## Section 2 — Endogenous skill bias of technical change (wpiea2023165-print-pdf)

## Source details

**Canonical URL:** [Section 2 — Endogenous skill bias of technical change (wpiea2023165-print-pdf)](https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023165-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2023/english/wpiea2023165-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2023/english/wpiea2023165-print-pdf.pdf.json)

---

### Model overview
- Purpose: build a formal model with an endogenous skill bias of technical change in developing countries and provide evidence; model yields the specification in equation (1).
- Key mechanism: the skill premium is influenced by (i) the supply of skilled labor relative to unskilled labor and (ii) the number of different machines that complement skilled labor relative to machines that complement unskilled labor. The relative number of skilled machines is determined by relative supply of skills and by the global relative availability of licences for purchase.

### The population and labor force
- Population: L = 1 consisting of portion q skilled workers and 1−q unskilled workers.
- Consumer utility (linear, pins down interest rate r for all t):
  - U_it = sum_{h=t}^{∞} G_ih (1 + r)^{−h+t}, where G is output consumed.
- Consumers earn wages and profits from any licences they hold.

### Production
- Final output (CES, linearly homogeneous):
  - Y_t = [ (y^s_t)^{(ε−1)/ε} + (y^u_t)^{(ε−1)/ε} ]^{ε/(ε−1)} with ε > 0.
- Relative prices of intermediates:
  - p^s_t / p^u_t = ( y^s_t / y^u_t )^{−1/ε}.
- Intermediate production (Romer (1990) style):
  - Skilled intermediate: y^s_it = (L^s_it)^{1−α} ∏_{j=1}^{T^s_t} X_{ijt}^{α}
  - Unskilled intermediate: y^u_it = A (L^u_it)^{1−α} ∏_{j=1}^{T^u_t} Z_{ijt}^{α}
  - A < 1 for unskilled labor (effective units); machines depreciate fully each period.
- Firm-level demand for each skilled machine type (marginal product = price):
  - X_{ijt} = [ α p^s_t / p_{X_{jt}} ]^{1/(1−α)} L^s_it.
- Own-price elasticity of demand for any machine = 1/(1−α); monopolist sets p_X = 1/α for all j,t.
- Economy-wide demand for each skill-biased machine:
  - X_t = α^{2/(1−α)} (p^s_t)^{1/(1−α)} q_t
- Economy-wide demand for each unskilled machine:
  - Z_t = A α^{2/(1−α)} (p^u_t)^{1/(1−α)} (1−q_t)
- Economy-wide intermediates:
  - y^s_t = T^s_t q_t^{1−α} X_t^{α}
  - y^u_t = T^u_t A^{1−α} (1−q_t)^{1−α} Z_t^{α}
- Constant returns to variety imply new machine types are always employed; increases in T^s relative to T^u or rises in q induce price adjustments.

### Prices and wages
- Definitions: p_t ≡ (p^s / p^u)^{1/(1−α)}, Q ≡ q / (A(1−q)), T ≡ T^s / T^u.
- After substitutions:
  - p_t = ( T^s q / (T^u A(1−q)) )^{−1/σ} ≡ (T Q)^{−1/σ}_t, where σ = ε + α − εα is the elasticity of substitution between skilled and unskilled labor.
- Relative wages (labor hired until wage equals marginal revenue product), with W_t ≡ W^s_t / W^u_t:
  - W_t = T_t p_t = T^{(σ−1)/σ}_t Q^{−1/σ}_t
- Interpretation:
  - Substitution effect: rise in relative skilled quantity reduces relative skilled wage via p.
  - Technology effect: rise in T increases relative physical productivity of skilled labor but lowers p and hence W; net sign depends on σ.

### Technology adoption and licences
- Empirical background (preserved facts):
  - Most countries acquire technologies from abroad through imports or transfers.
  - Imported technical change need not be skill-biased; some imports complement skilled labor and some complement unskilled workers.
  - Countries consider domestic factor market conditions before adopting methods.
  - Technology acquisition is modeled as purchases from abroad rather than home R&D for developing countries.
- Import pricing and licence costs:
  - It costs one unit of Y exported to import one machine (marginal cost unity).
  - Licence cost for a skilled machine: C^s; for unskilled: C^u, with relative cost:
    - C_t ≡ C^s_t / C^u_t = R^u_t / R^s_t ≡ 1 / R_t, where R is the skill-bias of the world’s available technologies.
- Licence values (P_X = 1/α and Ω ≡ (1−α) α^{(1+α)/(1−α)}):
  - Per-period profit from a skilled licence: π_x = Ω (p^s_t)^{1/(1−α)} q_t.
  - Skilled licence value:
    - V^s_t = Ω sum_{i=1}^{∞} q_{t+i} ( p^s_{t+i} )^{1/(1−α)} (1 + r)^{−i}
  - Unskilled licence profit: π_z = Ω (p^u_t)^{1/(1−α)} A(1−q_t).
  - Unskilled licence value:
    - V^u_t = A Ω sum_{i=1}^{∞} (1−q_{t+i}) ( p^u_{t+i} )^{1/(1−α)} (1 + r)^{−i}
- Ratio of licence values:
  - V_t = [ sum_{i=1}^{∞} q_{t+i} ( p^s_{t+i} )^{1/(1−α)} (1 + r)^{−i} ] / [ A sum_{i=1}^{∞} (1−q_{t+i}) ( p^u_{t+i} )^{1/(1−α)} (1 + r)^{−i} ]
- For constant Q and R, simplified:
  - V = Q^{(σ−1)/σ} T^{−1/σ}

### Steady state and comparative statics
- Free entry implies V^s = C^s and V^u = C^u so in steady state:
  - V = C
- Steady-state relationship:
  - T = Q^{(σ−1)/σ} R^{1/σ}
- Final equation for the skill premium:
  - W = Q^{σ−2} R^{σ−1}
- Comparative statics (log differentiation):
  - d log W / d log Q = (∂ log W / ∂ log T) (d log T / d log Q) − 1/σ
  - Simplified:
    - d log W / d log Q = σ−2
- Interpretation:
  - Substitution effect (conventional labor demand) = −1/σ.
  - Technology effect operates through d log T / d log Q; for σ > 1 a rise in Q leads to acquisition of more skilled machines (T rises).
  - For σ > 1 the technology effect dominates and rise in T raises skill premium; for σ < 1 effects reverse. The paper focuses on σ > 1 (empirically supported).

### Reinterpretation of canonical regression and empirical implications
- Canonical regression often estimated:
  - log W = α + β log Q + e, with implied traditional elasticity  ̃σ = −1/β.
- Mapping to the model:
  - In the directed-technical-change framework, β = σ − 2 (not β = −1/ ̃σ).
- Consequence: many existing coefficient estimates imply σ values that are lower and show less variation than implied ̃σ estimates. Example: Psacharopoulos & Hinchliffe (1972) coefficients imply σ ≈ 1.5–1.6 in the directed-technical-change framework.

