Beyond Average Effects: Identifying Signed Causal Effects under Latent Confounding via Multi-Environment Variance Shifts

A positive association between overnight commodity futures returns and equity opening returns does not establish causal transmission: both markets may react to the same unobserved news. Even a positive average causal effect can conceal positive and negative effects that partly cancel. We study what changes in volatility across a few environments can reveal about these two questions. Our model allows the causal slope to vary across observations and treatment to be confounded. Conditional on a pretreatment state, environments change only the scale of the treatment disturbance, while the joint distribution of the causal slope and latent common components remains unchanged. Under the model's assumptions, contrasts in second moments across two environments identify the mean and second moment of the causal slope. These moments yield exact joint bounds on its expected positive and negative parts: every pair in the resulting set is attained by a model matching the observed moments. With three environments having distinct, positive, and unknown scales, additional assumptions allow both signed effects to be point identified without recovering the full slope distribution. Simulations assess estimation and inference. In an application to Shanghai tin futures and Yunnan Tin equity returns, the estimated average causal effect is approximately 29 basis points per percentage-point tin innovation, after averaging over the observed state composition. Yet the moment-based bounds allow a negative effect with a magnitude as large as 55 basis points per percentage point—nearly twice the average effect. The same estimated moments thus admit both transmission that is nonnegative throughout and substantial cancellation between positive and negative effects.