## 9. Real GDP Forecasts (Y-O-Y growth rates)

## Source details

**Canonical URL:** [9. Real GDP Forecasts (Y-O-Y growth rates)](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10246.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10246.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10246.pdf.json)

---

### I. Introduction and headline forecast
- Focus: forecast of real investment in equipment and software (E&S), primary component of non-residential business fixed investment.
- Historical point: year-on-year growth rate of investment fell to minus 20 percent in 2009.
- Main forecast summary:
  - E&S investment will grow by about 10 percent on average over the 2010–12 period.
  - Long-run average growth thereafter of about 4 percent.
  - Contribution of investment to GDP growth is 0.8 percentage points on average over 2010–12.
  - Capital-to-output ratio will recover to the end-2008 level by the end of 2013 under most models considered.

### II. Modeling investment — approaches and key determinants
- Models evaluated:
  - Accelerator model (changes in real GDP up to 10 lags found statistically significant).
  - Tobin’s Q model (average Q constructed as ratio of market value of equities and credit liabilities to value of tangible assets); unadjusted Q performs better than tax-adjusted Q in R-squared; ratio of cash flow over nominal GDP improves fit.
  - Neoclassical (user cost of capital) model estimated by cointegration methods and VECM; elasticity estimated as one within VECM.
  - Bond market–based specifications (spreads, uncertainty, leverage, cash flow).
- Auxiliary variables incorporated into forecasting exercise:
  - Tobin’s Q
  - Uncertainty index (Nick Bloom)
  - Ratio of cash flow over nominal GDP
  - Spread between Baa Corporate bonds and the 10-year Treasury bill
  - Leverage ratio (debt/equity)
- Empirical regularities during the Great Recession:
  - Cash-flow/GDP increased, particularly striking during the Great Recession.
  - Spread between Baa corporate bonds and 10-year bill exceeded 500 basis points.
  - Nick Bloom’s uncertainty measure spikes during recessions.
  - Tobin’s Q dips at onset of recessions and recovers mid-to-late recession.
  - Debt/equity (leverage) behavior varies across recessions.

### III. Forecasts — VAR inputs and annual real GDP projections (Table 2)
- Annual GDP Growth (in percent) from VARs and WEO:
  - WEO: 2010 = 2.6; 2011 = 2.3; 2012 = 3.0; 2013 = 2.9; 2014 = 2.8; 2015 = 2.6
  - VAR Small: 2010 = 3.6; 2011 = 2.8; 2012 = 2.4; 2013 = 2.2; 2014 = 2.2; 2015 = 2.2
  - VAR Large: 2010 = 4.5; 2011 = 4.8; 2012 = 2.3; 2013 = 1.6; 2014 = 2.0; 2015 = 2.3

### IV. Forecasts by model type — principal quantitative results
- Accelerator model (fed with three GDP forecasts: large VAR, small VAR, WEO):
  - Large VAR-driven accelerator forecasts highest investment; negative for some quarters in 2013 before returning to long-run growth.
  - Small VAR-driven accelerator implies double-digit investment growth through mid-2012.
  - WEO-driven accelerator less optimistic for 2010–11.
- Tobin’s Q model (two representative versions: Q alone; Q plus cash flow), using large VAR forecasts:
  - Q-only forecast: about 12 percent in 2010 and 11 percent in 2011; long-run growth ~4 percent.
  - Q + cash-flow: 15 percent in 2010 and 12 percent in 2011 (cash-flow/GDP projected above historical average in 2010); growth rates decline as variables return to historical averages.
- Cost of capital (VECM) model:
  - VECM1 (small VAR GDP input): large double-digit rebound in 2010–11; long-run investment growth 4.5 percent.
  - VECM2 (large VAR GDP input): very strong recovery averaging 23.5 percent in 2010, followed by several quarters of negative growth in 2011–13, then return to 4.5 percent.
  - In both VECMs, E&S capital-output ratio returns by the end of 2014 to 41.9 percent (same value as middle of 2009:Q2).
- VAR-based unconditional forecasts:
  - Small VAR forecast for E&S investment: year-on-year investment growth reaches 11.5 percent in 2010:Q3, thereafter declining to around 3 percent y-o-y.
  - Large VAR forecast for E&S investment: growth close to 20 percent in 2010:Q4, driven by forecasted rise in Tobin’s Q and declines in uncertainty and spreads, offsetting decline in cash-flow/GDP.