### Estimation bias, publication bias, and hypothesis testing
- Measurement error causes attenuation bias toward zero; since most coefficient estimates are negative, attenuation bias tends to overestimate  ̃σ. In the framework, the bias would be towards values of σ= 2 from either direction.
- Reverse causation (wage premium affecting skill supply) can bias estimates; approaches to address include IV (compulsory schooling laws) and lags.
- If reverse causality is not fully dealt with and there is positive correlation between shifts in relative labor supply and labor demand:
  - a negative β-coefficient estimate is too small (in absolute value) relative to the true value;
  - a positive β-coefficient is too high relative to the true value.
  - This endogeneity tends to reinforce attenuation bias for true negative coefficients and lead to overestimates of  ̃σ; in the framework it leads to overestimates of σ regardless of coefficient sign.
- HILZ findings:
  - IV coefficients are on average 0.1 more negative than OLS coefficients.
  - Restricting to EMDEs using HILZ data yields a similar implied difference: only 0.1 for σ but implies a  ̃σ that is 0.4 lower.
- Publication bias works opposite to estimation biases: studies with low or insignificant β are less likely to be published, understating substitution elasticities.
- Testing implications in this framework:
  - Testing β= 0 in a 2-sided manner tests whether higher skill supply increases or decreases the wage premium.
  - If σ is insignificantly different from 2, technology and substitution effects approximately cancel and no change in wage inequality.
  - Testing Leontief (no substitution) amounts to testing β=−2.
  - σ= 1 (β=−1) is the condition under which a rise in supply of skilled labor does not lead to technical change that favors skilled workers (Cobb Douglas).
- HILZ bias-adjusted results:
  - OLS estimates decline to almost zero, increasing  ̃σ to 10 yet consistent with σ≈2.
  - HILZ preferred estimate accounting for estimation and publication bias is β=−0.27, implying:
    -  ̃σ= 3.7
    - σ= 1.73
    - HILZ 95% confidence interval for  ̃σ: [2;20]
    - Authors’ interval for σ: [1.5;1.9]
  - For EMDEs, combined effects yield bias-adjusted estimate very close to uncorrected mean at 2.1 with interval [1.4;4.2]; alternatively implies σ= 1.53 with interval about [1.3;1.8].

### Dynamics and estimation strategy
- Time-series/panel analogue:
  - log W_t = α_0 + α_1 log R_t + β log Q_t + e_t with R represented by a trend term.
- Dynamic specification example:
  - ∆log W_t = γ_0 − 1/σ ∆log Q_t + γ_1 [log W_{t−1} − (σ−2) log Q_{t−1}] + e_t
  - Coefficient on first difference of relative skill supply represents short-run substitution effect; its negative inverse provides an estimate of σ.
  - γ_1 indicates speed of adjustment; γ_1(σ−2) can back out σ.
- Framework is amenable to estimation with a non-linear restriction exploiting σ in both first-difference and lagged terms.

### New data and main empirical estimates
- Data sources:
  - Global panel 1970–2010 covering about 60 developing countries; labor supply from Barro and Lee (2018 update of 2013); Mincerian coefficients from Psacharopoulos & Patrinos (2018) and unpublished Barro & Lee (2001).
  - Aggregation from seven educational categories into two (skilled/unskilled) with constructions described for primary and tertiary cutoffs.
  - Latin America: SEDLAC December 2022 update; skill levels: 'low' 0-8 years, 'medium' 9-13 years, 'high' 14+ years; two cutoffs used (more than 8 years; more than 13 years).
- Global panel results (skilled = some tertiary/higher):
  - Estimated skill supply coefficient ≈ 0.15 in many specifications.
    - Example (column 1, Table 2, random effects): coefficient 0.15 yields:
      - traditional  ̃σ = -6.73
      - under new interpretation σ= 2.15, implying substitution effect = -0.47 and technology effect = 0.61
  - Tables 4 and 5 (skilled ≥ primary): coefficients positive but closer to zero; under new interpretation σ≈2.
  - Estimates fairly consistently around 0.15, implying σ= 2.15.
  - Standard errors suggest elasticity is significantly greater than 1.
- Latin America panel (higher cutoff):
  - Table 6 examples (Ln Relative Skill Supply: 13 years -0.19** (0.08); Year -0.01*** (0.00)):
    - Elasticity (beta+2) reported as 1.81***, 1.71***, 1.73*** in columns with standard errors (0.08)(0.07)(0.07).
    - Subs. effect -0.55***, -0.59***, -0.58***; Tech. effect 0.37***, 0.29***, 0.31***; Observations 246, 227, 232.
  - Table 7 (primary cutoff) examples:
    - Ln Relative Skill Supply: 8 years 0.20* (0.10); Year -0.02*** (0.01);
    - Elasticity (beta+2) 2.20*** 1.84*** 1.88***; Subs. effect -0.45*** -0.54*** -0.53***; Tech. effect 0.66*** 0.39*** 0.41***; Observations 246, 227, 232.
- Brazil (1981–2021) examples:
  - Table 8 (higher cutoff):
    - Ln Relative Skill Supply: 13 years -0.67*** (0.16); Year 0.02** (0.01);
    - Elasticity (inverse) 1.50*** 2.25** (0.37)(1.09); Elasticity (beta+2) 1.33*** 1.70*** 1.70***; Subs. effect -0.75*** -0.59*** -0.59***; Tech. effect 0.08 0.29*** 0.29***; Observations 363, 232, 232.
  - Table 9 (primary cutoff) examples:
    - Ln Relative Skill Supply: 8 years 0.32 (0.28); Year -0.04* (0.02);
    - Elasticity (beta+2) 2.32*** 1.80*** 1.82***; Subs. effect -0.43*** -0.56*** -0.55***; Tech effect 0.75*** 0.35*** 0.37***; Observations 363, 232, 232.
- Central America (selected results):
  - Table 10 (static, higher cutoff): country coefficients range from -0.21 (Honduras) to 0.20 (El Salvador). Panel coefficient 0.04 implies σ= 2.04; Observations vary by country (examples: 332, 222, 272, 71, 28).
  - Table 11 (constrained dynamic): regional σ= 1.67; example country elasticities (beta+2) include 1.79***, 1.62***, 1.14***, 1.64***, 1.74***, 1.67***.
  - Tables 12 and 13 (primary cutoff): most static specifications estimate positive coefficients implying elasticity values over 2; constrained dynamic estimates (elasticity (beta+2)) examples: 1.78***, 1.74***, 1.58***, 1.83***, 1.96***, 1.80***.

