## Section IV the empirical approach to analyzing the impact of Brexit and investment is

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---

### Related literature
- Links to studies on trade policy regime switches and firm behavior: Handley and Limão (2015, 2017).
- Closest in spirit to Crowley, Exton and Han (2018): estimate that new entries into exporting new products to the EU by UK firms would have been over 5 percent higher in 2016 absent increased trade policy uncertainty after the June 2016 referendum.
- Draws on literature measuring impact of uncertainty on investment: Bernanke 1983; Bloom et al. 2007; Bloom 2009; Gilchrist et al. 2014.
  - Bloom et al. (2007): firms subject to greater uncertainty are more cautious in investment.
  - Redl (2017): effects of uncertainty shocks in the UK depend on source; political uncertainty shows greater GDP response.
  - Smietanka et al. (2018): rise in macroeconomic uncertainty leads firms to adjust payout policies to secure additional cash.
  - Melolinna et al. (2018): firm-specific uncertainty was a stronger driver of firm investment than user cost of capital over last 20 years, particularly after the GFC.
- Methodological foundation: difference-in-difference methodology (Ashenfelter 1978; Ashenfelter and Card 1985); overview in Imbens and Wooldridge (2009).

### Fundamental determinants of business investment in the UK (aggregate analysis)
- UK GDP growth observations:
  - Average 2.5 percent between 2013-2015.
  - 1.8 percent in 2016.
  - 1.7 percent in 2017.
  - 2.8 percent averaged annually between 2000 and 2007.
- Empirical model (Bean (1981) specification, equation (1)):
  - ∆i = α + γ1 ∆y_{t-k} + γ2 u_{t-j} + γ3 ∆u_{t-j} + γ4 (i_{t-k} − y_{t-k-?}) + ε_t (as specified in text).
  - User cost of capital proxied by sum of real interest rate on 10-year Treasury bonds and depreciation rate.
  - Estimation period: 2000Q1-2015Q4.
  - Lag choices: k=4, j=5, i chosen to maximize fit.
- Baseline regression results (dependent variable: y/y business investment growth):
  - y/y GDP growth: 1.81*** 
  - y/y GDP growth, lag 4: 1.77*** 
  - log of user cost of capital, lag 9: -0.16*** 
  - y/y growth of user cost of capital, lag 5: -0.05* 
  - log of business investment to GDP(-5), lag 4: -0.67*** 
  - constant: -1.34*** 
  - observations: 60 
  - R-squared: 0.74 
  - robust standard errors; pval: *** p<0.01, ** p<0.05, * p<0.1
- Model performance:
  - Fit relatively high over sample; performs poorly for abrupt swings before the GFC; captures post-GFC investment dynamics well.
- Out-of-sample forecast (conditional on realized GDP and user cost of capital) for 2016Q1-2018Q1:
  - Cumulative real business investment in the 9 quarters since start of 2016 was 5.5 percent lower than implied by macroeconomic fundamentals.
  - Comparable BoE (2018) nominal underperformance estimate: 3-4 percent (BoE notes real effect likely higher); model yields 5 percent real terms for 2016Q2–2017Q2.
  - Forecast robustness: results robust to i) excluding current period GDP growth, ii) including lagged level of business investment, iii) estimating until 2014Q4 and projecting from 2015Q1.

### Counterfactual GDP and decomposition exercise
- Synthetic control counterfactual GDP path (average across 7 alternative model specifications):
  - Average difference between actual GDP and counterfactual GDP path: -1.7 percent as of 2018Q1 (in real terms).
  - Applying counterfactual GDP path to the investment forecast yields total “loss” of 6.6 percent since end-2015.
  - Interpretation: business investment would have been 1.1 percent higher absent the GDP slowdown, and 5.5 percent higher if “special factors” were absent.

