, 2005
Chief Strategist: Devina Mehra Analyst: Sri Raghunandhan N.L. US Sales: Email: [email protected] Email: [email protected] Email: [email protected] Email: [email protected]

Tel. No: 1-212-227 6611

UK & Europe Sales:

Tel.: 44-207-959 5300

Research Note issued by First Global Securities Ltd., India FG Markets, Inc. is a member of NASD/SIPC and is regulated by the Securities & Exchange Commission (SEC), US First Global (UK) Ltd. is a member of London Stock Exchange and is regulated by Financial Services Authority (FSA), UK

FIRST GLOBAL
India Research

www.first-global.us

Table of Contents
Particulars
n The Short Story n The Quick and Dirty Guide

Page Nos.
1-3 4-5 4 5 6-14 6 7 8 9 10 11 12-13 13 14 15-27 15-16 17-27 17-19 19-21 21-23 23-25 25-27 28-31 28 29 Page 50 30 30-31 31

The Background The Regression Analysis
n Section I: The Past: The Auto Story…a swift review l The growth down the years…has been cyclical in every category

Commercial Vehicles Passenger Vehicles (4-wheelers) Two-wheelers Three-wheelers Tractors
l The Interest rate Cycle l Government policies: Intended and Unintended Consequences l Exports: Indian Auto industry takes its first baby steps n Section II: The Analysis: The segment-wise Regression Analysis

Brief Methodology of Regression Analysis
n Segment-Wise Results

Commercial Vehicles Passenger Vehicles (4-wheelers) Two-wheelers Three-wheelers Tractors
n Section III: The Future: Which are the high growth automobile segments?

Commercial Vehicles Passenger Vehicles (4-wheelers) Two Wheelers Three Wheelers Tractors

FIRST GLOBAL
India Research

www.first-global.us

Particulars
n Appendix A: Key Variables and Estimates Data

Page Nos.
32-36 32 33 34 35 36 37-47 37 38 38 39 39 39 40 40 40 41 42-43 43 44-47 44 44-46 46 47 48 Page 51

Commercial Vehicles Passenger Vehicles (4-wheelers) Two-wheelers Three-wheelers Tractors
n Appendix B: The step-by-step Regression Model

The Multiple Regression Model The Concept of Detrending
u Methods of Detrending

Dummy Variables
u Dummy Variables for Multiple Groups u Format of Equation with multiple intercepts and slopes

Handling Autocorrelation
u Detecting Autocorrelation u Durbin-Watson d test: Decision rules u Remedial Measures for Autocorrelation

Centering and Scaling Accounting for Multicollinearity The Statistical Method that Accounts for Multicollinearity
u Principal Components Regression (PCR) u Computational Technique u Calculating the variance and Standard error of b* u Performing the T-Test n Appendix C: Bibliography

FIRST GLOBAL
India Research

www.first-global.us

Table of Illustrations
Sr. No.
Table 1

Index
Estimated (Domestic) Sales Growth and Sales Volumes in FY06 (Year-ending March ’06) Section I - The Past Section II - The Regression Analysis

Page Nos.
3 6 15 18 19 20 21 22 23 24 25 26 27 28 28 29 30 30 31 32 32 32 33 33 34 34 35 35 36 36 37 40

Table 2 Table 3 Table 4 Table 5 Table 6 Table 7 Table 8 Table 9 Table 10 Table 11

Key Variables used for Commercial Vehicles Regression Output for Commercial Vehicles Key Variables used for Passenger Vehicles Regression Output for Passenger Vehicles Key Variables used for Two Wheelers Regression Output for Two Wheelers Key Variables used for Three Wheelers Regression Output for Three Wheelers Key Variables used for Tractors Regression Output for Tractors Section III - The Future

Table 12 Table 13 Table 14 Table 15 Table 16

Our Model Domestic Sales estimates for Commercial Vehicles… Our Model Domestic Sales estimates for Passenger Vehicles… Our Model Domestic Sales estimates for Two Wheelers… Our Model Domestic Sales estimates for Three Wheelers… Our Model Domestic Sales estimates for Tractors… Appendix A

Table 17 Table 18 Table 19 Table 20 Table 21 Table 22 Table 23 Table 24 Table 25 Table 26

Key Variables used for Commercial Vehicles Key Variables and Estimated Sales (in numbers) Key Variables used for Passenger Vehicles Key Variables and Estimated Sales (in numbers) Key Variables used for Two Wheelers Key Variables and Estimated Sales (in numbers) Key Variables used for Three Wheelers Key Variables and Estimated Sales (in numbers) Key Variables used for Tractors Key Variables and EstimatedPage 52 numbers) Sales (in Appendix B

Table 27

Decision Rules of Durbin-Watson d test

FIRST GLOBAL
India Research

www.first-global.us

The Short Story
The trick in life is to get the cycle right. Not even Bill Clinton's best friends would credit him with being an economic genius. But he presided over the 8 best years for America, in the past 25 years. He just got the cycle right. Inadvertently, of course. The same is true for businesses, as well. In a recent interview, when asked about the rising ratings of the Tata management in recent times, Ratan Tata said, “I don’t give too much weightage to that because you’re the dog when you’re doing badly. If Tata Motors is in a loss, we say, look the market shrunk but our market share didn’t shrink. But nobody listens to you. Suddenly when the market booms again, the same company under the same management producing the same products just goes through the roof and everybody calls it a turnaround.” We’ve found that the bulk of investment returns The bottomline: the fortunes of Tata Steel and Tata Motors, as also their presence in the ‘Most Admired’, ‘Best Managed’, not to forget the ‘Biggest Gainers’, lists depends less on their management and more on where we are in the steel and automobile cycles. On a broader basis, as analysts, we’ve found that the bulk of investment returns come from the sector allocations, rather than in chasing up individual stock picks. This is especially true of a market like India, where fine market segmentation is still far away in most industries. For instance, the mid 2004- March 2005 market rally, you’d have been pretty well-off had you picked baskets of stocks with exposure to, say, steel, construction, auto components or housing finance; compared to finding the very best picks in Pharmaceuticals or refineries, which would’ve likely still lost you money. In Automobiles too, getting the cycle In Automobiles too, getting the cycle right is key. (After all, every single product category, including the ‘growth’ segments of cars and motorcycles has seen sales volume dip sometime or the other). We’d made our first attempts in this direction nearly a decade ago, when we constructed a forecasting model for Commercial Vehicles (CVs) based on various macro parameters. Though far less sophisticated than the one we have in this report, it proved to be pretty

come from the sector allocations, rather than in chasing up individual stock picks. This is especially true of a market like India, where fine market segmentation is still far away in most industries. For instance, the mid 2004- March 2005 market rally, you’d have been pretty well-off had you picked baskets of stocks with exposure to, say, steel, construction, auto components or housing finance; compared to finding the very best picks in Pharmaceuticals or refineries

right is key. We’d made our first attempts in this direction nearly a decade ago, when we constructed a forecasting model for Commercial Vehicles (CVs) based on various macro parameters. Though far less sophisticated than the one we have in this report, it proved to be pretty serviceable

Page 1

FY indicates Year Ending March

FIRST GLOBAL
India Research

www.first-global.us

serviceable. At the beginning of 1997, when market participants and the CV manufacturers were quibbling about whether industry sales volumes would grow by 10, 15 or 20%, we stuck out our necks and said that the FY98 would see a substantial decline in CV sales. The year ended with a 35% volume decline – a blow that hit CV manufacturers and their suppliers rather hard. Their stock prices got decimated. Two years of rather abysmal sales later, our model forecast an about 25% volume growth. At the time, we got separate calls from both the CV majors saying, “Please tone down your forecasts. We don’t expect anything more than 10% growth.” We stuck to our guns and FY 2000 saw a 24% growth in CV volumes. What we’ve brought you this time around is more ambitious and, in our view, more accurate. For one, we have attempted to model for and forecast sales for all segments of the automobile market. Plus we’ve employed more sophisticated statistical tools to We have attempted to model for and detrend and centre the independent variables and forecast sales for all segments of the to remove problems arising due to multicollinearity automobile market. Plus we’ve employed and auto-correlation. Our analysis of the Indian automotive sector is divided into two Volumes. This is Volume I, which carries the highlight of this piece - a Regression Analysis of as many as 5 segments, namely CVs, Passenger vehicles (4-wheelers), 2-wheelers, 3wheelers and tractors. We begin the report with a quick recap of the auto story so far and end it with a prognosis of the likely trends in sales during the coming years. The focus of this report is to forecast domestic sales for all automobile segments. We will deal with other issues like the export potential, the potential use of India as a sourcing base and/or a research & design hub, This is Volume I, which carries the highlight of this as well as individual company piece - a Regression Analysis of as many as 5 segments, outlooks & financials in our namely CVs, Passenger vehicles, 2-wheelers, 3-wheelers forthcoming pieces. However, as and tractors. We begin the report with a quick recap of we’ve said earlier, the key to investing the auto story so far and end it with a prognosis of the in this sector, as in most cyclical likely trends in sales during the coming years. The focus industries, is to get the big picture of this report is to forecast domestic sales for all right – and that’s exactly where this automobile segments... report should help.

more sophisticated statistical tools to detrend and centre the independent variables and to remove problems arising due to multicollinearity and auto-correlation

... the key to investing in this sector, as in most cyclical industries, is to get the big picture right – and that’s exactly where this report should help

For a quick peek at the results, turn the Page.
Page 2

FIRST GLOBAL
India Research

www.first-global.us

The Results (Pg. 28 Onwards)
Let’s cut to the chase: As per our model, the estimated Sales Growth and Sales Volumes for each automobile segment (domestic sales only) are as follows:

Table 1: Estimated (Domestic) Sales Growth and Sales Volumes in FY06 (Year-ending March ’06)

Commercial Passenger 2-wheelers 3-wheelers Tractors Vehicles Vehicles Sales V olume Sales Growth (%) 313,632 -1.4 1,257,736 18.5 6,905,351 14.2 341,497 5.8 224,585 -0.8

