Measuring the Effective Rate of Protection: Direct and Indirect Effects

Measuring the Effective Rate of Protection: Direct and Indirect EffectsAuthor(s): David B. HumphreySource: Journal of Political Economy, Vol. 77, No. 5 (Sep. - Oct., 1969), pp. 834-844Published by: The University of Chicago PressStable URL: http://www.jstor.org/stable/1829971 .

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Measuring the Effective Rate of Protection: Direct and Indirect Effects

David B. Humphrey San Francisco State College

The effective rate of protection (ERP) is concerned with determining the net effect of a tariff structure on domestic value added relative to its probable preprotection counterpart. A ranking of ERPs will shed light on the direction that protection may pull factors. As such, it is not at variance with the purposes of the Stolper-Samuelson theorem, Lerner's symmetry theorem, and other propositions in the theory of tariffs. The major divergence (in method) from traditional tariff analysis is that the ERP concept recognizes the possibility of tariffs on inputs and thus does not deal solely with protection on final selling prices.

Defining Dva,(Wva,) as domestic value added after (before) protection in the jth sector, the ERP is defined as (Dvaj/ Wvaj) - 1. If both Dva and Wva were known, the ERP calculation would be a simple matter. As it turns out, we only really know Dva but, with the help of an input-output table and computing each sector's level of nominal protection, we can presumedly approximate Wva. That is, as the domestic value of j(D V,) is equal to Dvaj plus the value of all intermediate use of domestic and imported i inputs into i(:& DVij), it follows that

Dvaj = DV,- DV (1)

The input-output table is used to compute :i DVij. Dividing (1) by estimated levels of nominal protection gives

Wva= DV V D Vil (2)

I would like to thank the University of California Computer Center (Berkeley) for making facilities and computer time available while I was a graduate student there. Comments by a referee have improved this paper. An earlier version was presented at the meeting of the Western Economic Association in 1968.

834



EFFECTIVE RATE OF PROTECTION 835

where t,(t1) represents the percentage rate of protection on final output (inputs). Behind (2) lie a number of important assumptions-the obvious one being that the preprotection value of j(WVj) is equal to DVj/(l + tj) for all j. Further, as (2) implies WVij = DVlj/(l + ti) for all i, we are additionally required to assume that there are no input substitution effects due to relative price changes concomitant with the incidence of protection.'

As can be seen from (2), the ERP is measured by deflating postprotection domestic values by the observed level of protection. The purpose of this paper is to show that even if measurement per se is not a problem (not likely in practice), the recent ERP computations performed for the United States (Basevi 1966), Common Market (Grubel and Johnson 1967), Argentina (Balassa 1966), and Pakistan (Soligo and Stern 1965) are likely to use an incorrect deflator. This is due to concentrating on the direct nominal protection effects on domestic prices and neglecting indirect protection effects on the costs (and hence prices) of sectors influenced by cost push inflation. In what follows we explain this bias, develop a general solution for its correction, and illustrate by computing corrected and uncorrected ERPs for Argentina for 1953.

Assume a three-sector economy-food (f), industry (i), and services (s) where tf and t2 > 0 (importables) but t8 = 0 (nontradable). From (2) we have for the f sector:

Wvaf _DVf _ DV,- _ DVs _ DV8f (3)

With t, = 0, it implies DVsf = WVSf. However, Dys (as well as DVsf) is likely to be composed directly and indirectly of protected inputs (that is, D Vs = Dvas + D Vfs + D Vts + D Vs, on a direct basis). Sector s is a nontradable in that there is no feasible competition from imports. Thus it is reasonable to assume that when direct inputs into s (that is, DVfs and D Vis) rise in price (due to the incidence of direct protection), Dvas will not necessarily absorb these cost increases and leave D Vs unaltered. This would be the case if s were an importable sector, however, for this is the core of the ERP analysis. Something akin to cost push inflation, therefore, is a feasible behavioral assumption for s. Thus, Dvas can be maintained either as an absolute or as a percentage and the protection-related input cost influences passed on. This raises D V, above WVs, to the extent the s sector

