Ragnar  Frisch (1971) - Cooperation between Politicians and Econometricians on the Formalization of Political Preferences

When I had to decide on what to say or not to say in the 45 minutes that are allotted to me, I was facing a big temptation. The temptation of elaborating on the difference between intelligence and wisdom. I might have started with the example of Évariste Galois, the famous mathematician. One of the most supreme mathematical geniuses that ever lived. His theory of transformation groups laid completely bare the nature of groups of algebraic equations. At the same time, Galois was a striking example of lack of wisdom. In a clash with political opponents, he accepted a duel on pistols, he was not a good shots man and he knew for certain that he would be killed in the duel. So therefore he spent the night before the duel in writing down at a desperate speed his mathematical testament. The next day he was shot and died the day after. I might have passed from this example to the example of Norbert Wiener, the famous American mathematician, known amongst others as being the founder of cybernetics. He too is dead, but much more recently. I had the great honour of knowing him personally and therefore could, so to speak, admire his supreme intelligence, so to speak face to face. At the same time he was naïve in the extreme. He wrote a book called God and Golem Incorporated with a long subtitle which I don’t remember exactly, but I do remember the meaning of it and the last words, which were something like this: An investigation on a topic where science impinges on religion. With his supreme intelligence he did not understand that what he was there talking about had nothing to do with religion at all. I might have given other examples and might have ended up by raising the question whether the scientist really discover the laws of nature or simply fool themselves by inventing something which has the appearance of being laws of nature. However I resisted this temptation, because I was afraid that it might give the impression, it might give the impression of being hostile to the physicists. And by all means, that is what I wanted to avoid. So I decided instead to present to you in all humility an example of the modern attempts called econometrics. Which is simply the attempt at passing from the talking stage to the computing stage in economics and social science. I want to make a plea for a new type of cooperation between politicians and econometricians. This new type of cooperation consists of formalising the preference function, which must underlie the very concept of an optimal economic policy. A preference function is simply a function of some other variables that enter into a description of the economy, the function being such that the maximisation of it can be looked upon as the definition of the goal to be obtained by the economic policy. How can we reach an expression for the numerical character of this function? And how can it be applied in practice? It is my firm conviction that an approach to economic policy through a preference function contains a key on the much needed reform in the methods of decision making in society at large in the world of today. On one hand we are facing crucial environmental factors which previously were and could be nearly completely neglected. A whole spectrum of production processes, still more or less exclusively by pecuniary gains, created enormous quantities of waste in the form of toxical matter, which it has left a society to handle. Similarly for the preservation of nature and for the relief of city congestions and for a variety of other questions concerning the welfare of humans. On the other hand, political discussions today come dangerously close to resembling a dog fight, where the global nature of and the interconnections between the basic questions have a tendency to get lost and only loud crying on striking partial aspects of inefficiencies and injustices counts. All this calls for radical and unconventional thinking about the decision making machinery in society at large. The preference function is a tool for defining the goal. Another important problem is to construct a model for the conditions, balance and equations under which we’re striving towards the goal has to proceed. But this latter question I shall not consider today. Since I am addressing two different groups, politicians and businessmen on the one hand and scientists on the other, the form of the presentation is a difficult question. Some parts in the sequel may perhaps be too technical for the liking of politicians and other parts too trivial for the liking of the scientists but this risk I’ll have to take. The preference function which I have in mind is the one that applies to the actual existing decision making authority in society. Whether this authority is a junta of powerful men or a democratic parliament. In the latter case one may also speak of the preference function of the individual political parties as distinct from the overall preference function that applies to the finally deciding body as this body is defined through the political machinery of the country. Therefore the preference function with which I am concerned is something very different from the welfare function about which one talks and writes a good deal in a very abstract part of economic theory. I shall not use my time this morning to correcting the various types of misunderstandings that have prompted some to maintain that a priori it is impossible to construct a preference function, applicably in practice. A sample of such misunderstandings was discussed in my contribution to the yearbook Les Prix Nobel in 1969. Instead I shall simply describe a method which I believe is applicable in practice. I have developed this method, not only through theoretical considerations but also through practical experiences based on conversation with high level politicians in developed countries and less developed countries, including the late Nehru of India and Nasser of Egypt. The econometrician, who through cooperation with politicians will try to formalise a preference function in a language which his electronic computer can understand, has to work in three stages. The first stage simply consists in the procedure that the econometrician uses his general knowledge of the political atmosphere in the country and in particular his knowledge of the atmosphere in the political party, consider if it is a question of formalising the preference function of a specific political party. This will give him, the expert, a tentative and preliminary notion of how the preference function aught to be shaped quantitatively. In the second stage, the econometrician will formulate a series of interview questions to the politicians. Here the expert will try to get a better approximation to the preference function which he is after. The system of questions in such interviews should be built up systematically in such a way that the expert, perhaps without the politicians even being aware of it, may get the information the expert is after. It is well known that people will not