### Summary and interpretation
- Reinterpretation: the reduced-form coefficient on log Q maps to σ−2 (not −1/ ̃σ). Under this mapping:
  - Negative coefficient estimates close to zero traditionally implying very high  ̃σ yield σ values just below 2.
  - The framework permits positive coefficient estimates and is more robust to estimation error and some publication biases.
- Preferred estimates implied by HILZ bias-adjusted coefficient estimates:
  - σ= 1.7 for the global sample.
  - σ= 1.5 for the subset of EMDEs.
- Main empirical findings:
  - Global results indicate a slightly positive relationship between relative supply of skills and the wage premium, implying an elasticity of 2–2.2 in many specifications.
  - Latin America and Central America results indicate elasticities around 2 or, when accounting for dynamics, 1.7–1.8.
- Interpretation: the absence of a large negative correlation between wage premia and quantities is viewed as technical change approximately cancelling the substitution effect rather than evidence of perfect substitutability.

### Policy implications
- Expanding education access to reduce within-country wage inequality may not be justified based on the modest effect on wage premia suggested by the results.
- Findings support:
  - Accounting for imperfect substitution in human capital measurement.
  - Enriching debate on human capital’s role in cross-country income differences.
  - Expectation of more broad-based effects of immigration on local wages.

### Suggested extensions and further research
- Encourage re-evaluation of previously excluded studies under the new framework.
- Possible extensions:
  - In-depth analysis of more countries with additional observations.
  - Alternative aggregations of skill types.
  - Applications accounting for worker experience.
  - Exploration of alternative proxies for external drivers of technology availability or adoption (trade, investment, upskilling in advanced economies).

*Source: wpiea2023165-print-pdf — content unit 2 (Section 2 and related empirical sections).*

### Section  2  builds  a  formal  model  with  an  endogenous  skill  bias  of  technical  change  in

### Section 2 builds a formal model with an endogenous skill bias of technical change in

### Model overview
- Purpose: build a formal model with an endogenous skill bias of technical change in developing countries and provide evidence; model yields the specification in equation (1).
- Key mechanism: the skill premium is influenced by (i) the supply of skilled labor relative to unskilled labor and (ii) the number of different machines that complement skilled labor relative to machines that complement unskilled labor. The relative number of skilled machines is determined by relative supply of skills and by the global relative availability of licences for purchase.

### The population and labor force
- Population: L = 1 consisting of portion q skilled workers and 1−q unskilled workers.
- Consumer utility (linear, pins down interest rate r for all t):
  - U_it = sum_{h=t}^{∞} G_ih (1 + r)^{−h+t}, where G is output consumed.
- Consumers earn wages and profits from any licences they hold.

### Production
- Final output is a CES aggregate of two intermediate types (linearly homogeneous):
  - Y_t = [ (y^s_t)^{(ε−1)/ε} + (y^u_t)^{(ε−1)/ε} ]^{ε/(ε−1)}   with ε > 0.
- Relative prices of intermediates:
  - p^s_t / p^u_t = ( y^s_t / y^u_t )^{−1/ε}.
- Intermediate production (building on Romer (1990)):
  - Skilled intermediate uses skilled labor L^s_it and T^s different machines:
    - y^s_it = (L^s_it)^{1−α} ∏_{j=1}^{T^s_t} X_{ijt}^{α}
  - Unskilled intermediate uses unskilled labor L^u_it and T^u different machines:
    - y^u_it = A (L^u_it)^{1−α} ∏_{j=1}^{T^u_t} Z_{ijt}^{α}
  - A < 1 for unskilled labor (effective units of labor); capital (machines) depreciates fully each period.
- Firm-level demand for each skilled machine type (marginal product equals price):
  - X_{ijt} = [ α p^s_t / p_{X_{jt}} ]^{1/(1−α)} L^s_it.
- Own-price elasticity of demand for any machine = 1/(1−α), implying each monopolist sets profit-maximizing price p_X = 1/α for all j,t.
- Economy-wide demand for each skill-biased machine:
  - X_t = α^{2/(1−α)} (p^s_t)^{1/(1−α)} q_t
- Economy-wide demand for each unskilled machine:
  - Z_t = A α^{2/(1−α)} (p^u_t)^{1/(1−α)} (1−q_t)
- Economy-wide intermediates output:
  - y^s_t = T^s_t q_t^{1−α} X_t^{α}
  - y^u_t = T^u_t A^{1−α} (1−q_t)^{1−α} Z_t^{α}
- New machine types always employed due to constant returns to variety; increases in T^s relative to T^u or rise in q induce price adjustments.

### Prices and wages
- Define p_t ≡ (p^s / p^u)^{1/(1−α)} and Q ≡ q / (A(1−q)), T ≡ T^s / T^u.
- After substitutions:
  - p_t = ( T^s q / (T^u A(1−q)) )^{−1/σ} ≡ (T Q)^{−1/σ}_t, where σ = ε + α − εα is the elasticity of substitution between skilled and unskilled labor.
- Relative wages (labor hired until wage equals marginal revenue product), with W_t ≡ W^s_t / W^u_t:
  - W_t = T_t p_t = T^{(σ−1)/σ}_t Q^{−1/σ}_t
- Interpretation:
  - Standard substitution effect: rise in relative skilled quantity reduces relative skilled wage via p.
  - Technology effect: rise in T increases relative physical productivity of skilled labor but lowers p and hence W; net sign depends on σ.

### Technology adoption
- Empirical background (key facts preserved from text):
  - Most countries acquire technologies from abroad through imports or transfers.
  - Imported technical change need not be skill-biased: some imports complement skilled labor (Caselli & Wilson, 2004); some imported capital complements unskilled workers and can lower the skill premium (Raveh and Reshef, 2016).
  - Countries consider domestic factor market conditions before adopting methods (examples: hammer mill in Kenya; can production in Tanzania and Thailand).
  - Technology acquisition is modeled as purchases from abroad rather than home R&D for developing countries.
- Technology import pricing and licence costs:
  - It costs one unit of Y exported to import one machine (marginal cost unity).
  - Cost of acquiring licence for a skilled machine: C^s; for unskilled: C^u, with relative cost captured by world technology skill-bias:
    - C_t ≡ C^s_t / C^u_t = R^u_t / R^s_t ≡ 1 / R_t, where R is the skill-bias of the world’s available technologies and the relative cost of importing skilled technologies is inversely related to R.
- Licence value (discounted present value of future profits), with P_X = 1/α and Ω ≡ (1−α) α^{(1+α)/(1−α)}:
  - Per-period profit from a skilled licence: π_x = Ω (p^s_t)^{1/(1−α)} q_t.
  - Skilled licence value:
    - V^s_t = Ω sum_{i=1}^{∞} q_{t+i} ( p^s_{t+i} )^{1/(1−α)} (1 + r)^{−i}
  - Unskilled licence profit: π_z = Ω (p^u_t)^{1/(1−α)} A(1−q_t).
  - Unskilled licence value:
    - V^u_t = A Ω sum_{i=1}^{∞} (1−q_{t+i}) ( p^u_{t+i} )^{1/(1−α)} (1 + r)^{−i}
- Ratio of licence values:
  - V_t = [ sum_{i=1}^{∞} q_{t+i} ( p^s_{t+i} )^{1/(1−α)} (1 + r)^{−i} ] / [ A sum_{i=1}^{∞} (1−q_{t+i}) ( p^u_{t+i} )^{1/(1−α)} (1 + r)^{−i} ]
- For constant Q and R, simplified:
  - V = Q^{(σ−1)/σ} T^{−1/σ}

