Estimating Network Spillovers under Dense Measurement Error

Aureo de Paula; Weining Wang; Yingxing Li

REVIEW 2 major objections 5 minor 262 references

Estimating Network Spillovers under Dense Measurement Error

T0 review · 2 major / 5 minor · reviewed 2026-08-01 · deepseek-v4-flash

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Pith's one-line read Network spillover effects can be estimated consistently under dense measurement error by first denoising the adjacency matrix as the sum of a low-rank and a sparse matrix.

desk verdict A genuinely useful rate result for network spillovers under structured measurement error, but the dense-noise headline is oversold and the key 1/n discount rests on conditions the paper never validates. read the letter →

arxiv 2607.19625 v1 pith:PHO5JNPK submitted 2026-07-21 econ.EM

Yingxing Li , Aureo De Paula , Weining Wang This is my paper · ORCID

classification econ.EM

keywords networkanalysismeasurementerrorlow-rankplussparsenuclearnormLASSOpenalizedGMMspatialspilloversdensenetworks

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

Spillover estimates in network models break down when the observed adjacency matrix is contaminated by dense measurement error: small elementwise errors accumulate along propagation paths, so standard GMM estimators stay biased even in large samples. This paper argues that if the true network is the sum of a low-rank component (pervasive but weak connections) and a sparse component (a few strong links), then a penalized denoising step can recover the signal well enough. The key theoretical result is that after denoising, the noise enters the spillover estimator only through a dimension-discounted rate R*_nT that is discounted by the network size n, so consistency holds even when the raw noise level does not vanish. The authors propose two estimators—a two-stage plug-in and a supervised GMM—and show in simulations that both reduce the RMSE of the spillover coefficient relative to naive GMM by roughly 50–80% across four network structures, including under endogenous measurement error. If correct, the finding matters because production, trade, and financial networks are dense and error-prone, and naive estimates can even violate stability conditions.

What carries the argument

The central object is the decomposition W = L0 + S0 + E, where L0 is low-rank (pervasive but individually weak links) and S0 is sparse (a few strong links), estimated by minimizing ½||W−L−S||_F² + ν_n||L||_* + τ_n Σ_{i≠j}|S_ij|, with nuclear norm and ℓ1 penalties. The argument then rests on showing that the estimation error cW−W0 affects the GMM objective only through bilinear forms that average the error against instruments and residuals; those averages are controlled by the nuclear norm of the low-rank error and the ℓ1 norm of the sparse error, producing the dimension-discounted rate R*_nT. The rate R*_nT is the machinery that converts a dense, elementwise-small error into an asymptoticall

What would settle it

Construct a network that violates the incoherence bound—for example a low-rank matrix with a few spiked rows added to a moderately dense sparse component—and simulate outcomes with dense measurement error. If the plug-in estimator's RMSE does not shrink toward the oracle rate O_p(1/√(nT)) as n grows (equivalently, if bias from the misattributed noise persists), the dimension-discount argument in Lemma 10(c) fails. The paper itself concedes the dominant-units case violates the bound and must be treated as pure sparse.

Watch

Extended reading notes

Core claim

The paper's central claim is that the inconsistency caused by dense measurement error in the adjacency matrix can be removed by imposing a low-rank-plus-sparse structure on the latent network. Formally, the plug-in estimator bθp(cW) that replaces the observed matrix W with a denoised estimate cW = bL + bS converges at rate O_p(R*_nT) + O_p(1/√(nT)), where R*_nT = (1+||B0||2)κ_n^{d+1}((r∨1)ρ_n + s_n)/n discounts the noise contribution by a factor 1/n. Because the recovery error enters the moment conditions only through bilinear forms, the low-rank part contributes O(r) effective directions and the sparse part contributes O(ms(S0)) entries, rather than all n². In contrast, using the noisy matr

Load-bearing premise

The true adjacency matrix must cleanly separate into a low-rank part with diffuse entries and a sparse part with bounded degree (incoherence condition inc(L0)·degmax(S0)≤1/16), and the measurement error must satisfy the conditional-moment bounds (E.8)–(E.10) of Lemma 10(c); if a real network has medium-rank, medium-entry structure or error that is too strongly correlated with outcomes, the denoising step misattributes noise to signal and the 1/n discount collapses.

Editorial extensions

If this is right

Consistency of spillover estimators can be restored in dense networks even when the measurement error is endogenous and does not vanish, as long as the latent network admits the low-rank-plus-sparse structure.
The plug-in estimator's error rate improves on naive GMM whenever R*_nT = o(w2n + w2n²); for networks with fixed or slowly growing rank and bounded sparsity, this condition holds even for constant noise levels.
The supervised estimator achieves the same rate as the plug-in estimator, so joint estimation does not sacrifice accuracy relative to two-stage denoising.
Because the estimator only depends on cW = bL + bS, the decomposition can be wrong in its economic interpretation without harming inference about the spillover parameter.

Reading between the lines

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

A testable extension is to apply the same denoising step to other network statistics that are nonlinear in the adjacency matrix—such as eigenvector centrality and the full Leontief inverse—to see whether the dimension-discounted noise property carries over; the paper's decomposition of the Leontief inverse suggests it should.
The theory suggests a hierarchy of measurement-error regimes: sparse errors are handled by elementwise-bounded arguments, while dense errors require structural signal (low-rank plus sparse); an estimator that adaptively detects which regime applies would be a natural next step.
If the 1/n discount is robust, applied researchers could use the method as a pre-processing step for spatial panels with distance-based weight matrices, without re-deriving the asymptotic theory case by case.
The paper's conditional-moment restrictions allow endogenous measurement error but bound its strength; an open question is how the rate degrades if the measurement error has heavier tails or long-range dependence that violates the variance bound.

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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. The paper is the first I've seen that takes low-rank-plus-sparse matrix recovery into the spatial-econometrics measurement-error problem, and the dimension-discounted rate R*_nT in Theorem 2 — where the denoising error enters as (r∨1)ρ_n/n instead of at the raw spectral level — is a real, nontrivial improvement over Lewbel et al. (2024) and over the naive-GMM bound. The L+S recovery rates in Theorem 1 follow from standard Agarwal/Wainwright arguments and look right. The plug-in and supervised estimators are clearly constructed, and the simulations are transparent: Table 1 shows a consistent 50–80% RMSE improvement over naive GMM across four DGPs.

The soft spots are in the framing and in the gap between the theory and the simulations. First, the abstract and intro say 'dense measurement error' in a way that suggests constant-level noise (σ_n ≥ c), but the theorems do not deliver consistency there — R*_nT = o(1) fails when w_{2n} ≍ √n. The paper is actually honest about this in Example 2, but the opening pages oversell it. Second, the headline 1/n noise discount goes through Lemma 10(c), whose conditional-moment conditions (E.8)–(E.10) are not in the main assumptions; Assumption 6(i) just punts to the appendix. If measurement error is dense and endogenous, as in their own motivating examples, ||E[ε_t|E]||_2 ≍ √n, so (E.8) fails and the endogeneity term is only discounted by 1/√n — the same order Proposition 1 says it removes. That is a load-bearing caveat for the rate comparison. Third, the simulations set σ_E = 0.3/n^0.7, so the measurement-error norms go to zero and the 'endogenous' case actually has vanishing endogeneity for both estimators. The 50–80% gain is then a vanishing-noise rate effect, not evidence for the consistency-restoration mechanism the paper motivates. That doesn't invalidate the method, but it means Table 1 doesn't test the paper's own hard regime.

Minor: the Theorem 3 proof is truncated in the version I read, and no code or data are shipped. The empirical applications are small-n (23 and 48 states) and illustrative.

Bottom line: this is a serious, technically competent paper with a real idea, and it deserves a referee even though I wouldn't accept it as-is. The fix is mostly honest framing: state plainly that the rate gain holds when w_{2n}/√n → 0 or under the conditional-moment conditions, validate (E.8)–(E.10) or bound the extra endogeneity term directly, and run at least one simulation with σ_n constant or slowly shrinking. With that revision it would be a solid contribution.