### Uncertainty measures and augmented aggregate model
- Uncertainty measures used to augment equation (1):
  - Economic Policy Uncertainty Index (EPU) by Baker et al. (2016).
  - London Stock Exchange Volatility Index.
  - Two macroeconomic policy uncertainty indices constructed using Jurado et al. (2015) methodology.
- Augmented model results (dependent variable: y/y business investment growth):
  - Select coefficients across specifications (1), (2), (4), (5):
    - y/y GDP growth: 1.74***; 1.80***; 1.76***; 1.80***.
    - y/y GDP growth, lag 4: 1.73***; 1.33***; 1.80***; 1.76***.
    - log of user cost of capital, lag 9: -0.21***; -0.15***; -0.17***; -0.17***.
    - y/y growth of user cost of capital, lag 5: -0.08***; -0.05*; -0.06*; -0.06*.
    - log of business investment to GDP(-5), lag 4: -0.71***; -0.69***; -0.71***; -0.71***.
    - log of EPU, lag 4: -0.02* (in one specification).
    - log of stock market volatility, lag 8: -0.05*** (in one specification).
    - macroeconomic uncertainty 1, lag 4: -0.01 (not significant).
    - macroeconomic uncertainty 2, lag 4: 0.002 (not significant).
    - Observations: 60; 58; 58; 56 respectively.
    - R-squared: 0.75; 0.78; 0.74; 0.74 respectively.
- Effect on forecast gap:
  - Adding EPU reduces the difference between predicted and actual business investment from 5.5 percent to 4.7 percent.
- Interpretation caveats:
  - Coefficients on uncertainty may not capture full impact (e.g., via GDP growth in subsequent quarters).
  - Measuring uncertainty is difficult; forward-looking, non-forecastable measures preferred but still problematic.
  - Aggregate results motivate firm-level analysis.

### Firm-level analysis: identification and data
- Conceptual channels by which Brexit could affect investment:
  - Increased uncertainty from switch in trade policy regime.
  - Increased expected future trade costs relative to pre-referendum expectations.
  - Sterling depreciation post-referendum could boost profits for firms with foreign sales.
- Identification strategy:
  - Use differentiation in firm-level exposure: foreign sales share (FSTS_i) interacted with potential trade costs (TC_i) under a “no deal” WTO scenario.
  - Specification (equation (2)):
    - inv_i = α + β X_i + γ FSTS_i + δ (FSTS_i × TC_i) + ε_i.
  - Expected signs:
    - γ (standalone FSTS_i): positive.
    - δ (interaction FSTS_i × TC_i): negative.
  - Empirical form: diff-in-diff on panel where dependent variable is post- minus pre-referendum fixed assets; pre-referendum fixed assets included in controls.
- Trade costs measure:
  - Sector-level WTO trade cost estimates from Berden et al. (2009) and Dhingra et al. (2016) used.
  - Select sector totals (Total):
    - Agriculture, forestry and fishing: 23.9
    - Mining and quarrying: 14.7
    - Food, drinks and tobacco: 24.3
    - Textiles, clothing, leather and footwear: 28.8
    - Solid fuels and oil refining: 17.4
    - Chemicals and man-made fibers: 15.7
    - Metals and metal goods: 11.0
    - Engineering and vehicles: 17.3
    - Electricity, gas and water: 6.0
    - Construction: 0.0
    - Distribution services: 21.0
    - Transport and storage: 14.1
    - Hotels and restaurants: 14.7
    - Financial intermediation: 25.4
    - Real estate, renting and business: 14.8
    - Education: 17.0
    - Health and social work: 17.0
    - Other services: 17.0
- Firm-level data and sample:
  - Balance sheet data for UK-listed non-financial companies from Datastream.
  - Focus on firms ending fiscal year in December-March.
  - After exclusions (missing data, outliers, FTSE100), sample size around 250-350 firms depending on specification.
  - Dependent variable: capital expenditure in the six quarters between 2016Q1 and 2017Q2, scaled by fixed assets at end-2015.
  - Control variables (as of end-2015): EBITDA, ROA, ROE, working capital, sales to fixed assets, total debt to common equity or total assets, interest paid on debt outstanding, market to book ratio, stock price volatility. FSTS measured as average annual value between 2013-2015.

