Testing the Neo-Classical and the Newtonian Theory of Production

Transcription

1 Tesng he Neo-Classcal and he Newonan Theory of Producon Ma Esola * & Ala Dannenberg # * Unversy of Easern Fnland Faculy of Socal Scences and Busness Sudes, Joensuu Campus # Unversy of Easern Fnland Deparmen of Busness, Joensuu Campus Presenaon n Fyskan pävä Unversy of Easern Fnland, Joensuu Campus, Fnland.

2 Defned Economc Laws of Producon 1s knd of regulary: Von Thünen, J.H. 185: The defnon of he concep of margnal producvy of producon facors. - Spllman, W.J. 1924: Decreasng margnal producvy. 2nd knd of regulary: Cobb, C.W. & Douglas, P.H Esmaed Cobb-Douglas -ype producon funcons for secoral producons. - Shakh, A. 1974: The esmaed aggregae level producon funcons have acually been accounng denes. 3rd knd of regulary: Nunes, L.A. e al. 1997: Scalng laws n he dsrbuons of frms value added, sales, and employmen n U.S. and Japanese daa We propose here 4h knd of regulary n producon: Un roo s observed n all producon daa n Fnnsh economy. Thus a me rend exss n flows of producon ha seems o be a general observaon hrough counres. Addonal opc of our sudy: We es Newonan heory agans he neoclasscal one n explanng ndusral flows of producon.

3 1. Measurng Producon and s Growh Knemacs Knemacs s he sudy of he geomery of moon; deals wh he mahemacal descrpon of moon n erms of poson, velocy, and acceleraon. Knemacs serves as a prelude o dynamcs, whch sudes force as he cause of changes n moon. Ohanan, H.C. Physcs, 2nd Ed. (1989) p. 25.

4 The 9 man producon secors n Fnland are: 1 = A (Agrculure, foresry and hunng) + B (Fshng), 2 = C (Mnng and quarryng) + D (Manufacurng) + E (Elecrcy, gas, and waer supply), 3 = F (Consrucon), 4 = G (Trade, repar of moor vehcles and household goods) + H (Hoels and resaurans), 5 = I (Transpor, sorage and communcaon), 6 = J (Fnancal nermedaon and nsurance), 7 = K (Real esae and busness acves), 8 = L (Admnsraon, socal secury) + M(Educaon), 9 = N (Healh and socal work) + O (Oher communy, socal and personal servces) + P (Household servce acves) - Fnancal nermedaon servces ndrecly measured. These secors cover he whole Fnnsh economy.

5 In Fnland, manufacurng s dvded n 13 secors: DA : Food producs, beverages and obacco, DB,DC: Texles, exle producs, leaher and leaher producs, DD: Wood and wood producs, DE: Pulp, paper and paper producs, publshng and prnng, DF: Refned peroleum producs, coke and nuclear fuel, DG: Chemcals and chemcal producs, DH: Rubber and plasc producs, DI: Oher non-meallc mneral producs, DJ: Basc meals and fabrcaed meal producs, DK: Machnery and equpmen, DL: Elecrcal and opcal equpmen, DM: Transpor equpmen, DN: Oher manufacurng and recyclng. These secors cover he whole Fnnsh manufacurng.

6 3, 2,5 2, 1,5 1, DA2 DBDC2 DD2 DF2 DG2 DH2 DI2 DM2 DN2 Fgure 1. Annual ndusral producon volumes a year 2 prces

7 24, 2, 16, 12, 8, 4, DE2 DK2 DJ2 DL2 Fgure 2. Annual ndusral producon volumes a year 2 prces

8 PA PBC PD PE PF PG Fgure 3. Indusral prces n manufacurng

9 PH PI PJ PK PL PM PN Fgure 4. Indusral prces n manufacurng

10 Secor ADF, vol. (Pr.) Indusry ADF, vol. (Pr.) ADF, prce (Pr.) (.99) DA.9 (.99) -2.6 (.1) (.8) DB+DC -.6 (.86) -3.6 (.1) 2.6 (.99) DD -.6 (.85) -2.7 (.9) (.44) DE -1.2 (.65) -2. (.3) (.63) DF 2.3 (.99) -1.9 (.32) (.99) DG -.5 (.89) -1. (.76) (.42) DH -.4 (.89) -1.4 (.59) 7.5 (.98) DI -.7 (.83) -2.2 (.21) (.22) DJ 1.9 (.99) -2.9 (.6) (.22) DK 1.2 (.99) -2.1 (.23) DL 1.5 (.99) -.1 (.94) DM -3.2 (.3) -1.5 (.51) DN -1. (.73) -2.5 (.12) Table 1: ADF un roo es resuls for all secors and ndusres

