## _wp1504 — Appendix A: Selected Empirical Findings on the Impact of Uncertainty

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### Theoretical channels and hypotheses
- Real-options
  - Core mechanism: uncertainty + sunk costs → option-value of waiting → depresses investment and entry (McDonald and Siegal 1986; Dixit 1989; Dixit and Pindyck 1994).
  - Pindyck (1993) distinction:
    - input cost uncertainty,
    - technical uncertainty.
  - Labor implications and hypothesis:
    - Hiring/firing costs include sunk components (Oi 1962; Abowd and Kramarz 2003).
    - Hypothesis 1: “Greater uncertainty is generally expected to negatively affect employment. The presence of significant levels of technological uncertainty may moderate this effect.”
- Information asymmetries and financing constraints
  - Greater uncertainty → tighter financing constraints via exacerbated information frictions (Greenwald and Stiglitz 1990a, 1990b, 1992; Greenwald, Stiglitz and Weiss 1984).
  - Smaller firms are on average less collateralized and more informationally opaque (Fazzari and others 1988; Gertler and Gilchrist 1994).
  - Hypothesis 2: “Greater uncertainty is expected to negatively affect employment, and this effect is likely to be more pronounced for smaller businesses.”
- Risk-preferences
  - Classical risk-aversion predicts lower output and altered input-mix under uncertainty (Sandmo 1971; Hartman 1972, 1973, 1976).
  - Prospect-theory / non-linear risk-preferences imply state-dependent responses; no clear uniform prediction.
  - Hypothesis 3: “Under the more classical and uniform risk-aversion assumption, greater uncertainty is expected to negatively affect employment. However, if risk-preferences are non-linear, then no clear prediction emerges.”

### Data, size classification, and uncertainty measures
- Data sources and coverage
  - U.S. Small Business Administration (SBA) database: annual data by size classes, available from 1988 to 2011.
  - U.S. macro series: Real GDP and GDP implicit price deflator (Federal Reserve Economic Data), S&P 500 (Yahoo Finance), Fuel price index (BLS).
  - Estimation sample for employment effects: 1988–2011.
  - Forecasting-estimation sample for regression-based uncertainty measures: 1960–2011 (generated series 1962–2011).
- Size classifications
  1. All businesses;
  2. Large businesses – businesses with ≥500 employees;
  3. Small businesses – businesses with <500 employees;
  4. Smaller businesses – businesses with <20 employees.
- Six alternative uncertainty measures
  - Survey-based (SPF):
    - ߪ௦௣௙௚ௗ௣,௧ଶ = SPF variance of GDP
    - ߪ௦௣௙௜௡ௗ,௧ଶ = SPF variance of industrial production
  - Regression-based (forecast-error variances; terms are measured in natural logarithms):
    - ߪ௚ௗ௣,௧ଶ = GDP uncertainty
    - ߪ௜௡௙௟,௧ଶ = inflation uncertainty
    - ߪ௦௣ହ଴଴,௧ଶ = S&P 500 uncertainty
    - ߪ௙௨௘௟,௧ଶ = fuel price uncertainty
- Construction and transformations
  - Regression baseline: AR(2) forecasting specification Z_t = α_0 + α_1 Z_{t-1} + α_2 Z_{t-2} + ε_t; uncertainty measured as variance of forecast error (squared residual).
  - Uncertainty variables enter specifications in natural logarithms (log).

### Empirical framework and estimation
- Partial-adjustment model
  - Representative firm partial-adjustment: EMP_t - EMP_{t-1} = λ (EMP_t^* - EMP_{t-1}); EMP^* modeled as function of dynamics, uncertainty, and expected GDP growth.
  - Estimated specification (notation preserved conceptually): ΔEMP_t = function(ΔGDP_t and lags, ΔEMP_{t-1} and lags, ln(uncertainty_t) and lags) + error.
  - Variables measured as logarithmic first differences (growth rates): ΔEMP_t and ΔGDP_t.
- Lag selection findings
  - Majority specifications: only one autoregressive lag of ΔEMP_t significant; ΔGDP effects captured by current and one lag; at most one lag of ln(uncertainty_t) significant.
- Estimation groups: All, Large (≥500), Small (<500), Smaller (<20).

### Main empirical findings (qualitative)
- Core stated conclusion:
  - “Uncertainty negatively affects the growth of employment and this impact appears to be concentrated primarily in the relatively smaller business category. The impact on the large business category is typically non-existent.”
- Summary of coefficient patterns
  - All businesses: uncertainty measures related to GDP, Inflation, S&P500 and Fuel prices generally have negative effects on employment growth; timing and magnitudes vary.
  - Large businesses (≥500): only Inflation and Fuel price uncertainty consistently dampen employment growth; uncertainty effects are typically smaller and often statistically insignificant.
  - Small (<500) and Smaller (<20) businesses: most uncertainty measures (survey-based and regression-based GDP, Inflation and Fuel) have negative and often statistically significant effects on employment growth.
  - Chow-tests reject equality of coefficients between Large and Small groups.

### Quantitative effects (selected exact figures preserved)
- Table 1 — mean growth of employment (annual percentage change)
  - All: Mean = 0.01103
  - Large (≥500): Mean = 0.01615
  - Small (<500): Mean = 0.00626
  - Small (<20): Mean = 0.00527
- Table 4.1 — Effect of one-s.d. increase on growth of employment (All; Large) — selected entries (asterisk denotes significance at least at 10%):
  - Growth of real GDP (ΔGDP) — All S1–S6: 0.0101*, 0.0092*, 0.0125*, 0.0105*, 0.0105*, 0.0081*.
  - Growth of real GDP lagged — All S1–S6: 0.0135*, 0.0156*, 0.0147*, 0.0167*, 0.0138*, 0.0174*.
  - Selected uncertainty effects (All / Large where reported):
    - ߪ௚ௗ௣,௧ଶ (GDP uncertainty): All 0.0058* / Large 0.0081
    - ߪ௚ௗ௣,௧ิଵ (lagged GDP uncertainty): All -0.0062* / Large -0.0054
    - ߪ௜௡௙௟,௧ிଵ (lagged inflation uncertainty): All -0.0043* / Large -0.0033*
    - ߪ௙௨௘௟,௧ (fuel price uncertainty): All -0.0058* / Large -0.0039*
- Table 4.2 — Effect of one-s.d. increase on growth of employment (Small groups) — selected entries:
  - Growth of real GDP (ΔGDP) — Small (<500) S1–S6: 0.0081*, 0.0081*, 0.0099*, 0.0098*, 0.0104*, 0.0078*.
  - Growth of real GDP (ΔGDP) — Small (<20) S1–S6: 0.0053*, 0.0076*, 0.0072*, 0.0082*, 0.0086*, 0.0068*.
  - Selected uncertainty effects (Small (<500) / Small (<20)):
    - ߪ௦௣௙௚ௗ௣,௧ଶ: -0.0019 / -0.0039*
    - ߪ௦௣௙௚ௗ௣,௧ிଵ: -0.0051* / -0.0044*
    - ߪ௦௣௙௜௡ௗ,௧: -0.0036* / -0.0037*
    - ߪ௚ௗ௣,௧ிଵ: -0.0074* / -0.0033*
    - ߪ௦௣ஹ଴଴,௧ிଵ: -0.0021* / -0.0012*
    - ߪ௙௨௘௟,௧: -0.0058* / -0.0041*
- Table 5 — Growth of Employment Specifications — Total Quantitative Effects (sum of significant effects; non-significant imputed 0.0)
  - All ܧ ത = 0.0110
    - Effects by measure (cells): 0      0      -0.0040*      -0.0043*      -0.0015*      -0.0058*       -0.0026         0.0255
  - Large (≥500) ܧ ത = 0.0161
    - Effects by measure (cells): 0                   0                   0                   -0.0033*                   0                   -0.0039*                   -0.0012                   0.0225
  - Small (<500) ܧ ത = 0.0063
    - Effects by measure (cells): -0.0051*      -0.0078*      -0.0074*      -0.0045*      -0.0021*      -0.0058*       -0.0055         0.0230
  - Smaller (<20) ܧ ത = 0.0053
    - Effects by measure (cells): -0.0083*      -0.0058*      -0.0033*      0      -0.0012*      -0.0041*      -0.0037          0.0075
  - Interpretation example (Smaller <20): one-s.d. increase in ߪ௦௣௙௚ௗ௣,௧ଶ reduces growth of employment by -0.0083 compared with mean 0.0053 (Table 4.2 illustrative computation preserved in source).
- Goodness-of-fit (selected R-squared ranges)
  - All and Large (Table 3.1): R-squared in the 75% to 87% range.
  - Small and Smaller (Table 3.2): R-squared in the 62% to 78% range.

