## _wp0468 - References

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---

### I. Introduction: problems and proposed solution
- Central empirical problems:
  - Inconsistent empirical estimates arising from omitted country-specific effects or endogenous variables.
  - Model uncertainty due to lack of clear theoretical guidance on choice of regressors.
- Estimation and identification strategy:
  - Systems Generalized Method of Moments Estimator (GMM) (Hansen (1982)) addresses endogeneity and omitted-variable bias by estimating a system (levels and differences) and instruments potentially endogenous explanatory variables with their own lagged values.
- Approaches to model uncertainty:
  - (i) arbitrarily select one model;
  - (ii) present results for all plausible models;
  - (iii) explicitly account for model uncertainty (preferred but challenging).
- Proposal:
  - Introduces Bayesian Model Averaging (BMA) as conceptually attractive but computationally difficult when the number of regressors is large: Number of models = 2^{k*}.
  - Proposes Limited Information Bayesian Model Averaging (LIBMA) which:
    - Incorporates dynamic panel estimation via GMM in a Bayesian robustness check.
    - Is limited-information (uses moment restrictions via GMM) rather than a full stochastic specification.
    - Controls for endogeneity through GMM, whereas prior literature often assumes exogenous regressors.

### II. Preliminaries on GMM: setup and properties
- Setup and notation:
  - x_t: n×1 vector of stochastic processes; θ: q×1 parameter vector from Θ ⊂ R^q.
  - h(x_t, θ): r×1 vector-valued function with moment condition E_P[h(x_t, θ_0)] = 0.
  - Sample average g_T(x_T, θ) ≡ (1/T) Σ_{t=1}^T h(x_t, θ).
- Key assumptions:
  - (A1) {w_t} is stationary and ergodic.
  - (A2) (a) E_P[w_t w'_t] exists and is finite; (b) E_P[w_{t+s} | w_t, w_{t-1}, ...] converges in mean square to zero.
  - (A3) (a) h(x, .) is continuously differentiable in Θ for each x; (b) h(., θ) and ∂h(., θ)/∂θ are Borel measurable for each θ ∈ Θ.
- Definitions and properties:
  - GMM estimator bθ_{G,T}(ω) minimizes g_T(x_T, θ)' W_{G,T} g_T(x_T, θ) with W_{G,T} positive definite weighting matrices.
  - First-order condition (interior optimum): [∂g_T/∂θ |_{θ=bθ}]' W_{G,T} g_T(x_T, bθ) = 0.
  - Long-run variance S ≡ Σ_{ν=-∞}^{∞} E_P[h(x_t, θ_0) h(x_{t-ν}, θ_0)']; S = lim_{T→∞} E_P[T g_T(x, θ_0) g_T(x, θ_0)'].
  - Optimal choice W_{G,T} = S^{-1} yields smallest asymptotic variance.
  - Consistent estimators of S: White (1980), Newey-West (1987) Bartlett kernel, Hansen (1982) truncated kernel, Andrews and Monahan (1992) automatic bandwidth.
  - Optimal GMM objective approximation: g_T(x_T, θ)' bS_T^{-1} g_T(x_T, θ) where bS_T is a consistent estimator of S.

### III. GMM in the Bayesian framework: Bayes estimator and limited information likelihood
- Motivation and methodological background:
  - Bayesian estimation traditionally requires a likelihood; recent work constructs likelihood analogues for moment problems (Zellner, Inoue, Kim).
  - Kim (2000, 2002) develops a limited-information Bayesian counterpart to classical GMM; this essay follows that approach.
- Bayes estimator aligned with GMM:
  - Posterior π_T(θ | x_T) defined on measurable space (Θ, G).
  - Quadratic loss in g_T: c(θ, δ) = [g_T(θ) − g_T(δ)]' W_T [g_T(θ) − g_T(δ)], transformable to quadratic in θ: c(θ, δ) = (θ − δ)' g W_T (θ − δ).
  - First order condition for Bayes estimator implies moment condition E_π[Ξ_T g_T(θ)] = 0 where Ξ_T = [∂g_T(θ)/∂θ |_{θ=bθ}]' W_T.
  - Lemma 1: Under second order conditions and Assumption (A3), GMM estimator bθ_{GMM} equals Bayes estimator bθ_B iff E_π[Ξ_T g_T(θ)] = 0 with {W_T} = {W_{G,T}}.
- Limited Information Likelihood (LIL):
  - Define family Q of probability measures absolutely continuous w.r.t. P satisfying moment constraints E_Q[g_T(x_T, θ)] = 0 and lim_{T→∞} E_Q[T g_T g_T'] = S.
  - Choose Q* ∈ Q minimizing Kullback-Leibler divergence I(Q || P) = ∫ ln(dQ/dP) dQ.
  - q*_P(θ) = dQ*/dP interpreted as an I-projection or Limited Information Likelihood (LIL).
  - Finite-sample LIL approximation:
    - q_{P,T}(x_T, θ) = K exp{ κ T g_T(x_T, θ)' S_T^{-1} g_T(x_T, θ) } with κ = −1/2 desirable and S replaced by consistent estimator bS_T.

