Estimating Parameters of Structural Models Using Neural Networks

Yanhao (Max) Wei; Zhenling Jiang

REVIEW 3 major objections 6 minor 7 references

Estimating Parameters of Structural Models Using Neural Networks

T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A neural net trained on simulated datasets estimates structural parameters and, on a consumer search model, beats simulated maximum likelihood in accuracy and cost.

desk verdict A useful, honest methods paper whose core trick predates it by years; the search-model application is strong, but the SMLE comparison and the missing SBI citations need fixing before publication. read the letter →

arxiv 2502.04945 v1 pith:OGW3AQWS submitted 2025-02-07 econ.EM stat.CO

Yanhao (Max) Wei , Zhenling Jiang This is my paper · ORCID

classification econ.EMstat.CO

keywords neuralnetworkestimatorstructuralestimationlimited-informationposteriormeansimulatedmaximumlikelihoodredundantmomentssequentialsearchsimulationcostmachinelearning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper develops a way to estimate the parameters of a structural econometric model without evaluating the likelihood or optimizing a simulated objective. The method simulates many datasets from the model under known parameter values, reduces each dataset to summary moments, and trains a shallow neural net to recognize the parameter value that generated each dataset. The paper proves that as the number of training datasets grows, the net's point estimate converges to the limited-information posterior mean $E(\theta|m)$, and with a cross-entropy loss it also converges to $\mathrm{Var}(\theta|m)$ or $\mathrm{Cov}(\theta|m)$ depending on the output specification. Because the net learns from training examples which moments carry information, it is less affected by redundant moments than GMM/SMM. In a consumer sequential search model, the neural net estimator achieves lower RMSE than smoothed simulated maximum likelihood across a wide range of computational budgets and gives better fit to real data.

What carries the argument

The object that carries the argument is the training distribution $P(\theta,m)$ induced by the model, the prior over $\Theta$, and the moment mapping, together with a shallow neural net trained to invert that mapping. The loss function is the engine: minimizing the cross-entropy loss (6) makes the net output converge to $[E(\theta|m),\mathrm{Var}(\theta|m)]$ or $[E(\theta|m),\mathrm{Cov}(\theta|m)]$ as $L$ grows. The proof adapts neural-net sieve asymptotics by letting the number of hidden units grow slowly, roughly proportional to $\sqrt{L}$, so that the function class is dense enough to approximate the target yet regularized enough to avoid overfitting. A KL-divergence projection argument explains why a normal-shaped loss still recovers the true conditional mean and variance for non-normal $P(\theta|m)$.

What would settle it

Run the paper's AR(1) Monte Carlo with the nine-moment specification of Table 2 but with $L$ raised to $10^6$; if NNE's RMSE rises above its single-moment benchmark, the claimed asymptotic robustness to redundant moments fails. Alternatively, in the search-model Monte Carlo put the true $\delta_0$ outside $\Theta$; if with a very large training set the estimates do not move from the boundary toward the true value, the Appendix A.2 check is not reliable.

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Extended reading notes

Core claim

The central claim is that parameter estimation can be recast as a supervised recognition problem. For any parametric model $y=q(x,\varepsilon;\theta)$ that can be simulated, draw training parameters $\theta^{(\ell)}$ uniformly from a compact space $\Theta$, simulate datasets conditional on the observed $x$, compute moments $m^{(\ell)}$, and train a shallow neural net $f:m\mapsto(\mu,V)$ to predict the generating parameter. With squared-error loss the fitted net converges in $L^2$ to $E(\theta|m)$ as the training size $L\to\infty$; with the normal-form cross-entropy loss it converges to $E(\theta|m)$ together with $\mathrm{Var}(\theta|m)$ (diagonal $V$) or $\mathrm{Cov}(\theta|m)$ (full $V$), without requiring $P(\theta|m)$ to be normal. This makes NNE a limited-information Bayesian estimator that avoids simulation noise in the objective, needs no smoothing factor, and is asymptotically robust to redundant moments. The application to a sequential search model shows the method recovering parameters with smaller RMSE than smoothed SMLE over a wide range of simulation burdens and producing better model fit on real hotel-search data.

