1. Input-Output Analysis in Current or Constant Prices: Does it Matter? Erik Dietzenbacher & Umed Temurshoev Faculty of Economic and Business University of Groningen This project is funded by the European Commission, Research Directorate General as part of the 7th Framework Programme, Theme 8: Socio-Economic Sciences and Humanities. Grant Agreement no: 225 281

2. Motivation Availability physical IO tables (PIOTs, single unit of mass) triggered discussion Treatment of waste (Hubacek & Giljum, 2003; Giljum & Hubacek, 2004; Giljum et al., 2004; Suh, 2004; Dietzenbacher, 2005; Dietzenbacher et al., 2009) Substantial differences with MIOTs (monetary IO tables) Weisz & Duchin (2006) reason: sectoral prices are not uniform for all deliveries

3. Motivation Example: 3-sector PIOT (million tons) and MIOT (billion DM) for Germany, 1990 land appropriation (hectares) Question: how much land used in each sector due to exports Results (in 1000 hectares): PIOT MIOT primary5,822.46,339.3 secondary 478.9 807.1 tertiary 544.5 134.9 total6,845.87,281.3

4. Motivation Example: 3-sector PIOT (million tons) and MIOT (billion DM) for Germany, 1990 land appropriation (hectares) Question: how much land used in each sector due to exports Results (in 1000 hectares): PIOT MIOT%diff primary5,822.46,339.3 -8.2 secondary 478.9 807.1 68.5 tertiary 544.5 134.9-75.2 total6,845.87,281.3 6.4

5. Research question Central question in this paper: To what extent do results differ between model based on IO table in current prices and model based on IO table in constant prices? Note: Results will be exactly the same if and only if each sector sells its goods and services for the same price Single sectoral deflator does the job Problem: deflators are cell-specific

6. Methodology Exercise: take a new final demand vector in current prices determine the effects for: sectoral gross outputs in constant prices employment Three approaches

7. Methodology Approach A: deflation after gross output calculations in current prices IO table in current prices input coefficients in current prices new final demands in current prices new gross outputs in current prices use gross output deflators new outputs in constant prices use labor coefficients (in current prices) new sectoral employment gross output deflators: total gross output sector j in constant prices divided by total gross output sector j in current prices

8. Methodology Approach B: gross output calculations in constant prices after deflation of final demands new final demands in current prices final demand deflators new final demands in constant prices IO tables in constant prices input coefficients in constant prices new gross outputs in constant prices use labor coefficients (in constant prices) new sectoral employment final demand deflators: final demands for good j in constant prices divided by final demands for good j in current prices

9. Methodology Approach C: using cell-specific deflators delivery (i,j) in constant prices divided by delivery (i,j) in constant prices final demand j in constant prices divided by final demand j in current prices

10. Methodology new final demands in current prices new gross outputs in current prices make a new IO table in current prices new delivery (i, j) in current prices = input coefficient (i, j) × new output j deflate new IO table (incl new final demands) in current prices using cell-specific deflators summation of each row new gross outputs in constant prices use labor coefficients (in constant prices) new sectoral employment

11. Methodology Observe: A (deflation of new outputs in current prices) requires gross output deflators only! B (calculation of outputs in constant prices after deflation of final demands) requires full IO table in constant prices C (cell-specific deflation) requires full IO table in constant prices (to determine the deflators)

12. Application Denmark, 2000-2007 IO tables in current prices IO tables in constant prices (base year 2000) Employment data 130 sectors new final demands = average of final demands over 2001-2007

13. Results, total gross outputs 2001200220032004200520062007Mean Economy-wide gross output, n = 130 (B-A)/A%0.011-0.033-0.0070.0120.0020.006-0.009-0.002 (C-A)/A%0.008-0.022-0.0020.0120.001 -0.010-0.002 (B-C)/C%0.003-0.011-0.0050.0000.0010.0050.002-0.001

14. Results, total gross outputs 2001200220032004200520062007Mean Economy-wide gross output, n = 130 (B-A)/A%0.011-0.033-0.0070.0120.0020.006-0.009-0.002 (C-A)/A%0.008-0.022-0.0020.0120.001 -0.010-0.002 (B-C)/C%0.003-0.011-0.0050.0000.0010.0050.002-0.001 %differences for total (economy-wide) gross outputs: very small 0.001-0.002% on average

15. Results, total gross outputs 2001200220032004200520062007Mean Economy-wide gross output, n = 130 (B-A)/A%0.011-0.033-0.0070.0120.0020.006-0.009-0.002 (C-A)/A%0.008-0.022-0.0020.0120.001 -0.010-0.002 (B-C)/C%0.003-0.011-0.0050.0000.0010.005 0.002-0.001 %differences for total (economy-wide) gross outputs: very small 0.001-0.002% on average further away from the base year 2000: one would expect larger differences no clear pattern over time

16. Results, total gross outputs 2001200220032004200520062007Mean Economy-wide gross output, n = 130 (B-A)/A%0.011-0.033-0.0070.0120.0020.006-0.009-0.002 (C-A)/A%0.008-0.022-0.0020.0120.001 -0.010-0.002 (B-C)/C%0.003-0.011-0.0050.0000.0010.005 0.002-0.001 large differences for B-A and C-A small differences for B-C intuition: B & C both use information from full IO tabel in constant prices A uses only gross output deflators