### Robustness, interpretation, and inference on mechanisms
- Robustness checks
  - Two distinct uncertainty constructions (SPF survey and forecasting-regression residuals).
  - Multiple economy-wide variables: GDP, industrial production, S&P500, inflation, fuel prices.
  - Additional experiments (longer AR lag lengths, augmented forecasting specifications with oil prices and Federal Funds Rate, rolling-window unconditional variances) leave core inferences intact.
  - Correlation between survey-based and regression-based GDP uncertainty measures: 0.75 (Table 2).
- Mechanism interpretation
  - Evidence consistent with information-asymmetry / financing-constraints channel: smaller firms more adversely affected by uncertainty.
  - Real-options and risk-preference channels not ruled out; financing-constraints explanation receives somewhat greater empirical support given size-differential patterns.
- Limitations and suggested extensions
  - Aggregate SBA data prevent disentangling dominant theoretical channel.
  - Cannot track firms that change size class over time.
  - Recommended: use firm- or industry-level panel data and incorporate structural industry characteristics (R&D intensity, high-tech status) to better separate channels.

### Policy implications (quantitative program figures preserved)
- Support measures and rationale
  - Targeted policies to alleviate financing constraints for smaller firms may help offset uncertainty-driven employment declines.
  - Examples of U.S. initiatives cited (preserved exact figures and FY dates from source):
    - supporting more than $53 billion in SBA loan guarantees to more than 113,000 small businesses;
    - awarding more than $221 billion in Federal contracts to small businesses (FY 2009 through April 30, 2011);
    - awarding more than $4.5 billion in research funding through the Small Business Innovation and Research Program during FY 2009 and FY 2010.
- Broader rationale
  - Large fraction of employment and business counts are in smaller categories; structural trends (globalization, banking consolidation) may favor large businesses, strengthening case for policies targeting smaller firms.

*Source: Appendix A, “Selected Empirical Findings on the Impact of Uncertainty,” excerpt from IMF working paper content unit _wp1504.*

### References................................................................................................225

### _wp1504 - References................................................................................................225

### Tables
- 1    Summary Statistics.................................................................................. 33
- 2.   Person Correlation Coefficients Uncertainly Measures........................................ 34
- 3.1 Growth of Employments Specifications. Dependent Variable: EMP
୲
.......................  35
- 3.2 Growth of Employment Specifications. Dependent Variable: EMP
୲
........................  37
- 4.1 Growth of Employment Specifications Dependent Variable: EMP
୲

 Quantitative Effect of one-s.d. Increase in Driving Variable................................. 39
- 4.2 Growth of Employment Specifications Dependent Variable: EMP
୲

 Quantitative Effect of one-s.d. Increase in Driving Variable................................. 41
- 5.   Growth of Employment Specifications Total Quantitative Effects..........................  43 

### Figures
- 1.   Growth of Total Employment..................................................................... 44
- 2.   Growth of Employment in Large (≥500 employees) Businesses............................. 44
- 3.   Growth of Employment in Small (<500 employees) Businesses............................. 44
- 4.   Growth of Employment in Small (<20 employees) Businesses.............................. 44

*Source: _wp1504 - References................................................................................................225*

### Appendix A. Selected Empirical Findings on the Impact of Uncertainty........................45

### Appendix A. Selected Empirical Findings on the Impact of Uncertainty

### I. Introduction
- Theory identifies alternative channels via which uncertainty can affect firms’ decisions related to capital investment outlays, entry, exit, production, R&D expenditures and choice of technology. Three broad classes dominate: real-options, information-asymmetry driven financing-constraints, and attitudes towards risk (risk-preferences).
- Literature examines uncertainty arising from demand, prices, input costs, cashflow, project returns, technological factors, regulatory and economic policy changes.
- Empirical focus of this appendix: effects of uncertainty on employment dynamics and potential differential effects across firm size (smaller versus larger businesses).
- Motivation:
  - No formal study previously examined the effect of uncertainty on employment; Bloom, Bond and van Reenen (2007) note higher uncertainty would make employment responses to demand shocks more cautious.
  - Post-2008 crisis policy debates emphasized employment effects; Leduc and Liu (2012), Mishkin (2011), Denis and Kannan (2013) find greater uncertainty reduced employment and economic activity.
- Main reported empirical finding preview:
  - “Our main findings are that uncertainty negatively affects the growth of employment and this impact appears to be concentrated primarily in the relatively smaller business category. The impact on the large business category is typically non-existent.”
- Paper organization (as described): Section II theoretical results and hypotheses; Section III overview of empirical literature; Section IV data sources and variables; Section V construction of uncertainty measures; Sections VI–VII empirical specification and results; Section VIII conclusions and policy discussion.

### II. Theoretical Considerations
- Broad theoretical channels and their implications for employment:

  A. Real-options
  - Core idea: uncertainty + sunk costs imply option-value of waiting, depressing investment and entry (McDonald and Siegal 1986; Dixit 1989; Dixit and Pindyck 1994).
  - Pindyck (1993) distinguishes:
    - input cost uncertainty (factor prices, regulatory interventions),
    - technical uncertainty (materials, R&D, time to build).
  - Simulation results: optimal capital stock decreases with input cost uncertainty and increases with technical uncertainty; optimal capital is far more sensitive to input cost uncertainty.
  - In R&D/technology choice models, demand uncertainty can generate a U-shaped relation between demand uncertainty and R&D; technological uncertainty can generate an inverted-U shaped relation between technological uncertainty and R&D.
  - Labor implications:
    - Hiring and firing costs include variable and fixed components; some are sunk (Oi 1962; Abowd and Kramarz 2003).
    - Adjustment-cost literature finds costs of adjusting labor are typically high (Sargent 1978; Kennan 1979; Nickell 1986; Hamermesh 1992; Hamermesh and Pfann 1996; Caballero and Engel 1993; Caballero and others 1997; Cooper and Willis 2009).
    - Real-options prediction for employment:
      - Hypothesis 1: “Greater uncertainty is generally expected to negatively affect employment. The presence of significant levels of technological uncertainty may moderate this effect.”
    - Real-options channel does not deliver clear small-versus-large firm divergence.

  B. Information asymmetries and financing constraints
  - Greater uncertainty exacerbates information asymmetries between borrowers and lenders, tightens financing constraints and lowers capital outlays (Greenwald and Stiglitz 1990a, 1990b, 1992; Greenwald, Stiglitz and Weiss 1984).
  - Increased uncertainty raises bankruptcy risk; firms relying on credit and outside equity markets face rationed credit; collateral can alleviate rationing (Campbell and Cochrane 1999).
  - Smaller firms are, on average, less able to offer collateral and more informationally opaque; thus, financing-constraint effects concentrate on smaller businesses (Fazzari and others 1988; Gertler and Gilchrist 1994).
  - Gertler and Gilchrist (1994) quoted: “…the informational frictions that add to the costs of external finance apply mainly to younger firms, firms with a high degree of idiosyncratic risk, and firms that are not collateralized. These are, on average, smaller firms.”
  - Financing-constraints prediction for employment:
    - Hypothesis 2: “Greater uncertainty is expected to negatively affect employment, and this effect is likely to be more pronounced for smaller businesses.”