Load-bearing premise

The load-bearing premise is the training design: $\theta$ is drawn uniformly from a hand-specified compact set $\Theta$ and every training dataset is simulated conditional on the same observed covariates $x$, so if the true parameter lies outside $\Theta$ or the real data's $x$ differs from the training $x$, the estimator's target $E(\theta|m)$ can be biased and the reported uncertainty is posterior spread under that prior, not a classical standard error.

Editorial extensions

If this is right

Researchers can estimate models whose likelihoods are intractable or non-smooth without choosing a likelihood-smoothing factor, because NNE never evaluates the likelihood.
Moment selection becomes less risky: asymptotically, adding moments can only weakly improve $E(\theta|m)$, so redundant moments do not create the finite-sample bias they create in GMM/SMM.
The network's second output provides a variance or covariance estimate as a byproduct, avoiding the need to derive separate standard-error formulas.
In the sequential search model, NNE achieves lower RMSE than smoothed SMLE at equal or lower simulation burden, and its implied model fit and counterfactual buy-rate increments are closer to the truth.
NNE gives the largest gains when simulation is the bottleneck; in models with closed-form likelihoods or where the main cost is solving the economic model, the paper expects little or no advantage.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The uncertainty output is a limited-information posterior dispersion under the training prior, not a frequentist standard error; users who want classical coverage should calibrate it on simulated validation data before drawing conclusions.
Because NNE consumes only moments, a pre-trained network could in principle estimate structural parameters from aggregate statistics without individual-level data, a privacy-preserving extension the authors list as future work.
The Appendix A.5 lasso-polynomial results suggest the neural net itself may not be essential: any flexible regressor that learns the inverse map from enough examples inherits the redundant-moment robustness, so the core recipe generalizes beyond shallow nets.

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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Two things to know. First, the core trick — regressing parameters on simulated moments with a neural net to approximate the posterior mean — is not new, and the paper's failure to cite the simulation-based inference literature (neural posterior estimation, ABC) will annoy referees. Second, the paper is more honest about what the estimator does than the abstract suggests: it converges to E(theta|m) under the training prior, not to the true theta, and the authors show in Appendix A.2 that a misspecified Theta pulls estimates. That is a real limitation of the method, not a hidden flaw.

What is genuinely useful: the econometric framing, the convergence results (standard sieve arguments, correctly stated), the redundant-moment robustness demonstration, and a serious application to a sequential search model where SMLE is genuinely painful. The Monte Carlo work is careful, the code is provided, and the authors are candid about when NNE will not help. The search-model results are the most convincing part: NNE beats smoothed SMLE even though the SMLE comparison uses an oracle choice of the smoothing factor lambda (Appendix A.3), which is the single most questionable design choice in the paper. That the advantage survives that handicap is evidence in the method's favor, though it also means the headline 'smaller RMSE' claim should be read as 'under a prior centered near the truth' — the MC design places the true parameters comfortably inside Theta.

Soft spots, in order of seriousness. First, the missing citations: the paper cites ABC in a footnote but not neural posterior estimation or related machine learning work. That is a significant novelty-framing gap. Second, the prior-dependence: the paper suggests checking whether the estimate falls inside Theta, but that diagnostic misses the common failure where Theta contains the truth but is off-center so the estimate is pulled inside Theta. The paper should either provide a better check or explicitly frame NNE as a Bayesian procedure. Third, the real-data model fit comparison has no uncertainty quantification; it is histograms and eyeballing. The fixed-x conditioning is a limitation the authors acknowledge, so I weigh it less.

Bottom line: this is a solid, useful methods paper for applied structural economists, with a real application and honest appendices. It needs revisions on novelty framing and the SMLE comparison, but the core is sound. I would send it to peer review, and I would cite it for the search-model application and the redundant-moment analysis.