### Firm-level results and robustness
- Main findings (Table 4, dependent variable: investment to fixed assets (in percent)):
  - Fixed assets to total assets: -0.42*** (cols 1-2); -0.38** (col 3); -0.27*** (col 4); -0.43*** (col 5).
  - EBITDA: 0.28 (col 1); 0.28 (col 2); 0.04 (col 3); 0.19 (col 4); 0.47* (col 5).
  - Sales to fixed assets: 0.002*** (cols 1-3,5); 0.001*** (col 4).
  - Total assets, log: -3.47* (cols 1-2); -3.91* (col 3); -1.38 (col 4); -3.03** (col 5).
  - Total debt to common equity: -0.08* (cols 1-3,5); -0.04* (col 4).
  - Market to book ratio: 0.0007 (col 1); 0.0006 (col 2); 0.01 (col 3); -0.0001 (col 4); -0.0009 (col 5).
  - Foreign sales to total sales (FSTS): 0.37* (col 1); 0.39* (col 2); 0.38 (col 3); 0.21** (col 4); 0.39* (col 5).
  - FSTS*WTO trade costs: -0.02** (col 1); -0.02** (col 2); -0.02* (col 3); -0.02** (col 4); -0.02** (col 5).
  - WTO trade costs (standalone, col 2): 0.18 (not significant).
  - Interest rate on debt (col 3): -0.05***.
  - Constant terms: 78.80*** (col 1); 76.24** (col 2); 84.96*** (col 3); 42.24*** (col 4); 77.09*** (col 5).
  - Sector dummies: YES in all specifications.
  - Observations: 270 (cols 1-2); 227 (col 3); 281 (col 4); 225 (col 5).
  - R-squared: 0.32; 0.32; 0.33; 0.30; 0.30 respectively.
  - Robust standard errors clustered at sector level; significance: *** p<0.01, ** p<0.05, * p<0.1.
- Robustness checks and alternative specifications:
  - Results robust to including standalone WTO trade costs and measure of cost of capital.
  - Results remain significant when:
    - Using 2016 investment as dependent variable.
    - Using alternative profitability measures (ROE, ROA) and cash measures (working capital).
    - Including stock price volatility.
    - Including dividend payouts per share.
    - Pooling pre- and post-referendum periods and estimating a 2-period panel (Appendix II).
  - Excluding firms with foreign assets > 50 percent of total assets preserves results (col 5).
  - Re-estimating equation (2) for 2014 and 2015: FSTS and FSTS×TC cease to be statistically significant in pre-referendum regressions.

### 2-period panel robustness (Appendix II)
- Panel regression setup:
  - inv_{i,t} = α + β X_{i,t} + σ I_{post} + γ1 FSTS_i + γ2 (FSTS_i × I_{post}) + δ (FSTS_i × TC_i × I_{post}) + ε_{i,t}
  - t = 0 for pre-referendum period (2014Q1-2015Q2) and t = 1 for post-referendum period (2016Q1-2017Q2).
- Selected estimation results (Table A2):
  - Fixed assets to total assets: -0.44*** (col 1); -0.41*** (col 2).
  - EBITDA: 0.00 (col 1); 0.00 (col 2).
  - Sales to fixed assets: 0.001 (col 1); 0.001* (col 2).
  - Total assets, log: -1.94** (col 1); -2.04* (col 2).
  - Total debt to common equity: -0.06*** (col 1); -0.06** (col 2).
  - Market to book ratio: 0.02*** (col 1); 0.02** (col 2).
  - Foreign sales to total sales (FSTS): 0.01 (col 1); -0.01 (col 2).
  - Post-referendum dummy: 2.23 (col 1); -0.003 (col 2).
  - FSTS*post-referendum: 0.19 (col 1); 0.25* (col 2).
  - FSTS*WTO Trade Costs*post-referendum: -0.01* (col 1); -0.01** (col 2).
  - Interest rate on debt (included in col 2): -0.001.
  - Constant: 71.85*** (col 1); 74.06*** (col 2).
  - Sector dummies included.
  - Observations: 512 (col 1); 426 (col 2).
  - R-squared: 0.25 (both columns).
  - Robust standard errors (clustered at sector level); significance: *** p<0.01, ** p<0.05, * p<0.1.
- Notes on variables:
  - Dependent variable: capital expenditure in 6 quarters between 2014Q1 and 2015Q2 or between 2016Q1 and 2017Q2, in percent of end-2013 or end-2015 fixed assets, respectively.
  - Fixed assets: net book value of plants, machinery and equipment.
  - Control variables: as of end-2013 or end-2015, in percent terms unless otherwise specified.
  - FSTS uses the average annual value between 2013-2015.
  - Column (2) includes the effective interest rate on outstanding debt.