Referee Report

2 major / 5 minor

Summary. The paper studies a panel spatial/network model Y_t = λ0 W0 Y_t + α + ι_t + X_t β0 + W0 X_t γ0 + ε_t in which the observed adjacency matrix W equals the latent matrix W0 plus a dense measurement error E. It models W0 as low-rank-plus-sparse and proposes two estimators: a plug-in GMM that first denoises W by nuclear-norm/ℓ1 penalization, and a supervised one-step GMM that jointly estimates θ and the network components. The main theoretical claims are: (i) recovery rates for (L0, S0); (ii) a plug-in estimation rate R*_nT that discounts the noise level by 1/n and is strictly smaller than the naive-GMM rate w2n + w2n²; (iii) Proposition 1, stating that under endogenous measurement error the plug-in rate contains no extra ρεE term. Simulations report 50–80% RMSE improvements across four DGPs, and two empirical applications illustrate the method. The proofs of the key rate results rely on conditional-moment restrictions (E.8)–(E.10) stated in Lemma 10(c) of the appendix.

Significance. The idea of combining low-rank-plus-sparse denoising of the adjacency matrix with spatial GMM is a useful and timely contribution. If the rates were established under primitive conditions, the paper would extend Lewbel et al. (2024) to dense measurement error and would offer a practical tool for input-output, trade, and financial networks. The paper also gives a careful reduction to known L+S recovery bounds, and the two applications illustrate potentially important economic consequences. However, the central rate comparison is built on conditional-moment assumptions that are not primitive and appear to fail under the paper's own endogenous-measurement-error model, and the simulations do not exercise the dense-noise regime the paper advertises. The headline claim of a 1/n noise discount is therefore not yet convincingly established.

major comments (2)

[§4 and Appendix E, Lemma 10(c), Theorem 2(a), Proposition 1] The 1/n noise discount in R*_nT is obtained in the proof of Lemma 10(c) from conditional-moment conditions (E.8)–(E.10). These are not part of Assumptions 1–8; Assumption 6(i) merely says that dependence between E and X_t is allowed 'subject to the conditional moment restrictions stated in Lemma 10(c)', which restates the missing conditions rather than giving primitive conditions. More seriously, under the paper's own Assumption 8 with non-vanishing σ_E, E[ε_t|E] has Euclidean norm of order √n. For the primitive pair (X_jt, ε_t), the conditional variance in (E.10) then contains a term μ^T A^T Cov(a)A μ with ∥μ∥² ≍ n, so the uniform bound Var(Σ_t a_t^T A b_t | E) ≲ T∥A∥_F² cannot hold with an n-independent constant. Consequently the step |E[B_nT(A)|E]| ≤ (2/n)∥ΔL∥_*∥P_E∥_2∥M_E∥_2∥Q_E∥_2, and Proposition 1's rate (12) with no ρεE term, are not justified in the dense endogenous regime. The
[§5.2, Table 1] The Monte Carlo design sets σ_E = 0.3/n^{0.7}. Then w2n ≍ n^{-0.2} → 0 and wmaxn ≍ n^{-0.7}√log n → 0, so the naive GMM estimator is already consistent under Theorem 2(b), and the 'endogenous' errors satisfy ∥E[ε_t|E]∥_2 = O_p(n^{-0.2}) → 0. The reported 50–80% RMSE reductions are thus a small-noise denoising gain rather than evidence for the paper's dense-measurement-error message; the ρ=0.7 rows do not exercise the conditions whose failure is discussed above. Please add simulations with σ_E constant (or at least w2n bounded away from zero) and with E[ε_t|E] non-vanishing, to verify the claimed improvement in the regime the paper is about.

minor comments (5)

[§5.2, Eq. (20)] The simulation uses a scalar ρ in ε_it = ρσ_ε Σ_j E_ij/√n + v_it, whereas Assumption 8 defines ρ_εE as a T×(n−1) matrix. Please clarify the relationship and match the notation.
[Table 1] The header layout is hard to parse: 'Exogenous Plug-in Supervised Plug-in Supervised...' would be clearer with a single panel and explicit column labels for T=1,5,15,50 and estimator type.
[Theorems 1 and 3] The tuning parameters are sometimes ν_n, τ_n and sometimes ν_nT, τ_nT. This notational inconsistency should be fixed, especially since Theorem 3 redefines them.
[§2.1, Example 2] The notation E|E|_{1,1} uses E both for the expectation operator and the error matrix; consider using 𝔼 or a different symbol for the error matrix expectation.
[Appendix D] Assumption 9, which is used for identification of the L+S decomposition, is introduced only in the appendix; it should be stated or referenced in Section 4 where Assumptions 1–8 appear.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: rates are derived from explicit assumptions and external benchmarks; the conditional-moment fragility is an assumption gap, not a circular reduction.

full rationale

The derivation chain is not circular. Theorem 1's matrix-recovery rates are direct applications of Agarwal et al. (2012) and Wainwright (2019, Thms 9.19/9.24), with tuning parameters chosen from the assumed noise bounds in Assumption 2 rather than from the target spillover parameter. Lemma 10 and Theorems 2–3 combine these recovery bounds with standard GMM expansions; the plug-in and supervised rates follow from the stated assumptions instead of from parameters fitted to the outcome. The improvement R*_nT = o(w2n + w2n^2) is a rate comparison, not an identity imposed by construction. Self-citations (de Paula et al. 2025; Graham & de Paula 2020) supply datasets and applied settings and are not load-bearing for the theoretical claims. The main fragility is that the 1/n discount in Lemma 10(c) is conditioned on the appendix-only conditional-moment restrictions (E.8)–(E.10), which are absent from the main assumptions and can fail in strongly endogenous dense-error regimes; the simulation design with sigma_E = 0.3/n^0.7 makes E[epsilon_t | E] = O_p(n^{-0.2}), so the 'endogenous' experiments do not exercise the failure regime. These are unvalidated-assumption and design concerns, not circularity: no step equates a fitted quantity with a prediction, and no load-bearing argument reduces to the authors' own unverified self-citation.

Assumptions & free parameters 4 free parameters · 8 assumptions · 0 invented entities

No new entities are invented: the low-rank/sparse decomposition is explicitly disclaimed as 'a flexible modelling device, not an economic interpretation' (Sections 2.1 and 3.1), and no independent falsifiable handle is claimed for L0 or S0 as separate objects. What the central claim rests on is a set of structural conditions (identifiability of the decomposition, spectral/max noise bounds, instrument exogeneity, and the Lemma 10(c) conditional-moment restrictions) plus data-driven tuning parameters.

free parameters (4)

ν_n (nuclear-norm penalty on L) = simulations: IQR(W)·√n; applications: C_L·bσ·√n, C_L by BIC
Sets the singular-value shrinkage threshold in Algorithm 1/2 (Eq. 6). Theory requires ν_n ∝ w2n; practice substitutes a robust scale of the observed matrix, making the effective denoising strength data-dependent.
τ_n (ℓ1 penalty on S off-diagonal) = simulations: 2·IQR(W)·log(n); applications: C_S·bσ·log(n), C_S by BIC
Soft-thresholding level for the sparse component (Eq. 6); determines how many weak links survive the denoising.
ξ_nT (supervised/GMM weight) = 1 in simulations
Balances the GMM objective against adjacency fit in Eq. 8; theory requires ξ = O(1) (and ξ = o(1) for the CLT) but gives no selection rule.
BIC-selected penalty constants C_L, C_S (applications) = chosen by BIC per application
Penalty magnitudes in the I-O, GDP, and tax applications; data-driven, so the reported λ̂ and network estimates embed these choices.

