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International Economics, Robert A. Mundell, New York: Macmillan, 1968, pp. 201-216.

The Nature of Policy Choices

Robert A. Mundell

The separate listing of targets (objects of policy) and instruments (vehicles of policy) has proved to be of considerable help in testing the consistency of systems of economic policy. To achieve a given target there must be an effective instrument, and to achieve various independent targets there must be at least an equal number of effective instruments. If a program includes more targets than instruments, at least one target cannot be fully attained; whereas if it contains more instruments than targets, there will be more than one way of achieving the combination of targets. Just as a mathematical system will be "overdetermined" or "underdetermined" if the number of variables differs from the number of equations, so a policy system will not generally have a unique attainable solution if the number of targets differs from the number of instruments. This reflects the rule made famous by Tinbergenl and it is of fundamental importance in the selection of a consistent program of economic policy.

Matching the number of instruments and targets is not of course a sufficient guide for policy. In the first place, instruments must be effective in the sense that they are capable of influencing to the necessary degree the target variable. An increase in a tariff that is already prohibitive, for example, cannot affect imports at all, whereas a tax on peanuts, although it may affect peanut production, would exert no important influence on the general level of effective demand. "Effectiveness," moreover, is partially a matter of degree: An increase in the discount rate may be effective in reducing the volume of credit up to the point where banks no longer borrow, but it would not be effective beyond it unless the banks were forced into the central bank by other instruments (for example, open market operations).

Consistency also requires that targets and instruments be mutually independent. For example, full employment and maximum output could not be considered targets if there is a unique functional relationship between the level of employment and of output, just as an adjustment of the exchange rate and certain applications of tariffs and export subsidies could produce equivalent effects on output and on the balance of payments.

The distinction between targets and instruments is, moreover, neither entirely unambiguous nor obvious. In Polak's apt phrase, targets refer to variables for which we "care," instruments to those for which we "do not care" [83]. But it is not easy to decide which variables we in fact care about. Nowadays, most people do not " care " about a change in the interest rate per se except insofar as it affects output or prices or the balance of payments although this was not true in many countries immediately after World War II; in the United States, for example, before the "Accord" of 1951 between the Treasury and the Federal Reserve (which permitted interest rates to rise), a prime object of Treasury policy was to defend the price of bonds. The same can be said for the exchange rate; thus, in 1925, some people in Britain "cared" about the traditional value of the pound sterling, but others (like Keynes) did not. Most people today do not "care" about the particular gold or foreign exchange value of a currency per se, although they do care, and strongly, that the gold value-whatever it happens to be-remain constant. "Defense of the dollar" is as much (or more) a part of U.S. policy today as "defense of the bond price" was in the early post-World War II period.

The difficulties of classification arise partially because targets and instruments are "hierarchial " in structure. Like the imputation view of production, in which inputs produce outputs that turn out to be only inputs at a higher stage in the hierarchy, the structure of a policy system includes instruments for the attainment of targets that are themselves only instruments on another level. Certainly the achievement of balance-of-payments equilibrium, or of a particular level of foreign reserves, and even maximum output and employment are only instruments for attaining higher welfare targets. There is also a sense in which the interest rate, the money supply, and the price level are simultaneously instruments and targets.

It really depends on the vantage point from which one views economic (or social) reality. A telephone call from the governor of a central bank may be the "instrument," while the "target" is an open market operation of the central bank; this, in turn, is the instrument for the achievement of a certain target level of bank reserves. Subsequently the latter is the instrument for attaining a certain level of interest rates or credit, a given degree of ease or tightness in the market, and, on a still higher stage, a prescribed level of effective demand. The latter is in turn the "instrument" used to stimulate given output and employment targets.

What is a target for one set of persons is an instrument for another; a certain degree of monetary expansion may be the target of a particular central bank technician, but it would be regarded by his superior as an instrument for attaining full employment. The hierarchial structure of economic policy process is thus flanked by a parallel bureaucratic structure controlling the links within the process.

