## Section 5.1 Theories of Misallocation

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### Overview and research questions
- Context: advanced economies face low productivity and potential growth coupled with high debt and limited fiscal and monetary policy space, prompting renewed interest in productivity and policies to boost output.
- Empirical background: most studies of resource misallocation focus on manufacturing or agriculture; only recently have service-sector estimates become available.
- Three central questions:
  - (1) how costly is the "excess misallocation" in the service sector?
  - (2) what are the drivers of "excess misallocation"?
  - (3) to what extent does this reflect structural differences between the manufacturing and service sectors?

### Key empirical findings (Portugal, firm-level data)
- Method: theoretical framework of Hsieh and Klenow (2009) with the three-factor extension of Dias et al. (2016).
- Counterfactual: closing the misallocation gap between services and manufacturing (making service-sector misallocation equal to manufacturing).
- Estimated aggregate effects (final model counterfactual translating sectoral gains into economy-wide effects):
  - Aggregate gross output (aggregate TFP) would increase by about 12 percent.
  - Aggregate value added (GDP) would increase by about 31 percent.
- Sectoral comparisons from other studies (preserved as reported):
  - Dias et al. (2016) for Portugal, 2004-2011: resource misallocation is, on average, 24 percentage points (p.p.) higher in services than in manufacturing when evaluated in terms of gross output, or around 40 p.p. higher when evaluated in terms of value added.
  - Garcia-Santana et al. (2015) for Spain, 2001-2007: efficiency gains are around 22 p.p. higher in services than in manufacturing.
  - Benkovskis (2015) for Latvia, 2007-2013: average misallocation gap of around 32 p.p. between the two sectors.
- Regularity: the result is not driven by a small number of industries; the majority of manufacturing industries rank among those with the lowest misallocation.

### Theoretical framework and identification (summary from Section 4)
- Aggregate production:
  - Y = ∏_{s=1}^S (Y_s)^{θ_s}, with ∑_{s=1}^S θ_s = 1 and θ_s = (P_s Y_s)/(P Y).
  - Industry gross output Y_s is a CES aggregate of M_s differentiated products with elasticity of substitution σ.
- Firm production function:
  - Y_si = A_si K_si^{α_s} H_si^{β_s} Q_si^{1−α_s−β_s}.
- Distortions (wedges):
  - Output distortion τ^y_si, capital distortion τ^k_si, labor distortion τ^h_si.
- TFPR definition and role:
  - TFPR_si = P_si A_si.
  - In absence of distortions TFPR equalizes across firms; distortions induce TFPR dispersion.
- Key decomposition:
  - ln(TFPR_si/TFPR^*_s) = α_s ln((1+τ^k_si)/(1+τ^k_s)) + β_s ln((1+τ^h_si)/(1+τ^h_s)) − ln((1−τ^y_si)/(1−τ^y_s)).
- Efficiency gains:
  - Industry gains: Y^*_s / Y_s (function of A_si and scaled TFPR).
  - Economy-wide gains: Y^* / Y = ∏_{s=1}^S (Y^*_s / Y_s)^{θ_s}.
  - Interpretation: potential gross-output (TFP) gains from reallocating existing inputs across firms within industries.

### Data and empirical setup
- Data source: Portuguese annual balance-sheet data from Informação Empresarial Simplificada (IES), available from 2006 onwards, covering virtually the universe of Portuguese non-financial firms.
- Variables used: gross output (production), value added, consumption of intermediate inputs, labor costs, employment, gross investment, depreciations, book values of gross and net capital stock.
- Sample sizes after cleaning:
  - 2008: 236,022 observations (from 375,783 raw).
  - 2010: 230,157 observations (from 370,326 raw).
- Sectoral composition in the cleaned dataset:
  - Employment (2008): Agric. 1.97, Manuf. 25.34, Serv. 72.69
  - Employment (2010): Agric. 2.04, Manuf. 23.69, Serv. 74.26
  - Gross output (2008): Agric. 2.42, Manuf. 34.46, Serv. 63.12
  - Gross output (2010): Agric. 1.92, Manuf. 32.71, Serv. 65.36
  - Value added (2008): Agric. 2.35, Manuf. 23.57, Serv. 74.08
  - Value added (2010): Agric. 1.76, Manuf. 22.24, Serv. 76.00
  - Number of firms (2008): Agric. 6,069, Manuf. 34,257, Serv. 195,696
  - Number of firms (2010): Agric. 6,351, Manuf. 32,096, Serv. 191,710
- Industry classification:
  - 3-digit NACE code (Rev. 2.1); 2008: 213 industries (16 agriculture, 101 manufacturing, 96 services); 2010: 215 industries (16 agriculture, 101 manufacturing, 98 services).
- Industry-level factor shares:
  - Use U.S. averages (1998–2010, BEA) to proxy undistorted shares: 46 percent intermediates, 33 percent labor compensation, 21 percent capital.

### Misallocation estimation choices and sensitivity
- Two sets of empirical assumptions:
  - Baseline model:
    - σ = 3.0; Trim 1 percent tails of scaled TFPR and TFP; Include all firms.
  - Final model:
    - σ = 4.5; Trim 2.5 percent tails of scaled TFPR and TFP; Exclude firms with 10 or less employees.
- Rationale: trimming and excluding very small firms address outliers and the higher presence of small firms in services.

### Key quantitative findings on efficiency gains (gross-output / TFP gains from within-industry reallocation)
- Baseline model (values preserved exactly):
  - 2008: Total 43.36; M 16.02; S 59.19; S−M 43.18
  - 2010: Total 49.33; M 16.81; S 66.46; S−M 49.65
- Final model (values preserved exactly):
  - 2008: Total 28.46; M 14.15; S 37.66; S−M 23.51
  - 2010: Total 31.28; M 14.43; S 40.82; S−M 26.39
- Interpretation:
  - Baseline: eliminating distortions would raise aggregate gross output (TFP) by about 43 percent in 2008 and about 49 percent in 2010; services show far greater inefficiency than manufacturing.
  - Final model: aggregate gains fall to about 28 percent (2008) and 31 percent (2010); services remain more inefficient but the gap narrows (S−M = 23.51 p.p. in 2008, 26.39 p.p. in 2010).
  - The reduction reflects the higher presence of small firms and outliers in services.