assumptions (8)

domain assumption Assumption 1(i)-(iii): L0 low-rank with ||L0||max = O(1/√(mr(L0)mc(L0))); S0 sparse with degmax(S0)²/min{mr(L0),mc(L0)} → 0
Makes the L+S decomposition identifiable and the recovery rates of Theorem 1 valid; unverified for the applications beyond one I-O singular-value plot.
domain assumption Assumption 2: ||E||2 ≤ w2n and ||E||max ≤ wmaxn with high probability, Eii = 0
Bounds the dense measurement error; the distinction between vanishing and non-vanishing spectral noise lives here and drives the rate comparisons.
domain assumption Assumption 4(iii): column sums of W0 uniformly bounded except J fixed columns; uniform stability of I − λW0
Needed for Lemma 8/9 (||(I−λW0)^{-1}||2 = O(n^{1/4})) and instrument relevance; rules out growing numbers of dominant units.
domain assumption Assumption 6(ii): instruments Z_t(M) satisfy E[ε|Z(M)] = 0; M pre-specified/exogenous
Standard SAR instrument validity; the paper notes this precludes M = W under endogenous E — the plug-in uses M = Ŵ, requiring the asymptotic argument of Lemma 10(c).
domain assumption Lemma 10(c) conditional-moment/variance conditions (E.8)-(E.10): for every E-measurable A, ||E[a_t b_t^T|E]||2 = Op(1) and Var(Σ a_t^T A b_t|E) ≲ T||A||F² over primitive pairs (X, Y, U, ε)
The 'operative restriction' that converts the L+S recovery error into the 1/n-discounted bilinear rate; unvalidated for real data, and the strongest driver of the headline rate improvement.
domain assumption Assumption 8: (ε_i, E_i,-i) jointly Gaussian with cross-covariance of order n^{-s}, s > 1/2
'Imposed solely to illustrate the rate' for endogenous measurement error (Proposition 1).
standard math External recovery results: Agarwal et al. (2012) Thm 1; Wainwright (2019) Thms 9.19/9.24; Chandrasekaran et al. (2009) Cor. 3
External benchmarks used for Theorem 1 and Lemma 1; assumed correct.
domain assumption Assumptions 3, 5, 6(i),(iii)-(iv), 7: compact parameter space, i.i.d. errors with 2+δ moments, strong-mixing covariates, full-rank moment limits
Standard GMM regularity for SAR panels; the authors explicitly flag the cross-sectional independence as strong but 'expositional'.

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Pith. "Pith review of Estimating Network Spillovers under Dense Measurement Error." pith.science (2026). https://pith.science/paper/PHO5JNPK

@misc{pith2026260719625,
  author       = {Pith},
  title        = {Pith review of: Estimating Network Spillovers under Dense Measurement Error},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PHO5JNPK}},
  note         = {Machine review of arXiv:2607.19625}
}

abstract

This paper analyzes spillover effects in spatial (network) models when the neighborhood (adjacency) matrix is contaminated by measurement error from reporting, aggregation, or disclosure imperfections, leading to inconsistent estimation of network effects. We introduce a regularization framework for the latent network that allows for sparse and/or low-rank structure and accommodates potential correlation between measurement errors and outcomes. We propose two estimators: (i) a two-stage procedure that first denoises the adjacency matrix and then incorporates the purified network into a regression analysis, and (ii) a Generalized Method of Moments (GMM) estimator that jointly estimates regression parameters and refines the network structure. We then establish strictly improved consistency rates for the spillover effect estimator relative to naive estimation ignoring measurement error. Simulations demonstrate that, in the presence of noisy networks, our approach reduces the root mean squared error of spillover estimates relative to conventional methods by approximately $50-80\%$. We apply our framework to examine the international spillover of economic growth, and the tax competition across U.S. states, illustrating that denoising might restore Leontief stability and yields improved estimates of spillovers.

Figures

Figures reproduced from arXiv: 2607.19625 by the authors.

**Figure 1.** Graphical representations of simulated adjacency matrices associated with different groups 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 1 10 20 1 10 20 to from w 0.0 Notes: Examples for the weight matrix formed by individuals who belong to different groups. The left one is the network graph and the right one is the heat map of the adjacency matrix. There are two groups, one of which has 6 members and the other h… view at source ↗

**Figure 2.** Graphical representations of the simulated adjacency matrix with dominant units. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 10 20 1 10 20 to from w 0.0 0.8 Notes: Examples for the weight matrix with dominant units. The left one is the network graph and the right one is the heat map of the adjacency matrix. There are 20 individuals and each individual connects to its neighbors with strength set by 0.25. The… view at source ↗

**Figure 3.** Heatmaps of 20 sectors from the 2002 Input-Output Table W (left), estimated sparse component Sb (centre), and estimated low-rank component Lb (right). The stripe pattern in Lb reveals pervasive systematic structure missed by a purely sparse representation. 0 5 10 15 20 0 5 10 15 20 to from w 0.00 0.25 0.50 0.75 1.00 0 5 10 15 20 0 5 10 15 20 to from w 0.00 0.25 0.50 0.75 1.00 0 5 10 15 20 0 5 10 15 20 to from w 0.00… view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Heatmaps of 20 sectors from the diffusion matrix (In − 0.7Wc) −1 (left), (In − 0.7Sb) −1 (centre), and the difference (right). Omitting the low-rank component eliminates the stripe pattern and distorts estimated spillover propagation by 68%. 3. Methodology We present t…

**Figure 5.** Figure 5: Heatmaps of different spatial weight matrices associated with 23 economies, including the raw weight matrix W2 (left), the estimated low-rank and sparse matrix Wc2 (center), and the estimated purely sparse matrix Sb (right). In the regression analysis, we evaluate the …

**Figure 6.** Figure 6: Graphical representation of different spatial weight matrix associated with 23 economies, including the estimated low-rank and sparse one Wc2 (left), the estimated lowrank one Lb (center) and the estimated purely sparse one Sb (right) [PITH_FULL_IMAGE:figures/full_fi…

**Figure 7.** Figure 7: Plots of eigenvector centrality associated with different weight matrices. Denote the low-rank and sparse components of our estimator Wc2 as Lb and Sb, i.e. Wc2 = Lb Wc2 + Sb Wc2 . From left to right, we provide the eigenvector centrality plots of Wc2, Lb Wc2 and Sb W…

**Figure 8.** Figure 8: Heatmaps of adjacency matrices associated with 48 states. From left to right, this figure provides the heatmaps associated with the row-normalized 0-1 geographic adjacency matrix Wg, the row-normalized inverse squared distance matrix W2, the estimated low-rank and spa…

**Figure 9.** Figure 9: Graphical representations of different weight matrices. From left to right, this figure provides the network representation for the row-normalized neighborhood weight matrix Wg, the row-normalized inverse squared distance matrix W2 and the estimated lowrank and sparse…

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Works this paper leans on

262 extracted references · 3 canonical work pages

[1]

and Romer, D

Mankiw, N.G. and Romer, D. and Weil, D.N. , title =. Quarterly Journal of Economics , year =
[2]

and Lewis, Randall , title =

Chandrasekhar, Arun G. and Lewis, Randall , title =. 2011 , note =

2011
[3]

Journal of Political Economy , year =

Fisman, Raymond and Wei, Shang-Jin , title =. Journal of Political Economy , year =
[4]

Journal of Financial Stability , year =

Upper, Christian , title =. Journal of Financial Stability , year =
[5]

Quantitative Finance , year =

Anand, Kartik and Craig, Ben and von Peter, Goetz , title =. Quantitative Finance , year =
[6]

and Duflo, Esther and Jackson, Matthew O

Banerjee, Abhijit and Chandrasekhar, Arun G. and Duflo, Esther and Jackson, Matthew O. , title =. Science , year =
[7]

Journal of Econometrics , year =

Griffith, Alexander , title =. Journal of Econometrics , year =
[8]

American Economic Review , year =

Acemoglu, Daron and Ozdaglar, Asuman and Tahbaz-Salehi, Alireza , title =. American Economic Review , year =

Show all 262 references

[9]

Under the hood: Issues in the specification and interpretation of spatial regression models , journal =

Luc Anselin , keywords =. Under the hood: Issues in the specification and interpretation of spatial regression models , journal =. 2002 , note =. doi:https://doi.org/10.1016/S0169-5150(02)00077-4 , url =

2002 doi
[10]

Lloyd , keywords =

C.D. Lloyd , keywords =. Assessing the effect of integrating elevation data into the estimation of monthly precipitation in Great Britain , journal =. 2005 , issn =. doi:https://doi.org/10.1016/j.jhydrol.2004.10.026 , url =

2005 doi
[11]

Lu and David W

George Y. Lu and David W. Wong , keywords =. An adaptive inverse-distance weighting spatial interpolation technique , journal =. 2008 , issn =. doi:https://doi.org/10.1016/j.cageo.2007.07.010 , url =

2008 doi
[12]

Increasing Returns and Economic Geography , urldate =

Paul Krugman , journal =. Increasing Returns and Economic Geography , urldate =
[13]

