References contributed by usersubmitted
- (The software industry uses computers and communication equipment that contain semiconductors, but it does not directly use semiconductors.) Communication Equipment Sector For 1997-2011, we estimate S Mï¢ with proprietary data from iSuppli Corp. on the annual semiconductor cost share of 14 different types of communication equipment. We aggregate the product-specific cost shares with domestic shipments weights that vary from year to year. For 2012, we use the share estimated for 2011. For 1990-96, we extrapolate back the 1997 share using the annual percent changes in the estimated worldwide semiconductor share in communication equipment; we estimate these shares from a variety of proprietary data sources.
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- Accordingly, for each type of IT capital, we construct contributions from data for the income share, capital input, and hours, extrapolating back from the 1987 contributions by splicing in values for these variables from the dataset we constructed for Oliner, Sichel, and Stiroh (2007). Capital Deepening for Non-IT Assets These contributions are calculated by subtracting the IT capital deepening contributions from the overall capital deepening contribution.
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Aizcorbe, Ana, Stephen D. Oliner, and Daniel E. Sichel. 2008. Shifting Trends in Semiconductor Prices and the Pace of Technological Progress. Business Economics 43(3): 2339.
- All of the NIPA data we use are from the release dated January 30, 2013. - 33 -Labor Hours (H) For 1974 to 2010, labor hours are from the MFP dataset. We extended the data to 2012 using the growth rate in hours of all persons in the nonfarm business sector from the P&C release.
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- All other series we use from the MFP data are also from that release. These data are available at http://www.bls.gov/mfp/mprdload.htm. See the spreadsheets titled “Historical Multifactor Productivity Measures (SIC 1948-87 linked to NAICS 1987-2011)†and “Information Capital by Asset Type for Major Sectors.†We used data from the release dated February 7, 2013.
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Baily, Martin Neil, James L. Manyika, and Shalabh Gupta. 2013. U.S. Productivity Growth: An Optimistic Perspective. International Productivity Monitor, no. 25, Spring.
Basu, Susanto, John G. Fernald, and Matthew D. Shapiro. 2001. Productivity Growth in the 1990s: Technology, Utilization, or Adjustment? Carnegie-Rochester Series on Public Policy 55: 117-65.
- Bayard, Kimberly, David Byrne, and Dominic Smith. 2013. The Scope of U.S. Factoryless Manufacturing. Available at http://www.upjohn.org/MEG/papers/baybyrsmi.pdf.
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- Brynjolfsson, Erik, and Andrew McAfee. 2011. Race Against the Machine: How the Digital Revolution is Accelerating Innovation, Driving Productivity, and Irreversibly Transforming Employment and the Economy. Digital Frontier Press.
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Byrne, David, and Carol Corrado. 2007. Prices for Communications Equipment: Rewriting a 46-Year Record. National Bureau of Economic Research conference paper, July.
- Capital Income To estimate capital income for each type of capital for the extension to 2011 and 2012, we use the following equation: capital incomej = [(R + j ï¤ - j ï ) jj Kp ] j T . We discuss each component of this equation below. Although we have suppressed the time subscript for expositional convenience, these estimates of capital income vary from year to year.
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Carmen M., Reinhart ; Kenneth S., Rogoff. (2009) This Time Is Different: Eight Centuries of Financial Folly. In: Economics Books.
Chwelos, P.D., Ernst. R. Berndt, and Iain M. Cockburn. 2008. “Faster, Smaller, Cheaper: An Hedonic Price Analysis of PDAs.†Applied Economics 40: 2839-56.
- Communication Equipment Sector We follow the same procedure described above for the computer sector. That is, we use ASM product shipments for communication equipment (NAICS category 3342) for 1987-2011; we then extrapolate back in time with the annual percent changes in ASM industry shipments and forward to 2012 with the percent change in a proxy series for current-dollar output of - 41 -communication equipment. The proxy variable is the product of the annual average level of the Federal Reserve's industrial production index for communication equipment and a price index for domestic output of this equipment constructed using the method described in Byrne and Corrado (2007). Because the Byrne-Corrado index is not yet available for 2012, we assume the 2012 percent change equaled that for 2011.