### Misallocation gap and value-added gains (final model assumptions)
- Closing the misallocation gap by reducing misallocation in services from 37.66 percent to 14.15 percent (bringing services to manufacturing levels in 2008) would lead to:
  - a 12 percent boost in aggregate gross output (or aggregate TFP), and
  - a 31 percent boost in aggregate value added (GDP).
- Value-added efficiency gains for 2008 (final model):
  - 71.75 percent for the whole economy,
  - 47.64 percent for manufacturing,
  - 84.05 percent for services.

### Drivers of excess misallocation (regression analysis and Gelbach decomposition)
- Four grouped categories of potential sources: a) adjustment costs; b) distortions to input prices; c) financial frictions; d) firm-specific markups.
- Empirical strategy:
  - Base regression: Z_s = a_0 + a_1 D_s + u_s, where Z_s = Y^*_s / Y_s and D_s = 1 for services.
  - Full model includes regressors X_1s = productivity shocks, X_2s = skewness of the TFP distribution, X_3s = proportion of young firms, plus interactions D_s X_is.
  - Gelbach decomposition used to attribute the sector gap to differences in regressor means (characteristics effects) and differences in regressor impacts (coefficients effects).

### Regression results (Gelbach decomposition, summary)
- Aggregate decomposition (Table 3, preserved numbers):
  - Difference in efficiency gains (services − manufacturing): 0.202 (8.31) in 2008; 0.205 (7.90) in 2010.
  - Explained difference: 0.225 (2.36) in 2008; 0.207 (2.45) in 2010.
  - Unexplained difference: −0.023 (−0.26) in 2008; −0.002 (−0.02) in 2010.
  - Number of industries: 154 in both years.
  - Robust t-statistics in parentheses.
- Key empirical conclusion:
  - The model fully accounts for the difference between the efficiency gains in the two sectors; the unexplained difference is not significantly different from zero in 2008 and 2010.

### a) Productivity shocks (dominant contributor)
- Contributions (services − manufacturing) to the explained difference (Table 3):
  - Productivity shocks: 0.175 (1.82) in 2008; 0.123 (1.64) in 2010.
    - characteristics effect: 0.027 (1.77) in 2008; 0.023 (2.17) in 2010.
    - coefficients effect: 0.148 (1.44) in 2008; 0.099 (1.23) in 2010.
- Interpretation:
  - Productivity shocks are the most important factor explaining misallocation differences.
  - The bulk of their contribution stems from the coefficients effect: shocks have a larger impact on misallocation in services than in manufacturing.
- Identification and mechanism:
  - TFP assumed AR(1); productivity shocks computed as the industry-level standard deviation of (a_si,t − a_si,t−1).
  - With adjustment costs or output-price rigidity, larger idiosyncratic shocks increase TFPR dispersion.
  - Evidence (Table 4 correlations) consistent with higher price rigidity and higher labor adjustment costs in services, making productivity shocks more impactful on misallocation in services.

### b) Sectoral firm-size structure (second contributor)
- Contributions (services − manufacturing) to the explained difference (Table 3):
  - Sectoral firm-size structure: 0.086 (2.60) in 2008; 0.113 (3.07) in 2010.
    - characteristics effect: 0.016 (2.15) in 2008; 0.002 (0.33) in 2010.
    - coefficients effect: 0.069 (2.00) in 2008; 0.112 (2.85) in 2010.
- Proxy and interpretation:
  - Skewness of the productivity distribution used as proxy (Fisher-Pearson).
  - Higher skewness (many low-productivity firms, few high-productivity firms) captures size-dependent distortions.
  - The bulk of the contribution comes from the coefficients effect: skewness has a larger impact in services.
- Supporting evidence:
  - corr(tfp,tfpr) much higher in services (0.696 in 2008) than manufacturing (0.431 in 2008), implying size-dependent distortions more prevalent in services.
  - Differences in the output wedge (services appear to benefit from output "subsidies" on average) may reflect higher informality in services.

### c) Proportion of young firms (net negative contribution)
- Contributions (services − manufacturing) to the explained difference (Table 3):
  - Importance of young firms: −0.036 (−0.96) in 2008; −0.029 (−0.97) in 2010.
    - characteristics effect: 0.021 (1.83) in 2008; 0.014 (1.70) in 2010.
    - coefficients effect: −0.057 (−1.32) in 2008; −0.042 (−1.37) in 2010.
- Interpretation:
  - The regressor produces opposing effects: the characteristics effect increases the misallocation difference while the coefficients effect reduces it; net impact is negative (−0.036 in 2008).
  - Young firms face higher rental costs of capital (evidence of credit constraints); young firms benefit from lower labor costs but face higher capital and output distortions.
  - The impact on misallocation from the proportion of young firms is lower in services; absent this effect the service–manufacturing gap would be larger.

### Mechanisms and sectoral differences (synthesis)
- Productivity shocks: their larger impact in services likely arises from higher output-price rigidity and higher labor adjustment costs in services.
- Size-dependent distortions: higher skewness and higher corr(tfp,tfpr) in services suggest policies or enforcement that favor small/low-productivity firms (possible role for informality).
- Financial frictions: young firms face higher capital costs consistent with credit constraints; these constraints have different impacts across sectors.
- Firm-specific markups and competition: direct measures omitted; competition effects captured indirectly via price rigidity and productivity distribution characteristics.