always act in the same way they say they would act in an interview. But still I think that valuable information can be attained in interviews provided the questions are wisely built up in a conversational manner and not simply performed by a youngster in opinion pole trade who asks people to put crosses in frames here or there in a questionnaire. The essence of what I have to say this morning will precisely be concerned with this conversational but at the same time systematic manner of forming the questions. In the third stage, the expert will go back to his electronic computer and feed in to it the numerical form of the preference function as he now sees it. The result will be an optimal socioeconomic path or development for the coming years. Optimality being defined with reference to the political party in question and in the preference function form as the expert now sees it. When the expert gets back to the politicians with his solution, the politicians will perhaps say The expert will understand more or less precisely what sort of changes in the preference function he will have to introduce in order that the optimal solution shall come near to that kind of development path which the politicians now say they want. This new solution the expert will bring back to the politician. This will lead to a dialogue back and forth between the expert and the politician. Step by step, one will in this way approach a situation where the politicians can say ‘alright, this is what we want.’ Or perhaps the expert will help to end up by saying politely: And the excellencies, being of course intelligent people, will understand the situation and will therefore acquiesce with a solution which may not be exactly what they want but which is at least closer to this than other forms of the social economic development path. Well, in this way each political party will be forced to recognise the consequences of their attitude and to admit this publicly. Even if we did not go further than this, something extremely important will be gained in clarifying the political discussions. But we should not stop there. We should proceed further to try to reach a political compromise on the formulation of a unified numerical preference function. Also in this search for a compromise an interaction process between the politicians and the experts should take place. The top political authority in a country based on political democracy, it will be the parliament, aught to devote most of its time and energy on a discussion of this compromise form of the preference function and on the consequences which such a form would entail. Instead of using practically all its time and effort on discussing and deciding upon one by one individual measures that have been proposed. This one by one method is, as I see it, a prehistoric method with regard to the preference function. In the rest of what I have to say I shall be particularly concerned with the interview technique and its systematic organisation. If time had permitted I would have wanted to go into the problem of how to measure the various variables. Some of the variables are fairly well known from current statistics such as the annual gross national product, the GNP, as the economists call it, and its growth rate. The number of unemployed, the visible trade balance and so forth. But for other variables it will be necessary to construct special kinds of indexes. For instance an index concerning the regional skews in the income distribution. But time will not permit me to go into this and in the sequel I shall just have to assume that measurements exist. The preference variables are those variables in the analytical model to which we want to apply a preference analysis. As socionomists with preference variables, we may speak of preferential variables. It’s only a special kind of variables which we want to include in the preference analyses. The main principle for inclusion of a variable in the set of preferential variables is that this variable is connected with an ethical or a humanitarian or a social or a consumptional or a justice desire about which common people can make up their minds without being experts in economic and social model building. As an exception to this we may include in the preferential set also one or more variables for the inclusion which we have to assume a certain amount of expert economic knowledge or the effects which this variable will have on the other variables in the economy. The visible trade balance, for instance, is an example in point. The inclusion of such a variable in the preferential set is prompted simply by our desire not to make the preferential analysis too complicated. But the ideal is not to include such a variable in the preferential set but leave its preferential aspects to be taken care of indirectly, through the effects on the variables that are included in the preferential set according to the main principle. Only in this way can we assure a comparability of the preference structure of the common man and that of the expert. In a democratic society this comparability is very important. For each of the preferential variables we will specify an interval in which the preferential variable shall lie in a given interval. The interval may be larger or smaller according to how analytically local we want to make the analysis. Local in this connection means local with respect to numerical variation and it has nothing to do with geographical or regional locality. The upper and lower bound of such a preference interval must of course be sufficiently different to make the distance perceptible from the viewpoint of preferences. But the differences must not be too large so as to deprive the comparison of any practical meaning. For instance a gross national product of say 500 times the volume in constant prices, which it has had over the last years, would have no understandable meaning. Instead of speaking about the upper and lower bound of a variable, we will speak of the preferred and the deferred bound, deferred is the opposite of preferred. May I have number 4... For the preference variable, X sub mu, we therefore would have two bounds, as you see, x sub mu, superscript pref, and x sub mu superscript def. This will define the interval. I shall have to say a few words on transitivity. Suppose that we have a system of preferences, which is such that whenever two different sets of magnitudes or the preference variables are given, it is always possible for the interviewed person to decide whether the formula of the two sets is preferred to him or deferred to him or whether the two combinations are indifferent to him. Then we say that the preference structure possesses the determinateness property. If we assume this, we may raise the following further question: Suppose that 3 different sets, A, B and C are given of the magnitudes of the preferential variables. If A has a certain preference relation to B, for instance the relation preferred to, and if B has the same preference relation to C, will then always A have this same preference relation to C? If so, we say that the preference structure has the