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A Layman’s Guide to Little/Mirrlees

Author(s):
International Monetary Fund. External Relations Dept.
Published Date:
March 1972
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George B. Baldwin

Two well-known Oxford professors, Ian Little and James Mirrlees, have written a manual on industrial cost-benefit analysis which has stirred up a lot of interest and a fair amount of dust.1 Some important development agencies have already announced adoption of the Little/Mirrlees approach; these include Britain’s Overseas Development Administration, West Germany’s Kreditanstalt für Wiederaufbau, and the United Nations Industrial Development Organization. The World Bank Group (the Bank, the International Development Association, and the International Finance Corporation, which assists private industry) has studied Little/Mirrlees to see whether any closer move toward it would be a useful refinement of present methods, which are already close to theirs (this is less true of IFC than of the Bank and IDA). Further experiments in applying Little/Mirrlees within the Bank are likely.

One of the major problems in evaluating Little/Mirrlees is understanding it. The Manual is not difficult for a reasonably well-trained economist to understand; but some of the subtleties and refinements have got in the way of getting agreement on what is new in Little/Mirrlees and what is not, what is essential and what is not. My own view is that their essential ideas are not new and their new ideas are not essential.

A First Approximation

The Manual’s central message can be simply stated. A valid assessment of an industrial project’s worth to an economy often requires the use of values that differ from the values used in the normal kind of business or financial appraisals. Economic appraisals frequently must be done with “shadow” prices, i.e., any assumed prices that differ from those that will actually be realized in the company’s own books (“market” prices). The particular shadow prices which Little and Mirrlees believe should be used are “world prices”; these represent a country’s actual trading opportunities. The resulting streams of annual costs and benefits should then be weighted (discounted) to reflect the differing times when they will occur. The discounting operation has the effect of translating future values into their present worth, allowing the streams of future costs and benefits to be summed into single figures. You then subtract the single cost figure from the benefit figure. If there is a surplus the project is said to have a favorable present social value, and is worth doing. Economists will at once recognize that Little and Mirrlees are relying on the familiar discounted cash flow method, using shadow prices, to test for a project’s net present worth.

Thus the basic approach of the Manual is not new. For those to whom the basic concepts may be hazy or unfamiliar, the Manual provides an admirable introductory explanation, free of mathematics or jargon. But the major innovation put forward by Little and Mirrlees—their big idea that has stirred up most of the interest and most of the dust—is their notion that all prices used in project calculation should be world prices. They are not satisfied with the procedure followed by many institutions (including, normally, the World Bank Group) whereby partial use is made of international values, e.g., applying them to major inputs and outputs that are or easily could be traded. They argue in favor of valuing all inputs at world prices, even the so-called nontraded inputs that normally cannot possibly be imported (i.e., electricity, construction, local transport, and labor). The reason Little and Mirrlees want to go “all the way” in using world prices for every input and output is to avoid the distortions which they feel creep into the calculations if only partial use is made of world prices. A cost-benefit calculation based partly on world prices and partly on domestic prices has to be put into a single currency through the use of an exchange rate. Little and Mirrlees don’t like exchange rates, not even “shadow” exchange rates based on “correcting” unrealistic official rates. In their view, no exchange rate, no matter how good, can overcome the distortion in relative values which arises whenever you combine values taken from different sets of prices (such as world prices and domestic prices). The use of one set of prices—world prices—bypasses this problem and, by taking all prices from one common pool, achieves a more valid ordering of the relative values used in constructing costs and benefits.2

If by some miracle of wisdom a country had developed its economic structure under conditions of free trade and free exchange rates, its investment decisions would continuously have been made in the light of world-wide trading opportunities; consequently, the relative values of home prices and world prices would today stand in an undistorted relationship to each other. This is hardly the world as we find it. Protection and other trade restrictions are everywhere, investment decisions have often been made outside the discipline and opportunities of world prices, and many exchange rates now serve to distort rather than to preserve true relationships between domestic and world values. Little and Mirrlees want to prevent this bad history from contaminating investment decisions. They want to avoid using some good prices (world prices of traded items) and some not-so-good prices (the domestic prices of nontraded inputs), which must then be merged by use of a (frequently bad) exchange rate. If all values can be measured in world prices, the problem is solved. In a neat display of inventiveness, Little and Mirrlees have “solved” this problem. But some of their critics say the cure is worse than the disease. This point is far and away the most controversial part of the Manual: just how much trouble is it worth to avoid using a foreign exchange rate, official or shadow?