### IV. Model uncertainty and Bayesian Model Averaging under limited information
- Bayesian model comparison:
  - Posterior odds for models M_1 and M_2:
    - p(M_1 | x_T) = q_T(x_T | M_1) p(M_1) / [ q_T(x_T | M_1) p(M_1) + q_T(x_T | M_2) p(M_2) ].
    - Posterior odds ratio: p(M_2 | x_T) / p(M_1 | x_T) = [ q_T(x_T | M_2) / q_T(x_T | M_1) ] × [ p(M_2) / p(M_1) ]; first term is Bayes factor B_{21}.
- Laplace approximation and BIC connections:
  - log q_T(x_T | M) ≈ log q_T(x_T | \hat θ, M) − (d/2) log n + O(1).
  - log B_{21} ≈ log q_T(x_T | \hat θ_2, M_2) − log q_T(x_T | \hat θ_1, M_1) − (d_2 − d_1)/2 log n + O(n^{-1/2}).
  - BIC = 2 log B_{21} ≈ 2[log q_T(x_T | \hat θ_2) − log q_T(x_T | \hat θ_1)] − (d_2 − d_1) log n + O(n^{-1/2}).
- Limited Information BIC (LIBIC) and LIBMA:
  - Replace full-information log-likelihood with LIL to obtain LIBIC:
    - LIBIC = 2[log q_{P,T}(x_T | \hat θ_2, M_2) − log q_{P,T}(x_T | \hat θ_1, M_1)] − (d_2 − d_1) log n.
  - With κ = −1/2 and LIL substitution:
    - LIBIC = 2[ κ T g_T(x_T, θ_2)' bS_T^{-1} g_T(x_T, θ_2) − κ T g_T(x_T, θ_1)' bS_T^{-1} g_T(x_T, θ_1) ] − (d_2 − d_1) log n.
  - Posterior model probabilities under limited information (LIBMA):
    - p(M_k | x_T) = exp( − 1/2 LIBIC_k ) p(M_k) / Σ_{j=1}^K exp( − 1/2 LIBIC_j ) p(M_j).
  - LIBMA: extension of BMA that uses LIBIC and LIL to average over models when only limited-information moment conditions (GMM) are available.
- Practical considerations:
  - BMA challenges: infeasibility when number of regressors k* large (2^{k*} models) and need to specify many priors.
  - LIBMA relaxes full-likelihood requirement and can control for endogeneity; still requires choices over model priors but offers a limited-information alternative.