Referee Report

3 major / 6 minor

Summary. The paper proposes a neural-net estimator (NNE) for structural econometric models. Training data are generated by simulating the model at parameter draws from a user-specified space Θ (typically uniform); a shallow neural net maps data moments to parameter estimates. The paper proves that, as the number of training datasets L grows, the NNE point estimate converges to the limited-information posterior mean E(θ|m) and, under a cross-entropy loss, to the posterior variance/covariance. The authors illustrate NNE on an AR(1) model, where they argue it is more robust to redundant moments than GMM/SMM, and on a consumer sequential-search model, where they report that NNE achieves lower RMSE than simulated maximum likelihood (SMLE) at lower computational cost and gives a better real-data model fit. The paper also provides convergence proofs, Monte Carlo studies, a real-data application, and links to code.

Significance. If the claims hold, NNE is a genuinely useful addition to the structural-estimation toolbox, particularly for models where likelihood/moment evaluation is simulation-heavy and where SMLE is sensitive to tuning choices such as smoothing factors. The theoretical results are correctly framed as translations of existing sieve convergence results for neural networks to the moments-to-parameters setting; the proofs are detailed and the Monte Carlo design is careful. The redundant-moment robustness is an interesting and credible property of the conditional-expectation target, and the ability to output a statistical-accuracy measure as a byproduct is practically valuable. The main caveat is that the estimator's target is the training-prior conditional mean, not the true parameter, and consequently the headline empirical claims are prior- and x-conditional.

major comments (3)

[Section 2.2, 2.4; Proposition 1] The convergence target in Proposition 1 is E(θ|m), where the expectation is taken under the training distribution with θ ~ Unif(Θ) and with all datasets generated conditional on the single observed x (Algorithm 2, step 1; Section 2.2). This is a prior-dependent, x-dependent object, not the true θ. The paper's language throughout, however, equates the NNE limit with recovering the true parameter: the abstract says the neural net 'tries to recognize the parameter value underlying that dataset,' and Section 4.3 states that 'NNE recovers the search model parameter well.' Because E(θ|m) is a Bayes estimator under the training prior, it is generally biased toward the prior center for any fixed true θ. Section A.2, Figure 12, shows exactly this mechanism: when the δ0 range is [-2,-1] or [-3,-1], the estimates fall between the range and the truth, i.e., they are pulled toward Θ. The suggested diagnostic ('check whether the estimate is inside Θ') cannot detect the more common failure where Θ contains the truth but is off-center and the estimate remains inside Θ while being pulled away from the truth. The authors should either reframe the core claims as being about the limited-information posterior mean, or provide conditions or evidence under which E(θ|m) is close to the true θ (e.g., highly informative moments, large n), and develop a more informative prior-sensitivity diagnostic.
[Section 4.3, Appendix A.3] The RMSE comparison in Figure 6 and the counterfactual in Table 3 give SMLE an oracle advantage: the smoothing factor λ = 7 is selected by grid search on the true θ (Appendix A.3, Figure 13), which requires knowledge of the truth and repeated SMLE estimation. This is a legitimate stress test, but the text does not emphasize the asymmetry in the other direction: the NNE training prior is centered on the true θ in the Monte Carlo design (δ0 = -4 lies in [-5,-2]; all βk lie in [-0.5,0.5]), so shrinkage toward the prior center can only reduce RMSE relative to a design with an off-center prior. The claim in Section 4.3 that 'Over a wide range of computational costs, NNE has a smaller RMSE than SMLE' is therefore a statement about this particular prior and data-generating process, not a general ranking of the two estimators. The authors should report results for true parameter values at the boundary or outside the training range, and clarify in the text that the reported RMSE is an average over the training prior rather than a frequentist average under a fixed true θ.
[Section 4.4, Figure 8] The real-data model-fit comparison rests on visual inspection of histograms: the text states that 'NNE seems to give a better model fit' and that SMLE 'can give a good fit on either the buy rate or the number of searches, but not both.' No statistical test or numerical fit measure is provided. This is load-bearing for the real-data section, since the true θ is unknown and RMSE cannot be computed. The authors should quantify the claim, for example, by reporting the fraction of bootstrapped datasets for which each estimator's predicted statistic is closer to the observed value, or by constructing posterior predictive intervals and reporting coverage for each of the three key statistics. Without such a test, the real-data fit comparison is anecdotal.