transitivity property. Or shorter that it is transitive. A few words on the mathematical form of a preference function. This mathematical form has nothing, has no role to play for the validity of the interview technique as such, except for the fact that we have to assume that the preference structure satisfies the determinateness criterion. Only when we get to the point of analysing the results of the interviews, we need to fall back on certain assumptions about the mathematical form of the preference function. This is simply the same kind of assumption as we make when we speak of special interpolation formula in any question of interpolation. Quite generally let a capital P, function of X1, X2, etc, capital P standing for preference, let that be the preference function and about this preference function we will to begin with make no other assumption that it possesses, continues partial derivatives. There you see, 7.1 simply is a definition of the partial derivative of the preference function. Then, besides this, when this is assumed, the existence of these partial derivatives, we have an equation as number 7.2, 7.2 is summation over capital P sub mu times X sub mu is equal to a certain number, a little s, times the preference function itself. This number s is the same as we speak of in productivity theory and called a scale function. If this s is constantly equal to 1, we speak of constant turns to scale. But there is nothing to prevent us from applying the same kind of reasoning also to the preference function. The equation 7.2 then is simply proven in this way, that you say nothing will prevent us in any point in space, the space X1, X2 etc, to compute the partial derivatives and divide the sum of these by the function itself and nothing will prevent us from calling this ratio the scale function, the little s. So therefore that is simply what is on the board as 7.2. The kind of specialisation, mathematical specialisations we want to introduce is as expressed in 7.3. Is this, assumptions about the nature of these preference coefficients or partial derivatives, if you like, assuming then as polynomials. You see that P, sub mu, super mu being constant and X sub mu super mu being the magnitude X raised to the power mu. Now, for preference comparisons, let us consider a pair of preference variables. X sub alpha and X sub beta, or shorter if you like alpha beta simply. This is a pair, alpha beta is a pair of two preference variables. A package in the pair alpha beta means a given magnitude of X alpha and a given magnitude of X beta. An interview question in the pair alpha beta means a comparison between two different packages. We may term them the package to the left and the package to the right respectively. Here you see an interview question therefore will contain four magnitudes of preferential variables. These four magnitudes are written in 8.1, namely X alpha, super script left, meaning the left side package, X beta left, X alpha right, X beta right. And the question to the interviewed person will simply be: Do you prefer the package to the left or the package to the right or are the two packages indifferent to you? In each pair alpha beta there will be formed a series of indifferent questions of this sort. But in each question the only information used will be the answer in the form either left or right or indifferent. In a conversational form of interview, there are certain conditions, or if you like assumptions, that must be made clear to the interviewed person. It must be emphatically explained to him that the questions are posed in what you make all the Santa Claus sense. This means that a question only pertains to what the interviewed person would choose if he had a free choice between the package to the left and the package to the right. The question of how these packages might come into being, that question is not raised at all. In particular it must be explained that the interviewed person must rid his mind completely of all sorts of what kind of economic and social policy one would have to apply in order to produce the considerations of the two packages. These ideas would lead into complicated and questionable reasoning which would result in no precise answer to the interview question at all. Now, I must explain what I mean by a run of package questions. The beginning of such a run is illustrated in this table 10.1, there are two sets of columns, one for the package to the left and one for the package to the right. And then a mark column to the left and a mark column to the right. On the first line of this little table, that is to say in the first interview questions, we enter the two outer magnitudes, the preferred bounds of X alpha and X beta, you see they are entered as the two outer magnitudes, outer of the two as the preferred. And the two inner magnitudes are entered as the deferred bounds. And on this first line the preferred magnitude of 1 of the variables is packed together with the deferred magnitude of the other. Now, what about the next question. On the first line, the answer might fall either to the left or to the right. In this table here it’s assumed that it has fallen to the left which is indicated by the hook in the left side mark column. And now in the rest of the questions we’ll arrange things in such a way that there is only one variable that is changed at a time. Experience has shown that this is an effective and easy arrangement which will lead to rapid convergence. According to the side to which the choice fell on the first line, we choose the variable to be changed in this run. There are two alternative ways of defining this, but I shall not insist on that, simply taking this table as an example, the case where it fell to the choice of the first line fell to the left. Then, on the next line, what? It has now been decided that which one of the four magnitude is to be changed. And in this table it will be X alpha superscript left. Now, for this variable we now enter on the third line, sorry, I should speak about the second line first. On the second line, we change this X alpha left, we change it from the preferred to the deferred magnitude. And this, now you see, leaving the other three magnitudes as unchanged. Now, this is the second line, as you see in the table. In reality it is not necessary at all to ask the question pertaining to the second line, because you see on this second line it is obvious that the answer must fall to the opposite side of that to which it fell on the first line. So when we enter this question at all, it’s simply for checking purposes and because of systematic reasons, we want to have one line on which the choice fell to the left and one where it fell to the right and this we now have. Therefore, now, on the third line we enter, as the magnitude in the very first column, that is the variable that is to be changed, we enter the arithmetic, unweighted average of the two magnitudes we find in this column on the first two lines. Where one was to the left and the other to the right. This is indicated you see in the table. Now, in all the rest we will arrange things in such a way that we