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- Computer Sector For 1978-2012, we measure pC with the NIPA price index for final sales of computers and peripheral equipment (NIPA table 1.2.4, line 17). For earlier years, we extrapolate back the 1978 level with the percent change in the NIPA price index for private fixed investment in computers We compute the rate of change in each relative price as the percent change from the prior year’s price ratio, not as a log difference. Although growth accounting studies typically use the log difference approximation to calculate rates of change, this approximation is inaccurate for percent changes as large as those observed for the relative prices of computers and semiconductors. - 43 -and peripheral equipment (NIPA table 1.5.4, line 32), trend-adjusted to decline one percentage point faster per year. This trend adjustment accounts for the difference in the average annual decline over 1978-95 between the price indexes for private fixed investment in computers and final sales of computers.
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- Computer Sector For 1987 to 2011, we used Census Bureau data from the Annual Survey of Manufacturers (ASM) on product shipments of computer and peripheral equipment (NAICS category 3341).
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Congressional Budget Office. 2013. The Budget and Economic Outlook: Fiscal Years 2013 to 2023. Washington (August). Available at http://www.cbo.gov/sites/default/files/cbofiles/attachments/43907-BudgetOutlook.pdf.
- Contribution of Capital Deepening in the Nonfarm Business Sector Overall Capital Deepening For 1974 to 2010, the contribution of overall capital deepening to growth in labor productivity is calculated as the product of: 1) the log difference of the capital-hours ratio (using real capital input) and 2) capital’s income share. Our income shares are time varying and not period averages.30 The data for the capital-hours ratio and the income shares are from the MFP dataset.
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Copeland, Adam. 2013. “Seasonality, Consumer Heterogeneity and Price Indexes: the Case of Prepackaged Software.†Journal of Productivity Analysis 39: 47-59.
Corrado, Carol, and Charles Hulten. 2012. Innovation Accounting. The Conference Board, Economics Program Working Paper No. 12-04, October.
Corrado, Carol, Charles Hulten, and Daniel Sichel. 2009. “Intangible Capital and U.S. Economic Growth.†Review of Income and Wealth 55(3): 661-85.
Corrado, Carol, Jonathan Haskel, Cecilia Jona-Lasinio, and Massimiliano Iommi. 2012. “Intangible Capital and Growth in Advanced Economies: Measurement Methods and Comparative Results.†IZA Discussion Paper No. 6733, July.
- Cowen, Tyler. 2011. The Great Stagnation: How America Ate All the Low-Hanging Fruit of Modern History, Got Sick, and Will (Eventually) Feel Better Again. Dutton. - 30 -Doherty, Maureen. 2013. Reflecting Factoryless Goods Production in the U.S. Statistical System. Available at http://www.upjohn.org/MEG/papers/Doherty_Reflecting%20Factoryless%20GoodsProduction.p df.
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- Depreciation Rate (δj) For equipment and software, nonresidential structures, and tenant-occupied rental housing, we use depreciation rates reported in the MFP dataset through 2010. For 2011 and 2012, we use the value reported for 2010. For land and inventories, the depreciation rate is zero. For IT assets, we use a parallel procedure.
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- Expected Nominal Capital Gain/Loss (Î j) For each type of capital, we calculated Î j as a three-year moving average of the percent change in the price of asset j (pj). The moving average serves as a proxy for the unobserved - 38 -expectation of price change. Through 2010, the pj series are the investment price indexes from the MFP dataset. Except for land, each pj series was extended to 2011 and 2012 using the growth rate of the corresponding series for NIPA investment prices.31 For land, we extended prices to 2011 and 2012 using the average growth rate of land prices in the MFP dataset from 2007 to 2010. Current-dollar Productive Capital Stock (pjKj) For each asset, this series is simply the product of the real productive stock (Kj) and the asset price index (pj), both of which are discussed above.
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- Fernald, John. 2012. Productivity and Potential Output before, during, and after the Great Recession. Federal Reserve Bank of San Francisco Working Paper 2012-18. Available at http://www.frbsf.org/publications/economics/papers/2012/wp12-18bk.pdf.
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- Finally, for years before 1990, we extrapolate back the 1990 share using the annual percent changes in the share constructed in Oliner and Sichel (2002) using data from the Semiconductor Industry Association. See the data appendix in Oliner and Sichel (2002) for details. - 46 -Other Final-output Sector. To estimate S O
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- Flamm, Kenneth. 2007. The Microeconomics of Microprocessor Innovation. National Bureau of Economic Research conference paper, July.