minor comments (6)

[Section 2.2, Algorithm 1] The AR(1) moment is defined as m = (1/(n-1)) Σ y_i y_{i-1}, which is an uncentered autocovariance. For a zero-mean stationary AR(1) this is fine, but the text calls it 'the covariance between yi and its own lag'; please state explicitly that the mean is zero or use centered moments.
[Section 3.3, Table 2] The table notes state that numbers in parentheses are standard errors. These are Monte Carlo standard errors of the reported bias and RMSE, not standard errors of the parameter estimates; please label them as 'Monte Carlo standard errors' to avoid confusion.
[Section 4.1] The outside option utility is specified as ui0 = η + εi0, but the distribution of εi0 is not stated. Presumably εi0 ~ N(0,1) as for the other εij, but this should be made explicit.
[Section 4.3, first paragraph] The Monte Carlo design sets J = 30, while the real data have J = 33 or 34. Since the neural net is trained for a fixed x (including the ranking positions), the trained NNE is not directly applicable to a different J; the text should acknowledge this and clarify that the Monte Carlo and real-data applications each retrain on their respective x.
[Section 5, third paragraph] The discussion of pre-trained NNE correctly notes the dependence on x, but it should also mention dependence on the sample size n; the training is conditional on a fixed n, and Section 4.5 retrains at each n. This limitation should be stated explicitly.
[Appendix B, Lemma 1] In the verification of condition 5, the text says 'we will use the sup norm ∥·∥∞ as this metric when applying condition 3.5M' and then states that the covering number 'cannot grow too fast.' Since this is a standard sieve condition, it is acceptable, but a precise rate (e.g., u_L ∝ √L, b_L ∝ log L, as given earlier in the appendix) would make the proof self-contained.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: NNE's convergence to E(theta|m) is a standard regression limit derived from external sieve results, and the prior-conditional nature of the target is transparently acknowledged.

full rationale

The paper's central theoretical claim, Proposition 1, is that the neural net trained with MSE loss converges to E(theta|m) as L grows. This is a direct application of existing neural-network sieve asymptotics (White 1989, White 1990, Chen 2007), which are external references, not self-citations. The target E(theta|m) is defined as the conditional expectation under the training distribution induced by the uniform prior over Theta and the structural model; the proof in Appendix B verifies the sieve conditions for this specific target. This is a derivation, not a circular reduction: the estimator is constructed to minimize a loss, and the proposition characterizes the population minimizer. The robustness-to-redundant-moments claim follows from the monotonicity of conditional expectation as m expands, which the paper states and then verifies numerically in Section 3 and Table 5. The application to the search model is a Monte Carlo demonstration with the true parameter placed inside Theta, not a claim that NNE consistently estimates theta outside the prior support; Section A.2 explicitly studies misspecified Theta and reports shrinkage toward Theta. Thus potential prior-dependence is disclosed as a limitation rather than hidden or relabeled. There are no load-bearing self-citations, no imported uniqueness theorems from the authors' own prior work, and no fitted parameters renamed as predictions. The paper's derivation chain is self-contained given its stated assumptions, and the empirical comparisons are genuine out-of-sample validation exercises within the Monte Carlo design. Score 0 reflects the absence of circular steps.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

No new physical or structural entities are postulated. The estimator's behavior is governed by three chosen inputs: the prior support Theta, the moment vector m, and the network width; the first and third are explicitly acknowledged as tuning choices, while the second is a modeling choice that the paper argues is non-critical due to redundant-moment robustness.

free parameters (3)