  C. Risk-preferences
  - Classical risk-aversion models (Sandmo 1971; Hartman 1972, 1973, 1976) predict risk-aversion leads firms to choose lower output and alter input-mix; empirical evidence shows greater uncertainty alters input-mix and lowers capital-labor ratios (Ghosal 1991, 1995).
  - Prospect-theory / non-linear risk-preferences (Kahneman and Tversky 1979; Bowman 1980, 1982; Fiegenbaum and Thomas 1988; Abdellaoui et al. 2007; Levy and Levy 2002) imply complex, state-dependent behavior; agents may be risk-seeking or risk-averse depending on returns.
  - Prediction ambiguity:
    - Hypothesis 3: “Under the more classical and uniform risk-aversion assumption, greater uncertainty is expected to negatively affect employment. However, if risk-preferences are non-linear, then no clear prediction emerges.”

### III. Empirical Evidence (Selected)
- The empirical literature is extensive; Appendix A provides a summary table (not reproduced here) covering:
  - variables used to measure uncertainty (GDP, inflation rate, prices, input costs, energy prices, stock indices, etc.);
  - statistical constructs capturing uncertainty (unconditional variance, conditional variance from forecasting regressions, survey measures);
  - levels of aggregation (firm/industry, macroeconomic);
  - estimated qualitative and quantitative effects on production, investment, R&D, inventories, entry/exit, plant openings/closings.
- Evidence on small versus large firms (primarily from investment studies):
  - Ghosal and Loungani (2000): uncertainty negatively affects investment, with greater negative impact in industries dominated by smaller firms.
  - Lensink and others (2005): uncertainty negatively impacts investment size; smaller firms have lower probability of investing when uncertainty increases.
  - Ghosal (1991): uncertainty negatively affects capital-labor ratios; larger firms’ input-mix less affected.
  - Bianco and others (2012): small family firms’ investments more negatively affected by uncertainty than larger non-family firms.
  - Ghosal and Loungani (1996): negative impact on investment concentrated in competitive/atomistic industries.
  - Li (2008): market uncertainty encourages venture capital firms to delay investing; Li and Mahoney (2011) find venture capitalists defer projects in volatile industries.
- Overall empirical impression: uncertainty may differentially affect smaller and larger firms; evidence is consistent with information-asymmetry / financing-constraints being an important mechanism.

### IV. Data Description
- Data sources used in empirical analysis:
  - U.S. Small Business Administration (SBA) database:
    - Annual data on economic and business variables by ‘size of businesses’ typically over the period 1988 to 2011.
    - Data are aggregated and presented by alternative size classes based on number of employees.
    - SBA employment data by business size classification available from 1988 onward.
  - U.S. macroeconomic series:
    - Real GDP and GDP implicit price deflator from Federal Reserve Economic Data.
    - S&P 500 stock price index from Yahoo Finance.
    - Fuel price index from U.S. Bureau of Labor Statistics (BLS) (contains gasoline, electricity, natural gas, heating oil, among others).
- Size classifications used:
  1. ‘All’ businesses;
  2. ‘Large’ businesses – businesses with ≥500 employees;
  3. ‘Small’ businesses – businesses with <500 employees;
  4. ‘Smaller’ businesses – businesses with <20 employees.
- Rationale for cutoffs:
  - 500 employee cutoff is standard used by the U.S. SBA and serves as baseline.
  - <20 cutoff considered because: (a) 500 employees is relatively large, (b) data with <20 consistent for employment and number of businesses, (c) large percentage of truly small businesses fall in this category.
- Empirical implementation:
  - Employment specifications estimated for each of the four groupings (1–4).
  - Figures and summary statistics (Figures 4, Table 1) display time paths and summary stats for employment growth by size class (not reproduced here).

### V. Measuring Uncertainty
- Uncertainty can arise from demand, input costs, and technical/project factors, as well as regulatory and policy interventions (Pindyck 1993; Dixit and Pindyck 1993, 1994).
- Because the data are U.S.-wide and aggregated by firm size, uncertainty measures are created using macroeconomic indicators.
- Alternative measures aim to capture:
  - overall uncertainty about macroeconomic conditions;
  - uncertainty arising from the cost side (input/fuel prices, etc.).
- (Construction details of specific uncertainty measures are described in later sections of the original paper.)

### Key Empirical Conclusion (as stated)
- Uncertainty negatively affects the growth of employment, with the impact concentrated primarily among relatively smaller businesses; impacts on large businesses are typically non-existent.

*Source: Appendix A, “Selected Empirical Findings on the Impact of Uncertainty” (excerpt).*

### Section 3, various papers in the literature have used a range of variables to measure uncertainty

### Section 3, various papers in the literature have used a range of variables to measure uncertainty

### Conceptual frameworks and overall approach
- Two alternative conceptual frameworks are used to construct uncertainty measures:
  - Survey-based: forecasts from the Survey of Professional Forecasters (SPF) provided by the Federal Reserve Bank of Philadelphia (spf denotes ‘survey of professional forecasters’).
  - Regression-based: forecasting-specification residual variance (conditional variance of forecast errors) from estimated time-series models.
- Six alternative variables are used to measure uncertainty (see below).
- Aim: ensure inferences are not dependent on a specific conceptual approach or single variable.

### Survey-based measures (SPF)
- Data source: Survey of Professional Forecasters (Federal Reserve Bank of Philadelphia).
- Forecasts: quarterly and annual forecasts for current year and following year; respondents attach probabilities over pre-assigned intervals; Philadelphia Fed reports mean probabilities as a histogram.
- Variables used from SPF to construct uncertainty:
  - Forecasts for growth of GDP.
  - Forecasts for growth of industrial production.
- Construction: within-year variance of survey forecasts for growth of GDP and industrial production (procedure common in the literature; Lensink, Bo and Sterken (2001, p.104-105) referenced).
- Survey-based measures labeled in the source as ߪ௦௣௙௚ௗ௣,௧ଶ and ߪ௦௣௙௜௡ௗ,௧ଶ.

### Regression-based measures (forecast-error variance)
- Procedure:
  - Assume representative firm uses a forecasting specification to predict future values of a variable (Z = real GDP growth, inflation rate, growth of S&P500 stock index, growth of real fuel prices).
  - Estimate forecasting regression; predicted values = forecastable component; residuals = unpredictable component.
  - Measure uncertainty as the variance of the forecast error (squared residual).
- Forecasting sample and rationale:
  - Available data for macroeconomic variables used from 1960 to 2011 (BLS fuel price indices available starting 1960).
  - Terminal period is 2011 (same as last period for which U.S. SBA data were available when the paper began).
  - Longer time series (1960-2011) used to obtain precisely estimated forecasting-equation parameters and recover reliable residuals; generated time-series for uncertainty measures are over the period 1962-2011.
  - Actual estimation of effects of uncertainty uses data over the period 1988-2011 (SBA employment data availability).
- Forecasting specification baseline:
  - AR(2) (second-order autoregressive) specification used as baseline forecasting model.
  - Specification (1) in source: Z_t = α_0 + α_1 Z_{t-1} + α_2 Z_{t-2} + ε_t.
  - Residual formula (2) and squared residual used as measure of uncertainty.
- Regression-based uncertainty measures obtained (denoted in source):
  - ߪ௚ௗ௣,௧ଶ (for real GDP growth)
  - ߪ௜௡௙௟,௧ଶ
  - ߪ௦௣ହ଴଴,௧ଶ
  - ߪ௙௨௘௟,௧ଶ

### Specific variables used to construct uncertainty measures
- 1. Real GDP growth — captures economy-wide demand and supply conditions; used in Driver and others (2005), Asteriou and others (2005), Bloom (2009).
- 2. Inflation rate — annual percentage growth of the GDP deflator; captures input and product price uncertainty and effects on firms’ real borrowing rates; used in Huizinga (1993), Fountas and others (2006), Elder (2004).
- 3. Stock prices — S&P500 stock price index; forward-looking indicator of investor and business confidence; used in Bloom (2009), Chen and others (2011), Bloom and others (2007), Greasley and others (2006), Stein and others (2010).
- 4. Real fuel price growth — BLS price index of commonly used fuels, deflated by the implicit GDP deflator; proxy for critical input (fuel/energy) price uncertainty; used in Koetse and others (2006), Kilian (2008), Guo and others (2005).
- Note: The source uses six alternative measures of uncertainty overall: the two SPF-based measures (GDP and industrial production within-year variances) and the four regression-residual-based measures listed above.