### Policy implications and recommendations (drawn from empirical findings)
- Reduce output price rigidity in services by boosting product market competition to increase allocative efficiency.
- Avoid size-contingent laws or policies (special credit lines, labor subsidies targeted by firm size) that sustain unproductive firms and increase misallocation.
- Reduce financial frictions and credit constraints for young firms to enable growth of productive entrants and raise aggregate productivity.
- Note: authors plan further work exploring structural reforms of tax and expenditure policies and sectoral effects of tax rate changes.

### Robustness and sensitivity (Appendix summary)
- Key robustness results (selected rows from Table A1, values preserved):
  - 1) Baseline model (2008 total / M / S): 43.36 / 16.02 / 59.19; (2010) 49.33 / 16.81 / 66.46.
  - 2) σ = 4.5: 63.48 / 19.93 / 90.65 (2008); 71.55 / 20.33 / 100.84 (2010).
  - 3) Trimming = 2.5%: 36.35 / 16.36 / 47.43 (2008); 31.07 / 0.00 / 17.12 (2010).
  - 4) Employment > 10: 28.31 / 12.92 / 38.33 (2008); 25.41 / 13.43 / 41.68 (2010).
  - 8) Final model (combined changes): 28.46 / 14.15 / 37.66 (2008); 23.51 / 14.43 / 40.82 (2010).
- Additional robustness insights:
  - Higher σ implies higher estimated efficiency gains.
  - Trimming outliers and excluding very small firms reduce estimated gains, especially in services.
  - Micro firms (Empl <= 5) show much higher estimated efficiency gains (e.g., All firms 43.36 vs Empl <= 5: 87.04 in 2008 under baseline).
  - Using a 5-digit industry classification lowers global efficiency gains somewhat but does not eliminate the sectoral gap.

### Conclusions (from regression analysis and broader results)
- Higher allocative inefficiency in the service sector is a broad regularity across industries in Portugal, not driven by a few outliers.
- Conservative estimate for Portugal (2008): resource misallocation was around 24 percentage points higher in services than in manufacturing.
  - Closing this gap would yield: a 12 percent boost in aggregate gross output (TFP) and a 31 percent boost in aggregate value added (GDP).
- Regression-based attribution:
  - Productivity shocks are the most important factor for the sectoral misallocation differences (driven by differential impacts).
  - Sectoral firm-size structure (skewness) is the second most important factor (likely reflecting informality and size-contingent distortions).
  - Proportion of young firms contributes but with a lower impact in services due to differential wedges and constraints.

*Source: Section 5.1 "Theories of Misallocation" and Sections 4 and 5.3 from content unit _wp16220.*

### 5.1  Theories of Misallocation ........................................................................................1

### 5.1  Theories of Misallocation

### Overview and research questions
- Context: advanced economies face low productivity and potential growth coupled with high debt and limited fiscal and monetary policy space, prompting renewed interest in productivity and policies to boost output.
- Empirical background: most studies of resource misallocation focus on manufacturing or agriculture; only recently have service-sector estimates become available.
- Three central questions posed:
  - (1) how costly is the "excess misallocation" in the service sector?
  - (2) what are the drivers of "excess misallocation"?
  - (3) to what extent does this reflect structural differences between the manufacturing and service sectors?

### Key empirical findings (Portugal, firm-level data)
- Method: theoretical framework of Hsieh and Klenow (2009) with the three-factor extension of Dias et al. (2016).
- Counterfactual: closing the misallocation gap between services and manufacturing (making service-sector misallocation equal to manufacturing).
- Estimated aggregate effects:
  - Aggregate gross output (aggregate TFP) would increase by about 12 percent.
  - Aggregate value added (GDP) would increase by about 31 percent.
- Sectoral comparisons from other studies (preserved as reported):
  - Dias et al. (2016) for Portugal, 2004-2011: resource misallocation is, on average, 24 percentage points (p.p.) higher in services than in manufacturing when evaluated in terms of gross output, or around 40 p.p. higher when evaluated in terms of value added.
  - Garcia-Santana et al. (2015) for Spain, 2001-2007: efficiency gains are around 22 p.p. higher in services than in manufacturing.
  - Benkovskis (2015) for Latvia, 2007-2013: average misallocation gap of around 32 p.p. between the two sectors.
- Regularity: result is not driven by a small number of industries; the majority of manufacturing industries rank among those with the lowest misallocation.

### Drivers of excess misallocation (regression analysis)
- Overall conclusion: structural differences between the two sectors can fully explain the higher levels of allocative inefficiency in the service sector.
- Main contributing factors (in order of importance):
  - Idiosyncratic productivity shocks:
    - Mechanism: productivity shocks affect allocative efficiency in the presence of capital/labor adjustment costs and/or output-price rigidity.
    - Role: most important factor contributing to misallocation differences between sectors.
    - Additional nuance: the contribution stems more from different impacts of shocks across sectors than from differences in the magnitude of the shocks themselves.
  - Sectoral firm-size structure (proxied by skewness of the productivity distribution):
    - Mechanism: a higher proportion of low-productivity firms in services increases right-skewness of the productivity distribution.
    - Role: second most important factor; contributes to higher misallocation due to prevalence of size-dependent policies.
  - Proportion of young firms:
    - Finding: young firms face higher rental costs of capital than older firms, interpreted as evidence of credit constraints from financial institutions (lack of credit history or insufficient guarantees).
    - Net contribution: negative—meaning that, absent this effect, the difference in misallocation between services and manufacturing would be even larger.

### Policy implications and recommendations
- Targeted measures to reduce within-industry misallocation, particularly in services:
  - Boost competition to reduce output price rigidity in the service sector.
  - Avoid size-contingent laws that may support the survival of unproductive firms.
  - Reduce barriers to growth by eliminating credit constraints imposed by financial institutions on young firms.
- Expected outcome: implementing such measures can contribute to increasing aggregate TFP and aggregate value added (GDP).