### Steady state and comparative statics
- Free entry implies V^s = C^s and V^u = C^u so in steady state:
  - V = C
- Steady-state relationship between technologies and fundamentals:
  - T = Q^{(σ−1)/σ} R^{1/σ}
- Final equation for the skill premium:
  - W = Q^{σ−2} R^{σ−1}
- Comparative statics (differentiation of log W):
  - d log W / d log Q = (∂ log W / ∂ log T) (d log T / d log Q) − 1/σ
  - Simplified to:
    - d log W / d log Q = σ−2
  - Interpretation:
    - Substitution effect (conventional labor demand) = −1/σ.
    - Technology effect operates through d log T / d log Q and, for σ > 1, a rise in Q leads to acquisition of more skilled machines (T rises).
    - For σ > 1 the technology effect dominates and rise in T raises skill premium; for σ < 1 effects reverse. The paper focuses on σ > 1 (empirically supported).

### Section 3 preview: Elasticity of substitution reinterpreted
- Canonical regression often estimated:
  - log W = α + β log Q + e, with implied traditional elasticity  ̃σ = −1/β.
- Mapping to the model:
  - In the directed-technical-change framework, β = σ − 2 (not β = −1/ ̃σ).
- Empirical implications and examples from literature:
  - Katz & Murphy (1992) and others established consensus elasticity ≈ 1.5 for U.S. studies (traditional interpretation).
  - HILZ (2022) report an unadjusted average regression coefficient whose implied ̃σ is 1.8 for all countries and 2.4 for the United States; interquartile ranges and bias-corrected means reported (maintained as described).
  - For developing countries: Psacharopoulos & Hinchliffe (1972) report ̃σ in 2.1 to 2.5 range; HILZ meta-study reports mean ̃σ = 2.1 for developing countries and bias-corrected mean ̃σ = 2.1 with [1.4;4.2] interval.
  - Re-interpretation under model: many existing coefficient estimates imply σ values that are lower and show less variation than implied ̃σ estimates. Example: Psacharopoulos & Hinchliffe (1972) coefficients imply σ ≈ 1.5–1.6 in the directed-technical-change framework.
- Consequences:
  - Directed-technical-change framework produces much smaller variation in implied elasticity estimates because β maps to σ − 2 rather than to the inverse −1/ ̃σ; taking inverses of small coefficients inflates variation in ̃σ estimates.

*Source: wpiea2023165-print-pdf (Section 2) — IMF working paper content unit*

### 2.  In HILZ, the interquartile range ofβestimates implies considerable variation in  ̃σbut not

### 2.  In HILZ, the interquartile range ofβestimates implies considerable variation in  ̃σbut not σ, which remains close to the consensus of 1.5.

### 3.2 Estimation bias, publication bias, and hypothesis testing
- Measurement error can cause attenuation bias, which tends to move estimated coefficients towards zero. Since most coefficient estimates are negative, attenuation bias would tend to overestimate  ̃σ. In the framework, the bias would be towards values of σ= 2 from either direction.
- Systematic mismeasurement could also bias the coefficient, though not necessarily towards zero.
- Identification and interpretation of β rely on the assumption that quantities affect prices and not the other way around. Reverse causation (wage premium affecting skill supply through migration or education choices) can bias estimates. Examples of approaches to address reverse causation include instrumental variables (compulsory schooling laws) and exploiting exogenous variation (school colleges and synthetic controls). In the absence of such options, using lags of quantities can mitigate reverse causation.
- If reverse causality is not fully dealt with, and there is a positive correlation between shifts in relative labor supply and labor demand, then:
  - a negative β-coefficient estimate is too small (in absolute value) relative to the true value;
  - a positive β-coefficient is too high relative to the true value.
  - Endogeneity of this form would tend to reinforce attenuation bias for true negative coefficients and thus lead to overestimates of  ̃σ. In the framework, it would lead to overestimates of σ regardless of the coefficient sign.
- HILZ document the role of attenuation and endogeneity bias and observe that IV methods can address both issues; they find that IV coefficients are on average 0.1 more negative than OLS coefficients.
  - Restricting to EMDEs using HILZ data yields a similar implied difference: only 0.1 for σ but implies a  ̃σ that is 0.4 lower.
  - More generally, the proposed framework makes inferred elasticities much more robust to estimation error.
- Publication bias works in the opposite direction to estimation biases:
  - Studies with β coefficients that are low or insignificantly different from zero (failing to reject the null of perfect substitutability) are less likely to be published, leading to understatement of substitution elasticities.
  - Publication bias may understate the number of studies that produce positive coefficients (theoretically-inconsistent negative values for  ̃σ), possibly explaining why the share of weakly positive coefficient values is less than 5 percent for the full set of studies and for the EMDE subsample.
- The proposed framework changes the interpretation and incentives around hypothesis testing:
  - Testing β= 0 in a 2-sided manner allows reduced-form testing of whether a higher skill supply increases or decreases the wage premium.
  - If σ is insignificantly different from 2, the technology and substitution effects are approximately equal and there is no change in wage inequality.
  - Testing whether types of labor can’t be substituted at all (Leontief) amounts to testing whether β=−2 in this framework.
  - σ= 1 (β=−1) is the only condition under which a rise in the supply of skilled labor does not lead to technical change that favors skilled workers and implies Cobb Douglas production technology.
- HILZ results after controlling for publication bias:
  - OLS estimates decline to almost zero, which increases  ̃σ to 10 yet is consistent with σ≈2.
  - HILZ preferred estimate accounting for estimation and publication bias is β=−0.27, implying:
    -  ̃σ= 3.7
    - σ= 1.73
    - HILZ 95% confidence interval for  ̃σ: [2;20]
    - The authors’ interval: [1.5;1.9]
  - For EMDEs, combined effects of publication and estimation bias yield a bias-adjusted estimate very close to the uncorrected mean at 2.1 with an interval of [1.4;4.2]. It alternatively implies σ= 1.53 with an interval of about [1.3;1.8].

