CHAPTER 3 DATABASE AND METHODOLOGY In the present chapter, sources of database used and methodology applied for the empirical analysis has been presented The whole chapter has been divided into three sections Section 3 explains the sources of database used and construction of relevant variables for the empirical analysis In Section 32, different methodologies have been explained in details which are used for the empirical analysis Final section concludes the whole chapter 3 Database For the study purpose, six input-output transaction tables (IOTTs) for the years 983-84, 989-90, 993-94, 998-99, 2003-04 and 2006-07 of Indian economy have been utilized All the Input-Output tables are provided after every five years by Central Statistical Organization (CSO), Government of India Following table shows the classification of sectors of all IOTTs with year of publication:- Table 3: Sectoral Classification for all Input Output Transaction Tables (IOTTs) S No IOTT Year of Publication No of Sectors 983-84 990 60 2 989-90 997 5 3 993-94 2000 5 4 998-99 2005 5 5 2003-04 2008 30 6 2006-07 20 30 Source: Author s Elaboration The actual Input-Output table for 983-84 & 993-94 divide the whole economy into 60 and 5 sectors respectively whereas for 2006-07, number of sectors has been
increased to 30 due to some additions of new sectors as well as through further disaggregation of some of the existing one Further, recent Economic Surveys, from 2007-08 to 202-3 provided by Ministry of Finance, Government of India, have been utilized to analyze the demand pattern during financial crisis As per the Appendix III, IOTT of 983-84, shows the sector classification which is equal to 5 Appendix IV explained that the CSO itself aggregates all these 5 sectors to 60 sectors which is followed by our study Due to negligible output of two sectors which are Ownership of Dwelling and Public Administration they have been merged into Other Services That is why for the study purpose, the given Input/Output tables have been adjusted to aggregate the whole economy into 58 sectors (see Appendix Table A7 for detail) These matrices provide the detailed input flow among each sector of the economy To neutralize the effect of change in prices, the values of Input/Output tables have been deflated at 2003-04 prices Hence, all the variables are measured at 2003-04 prices For structural decomposition analysis, following Saxena et al (203), the absorption matrices (commodity by industry matrix) representing input flows of an economy, of three Input/Output tables 983-84, 993-94 and 2006-07 have been used For analyzing the pre- and post-reforms periods separately, two ranges of output change have been studied viz, output growth from 983-84 to 993-94 considered as output change in Pre-reforms period and output growth from 993-94 to 2006-07 considered as Post-reforms period For calculating the linkages, absorption matrix (commodity by industry matrix representing input flows) of all six tables, provided by the Central Statistical Organization (CSO), New Delhi, have been utilized These matrices provide the detailed input flow among each sector of the economy For time-series regression analysis, time-series data on five variables have been culled out from Handbook of Statistics on Indian Economy, provided by RBI The complete description of every variable is mentioned in Table 32 See Appendix Tables A, A2 and A3 for detail 8
Table 32: Description of Variables Used for VAR Analysis Nature SNo Variable Description Dependent ln(share) Log of Share of Services Sector in Total GDP 2 ln(open) Log of Openness constructed as follows: (Total Exports + Total Imports) / Total GDP Independent 3 ln (GCF) Log of Gross Capital Formation 4 ln(fdi) Log of Net Foreign Direct Investment Inflows 5 LNGNPPC Log of Per-Capita GNP Notes: Nature of variable is defined only to estimate the regression in the first instance As in VAR analysis, every variable is endogenous variable, so while doing VAR analysis, every variable is assumed as endogenous one Source: Author s Elaboration 32 Methodological Background for the Analysis For analysis purpose, two types of methodologies have been utilized viz, deterministic analysis using Input/Output tables and regression analysis using time series data on required variables Following two subsections explain the two types of methodologies used for the empirical analysis in Chapter 4, 5 and 6 32 Deterministic Approach Using Input/Output Analysis An input output table is made up of rows and columns, row representing sectoral output and the column representing sectoral purchases The figure entered in each column of the table describes the input structure of the corresponding sector, whereas each row shows what happens to the corresponding output sector The system includes an integrated set of supply and use tables or matrices as well as symmetric input output tables or matrices They provide a detailed analysis of the process of production and use of products and the income generated in that production Symmetric means there are same classifications (groups of products) which are used in both rows and columns The input output tables serve a coordinating framework for economic statistics, both conceptually for ensuring the consistency of the definitions and classifications used and 82
