ABSTRACT
The economic process within a given economic system takes place in time. Like the physicist or the astronomer, we can by constant observation and measurement register all the quantities marking the course of the economic process, large or small, either in aggregates or in individual units. In the contemporary exchange economy we can follow the curves through time of prices, of the quantities of goods purchased, of the quantities of particular goods produced, of income, of the quantity of money, of the level of investment, of the number of unemployed, of the level of particular taxes, of the level of tariff revenue, etc., and follow, in each case, the course through time of each of these particular economic variables. In this way we obtain a description in as much detail as we wish of the course of economic variables through time. We can, if we like go back to the separate variables of the individual economic units engaged, or we may limit ourselves to registering the curve through time of macro-economic aggregates. Which variables he registers depends on the problem in which the economist is interested. It is obvious that registering and describing variables simply for their own sake is senseless. One must be equipped with meaningful questions when approaching the real world, if one is to know what phenomena to observe. Such meaningful, questions can only be obtained from a sound theoretical analysis of the real world which will enable us to form hypotheses as to the relationships between economic quantities. One task of economic analysis is to explain the historical course of the economic process. (For example, why did the prices of particular goods rise in a particular period, while the prices of other goods fell? Why has the national income of a country fallen in a particular period ?) Another task of economic analysis is to give an account of how the course of the economic process will develop from a particular initial condition under particular assumptions. (For example, how will the course of a country’s economy develop from today onwards if wages are raised by a particular amount ?) Of the two tasks the second is undoubtedly the more important and one might even say the real task of economic analysis. Historical description for its own sake is not the task of economic science. Only in so far as the analysis of the past provides us with knowledge that is relevant to the shape of things to come is there any sense in the economist studying the past. The solution of the two problems requires, just as it does in the natural sciences, a close interaction between the theoretical and the empirical, or between the analysis and the exact observation of the real world.
In studying the course through time of an economic variable we must first distinguish between two sorts of phenomenon. The process of an economic variable through time appears either as stationary or as changing (evolving). An economic variable may be said to be stationary through time if the value of the variable does not change, that is, if the curve through time of the variable is parallel to the time axis.( 1 ) Thus the prices of goods are behaving in a stationary way if they do not vary. The national income is stationary if its quantity does not change through time. On the other hand, the behaviour of an economic variable through time is non-stationary, or changing, or evolving, if its value is subject to changes. Correspondingly, we may say that an economy is stationary (or changing) if the values of all the variables are constant through time (or not constant). It is, of course, possible that many economic phenomena are changing from the micro-economic point of view, but stationary from the macro-economic point of view. Thus the population as a whole may be stationary when the size of individual families is by no means stationary. Similarly, the value of total net investment may be stationary even if the net investment of individual economic units is not stationary. We must notice, further, that particular variables may be stationary without the economy as a whole being stationary. The fact that positive net investment remains stationary at a particular level does not mean that the economy as a whole is stationary. With net investment at a constant rate and positive, the quantity of real capital in the economy is growing constantly per unit of time so that the total of capital is not constant.
It is the task of economic theory, as we have emphasised, to explain the course through time of a system of economic variables. Such an explanation can be given in two different ways. If one is using an analysis where the relations between the relevant variables relate to the same moment of time, or to the same period of time, then we may speak of a “static” analysis or “static” theory. A relationship in which the values of the variables relate to the same point of time, or to the same period, may correspondingly be described as a “static” relationship. On the other hand, if the explanation contains relationships between relevant variables the values of which do not all relate to the same point of time or period of time, then we may speak of “dynamic” analysis or “dynamic” theory. The relationships themselves, if they possess this characteristic, may be described as “dynamic” relationships.
Examples of static relationships have occurred frequently in the previous sections. If we formulate the demand plans of a household in the following way:
“If the price of a good in the coming period is p 1 then the household (ceteris paribus) will buy the quantity x 1; if, on the other hand, the price in the coming period is p 2 then the household will (ceteris paribus) buy an amount x 2, etc.”
then the relationship described between the price and the quantity demanded is a static relationship.
If the savings plan of a household is formulated in the following way:
“If the income in the coming period is e 1 then, at the prices of goods expected in the period, a sum of s 1 will be saved; if, on the other hand, the income in the coming period is e 2, then (ceteris paribus) the sum s 2 will be saved, etc.”
then, again, there is a static relationships between expected income and planned savings. The supply function deduced earlier for a suppher acting as a quantity-adjuster was similarly a static relationship. The reader will be able to work out further examples for himself.
We have noticed examples of dynamic relationships in discussing the problems of long-term planning. If one assumes that the demand of a household for a particular good depends in the coming period (ceteris paribus) not only on the price of the good in the coming period, but also on the expected prices in later periods, then there is a relationship between variables which relate to different points or periods in time.