### V. Model-specific numerical summaries (selected figures from Table 3)
- Annual E&S Investment Growth (in percent) — selected entries:
  - VAR Small: 2010 = 8.8; 2011 = 4.9; 2012 = 3.2; Average (2010–12) = 5.6
  - VAR Large: 2010 = 11.3; 2011 = 11.3; 2012 = 4.6; Average = 11.3
  - Accelerator Small: 2010 = 11.3; 2011 = 14.7; 2012 = 9.1; Average = 11.3
  - Accelerator Large: 2010 = 14.7; 2011 = 9.1; 2012 = 10.5; Average = 11.3
  - Tobin’s Q Baseline: 2010 = 13.1; 2011 = 10.9; 2012 = 4.6; Average = 9.1
  - Tobin’s Q with CF: 2010 = 15.2; 2011 = 19.6; 2012 = 9.4; Average = 10.5
  - User Cost VECM1: 2010 = 11.9; 2011 = 10.9; 2012 = 4.6; Average = 9.5
  - User Cost VECM2: 2010 = 15.0; 2011 = 12.1; 2012 = 4.4; Average = 10.4
- E&S Contribution to GDP Growth (in percentage points) — selected entries:
  - VAR Small: 2010 = 0.6; 2011 = 0.4; 2012 = 0.2; Average = 0.4
  - VAR Large: 2010 = 0.9; 2011 = 1.2; 2012 = 0.4; Average = 0.8
  - Accelerator Small: 2010 = 0.9; 2011 = 0.8; 2012 = 0.8; Average = 0.8
  - Tobin’s Q Baseline: 2010 = 0.9; 2011 = 0.8; 2012 = 0.8; Average = 0.7
  - Tobin’s Q with CF: 2010 = 1.0; 2011 = 1.5; 2012 = 0.8; Average = 0.8
  - User Cost VECM1: 2010 = 0.8; 2011 = 0.8; 2012 = 0.4; Average = 0.7
  - User Cost VECM2: 2010 = 1.1; 2011 = 1.1; 2012 = 0.2; Average = 0.7
- E&S Capital-Output Ratio (reported to three decimals) — selected entries:
  - VAR Small: 2010 = 0.398; 2011 = 0.391; 2012 = 0.387
  - VAR Large: 2010 = 0.398; 2011 = 0.393; 2012 = 0.398
  - Accelerator Small: 2010 = 0.401; 2011 = 0.400; 2012 = 0.406
  - Tobin’s Q Baseline: 2010 = 0.399; 2011 = 0.397; 2012 = 0.409
  - Tobin’s Q with CF: 2010 = 0.402; 2011 = 0.400; 2012 = 0.400
  - User Cost VECM1: 2010 = 0.404; 2011 = 0.404; 2012 = 0.406
  - User Cost VECM2: 2010 = 0.402; 2011 = 0.405; 2012 = 0.409

### VI. Forecast uncertainty (95 percent confidence intervals, selected entries from Table 4)
- VAR-Small 2010: Low = 3.9; High = 13.7
- VAR-Large 2010: Low = 9.9; High = 17.7
- Accelerator-Small 2010: Low = 8.4; High = 17.3
- Accelerator-Large 2010: Low = 10.7; High = 20.9
- Tobin’s Q 2010: Low = 0.1; High = 23.2
- Tobin’s Q with CF 2010: Low = 4.7; High = 24.1
- User Cost VECM1 2010: Low = -13.8; High = 47.2
- User Cost VECM2 2010: Low = -0.5; High = 49.5
- Comment: Confidence bands are particularly large for Tobin’s Q and VECM1 models, reflecting parameter and regressor-forecast uncertainty.

### VII. Comparison with other forecasts (annual business investment growth, selected entries from Table 5)
- WEO aggregate business investment: 2010 = 5.0; 2011 = 8.9
- Consensus Average: 2010 = 2.5; 2011 = 7.4
- VAR Small aggregate business investment: 2010 = -0.3; 2011 = 3.1
- VAR Large aggregate business investment: 2010 = 3.0; 2011 = 11.4
- Accelerator Small (aggregate business investment): 2010 = 2.7; 2011 = 7.7
- Tobin’s Q (aggregate): 2010 = 4.2; 2011 = 14.4
- User Cost of Capital VECM1: 2010 = 1.8; 2011 = 7.7
- User Cost of Capital VECM2: 2010 = 4.0; 2011 = 8.7