Page 3

FIRST GLOBAL
India Research

www.first-global.us

The Quick and Dirty Guide
The Background
n

The Auto industry has had a direct linkage with the economic growth of the country – though the variables impacting the various segments have been somewhat different; with Industrial growth directly affecting Commercial vehicle sales and Agricultural growth driving tractor sales. Some estimates show that for every increase of 1% in the GDP, there will be a corresponding increase of 1.5-2% in road traffic. The Indian auto sector grew at a very rapid pace of 16% in FY2005, whereas the global auto sector witnessed a decline of 2% during the same period. Besides factors like the different stage of economic growth (very early days yet for India), attractive demographics (a young and growing working population), the major driver of this growth has been the sliding interest rates.

n

Certain government policies have also had intended and unintended consequences for the automobile market. For example, the stringent auto emission norms in several parts of the country resulted in a more rapid replacement cycle, as well as the availability of upgraded vehicles. The Auto Policy of 2002 facilitated the automatic approval of foreign equity investment of up to 100% of the manufactured automobiles and components. During the next 3-4 years, the industry will pump in as much as $5 bn, out of which the FDI would be close to $3 bn (Source: SIAM).

n

Exports are a large potential area to drive growth and also to diversify market risk, where Indian companies have just started to take their first baby steps. Not just the recognised cyclical categories like CVs, but even all other auto segments have shown sales declines sometime or the other. Hence catching the cycle is key for this industry.

n

Not just the recognised cyclical categories like CVs, but even all other auto segments have shown sales declines sometime or the other

Page 4

FIRST GLOBAL
India Research

www.first-global.us

The Regression Analysis (Pg. 15 onwards)
n

Various factors possibly influence the expected demand in auto segments, all of which have been tried and tested in order to obtain the key drivers. These can be broadly classified as variables capturing growth in various GDP/ Income/ consumption components, variables representing the cost and quantum of credit, the vehicle selling prices, variables relating to price and quantum of petrol/diesel, demographic variables (eg, working population for passenger vehicles, rural population for tractors) plus qualitative variables to capture discontinuities in the industry. As regards the dependent variable, we tried both Sales Volumes, as well as Vehicle Population for each Automobile segment. We also attempted linkages for same year data and lagged data. The taking of data spanning over a period of 24 years has also led to the effect of business cycles being factored in. The model has been perfected by the use of remedial measures for handling problems of spurious correlation, autocorrelation and Multicollinearity.

n

n n

n

Various factors possibly influence the expected demand in auto segments, all of which have been tried and tested in order to obtain the key drivers. These can be broadly classified as variables capturing growth in various GDP/ Income/ consumption components, variables representing the cost and quantum of credit, the vehicle selling prices, variables relating to price and quantum of petrol/diesel, demographic variables (eg, working population for passenger vehicles, rural population for tractors) plus qualitative variables to capture discontinuities in the industry

Page 5

FIRST GLOBAL
India Research

www.first-global.us

Section I: The Past
The Auto Story…a swift review
Here’s a quick recap of the auto industry’s growth down the years.

l The growth down the years…has been cyclical in

every category
Given India’s nascent stage of growth, the automobile industry has, unsurprisingly, been a growth industry. The more surprising fact has been the cyclical nature of the growth even at a comparatively low base. As the graphs below show, the industry has seen significant ups Given India’s nascent stage of and downs in sales volumes, with annual growth growth, the automobile industry has, rates even going into the negative territory for every unsurprisingly, been a growth industry. single product category. For example, let alone The more surprising fact has been the traditionally recognised cyclical categories like CVs, cyclical nature of the growth even at a growth in even the car category went into negative comparatively low base territory in FY89, FY99 and FY01 (YE March). Hence while India’s long-term growth story may remain intact, it’s still vital to project what the growth rates would be on an annual basis. After all, a year or two of sales decline can take a heavy toll on the auto companies.

Let alone traditionally recognised cyclical categories like CVs, growth in even the car category went into negative territory in FY89, FY99 and FY01 (YE March). Hence while India’s long-term growth story may remain intact, it’s still vital to project what the growth rates would be on an annual basis. After all, a year or two of sales decline can take a heavy toll on the auto companies

Page 6

FIRST GLOBAL
India Research

www.first-global.us

Commercial Vehicles
Commercial Vehicles domestic sales volume over the years…

350 300

Sales Volume (000's)

250 200 150 100 50 0

79-80

80-81

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

91-92

92-93

93-94

94-95

96-97

01-02

02-03 02-03

03-04 03-04

95-96

97-98

98-99

99-00

Years M & HCVs LCVs Total CVs

Commercial Vehicles: Annual Domestic Sales volume growth trend

50% 40% 30% 20%

% change

10% 0%

80-81

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

91-92

92-93

93-94

94-95

96-97

00-01

01-02

95-96

97-98

98-99

99-00

-10% -20% -30% -40% -50%

Years M & HCVs LCVs Total CVs

Page 7

00-01

04-05

04-05

FIRST GLOBAL
India Research

www.first-global.us

Passenger Vehicles (4-wheelers)
Passenger Vehicles domestic sales volume over the years…

1200 1000
Sales Volume (000's)

800 600 400 200 0

79-80

80-81

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

91-92

92-93

93-94

94-95

96-97

01-02

02-03 02-03

03-04 03-04

95-96

97-98

98-99

99-00

Years Passenger Cars UVs MPVs Total Passenger Vehicles

Passenger Vehicles: Annual Domestic Sales volume growth trend

80% 60% 40%
% change

20% 0%

80-81

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

91-92

92-93

93-94

94-95

96-97

00-01

01-02

95-96

97-98

98-99

99-00

-20% -40% -60%

Years Passenger Cars UVs MPVs Total Passenger Vehicles

Page 8

00-01

04-05

04-05

FIRST GLOBAL
India Research

www.first-global.us

Two-wheelers
Two Wheelers domestic sales volume over the years…

7 6
Sales Volume (000's)

5 4 3 2 1 0

79-80

80-81

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

91-92

92-93

93-94

94-95

96-97

01-02

02-03 02-03

03-04 03-04

95-96

97-98

98-99

99-00

Years Scooters / Scooterettee Motorcycles / Step Through Mopeds Total Two Wheelers

Two Wheelers: Annual Domestic Sales volume growth trend

60% 50% 40% 30%
% change

20% 10% 0%

80-81

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

91-92

92-93

93-94

94-95

96-97

00-01

01-02

95-96

97-98

98-99

99-00

-10% -20% -30% -40% -50%

Years Scooters / Scooterettee Motorcycles / Step Through Mopeds Total Two Wheelers

Page 9

00-01

04-05

04-05

% change
100 150 200 250 300 350 50 0 -10% 10% 20% 30% 40% 0%

Sales Volume (000's)

India Research

FIRST GLOBAL

-30%

-20%

80-81 80-81 81-82 82-83 83-84 84-85 85-86 86-87 87-88 88-89 89-90 90-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 99-00 00-01 01-02 02-03 03-04 04-05
Years

79-80

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

www.first-global.us

Three-wheelers

Three Wheelers domestic sales volume over the years…

Three Wheelers: Annual Domestic Sales volume growth trend

Page 10
Three Wheelers

91-92

Years

92-93

Three Wheelers

93-94

94-95

95-96

96-97

97-98

98-99

99-00

00-01

01-02

02-03

03-04

04-05

% change
100 150 200 250 300 50 0 10% 20% 30% 40% 50% 60% 70% 0%

Sales Volume (000's)

India Research

FIRST GLOBAL

-30%

-20%

80-81

81-82

82-83

83-84

84-85

85-86

86-87

87-88

88-89

89-90

90-91

www.first-global.us

Tractors

Tractors domestic sales volume over the years…

Tractors: Annual Domestic Sales volume growth trend

Page 11
90-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 99-00 00-01 01-02 02-03 03-04 04-05
Years Tractors

91-92

Tractors

Years

92-93

93-94

94-95

95-96

96-97

97-98

98-99

99-00

00-01

01-02

02-03

03-04

04-05

-10%

79-80 80-81 81-82 82-83 83-84 84-85 85-86 86-87 87-88 88-89 89-90

FIRST GLOBAL
India Research

www.first-global.us

l The Interest rate Cycle
India’s auto cycle has also been aligning itself with the world on another front, which is its dependence on credit. While financing was always a large part of the CV story, it has lately become a key driver for even passenger vehicles. It is therefore no coincidence that most auto categories took off around 2000, when the interest rates dipped significantly. (see graph below). Of course, what the long-term data does not capture completely is the lowering of the financing spread over the Bank While financing was always a Rate as banks go in for sub-PLR lending, thus large part of the CV story, it has lately lowering the effective financing rates even more.

become a key driver for even passenger vehicles. It is therefore no coincidence that most auto categories took off around 2000, when the interest rates dipped significantly

Prime Lending Rate (PLR) over the years… (PLR Lower Limit)
20 18 16 14 12 10 8 6 4 2 0 78-79 79-80 80-81 81-82 82-83 83-84 84-85 85-86 86-87 87-88 88-89 89-90 90-91 91-92 92-93 93-94 94-95 95-96 96-97 97-98 98-99 99-00 00-01 01-02 02-03 03-04 04-05
Years

Source: RBI Page 12

PLR Lower Limit

FIRST GLOBAL
India Research

www.first-global.us

The growth in CV was phenomenal during 2001-04, with a CAGR of 25% witnessed during the period, while the industry grew at an incredible 36.5% in FY04 and a healthy 22% in FY05 (YE March). With a growth of almost 14% in car sales during 2004, India has emerged as the fastest-growing car market in the world and has outstripped even China’s estimated growth of 13.7% last The growth in CV was year. The two and three-wheeler segments have been phenomenal during 2001-04, with a growing consistently at 10% during the last ten years CAGR of 25% witnessed during the and posted a growth of 15.6% and 20% respectively period, while the industry grew at during the last year. FY04 and FY05 have been good an incredible 36.5% in FY04 and a years for tractors as well, with growth of over 18% pa.