always have the following situation: When a question has been asked and answered, when we look back in the table, we will always find that there is one line on which the answer fell to the opposite side of that in which it fell on the last line. We make use of this by saying that in the subsequent question we take in this column of the variable, of the changing variable, we take the isometric average, leaving the other three as unchanged. You look backwards in the table, that is to say you look backwards in the table until you find a line where the choice fell to the opposite side of the one to which it fell in the last question, such a line will always exist, call this the opposition line. And then take the average between the two. Now, it’s very interesting to note how rapidly this procedure will converge. You can really, already at a very early stage of this game, you can guess fairly approximately where the indifference point will lie. You can guess by noticing the time it takes for the interviewed person before he reaches his answer. This reflection time will increase all the time, you can even watch it by a stop watch if you like and then guess. So in this way it is possible to reach very easily and quickly a situation where the interviewed person will say or the expert may say ‘the changes are so small that I don’t need to bother about them.’ So much for the interview technique as such. Under such types of assumptions, as we have discussed there is fortunately not necessary to investigate by interviews all the pairs in a given list of preferential variables. Take for instance the case of linear preference coefficients. That’s to say a constant term plus a term multiplied by the magnitude of the variable. It’s easy to see that what you actually get out of such an interview is the 3 ratios which are indicated in 12 of 1, the constant term in alpha divided by the constant term in beta. Second the linear term in alpha divided by the constant term in beta and the linear term in beta divided by the constant term in beta. And similarly this is what you would get if you made an alpha beta run. Similarly 12.2 indicates the three ratios you would get by an interview run in the beta gamma pair. Then, if you have that, it is really not necessary to make the alpha gamma pair by interviews. Because that would mean obtaining the three ratios in 12.3. And you see, from 12.4 you see that each of these three ratios which you would have gotten, out of the pair alpha gamma, these three ratios are already known from the two pairs you have had, namely alpha beta and beta gamma. As a curious, you may ask this question: What is the smallest number of pairs? You will have to consider a minimal set of pairs. If you should have a set where the number of pairs is as small as possible, and at the same time it is possible from direct interviews in these pairs in the minimal set, you can derive everything you need from any other combination in a whole list of variables. This number is N, if N is the number of preferred set variables, this number is equal to N to the power N minus 2. So you see it’s an enormous number, which means that you have an enormous degree of freedom in choosing those pairs which are needed to consider by interview questions. I will end up by indicating to you very briefly a concrete example from the Norwegian economy. It was in October 1970, I made an interview experiment with a high ranking civil servant in the Norwegian ministry of finance. The computations made in that illustrate some of the previously explained principles and will therefore be considered briefly. First we had to decide on the list of preferential traits. This interviewed person made a list of 17 different things which we should like to discuss. Out of these, the first five were selected for interviewing. These five preferential variables are indicated in this slide, 13.1. It was a next-year analysis, that is to say next year as seen from 1970. Of course, we could have made an interview concerning a longer range, but this was not done in this case. The first variable was number of unemployed, X1, growth rate of the GNP, the gross national product, that was variable number 2. And that was preferred and deferred bounds, plus 6 and plus 2 and for number of unemployed it’s indicated 10,000, 23,000. Now number 3, regional skewness of income, that had to be considered by a specially constructed index between 0% and 40%. Then the conception price change, of course, if you look in the newspapers you will see every day people speak about the rise in consumption prices. So here the two bounds were plus 2% and plus 7%, we didn’t dare to introduce a minus here. Now, the visible trade balance in the Norwegian krone, minus 3 milliards and 11 milliards. I’ll just indicate very briefly to you the kind of table summarising the interview questions. I shall not discuss them in detail but just to indicate to you. That’s, you see the upper part of it, and then you can see the lower part. This is just to give you a smattering of the kind of figures we obtain. These figures tell their own and very interesting story. And I shall mention only one point which was connected with the fact that we assumed in this case constant preference coefficients, we knew full well that this was an assumption that was not very realistic in the case of such large differences in the interview bounds as we had, but nevertheless we made it. And a very interesting thing came out. If you take the comparison number 2.5, growth rate of the gross national product, and the visible trade balance. It turned out that this high ranking civil servant in the ministry of finance, he would be willing to sacrifice no less than 1 whole percent of the annual increase in the GNP in order to obtain as little as 123 million kroner improvement in the visible trade. Well, how can that be? That looks very serious. But a further scrutiny showed that it is perfectly consistent with all the answers to the previous questions. And the explanation is of course simply this: That the interviews were arranged in such a way that in the indifference point there entered a very great deficit in the visible trade balance. That is to say here a red lamp has been lit, so to speak, which made him afraid, and that is why he was willing to sacrifice so much of the GNP. Another interesting feature of these results were that it was possible to make a checking, we know that from... We made the runs 1.2 and 2.3. From these runs we should be able to compute also what would have been the result of a 1.3 comparison. Now, what is on the board now indicates that the ratio P1 and P3 is plus decimal point 675. While the product of P1 over P2 and P2 over P3, which should of course amount to the same. That is equal to, well, the figures are indicated, minus 0.1153 times minus 6.25 and with slight accuracy this is equal to plus 0.723. And of course, in view of the fact that so few questions were involved in this question, I think that this triangular test was fulfilled fairly well. This is all I wanted to say today and I thank you very much for your attention, thank you.