17. Results, aggregation 2001200220032004200520062007Mean Economy-wide gross output, n = 130 (B-A)/A%0.011-0.033-0.0070.0120.0020.006-0.009-0.002 (C-A)/A%0.008-0.022-0.0020.0120.001 -0.010-0.002 (B-C)/C%0.003-0.011-0.0050.0000.0010.0050.002-0.001 Economy-wide gross output, n = 56 (B-A)/A%0.0280.0260.0420.0330.001-0.009-0.0050.017 (C-A)/A%0.0220.0230.0380.0280.000-0.008-0.0100.013 (B-C)/C%0.0060.004 0.0060.001-0.0010.0060.003 aggregation increases the %differences the maximum difference is 0.042%

18. Results, aggregation 2001200220032004200520062007Mean Economy-wide gross output, n = 130 (B-A)/A%0.011-0.033-0.0070.0120.0020.006-0.009-0.002 (C-A)/A%0.008-0.022-0.0020.0120.001 -0.010-0.002 (B-C)/C%0.003-0.011-0.0050.0000.0010.0050.002-0.001 Economy-wide gross output, n = 56 (B-A)/A%0.0280.0260.0420.0330.001-0.009-0.0050.017 (C-A)/A%0.0220.0230.0380.0280.000-0.008-0.0100.013 (B-C)/C%0.0060.004 0.0060.001-0.0010.0060.003 aggregation increases the %differences the maximum difference is 0.042% aggregation affects B-A and C-A more than it affects B-C (differences remain very small)

19. Results, employment total economy-wide employment very similar conclusions: - extremely small differences - no clear pattern over time - same distinction between B and C versus A but: aggregation does NOT tend to increase the differences (averages over 7 years even decrease) 2001200220032004200520062007Mean Economy-wide employment, n = 130 (B-A)/A%0.010-0.0100.0050.011-0.004-0.015-0.027-0.004 (C-A)/A%0.007-0.0050.0050.006-0.004-0.012-0.019-0.003 (B-C)/C%0.003-0.0050.0000.0050.000-0.003-0.008-0.001 Economy-wide employment, n = 56 (B-A)/A%0.0050.0000.0070.022-0.005-0.012-0.0070.001 (C-A)/A%0.002-0.0010.0040.013-0.004-0.008-0.0050.000 (B-C)/C%0.003 0.0020.0030.009-0.001-0.005-0.0020.001

20. Results, sectoral level differences at sectoral level are larger largest positive difference: 3.297% (B-A) and 3.280% (C-A) in 2007 manufacturing of office machinery and computers (0.06% of national output) largest negative differences: manufacturing and distribution of gas (approx 0.5% of national output) 2001 2002 20032004200520062007Mean (B-A)/A%, n = 130 Min-1.278-2.562-1.586-0.862-0.588-1.215-1.708-1.400 Max0.4720.3070.3480.6350.5201.7473.2971.046 (C-A)/A%, n = 130 Min-1.321-2.542-1.565-0.850-0.584-1.090-1.395-1.335 Max0.4630.3030.3460.6320.4901.6793.2801.028 (B-C)/C%, n = 130 Min-0.055-0.255-0.214-0.279-0.071-0.270-0.409-0.222 Max0.0700.0630.0690.1100.1230.5750.8680.268

21. Results, sectoral level differences between B and C: for only 3 (out of 910 cases) differences larger than 0.4% 2001 2002 20032004200520062007Mean (B-A)/A%, n = 130 Min-1.278-2.562-1.586-0.862-0.588-1.215-1.708-1.400 Max0.4720.3070.3480.6350.5201.7473.2971.046 (C-A)/A%, n = 130 Min-1.321-2.542-1.565-0.850-0.584-1.090-1.395-1.335 Max0.4630.3030.3460.6320.4901.6793.2801.028 (B-C)/C%, n = 130 Min-0.055-0.255-0.214-0.279-0.071-0.270-0.409-0.222 Max0.0700.0630.0690.1100.1230.5750.8680.268

22. Results, sectoral level

23. Conclusion at sectoral level: differences may occasionally be > 1.0% but in these cases sectoral output < 1.0% of national output

24. Conclusions A = model in current prices + gross output deflators B = model in constant prices C = model in current prices + cell-specific deflators B & C very close to each other, versus A at sectoral level: few differences > 1%, for sectors with output < 1% of national output (results for employment are exactly the same) at level of total economy-wide outputs and employment: differences are extremely small

25. Conclusions new final demand vector: average of final demand vectors 2001-2007 what about out of sample vectors? size doesnt matter!! multiply new final demand vector with k then outcomes (outputs, employment) are multiplied with k %differences will remain the same composition of the new final demand vector may matter

26. Conclusions future extensions: further aggregation (28, 14, 7, 3 sectors) are the results unique for Denmark 2001-2007? what if constant price tables are not available every year (2003: constant prices 2007: current prices, gross output + final demand deflators are B & C still so close to each other?)