## 1. Dynamics of Gross Fixed Capital Formation (GFCF)

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### Key facts on investment dynamics
- Real gross fixed capital formation (GFCF) has dropped by 20 percent over 2007–10.
- As a share of GDP, investment has declined by 5.4 percent during 2007–10 and now remains about 3 percent of GDP lower relative to its pre-crisis level.
- The post-GFC investment weakness resulted in a downward level shift in GFCF because recovery after 2010 was insufficient to compensate for losses incurred during the GFC.

### Macro implications of the investment slowdown
- Drop in labor productivity growth
  - Labor productivity (per standard production function) implied relationship: Y/L = A (K/L)^α, where Y is real output, K is capital stock, L is labor input, A is total factor productivity, and α is capital share.
  - Reduction in the capital-to-labor ratio driven by weak investment directly adversely affects labor productivity.
  - Denmark evidence: slowdown in labor productivity growth from close to 2 percent in 2010 to close to 0 percent in 2016, with contributions from the capital-to-labor ratio slowing from 0.7 percent in 2010 to -0.3 percent in 2016.
  - Note: Using output-to-hours worked ratio shows a smaller deceleration in labor productivity growth: from 1.1 percent in 2010 to 0.4 percent in 2016.
- Surge in the current account surplus
  - National accounts identity: current account balance (CAB) = aggregate savings minus investment (CAB = S - I).
  - In Denmark, both aggregate savings and investment declined after the GFC; starting from 2010, savings recovered and surpassed their pre-crisis peak in 2016, while investment recovery was sluggish.
  - The current account surplus increased from less than 2 percent of GDP in 2007 to 8 percent of GDP in 2016, largely driven by the slowdown in the investment-to-GDP ratio following the GFC.

### Purpose and roadmap of the paper
- Purpose: analyze the determinants of the investment slowdown in Denmark and identify policies to boost investment.
- Roadmap:
  - Section B: stylized facts on investment dynamics in Denmark.
  - Section C: review of determinants of investment slowdown discussed in the literature and illustration using Danish data.
  - Section D: empirical analysis using the baseline and augmented versions of the accelerator model.
  - Section E: (continues beyond excerpt).

### Investment dynamics in Denmark: stylized facts
- Total investment in Denmark peaked at 24 percent of GDP before the crisis and dropped to 18 percent of GDP in 2010.
- Real GFCF has declined by 20 percent between 2007–10, resulting in a downward level shift.
- As a share of GDP, GFCF declined by 5.4 percent from peak to trough between 2007–10.
- Nominal GFCF-to-GDP ratio decline in Denmark is more pronounced than in EU peers; real GFCF-to-GDP ratio decline is less pronounced but still larger than peers.
- Decomposition by asset classes: almost all asset classes declined post-GFC, except investment in intellectual property products.
- Decomposition by institutional sectors: the decline was mainly driven by the private sector; public sector expanded partially offsetting the decline (expansion supported by countercyclical government measures).
- Infrastructure and public capital spending:
  - Denmark’s infrastructure quality ranked 12th best in the world (World Economic Forum).
  - Government capital spending-to-GDP ratio in Denmark is one of the highest among EU peers (data for 2016 reported).
- Sectoral drivers:
  - Shift-share analysis of GFCF-to-GVA ratio over 2007–16: the decline of 4.7 percent over 2007–16 was mainly driven by within-factors (5.1 percent).
  - Some sectors (mining, manufacturing, electricity, transport, financial) saw a post-GFC GFCF-to-GVA ratio increase by 1.4 percent in total, but this was more than offset by declines in other sectors.