healthy 22% in FY05 (YE March)

l Government policies: Intended and Unintended

Consequences
The advantages of the post-liberalisation era, coupled with the relaxation of government policies, helped the industry to change track. The combination of allowing FDI and more stringent auto emission norms meant that the Indian automobile industry had to upgrade in a hurry. An accelerated replacement cycle, demand driven by availability of more attractive models and The combination of allowing FDI and easy financing, all combined to boost growth to higher more stringent auto emission norms meant levels. The automobile industry grew at a compound annual growth rate (CAGR) of 22% between the period 1992-1997. With investments exceeding Rs. 500,000 mn, the turnover of the automobile industry exceeded Rs. 595,180 mn in FY03. Including the turnover of the auto-component sector, the Indian automotive industry’s turnover, which was above Rs. 840 billion (bn) in FY03, is estimated to have exceeded Rs.1,000 bn in FY04. The higher turnover targets and an aggressive exports strategy were met by enhancing production capacities. The production of total vehicles increased from 4.2 mn in FY99 to 7.3 mn during FY04. It is likely that the production of vehicles will exceed 10 mn during the next couple of years. Inorganic growth and technology transfers played a vital role in this growth. India registered the fastest growth of 30% among the top 15 passenger car producing countries in the world during 2004 (Source: OICA). Between FY99 and FY04, output of commercial vehicles grew by 2.8 times, as compared to the increase of 2.2 times in passenger cars. The two-wheeler output now continues to dominate the volume statistics of the sector.
Page 13

that the Indian automobile industry had to upgrade in a hurry. An accelerated replacement cycle, demand driven by availability of more attractive models and easy financing, all combined to boost growth to higher levels

FIRST GLOBAL
India Research

www.first-global.us

l Exports: Indian Auto industry takes its first baby steps
Exports Volume trend over the years…
Exports
400 350 700 600 500 400 300 200 100 0 95-96 96-97 97-98 98-99 99-00 00-01 01-02 02-03 03-04 04-05 Years
Commercial Vehicles Three Wheelers Passenger Vehicles Total Vehicles Two Wheelers

Sales Volume (000's)

300 250 200 150 100 50 0

Between April 1997 and March 2005, India’s automobile exports have gone up by more than three times to cross 615,000 units. In value terms, automobile exports crossed the one billion dollar mark for the first time in Between April 1997 and March 2005, India’s the beginning of 2004. Though it is early automobile exports have gone up by more than three days yet, the Indian automobile sector is times to cross 615,000 units. In value terms, becoming part of the global set. While automobile exports crossed the one billion dollar mark this report addresses the estimation for the first time in the beginning of 2004. Though it is of domestic sales, we will deal with early days yet, the Indian automobile sector is the export market potential in one becoming part of the global set of our forthcoming pieces. Exports in the Commercial vehicles segment have grown at CAGR of 11% since 98-99, for two-wheeler for the same period the growth is higher at 21.5%. During FY05, Commercial vehicles exports showed the highest growth of 75.6%, albeit from a small base. Coming to two-wheelers, motorcycles were the drivers, with foreign shipments growing 42.9%. Three-wheelers grew incredibly at 112% since 01-02, but in FY05 it was the only segment, which witnessed a fall in numbers, declining 5.7%. In the passenger vehicle segment, with the entry of MNCs, exports have been rising, as many of them like Honda and Hyundai are using the country as an export base. Passenger segment exports have grown at CAGR Page 14 of 46% from FY00 to FY04 (YE March). Hyundai’s Exports saw a staggering growth of 95% in the year FY05 over FY04, with a sale of 82,093 cars.
Page 14

Total Vehicles (000's)

FIRST GLOBAL
India Research

www.first-global.us

Section II: The Analysis
The segment-wise Regression Analysis
Sales of the automobile segment are potentially impacted by a number of parameters. We did extensive testing to come up with the most significant of these, which have been factored into the final model. This section takes a detailed look at the conclusions of the Regression Analysis and also arrives at the most high growth segments in the future in terms of sales.

Brief Methodology of Regression Analysis
n

Various factors possibly influence the expected demand in auto segments, all of which have been tried and tested in order to obtain the key drivers. The potentially significant variables included variables capturing growth in The potentially significant variables included various GDP/ Income/ consumption variables capturing growth in various GDP/ Income/ components, growth in average selling consumption components, growth in average selling prices of the vehicles, variables prices of the vehicles, variables representing the representing the cost and quantum of cost and quantum of credit, variables relating to credit, variables relating to price and price and quantum of petrol/diesel, demographic quantum of petrol/diesel, demographic variables (eg, working population for passenger variables (eg, working population for vehicles, rural population for tractors) plus passenger vehicles, rural population for qualitative variables to capture discontinuities in tractors) plus qualitative variables to capture discontinuities in the industry the industry (eg, delicensing) (eg, delicensing). As regards the dependent variable, we tried both Sales Volumes, as well as Vehicle Population for each Automobile segment. However, in all cases the fit was better with the Population figure. Vehicle Population was defined as total registered vehicles in India at the beginning of the year, plus that year’s annual sales and less the estimated nonfunctional/junked vehicles for the year. We also attempted linkages for same year data and Page 15 lagged data.

n

n

As regards the dependent variable, we tried both Sales Volumes, as well as Vehicle Population for each Automobile segment. However, in all cases the fit was better with the Population figure

n

The taking of data spanning over a period of 25 years has also led to the effect of business cycles being factored in.
Page 15

FIRST GLOBAL
India Research

www.first-global.us

The statistically inclined can see Appendix B for the Regression Methodology and Appendix A for the data used. Very briefly, we followed these steps to take care of some of the pitfalls of traditional Regression analysis (those not interested in even this summary can skip to page 17 for the variables used, or even further to Page 28 for the final estimates):

Detrending
Data involving economic time series, such as PDI and industrial production, in regression often tend to move in the same direction, reflecting a high R2 value, which may not reflect the true association and may reflect only the common trend present in them. Use of Detrending variable in the equation is necessary for handling this spurious correlation.

Removal of Autocorrelation
Autocorrelation among the residual values have to be removed to satisfy the assumption of a linear regression model (Autocorrelation is defined as the correlation of a variable with itself. For example, Agricultural production in one year will be correlated to the Agricultural Production in preceding years). Those interested in the use of the Durbin Watson d-statistic, Prais-Winsten transformation et al used to Autocorrelation among the remove Autocorrelation are referred to the Appendix B. residual values have to be

removed to satisfy the assumption of a linear regression model

Centering and Scaling
Centering and scaling of independent variables has been done to normalize the variable, i.e. to obtain Mean of 0 and a constant variance.

Handling Multicollinearity
Multicollinearity can be defined as the presence of high correlations between predictor variables in multiple regression. Multicollinearity has been handled by using the Principal Components Regression model, which involves the use of Eigen Values and Eigen Vectors (See Appendix B for details).
Page 16

FIRST GLOBAL
India Research

www.first-global.us

Segment-Wise Results
For each segment, many variables were tried and tested before arriving at the key drivers. All the variables were tested for the cobweb phenomenon, i.e., variables were tested even with lag as they might fit better. The model has used data upto 2003-04. The key drivers have been selected on basis of the part played by them in variance of the independent variable. The selection has been made on the basis of the fit of the variable i.e., R2 , the eigen values obtained and T-Statistics.

For each segment, many variables were tried and tested before arriving at the key drivers. All the variables were tested for the cobweb phenomenon, i.e., variables were tested even with lag as they might fit better. The model has used data upto 2003-04

Commercial Vehicles
The Independent variables tested were: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) Index of industrial production (IIP) Wholesale Price Index of Commercial Vehicles Cumulative credit amount outstanding for transport operators by Commercial Banks Credit limit for transport operators by Commercial Banks Working and total population GDP growth rates GDP service sector growth rates Prime Lending Rates and bank rates Diesel prices Crude oil consumption and crude oil imports Index of total imports Index of total exports Dummy Variable for pre and post delicensing
Page 17

FIRST GLOBAL
India Research

www.first-global.us

The Dependent variables tried out were: Annual Domestic Sales Volume and Vehicle Population. Vehicle Population was defined as total registered vehicles in India at the beginning of the year, plus that year’s annual sales and less the estimated non-functional/junked vehicles for the year. The latter turned out to be better for modelling purposes. As far as the independent variables were concerned, while several variables were significant individually (on a simple regression basis), after the entire rigorous process detailed in Appendix B, these were the key variables identified that explained most of the changes in Commercial Vehicle sales:

Table 2: Key Variables used for Commercial Vehicles
Dependent Variable Vehicle Population Independent Variables Main Variables: Index of Industrial Production (with lag), WPI of commercial vehicles (same year), Credit Amount OS for Transport Operators (with lag), Working Population (with lag), Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

The key drivers are as follows: 1) Growth in industrial production directly contributes to the sales and the nature of technology used in the majority of commercial vehicles. The Index of Industrial Production has been taken from CSO (Central Statistical Organisation) data (FY05 growth: 7%). 2) Wholesale Price Index of Commercial Vehicles: The trend in the WPI for CVs highlights the price elasticity of demand and shows the relationship between rising prices and its cascading effect on the growth rates of annual demand. Not surprisingly, this is one variable where the same year data has a better fit than the lagged version, as it is the prevailing prices that impact the purchase decision. The data of WPI, as also its estimated value, has been taken from CMIE (FY06 growth: 2.9%). 3) Easy availability of finance schemes for transport operators and the level of funding provided by scheduled commercial banks is a major demand driver. The variable for FY05 has been estimated as a ratio of banking component of GDP. The variable taken represents the total credit amount outstanding for transport operators given by all scheduled commercial banks (FY05 growth: 7.2%). 4) The growth in working population also has an impact on road transport scenario, especially as this mode of transport is more preferred than railways. The working population represents the working population on register taken from RBI database. The working population has been estimated as a percentage of total working age population, working age population refers to population between the age group of 15 to 65 (FY05 growth: 1.8%).
Page 18

All the key drivers, except for the WPI for CVs, have been taken with a lag as they were fitting better i.e. the data for FY05 has been used to forecast CV sales for FY06 (YE March).
Page 18

FIRST GLOBAL
India Research

www.first-global.us

The final model and statistics are as follows:

Table 3: Regression Output for Commercial Vehicles
Regression Output
R Square Adj. R Square No. of Observations X Coefficients Prior Period (1980-1991) X Coefficients Std Err of Coef. Full Period (1980-2004) X Coefficients Std Err of Coef. Full Period Dummy Variable Coef Std Err of Coef. t - value f - value 99.95% 99.91% 24 IIP Index 27194 8735 WPI -8168 8596 Crd Amt OS -9.49E-06 9.46E-06 Wrk. Popln on Reg -0.0007 0.052