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- For 1974 to 1986, the BLS does not make available the needed IT detail on their website.
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- For 1974 to 1986, we difference splice in the income shares that we constructed for Oliner, Sichel, and Stiroh (2007). To extend the income shares for each IT asset to 2011 and 2012, we use a procedure parallel to the one described for the pieces that add up to total capital.
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- For 2009-2012 we extended the BLS series using annual growth rates for real output and currentdollar output in the nonfarm business sector from the NIPAs.29 We measured p as an implicit price deflator, constructed as the ratio of current-dollar nonfarm business output to real nonfarm business output from the MFP dataset for the period 1974-2008. For 2009-2012, we extended the series for p using annual growth rates constructed from the NIPA data on real output and current-dollar output in the nonfarm business sector.
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- For 2011 to 2012, we extended the series for the contributions using a procedure exactly parallel to that for the components of overall capital deepening.
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- For equipment and software and nonresidential structures, we used the price series from NIPA table 5.3.4. For inventories, we used the implicit price deflator for nonfarm inventories from NIPA table 5.7.9B. For tenantoccupied rental housing, we used the price series for investment in multifamily residential structures from NIPA table 5.3.4. For each type of IT capital, we used prices from NIPA table 5.5.4. As part of the MFP dataset, under the heading “Additional Available Measures,†BLS provides spreadsheets for 1987-2010 Rental Price Detail Measures by Asset Type for both manufacturing and non-manufacturing industries.
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Gordon, Robert J. 2013. U.S. Productivity Growth: The Slowdown Has Returned After a Temporary Revival. International Productivity Monitor, no. 25, Spring.
- Grimm, Bruce. 1998. Price Indexes for Selected Semiconductors, 1974-96. Survey of Current Business 78 (February): 8-24.
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- Holdway, Michael. 2001. “An Alternative Methodology: Valuing Quality Change for Microprocessors in the PPI.†Unpublished paper presented at Issues in Measuring Price Change and Consumption Conference, Bureau of Labor Statistics, Washington DC, June 5-8, 2000.
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- Holdway, Michael. 2011. “Hedonic Methods in the Producer Price Index.†Available at http://www.bls.gov/ppi/ppicomqa.htm.
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- ï¢ , note that equation A22 in Oliner and Sichel (2002) shows that: S ï =  1i S ii ï¢ï (1+ ï± ), which can be written with explicit sectoral notation as S ï = [ S CC ï¢ï + S SWSW ï¢ï + S MM ï¢ï + S OO ï¢ï ](1+ ï± ). Solving this equation for S O ï¢ yields S O ï¢ = )1( ])[1( ï±ï ï¢ïï¢ïï¢ïï±ï  ï€«ï€«ï€«ï€ O S MM S SWSW S CCS . The data sources for all series on the right-hand side of this expression have been discussed above. - 47 -
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- ï¢ , S O ï¢ ) Computer Sector For 1997-2011, we estimate S Cï¢ with proprietary data from iSuppli Corp. on the annual semiconductor cost share of seven different types of computing equipment. We aggregate the product-specific cost shares with domestic shipments weights that vary from year to year. For - 45 -2012, we use the share estimated for 2011. For 1990-96, we extrapolate back the 1997 share using the annual percent changes in the estimated worldwide semiconductor share in computing equipment; we estimate these shares from a variety of proprietary data sources. Finally, for years before 1990, we set the cost share to be a shipment-weighted average of the cost shares for personal computers and all other computing equipment; in this calculation, we use the semiconductor cost shares from 1997, the earliest year for which we have the iSuppli data. Software Sector We set S SW ï¢ to zero because semiconductors are not a direct input to software production.
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- Income Shares (αj) Total Capital For 1974 to 2010, the income share for total capital is from the MFP dataset. To extend this series to 2011 and 2012, we construct capital income for the five categories of total capital that BLS provides: equipment and software, nonresidential structures, inventories, tenantoccupied rental housing, and land. We sum these estimates to generate an estimate of total capital income. The share is then the ratio of this estimate of capital income to total income in the nonfarm business sector. Finally, we take this estimate of the capital income share and difference splice it to the 2010 value of the published BLS series for the capital income share to obtain estimates of the income share for 2011 and 2012. With an estimate of the income share for capital in hand, the income share for labor equals unity minus the income share for capital. - 37 -IT Capital For 1987 to 2010, the income shares for each type of IT capital are from the MFP dataset.
