Using panel data comprising firm-level information drawn from groups within manufacturing industry which have experienced the most significant tariff reduction, this study investigates the trend in productivity growth since 1991-92. The sample of 2300 firms and 11009 observations, spanning the period 1988-89 to 1997-98 is, as far as we are aware, very likely the largest assembled for the purpose thus far. We find no evidence of a shift in productivity growth since the onset of reforms. The result is evaluated in relation to the changes till date in the policy regime in the Indian economy.

* For advice and\or discussion we thank Sangamitra Das, K.L. Krishna, Arunava Sen and B.P. Vani. Responsibility is ours. For support and financial assistance we thank the Centre for Development Studies, Thiruvananthapuram and the Indian Institute of Management, Kozhikode, respectively.

I. __Introduction__

In a review of research on total factor productivity growth (TFPG) in manufacturing industry in the *eighties* we had observed that there remained a puzzle in that two differing methods of estimation – the growth accounting method and the econometric one, respectively – produced divergent results. In this paper we do not address this issue which remains of some importance to scholarship on the estimation of productivity growth in India. Instead, we move on to study the *nineties*. This followed from the fact that both our perception and our own priorities have evolved since our last paper. Principally, it had struck us that considering the best received work had posited a relationship between TFPG and, what may be referred to as liberal policy regimes, the nineties are a more appropriate period for a test of the relationship between TFP growth and the change in the policy regime. For after all in the eighties we had "not seen nothing yet", so to speak. The changes initiated in 1991 dwarf anything by way of liberalisation that may have taken place during the preceding decade. If this view is acceptable, and to us it appears eminently so, the data of the nineties would serve as a better test bed than any other period thus far. In this paper we present results of a test for a shift in productivity growth since 1991. We would expect any shift in productivity to occur in those sectors of manufacturing where the reforms have been most pronounced. It is widely held that the defining character of these reforms is the greater openness of the Indian economy. Therefore we have focussed on those sectors where trade has been liberalised. While we are aware of many dimensions to trade liberalisation, for the purpose of this study we define trade liberalisation as significant reductions in the tariff rate.

To investigate the existence of a shift in the growth of productivity since the introduction of trade reforms in the Indian economy, data for a panel of 2300 firms, spread over five industry groups at the two digit level of the NIC 1987, yielding 11009 observations was assembled from the data base on electronic medium (PROWESS) of the Centre for Monitoring the Indian Economy (CMIE). On the basis of the record of tariff reduction since 1991 the industry groups chosen were machinery, transport equipment and parts, textiles, textile products and chemicals. It was attempted to be seen that, as far as possible, the industries subjected to significant tariff reductions are included. The data on tariff reductions used for this study is presented in Balakrishnan, Pushpangadan and Suresh Babu (2000; henceforth BPS). The period 1988-89 to 1997-98 was chosen for the study, 1997-98 having been the last complete financial year for which data was available at the time of commencement of the study. The study investigated a shift in productivity growth from the year 1991-92.

II. __Methodology__

From Hall (1988) we have a methodology whereby estimation of a single equation yields both an estimate of the price-marginal cost ratio and of productivity. This methodology has been widely applied in empirical analyses of the consequence of trade reforms for competition and productivity growth in different economies for different periods, and we have proceeded accordingly.

Specify the production function for firm *i* in industry *j* at time t as:

(1) Y_{ijt} = A_{jt}f_{it}G(L_{ijt}, K_{ijt}, M_{ijt})

where Y, K, L and M stand for output, capital, labour and materials inputs, respectively, A_{jt} is an index of industry-specific index of Hicks-neutral technical and f_{it} is a parameter allowing for firm-specific differences. Totally differentiating (1) and dividing through by Y, we have

(2) (dY/Y)_{ijt} = (d Y/d L)(dL/Y)_{ijt} + (d Y/d K)(dK/Y)_{ijt}

+ (d Y/d M)(dM/Y)_{ijt} + (dA/A)_{jt} + (df/f_{)it}.