I Corden (1966) has shown that if this assumption is not met, the result is always an overstatement of the ERP. The nonfulfillment of this assumption can be circum- vented with the calculation of dynamic input-output coefficients (Arrow and Hoffen- berg 1959) in order to derive the appropriate preprotection input-output coefficients used in determining Et WVj,. An easier alternative would be to estimate the ERP under a (elasticity of substitution) = 0-the assumption used here-and a = 1 (Humphrey and Tsukahara, in press). This would then give an interval of substitution bias.



836 JOURNAL OF POLITICAL ECONOMY

directly or indirectly (via other cost push sectors) uses these protected inputs.2 The net result of the usual ERP calculation is then to overstate preprotection input values (DVf/[l + tj] > WV8,), understate (3), and hence overstate ERPf. Similarly, the bias is in the same direction for ERPj, to the extent that it too uses DV, as an input. Calling the f subscripts s and the s subscripts f in (3), we can see that Wva, is overstated, making ERP. understated.3 In summary, the ERPs for sectors in competition with imports are overstated, while for all sectors influenced by cost push inflation they are understated.4

Corden (1966) has raised a similar line of criticism concerning nontradables and the ERP. To wit: as the incidence of protection switches domestic demand from imports to domestic production of importables (which use nontradable inputs directly and indirectly), it will result in an increase in the demand for nontradable output. In the absence of excess capacity in this sector and/or general unemployment, the consequent output expansion may be forthcoming only at increased prices. The distinction between tradable and nontradable inputs is put in terms of price elasticities. That is, with either infinitely elastic competitive foreign supply (Corden's importables) or demand (his exportables), cost increases will not raise output prices. Lacking an infinitely elastic demand, it follows that, " If nontraded inputs were ... in infinitely elastic supply, they could indeed be treated like traded inputs" (Corden 1966, p. 228). As this supply condition also is not met, Corden's solution is to compute the ERP1 in terms of Dvaj plus direct and indirect nontraded input value added into j.

In having supply elasticities be the decision criteria for inclusion or exclusion in the ERP, Corden is seemingly concerned only with movements along the supply curve, while our bias deals only with upward shifts (external diseconomies). That is, even with an infinitely elastic nontradable supply curve in Corden's terms (for example, excess capacity and general unem-

2 Simply put, the pricing assumptions which form the basis of the ERP concept- that postprotection prices cannot be more than preprotection prices plus protection- are applicable only to domestic sectors which are competitive with imports, for only here is it infeasible to pass cost increases on. Thus, deflating postprotection values by observed protection levels will not always give preprotection values.

3 Here Wva, = DV,/(1 + t,) - DV.,/(1 + t:) - DVfs/(l + to) - DVf,(1 + tf). We saw, however, that DV. > WV, even though t, = 0 may be observed. In effect, to obtain a correct WV,, t, must be > 0. This then deflates D V. by a greater absolute amount than it deflates D V,,, making the corrected Wva, smaller than a Wva, computed with t, = 0. Thus the usually computed Wva, is overstated, resulting in the consequent understatement of ERP..

4 Corden assumed that the price elasticity of demand for exportables (and the supply of importables) was infinite. Here any input cost increase only lowers Dva, leaving final prices unchanged. As we deal with Argentina, whose export elasticity of demand is less than infinite, we recognize that part of the input cost rise can be passed on in much the same manner as exists for nontradable sectors. Furthermore, treating the Argentine exportable sectors as Corden suggests yielded spurious ERP calculations. Thus we treat exportables as if they were nontradables.




ployment), our bias would still influence the ERP calculation to the extent that nontradables (or exportables for Argentina) use protected inputs.5

Generalizing, Corden elaborates a demand pull inflationary effect on nontradable sectors while our analysis emphasizes cost push. It is apparent that if these two inflationary effects could be estimated, it would then again be possible to compute the ERPj in terms of Dvaj and Wvaj, regardless of nontradable supply elasticities and/or importable indirect use of protected inputs (via direct use of nontradable inputs which directly use protected importables). This inflationary estimation is central to our proposed correction for the ERP calculations already performed. However, we can only correct for cost push elements. Thus, our correction is most useful in situations where cost push influences outweigh demand pull causes. Such is the case for our illustration-Argentina (Diaz Alejandro 1965; Humphrey in press).

