  We propose a conceptual framework for counterfactual and welfare analysis for
approximate models. Our key assumption is that model approximation error is the
same magnitude at new choices as the observed data. Applying the framework to
quasilinear utility, we obtain bounds on quantities at new prices using an
approximate law of demand. We then bound utility differences between bundles
and welfare differences between prices. All bounds are computable as linear
programs. We provide detailed analytical results describing how the data map to
the bounds including shape restrictions that provide a foundation for plug-in
estimation. An application to gasoline demand illustrates the methodology.