Econometrics of Network Models , booktitle=

Paula, Áureo de , editor=. Econometrics of Network Models , booktitle=. 2017 , pages=

2017
[14]

, title =

Cressie, N. , title =
[15]

2009 , publisher =

Introduction to Spatial Econometrics , author =. 2009 , publisher =

2009
[16]

American Economic Review , volume =

Strategic Interaction and Networks , author =. American Economic Review , volume =. 2014 , doi =

2014
[17]

Journal of Statistical Software , author=

Regularization Paths for Generalized Linear Models via Coordinate Descent , volume=. Journal of Statistical Software , author=. 2010 , pages=. doi:10.18637/jss.v033.i01 , number=

2010 doi
[18]

and Willsky, Alan S

Chandrasekaran, Venkat and Sanghavi, Sujay and Parrilo, Pablo A. and Willsky, Alan S. , booktitle=. Sparse and low-rank matrix decompositions , year=
[19]

Geographical Analysis , volume =

Getis, Arthur and Aldstadt, Jared , title =. Geographical Analysis , volume =
[20]

Journal of Regional Science , volume =

Corrado, Luisa and Fingleton, Bernard , title =. Journal of Regional Science , volume =
[21]

A Singular Value Thresholding Algorithm for Matrix Completion , journal =

Cai, Jian-Feng and Cand\`. A Singular Value Thresholding Algorithm for Matrix Completion , journal =. 2010 , doi =

2010
[22]

Econometrica , volume =

The granular origins of aggregate fluctuations , author =. Econometrica , volume =. 2011 , publisher =

2011
[23]

Journal of Economic Perspectives , volume =

From micro to macro via production networks , author =. Journal of Economic Perspectives , volume =. 2014 , publisher =

2014
[24]

2008 , volume =

Social and economic networks , author =. 2008 , volume =

2008
[25]

Goyal and J

S. Goyal and J. L. Moraga-Gonz\'. Learning in networks , journal =
[26]

E. J. Cand. Robust principal component analysis? , journal =
[27]

Jackson , title =

Matthew Elliott and Benjamin Golub and Matthew O. Jackson , title =. 2014 , publisher =

2014
[28]

2012 , volume =

Stefano Battiston and Michelangelo Puliga and Rahul Kaushik and Paolo Tasca and Guido Caldarelli , title =. 2012 , volume =

2012
[29]

2007 , publisher =

Hans Degryse and Gregory Nguyen , title =. 2007 , publisher =

2007
[30]

2015 , doi =

Vulnerable banks , journal =. 2015 , doi =

2015
[31]

Chandrasekaran and S

V. Chandrasekaran and S. Sanghavi and P. A. Parrilo and A. S. Willsky , title =. SIAM Journal on Optimization , year =
[32]

Wright and A

J. Wright and A. Y. Yang and A. Ganesh and S. S. Sastry and Y. Ma , title =. IEEE Transactions on Pattern Analysis and Machine Intelligence , year =
[33]

W. W. Hager , title =. SIAM Review , year =
[34]

Barrot and J

J.-N. Barrot and J. Sauvagnat , title =. The Quarterly Journal of Economics , year =
[35]

Available at SSRN 3963526 , year =

Network regressions and supervised centrality estimation-supplemental materials of proof , author =. Available at SSRN 3963526 , year =
[36]

Input linkages and the transmission of shocks: Firm-level evidence from the 2011 T

Boehm, Christoph E and Flaaen, Aaron and Pandalai-Nayar, Nitya , journal =. Input linkages and the transmission of shocks: Firm-level evidence from the 2011 T. 2019 , publisher =

2011
[37]

F. X. Diebold and K. Yilmaz , title =. Journal of Econometrics , year =
[38]

Forni and L

M. Forni and L. Reichlin , title =. Review of Economics and Statistics , year =
[39]

Golub and M

B. Golub and M. O. Jackson , title =. American Economic Journal: Microeconomics , year =
[40]

V. M. Carvalho , title =. Journal of Economic Perspectives , year =
[41]

Networks, Shocks, and Systemic Risk , booktitle =

Acemoglu, Daron and Ozdaglar, Asuman and Tahbaz-Salehi, Alireza , isbn =. Networks, Shocks, and Systemic Risk , booktitle =. 2016 , month =. doi:10.1093/oxfordhb/9780199948277.013.17 , url =

2016
[42]

Testing community structure for hypergraphs , year =

Yuan, Mingao and Liu, Ruiqi and Feng, Yang and Shang, Zuofeng , journal =. Testing community structure for hypergraphs , year =
[43]

2012 , publisher =

Global shell games: Testing money launderers' and terrorist financiers' access to shell companies , author =. 2012 , publisher =

2012
[44]

2023 , publisher =

Spatial statistics for data science: Theory and practice with R , author =. 2023 , publisher =

2023
[45]

2005 , publisher =

Spatial statistics , author =. 2005 , publisher =

2005
[46]

2015 , publisher =

Statistics for spatial data , author =. 2015 , publisher =

2015
[47]

Geographical Analysis , year =

Geographical and temporal weighted regression , author =. Geographical Analysis , year =
[48]

Journal of Business & Economic Statistics , volume =

Bayesian model averaging for spatial autoregressive models based on convex combinations of different types of connectivity matrices , author =. Journal of Business & Economic Statistics , volume =. 2022 , publisher =

2022
[49]

2020 , publisher =

The econometric analysis of network data , author =. 2020 , publisher =

2020
[50]

The Quarterly Journal of Economics , volume =

Does electoral accountability affect economic policy choices? Evidence from gubernatorial term limits , author =. The Quarterly Journal of Economics , volume =. 1995 , publisher =

1995
[51]

2019 , publisher =

High-dimensional statistics: A non-asymptotic viewpoint , author =. 2019 , publisher =

2019
[52]

American Economic Review , year =

Incumbent behavior: Vote-seeking, tax-setting, and yardstick competition , author =. American Economic Review , year =
[54]

Econometrics Journal , volume =

Ignoring measurement errors in social networks , author =. Econometrics Journal , volume =. 2024 , publisher =

2024
[55]

IFAC Proceedings Volumes , volume =

Sparse and low-rank matrix decompositions , author =. IFAC Proceedings Volumes , volume =. 2009 , publisher =

2009
[57]

2023 , archiveprefix =

Victor Chernozhukov and Chen Huang and Weining Wang , title =. 2023 , archiveprefix =. 2105.07424 , primaryclass =

2023 arXiv
[58]

Community detection with nodal information: Likelihood and its variational approximation , year =

Weng, Haolei and Feng, Yang , journal =. Community detection with nodal information: Likelihood and its variational approximation , year =
[59]

Franco and Yu, Yi and Feng, Yang , journal =

Saldana, D. Franco and Yu, Yi and Feng, Yang , journal =. How many communities are there? , year =
[60]

2023 , issn =

Huang, Sihan and Sun, Jiajin and Feng, Yang , journal =. 2023 , issn =. doi:10.1080/01621459.2023.2244731 , publisher =

2023
[61]

2023 , number =

Sihan Huang and Haolei Weng and Yang Feng , journal =. 2023 , number =

2023
[62]

1950 , archiveprefix =

Max Woodbury , title =. 1950 , archiveprefix =

1950
[63]

2008 , archiveprefix =

Karim Lounici , title =. 2008 , archiveprefix =. 0811.2281 , primaryclass =

2008 arXiv
[64]

Linear Algebra and its Applications , title =

Queir. Linear Algebra and its Applications , title =. 1995 , pages =

1995
[65]

Performance bounds for parameter estimates of high-dimensional linear models with correlated errors , year =

Wu, Wei-Biao and Wu, Ying Nian , journal =. Performance bounds for parameter estimates of high-dimensional linear models with correlated errors , year =
[66]

and Pearce, Charles E

Lu, L.-Z. and Pearce, Charles E. M. , journal =. Some new bounds for singular values and eigenvalues of matrix products , year =
[67]

2018 , archiveprefix =

Alexandre Belloni and Victor Chernozhukov and Denis Chetverikov and Christian Hansen and Kengo Kato , title =. 2018 , archiveprefix =. 1806.01888 , primaryclass =

2018 arXiv
[68]