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- IT Capital Deepening For 1987 to 2010, capital deepening contributions for each type of IT capital are calculated as the product of: 1) the log difference of the capital-hours ratio using real capital input for each type of IT (computer hardware, software, and communication equipment) and 2) the income share for that type of capital. The data for capital input, hours, and the income shares for each type of IT capital are from the MFP dataset.
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Jorgenson, Dale W. 2001. Information Technology and the U.S. Economy. American Economic Review 91(1): 1-32. - 31 -Jorgenson, Dale W., Mun S. Ho, and Kevin Stiroh. 2005. Productivity: Information Technology and the American Growth Resurgence (volume 3). MIT Press.
- Jorgenson, Dale W. 2012. A Prototype Industry-Level Production Account for the United States, 1947-2010. Presentation at the WIOD Conference, Groningen, The Netherlands, April 25.
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Kahn, James A., and Robert W. Rich. 2013. Update to “Tracking Productivity in Real Time,†Current Issues in Economics and Finance 12(8), November 2006. Federal Reserve Bank of New York. Available at http://www.newyorkfed.org/research/national_economy/richkahn_prodmod.pdf.
Kendrick, John W. 1961. Productivity Trends in the United States. National Bureau of Economic Research. Princeton University Press. Available at http://www.nber.org/books/kend61-1.
- Non-Depreciable Assets (Inventories and Land) To extend the stock of inventories to 2011, we take the productive stock in 2010 and add the NIPA value for the change in real private inventories for 2011. Then, to extend forward to 2012, we add the 2012 value of the change in inventories to the estimated 2011 stock. - 36 -To extend the stock of land to 2011 and 2012, we assume that the real productive stock of land in 2011 and 2012 changed at the average annual rate from 2007 to 2010. Labor Composition (q) BLS measures the change in labor composition as the difference between the growth rate of labor input and that of labor hours. To calculate labor input, BLS divides the labor force into a number of age-sex-education cells, and then constructs a weighted average of growth in hours worked in each cell, with the weight for each cell equal to its share of total labor compensation.
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Oliner, Stephen D., and Daniel E. Sichel. 1994. “Computers and Output Growth Revisited: How Big is the Puzzle?†Brookings Papers on Economic Activity 1994(2): 273-334.
Oliner, Stephen D., and Daniel E. Sichel. 2000. The Resurgence of Growth in the Late 1990s: Is Information Technology the Story? Journal of Economic Perspectives 14 (Fall): 3-22.
- Oliner, Stephen D., and Daniel E. Sichel. 2002. Information Technology and Productivity: Where Are We Now and Where Are We Going? Federal Reserve Bank of Atlanta Economic Review 87 (Third Quarter): 15-44.
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Pillai, Unni. 2013. A Model of Technological Progress in the Microprocessor Industry. Forthcoming in Journal of Industrial Economics. Available at http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1873992.
- Productive Stocks To extend the capital deepening contributions to 2011 and 2012 as described above, we used productive capital stocks to measure capital input for each category of capital, in accord with BLS methodology. For the calculations for total capital, we need productive stocks for each - 35 -of the capital categories we use to sum up to total capital (equipment, nonresidential structures, inventories, tenant-occupied rental housing, and land). For the calculations for IT capital, we need productive stocks for each of the IT capital categories (computer hardware, software, and communication equipment).
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- Real Output (Y), Current-dollar Output (pY), and Price Index (p) for the Nonfarm Business Sector Data for real output and current-dollar output for 1974-2008 are from the MFP dataset.
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- Real Output per Hour in the Nonfarm Business Sector (Y/H) Data from 1974 through 2008 are from the tables the BLS makes available with its multifactor productivity (MFP) release. We used the version of the MFP data released on March 21, 2012.27 For 2009-2012, we extended the BLS series using the annual growth rate of BLS’ series for output per hour in the nonfarm business sector from its quarterly Productivity and Cost (P&C) Release.28 We used data from the P&C release starting in 2009 so as to incorporate revisions to real output in the nonfarm business sector in the BEA’s 2012 annual revision of the National Income and Product Accounts (NIPAs).