### Determinants of the investment slowdown
- Output (accelerator model)
  - Baseline accelerator model supports importance of output for investment dynamics, but residuals show GFCF has fallen beyond levels explained by output in much of the post-GFC period.
  - Residuals converged to zero more recently, though stronger investment would be expected given ultra-low borrowing costs.
- Additional impediments identified in literature and evidence
  - Debt overhang: GFC led to an increase in private leverage; highly indebted firms less responsive to demand fluctuations.
  - Uncertainty: uncertainty about future economic conditions can postpone lumpy, irreversible investment.
  - Financial constraints: reduced collateral values made bank lending for investment more difficult.
  - Weak competition: greater market concentration and reduced competition reduce incentives for investment.
  - Tax burden: effective tax rates and tax-base provisions affect return on investment projects.
  - Stringent product and labor market regulations: can create barriers to entry/exit and reduce incentives for investment; tightening has stronger effects than relaxation.
  - Intangible assets: shift toward intangibles can lead to understatement of private investment and different association with output.
- Denmark-specific impediments
  - Firm survey (EIB – EIBIS 2017): skilled labor shortages and uncertainty about the future are the largest investment constraints; capacity constraints rank high among EU peers.
  - Leverage: leverage in Denmark has risen since 2001 in all sectors except general government; leverage picked up around 2010 and started declining since then but remains elevated; largest build-up in private non-financial sector.
  - Denmark’s leverage reached a historical peak of about 210 percent of GDP at the outset of the crisis.
  - Product market regulation (PMR): Denmark’s PMR is relatively less restrictive compared to OECD countries and has improved over 1998–2013, but scope exists for deregulation in electricity, gas, retail, and rail sectors.

### Empirical analysis: accelerator model results
- Baseline accelerator model (Denmark, quarterly lags)
  - Most coefficients of 12 lagged output variables and their sum are significant, supporting accelerator hypothesis.
  - Table 1 estimation summary:
    - Coefficient vector (reported beginning values): 0.22 0.25** 0.33** 0.45*** 0.27* 0.41*** 0.47*** 0.24** 0.36** 0.27* 0.46*** 0.29* ‐14.76 0.02***.
    - Observations 76.
    - R-squared 0.476.
    - Sum of βs 1.475.
    - Standard error (sum of βs) 0.625.
    - t-stat (sum of βs) 2.360.
  - Residuals from baseline: persistently negative following the GFC (GFCF fell beyond output-explained level); Denmark had highest positive residuals pre-GFC and most pronounced negative unexplained component immediately post-GFC among peers.
  - Sectoral and category regressions: residuals turn negative post-GFC and remain negative through 2016 in most sectors and many GFCF categories (exceptions: financial and insurance activities sector shows positive, large residual; communications equipment category shows positive spike in 2014–15).
- Augmented accelerator model (additional controls: leverage, price markups, product market reforms, policy uncertainty)
  - Inclusion of additional controls removes persistence of negative residuals following GFC, implying factors beyond output matter.
  - Panel regressions for OECD countries (annual data, 3 lags of output) confirm:
    - Non-financial corporate leverage has a negative and significant effect on investment.
    - Competitiveness proxied by price markup has a significant negative effect (low competition adversely affects investment).
    - Policy uncertainty (EU-level) has a negative and significant effect.
    - Impact of product market reform variable is insignificant in this panel specification (possible low variability of interpolated 5-year PMR index or reverse causality).
  - Table 2 estimation summary (fixed effects, annual data 1999–2016):
    - Reported Coefficient row: 0.57*** 0.21*** 0.36***‐43.71*27.28   ‐2.10**   ‐0.04**   ‐2,881.51**
    - Standard error row: (0.07)  (0.03)  (0.06)(23.48)(15.93)   (0.95)    (0.01)    (1,319.04)
    - Observations 283.
    - R-squared 0.87.
    - Sum of βs 1.720.
    - Standard error (sum of βs) 0.194.
    - t-stat (sum of βs) 8.849.