### 3.3 Dynamics
- Time-series/panel analogue: log W_t = α_0 + α_1 log R_t + β log Q_t + e_t with R represented by a trend term.
- Dynamic specifications distinguish short-run substitution effects and longer-run technology responses; wage premia may initially contract after a rise in skill supply but subsequently expand.
- Example dynamic specification:
  - ∆log W_t = γ_0 − 1/σ ∆log Q_t + γ_1 [log W_{t−1} − (σ−2) log Q_{t−1}] + e_t
  - γ_0 captures the linear trend; additional trend terms could be incorporated.
  - Coefficient on the first difference of relative skill supply represents the short-run substitution effect; its negative inverse provides an estimate of σ.
  - γ_1 indicates speed of adjustment to the static/long-run equilibrium; together with γ_1(σ−2) it can be used to back out another estimate of σ.
  - The framework is amenable to estimation with a non-linear restriction exploiting σ in both first-difference and lagged labor supply terms.

### 4 New data and estimates

- Data sources:
  - Global panel: constructed from 1970 to 2010, extending coverage to about 60 developing countries, building on Caselli & Coleman (2006). Labor supply data from the 2018 update of Barro and Lee (2013) reporting share of population aged 15-64 in seven educational categories. Mincerian coefficients from Psacharopoulos & Patrinos (2018) and unpublished Barro & Lee (2001) duration information used to calculate wage premia and aggregates.
    - Labor supply data are available in 5-year periods; Mincerians have varying frequencies. Observations from the period preceding the Mincerian estimate are used to allow for lags (e.g., a Mincerian for 2000 or 2004 allocated labor supply for 2005).
  - Aggregation from seven categories into two (skilled/unskilled):
    - For primary cutoff:
      - L_unskilled = L_no education + W_some primary L_some primary
      - L_skilled = L_completed primary + W_some secondary L_some secondary + W_completed secondary L_completed secondary + W_some higher L_some higher + W_completed higher L_completed higher
      - W_i constructed using Mincerian earnings coefficients and years of schooling between categories; W_i measured relative to completed primary education for skilled aggregates.
    - For tertiary cutoff analogous construction performed.
  - Latin America: SEDLAC December 2022 update (CEDLAS & World Bank (2009) methodology). SEDLAC skill levels: 'low' 0-8 years, 'medium' 9-13 years, 'high' 14+ years. Two cutoffs used:
    - skilled = more than 8 years (medium+high, roughly equivalent to completed primary)
    - skilled = more than 13 years (high only, roughly equivalent to some tertiary)
    - Wages by level are in the data; frequency typically annual.
- Global panel results:
  - Tables 2 and 3: skilled defined as some tertiary/higher education. In all specifications, estimated skill supply coefficient is slightly positive.
    - Traditional interpretation produces negative/nonsensical  ̃σ values; under the paper’s interpretation (“Elasticity (beta+2)”), σ is slightly higher than 2 and small positive coefficients represent substitution effects slightly outweighed by directed technology effects.
    - Example (column 1, Table 2, random effects): coefficient 0.15 yields:
      - traditional  ̃σ = -6.73
      - under new interpretation σ= 2.15, implying substitution effect = -0.47 and technology effect = 0.61
    - Fixed effects, between effects, country-specific AR(1), period dummies, and higher-order trend terms do not materially alter results.
    - Estimates are fairly consistently around 0.15, implying σ= 2.15.
  - Tables 4 and 5: skilled defined as at least primary education. Coefficients positive but much closer to zero; under new interpretation σ≈2.
  - Standard errors suggest the elasticity is significantly greater than 1 (implying absence of directed technical change if interpreted as Cobb Douglas). σ>1 means a rise in skill supply would raise its share of labor income. Trend term and period dummies were insignificant or negative.
- Latin America panel (SEDLAC):
  - Figures show broadbased increase in skill supply; skill premium has not fallen consistently, especially at higher education cutoff.
  - Table 6 (higher education cutoff, country dummies included):
    - Column 1 (static canonical): significantly negative coefficient; traditional interpretation implies  ̃σ >5, while framework implies σ= 1.81 with substitution effect slightly outweighing technology effect.
    - Column 2 (dynamic per equation 20): inverse of coefficient on first difference term = -0.11 implies inverse elasticity of 9.2; steady-state/long-run elasticity = 1.71. Substitution and technology effects: -0.59 and 0.29.
    - Column 3 (non-linear constraint enforcing equivalence): results close to steady-state relationship from unrestricted regression.
  - Table 7 (primary cutoff):
    - Column 1 static: coefficient positive implying unfeasible  ̃σ under traditional view but σ= 2.2 under new framework (technology effect exceeds substitution effect).
    - Column 2 dynamic: coefficient on first difference positive (implies unfeasible negative elasticity even under new framework). Constrained approach estimates σ= 1.88.
- Single time series for Brazil (1981-2021):
  - Table 8 (primary cutoff):
    - Coefficient -0.67 implies traditional  ̃σ= 1.5 and σ= 1.33 in new framework.
    - Dynamic specification: inverse of first-difference coefficient (-0.45) implies elasticity 2.25, similar to steady-state/long-run elasticity 1.7. Constrained estimate matches steady-state.
  - Table 9 (higher education cutoff):
    - Static specification yields non-feasible traditional elasticity; dynamic specification’s low first-difference coefficient implies very high inverse elasticity.
    - Elasticity from dynamic model steady-state and constrained estimate = 1.8 (closer to tertiary cutoff value).
- Central American countries (Costa Rica, Dominican Republic, El Salvador, Honduras, Panama; roughly 1991-2021):
  - Supply of skills increased notably; decline in wage premium less apparent.
  - Table 10 (static, higher education cutoff, survey method dummies included):
    - Coefficients range from -0.21 (Honduras) to 0.20 (El Salvador).
    - Panel coefficient 0.04 implies σ= 2.04 and directed technology effect marginally outweighs substitution effect.
  - Table 11 (constrained dynamic specification): estimates σ= 1.67 for the region, with most countries close to that value.
  - Tables 12 and 13 (primary cutoff): most static specifications estimate positive coefficients and thus, in the framework, elasticity values of over 2.

