Chapter 5 DETERMINANTS OF FDI IN INDIA: AN ECONOMETRIC ANALYSIS The aim of this chapter is to identify the determinants of FDI inflows in vanous industries and states of India, as well as those for aggregate inflows, by employing tools of applied econometrics. We employ panel models for examining the determinants of FDI across industries and states of India. FDI inflows across industries and states over a period of time are examined in terms of various industry and state-specific explanatory variables. Accordingly, panels ofFDI inflows across industries and states are constructed. We also analyse the determinants of aggregate FDI inflows in India in terms of specific macroeconomic parameters using simple time series data. The chapter is organised into four sections. Section 1 sets up the testable hypotheses. Section 2 specifies the econometric models for estimation, discusses the data and variables and explains the econometric methodology employed. Section 3 reports and analyses the results. Section 4 gives a synthesis of the main findings. 5.1 TESTABLE HYPOTHESES We categorise our hypotheses into three groups. The first group looks at industry- specific determinants of FDI. The second group focuses on state-level characteristics. The third and final group comprises macro-level determinants of aggregate FDI flows. 106
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Chapter 5
DETERMINANTS OF FDI IN INDIA: AN ECONOMETRIC
ANALYSIS
The aim of this chapter is to identify the determinants of FDI inflows in vanous
industries and states of India, as well as those for aggregate inflows, by employing tools
of applied econometrics.
We employ panel models for examining the determinants of FDI across industries and
states of India. FDI inflows across industries and states over a period of time are
examined in terms of various industry and state-specific explanatory variables.
Accordingly, panels ofFDI inflows across industries and states are constructed. We also
analyse the determinants of aggregate FDI inflows in India in terms of specific
macroeconomic parameters using simple time series data.
The chapter is organised into four sections. Section 1 sets up the testable hypotheses.
Section 2 specifies the econometric models for estimation, discusses the data and
variables and explains the econometric methodology employed. Section 3 reports and
analyses the results. Section 4 gives a synthesis of the main findings.
5.1 TESTABLE HYPOTHESES
We categorise our hypotheses into three groups. The first group looks at industry
specific determinants of FDI. The second group focuses on state-level characteristics.
The third and final group comprises macro-level determinants of aggregate FDI flows.
106
5.1.1 Industry-level hypotheses
Industry size
Among various industry-level characteristics that are likely to be significant
determinants of inward FDI, we identify the size of the industry as a crucial factor.
Larger industries have well-developed markets for final products in the host country,
along with established input suppliers and skilled labour, resulting in several external
economies of scale ( orindustry size). These industries also perhaps belong to sectors in
which the host nation enjoys comparative advantage. Accordingly, we may expect more
FDI to flow into these sectors.
Empirical research on role of industry size as a determinant of FDI has been relatively
limited. This is, because, the thrust of the empirical literature on determinants of FDI
has been largely on macro-level country-specific determinants (e.g. size of the host
country market). Industry-specific studies, however, have found evidence of industry
size being a significant and positive determinant of FDI (e.g. Morgan and Wakelin
(1999), in an empirical study of the determinants of FDI in different categories of the
U.K. food industry).
Labour intensity
Given the intrinsic features of FDI in terms of specific ownership attributes (e.g. money
assure foreign investors about regular participation of labour in production, apart from
indicating fewer disruptions in production schedules. We expect states with better
industrial relations to attract more FDI.
Degree of industrialisation
Ownership advantages of FDI can be exploited more meaningfully in manufacturing
and service sectors. More industrialised locations have larger presence of manufacturing
and service activities. These locations also offer a more enabling environment for FDI.
Accordingly, we hypothesise that FDI will show a higher propensity to flow into the
states that are more industrialised.
Technological capabilities and infrastructure
R&D initiatives undertaken at the state-level reflect the quality of technological
infrastructure available in the states. Higher R&D initiatives not only improve the
quality of existing technological infrastructure, but also enhance technological
capabilities. These are expected to act as 'pull' factors for FDI, since availability of
indigenous technological capabilities can help foreign firms in exploiting their
111
ownership advantages better. We hypothesise FDI flows to be positively related to the
level of technological capability and infrastructure of the states.
5.1.3 Macro-level hypotheses
Market size
We have already discussed the importance of host country market size as a determinant
for incoming FDI. Earlier, in chapter 3, we have mentioned various empirical studies
that have identified market size as a significant factor influencing FDI flows for
developed countries, LDCs, as well as the Indian economy. In the present study, we
would like to study the effect of the domestic market size on aggregate FDI inflows into
India. We expect FDI to be positively related to the size of the domestic market.
