University of Pennsylvania ScholarlyCommons Business Economics and Public Policy Papers Wharton Faculty Research 8-11-2003 IT Investment and Hicks' Composite-Good Theorem: The U.S. Experience Jaime Marquez Shing-Yi Wang Follow this and additional works at: http://repository.upenn.edu/bepp_papers Part of the Business Commons, Economics Commons, and the Public Affairs, Public Policy and Public Administration Commons Recommended Citation Marquez, J., & Wang, S. (2003). IT Investment and Hicks' Composite-Good Theorem: The U.S. Experience. FRB International Finance Discussion Paper No.767, http://dx.doi.org/10.2139/ssrn.425003 This paper is posted at ScholarlyCommons. http://repository.upenn.edu/bepp_papers/17 For more information, please contact repository@pobox.upenn.edu.
IT Investment and Hicks' Composite-Good Theorem: The U.S. Experience Abstract We study whether aggregation residuals in U.S. private investment in information technology (IT) exhibit a predictable pattern that is consistent with Hicks' composite-good theorem and that may be used for forecasting. To determine whether one can extract such a pattern, we apply the general-to-specific strategy developed by Krolzig and Hendry (2001). This strategy combines ordinary least squares with a computerautomated algorithm that selects a specification based on coefficients' statistical significance, residual properties, and parameter constancy. Then, we derive the testable implications from Hicks' theorem and evaluate them with econometric formulations; we find qualified support for these implications. Having obtained these formulations, we evaluate their ex-post predictive accuracy and compare it to that of an autoregressive model. The key finding is that ignoring movement in relative prices results in a loss of information for predicting aggregation residuals. Keywords aggregation errors, fisher aggregates, divisia aggregate, general-to-specific Disciplines Business Economics Public Affairs, Public Policy and Public Administration This working paper is available at ScholarlyCommons: http://repository.upenn.edu/bepp_papers/17
Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 767 June 2003 IT Investment and Hicks Composite-Good Theorem: The U.S. Experience Jaime Marquez and Shing-Yi Wang NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/.
IT Investment and Hicks Composite-Good Theorem: The U.S. Experience Jaime Marquez and Shing-Yi Wang * Abstract: We study whether aggregation residuals in U.S. private investment in information technology (IT) exhibit a predictable pattern that is consistent with Hicks composite-good theorem and that may be used for forecasting. To determine whether one can extract such a pattern, we apply the general-to-specific strategy developed by Krolzig and Hendry (2001). This strategy combines ordinary least squares with a computer-automated algorithm that selects a specification based on coefficients statistical significance, residual properties, and parameter constancy. Then, we derive the testable implications from Hicks theorem and evaluate them with econometric formulations; we find qualified support for these implications. Having obtained these formulations, we evaluate their ex-post predictive accuracy and compare it to that of an autoregressive model. The key finding is that ignoring movement in relative prices results in a loss of information for predicting aggregation residuals. Keywords: Aggregation Errors, Fisher Aggregates, Divisia Aggregate, General-to-Specific. * Corresponding author. e-mail address is jaime.marquez@frb.gov. We would like to thank Joe Gagnon, David Hendry, Jane Ihrig, David Lebow, and Joel Prakken for their detailed comments. We also benefited from conversations with Flint Brayton, Neil Ericsson, and Dale Henderson; we are also grateful to participants in the International Finance Workshop series for their remarks. Our calculations are based on PcGets; see Hendry and Krolzig (2001). The views in this paper are solely the responsibility of the authors and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System.
