IMPLEMENTING PARETO OPTIMALITY THROUGH BUSINESS MANAGEMENT (THROUGH STOCK MARKETS) IN INDIA ’S MANUFACTURING SECTOR
Soumitra K. Mallick Indian Institute of Social Welfare & Business Management, Management House, College Square West, Kolkata 700 073, India;
[email protected]; March 2006; Abstract : This paper analyzes and models the problem of implementing social welfare through business management in the Indian manufacturing sector by utilizing data contained in an estimated dynamic (stock market) asset pricing model for India(developed by the author) of its manufacturing sector. It is argued that the pricing model contains enough information to make inferences about demand and hence welfare and therefore makes a case against using exogenous social welfare weights. A measurement of the elas ticities is done to capture the operation of the Law of Demand in the market for manufacturing companies shares. However, interest cost of companies becomes a key factor in ensuring existence of stock market equilibrium. Key words: Indian Asset Price equati on, Law of Demand, manufacturing sector stock markets, social welfare, business management, interest cost.(JEL Classification C60,D90, G13)
1.Introduction THE INTERACTION of social welfare and individual efficiency is summarized in Economic Theory in terms of the two Classical Theorems of Welfare Economics (Arrow & Hahn (1971)). General Competitive Equilibrium is Pareto Optimaland any Pareto Optimal allocation can be obtained as a General Competitive Equilibrium through lumpsum taxes and transfers, if preferences do not violate the assumption of nonsatiation.Here Pareto Optimality can be considered to be the appropriate notion of Social Welfare, which is defined as an allocation such that no individual can be made better off without making someone else worse off with the total available goods by altering the allocation.This is the most liberal notion of Social Welfare in which every person’s individual welfare is given same weightage as anyone else’s. Thus the test for optimal social welfare is based only on the available set and quantity of goods and their allocations,as long as no one becomes satisfied with any particular allocation of goods when he can still have more of any. The notion of General Competitive Equilibrium implies that the prices and the allocations have attained a state of allocation such that each individual maximizes his welfare subject to his budget constraint, and all available goods are allocated. If prices are positive it is straight forward to show that changing the equilibrium allocation will have to take something away from someone to give to anyone else,and with monotonic preferences, this will reduce his welfare, therefore the allocation is Pareto Optimal. The efficiency attained at the individual level in a perfectly competi2
tive market system is essential to achieve both aggregate efficiency in terms of general equilibrium and maximum social welfare in the sense of Pareto Optimality. These theorems are therefore not a good guide to discussing the process of attaining individual efficiency by managing individual affairs whether they be the affairs of consumers or producers, as apart from the technical requirement that demand functions satisfy the Law of Demand,and supply functions are conceived of as negative demand, and Walras’ Law holds, nothing more is required (Sonnenschein(1973)). In the context of the present market perhaps to compensate for this not requiring any explicit management in the market the notion of Pareto Optimality has been conceived of which requires very little management by the central planner except lumpsum taxes and transfers (second theorem). The literature on Moral Hazard and Adverse Selection introduces the problems of achieving Pareto Optimality in individual contract situations where information asymmetry creates resources to be lost because of moral hazard and adverse selection. In such situations various incentive schemes can be devised which ensures truth telling on the part of all,thus creating conditions necessary for Pareto Optimality to be achieved. From these contract theoretic models therefore Managerial Effectiveness is judged in being able to devise appropriate compensation schemes to implement first best.However the General Equilibrium of such individual contracts are difficult to envisage as there can be so many types of contracts and so many types of cheating that it would be impossible for a central planner to know why his notion of social welfare, even in the sense of Pareto Optimality,is not being implemented out there in the market. Therefore, at the very least Management 3