, journal =

Thompson, Robert C. , journal =. 1972 , number =

1972
[69]

Linear hypothesis testing in dense high-dimensional linear models , year =

Zhu, Yinchu and Bradic, Jelena , journal =. Linear hypothesis testing in dense high-dimensional linear models , year =
[70]

2015 , number =

Belloni, Alexandre and Chernozhukov, Victor and Kato, Kengo , journal =. 2015 , number =

2015
[71]

A general theory of hypothesis tests and confidence regions for sparse high dimensional models , year =

Ning, Yang and Liu, Han , journal =. A general theory of hypothesis tests and confidence regions for sparse high dimensional models , year =
[72]

Generalized econometric models with selectivity , year =

Lee, Lung-Fei , journal =. Generalized econometric models with selectivity , year =
[73]

Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models , year =

Lee, Lung-Fei , journal =. Asymptotic distributions of quasi-maximum likelihood estimators for spatial autoregressive models , year =
[74]

2011 , number =

Belloni, Alexandre and Chernozhukov, Victor , journal =. 2011 , number =

2011
[75]

Testing cross-section correlation in panel data using spacings , year =

Ng, Serena , journal =. Testing cross-section correlation in panel data using spacings , year =
[76]

Financial network systemic risk contributions , year =

Hautsch, Nikolaus and Schaumburg, Julia and Schienle, Melanie , journal =. Financial network systemic risk contributions , year =
[77]

Semiparametric efficiency bounds for high-dimensional models , year =

Jankova, Jana and van de Geer, Sara , journal =. Semiparametric efficiency bounds for high-dimensional models , year =
[78]

and Kwon, Jaimyoung , journal =

Bickel, Peter J. and Kwon, Jaimyoung , journal =. Inference for semiparametric models: some questions and an answer , year =
[79]

2023 , volume =

Ata, Baris and Belloni, Alexandre and Candogan, Ozan , journal =. 2023 , volume =

2023
[80]

Shrinkage estimation of network spillovers with factor structured errors , year =

Higgins, Ayden and Martellosio, Federico , journal =. Shrinkage estimation of network spillovers with factor structured errors , year =
[81]

2025 , journal =

Aureo de Paula and Imran Rasul and Pedro Souza , title =. 2025 , journal =

2025
[82]

High dimensional covariance matrix estimation in approximate factor models , year =

Fan, Jianqing and Liao, Yuan and Mincheva, Martina , journal =. High dimensional covariance matrix estimation in approximate factor models , year =
[83]

Bagging predictors , year =

Breiman, Leo , journal =. Bagging predictors , year =
[84]

Gaussian approximation for high dimensional time series , year =

Zhang, Danna and Wu, Wei Biao , journal =. Gaussian approximation for high dimensional time series , year =
[85]

Robustify financial time series forecasting with bagging , year =

Jin, Sainan and Su, Liangjun and Ullah, Aman , journal =. Robustify financial time series forecasting with bagging , year =
[86]

and Ng, S

Bai, J. and Ng, S. , journal =. 2002 , pages =

2002
[87]

Efficient

Lee, Lung-Fei and Yu, Jihai , journal =. Efficient. 2014 , number =

2014
[88]

Select the valid and relevant moments: An information-based lasso for GMM with many moments , year =

Cheng, Xu and Liao, Zhipeng , journal =. Select the valid and relevant moments: An information-based lasso for GMM with many moments , year =
[89]

, publisher =

van der Vaart, Aad W. , publisher =. 2000 , volume =

2000
[90]

High-dimensional probability , year =

Vershynin, Roman , publisher =. High-dimensional probability , year =
[91]

, journal =

Manski, Charles F. , journal =. Identification of endogenous social effects: The reflection problem , year =
[92]

Econometrics of network models , year =

de Paula, Aureo , booktitle =. Econometrics of network models , year =
[93]

Lasso-type GMM estimator , year =

Caner, Mehmet , journal =. Lasso-type GMM estimator , year =
[94]

Annals of Statistics , title =

Victor Chernozhukov and Wolfgang H\". Annals of Statistics , title =. 2021 , number =

2021
[95]

Multivariate regression models for panel data , year =

Chamberlain, Gary , journal =. Multivariate regression models for panel data , year =
[96]

On the pooling of time series and cross section data , year =

Mundlak, Yair , journal =. On the pooling of time series and cross section data , year =
[97]

2019 , number =

Jin, Fei and Lee, Lung-Fei , journal =. 2019 , number =

2019
[98]

2019 , archiveprefix =

Mehmet Caner and Anders Bredahl Kock , title =. 2019 , archiveprefix =. 1811.08779 , primaryclass =

2019 arXiv
[99]

and Prucha, Ingmar R

Kuersteiner, Guido M. and Prucha, Ingmar R. , journal =. Dynamic spatial panel models: Networks, common shocks, and sequential exogeneity , year =
[100]

Instrumental quantile regression inference for structural and treatment effect models , year =

Chernozhukov, Victor and Hansen, Christian , journal =. Instrumental quantile regression inference for structural and treatment effect models , year =
[101]

2020 , type =

Xu, Xiu and Wang, Weining and Shin, Yongcheol , title =. 2020 , type =

2020
[102]

Journal of Econometrics , title =

Zhu, Xuening and Wang, Weining and Wang, Hansheng and H. Journal of Econometrics , title =. 2019 , number =

2019
[103]

Journal of Econometrics , title =

H. Journal of Econometrics , title =. 2016 , number =

2016
[104]

Diebold, Francis X. and Y. Journal of Econometrics , title =. 2014 , number =

2014
[105]

and Yilmaz, Kamil , journal =

Diebold, Francis X. and Yilmaz, Kamil , journal =. 2012 , number =

2012
[106]

, journal =

Newey, Whitney K. , journal =. Semiparametric efficiency bounds , year =
[107]

2011 , number =

Cai, Tony and Liu, Weidong and Luo, Xi , journal =. 2011 , number =

2011
[108]

Elements of causal inference , year =

Peters, Jonas and Janzing, Dominik and Sch. Elements of causal inference , year =
[109]

Another look at the instrumental variable estimation of error-components models , year =

Arellano, Manuel and Bover, Olympia , journal =. Another look at the instrumental variable estimation of error-components models , year =
[110]

, journal =

Thompson, Robert C. , journal =. Interlacing inequalities for invariant factors , year =
[111]

, journal =

Newey, Whitney K. , journal =. The asymptotic variance of semiparametric estimators , year =
[112]

, title =

Graham, Bryan S. , title =. 2016 , type =

2016
[113]

Estimating a spatial autoregressive model with an endogenous spatial weight matrix , year =

Qu, Xi and Lee, Lung-Fei , journal =. Estimating a spatial autoregressive model with an endogenous spatial weight matrix , year =
[114]

Formulation and estimation of dynamic models using panel data , year =

Anderson, Theodore Wilbur and Hsiao, Cheng , journal =. Formulation and estimation of dynamic models using panel data , year =
[115]

2019 , archiveprefix =

Alexandre Belloni and Mingli Chen and Victor Chernozhukov , title =. 2019 , archiveprefix =. 1607.00286 , primaryclass =

2019 arXiv
[116]

Epskamp, Sacha and Waldorp, Lourens J. and M. Multivariate Behavioral Research , title =. 2018 , number =

2018
[117]

Inference on treatment effects after selection among high-dimensional controls , year =

Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian , journal =. Inference on treatment effects after selection among high-dimensional controls , year =
[118]

Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors , year =

Chernozhukov, Victor and Chetverikov, Denis and Kato, Kengo , journal =. Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors , year =
[119]

, journal =

Freedman, David A. , journal =. On tail probabilities for martingales , year =
[120]

2000 , volume =

van de Geer, Sara , publisher =. 2000 , volume =

2000
[121]

, booktitle =

Burkholder, Donald L. , booktitle =. Sharp inequalities for martingales and stochastic integrals , year =
[122]

2000 , number =

Blundell, Richard and Bond, Stephen , journal =. 2000 , number =

2000
[123]

Network vector autoregression , year =

Zhu, Xuening and Pan, Rui and Li, Guodong and Liu, Yuewen and Wang, Hansheng , journal =. Network vector autoregression , year =
[124]

Multivariate spatial autoregressive model for large scale social networks , year =