With this summary introduction we can take a closer look at some of the main features of the Little/Mirrlees approach.

Social Profitability and Private Profitability

Little and Mirrlees begin by pointing out the many similarities between the calculation of an industrial project’s private and its economic or social profitability. Both calculations start with the problem of estimating future income (i.e., “benefits”) and costs (capital and operating). The cost and benefit estimates are both made up of two elements: (1) the number of physical units involved plus (2) the price used to value each physical element. “The essence of a cost-benefit analysis is that it does not accept that actual receipts adequately measure social benefits, and actual expenditures social costs. But it does accept that actual receipts and expenditures can be suitably adjusted so that the difference between them … will properly reflect the social gain” (pp. 22-23).

A second but less crucial feature of their system is the emphasis given to savings. Little and Mirrlees feel that resources for investment are so often a critical constraint that they deserve to occupy a central role in evaluating projects. Their handling of this problem, by converting a project’s cash flow into a pure savings flow stripped of all consumption elements, is neat, and deserves discussion. But not until we look further at what they have to say about the use of world prices.

Why World Prices?

“If you can get more refrigerators by exporting bicycles to pay for them, than by diverting resources from making bicycles to making refrigerators at home, it is clearly right to make and export the bicycles and import the refrigerators. But whether this is in fact the case, requires a knowledge both of the relative costs of production at home, and of world prices and market conditions” (p. 85). The reason for relating everything to world prices is not because they are “more rational” than domestic prices but simply because “they represent the actual terms on which the country can trade” (p. 92). So it is logical to argue that all internationally traded goods—i.e., those which the country actually imports or exports, regardless of whether the project itself will do so—should be valued at their c.i.f. (for imports) or f.o.b. (for exports) prices. But what should we do with nontraded inputs and outputs? (The main nontraded inputs are domestic transportation, construction, electricity, land, and labor; other minor ones can be thought of, e.g., water and waste disposal, telecommunications, advertising, banking services, maintenance and repair services.)

Obviously a dollar’s worth of future consumption is never worth a full dollar to us today.

Little and Mirrlees say that since traded goods are valued in world prices, nontraded goods must be similarly valued; “only thus can we ensure that we are valuing everything in terms of a common yardstick.” Note that a “common yardstick” may refer either to use of a common currency, (e.g., all values expressed in either dollars or rupees), or to the use of a common source of values (e.g., world prices, instead of a mixture of world prices and domestic prices). All methods of project appraisal require the use of a common currency, but only Little/Mirrlees requires the use of both a common currency and a common source for all values used. The problem of trying to express all values in a single currency where they will stand in a right relationship to each other can be solved either by using “a special accounting price for foreign exchange” (a shadow exchange rate) or by revaluing domestic resources in terms of world prices; the latter is the method recommended in the Manual. Once all values are established in terms of world prices, it does not matter whether they are left in U.S. dollars or converted into domestic rupees (the two illustrative currencies used in the Manual). If a complete set of costs and benefits are converted from dollars into rupees any exchange rate can be used, since all values will retain a constant relationship to each other. But this is not true if some values are taken from world prices and some are taken from domestic prices and the two sets are then put into a single currency by using an exchange rate. This will change the relationships among different values and distort the estimate of the relationship between foreign and domestic resources.

Using Input/Output Analysis to Chase Down Traded items

Little and Mirrlees advance both pragmatic and theoretical reasons for wanting to anchor all cost-benefit values in world prices. Their pragmatic reason is that world prices represent actual trading opportunities, which heavily influence domestic investment decisions. Every industrial investment decision involves the “make or buy” decision involved in the refrigerator and bicycle quotation cited earlier. The development process involves a steady expansion of the demand for imports, and the only way to pay for them, in the long run, is to produce for export only those things a country can produce best. To make the most of its opportunities a country must deploy its resources (fundamentally, its land and its labor force) in ways which give it the most for its money, i.e., the most foreign exchange (either earnings or savings) for domestic resources used. And the only way to do this in a complete and theoretically consistent manner is to chase down all the inputs used by a project, direct and indirect, until all the potentially tradable items have been valued in world prices, leaving only land and labor. Land is dismissed as relatively unimportant in most industrial projects. But in valuing labor, Little and Mirrlees argue that even labor’s own inputs (i.e., its consumption) should be valued in terms of world prices (they give us some help by suggesting how this refinement might be achieved).

