arXiv 4 Aug 2026 · Econometrics
arXiv:2608.03486 · PDF · Extracted main text
We develop a fully nonlinear structural vector autoregressive framework in which the contemporaneous structural mapping may be nonlinear and non-additive. Identification is achieved by exploiting variation in the conditional distributions of the mutually independent structural shocks induced by an observed exogenous variable. Specifically, a general contrastive learning framework that makes use of this variation together with the assumed exponential-family structure is employed to recover the shocks. Existing independent innovation analysis results identify such shocks only up to arbitrary componentwise invertible transformations, which is generally insufficient for structural econometric analysis. We strengthen this result by imposing a structured exponential-family specification for the conditional shock distributions. With the imposed sufficient statistics, the remaining ambiguity is reduced to a one-parameter transformed-scale map for each shock. We then show that, under a logistic specification used for the natural parameters, the identification is further strengthened up to permutation and componentwise sign changes. Once the shocks have been recovered, the fully nonlinear structural vector autoregression can be estimated using feed-forward neural networks, motivated by their universal approximation capabilities. The empirical application studies asymmetries in the responses of U.S. industrial production to the real oil price shock. We find modest asymmetries with respect to the sign of the shock and state of the economy. The accompanying R package iiasvar implements the introduced methods.
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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 | Herrera A. M., Lagalo L. G., Wada T (2011) Oil price shocks and industrial production: is the relationship linear? | 1.000 | 6 | 3 | 100% |
| 2 | Morioka H., Hälvä H., Hyvärinen A (2021) Independent innovation analysis for nonlinear vector autoregressive process | 0.952 | 22 | 6 | 86% |
| 3 | Hornik K., Stinchcombe M., White H (1989) Multilayer feedforward networks are universal approximators | 0.928 | 4 | 4 | 100% |
| 4 | Jurado K., Ludvigson S., Ng S (2015) Measuring uncertainty | 0.928 | 4 | 3 | 100% |
| 5 | Koop G., Pesaran M., Potter S (1996) Impulse response analysis in nonlinear multivariate models | 0.843 | 3 | 3 | 100% |
| 6 | Virolainen S (2026) iiasvar: Fully nonlinear structural vector autoregression framework based on independent innovation analysis | 0.843 | 3 | 3 | 100% |
| 7 | Lanne M., Meitz M., Saikkonen P (2017) Identification and estimation of non-Gaussian structural vector autoregressions | 0.737 | 3 | 2 | 100% |
| 8 | Lanne M., Virolainen S (2025) A Gaussian smooth transition vector autoregressive model: An application to the macroeconomic effects of severe weather shocks | 0.737 | 3 | 2 | 100% |
| 9 | Virolainen S (2026) Identification by non-Gaussianity in structural smooth transition vector autoregressive models | 0.644 | 2 | 2 | 100% |
| 10 | Hansen B. E (1994) Autoregressive conditional density estimation | 0.511 | 2 | 2 | 50% |
Showing the top 10 of 25 scored citations.