Empirical Studies




Panel Discussion
O. Kyn:

The purpose of today’s panel discussion is to sum up and evaluate the results o our symposium. We should discuss at least three major topics: First the methodological problems. We have had many papers using a number of different methods for estimating factor productivities. Are these methods satisfactory or should new methods be developed. Secondly, we should discuss the empirical results. Do they tell us anything about individual countries. Can we make any conclusions from international comparisons. Finally, we should discuss the question of influence of economic systems on factor productivity. I would like to ask the members of the panel to start with their opening statements.


G.  Tintner:

First of all I would like to thank for the invitation to this very interesting symposium. Especially it was nice to speak to the East European colleagues. The general impression from this conference is very difficult to formulate, because so many papers were presented. It is interesting that the methodology of study of production is not very different in the East and in the West. That is an important result. Regarding the possibilities of new methods, I am very much in favour of applying the systems theory. The idea of sequential machines as suggested by Gottinger may be quite fruitful. Personally I would stress the importance of stochastic influences. In my opinion the aggregation problem is fundamental to the study of production. As economists we should not be very attracted to deter­ministic considerations in this field. I have been wondering whether the theory of aggregation as it has been developed especially by French and American economists is very much to the point; whether we should not shift to a more stochastic point of view.
I would very much like to advocate the method of principal components as an Aggregation-Principle as it had been first developed by Prof. Stone in Cambridge. It is perhaps simple minded, and there is a lot of difficulties with it, hut I think it is more to the point than various kinds of theoretical considerations on index numbers and aggregates which are deterministic. It may be interesting to go into the history of production theory. Here in Germany we should remember that great impulses to production theory really came from outstanding German economists, and especially from von Thünen who had an extreme influence on Marshall. And let me remind you that von Thünen was also motivated if not by what we would call today “econometrics”, but certainly by empirical considera­tions from his own experience with German agriculture. So there is an interesting historical background to this symposium if you like, and the debates about the capital theory, which are now taking place between Cambridge, Mass., and Cambridge, England, can perhaps be resolved by going back to the sources.


Z. Roman:

Mr. Chairman, we have had 27 papers and so very little time was left for discussion. Nevertheless, the critical spirit was high, and all the major remarks which could have been raised were raised. So let us not discuss the details today, We all have the feeling that we can start further research and improve our methodology. The measurement of total factor productivity dominated this conference, except in the field of international comparisons of relative levels of productivity. Seemingly in this field we face a lack of relevant data. Nevertheless. I think we should direct our effort even in this field to the introduction of the total factor productivity indicators as one of the explanatory tools. Another point of view the approach of production functions dominated over traditional index number methods. Only two or three papers used the traditional method of computing index numbers of total factor productivity and at least fifteen papers used production functions. This indicates the great interest in production functions and the expected value attached to this method for explaining the major factors influencing the rates of growth. I think very worth­while was the paper of Brown. Neuberger und Licari, who by combining these two approaches illuminated the relationship and controversy between them, Concerning production functions I think that there is a growing discrepancy between the power of computer facilities and the lack of relevant data. The intellectual capacity to develop more and more sophisticated methods and to process by computers a very large number of alternative variants is frustrated b~ lack of reliable data. In many cases this cannot be overcome because both the number of countries and the timespan of the time series are limited. It is my con­clusion from the symposium that this sets very heavy limits to generalizations about macro-economic growth and, even more, to explaining differences among individual countries.
Production functions are appropriate only if a large number of observations is available. In the case of individual countries we are bound to the historical time. so that it is very difficult to explain the particular growth characteristics of indi­vidual countries. Few papers went beyond production function analysis to factors influencing the growth of productivity. At least in some sections there were doubts about the possibility to isolate the influence of individual factors upon growth and to point out the key factors of growth of productivity. Some papers emphasized more capital others the quality of manpower. These are extremes because all factors in balance are needed to facilitate fast growth. We had only two papers about relative levels of productivity and it was suggested in discussion that marginal analysis should have been used in these comparisons. On the other hand it was argued that unlike in the case of rates of growth in international comparisons marginal productivities ma~ be unreliable. This may not be the best answer to these questions but I would like to remind the words of Oscar Morgenstern. He raised many times the question of the accuracy of measurement and warned us that errors can accumulate and result in misleading conclusions.-- The main problem in comparisons of productivity levels, as I see it. is that they are based on isolated signals from the economy and that they lack consistency. This is not the case with the analysis of growth based on national accounts in which the consistency of different parts of the economy is always checked. For comparisons concerning only industry in a single period of time it is very difficult to check the results with the overall level of development. Finally, I would like to emphasize the message of two papers which are not very closely related to the majority of the other papers. The first one is the paper of Yanakiev who emphasized the practical applications of the research on productivity. It is very important to evaluate the marginal productivity of research from the point of view of both theory and economic policy. The second paper which I think is very important is the paper of Montias and Sturm which stressed two
at least for me— very natural points. First, that productivity or efficiency is not the ultimate goal of economies rather than a derived goal. Secondly, that the system characteristics and rules have a very great impact on economic growth and productivity. However, I have some doubts about the quantitative analysis of the impact of the system rules with the help of production functions or other very formalized instruments of econometric analysis. Thank you.