From the first order conditions for profit maximisation of a firm in Cournot equilibrium the expression for the physical marginal product(s) can be written as:

(3a) (d Y/d L)_{ijt} = (w/p)_{jt}{1/[1+(s_{ij}/e_{j})]} = (w/p)_{jtm ij}

(3b) (d Y/d K)_{ijt} = (r/p)_{jt}{1/[1+(s_{ij}/e_{j})]} = (r/p)_{jtm ij}

(3c) (d Y/d M)_{ijt} = (n/p)_{jt}{1/[1+(s_{ij}/e_{j})]} = (n/p)_{jtm ij}

where p is the product price, w, r and n are the price of labour, capital and materials, respectively, s_{ij} is the market share of firm i in industry j, and m is the mark-up (price-marginal cost ratio).

Anticipating the estimation to follow, which takes the form of estimating production functions for whole industries, it is assumed that the mark-up varies across industries alone, implying that it is common to firms. Now, substituting (3a)-(3c) into (2) and re-arranging terms, we have:

(4) (dY/Y)_{ijt} = m _{j}[(wL/PY)(dL/L)+(rK/PY)(dK/K)+(nM/PY)(dM/M)]_{ijt }

+ (dA/A)_{jt} + (df/f_{)it}.

Denote the factor shares (wL/PY), (rK/PY) and (nM/PY) as a _{l}, a _{k} and a _{m}, respectively (4) may be re-witten as:

(5) (dlnY)_{ijt} = m _{j}[a _{l}(dlnL) + a _{m}(dlnM) + a _{k}(dlnK)]_{ijt } + (dA/A)_{jt} + (df/f)_{it}.

Denoting the sum of factor shares as b /m , where b is the returns-to-scale parameter, we can re-write (5) as the production function in intensive form:

(6) dy_{ijt} = m _{j}[a _{l}dl+a _{m}dm]_{ijt} + (b j-1)(dK/K)_{ijt} + (dA/A)_{jt} + (df/f)_{it.}

where the variables y, l and m equal ln(Y/K), ln(L/K) and ln(M/K), respectively.

In an estimate of (6) the productivity term (dA/A)_{jt}, which can be thought of as the rate of productivity growth for industry j, is captured by a constant term B_{0j}. Next, (df/f)_{it} may be decomposed into a firm-specific effect g_{it} and a disturbance term u_{it}. The resulting specification can be used to test for changes in the extent of competition and in productivity growth due to trade reforms. The change in the price-cost ratio can be investigated by adding an interactive slope dummy to the sum of the changes in variable inputs in (6) and a shift in the level of productivity growth can be accounted for by an intercept dummy. Incorporating these would give rise to the estimating equation:

(7) dy_{ijt} = B_{oj} + B_{1j}dx_{ijt} + B_{2j}[Ddx_{ijt}] + B_{3j}dk_{ijt} + B_{4j}D + g_{it} + u_{it}

where

B_{1} = m

B_{3} = (b -1)

dx = [a _{l}dl+a _{m}dm]

dk = dK/K, and

D is a dummy accounting for the (policy) regime in place during any particular historical phase. Given our interest in this study the dummy takes the value zero prior to 1991 and one from that date on. Moreover, in this study we remain interested only in the behaviour of productivity growth.

Notice from (6) that there is a firm-specific factor in the form of f_{it} to take care of. We follow standard practice and allow for the possibility of this standing either for fixed or for random effects. In this study separate estimates under each assumption are presented and the Hausman test used to choose among these.

Finally, if B_{3} is not significantly different from zero in an estimate of (7) we may conclude that the technology is characterised by constant returns-to-scale. Further, since there has been evidence of an impact of trade reforms on the scale parameter in some economies it would be advisable to allow for it in estimation. This is done by adding an interactive slope dummy to `dk' which yields:

(8) dy_{ijt} = B_{oj} + B_{1j}dx_{ijt} + B_{2j}[Ddx_{ijt}] + B_{3j}dk_{ijt} + B_{4j}D + B_{5j}[Ddk_{ijt}] + g_{it} + u_{it}.