as an accounting framework for ensuring the numerical consistency of data drawn from different sources As an analytical tool, input-output data provides macro-economic models linking final demand and products output levels Input output analysis also serves a number of other analytical uses Static input output analysis can be studied independently of the system of national accounts as well This section will first introduce static input-output analysis as inter-industry analysis assuming that one industry produces one good (homogeneity assumption) and explain the related models and applications Then the real economic life situation will be considered where an industry produces products and by-products and the compilation of symmetric input output tables will be described It may be remembered that supply and use tables represent intermediate stage between basic statistic and symmetric input output tables 32 Static Input Output Analysis The productive process of a complete economic system can be described in a unified way through inter-industry (or input-output) transactions table and analysis As will be seen, an input-output table is a convenient form of presentation to depict the destinations of the outputs of individual industries over a given period of time and the origins of the costs associated with these outputs The inter-industry analysis has two phases: (i) the Input/Output table which gives inter-industry accounting and provides consistency checks to the national income estimates; and (ii) Input/Output model which is used for projections, perspective planning and many other applications The three basic elements of the inter-industry analysis are that (i) it classifies economy into various productive industries usually called sectors (say n sectors), (ii) it considers both uses ie the intermediate uses and final uses and (iii) it considers the availability of a product (good or service) with time dimension which is usually taken as one year The equivalence relation of the availability of a product and its utilization is described below: Intermediate use + Consumption + Fixed capital formation + Change in stock + Export Import = Current production 83
322 Input-Output Table For a sector the equivalence relation can be visualized as a row If we consider such relations for all the n sectors of the economy, we get an array in the form of a tabular arrangement of n rows This tabular arrangement augmented by a row of sectoral value added is termed as the Input/Output table of the economy The table 33 depicts all the inter-industry transactions of the economy More specifically a row in an Input/Output table shows the sales made by one economic sector to various sectors and final uses, whereas a column shows what the sector purchased from different sectors and primary inputs (value added components of incomes) Table 33: Input Output Transaction Table with n Sectors Intermediate-Use Final Use Gross To 2 j n Cons FCF CIS Exp Imp Output From (-) 2 j n c f s e m 2 2 22 2j 2n c 2 f 2 s e 2 m 2 2 i i i2 in ci f i s ei mi i n n n2 nj nn cn f n s en mn n Primary Inputs V V 2 V j V n Total 2 j n C F S E M Notes: Cons = Consumption; FCF = Fixed Capital Formation; CIS = Change in Stocks; Exp = Exports; Imp = Imports Source: Author s Elaboration Notations: Using the following notations (in value terms) : Output of i th product used as input in j th industry i : Total output of the i th product, i =, 2,, n c i : Consumption (household and government) of the i th product 84
fi : Fixed capital formation out of the i th product si : Net change in stock (closing - opening) of ith product ei : Export of the i th product mi : Import of the ith product V i : Gross Value Added of the ith sector (industry) Y i : Total final use of i th product Y i = ci + f i + s i + e i - m i, i =, 2,, n (3) The general equilibrium balance equivalence relation equation can be written as, i + i2 + in + c i + f i + s i + e i - m i = i, i =, 2,, n (32) This system of n equations is called the Input Output system 323 The Four Quadrants The distinction commonly made in economic analysis between the production of goods and services and their final utilization is reflected in the four divisions in form of the quadrants of Input-Output Table The producing sectors are placed in the quadrant-i while the final demand vectors in the quadrant-ii The quadrant-i shows the intermediate transactions ie the flows of goods and services which are both produced and consumed in the process of current production Quadrant-II shows the sales by the producing industries to final uses such as private consumption, government consumption, fixed capital formation, change in stocks and net exports Quadrants I and II together allocate the total output of each industry in the economy Quadrant-III shows the primary (factor) inputs and consumption of fixed capital that are required by each producing industry, thus constituting the gross value added in each industry Quadrants I and III together show the total inputs used in production by each industry in the economy Quadrant-IV records the totals of the various categories of final demand, conceptually representing the familiar GDP expenditure components It is interesting to note in the above static input output table, quadrant-ii and quadrant-iii are equal demonstrating that sum total of primary inputs and sum total of final uses is equal Thus equivalence of income and expenditure approach is used for estimating GDP Again, sum total of outputs produced less sum total of all intermediate 85