### Broader implications for developing countries and structural transformation
- Relevance:
  - Duarte and Restuccia (2010): differences in productivity in services and agriculture across countries are key factors behind overall productivity differences.
  - Hsieh and Klenow (2009): reducing misallocation in manufacturing to U.S. levels would increase productivity by 30-50 percent in China and 40-60 percent in India.
- Extension: if significant service-versus-manufacturing allocative-efficiency differences like those documented for Portugal, Spain, or Latvia exist in other countries, the role of resource misallocation in explaining international productivity gaps may be even larger than estimates based solely on manufacturing data suggest.

*Source: Section 5.1 "Theories of Misallocation" from the provided IMF content unit.*

### Section 4 computes misallocation in the manufacturing and service sectors and discusses

### _wp16220 - Section 4 computes misallocation in the manufacturing and service sectors and discusses

### Theoretical framework: model and identification
- Economy with a single final good Y produced by a representative firm combining S industries with Cobb-Douglas aggregator:
  - Y = ∏_{s=1}^S (Y_s)^{θ_s}, with ∑_{s=1}^S θ_s = 1 and θ_s = (P_s Y_s)/(P Y).
- Industry gross output Y_s is a CES aggregate of M_s differentiated products with elasticity of substitution parameter σ.
- Firm-level gross output Y_si produced with a Cobb-Douglas function of three factors:
  - Y_si = A_si K_si^{α_s} H_si^{β_s} Q_si^{1−α_s−β_s}, where A_si is firm i’s TFP, K capital, H labor, Q intermediate inputs.
- Three types of distortions (wedges) introduced:
  - Output distortion τ^y_si (tax/subsidy on revenues),
  - Capital distortion τ^k_si (tax/subsidy on capital services),
  - Labor distortion τ^h_si (tax/subsidy on labor costs).
- Definition and role of TFPR:
  - TFPR_si = P_si A_si.
  - In the absence of distortions TFPR is equalized across firms within an industry; distortions induce TFPR dispersion.
- Decomposition and implications:
  - ln(TFPR_si/TFPR^*_s) = α_s ln((1+τ^k_si)/(1+τ^k_s)) + β_s ln((1+τ^h_si)/(1+τ^h_s)) − ln((1−τ^y_si)/(1−τ^y_s)).
  - Scaled TFPR above one signals a firm is being “taxed” and would expand output if distortions were removed; scaled output wedge above one signals a firm benefits from output subsidies and would shrink if subsidies were removed.
- Industry and economy-wide gross-output (TFP) gains from reallocation:
  - Industry: Y^*_s / Y_s expressed as a function of firm-level A_si and scaled TFPR (equations (14)–(15)).
  - Economy: Y^* / Y = ∏_{s=1}^S (Y^*_s / Y_s)^{θ_s} (equation (16)).
  - Interpretation: potential efficiency gains equal potential gross-output (or TFP) gains obtained by reallocating existing inputs across firms within industries; gains are larger when more productive firms face higher distortions or when dispersion of scaled TFPR is larger.

### Data and empirical setup
- Firm-level data source:
  - Portuguese annual balance-sheet data from Informação Empresarial Simplificada (IES), available from 2006 onwards, covering virtually the universe of Portuguese non-financial firms.
  - Variables used: gross output (production), value added, consumption of intermediate inputs, labor costs (wages and benefits including social security contributions), employment (average number of employees), gross investment, depreciations, book values of gross and net capital stock.
- Sample sizes after cleaning (strictly positive values for required variables):
  - 2008: 236,022 observations (from 375,783 raw).
  - 2010: 230,157 observations (from 370,326 raw).
- Sectoral composition in the cleaned dataset (percentages and counts):
  - Employment (2008): Agric. 1.97, Manuf. 25.34, Serv. 72.69
  - Employment (2010): Agric. 2.04, Manuf. 23.69, Serv. 74.26
  - Gross output (2008): Agric. 2.42, Manuf. 34.46, Serv. 63.12
  - Gross output (2010): Agric. 1.92, Manuf. 32.71, Serv. 65.36
  - Value added (2008): Agric. 2.35, Manuf. 23.57, Serv. 74.08
  - Value added (2010): Agric. 1.76, Manuf. 22.24, Serv. 76.00
  - Number of firms (2008): Agric. 6,069, Manuf. 34,257, Serv. 195,696
  - Number of firms (2010): Agric. 6,351, Manuf. 32,096, Serv. 191,710
- Industry classification and aggregation:
  - Analyses conducted at 3-digit NACE code (Rev. 2.1) level.
  - 2008: 213 industries (16 agriculture, 101 manufacturing, 96 services).
  - 2010: 215 industries (16 agriculture, 101 manufacturing, 98 services).
- Industry-level factor shares:
  - Use average factor shares observed in the U.S. during 1998–2010 (BEA) to proxy undistorted shares; motivation is that with three factors the model cannot separately identify average wedges and input elasticities.
  - Aggregate gross output composition (1998–2010, U.S.): 46 percent consumption of intermediate inputs, 33 percent labor compensation, 21 percent compensation to capital owners.
- Notes:
  - Worker compensation in IES includes salaries and other labor costs (pension contributions, fringe benefits), consistent with BEA measure.
  - Approximate concordance used between Portuguese and U.S. industry classifications where necessary.

### Misallocation in the manufacturing and service sectors: estimation choices and sensitivity
- Important empirical choices affect estimated misallocation: value of σ (elasticity of substitution), treatment of outliers, and sample inclusion rules for firms.
- Two sets of assumptions presented and compared:
  - Baseline model:
    - σ = 3.0 (value usually assumed in the literature).
    - Trim 1 percent tails of the scaled TFPR and TFP distributions.
    - Include all firms in the dataset.
  - Final model:
    - σ = 4.5 (the average sigma estimated for Portugal).
    - Trim 2.5 percent tails of the scaled TFPR and TFP distributions.
    - Exclude very small firms (firms with 10 or less employees).
- Rationale:
  - Trimming and excluding very small firms address outliers and the higher presence of small firms in services, which disproportionately affect service-sector misallocation estimates.

