arXiv 12 Jan 2025 · Econometrics
arXiv:2501.06777 · PDF · DOI · OpenAlex · Extracted main text
Identifying structural parameters in linear simultaneous-equation models is a longstanding challenge. Recent work exploits information in higher-order moments of non-Gaussian data. In this literature, the structural errors are typically assumed to be uncorrelated so that, after standardizing the covariance matrix of the observables (whitening), the structural parameter matrix becomes orthogonal -- a device that underpins many identification proofs but can be restrictive in econometric applications. We show that neither zero covariance nor whitening is necessary. For any order $h>2$, a simple diagonality condition on the $h$th-order cumulants alone identifies the structural parameter matrix -- up to unknown scaling and permutation -- as the solution to an eigenvector problem; no restrictions on cumulants of other orders are required. This general, single-order result enlarges the class of models covered by our framework and yields a sample-analogue estimator that is $\sqrt{n}$-consistent, asymptotically normal, and easy to compute. Furthermore, when uncorrelatedness is intrinsic -- as in vector autoregressive (VAR) models -- our framework provides a transparent overidentification test. Monte Carlo experiments show favorable finite-sample performance, and two applications -- "Returns to Schooling" and "Uncertainty and the Business Cycle" -- demonstrate its practical value.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Davis, R. and Ng, S (2023) Time series estimation of the dynamic effects of disaster-type shocks | 1.000 | 7 | 3 | 100% |
| 2 | Bonhomme, S. and Robin, J.-M (2009) Consistent noisy independent component analysis | 0.737 | 3 | 2 | 100% |
| 3 | Ludvigson, S. C., Ma, S., and Ng, S (2021) Uncertainty and business cycles: exogenous impulse or endogenous response? | 0.693 | 6 | 1 | 100% |
| 4 | Card, D (1993) Using geographic variation in college proximity to estimate the return to schooling | 0.644 | 4 | 1 | 100% |
| 5 | Deaton, A (1988) Quality, quantity, and spatial variation of price | 0.644 | 2 | 2 | 100% |
| 6 | Lanne, M., Meitz, M., and Saikkonen, P (2017) Identification and estimation of non-gaussian structural vector autoregressions | 0.644 | 2 | 2 | 100% |
| 7 | Hyvärinen, A (2013) Independent component analysis: recent advances | 0.644 | 2 | 2 | 100% |
| 8 | Lewis, D. J (2021) Identifying shocks via time-varying volatility | 0.585 | 3 | 1 | 100% |
| 9 | McCullagh, P (1984) Tensor notation and cumulants of polynomials | 0.511 | 2 | 1 | 100% |
| 10 | Card, D (2001) Estimating the return to schooling: Progress on some persistent econometric problems | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 40 scored citations.