Returns to Capital
We attempt to study three related determinants ·in this category. These are stock market
returns, FII investment and non-resident deposits.
Stock market returns
Higher returns from domestic stock markets indicate higher returns on the equity capital
invested in the host economy. Though returns from stock markets are not considered
traditional determinants of FDI, neo-classical trade theory identifies differences in rates
of return as the main reason behind movement of capital across nations. In that sense,
stock market returns may reflect the incentive for capital movement. We would like to
study the impact of returns from stock markets on incoming FDI. We expect stock
market returns to have a positive relationship with FDI flows.
112
FII inflows
FII inflows into a host economy are intricately linked to returns from stock markets.
Portfolio investments by Fils are determined on the basis of their perceptions regarding
risks and returns from the host economy. These inflows usually increase if the risk··
return expectations are favourable. Higher FII inflows, reflecting positive expectations
about returns from the host economy, can encourage FDI flows. Accordingly, we
hypothesise FDI flows to be positively related to FII inflows.
Inflows of non-resident bank deposits
Bank deposits by expatriates respond favourably to the difference in interest rates
between source and host countries. Host country deposit rates reflect the nature of
returns to capital in that country. Higher inflows of non-resident deposits in response to
higher deposit rates (i.e. higher returns on capital) can motivate FDI flows, according to
the principle of capital arbitrage. We expect FDI flows to be positively related to
inflows of non-resident deposits.
( Export-orientation
Greater export-orientation of the host economy is expected to attract more FDI of the
'export-oriented' variety (Singh and Jun, 1995), Studies on India, however, suggest
greater inflow ofFDI ofthe 'domestic market-oriented' variety, rather than the 'export
oriented' type (Guha and Ray, 2001). We would like to revisit the issue in the present
study.
113
5.2 ECONOMETRIC MODEL SPECIFICATION, DATA AND VARIABLES,
AND ECONOMETRIC METHODOLOGY
5.2.1 Econometric model specification
We specify econometric models for testing our three sets of hypotheses.
Industry and state-level hypotheses
For industry and state-level hypotheses, we posit the following panel regression model:
(1) i=l,2, ....... N; t=l,2, ...... T; where
yit: FDI inflow in i-th industry in period 't'(or in i-th state in period 't').
xit: Vector of specific characteristics for i-th industry in period 't' (or i-th state in
period 't').
a1: the individual effect for the ith industry (or state) assumed to be constant
over time.
Eit : the stochastic error term.
Macro-level hypotheses
We propose a simple time series model for our macro-level analysis.
Yt= a+ f3xt + Et; (2) t=l,2, ...... T;,where
Yt : Aggregate FDI inflow in period t .
x1 : Vector of specific macro-economic parameters for period t.
E 1 : the stochastic error terriL
5.2.2 Data and variables
Our study employs panel models for identifying the determinants of FDI at the industry,
state and country levels. The variables are constructed accordingly.
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5.2.2.1 Dependent variable (FDI)
We use actual FDI inflows as the dependent variable for testing our industry-level
hypothese~. Data on annual FDI inflows on an industry-wise basis are compiled by the
Secretariat for Industrial Assistance (SIA), Department of Industrial Promotion and
Policy, Ministry of Industry, Government of India. FDI data has been obtained from
annual issues of the SIA newsletters (2000 and 2002).
Unlike industry, data on actual FDI inflows on a state-wise basis, however, are not
available before the year 2000. Due to this data constraint, we proxy actual FDI inflows
by approved FDI flows. Approvals indicate investment intentions of foreign investors.
These intentions are influenced by the various state-level characteristics that we have
hypothesised. Accordingly, we expect results obtained by using FDI approvals to reflect
accurately the nature of relationship between incoming FDI and various explanatory
variables. Data on FDI approvals is also maintained by the SIA and was obtained from
the same sources mentioned above.
We take aggregate FDI inflows as the dependent variable for our country-level analysis.
Information on aggregate FDI inflows into India is available with both the SIA and the
RBI. On the present occasion, we use the RBI data. 38
5.2.2.2 Explanatory variables
5.2.2.2a Industry-level analysis
Industry size
We employ three variables for capturing industry size. The first of these is share of sales
of a particular industry in total industrial sales (salesxsales) for a given year.