### Key quantitative findings on efficiency gains (misallocation)
- Table of efficiency gains (gross-output or TFP gains from reallocating resources within industries) — values preserved exactly as reported:

  - Baseline model (2008 and 2010):
    - 2008: Total 43.36; M 16.02; S 59.19; S−M 43.18
    - 2010: Total 49.33; M 16.81; S 66.46; S−M 49.65

  - Final model (2008 and 2010):
    - 2008: Total 28.46; M 14.15; S 37.66; S−M 23.51
    - 2010: Total 31.28; M 14.43; S 40.82; S−M 26.39

- Interpretation of these numbers:
  - Under the baseline model, eliminating distortions and equalizing TFPR across firms would increase aggregate gross output (or TFP) by:
    - about 43 percent in 2008 and about 49 percent in 2010.
  - Under the baseline model, estimated sectoral efficiency gains:
    - Services: about 59 percent in 2008 and 66 percent in 2010.
    - Manufacturing: about 16 percent in 2008 and 17 percent in 2010.
    - Thus services show far greater inefficiency than manufacturing under baseline assumptions.
  - Under the final model (higher σ, more trimming, exclude very small firms):
    - Aggregate gains fall to about 28 percent in 2008 and 31 percent in 2010.
    - Services remain substantially more inefficient than manufacturing, but the gap narrows:
      - S−M = 23.51 p.p. in 2008 and 26.39 p.p. in 2010.
  - The reduction in estimated service-sector misallocation under the final model reflects:
    - a higher presence of small firms in services,
    - a higher frequency of outliers in the service sector; excluding small firms and trimming more has a larger downward effect on the service-sector efficiency gain estimates.
- Pattern across industries:
  - Figures (referenced in text) indicate that the higher service-sector levels of efficiency gains are not driven by a small number of outlier industries.
  - Instead, a systematic pattern: the bulk of manufacturing industries rank among the lowest TFP-gain industries, while the bulk of service industries rank among the highest TFP-gain industries.
  - Example statistics from the figures (2008, baseline vs final):
    - Among the 50 percent of industries with the lowest TFP gains (77 industries), only 11 industries (14.7 percent) belong to the service sector in Figure 1, and only 13 industries (17.3 percent) belong to the service sector in Figure (continued in source).

### Empirical implications emphasized in Section 4
- Misallocation calculations use the three-factor extension of Hsieh and Klenow (2009, 2011), allowing separate identification of capital, labor and intermediate-input wedges from firm-level gross output and input cost data, given σ, α_s and β_s.
- Efficiency gains computed fix total inputs and reallocate them across firms within industries; thus potential gross-output gains coincide with potential TFP gains.
- The magnitude of estimated aggregate and sectoral misallocation is sensitive to:
  - choice of σ,
  - trimming of extreme values in scaled TFPR and TFP distributions,
  - inclusion or exclusion of very small firms (notably prevalent in services).

*Source: _wp16220 - Section 4 computes misallocation in the manufacturing and service sectors and discusses*

### 2.  This result shows that the presence of higher levels of inefficiency is a widespread

### _wp16220 - 2.  This result shows that the presence of higher levels of inefficiency is a widespread

### Misallocation gap and aggregate gains (final model assumptions)
- Closing the misallocation gap by reducing misallocation in the service sector from 37.66 percent to 14.15 percent (bringing services to manufacturing levels in 2008) would lead to:
  - a 12 percent boost in aggregate gross output (or aggregate TFP), and
  - a 31 percent boost in aggregate value added (GDP).
- Value-added efficiency gains for 2008 under the ”final model” assumptions:
  - 71.75 percent for the whole economy,
  - 47.64 percent for manufacturing, and
  - 84.05 percent for services.
- Note on computation: The efficiency gains in terms of gross output are computed as (1.3766/1.1415) θ_s, where θ_s is the share of the service sector in aggregate gross output. The value-added efficiency gains are computed using equation (24) in Dias et al. (2016).

### Motivation for investigating determinants of the misallocation gap
- The large estimated gains motivate a detailed investigation of determinants explaining the misallocation gap between manufacturing and services.
- The paper proceeds to use regression analysis and the Gelbach decomposition to identify the most relevant factors.

### Theories of misallocation — four grouped categories
- The paper groups potential sources of misallocation in four categories: a) adjustment costs; b) distortions to input prices; c) financial frictions; and d) firm-specific markups.

- a) Adjustment costs
  - The Hsieh and Klenow (2009) model is static and assumes instantaneous adjustments; short-term deviations and adjustment costs will show up as misallocation in the static model.
  - Asker et al. (2014) and others show that firms facing idiosyncratic productivity shocks and capital adjustment costs generate dispersion in marginal revenue products of capital; what appears inefficient statically may be dynamically efficient.
  - Key implication: As the volatility of TFP shocks increases, so does the dispersion of the marginal product of inputs; volatility of TFP shocks may therefore increase TFPR dispersion and misallocation through higher dispersion of capital and/or labor wedges (see equation (13)).
  - Price stickiness is another source: the static model assumes a one-to-one contemporaneous negative relationship between productivity (A_si) and prices (P_si) (see equation (5)). In reality price rigidity and asymmetric responses to shocks can increase TFPR dispersion via the output wedge.
  - Footnote: Our framework cannot distinguish productivity shocks from other time-varying shocks (demand shocks, natural disasters, changes to informal barriers, etc.); the term "productivity shocks" is used broadly to cover these.