1112 14535

-17430 13770

5.41E-06 1.81E-05

1.71 0.069

-364280 1120849 3.11 2919 -4.00 2.71 2.01

Passenger Vehicles (4-wheelers)
The variables tested were: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) Personal Disposable Income Cumulative credit amount outstanding for vehicles by Commercial Banks Credit limit for vehicles by Commercial Banks Working, urban and total population GDP growth rates Prime Lending Rates and bank rates Diesel and petrol prices Crude oil consumption and crude oil imports Index of total imports Index of total exports Dummy Variable for pre and post delicensing
Page 19

FIRST GLOBAL
India Research

www.first-global.us

The Dependent variables tried out were: Annual Domestic Sales Volume and Vehicle Population. The key variables that explained most of the changes in Passenger Vehicle sales were:

Table 4: Key Variables used for Passenger Vehicles
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI of motor vehicles (same year), Credit Amount OS for Vehicles, Vehicle parts etc (with lag), Working Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

The key drivers are as follows: 1) Personal Disposable Income (PDI): Increased disposable income, change in lifestyle and lack of public transport facilities have fuelled the growth in passenger vehicles. PDI has been taken at nominal prices. Personal Disposable Income for FY05 has been estimated as a ratio of GDP (FY05 growth: 12.6%). 2) Wholesale Price Index of Passenger Vehicles: The trend in the WPI highlights the price elasticity of demand and shows the relationship between rising prices and its cascading effect on the growth rates of annual demand. As prevailing prices impact the purchase decision, the same year data has a better fit. The WPI data has been taken from CMIE (FY06 growth: 2.8%). 3) Easy availability of finance schemes, aggressive promotion of vehicle loans by banks and declining interest rates has played a vital role. The variable for FY05 has been estimated as a ratio of banking component of GDP. The variable taken represents the total credit amount outstanding for vehicles given by all scheduled commercial banks (FY05 growth: 7.2%). 4) Increase in working population has also contributed its share in the growth – quite logically so, as this would constitute the car buying population. The working population has been estimated as a ratio of total working age population (FY05 growth: 1.8%). All the three key drivers, except WPI have been taken with lag as they were fitting better.

Page 20

FIRST GLOBAL
India Research

www.first-global.us

The final model and statistics are as follows:

Table 5: Regression Output for Passenger Vehicles
Regression Output
R Square Adj. R Square No. of Observations X Coefficients Prior Period (1980-1991) X Coefficients Std Err of Coef. Full Period (1980-2004) X Coefficients Std Err of Coef. Full Period Dummy Variable Coef Std Err of Coef. t - value f - value 99.88% 99.81% 24 PDI 1.19E-06 4.72E-07 WPI -34526 76674 Crd Amt OS -4.28E-05 9.7E-05 Wrk. Popln on Reg 0.06 0.35

4.1E-07 8.5E-07

-20916 145076

5.6E-06 0.0002

0.05 0.47

633517 6284558 2.51 1315 -2.03 3.20 2.56

Two-wheelers
The variables tested were: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) Personal Disposable Income Cumulative credit amount outstanding for vehicles by Commercial Banks Credit limit for vehicles by Commercial Banks Working, urban and total population GDP growth rates Prime Lending Rates and bank rates Petrol prices Crude oil consumption and crude oil imports Index of total imports Index of total exports Dummy Variable for pre and post delicensing
Page 21

FIRST GLOBAL
India Research

www.first-global.us

The key variables that explained most of the changes in Passenger Vehicle sales were:

Table 6: Key Variables used for Two Wheelers
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI for two wheelers (same year), Credit Amount OS for Vehicles, Vehicle parts etc (with lag), Working Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

The key drivers are as follows: 1) Post the liberalisation, the overall economic growth has primarily resulted in an increase in the rural and urban disposable income, which is a major demand driver for two-wheelers. PDI has been taken at nominal prices. Personal Disposable Income for FY05 has been estimated as a ratio of GDP (FY05 growth: 12.6%). 2) Wholesale Price Index of Two Wheelers: The WPI For Two Wheelers is the weighted average indicator of motorcycles, scooters and mopeds, which shows the sensitivity of demand to the rise in two-wheeler prices. As prevailing prices impact the purchase decision, the same year data has a better fit. The WPI data has been taken from CMIE (FY06: 2.8%). 3) Finance schemes available at attractive rates have also induced consumer to go in for purchases of two-wheelers. The variable for FY05 has been estimated as a ratio of banking component of GDP. The variable taken represents the total credit amount outstanding for vehicles given by all scheduled commercial banks (FY05 growth: 7.2%). 4) India has one of the youngest demographic profiles in the world and the working population has been growing rapidly – a factor which is a driver for two-wheeler sales. The working population has been estimated as a ratio of total working age population (FY05 growth: 1.8%). All the three key drivers, except WPI have been taken with lag as they were fitting better.

Page 22

FIRST GLOBAL
India Research

www.first-global.us

The final model and statistics are as follows:

Table 7: Regression Output for Two Wheelers
Regression Output
R Square Adj. R Square No. of Observations X Coefficients Prior Period (1980-1991) X Coefficients Std Err of Coef. Full Period (1980-2004) X Coefficients Std Err of Coef. Full Period Dummy Variable Coef Std Err of Coef. t - value f - value 99.95% 99.93% 24 PDI 4.57E-06 9.08E-07 WPI -202699 179871 Crd Amt OS -0.0002 0.0001 Wrk. Popln on Reg 0.199 0.678

1.6E-06 1.8E-06

-27683 299031

1.79E-06 0.0003

0.298 1.004

14822346 10279996 5.03 3417 -3.34 3.07 2.29

Three-wheelers
The variables tested were: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) Personal Disposable Income Cumulative credit amount outstanding for vehicles by Commercial Banks Credit limit for vehicles by Commercial Banks Working and total population GDP growth rates GDP industry growth rates GDP service sector growth rates Prime Lending Rates and bank rates Petrol prices and diesel prices Crude oil consumption and crude oil imports Index of total imports Index of total exports Dummy Variable for pre and post delicensing
Page 23 Page 23

FIRST GLOBAL
India Research

www.first-global.us

The key variables that explained most of the changes in Three-Wheeler sales were:

Table 8: Key Variables used for Three Wheelers
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI for three-wheelers (same year), Credit Amount OS for Vehicles, Vehicle parts etc (with lag), Working Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

The key drivers are as follows: 1) Increase in the Personal Disposable Income has been a major demand driver. PDI has been taken at nominal prices. Personal disposable income for FY05 has been estimated as a ratio of GDP (FY05 growth: 12.6%). 2) Wholesale Price Index of Three Wheelers: The WPI for three-wheelers shows how the rise in prices have been affecting the growth rates of annual demand. As prevailing prices impact the purchase decision, the same year data has a better fit. The WPI data has been taken from CMIE (FY06 growth: 2.8%) 3) Most of the three-wheelers that are purchased are financed. In addition to the finance provided by banks, a small percentage of that amount has to be contributed by the transport operator. The variable for FY05 has been calculated as a ratio of the banking component of GDP. The variable taken represents the total credit amount outstanding for vehicles given by all scheduled commercial banks (FY05 growth: 7.2%). 4) Three wheelers are largely used in rural and urban areas for public transportation. Due to poor transport facilities in rural India, the growth in the working population has affected the growth in 3-wheelers. The working population has been estimated as a ratio of total working age population (FY05 growth: 1.8%). All the three key drivers, except WPI have been taken with lag as they were fitting better.

Page 24

FIRST GLOBAL
India Research

www.first-global.us

The final model and statistics are as follows:

Table 9: Regression Output for Three Wheelers
Regression Output
R Square Adj. R Square No. of Observations X Coefficients Prior Period (1980-1991) X Coefficients Std Err of Coef. Full Period (1980-2004) X Coefficients Std Err of Coef. Full Period Dummy Variable Coef Std Err of Coef. t - value f - value 99.89% 99.81% 24 PDI 1.51E-07 6.21E-08 WPI 3257 107811 Crd Amt OS -1.8E-06 9.9E-06 Wrk. Popln on Reg -0.0019 0.0563

1.85E-07 1.37E-07

-210428 194260

9.92E-07 1.63E-05

0.04 0.07

-216325 742412 3.41 1373 -3.44 3.05 2.03

Tractors
The variables tested were: 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11) 12) 13) Agricultural Production Personal Disposable Income Cumulative credit amount outstanding for vehicles by Commercial Banks Credit limit for vehicles by Commercial Banks Working, rural and total population GDP growth rates GDP agricultural growth rates Prime Lending Rates and bank rates Diesel prices Crude oil consumption and crude oil imports Index of total imports Index of total exports
Page 25

Dummy Variable for pre and post delicensing
Page 25

FIRST GLOBAL
India Research

www.first-global.us

The key variables that explained most of the changes in Passenger Vehicle sales were:

Table 10: Key Variables used for Tractors
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI for motor vehicles (same year), Agricultural Production (with lag), Rural Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

The key drivers are as follows: 1) The size of the land holding put for cultivation by farmers, cropping intensity, soil conditions and most importantly, timely and agricultural production. The data of agricultural production represents cumulative production figures, as taken from CSO (Central Statistical Organisation) data and estimates for FY05 have been calculated based on guidance given by Ministry of Statistics and Programme implementation (FY05 growth: 3.3%). 2) Wholesale Price Index of Tractors : The WPI of motor vehicles represent the overall trend in prices in the industry and the effect of the same on tractor segment. The WPI data has been taken from CMIE (FY06 growth: 2.8%) 3) Another major driver of the upsurge in the demand for tractors is the farmer’s income, which in turn, depends on yield, productivity per acre of farming and the price realized on commodities. PDI has been taken at nominal prices. Personal Disposable Income for FY05 has been estimated as a ratio of GDP (FY05 growth: 12.6%). 4) As the rural population increases, the area under irrigation also increases, thus leading to a cascading effect on the demand of tractors. The present estimates indicate that 65% of the total irrigation potential has been achieved in India, which still leaves a sizeable area for irrigation. The rural population has been estimated as a ratio of total population after adjusting for the declining rural population ratio. (FY05 growth: 1.7%). All the three key drivers, except WPI have been taken with lag as they were fitting better.