### Diving deeper: leverage and product market reforms
- Leverage and long-run investment
  - Historical analysis using macrofinancial history database (1870–2013) for 17 advanced economies shows Denmark historically among the most leveraged.
  - At the outset of the crisis, Denmark’s leverage peaked at about 210 percent of GDP.
  - Investment-to-GDP ratio in Denmark has been relatively low since the 1970s and dropped rapidly following the GFC.
  - Regression discontinuity finds a leverage tipping point γ at which 15-year real investment growth declines rapidly:
    - Estimated tipping point γ = 87.8 percent of GDP.
    - Graphical analysis shows investment growth drops rapidly and becomes negative from the 87.8 percent discontinuity point onward.
    - Given Denmark’s leverage above 200 percent of GDP, leverage is indicated as an impediment to long-run investment growth.
- Product market reforms (PMR) and investment
  - Three empirical specifications used:
    - Model 1 (country-level reforms → aggregate investment): product market reforms have a statistically significant medium-term impact on investment; on the 5th year following reform, real investment is 4.5 percentage points higher relative to no-reform baseline.
    - Model 2 (country-level reforms → sectoral investment): product market reforms increase sectoral real investment in medium-term; average sector gains about 4 percentage points relative to no-reform baseline.
    - Model 3 (difference-in-difference with sectoral exposure Exp_s): sectors with higher “natural” turnover rates (75th percentile vs 25th percentile of U.S. distribution) see larger investment gains; at the 5th year following reform, cumulative investment gain is about 0.8 percent (differential effect).
  - Channels: PMR can boost investment by lowering markups, reducing costs of capital adjustment, affecting ownership structure, and boosting productivity and employment.
  - Denmark’s PMR standing (components, 2013) indicates scope for further deregulation in network sectors (electricity, rail, telecom, postal, gas) in areas of entry barriers, public ownership, vertical integration, market structure, and in the retail sector in areas of licenses/permits, regulation of large outlets, protection of existing firms, regulation of opening hours, and price controls.

### Conclusions and policy recommendations
- Main conclusions
  - The post-GFC weakness in Denmark’s aggregate investment cannot be fully explained by output slowdown; investment fell beyond the level explained by output movements in most of the post-GFC period.
  - The augmented accelerator model indicates additional significant factors: high leverage, weak competition (high markups), and elevated policy uncertainty.
  - Panel evidence for advanced economies shows that reductions in leverage and product market reforms can boost investment in the medium term.
- Policy recommendations
  - Reduce debt-bias
    - Leverage increased at the outset of the crisis and remains elevated despite recent declines.
    - Tax policy measures aimed at reducing “debt-bias” would reduce private sector vulnerabilities and promote additional investment.
  - Enhance competition
    - Regulations could be eased further in some sectors (network and retail sectors highlighted).
    - Specific gaps from OECD EU frontier: public ownership, vertical integration, market structure (network); licensing, regulation of large outlets, protection of existing firms, shop opening hours, price controls (retail).
    - Example: liberalizing the Planning Act to allow construction of hypermarkets that combine supermarkets and department stores was noted as warranted by the Productivity Commission.
  - Macroeconomic benefits from higher investment
    - Counterfactual simulation: 2 percentage points higher annual real investment over the 2018-22 period would result in 0.7 percent higher real output relative to the baseline in 2022.
    - Higher investment supported by PMR reforms would help reduce the current account surplus:
      - Cacciatore and others (2016): New Keynesian model — PMR reforms increase firm entry and investment, reducing current account balance.
      - Culiuc and Kyobe (2017): local projections — PMR reforms in advanced economies have a negative short-term effect on the current account balance.

### Annex I — Shift-Share Analysis of Investment Dynamics (methodology)
- Purpose: Decompose changes in the aggregate investment-to-output ratio into within-sector (changes in investment within a sector) and between-sector (changes in sectoral shares in aggregate output) effects using a shift-share methodology.
- Two-period, multi-sector decomposition formulae used to yield a breakdown into within- and between-effects that gauge their magnitude on aggregate investment-to-output dynamics.