- b) Distortions to input prices
  - Distortions to factor prices (credit allocation, subsidies, tax incentives, labor and product regulations) can misallocate resources across firms (Hsieh and Klenow (2009), Guner et al. (2008), Restuccia and Rogerson (2008)).
  - In Portugal, many regulations tend to benefit small and medium-sized firms, including:
    - i) less bureaucratic processes for worker dismissals;
    - ii) less costly conditions regarding the provision of health care services;
    - iii) smaller fines for labor law breaches;
    - iv) better accessibility conditions (including reduction of social contributions) to subsidized employment creation, worker training and professional internship programs;
    - v) better accessibility conditions to investment subsidies, including access to specific investment programs;
    - vi) access to specific fiscal benefits (smaller taxes on profits).
  - Empirical strategy: use skewness of the industry TFP distribution as a summary measure to characterize industry structure (high skewness = many low-productivity firms and a few very high-productivity firms). Skewness is used to capture size-dependent distortions while mitigating endogeneity issues by focusing on TFP rather than employment or gross output.
  - Interpretation: correlation between skewness and misallocation measures the importance of size-dependent distortions; linking productivity to individual wedges helps infer whether less productive firms are taxed or subsidized and the source of such policies.

- c) Financial frictions
  - Financial frictions can prevent highly productive but credit-constrained firms from expanding (Midrigan and Xu (2014), Moll (2014), Gilchrist et al. (2013), Banerjee and Moll (2010), Hosono and Takizawa (2012)).
  - Alternatively, financial frictions may disproportionately affect larger firms with larger financing needs (Buera et al. (2011)).
  - Empirical proxies: investigate misallocation variation with firm age to capture young firm constraints versus size-dependent price distortions.
    - If distortions operate through input price differences favoring small firms, expect a positive relationship between firm size and TFPR or the capital/labor wedge (returns to additional inputs lower in smaller firms).
    - If financial market failures constrain young firms, expect a negative relationship between firm age and the capital wedge (many young firms fail to grow due to credit access limits).
    - Both phenomena may coexist (small firms benefiting from lower capital costs and young firms facing capital constraints).

- d) Firm-specific markups
  - Imperfectly competitive output markets with firm-specific markups can generate misallocation identified by the static model (Peters (2013), Syverson (2004a,b)).
  - In such models high TFPR may indicate market power (higher markups) rather than being a sign of constraint/taxation.
  - Industry-level misallocation is expected to be negatively correlated with the level of competition.
  - Measuring competition directly is difficult; common statistics (concentration ratios, advertising intensity, price-cost margins, Herfindahl, Ellison and Glaeser indices, sunk entry costs, international exposure) have limitations and may misrepresent competitive pressures (e.g., exports alter effective competition).
  - Consequence for empirical model: no direct competition measure is included; instead, competition effects are captured indirectly via price rigidity and productivity distribution characteristics. Higher skewness may serve as an indirect measure of lower competition.

### Empirical approach — Gelbach decomposition and regression setup
- Definitions:
  - Efficiency gains in industry s are Z_s = Y*_s / Y_s.
  - Dummy D_s = 1 if industry is service, 0 if manufacturing.
- Base cross-section regression:
  - Z_s = a_0 + a_1 D_s + u_s (equation (17)); coefficient a_1 measures the difference in efficiency gains between service and manufacturing sectors.
- Full model allowing differential impacts of regressors:
  - Regressors: X_1s = productivity shocks, X_2s = skewness of the TFP distribution, X_3s = proportion of young firms.
  - Full model:
    - Z_s = a_0 + a_1 D_s + b_1 X_1s + c_1 D_s X_1s + b_2 X_2s + c_2 D_s X_2s + b_3 X_3s + c_3 D_s X_3s + v_s (equation (18)).
  - Interpretation:
    - c_i measures difference in impact of X_is between services and manufacturing.
    - a_1 in the full model (â_full_1) is the residual difference in efficiency gains not accounted for by included regressors.
- Gelbach decomposition of omitted variable bias (Gelbach (2016)):
  -  â_base_1 = â_full_1 + ˆθ_1 ˆb_1 + ˆμ_1 ˆc_1 + ˆθ_2 ˆb_2 + ˆμ_2 ˆc_2 + ˆθ_3 ˆb_3 + ˆμ_3 ˆc_3 (equation (19)).
  - Components:
    - â_base_1 and â_full_1 are OLS estimates of a_1 in the base and full models, respectively.
    - ˆb_i and ˆc_i (i=1,2,3) are OLS estimates of b_i and c_i in the full model.
    - ˆθ_i and ˆμ_i are OLS estimates from simple regressions X_is = b_i0 + θ_i D_s + ε_is and D_s X_is = c_i0 + μ_i D_s + ε_is, respectively.
  - Intuition for interpretation:
    - â_base_1 = observed difference in efficiency gains between services and manufacturing (in the base model).
    - â_full_1 = remaining unexplained difference after including regressors.
    - ˆθ_i = difference in the mean of X_is between service and manufacturing sectors.
    - ˆμ_i = mean of D_s X_is in the service sector.
    - Total contribution of regressor X_is to the sector gap is ˆθ_i ˆb_i + ˆμ_i ˆc_i.
    - X_is accounts for the sector difference if either: i) its mean differs across sectors (ˆθ_i ≠ 0), or ii) its impact differs across sectors (ˆc_i ≠ 0).

*Italic source attribution: _wp16220 - 2.  This result shows that the presence of higher levels of inefficiency is a widespread*

### 5.3    Regression analysis

### _wp16220 - 5.3    Regression analysis

### Regression results overview
- The Gelbach decomposition results (Table 3) for 2008 and 2010:
  - Difference in efficiency gains (services minus manufacturing): 0.202 (8.31) in 2008; 0.205 (7.90) in 2010.
  - Explained difference: 0.225 (2.36) in 2008; 0.207 (2.45) in 2010.
  - Unexplained difference: −0.023 (−0.26) in 2008; −0.002 (−0.02) in 2010.
  - Number of industries: 154 in both years.
  - Note: Robust t-statistics in parentheses. Efficiency gains are obtained assuming case (8) in Table 2.
- Decomposition structure:
  - For each regressor X_is, total contribution = characteristics effect (difference in regressor means across sectors) + coefficients effect (difference in regressor impacts across sectors).
- Key empirical conclusion:
  - The model fully accounts for the difference between the efficiency gains in the two sectors: the unexplained difference (â^full_1) is not significantly different from zero in 2008 and 2010.
  - Ordering industries by unexplained efficiency gains in 2008: among the 50 percent of industries with the lowest TFP gains (77 industries), 43 industries (58.1 percent) belong to the service sector (compared to 17.3 percent in Figure 2).