But an over-all view is necessary. Fiscal experts in the Treasury have to evaluate the general effects of tax changes while monetary experts of the central bank should understand the relationships among money, velocity of circulation, interest rates, and employment; all must have some knowledge of the influence of their policies on the balance of payments. But at a certain stage, when a dilemma of importance arises, there is the problem of selecting a program after examining the full gamut of policy alternatives. This usually requires some generalized knowledge of the degrees of effectiveness of different policy prescriptions.

It will be found in most cases that each instrument influences al1 target variables, although the relative impact of a given set of instruments on a certain pattern of targets, if they are independent, will nevertheless be different. A useful guide that can be used in this connection is the principle of effective market classification, according to which an instrument should be matched with the target on which it exerts the greatest relative influence. The application of this rule, which takes into account the fact that "comparative advantages" of instruments are different with respect to different targets, reduces the unfavorable side effects of policies and hence minimizes the magnitude of the adjustments that must be made when an instrument is "attached" to a target that is not appreciably out of equilibrium.

In the final stages of policymaking, however, qualitative information alone is generally not sufficient. To decide which sets of policy responses are likely to be appropriate, some judgment about the likely magnitude of the required adjustment is necessary. It would be unusual, for example, if a country considering devaluation of its currency were to be entirely indifferent to the magnitude of the devaluation required; this judgment requires at least a crude estimate of relevant elasticities, wealth liquidity, and redistribution effects involved. Similarly, an expansive fiscal policy might be under consideration, bit it may be known in advance that limitations exist as to the permissible soize of budget deficits. The degree of effectiveness of fiscal policy will play an important role in the decision to use fiscal policy at all.

What this means is that there are either institutional barriers to the free adjustment of particular instruments or that, after a point, the instrument itself becomes a target or at least impinges on other targets that have not been  explicitly taken into account. Variations in interest rates, for example, may be entirely permissible within some ranges but not in others, just as in the present system of international payments, free adjustment of exchange rates for IMF members is permissible within the 1 per cent margin on either side of parity but not outside this margin (except in unusual cases).

Accordingly, before a policy program is formulated in its final stages, there must be preparatory quantitative work examining the effectiveness of various instruments to establish whether the extent of the adjustment needed is within the realm of political possibility. Otherwise, alternative methods must be sought.2

Employment and the Balance of Payments

Some of the above precepts can be illustrated by the problems likely to be encountered in pursuing two "targets" that have become recognized as extremely important in the post-World War II years: "full employment without inflation" and "balance-of-payments equilibrium."

It will be apparent at the outset that the mere specification of these goals as "targets " involves a great deal of ambiguity and implicit assumptions about the economic system. In the first place, the expression "full employment without inflation" seems to involve two targets, rather than one, since the attainment of full employment is certainly different from the attainment of price stability. Post-World War II literature has, however, frequently assumed that an increase in effective demand leads to an expansion of employment and of output up to the point of full employment; further increases will cause inflation. The underlying implicit assumption is that the aggregate supply curve, reflecting the marginal costs of firms (on the assumption of competition), is perfectly elastic up to the point of full employment, and completely inelastic after that point, at any given monthly wage. This assumption is not generally satisfied in reality, first, because of diminishing returns at constant wage rates and, second, because wage rates, determined through the collective bargaining process, are influenced by the level of activity as bargaining power shifts back and forth between management and labor with the contraction or expansion of economic activity. But in extreme cases -high unemployment or rapid price increases- it is usually not difficult to determine whether inflation or unemployment is the major problem, and therefore in which direction the authorities should try to push aggregate demand. For this reason there is some justification for lumping full employment and stable prices together as a single target, provided this is recognized as only an approximate description of a set of very complicated economic facts.