### Annex II — The Accelerator Model (methodology)
- Framework: investment I_{i,t} depends on desired stock of capital K^*_{i,t}, its lags, and depreciation δ_{i}; accelerator postulate ΔK^*_{i,t} = κ_i ΔY_{i,t}.
- Baseline empirical specification: lagged output included to alleviate endogeneity; α_i country fixed effects; ε_{i,t} i.i.d. error.
- Augmented specification: additional determinants P_{i,t} included to capture factors driving investment; significance of γ coefficients evaluates importance of these factors.
- Estimation: fixed effects panel estimator with standard errors corrected for autocorrelation, heteroskedasticity, and intra-group correlation; alternative specifications include sectoral panels and country-specific time series regressions.

*Source: wp18161 - 1. Dynamics of Gross Fixed Capital Formation (GFCF).*

### 1. Dynamics of Gross Fixed Capital Formation (GFCF)............................................15

### Dynamics of Gross Fixed Capital Formation (GFCF)

### Key facts on investment dynamics
- Real gross fixed capital formation (GFCF) has dropped by 20 percent over 2007–10 (Figure 1, left panel).
- As a share of GDP, investment has declined by 5.4 percent during 2007–10 and now remains about 3 percent of GDP lower relative to its pre-crisis level (Figure 1, right panel).
- The post-GFC investment weakness resulted in a downward level shift in GFCF because recovery after 2010 was insufficient to compensate for losses incurred during the GFC.

### Macro implications of the investment slowdown
- Drop in labor productivity growth
  - Using the standard production function, labor productivity can be defined as: ௒ ௅ ቀܣൌ ௄ ௅ ቁ ஈ , where Y is the real output, K is the stock of capital, L is the labor input, A is the total factor productivity, and α is a constant measuring the share of capital in total output.
  - The formula implies that a reduction in the capital-to-labor ratio driven by weak investment has a direct adverse effect on labor productivity.
  - Evidence for Denmark: the rapid decline in investment following the GFC was associated with a slowdown in labor productivity growth from close to 2 percent in 2010 to close to 0 percent in 2016, suppressed by the slowdown of contributions from the capital-to-labor ratio from 0.7 percent in 2010 to -0.3 percent in 2016 (Figure 2, left and right panels).
  - Note (footnote 3 in source): Using output-to-hours worked ratio shows a smaller deceleration in labor productivity growth: from 1.1 percent in 2010 to
- Surge in the current account surplus
  - By the national accounts identity, the current account surplus equals aggregate savings minus investment (CAB = S-I).
  - In Denmark, both aggregate savings and investment declined after the GFC. Starting from 2010, savings recovered and surpassed their pre-crisis peak in 2016, while investment recovery was sluggish.
  - The current account surplus increased from less than 2 percent of GDP in 2007 to 8 percent of GDP in 2016, largely driven by the slowdown in the investment-to-GDP ratio following the GFC.

### Purpose and roadmap of the paper
- Purpose: analyze the determinants of the investment slowdown in Denmark and identify policies to boost investment.
- Roadmap (sections as presented in the source):
  - Section B: stylized facts on investment dynamics in Denmark.
  - Section C: review of determinants of investment slowdown discussed in the literature and illustration using Danish data.
  - Section D: empirical analysis using the baseline and augmented versions of the accelerator model.
  - Section E: (continues in source beyond excerpt).