*Italic source attribution: wpiea2023165-print-pdf — content unit 2 (section excerpts on estimation bias, dynamics, and new data and estimates).*

### 2.  The dynamic specifications yield estimates of around 1.8.  The trend terms in the static

### 2.  The dynamic specifications yield estimates of around 1.8.  The trend terms in the static

### Summary and interpretation
- For the Central America region:
  - Many static specifications for higher and primary cutoffs imply unfeasible elasticities under the traditional interpretation.
  - By the authors' reinterpretation, σ≈2 for higher education and a little more for primary education.
  - Dynamic specifications yield Central American elasticities of 1.7-1.8, matching those for Brazil and Latin America as a whole.
  - Variation within Central America across individual countries is at least as large as variation between the region and the rest of Latin America.
  - Mollick (2008) finds coefficients of ̃σ≈2 and thus σ≈1.5 for Mexico.
- For global data:
  - The authors' coefficient estimates differ from the negative coefficients produced by Psacharopoulos & Hinchliffe (1972) and are toward the extreme end of the HILZ meta study for EMDEs.
  - The global estimate for the value of the elasticity is comparatively high; positive estimates would be more prone to exclusion owing to publication bias.
  - Even extreme values of σ are not that different in the authors' framework, unlike in traditional interpretations.
  - Regional analyses that permit dynamics align more closely with existing studies.
  - Manacorda et al (2010) imply values of 1.6-1.8 for σ.
  - The Latin America analysis is aligned with the HILZ bias-adjusted mean for all countries.

### Model, reinterpretation, and main quantitative implications
- The paper introduces a model of directed technical change for EMDEs drawing on Acemoglu (1998) and Kiley (1999), modeling an EMDE licence holder choosing whether to import machines of a particular type to sell locally.
- Key reinterpretation:
  - In the authors' framework, the coefficient on the canonical reduced-form regression of relative wages on relative quantities is σ−2, not −1/̃σ.
  - Viewed this way, elasticities near the existing consensus remain close: negative coefficient estimates close to zero, which traditionally imply very high elasticity values, would yield σ values of just below 2.
  - The framework permits positive coefficient estimates, is more robust to estimation error, and mitigates a source of publication bias.
- Preferred estimates implied by HILZ bias-adjusted coefficient estimates:
  - σ= 1.7 for the global sample.
  - σ= 1.5 for the subset of EMDEs.

### Empirical contributions and quantitative results
- Data construction:
  - Global panel of relative skill supply and relative quantities for large-panel analysis.
  - Latin America panel to facilitate dynamics.
- Main empirical findings:
  - Global results indicate a slightly positive relationship between the relative supply of skills and the wage premium, implying an elasticity of 2-2.2.
  - Latin America results, including Central America, indicate elasticities of around 2 or, once accounting for dynamics, 1.7-1.8, aligning with the consensus.
- Interpretation:
  - The absence of a large correlation between wage premia and quantities is viewed as technical change approximately cancelling the substitution effect rather than evidence of perfect substitution.

### Policy implications
- Prioritizing expanded education access to reduce within-country wage inequality may not be justified based on the modest effect on wage premia suggested by the results.
- The finding of imperfect substitution, even when the reduced-form correlation is weak (Banerjee & Duflo, 2005), supports:
  - Accounting for imperfect substitution in human capital measurement.
  - Enriching the debate on the role of human capital in explaining cross-country income differences (Jones, 2014; Caselli & Ciccone, 2019).
  - Expectation of more broad-based effects of immigration on wages of the local population (Borjas et. al, 2012).

### Suggested extensions and further research
- Encourage bringing previously condemned studies to light under the new framework to stimulate more research.
- Possible extensions include:
  - In-depth analysis of more countries with perhaps more observations.
  - Alternative forms of aggregating skill types.
  - Applications of the framework to innovations that account for worker experience.
  - Exploration of alternative proxies for external drivers of technology availability or adoption, including observables like trade, investment, or measures of upskilling in advanced economies, or unobservables backed out for advanced economies using the directed technical change modelling framework.