### a) Productivity shocks
- Table 3 contributions (services − manufacturing) to the explained difference (2008 / 2010):
  - a) Productivity shocks: 0.175 (1.82) in 2008; 0.123 (1.64) in 2010.
    - a1) characteristics effect: 0.027 (1.77) in 2008; 0.023 (2.17) in 2010.
    - a2) coefficients effect: 0.148 (1.44) in 2008; 0.099 (1.23) in 2010.
- Main findings:
  - Productivity shocks emerge as the most important factor explaining misallocation differences between the two sectors.
  - The contribution of productivity shocks stems mostly from the coefficients effect: the impact of productivity shocks on misallocation is significantly higher in the service sector than in manufacturing.
- Identification note:
  - TFP is assumed to follow an AR(1): a_si,t = μ_s + ρ_s a_si,t−1 + φ_s υ_si,t with υ_si,t ∼ N(0,1). φ_s measures productivity shocks. Productivity shocks are computed as the industry-level standard deviation of (a_si,t − a_si,t−1).
- Mechanism and further evidence:
  - With adjustment costs or output-price rigidity, larger idiosyncratic productivity shocks generate greater variation in TFPR across firms -> greater misallocation.
  - For differential sectoral impacts, input adjustment costs or price rigidity must vary across industries.
  - Table 4 (2008) correlations between regressors and industry-level standard-deviations of scaled TFPR and scaled wedges:
    - sd(tau_k): Manuf 0.114 / Serv 0.059; Manuf 0.212 / Serv −0.089; Manuf 0.302 / Serv 0.225 (columns correspond to TFP-shocks / Sectoral structure / Share young firms as regressors paired with sd of wedges and sd(tfpr) — see table layout).
    - sd(tau_h): Manuf 0.108 / Serv 0.418; Manuf 0.084 / Serv 0.241; Manuf 0.308 / Serv 0.233.
    - sd(tau_y): Manuf 0.342 / Serv 0.393; Manuf 0.299 / Serv 0.163; Manuf 0.398 / Serv 0.160.
    - sd(tfpr): Manuf 0.337 / Serv 0.456; Manuf 0.264 / Serv 0.228; Manuf 0.359 / Serv 0.153.
  - Interpretation:
    - Productivity shocks are not very correlated with the standard-deviation of the capital wedge, especially in services.
    - Productivity shocks are more correlated with labor-wedge and output-wedge dispersion in services than in manufacturing.
    - Evidence is consistent with higher price rigidity and higher labor adjustment costs in the service sector (cited literature: Fabiani et al. (2006), Dias et al. (2015), Martin (1993), Gopinath and Itskhoki (2010), ECB (2006)).
    - Proposed channel: higher output price rigidity and higher labor adjustment costs in services explain the higher impact of productivity shocks on misallocation in services.

### b) Sectoral firm-size structure
- Table 3 contributions (services − manufacturing) to the explained difference (2008 / 2010):
  - b) Sectoral firm-size structure: 0.086 (2.60) in 2008; 0.113 (3.07) in 2010.
    - b1) characteristics effect: 0.016 (2.15) in 2008; 0.002 (0.33) in 2010.
    - b2) coefficients effect: 0.069 (2.00) in 2008; 0.112 (2.85) in 2010.
- Proxy and interpretation:
  - Sectoral firm-size structure proxied by skewness of the productivity distribution (Fisher-Pearson formula).
  - Higher skewness implies many low-productivity firms and few firms with productivity far above the mean; used as a summary of industry-level characteristics that affect size-dependent distortions.
  - The bulk of the contribution comes from the coefficients effect: the impact of skewness is larger in services.
- Supporting correlations (Table 5, average of industry-level correlations):
  - corr(tfp,tau_k): Manuf 0.291 / Serv 0.387 (2008); Manuf 0.303 / Serv 0.384 (2010).
  - corr(tfp,tau_h): Manuf 0.407 / Serv 0.314 (2008); Manuf 0.442 / Serv 0.297 (2010).
  - corr(tfp,tau_y): Manuf 0.156 / Serv 0.046 (2008); Manuf 0.167 / Serv 0.026 (2010).
  - corr(tfp,tfpr): Manuf 0.431 / Serv 0.696 (2008); Manuf 0.448 / Serv 0.693 (2010).
  - corr(tfp,tfpr+tau_y): Manuf 0.437 / Serv 0.424 (2008); Manuf 0.462 / Serv 0.419 (2010).
- Mechanism:
  - Higher positive correlation between productivity and TFPR in services (0.70 in services vs. 0.43 in manufacturing in 2008) implies size-dependent distortions more prevalent in services.
  - Figure 3 (firm-level local trends):
    - Less productive firms appear subsidized (negative log scaled TFPR for low-productivity firms) in both sectors, via relatively lower capital and labor costs.
    - Manufacturing: firms on average face output "taxes" (negative log scaled output wedge) for many productivity levels, offsetting capital and labor "subsidies".
    - Services: firms appear to benefit from output "subsidies" on average, adding to capital and labor "subsidies" for less productive firms.
  - This difference in the output wedge explains the higher corr(tfp,tfpr) in services; corr(tfp,tau_y) is lower in services (0.047) vs manufacturing (0.155) in 2008.
  - Hypothesized source of output-wedge difference: higher informality in services (firms misreporting sales) makes them appear less productive while benefiting from output subsidies in the model.