Referring to the example used earlier, where D Vf/(l + tJ) > WV f, because D V8 has risen via protection-induced cost push inflation, our correction is merely to estimate the amount of inflation and use this estimate to redefine t,. Thus dividing by a new t3 effectively deflates DVsf of its cost push price rise, making D Vf/(l + new tJ) WVSf if demand pull effects are negligible.

The application of this concept can take many forms in practice. For example, is one concerned only with estimating and correcting for the direct plus indirect protection-induced cost effects from material inputs, or is it necessary that these effects be added to estimated labor and profit cost changes concomitant with a general increase in the cost of living? Further, these initial cost changes can engender additional (but usually smaller) labor and profit changes in a sequential manner.

To illustrate our analysis, we computed the Argentine ERP in the following four ways:

A. By using only the observed nominal protection rates to deflate postprotection values to obtain preprotection values- this is the method employed (Basevi 1966, Grubel and Johnson 1967, and Soligo and Stern 1965) and forms a basis for com- parison.

B. By using (A), but including cost push effects due to using protected importable material inputs in the nontradable and exportable sectors.

5If the demand for exportables were infinitely elastic, and no nontradables used protected inputs directly, then our bias from material inputs would be zero. However, a bias from factor inputs would exist if the price of these inputs rose with the likely rise in the cost of living resulting from the imposition of a protection structure. This would then make DV, > WV., even after its deflation by the observed t,, and hence the same cost push bias would be present.




C. By using (B), but adding the likely first round induced labor cost changes (due to a rise in the cost of living) along with the reaction of profit receivers also attempting to maintain their relative position.

D. By using (C), but continuing the cumulative labor-profit cost interaction until we deem the marginal significance minor.

In our opinion, since (D) incorporates the full cost push effect-materials, labor, profits-it represents the preferred deflator.

The nominal protection rates of (A) were derived by dividing j import value at peso user's prices byj import value at peso c.i.f. prices. Any value difference is thus indicative of protection (Argentine Republic 1962, p. 105 and table 20). As all peso values do not translate into U.S. dollars at the same ratio, (A) was further corrected for the existence of multiple exchange rates. We chose the "free" rate as representing equilibrium and placed other rates in relation to it. Direct subsidies and taxes, if not reflected in the ratio of peso import values, are not otherwise included. Estimation of (A) is hampered by the fact that actual protection, if prohibi- tive, will not be reflected here, for our procedure implicitly weights the protection level on an import value basis. Thus, no imports, no weight.

Deflator (A) is used, via appropriate weighting and a special inverse matrix, to derive deflator (B). Deflator (B) will raise the cost-of-living index which, in turn, raises money wages. The percentage rise in money wages, again appropriately weighted and using the same matrix inverse, results in a further cost increase. Adding this increase to that obtained from assuming that profits are a constant percentage of final prices gives deflator (C). Continuing the interaction between labor and profit costs until the marginal effects on the cost of living are small gives us deflator (D). Dividing postprotection output and input values by each of the four deflators yields a set of four estimates of preprotection output and input values from which various ERPs can be obtained readily.6

Our calculation process took the following form:

DVA.[T*.DV- (1R.T*.A*DV)]* - I= ERP (4)

as a diagonal matrix when the result of (IR T* . A DV) is placed as a diagonal on a 29 x 29 zero matrix before the bracketed subtraction is performed and where

D VA = 29 x 29 diagonal matrix with Dvaj as elements; T = 29 x 29 diagonal matrix containing 1 plus the percent-

age deflators-(A)-(D) above-as elements;

6 The Appendix shows, in greater detail, how deflators (A)-(D) were actually obtained.




* = the operation of individually inverting each element in the matrix (not a matrix inverse);

DV = 29 x 29 diagonal matrix with elements D Vj (postprotection value of j supply);

1 R = 1 x 29 (row) matrix consisting only of ones; A = 29 x 29 matrix of input-output coefficients (that is,

DVij/DVj, recalling that DVij consists of imported and domestic inputs); and

I = 29 x 29 identity matrix.