inputs gives quadrant-iii demonstrating that production and income approach give the same result Thus the arithmetical identity of the three approaches of estimating GDP Further it is also seen that input output account is nothing but extensive desegregation of production account 324 Assumptions The system developed through the input-output analysis to start with postulates three main assumptions: (i) Homogeneity assumption: Each sector producers a single output with a single input structure and there is no automatic substitution between the outputs of different sectors This assumption requires (a) that all products of a single sector should either be perfect substitutes for one another or they should be produced in strictly fixed proportions (b) that each sector should have a single input structure and (c) that there should be no substitution between the products of different sectors (ii) Proportionality assumption : the inputs into each sector are a linear function only of the level of output of that sector, that is, the amount of each kind of input absorbed by the particular sector goes up or down in different proportion to the increase or decrease in that sector's total output (iii) Additivity assumption: the total effect of carrying out production in several sectors is the sum of separate effects Any form of external dependence is thus ruled out 325 The input-output model: Using notations, the equivalence relations described in above section represent the following set of n balance equations: i + i2 + + + + in + Y i = i, i =, 2,, n (33) It may be noted that these equations are what is presented in the rows of above input output table This set of equations is also called the input output system The above n equations involve n square plus n unknowns and therefore cannot be solved However for given final demand (Y) assuming constant technology the unknowns in the equations can be reduced to just n, thus making it possible to find a unique solution of equations giving the value of output for a given final demand 86
Denoting, a = / j for the input output coefficient representing the output of sector i absorbed by sector j per unit of output of sector j, and assuming it to be constant, we get i n Y i j j n a j Y i, (< i <n) (34) These equations can be conveniently written in matrix notations as = A + Y, or, (I-A) = Y or, = (I-A) - Y (35) This is the static input-output open model put forward by W Leontief It has been obtained by exploiting the relationship in the rows of the input output system It is clear from above that the input-output system attains equilibrium in terms of supply and demand Thus, the input-output analysis is an economic application of general equilibrium theory Having the coefficient matrix A, known from earlier results, for a given final demand vector Y the model determines the sectoral output levels This model also has several other applications The model is open as it considers the labour supply open In a closed model labour is considered as an industry consuming household consumption and producing labour for the system Further the model is static as it does not consider capital stock requirements for the system A dynamic model would include additional requirements of capital stock to produce additional output within the model The basic requirement of Input/Output analysis is the transaction table of the whole economy This table provides the matrix representation of the national economy into given number of sectors The transaction matrix becomes square matrix of order depends upon the total number of sectors divided Following matrix shows the three sector interdependent economy 87
2 3 2 22 23 3 32 33 3 3 (36) Further, the technological matrix (A) can be constructed by using the following formula: a a2 a3 A a2 a22 a 23 and a a3 a32 a 33 33 x j (37) And by using the relation 35, one can easily obtain Leontief inverse The following is the famous Leontief inverse ( I ) A : l l l 2 3 ( I A) l l l 2 22 23 l l l 3 32 3333 where I is the identity matrix of order 3 (38) The beauty of ( I ) A is that it behaves as a unit device to capture all the direct and indirect effects of a unit increase in final demand in the economy and its elements can be used to explain the demand linkages 322 Structural Decomposition Analysis This methodology is just an extension of the standard Leontief Input-Output formula given as: ( I A) F According to this formula, the change in output () over the period may be due to change in final demand (F) or due to the change in technological relations ( I A) or due to change in both (the interaction component in this study takes care of this change) Following Forssell (988), final demand vector has been further bifurcated into five demand categories viz, private consumption expenditure (P), government consumption expenditure (G), gross investment (I), exports () and imports (I) In 88
