A WELFARE-BASED MEASURE PRODUCTIVITY GROWTH WITH ENVIRONMENTAL EXTERNALITIES. Kelly Chaston* Gregory Swinand** Frank Gollop** and Richard Arnott**

Transcription

1 A WELFARE-BASED MEASURE OF PRODUCTIVITY GROWTH WITH ENVIRONMENTAL EXTERNALITIES Kelly Chaston* Gregory Swnand** Frank Gollop** and Rchard Arnott** September 1997 Prelmnary draft: Please do not cte or quote wthout the permsson of the authors. ** Department of Economcs * Department of Economcs Boston College Davdson College Chestnut Hll, MA Davdson, NC U.S.A. U.S.A.

2 A Welfare-Based Measure of Productvty Growth wth Envronmental Externaltes * The negatve mpact of envronmental regulatons on productvty growth as conventonally measured s well documented n the lterature (e.g., Gollop and Roberts (1983)). Snce the conventonal measure of productvty growth accounts for the hgher producton costs caused by the envronmental regulatons but not the benefts resultng from reduced polluton, ths result s not surprsng. It does, however, rase the ssue of whether, n ths context, the conventonal measure of productvty growth s n fact measurng what we want t to measure. If we want to measure the rate of techncal progress, then we would lke somehow to net out the effects of envronmental regulaton. And f we want to measure how rapdly socety s gettng better at combnng a gven set of nputs to produce welfare, then we would want to nclude the benefts from polluton reducton. The problem s llustrated dagrammatcally n Fgure 1 whch plots the productonpossbltes fronter before (PPF 0 ) and after (PPF 1 ) a productvty mprovement, wth respect to a generc numérare consumpton good (whch ncludes nvestment) and ar qualty, holdng nputs fxed. In the absence of envronmental regulaton, the pre-mprovement equlbrum s at A snce the producer prce of ar qualty s zero, and the post-mprovement equlbrum s at B. Envronmental regulaton s modeled smply as a floor on ar qualty, a. Wth envronmental regulaton fxed at a, the pre-mprovement equlbrum s at C and the post-mprovement equlbrum s at D. Fnally, the effcent producton pont where the ndfference curve s tangent to the producton-possblty fronter s at E pror to the mprovement and at F afterwards. Suppose, for the sake of argument, that the envronmental regulaton s appled between the tmes at whch PPF 0 and PPF 1 apply. Then the equlbrum over ths tme perod shfts from A to D. The ssue s how the productvty mprovement should be measured. The conventonal procedure s to gnore ar qualty, whch s tantamount to accordng t a zero prce n productvty * Thanks to Alexander Kalenk for preparaton of the dagrams. 1

3 measurement. Accordngly, the productvty mprovement over the perod s measured as A D, and the proportonal productvty mprovement as A D. If the envronmental regulaton had not O A A B been mposed, the correspondng magntudes would be A B and. It s evdent that the O A envronmental regulaton causes the measured productvty mprovement to decrease. INSERT FIGURE 1 HERE Now suppose that n the pre-mprovement stuaton a mnmum ar qualty regulaton of a s n place and that n the post-mprovement stuaton the mnmum regulated ar qualty a s hgher. Ths scenaro s shown n Fgure 2. The equlbrum then shfts from C to G. Accordng to the conventonal measure whch gves a zero prce to ar qualty, the productvty mprovement s cg and the proportonal productvty mprovement cg. But at C, there s a margnal cost or Oc producer prce to producng ar qualty. If one were to use ths producer prce n evaluatng natonal ncome, measured as the heght of the ntersecton pont of the prce lne tangent to C wth the vertcal axs, the pre-mprovement natonal ncome would be O C and the post-mprovement natonal ncome O G, wth a productvty gan of G C and a proportonal productvty gan of G C. A problem wth ths procedure s that t measures natonal ncome wth mnmum ar O C qualty as a reference pont. But there s no natural mnmum ar qualty. A superor procedure s to measure natonal ncome relatve to maxmum ar qualty. Ths s superor for two reasons. Frst, there s a natural maxmum ar qualty clean ar. Second, standard natonal accountng measures do not nclude clean ar. Under ths alternatve procedure, polluton s treated as a bad and subtracted from GNP. Real ncome n the pre-mprovement stuaton s then measured as the heght of the ntersecton pont of the prce lne tangent to C wth the vertcal lne through O, O C. Post-mprovement natonal ncome s O G, the productvty gan C G and the proportonal productvty gan C G. Ths measure of productvty gan fals to correct for the O C loss n productvty due to the strcter envronmental regulatons but does value the reducton n 2