Page 26

FIRST GLOBAL
India Research

www.first-global.us

The final model and statistics are as follows:

Table 11: Regression Output for Tractors
R Square Adj. R Square No. of Observations X Coefficients Prior Period (1980-1991) X Coefficients Std Err of Coef. Full Period (1980-2004) X Coefficients Std Err of Coef. Full Period Dummy Variable Coef Std Err of Coef. t - value f - value 99.95% 99.92% 24 PDI 3.32E-07 2.82E-07 WPI -5302 51444 Cumi Agri Prod -0.0006 0.0005 Rural Popln 0.005 0.021

7.06E-08 5.09E-07

-10021 78101

0.0004 0.001

0.022 0.027

5002076 1957559 4.18 3153 -3.47 3.05 2.22

Page 27

FIRST GLOBAL
India Research

www.first-global.us

Section III: The Future
Which are the high growth automobile segments?
Commercial Vehicles
(Listed stocks: Tata Motors, Ashok Leyland, Eicher Motors, M&M, Swaraj Mazda…)
The shift from the rigid axle vehicle to multi axle vehicle has increased the demand from 2001-02. Along with that, the reduction in the replacement cycle of commercial vehicles from 18 years to 12-14 years has also boosted the demand in this sector.

Table 12: Our Model Domestic Sales estimates for Commercial Vehicles…
Regression Model Estimate (YE March) March ’05 March ’06 Units 318,194 313,632 Growth 18.7% -1.4% Actual Figures 318,438 Industry Consensus Units (Source) 282,137 (SIAM) 350,282 (Tata Motors)

The model had got the CV sales estimate right in FY05. Based on a IIP growth of 7%, borrowings growth of 7.2% and working population growth of 1.7% in FY05 and estimated WPI growth of 2.9% in FY06, the model estimates a Based on a IIP growth of 7%, borrowings 1.4% decline in CV sales in FY06. While growth of 7.2% and working population growth of the estimate may not be exact, we are fairly 1.7% in FY05 and estimated WPI growth of 2.9% confident about its general direction. A cyclical in FY06, the model estimates a 1.4% decline in CV downturn is on the cards, resulting in a low sales in FY06. While the estimate may not be to negative sales growth figure. More exact, we are fairly confident about its general worrisome is the fact that the industry direction. A cyclical downturn is on the cards, continues to be fairly upbeat, estimating resulting in a low to negative sales growth figure a 11.7% growth, which may cause problems if production and inventory levels are not adjusted in time.
Page 28

FIRST GLOBAL
India Research

www.first-global.us

Passenger Vehicles (4-wheelers)
(Listed stocks: Maruti, Tata Motors…)
Cost control through higher indigenisation, better supply chain management and value engineering, along with strong brands, are the critical factors for success in this segment, which includes cars, utility vehicles and multi-purpose vehicles. Networking with car finance providers and a large after sales service network is also essential.

Table 13: Our Model Domestic Sales estimates for Passenger Vehicles…
Regression Model Estimate (YE March) March ’05 March ’06 Units 1,061,872 1,257,736 Growth 17.7% 18.5% Actual Figures 1,061,290 Industry Consensus (SIAM) Units 1,008,842 1,129,903

The passenger vehicle sector recorded a sales 17.8% growth in FY05 due to a number of factors, such as the low interest rates and easy availability of finance. With these benefits continuing in the current year as well (in spite of some uptick in interest rates), the manufacturers of passenger vehicles expect to witness similar growth this year (2005-06). Our model, which had estimated FY05 sales quite accurately, now forecasts a bumper year with 1520% volume growth – in fact, better than the industry Our model, which had consensus numbers. estimated FY05 sales quite

accurately, now forecasts a bumper year with 15-20% volume growth – in fact, better than the industry consensus numbers

Page 29

FIRST GLOBAL
India Research

www.first-global.us

Two Wheelers
(Listed stocks: Bajaj Auto, Hero Honda, TVS Motors, Kinetic…)
This is the other individual buyer driven segment, and is also likely to see buoyant growth – not surprising, given the youthful demographic profile of the country’s population. Based on the independent variable values for FY05, this segment is estimated to see nearly 14% plus growth in FY06. Based on the

independent variable values for FY05, this segment is estimated to see nearly 14% plus growth in FY06.

Table 14: Our Model Domestic Sales estimates for Two Wheelers…
Regression Model Estimate (YE March) March ’05 March ’06 Units 6,045,615 6,905,351 Growth 16.2% 14.2% Actual Figures 6,208,860 Industry Consensus (SIAM) Units 6,062,465 6,850,585

Three Wheelers
(Listed stocks: M&M, Bajaj Auto, Bajaj Tempo…)
India is the largest producer and consumer of 3-wheeler vehicles. Used in the rural and urban areas for public transportation, it has been growing at a CAGR of 11.1% since 2000, due to aggressive exports in this segment.

Table 15: Our Model Domestic Sales estimates for Three Wheelers…
Regression Model Estimate (YE March) March ’05 March ’06 Units 322,931 341,497 Growth 22.8% 5.8% Page 30 322,442 Actual Figures Industry Consensus (SIAM) Units 282,137 N.A.

FIRST GLOBAL
India Research

www.first-global.us

Our model forecasts thin growth in this market – at least in FY06. This market is expected to shrink in the future due to the introduction of stringent pollution guidelines in the cities, increasing private vehicle population and increasing competition in rural public transport.

Our model forecasts thin growth in this market – at least in FY06

Tractors
(Listed stocks: M&M, Punjab Tractors, Eicher Motors, Escorts Ltd…)
Despite being the largest tractor market in the world, the tractor penetration level in India is low at 11 per 1,000 hectare of Gross Cropped Area (GCA), as compared to the estimated world average of 19 tractors per 1,000 hectare of GCA. Unfortunately FY06 is unlikely to be a good year for this industry, with our model estimating flat sales.

Unfortunately FY06 is unlikely to be a good year for this industry, with our model estimating flat sales

Table 16: Our Model Domestic Sales estimates for Tractors…
Regression Model Estimate (YE March) March ’05 March ’06 Units 226428 224585 Growth 17.3% -0.8% 225,000 Actual Figures Industry Consensus (TMA) Units 200,000-225,000 N.A

Page 31

FIRST GLOBAL
India Research

www.first-global.us

Appendix A: Key Variables and Estimates Data
Commercial Vehicles
Table 17: Key Variables used for Commercial Vehicles
Dependent Variable Vehicle Population Independent Variables Main Variables: Index of Industrial Production (with lag), WPI of commercial vehicles (same year), Credit Amount OS for Transport Operators (with lag), Working Population (with lag), Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

Table 18: Key Variables and Estimated Sales (in numbers)
(YE March) 1980-81 1981-82 1982-83 1983-84 1984-85 1985-86 1986-87 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 Vehicle Popln. 716,000 786,000 860,000 941,000 1,045,000 1,090,000 1,229,000 1,383,000 1,457,000 1,603,000 1,687,000 1,872,000 1,967,000 2,083,000 2,217,000 2,480,000 2,748,000 3,064,000 3,094,000 3,277,000 3,582,000 3,714,000 3,851,000 3,993,000 IIP Index 39 43 47 49 52 56 61 67 72 78 84 91 92 94 100 109 123 131 140 145 155 163 167 177 189 202 WPI 66.2 69.3 70.5 67 67.9 73.7 78.3 81 86.7 95.5 103.5 111 117 118 124.4 135.9 146.1 151.5 157.4 165.4 175.5 178 185.9 188 196.9 202.5 Credit Amount Wrk. Popln Outstanding (Rs.) on Reg. 9,142,600,000 12,182,900,000 15,231,700,000 19,086,500,000 22,572,900,000 23,976,700,000 26,019,100,000 25,575,300,000 27,646,900,000 29,883,600,000 36,392,600,000 35,806,500,000 37,432,000,000 37,573,800,000 39,568,900,000 39,569,000,000 45,774,800,000 78,117,250,000 64,684,900,000 70,733,900,000 80,750,000,000 87,010,000,000 93,230,000,000 Page 32 94,090,000,000 105,107,600,000 112,622,300,000 16,200,000 17,840,000 19,750,000 21,950,000 23,550,000 26,270,000 30,130,000 30,250,000 30,050,000 32,780,000 34,630,000 36,300,000 36,760,000 36,280,000 36,690,000 36,740,000 37,430,000 39,140,000 40,090,000 40,370,000 41,340,000 42,000,000 41,170,000 41,390,000 42,380,000 43,140,000 Actual Sales 75,083 82,449 90,559 90,790 98,929 96,722 103,693 118,559 117,413 124,444 141,782 139,015 120,636 142,703 168,919 200,083 221,676 143,814 129,822 161,611 136,585 146,671 190,682 260,345 318,438 Esti. Sales 78,826 83,794 87,365 87,532 90,958 102,611 111,268 109,478 117,104 130,544 140,944 142,636 106,795 142,069 166,665 195,700 228,535 152,155 148,139 160,081 138,813 144,040 184,900 252,034 318,194 313,632

Page 32

FIRST GLOBAL
India Research

www.first-global.us

Passenger Vehicles (4-wheelers)
Table 19: Key Variables used for Passenger Vehicles
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI of motor vehicles (same year), Credit Amount OS for Vehicles, Vehicle parts etc (with lag), Working Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