### Interpretation, caveats, and conclusion
- Main interpretation:
  - Anticipated Brexit-related trade effects have weighed on firm investment in the UK after the referendum.
  - Post-referendum sterling depreciation has likely contributed positively to investment by more foreign-oriented firms (positive standalone FSTS coefficient).
- Caveats and limitations:
  - Interaction term FSTS×TC captures both uncertainty and expectations channels; does not identify which channel is more important.
  - Aggregate results where uncertainty measures had weak impact might suggest expectations channel more important, but measurement issues persist.
  - Firm-level identification based on differentiation in exposure does not capture average change in uncertainty affecting all firms.
  - Sample limited to listed companies; does not capture firm-size heterogeneity. Sample covers about 10 percent of private non-financial firms’ investment in 2016.
- Conclusion summary:
  - Aggregate analysis: investment underperformed fundamentals by 5.5 percent in 2016Q1-2018Q1; part of the underperformance (1.1 percentage points) attributable to slower GDP growth relative to a counterfactual; remaining underperformance linked to “special factors.”
  - Firm-level analysis: potential future trade costs under a “no deal” WTO scenario interacted with firms’ foreign exposure significantly reduced post-referendum investment; sterling depreciation partly offset this effect for more foreign-oriented firms.

*Source: wp18247 - Section IV the empirical approach to analyzing the impact of Brexit and investment is (IMF working paper content).*

### Section IV the empirical approach to analyzing the impact of Brexit and investment is

### Section IV the empirical approach to analyzing the impact of Brexit and investment is

### Related literature
- Links this paper to studies on trade policy regime switches and firm behavior: Handley and Limão (2015, 2017).
- Closest in spirit to Crowley, Exton and Han (2018): estimate that new entries into exporting new products to the EU by UK firms would have been over 5 percent higher in 2016 absent increased trade policy uncertainty after the June 2016 referendum.
- Draws on literature measuring impact of uncertainty on investment: Bernanke 1983, Bloom et al. 2007, Bloom 2009, Gilchrist et al. 2014.
  - Bloom et al. (2007): firms subject to greater uncertainty are more cautious in investment.
  - Redl (2017): effects of uncertainty shocks in the UK depend on source; political uncertainty shows greater GDP response.
  - Smietanka et al. (2018): rise in macroeconomic uncertainty leads firms to adjust payout policies to secure additional cash.
  - Melolinna et al. (2018): firm-specific uncertainty was a stronger driver of firm investment than user cost of capital over last 20 years, particularly after the GFC.
- Methodological foundation: difference-in-difference methodology (Ashenfelter 1978; Ashenfelter and Card 1985); overview in Imbens and Wooldridge (2009).