38 See RBI (2002).
115
salesxsa/esu = (Sales of i-th industry in year 't') I Total industrial sales in year
't'.
Industry size is also measured by Sales, which reflects the value of total sales for
industry 'i' in year 't'.
The third variable used for industry size is GV AXGVA, which is the share of Gross
Value Added (GVA) by industry 'i' in year 't" in total industry GVA for year 't'.
GVAxGVAu = (GV A for i-th industry in year't')l Total industrial GV A in year
't'.
The data for industry-wise sales39 and GV A 40 have been obtained from the Corporate
Sector (May 2002) report brought out by the Centre for Monitoring Indian Economy
(CMIE).
Labour intensity
We measure labour-intensity of an industry by the share of wages and salaries of a
particular industry, i.e. the total wage bill, in industrial GV A. The variable is expressed
as wsxGVA, where,
wsxGVAit =(Wages and salaries for i-th industry in year 't') I (Total GVA fori-
th industry in year 't')
This variable fails to make a distinction between skilled and unskilled labour intensity.
Due to Jack of disaggregated data on wages and salaries for skilled and unskilled labour,
our variable reflects labour-intensity as a whole. The result, therefore, may be distorted
39 Sales are defined as Income generated from main business activities like sale of goods and services, fiscal benefits, trading income. It also includes internal transfers but excludes expenses capitalized. See CMIE (2002).
116
in reporting the essence of the labour-intensity hypothesis. We_would like to clarify that
though we expect FDI to flow more into capital-intensive industries, given the
significance of skilled labour as a determinant of FDI, we should ideally employ
variables that measure labour-intensities separately in terms of skilled and unskilled
components.
Data on wages and salaries have been taken from the CMIE data source cited earlier.
Export-orientation
Export-orientation is measured by the volume of exports from a particular industry as a
proportion of total industrial sales. The variable is expressed as expxsales, where
expxsalesit = (Total export earnings41 for i-th industry in year 't') I (Total sales
for i-th industry in year 't')
Data on export earnings and industrial sales have been obtained from the CMIE data
source.
Import-intensitv
We measure import-intensity by the volume of imports for an industry as a proportion
of total industrial sales. The variable is expressed as impxsales, where
impxsalesit = (Total import expenses42 for i-th industry in year 't') I (Total sales
for i-th industry in year 't')
Data for import earnings have been taken from the CMIE data source.
40 GV A is defmed as the sum of wages and salaries, interest payments, rent paid, profit before tax, and depreciation. Interest and rent payments are net of receipts, while profit before tax is net of non-recurring transactions. See CMIE (2002) 41 Total exports are defined as total forex earnings, including earnings from export of goods on FOB value, as well as forex earnings from services. See CMIE (2002).
117
Profitability
Profitability of industries is measured by the share of profit after tax (PAT) (net of non-
recurring transactions) in total sales of an industry. The variable is expressed as
pat.xsales, where,
Pat.xsalesit = (Total profits after tax for i-th industry in year 't') I (Total sales for
i-th industry in year 't')
Data on profit after tax has been taken from CMIE.
Advertisement-intensitv
We use the share of advertising expenses, as a proportion of total industrial sales, as a
measure of advertisement-intensity. The variable is expressed as advtxsales, where
advtxsalesit = (Total advertising expenditure for i-th industry in year 't') /
(Total sales for i-th industry in year 't')
Data on advertising expenses43 has also been collected from the CMIE.
A note on the CMIE data source is given in Appendix 1.
For the industry-level analysis, we estimate the panel regression model specified in the
earlier section for two different data sets. The first data set comprises eighteen
manufacturing industries. These are: metallurgical, fuels, electrical equipment,
42 Total import expenses include the CIF value of import of raw materials, stores, import of capital goods and also foreign exchange outgo on royalty, know-how, fees, dividend, interest etc. See CMIE (2002). 43 Advertising cost is defmed as the expenditure incurred on advertising. It also includes marketing expenditure such as rebates, discounts and commissions. See CMIE (2002).
118
The second data set includes services, hotel & tourism, and trading, in addition to the
eighteen manufacturing industries. However, due to lack of data on advertising cost for
services, we had to drop advtxls as an explanatory variable from the second variation.
The time period for estimation is 1994-95 to2000-01.
5.2.2.2b State-level analysis
Market size
We capture the size of domestic market for states through annual per capita net state
domestic product (SDP) at current prices. The variable is expressed as pcnsdp. Per
capita net SDP is an income proxy of the market size, reflecting the purchasing power.
