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Applied macroeconomists frequently use impulse response estimators motivated by linear models. We study whether the estimands of such procedures have a causal interpretation when the data generating process is in fact nonlinear. We show that vector autoregressions and linear local projections onto observed shocks or proxies identify weighted averages of causal effects regardless of the extent of nonlinearities. By contrast, identification approaches that exploit heteroscedasticity or non-Gaussianity of latent shocks are highly sensitive to departures from linearity. Our analysis is based on new results on the identification of marginal treatment effects through weighted regressions, which may also be of interest to researchers outside macroeconomics.
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This content will become publicly available on November 1, 2026
Beyond the Diagonal Reference Model: Critiques and New Directions in the Analysis of Mobility Effects
Over the past decade there has been a striking increase in the number of quantitative studies examining the effects of social mobility, with almost all based on the diagonal reference model (DRM). We make four main contributions to this rapidly expanding literature. First, we show that under plausible values of mobility effects, the DRM will, in many cases, implicitly force the underlying mobility linear effect toward zero. In addition, we show both mathematically and through simulations that the mobility effects estimated by the DRM are sensitive to the size and sign of the origin and destination linear effects, often in ways that are unlikely to be intuitive to applied researchers. This finding clarifies why, contrary to expectations, applied researchers have generally found mixed evidence of mobility effects. Second, we generalize the identification problem of conventional mobility effect models by showing that the DRM and related methods can be viewed as special cases of a bounding analysis, where identification is achieved by invoking extremely strong assumptions. Finally, and importantly, we present a new framework for the analysis of mobility tables based on the identification and estimation of joint parameter sets, introducing what we call the structural and dynamic inequality model. We show that this model is fully identified, relies on much weaker assumptions than conventional models of mobility effects, and can be treated both as a descriptive model and, if additional assumptions are invoked, as a causal model. We conclude with an agenda for further research on the consequences of socioeconomic mobility.
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- Award ID(s):
- 1948310
- PAR ID:
- 10649358
- Publisher / Repository:
- Sage
- Date Published:
- Journal Name:
- Sociological Methods & Research
- Volume:
- 54
- Issue:
- 4
- ISSN:
- 0049-1241
- Page Range / eLocation ID:
- 1339 to 1395
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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