*Source: wp18161 - 1. Dynamics of Gross Fixed Capital Formation (GFCF).*

### 0.4 percent in 2016.

### wp18161 - 0.4 percent in 2016.

### Investment dynamics in Denmark: stylized facts
- Total investment in Denmark peaked at 24 percent of GDP before the crisis and dropped to 18 percent of GDP in 2010.
- Real GFCF has declined by 20 percent between 2007–10, resulting in a downward level shift.
- As a share of GDP, GFCF declined by 5.4 percent from peak to trough between 2007–10.
- Nominal GFCF-to-GDP ratio decline in Denmark is more pronounced than in EU peers; real GFCF-to-GDP ratio decline is less pronounced but still larger than peers.
- Decomposition by asset classes: almost all asset classes declined post-GFC, except investment in intellectual property products.
- Decomposition by institutional sectors: the decline was mainly driven by the private sector; public sector expanded partially offsetting the decline (expansion supported by countercyclical government measures).
- Infrastructure and public capital spending:
  - Denmark’s infrastructure quality ranked 12th best in the world (World Economic Forum).
  - Government capital spending-to-GDP ratio in Denmark is one of the highest among EU peers (reported are the data for 2016).
- Sectoral drivers:
  - Shift-share analysis of GFCF-to-GVA ratio over 2007–16: the decline of 4.7 percent over 2017–16 was mainly driven by within-factors (5.1 percent). (Figure 7 text as reported.)
  - Some sectors (mining, manufacturing, electricity, transport, financial) saw a post-GFC GFCF-to-GVA ratio increase by 1.4 percent in total, but this was more than offset by declines in other sectors.

### Determinants of the investment slowdown
- Output (accelerator model):
  - Baseline accelerator model supports importance of output for investment dynamics, but residuals show GFCF has fallen beyond levels explained by output in much of the post-GFC period.
  - Residuals converged to zero more recently, though stronger investment would be expected given ultra-low borrowing costs.
- Additional impediments identified in literature and evidence:
  - Debt overhang: GFC led to an increase in private leverage; highly indebted firms less responsive to demand fluctuations.
  - Uncertainty: uncertainty about future economic conditions can postpone lumpy, irreversible investment.
  - Financial constraints: reduced collateral values made bank lending for investment more difficult.
  - Weak competition: greater market concentration and reduced competition reduce incentives for investment.
  - Tax burden: effective tax rates and tax-base provisions affect return on investment projects.
  - Stringent product and labor market regulations: can create barriers to entry/exit and reduce incentives for investment; tightening has stronger effects than relaxation.
  - Intangible assets: shift toward intangibles can lead to understatement of private investment and different association with output.
- Denmark-specific impediments:
  - Firm survey (EIB – EIBIS 2017): skilled labor shortages and uncertainty about the future are the largest investment constraints; capacity constraints rank high among EU peers.
  - Leverage: leverage in Denmark has risen since 2001 in all sectors except general government; leverage picked up around 2010 and started declining since then but remains elevated; largest build-up in private non-financial sector. Denmark’s leverage reached a historical peak of about 210 percent of GDP at the outset of the crisis.
  - Product market regulation (PMR): Denmark’s PMR is relatively less restrictive compared to OECD countries and has improved over 1998–2013, but scope exists for deregulation in electricity, gas, retail, and rail sectors.