Uniform prior support Theta for search model = eta in [2,5], delta0 in [-5,-2], delta1 in [-0.25,0.25], beta_k in [-0.5,0.5]
Chosen by hand; defines the target posterior E(theta|m). If Theta excludes the true theta, estimates are biased toward Theta (Appendix A.2, Figure 12).
Hidden nodes in shallow NN = 64 for L*=1e4
Selected by validation loss (Appendix A.1); the paper shows estimates are insensitive, so it is a minor free parameter.
Moment vector m = 46 moments for main search-model results
Hand-selected from means, covariances, and consumer-level aggregates (Section 4.2); alternative specifications are tested in Table 5.

assumptions (4)

standard math Sieve convergence results for single-hidden-layer neural networks (Chen 2007, White 1990): neural nets with slowly growing capacity are dense in continuous function space and their empirical loss minimizers converge to the population minimizer.
Used in Lemma 1 and Propositions 1-3 (Appendix B).
domain assumption The econometric model q can be simulated and the selected moments m identify the parameter theta.
State in Section 2.2: 'we would require that the parameter theta is identified by the moments selected into m'.
domain assumption Training and application use the same observed covariates x.
Section 2.2: 'all training datasets are generated conditional on the same observed x'; real data must share this x for the mapping to apply.
ad hoc to paper The prior theta ~ U(Theta) is a reasonable representation of the researcher's uncertainty; the true theta is in Theta.
The method defines its target as the posterior under this prior; validity as an estimator requires the prior not to dominate (Appendix A.2).

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Cite this review

Pith. "Pith review of Estimating Parameters of Structural Models Using Neural Networks." pith.science (2026). https://pith.science/paper/OGW3AQWS

@misc{pith2026250204945,
  author       = {Pith},
  title        = {Pith review of: Estimating Parameters of Structural Models Using Neural Networks},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OGW3AQWS}},
  note         = {Machine review of arXiv:2502.04945}
}

read the original abstract

We study an alternative use of machine learning. We train neural nets to provide the parameter estimate of a given (structural) econometric model, for example, discrete choice or consumer search. Training examples consist of datasets generated by the econometric model under a range of parameter values. The neural net takes the moments of a dataset as input and tries to recognize the parameter value underlying that dataset. Besides the point estimate, the neural net can also output statistical accuracy. This neural net estimator (NNE) tends to limited-information Bayesian posterior as the number of training datasets increases. We apply NNE to a consumer search model. It gives more accurate estimates at lighter computational costs than the prevailing approach. NNE is also robust to redundant moment inputs. In general, NNE offers the most benefits in applications where other estimation approaches require very heavy simulation costs. We provide code at: https://nnehome.github.io.

Figures

Figures reproduced from arXiv: 2502.04945 by the authors.

**Figure 1.** Training Examples in NNE y (ℓ) = q(x, ε (ℓ) ; θ (ℓ) ). The collection {θ (ℓ) , {y (ℓ) , x}} constitutes a training example. An illustration is given in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗

**Figure 2.** Estimation of AR(1) 16 [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗

**Figure 3.** Distributions of Estimates for AR(1) with Redundant Moments [PITH_FULL_IMAGE:figures/full_fig_p018_3.png] view at source ↗

Figures from the paper (12 more)

**Figure 4.** Figure 4: NNE’s Estimates for Search Model in Monte Carlo [PITH_FULL_IMAGE:figures/full_fig_p023_4.png]

**Figure 5.** Figure 5: SMLE’s Estimates for Search Model in Monte Carlo [PITH_FULL_IMAGE:figures/full_fig_p024_5.png]

**Figure 6.** Figure 6: RMSE vs. Computational Cost for Search Model in Monte Carlo [PITH_FULL_IMAGE:figures/full_fig_p025_6.png]

**Figure 7.** Figure 7: Model Fit on Key Statistics in Monte Carlo [PITH_FULL_IMAGE:figures/full_fig_p026_7.png]

**Figure 8.** Figure 8: Model Fit on Key Statistics in Real Data [PITH_FULL_IMAGE:figures/full_fig_p029_8.png]

**Figure 9.** Figure 9: Estimation of Search Model with Different Data Sizes [PITH_FULL_IMAGE:figures/full_fig_p031_9.png]

