The effects of import quotas on national welfare: comment.

Tower, Edward

1. Introduction

Recently in this journal, Palivos and Yip (1997a) married real and monetary analysis to provide an intriguing new argument for protection. Is this an idea that international agencies like the World Trade Organization and the World Bank should educate their member countries about?

The authors consider an economy with differential cash-in-advance constraints, fiat money, and no interest payments on cash. They argue that the first-best policy in such an economy is differential consumption taxes and, if the exportable is cash intensive, a second-best policy is an import quota. In this Comment, we argue that paying interest on cash (or equivalently deflating the economy) is better than differential taxation because it is administratively simpler and cheaper; for variants of the model, it is welfare superior, and less susceptible to manipulation by rent seekers.

This issue is most relevant for high-inflation economies, for they have the highest interest rates and hence the highest opportunity costs of holding money. Such economies are typically developing.

2. The Palivos-Yip Argument

Here is a simple exposition of the Palivos-Yip argument. Consider a hypothetical small economy, which we will call Ghana. It imports wheat and exports cocoa. It produces and consumes both goods. At time T, its producer prices measured in local currency (cedis) are [P.sub.w] and [P.sub.c], respectively. There are no explicit taxes, so these are also nominal prices paid by consumers. To consume a unit of cocoa at time T, our consumer must acquire the purchase price in non-interest-bearing cash at time T - [Phi] and hold it for [Phi] periods. Thus, the present value at time T of the cost of consuming a unit of cocoa at time T is [P.sub.c][e.sup.i[Phi]], where i is the nominal interest rate on other securities. There is no cash-in-advance requirement for consuming wheat, so the present value at time T of the cost of consuming a unit of wheat at time T is just the purchase price [P.sub.w]. The relative price of cocoa to consumers is [P.sub.c][e.sup.i[Phi]]/[P.sub.w] [approximately equal to] [1 + i[Phi]][P.sub.c]/[P.sub.w]. Since [P.sub.c]/[P.sub.w] is the relative producer price of cocoa, consumers pay an implicit ad valorem tax of i[Phi] on cocoa. Since there is no social opportunity cost associated with money creation, this tax is inefficient. It could be offset with an explicit tax on wheat consumption or subsidy on cocoa consumption. Alternatively, it could be offset by taxes on international trade, but this would distort production decisions so, as the authors note elsewhere (Palivos and Yip 1997b), trade intervention is inferior to differential consumption taxes.(1)

3. Paying Interest on Money

An alternative solution emphasized by Friedman (1959, 1969) is to pay interest on money. If money bears the same interest rate that securities do, then there is no implicit tax on cocoa, and consumption is optimized. Equivalently, as Friedman points out and the authors note elsewhere (Palivos and Yip 1997b), the economy could be deflated at the real rate of interest, so the money interest rate falls to zero, and there is no need to pay interest on money.

How do the various policies compare? In this model, it makes no difference whether wheat consumption bears a tax or cedis carry interest. However, in more general models, for several reasons, payment of the optimum interest rate on cash will be superior:

(i) Taxes or subsidies to consumption or trade evoke attempts to trick the authorities through tax evasion, smuggling, or falsification of invoices. These activities and official efforts to combat them squander resources.

(ii) If our representative citizen must work to obtain goods, a consumption tax on goods will cause him to superoptimally economize on money and substitute leisure for goods.

(iii) Suppose I live closer to a bank than you do, so I hold cash for a shorter period before each purchase than you do. In this case, we have different cash-in-advance requirements and different consumption taxes should be levied on the two of us. But if interest is paid on cash, resource allocation is optimized with one interest rate for all.

(iv) Suppose our representative citizen can economize on money balances by transforming leisure into transactions services, so the cash-in-advance constraint [Phi] is endogenous. He will choose a suboptimal quantity of money unless it pays the appropriate interest.