A more serious problem with the target of  "full employment without inflation" relates to its closed-economy connotation. If one is dealing with a closed economy (such as the world as a whole or -to a lesser extent- the Soviet or non-Soviet bloc), a stable price level is not an unreasonable practical goal. As the closed economy expands, the increase in real income can be distributed through wage increases more or less in line with productivity growth (maintaining reasonable price stability) or through falling prices also in line with productivity growth (maintaining constant money wages, but growing real wages). The second method is theoretically preferable, because it permits a competitive interest payment (in real terms) on money balances; because these bear little or no social cost optimal money holdings require a return be paid on money. But a fact of life at the present time is the of some degree of wage rigidity downward and, because of this fact, economists all over the world typically recommend a system of expanding tith growth) and constant prices even if this is at the expense of optimal tholdings.

For a single economy facing the rest of the world, however, it is far from clear that price stability should be treated as a target of policy. If it means stability of a price index of home-produced goods, it means (literally interpreted in a world of fixed exchange rates) no possibility of relative price changes in the world as a whole. If the prices of German goods, Italian goods, Indian goods, and American goods are all stabilized, then the international price mechanism cannot function at all under fixed exchange rates. It is clear, therefore, that the goal of price stability must be very cautiously interpreted in an international context. If an implicit goal is a system of fixed rates of exchange, what is required is differential rates of inflation between countries: Surplus countries should let prices go up while deficit countries should either prevent hem from going up or let them fall, depending on how the " burden of adjustment" is to be divided.

There appear to be even greater ambiguities connected with the target of balance-of-payments equilibrium." The balance of payments reflects the budget of the community as a whole excepting the monetary authorities; after netting out home-produced and home-consumed goods, and home-issued and home-bought securities, the "balance" is the difference between the balance of the goods plus securities sold and bought abroad. Any gap must be settled in money acceptable to foreign central banks -gold or liquid assets. Strictly speaking, a balance-of-payments deficit does not, per se, cause any discomfort. The man in the street does not care about a balance-of-payments deficit. Discomfort arises from the actions that a dwindling level of foreign reserves will necessitate. The man in the street will care about these actions insofar as they must affect him directly or indirectly.

To some extent, therefore, it is stocks rather than flows that people do worry about, and should worry about. The balance of payments is a flow over time that, when added up from a certain date, implies a change in the stock of foreign reserves between the two dates. In turn, significant changes in the stock of reserves will induce discomfort. If reserves begin to accumulate rapidly, the country will realize that it is investing too large a portion of its savings in an asset that yields no return (for example, gold or a creditor position at the IMF) or only a small return (for example, foreign exchange balances). And if reserves get too low, the country will be placed at the mercy of foreign private speculators or central banks or else be forced into precipitate action at inopportune times. Reaction to excessively low reserves is, of course, usually more rapid than reaction to unnecessarily high reserves.

There is an analogy in this to the budget of the government. Economists have become accustomed to regard the budget deficit -as it is altered through changes in taxes or government spending- as an instrument of policy The man in the street has no objections to budget deficits, but he has, in many countries, strong objections to increases in the public debt, arguing, rationally or otherwise, by analogy with his own budgetary problems as an individual. Of course, the rub is that the budget deficit always leads to an increase in the public debt. But again the discomfort is produced by the stock of outstanding debt and its implied tax liabilities rather than by the flow of the deficit over time. In the same way, individuals, as citizens, would be worried about an excessive accumulation of external debt rather than about the position of the balance of payments at any instant of time.

Related to the importance of stocks of reserves is a problem concerning the consistency of domestic decisions in relation to the rest of the world. Under one definition of the over-all balance-of-payments position -a perfectly symmetrical definition-  the sum total of the balances of payments of all countries in any one period of time is zero, so that there is no inconsistency if every country aims for a precise balance at all points in time. But in practice an asymmetrical definition of the balance-of-payments position is generally used. If gold were the only type of international reserve, the sum of the external positions of all countries would add up not to zero but to the amount of new gold finding its way into the monetary reserves of the central banks. The reason is that South Africa and other gold-producing countries treat the export of gold just like any other commodity export, whereas the import of gold into the coffers of central banks is excluded from ordinary imports. For this reason it is possible for each and every country to have a balance-of-payments surplus when monetary gold holdings of the world are increasing, which is the case whenever gold production exceeds the current use of gold for the arts and for private hoarding.