**Figure 10.** Figure 10: A Shallow Neural Network A Appendix A.1 Number of hidden nodes [PITH_FULL_IMAGE:figures/full_fig_p033_10.png]

**Figure 11.** Figure 11: Estimates with Different Neural Net Configurations [PITH_FULL_IMAGE:figures/full_fig_p034_11.png]

**Figure 12.** Figure 12: Sensitivity Analysis of NNE to Θ A.2 Parameter space Θ In NNE, the parameter values of the econometric model in training and validation sets are drawn from a parameter space Θ. A practical question is how NNE will behave if Θ fails to contain the true value of θ. We e…

**Figure 13.** Figure 13: Optimal Smoothing Factor in SMLE NNE 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 Actual SD Learned SD SMLE 0.00 0.05 0.10 0.15 0.20 0.25 0.00 0.05 0.10 0.15 0.20 0.25 Actual SD Asymptotic SE Notes: Each point represents one parameter in the search mode…

**Figure 14.** Figure 14: Estimates of Statistical Accuracy 36 [PITH_FULL_IMAGE:figures/full_fig_p036_14.png]

**Figure 15.** Figure 15: Indirect Inference for AR(1) moment used by SMM in Section 3.1. Thus, the consequent indirect inference estimator for β is effectively the same as the SMM illustrated in [PITH_FULL_IMAGE:figures/full_fig_p038_15.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

7 extracted references · 5 canonical work pages

[1]

Small-sample Bias in GMM Estimation of Covariance Struc- tures,

Altonji, Joseph G and Lewis M Segal (1996) “Small-sample Bias in GMM Estimation of Covariance Struc- tures,” Journal of Business & Economic Statistics , 14 (3), 353–366. Andersen, Torben and Bent Sorensen (1996) “GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study,” Journal of Business and Economic Statistics , 14 (3). Athey, Susan (2018)...

work page 1996
[3]

Search Personalization using Machine Learning,

Yoganarasimhan, Hema (2020) “Search Personalization using Machine Learning,” Management Science, 66 (3), 1045–1070. Yoganarasimhan, Hema, Ebrahim Barzegary, and Abhishek Pani (2023) “Design and Evaluation of Optimal Free Trials,”Management Science, 69 (6), 3220–3240. Zhang, Mengxia and Lan Luo (2023) “Can Consumer-posted Photos Serve as a Leading Indicato...

work page 2020
[6]

Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Ar- bitrary Mappings,

(1990) “Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Ar- bitrary Mappings,” Neural Networks,

work page 1990
[27]

Choosing the Number of Instruments,

Donald, Stephen G. and Whitney K. Newey (2021) “Choosing the Number of Instruments,” Econometrica, 69 (5). Du, Simon, Jason Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai (2019) “Gradient Descent Finds Global Minima of Deep Neural Networks,” International Conference on Machine Learning ,

work page 2021
[32]

Large-scale Cross-category Analysis of Consumer Review Content on Sales Conversion Leveraging Deep Learning,

Liu, Xiao, Dokyun Lee, and Kannan Srinivasan (2019) “Large-scale Cross-category Analysis of Consumer Review Content on Sales Conversion Leveraging Deep Learning,” Journal of Marketing Research , 56 (6), 918–943. Newey, Whitney K. (2007) “Generalized Method of Moments,” MIT OpenCourseWare: New Econometric Methods. Pakes, Ariel, Michael Ostrovsky, and Steve...

work page 2019
[97]

Deep Learning for Individual Heterogeneity: an Automatic Inference Framework,

Farrell, Max H, Tengyuan Liang, and Sanjog Misra (2021b) “Deep Learning for Individual Heterogeneity: an Automatic Inference Framework,” arXiv preprint arXiv:2010.14694 . 47 Farrell, Max, Tengyuan Liang, and Sanjog Misra (2021a) “Deep Neural Networks for Estimation and Infer- ence,” Econometrica, 89 (1), 181–213. Gelman, Andrew, John B. Carlin, Hal S. Ste...