III. __Estimation__

Equation (8), was estimated by OLS with and without group-dummies and by feasible generalised least squares, yielding the OLS, `within’ and `between’ estimators, respectively. The Hausman Test (Chi-square: 384.5) favoured the within transformation applicable to a fixed-effects model. The estimation of firm-level production functions is particularly prone to the classical problem of identification. We take the view that in the short-run the capital stock is not a variable for the firm while employment is a quasi-fixed input – as opposed to capital services and manhours, respectively, which may be varied with current output - allowing their use as instruments for the endogenous input `materials’. Thus `dx_{ijt}` was instrumented by its predicted value with the prediction equation having contained the current capital stock and employment per period. The instrumental-variables estimate of (8), now without the time dummy for the mark-up, maintaining a fixed-effects model, is presented in the table below. The estimated coefficient (B_{3}) of the time dummy indicates no improvement in productivity growth. Indeed it signals a statistically significant decline in the growth of total factor productivity after 1991-92.

__Testing for a shift in productivity growth__

Regression is dy_{ijt} = B_{oj} + B_{1j}dx_{ijt} + B_{2j}dk_{ijt} + B_{3j}D + B_{4j}[Ddk_{ijt}] + g_{it} + u_{it}

D=0 for year < 1991-92 else D=1

B |
B |
B |
B |

1.07 (0.015) |
-0.27 (0.024) |
-0.01* (0.001) |
0.07 (0.025) |

standard errors in parentheses; * denotes statistical significance at the

five-percent level

The above regression is based on the assumption of `poolability’ of the separate industry-group panels in the data set. Therefore, a test for poolability was conducted and resulted in an F-statistic of 1.1 implying that the null hypothesis that the data may be pooled cannot be rejected.

IV. __Conclusion__

We would like to draw attention to the fact that we now have a set of results, due to all and one of us, which are mutually consistent. First, we have presented here TFP estimates based on econometric estimates of firm-level data from the CMIE. Secondly, one of us, has produced estimates of TFPG for industry aggregates from ASI data using the growth accounting method. However, the coverage did vary purposively. Both the studies use gross production as the output variable precluding any debate about the measurement of value added likely to emerge otherwise. Neither of these studies reveal an acceleration in productivity growth since 1991. Note, then, that the problem of divergent trends observed in the case of the estimates for the eighties does not exist in the case of the estimates provided by us for the nineties. What is of greater interest to us though is to find the original result in Balakrishnan and Pushpangadan (1994) holding good across time periods, data sources, coverage, definitions of the output variable and the methodologies of estimation.

As far as we are aware, there exist two other studies of TFPG in Indian manufacturing that use firm-level panel data and are based on the econometric estimation of the production function. The near exemplary work of Srivastava, however, looks at a period prior to 1991, which due to the subsequent change in the policy regime interest is now only of academic interest. On the other hand, Krishna and Mitra (1998) study productivity growth after 1991 and report statistically significant increase in productivity growth in 4 industry groups chosen by them. However, we would like to express some reservations regarding their data base. We find that the construction of the inputs variables, both capital and labour, in their work leaves something to be desired. Here it is of interest to note the comment of Grilliches that measurement is one of the single most important problems in the estimation of productivity. He has gone to state eight sources of measurement error among which is "the improper measurement of inputs over time". In our view, a major contribution of our paper is to move a little closer to the best practice without of course satisfying all of Grilliches’ requirements. Interested readers may wish to compare the methodology of variable construction used by us, provided in the Appendix, and that used by authors.

That the reforms initiated in 1991 may not have led to noticeable productivity gains does not particularly surprise us. In our earlier work we have referred to the absence of conclusive arguments linking a liberal policy regime and productivity growth in theory, or of any overwhelming evidence of the same. Interestingly, this is also a view held by observers who are not mainstream economists. Thus we have an observation that was made as early as on the eve of the first General Election in the country held after the launching of the economic reforms: "One kind of reforms pertain to a few crucial decisions: such as the decision to reduce tariff barriers, to de-licence industries and dismantle the licence-permit raj. Another, more subtle reform measure is the setting up of new institutions and of the adjustment of existing ones. These include independent regulatory structures to coagulate (*sic*) investment, to improve the efficiency of labour and capital and in general to step up on productivity and efficacy." We believe that this an apposite appraisal.