Table 20: Key Variables and Estimated Sales (in numbers)
(YE March) 1980-81 1981-82 1982-83 1983-84 1984-85 1985-86 1986-87 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 Vehicle Popln. 1,160,000 1,243,000 1,385,000 1,455,000 1,607,000 1,780,000 2,007,000 2,295,000 2,486,000 2,736,000 2,954,000 3,205,000 3,361,000 3,569,000 3,841,000 4,204,000 4,662,000 5,056,000 5,556,000 6,143,000 7,058,000 7,571,000 8,051,000 8,710,000 PDI (Rs.) 913,480,000,000 1,206,420,000,000 1,388,690,000,000 1,531,260,000,000 1,813,590,000,000 2,022,450,000,000 2,243,710,000,000 2,509,200,000,000 2,863,280,000,000 3,402,920,000,000 3,922,230,000,000 4,611,920,000,000 5,270,180,000,000 6,113,900,000,000 7,076,920,000,000 8,347,640,000,000 9,491,910,000,000 11,275,410,000,000 12,531,420,000,000 14,618,270,000,000 16,119,280,000,000 17,908,280,000,000 19,675,770,000,000 21,089,350,000,000 23,663,490,000,000 26,653,020,000,000 WPI 44.8 46.3 47.8 48 50.8 56.4 59.4 62.1 67.7 75.6 82.1 91.2 98 100 107.6 116.6 124.5 129.3 133.4 137.6 146.1 149.2 149.6 149.9 157.3 Credit Amount Outstanding (Rs.) 11,885,380,000 15,837,770,000 19,801,210,000 24,812,450,000 29,344,770,000 31,169,710,000 33,824,830,000 33,247,890,000 35,940,970,000 38,848,680,000 47,310,380,000 46,548,450,000 48,661,600,000 48,845,940,000 51,439,570,000 29,620,700,000 43,830,900,000 74,216,100,000 60,770,500,000 79,134,700,000 80,560,000,000 89,000,000,000 110,900,000,000 115,530,000,000 120,432,400,000 Wrk. Popln on Reg. 16,200,000 17,840,000 19,750,000 21,950,000 23,550,000 26,270,000 30,130,000 30,250,000 30,050,000 32,780,000 34,630,000 36,300,000 36,760,000 36,280,000 36,690,000 36,740,000 37,430,000 39,140,000 40,090,000 40,370,000 41,340,000 42,000,000 41,170,000 41,390,000 42,380,000 43,140,000 Actual Sales 52,680 59,519 67,253 84,852 123,926 138,429 183,599 195,008 137,230 152,732 145,929 202,075 203,283 257,971 327,967 417,762 506,301 518,029 493,565 733,641 690,560 675,116 707,198 900,752 1,061,290 Esti. Sales 40,255 57,912 77,601 105,219 113,702 132,854 182,041 184,114 152,668 156,039 138,752 178,264 221,436 278,145 338,733 430,149 489,481 509,109 539,256 610,074 672,350 721,463 801,846 843,916 1,061,872 1,257,736

161.6 129,042,800,000 Page 33

Page 33

FIRST GLOBAL
India Research

www.first-global.us

Two-wheelers
Table 21: Key Variables used for Two Wheelers
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI for two wheelers (same year), Credit Amount OS for Vehicles, Vehicle parts etc (with lag), Working Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

Table 22: Key Variables and Estimated Sales (in numbers)
(YE March) 1981-82 1982-83 1983-84 1984-85 1985-86 1986-87 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 Vehicle Popln. 1,243,000 1,385,000 1,455,000 1,607,000 1,780,000 2,007,000 2,295,000 2,486,000 2,736,000 2,954,000 3,205,000 3,361,000 3,569,000 3,841,000 4,204,000 4,662,000 5,056,000 5,556,000 6,143,000 7,058,000 7,571,000 8,051,000 8,710,000 PDI (Rs.) 1,206,420,000,000 1,388,690,000,000 1,531,260,000,000 1,813,590,000,000 2,022,450,000,000 2,243,710,000,000 2,509,200,000,000 2,863,280,000,000 3,402,920,000,000 3,922,230,000,000 4,611,920,000,000 5,270,180,000,000 6,113,900,000,000 7,076,920,000,000 8,347,640,000,000 9,491,910,000,000 11,275,410,000,000 12,531,420,000,000 14,618,270,000,000 16,119,280,000,000 17,908,280,000,000 19,675,770,000,000 21,089,350,000,000 23,663,490,000,000 26,653,020,000,000 WPI 38.5 40.7 41.4 45.8 50.8 52.8 53.4 54.8 62 67.3 72.9 76.3 83 89 96.4 103.2 106.8 110.7 114.3 123.3 125.7 125.8 131.4 135.5 139.3 Credit Amount Outstanding (Rs.) 15,837,770,000 19,801,210,000 24,812,450,000 29,344,770,000 31,169,710,000 33,824,830,000 33,247,890,000 35,940,970,000 38,848,680,000 47,310,380,000 46,548,450,000 48,661,600,000 48,845,940,000 51,439,570,000 29,620,700,000 43,830,900,000 74,216,100,000 60,770,500,000 79,134,700,000 80,560,000,000 89,000,000,000 110,900,000,000 115,530,000,000 120,432,400,000 129,042,800,000 Wrk. Popln on Reg. 17,840,000 19,750,000 21,950,000 23,550,000 26,270,000 30,130,000 30,250,000 30,050,000 32,780,000 34,630,000 36,300,000 36,760,000 36,280,000 36,690,000 36,740,000 37,430,000 39,140,000 40,090,000 40,370,000 41,340,000 42,000,000 41,170,000 41,390,000 42,380,000 43,140,000 Actual Sales 591,381 759,031 855,432 1,107,185 1,354,112 1,397,902 1,556,918 1,639,087 1,759,499 1,808,272 1,608,623 1,503,352 1,788,269 2,131,101 2,544,317 2,838,761 2,917,351 3,303,425 3,693,541 3,634,378 4,203,725 4,812,126 5,365,013 6,208,860 Esti. Sales 570,661 750,649 887,254 1,088,847 1,329,653 1,420,278 1,539,189 1,636,583 1,749,587 1,828,653 1,393,638 1,626,108 1,959,220 2,175,338 2,589,294 2,723,614 2,853,262 3,180,140 3,653,567 3,811,107 4,240,214 4,904,958 5,233,522 6,045,615 6,905,351

Page 34 Page 34

FIRST GLOBAL
India Research

www.first-global.us

Three-wheelers
Table 23: Key Variables used for Three Wheelers
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI for three-wheelers (same year), Credit Amount OS for Vehicles, Vehicle parts etc (with lag), Working Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

Table 24: Key Variables and Estimated Sales (in numbers)
(YE March) 1981-82 1982-83 1983-84 1984-85 1985-86 1986-87 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 Vehicle Popln. 1,243,000 1,385,000 1,455,000 1,607,000 1,780,000 2,007,000 2,295,000 2,486,000 2,736,000 2,954,000 3,205,000 3,361,000 3,569,000 3,841,000 4,204,000 4,662,000 5,056,000 5,556,000 6,143,000 7,058,000 7,571,000 8,051,000 8,710,000 PDI (Rs.) 1,206,420,000,000 1,388,690,000,000 1,531,260,000,000 1,813,590,000,000 2,022,450,000,000 2,243,710,000,000 2,509,200,000,000 2,863,280,000,000 3,402,920,000,000 3,922,230,000,000 4,611,920,000,000 5,270,180,000,000 6,113,900,000,000 7,076,920,000,000 8,347,640,000,000 9,491,910,000,000 11,275,410,000,000 12,531,420,000,000 14,618,270,000,000 16,119,280,000,000 17,908,280,000,000 19,675,770,000,000 21,089,350,000,000 23,663,490,000,000 26,653,020,000,000 WPI 3.6 3.8 3.8 4.1 4.6 4.7 4.7 4.9 5.6 5.9 6.4 6.8 7 7.5 8.2 8.6 9 9.4 10.2 10.5 11.1 11.3 11.5 11.8 12.2 Credit Amount Outstanding (Rs.) 15,837,770,000 19,801,210,000 24,812,450,000 29,344,770,000 31,169,710,000 33,824,830,000 33,247,890,000 35,940,970,000 38,848,680,000 47,310,380,000 46,548,450,000 48,661,600,000 48,845,940,000 51,439,570,000 29,620,700,000 43,830,900,000 74,216,100,000 60,770,500,000 79,134,700,000 80,560,000,000 89,000,000,000 110,900,000,000 115,530,000,000 120,432,400,000 129,042,800,000 Wrk. Popln on Reg. 17,840,000 19,750,000 21,950,000 23,550,000 26,270,000 30,130,000 30,250,000 30,050,000 32,780,000 34,630,000 36,300,000 36,760,000 36,280,000 36,690,000 36,740,000 37,430,000 39,140,000 40,090,000 40,370,000 41,340,000 42,000,000 41,170,000 41,390,000 42,380,000 43,140,000 Actual Sales 33,470 37,673 41,886 48,944 53,312 60,872 68,052 80,227 83,348 89,448 79,790 64,321 84,307 110,504 144,841 198,463 215,138 189,082 172,135 181,899 200,276 231,529 268,702 322,442 Esti. Sales 22,179 38,677 39,312 55,580 70,273 49,896 73,580 86,726 87,425 78,007 68,998 90,636 104,652 126,900 131,213 157,966 173,823 179,331 197,313 205,948 222,138 234,563 247,505 322,931 341,497

Page 35

FIRST GLOBAL
India Research

www.first-global.us

Tractors
Table 25: Key Variables used for Tractors
Dependent Variable Vehicle Population Independent Variables Main Variables: Personal Disposable Income (with lag), WPI for motor vehicles (same year), Agricultural Production (with lag), Rural Population (with lag) Adjustment Variables: Dummy Variable for Licence Raj, Detrending Variable