### Fundamental determinants of business investment in the UK (aggregate analysis)
- Recent UK GDP growth:
  - Average 2.5 percent between 2013-2015.
  - 1.8 percent in 2016.
  - 1.7 percent in 2017.
  - 2.8 percent averaged annually between 2000 and 2007.
- Empirical model: Bean (1981) specification (equation (1)):
  - ∆i = α + γ1 ∆y_{t-k} + γ2 u_{t-j} + γ3 ∆u_{t-j} + γ4 (i_{t-k} − y_{t-k-?}) + ε_t (as specified in text).
  - User cost of capital proxied by sum of real interest rate on 10-year Treasury bonds and depreciation rate.
  - Estimation period: 2000Q1-2015Q4.
  - Lag choices: k=4, j=5, i chosen to maximize fit.
- Baseline regression results (Table 1, dependent variable: y/y business investment growth):
  - y/y GDP growth: 1.81*** 
  - y/y GDP growth, lag 4: 1.77*** 
  - log of user cost of capital, lag 9: -0.16*** 
  - y/y growth of user cost of capital, lag 5: -0.05* 
  - log of business investment to GDP(-5), lag 4: -0.67*** 
  - constant: -1.34*** 
  - observations: 60 
  - R-squared: 0.74 
  - robust standard errors; pval: *** p<0.01, ** p<0.05, * p<0.1
- Model performance:
  - Fit relatively high over sample, performs poorly for abrupt swings before the GFC; captures post-GFC investment dynamics well.
- Out-of-sample forecast (conditional on realized GDP and user cost of capital) for 2016Q1-2018Q1:
  - Cumulative real business investment in the 9 quarters since start of 2016 was 5.5 percent lower than implied by macroeconomic fundamentals.
  - Comparable BoE (2018) nominal underperformance estimate: 3-4 percent (BoE notes real effect likely higher); model yields 5 percent real terms for 2016Q2–2017Q2.
  - Forecast robustness: results robust to i) excluding current period GDP growth, ii) including lagged level of business investment, iii) estimating until 2014Q4 and projecting from 2015Q1.

### Counterfactual GDP and decomposition exercise
- Synthetic control counterfactual GDP path (average across 7 alternative model specifications):
  - Average difference between actual GDP and counterfactual GDP path: -1.7 percent as of 2018Q1 (in real terms).
  - Applying counterfactual GDP path to the investment forecast yields total “loss” of 6.6 percent since end-2015.
  - Interpretation: business investment would have been 1.1 percent higher absent the GDP slowdown, and 5.5 percent higher if “special factors” were absent.

### Uncertainty measures and augmented aggregate model
- Uncertainty measures used to augment equation (1):
  - Economic Policy Uncertainty Index (EPU) by Baker et al. (2016).
  - London Stock Exchange Volatility Index.
  - Two macroeconomic policy uncertainty indices constructed using Jurado et al. (2015) methodology.
- Augmented model results (Table 2, dependent variable: y/y business investment growth):
  - Specification highlights:
    - Columns reported as (1), (2), (4), (5) with different uncertainty measures.
  - Select coefficients:
    - y/y GDP growth: 1.74***, 1.80***, 1.76***, 1.80*** across specs.
    - y/y GDP growth, lag 4: 1.73***, 1.33***, 1.80***, 1.76***.
    - log of user cost of capital, lag 9: -0.21***, -0.15***, -0.17***, -0.17***.
    - y/y growth of user cost of capital, lag 5: -0.08***, -0.05*, -0.06*, -0.06*.
    - log of business investment to GDP(-5), lag 4: -0.71***, -0.69***, -0.71***, -0.71***.
    - log of EPU, lag 4: -0.02* (in one specification).
    - log of stock market volatility, lag 8: -0.05*** (in one specification).
    - macroeconomic uncertainty 1, lag 4: -0.01 (not significant).
    - macroeconomic uncertainty 2, lag 4: 0.002 (not significant).
    - Observations: 60, 58, 58, 56 respectively.
    - R-squared: 0.75, 0.78, 0.74, 0.74 respectively.
- Effect on forecast gap:
  - Adding EPU reduces the difference between predicted and actual business investment from 5.5 percent to 4.7 percent.
- Interpretation caveats:
  - Coefficients on uncertainty may not capture full impact (e.g., via GDP growth in subsequent quarters).
  - Measuring uncertainty is difficult; forward-looking, non-forecastable measures preferred but still problematic.
  - Aggregate results motivate turning to firm-level analysis.