(v) Suppose that producers are subject to differential cash-in-advance requirements on their intermediate inputs. Then if their proportions are variable, they too should be subject to differential rates of taxation on their intermediate inputs and, even if they use intermediate inputs in fixed proportions, they should be subject to differential rates of taxation on output. If exporters are subject to differential cash-in-advance requirements on their exports, differential rates of taxation on exports are required. However, one interest rate on cash would fix the problem.

These arguments convince us that any combination of taxes or subsidies on consumption, production, and trade is less than first best and is likely in practice to waste resources on the calculation and recalculation of second-best (or conceivably first best) optima as technology, endowments, and tastes change. Paying interest on money means the first best is achievable and that economists who specialize in calculating second-best optima can be reemployed elsewhere.

Finally, since the calculation of any optimum tax/subsidy scheme will be complex, in practice such schemes invite rent seeking in the legislative process.

4. Currency Boards and the Gold Standard

Suppose our analysis is of a country with a currency that is backed 100% by foreign securities that pay interest rate f.(2) In this case, holding each unit of domestic currency creates currency board revenue at a rate of f. For optimality, this interest rate f should be paid on currency. If the currency board holds only gold and the currency is pegged to gold, since gold pays no interest, the currency should pay no interest either.

5. Shadow Prices and Immiserizing Growth

Once the proper interest rate is paid on money so there are no distortions, shadow prices become market prices. This means that project evaluation can be carried out by just looking at market prices. This simplifies the process of project evaluation. Moreover, the paradoxes of immiserizing growth disappear.(3)

6. Financial Repression and the Argument for Protection

Developing economies frequently exhibit high rates of inflation so their governments can collect the inflation tax. McKinnon (1973) notes that, to the extent that cash holdings and deposits serve as a vehicle for turning savings into investment, reduced real interest payments on money and deposits implicitly tax investment.(4) To keep the demand for domestic currency high, these same countries typically restrict permissible holdings of foreign securities, discourage the development of domestic securities markets, impose high reserve requirements on the banking system (with no interest payments on reserves), and require advance deposits of domestic currency prior to importing (with no interest rate paid on these deposits). These are all elements of financial repression, which shrinks welfare and economic growth. Our prototype is, in effect, an economy where the cash-in-advance requirement for imports is high and cash held prior to importing bears a zero nominal interest rate, the cash held (as deposits) prior to domestic market purchases bears a positive nominal but negative real interest rate, and the cash held as currency prior to domestic market purchases bears a zero nominal interest rate. In such an economy, reducing the repression of financial and international markets through lower inflation, freer trade, and sensible consumption and/or factor taxes is especially desirable.(5)

Appendix: Technical Notes on the Palivos-Yip Models

The expression for the tariff equivalent of the optimum quota in Palivos and Yip (1997a) does not depend on the interest rate. Thus, it appears that the distortion that drives the need for a trade or tax intervention in Palivos and Yip (1997a) is something other than the gap between the interest rates on money and alternative assets.

In fact, there is no conflict between the logic of this comment and Palivos and Yip (1997a). The mathematics in Palivos and Yip (1997a) implicitly assumes an interest rate of 100%.(6) For clarity, we reproduce the mathematics of Palivos and Yip (1997a) with the interest rate explicit.

There is non-interest-bearing fiat money. The money stock is [Mathematical Expression Omitted]. The monetary authority lends money out, earning an interest rate i. It distributes this seignorage as a lump sum to each agent at the end of his single period of life. At the same time, the agent earns income [p.sub.1][X.sub.1] + [p.sub.2][X.sub.2] and receives the lump sum distribution of tariff revenue earned S. This is balanced by the individual's expenditure at the end of his life: [p.sub.1][D.sub.1] + [p.sub.2][D.sub.2] plus the interest the individual must pay at the end of his life in order to acquire money balances M at the beginning of the period in order to satisfy his cash-in-advance constraint. Thus, our agent's budget constraint is

[Mathematical Expression Omitted],

which is identical to Equation 2 in Palivos and Yip (1997a) except that the coefficients of 1 on M and [Mathematical Expression Omitted] have been replaced by i. The rest of the analysis in Palivos and Yip (1997a) stays intact. However, the [Gamma] in Palivos and Yip's Equation 8 is now defined as i[[[Phi].sub.2] - [[Phi].sub.1]]/[1 + [[Phi].sub.1]i]. In the limit as i (the excess of the interest rate on assets alternative to money) above that on money approaches zero, the need for a quota or commodity tax disappears.