and Social Welfare have to have purposes of their own. In a recent project completed for the Planning Commission of India, we have investigated in a loose sense, what can be called this divergence of objectives. Taking the function of Stock Market Financing of three different sectors, which incorporate thei r own contractual structures, we have investigated, how structure of individual contracts with shareholders measured by profitability, risk, liquidity and growth and the result of their management as evidenced by the positive diection of change in their an nual values, affect the allocation of capital through the pricing mechanism. If it can be shown that Indian industry knows how to make efficient contracts between investors of capital operating through stock markets and their managers operating within the firms then the theoretical relations between market prices of shares and their properties, as envisaged through individually efficient trades and aggregate market clearing should be observable in terms of data.We have seen such evidence in terms of data co vering over a decade in the nineties (Sarkar, Roy, Mallick, Duttachaudhuri, Chakraborty (2001), Mallick, Sarkar, Roy, Duttachaudhuri, Chakraborty (2006)). In the next section I discuss the Indian manufacturing sector context to drive home the theoretical argument and to demonstrate the nature of steps necessary in utilizing the elasticities to derive the welfare function. The regression estimates ha ve been taken from Mallick et. al. (2001, 2006). 2.Dynamic Model 2.1.Dataset Data for the regression estimates is obtained from the Prowess database of
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Centre for Monitoring Indian Economy. It is a pooled database covering the period 1988-2001. Prowess provides information on around 7638 companies. These account for more than seventy per cent of the economic activity in the organised industrial sector of India. These data has been compiled from the audited annual accounts of all public limited companies in India which furnish annual returns with Registrar of Companies and are listed on the Bombay Stock Exchange. All the variables have been normalized to Rs.100 of investment in the stocks (referred to as paid up value) at the respective dates.We have used annual series of all the variables, described below, for the period 2000-1990. While higher frequency series for some of the variables are available, since matching series for all the variables are not contained in the database, we have analysed data for years ending 31st December for all variables for the companies for which data are available. 2.2 Manufacturing Sector Data The only sector that has been considered in isolation from the market dataset is the manufacturing sector. The reason being that the only sector that has a large number of surviving firms between 1990 and 2000 is this sector. Three stages in the algorithm are carried out with respect to this dataset. The 2000-1990 average growth model is fitted as also the 2000-1999 annual growth model is fitted. The fits as well as the errors are then compared to ensure that the errors are uncorrelated. The total number of firms in the first dataset is 392 and in the other case is 2031.The other portfolio in terms of company grouping we have considered is the ”blue chip” companies portfolio described later. 2.2 The Model
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We consider the following time series model for dynamic price formation in Indian Stock Markets. Pt+1 − Pt = At + B1t N Wt + B2t DEt + B3t P It + B4t DIVt + B5t ICt + B6t Et δ NWt + B7t Et δ DEt + B8t Et δ PIt + B9t Et δ DIVt + B10t Et δ ICt +t , t N (0,σ 2t ) where, Pt = closing price of shares at 31st December of the year t, N Wt = Net worth per outstanding equity share at 31st December of the year t, P It = Profit for the year t after adding back the interest cost, per outstanding equity share at 31st December of the year t, DEt = Debt-Equity ratio at 31st December of the year t, DIVt = Dividend declared during year t per outstanding equity share at 31st December of the year t, ICt = Interest cost for the year t, δ N Wt = N Wt+1 −N Wt , is the first forward difference in NW, δ P It = P It+1 −P It , is the first forward difference in PI, δ DEt = DEt+1 −DEt , is the first forward difference in DE, δ DIVt = DIVt+1 − DIVt , is the first forward difference in DIV, δ ICt = ICt+1 − ICt , is the first forward difference in IC, Et is the forward looking Rational Expectations operator with respect to 31st December of year t,{epsilont is a random error term normally distributed with mean 0 and variance matrix σ 2t > 0 We shall jointly test for the fit of the model as well as the properties of the error terms hypothesized, with annual data over the period 1990-2000.The econometric testing of a time series model of this form, which consists of a large cross- section of companies at any given t can be carried out along two directions. The first method is the traditional Vector Auto Regression method of the Box-Jenkins type. In such a method the entire panel data pooled across firms and time periods has to be studied in integrated form to
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give GLS estimates by this ARIMA model. This has the potential dimensionality cost of there being around 2500 firms for each of the years 1990-2000 with twelve variables, which could potentially become a 2500 X 10 X 12 matrix requiring high computing time and memory costs. Besides, with a linear model specification such as ours, the nonlinearity involved in the historical behavior of stock prices would not be readily evident till we change our specification and fit a nonlinear model all over again. This prompts us to carry out the Time Series GLS regression in a ”nested” procedure similar in many respects with that suggested by Granger & Newbold (1977) and consists of the following algorithm. This algorithm uses the residual matrix of nested models to set up an objective function based on correlations amongst the nested residuals. While this procedure helps in time series estimation of the parameters along the Granger et. al. approach, it also provides a new procedure for estimating TVP (Time Varying Parameter) problems (see also Rao (2000)), without using any exogenous cost minimization objectives. In the first step we break up the pooled time series ARIMA model into nested models identified by years as follows: [Pt+1 −Pt ] = [At +historicalvariablei,t +expectationvariablei,t +epsilont ]CXT