### Measurement choices, transformations, and robustness
- Uncertainty measures enter empirical specifications in natural logarithms (log) because mean values of uncertainty variables vary enormously across measures (see Table 1 in source); using logs avoids pure scaling effects and does not change inferences related to small versus large business differences.
- Baseline forecasting model: AR(2); results robust to including longer lag lengths and alternative specifications (experiments commented in Section VII of source).
- Correlation between survey-based and regression-based GDP uncertainty measures: 0.75 (from Table 2 in source).

### Partial-adjustment empirical framework for employment
- Theoretical basis: partial-adjustment model from quadratic cost-minimizing framework (representative firm minimizes disequilibrium and adjustment costs).
- Representative firm partial-adjustment equation (4) in source:
  - EMP_t - EMP_{t-1} = λ (EMP_t^* - EMP_{t-1}).
  - EMP^* (optimal employment) modeled as function of its intertemporal dynamics, uncertainty, and expectations of macroeconomic conditions (expected GDP growth).
- Expected GDP growth replaced by its forecasting equation; combining leads to equation (6) and then to estimated partial-adjustment specification (7).
- Estimated empirical specification (7) (notation preserved from source):
  - ΔEMP_t = (1/λ)Φ(ΔGDP_t, lags) + Ψ(ΔEMP_{t-1}, lags) + Χ(ln(uncertainty_t), lags) + error.
  - In source notation: ܲܯܧ	
ሶ
௧  etc., with ߪ(·),௧ଶ denoting uncertainty in natural logs.
- Variables measured in logarithmic first differences (growth rates): ΔEMP_t and ΔGDP_t.
- Lag selection findings from experiments:
  - Majority specifications: only one autoregressive lag of ΔEMP_t significant; in a few specs two lags significant.
  - ΔGDP effects captured by current and one lag.
  - At most one lag of the uncertainty variable ln(ߪ(·),t) significant.

### Data coverage and estimation samples
- Macroeconomic forecasting-estimation sample for constructing regression-based uncertainty measures: 1960-2011 (generated series 1962-2011).
- Estimation of employment effects uses annual SBA data over 1988-2011.
- Four aggregated employment groups estimated with specification (7):
  - (1) All businesses;
  - (2) Large businesses (≥500 employees);
  - (3) Small businesses (<500 employees);
  - (4) Smaller businesses (<20 employees).

### Estimation strategy and reported results (structure described)
- Presentation sequence in source:
  - Tables 3.1 and 3.2: estimates from specification (7) — statistical significance and qualitative inferences.
  - Tables 4.1 and 4.2: quantitative effects computed as effect of a one-standard-deviation increase in uncertainty on growth of employment.
  - Table 5: total quantitative effects aggregated and systematized, showing quantitative effects of uncertainty and relative effects versus GDP growth.
- Note in source: differences in mean variable values across regressions complicate direct interpretation of coefficients; hence one-standard-deviation computations and aggregation are used to convey magnitudes.

*Source: _wp1504 - Section 3, various papers in the literature have used a range of variables to measure uncertainty*

### 3.1 presents estimates for All and Large businesses, and Table 3.2 presents estimates for the

### _wp1504 - 3.1 presents estimates for All and Large businesses, and Table 3.2 presents estimates for the

### Model fit and core coefficient estimates
- Goodness-of-fit:
  - For All and Large businesses (Table 3.1), the ܴଶݏ′ are in the 75% to 87% range.
  - For Small and Smaller size classes (Table 3.2), the ܴଶݏ′ are in the 62% to 78% range.
- Autocorrelation:
  - Estimates of the first-order autocorrelation coefficient, ρ, are relatively low on average (both tables).
- Uncertainty effects on employment growth:
  - For All businesses: uncertainty related to GDP, Inflation, S&P500 and Fuel prices have a negative effect on the growth of employment; timing and magnitudes vary.
  - For Large businesses: only Inflation and Fuel price uncertainty dampen growth of employment; estimated coefficients are smaller than for All businesses.
  - For Small and Smaller businesses: uncertainty related to two survey-based measures, and GDP, Inflation and Fuel prices have a negative effect on growth of employment; mixed inferences for Inflation and S&P500 based measures.
- Selected coefficient examples and statistical significance (imputing 0.0 for statistically insignificant coefficients):
  - Survey-based GDP uncertainty measure (ߪ௦௣௙௚ௗ௣ଶ):
    - All group (Table 3.1, col. S1): 0.0
    - Large group (Table 3.1, col. S1): 0.0
    - Small group (Table 3.2, col. S1): -0.0039 (p-value 0.008)
  - Forecasting-based measure (ߪ௚ௗ௣ଶ):
    - All: -0.0002 (statistically significant)
    - Large: 0.0
    - Small: -0.0038 (statistically significant)
- Statistical tests:
  - Chow-tests reject the null hypothesis of equality of coefficients between the Large and Small groups.

### GDP growth and employment dynamics
- GDP growth included as control and through lagged dynamics; has significant and positive effect on growth of employment regardless of firm size.
- Magnitude comparisons:
  - For Large firms, GDP growth has a larger positive effect in a 51% to 74% range.
  - For the Smaller group (<20 employees), the effects range from 6% to 47%.
- Relative importance:
  - Quantitative effects of GDP growth are consistently larger than those of uncertainty (ߪശതതത versus ܲܦܩതതതതത).

### Quantitative effects (Tables 4.1, 4.2 and Table 5 summary)
- Methodology:
  - Tables 4.1 and 4.2 report the effect of a one-standard-deviation (one-s.d.) increase in each independent variable on growth of employment.
  - Numbers are changes in growth of employment; asterisk * denotes statistical significance at least at the 10% level.
  - Illustrative numeric example for the Smaller (<20) group:
    - For ߪ௦௣௙௚ௗ௣ശ, column S1 values are -0.0039 and -0.0044; both statistically significant.
    - Total effect = sum = -0.0083.
    - Mean growth of employment for Smaller (<20) = 0.0053.
    - Interpretation: a one-s.d. increase in ߪ௦௣௙௚ௗ௣ശ reduces growth of employment by 0.0083 (compared with mean 0.0053).
- Aggregate comparisons:
  - Difference between Large (>500 employees) and Small (<500 employees) is dramatic: Small group effect is about 4.5 times larger than the Large group.
  - Total quantitative effect for the Smaller (<20) group is somewhat smaller than for the Small (<500) size group, implying intermediate size classes may experience larger effects.
- Reporting convention for Table 5:
  - Only statistically significant effects (at least 10% level) are reported; non-significant assigned 0.0.
  - Column ߪଶതതത reports the mean value of all numbers in that row: interpreted as average estimated quantitative effect of uncertainty for that size class.
  - Column ܲܦܩതതതതത is interpreted similarly for GDP growth.

### Robustness checks
- Two distinct uncertainty-construction approaches used:
  - Survey of professional forecasters (Federal Reserve Bank of Philadelphia surveys).
  - Forecasting-regression generated measure using forecast errors.
- Multiple economy-wide variables used to measure uncertainty: GDP, industrial production, S&P500, inflation and fuel prices.
- Additional checks (not tabulated in paper due to space) that leave core inferences intact:
  - Forecasting specification (1) estimated using longer autoregressive lag lengths to generate uncertainty measures.
  - Augmented forecasting specifications including growth of oil prices and Federal Funds Rate.
  - Use of unconditional variance of GDP growth and other variables over rolling windows of three, five and seven years.
- Conclusion: results related to the impact of uncertainty on growth of employment remain intact across these checks.