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Reinhart, Carmen M., and Kenneth S. Rogoff. 2009. This Time is Different: Eight Centuries of Financial Folly. Princeton University Press.
- Semiconductor Sector For 1977-2012, the data source for pS is the internal Federal Reserve price index for integrated circuits (NAICS product class 3344131 back to 1992, linked to the analogous index for SIC code 36741 for 1977-92). For the years before 1977, we extrapolate back using the price index for memory chips in Grimm (1998). Because Grimm's index covers a narrower set of chips than the Federal Reserve index, we level-adjust the annual percent changes in Grimm's index by the ratio of the percent change in the Federal Reserve index to that in Grimm's index between 1977 and 1978, the earliest overlap period. Semiconductors as a Share of Current-dollar Input Costs ( S C ï¢ , S SW ï¢ , S M
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- Semiconductor Sector Here too we rely on Census shipments data. For 1987-2011, we use ASM product shipments for integrated circuits (NAICS category 3344131). We then extrapolate back in time with the annual percent changes in ASM industry shipments for semiconductors and related devices (NAICS code 334413), the closest available industry to integrated circuits. For 2012, we extrapolate the 2011 level of the ASM product shipments forward using the annual percent change in current-dollar shipments of integrated circuits calculated by Federal Reserve staff.
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- Shenoy, Sunil R., and Akhilesh Daniel. 2006. Intel Architecture and Silicon Cadence: The Catalyst for Industry Innovation. Intel white paper.
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- Software Sector For 1995 to 2011, we used NIPA data on current-dollar final sales of software, adjusted to exclude own-account software produced by the government. The data are in supplemental NIPA tables posted at http://www.bea.gov/national/info_comm_tech.htm under the headings GDP and Final Sales of Software and Software Investment and Prices, by Type.
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- Software Sector For 1995-2011, pSW is an implicit price deflator for final sales of software excluding ownaccount software produced by the government. Using NIPA data, we calculate this deflator as the ratio of current-dollar final sales excluding government own-account software (the series pSWYSW described above) to a chain aggregate of real software outlays with the same coverage.
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- Tax Adjustment (Tj) For each asset j, this adjustment is Tj = (1 - c - ï´v)/(1 - ï´), where c is the rate of investment tax credit, ï´ is the corporate tax rate, and v is the present value of $1 of tax depreciation allowances. We include a tax term (Tj) for each asset in the capital income and income share variables we construct. Through 2010, we construct the tax terms from the MFP dataset.32 For 2011 and 2012, we use the 2010 value of each tax term.
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- The data for this calculation come from the supplemental NIPA tables posted at http://www.bea.gov/national/info_comm_tech.htm under the headings GDP and Final Sales of Software and Software Investment and Prices, by Type. We extrapolate the 1995 level of the price deflator back in time and the 2011 level forward to 2012 with the annual percent change in the NIPA price index for private fixed investment in software (NIPA table 1.5.4, line 33). We did not use a trend adjustment because the price series for software investment fell at a similar rate on average over 1995-2011 as the price deflator for final sales of software.
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- The extension from 2010 to 2011 and 2012 only requires data on the components for those years, but we compile data for each component back to 1974 because the steady-state calculations require the full history.
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- Through 2010, our measure of the change in labor composition is from the MFP dataset. For 2011 and 2012, we assumed that the change in labor composition generated a contribution of 0.25 percentage point to growth in labor productivity.
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- VSLI Research Inc. (2006). Did Acceleration from a Three to Two Year Node Life Really Occur? The Chip Insider, April 6.
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Wasshausen, Dave, and Brent R. Moulton. 2006. “The Role of Hedonic Methods in Measuring Real GDP in the United States.†Available at http://bea.gov/papers/pdf/hedonicGDP.pdf. - 32 -DATA APPENDIX This appendix describes the data series used in the paper. All data are annual and cover the period from 1974 to 2012.
- We extrapolated the 1995 level back to earlier years and the 2011 level forward to 2012 using the annual percent changes in the NIPA series for private fixed investment in software (NIPA table 1.5.5, line 33).
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