  In policy research, one of the most critical analytic tasks is to estimate
the causal effect of a policy-relevant shift to the distribution of a
continuous exposure/treatment on an outcome of interest. We call this problem
shift-response function (SRF) estimation. Existing neural network methods
involving robust causal-effect estimators lack theoretical guarantees and
practical implementations for SRF estimation. Motivated by a key
policy-relevant question in public health, we develop a neural network method
and its theoretical underpinnings to estimate SRFs with robustness and
efficiency guarantees. We then apply our method to data consisting of 68
million individuals and 27 million deaths across the U.S. to estimate the
causal effect from revising the US National Ambient Air Quality Standards
(NAAQS) for PM 2.5 from 12 $\mu g/m^3$ to 9 $\mu g/m^3$. This change has been
recently proposed by the US Environmental Protection Agency (EPA). Our goal is
to estimate, for the first time, the reduction in deaths that would result from
this anticipated revision using causal methods for SRFs. Our proposed method,
called {T}argeted {R}egularization for {E}xposure {S}hifts with Neural
{Net}works (TRESNET), contributes to the neural network literature for causal
inference in two ways: first, it proposes a targeted regularization loss with
theoretical properties that ensure double robustness and achieves asymptotic
efficiency specific for SRF estimation; second, it enables loss functions from
the exponential family of distributions to accommodate non-continuous outcome
distributions (such as hospitalization or mortality counts). We complement our
application with benchmark experiments that demonstrate TRESNET's broad
applicability and competitiveness.