addition to this, following Saxena et al (203), the same methodology of calculating the sources of output growth has been further modified by adding the interaction term effect By using Leontief s formula, the value of output in the given year can be written as follows: ( I A) P G I E M (39) As per the structural decomposition analysis, the total growth in output has been divided into four major components and each component is composed of five more components, such as the growth of private consumption; the growth of government consumption; the growth of gross investment; the growth of exports and the growth of imports The first four of these effects have positive sign and the last effect has a negative sign because imports are a substitute for domestic output as another source of supply Any growth of imports is evaluated as if it had been a loss to the domestic production If the growth effect of imports is large enough or the initial amount of imported products is greater than output, the total growth effect may even be negative (Forssell, 988) The first component ie, effect of average growth of final demand is analyzed in order to reveal how much output in each industry would have changed if all elements of a particular final demand category were growing at the same rate One can use this component for comparison purpose only in case of aggregate change in final demand (ie, not suitable for comparison in case of further disaggregation of final demand category) Guill (979) explains that this component is equivalent to the difference of final expenditure in period t and period zero One can calculate the extent of this component by estimating the following equation: d L ( I A) g L 0 L 0 (30) where d represents the change in output; L shows the different demand categories such as private consumption expenditure, government expenditure, gross Investment, exports and imports; Subscript 0 represents the values pertaining to the initial year and g L is the 89
average growth rate of different demand categories between the initial and the final year respectively, and can be calculated as: g p 58 58 P P ti i i 58 i P 0i 0i (3) where i refers to sector number and g p stands for the average rate of private consumption expenditure between the initial year and the terminal year (t) The above formula represents the average growth rate of private consumption expenditure over the years One can also calculate the average growth rates for other demand categories as well by using the same formula The second component of change in final demand ie, changes in the composition of final demand refer to the difference between the actual sectoral final demand element and the sectoral final demand element calculated according to the average growth rate of the related final demand category Guill (979) measures this component by subtracting that vector of final demand of year t which is constructed by distributing total final demand of year t according to the industrial composition of final demand in year zero from the actual final demand vector of year t The effect of change in the composition of final demand category is analyzed in order to find out how much deviations of actual growth of sectors from average growth of a particular final demand category have caused structural changes in industrial output These changes are exogenous to the production system under consideration Thus, the first effect tells us what would have happened to industrial output if all final demand elements were growing at the average growth rate whereas the second component explains what actually happened since in actuality all final demand elements do not grow at the average growth rate Both effects assumed that technology remains constant Following is the formula to calculate the proportion of this component in total change in final demand over the study period 90
d L L g L ( I A) 0 L t 0 L 0 (32) Further, the third component of output change measures the effect of change in technology on output keeping final demand as constant In other words, the estimation of this effect reveals how much output in each industry has changed due to change in the input-output coefficients It can be estimated by subtracting Leontief inverse matrix of initial period from inverse of terminal year and then multiplied with final demand vector of initial period Mathematically, it can be written as follows: ( ) ( ) t d L I A I A L (33) 0 0 The last component of output change measures the differential effect of final demand change due to technological change, on industrial output This component emerges as a residual when the same year weights are used for both the final demand change and technological change components of total output change and shows the interaction effect of final demand change and technology change on output change Venkatramaiah et al (984) defined this component as the measuring rod of differential effect of technological change due to change in the final demand, on industrial output d L I A I A ( ) ( ) L L t 0 t 0 (34) 322 Contribution of Different Final Demand Categories One can also measure the contribution of separate demand factors like private consumption, government consumption, gross investment, exports and imports to output growth between the initial and the final year Following expression is used to calculate the contribution of private consumption expenditure in output change between two periods: d P d P d P d P d P (35) 2 3 4 where subscripts to 4 shows the proportion of its changes from all four sources of output growth mentioned in previous sub-section 9