### Empirical analysis: accelerator model results
- Baseline accelerator model (Denmark, quarterly lags):
  - Most coefficients of 12 lagged output variables and their sum are significant, supporting accelerator hypothesis.
  - Table 1 estimation summary:
    - Coefficients (1 … 12 and others) as reported in Table 1 (coefficient vector begins with 0.22 0.25** 0.33** 0.45*** 0.27* 0.41*** 0.47*** 0.24** 0.36** 0.27* 0.46*** 0.29* ‐14.76 0.02***).
    - Observations 76.
    - R-squared 0.476.
    - Sum of s 1.475.
    - Standard error (sum of s) 0.625.
    - t-stat (sum of s) 2.360.
  - Residuals from baseline: persistently negative following the GFC (GFCF fell beyond output-explained level); Denmark had highest positive residuals pre-GFC and most pronounced negative unexplained component immediately post-GFC among peers.
  - Sectoral and category regressions: residuals turn negative post-GFC and remain negative through 2016 in most sectors and many GFCF categories (exceptions: financial and insurance activities sector shows positive, large residual; communications equipment category shows positive spike in 2014–15).
- Augmented accelerator model (additional controls: leverage, price markups, product market reforms, policy uncertainty):
  - Inclusion of additional controls removes persistence of negative residuals following GFC, implying factors beyond output matter.
  - Panel regressions for OECD countries (annual data, 3 lags of output) confirm:
    - Non-financial corporate leverage has a negative and significant effect on investment.
    - Competitiveness proxied by price markup has a significant negative effect (low competition adversely affects investment).
    - Policy uncertainty (EU-level) has a negative and significant effect.
    - Impact of product market reform variable is insignificant in this panel specification (possible low variability of interpolated 5-year PMR index or reverse causality).
  - Table 2 estimation summary (fixed effects, annual data 1999–2016):
    - Reported Coefficient row (as presented): 0.57*** 0.21*** 0.36***‐43.71*27.28   ‐2.10**   ‐0.04**   ‐2,881.51**
    - Standard error row (as presented): (0.07)  (0.03)  (0.06)(23.48)(15.93)   (0.95)    (0.01)    (1,319.04)
    - Observations 283.
    - R-squared 0.87.
    - Sum of s 1.720.
    - Standard error (sum of s) 0.194.
    - t-stat (sum of s) 8.849.

### Diving deeper: leverage and product market reforms
- Leverage and long-run investment:
  - Historical analysis using macrofinancial history database (1870–2013) for 17 advanced economies shows Denmark historically among the most leveraged.
  - At the outset of the crisis, Denmark’s leverage peaked at about 210 percent of GDP.
  - Investment-to-GDP ratio in Denmark has been relatively low since the 1970s and dropped rapidly following the GFC.
  - Regression discontinuity (Gaspar and others (2016) methodology) finds a leverage tipping point γ at which 15-year real investment growth declines rapidly:
    - Estimated tipping point γ = 87.8 percent of GDP.
    - Graphical analysis shows investment growth drops rapidly and becomes negative from the 87.8 percent discontinuity point onward.
    - Given Denmark’s leverage above 200 percent of GDP, leverage is indicated as an impediment to long-run investment growth.
- Product market reforms (PMR) and investment:
  - Three empirical specifications used:
    - Model 1 (country-level reforms → aggregate investment): results show product market reforms have a statistically significant medium-term impact on investment; on the 5th year following reform, real investment is 4.5 percentage points higher relative to no-reform baseline.
    - Model 2 (country-level reforms → sectoral investment): product market reforms increase sectoral real investment in medium-term; average sector gains about 4 percentage points relative to no-reform baseline.
    - Model 3 (difference-in-difference with sectoral exposure Exp_s): sectors with higher “natural” turnover rates (75th percentile vs 25th percentile of U.S. distribution) see larger investment gains; at the 5th year following reform, cumulative investment gain is about 0.8 percent (differential effect).
  - Channels: PMR can boost investment by lowering markups, reducing costs of capital adjustment, affecting ownership structure, and boosting productivity and employment.
  - Denmark’s PMR standing (components, 2013) indicates scope for further deregulation in network sectors (electricity, rail, telecom, postal, gas) in areas of entry barriers, public ownership, vertical integration, market structure, and in the retail sector in areas of licenses/permits, regulation of large outlets, protection of existing firms, regulation of opening hours, and price controls.