It is not easy to value the nontraded inputs in world prices. The general procedure is to take each such input (power, construction, transport, or labor) and break it down into its own inputs; these in turn will consist of items that are traded and items that are non-traded. The latter are in turn broken down into traded and nontraded items, etc., etc. The only way this chain can be followed back very far is through a detailed input/output table for the economy as a whole. Few less developed countries have in existence a table that is detailed enough to permit the needed calculations for more than a few simple industries. If no such table is available, rough-and-ready approximations to world values can be used. These approximations or “conversion factors” are based on the ratio of domestic costs of a representative sample of, say, construction items (wood, cement, steel, fuel, etc.) to the world price of these items. This ratio is based on using the official exchange rate; the reciprocal of the ratio is then used to adjust the domestic cost of nontraded inputs to values closer to what they would be if the complete input/output method had been rigorously followed. This conversion factor is in effect a way of correcting for the overvaluation of an exchange rate; however, it does it on an average basis and not with the precision theoretically achievable if all nontraded inputs could be decomposed into their ultimate traded elements which could then be valued in world prices.

The Price of Labor

There is nothing particularly new or distinctive in the Little/Mirrlees treatment of this much-discussed question. Most of the labor used in industry comes from a labor-surplus rural sector, and its departure involves little or no loss of agricultural production, i.e., its opportunity cost (equal to its marginal productivity) is typically very low. However, industrial labor is usually paid considerably more than the agricultural subsistence wage. Some of this excess over what labor could earn in agriculture is a necessary cost of making it available at industrial locations; but some of the excess is an artificial creation of trade union policies, needlessly high minimum wages, or employer “softness” in relation to what he could pay if he wanted to pay no more than a competitive wage. So the proper domestic price for valuing labor is a shadow wage that lies somewhere between its actual market rate and an agricultural subsistence wage. A good deal of judgment is involved in settling on a figure (since the cost stream stretches over many years, there is no reason for using a constant shadow price throughout the project life if there is any reasonable basis for varying it).

But Little and Mirrlees do not let the domestic shadow price of labor determine its value in project costs. A domestic shadow price reflects only labor’s relative scarcity in the domestic economy; once this has been estimated, this domestic value must then be converted into a world price. In theory this can be done—as explained above—by decomposing labor’s consumption into traded items; but in practice either a specific conversion factor or the standard conversion factor would almost always be used.

Adjusting for a Projects “Commitment to Consumption”

With nations, as with individuals, there is a never-ending tug-of-war between consumption and savings. The ultimate purpose of all economic activity is to raise living standards, which means raising consumption. But it is nonconsumption out of present income (savings) which provides the resources for the investment necessary to assure higher consumption tomorrow. Hence the battle between consumption today and consumption tomorrow. Little/Mirrlees have an unusually clear discussion of this classical problem, although their operational advice seems unnecessarily complicated.

Obviously a dollar’s worth of future consumption is never worth a full dollar to us today. Future values always stand at a discount compared to the present, and the more distant the future, the greater the discount. The specific rate at which future consumption is discounted is called the consumption rate of interest (economists often call this the social discount rate, a more ambiguous term). This is not the discount rate Little and Mirrlees use in discounting cost-benefit streams. Why not? Because projects generate future savings as well as future consumption. Indeed, Little and Mirrlees believe that savings are so difficult to generate, and so important to future consumption, that the main test of a project’s economic merit in almost all less developed countries should be its ability to generate savings. There is no reason why future savings should carry the same discount rate as future consumption. So it may look at first as though future consumption will have to be discounted at one rate and future savings at another. To avoid this, Little/Mirrlees revalue future consumption in terms of savings: this gives us a unified benefit stream, a “cash flow” stripped of its consumption elements so that it represents only savings. These can then be discounted at a single rate; the rate at which savings are discounted is called the “accounting rate of interest” (ARI). This is the discount rate to use in calculating the present worth of a project’s cost and benefit streams.