Table 1 gives us the Argentine ERPs under the four definitions of deflators submitted above. Minus signs reflect a net tax effect on Dva due to the protection structure. The asterisks signify that Wva was negative in the ERP calculation-an absurd result yielding a spurious ERP. It implies that the preprotection value of j output is less than the sum of its intermediate input value. This requires D Vj/(1 + tj) < hi D Vfj/(1 + t,) from (2). Its cause may involve (a) input substitution to a price change; (b) over- stating (underestimating) tj(t,) ;7 or (c) the cost push bias we describe in this paper. That the removal of the cost push bias will at least reduce the number of negative Wvas we obtain is seen in table 1. As more and more cost effects of our deflators are introduced-moving from columns (1) to (4) in table 1-we reduce the number of spurious calculations from eleven to three. However, the ERPs we derive may still be overstated for importable sectors (understated for nontradable and exportable sectors), if Corden's demand inflation bias is not fully accounted for with our cost push sequence.

Ranking the ERPs of column (4) will give some idea of the direction in which protection will pull resources (if they are responsive to price incen- tives). Given that our classification of sectors is correct, column (4) tells us (surprisingly) that the importable sectors comprise the highest six and lowest six ERPs. Exportable sectors are below the median (three out of four) while nontradables are above the median (five out of nine). Generaliz- ing, this means that resources will move mainly from one importable sector to another-roughly, from finished consumer and intermediate goods to intermediate and capital goods sectors.8

7 This is suggested by Ellsworth (1966) to be the most probable cause for the spurious results of Soligo and Stern (1965).

8 The high positive ERP values shown for sectors 3 and 24 lie in the hard-to-believe range while sectors 11, 16, and 25 are definitely spurious. Sector 24, for example, moves from -5.95, -7.21, 77.38, and 12.95 in ERP value. That is, with Dva24 and WV24 constant, adding our cost effects to this importable sector will raise (lower) the computed Wva24 positive (negative) value, and so change the ERP as we move from column (1) to (4) in table 1. See Ellsworth (1966, pp. 402-4) for a graphic demonstra- tion of a similar process, but concerning the tj and tj estimations. In our case this result is expected, but also serves to emphasize that an ERP computed with a - Wva in column (1) or (2) may not yield a believable ERP for column (4), since it apparently started out with more bias than our correction is capable of eliminating.




10

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Column (4) shows the percentage that Argentine Dva can exceed Wva at unadjusted exchange rates. Corden has argued that the ERPs need to be modified to the extent that exchange rate adjustment is necessary to maintain internal and external balance (one of his assumptions). As this balance deals with the stability of relative prices (domestic and international), the argument for exchange rate adjustment following the ERP calculation can be put in terms of purchasing power exchange rates. That is, looking at sector 1, at a constant exchange rate, factors employed here can buy approximately 59 percent more foreign goods as a result of the protection structure (assuming no output or factor employment change as yet). At the same time, we found that our cost-of-living index rose by 65 percent when deflator (D) was estimated. If we say that the international purchasing power "market basket" is best reflected by the composition of the cost-of- living index, then it makes sense to "correct" the ERPs in column (4) by subtracting this price level rise. This correction gives column (5).9 The operation will not change the relative ranking of ERPs but will show to a greater extent the real tax and subsidy effects of the protection structure- both internationally and domestically.