### Discussion, interpretation, and policy implications
- Main finding:
  - Employment growth in Large businesses is largely insensitive to uncertainty; only GDP and stock price uncertainty show negative and significant effects on Large businesses.
  - Almost all uncertainty coefficients are significant for Small and Smaller business groups: uncertainty dampens employment growth and effects concentrate in Smaller (<20 employees) and Small (<500 employees) groups.
- Theoretical interpretation:
  - Results broadly support theoretical models discussed in Section II.
  - Real-options and risk-preference theories do not give clear firm-size differential predictions; information-asymmetry/financing-constraints theory predicts smaller firms are most adversely affected by uncertainty.
  - Authors find somewhat greater support for the financing-constraints channel given the empirical patterns.
- Policy relevance and existing U.S. measures cited (FY and counts preserved exactly as in source):
  - Recent U.S. initiatives include:
    - supporting more than $53 billion in SBA loan guarantees to more than 113,000 small businesses;
    - awarding more than $221 billion in Federal contracts to small businesses (FY 2009 through April 30, 2011);
    - awarding more than $4.5 billion in research funding through the Small Business Innovation and Research Program during FY 2009 and FY 2010.
  - Such initiatives and appropriate lending policies can help ease financing-constraints faced by smaller businesses in times of economic and financial distress and may help alleviate some negative impacts of uncertainty on smaller businesses.
- Broader rationale for policy focus on small businesses:
  - Large fraction of employment and businesses fall into smaller categories.
  - Structural factors (e.g., globalization, banking sector consolidation) may favor large businesses, strengthening case for policies targeting smaller firms.

### Limitations and suggested extensions
- Data limitations:
  - Use of U.S. Small Business Administration aggregate data prevents disentangling which theoretical channel (real-options versus financing-constraints) is dominant.
  - Cannot track firms that change size class over time, which may bias attribution of employment growth to size classes.
- Recommended extensions:
  - Use firm- or industry-level data to better test model predictions and disentangle information-asymmetry versus real-options channels.
  - Examine role of structural industry characteristics (R&D and innovation intensity) as moderators of the uncertainty–employment relationship; R&D intensity or high-tech industry status could be used alongside firm size.

*Source: Excerpt from the provided IMF working paper content unit (_wp1504) covering Tables 3.1, 3.2 and discussion sections VIII and robustness checks.*

### References

### _wp1504 - References

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### Table 1. Summary Statistics
- Variable: 1. Growth of Employment — EMP Size: All
  - Mean: 0.01103
  - Std. Dev.: 0.02258
  - C.V.: 204.7
- Variable: 1. Growth of Employment — EMP Size: Large w ≥500 employees
  - Mean: 0.01615
  - Std. Dev.: 0.02537
  - C.V.: 157.1
- Variable: 1. Growth of Employment — EMP Size: Small w <500 employees
  - Mean: 0.00626
  - Std. Dev.: 0.02158
  - C.V.: 344.7
- Variable: 1. Growth of Employment — EMP Size: Small w <20 employees
  - Mean: 0.00527
  - Std. Dev.: 0.01281
  - C.V.: 243.1
- Variable: 2. Growth of Real GDP
  - Mean: 0.02550
  - Std. Dev.: 0.01814
  - C.V.: 71.1
- Variable: 3. Uncertainty Measures — ߪ௦௣௙௚ௗ௣,௧ଶ
  - Mean: 0.17861
  - Std. Dev.: 0.25266
  - C.V.: 141.4
- Variable: 3. Uncertainty Measures — ߪ௦௣௙௜௡ௗ,௧ଶ
  - Mean: 0.51206
  - Std. Dev.: 0.73873
  - C.V.: 144.2
- Variable: 3. Uncertainty Measures — ߪ௚ௗ௣,௧ଶ
  - Mean: 0.00027
  - Std. Dev.: 0.00052
  - C.V.: 192.6
- Variable: 3. Uncertainty Measures — ߪ௜௡௙௟,௧ଶ
  - Mean: 0.00003
  - Std. Dev.: 0.00005
  - C.V.: 166.7
- Variable: 3. Uncertainty Measures — ߪௌ௉ହ଴଴,௧ଶ
  - Mean: 0.01836
  - Std. Dev.: 0.01920
  - C.V.: 104.6
- Variable: 3. Uncertainty Measures — ߪ௙௨௘௟,௧ଶ
  - Mean: 0.00842
  - Std. Dev.: 0.01281
  - C.V.: 152.1

Notes:
- 1. C.V. denotes coefficient of variation (percent).

*Source: _wp1504 - References (PDF).*

### 2. The uncertainty variables are:

### _wp1504 - 2. The uncertainty variables are:

### Definitions of uncertainty variables
- Survey of Professional Forecasters (SPF) uncertainty measures:
  - ߪ௦௣௙௚ௗ௣,௧ଶ = survey of professional forecasters variance of GDP
  - ߪ௦௣௙௜௡ௗ,௧ଶ = survey of professional forecasters variance of industrial (manufacturing) production
- Forecasting-regression generated (Estimation generated) uncertainty measures:
  - ߪ௚ௗ௣,௧ଶ = GDP uncertainty
  - ߪ௜௡௙௟,௧ଶ = inflation uncertainty
  - ߪ௦௣ହ଴଴,௧ଶ = S&P 500 uncertainty
  - ߪ௙௨௘௟,௧ଶ = fuel price uncertainty
- Note: The uncertainty terms are measured in natural logarithms.

### Table 2 — Pearson Correlation Coefficients (Uncertainty Measures)
- Correlation matrix entries (Pearson coefficients; p-values in parentheses):
  - ߪ௦௣௙௚ௗ௣,௧ଶ with:
    - ߪ௦௣௙௚ௗ௣,௧ଶ: 1.0000
    - ߪ௦௣௙௜௡ௗ,௧ଶ: 0.6543 (0.001)
    - ߪ௚ௗ௣,௧ଶ: 0.7510 (0.001)
    - ߪ௜௡௙௟,௧ଶ: 0.4144 (0.044)
    - ߪ௦௣ହ଴଴,௧ଶ: 0.4083 (0.048)
    - ߪ௙௨௘௟,௧ଶ: 0.4381 (0.032)
  - ߪ௦௣௙௜௡ௗ,௧ଶ with:
    - ߪ௦௣௙௚ௗ௣,௧ଶ: 0.6543 (0.001)
    - ߪ௦௣௙௜௡ௗ,௧ଶ: 1.0000
    - ߪ௚ௗ௣,௧ଶ: 0.7772 (0.001)
    - ߪ௜௡௙௟,௧ଶ: 0.6002 (0.002)
    - ߪ௦௣ହ଴଴,௧ଶ: 0.4559 (0.025)
    - ߪ௙௨௘௟,௧ଶ: 0.6358 (0.001)
  - ߪ௚ௗ௣,௧ଶ with:
    - ߪ௦௣௙௚ௗ௣,௧ଶ: 0.7510 (0.001)
    - ߪ௦௣௙௜௡ௗ,௧ଶ: 0.7772 (0.001)
    - ߪ௚ௗ௣,௧ଶ: 1.0000
    - ߪ௜௡௙௟,௧ଶ: 0.6941 (0.001)
    - ߪ௦௣ହ଴଴,௧ଶ: 0.5501 (0.005)
    - ߪ௙௨௘௟,௧ଶ: 0.6934 (0.001)
  - ߪ௜௡௙௟,௧ଶ with:
    - ߪ௦௣௙௚ௗ௣,௧ଶ: 0.4144 (0.044)
    - ߪ௦௣௙௜௡ௗ,௧ଶ: 0.6002 (0.002)
    - ߪ௚ௗ௣,௧ଶ: 0.6941 (0.001)
    - ߪ௜௡௙௟,௧ଶ: 1.00000
    - ߪ௦௣ହ଴଴,௧ଶ: 0.4047 (0.050)
    - ߪ௙௨௘௟,௧ଶ: 0.6288 (0.001)
  - ߪ௦௣ହ଴଴,௧ଶ with:
    - ߪ௦௣௙௚ௗ௣,௧ଶ: 0.4083 (0.048)
    - ߪ௦௣௙௜௡ௗ,௧ଶ: 0.4559 (0.025)
    - ߪ௚ௗ௣,௧ଶ: 0.5501 (0.005)
    - ߪ௜௡௙௟,௧ଶ: 0.4047 (0.050)
    - ߪ௦௣ହ଴଴,௧ଶ: 1.0000
    - ߪ௙௨௘௟,௧ଶ: 0.3688 (0.076)
  - ߪ௙௨௘௟,௧ଶ with:
    - ߪ௦௣௙௚ௗ௣,௧ଶ: 0.4381 (0.032)
    - ߪ௦௣௙௜௡ௗ,௧ଶ: 0.6358 (0.001)
    - ߪ௚ௗ௣,௧ଶ: 0.6934 (0.0002)
    - ߪ௜௡௙௟,௧ଶ: 0.6288 (0.001)
    - ߪ௦௣ହ଴଴,௧ଶ: 0.3688 (0.076)
    - ߪ௙௨௘௟,௧ଶ: 1.0000