*Source: wpiea2023165-print-pdf*

### References

### wpiea2023165-print-pdf - References

### References
- [1]Acemoglu, D. (1998), Why do new technologies complement skills?  Directed technical change and wage inequality, Quarterly Journal of Economics, vol. 113(4)
- [2]Acemoglu, D. (2002), Directed technical Change, Review of Economic Studies, vol. 69(4)
- [3]Acemoglu, D. & F. Zilibotti (2001), Productivity Differences, Quarterly Journal of Economics, vol. 116(2)
- [4]Angrist,  J.  (1995),  The  Economic  Returns  to  Schooling  in  the  West  Bank  and  Gaza  Strip, American Economic Review, vol. 85(5)
- [5]Atkinson, A. (2015), Inequality:  What can be done?, Harvard University Press
- [6]Atkinson, A. & J. Stiglitz (1969), A new view of technological change, Economic Journal, vol. 79(1)
- [7]Banerjee, A. & E. Duflo (2005), Growth Theory through the Lens of Development Economics,in Durlauf & Aghion, (eds.),Handbook of Economic Growth, Elsevier Science Ltd.-North Holland: 2005, Vol. 1A
- [8]Behar, A. (2009), Directed Technical change, the Elasticity of Substitution and Wage Inequality in Developing Economies. Oxford Department of Economics Discussion Paper, 467
- [9]Behar, A. (2013), The endogenous skill bias of technical change and inequality in developing countries, IMF Working Paper WP/13/50
- [10]Behar, A. (2016), The endogenous skill bias of technical change and wage inequality in developing countries, The Journal of International Trade  Economic Development, Taylor  Francis Journals, vol. 25(8)
- [11]Barro, R. & J. Lee (2001), International data on educational attainment:  updates and implications, JOxford Economic Papers, vol. 53(3)
- [12]Barro, R. & J. Lee (2013), A new data set of educational attainment in the world, 1950–2010, Journal of Development Economics, vol. 104
- [13]Berman,  E.  &  S.  Machin  (2000),  Skill-biased  technology  transfer:  evidence  of  factor  biased technical change in developing countries, Oxford Review of Economic Policy, vol. 16(3)
- [14]Berndt, E. & L. Christensen (1973), The Internal Structure of Functional Relationships:  Separability, Substitution and Aggregation, Review of Economic Studies vol. 40(3)
- [15]Blum, B. (2009), Endowments, Output, and the Bias of Directed Innovation, Review of Economic Studies (2010) vol. 77
- [16]Borjas, G., J. Grogger & G. Hanson, 2012, Comment:  On Estimating Elasticities of Substitution, Journal of the European Economic Association, vol. 10(1)
- [17]Bowlus, A., L. Lochner, C. Robinson & E. Suleymanoglu (2021), Wages, Skills, and Skill-Biased Technical Change:  The Canonical Model Revisited, CESifo Working Paper 9212
- [18]Carneiro, P., K. Liu & K Salvanes (2023), The supply of skill and endogenous technical change: evidence from a college expansion reform, Journal of the European Economic Association, vol. 21(1)
- [19]Caselli, F. (2005), Accounting for Cross-Country Income Differences, in P. Aghion & S. Durlauf (eds.) Handbook of Economic Growth, Elsevier
- [20]Caselli, F. & A. Ciccone (2019), The Human Capital Stock:  A Generalized Approach:  Comment, American Economic Review, vol. 109(3)
- [21]Caselli, F. & W. Coleman (2006), The World Technology Frontier, American Economic Review, vol. 96(3)
- [22]Caselli, F. & D. Wilson (2004), Importing Technology, Journal of Monetary Economics, vol. 51(1)
- [23]CEDLAS & World Bank (2009), A guide to the SEDLAC socio-economic database for Latin America and the Caribbean
- [24]Christenko, A., ˇ Z. Martinaitis & P. Kr ̄uminas (2022), From Socialism to Capitalism: Low-Skill-Biased Change in the Baltics during the Transition and Beyond, TalTech Journal of European Studies, vol. 13(1)
- [25]Ciccone  &  Peri  (2005),  Long-run  substitutability  between  more  and  less  educated  workers: evidence from US States, 1950-1990, The Review of Economics and Statistics, vol. 87(4)
- [26]Eaton, J. & S. Kortum (2001), Trade in Capital Goods, European Economic Review, vol. 45(7)
- [27]Epifani, P. & G. Gancia (2008), The skill bias of world trade, Economic Journal, vol. 118
- [28]Esposito, P. & R. Stehrer (2009), The sector bias of skill-biased technical change and the rising skill premium in transition economies, Empirica vol. 36
- [29]Fernandez, M.  J Messina (2018), Skill premium, labor supply, and changes in the structure of wages in Latin America, Journal of Development Economics, vol. 135
- [30]Fransman, M. (1985), Conceptualising Technical Change in the Third World in the 1980s:  An Interpretive Survey, Journal of Development Studies, vol. 21(4)
- [31]Freeman, R. (1986), Demand for Education, in Ashenfelter & Layard (eds), Handbook of labor Economics Vol 1, Elsevier / North Holland
- [32]Gallego,  F.  (2012),  Skill  premium  in  Chile:   Studying  skill  upgrading  in  the  South,  World Development vol. 40(3)
- [33]Gindling, T. & W. Sun (2002), Higher education planning and the wages of workers with higher education in Taiwan, Economics of Education Review vol. 21
- [34]Hamermesh, D. (1993), Labor Demand, Princeton University Press
- [35]Havranek,  T.,  Z Irsova,  L Laslopova,  & O Zeynalova (2022),  Publication and Attenudation Biases in Measuring Skill Substitution, Review of Economics and Statistics, preprint
- [36]Hendricks,  L.  (2002),  How  Important  Is  Human  Capital  for  Development?   Evidence  from Immigrant Earnings, American Economic Review vol. 92(1)
- [37]Hicks, J. (1963), The theory of wages, 2nd edition, Macmillan
- [38]Jones, B. (2014), The human capital stock:  a generalized approach, American Economic Review vol. 104(11)
- [39]Karabarbounis, L & B Neiman (2013), The Global Decline of the Labor Share, The Quarterly Journal of Economics vol. 129(1)
- [40]Katz & Murphy (1992),  Changes in relative wages,  1963-1987:  Supply and demand factors, Quarterly Journal of Economics, vol. 107(1)
- [41]Kiley, M. (1999), The supply of skilled labor and skill-biased technical progress, the Economic Journal, vol. (109)
- [42]Klenow, P. & A. Rodriguez-Clare (1997), The Neoclassical Revival in Growth Economics:  Has It Gone Too Far?, NBER Macroeconomics Annual vol. 12
- [43]Knight, J. (1979), Black Wages and Choice of Techniques in South Africa, Oxford Bulletin of Economics and Statistics, vol. 41(2)
- [44]Knight, J. & R. Sabot (1987), Educational expansion, government policy and wage compression, Journal of Development Economics vol 26(2)
- [45]Lavely,  W.,  X. Zhenyu,  L. Bohua & R. Freedman (1990),  The Rise in Female Education in China:  National and Regional Patterns, The China Quarterly vol. 121
- [46]Li,  B.  (2010),  Multinational  production  and  choice  of  technologies:  New  evidence  on  skill-biased technological change from China, Economics Letters vol. 108
- [47]Manacorda, M., C. Sanchez-Paramo & N. Schady (2010), Changes in Returns to Education in Latin America:  The Role of Demand and Supply of SKills, Industrial and Labor Relations Review, vol.63 (2)
- [48]Mollick, A. (2008), The Rise of the Skill Premium in Mexican Maquiladoras, the Journal of Development Studies, vol. 44(9)
- [49]Okoye,  D.  (2016),  Appropriate  technology  and  income  differences,  International  Economic Review, vol. 57(3)
- [50]Psacharopoulos, G. & K. Hinchliffe (1972), Further Evidence on the Elasticity of Substitution among Different Types of Educated labor, Journal of Political Economy, vol. 80(4)
- [51]Psacharopoulos,  G.  &  H.  Patrinos  (2004), Returns to Investment in Education:  A Further Update, Education Economics, vol. 12(2)
- [52]Psacharopoulos,  G.  &  H.  Patrinos  (2018),  Returns  to  investment  in  education:  a  decennial review of the global literature, Education Economics vol. 26(5)
- [53]Raveh, O. & A. Reshef (2016), Capital imports composition, complementarities, and the skill premium in developing countries, Journal of Development Economics, vol. 118
- [54]Romer, P. (1990), Endogenous technological change, Journal of Political Economy, vol. 98(5)
- [55]Savvides,  A. & M. Zachariadis (2005),  International technology diffusion and the growth of TFP in the manufacturing sector of developing economies, Review of Development Economics, vol. 9(4)
- [56]Serrano,  L. & M. Timmer (2002),  Is technical change directed by the supply of skills?  The case of South Korea, Economics Letters vol. 76
- [57]Teulings,  C.  &  T.  van  Rens  (2008),  Education,  Growth  and  Income  Inequality,  Review  of Economics and Statistics, vol, 90(1)
- [58]Thoenig, M. & T. Verdier (2003), A Theory of Defensive Skill-Biased Innovation and Globalization, American Economic Review, vol. 93(3)
- [59]Van der Berg, S. (2001), Resource shifts in South African Schools after the political transition, Development Southern Africa vol. 18(4)
- [60]Wooldridge, J. (2002), Econometric Analysis of Cross Section and Panel Data, MIT Press