Our understanding of the relevant theory is that the route from increased competition and\or the liberalisation of trade to higher productivity growth is less than clearly defined. So much so that a reasonable position to adopt, it appears to us, would be that it is an empirical issue. The discovery here of the absence of any significant improvement in productivity growth since 1991-92 lends itself to two interpretations. Either the period studied is too soon after the launching of reforms for there to have emerged the, allegedly inevitable, increase in the rate of productivity growth or the policy instruments employed are inadequate to the task. However, we would like to propose a further dimension to the interpretation of this result. The reforms have thus far remained mainly macroeconomic in nature. Productivity growth may well have strong microeconomic foundations which remain to be addressed.

__References__

Balakrishnan, P. (1996) ‘Economic Reforms, Competition and Productivity Growth in India:

A Panel Study of the Manufacturing Sector’, Background paper for The World

Bank’s `India: Country Economic Memorandum’, mimeo: Indian Statistical Institute,

Delhi Centre, New Delhi.

Balakrishnan, P. and K. Pushpangadan (1994) "Total factor productivity growth in

manufacturing industry: A fresh look", Economic and Political Weekly’, 29, 2028-35.

Balakrishnan, P. and K. Pushpangadan (1998) "What do we know about productivity

growth in Indian industry?", `Economic and Political Weekly’, 33, 2241-6.

Balakrishnan, P., K. Pushpangadan and M. Suresh Babu (2000) "Liberalisation, Competition

and Productivity Growth in Indian Manufacturing" mimeo: Indian Institute of

Management, Kozhikode and Centre for Development Studies, Thiruvananthapuram

Baltagi, B.H. (1995) `Econometric Analysis of Panel Data’, Chichester, U.K.: John Wiley.

Dennison, E.F. (1967) `Why Growth Rates Differ: Post-War Experience in Nine Western

Countries, Washington, D.C.: The Brookings Institution.

Goldar, B.N. (1986) `Productivity Growth in Indian Industry’ New Delhi: Allied Publishers.

Grilliches, Z. (1994) "Productivity, research and development, and the data constraint",

`American Economic Review’ 84, 1-23.

Grilliches, Z. and J. Mairesse (1998) "Production Functions: The Search for Identification", in

`Steinar Storm (ed.) `Econometrics and Economic Theory in the Twentieth Century: The

Ragnar Frisch Centenary Symposium’, Cambridge: Cambridge Unviersity Press.

Hall, R. (1988) "The relation between price and marginal cost in U.S. industry", *`Journal of*

*Political Economy'*, 96, 921-47.

Harrison, A. (1994) "Productivity, imperfect competition and trade reform: theory and

evidence", `Journal of International Economics’, 36, 53-73.

Hsiao, C. (1986) `*The Analysis of Panel Data'*, Cambridge:* *Cambridge University Press*.*

Klette, T.J. (1999) "Market Power, Scale Economies and Productivity: Estimates from a Panel

of Establishment Data", `The Journal of Industrial Economics’, 67, 451-76.

Krishna, P. and D. Mitra (1998) "Trade liberalisation, market discipline and productivity

growth: New Evidence from India", `Journal of Development Economics’, 56, 447-462.

Mishra, J. (1996) "*Towards a Consensus on Power*", `The Economic Times', New Delhi, April

22.

Srivastava, V. (1996) `Liberalisation, Productivity and Competition: A Panel Study of Indian

Manufacturing’, Delhi: OUP.

Suresh Babu, M. (2000) "Total Factor Productivity in Manufacturing: Some Further Results",

mimeo: Centre for Development Studies, Thiruvananthapuram.