Throwing out sectors 11, 16, and 25, this means that 14 sectors (54 percent) are, on balance, presumedly taxed via the protection structure. As might be expected, the proportion of importable sectors taxed is lower than that for exportables. These figures, however, would be different if the sector aggregation level of the Argentine matrix were different.

In summary, we have demonstrated that a bias can exist in calculations of the ERP performed to date, shown how it enters indirectly (via cost push) when nontradable and exportable sectors are protected inputs, explained its similarity to Corden's bias, have presented a general solution (estimating the protection-related inflationary effects), and shown illustra- tive calculations for Argentina which indicate that our solution reduces the number of spurious calculations and is thus important as well as workable.

Appendix

We used (Rasmussen 1957) to develop our cost push model. In order of actual calculation we have:

(1) P1 = {CANCEL.[M.(I - 4)]'Pm} + Pm* (2) COL1 = COLW*P1 (3) W = R.(COL1 - LPROD)

9 Since we assumed that any change in the cost of living generates an equal change in money wages, we are in effect using the wage level change for the exchange rate adjustment. Alternatively, the values of deflator (D) could be weighted by the composition of GNP and used, as a " GNP price index," for the exchange rate adjustment. If this latter index were used, the resulting exchange rate adjustment would probably have been larger than 65 percent.




(4) P2 = CANCEL .[K-(I -A)-1]' W (5) PR= P*.(P2 + P1) (6) P3 = CANCEL - [P - (I -A) ']'.PR

(7) COL2 = COLW.(P3 + P2)

and so on until COL7 and P15 have been derived. The matrices are defined as:

Pm = 29 x 1 matrix with elements made up of the computed nominal level of protection for each sector-1953 ratio of imports at user prices to c.i.f. prices corrected for multiple exchange rates;

(I - A) -1 = 29 x 29 inverse matrix for 1953, where A represents a matrix consisting only of nontradable and exportable sectors which experience only cost effects-from importables and themselves;

M = 29 x 29 matrix made up of import and importable input-output coefficients-these sectors have their final prices determined by the level of protection but here act as weights for the final price changes of sectors in A;

CANCEL = 29 x 29 diagonal matrix with ones for the A sectors but zeros for M sectors-this cancels out the previously generated cost effects (that is, [M.(I - A)-1]' Pm) for importables which otherwise would raise their final price;

Pm* = 29 x 1 matrix composed of the same elements as Pm except have zeros for A sectors making the final prices in P1 for M sectors equal to the level of nominal protection;

P1 = 29 x 1 matrix showing the percentage change in final prices due to direct and indirect cost effects stemming from the protection structure for A sectors and only the level of nominal protection for M sectors;

COL W = 1 x 29 matrix with elements showing the percentage importance of each j sector in the Argentine cost-of-living index-cost-of- living weights;

COL1 = 1 x 1 matrix indicating the percentage change in the cost of living due to the percentage change in final prices (that is, P1);

LPROD = 1 x 1 matrix showing the likely percentage change in labor productivity (assumed constant between all j sectors)-we used LPROD = 0;

R = 29 x 1 matrix with elements indicating the degree that cost-of- living increases, after accounting for any change in labor productivity, are likely to be passed on as wage increases for each sector (via scalar multiplication)-we assumed that real wages can be maintained making the R matrix consist only of ones;

W = 29 x 1 matrix indicating the resultant percentage change in labor costs for each j sector;

K = 29 x 29 diagonal matrix with elements representing the percentage labor cost (wages and salaries) is of total domestic output value for each j sector;

P2 = 29 x 1 matrix of percentage final price changes from direct and indirect labor cost changes (premultiplying by CANCEL means that we have zero price changes for M sectors, as their final prices are not affected by cost changes);




IS* = 29 x 29 diagonal matrix with elements 1/(1 - P%), showing the multiplier effect necessary to maintain "profits" as a constant percentage of final price (FP = (Dvaj - wages and salaries j)! total domestic output value);

PR = 29 x 1 matrix indicating the percentage change in "profit" cost concomitant with the behavioral assumption in P* that percentage profit rates are maintained;

P3 = 29 x 1 matrix showing the percentage change in final prices of the 4 sectors (the M sectors have a zero change through using CANCEL) due to the maintenance of percentage profit rates;

P = 29 x 29 diagonal matrix with elements P1; and = matrix transpose.