Table 26: Key Variables and Estimated Sales (in numbers)
(YE March) 1981-82 1982-83 1983-84 1984-85 1985-86 1986-87 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05 2005-06 Vehicle Popln. 636,225 690,987 748,013 802,551 855,823 893,284 969,700 1,053,377 1,144,981 1,245,241 1,354,951 1,474,982 1,606,284 1,749,895 1,906,949 2,078,688 2,266,464 2,452,909 2,649,322 2,819,414 2,950,441 3,031,927 3,130,970 PDI (Rs.) 1,206,420,000,000 1,388,690,000,000 1,531,260,000,000 1,813,590,000,000 2,022,450,000,000 2,243,710,000,000 2,509,200,000,000 2,863,280,000,000 3,402,920,000,000 3,922,230,000,000 4,611,920,000,000 5,270,180,000,000 6,113,900,000,000 7,076,920,000,000 8,347,640,000,000 9,491,910,000,000 11,275,410,000,000 12,531,420,000,000 14,618,270,000,000 16,119,280,000,000 17,908,280,000,000 19,675,770,000,000 21,089,350,000,000 23,663,490,000,000 26,653,020,000,000 WPI 46.3 47.8 48 50.8 56.4 59.4 62.1 67.7 75.6 82.1 91.2 98 100 107.6 116.6 124.5 129.3 133.4 137.6 146.1 149.2 149.6 149.9 157.3 161.6 Cum. Agri. Prod. 4,376,366,400 4,712,272,900 5,046,002,800 5,386,563,200 5,718,714,700 6,061,176,600 6,406,215,200 6,756,465,600 7,146,027,000 7,562,343,000 7,998,848,600 8,441,216,500 8,868,725,200 9,301,813,900 9,789,812,900 10,272,995,200 10,775,355,200 11,269,025,200 11,783,455,200 12,314,655,200 12,827,505,200 13,359,245,200 13,835,115,200 14,308,335,200 14,776,683,200 Rural Popln. 504,000,000 514,000,000 526,000,000 537,000,000 549,000,000 561,000,000 573,000,000 585,000,000 598,000,000 611,000,000 623,000,000 634,000,000 644,000,000 657,000,000 668,000,000 679,000,000 690,000,000 701,000,000 713,000,000 724,000,000 737,000,000 750,000,000 763,000,000 776,000,000 789,000,000 Actual Sales 71,908 73,849 77,756 76,978 77,349 63,135 103,215 112,768 123,205 134,608 147,067 160,679 175,551 191,799 209,551 228,946 250,137 254,439 270,000 249,572 215,609 170,000 190,000 225,000 Esti. Sales 85,708 55,230 70,078 87,909 71,011 77,016 96,716 111,923 134,841 124,825 142,446 162,094 179,949 195,772 219,092 235,656 242,750 242,330 241,614 251,962 230,038 192,716 176,931 226,428 224,585

Page 36

FIRST GLOBAL
India Research

www.first-global.us

Appendix B: The step-by-step Regression Model
The Multiple Regression Model
First, the basic regression equation with the dependent/ response variable y that spans n years and k independent variables, x1, x2, …xk. Assume that in the region of the x’s defined by the data, y is related approximately linearly to the variables. The aim of response function analysis in the automobile segment is to diagnose the influence of variation among input variables on the annual radial growth of vehicle population using a model of the form:

Eq. 1
Here, yi is a measure of the vehicle population at the ith year, xji is the ith year data on the jth variable. (While we did try Sales Volume also as a potential dependent variable, in each case, the use of Vehicle Population gave a better fit.) In addition to this, for the purpose of testing hypotheses and calculating confidence intervals, it is assumed that ε is normally distributed. Using matrix notation, the model in Eq. 1 can be written:

Eq. 2

The least squares estimator β=(β0, β1, β2, … βk)’ of the regression coefficients of the variables is β = b= (X’X)-1 X’y and the variance-covariance matrix of the estimated regression coefficients in vector b is Var(b)=σ2 (X’X)-1 (Draper and Smith 1981, Myers 1986). Each column of X represents measurements for a particular variable.
Page 37

FIRST GLOBAL
India Research

www.first-global.us

The Concept of Detrending
In most multiple regression analysis involving time-series data, it is common practice to introduce the time or trend variable, in addition to several explanatory variables for the following reasons: a) To uncover the trend of the dependent variable over time. The objective may not be to determine the causes of upward or downward trend, but to describe the data over time. b) The trend variable can be used as a surrogate for a basic variable affecting Y. In the automobile industry, the vehicle sales increases along with the increase in the working population, which may very well have some (linear) relationship with time. c) Another reason for introducing the trend variable is to avoid the problem of spurious correlation. Data involving economic time series, such as PDI and industrial production, in regression often tend to move in the same direction, reflecting a high R2 value, which may not reflect the true association and may reflect only the common trend present in them.

u

Methods of Detrending

1) One can detrend by introducing a trend variable. For instance, in case of the automobile industry, detrending has been accomplished by introducing a variable, which has values from 1 to 24 representing the time-series. 2) Alternatively, one can detrend Y and X and run the regression on detrended Y and X. Assuming a linear time trend, the detrending can be affected by the three-stage procedure discussed. It involves regressing Y on detrending variable, then X on detrending variable, then finally regress the residuals of both regressions, which are free from the influence of time. Computationally, the first method is more economical than the second method, and has been used by us.

Page 38

FIRST GLOBAL
India Research

www.first-global.us

Dummy Variables
A dummy variable is a numerical variable used in regression analysis to represent subgroups of the sample in your study. In research design, a dummy variable is often used to distinguish different treatment groups. In the simplest case, we would use a 0,1 dummy variable where a person is given a value of 0 if they are in the control group or a 1 if they are in the treated group.

u

Dummy Variables for Multiple Groups

Dummy variables are useful because they enable us to use a single regression equation to represent multiple groups. This means that we don’t need to write out separate equation models for each subgroup. The dummy variables act like ‘switches’ that turn various parameters on and off in an equation. In case of the automobile industry, dummy variables can be brought into play to represent the influence of the "License Raj", sub-groups of two time-periods representing before and after 'Licence Raj' can be easily established.

u

Format of Equation with multiple intercepts and slopes
Eq. 3

Y = α 1 + α 2 Di + β1 X1 + β2 X2 + β3 X3 + β4 (Di X1) + β5 (Di X2) + β6 (Di X3) + ε

In case of the automobile sector’s analysis, the dummy variable is multiplied with each of the explanatory variable, which results in the obtaining of differential slopes and intercepts. In the commercial segment, the first period has been coded 1, then the equation for the period would be:
Y = (α1 + α2)+ (β1+β4) X1 + (β2 + β5) X2 + (β3 + β3 ) X3 + ε

The second period has been coded 0, then the equation would be:
Y = α1 + β1 X1 + β2 X2 + β3 X3 + ε

Page 39

FIRST GLOBAL
India Research

www.first-global.us

Handling Autocorrelation
The term autocorrelation may be defined as correlation between members of series of observations ordered in time [as in time series data] or space [as in cross-sectional data]. In regression context, the classical linear regression model assumes that such autocorrelation does not exist in the disturbances (i.e., residual values ei). However, in the real world, Autocorrelation does exist. For example, Agricultural production in one year is correlated to that in the previous year. Hence adjustments are required to use time series data for regression purposes.

u

Detecting Autocorrelation

The most celebrated test for detecting serial correlation is that developed by statisticians Durban and Watson. It is popularly known as the Durban-Watson d statistic, which is defined as

Eq. 4 which is simply the ratio of the sum of squared differences in successive residuals to the RSS. Note that in the numerator of the d statistic, the number of observations is n-1 because one observation is lost in taking successive differences. The calculation the d-statistic to be followed by obtaining the critical dl and du values from the d table. After that, one can follow the decision rules given in the following table:

u

Durbin-Watson d test: Decision rules
Table 27: Decision Rules of Durbin-Watson d test
Null Hypothesis No positive autocorrelation No positive autocorrelation No negative autocorrelation No negative autocorrelation No autocorrelation, positive or negative Decision Reject No decision Reject No decision If 0 < d < dL dL ≤ d ≤ dU 4 - dL < d < 4 4 - d U ≤ d ≤ 4 - dU dU < d < 4 - dU

Page Do not reject 40 Page 40

FIRST GLOBAL
India Research

www.first-global.us

u

Remedial Measures for Autocorrelation

Since the disturbances et are unobservable, the nature of serial correlation is often a matter of speculation or practical exigencies. In practice, it is usually assumed that the et follow the first-order autoregressive scheme, viz.,

Where |ρ| < 1. The ρ can be calculated based on Durbin-Watson d statistic, which gives the following relationship:

Which can be deduced as follows: ρ = 1 – d/ 2 The next step is deriving new values of X and Y using ρ. The new values can be obtained as follows: New Values of X = (Xt – Xt-1 * ρ) Similarly, new values of Y have to be calculated. As mentioned earlier, in the d statistic, the number of observations is n-1 because one observation is lost in taking successive differences. This problem is over come by using Prais-Winsten transformation, where the first value is calculated using: First Value of X = Old Value * (1 - √ρ2).

Eq. 5

Page 41

FIRST GLOBAL
India Research

www.first-global.us

Centering and Scaling
The multiple linear regression model in Equations 1 and 2 can be written in alternative forms by either centering and scaling or standardizing the independent variables. Suppose that the independent variables (each column of X) are centered and scaled, i.e., xji, the ith year measurement on the jth variable (xj) in the natural units, is transformed into xji as follows:

Where

The process of centering and scaling allows for an alternative formulation of Eq. 1 as follows:

Eq. 6 Consider the model formulation in Eq. 6. Separating the first column of ones (1) from the X matrix results in the model form Eq. 7 In this form, β∗=(β∗1 , β∗2, … β∗ k)’ is the vector of coefficients, apart from the intercept and X∗ is then n ⋅ k matrix of centered and scaled independent variables. The notation 1 is used to denote an n-vector of ones. Centering and scaling makes X∗∋ X∗ the k ⋅ k correlation matrix of the independent variables. Let the vector b∗ =(b∗1, b∗2 , … b∗k )’ be the least squares estimator of β∗.

Page 42

FIRST GLOBAL
India Research

www.first-global.us

If a data set is used to fit the centered and scaled model of Eq. 6, one can obtain the estimated coefficients in the original model of Eq. 1 using the following transformation:

The estimate of the intercept is obtained by computing

Where b∗j are estimates from the centered and scaled model of Eq. 7 and b∗0 = mean of y.

Accounting for Multicollinearity
The presence of high correlations between predictor variables is Multicollinearity. In a multiple regression with more than one X variable, two or more X variables are collinear, if they are nearly linear combinations of each other. For eg. As industrial production increases more employment is generated and hence, growth in working population. Multicollinearity can make the calculations required for the regression unstable, or even impossible. It can also produce unexpectedly large estimated standard errors for the coefficients of the X variables involved. Multicollinearity is also known as collinearity and ill conditioning. When the independent variables show mild collinearity, coefficients of a response function may be estimated using the classical method of least squares. Because variables are often highly intercorrelated, use of ordinary least squares (OLS) to estimate the parameters of the response function results in instability and variability of the regression coefficients. When the variables exhibit multicollinearity, estimation of the coefficients using OLS may result in regression coefficients much larger than the physical or practical situation would deem reasonable (Draper and Smith 1981); coefficients that wildly fluctuate in sign and magnitude due to a small change in the dependent or independent variables; and coefficients with inflated standard errors that are consequently nonsignificant.