Market size can also be measured in terms of the absolute value of net SDP. However,
we have constructed pcnsdp after normalising absolute values ofNSDP by population.
Values of pcnsdp have been obtained from the annual Economic Survey (2002-03)
published by the Ministry of Finance, Government of India.
Infrastructure
In our analysis, we focus specifically upon three major components of infrastructure.
These are transport infrastructure, electricity, and telecommunication, respectively. We
measure transport infrastructure through two variables: raildensity and rddensity. While
raildensity indicates the state-wise density of rail route length per '000 sq. km. of area,
rddensity is state-wise density of road length per '000 sq. km. of geographical area.
Data for both these variables have been obtained from the Infrastructure report44
brought out by the CMIE.
44 See CMIE (2003).
119
We measure availability of electricity through per capita electricity consumption in
states. The variable is expressed as pcelecon. Data on state-level per capita electricity
consumption has been taken from the Annual Report (2001-02) on the Working of State.
Electricity Boards & Electricity Departments brought out by the Planning Commission.
Finally, we try to capture the availability of telecommunication services by delciricle,
which measures circle-wise direct exchange lines (provided by BSNL & MTNL) in
'000 numbers for every state. Data on number of circle-wise direct exchange lines has
also been obtained from the CMIE database cited above.
Quality of industrial relations
Quality of industrial relations in various states is measured by number of mandays lost
on account of strikes and lockouts. The variable is expressed as mtmdays. Information
on number of mandays lost annually, state-wise, has been obtained from various issues
of the Handbook of Indhstrial Statistics published by the Department of Industrial
Promotion & Policy (DIP&P), Government oflndia.
Degree of industrialisation
We use the share of non-agricultural domestic product in net SDP at current prices, as a
measure for degree of industrialisation. The variable is expressed as nonagrdp.
nonagrdpit = 1- (Net domestic product from agriculture in i-th state in year
't')/(Total net domestic product in i-th state in year 't')
Values of nonagrdp for different states have been calculated on the basis of sectoral and
aggregate estimates for SDPs from the National Accounts Statistics compiled by the
Central Statistical Organisation (CSO).
120
Technological Capabilities and Infrastructure
We have tried to quantify the level of technological capabilities and infrastructure at
state-level in terms of share of R&D expenditure as a proportion of per capita net SDP
for each state. The variable is expressed as rdpcnsdp.
rdpcnsdpu = (Total R&D expenditure by state 'i' m year 't') I (Per capita
NSDP for state 'i' in year 't')
The values of rdpcnsdp has been estimated on the basis of data on state-level R&D
expenditure, compiled from statistics released by the Department of Science and
Technology in various issues of the Handbook of Industrial Statistics brought out by the
Ministry of Industry, Government of India.
The panel regression model specified in the earlier section has been estimated for
sixteen states of the country. These are: Andhra Pradesh, Assam, Bihar,, Gujarat,
We find that the coefficient of gdpgr is statistically insignificant. The result does not
confirm our hypothesis that FDI in India responds positively to growth in domestic
market size and also contradicts the findings of several empirical studies. The short
length of the time series can probably explain the result. Variations in real GDP growth
during this period (1992-93 - 2001-02) have been in the range of only around 3 .. 5
percentage points. Estimation of GDP growth over a longer time series might produce
different results.
Returns to capital
Stock market returns
The coefficient of peratio is found to be negatively significant. The result confirms our
hypothesis and indicates that FDI flows respond positively to lower values of peratio,
which arise when earnings from stock rrtarkets increase relative to prices. There is
therefore clear evidence ofFDI inflows being sensitive to returns from stock markets.
FII inflows
The coefficient of jiiinvnet is positively significant confirming our hypothesis. Thus,
there' is evidence that higher FII inflows, which occur from favourable expectations of
returns from the host economy, appear to encourage FDI also, through a 'demonstration
effect'. Since FII inflows are· strongly related to returns from stock markets, the latter
appear to be a major factor behind not only higher FII inflows, but also FDI flows.
Non-resident deposits
The coefficient of nridepnet is statistically insignificant. Thus, higher inflows of NRI
deposits are not a significant determinant for FDI
138
Export-orientation
The coefficient of exportGDP is also insignificant, The result corroborates the earlier
findings from the panel regression analysis, which suggest that export-intensity is not a
significant determinant ofFDI in India. FDI in India, therefore, is not export--oriented.