### c) Importance of young firms
- Table 3 contributions (services − manufacturing) to the explained difference (2008 / 2010):
  - c) Importance of young firms: −0.036 (−0.96) in 2008; −0.029 (−0.97) in 2010.
    - c1) characteristics effect: 0.021 (1.83) in 2008; 0.014 (1.70) in 2010.
    - c2) coefficients effect: −0.057 (−1.32) in 2008; −0.042 (−1.37) in 2010.
- Findings:
  - The regressor contributes two opposing effects:
    - The characteristics effect (difference in means) increases the misallocation difference (2.1 p.p. in 2008).
    - The coefficients effect (difference in impacts) decreases the misallocation difference (−5.7 p.p. in 2008).
  - Net total impact of this regressor is negative: −3.6 p.p. in 2008.
  - Interpretation: the impact on misallocation from the proportion of young firms is lower in the service sector; absent this effect, the misallocation gap would be even larger.
- Figure 4 and channels:
  - Young firms benefit from lower labor costs (lower scaled labor wedge) but face higher distortions (higher TFPR) due to higher capital costs and higher output distortions.
  - Higher capital costs for young firms linked to credit constraints (lack of credit history or insufficient guarantees).
  - Correlations (Table 4) show the proportion of young firms correlates less with standard deviations of wedges in services than in manufacturing, implying all distortions contribute to the lower impact of this regressor in services.
  - Output distortions in young firms are much less important in services than in manufacturing, contributing to the smaller contrast between younger and older firms in services.

### Conclusions (from regression analysis and broader results)
- Cross-sectional and decomposition findings:
  - Higher allocative inefficiency in the service sector is a broad regularity across industries, not driven by a few outlier industries.
  - Conservative estimates for Portugal: resource misallocation in 2008 was around 24 percentage points higher in the service than in the manufacturing sector.
    - Closing this misallocation gap (reducing service sector misallocation to manufacturing levels) would lead to:
      - a 12 percent boost in aggregate gross output (or aggregate TFP),
      - and a 31 percent boost in aggregate value added (GDP).
- Regression-based attribution:
  - Productivity shocks are the most important factor for sectoral misallocation differences; this predominately reflects differences in impacts (coefficients), not in shock magnitudes.
  - Likely origin of this channels: higher output-price rigidity and higher labor adjustment costs in services.
  - Sectoral firm-size structure (skewness) is the second most important factor; higher impact in services likely reflects higher informality that complicates tax enforcement.
  - The proportion of young firms affects misallocation differences but has a lower impact in services; linked to credit constraints on young firms.

### Policy implications (drawn from the empirical findings)
- Increasing product market competition in the service sector (to reduce output price rigidity) would increase allocative efficiency and boost aggregate productivity.
- Size-contingent policies (special lines of credit with subsidized interest rates and/or labor subsidies) that support small/medium firms can sustain unproductive firms and thereby increase misallocation, with negative effects on aggregate productivity — indicating a potential trade-off between employment creation and aggregate productivity.
- Reducing financial constraints on young firms would contribute to increasing aggregate productivity.
- The authors note future work plans to explore structural reforms of tax and expenditure policies and sectoral effects of tax rate changes.

### Appendix — Misallocation under alternative assumptions (robustness)
- Baseline assumptions:
  - σ = 3; trimming top and bottom 1.0 percent tails of scaled TFPR and TFP distributions; inclusion of all firms in retained industries.
  - Industry-specific rental price of capital R_s = δ_s + 0.05 (depreciation rate + 5 percent real interest); intermediate input price Z_s = 1.
- Table A1: Efficiency gains (selected rows, percent) — all numbers preserved as in source (rows correspond to variants):
  - 1) Baseline model (2008 total / M / S): 43.36 / 16.02 / 59.19; (2010) 49.33 / 16.81 / 66.46.
  - 2) σ = 4.5: 63.48 / 19.93 / 90.65 (2008); 71.55 / 20.33 / 100.84 (2010).
  - 3) Trimming = 2.5%: 36.35 / 16.36 / 47.43 (2008); 31.07 / 0.00 / 17.12 (2010) — (numbers as listed in table).
  - 4) Employment > 10: 28.31 / 12.92 / 38.33 (2008); 25.41 / 13.43 / 41.68 (2010).
  - 8) Final model (combined changes): 28.46 / 14.15 / 37.66 (2008); 23.51 / 14.43 / 40.82 (2010).
  - Note: M stands for manufacturing and S for services; S-M is the difference between the service and the manufacturing sectors; the total also includes firms from agriculture.
- Robustness insights:
  - Higher σ implies higher estimated efficiency gains; increasing σ from 3 to 4.5 raises the sectoral gap (e.g., difference increases from ~43 p.p. to ~71 p.p. in 2008).
  - Trimming outliers (2.5% tails) reduces estimated gains, especially in services — indicating outliers concentrated in the service sector contribute to baseline gap.
  - Minimum firm size: micro and small firms display much higher efficiency gains than larger firms (Table A2). Examples (baseline assumptions, 2008):
    - All firms: 43.36 (Total).
    - Empl <= 5: 87.04 (Total).
    - Empl > 5: 31.54 (Total).
    - Empl > 10: 28.31 (Total).
  - Restricting to firms with more than 10 employees reduces total efficiency gains and narrows the services–manufacturing gap (e.g., difference drops from 43 p.p. to 25 p.p. in 2008).
  - Final model (σ=4.5, trimming=2.5%, employment>10): efficiency gains ~28 percent in 2008 and ~31 percent in 2010; differences between services and manufacturing drop to about 24 p.p. (2008) and 26 p.p. (2010).
- Overall robustness conclusion:
  - A significant difference in allocative efficiency between manufacturing and services is robust to alternative assumptions about σ, outlier treatment, and firm-sample selection.
  - Additional sensitivity: using a 5-digit industry classification lowers global efficiency gains somewhat but does not eliminate the large sectoral gap (example: final model difference 17.64 p.p. in 5-digit 2008 vs 23.51 p.p. in 3-digit).

*Source: _wp16220 - 5.3    Regression analysis*

### References

### _wp16220 - References

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*References list as presented in the source PDF _wp16220 - References.*

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