### V. Statistics and computational aspects for the robustness analysis
- Model space and prior specification:
  - k* possible regressors; K = 2^{k*} possible models M_j.
  - Represent model M_j as binary length-k* vector (1 = variable included, 0 = excluded).
  - Prior uses a single hyper-parameter k = expected model size; equal inclusion probability for each variable = k/k*.
  - Prior probability for model M_j:
    - p(M_j) = (k/k*)^{k_j} (1 − k/k*)^{1−k_j} where k_j is number of included variables in M_j.
  - Prior odds ratio between M_j and M_l:
    - p(M_j)/p(M_l) = (k/k*)^{k_j − k_l} (1 − k/k*)^{k_j − k_l}.
- Posterior model probabilities and model averaging formulas:
  - Posterior model probability with LIBIC weights:
    - p(M_j | x_T) = exp( − 1/2 LIBIC_j ) p(M_j) / Σ_{l=1}^{2^{k*}} exp( − 1/2 LIBIC_l ) p(M_l).
  - Posterior mean of parameter θ_k:
    - E(θ_k | x_T) = Σ_{j=1}^{2^{k*}} p(M_j | x_T) E(θ_k | x_T, M_j).
  - Posterior variance of θ_k:
    - Var(θ_k | x_T) = Σ_{j=1}^{2^{k*}} p(M_j | x_T) [ Var(θ_k | x_T, M_j) + E(θ_k | x_T, M_j)^2 ] − E(θ_k | x_T)^2.
- Inclusion and sign metrics:
  - Posterior inclusion probability for regressor k:
    - p(θ_k ≠ 0 | x_T) = Σ_{M_j: θ_k ≠ 0} p(M_j | x_T).
  - Decision rule: if p(θ_k ≠ 0 | x_T) > p(θ_k ≠ 0) = k/k*, variable has high marginal contribution.
  - Posterior mean and variance conditional on inclusion: divide unconditional posterior mean and variance by posterior inclusion probability.
  - Sign certainty probability:
    - sign certainty for θ_k = p[ sgn(θ_k) = sgn E(θ_k | D) | D, θ_k ≠ 0 ] = Σ_{j=1}^{2^{k*}} p(M_j | x_T) p[ sgn(θ_k) = sgn E(θ_k | x_T) | M_j, x_T ].

### VI. Conclusion: contribution and applications
- Main contribution:
  - Develops theoretical background and computational aspects for Limited Information Bayesian Model Averaging (LIBMA).
  - LIBMA provides a coherent Bayesian framework that:
    - Accounts explicitly for model uncertainty via model averaging.
    - Relaxes full-information likelihood assumptions by using GMM-based Limited Information Likelihood.
    - Controls for endogeneity through GMM instrumentation.
- Potential applications highlighted:
  - Investigations of competing hypotheses.
  - Parameter estimation robust to model specification.
  - Empirical growth and poverty analyses, including an example application by Ghura, Leite, and Tsangarides (2002) on elasticity of poor income with respect to average income and macroeconomic policy effects on poverty.
  - Cross-country convergence and robust patterns of growth behavior analysis using LIBMA.

*Source: _wp0468 - References*

### References .............................................................................................................

### _wp0468 - References

### I. Introduction: problems and proposed solution
- Identifies two central empirical problems:
  - Inconsistent empirical estimates arising from omitted country-specific effects or endogenous variables.
  - Model uncertainty due to lack of clear theoretical guidance on choice of regressors.
- Notes that systems Generalized Method of Moments Estimator (GMM) (Hansen (1982)):
  - Addresses endogeneity and omitted-variable bias simultaneously by estimating a system (levels and differences).
  - Instruments potentially endogenous explanatory variables with their own lagged values.
- Discusses options for dealing with model uncertainty:
  - (i) arbitrarily select one model;
  - (ii) present results for all plausible models;
  - (iii) explicitly account for model uncertainty (preferred but challenging).
- Introduces Bayesian Model Averaging (BMA) as conceptually attractive but with implementation difficulties when the number of regressors is large:
  - Number of models = 2^{k*}.
  - Requires specifying priors for all relevant parameters.
- Proposes Limited Information Bayesian Model Averaging (LIBMA):
  - Incorporates dynamic panel estimation via GMM in a Bayesian robustness check.
  - Two relaxations relative to standard BMA:
    - LIBMA is limited-information (moment restrictions via GMM) rather than full stochastic specification.
    - LIBMA can control for endogeneity through GMM, whereas prior literature often assumes exogenous regressors.