The social income stream (consumption plus savings) to be generated by a project is stripped of its consumption element by taking the consumption element out of both labor income and returns to capital. On the labor side this adjustment is made automatically by defining labor’s cost in terms of its consumption only. Since only this consumption cost is deducted from project income, anything labor saves remains in the net benefit stream. The elimination of consumption from the returns paid to the owners of capital is accomplished by applying to the project’s estimated incremental capital income an estimate of the general marginal propensity to consume of those who receive interest and dividends (for some reason no offsetting allowance is made for any extra government consumption which may result from tax revenue generated by a project).

Thus the use of a shadow price for labor increases the benefit stream while the adjustment for consumption out of profits reduces the stream: one wonders how near the truth one would be if neither of these offsetting adjustments were made! But at least Little/Mirrlees give us a complete, easy-to-understand lesson in why a “commitment to consumption” is “bad” and how they think it ought to be eliminated from the cost-benefit calculation.

What Discount Rate to Use?

As noted, in the Little/Mirrlees system (as in many others) the investment test used is a project’s present social value,3 the difference between the present values of the benefit and cost streams. These present values are, of course, critically dependent on the discount rate used; different rates can change not only the size of the present social value but can make a positive value turn negative. So the specific ARI is important. The Little/Mirrlees rule for choosing the right discount rate is the same as that used by many others, including the World Bank Group: “… the accounting rate of interest should be kept as high as possible consistent with there being as much investment as savings permit” (p. 96). (“Savings” here means domestic plus foreign savings, the latter being net capital inflow.) If a too-low ARI is chosen there will be excessive investment, a balance of payments deficit, and underuse of resources. Recognizing these limits and choosing a rate that will steer the right course between them is a matter of good judgment. Little and Mirrlees think most developing countries ought to use a rate around 10 per cent in real terms, i.e., after inflation; some countries might use even 15 per cent. Rather than worry about the exact correctness of the ARI, Little and Mirrlees sensibly suggest the trial use of three rates—high, low, and medium—to sort out the “obviously good” and the “obviously bad” projects, with marginal ones to be put off until the authorities see how large the investment program will be and whether any clearly better projects come along to displace the marginal candidates.

A Project’s Balance of Payments, Employments and Future Consumption Effects

One of the attractive features claimed for the Little/Mirrlees approach is that it provides a comprehensive project evaluation test. Once it is determined that a project has a positive PSV when world prices are used, one can be confident that it will fulfill all important economic objectives for which projects are often specifically tested.4 This applies to a project’s impact on the balance of payments, on employment, and on society’s claims for future consumption. By valuing all project inputs and outputs at world prices (i.e., in terms of their foreign exchange value), “import-substitution and exporting is encouraged to the maximum desirable extent.” Once the authorities have persuaded project appraisers to use correct values (i.e., world prices) in their cost-benefit studies then “the right way to control the balance of payments is to concentrate on high-yielding projects, and not to try to do more investment than saving, tax policies, and foreign aid, allow.” By valuing labor’s shadow wage also in terms of foreign exchange (which may put a lower value on labor’s consumption inputs than domestic prices do) “producers are encouraged to use labor, instead of imported inputs, to the maximum desirable extent.” Finally, as we have seen, the problem of balancing consumption today against consumption tomorrow is handled by use of a shadow wage rate—e.g., a low shadow wage encourages labor-intensive projects, the main expression of consumption today over consumption tomorrow.

Controversial Points

Toward the end of the Little/Mirrlees volume one comes upon this self-description: “The methods of project appraisal described in this Manual, depending as they do on relatively crude methods of estimating accounting prices, can be thought of as a first step in the harnessing of the whole range of production decisions to social ends…. The methods suggested do not depend upon the prior analysis of reliable and sophisticated planning models. They are practicable: and are likely to be accurate enough to exclude all definitely bad projects, and allow all definitely good ones. Small mistakes on marginal projects are less important” (p. 188). Admirable goals for any appraisal method— reliability, simplicity, feasibility. At most points, the Manual meets these tests; at a few points it fails them.

Little and Mirrlees do not expect their Manual to give individual project analysts everything they need to go out and make valid cost-benefit studies of industrial projects. They acknowledge that they have really written a textbook of appraisal theory, not a how-to-do-it manual for men on the firing line. Furthermore, the textbook is meant for the education and guidance of a small group of high-powered economists who, the authors hope, will be found presiding over development planning at the center of things in every country. They urge every country to prepare a much shorter manual5 of its own, telling ministries and development banks how to do economic cost-benefit studies and giving them the necessary accounting prices.