This does not imply consistency in the targets of each country, as the external surpluses planned by all countries - as they attempt to let reserves grow with trade or some other measure of growth-may add up to more than the net accretions of gold into monetary reserves. (This, of course, is the crux of the liquidity problem of the present decade: Most countries desire a balance-of-payments surplus to finance a level of desired reserves growing at a faster rate than actual reserves; the demand of all countries cannot in this way be satisfied, thus threatening progressive contractionary employment or restrictive trade policies). Every country cannot have a surplus of an arbitrary size, since the sum of the surpluses is limited to the growth of the gold reserves.

There are additional reasons, based on accounting practices, why the balances of payments of all countries do not sum to zero. Countries do not all follow the same practice in recording various transactions in the balance of payments. Thus, a deposit by German commercial banks in New York would counted in the United States as an item financing a U.S. deficit, according to the pre-Bernstein Department of Commerce definition, but there would be no offsetting surplus in German accounts, since the transaction would be treated in Germany as a capital outflow. These are technical questions of definition, but they have real significance insofar as policy becomes conditioned to particular accounting practices.3

The ambiguities do not end with problems of asymmetries in the definition of the balance-of-payments position. Discomfort is provided by a bad composition of the balance. Thus there was a sense in which Canada had a continuing external equilibrium during the period 1950-1962 when the exchange rate was (in varying degrees) flexible and the level of official reserves remained approximately constant. But the composition of the balance, achieved through an import surplus financed by capital inflows from the United States, was a source of considerable worry. What is involved here is an additional goal implicit in the system: the level of the net external indebtedness. Increasing indebtedness causes discomfort because it introduces present feelings of future insecurity. Just as the composition of output is important (the division of output between investment and consumption affects additional growth targets), so an appropriate composition of the balance of payments is a ligitimate target of policy.

Mathematical Aspects of the Theory of Policy

Some of these considerations are worth formalizing mathematically, as a convenient introduction to some of the work in the following chapters. We can start with the statical policy solutions outlined by Tinbergen.

Tinbergen's rule-that consistent, determinate policy systems require an equal number of targets and instruments-reflects the mathematical fact that an equal number of variables and equations is necessary for a mathematical system to have a unique solution. Suppose that we have two instrumental variables, a and b, and one target variable X. Then, generally, a and b will each affect X so that

X = X(a, b).                                                   (1) 

If we now set X at some target level, say X0, then the target will be achieved whenever

X0 = X(a, b)    holds.                                               (2)

Figure 14-1

The function (2) may be plotted on a graph (Figure 14-1) with the instruments on the abscissa and ordinate. The graph shows that there is a single-fold infinity of ways of setting a and b to achieve the target for X. The X0X0 could, for example, illustrate the requirements of internal balance as functions of the interest rate a and the level of taxes b, as discussed in Chapter 16. This case of redundancy is the policymaker's delight because he has a great variety of ways to achieve a single target.

As a second case we may assume the same two instruments but two target variables, X and Y, each of which are functions of the instrumental variables. Mathematically we have

and when we set target levels X0 and Y0 we get a determinate system

which can be plotted in Figure 14-2. Here the policymaker has no but to set the instruments at the levels al and bl if he wants to achieve the targets; only at a1 and bl are X = X0 and Y = Y0. Again the example of

Figure 14-2

Chapter 16 may be used in illustration, where, as before, the X0X0 line is the internal balance schedule, and the Y0Y0 line is the foreign balance schedule.