J. M. Montias:

Mr. Roman, as a true statistician made a good census of the papers and classified them in a very helpful way. I will not do that, I will be more impressionistic, and just touch on the few points that seem to me to be of interest without being exhaustive at all. I was surprised by the extraordinary variety of specifications that have been tried out in the production functions, specifications that seem to me to be not of an experimental nature but rather of a theoretical nature. So far I have not been able to see their theoretical justification, the a priori justification, for using one type of specification let us say CES, homothetic, non­homothetic, with material inputs, without material inputs rather than the other. This is perhaps justified at this stage of the game. We want to see whether it is possible to specify production functions in very many different forms and to see whether any reasonable results come out. But I don’t think we should be misled at this point on the value of the results when a great many forms of specification have been tried out. We know that if we try out many specifications we can by chance find one that will fit any set of data. This does not necessarily mean that the high R2 will be particularly meaningful. The next stage is to really start testing hypotheses. To speculate theoretically on the kind of production function that is likely to be the most appropriate for a particular country or group of countries and then to test some hypotheses on this basis. In other words. we must avoid “fishing for hypotheses”. We must make an apriory specification. and then if this doesn’t work, say o.k.. let us work on the theory. and let us try to see why it has not worked, rather than use the computer for testing the whole mass of other specifications which might possibly fit the data better. These very obvious points were made by Tjalling Koopmans and by others already many years ago. I do not think that the papers reflected this particular methodological view point sufficiently. Speaking about the actual results, it struck me that the CES production function estimations for the Western countries came out with elasticity of substitution close to one.
For example refering to Mairesse’s paper. Norway and France came out with elasticities of substitution either equal to one or above one depending on the particular assumptions used: and the elasticity of substitution in West Germany and other West European countries tended to be fairly high, of the order of .8 or above. Whereas in the work of Miss Desai, Brown-Neuberger-Licari, Toda and others it
came out that the elasticity of substitution for the Soviet Union and other East European countries was of the order of .1 to .3 both in individual sectors and in the aggregate production functions, which is very low, indeed. Is this something that reflects system or policy differences? Is it conceivable that the additions to capital are misdirected in the centralized economies? Are there possibly longer time lags in the utilization of capital. longer gestation periods that cause the apparently very low implicit rates of returns and consequently the difficulties in substituting capital for labour. Are there any tests that might enable us to get at this question and to see whether in international comparisons the differences between elasticities are real or only apparent. and if they are real what they might be due to? I suggest that when looking at the socialist countries in greater detail quite substantial differences in the system rules by which they are regulated and operated, can be found. In particular, in Hungary and Poland in recent years, investment has become increasingly decentralized. It would be very interesting to see perhaps not now but in two or three years when the reforms have settled down and when data have become available for a span of four or five years whether the elasticity of substitution might rise in those countries where investment has been decentralized and where enterprises use economic criteria in deciding on investment. This would be in effect a test of the hypothesis that a high degree of centralization has an adverse effect on the elasticity of substitution. What other system aspects have been found in these works? One, which has not been stressed very much, is that the specification of the form of the production function may reflect important aspects of the system in which the production function has been tested. I am thinking in particular of assumptions about cost minimization or profit maximization in the works of Frohn and Mairesse and some others. Some estimations have been made under the assumption that the marginal value product of a factor is equal to its price. Frohn has shown very interestingly that one can get slightly more leverage if profit maximization as well as cost minimization is assumed. Clearly, this is the kind of assumption which can be made more easily in Western market economies than in East European economies. More experiments should be made to see the consequences of adding this kind of assumption for the Soviet Union and Eastern Europe.
Finally I want to make one brief reference to the discussion about the rates of growth of labour productivities in Czechoslovakia and France. It turned out that labour productivity in the French industry is on average 20% higher than in Czechoslovakia, but if one normalizes the size distribution of establishments the difference in favour of France is much greater, of the order of 40%. In other words, the French establishments of the same size as the Czech establishments seem to be much more efficient. What drives the French productivity down is