If one assumes that the planned supply for the coming period depends on the actual price of the previous period, that is:
xt = f(Pt -1)
where x t is the planned supply for the coming period, and p t-1 the price in the previous period, then we have a dynamic relationship between two variables.
If we assume that the value C t for total consumption in an economy in the period t depends on the national income y t-1 in the previous period t -1 so that
Ct = f(yt -1),
then again we are working with a dynamic relationship.
For the understanding of modern theory it is necessary to maintaincomplete clarity as between the pair of concepts “static” and “dynamic” on the one hand, and “stationary” and “changing” on the other hand.The concepts “static” and “dynamic” have been used in economicsin many different ways, so that it is impossible to be clear unless aprecise definition is given. The definitions used here were introducedinto economic theory by Ragnar Frisch in 1928 and today have beenaccepted by the majority of theoretical economists in all countries.( 1 ) It is essential to understand that in modern theory “statics” and “dynamics” refer to a particular mode of treatment or type of analysis of the phenomena observed, while the adjectives “stationary” and “changing” describe the actual economic phenomena. A static ordynamic theory is a particular kind of explanation of economicphenomena; and, indeed, stationary and changing phenomena can besubmitted either to a static or to a dynamic analysis. We shall becomeacquainted in the next section with examples.
From the definition of the concept of dynamics it follows that a theory is not to be considered as dynamic simply because it introduces expectations. Whether that is the case or not depends simply on whether or not the expected values of the single variables relate to different periods, or points, of time.
In addition to the method of analytical dynamics for analysingthe course of the economic process within a given economic system, there is also what, following Frisch, we may describe as “historical dynamics”, which is concerned with the development of the economic system or its institutional framework, within which the economic process takes its course. This kind of historical dynamics lies outside the boundaries of economic theory. Its problems belong mainly to economic history and sociology. In historical dynamics one is interested in different types of environment, and in problems of the transition from one type of environment to another; in analytical dynamics one is interested in the course of the economic process within a given type of environment.
The necessity for, and significance of, a dynamic treatment in theoretical analysis depends on the fact that the adjustment of the economy to changes in the data underlying economic plans takes time. (We shall consider the concept of “data” in the next section.) Thus, changes in income in one period often only take effect in later periods on the decisions of households as to their consumption. Changes in prices influence the supply plans of the entrepreneur often only in subsequent periods, etc. It is these “lags” as they have been called in modern theory, with which the change of one variable works on another variable, which make necessary the use of dynamic relationships in explaining the economic world. In addition, there is the fact, as we have seen, that certain variables depend among other things on the rate of growth of other variables (for example, the demand for a good may depend on the rate of change of prices); and a speed is always a quantity in the calculation of which two different points of time are involved. Problems involving rates of growth therefore require the use of dynamic relationships.
The role of lags in the process through time of the economy has been presented in a very clear way in Tinbergen’s “Arrow” diagram.( 1 ) Let us assume that there are four variables, quantities A, B, C and D, in the explanation of an economic process. In the adjoining diagram the points in horizontal rows represent the course through time of the single variables, that is, the values of the variables at the consecutive moments of time t – 1, t, t + 1, t + 2, and t + 3.
It is the business of theory to explain the observed development of these variables. It is therefore necessary to know how the change in the value of a variable at one point of time affects the values of other variables at different points of time. For this purpose the theory will assume particular inter-temporal relationships between the variables, and then will examine what the course through time of the four variables will be according to different assumptions, and will compare the theoretical results with the empirical facts. We may assume, for example, that changes in A affect the variable B in the same period, but affect the variable C one period later, i.e. with a lag of one period. In the Arrow diagram this is represented by the arrows from A to B and from A to C. We may assume, further, that changes in C bring about changes in D and A with a lag of two time-periods, as is portrayed in the Arrow diagram by the corresponding arrows from C to D and C to A. A change in A at the point of time t can then be the primary cause of a change in C at time t + 1, and a secondary cause of a change in D at time t + 3. On the other hand, a change in C results two periods later in a change in A. This causal interdependence between the relevant variables is graphically expressed in this Arrow diagram.
The Arrow diagram also makes it especially clear that dynamic relations always involve propositions about inter-temporal causal relationships between economic variables. A dynamic theory shows how in the course of time a condition of the economic system has grown out of its condition in the previous period of time. It is this form of analysis which has central importance for the study of the processes of economic development, be they short-run or long-run processes. Sequence analysis (or process analysis) is only possible in the context of a dynamic theory, that is, of a theory which involves at least one dynamic relation. Sequence analysis is not possible in static theory. because this type of theory works only with relations between variables which relate to the same period or point of time.
Now we have clarified this fundamental distinction between a static and a dynamic treatment of economic phenomena, we are in a position to turn to one of the main problems of economic theory: that of the interaction between the plans or dispositions of the individual economic units engaged. The relationships considered in this chapter will play an important role in the analysis of the problem of equilibrium, which we shall now discuss by means of a number of examples.