### Conclusions and policy recommendations
- Main conclusions:
  - The post-GFC weakness in Denmark’s aggregate investment cannot be fully explained by output slowdown; investment fell beyond the level explained by output movements in most of the post-GFC period.
  - The augmented accelerator model indicates additional significant factors: high leverage, weak competition (high markups), and elevated policy uncertainty.
  - Panel evidence for advanced economies shows that reductions in leverage and product market reforms can boost investment in the medium term.
- Policy recommendations (targeted areas and expected macro effects):
  - Reduce debt-bias:
    - Leverage increased at the outset of the crisis and remains elevated despite recent declines.
    - Tax policy measures aimed at reducing “debt-bias” would reduce private sector vulnerabilities and promote additional investment.
  - Enhance competition:
    - Regulations could be eased further in some sectors (network and retail sectors highlighted).
    - Specific gaps from OECD EU frontier: public ownership, vertical integration, market structure (network); licensing, regulation of large outlets, protection of existing firms, shop opening hours, price controls (retail).
    - Example: liberalizing the Planning Act to allow construction of hypermarkets that combine supermarkets and department stores was noted as warranted by the Productivity Commission.
  - Macroeconomic benefits from higher investment:
    - Counterfactual simulation: 2 percentage points higher annual real investment over the 2018-22 period would result in 0.7 percent higher real output relative to the baseline in 2022.
    - Higher investment supported by PMR reforms would help reduce the current account surplus (national accounts identity and supporting theoretical/empirical studies).
      - Cacciatore and others (2016): New Keynesian model — PMR reforms increase firm entry and investment, reducing current account balance.
      - Culiuc and Kyobe (2017): local projections — PMR reforms in advanced economies have a negative short-term effect on the current account balance.

*Source: IMF staff chapter (wp18161 - 0.4 percent in 2016.)*

### REFERENCES

### wp18161 - REFERENCES (Annexes I–II extracted methodology)

### Shift-Share Analysis of Investment Dynamics (Annex I)
- Purpose: Decompose changes in the aggregate investment-to-output ratio into within-sector (changes in investment within a sector) and between-sector (changes in sectoral shares in aggregate output, a structural shift) effects using a shift-share methodology.
- Two-sector, two-period illustration:
  - Variables: Yi (sector i output), INVi (sector i investment); superscripts 0 and T denote beginning and end of period.
  - Aggregate investment-to-output ratio at time T expressed and decomposed as shown in equations (1.1)–(1.4).
  - Key decomposition expressions:
    - Difference in investment ratios between time 0 and T: equation (1.2) and alternative form equation (1.3).
    - Base-invariant decomposition using period averages as weights: equation (1.4) (bars indicate the arithmetic average over period [0, T]).
- Multi-sector extension:
  - Expression (1.5) generalizes (1.4) for N sectors and yields a breakdown into within- and between-effects that can be used to gauge the magnitude of each component.
- Use: The breakdown (within- vs between-effects) is intended to gauge the magnitude of within- and between-effects on aggregate investment-to-output dynamics.

### The Accelerator Model (Annex II)
- Framework: Adopted following IMF (2015) and EC (2017) to model investment dynamics.
- Basic model structure:
  - Investment in time t and country i (I_{i,t}) is a function of a desired stock of capital (K^*_{i,t}), its lags (up to N periods) to account for inertia, and the capital depreciation rate (δ_{i}): see equation (2.1).
  - Accelerator postulate: proportional relationship between changes in desired stock of capital and changes in output: ΔK^*_{i,t} = κ_i ΔY_{i,t} (equation (2.2)).
  - Baseline empirical specification (lagging output by one year to alleviate endogeneity): equation (2.3), where α_i is the country-specific fixed effect and ε_{i,t} is the i.i.d. error.
- Augmented specification:
  - Baseline can be augmented to include additional determinants P_{i,t} (factors driving investment, including those affected by policies): equation (2.4).
  - The significance of γs (coefficients on P) informs their importance in explaining the post-GFC investment slowdown.
- Estimation:
  - Model estimated using fixed effects panel estimator.
  - Standard errors are corrected for autocorrelation, heteroskedasticity, and intra-group correlation.
  - Alternative specifications: panel of sectors within countries (sector-specific fixed effects regressions) or individual countries/sectors (time series regressions).
- Note (footnote 17): See Jorgenson and Siebert (1968) for a theoretical derivation of the accelerator model and Oliner and others (1995) for an empirical specification based on the theory.

*Source: wp18161 - REFERENCES (Annex I and Annex II methodology).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18161.pdf_