These identities will be used to measure the total individual effect of a final demand category on the total output change It separates certain components and in this way it helps us to understand better that what has happened in the economy Thus, the change in output is the result of four different effects and the sum total of values of all the effects should be equal to the total change in output 3222 Steps to Apply the Structural Decomposition Analysis to the Data The following four steps have been followed to calculate the share of four components in change in output from initial year to final year ) Converted the values of both tables into the same base year; 2) Calculated the technology coefficient matrix for Leontief Inverse; 3) Calculated the average growth rate of the different categories of final demand; 4) In the last step, the four main sources of economic growth has been estimated to know the percentage share of each factor responsible for the output change over the years and interpret the results accordingly 323 Calculation of Linkages Before calculating the forward and backward linkages, the study focuses on production and demand linkages by using simple Input-Output analysis The production linkages have been explained by using the technology coefficient matrix (A) The procedure to calculate technology coefficient is given as follows: a a2 a3 A a2 a22 a 23 and a a3 a32 a 3333 x j (36) where x is the amount of commodity i used in sector j, j is sum of intermediate and final demand, the and a, technology coefficient, represents the proportion of input i required in sector j for its production and hence can be used to explain production linkages 92
( I ) However, for interpreting the demand linkages, the famous Leontief inverse A has been calculated Where I is the identity matrix of order 3 and A is the technology coefficient matrix calculated as above The as: l l l 2 3 ( I A) l l l 2 22 23 l l l 3 32 3333 ( I ) A matrix then looks like (37) The beauty of ( I ) A is that it behaves as a unit device to capture all the direct and indirect effects of a unit increase in final demand in the economy and its elements can be used to explain the demand linkages 323 Chenery Watanabe Method As per Chenery Watanbe method, backward and forward linkages can be calculated by using the following formulas: Backward Linkages (38) where denotes the backward linkage of sector j for the Chenery- Watanabe a denotes the input coefficient matrix Forward Linkages (39) where denotes the backward linkage of sector i, b is the output coefficient of sector i to sector j 93
3232 Rasmussen Method Rasmussen (956) proposed to use the column (or row) sums of the Leontief inverse, ( I ) A, to measure intersectoral linkages The backward and forward linkage, based on this method, is defined as the column and row sums of the Leontief inverse matrix In a mathematical way: n (320) BackwardLinkage l and Forward Linkages l i j n A more refined way to calculate linkages on the basis of inverse matrix is as follows: n / n l / n l Backward Linkage / n l / n l i j and Forward Linkage n n n n 2 2 i j i j n (32) 3233 Key Sectors If the values of both backward and forward linkages of sector are all above the corresponding average, the sector is called Key Sector Key Sector are denoted by K, If only the backward linkages of sector are greater than the average, the sector can be termed a strong backward linkages sector Strong backward linkages are denoted by B Similarly, if only the forward linkages of sector are greater than the average, the sector is called a strong forward linkages sector Strong forward linkages are denoted by F The fourth group refers to the weak linkages category This is the case where a sector s backward linkages and forward linkages are less than one Weak linkages are denoted by L 324 Vector Auto Regression (VAR) Modeling In economics, it is quite common to have models where some variables are not only explanatory variables for a given dependent variable, but they are also explained by the variables that are used to determine the dependent variable In those cases, we have models of simultaneous equations, in which it is necessary to clearly identify 94
