Constructing Price and Quantity Indices - Assignment Example

Running Head: Index Numbers and TFP Change Index Numbers and TFP Change.docx Insert name Institution Q1. Constructing price and quantity indices (a). From the table below, we can note that the indices have different values in results. The main reason for the variations is the variables used in price weight co-variance. Laspeyres considers the quantity and price of previous year when determining the index while Paasche considers only the quantity of the previous year OZ ZIL PASS P_OZ P_Z P_PASS Laspeyres Index Paasche’s Index Fisher Index 1986 4188000 460000 2149 9757 70 107 100 100.00 100.00 1987 4265000 504000 2247 9064 72 102 92.91 94.62 93.76 1988 4285000 451000 2199 8947 69 97 98.71 99.16 98.93 1989 3974000 458000 1760 8618 65 99 96.32 89.34 92.76 1990 4547000 397000 1566 8327 77 98 96.64 110.55 103.36 1991 4840000 529000 1455 7919 81 88 95.11 101.26 98.14 1992 5510000 528000 1653 7314 87 84 92.38 105.15 98.56 1993 5317000 556000 1583 7054 83 72 96.44 93.08 94.74 1994 5896000 590000 1537 6478 87 70 91.85 101.85 96.72 1995 6248000 436000 1510 5983 91 67 92.38 97.85 95.07 1996 6316000 393000 1459 5789 89 73 96.76 97.80 97.28 1997 6087000 353000 1517 5369 86 66 92.75 89.38 91.05 1998 6532000 376000 1409 5341 88 69 99.48 106.75 103.05 1999 6618000 371000 1601 5280 88 65 98.86 100.16 99.51 2000 6631000 365000 1533 5231 89 65 99.07 99.27 99.17 Fisher is substitute effect of the two. It is calculated by finding the square root of the two indices. The graph below shows the trend taken by the indices. From the graph above, it can be noted that the indices have a similar trend except that they have different figures. The figures shown by Paasache quantity index appears to be greater than those other type of indices except in the years 1989, 1993 and 1997. There is no unique explanation for the variation except for the covariance figures used. It can be noted from the graph that except the three mentioned years, the trend of Fisher index is below and above Lapeyres index. (b) Laspeyres, Paasche and Fisher price indexes for the three outputs using Direct method The direct method will not be preferable for these tasks because the amount of time required to calculate the indices is high. It also requires care while calculating the components the indices 1) Laspeyres - Type:  pj * |qk|  pppj/k * |wk| PPPLj/k = ---------------- = -----------------------  pk * |qk|  |wk| where PPPLj/k - Laspeyres-PPP for the aggregate pppj/k- PPPs for basic headings wk - nominal values for basic headings 2) Paasche - Type:  pj * |qj|  |wj| (I.2) PPPPj/k = --------------- = ------------------  pk * |qj| |wj| / pppj/k where PPPPj/k - Paasche -PPP for the aggregate (Country „j“ to Country „k“), pppj/k- ppp for basic headings wj - nominal value for basic headings in Country „J“. SHAZAM out Welcome to SHAZAM (Double Precision) v11.0 - JUNE 201 WIN-XP PAR= 78 ...NOTE..CURRENT WORKING DIRECTORY IS: C:\Documents and Settings\user\My Documents\SHAZAM |_SAMPLE 1 15 _|_|_* quantity, in hundreds of thousands. _|_|_READ Q1 Q2 Q3 ...NOTE.. 3 VARIABLES AND 15 OBSERVATIONS STARTING AT OBS 1 _|_|_* Quantity prices for farmer. _|_|_READ P1 P2 P3 ...NOTE.. 3 VARIABLES AND 15 OBSERVATIONS STARTING AT OBS 1 _|_|_* Compute a price index - base period is 1. _|_|_GEN1 PBASE1=P1:1 _|_|_GENR PINDEX1=100*P1/PBASE1 _|_|_* Compute an aggregate price index _|_|_INDEX P1 Q1 P2 Q2 P3 Q3 / BASE=1 PAASCHE=PALL REQUIRED MEMORY IS PAR= 3 CURRENT PAR= 78 BASE PERIOD IS OBSERVATION 1 PAASCHE WILL BE STORED AS VARIABLE: PALL PRICE INDEX QUANTITY DIVISIA PAASCHE LASPEYRES FISHER DIVISIA PAASCHE LASPEYRES FISHER 1 1.000 1.000 1.000 1.000 0.4089E+08 0.4089E+08 0.4089E+08 0.4089E+08 2 0.929 0.929 0.929 0.929 0.4165E+08 0.4165E+08 0.4165E+08 0.4165E+08 3 0.917 0.917 0.917 0.917 0.4184E+08 0.4184E+08 0.4184E+08 0.4184E+08 4 0.883 0.883 0.883 0.883 0.3881E+08 0.3881E+08 0.3881E+08 0.3881E+08 5 0.854 0.854 0.854 0.854 0.4439E+08 0.4439E+08 0.4439E+08 0.4439E+08 6 0.812 0.812 0.812 0.812 0.4726E+08 0.4726E+08 0.4726E+08 0.4726E+08 7 0.750 0.750 0.750 0.750 0.5380E+08 0.5380E+08 0.5379E+08 0.5380E+08 8 0.723 0.723 0.723 0.723 0.5192E+08 0.5192E+08 0.5192E+08 0.5192E+08 9 0.664 0.664 0.664 0.664 0.5757E+08 0.5757E+08 0.5757E+08 0.5757E+08 10 0.614 0.614 0.614 0.614 0.6098E+08 0.6099E+08 0.6097E+08 0.6098E+08 11 0.594 0.594 0.594 0.594 0.6164E+08 0.6165E+08 0.6163E+08 0.6164E+08 12 0.551 0.551 0.551 0.551 0.5940E+08 0.5942E+08 0.5939E+08 0.5940E+08 13 0.548 0.548 0.548 0.548 0.6374E+08 0.6376E+08 0.6373E+08 0.6374E+08 14 0.542 0.541 0.542 0.542 0.6458E+08 0.6460E+08 0.6457E+08 0.6458E+08 15 0.537 0.536 0.537 0.537 0.6470E+08 0.6472E+08 0.6469E+08 0.6471E+08 |_GENR PALL=100*PALL _|_|_GENR OBS=TIME(0) _|_|_FORMAT(F10.0,5X,2F13.2) _|_|_PRINT OBS PINDEX1 PALL / FORMAT OBS PINDEX1 PALL 1. 100.00 100.00 2. 92.90 92.91 3. 91.70 91.70 4. 88.33 88.33 5. 85.34 85.36 6. 81.16 81.19 7. 74.96 75.00 8. 72.30 72.33 9. 66.39 66.43 10. 