Ragnar Frisch (1971)

Cooperation between Politicians and Econometricians on the Formalization of Political Preferences

Ragnar Frisch (1971)

Cooperation between Politicians and Econometricians on the Formalization of Political Preferences

Comment

In 1968 the Swedish National Bank made an agreement with the Nobel Foundation and the Royal Swedish Academy of Sciences to sponsor a new prize now entitled “The Sveriges Riksbank Prize in Economic Sciences to the Memory of Alfred Nobel”. The first prize was shared between the two econometricians Ragnar Frisch and Jan Tinbergen in 1969. Frisch was then an old man and only visited the Lindau meetings once before he passed away. During the 1950’s and 60’s, he had been engaged in helping India and Egypt in formulating decision models for economic planning by devising mathematical programming techniques to be used in electronic computing machines (as they were called). The first half of his lecture in Lindau describes in general terms his ideas about the so-called preference function. This is a function to be formulated in interviews between the econometrician (called the expert) and politicians and other decision makers. Using the preference function, the idea is then for the expert to feed it into the computer, show the results to the politicians and in an iterative process try to improve on the preference function. Sometimes this process will converge to a final solution, but sometimes the expert will have to tell the politicians that they have to strike out one or more of their wishes. In the second half of the lecture, which is more difficult to follow, Frisch becomes more technical and starts using mathematical formulae shown on slides that are not presented here. It is of some interest to note that Frisch is speaking before an audience mainly consisting of physicists and physics students. With his mathematical approach to the science of economics, econometrics, many of his ideas are close to the ones used in theoretical and mathematical physics. In his Prize lecture in Stockholm, held in June 1970, there is also a long section on the symmetry problem of particle physics!

Anders Bárány

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