### II. Preliminaries on GMM: setup and properties
- Setup and notation:
  - x_t: n×1 vector of stochastic processes; θ: q×1 parameter vector from Θ ⊂ R^q.
  - h(x_t, θ): r×1 vector-valued function with moment condition E_P[h(x_t, θ_0)] = 0.
  - Sample average g_T(x_T, θ) ≡ (1/T) Σ_{t=1}^T h(x_t, θ).
- Assumptions:
  - (A1) {w_t} is stationary and ergodic.
  - (A2) (a) E_P[w_t w'_t] exists and is finite; (b) E_P[w_{t+s} | w_t, w_{t-1}, ...] converges in mean square to zero.
  - (A3) (a) h(x, .) is continuously differentiable in Θ for each x; (b) h(., θ) and ∂h(., θ)/∂θ are Borel measurable for each θ ∈ Θ.
- Definitions and properties:
  - GMM estimator bθ_{G,T}(ω): minimizes g_T(x_T, θ)' W_{G,T} g_T(x_T, θ) with W_{G,T} positive definite weighing matrices.
  - First-order condition (interior optimum): [∂g_T/∂θ |_{θ=bθ}]' W_{G,T} g_T(x_T, bθ) = 0.
  - Long-run variance S ≡ Σ_{ν=-∞}^{∞} E_P[h(x_t, θ_0) h(x_{t-ν}, θ_0)']; S = lim_{T→∞} E_P[T g_T(x, θ_0) g_T(x, θ_0)'].
  - Optimal choice W_{G,T} = S^{-1} yields smallest asymptotic variance.
  - Consistent estimators of S: White (1980), Newey-West (1987) Bartlett kernel, Hansen (1982) truncated kernel, Andrews and Monahan (1992) automatic bandwidth.
  - Optimal GMM objective approximation: g_T(x_T, θ)' bS_T^{-1} g_T(x_T, θ) where bS_T is consistent estimator of S.

### III. GMM in the Bayesian framework: Bayes estimator and limited information likelihood
- Motivation:
  - Bayesian estimation traditionally requires likelihood; recent work constructs likelihood analogues for moment problems (Zellner, Inoue, Kim).
  - Kim (2000, 2002) develops a limited-information Bayesian counterpart to classical GMM; this essay follows that approach.
- Bayes estimator aligned with GMM:
  - Define posterior π_T(θ | x_T) on measurable space (Θ, G).
  - Loss function quadratic in g_T: c(θ, δ) = [g_T(θ) − g_T(δ)]' W_T [g_T(θ) − g_T(δ)], transformable to quadratic in θ: c(θ, δ) = (θ − δ)' g W_T (θ − δ).
  - First order condition for Bayes estimator with that loss implies moment condition E_π[Ξ_T g_T(θ)] = 0 where Ξ_T = [∂g_T(θ)/∂θ |_{θ=bθ}]' W_T.
  - Lemma 1: Under second order conditions and Assumption (A3), GMM estimator bθ_{GMM} equals Bayes estimator bθ_B iff E_π[Ξ_T g_T(θ)] = 0 with {W_T} = {W_{G,T}}.
- Limited Information Likelihood (LIL):
  - Define family Q of probability measures absolutely continuous w.r.t. P satisfying moment constraints E_Q[g_T(x_T, θ)] = 0 and lim_{T→∞} E_Q[T g_T g_T'] = S.
  - Choose Q* ∈ Q minimizing Kullback-Leibler divergence I(Q || P) = ∫ ln(dQ/dP) dQ.
  - q*_P(θ) = dQ*/dP interpreted as an I-projection or Limited Information Likelihood (LIL).
  - Finite-sample LIL approximation: q_{P,T}(x_T, θ) = K exp{ κ T g_T(x_T, θ)' S_T^{-1} g_T(x_T, θ) } with κ = −1/2 desirable and S replaced by consistent estimator bS_T.

### IV. Model uncertainty and Bayesian Model Averaging under limited information
- Bayesian hypothesis testing and Bayes factors:
  - For models M_1 and M_2, posterior odds p(M_1 | x_T) = q_T(x_T | M_1) p(M_1) / [ q_T(x_T | M_1) p(M_1) + q_T(x_T | M_2) p(M_2) ].
  - Posterior odds ratio p(M_2 | x_T) / p(M_1 | x_T) = [ q_T(x_T | M_2) / q_T(x_T | M_1) ] × [ p(M_2) / p(M_1) ]; first term is Bayes factor B_{21}.
- Laplace approximation and BIC:
  - Using Laplace approximation for marginal likelihood q_T(x_T | M) yields Schwarz criterion and BIC approximations:
    - log q_T(x_T | M) ≈ log q_T(x_T | \hat θ, M) − (d/2) log n + O(1).
    - log B_{21} ≈ log q_T(x_T | \hat θ_2, M_2) − log q_T(x_T | \hat θ_1, M_1) − (d_2 − d_1)/2 log n + O(n^{-1/2}).
    - BIC = 2 log B_{21} ≈ 2[log q_T(x_T | \hat θ_2) − log q_T(x_T | \hat θ_1)] − (d_2 − d_1) log n + O(n^{-1/2}).
- Limited Information BIC (LIBIC) and LIBMA:
  - Replace full-information log-likelihood with LIL (20) in BIC derivation to obtain LIBIC:
    - LIBIC = 2[log q_{P,T}(x_T | \hat θ_2, M_2) − log q_{P,T}(x_T | \hat θ_1, M_1)] − (d_2 − d_1) log n.
    - Using κ = −1/2 and LIL gives LIBIC explicitly as:
      LIBIC = 2[ κ T g_T(x_T, θ_2)' bS_T^{-1} g_T(x_T, θ_2) − κ T g_T(x_T, θ_1)' bS_T^{-1} g_T(x_T, θ_1) ] − (d_2 − d_1) log n.
  - Posterior model probabilities under limited information (LIBMA):
    - p(M_k | x_T) = exp( − 1/2 LIBIC_k ) p(M_k) / Σ_{j=1}^K exp( − 1/2 LIBIC_j ) p(M_j).
  - LIBMA: extension of BMA that uses LIBIC and LIL to average over models when only limited-information moment conditions (GMM) are available.
- Practical issues with BMA and how LIBMA addresses them:
  - BMA challenges: infeasibility when number of regressors k* large (2^{k*} models) and need to specify many priors.
  - LIBMA uses GMM/LIL to relax full-likelihood requirement and can control for endogeneity; still requires choices over model priors but offers a limited-information alternative.