**Appendix**

__Data base__

The data for the present exercise is drawn from the CMIE's database PROWESS. CMIE provides information for approximately 7000 firms registered with the Bombay Stock Exchange, limiting itself to public limited companies. It should be noted that public limited companies in India account for almost 50% of the labour force and 80% of the fixed capital of the private sector factories while contributing to around 60% of the output and 70% of the value added.

We commenced with a sample of 3000 firms from industry groups with significant tariff reduction. Firms for which unacceptable values were recorded for certain variables, such as negative or zero values for fixed assets, and those for which a continuous time-series was unavailable were subsequently excluded from the sample. As it is not mandatory for the firms to report the balance sheet and other details to the data-collecting agency information for some years were found missing for certain firms. This does not mean that the firms have exited from the industry. Inference drawn from the study, thus, must be limited to the public limited companies and cannot be used to understand the entry and exit behaviour of firms. The final data set comprised information for 2300 firms for the ten-year period 1988-89 to 1997-98. For the precise number of firms and the number of observations in the separate industry groups see BPS (2000).

__Variable construction__

As the balance-sheet data is provided in nominal terms the conversion of these values into a measure of the underlying quantities is the principal data-processing involved in the estimation of production functions. This was done by deflating these nominal values using appropriate price deflators. We discuss the procedure in detail.

Output: CMIE provides information on the value of output of firms in an industry group. This was deflated by the industry specific wholesale price index. The source of the price index used is "Index Numbers of Wholesale Prices in India, base 1981-82=100", Ministry of Industry, Government of India.

Capital: A daunting task awaits the empirical researcher setting out to measure the capital stock. While we are aware of the controversies and debates with regard to this issue we believe that the empirical procedure applied in the present study lives up to the task of capturing this input to the extent of providing a reasonable estimate of the variable. While most of the current studies use the book value of fixed assets deflated by a investment goods deflator, mostly the wholesale price index for Machinery and Machine Tools, this is plain wrong, for it for it makes no allowance for vintage. The methodology we have used is based on that in Srivastava (1996). It is explained below.

CMIE provides information from balance sheets on gross fixed assets and its components along with depreciation. From this investment can be obtained as the difference between the current and lagged values. This enables one to use the perpetual inventory method (PIM) to arrive at an estimate of capital stock. However, straightforward application of PIM is not possible as the balance-sheet figures for capital are at historic cost, which has to be converted into asset value at replacement cost. To appreciate this, note that the perpetual inventory method implies

P_{t+1} K_{t+1} = P_{t+1}(1-d ) P_{t}K_{t} + P_{t+1} I_{t+1}

where `K’ is the quantity of capital, `P’ its price, `I’ is investment and d the depreciation rate.

However, this procedure is valid only if the base-year capital stock can be written as `P_{0}K_{0 }`. But this is not the case as in the base-year too the firms’ asset mix is valued at historic cost. The value of capital at replacement cost for the base year is arrived by revaluing the base year capital. The method adopted for this generally involves an element of arbitrariness and the most one can arrive at is an approximation. Our estimation rests on three crucial assumptions.

(a) We treat 1997 as the base year due the availability of a greater number of observations if we take a later year in the sample as the base. We assume that the earliest vintage in the capital mix dates from 1977, or from the year of incorporation if it is after 1977. 1977 itself was chosen because the life of machinery is assumed to be twenty years from as noted in the `Report of the Census of Machine Tools 1986’ of the Central Machine Tools Institute, Bangalore (`National Accounts Statistics: Sources and Methods’, New Delhi: Central Statistical Organisation, 1989).

(b) The price of capital changes at a constant rate p =P_{t}/P_{t-1} from 1977 or the year of incorporation up to 1997. The values for p were arrived from a series of price deflators constructed from CSO's data on gross fixed capital formation published in various issues of the National Accounts Statistics (NAS).

(c) Similar to the price of capital we assume that investment also changes by a constant rate

g= I_{t}/I_{t-1}. The growth of fixed capital formation at 1980-81 prices, taken from various issues of NAS, is applied in the case of all the firms. Depending on the year of incorporation firms will have different annual average growth after 1977.