11 The Augmened Dckey-Fuller es shows ha n all me seres he exsence of un roo canno be rejeced a crcal level.1. Un roo n me seres x n,n... 1,,1,... corresponds o: x n x n f ( n), 1 1, where α s consan and f(n) an unknown funcon. The soluon of hs frs order dfference equaon x n x n 1 n f (1 ) shows ha a lnear or a more complcaed me rend exss n x n because number n measures he order of he me nerval n dscree me. The neo-classcal assumpon ha frms produce a an equlbrum flow n a me un s hus rejeced n every secor and ndusry n Fnland.

12 Conclusons 1 A lnear or a more complcaed me rend s observed n producon n every secor and ndusry n Fnland. Non-zero acceleraon n accumulaed producon s hus observed a every secor and ndusry. The esmaed non-zero acceleraons for accumulaed secoral producons are n conflc wh he neo-classcal heory ha assumes frms o produce a her profmaxmzng equlbrum volume flows.

13 2. Theores of Frms Behavor Le he annual prof funcon Π( /y), y=year, of a frm be ( ) p( ) q( ) C( q( )), where p()( /kg) s he prce of he produc of he frm, q()(kg/y) he annual flow of producon, and C(q)( /y) he cos funcon of he frm Neo-classcal Theory of a Frm In he neoclasscal framework, he me passage s absraced away, and he frm s producon s modelled as a sac opmzaon problem: q p C'( q) q * f ( p), (1) where q* s he frm s annual prof maxmzng flow of producon.

14 If he neoclasscal heory s rue, we should observe zero acceleraon n producon a every secor and ndusry, because he heory assumes ha frms produce a her prof maxmzng flow of producon. However, n all secors and ndusres he assumpon of zero acceleraon n producon was rejeced, and a lnear or more complcaed me rend was observed n producon flows. Thus we need a heory of producon where me passage s ncluded Newonan Theory of a Frm 1 mq'( ) q q'( ) 1 m q. (2) The frm s acceleraon of producon q () s explaned by he frm s margnal profably Π/ q, whch s he force acng upon he producon. Consan m s nerpreed as he neral mass of producon of he frm. In our esng, we approxmae / q by average profably / q. 1 Esola 21: A Dynamc Theory of a Frm: An Applcaon of Economc Forces. Advances n Complex Sysems.

15 Suppose he prce a secor follows he followng process (3) ), sn( ) sn( ) ( b b a b b a a a p where a j are consans and b j are he frequency and phase parameers of busness cycles. The cos funcon C (q (),) ( /y) of frm s assumed as follows: ), ( ) ( 2 1 ) ( ) ), ( ( q c q c q c c q C where he las erm represens possble decreasng coss wh me due o echnologcal developmen. The margnal prof funcon s hen ). sn( ) sn( ) ( ) ( ) ( b b a b b a c a q c c a q

16 The dfferenal equaon n (2) becomes hus he followng: ), sn( ) sn( ) ( ) ( ' b b a b b a z q c z m q The soluon of he above equaon s: (4), ) cos( ) sn( ) cos( ) sn( ) ( m c e B b b B b b B b B b B B B q where, c a z c a z where B j are consans.