5.4 A SYNTHESIS
In this section, we try to present a synthesis of the results that we have obtained from
our industry-level, state-level and country-level analyses.
Industry-level analysis
Industry size is clearly a significant determinant of FDI in India. Industries with larger
sizes are seen to attract more FDI.
Although we expected FDI to flow into more capital-intensive industries, the positive
and significant coefficient of labour-intensity perhaps reflects the propensity of foreign
firms to invest in skill-intensive activities. These industries offer foreign firms ample
scope for exploiting their ownership advantages.
Import-intensity also emerges as a significant determinant of incoming FDI. Like skill
intensive industries, industries using more imported inputs in production offer foreign
firms considerable opportunities for better exploiting their ownership advantages again.
On account of better access to foreign inputs like imported raw materials, stores, capital
goods, know-how etc. multinationals are expected to be much more competitive than
domestic firms in import-intensive industrie~ and hence these are the sectors which may
attract larger FDI.
139
We had expected FDI to flow into more profitable industries. The results vindicate our
expectation. Profitability has a positive and significant impact on the level of FDI.
Results appear to be somewhat inconclusive with respect to advertising-intensity. If at
all, our results show that FDI is likely to be attracted to relative advertisement-intensive
· industries in India.
We have, however, obtained fairly clear evidence of FDI in India not being export-
oriented. Our results in this regard appear to confirm earlier findings of empirical
research, which point to FDI in India being more of the 'domestic market-oriented'
variety. The direction of causality between FDI and exports in India remains an
important agenda for future research47.
State--level analysis
The 'domestic market-oriented' nature of FDI in India gathers stronger evidence from
the results obtainkd in our state-level analysis. Market size is found to be a highly
significant locational determinant for FDI flows. It is clear that the advantages of scale
economies offered by large markets are important factors influencing FDI decisions in
India.
We have obtained interesting results regarding the role of infrastructure in motivating
FDI. We find that availability of electricity and communication facilities are critical
factors in deciding FDiflows. Rail and road networks, however, are not significant: Our
findings indicate that FDI has a clear tendency to locate close to markets for final
products. This tendency strengthens the decision to enter large markets and reinforces
47 Though FDI has not been found to be attracted to export-oriented industries, there is empirical evidence indicating that FDI has led to diversification of exports from traditional to non-traditional sectors in India. See Banga (2003).
140
the significance of market size~ We further argue that FDI in India probably has a larger
concentration in non-tradeables, for which, the locations of producers and consumers
are usually the same, thereby reducing the importance of facilities required for physical
shipment of goods. The significance of electricity and communication facilities also
points to the entry of FDI into sectors where the availability of these inputs is vital, i.e.
high technology, knowledge-intensive activities.
We hypothesised that more industrialised states are likely to attract greater FDI. Our
results point to similar conclusions. Degree of industrialisation of states is found to be a
significant determinant of FDI flows.
We did not find FDI flows to be sensitive to the quality of industrial relations.
The role of technological capabilities and infrastructure in attracting FDI is indeed ·a
significant result of our study., The positive significance of R&D expenditure at the
state-level to FDI flows clearly demonstrates the importance of possessing quality
teclmological infrastructure and technological capabilities at the local level for
attracting FDI. Our earlier results from the industry-level analysis, which point to the
inclination of FDI to move into skill-intensive industries, also acquire significance in
this regard. Availability of indigenous technological capabilities certainly enables
foreign firms to better utilise their ownership advantages.
Macro-level analysis
Our study of determinants of aggregate FDI inflows does not indicate market size to be
a significant determinant ofFDI. We attribute this result to the limited span of the time
series. However, it is important to mention in this context that we had employed growth
in GDP as our measure of market size. This measure is an indicator of potential market
141
size, rather than current size. It is possible that the results might have been different had
we used measures for the current size.
With respect to returns to capital, our findings regarding response of FDI flows to stock
market returns are indeed interesting. We find FDI flows to be positively related to
stock market returns. The results indicate that among other things, the returns earned on
equity capital deployed are important factors behind FDI decisions. We also find FII
inflows to positively encourage FDI through a 'demonstration effect'. This finding
markets and higher FII inflows are likely to encourage greater FDI flows into India. We
do not find inflows of non-resident deposits to be a significant determinant ofFDI.
We also find that FDI in India does not respond to exports. This reinforces our earlier
results that market size acts as a strong 'pull' factor for FDI in India. Our results appear
to confirm that FDI in India is essentially 'domestic market-oriented'.