which are the endogenous and which are the exogenous variables The decision regarding such a differentiation among variables was heavily criticized by Sims (980) According to him, if there is simultaneity among a number of variables, then all these variables should be treated in same way In other words, there should be no distinction between endogenous and exogenous variables Therefore, once this distinction is abandoned, all variables are treated as endogenous This means that in its general reduced form each equation has the same set of regressors which leads to the development of VAR models When we are not confident that a variable is really exogenous, we have to treat each variable symmetrically For example, the time series Y t that is affected by current and past values of t and, simultaneously, the time series t to be a series that is affected by current and past values of the this case we will have the simple bi-variate model given by: t 0 2 t t 2 t yt Y t series In y x y x u (322) x y y x u (323) t 20 2 t 2 t 22 t xt where we assume that both Yt and t are stationary and u yt andu xt are uncorrelated white noise error terms Equations (322) and (323) constitute a first order VAR model; because the longest lag length is unity These equations are not reduced form equations since Y t has a contemporaneous impact on t (given by 2 ), and t has a contemporaneous impact on Y t (given by 2 ) Rewriting the system with the use of matrix algebra, we get: 2 yt 0 2 yt uyt 2 x t 20 2 22 x t u xt (324) Or Bz z u (325) t 0 t t 95
where B 2 2, z t y, t x t, 0 0 20 2 2, and 22 u t u yt u xt Multiplying both sides by t 0 t t B, we obtain: z A A z e (326) where A 0 B 0, A B and e t B ut For purpose of notational simplification we can denote as a i0 the i th element of the vector A 0, a the element in row i and the column j of the matrix A and e it as the i th element of the vector e t Using this we can rewrite the VAR model as: y a a y a x e (327) t 0 t 2 t t x a a y a x e (328) t 20 2 t 22 t 2t To distinguish between the original VAR model and the system we have just obtained, we call the first a structural or primitive VAR system and the second a VAR in standard (or reduced) form It is important to note that the new error terms composites of the two shocks as: u yt and u xt Since e t B ut et and e 2t, are we can obtain et and e 2t e ( u u )/( ) (329) t yt 2 xt 2 2 e ( u u )/( ) (330) 2t xt 2 yt 2 2 Since u yt and u xt are white noise processes, it follows that both et and e 2t are white noise processes as well 324 Testing for Causality One of the good features of VAR models is that they allow us to test for the direction of causality Causality in econometrics is somewhat different to the concept in 96
everyday use; it refers more to the ability of one variable to predict (and therefore cause) the other Suppose two variables, say Yt and t, affect each other with distributed lags The relationship between those variables can be captured by a VAR model In this case it is possible to have that a) Y t causes t, b) t causes Y t, c) there is bi-directional feedback (causality among the variables), and finally d) the two variables are independent The problem is to find an appropriate procedure that allows us to test and statistically detect the cause and effect relationship among the variables I) The Granger Causality Test Granger (969) developed a relatively simple test that defined causality as follows: a variable Y t is said to Granger-cause t, if t can be predicted with greater accuracy by using past values of the Yt variable rather than not using such past values, all other terms remaining unchanged The Granger causality test for the case of two explanatory variables following VAR model: Y t and t, involves as a first step the estimation of the n y a x y e t i ti j t j t i j m (33) n x a x y e t 2 i ti j t j 2t i j m (332) where it is assumed that both e 2t and e t are uncorrelated white-noise error terms In this model we can have the following different cases: Case : the lagged x terms in (33) may be statistically different from zero as a group, and the lagged y terms in (332) not statistically different from zero In this case we have that x t causes y t 97
Case 2: the lagged y terms in (332) may be statistically different from zero, and the lagged x terms in (33) is not statistically different from zero In this case we have that y t causes x t Case 3: both sets of x and y terms are statistically different from zero in (33) and (332), so that we have bi-directional causality Case 4: both sets of x and y terms are not statistically different from zero in (33) and (332), so that x t is independent of y t The Granger causality test, then, involves the following procedure First, estimate the VAR model given by equations (33) and (332) Then check the significance of the coefficients and apply variable deletion tests first in the lagged x terms for equation (33), and then in the lagged y terms in (332) According to the results of the variable deletion tests we may conclude about the direction of causality based upon the four cases mentioned above To explain the growth of services sector of Indian economy, VAR approach has been estimated by using time-series data on selected variables as per the analysis 33 Concluding Remark All of the above mentioned methodologies would be applied to gauge the structural changes and the role of services sector in Indian economy The next three empirical chapters present the empirical application of the above methodologies In Chapter 4, Time-series regression analysis has been applied and the results have been discussed Chapter 5 and Chapter 6 present the deterministic analysis using Input- Output approach 98