### Firm-level analysis: identification and data
- Conceptual channels by which Brexit could affect investment:
  - Increased uncertainty from switch in trade policy regime.
  - Increased expected future trade costs relative to pre-referendum expectations.
  - Sterling depreciation post-referendum could boost profits for firms with foreign sales.
- Identification strategy:
  - Use differentiation in firm-level exposure: foreign sales share (FSTS_i) interacted with potential trade costs (TC_i) under a “no deal” WTO scenario.
  - Specification (equation (2)):
    - inv_i = α + β X_i + γ FSTS_i + δ (FSTS_i × TC_i) + ε_i.
  - Expected signs:
    - γ (standalone FSTS_i): positive (sterling depreciation and global growth boost foreign-oriented firms).
    - δ (interaction FSTS_i × TC_i): negative (higher expected future trade costs and uncertainty reduce investment).
  - Empirical form: diff-in-diff on panel where dependent variable is post- minus pre-referendum fixed assets; pre-referendum fixed assets included in controls.
- Trade costs measure:
  - Sector-level WTO trade cost estimates from Berden et al. (2009) and Dhingra et al. (2016) used (Table 3: cost under WTO provisions; tariffs, non-tariff costs, total).
  - Select sector totals (Total):
    - Agriculture, forestry and fishing: 23.9
    - Mining and quarrying: 14.7
    - Food, drinks and tobacco: 24.3
    - Textiles, clothing, leather and footwear: 28.8
    - Solid fuels and oil refining: 17.4
    - Chemicals and man-made fibers: 15.7
    - Metals and metal goods: 11.0
    - Engineering and vehicles: 17.3
    - Electricity, gas and water: 6.0
    - Construction: 0.0
    - Distribution services: 21.0
    - Transport and storage: 14.1
    - Hotels and restaurants: 14.7
    - Financial intermediation: 25.4
    - Real estate, renting and business: 14.8
    - Education: 17.0
    - Health and social work: 17.0
    - Other services: 17.0
- Firm-level data and sample:
  - Balance sheet data for UK-listed non-financial companies from Datastream.
  - Focus on firms ending fiscal year in December-March.
  - After exclusions (missing data, outliers, FTSE100), sample size around 250-350 firms depending on specification.
  - Dependent variable: capital expenditure in the six quarters between 2016Q1 and 2017Q2, scaled by fixed assets at end-2015.
  - Control variables (as of end-2015): EBITDA, ROA, ROE, working capital, sales to fixed assets, total debt to common equity or total assets, interest paid on debt outstanding, market to book ratio, stock price volatility. FSTS measured as average annual value between 2013-2015.

### Firm-level results and robustness (Table 4)
- Key finding: interaction term FSTS × WTO trade costs is negative and statistically significant, indicating potential future trade costs have a negative impact on firm investment post-referendum; standalone FSTS is positive and statistically significant.
- Summary of select coefficient estimates from Table 4 (dependent variable: investment to fixed assets (in percent)):
  - Fixed assets to total assets: -0.42*** (cols 1-2), -0.38** (col 3), -0.27*** (col 4), -0.43*** (col 5).
  - EBITDA: 0.28 (col 1), 0.28 (col 2), 0.04 (col 3), 0.19 (col 4), 0.47* (col 5).
  - Sales to fixed assets: 0.002*** (cols 1-3,5), 0.001*** (col 4).
  - Total assets, log: -3.47* (cols 1-2), -3.91* (col 3), -1.38 (col 4), -3.03** (col 5).
  - Total debt to common equity: -0.08* (cols 1-3,5), -0.04* (col 4).
  - Market to book ratio: 0.0007 (col 1), 0.0006 (col 2), 0.01 (col 3), -0.0001 (col 4), -0.0009 (col 5).
  - Foreign sales to total sales (FSTS): 0.37* (col 1), 0.39* (col 2), 0.38 (col 3), 0.21** (col 4), 0.39* (col 5).
  - FSTS*WTO trade costs: -0.02** (col 1), -0.02** (col 2), -0.02* (col 3), -0.02** (col 4), -0.02** (col 5).
  - WTO trade costs (standalone, col 2): 0.18 (not negative or significant here).
  - Interest rate on debt (col 3): -0.05***.
  - Constant terms: 78.80*** (col 1), 76.24** (col 2), 84.96*** (col 3), 42.24*** (col 4), 77.09*** (col 5).
  - Sector dummies: YES in all specifications.
  - Observations: 270 (cols 1-2), 227 (col 3), 281 (col 4), 225 (col 5).
  - R-squared: 0.32, 0.32, 0.33, 0.30, 0.30 respectively.
  - Robust standard errors clustered at sector level; significance: *** p<0.01, ** p<0.05, * p<0.1.
- Robustness checks and alternative specifications:
  - Results robust to including standalone WTO trade costs and measure of cost of capital.
  - Results remain significant when:
    - Using 2016 investment as dependent variable.
    - Using alternative profitability measures (ROE, ROA) and cash measures (working capital).
    - Including stock price volatility.
    - Including dividend payouts per share.
    - Pooling pre- and post-referendum periods and estimating a 2-period panel (Appendix II).
  - Excluding firms with foreign assets > 50 percent of total assets (to remove large multinationals) preserves results (col 5).
  - Re-estimating equation (2) for 2014 and 2015: FSTS and FSTS×TC cease to be statistically significant in pre-referendum regressions, supporting interpretation that effects are post-referendum.
- Coverage note:
  - Sample of listed companies captures capital expenditure accounting for around 10 percent of total investment by private non-financial firms in 2016.