the presence of very small establishments of 15 to 25 workers that seem to have a very low productivity. It is the difference in the partitioning of production units in the economy -- as Hurwicz expressed it -- that seems to have an considerable effect on productivity. One question --  which came up in discussion with Kyn -- is whether the small French firms may be necessary to provide inputs and subcontracts for the larger firms, and therefore may make possible the higher productivity of the larger firms. I think, these are interesting system-oriented questions. When more disaggregated work on production functions will be done it might possibly throw some light on productivity differences, and on the unexplained parts of the residual


P. Zarembka:

In concluding this symposium it might be worthwhile to think about why we are interested in improving productivity. Often as economists we lose sight of deeper motivations for studying those particular questions that occupy so much of our own creative time.
In looking rather carefully through the papers only Yanakiev gave some indication in this introductory remarks of broader purposes, “the well-being of the members of our society depends much on the level and growth of labour productivity as it creates the basis for harmonic economic and cultural development”. One implication of the remark is that any society which has not been able to provide the basic food, clothing, shelter, and medical services of all of its members commits violence against the dignity of the human being; thus, harmony at least requires these basic needs to be satisfied. Unfortunately, most countries of the world either do not or cannot provide such basic needs for all their people. Many developing countries fall, at the present. in the category of those who cannot, and the prospects for the improvement in the world food situation is not bright.
The second implication of Yanakiev’s comment, as I understand it, is that beyond the basic needs the level and growth of labour productivity aids the development of fuller, more creative members of society. While I am sure that high labour productivity is a necessary condition, economists often seem to work as if the development of society comes
part passu with increasing labour productivity and thus specialize their field of inquiry to rather narrow issues of commodity production. It would be more healthy, however, to turn the issue upside down and ask not only how to produce more commodities but also how to change working conditions so that productive activity itself becomes a more creative and rewarding process. Particularly in the coming decades when growth rates will also certainly fall and will more frequently even be negative, it seems all the more appropriate that we move behind the level of output of commodities to the methods in which these commodities are produced and to reconsider which commodities ought to be produced.


O. Kyn:

Thank you for the very interesting introductory statements. Would anybody like to respond?

R.  Yanakiev:

I very much liked the statement that we also need to create better working conditions. And I think that the better working conditions the better living standard which we arrive to by raising productivity are also factors for the further increase of productivity. But I would like to speak about another problem here that we as economists should also consider when doing research. I would like to discuss here an important problem which was out of sight during our symposium. It is comparatively easy to make a list of research work to be done. We may continue to study productivity concepts and measurements, productivity behaviour, production functions, indices, international comparisons, the factors and causes of productivity change. the policy to raise the productivity in a country, etc. All these are possible lines of research. This is not enough. We must be more specific and estimate also the amount of time and the probability of returns from research in each direction, the prospective costs of the particular study. After that we can choose and direct the limited resources to a particular study. As economists we should not forget the difficult but important problem of estimating costs and benefits. And since we are discussing here productivity we must face up also this important problem of the economy of research.