17 Ind. Cons. (T-sa.) Tme (T) Sn(b +b 1 ) (T) Sn(b 2 +b 3 ) (T) R 2 B-G, F- Pr 1. DA.4 (12.9). (12.2).6 (16.9).94. DB+DC.5 (59.8).5 (43.9).98.1 DD.7 (18.8). (7.8) -.2 (-6.3) DE -9.8 (-15.3).1 (3.9) -1.7 (-16.4).91.1 DF 1. (18.5).3 (3.5).28.2 DG.6 (26.4). (19.7) -.1 (-6.6).94. DH.4 (27.7) -.1 (-7.2) -.7 (-32.3).97.2 DI.4 (21.9).1 (5.2).6 (24.8).97. DJ.3 (9.2) 2.2 (19.8) -.3 (-5.3).95.2 DK.4 (28.8) -.6 (-35.4). (2.6) DL 1.1 (82.8) -.4 (-2.2).1 (6.5) DM.5 (19.8). (21.4).1 (5.) DN.3 (17.9).7 (28.6).96. Table 2. Esmaed models (3) for ndusral prces 1 B-G, F-Pr. s he probably of rejecng he null hypohess of no auocorrelaon n resduals n Breusch-Godfrey seral correlaon es.

18 Tesng he wo Theores of Producon We esmae equaons (1), (2), and (4) by usng annual daa of 13 manufacurng ndusres n Fnland a Only manufacurng daa s used, because hese mcro level heores su beer for mcro level daa. Because he funconal form n Eq. (1) can be any, we esed several funconal forms for he neo-classcal equaon q=f(p). However, because p, p 2, sn(p), and exp(p) correlae a every ndusry abou.9, only one of hem can be used n he esmaed equaon. We chose he bes f for every ndusry. The esmaon resuls for he Newonan model (2) are n Table 3, hose for he neo-classcal heory n Eq. (1) are n Table 4, and hose for he Newonan model (4) are n Table 5. Noce ha n (1) and (4) we model he flow of producon, and n (2) he acceleraon of producon.

19 Indusry Un prof (T-sa.) R 2 B-G, F-Pr. DA (2.5).1.29 DD (2.5).1.55 DE (3.2).7.13 DG 11.1 (3.5).7.7 DH 91.8 (3.3).5.99 DI 93.7 (2.5).1.5 DJ (4.6) DK (4.) DL (6.3).36. Table 3: Esmaed Newonan models (2) for manufacurng ndusres

20 Ind. Cons. (Tsa.) Prce (Tsa.) Prce 2 (T-sa.) Sn(Prce) (Tsa.) R 2 B-G, F- Pr. DA (2.1) (2.6).18. DB+DC (26.3) (-11.9).82. DD (21.1).25. DE (46.8).79. DF (1.3).. DG 45.7 (5.2) (1.6).78. DH (-2.6) 17. (14.9).87. DI (11.9) 47.8 (7.9).66. DJ (27.2).78. DK (3.3) (6.1).54. DL (9.8) (-8.5).69. DM (54.6).. DN 368. (12.5) (7.).6. Table 4: Esmaed neo-classcal models (1) for manufacurng ndusres

21 Ind. Cons. (T) Tme (T) Exp(h ) (T) Sn(b 2 ) (T) Cos(b 2 ) (T) Sn(b +b 1 ) (T) Cos(b +b 1 ) (T) DA (29.9) 46.6 (25.1) (-7.8) (-2.4).97.5 DB+ DC (72.2) -28. (-29.3) -84. (-6.2) (8.2).97. DD (17.8) 31.6 (21.2) (7.6).95.5 DE (42.6) 15.1 (39.4) (-4.5) (-2.1) DF 23.3 (18.2) -. (-4.1) 14.6 (4.4).69.7 DG 58.4 (22.2) 39.6 (32.1) (-2.8).97.3 DH (2.5) 24. (32.9) 43.9 (4.6).97.3 R 2 B-G, F- Pr. DI (44.5) 7.5 (8.5). (7.1) (-9.9) (-7.3) (-3.3).96.1 DJ (9.7) 95.4 (27.4). (7.1) (-4.2).98.5 DK (19.5) 68.3 (16.4). (9.) (3.3) (-4.1).96.2 DL 87.4 (72.6) 315. (2.5) (-2.6).99.3 DM 813. (81.6) (-6.3) -4.8 (-2.9).6.1 DN (69.4). (5.3) (-6.4) (-2.6) (-5.7).85. Table 5: Esmaed Newonan models (4) for manufacurng ndusres