As a third case we again have the two instruments a and b, but this time three target variables, X, Y, and Z, so that

If we now set target values X0, Y0, and Z0, we have three equations in two unknowns,

which we can plot on Figure 14-3. There are three points of intersection but at none of them are all three equations satisfied; one of the targets is not reached. The monetary-fiscal policy mix example may again be used for illustration with the new target variable, Z, denoting, for example, the rate of economic growth and Z0 its target levell. Then if an economy were following the

Figure 14-3

monetary-fiscal policy mix represented by the point H, it would have a balanceof-payments deficit, excess unemployment, and a rate of growth below its target rate, as, for example, the United States experienced in 1961 and 1962.

The point H presents a policy dilemma. Those who regarded the balance of payments and full employment as the primary targets (neglecting growth) would urge higher interest rates and a budget deficit to get toward the point alpha, Those who advocated higher growth and employment, neglecting the balance of payments, would urge a budget deficit and lower interest rates to get to the point beta . And those who stressed secular growth and the balance of payments, to the exclusion of the level of employment, would urge lower interest rates and higher taxes to get to the point gamma.

Actual policy makers, hovering in indecision, may indeed elect to remain at H. It is quite possible, in fact, that H is the best of a set of bad positions as represented by planners' preferences. (We can conceive of planners' preference functions-to be sure a mere toy-reaching an apex at the point H.)

Anatomy of Policy Failure

An equal number of instruments and targets is not, however, a sufficient condition for establishing a solution to a policy problem. Failure may result from (1) a lack of independence in the targets, (2) multiple solutions, or (3) limitations on the variability of the instruments.

The first case is illustrated in Figure 14-4, where the X0X0 and Y0Y0 lines

Figure 14-4

are parallel (a result that could occur in the illustrative example if capital is immobile). Mathematically this means that the Jacobian is singular, that is,

The second case results from nonlinearities in the schedules, as illustrated in Figure 14-5, which can give rise to multiple intersections; in the graph alpha, beta, and gamma are all solutions to the system. This result is unlikely in the illustrative example, but it is not impossible if certain reverse transfer conditions or interest rate effects on the composition of the trade balance occur.

A third case of failure results from intersections outside the feasible zone of variation of the instruments, as indicated in Figure 14-6. Suppose for political or economic reasons a and b are restricted to the shaded area. Then the solution alpha cannot be attained. In the illustrative example this case is possible and even likely if the degree of disequilibrium is very high. Political considerations may limit the "doses" of monetary and fiscal policy. But there may be ecosonomic reasons limiting its use as well, for example, the interest rate implied by alpha may be outside the scope of manipulation by the central bank.

Figure 14-5

Figure 14-6

Incomplete Information and Policy Dynamics

If we have conplete information about the system, we need only solve the equations for the changes in the instrumental variables needed to eliminate any discrepancy betweent he target values of the target variables and their actual values. Retaining only the linear terms of a taylor series, from

By substituting the (known) values of X0-X and Y0-Y, the policy problem is solved (once the problems of existence and uniqueness have been been settled).

The fact is, however, that we never (or hardly ever) have complete information. The values of the coefficients deltaX / delta a, deltaX / delta b, deltaY / delta a, and deltaY / delta b may not be known, and they may even change over time. To be sure, as econometrics progresses it may be expected that information will improve over time. But in the meantime policy must be guided somehow, and to this end we need means of getting to the target equilibrium without having full information about its position.

It is here that economic dynamics becomes relevant. We want to find the equilibrium solution without knowing exactly where it is. To do this we can make use of our understanding of the stability of particular dynamic processes, since knowledge of stability conditions never (again, hardly ever) requires complete information about the parameters. If we can invent a set of rules for policymakers to follow -a set of rules that is not contingent on complete knowledge of the whole system- we will have found a way of compensating for our lack of complete information.

The analogy to the correspondence principle readily presents itself. Marshall, Hicks, Samuelson, and others made use of stability conditions to derive meaningful theorems in comparative statistics; the conformity that seemed to exist between "well-behaved" dynamic systems and "normal" comparative-static results Samuelson termed the correspondence principle. The same relation can be exploited, but in a different way, in policy systems.