J.   M. Montias:

One question which we really did not get to and which somebody more competent than I should discuss is what have we learned from Nuti and others about the importance of reswitching and capital reversal phenomena for the production function work which has been done here und for the assumptions which have been made. This is a very interesting question which came out a few times in the conference and has not been resolved.

P.  Zarembka:
One interpretation of what it means for an economy to reswitch is to say that more than one price-plane supports the same technology. In other words at least two price-planes support one technology. When I used the words ‘~two price­planes” that includes wage rates. Now, if two price-planes support the same technology, then also two separate wage rates support the same technology. And that in turn means that there is no unambiguous definition of what we mean by marginal productivity. If the same technology is associated with two different wage rates, then the term marginal productivity has no meaning. People often think that the reswitching debate has more to do with questions of aggregation in production functions, but there is an important implication for all kinds of empirical work involving concepts like marginal productivity.
O. Kyn:
This is also raising a very crucial question about the methodology of estimation. There seemed to have been an agreement, at least in some sections, that the aggregate production function could be accepted as an approximate tool for forecasting the behaviour of whole economies, but that it is not good for the theory of distribution of income. Many of the estimates of production functions for Western Europe were obtained from marginal productivity conditions. Does it mean that this method was totally wrong?

P.  Zarembka:
Yes! (The audience is laughing). 

I would also say yes, and in very clear terms. Because when you aggregate capital stock with a set of prices some wage rates and profit rates in those prices are implicit. And then, when you do your calculations you find the marginal productivity of capital and the wage rate implicit in the production function. There you are. You are very lucky if the marginal product of capital is equal to the profit rate you had in your original prices. If they differ, then there is no real meaning you can attach to your estimates.
D. W. Green:
Using this method for Western economies we often reverse the conclusion. We conclude that we have learned something about technology, for example that the elasticity of substitution is equal to 1. Whereas in fact, this kind of estimation should lead only to the conclusion that the distribution of income is quite stable. And it is stable irrespective of what the functional form of technology is.


O. Kyn:
That is an extremely important issue. Yesterday we have learned from the paper of Toda that if one tries to estimate the elasticity of substitution for the Soviet economy from distribution of income one gets exactly the same result, namely that the elasticity of substitution is equal to 1. While the direct estimation by regressing output on capital and labour inputs gives much lower elasticity of substitution. I would like to ask those who estimated the production functions for Western countries whether they tried also direct estimation?

J.   Mairesse:
We found from the French and Norwegian firms’ data that the direct estimate of the elasticity of substitution for the whole industry was about 1 in Norway and let us say 3 in France, while the indirect estimate was .8 or .9 in both France and Norway. But when you look at the individual estimates at the level of branches then you don’t find any correlation between the direct and indirect estimates of elasticity of substitution. In fact, the rank correlation was negative. The direct estimates go from .5 up to 2 or 3, while the indirect estimates were much more gathered around .8 and .9.
S.  K. Kuipers:
I made direct and indirect estimates for my country and my conclusions are the same as Mairesse’s. When the elasticity of substitution is estimated in the neo­classical framework, that is via factor price equations, then the values are in the neighbourhood of .5 or .6. But in direct estimates the elasticity of substitution is much higher. Another important point is that the factor elasticities of production derived from direct estimates, do not coincide with the factor shares what you would expect if you were estimating the production function via indirect methods. So, according to my experience, there is no reason for using the neo­classical equality between the wage-rental-ratio and the ratio of factor produc­tivities in estimating the production function. I would warn against doing that. Zarembka and Nuti showed the theoretical reasons: capital reversal, reswitching and other anomalies, but also the empirical experience suggests that it is an unjustified procedure.
P.  Zarembka:
I have some remarks. The first is that sometimes it is thought that the Cambridge (England) critique has to do only with the aggregate production function. But what it really has to do with is whether capital can be used as an argument in a production function. This means that the critique is equally relevant at the sector level as at the aggregate level. The problem cannot be settled by going to the sectoral level instead of estimating the aggregate production function. The second thing is that one of the interpretations you can .give to the reswitching debate is to ask yourself the question what is the shadow price of labour. Reswitching says that there is no unique shadow price of labour. Now, suppose we turn this around and say the issue about the uniqueness of shadow price of labour is an empirical issue. Incidentally, I doubt that this issue will ever be settled in one way or another. Suppose for the moment that the shadow price of labour is indeed unique. That still does not mean that there is a smooth marginal productivity function, a smooth shadow price of labour function. What is the implication of that? The implication of the fact that this function is not smooth is that it is not a shadow price or the marginal productivity of labour that determines wages. but rather the other way around. The expected changes in wages which are determined by other, say sociological or political,factors deter­mine which technology firms adopt. In other words, switch the order of causation from technology determining wages to expected changes in wages determining technology.
M. J. Beckmann:
In equilibrium it is always both ways and you cannot say one causes the other. In equilibrium both wages and technology are determining each other.
D. M. Nuti:
In the general equilibrium model but not in the kind of model we are discussing here!
M. J. Beckrnann:
It depends how you interpret it.
You mean that it is a general equilibrium production function that you are estimating
M. J. Beckmann:
It should be