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0 Billion of 1996 Dollars GDP by Expenditure (a) GDP by Sector (b) GDP by Product (c) 0.0-2.5 Percent of GDP GDP by Expenditure GDP by Sector GDP by Product -50-100 Expenditures Sector Product Mean -6.5-3.49-7.45 Std. Dev. 14.8 2.61 7.92 ADF* -1.76-2.03-2.98-5.0 Expenditures Sector Product Mean -0.11-0.05-0.11 Std. Dev. 0.21 0.04 0.12 ADF* -1.435-1.72-2.59 Billion of 1996 Dollars 0.0 Percent of Own Aggregate 0-50 Consumption (d) Imports (e) Exports (f) Investment (g) -2.5 Consumption Imports Exports Investment Consumption Investment Exports Imports -5.0 Consumption Investment Exports Imports -100 Mean -8.2-30.6-8.53-11.65 Std. Dev. 9.0 25.5 6.87 9.92 ADF* 0.83 0.73-1.04-2.03 Mean -0.15-2.60-1.46-1.71 Std. Dev. 0.14 1.86 1.48 1.77 ADF* 0.01-0.17-1.62-2.76 * ADF test uses three lags and a constant; the 5% critical value is 2.91. Iljxuh 4= Djjuhjdwlrq Uhvlgxdov lq X1V1 Qdwlrqdo Lqfrph dqg Surgxfw Dffrxqwv1 Vrxufh= Vxuyh ri Fxuuhqw Exvlqhvv1 @ Djjuhjdwlrq uhvlgxdo iru JGS e w sh ri H{shqglwxuh +QLSD wdeoh 415,1 K Djjuhjdwlrq uhvlgxdo iru JGS e w sh ri Vhfwru +QLSD wdeoh 41:,1 S Djjuhjdwlrq uhvlgxdo iru JGS e w sh ri Surgxfw +QLSD wdeoh 417,1 _ Djjuhjdwlrq uhvlgxdo iru Frqvxpswlrq +QLSD wdeoh 516,1 e Djjuhjdwlrq uhvlgxdo iru Lpsruwv ri Jrrgv dqg Vhuylfhv +QLSD wdeoh 717,1 s Djjuhjdwlrq uhvlgxdo iru H{sruwv ri Jrrgv dqg Vhuylfhv +QLSD wdeoh 717,1 } Djjuhjdwlrq uhvlgxdo iru Sulydwh Il{hg Lqyhvwphqw +QLSD wdeoh 818,1 43
0 Billion of 1996 Dollars Billion of 1996 Dollars 0-50 -50 Published Residual for Aggregate Investment (a) Computed Residual for Investment in Non-residential Structures (b) -100-100 0 Billion of 1996 Dollars 0 Billion of 1996 Dollars -50-50 -100 Computed Residual for Investment in Equipment and Software (c) -100 Computed Residual for Residential Investment (d) 0 Billion of 1996 Dollars 0.0 Percent -50-2.5-100 Computed Residual for Investment in Information Processing Equipment (e) -5.0 Computed Residual for Investment in Information Processing Equipment and Software Relative to Own Fisher Aggregate Iljxuh 5= Djjuhjdwlrq Uhvlgxdov lq Djjuhjdwh Sulydwh Lqyhvwphqw1 Vrxufh= Vxuyh ri Fxuuhqw Exvlqhvv1 @ Djjuhjdwlrq uhvlgxdo iru Sulydwh Lqyhvwphqw +odvw olqh ri QLSD wdeoh 818,1 K Frpsxwhg e dxwkruv dv wkh glhuhqfh ehwzhhq Sulydwh Lqyhvwphqw lq Vwuxfwxuhv dqg wkh vxp ri h{shqglwxuhv rq Qrq0uhvlghqwldo Exloglqjv/ Xwlolwlhv/ Plqlqj H{sorudwlrq/ Vkdiwv dqg Zhoov/ Rwkhu Qrq0uhvlghqwldo Vwuxfwxuhv1 S Frpsxwhge dxwkruvdvwkhglhuhqfhehwzhhqwkhilvkhudjjuhjdwhirusulydwhlqyhvwphqwri Htxlsphqw dqg Vriwzduh dqg wkh vxp ri Lqirupdwlrq Surfhvvlqj Htxlsphqw dqg Vriwzduh/ Lqgxvwuldo Htxlsphqw/ Wudqvsruwdwlrq Htxlsphqw/ Rwkhu +Htxlsphqw dqg Vriwzduh,1 _ Frpsxwhg e dxwkruv dv wkh glhuhqfh ehwzhhq wkh Ilvkhu djjuhjdwh iru Sulydwh Lqyhvwphqw lq Uhvlghqwldo dqg wkh vxp ri Vlqjoh0idplo Vwuxfwxuhv/ Pxowlidplo Vwuxfwxuhv/ Rwkhu Uhvlghqwldo Vwuxfwxuhv/ dqg Uhvlghqwldo Htxlsphqw1 e Frpsxwhg e dxwkruv dv wkh glhuhqfh ehwzhhq Ilvkhu djjuhjdwh iru Sulydwh Il{hg Lqyhvwphqw lq Lqirupdwlrq Surfhvvlqj Htxlsphqw dqg Vriwzduh dqg wkh vxp ri Lqyhvwphqw lq Frpsxwhuv dqg Shulskhudo Htxlsphqw/ Vriwzduh/ dqg Rwkhu Lqirupdwlrq Surfhvvlqj Htxlsphqw dqg Vriwzduh1 44
300 Aggregate Price Index for Investment Price Index for Investment in Information Technology 150 Real Effective Exchange Rates 200 125 IMF (USD/FX) 1990 = 100 100 100 FRB(FX/USD) January 1997 = 100 25 US Dollars per barrel Unit value of Oil Imports 10.0 7.5 Percent fed. funds rate 30-year 10-year CPI Inflation 20 5.0 15 2.5 0.0 Iljxuh 6= Hyroxwlrq ri H{sodqdwru Yduldeohv1 Vrxufh= Vxuyh ri Fxuuhqw Exvlqhvv/ Exuhdx ri Oderu Vwdwlvwlfv/ Lqwhqudwlrqdo Prqhwdu Ixqg/ dqg Ihghudo Uhvhuyh Erdug1 45