### Figures and Tables listed in References section
- Figure 1:  Skill supply and wage premium (primary)
- Figure 2:  Skill supply and wage premium (tertiary)
- Table 1:  Existing literature:  coefficients and implied elasticities
- Table 2:  Global panel, higher cutoff, by estimation method
  - Key reported numeric entries include Skill supply 0.15*** 0.25*** 0.05 0.12*** 0.14*** (standard errors in parentheses), Constant 1.66*** 2.01*** 1.35*** 1.62*** 1.73***, Elasticity (inverse) -6.73*** -4.03*** -19.67 -8.02*** -6.94***, Elasticity2.15*** 2.25*** 2.05*** 2.12*** 2.14***, Subs. effect -0.47*** -0.44*** -0.49*** -0.47*** -0.47***, Tech. effect 0.61*** 0.69*** 0.54*** 0.60*** 0.61***, Observations 204 204 204 190 204.
- Table 3:  Global panel, higher cutoff, by sample
  - Examples of reported values: Skill supply 0.15*** 0.16* 0.25*** 0.08 0.14***; Elasticity (inverse) -6.73*** -6.19* -4.05*** -12.91 -7.00***; Elasticity2.15*** 2.16*** 2.25*** 2.08*** 2.14***; Observations 204 146 178 127 127.
- Table 4:  Global panel, secondary cutoff, by estimation method
  - Examples: Skill supply 0.04*** 0.09*** 0.00 0.01*** 0.03***; Constant 0.34*** 0.37*** 0.35*** 0.36*** 0.36***; Elasticity (inverse) -26.21*** -11.21*** -1682.32 -80.32*** -31.61***; Elasticity (beta+2) 2.04*** 2.09*** 2.00*** 2.01*** 2.03***; Observations 204 204 204 190 204.
- Table 5:  Global panel, secondary cutoff, by sample
  - Examples: Skill supply 0.04*** 0.04* 0.05*** 0.03** 0.03***; Elasticity (inverse) -26.21*** -26.89* -19.21*** -35.51** -31.59***; Elasticity (beta+2) 2.04*** 2.04*** 2.05*** 2.03*** 2.03***; Observations 204 146 178 127 127.
- Table 6:  Latin America panel, higher cutoff
  - Examples: Ln Relative Skill Supply: 13 years -0.19** (0.08); Year -0.01*** (0.00); Elasticity (inverse) 5.39** 9.20* (2.18)(5.17); Elasticity (beta+2) 1.81*** 1.71*** 1.73*** (0.08)(0.07)(0.07); Subs. effect -0.55*** -0.59*** -0.58***; Tech. effect 0.37*** 0.29*** 0.31***; Observations 246 227 232.
- Table 7:  Latin America panel, primary cutoff
  - Examples: Ln Relative Skill Supply: 8 years 0.20* (0.10); Year -0.02*** (0.01); Elasticity (inverse) -4.98** -6.77 (2.41)(4.15); Elasticity (beta+2) 2.20*** 1.84*** 1.88***; Subs. effect -0.45*** -0.54*** -0.53***; Tech. effect 0.66*** 0.39*** 0.41***; Observations 246 227 232.
- Table 8:  Brazil, higher education cutoff
  - Examples: Ln Relative Skill Supply: 13 years -0.67*** (0.16); Year 0.02** (0.01); Elasticity (inverse) 1.50*** 2.25** (0.37)(1.09); Elasticity (beta+2) 1.33*** 1.70*** 1.70***; Subs. effect -0.75*** -0.59*** -0.59***; Tech. effect 0.08 0.29*** 0.29***; Observations 363 232 232.
- Table 9:  Brazil, primary education cutoff
  - Examples: Ln Relative Skill Supply: 8 years 0.32 (0.28); Year -0.04* (0.02); Elasticity (inverse) -3.09 11.70 (2.62)(26.99); Elasticity (beta+2) 2.32*** 1.80*** 1.82***; Subs. effect -0.43*** -0.56*** -0.55***; Tech effect 0.75*** 0.35*** 0.37***; Observations 363 232 232.
- Table 10:  Central America:  Static specification, higher education cutoff
  - Country columns include C. Rica, Dom. Rep., El Salv., Honduras, Panama, All. Example entries: Ln Relative Skill Supply: 13 years 0.10 -0.07 0.20 -0.21 -0.10 0.04; Year -0.01** -0.01 -0.02*** -0.01 -0.00 -0.01**; Elasticity (inverse) -9.86 15.11 -5.02 4.80 9.92 -24.19; Elasticity (beta+2) 2.10*** 1.93*** 2.20*** 1.79*** 1.90*** 2.04***; Observations 332 222 272 71 28.
- Table 11:  Central America:  Constrained dynamic specification, higher education cutoff
  - Examples: Constant -39.90 -14.89 -121.64*** -133.48*** 0.53*** 0.32***; Lagged premium -0.66** -1.10*** -0.99*** -0.43** -0.98*** -0.73***; Lagged skill supply -0.14* -0.42** -0.85* -0.16 -0.26* -0.24***; Elasticity (beta+2) 1.79*** 1.62*** 1.14*** 1.64*** 1.74*** 1.67***; Subs. effect -0.56*** -0.62*** -0.87*** -0.61*** -0.58*** -0.60***; Tech. effect 0.35*** 0.24** 0.02 0.25** 0.31*** 0.27***; Observations 322 121 242 212 120.
- Table 12:  Central America:  Static specification, primary cutoff
  - Examples: Ln Relative Skill Supply: 8 years 0.28*** 0.80*** 0.31 0.29 -0.35* 0.23***; Year -0.01*** -0.06*** -0.02*** -0.03** 0.01 -0.02**; Elasticity (inverse) -3.52*** -1.25*** -3.26* -3.39 2.82* -4.44***; Elasticity (beta+2) 2.28*** 2.80*** 2.31*** 2.29*** 1.65*** 2.23***; Observations 332 222 272 71 28.
- Table 13:  Central America:  Constrained Dynamic Specification Primary, by country
  - Examples: Constant 0.43** 0.59*** 0.79*** 72.22*** 0.56*** 0.60**; Lagged premium -0.73** -1.05*** -1.19*** -0.38** -0.70*** -0.65**; Lagged skill supply -0.16* -0.27 -0.51** -0.06 -0.03 -0.13; Elasticity (beta+2) 1.78*** 1.74*** 1.58*** 1.83*** 1.96*** 1.80***; Subs. effect -0.56*** -0.57*** -0.63*** -0.55*** -0.51*** -0.55***; Tech. effect 0.34*** 0.32*** 0.21*** 0.38** 0.47*** 0.36***; Observations 322 121 242 212 120.

*Content and exact numeric values preserved from the source PDF section "References".*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2023/english/wpiea2023165-print-pdf.pdf_