J. Mairesse:
I think that when we consider the neo-classical theory on the micro-economical level we can very well accomodate all the reswitching problems. It will never bother, I guess, somebody like Arrow or even Wicksell in the old times. When you say that marginal productivity for two techniques may be equal to wages you can still define marginal productivity. What you say is that it is not a monotonous function or that it does not have the right shape. But this is another problem. I do not think that this can disprove the heart of neo-classical theory. Some parables may be defeated, but not the general equilibrium model which is the real heart of it.
O. Kyn:
May I know from our colleagues of Cambridge-School whether they would accept the direct estimate of production functions as a kind of surrogate description of reality if no distributional conclusions are implied?
I think you get it wrong in the same way as before because you would have to assume that there is a general equilibrium system behind the production function. But as far as I am concerned you can go ahead with it. (Laughter).
P.  Zarernhka:

Rorna dixit! (laughter)  I would say that you can go ahead and estimate production functions without using marginal productivity conditions, but even if you believe in “neo-classical economics” there is no guarantee that your data are good enough and even that the concepts are well enough defined to get good estimates of second order parameters like the elasticity of substitution. So I would reiterate the remark made earlier in the conference, namely that I would not go much beyond the simple kind of production function like the Cobb-Douglas.

G. Tintner:
I think we ought to look at these problems from a stochastic point of view and consider production functions as statements about mathematical expectations of variables. There was a similar problem between micro-physics and macro-physics, but in physics the situation is such that the law of large numbers can be applied whereas in economics, with some exceptions, we have only very few firms in a given branch. The results are, therefore, extremely dubious and so I think that Zarembka is perfectly right in saying that we probably do not have enough data to talk about the curvature of production functions. Even our results about the slope are somewhat dubious.

M. J. Beckmann:
It cannot be settled on a priori grounds whether we have enough data or not. If you would limit yourself to one type of production function you would artificially limit the questions you can ask. Is the world still Cobb-Douglas or is it perhaps nonhomothetic? Is the elasticity of substitution varying and which way? Is there any systematic relationship in it? Things like that should be questioned. 

P.  Zarembka:
I have personally never said that I believe in the Cobb-Douglas world, and in my own empirical work over the years I did not take the Cobb-Douglas production function a priori. It is rather my empirical experience that I cannot estimate the elasticity of substitution.

M. J. Beckmann:
But you can proceed in a different way. We tried to estimate the differential equa­tions rather than directly the production functions which has something to do with the previous discussion about the way of estimating production functions. When you estimate the differential equations you can also raise the question of type of technical change. There are many ways of skipping this step but then you wind up with such statements like  "it doesn’t make sense" or “you cannot do that” etc.