### VIII. Model diagnostics and empirical notes
- Structural breaks: Chow tests indicate structural break around 1984 (Great Moderation) in several relationships; when evidence of breaks, post-1984 samples used.
- Goodness of fit:
  - Accelerator and E&S specifications generally deliver higher R-squared and lower residual standard errors than Tobin’s Q and neoclassical single-equation specifications.
- Bond-market specifications:
  - When run in levels, spread sometimes has unexpected sign; in year-on-year changes the spread has the expected sign and is significant.
  - Key significant bond-market predictors (post-1984): leverage and cash-flow/GDP.
- Practical forecasting note: Tobin’s Q models augmented with cash flow tend to predict stronger investment given high cash-flow/GDP in the Great Recession, implying a larger negative shock to residuals to match observed 2008–09 investment collapse.

### IX. Overall assessment and conclusion
- Several representative econometric models forecast a moderate-strength rebound in E&S investment over 2010–11, reaching double-digit growth rates in 2010 and 2011, then tapering to single-digit growth and eventually the long-run average of 4–5 percent.
- Average E&S investment growth over 2010–12 across models is about 10 percent per year.
- Contribution of E&S investment to GDP growth: 0.8 percentage point on average over 2010–12.
- Considerable uncertainty surrounds forecasts, with wide 95 percent confidence intervals and sensitivity to assumptions about financial conditions (spreads), uncertainty, Tobin’s Q, and cash-flow behavior.

*Source: IMF Working Paper content unit "_wp10246 - 9. Real GDP Forecasts (Y-O-Y growth rates)".*

### References..............................................................................................................

### _wp10246 - References..............................................................................................................

### Major sections
- References......................................................................................................................................20
- Appendix........................................................................................................................................21

### Tables
- 1. Models of Investment..................................................................................................................7
- 2. Annual GDP Growth.................................................................................................................10
- 3. Summary E&S Investment........................................................................................................17
- 4. Annual Business Investment Growth........................................................................................18

### Figures
- 1. Real GDP, Investment and Capital Stock....................................................................................4
- 2. Evolution of Determinants of Investment....................................................................................8
- 3. Evolution of Determinants of Investment....................................................................................9
- 4. E&S Investment Forecasts (Y-O-Y growth rates), Accelerator Model.....................................11
- 5. E&S Investment Forecasts (Y-O-Y growth rates), Tobin’s Q model........................................12
- 6. Investment Forecasts (Y-O-Y growth rates), User Cost of Capital Model................................14
- 7. Historical and Predicted E&S Capital-Output Ratio, Cost of Capital Model............................14
- 8. Investment Forecasts (Y-O-Y growth rates)..............................................................................15

*Source: _wp10246 - References (PDF), pages and list as provided in the source content.*

### 9. Real GDP Forecasts (Y-O-Y growth rates)..............................................................................

### 9. Real GDP Forecasts (Y-O-Y growth rates)

### I. Introduction and headline forecast
- Focus: forecast of real investment in equipment and software (E&S), primary component of non-residential business fixed investment.
- Key historical point: year-on-year growth rate of investment fell to minus 20 percent in 2009.
- Main forecast summary:
  - E&S investment will grow by about 10 percent on average over the 2010–12 period.
  - Long-run average growth thereafter of about 4 percent.
  - Contribution of investment to GDP growth is 0.8 percentage points on average over 2010–12.
  - Capital-to-output ratio will recover to the end-2008 level by the end of 2013 under most models considered.

*Source: authors’ organization of paper (sections II–V).*

### II. Modeling investment — approaches and key determinants
- Models evaluated:
  - Accelerator model (changes in real GDP up to 10 lags found statistically significant).
  - Tobin’s Q model (average Q constructed as ratio of market value of equities and credit liabilities to value of tangible assets); unadjusted Q performs better than tax-adjusted Q in R-squared; ratio of cash flow over nominal GDP improves fit.
  - Neoclassical (user cost of capital) model estimated by cointegration methods and VECM; elasticity estimated as one within VECM.
  - Bond market–based specifications (spreads, uncertainty, leverage, cash flow).
- Auxiliary variables incorporated into forecasting exercise:
  - Tobin’s Q
  - Uncertainty index (Nick Bloom)
  - Ratio of cash flow over nominal GDP
  - Spread between Baa Corporate bonds and the 10-year Treasury bill
  - Leverage ratio (debt/equity)
- Notable empirical regularities during the Great Recession:
  - Cash-flow/GDP increased, particularly striking during the Great Recession.
  - Spread between Baa corporate bonds and 10-year bill exceeded 500 basis points.
  - Nick Bloom’s uncertainty measure spikes during recessions.
  - Tobin’s Q dips at onset of recessions and recovers mid-to-late recession.
  - Debt/equity (leverage) behavior varies across recessions.