### Table 3.1 — Growth of employment specifications (All; Large (≥500 Employee) Businesses)
- Dependent Variable: ܲܯܧ௧ = Growth (annual percentage change) of employment
- Main regressors and selected coefficients (p-values in parentheses). An * denotes significance at least at the 10% level.
  - Const. (All / Large):
    - All: -0.0264* (0.001), -0.0273* (0.001), -0.0239* (0.087), -0.0486* (0.023), -0.0314* (0.001), -0.0493* (0.001)
    - Large: -0.0183* (0.055), -0.0197* (0.001), -0.0087 (0.653), -0.0555* (0.048), -0.0243* (0.013), -0.0382* (0.001)
  - Lagged employment ܲܯܧ௧ିଵ:
    - All: -0.2261 (0.122), -0.3510* (0.070), -0.3517* (0.034), -0.4135* (0.048), -0.2208 (0.128), -0.4797* (0.0142)
    - Large: 0.1390 (0.202), 0.1867* (0.038), -0.0015 (0.992), 0.1216 (0.204), 0.1703* (0.041), 0.0185 (0.869)
  - Growth of real GDP ܲܦܩ௧:
    - All: 0.5624* (0.006), 0.5110* (0.001), 0.6924* (0.001), 0.5858* (0.001), 0.5854* (0.001), 0.4492* (0.001)
    - Large: 0.6119* (0.009), 0.5776* (0.001), 0.7452* (0.000), 0.5833* (0.001), 0.6129* (0.001), 0.5121* (0.001)
  - Growth of real GDP lagged ܲܦܩ௧ିଵ:
    - All: 0.7489* (0.002), 0.8648* (0.001), 0.8168* (0.002), 0.9315* (0.001), 0.7659* (0.001), 0.9676* (0.001)
    - Large: 0.6213* (0.002), 0.5711* (0.005), 0.6656* (0.003), 0.5516* (0.010), 0.5674* (0.003), 0.6839* (0.002)
- Selected uncertainty variable coefficients (All / Large) — coefficients shown where reported:
  - ߪ௦௣௙௚ௗ௣,௧ଶ (SPF GDP variance):
    - All: 0.0002 (0.950), -0.0025 (0.112), -0.0025 (0.112)
    - Large: 0.0010 (0.799), -0.0008 (0.696), -0.0008 (0.696)
  - ߪ௦௣௙௜௡ௗ,௧ଶ (SPF industrial variance):
    - All: -0.0017 (0.221), -0.0017 (0.262)
    - Large: -0.0019 (0.237), 0.0009 (0.613)
  - ߪ௚ௗ௣,௧ଶ (GDP uncertainty):
    - All: 0.0030* (0.063)
    - Large: 0.0042 (0.125)
  - ߪ௚ௗ௣,௧ିଵ (lagged GDP uncertainty):
    - All: -0.0032* (0.049)
    - Large: -0.0028 (0.178)
  - ߪ௜௡௙௟,௧ଶ (inflation uncertainty):
    - All: 0.0004 (0.795)
    - Large: -0.0015 (0.465)
  - ߪ௜௡௙௟,௧ିଵ (lagged inflation uncertainty):
    - All: -0.0026* (0.027)
    - Large: -0.0020* (0.091)
  - ߪ௦௣ହ଴଴,௧ଶ (S&P 500 uncertainty):
    - All: -0.0004 (0.541)
    - Large: 0.0001 (0.903)
  - ߪ௦௣ହ଴଴,௧ିଵ (lagged S&P 500 uncertainty):
    - All: -0.0014* (0.099)
    - Large: -0.0013 (0.158)
  - ߪ௙௨௘௟,௧ଶ (fuel price uncertainty):
    - All: -0.0038* (0.002)
    - Large: -0.0026* (0.081)
  - ߪ௙௨௘௟,௧ிଵ (lagged fuel price uncertainty):
    - All: -0.0017 (0.150)
    - Large: -0.0017 (0.159)
- Goodness-of-fit and autocorrelation (selected):
  - R-squared (ܴଶ) All: 0.806, 0.825, 0.833, 0.819, 0.819, 0.882
  - R-squared (ܴଶ) Large: 0.752, 0.764, 0.798, 0.770, 0.762, 0.789
  - First-order autocorrelation coefficient (ρ) All: 0.177, 0.225, 0.147, 0.264, 0.036, -0.133
  - ρ Large: 0.144, 0.113, 0.051, 0.158, 0.079, -0.067

### Table 3.2 — Growth of employment specifications (Small (<500 Employee) and Small (<20 Employee) Businesses)
- Dependent Variable: ܲܯܧ௧
- Selected coefficients (p-values in parentheses). An * denotes significance at least at the 10% level.
  - Const. (Small <500 / Small <20):
    - Small (<500): -0.0359* (0.001), -0.0346* (0.001), -0.0563* (0.001), -0.0687* (0.016), -0.0370* (0.001), -0.0480* (0.001)
    - Small (<20): -0.0192* (0.001), -0.0153* (0.001), -0.0384* (0.001), -0.0279 (0.151), -0.0174* (0.001), -0.0221* (0.013)
  - Lagged employment ܲܯܧ௧ିଵ:
    - Small (<500): -0.4107* (0.012), -0.5815* (0.002), -0.4837* (0.007), -0.5318* (0.018), -0.3907* (0.042), -0.5465* (0.004)
    - Small (<20): 0.0943 (0.594), -0.0239 (0.873), -0.0322 (0.862), 0.1030 (0.637), 0.1013 (0.581), 0.0136 (0.941)
  - Growth of real GDP ܲܦܩ௧:
    - Small (<500): 0.4495* (0.046), 0.4492* (0.001), 0.5554* (0.002), 0.5503* (0.001), 0.5806* (0.001), 0.4363* (0.001)
    - Small (<20): 0.2969* (0.007), 0.4223* (0.001), 0.3990* (0.001), 0.4519* (0.001), 0.4792* (0.001), 0.3781* (0.001)
  - Growth of real GDP lagged ܲܦܩ௧ିଵ:
    - Small (<500): 0.7867* (0.001), 0.8903 (0.001), 0.7612* (0.003), 0.8475* (0.004), 0.7603* (0.003), 0.9219* (0.001)
    - Small (<20): 0.1232 (0.315), 0.0676 (0.532), 0.1040 (0.473), 0.0551 (0.723), 0.0625 (0.671), 0.1813 (0.1053)
- Selected uncertainty variable coefficients (Small groups):
  - ߪ௦௣௙௚ௗ௣,௧ଶ (SPF GDP variance):
    - Small (<500): -0.0014 (0.658)
    - Small (<20): -0.0028* (0.063)
  - ߪ௦௣௙௚ௗ௣,௧ிଵ:
    - Small (<500): -0.0039* (0.008)
    - Small (<20): -0.0031* (0.004)
  - ߪ௦௣௙௜௡ௗ,௧:
    - Small (<500): -0.0025* (0.051)
    - Small (<20): -0.0026* (0.001)
  - ߪ௦௣௙௜௡ௗ,௧ிଵ:
    - Small (<500): -0.0029* (0.014)
    - Small (<20): -0.0015* (0.039)
  - ߪ௚ௗ௣,௧:
    - Small (<500): 0.0004 (0.819)
    - Small (<20): -0.0015 (0.236)
  - ߪ௚ௗ௣,௧ிଵ:
    - Small (<500): -0.0038* (0.010)
    - Small (<20): -0.0017* (0.063)
  - ߪ௜௡௙௟,௧:
    - Small (<500): -0.0010 (0.594)
    - Small (<20): -0.0014 (0.208)
  - ߪ௜௡௙௟,௧ிଵ:
    - Small (<500): -0.0027* (0.075)
    - Small (<20): -0.0003 (0.809)
  - ߪ௦௣ହ଴଴,௧:
    - Small (<500): -0.0001 (0.861)
    - Small (<20): -0.0003 (0.562)
  - ߪ௦௣ହ଴଴,௧ிଵ:
    - Small (<500): -0.0020* (0.030)
    - Small (<20): -0.0012* (0.036)
  - ߪ௙௨௘௟,௧:
    - Small (<500): -0.0038* (0.003)
    - Small (<20): -0.0027* (0.0033)
  - ߪ௙௨௘௟,௧ிଵ:
    - Small (<500): -0.0006 (0.692)
    - Small (<20): -0.0001 (0.899)
- Goodness-of-fit and autocorrelation (selected):
  - R-squared (ܴଶ) Small (<500): 0.749, 0.796, 0.773, 0.741, 0.755, 0.795
  - R-squared (ܴଶ) Small (<20): 0.745, 0.768, 0.724, 0.629, 0.667, 0.754
  - ρ Small (<500): 0.124, 0.134, 0.241, 0.213, 0.111, 0.160
  - ρ Small (<20): 0.001, 0.063, 0.117, 0.066, 0.113, 0.095