where C is the number of companies in the data set T is the time ” horizon” which in this case is 1990-2000. Bi,t is the coefficient on historical variable i at time t where i is the indicator as follows: i = 1 => N W i = 2 => DE i = 3 => P I
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i = 4 => DIV i = 5 => IC
The historical variables are, as given above, the expectation variables follow the same order , i.e., i = 6 => E δ N W i = 7 => E δ DE i = 8 => E δ P I i = 9 => E δ DIV i = 10 => E δ IC
This is the basic time series model with the time (t) subscripts depending on the portfolio . In the second step, we break up this general ARIMA (1,1,1) specification into first a ”bootstrap” average growth model as follows: P2000 − P1990 = A + B1 N W1990 + B2 DE1990 + B3 P I1990 + B4 DIV1990 + B5 IC1990 +B6 E1990 δ NW2000−1990 +B7 E1990 δ DE2000−1990 +B8 E1990 δ PI2000−1990 + B9 E1990 δ DIV2000−1990 + B10 E1990 δ IC2000−1990 where, E1990 δN W2000−1990 = N W2000−N W 1990 , E1990 δDE2000−1990 = DE2000 − DE1990 , E1990 δP I2000−1990 = P I 2000 − P I 1990 E1990 DIV2000−1990 = DIV2000 - DIV1990 E1 990 δIC2000−1990 = IC2000 - IC1990
Thus, here the dependent variable is the total price differential over the decade. Any of the coefficients B6 toB10 isthe”averagegrowth”coef f icientinthesensethat B6 E1990 δN W2000−1990 = 10 B6 E1990 N W2000−1990 /10 This model serves as the ”bootstrap” model for the decade of the 90s. In the third step, the linear growth assumption along with the 10-year horizon
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assumption is relaxed to test a set of four ”nested” models, one for each year as follows: Retn = An +historicalvariablei +expectationvariablei +n , n = 2000 . . . 1990. And growth is taken over 1-year periods working back from 2000 for each n=1,2 and 3, and expectations is forward looking over the one year. Thus for e.g. B16 E1 δN W1 = B6 (N W2000 − N W1999 ) and so on Retn =Pn+1 - Pn Granger and Newbold (1977) argued that this is a valid procedure for obtaining the Time-Series properties of Stock Price, provided, the residual matrix [ ] does not show significant serial correlation. Therefore the final step in this algorithm is to check for the correlation in the [ ] matrix from the four nested models obtained in step 3. (Since the overall fit will not change much due to the presence of interest cost along with profit in the time series analysis , we only explore the first three annual data sets, taking on faith as before that the long run average growth model will fit better. This may remain as a weakness of the present study.) If the significance of serial correlation is low then this may also be considered as an algorithmic procedure for cointegration of stock price variables. We test these coincident hypotheses with the overall dynamics in the paper,in the following sections. 2.MANUFACTURING SECTOR ESTIMATES The estimated equation for the manufacturing sector is as follows: P2000 - P1990 = -49.98 +3.75 NW1990 −3.89DE1990 +2.691P I1990 +2.184IC1990 + 25.5DIV1990 +3.81GN W2000−1990 4.04GDE2000−1990 +1.96GP I2000−1990 +35.35GDV2000−1990 + 0.61GIC2000−1990 P refers to price, NW is networth, DE is debt-equity, PI is profit, IC is
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interest cost, DIV is dividend, GNW is growth in networth, GDE is growth in DE, GPI is growth in Profit, GDV is growth in Dividend, GIC is growth in interest cost, all in terms of per normalized share of Rs.100. ELASTICITIES AND MARKET EQUILIBRIUM The price elasticities are as follows : EPI = + 1.96 EDE = - 4.04 EDV = + 35.35 EIC = + 0.61 ENW = + 3. 81 Thus, stocks trade at higher prices at the year’s end if higher profits have accumulated over the year, the risk in terms of debt-equity ratio in the investment have been reduced, but more dividends have been distributed and more governement controls have been put in place through a higher interest rate and the overall net worth of the companies have increased. Since, profit, dividends and net worth are positive contributors to shareholder wealth and risk is negative, hence the signs verify that the requirements of the Law of Demand, are satisfied, statistically. The role of interest cost is ambiguous in terms of theory, so I am not discussing it here (Mallick et. al.(2005)). In calculating the return elasticities,since all calculations have been done on the basis of normalized share which means Rs.100 invested in terms of market price at the initial date hence first differences in the estimated model have been used in scale to calculate elasticities. Otherwise the elasticity model will have to be estimated dividing by initial price which will scale down magnitudes by order of hundreds often, and errors in fits by the Least Squares method, which has been carried out here, may be significant due to flatness of gradients1 Hence, 1
I thank M.Ramachandran, B.Friedman for pointing out this observation.