### V. Statistics and computational aspects for the robustness analysis
- Model space and priors:
  - k* possible regressors; K = 2^{k*} possible models M_j.
  - Represent model M_j as binary length-k* vector (1 = variable included, 0 = excluded).
  - Prior: adopt single hyper-parameter k = expected model size; equal inclusion probability for each variable = k/k*.
  - Prior probability for model M_j: p(M_j) = (k/k*)^{k_j} (1 − k/k*)^{1−k_j} where k_j is number of included variables in M_j.
  - Prior odds ratio between M_j and M_l: p(M_j)/p(M_l) = (k/k*)^{k_j − k_l} (1 − k/k*)^{k_j − k_l}.
- Posterior model probabilities and averaging:
  - Posterior model probability with LIBIC weights:
    - p(M_j | x_T) = exp( − 1/2 LIBIC_j ) p(M_j) / Σ_{l=1}^{2^{k*}} exp( − 1/2 LIBIC_l ) p(M_l).
  - Posterior mean of parameter θ_k:
    - E(θ_k | x_T) = Σ_{j=1}^{2^{k*}} p(M_j | x_T) E(θ_k | x_T, M_j).
  - Posterior variance of θ_k:
    - Var(θ_k | x_T) = Σ_{j=1}^{2^{k*}} p(M_j | x_T) [ Var(θ_k | x_T, M_j) + E(θ_k | x_T, M_j)^2 ] − E(θ_k | x_T)^2.
- Inclusion and sign metrics:
  - Posterior inclusion probability for regressor k:
    - p(θ_k ≠ 0 | x_T) = Σ_{M_j: θ_k ≠ 0} p(M_j | x_T).
  - If p(θ_k ≠ 0 | x_T) > p(θ_k ≠ 0) = k/k*, variable has high marginal contribution.
  - Posterior mean and variance conditional on inclusion: divide unconditional posterior mean and variance by posterior inclusion probability.
  - Sign certainty probability:
    - sign certainty for θ_k = p[ sgn(θ_k) = sgn E(θ_k | D) | D, θ_k ≠ 0 ] = Σ_{j=1}^{2^{k*}} p(M_j | x_T) p[ sgn(θ_k) = sgn E(θ_k | x_T) | M_j, x_T ].

### VI. Conclusion: contribution and applications
- The paper develops theoretical background and computational aspects for Limited Information Bayesian Model Averaging (LIBMA).
- LIBMA provides a coherent Bayesian framework that:
  - Accounts explicitly for model uncertainty via model averaging.
  - Relaxes full-information likelihood assumptions by using GMM-based Limited Information Likelihood.
  - Controls for endogeneity through GMM instrumentation.
- Potential applications highlighted:
  - Investigations of competing hypotheses.
  - Parameter estimation robust to model specification.
  - Empirical growth and poverty analyses: example application by Ghura, Leite, and Tsangarides (2002) on elasticity of poor income w.r.t. average income and macroeconomic policy effects on poverty.
  - Cross-country convergence and robust patterns of growth behavior analysis using LIBMA.