### Table 4.1 — Quantitative effect of one-s.d. increase in driving variables (All; Large)
- Dependent variable: ܲܯܧ௧
- Mean growth of employment:
  - Size Group: All Businesses — Mean growth of employment=0.0110
  - Size Group: Large (≥500 Employee) Businesses — Mean growth of employment=0.0161
- Effect of one-standard-deviation increase (selected; asterisk denotes significance at least at the 10% level):
  - Growth of real GDP ܲܦܩ௧:
    - All S1–S6: 0.0101*, 0.0092*, 0.0125*, 0.0105*, 0.0105*, 0.0081*
    - Large S1–S6: 0.0110*, 0.0104*, 0.0134*, 0.0105*, 0.0110*, 0.0092*
  - Growth of real GDP lagged ܲܦܩ௧ิଵ:
    - All S1–S6: 0.0135*, 0.0156*, 0.0147*, 0.0167*, 0.0138*, 0.0174*
    - Large S1–S6: 0.0112*, 0.0103*, 0.0119*, 0.0099*, 0.0102*, 0.0123*
  - Selected uncertainty effects (All / Large, where reported):
    - ߪ௦௣௙௚ௗ௣,௧ଶ: All 0.0003; Large 0.0014
    - ߪ௦௣௙௚ௗ௣,௧ிଵ: All -0.0036; Large -0.0011
    - ߪ௦௣௙௜௡ௗ,௧: All -0.0024; Large -0.0027
    - ߪ௦௣௙௜௡ௗ,௧ிଵ: All -0.0023; Large 0.0013
    - ߪ௚ௗ௣,௧: All 0.0058*; Large 0.0081
    - ߪ௚ௗ௣,௧ிଵ: All -0.0062*; Large -0.0054
    - ߪ௜௡௙௟,௧: All 0.0007; Large -0.0025
    - ߪ௜௡௙௟,௧ிଵ: All -0.0043*; Large -0.0033*
    - ߪ௦௣ହ଴଴,௧: All -0.0004; Large 0.0001
    - ߪ௦௣ହ଴଴,௧ிଵ: All -0.0015*; Large -0.0013
    - ߪ௙௨௘௟,௧: All -0.0058*; Large -0.0039*
    - ߪ௙௨௘௟,௧ிଵ: All -0.0026; Large -0.0026
- Notes:
  - The reported numbers measure the effect of a one-standard-deviation increase in the relevant independent variable on growth of employment by size category.
  - The effects of lagged dependent variable are not reported in this table.

### Table 4.2 — Quantitative effect of one-s.d. increase in driving variables (Small groups)
- Dependent variable: ܲܯܧ௧
- Mean growth of employment:
  - Size Group: Small (<500 Employee) Businesses — Mean growth of employment=0.0063
  - Size Group: Small (<20 Employee) Businesses — Mean growth of employment=0.0053
- Effect of one-standard-deviation increase (selected; asterisk denotes significance at least at the 10% level):
  - Growth of real GDP ܲܦܩ௧:
    - Small (<500) S1–S6: 0.0081*, 0.0081*, 0.0099*, 0.0098*, 0.0104*, 0.0078*
    - Small (<20) S1–S6: 0.0053*, 0.0076*, 0.0072*, 0.0082*, 0.0086*, 0.0068*
  - Growth of real GDP lagged ܲܦܩ௧ிଵ:
    - Small (<500) S1–S6: 0.0142*, 0.0160, 0.0137*, 0.0152*, 0.0137*, 0.0166*
    - Small (<20) S1–S6: 0.0022, 0.0012, 0.0018, 0.0009, 0.0011, 0.0033
  - Selected uncertainty effects (Small (<500) / Small (<20), where reported):
    - ߪ௦௣௙௚ௗ௣,௧ଶ: -0.0019 / -0.0039*
    - ߪ௦௣௙௚ௗ௣,௧ிଵ: -0.0051* / -0.0044*
    - ߪ௦௣௙௜௡ௗ,௧: -0.0036* / -0.0037*
    - ߪ௦௣௙௜௡ௗ,௧ிଵ: -0.0042* / -0.0021*
    - ߪ௚ௗ௣,௧: 0.0008 / -0.0029
    - ߪ௚ௗ௣,௧ிଵ: -0.0074* / -0.0033*
    - ߪ௜௡௙௟,௧: -0.0017 / -0.0023
    - ߪ௜௡௙௟,௧ிଵ: -0.0045* / -0.0005
    - ߪ௦௣ஹ଴଴,௧: -0.0001 / -0.0003
    - ߪ௦௣ହ଴଴,௧ிଵ: -0.0021* / -0.0012*
    - ߪ௙௨௘௟,௧: -0.0058* / -0.0041*
    - ߪ௙௨௘௟,௧ிଵ: -0.0009 / -0.0001
- Notes:
  - The notes for this table are the same as for Table 3.2. An asterisk denotes that the estimated effect is significant at least at the 10% level.
  - For each specification’s regression statistics (ܴଶ and ρ), see Table 3.2.

*Italic: Source content unit: _wp1504 - 2. The uncertainty variables are:*

### 2. The reported numbers above measure the effect of a

### _wp1504 - 2. The reported numbers above measure the effect of a

### Growth of Employment Specifications — Total Quantitative Effects (Table 5)
- All ܧ ത = 0.0110
  - Effects by measure (cells): 0      0      -0.0040*      -0.0043*      -0.0015*      -0.0058*       -0.0026         0.0255
- Large(>500) ܧ ത = 0.0161
  - Effects by measure (cells): 0                   0                   0                   -0.0033*                   0                   -0.0039*                   -0.0012                   0.0225
- Small(<500) ܧ ത = 0.0063
  - Effects by measure (cells): -0.0051*      -0.0078*      -0.0074*      -0.0045*      -0.0021*      -0.0058*       -0.0055         0.0230
- Smaller(<20) ܧ ത = 0.0053
  - Effects by measure (cells): -0.0083*      -0.0058*      -0.0033*      0      -0.0012*      -0.0041*      -0.0037          0.0075

Notes (from source):
- 1. From Tables 4.1 and 4.2, we take the sum of the significant coefficients of each effect (e.g., ߪ௦௣௙௚ௗ௣ଶ); these are the reported numbers above in each cell. If a particular coefficient is not statistically significant at the 10% level, we impute a value of zero for the above table.
- 2. ܧ ത is the mean growth (annual percentage change) of employment, by size category.
- 3. The term ߪ ശ തതത is the average uncertainty effect, across the different measures. The term ܲܦܩ തതതതതത is the average GDP effect, across the different specifications.
- The reported numbers measure the effect of a one-standard-deviation increase in the relevant independent variable on growth of employment by size category. See section 7.2 for details.
- To keep the table compact, the effects of lagged dependent variable are not reported.