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Z(N W, DE, P I, DV, IC) = 3.75N W1990 − 3.89DE1990 + 2.691P I1990 + 2.184IC1990 +25.5DIV1990 +3.81GN W2000−1990 4.04GDE2000−1990 +1.96GP I2000−1990 + 35.35GDV2000−1990 + 0.61GIC2000−1990 is the excess demand function. THEOREM If demand for shares are positively varying with interest costs, then, equilibrium will exist in the Indian manufacturing shares market if : 3.75N W1990 − 3.89DE1990 + 2.691P I1990 + 2.184IC1990 + 25.5DIV1990 + 3.81GN W2000−1990 4.04GDE2000−1990 +1.96GP I2000−1990 +35.35GDV2000−1990 + 0.61GIC2000−1990 ≥ 49.98. PROOF: Demand for shares in the manufacturing shares market is positive if Z>0 and P2000 - P1990 ≥ 0. In terms of demand theory it is justified in Mallick et.al.(2005) why the signs of the coefficients will be as they are above, and, given the assumption with respect to interest costs, positive returns on the market on average are necessary for shares to be in demand . Also, if P1990 P2000 is considered the price in terms of which Z exhibits negative slope as required by the Law of Demand, it is easy to verify P1990 − P2000 ≤ 0 if Z ≥ 49.98 and returns are positive. Hence from the Sonnenschein(1973) theorem it is proved that within the price space Walras’ Law holds in the Indian manufacturing shares market statistically (i.e. with respect to the estimated Regression Equation on the manufacturing sector on average (Judge, Hill, Griffiths, Lutkepohl & Lee (1994))) and demand functions are positive and continuous under the 11
stated condition hence equilibrium will exist, hence the above result. The proof is by factorization of the inequality (Hardy, Littlewood & Polya (1992)) to set up two inequalities and then integrate the two again by addition as in the fundamental theorem of Calculus (Rudin(1976)) and is an alternative to Geanokoplos and Shafer (1990) in that it does not use dimensionality. Q.E.D. CONCLUSION The estimated market pricing equations for the manufacturing sector can be differentiated and integrated to analyse the various kind of demand and supply functions,with respect to financial management. This note makes it theoretically possible from the fundamental theorem of calculus (Rudin (1976)) to estimate the welfare function varying with various fundamentals in the Indian manufacturing sector stock market by showing the existence of Law of Demand consistent elasticities, which in turn ensure t he existence of all derivatives with the right signs and therefore their integrals. The welfare achieved through such equilibrium asset price relationship will be the Pareto Optimal level of welfare. However, a lot of work remains on this if someone is to estimate the exact welfare functions and levels from the pricing equations. To use the result of this paper to form a prescription of how the Pareto Optimal (dynamic) level of welfare can be implemented by managing finance functions of manufacturing companies in India using time series stock market data, requires further analy sis. But at the very least the Sonnenschein result (also Debreu (1958)) comes to bear on the more than one decade long study. Traders in the stock market in India respond to certain variables in certain quantifiable ways, which therefore measures how the various variables can
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be managed to improve the welfare of the participants. It is impossible to say from here on what will happen to the rest of the investors and their entreprises, who were non participants in the stock market, during this period. The cha racterizing inequality only gives a set of consistent fundamentals to be able to estimate the welfare function. However, the hypothesized scheme of controling social welfare through business management through a functioning stock market will work , iff the re is demand for the shares which this paper conjectures is related to the assumption regarding positive elasticity of share demand with tespect to interest cost and growth in interest cost in Indian stock markets, in general. (Mallick et. al. (2005, 2006))
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