Page 43

FIRST GLOBAL
India Research

www.first-global.us

The Statistical Method that Accounts for Multicollinearity
Principal Components Regression is a technique to handle the problem of Multicollinearity and
produce stable and meaningful estimates for regression coefficients. For eg. The dependence of working population on industrial production has been eliminated by use of Principal components regression model. The estimators of the parameters in the response function, obtained after performing PCR, are referred to as principal component estimators (Gunst and Mason 1980). Fritts (1976) refers to the values of these estimators as elements of the response function.

u

Principal Components Regression (PCR)

Principal components regression (PCR) is a method for combating multicollinearity and results in estimation and prediction better than ordinary least squares when used successfully (Draper and Smith 1981, Myers 1986). With this method, the original k variables are transformed into a new set of orthogonal or uncorrelated variables called principal components of the correlation matrix. This transformation ranks the new orthogonal variables in order of their importance and the procedure then involves eliminating some of the principal components to effect a reduction in variance. After elimination of the least important principal components, a multiple regression analysis of the response variable against the reduced set of principal components is performed using ordinary least squares estimation (OLS). Because the principal components are orthogonal, they are pair-wise independent and hence, OLS is appropriate. Once the regression coefficients for the reduced set of orthogonal variables have been calculated, they are mathematically transformed into a new set of coefficients that correspond to the original or initial correlated set of variables. These new coefficients are principal component estimators (Gunst and Mason 1980).

u

Computational Technique
Let X* be the centered and scaled n ⋅ k data matrix as given in Eq. 7. The k ⋅ k correlation matrix of the variables is then C=X*’ X. Let λ1, λ2, ... λk, be the Eigenvalues of the correlation matrix, and V = [v1 v2 .. vk ] be the k ⋅ k matrix consisting of the normalized eigenvectors associated with each Eigenvalue. The vectors, vj = ( v1 v2 .. vk )’, are the normalized solutions such that v j‘v j =1 and v j‘v i =0 for i≠j. That is, the Eigenvectors have unit length and are orthogonal to one another. Hence the Eigenvector matrix V is orthonormal, i.e., V V’ = 1. Now, consider the model formulation given in Eq. 7. One can write the original Page 44 regression model (Eq. 7) in the form
Page 44

FIRST GLOBAL
India Research

www.first-global.us

or Eq. 8

Where Z=X*V and α = V’β*. Z is an n ⋅ k matrix of principal components and α = (α1 , α2, .. αk ) is a k ⋅ 1 vector of new coefficients. The model formulation in Eq. 8 can be expanded as

Where z1, z2, …, zk are the k new variables called principal components of the correlation matrix. Hence, the model formulation in Eq. 8 is nothing more than the regression of the response variable on the principal components, and the transformed data matrix Z consists of the k principal components. For the model in Eq. 8 the principal components are computed using: Z = X*V Eq. 9

Where X* is the n ⋅ k matrix of centered and scaled variables without the column of ones, and V is the k ⋅ k orthonormal matrix of eigenvectors. The principal components are orthogonal to each other, i.e.:
Eq. 10

Equation 10 shows that z’j z j = λ and z’j z i = 0, i ≠j. From Eq. 9, one can see that the principal components are simply linear functions of the centered and scaled variables and the coefficients of this linear combination are the eigenvectors. For example, the elements of the jth principal component, zj, are computed as follows:
Eq. 11 Where v1j, v2j,… vkj are elements of the eigenvector associated with λj, and x*j ’s are the centered and scaled variables obtained using Eq. 6. Note that

Page 45

FIRST GLOBAL
India Research

www.first-global.us

and the sum of squares of zj is λj. Since summation of λj is k, then total sum of squares,

is k.. zj accounts for λj of the total variance. If the response variable (y) is regressed against the k principal components using the model in Eq. 8, then the least squares estimator for the regression coefficients in vector α is the vector

and the variance-covariance matrix of the estimated coefficients in vector α is given by

If all of the k principal components are retained in the regression model of Eq. 8, then all that has been accomplished by the transformation is a rotation of the k original variables. The Standard error is obtained by taking the square root of the variance.

u

Calculating the variance and Standard error of b*

The variance and standard error of the coefficients in vector b* can be computed easily, given the variance and standard error of the estimated coefficients in vector αj. In matrix notation, it can be written as follows:

The standard error can be calculated by simply taking the square root of the variance of the coefficients.
Page 46

FIRST GLOBAL
India Research

www.first-global.us

u

Performing the T-Test
To test a hypothesis about the significance of the influence of a variable (H0: β*j = 0 vs. Ha : β*j == 0) using the principal component estimators, Mansfield et al. (1977) and Gunst and Mason (1980) have shown that the appropriate statistic to use is:

Where MSE = σ2

Page 47

FIRST GLOBAL
India Research

www.first-global.us

Appendix C
Bibliography
Sources of Data:
Journal of Public Transportation, Vol. 8, No. 1, 2005 Statistical Profile: 1994, Association of Indian Automobile Manufacturers Sales Statistics: SIAM India Database on Indian Economy: RBI RBI Banking Statistics Energy Prices & Taxes, 1st Quarter 2005 – International Energy Organization (IEA) Energy Statistics 2001: CMIE National Income Statistics 2001: CMIE Industry Growth and Agricultural Growth Predictions: Central Statistical Organisation Ministry of Statistics & Programme Implementation

Sources for construction of Regression Model:
Basic Econometrics: Damodar N. Gurjrati Research Papers
n n n

Draper and Smith 1981, Myers 1986 on estimation of regression coefficients Gunst and Mason 1980 on Principal components regression Fritts (1976) on Elements of the response function
Page 48

FIRST GLOBAL
India Research

www.first-global.us

FG Markets, Inc.
90 John Street, Suite 703, New York, NY 10038

FIRST GLOBAL (UK) Ltd.
Rivington House, 82, Great Eastern Street, London EC2A 3JL, United Kingdom

Dealing Desk (US):
Tel. No: 1-212-2276611 email: [email protected]

Dealing Desk (UK & Europe):
Tel. No: 00-44-207-959 5300 email: [email protected]

The information and opinions in this report were prepared by First Global. Information contained herein is based on data obtained from recognized statistical services, issuer reports or communications, or other sources, believed to be reliable. However, such information has not been verified by us, and we do not make any representations as to its accuracy or completeness. Any statements nonfactual in nature constitute only current opinions, which are subject to change. First Global does not undertake to advise you of changes in its opinion or information. First Global and others associated with it may make markets or specialize in, have positions in and effect transactions in securities of companies mentioned and may also perform or seek to perform investment banking services for those companies. Whilst all reasonable care has been taken to ensure the facts stated and the opinions given are fair, neither First Global (UK) Limited nor FG Markets, Inc. nor any of their affiliates shall be in any way responsible for its contents, nor do they accept any liability for any loss or damage (including without limitation loss of profit) which may arise directly or indirectly from use of or reliance on such information. First Global (or one of its affiliates or subsidiaries) or their officers, directors, analysts, employees, agents, independent contractors, or consultants may have positions in securities or commodities referred to herein and may, as principal or agent, buy and sell such securities or commodities. An employee, analyst, officer, agent, independent contractor, a director, or a consultant of First Global, its affiliates, or its subsidiaries may serve as a director for companies mentioned in this report. First Global and its affiliates may, to the extent permitted under applicable law, have acted upon or used the information prior to or immediately following its publication, provided that we could not reasonably expect any such action to have a material effect on the price. This memorandum is based on information available to the public. No representation is made that it is accurate or complete. This memorandum is not an offer to buy or sell or a solicitation of an offer to buy or sell the securities mentioned. The investments discussed or recommended in this report may not be suitable for all investors. Investors must make their own investment decisions based on their specific investment objectives and financial position and using such independent advisors as they believe necessary. Where an investment is denominated in a currency other than the investor's currency, changes in rates of exchange may have an adverse effect on the value, price of, or income derived from the investment. There may be instances when fundamental, technical, and quantitative opinions may not be in concert. Past performance is not necessarily a guide to future performance. Income from investments may fluctuate. The price or value of the investments to which this report relates, either directly or indirectly, may fall or rise against the interest of investors. There are risks inherent in international investments, which may make such investments unsuitable for certain clients. These include, for example, economic, political, currency exchange rate fluctuations, and limited availability of information on international securities. The value of investments and the income from them may vary and you may realize less than the sum invested. Part of the capital invested may be used to pay that income. In the case of higher volatility investments, these may be subject to sudden and large falls in value and you may realize a large loss equal to the amount invested. Some investments are not readily realizable and investors may have difficulty in selling or realizing the investment or obtaining reliable information on the value or risks associated with the investment. Where a security is denominated in a currency other than sterling (for UK investors) or dollar (for US investors), changes in exchange rates may have an adverse effect on the value of the security and the income thereon. The tax treatment of some of the investments mentioned above may change with future legislation. The investment or investment service may not be suitable for all recipients of this publication and any doubts regarding this should be addressed to your broker. While First Global has prepared this report, First Global (UK) Ltd. and FG Markets, Inc. is distributing the report in the UK & US and accept responsibility for its contents. Any person receiving this report and wishing to effect transactions in any security discussed herein should do so only with a representative of First Global (UK) Ltd. or FG Markets, Inc. First Global (UK) Limited is regulated by FSA and is a Member firm of the London Stock Exchange. FG Markets, Inc. is regulated by SEC and is a member of National Association of Security Dealers (NASD) and Securities Investor Protection Corporation (SIPC). FG Markets, Inc., its affiliates, and its subsidiaries make no representation that the companies which issue securities which are the subject of their research reports are in compliance with certain informational reporting requirements imposed by the Securities Exchange Act of 1934. Sales of securities covered by this report may be made only in those jurisdictions where the security is qualified for sale. Additional information on recommended securities is available on request. This report may not be resold or redistributed without the prior written consent of First Global.

Page 49

Sponsor Documents

Or use your account on DocShare.tips

Hide

Forgot your password?

Or register your new account on DocShare.tips

Hide

Lost your password? Please enter your email address. You will receive a link to create a new password.

Back to log-in

Close