### Interpretation, caveats, and conclusion
- Main interpretation:
  - Anticipated Brexit-related trade effects have weighed on firm investment in the UK after the referendum.
  - Post-referendum sterling depreciation has likely contributed positively to investment by more foreign-oriented firms (positive standalone FSTS coefficient).
- Caveats and limitations:
  - Interaction term FSTS×TC captures both uncertainty and expectations channels; does not identify which channel is more important.
  - Aggregate results where uncertainty measures had weak impact might suggest expectations channel more important, but measurement issues persist.
  - Firm-level identification based on differentiation in exposure does not capture average change in uncertainty affecting all firms.
  - Sample limited to listed companies; does not capture firm-size heterogeneity. Sample covers about 10 percent of private non-financial firms’ investment in 2016.
- Conclusion summary:
  - Aggregate analysis: investment underperformed fundamentals by 5.5 percent in 2016Q1-2018Q1; part of the underperformance (1.1 percentage points) attributable to slower GDP growth relative to a counterfactual; remaining underperformance linked to “special factors.”
  - Firm-level analysis: potential future trade costs under a “no deal” WTO scenario interacted with firms’ foreign exposure significantly reduced post-referendum investment; sterling depreciation partly offset this effect for more foreign-oriented firms.

*Source: wp18247 - Section IV the empirical approach to analyzing the impact of Brexit and investment is (IMF working paper content).*

### References

### References

### Key citations
- Allard-Prigent, C., Audenis, C., Berger, K., Carnot, N., Duchene, S. and F. Pesin (2002), Modèle Econométrique de Simulation et d’Analyse Générale de l’Economie, French Ministry of Economy, Finance and Industry 2002.
- Ashenfelter, O. (1978), Estimating the Effect of Training Programs on Earnings, Review of Economics and Statistics 6 (1), 47–57.
- Ashenfelter, O. and D. Card (1985), Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs, Review of Economics and Statistics, 67 (4), 648–60.
- Baker, S. R., Bloom, N. and S. J. Davis (2015), Measuring Economic Policy Uncertainty, Technical Report, National Bureau of Economic Research.
- Bank of England (2018), Inflation Report, February 2018.
- Bean, C. B. (1981), An Econometric Model of Manufacturing Investment in the UK, The Economic Journal 91 (361), 106-121.
- Berden, K., Francois, J., Tamminen, S., Thelle, M. and P. Wymenga (2009), Non-Tariff Measures in EU-US Trade and Investment – An Economic Analysis, Ecorys report prepared for the European Commission, Reference OJ 2007/S180219493.
- Bernanke, B. (1983), Irreversibility, Uncertainty, and Cyclical Investment, Quarterly Journal of Economics, 98, 85-106.
- Bloom, N. (2009), The Impact of Uncertainty Shocks, Econometrica, 77, 623-685.
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### Appendix I. Measuring Macroeconomic Uncertainty

### Definition and approach
- Jurado et al. (2015) define h-period ahead uncertainty in the variable y_t as:
  - U_t(h) = E[ (y_{t+h} - E[y_{t+h} | I_t])^2 | I_t ], (A1)
  - where I_t stands for the information set available to forecasters at period t.
- A macroeconomic uncertainty index is an average of uncertainty measures of individual series y.