I do not think that one can say generally that CES and more sophisticated production functions cannot be used according to empirical experience. If there is not enough correlation information in time series to estimate more sophisticated production functions it is good enough to use the simple Cobb-Douglas function. But if you, for instance, try to estimate from cross-section data then you might have enough information for getting the curvature of isoquants and then you can estimate CES production functions and probably even more sophisticated types.
J. Mairesse:
I want to add one point to what Frohn said. It is true that when you go to cross-section estimations you have usually plenty of data so that you will get very precise estimates. But the problem is that you can have a specification error or an error of measurement. I tried to show, and Ringstad and Griliches showed it even better, that when you estimate production functions from data on 10.000 firms or so you must be very careful about their quality. For example, if you assume errors in measurement of capital, which may be very probable, then your estimates become less precise and you can have large biases. In fact, my conclusion was very similar as Griliches’ that the estimation of the elasticity of substitution with cross-section data was very difficult, if not impossible.
Mr. Chairman, what strikes me at this symposium is that almost everybody was using some kind of aggregate production function with disembodied technical change. I myself think that for empirical work in production theory it would be much better to try some kind of vintage model, in which there exist sufficient substitution possibilities cx
ante but only bounded substitutibility for production processes which are using capital goods produced in the past. Of course, there may not be enough data to estimate such a model. I think that one of the first things which have to be done in this field is to collect more data so that it would become possible to differentiate between different kinds of capital goods and to take account of embodied technical progress.
R. Evenson:
May I make one comment on the use of the productivity measurement? In spite of the doubts that have emerged here, many of the countries that we are concerned with have had extraordinary economic performances in the period of last 20 years or so. Quite a number of these countries have increased substantially the available goods and services and while many of them may have pursued different distributional policies, one would have to be hard pressed to reach the conclusion that they had not done really extraordinarily well. Can developing countries who seek to realize at least a small fraction of this kind of economic success gain from these productivity measurements any insight as to how to do it?
D. M. Nuti:
At the end of a conference like this I would like to return to the problems that we face and have to look at. One problem that has been bothering me is the question of sectoral studies. I think, we all take for granted that a sector is a sector. But a sector is an arbitrary horizontal partitioning of production activities in an economy and this is the way data are collected because it is convenient. Perhaps we might think of that differently. We ought to rearrange our information in such a way that we transform our data into data for some notional vertically integrated sectors so that we get a really sharp focus on commodities rather than on sectors which are clearly arbitrary subdivisions made by engi­neers and statisticians. Then the question is: how far should we go with vertical integration? Should we stop at the production of direct inputs or should we go as far as wage goods. I think these problems are major and if we look at sectors like this we might get very different results
I think that at least in market economies it is impossible to go very far in switching from sectors to commodities. You will not find enough supplementary data, for instance, on wage levels. Such data are available only for firms and sectors. Perhaps it would be good to have always two sets of data but presently we cannot get very far in this direction
D. M.Nuti:
I would not be so pessimistic, because from input/output tables you can obtain the raw data for any notion of sector you care to invent.
O. Kyn:
We have all measured the factor productivity or estimated production functions using either GNP or gross value of output on the left sides of our equations. But the Montias-Sturm paper as well as Zarembka’s statement at the beginning of the panel discussion remind us that it may be questionable whether these are really proper measures of the achievements of society, of the social and economic progress
Z. Roman:
I feel very deeply that they are definitely not the proper measures of efficiency in a broader sense. Nevertheless, we have to keep these indicators. We should, however, add a whole set of additional social and economic indicators. I can see that many different experiments will be performed to broaden the scope of indicators used for aggregating the social and economic performance.
P. Zarembka:
I certainly think we have to move beyond such concepts as GNP in describing the conditions in both socialist and capitalist societies. In fact, the “limits to growth” literature which is developing suggests that the world may come to a zero growth. I would go beyond that and say, perhaps, even to a negative growth. That implies that moving towards other measures of economic performance will be forced upon us. We will not be willing to look on a number that stays constant so that we will want to turn to some other indicator.
O. Kyn:
Thank you very much and by that we close the symposium.





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