Using the values of p and `g’, we arrive at a revaluation factor R^{G} to arrive at a measure of the capital stock at replacement cost for the base year. This is done as follows. Suppose the gross fixed assets at historic costs can be defined as

GFA_{t}^{h} = P_{t}I_{t} + p_{t-1} I_{t-1} + p_{t-2} I_{t-2}+ ...

which can be rewritten as

(1+g)(1+p )

GFA_{t}^{h} = P_{t}I_{t} ------------------- and similarly

(1+g)(1+p )- 1

gross fixed assets at replacement costs can be written as

GFA_{t}^{r} = P_{t}I_{t} + P_{t} I_{(t-1)}+ P_{t}I_{(t-2)} + .....

which can be re-written as

GFA_{t}^{r } = P_{t}I_{t} (1+g)

----------

g

then the revaluation factor R^{G} , defined as the ratio of the value of the asset at replacement cost to the value of the asset at historic cost will be, if the earliest vintage of capital dates back infinitely,

R^{G} = (1+g)(1+p ) -1

-----------------

g(1+p ) .

In this study we assumed that the capital stock has finite economic life. Now the revaluation factor becomes

R^{G} = [ (1+g)t ^{+1} -1] (1+p )t [ (1+g)(1+p ) - 1]

---------------------------------------------

g([(1+g)(1+p )]t ^{+1} - 1)

where t is the life of the machine.

Using the revaluation factor thus obtained we convert the capital in the base-year into capital at replacement costs in current prices. We then deflate this value to arrive at a measure of the capital stock in real terms for the base year. The price deflator used is the price index for machinery and machine tools as plant and machinery account for 71.5 percent of GFA. Subsequent years’ investment, GFA_{t} - GFA_{t-1}, is added to the capital stock existing at every time period using the perpetual-inventory method.

It should be noted that we have used gross values of capital in our estimates. Dennison (1967) argues that a correct measure falls somewhere in between the gross stock and the net stock advocating the use of a weighted average of the two with higher weight for the gross as the true value is expected to be closer to it. Empirically implementing this runs into a problem in the Indian context as the figure for capital consumption is difficult to arrive at. Moreover, one often encounters the question of the reliability of the depreciation values reported by the firms as most of these are calculated as per the allowances by the income tax authorities. Another related problem is the computation of the revaluation factor for the net capital stock. This demands the use of accounting depreciation rates as well as the economic depreciation rates. Economic depreciation rates can be exogenously determined, endogenously determined or arrived using the one-hoss-shay model. The first one implies borrowing a set of estimates for some other economy, the second one makes use of the assumption of straight line depreciation and the third assumes that the depreciation during the life of a machine is zero and is one hundred percent at the end of the life of the machine. Limitations regarding the three measures are well recognised in the literature. Ambiguity exists on the treatment of depreciation due to obsolescence and depreciation due to physical deterioration. This poses further problems, as one has to deal with the concepts of obsolescence and aging, retirement and discarding (mortality) and the service life of the capital stock. Data requirements to untangle these issues are more demanding than what is available at present. Thus we prefer gross values to net values.

Labour: The expenditure on `wages and salaries' was converted into a measure of labour input of firms by administering an estimated average total compensation to labour in the firm's industry for that year. The resulting measure may be seen as labour expressed in `efficiency units'. The average compensation by industry was computed by dividing each industry's total emoluments by total labour hours from the Annual Survey of Industries (ASI). As, at time of our investigation, ASI data was available only upto 1995-96 we have used extrapolated values for the subsequent years.

Materials: The value of the materials bill was deflated by a materials input-price index. The Input-Output coefficients for 1989-90 have been used as weights to combine the wholesale prices of the relevant materials. The source of the weights is CSO's input-output table for 1989-90 and the relevant price indices were taken from "Index Numbers of Wholesale Prices in India, base 1981-82=100", Ministry of Industry, Government of India.