### Construction procedure (three-step, following Jurado et al. (2015))
- Step 1: Apply a principal component regression to a range of macroeconomic and financial variables and extract a subset of principal components (PCs).
- Step 2: For each macro variable, estimate a VAR consisting of that variable and the principal components from step 1. Use the residuals from the VAR to calculate the uncertainty index in (A1).
- Step 3: Aggregate the individual uncertainty series by averaging to derive the macroeconomic uncertainty index.

### Implementation for the UK
- Data:
  - 29 variables listed in Table A1 (grouped by Output and income; Labor market; Housing; Consumption and orders; Money and credit; Bond and interest rates, stock market; Prices).
  - Data frequency: quarterly.
  - Sample period: 2000Q1 to 2018Q1.
  - Source: Haver Analytics.
- VAR specification:
  - Three first principal components and a square of the first principal component are used in the VAR for macroeconomic index 1.
  - PCs for the squared macroeconomic variables are added to the VAR when constructing macroeconomic index 1.
  - Number of lags for macroeconomic index 1: L = 2.
  - Macroeconomic index 2: remove PCs for the squared variables and set L = 4.
- The chart (not reproduced here) plots the computed macroeconomic uncertainty indices against the Economic Policy Uncertainty (EPU) index with all variables standardized.

### Appendix II. Firm-level Analysis: Robustness

### 2-period panel regression setup
- Panel regression equation (A2):
  - inv_{i,t} = α + β X_{i,t} + σ I_{post} + γ1 FSTS_i + γ2 (FSTS_i × I_{post}) + δ (FSTS_i × TC_i × I_{post}) + ε_{i,t}
  - where t = 0 for pre-referendum period (2014Q1-2015Q2) and t = 1 for post-referendum period (2016Q1-2017Q2).
  - I_{post} is an indicator equal to 1 when t = 1.
  - Control variables X_{i,t} are as of 2014Q2 when t = 0 and as of 2015Q4 when t = 1.
  - FSTS is foreign sales to total sales; interaction term FSTS × I_{post} allows different impact across periods.

### Table A2: Business Investment and Brexit Process — 2-Period Panel Regression (Dependent variable: investment to fixed assets)
- Estimation results (two columns reported):
  - Fixed assets to total assets: -0.44*** (col 1), -0.41*** (col 2)
  - EBITDA: 0.00 (col 1), 0.00 (col 2)
  - Sales to fixed assets: 0.001 (col 1), 0.001* (col 2)
  - Total assets, log: -1.94** (col 1), -2.04* (col 2)
  - Total debt to common equity: -0.06*** (col 1), -0.06** (col 2)
  - Market to book ratio: 0.02*** (col 1), 0.02** (col 2)
  - Foreign sales to total sales (FSTS): 0.01 (col 1), -0.01 (col 2)
  - Post-referendum dummy: 2.23 (col 1), -0.003 (col 2)
  - FSTS*post-referendum: 0.19 (col 1), 0.25* (col 2)
  - FSTS*WTO Trade Costs*post-referendum: -0.01* (col 1), -0.01** (col 2)
  - Interest rate on debt: (included in col 2) -0.001
  - Constant: 71.85*** (col 1), 74.06*** (col 2)
- Additional reporting details:
  - Sector dummies included.
  - Observations: 512 (col 1), 426 (col 2)
  - R-squared: 0.25 (both columns)
  - Robust standard errors (clustered at sector level).
  - Significance notation: *** p<0.01, ** p<0.05, * p<0.1

### Notes on variables and measurement
- Dependent variable: capital expenditure in 6 quarters between 2014Q1 and 2015Q2 or between 2016Q1 and 2017Q2, in percent of end-2013 or end-2015 fixed assets, respectively.
- Fixed assets: net book value of plants, machinery and equipment.
- Control variables: as of end-2013 or end-2015, in percent terms unless otherwise specified.
- FSTS uses the average annual value between 2013-2015 to include firms reporting FSTS only every few years.
- In column (2) the effective interest rate on outstanding debt is added as an explanatory variable.

*Source: wp18247 - References (PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2018/wp18247.pdf_