142
A Note on the Data
Data on various explanatory variables for industry has been obtained from the database of the Centre for Monitoring Indian Econom/8 (CMIE). The CMIE accumulates data on an annual basis for a select sample of companies, which include both public and private companies. The sample varies in terms of number of companies covered each year. The nature of co~panies covered in terms of ownership during the period under consideration (1994-95- 2000-01) is given below:
Distribution of Companies according to Ownership (in numbers) Industry 1994- 1995-96 1996- 1997-98 1998-99 1999-00 2000-01 groups 95 97 Manufacturing 3774 4372 4436 4268 4126 4225 4207
The above companies account for 74 per cent of the gross value added in the industrial sector of the country and 78 per cent of the total value of output in the manufacturing sector. There were, however, certain inconsistencies in the classification of industries between the CMIE and the SIA. While the CMIE broadly follows the Annual Survey of Industries (ASI) classification of the Central Statistical Organisation (CSO), the SIA data is classified
48 See CMIE (2002).
143
differently. In order to make the two sets of data compatible, the following matching exercise has been carried out:
Industries: SIA Industries: CMIE Modified format (1) (2) (3)
Metallurgical (ferrous, non- Ferrous metals, non-ferrous The four industries m (2) ferrous, special alloys, metals, mmmg, metals & have been grouped together mining & miscellaneous) metal products under metallurgy. Fuels (power, oil refinery, Petroleum products and The two industries in (2) have fuels) electricity been grouped together under
fuels. Electrical equipment Electrical equipment and The two industries in (2) have (electrical equipment, electronics (including been grouped together under computer software, computer computer) electrical equipment. hardware, electronics) Transportation industry Automobiles (including The two industries in (2) have (air/sea transport, passenger cars) and auto been grouped together under automobiles, passenger cars, ancillaries transportation. auto ancillaries, ports) Industrial machinery, Non-electrical machinery FDI for industries in ( 1) has machine tools, agricultural been accumulated to machinery, earth-moving represent FDI Ill non-machinery, miscellaneous 1 electrical machinery mechanical and engineering, commercial office & household equipment Fertilisers Fertilisers No change Chemicals (other than Chemicals No change fertilisers) Drugs & phannaceuticals Drugs & pharmaceuticals No change Textiles Textiles No change Paper & pulp including paper Paper & paper products No change products Sugar Sugar No change Fennentation industries Beverages & tobacco The industry in (2) has been
represented under fermentation industries
Food processing (food Food products Food products in (2) has been products & marine products) represented under food
processing Vegetable oils & vanaspati Vegetable oils & products No change Rubber goods Rubber and rubber products No change Soaps, cosmetics & .toiletries Soaps and detergents Industry Ill (2) has been
represented as soaps & detergents
Leather, leather goods & Leather products Industry m (2) has been pickers represented as leather. Cement & gypsum Cement Industry in (2) has been
represented as cement Services Services No change Hotel & tourism Hotel & tourism No change Trading Trading No change
144
Some industries from SIA had to. be excluded, as they could not be matched with the CMIE industries. These are: boilers & steam generating plants, prime movers other than electrical, telecommunication, medical and surgical appliances, industrial instruments, scientific instruments, photographic raw film and paper, dye stuffs, glue & gelatine, glass, ceramics and consultancy.
145
Appendix2 A Note on Principal Component Regression Method
The principal component method is a popular method used in applied econometrics for overcoming multicollinearity problems. The basic method (Maddala, 2001) can be outlined as follows: Let there be x 1, x2, .......... xk explanatory variables in a regression model. Let it be further assumed that these variables are correlated. For x~, x2, .......... xk explanatory variables, there can be z1, z2, .......... zk linear functions, which can be represented as:
The a's in (1) can be chosen in such a way so that Var(zl) is maximised subject to: 2 2 2 1 (2) a, +a2 + ............... +ak = .... .
By maximizing the variances of the linear functions (z1, z2, etc) subject to the condition that sum of the squares of the coefficients will be equal to 1, k solutions can be obtained, corresponding to which k linear functions z 1, z2, .......... zk can be constructed. These are the principal components of the k explanatory variables. They can be ordered as:
Var(z1) > Var(z2) > .......... Var(zk) z1, which has the highest variance is the first principal component, followed by z2, the second principal component etc. These principal components are orthogonal or uncorrelated, unlike the x's.