The weakest—and certainly the most contentious— of the various steps recommended by Little/Mirrlees is the extent to which they go in using world prices. They want us to use them for all cost and benefit values, not just for important items that are actually traded, or could be. To do this involves a lot of trouble for a doubtful advantage. It is a lot of trouble because of the need to use input/output data that usually do not exist with nearly the accuracy needed to yield accurate results —and there seems little advantage in substituting the distortions of bad input/output data, or the approximations of conversion factors, for those arising from overvalued exchange rates. It is not even true that Little and Mirrlees get rid of exchange rates entirely, since some world prices will be in U.S. dollars, some in deutsche mark, some in yen, etc., and these can be merged only by using exchange rates. So part of the exchange rate problem is simply pushed outside the country. In most countries, it appears far simpler and sufficiently accurate to use:

  • 1. world prices for the actually traded major capital and current inputs, and for the outputs;

  • 2. domestic factor costs (at either shadow or market prices as judged appropriate) for the nontraded inputs; and then to

  • 3. convert these foreign and domestic values into a single currency by resort to an exchange rate (again, using any reasonable rate if the official rate is felt badly out of line).

In a majority of industrial projects distortions in the values of nontraded inputs simply will not be important. Electricity rarely comprises more than 4-5 per cent of manufacturing costs, so a 20 per cent distortion of its value will affect total costs by only 1 per cent. Distortions in internal transport costs for capital and operating costs are unlikely to run more than the same order of magnitude. The construction element in plant capital costs is larger and may run 15-30 per cent; at least half of this will consist of labor costs which, as with operating labor costs, can be adjusted to an “economic” value through the use of a shadow wage. The distortion arising from using domestic currency to price labor’s shadow wage is likely to be less than the margin of error inherent in deciding what shadow wage to use. Thus, when one looks at the relative unimportance of all the nontraded inputs, except labor, in a majority of industrial projects, refinements in these values begin to look relatively unimportant. Cost-benefit analysis simply does not work to the order of precision to which Little and Mirrlees want to take us.

Labor operating costs, which are important in most industrial or agricultural projects, can be handled satisfactorily by sensitivity analysis, i.e., by trying two or three different values to see how much difference it makes to the final result. There is no point in going to a lot of trouble to establish a doubtful accuracy for values that do not change a conclusion reached with more easily established, well-reasoned values. Little and Mirrlees make a good case for using sensitivity analysis when discussing the “fuzziness” surrounding the ARI; they might well have extended its use to other cost-benefit values. I cannot help concluding that this particular feature of the Little/Mirrlees methodology—the world-pricing-of-nontraded-inputs feature that has caused so much argument—is a tempest in a teapot. I doubt it will catch on, and it will not matter much if it doesn’t. There is plenty of wisdom in the basic Little/Mirrlees approach without trying to make everything depend on their controversial method of valuing a project’s nontraded inputs.

The Little/Mirrlees manual is Volume II of the Organization for Economic Cooperation and Development’s two-volume Manual of Industrial Project Analysis in Developing Countries, with the subtitle “Social Cost-Benefit Analysis” (Paris, 1969, 280 pp.). Volume I, “Methodology and Case Studies,” was written by a French consulting firm and deals with aspects of appraisals other than their social profitability (Paris, 1968, 451 pp.). The methods explained in the Manual are intended for industrial projects only. The reason for not applying the method to other sectors (except perhaps agriculture) is the methodology’s dependence on sectors where “sales to individuals or firms … offer at least a good starting point for the estimation of benefits” (p. 31). Page references in this article are to Volume II of the Manual unless otherwise stated.

The key value of labor is brought into this system of world prices at its proper relative value by first giving it a hypothetical or shadow price in terms of its domestic scarcity and then translating this into its world-price equivalent.

This is the test they recommend for any agency or government that has access to an unlimited source of investment funds. Where investment funds are limited, they suggest a profitability ratio constructed by putting the net social value over the present value of the project’s capital cost (the use of a denominator acknowledges the scarcity of the resource expressed in it and the consequent need to make decisions according to its productivity).

Theorists claim that all the leading project evaluation tests (e.g., the internal rate of return, B/C ratio, or effective protection tests) share this quality if “correct” economic values are used in the calculations.

Britain’s Overseas Development Administration has prepared just such a manual for its own use, based explicitly on the Little/Mirrlees Manual. ODA’s Manual of Project Appraisal is scheduled for publication this year.

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