### III. Forecasts — VAR inputs and annual real GDP projections (Table 2)
- Annual GDP Growth (in percent) from VARs and WEO:
  - WEO: 2010 = 2.6; 2011 = 2.3; 2012 = 3.0; 2013 = 2.9; 2014 = 2.8; 2015 = 2.6
  - VAR Small: 2010 = 3.6; 2011 = 2.8; 2012 = 2.4; 2013 = 2.2; 2014 = 2.2; 2015 = 2.2
  - VAR Large: 2010 = 4.5; 2011 = 4.8; 2012 = 2.3; 2013 = 1.6; 2014 = 2.0; 2015 = 2.3

### IV. Forecasts by model type — principal quantitative results

A. Traditional single-equation models (accelerator, Tobin’s Q, user cost of capital)
- Accelerator model (fed with three GDP forecasts: large VAR, small VAR, WEO):
  - Large VAR-driven accelerator forecasts highest investment; negative for some quarters in 2013 before returning to long-run growth.
  - Small VAR-driven accelerator implies double-digit investment growth through mid-2012.
  - WEO-driven accelerator less optimistic for 2010–11.

- Tobin’s Q model (two representative versions: Q alone; Q plus cash flow), using large VAR forecasts:
  - Q-only forecast: about 12 percent in 2010 and 11 percent in 2011; long-run growth ~4 percent.
  - Q + cash-flow: 15 percent in 2010 and 12 percent in 2011 (cash-flow/GDP projected above historical average in 2010); growth rates decline as variables return to historical averages.

- Cost of capital (VECM) model:
  - VECM1 (small VAR GDP input): large double-digit rebound in 2010–11; long-run investment growth 4.5 percent.
  - VECM2 (large VAR GDP input): very strong recovery averaging 23.5 percent in 2010, followed by several quarters of negative growth in 2011–13, then return to 4.5 percent.
  - In both VECMs, E&S capital-output ratio returns by the end of 2014 to 41.9 percent (same value as middle of 2009:Q2).

B. VAR-based unconditional forecasts (Section III.B.)
- Small VAR forecast for E&S investment:
  - Year-on-year investment growth reaches 11.5 percent in 2010:Q3, thereafter declining to around 3 percent y-o-y.
- Large VAR forecast for E&S investment:
  - Growth close to 20 percent in 2010:Q4, driven by forecasted rise in Tobin’s Q and declines in uncertainty and spreads, offsetting decline in cash-flow/GDP.

### V. Model-specific numerical summaries (Table 3 — Annual E&S investment growth, E&S contribution to GDP growth, E&S capital-output ratio)
- Annual Investment Growth (in percent) — selected entries from Table 3:
  - VAR Small: 2010 = 8.8; 2011 = 4.9; 2012 = 3.2; Average (2010–12) = 5.6
  - VAR Large: 2010 = 11.3; 2011 = 11.3; 2012 = 4.6; Average = 11.3
  - Accelerator Small: 2010 = 11.3; 2011 = 14.7; 2012 = 9.1; Average = 11.3
  - Accelerator Large: 2010 = 14.7; 2011 = 9.1; 2012 = 10.5; Average = 11.3 (note: table aligns multiple columns; above captures reported numerical values)
  - Tobin’s Q Baseline: 2010 = 13.1; 2011 = 10.9; 2012 = 4.6; Average = 9.1
  - Tobin’s Q with CF: 2010 = 15.2; 2011 = 19.6; 2012 = 9.4; Average = 10.5
  - User Cost VECM1: 2010 = 11.9; 2011 = 10.9; 2012 = 4.6; Average = 9.5
  - User Cost VECM2: 2010 = 15.0; 2011 = 12.1; 2012 = 4.4; Average = 10.4

- E&S Contribution to GDP Growth (in percentage points) — selected entries:
  - VAR Small: 2010 = 0.6; 2011 = 0.4; 2012 = 0.2; Average = 0.4
  - VAR Large: 2010 = 0.9; 2011 = 1.2; 2012 = 0.4; Average = 0.8
  - Accelerator Small: 2010 = 0.9; 2011 = 0.8; 2012 = 0.8; Average = 0.8
  - Tobin’s Q Baseline: 2010 = 0.9; 2011 = 0.8; 2012 = 0.8; Average = 0.7
  - Tobin’s Q with CF: 2010 = 1.0; 2011 = 1.5; 2012 = 0.8; Average = 0.8
  - User Cost VECM1: 2010 = 0.8; 2011 = 0.8; 2012 = 0.4; Average = 0.7
  - User Cost VECM2: 2010 = 1.1; 2011 = 1.1; 2012 = 0.2; Average = 0.7