4 polluton at the pre-mprovement producer prce. INSERT FIGURE 2 HERE In contrast, when ar qualty s gven a zero prce, the proportonal productvty gan s the same whether measured wth reference to O or O. Accordngly, we advocate usng O as the approprate orgn. If ths s done, t s natural to defne smoke to be the qualty of clean ar mnus the actual qualty of the ar. Fgure 3 portrays ths conventon. There are then three measures of productvty mprovement n the movement of the economy from C to G, whch dffer accordng to how smoke s valued. The frst s the conventonal measure, whch we denote by I 0 the ndex of productvty mprovement where smoke s prced at zero 1 : I 0 = gc Oc. The second s the measure usng the (negatve) producer prce of smoke at the pre-mprovement equlbrum, whch we denote by I p : I p = G C /O C. And the thrd s the measure usng the (negatve) consumer prce of smoke at the pre-mprovement equlbrum, whch we denote by I q : I q = G C /O C. If the consumer prce exceeds the producer prce n absolute value, whch seems reasonable emprcally, then G C > G C > gc and Oc > O C > O C, whch together mply that I q > I p > I 0. INSERT FIGURE 3 Several comments are n order. Frst, all three ndexes measure the proportonal productvty mprovement as the change n real ncome dvded by real ncome, where real ncome s measured as the value of consumpton and nvestment mnus the cost of smoke; they dffer n how they cost smoke. Second, what s the true proportonal productvty mprovement? Ths reduces to the queston of what s true real ncome. Wetzman (1976) provdes one answer for the stuaton where there s no smoke: True real ncome s the current value of the Hamltonan where the obectve s the maxmzaton of the present value of consumpton, and therefore equals consumpton plus nvestment. How mght ths measure be adapted to nclude smoke? One possblty s to replace consumpton n the defnton by consumpton mnus the utlty cost of 1 The subscrpts on the productvty ndexes are chosen usng the optmal tax theory conventon that p denotes a producer prce and q a consumer prce. 3

5 smoke, or equvalently that level of consumpton whch, n the absence of smoke, would provde the same level of utlty as the current stuaton. Accordng to ths defnton, real natonal ncome n the pre-mprovement stuaton would be OĈ and n the post-mprovement stuaton would be ĜĈ OĜ, and the ndex of productvty mprovement would be. Ths measure s of conceptual OĈ nterest but, because t depends on the propertes of the utlty functon outsde the range of observaton, s not emprcally mplementable. The above dscusson lays out the basc theory on the smplfyng assumpton that nputs are fxed. The next secton provdes emprcally-mplementable measures of I 0, I p, and I q, whch account for changes n the economy s nputs. II. Emprcal Measures We employ the followng notaton p y w s ε σ I market prce of good, = 1,..., m output of good market prce of nput, = 1,...n quantty of nput smoke margnal cost of reducng smoke by one unt margnal beneft of reducng smoke by one unt ndex of total factor productvty growth The conventonal measure of growth n total factor productvty s I * = ( p y M ) ẏ y ẋ ( w M ), (1) where M p y = w s real natonal ncome. The frst term on the rght-hand sde s the value-share weghted average of the growth rate of outputs, and the second term s the value-share weghted average of the growth rate of nputs. The measure s derved n Jorgenson and Grlches (1967) and Jorgenson, Gollop, and Fraumen (1987), nter ala, on the assumptons that 4

6 producton exhbts constant returns to scale, all markets are compettve, and all outputs are marketed. The ssue at hand s how ths measure needs to be modfed when there s an unmarketed output. The tradtonal procedure s smply to gnore the unmarketed output, n whch case (1) contnues to apply, so that I 0 = I * (2) Pttman (1983) proposed a measure that treats smoke as an undesrable output. Natonal ncome s defned as M p p y εs, where ε>0 s the margnal cost of reducng smoke by one unt. Natonal ncome s defned usng clean ar as the reference pont, and values smoke as the negatve of ts margnal cost or producer cost. We refer to ths as the producer-cost measure of growth n total factor productvty: I p = ( p y M p ) ẏ y ( εs M p ) ṡ s ( w w ) ẋ (3) Note that, because of general equlbrum effects, the measured growth n total factor productvty wll dffer dependng on whether the reducton n smoke s acheved through taxaton (wth the revenue beng returned to consumers as a lump sum) or regulaton. Frst, the market-clearng prces wll dffer. Second, snce (under the assumptons of constant returns to scale and perfect competton) the prces of all goods equal the correspondng unt costs: wth regulaton alone, p y = w ; wth taxaton alone p y = w +τs, where τ=ε s the tax rate on smoke, and wth both taxaton and regulaton p y = w +τswhere τ ε n general. The measure we propose s analogous to Pttman s except that smoke s valued at ts (negatve) shadow consumer prce, σ the margnal rate of substtuton between smoke and a numérare composte commodty. Thus, I q = ( p y M q ) ẏ y ( σs M q ) ṡ s ( w w ) ẋ (4) where M q p y σs. When the level of smoke s controlled only by regulaton, 5