All data, except for COLW, are from Argentine Republic (1962), or from independent assumptions (for instance, LPROD = 0, and R consists only of ones). Thus, R can consist of values S 1, making real wages rise or fall, but the difficulty is in deciding what values are appropriate.

COL W was obtained by assigning input-output sector classifications of the Argentine Republic publication (1962) to the percentage compositions of private consumption shown in Panorama de la Economia Argentina (1958, p. 238). The deflators used to compute the ERPs of table 1 are related to the above sequential model in the following manner: deflator (A) = Pm; (B) = P1; (C) = P1 + P2 + P3; and (D) = P1 + P2 + P3 + .. + P15. Other works influencing the construction of this sequence were (Cohen 1966; Dow 1956; and Eckstein and Fromm 1959, pp. 34-38).

References

Argentine Republic. Consejo Federal de Inversiones. Relevamiento de la Estructura Regional de la Economia Argentina. Vol. 2, pt. 2. Buenos Aires, 1962.

Arrow, K., and Hoffenberg, M. A Time Series Analysis of Interindustry Demands. Amsterdam: North-Holland (for the RAND Corp.), 1959.

Balassa, B. "Integration and Resource Allocation in Latin America." Paper presented at the Cornell Latin American Year Conference, April 1966, at Cornell University.

Basevi, G. "The U.S. Tariff Structure: Estimates of Effective Rates of Protec- tion of U.S. Industries and Industrial Labor." Rev. Econ. Statis. 68, no. 2 (May 1966): 147-60.

Cohen, B. I. "Measuring the Short-Run Impact of a Country's Import Restrictions on Its Exports." Q.J.E. 80, no. 3 (August 1966): 456-62.

Corden, W. "The Structure of a Tariff System and the Effective Protective Rate." J.P.E. 74, no. 3 (June 1966):221-37.

Diaz Alejandro, C. F. Exchange Rate Devaluation in a Semi-Industrialized Country. M.I.T. Monographs in Economics. Cambridge, Mass.: M.I.T. Press, 1965.

Dow, J. C. R. "Analysis of the Generation of Price Inflation. A Study of Cost and Price Changes in the United Kingdom 1946-54." Oxford Econ. Papers 8, no. 3 (October 1956):260-301.

Eckstein, O., and Fromm, G. Steel and Post- War Inflation. U.S. Congress, Joint Econ. Committee, Study Paper no. 2, November 1959.



EFFECTIVE RATE OF PROTECTION

Ellsworth, P. T. "Import Substitution in Pakistan-Some Comments." Pakistan Development Rev. 6, no. 3 (Autumn 1966):395-407.

Grubel, H., and Johnson, H. G. " Nominal Tariffs, Indirect Taxes and Effective Rates of Protection: The Common Market Countries 1959." Econ. J. 77, no. 308 (December 1967):761-76.

Humphrey, D. "Changes in Protection and Inflation in Argentina, 1953-66." Oxford Econ. Papers, in press.

Humphrey, D., and Tsukahara, T., Jr. "On Substitution and the Effective Rate of Protection." Internat. Econ. Rev., in press.

Panorama de la Economia Argentina. Vol. 1, no. 6 (September 1958), Buenos Aires.

Rasmussen, P. N. Studies in Inter-Sectorial Relations. Amsterdam: North- Holland, 1957.

Soligo, R., and Stern, J. "Tariff Protection, Import Substitution and Invest- ment Efficiency." Pakistan Development Rev. 5, no. 2 (Summer 1965): 250-70.



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Measuring the Effective Rate of Protection: Direct and Indirect Effects