Zhu, Xuening and Huang, Danyang and Pan, Rui and Wang, Hansheng , journal =. Multivariate spatial autoregressive model for large scale social networks , year =
[125]

1991 , number =

Arellano, Manuel and Bond, Stephen , journal =. 1991 , number =

1991
[126]

Invariant causal prediction for nonlinear models , year =

Heinze-Deml, Christina and Peters, Jonas and Meinshausen, Nicolai , journal =. Invariant causal prediction for nonlinear models , year =
[127]

Lam, Clifford and Souza, Pedro C. L. , journal =. Estimation and selection of spatial weight matrix in a spatial lag model , year =
[128]

2016 , journal =

Auerbach, Eric , title =. 2016 , journal =

2016
[129]

2024 , journal =

Wang, Yike and Otsu, Taisuke , title =. 2024 , journal =

2024
[130]

Econometrica , volume =

Panel data models with interactive fixed effects , author =. Econometrica , volume =
[131]

and Liu, Han , journal =

Neykov, Matey and Ning, Yang and Liu, Jun S. and Liu, Han , journal =. A unified theory of confidence regions and testing for high-dimensional estimating equations , year =
[132]

Hypothesis testing in high-dimensional regression under the

Javanmard, Adel and Montanari, Andrea , journal =. Hypothesis testing in high-dimensional regression under the. 2014 , number =

2014
[133]

, journal =

Zhang, Cun-Hui and Zhang, Stephanie S. , journal =. Confidence intervals for low dimensional parameters in high dimensional linear models , year =
[134]

Annals of Statistics , title =

van de Geer, Sara and B. Annals of Statistics , title =. 2014 , number =

2014
[135]

Test , title =

Dezeure, Ruben and B. Test , title =. 2017 , number =

2017
[136]

2016 , journal =

Manresa, Elena , title =. 2016 , journal =

2016
[137]

Social networks with unobserved links , year =

Lewbel, Arthur and Qu, Xi and Tang, Xun , journal =. Social networks with unobserved links , year =
[138]

Double/debiased machine learning for treatment and structural parameters , year =

Chernozhukov, Victor and Chetverikov, Denis and Demirer, Mert and Duflo, Esther and Hansen, Christian and Newey, Whitney and Robins, James , journal =. Double/debiased machine learning for treatment and structural parameters , year =
[139]

Simultaneous inference for high-dimensional linear models , year =

Zhang, Xianyang and Cheng, Guang , journal =. Simultaneous inference for high-dimensional linear models , year =
[140]

Semiparametric efficiency in

Chen, Xiaohong and Hong, Han and Tarozzi, Alessandro , journal =. Semiparametric efficiency in. 2008 , number =

2008
[141]

Inference for high-dimensional instrumental variables regression , year =

Gold, David and Lederer, Johannes and Tao, Jing , journal =. Inference for high-dimensional instrumental variables regression , year =
[142]

Journal of Political Economy , volume =

Linear social interactions models , author =. Journal of Political Economy , volume =
[143]

Identification and estimation of econometric models with group interactions, contextual factors and fixed effects , year =

Lee, Lung-Fei , journal =. Identification and estimation of econometric models with group interactions, contextual factors and fixed effects , year =
[144]

2017 , number =

Yang, Kai and Lee, Lung-fei , journal =. 2017 , number =

2017
[145]

Specification and estimation of social interaction models with network structures , year =

Lee, Lung-Fei and Liu, Xiaodong and Lin, Xu , journal =. Specification and estimation of social interaction models with network structures , year =
[146]

2018 , pages =

Fan, Jianqing and Wang, Weichen and Zhong, Yiqiao , journal =. 2018 , pages =

2018
[147]

, journal =

Agarwal, Alekh and Negahban, Sahand and Wainwright, Martin J. , journal =. Noisy matrix decomposition via convex relaxation: Optimal rates in high dimensions , year =
[148]

2021 , archiveprefix =

Junhui Cai and Dan Yang and Wu Zhu and Haipeng Shen and Linda Zhao , title =. 2021 , archiveprefix =. 2111.12921 , primaryclass =

2021 arXiv
[149]

2020 , pages =

Chanpuriya, Sudhanshu and Musco, Cameron and Sotiropoulos, Konstantinos and Tsourakakis, Charalampos , booktitle =. 2020 , pages =

2020
[150]

Journal of Econometrics , title =

Chen, Cathy Yi-Hsuan and H. Journal of Econometrics , title =. 2022 , number =

2022
[151]

Monitoring network changes in social media , year =

Chen, Cathy Yi-Hsuan and Okhrin, Yarema and Wang, Tengyao , journal =. Monitoring network changes in social media , year =
[152]

Hashem , journal =

Chudik, Alexander and Pesaran, M. Hashem , journal =. 2013 , number =

2013
[153]

2009 , number =

Fan, Jianqing and Feng, Yang and Wu, Yichao , journal =. 2009 , number =

2009
[154]

2016 , number =

Gamble, Jennifer and Chintakunta, Harish and Wilkerson, Adam and Krim, Hamid , journal =. 2016 , number =

2016
[155]

2024 , journal =

Dapeng Shi and Tiandong Wang and Zhiliang Ying , title =. 2024 , journal =

2024
[156]

and Hou, Li , journal =

Jin, Baisuo and Wu, Yuehua and Rao, Calyampudi R. and Hou, Li , journal =. Estimation and model selection in general spatial dynamic panel data models , year =
[157]

Estimation and variable selection for high-dimensional spatial dynamic panel data models , year =

Hou, Li and Jin, Baisuo and Wu, Yuehua , journal =. Estimation and variable selection for high-dimensional spatial dynamic panel data models , year =
[158]

A social interactions model with endogenous friendship formation and selectivity , year =

Hsieh, Chih-Sheng and Lee, Lung Fei , journal =. A social interactions model with endogenous friendship formation and selectivity , year =
[159]

Peer effects and endogenous social interactions , year =

Koen Jochmans , journal =. Peer effects and endogenous social interactions , year =
[160]

Estimation of peer effects in endogenous social networks: Control function approach , year =

Johnsson, Ida and Moon, Hyungsik Roger , journal =. Estimation of peer effects in endogenous social networks: Control function approach , year =
[161]

Hashem and Reese, Simon , journal =

Kapetanios, George and Pesaran, M. Hashem and Reese, Simon , journal =. Detection of units with pervasive effects in large panel data models , year =
[162]

Journal of Business & Economic Statistics , year =

Lee, Lung-Fei and Yang, Chao and Yu, Jihai , title =. Journal of Business & Economic Statistics , year =
[163]

, journal =

Masten, Matthew A. , journal =. Random coefficients on endogenous variables in simultaneous equations models , year =
[164]

, journal =

Parekh, Ankit and Selesnick, Ivan W. , journal =. Improved sparse low-rank matrix estimation , year =
[165]

Identification of unknown common factors: Leaders and followers , year =

Parker, Jason and Sul, Donggyu , journal =. Identification of unknown common factors: Leaders and followers , year =
[166]

Hashem and Yang, Cynthia Fan , journal =

Pesaran, M. Hashem and Yang, Cynthia Fan , journal =. Econometric analysis of production networks with dominant units , year =
[167]

Hashem and Yang, Cynthia Fan , journal =

Pesaran, M. Hashem and Yang, Cynthia Fan , journal =. Estimation and inference in spatial models with dominant units , year =
[168]

Proceedings of the 29th International Conference on Machine Learning , title =

Richard, Emile and Savalle, Pierre-Andr\'. Proceedings of the 29th International Conference on Machine Learning , title =. 2012 , pages =

2012
[169]

2004 , volume =

Srebro, Nathan and Rennie, Jason and Jaakkola, Tommi , booktitle =. 2004 , volume =

2004
[170]

Grouped network vector autoregression , year =

Zhu, Xuening and Pan, Rui , journal =. Grouped network vector autoregression , year =
[171]

New directions in spatial econometrics , year =

Anselin, Luc and Florax, Raymond , publisher =. New directions in spatial econometrics , year =
[172]

and Prucha, Ingmar R

Kelejian, Harry H. and Prucha, Ingmar R. , journal =. A generalized moments estimator for the autoregressive parameter in a spatial model , year =
[173]