### Figures (visuals referenced)
- Figure 1: Growth of Total Employment (visual referenced; data summarized in Table 5).
- Figure 2: Growth of Employment in Large (≥500 employees) Businesses.
- Figure 3: Growth of Employment in Small (<500 employees) Businesses.
- Figure 4: Growth of Employment in Small (<20 employees) Businesses.

### Appendix A — Selected Empirical Findings on the Impact of Uncertainty (high-level synthesis)
- Scope: Papers show a range of uncertainty measures (GDP, inflation, prices, energy prices, stock prices, survey measures), statistical constructs (unconditional variance, conditional variance, survey measures), aggregation levels (firm, industry, macro), and estimated quantitative/qualitative effects.
- Representative empirical findings (preserve original phrasing and numeric detail):
  - Lensink, van Steen, Sterken (Survey of 1,097 Dutch firms in 1999): Conditional variance/mean — Uncertainty has a negative impact on the size of investment; smaller firms have a lower probability to invest if uncertainty increases.
  - Koetse, van der Vlist, de Groot (Survey of 135 plant locations in Netherlands in 1998): Survey based — Uncertainty has a larger influence on decision making in small firms than in large firms specifically for investment in energy-saving technologies.
  - Bo and Sterken (Data for 41 Dutch listed firms from 1984 to 1995): Conditional variance. ARCH model — Cross-effect of the interest rate volatility and debt on investment is positive; effect stronger for highly indebted firms.
  - Driver and Whelan (Disaggregated survey data of Ireland in 1995): Subjective descriptions — No strong effect of risk due to convexities; risk affected timing of investment for between a quarter and a third of the sample.
  - Oriani and Sobrero (Data for 290 manufacturing firms in UK from 1989 to 1998): Absolute percentage difference. Inverse of the median age — U-shaped relationship between market uncertainty and value of investment; inverted U-shaped relationship between technological uncertainty and value of R&D capital.
  - Bianco et al. (Data for 2,959 Italian private companies from 1996 to 2007): Coefficient of variation — Family firms’ investments are significantly more sensitive to uncertainty than nonfamily firms.
  - Bloom, Bond, Van Reenen (Data for 672 UK manufacturing firms from 1972 to 1991): Std. deviation of daily stock returns — Effects of uncertainty are large; uncertainty distribution halves the first year investment response to demand shocks.
  - Caglayan, Maioli, Mateut (Data across Belgium, Finland, France, Italy, Spain 1999–2007): First, one standard deviation change in sales uncertainty leads to four percent change in inventory stock. Second, sales uncertainty has indirect effects via net trade credit and liquidity; impact positive/significant when financial strength is low, becomes insignificant beyond a threshold.
  - Ghosal and Loungani (Data for 254 US 4-digit SIC manufacturing industries 1958–1989): Rolling regression based conditional std. deviation — Negative relationship between investment and price uncertainty only in competitive industries; One percentage increase in price uncertainty estimated to cause the ratio of gross industry investment (I/K) decrease by 0.358 for most competitive industries.
  - Fuss and Vermeulen (Survey of 279 firms 1987–2000 and 319 firms 1987–1999): Theil index — One standard deviation increases in demand uncertainty estimated to reduce 6% of the average investment ratio.
  - Ghosal and Loungani (Data for 330 US SIC 4-digit manufacturing industries 1958–1991): Rolling regression based conditional std. deviation — Investment-uncertainty relationship negative and greater in industries dominated by small firms.
  - Gilchrist, Sim, Zakrajšek (Simulated data for 10,000 firms 1962:Q1 to 2012:Q3): Structural vector autoregression — Uncertainty affects financial conditions by significantly altering credit spreads.
  - Huizinga (Data for 450 U.S. SIC 4-digit industries 1954–1989): Bivariate ARCH model — Increased uncertainty about real wages portends an immediate and large drop in capital expenditures.
  - Stein and Stone (Data for 2,230 US manufacturing firms 1996–2009): Expected volatility — Negative and statistically significant relationship between uncertainty and investment; coefficients larger after addressing endogeneity.
  - Folta and O’Brien (Data for 2,230 US manufacturing firms 1996–2009 and 17,897 firms 1980–1999): Square root of conditional variance. GARCH model — Effect of uncertainty on entry is non-monotonic and U-shaped; uncertainty has a potent effect on entry even after controlling for firm resource profiles.
  - Baker, Bloom, Davis (Index of economic policy uncertainty 1985–2011): VAR model — High policy uncertainty in 2010 and 2011 reflects tax and monetary policy concerns; a rise in policy uncertainty associated with substantially lower levels of output and employment compared with actual changes since 2006.
  - Driver, Temple, Urga (Aggregate UK manufacturing 1972–1999): Time-series conditional volatility. GARCH model — Uncertainty variable negatively significant at the 5% level for machinery; negative but not significant for building.
  - Greasley and Madsen (US investment 1920–1938): Tobin’s q, Real stock prices — Effects of uncertainty on expected marginal profitability of capital can explain around 80% of the actual fall in the business fixed investment ratio in 1930.
  - Kilian (Monthly oil production data since 1973): OLS — Exogenous oil supply shocks lead to a sharp drop in real GDP growth and a spike in CPI inflation.
  - Guo and Kliesen (Daily futures 1983–2004): Realized variance series — Oil price volatility has a negative and significant effect on future GDP growth over 1984–2004.
  - Elder (U.S. data 1966–2000): MGARCH-M VAR model — One standard deviation increase in inflation uncertainty tends to reduce real economic activity by about 22 basis points in the post-1982 period.
  - Denis and Kannan (Monthly data June 1984 to September 2011): VAR model — Uncertainty has a substantial effect on UK industrial production, unemployment and GDP.
  - Ghosal (125 U.S. manufacturing industries 1968–1977): Standard deviation — Significant negative relationship between demand uncertainty and the capital-labor ratio; increase in firm size counteracts this negative influence.
  - Ghosal (196 U.S. industries 1973–1986): IV Estimation — Price uncertainty has a statistically significant and quantitatively large negative impact on the number of firms in an industry.
  - Li (46,976 portfolio company-round pairs in U.S. 1975–2005): Weibull regression model — Market uncertainty encourages venture capital firms to delay investing at each round.
  - Podoynitsyna et al. (Sample of 385 NTVs): OLS multiple regression — Real option reasoning does not always perform better under conditions of higher uncertainty.
  - Li and Mahoney (22,164 venture investments 1980–2007): Accelerated-failure-time models — Venture capitalists tend to defer new investment projects in target industries with substantial market volatility; delay effect reduced if sales growth is high or competition intense.
  - Li, Dan (346 new ventures 1990–2005): Heckman two-stage regressions — Inverted U-shaped relationship between market uncertainty and likelihood of forming multilateral R&D alliances.
  - Freel (UK SMEs survey 1996, 1998, 2000): Discriminant functions — Higher levels of innovation in manufacturing firms associated with higher perceptions of supplier uncertainty; in service firms associated with higher perceptions of human resource uncertainty.
  - Drakos and Konstantinou (Data of 51,881 plant-year observations for Greece 1994–2005): GARCH model — Increase in measure of real oil price uncertainty by 0.01 reduces the probability of investment action by 0.46 percent; smaller plants are influenced more by rising real oil-price uncertainty.

- Cross-cutting implication: Uncertainty—measured in a variety of ways—tends to exert negative effects on investment, hiring, entry, and other firm-level decisions, with effects often larger for smaller or more financially constrained firms; quantitative magnitudes vary by measure, model, and sample.

*Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1504.pdf*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp1504.pdf_