0 Percent of IT Investment -5 Actual Fitted for Model M3 Estimated Parameters (standard errors) R/Y = + 0.6099*R/Y(t-1) - 40.92 + 25.75*w - 2.96*w.sqrd (0.0825) (11.8) (4.87) (0.566) Effect of "9/11" Dummy + 0.1833*p.sqrd - 45.07*q + 66.42*q.sqrd + 0.6701*r (0.059) (13.5) (19.9) (0.306) -10 + 0.1346*r(t-1) - 0.08852*r.sqrd - 0.09052*Trend + 2.581*d911 (0.0609) (0.0417) (0.0525) (0.49) SER: 0.448809 R.SQRD: 0.98507 (1988.2-2002.3) mean(r/y): -4.86629 var(r/y): 10.7005 1988 1990 1992 1994 1996 1998 2000 2002 120 Contribution of Relative Price of IT Investment (1987=100) 110 Estimated Effect of w= (25.75*w - 2.96*w.sqrd)*100/value in 1987Q1 Estimated Standard Deviation: 4:6 100 1988 1990 1992 1994 1996 1998 2000 2002 Iljxuh 7= Hpslulfdo Uhvxowv iru Prgho P60Ilwwhg Ydoxhv dqg Hhfw ri Uhodwlyh Sulfh ri LW Lqyhvwphqw 46
Percent of Aggregate Percent of Aggregate 0 1-step Forecasts Actual 0 Multi-step Forecasts Actual -5-5 -10 Model M3 RMSE 1.1% -10 Model M3 RMSE 1.6% 2000 2001 2002 2003 2000 2001 2002 2003 0 1-step Forecasts Actual 0 Multi-step Forecasts Actual -5-5 -10 Model AR(5) RMSE 1.3% -10 Model AR(5) RMSE 3.0% 2000 2001 2002 2003 2000 2001 2002 2003 Iljxuh 8= <8( Frqghqfh Lqwhuydov iru H{0srvw Iruhfdvwv ri Uhvlgxdov lq LW Lqyhvwphqw 47
Table 1: Parsimonious Model of Aggregation Residuals Private Investment in Information Equipment a Ordinary Least Square Estimation Results - 1987:Q1-2002:Q3 Sensitivity to Model Specification b M1 M2 M3 M4 M5 M6 Significant short-run price effects Linear w, p, q, r w, p, q w, q, r w, q w, q w, q Nonlinear w w, p, q w, p, q, r w, p, q w, p, q w, p, q Significant long-run price effects Linear w, r w, p, q w, q, r w, q w w, q Nonlinear w w, p, q w, p, q w, q w, q w, q Is Trend Significant? no yes no yes yes yes Adj. R 2 0.98 0.98 0.99 0.98 0.98 0.98 SER (percent) 0.46 0.45 0.45 0.45 0.47 0.45 Number of Parameters 11 14 12 13 11 13 /DJJHG'HS9DULDEOH 0.56 0.50 0.61 0.58 0.62 0.58 (std. error) (0.09) (0.10) (0.08) (0.09) (0.09) (0.09) Hypothesis Testing c Properties of Disturbances Normality 0.62 0.51 0.91 0.43 0.51 0.44 Serial Correlation 0.82 0.31 0.50 0.87 0.60 0.87 Homoskedasticity 0.14 0.84 0.56 0.40 0.48 0.40 Parameter Stability Exclude Half Sample 0.09 0.32 0.62 0.42 0.10 0.42 Exclude Last Eight Obs. 0.10 0.09 0.06 0.02* 0.14 0.02* Forecasts Error (RMSE) d Multi-step Ahead 1.78 2.01 1.64 1.80 3.66 1.80 One-step Ahead 1.04 1.13 1.11 1.08 1.40 1.08 a Aggregation residual for Private Investment in Information Equipment (NIPA table 5.5): difference between the BEA aggregate for nonresidential, private investment in information equipment and the sum of investment in computers and peripheral equipment, software, and other information processing equipment and software. q: Real effective exchange rate, r: Real interest rate, p: Price of oil relative to aggregate s own price w: Price of computer equipment purchases relative to aggregate s own price b Models differ in their choice of exchange-rate and interest-rate measures: Real Interest Rate Real Effective Federal Funds 10-year 30-year Exchange Rate IMF-Narrow M1 M2 M3 FRB-Broad M4 M5 M6 c Significance level needed to reject the associated hypothesis; an entry less than 0.05 means that one can reject the null hypothesis at the five percent significance level-denoted with an asterisk. d Root mean squared error over 2000:Q4 to 2002:Q3. 15