What is the relationship between the results in Palivos and Yip (1997a) and Palivos and Yip (1997b)? In Palivos and Yip (1997a, Equation 15), the authors (after removal of an extraneous [p.sup.*] from the right-hand side) provide an expression for the tariff equivalent of the optimum import quota. In Palivos and Yip (1997b, Equation 29), they provide an expression for the optimum import tariff in a "dynamic generalized cash-in-advance model." Using the modified definition of [Gamma] and recognizing that [Gamma] [equivalent to] [Delta], [Epsilon] [equivalent to] [Alpha][e.sup.d], and [Sigma] [equivalent to] ([Alpha] - 1)[e.sup.s], the expression for the tariff equivalent of the optimum quota in Palivos and Yip (1997a) is identical to the expression for the optimum import tariff in Palivos and Yip (1997b). This equality is to be expected in a competitive environment for certain classes of model.

1 Of course, if wheat is the cash-intensive commodity and trade intervention is the policymaker's only option, a subsidy to trade is the appropriate policy.

2 For an argument for 100% reserve requirements, see Friedman (1959).

3 For an intuitive discussion of shadow pricing and project evaluation, see Tower (1991). Incidently, like Alam (1981) and Palivos and Yip, Bhagwati and Srinivasan (1981) recognize that, in the presence of a quota, growth does not immiserize.

4 For discussion of financial repression, also see World Bank (1989).

5 None of these conclusions are altered when we consider an optimal tax framework. Dixit (1985) points out that, in an optimal tax framework, only those items that enter the utility function directly should be taxed. Thus, in such a framework, money, production, and trade should all be kept free of tax. Also see Kimbrough (1986).

6 T. Palivos suggested this interpretation to us.

References

Alam, Shahid. 1981. Welfare implications of growth under quotas. Economics Letters 8:177-80.

Bhagwati, Jagdish N., and T. N. Srinivasan. 1981. The evaluation of projects at world prices under trade distortions: Quantitative restrictions, monopoly power in trade and nontraded goods. International Economic Review 22: 385-99.

Dixit, Avanish. 1985. Tax policy in open economies. In Handbook of public economics, volume 1, edited by Alan Auerbach and Martin Feldstein. Amsterdam: North Holland, pp. 313-74.

Friedman, Milton. 1959. A program for monetary stability. New York: Columbia University Press.

Friedman, Milton. 1969. The optimum quantity of money and other essays. Chicago: Aldine.

Kimbrough, Kent. 1986. The optimum quantity of money role in the theory of public finance. Journal of Monetary Economics 18:277-84.

McKinnon, Ronald I. 1973. Money and capital in economic development. Washington, DC: The Brookings Institution.

Palivos, Theodore, and Chong K. Yip. 1997a. The effects of import quotas on national welfare: Does money matter? Southern Economic Journal 63:751-60.

Palivos, Theodore, and Chong K. Yip. 1997b. The gains from trade for a monetary economy once again. Canadian Journal of Economics 30:208-23.

Tower, Edward. 1991. On shadow prices, effective protection, and domestic resource cost. In Companion to economic thought, edited by David Greenaway, Michael Bleaney, and Ian Steward (eds.), Companion to Economic Thought, London: Routledge, 1991, 614-33. Reprinted in A guide to modern economics, London: Routledge, 1996.

World Bank. 1989. World development report 1989: Financial systems and development. New York: Oxford University Press.

Professor Gokcekus is also a scholar-in-residence at Duke University and Professor Tower is a regular visitor at the University of Auckland. Thanks go to Kent Kimbrough and Theodore Palivos for helpful comments.