- E&S Capital-Output Ratio in the Forecast — selected entries (values reported to three decimals):
  - VAR Small: 2010 = 0.398; 2011 = 0.391; 2012 = 0.387
  - VAR Large: 2010 = 0.398; 2011 = 0.393; 2012 = 0.398
  - Accelerator Small: 2010 = 0.401; 2011 = 0.400; 2012 = 0.406
  - Tobin’s Q Baseline: 2010 = 0.399; 2011 = 0.397; 2012 = 0.409
  - Tobin’s Q with CF: 2010 = 0.402; 2011 = 0.400; 2012 = 0.400
  - User Cost VECM1: 2010 = 0.404; 2011 = 0.404; 2012 = 0.406
  - User Cost VECM2: 2010 = 0.402; 2011 = 0.405; 2012 = 0.409

### VI. Forecast uncertainty (Table 4 — 95 percent confidence intervals for annual E&S investment growth)
- Representative 95 percent confidence intervals (selected entries):
  - VAR-Small 2010: Low = 3.9; High = 13.7
  - VAR-Large 2010: Low = 9.9; High = 17.7
  - Accelerator-Small 2010: Low = 8.4; High = 17.3
  - Accelerator-Large 2010: Low = 10.7; High = 20.9
  - Tobin’s Q 2010: Low = 0.1; High = 23.2
  - Tobin’s Q with CF 2010: Low = 4.7; High = 24.1
  - User Cost VECM1 2010: Low = -13.8; High = 47.2
  - User Cost VECM2 2010: Low = -0.5; High = 49.5
- Comment: Confidence bands are particularly large for Tobin’s Q and VECM1 models, reflecting parameter and regressor-forecast uncertainty.

### VII. Comparison with other forecasts (Table 5 — annual business investment growth)
- WEO and Consensus vs. VARs and model outputs (selected entries):
  - WEO aggregate business investment: 2010 = 5.0; 2011 = 8.9
  - Consensus Average: 2010 = 2.5; 2011 = 7.4
  - VAR Small aggregate business investment: 2010 = -0.3; 2011 = 3.1
  - VAR Large aggregate business investment: 2010 = 3.0; 2011 = 11.4
  - Accelerator Small (aggregate business investment) 2010 = 2.7; 2011 = 7.7
  - Tobin’s Q (aggregate) 2010 = 4.2; 2011 = 14.4
  - User Cost of Capital VECM1 2010 = 1.8; 2011 = 7.7
  - User Cost of Capital VECM2 2010 = 4.0; 2011 = 8.7

### VIII. Model diagnostics and empirical notes (selected)
- Structural breaks: Chow tests indicate structural break around 1984 (Great Moderation) in several relationships; when evidence of breaks, post-1984 samples used.
- Accelerator and E&S specifications generally deliver higher R-squared and lower residual standard errors than Tobin’s Q and neoclassical single-equation specifications.
- Bond-market specifications:
  - When run in levels, spread sometimes has unexpected sign; in year-on-year changes the spread has the expected sign and is significant.
  - Key significant bond-market predictors (post-1984): leverage and cash-flow/GDP.
- Practical forecasting note: Tobin’s Q models augmented with cash flow tend to predict stronger investment given high cash-flow/GDP in the Great Recession, implying a larger negative shock to residuals to match observed 2008–09 investment collapse.

### IX. Overall assessment and conclusion
- Several representative econometric models forecast a moderate-strength rebound in E&S investment over 2010–11, reaching double-digit growth rates in 2010 and 2011, then tapering to single-digit growth and eventually the long-run average of 4–5 percent.
- Average E&S investment growth over 2010–12 across models is about 10 percent per year.
- Contribution of E&S investment to GDP growth: 0.8 percentage point on average over 2010–12.
- Considerable uncertainty surrounds forecasts, with wide 95 percent confidence intervals and sensitivity to assumptions about financial conditions (spreads), uncertainty, Tobin’s Q, and cash-flow behavior.

*Source: IMF Working Paper content unit "_wp10246 - 9. Real GDP Forecasts (Y-O-Y growth rates)".*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10246.pdf_