We develop non-asymptotically justified methods for hypothesis testing about the $p-$dimensional coefficients $\theta^{*}$ in (possibly nonlinear) regression models. Given a function $h:\,\mathbb{R}^{p}\mapsto\mathbb{R}^{m}$, we consider the null hypothesis $H_{0}:\,h(\theta^{*})\in\Omega$...

We study the finite sample behavior of Lasso-based inference methods such as post double Lasso and debiased Lasso. Empirically and theoretically, we show that these methods can exhibit substantial omitted variable biases (OVBs) due to Lasso not selecting relevant controls. This phenomenon can be...

The classic third degree price discrimination (3PD) model requires the knowledge of the distribution of buyer valuations and the covariate to set the price conditioned on the covariate. In terms of generating revenue, the classic result shows that 3PD is at least as good as uniform pricing. What...