7 p y = w, etc. as above. It mght appear that the measure we propose s ad hoc. It can, however, be derved from basc prncples, whch strengthens ts appeal. Start wth a representatve ndvdual s utlty functon, U = U(y 1,..., y m, s). Totally dfferentate the utlty functon wth respect to tme. U = U ẏ + U s ṡ. (5) It makes no dfference for a measure of productvty growth whch good s taken as the numérare; let t be good one. Then usng the frst-order condtons from the ndvdual s optmzaton problem: U U 1 = p ẏ σṡ = (p y ) ẏ y (σs) ṡ s. (6) If we defne M q to be real natonal ncome, then (6) s growth of natonal ncome evaluated at consumer prces (ncludng the consumer shadow prce of smoke). And U = U 1 M ( p y q M q ) ẏ ( σs ) ṡ y M q s (7) gves a measure of the rate of growth of natonal ncome. Then f we subtract off the rate of growth of nputs, we have the welfare-based measure of total factor productvty growth, (4). Ths welfare-based measure of productvty growth has a nce feature. Holdng nputs fxed, the rate of productvty growth has the same sgn as the drecton of change of utlty or welfare. Nether I o nor I p has ths property. We now relate the varous productvty measures. To do so, note that all the productvty measures can be wrtten as I(ρ) = A ρṡ C, (8) B ρs A p ẏ, B p y, and C w ẋ, and ρ s the shadow prce of smoke used n the w 6

8 productvty measure, wth ρ=0 for I 0, ρ=ε for I p, and ρ=σ for I q. Then di(ρ) dρ = ṡ B ρs = ρṡ)s Bṡ + As +(A = 2 (B ρs) (B ρs) 2 sb (B ρs) 2 ( ṡ s + A B ) (9) If, therefore, the rate of growth of market output, A, exceeds (falls short of) the rate of growth of B smoke, then measured productvty growth s ncreasng (decreasng) n ρ, the shadow prce of smoke used n the productvty measure. In the case of central nterest, where envronmental regulaton s becomng ncreasngly strngent so that ṡ s + A B > 0, I > I > I q p 0. Also, usng (8) I(ρ 1 ) I(ρ 0 ) = A ρ 1ṡ B ρ 1 s A ρ 0ṡ B ρ 0 s = sb(ρ 1 ρ 0 )( ṡ s + A B ) (B ρ 1 s)(b ρ 0 s) (10) for any par of values of ρ 0 and ρ 1. Whch measure of productvty growth s superor depends on the ntent of the measure. If the ntent s to measure the rate at whch welfare s ncreasng, nettng out the growth rate of nputs, then I q s the approprate measure. III. Concludng Comments The paper developed a measure of total factor productvty growth desgned to account for the benefcal effects of envronmental regulaton whch we termed a welfare-based measure of productvty growth. To make the essental ponts as starkly as possble, we employed a very smple descrpton of an economy. The theory of productvty measurement has been extended to nclude taxes and subsdes, ntermedate nputs, publc servces, mports and exports, non-constant returns to scale, and non-compettve prcng. The welfare-based measure of productvty growth we have presented could be generalzed to treat all these extensons. To operatonalze the welfare-based measure of productvty growth requres not only 7

9 makng these extensons, but also measurng the margnal beneft from envronmental mprovement, whch s notorously dffcult. Nevertheless, the usefulness of the measure has already been demonstrated n practcal applcatons (Chaston (1997) and Swnand (1997)). 8

10 REFERENCES Chaston, K. (1997). Productvty Measurement n the Presence of Externaltes: An Example from the Electrc Power Industry. Unpublshed Ph.D. thess. Boston College. Gollop, F. and Roberts. M. (1983). Envronmental Regulatons and Productvty Growth: The Case of Fossl-Fueled Electrc Power Generaton. Journal of Poltcal Economy 91, Gray, W. (1987). The Cost of Regulaton: OSHA, EPA and the Productvty Slowdown. Amercan Economcs Revew 77, Jorgenson, D., Gollop, F., and Fraumen, B. (1987). Productvty and U.S. Economc Growth. Cambrdge, MA: Harvard Unversty Press. Jorgenson, D., Grlches, Z. (1967). The Explanaton of Productvty Change. Revew of Economc Studes 34, Pttman, R. (1983). Multlateral Productvty Comparsons wth Undesrable Output. The Economc Journal 93, Swnand, G. (1996). Incorporatng Envronmental Polluton nto Productvty Growth Measures: U.S. Agrculture Mmeo, Boston College. Wetzman, M. (1976). On the Welfare Sgnfcance of Natonal Product n a Dynamc Economy. Quarterly Journal of Economcs 90,

11 Fgure Legends Fgure 1: Pre- and post- mprovement producton-possblty fronters. Fgure 2: Productvty mprovement usng producer prces wth strengthenng envronmental regulaton. Fgure 3: Four measures of productvty mprovement wth strengthenng envronmental regulaton: conventonal gc, usng producer prce for smoke G C, usng consumer Oc O C prce for smoke ( G C / O C ) and usng utlty ĜĈ. OĈ 10

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