Journal of Econometrics , title =

Bramoull. Journal of Econometrics , title =. 2009 , number =

2009
[174]

and Prucha, Ingmar R

Kelejian, Harry H. and Prucha, Ingmar R. , journal =. A generalized spatial two-stage least squares procedure for estimating a spatial autoregressive model with autoregressive disturbances , year =
[175]

2007 , number =

Lee, Lung-Fei , journal =. 2007 , number =

2007
[176]

2022 , doi =

Xiu Xu and Weining Wang and Yongcheol Shin and Chaowen Zheng , journal =. 2022 , doi =

2022
[177]

2022 , archiveprefix =

Yong Cai , title =. 2022 , archiveprefix =. 2210.10024 , primaryclass =

2022
[178]

2018 , booktitle =

Dan, Chen and Hansen, Kristoffer Arnsfelt and Jiang, He and Wang, Liwei and Zhou, Yuchen , title =. 2018 , booktitle =

2018
[179]

and Zhou, Douglas and Cai, David , journal =

Barranca, Victor J. and Zhou, Douglas and Cai, David , journal =. Low-rank network decomposition reveals structural characteristics of small-world networks , year =
[180]

Recovering low-rank and sparse matrix based on the truncated nuclear norm , year =

Cao, Feilong and Chen, Jiaying and Ye, Hailiang and Zhao, Jianwei and Zhou, Zhenghua , journal =. Recovering low-rank and sparse matrix based on the truncated nuclear norm , year =
[181]

Reconstruction from randomized graph via low rank approximation , year =

Wu, Leting and Ying, Xiaowei and Wu, Xintao , booktitle =. Reconstruction from randomized graph via low rank approximation , year =
[182]

, journal =

Fang, Chunsheng Victor and Kohram, Mojtaba and Ralescu, Anca L. , journal =. Spectral regression with low-rank approximation for dynamic graph link prediction , year =
[183]

and Golovach, Petr A

Fomin, Fedor V. and Golovach, Petr A. and Panolan, Fahad , journal =. Parameterized low-rank binary matrix approximation , year =
[184]

Journal of the ACM , title =

Cand. Journal of the ACM , title =. 2011 , number =

2011
[185]

Sparse approximate solutions to linear systems , year =

Natarajan, Balas Kausik , journal =. Sparse approximate solutions to linear systems , year =
[186]

, journal =

Recht, Benjamin and Fazel, Maryam and Parrilo, Pablo A. , journal =. Guaranteed minimum-rank solutions of linear matrix equations via nuclear norm minimization , year =
[187]

A new primal-dual algorithm for minimizing the sum of three functions with a linear operator , year =

Yan, Ming , journal =. A new primal-dual algorithm for minimizing the sum of three functions with a linear operator , year =
[188]

A three-operator splitting scheme and its optimization applications , year =

Davis, Damek and Yin, Wotao , journal =. A three-operator splitting scheme and its optimization applications , year =
[189]

Weighted low-rank approximations , year =

Srebro, Nathan and Jaakkola, Tommi , booktitle =. Weighted low-rank approximations , year =
[190]

, booktitle =

Razenshteyn, Ilya and Song, Zhao and Woodruff, David P. , booktitle =. Weighted low rank approximations with provable guarantees , year =
[191]

and Mahony, Robert and Hua, Yingbo , journal =

Manton, Jonathan H. and Mahony, Robert and Hua, Yingbo , journal =. The geometry of weighted low-rank approximations , year =
[192]

PLoS One , title =

Guillemot, Vincent and Beaton, Derek and Gloaguen, Arnaud and L. PLoS One , title =. 2019 , number =

2019
[193]

2024 , volume =

Feng, Junlong , journal =. 2024 , volume =

2024
[194]

, title =

Wainwright, Martin J. , title =. 2019 , publisher =

2019
[195]

2021 , number =

Chen, Yuxin and Fan, Jianqing and Ma, Cong and Yan, Yuling , journal =. 2021 , number =

2021
[196]

The geometry of graphs and some of its algorithmic applications , year =

Linial, Nathan and London, Eran and Rabinovich, Yuri , journal =. The geometry of graphs and some of its algorithmic applications , year =
[197]

and Willsky, Alan S

Chandrasekaran, Venkat and Parrilo, Pablo A. and Willsky, Alan S. , booktitle =. Latent variable graphical model selection via convex optimization , year =
[198]

The Journal of Machine Learning Research , volume =

Clustering partially observed graphs via convex optimization , author =. The Journal of Machine Learning Research , volume =. 2014 , publisher =

2014
[199]

and Romberg, Justin , journal =

Davenport, Mark A. and Romberg, Justin , journal =. An overview of low-rank matrix recovery from incomplete observations , year =
[200]

2024 , volume =

Cui, Liyuan and Hong, Yongmiao and Li, Yingxing and Wang, Junhui , journal =. 2024 , volume =

2024
[201]

Matrix completion methods for causal panel data models , year =

Athey, Susan and Bayati, Mohsen and Doudchenko, Nikolay and Imbens, Guido and Khosravi, Khashayar , journal =. Matrix completion methods for causal panel data models , year =
[202]

Inference for heterogeneous effects using low-rank estimations , year =

Chernozhukov, Victor and Hansen, Christian Bailey and Liao, Yuan and Zhu, Yinchu , institution =. Inference for heterogeneous effects using low-rank estimations , year =
[203]

Inference for low-rank models , year =

Chernozhukov, Victor and Hansen, Christian and Liao, Yuan and Zhu, Yinchu , journal =. Inference for low-rank models , year =
[204]

Targeting interventions in networks , year =

Galeotti, Andrea and Golub, Benjamin and Goyal, Sanjeev , journal =. Targeting interventions in networks , year =
[205]

and Laskey, Kathryn Blackmond and Leinhardt, Samuel , journal =

Holland, Paul W. and Laskey, Kathryn Blackmond and Leinhardt, Samuel , journal =. Stochastic blockmodels: First steps , year =
[206]

and Ozdaglar, Asuman and Tahbaz-Salehi, Alireza , journal =

Acemoglu, Daron and Carvalho, Vasco M. and Ozdaglar, Asuman and Tahbaz-Salehi, Alireza , journal =. The network origins of aggregate fluctuations , year =
[207]

arXiv preprint arXiv:1904.00136 , year=

Estimating spillovers using imprecisely measured networks , author=. arXiv preprint arXiv:1904.00136 , year=

1904 arXiv
[208]

arXiv preprint arXiv:2410.10772 , year=

Minimax rates for the linear-in-means model reveal an identifiability-estimability gap , author=. arXiv preprint arXiv:2410.10772 , year=
[209]

Review of Economics and Statistics , pages=

Estimating peer effects using partial network data , author=. Review of Economics and Statistics , pages=. 2025 , publisher=

2025
[210]

, journal =

Killworth, Peter and Bernard, H. , journal =. Informant accuracy in social network data , year =
[211]

2015 , pages =

Jeon, Kwon Chan and Goodson, Patricia , journal =. 2015 , pages =

2015
[212]

1989 , number =

Anselin, Luc , institution =. 1989 , number =

1989
[213]

, journal =

Holloway, Garth and Lacombe, Donald and LeSage, James P. , journal =. Spatial econometric issues for bio-economic and land-use modelling , year =
[214]

Recent developments in factor models and applications in econometric learning , year =

Fan, Jianqing and Li, Kunpeng and Liao, Yuan , journal =. Recent developments in factor models and applications in econometric learning , year =
[215]

2013 , journal =

Xi Luo , title =. 2013 , journal =

2013
[216]

Econometrica , title =

Ballester, Coralio and Calv. Econometrica , title =. 2006 , number =

2006
[217]

Journal of Business & Economic Statistics , volume=

Who is the key player? A network analysis of juvenile delinquency , author=. Journal of Business & Economic Statistics , volume=. 2021 , publisher=

2021
[218]

, booktitle =

Borgatti, Stephen P. , booktitle =. The key player problem , year =
[219]

, journal =

Borgatti, Stephen P. , journal =. Identifying sets of key players in a social network , year =
[220]

The international trade network: Empirics and modeling , year =

Fagiolo, Giorgio , booktitle =. The international trade network: Empirics and modeling , year =
[221]