The dynamic stability literature asks whether a system is stable under a given set of dynamic postulates, and then makes use of the information about stability to deduce comparative-statics results. The policy literature, on the other hand, asks how instruments should be allocated to targets, or how "prices" should be allocated to "markets."

The principle to be followed is to assign instruments to targets in such a way as to ensure that the dynamic system implied by the policy rules is a stable system. It is this principle that I have called the principle of effective market classification, and the guide to be followed is that instruments should be allocated to targets which they influence most directly.

Alternative Mathematical Formulations

There are two ways of posing the problem in a formal mathematical way. One is to specify how the instruments should be adjusted over time in relation to each target variable or market. In linear differential form, for example, we could write the two-target, two-instrument system as follows:

where X and Y may now be so taken as discrepancies from their target values. The eij's are dynamic policy parameters indicating the direction and speed at which instruments change in relation to targets. For example, if X and Y represented inflationary pressures (unemployment, if negative) and the balance-of-payments surplus (in excess of the desired surplus), and a and b denoted interest rate and tax policies respectively, ell and e2l would state how slowly the interest rate would be required to adjust to unemployment and to the balance of payments, while e12 and e22 would similarly determine the specified rates at which taxes or government spending should be altered.

The other way of posing the problem is to specify the weight given to each target variable in determining the movement of each instrument. Mathematically this is equivalent to writing

There is therefore no difference between them in the linear case. From an institutional point of view, however, (18) and (19) would be more revealing if institutions were set up on a " target basis " (had specific functions to perform) while (20) and (21) would be more revealing if institutions were set up on an instrument basis (had specific tools to manipulate). Since the central bank and Treasury may be best conceived of as having instruments to control (money or interest rates, and taxes or government spending), we shall use, for illustrative purposes, (20) and (21).

Now (20) and (21) are written in completely general terms (except for the assumption of linearity). After linearizing the system to make X(a, b) and Y(a, b) explicit functions we get

where the Aij's depend on initial conditions and the lambda's are the roots of the following equation:  

The policy problem is to find values for the "weights" Kij that will make the roots of (27) negative if real, and have negative real parts if complex. This amounts to making the coefficient of lambda and the determinant positive, stability conditions of the system.

Equation (27) may be simplified notationally to

It is at once clear that it is not necessary to know each of the slopes Xa, Xb, Ya and Yb to develop a stable policy system, for we can always find a way of making two of the Kij's equal to zero. Suppose, for example, Delta > 0. Then setting K12 = K21 = 0 ensures the first stability condition if Kll and K22 have the same sign. We also have to make KllXa + K22 Yb < 0. If Xa and Yb have the same sign, giving both Kll and K22, the opposite sign ensures all stability conditions; and if Xa and Yb have opposite signs, say, Xa < 0 and Yb > 0, then negative values of both Kll and K22 are sufficient to ensure stability. A stable system can always be found without knowing the values of all the slopes.4

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Notes

1 See, for example, ([100], chap. V).

2 Introduction to Chapter 14 adapted from " The Nature of Policy Choice", Banca Nazionale del Lavoro Quarterly Review, LXV1 (September 1963).

3 For a review of the major asymmetries see Høst-Madsen [26].

4 For a discussion of the complications associated with the general case see Chapter 21 of this book. Decentralization is always possible if the so-called Hicks conditions of perfect stability are satisfied.

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Literature Cited

[26] P. HØST-MADSEN, "Asymmetries between Balance of Payments Surpluses and Deficits," I.M.F. Staff Papers, 9, 182-199 (1962).

[83] J. J. POLAK, "International Coordination of Economic Policy," IMF Staff Papers, 9, 151 (July 1962).

[100] J. TINBERGEN, On the Theory of Economic Policy. Amsterdam: North Holland, 1952.


© Copyright Robert A. Mundell, 1968