22 2,8 1,4 2,4 1,2 2, 1, 1,6 8 1, DA2 1*PA DBDC2 1*PBC Fgure 5. Prce and volume of producon n an ndusry

23 1,8 1,6 1,4 1,2 1, , 7, 6, 5, 4, 3, 2, 1, DD2 1*PD DE2 1*PE Fgure6. Prce and volume of producon n an ndusry

24 1,6 1,4 1,2 1, , 1,8 1,6 1,4 1,2 1, DF2 1*PF DG2 1*PG Fgure7. Prce and volume of producon n an ndusry

25 1,2 1,4 1, 1,2 8 1, DH2 1*PH DI2 1*PI Fgure 8. Prce and volume of producon n an ndusry

26 5, 6, 4, 5, 3, 4, 3, 2, 2, 1, 1, DJ2 1*PJ DK2 1*PK Fgure 9. Prce and volume of producon n an ndusry

27 24, 1,4 2, 1,2 16, 1, 12, 8 8, 6 4, DL2 1*PL DM2 1*PM Fgure1. Prce and volume of producon n an ndusry

28 1,4 1,2 1, DN2 1*PM Fgure12. Prce and volume of producon n an ndusry

29 Comparson of Neo-classcal Model (1) and Newonan Model (4) 2,8 2,8 2,4 2,4 2, 2, 1, ,6 1, ,6 1, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DA Newonan model (4) for DA

30 Comparson of Neo-classcal Model (1) and Newonan Model (4) 1,4 1,4 1,2 1,2 1, 1, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DB+DC Newonan model (4) for DB+DC

31 Comparson of Neo-classcal Model (1) and Newonan Model (4) 2, 2, 1,6 1, , , Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DD Newonan model (4) for DD

32 Comparson of Neo-classcal Model (1) and Newonan Model (4) 2, 8, 1,6 7, 6, , , 4, 3, 2, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DE Newonan model (4) for DE

33 Comparson of Neo-classcal Model (1) and Newonan Model (4) 1,2 1,2 1, 1, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DF Newonan model (4) for DF

34 Comparson of Neo-classcal Model (1) and Newonan Model (4) 2, 2, 1,6 1,6 6 1,23 1, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DG Newonan model (4) for DG

35 Comparson of Neo-classcal Model (1) and Newonan Model (4) 1,2 1,2 1, 1, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DH Newonan model (4) for DH

36 Comparson of Neo-classcal Model (1) and Newonan Model (4) Resdual Acual Fed 1,4 1,2 1, Resdual Acual Fed 1,4 1,2 1, Neo-classcal model (1) for DI Newonan model (4) for DI

37 Comparson of Neo-classcal Model (1) and Newonan Model (4) 5, 6, 2, 1,5 1, , -1, , 3, 2, 1, , 4, 3, 2, 1, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DJ Newonan model (4) for DJ

38 Comparson of Neo-classcal Model (1) and Newonan Model (4) 6, 6, 5, 5, 3, 4, 4, 3, 2, 3, 8 2, 1, 2, 4 1, 1, -1, -4-2, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DK Newonan model (4) for DK

39 Comparson of Neo-classcal Model (1) and Newonan Model (4) 25, 25, 8, 4, -4, 2, 15, 1, 5, 4, 3, 2, 1, 2, 15, 1, 5, -5, -8, -1, -12, , Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DL Newonan model (4) for DL

40 Comparson of Neo-classcal Model (1) and Newonan Model (4) 1, 1, Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DM Newonan model (4) for DM

41 Comparson of Neo-classcal Model (1) and Newonan Model (4) Resdual Acual Fed Resdual Acual Fed Neo-classcal model (1) for DN Newonan model (4) for DN

42 Conclusons 2 Newonan model (2) gves some suppor for un profably as he force causng acceleraon n ndusral producons, bu he suppor s no mpressve. Newonan model (4) works beer han he neo-classcal one (1) n every ndusry. The rae of explanaon and he auocorrelaon problem n resduals are mproved remarkably n every ndusry. A cyclcal erm n producon s observed n every ndusry, and also a lnear or an exponenal me rend. The assumed model for ndusral prces works also reasonably well.

43 Thank You for Your Aenon! Commens Welcome!