, journal =

Guo, Liang and Wang, Sizhu and Xu, Nicole Z. , journal =. 2023 , number =

2023
[222]

What's new in economic sanctions? , year =

Hufbauer, Gary Clyde and Jung, Euijin , journal =. What's new in economic sanctions? , year =
[223]

and Goldberg, Pinelopi K

Fajgelbaum, Pablo D. and Goldberg, Pinelopi K. and Kennedy, Patrick J. and Khandelwal, Amit K. , journal =. The return to protectionism , year =
[224]

Review of Economics and Statistics , title =

K. Review of Economics and Statistics , title =. 2019 , number =

2019
[225]

Review of Economic Studies , title =

Calv. Review of Economic Studies , title =. 2009 , number =

2009
[226]

American Economic Review , title =

Acemoglu, Daron and Garc. American Economic Review , title =. 2015 , number =

2015
[227]

SIAM Journal on Numerical Analysis , volume =

Splitting algorithms for the sum of two nonlinear operators , author =. SIAM Journal on Numerical Analysis , volume =. 1979 , publisher =

1979
[228]

2016 , archiveprefix =

Tom Goldstein and Christoph Studer and Richard Baraniuk , title =. 2016 , archiveprefix =. 1411.3406 , primaryclass =

2016 arXiv
[229]

Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances , year =

Lee, Lung-Fei , journal =. Best spatial two-stage least squares estimators for a spatial autoregressive model with autoregressive disturbances , year =
[230]

and Chen, Rong , title =

Chen, Bin and Chen, Elynn Y. and Chen, Rong , title =. 2023 , institution =

2023
[231]

Paul , title =

Elhorst, J. Paul , title =. Spatial Econometrics: From Cross-Sectional Data to Spatial Panels , year =
[232]

Spatial panel econometrics , year =

Anselin, Luc and Gallo, Julie Le and Jayet, Hubert , booktitle =. Spatial panel econometrics , year =
[233]

Some recent developments in spatial panel data models , year =

Lee, Lung-Fei and Yu, Jihai , journal =. Some recent developments in spatial panel data models , year =
[234]

Autoregressive models for matrix-valued time series , year =

Chen, Rong and Xiao, Han and Yang, Dan , journal =. Autoregressive models for matrix-valued time series , year =
[235]

Consumption network effects , year =

de Giorgi, Giacomo and Frederiksen, Anders and Pistaferri, Luigi , journal =. Consumption network effects , year =
[236]

and Galeotti, Andrea , journal =

Fainmesser, Itay P. and Galeotti, Andrea , journal =. Pricing network effects , year =
[237]

Proceedings of the National Academy of Sciences , title =

Araujo, Rafael and Assun. Proceedings of the National Academy of Sciences , title =. 2023 , number =

2023
[238]

2018 , volume =

de Nooy, Wouter and Mrvar, Andrej and Batagelj, Vladimir , publisher =. 2018 , volume =

2018
[239]

Journal of Political Economy , volume=

Social networks with unobserved links , author=. Journal of Political Economy , volume=. 2023 , publisher=

2023
[240]

Specification and estimation of network formation and network interaction models with the exponential probability distribution , year =

Hsieh, Chih-Sheng and Lee, Lung-Fei and Boucher, Vincent , journal =. Specification and estimation of network formation and network interaction models with the exponential probability distribution , year =
[241]

Han, Xiaoyi and Hsieh, Chih-Sheng and Ko, Stanley I. M. , journal =. Spatial modeling approach for dynamic network formation and interactions , year =
[242]

2021 , institution =

Shin, Yongcheol and Thornton, Michael Alan , title =. 2021 , institution =

2021
[243]

and Duflo, Esther and Jackson, Matthew O

Banerjee, Abhijit and Chandrasekhar, Arun G. and Duflo, Esther and Jackson, Matthew O. , journal =. The diffusion of microfinance , year =
[244]

, booktitle =

Stark, Tobias H. , booktitle =. 2018 , pages =

2018
[245]

A survey on network data collection , year =

Donghao Zhou and Zheng Yan and Yulong Fu and Zhen Yao , journal =. A survey on network data collection , year =
[246]

Data collection for social network research , year =

Garry Robins and David Bright and Laurin Weissinger and Pat Stys , journal =. Data collection for social network research , year =
[247]

2021 , publisher =

Adams, jimi and Santos, Tatiane and Williams, Venice Ng , booktitle =. 2021 , publisher =

2021
[248]

McCormick and Tian Zheng , journal =

Tyler H. McCormick and Tian Zheng , journal =. 2015 , number =

2015
[249]

2024 , number =

Matteo Barigozzi and Haeran Cho and Dom Owens , journal =. 2024 , number =

2024
[250]

, booktitle =

Belloni, Alexandre and Chernozhukov, Victor and Hansen, Christian B. , booktitle =. 2013 , pages =

2013
[251]

Chen and Jianqing Fan and Xuening Zhu , journal =

Elynn Y. Chen and Jianqing Fan and Xuening Zhu , journal =. Community network auto-regression for high-dimensional time series , year =
[252]

Journal of Econometrics , title =

Chen, Cathy Yi-Hsuan and H. Journal of Econometrics , title =. 2019 , number =

2019
[253]

2016 , publisher =

Zenou, Yves , booktitle =. 2016 , publisher =

2016
[254]

and McCormick, Tyler H

Breza, Emily and Chandrasekhar, Arun G. and McCormick, Tyler H. and Pan, Mengjie , journal =. 2020 , number =

2020
[255]

Candelaria and Takuya Ura , journal =

Luis E. Candelaria and Takuya Ura , journal =. Identification and inference of network formation games with misclassified links , year =
[256]

Rossi and Nesreen K

Ryan A. Rossi and Nesreen K. Ahmed , booktitle =
[257]

, journal =

Stewart, Gilbert W. , journal =. 1980 , number =

1980
[258]

How to generate random matrices from the classical compact groups , year =

Francesco Mezzadri , journal =. How to generate random matrices from the classical compact groups , year =
[259]

Low-rank and sparse matrix factorization with prior relations for recommender systems , year =

Wang, Jie and Zhu, Li and Dai, Tao and Xu, Qiannan and Gao, Tianyu , journal =. Low-rank and sparse matrix factorization with prior relations for recommender systems , year =
[260]

Matrix completion with noise , year =

Candes, Emmanuel J and Plan, Yaniv , journal =. Matrix completion with noise , year =
[261]

2014 , number =

Olga Klopp , journal =. 2014 , number =

2014
[262]

2024 , publisher =

Bingyan Wang and Jianqing Fan , journal =. 2024 , publisher =

2024
[263]

A machine learning approach to economic complexity based on matrix completion , year =

Gnecco, Giorgio and Nutarelli, Federico and Riccaboni, Massimo , journal =. A machine learning approach to economic complexity based on matrix completion , year =
[264]

A connectedness constraint for learning sparse graphs , year=

Sundin, Martin and Venkitaraman, Arun and Jansson, Magnus and Chatterjee, Saikat , booktitle=. A connectedness constraint for learning sparse graphs , year=

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [1]

and Romer, D

Mankiw, N.G. and Romer, D. and Weil, D.N. , title =. Quarterly Journal of Economics , year =

[2] [2]

and Lewis, Randall , title =

Chandrasekhar, Arun G. and Lewis, Randall , title =. 2011 , note =

2011

[3] [3]

Journal of Political Economy , year =

Fisman, Raymond and Wei, Shang-Jin , title =. Journal of Political Economy , year =

[4] [4]

Journal of Financial Stability , year =

Upper, Christian , title =. Journal of Financial Stability , year =

[5] [5]

Quantitative Finance , year =

Anand, Kartik and Craig, Ben and von Peter, Goetz , title =. Quantitative Finance , year =

[6] [6]

and Duflo, Esther and Jackson, Matthew O

Banerjee, Abhijit and Chandrasekhar, Arun G. and Duflo, Esther and Jackson, Matthew O. , title =. Science , year =

[7] [7]

Journal of Econometrics , year =

Griffith, Alexander , title =. Journal of Econometrics , year =

[8] [8]

American Economic Review , year =

Acemoglu, Daron and Ozdaglar, Asuman and Tahbaz-Salehi, Alireza , title =. American Economic Review , year =