61.32 61.35 11. 59.33 59.36 12. 55.03 55.06 13. 54.74 54.77 14. 54.11 54.14 15. 53.61 53.64 The substitution effect have a bring an effect on quantity index and price coefficient of variations. In 1989 the effects have offset, with the quantity index very close to the Fisher price index. The levels effect generally dominates driven by the increasing dispersion in quantities over time. Q2 Measuring TFP change using the Tornqvist and Fisher indices Indices Of Changes Rel. To Previous Observation: Cumulative Indices Year Fisher Tornqvist CUMULATIVE INDICES 1986 1 1 1987 0.9005 0.9005 0.9005 0.9005 1988 1.0252 1.0252 0.9232 0.9232 1989 0.9017 0.9017 0.8324 0.8324 1990 1.1445 1.1445 0.9527 0.9527 1991 1.0754 1.0754 1.0246 1.0246 1992 1.1529 1.1529 1.1812 1.1813 1993 0.9809 0.9809 1.1587 1.1587 1994 1.1186 1.1186 1.2961 1.2961 1995 1.0698 1.0698 1.3866 1.3866 1996 1.0035 1.0035 1.3915 1.3915 1997 0.9605 0.9605 1.3365 1.3365 1998 1.0778 1.0778 1.4405 1.4405 1999 1.0245 1.0245 1.4758 1.4758 2000 0.9953 0.9953 1.4688 1.4688 (b) Total factor productivity index using the Tornqvist and Fisher index formulae for period from 1986 to 2000 for both formulae. From the table above which is an extract of outputs from TFPIP, we can note that total factor productivity index is similar in the case of Tornqvist and Fisher index formula both in indices of changes to relative to previous observation and cumulative indices. The trend taken by the indices of total productivity over the period from 1986-2000 is shown in the graphs below. The graph indicates that productivity index fluctuated from time to time which is not a good sign to production. The fluctuating indices show variability in adaption in long term technological change and producers. Only two periods that has a similar index as the base year 1986 that is 1996 and 2000. 4 years that is 1987, 1989, 1993 and 1997 have their total facto productivity indices below one which means that production was below the base year in terms of efficiency in using factors of production. The other years had their indices above one. The year 1992 had the highest index while the lowest index was in 1989. The fluctuation is a clear indication that the use of factors of production was not producing similar outputs annually either because of changes in technology of production or changes in the prices of the output. Looking at the year 1995 for both indices of changes relative to previous observation it can be noted that the index increased by 7% meaning the efficiency increased during that period and there was advancement in production compared to previous year. In analysing the year 2000, it can be noted that the index decreased to 0.9953 which is equivalent to 1 when rounded off to 2 decimal points but it is less than 0.5% decrease in advancement. Q3 3 Measuring TFP change using the Malmquist index (a) Malmquist total factor productivity change for the 43 farms assuming constant returns to scale and an input orientation (b) Malquist total factor productivity change e for the farms as represented on the table above shows that 11 farms had their index decreased, two farms had their index equal to one while 30 had their indexes more than one. The table also shows that these farms had their technical efficiency change increased as well as technological change. The farms that had decreased total factor of productivity change had their technical efficiency change, technological change and scale efficiency change decayed. Out of the 11 farms that had their index lower than one, only one had a decayed technological change. The others had a technological change of more than one. However it should be noted that one of those farms that had total factor productivity change index of more than one showed a decline in technological change. The lowest index for the firms was 0.769 for farm 30 while farm 33 had the highest index of 1.249. if you look at this two farms, it can be noted that they had a slight difference they had a huge difference in technical and scale efficiency changes. This means the reduction in total productivity was contributed by management incompetence. It should be noted that average Malquist total factor productivity change improved by 2.7% for all the farms and was contributed by technological change and pure technical efficiency change by 3.3% and 0.5% respectively. The average was reduced by a reduction in technical efficiency change by 0.05% and scale efficiency change of 1.1%. in essence it means that there was increased in production due to technological and pure technical efficiency change. This means that there was managerial competence in managing labour and technology. However the management had distorted slight scale efficiency and decayed technological efficiency. From the findings, it can be concluded that the 43 farms had total factor productivity change improved due to technological change and pure technical efficiency change. Appendix 2: output file Read More