*Source: _wp0468 - References (IMF working paper content supplied).*

### References

### References

### Econometric methods and estimators
- Andrews, D., and J. C. Monahan, 1992, “An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator,” Econometrica, Vol. 60 (July), pp. 953-66.
- Hansen, L. P., 1982, “Large Sample Properties of Generalized Methods of Moments Estimators,” Econometrica, Vol. 50 (July), pp. 1029-54.
- Newey, W., and K. West, 1987, “Hypothesis Testing with Efficient Method of Moments Estimation,” International Economic Review, Vol. 28 (no. 3), pp. 777-87.
- White, H., 1980, “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity,” Econometrica, Vol. 48 (May), pp. 817-38.
- White, H., 1982, “Maximum Likelihood Estimation of Misspecified Models,” Econometrica, Vol. 50 (January), pp. 1-25.
- Tierney L., and J. B. Kadan, 1986, “Accurate Approximations for Posterior Moments and Marginal Densities,” Journal of American Statistical Association, Vol. 81, pp. 82-86.

### Bayesian methods, model averaging, and selection
- Hoeting, J. A., and others, 1999, “Bayesian Model Averaging: A Tutorial,” Statistical Science, Vol. 14 (No. 4), pp. 382-417.
- Kass, R. and A. Raftery, 1995, “Bayes Factors,” Journal of the American Statistical Association, Vol. 90 (no. 430), pp. 773-95.
- Madigan, D., and A. Raftery, 1994, “Model Selection and Accounting for Model Uncertainty in Graphical Models Using Occam's Window,” Journal of American Statistical Association, Vol. 63, pp. 1535-46.
- Raftery, A. E., 1994, “Bayesian Model Selection in Social Research,” in Sociological Methodology, ed. by Peter V. Marsden, (Cambridge, Massachusetts: Blackwells), pp. 111-96.
- Raftery, A. E., 1996, “Approximate Bayes Factors and Accounting for Model Uncertainty in Generalized Linear Models,” Biometrika, Vol. 83, pp. 251-66.
- Kim, J. Y., 2000, “The Generalized Method of Moments in the Bayesian Framework and a Model and Moment Selection Criterion,” Working Paper (Albany: State University of New York).
- Kim, J. Y., 2001, “Bayesian Limited Information Analysis in the GMM Framework,” Working Paper (Albany: State University of New York).
- Kim, J. Y., 2002, “Limited Information Likelihood and Bayesian Analysis,” Journal of Econometrics, Vol. 107 (March), pp. 175-93.
- Inoue, A., 2001, “A Bayesian Method of Moments in Large Samples,” Working Paper (Raleigh: North Carolina State University).
- Zellner, A., 1996, “Bayesian Method of Moments/Instrumental Variable (BMOM/IV) Analysis of Mean and Regression Model,” in Modeling and Prediction Honoring Seymour Geisser, ed. by J.C. Lee, W.C. Johnson, and A. Zellner (New York: Springer), pp. 61-74.
- Zellner, A., 1997, “The Bayesian Method of Moments (BMOM): Theory and Application,” in Advances in Econometrics Vol. 12, ed. by T. Fomby, R. C. Hill (Greenwich, Connecticut: JAI press), pp. 85-105.

### Information-theoretic and entropy-based approaches
- Csiszar, I., 1975, “I-divergence Geometry of Probability Distributions and Minimization Problems,” Annals of Probability, Vol. 3 (no. 1), pp. 146-58.
- Golan, A., G. Judge, and D. Miller, 1996, Maximum Entropy Econometrics: Robust Estimation with Limited Data (Chichester: Wiley & Sons).

### Growth, development, and policy-related studies
- Brock, W., and S. Durlauf, 2001, “Growth Empirics and Reality,” World Bank Economic Review, Vol. 15 (no. 2), pp. 229-72.
- Doppelhofer, G., R. I. Miller, and X. Sala-i-Martin, 2000, “Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (BACE) Approach,” Working Paper No. 7750 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Ghura, D., C. Leite, and C. Tsangarides, 2002, “Is Growth Enough? Macroeconomic Policy and Poverty Reduction,” IMF Working Paper No. 02/118 (Washington: International Monetary Fund).
- Leamer, E., 1978, Specification Searches: Ad Hoc Inference with Non-experimental Data, (New York: Wiley & Sons).

*Source: _wp0468 - References*

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