arXiv 2021
[107]

Network Dependence Can Lead to Spurious Associations and Invalid Inference,

Lee, Youji and Elizabeth L. Ogburn (2021) “Network Dependence Can Lead to Spurious Associations and Invalid Inference,” Journal of the American Statistical Association , 116 (535), 1060–1074. Lewis, Greg and Vasilis Syrgkanis (2018) “Adversarial generalized method of moments,” arXiv preprint arXiv:1803.07164. Li, Hao, Zheng Xu, Gavin Taylor, Christoph Stu...

arXiv 2021

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.

[1] [1]

Small-sample Bias in GMM Estimation of Covariance Struc- tures,

Altonji, Joseph G and Lewis M Segal (1996) “Small-sample Bias in GMM Estimation of Covariance Struc- tures,” Journal of Business & Economic Statistics , 14 (3), 353–366. Andersen, Torben and Bent Sorensen (1996) “GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study,” Journal of Business and Economic Statistics , 14 (3). Athey, Susan (2018)...

work page 1996

[2] [3]

Search Personalization using Machine Learning,

Yoganarasimhan, Hema (2020) “Search Personalization using Machine Learning,” Management Science, 66 (3), 1045–1070. Yoganarasimhan, Hema, Ebrahim Barzegary, and Abhishek Pani (2023) “Design and Evaluation of Optimal Free Trials,”Management Science, 69 (6), 3220–3240. Zhang, Mengxia and Lan Luo (2023) “Can Consumer-posted Photos Serve as a Leading Indicato...

work page 2020

[3] [6]

Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Ar- bitrary Mappings,

(1990) “Connectionist Nonparametric Regression: Multilayer Feedforward Networks Can Learn Ar- bitrary Mappings,” Neural Networks,

work page 1990

[4] [27]

Choosing the Number of Instruments,

Donald, Stephen G. and Whitney K. Newey (2021) “Choosing the Number of Instruments,” Econometrica, 69 (5). Du, Simon, Jason Lee, Haochuan Li, Liwei Wang, and Xiyu Zhai (2019) “Gradient Descent Finds Global Minima of Deep Neural Networks,” International Conference on Machine Learning ,

work page 2021

[5] [32]

Large-scale Cross-category Analysis of Consumer Review Content on Sales Conversion Leveraging Deep Learning,

Liu, Xiao, Dokyun Lee, and Kannan Srinivasan (2019) “Large-scale Cross-category Analysis of Consumer Review Content on Sales Conversion Leveraging Deep Learning,” Journal of Marketing Research , 56 (6), 918–943. Newey, Whitney K. (2007) “Generalized Method of Moments,” MIT OpenCourseWare: New Econometric Methods. Pakes, Ariel, Michael Ostrovsky, and Steve...

work page 2019

[6] [97]

Deep Learning for Individual Heterogeneity: an Automatic Inference Framework,

Farrell, Max H, Tengyuan Liang, and Sanjog Misra (2021b) “Deep Learning for Individual Heterogeneity: an Automatic Inference Framework,” arXiv preprint arXiv:2010.14694 . 47 Farrell, Max, Tengyuan Liang, and Sanjog Misra (2021a) “Deep Neural Networks for Estimation and Infer- ence,” Econometrica, 89 (1), 181–213. Gelman, Andrew, John B. Carlin, Hal S. Ste...

arXiv 2021

[7] [107]

Network Dependence Can Lead to Spurious Associations and Invalid Inference,

Lee, Youji and Elizabeth L. Ogburn (2021) “Network Dependence Can Lead to Spurious Associations and Invalid Inference,” Journal of the American Statistical Association , 116 (535), 1060–1074. Lewis, Greg and Vasilis Syrgkanis (2018) “Adversarial generalized method of moments,” arXiv preprint arXiv:1803.07164. Li, Hao, Zheng Xu, Gavin Taylor, Christoph Stu...

arXiv 2021