Discrete Temporal Models of Social Networks

We propose a family of statistical models for social network evolution over time, which represents an extension of Exponential Random Graph Models (ERGMs). Many of the methods for ERGMs are readily adapted for these models, including maximum likelihood estimation algorithms. We discuss models of this type and their properties, and give examples, as well as a demonstration of their use for hypothesis testing and classification. We believe our temporal ERG models represent a useful new framework for modeling time-evolving social networks, and rewiring networks from other domains such as gene regulation circuitry, and communication networks

Revenue Equivalence Revisited

The conventional wisdom in the auction design literature is that first price sealed bid auctions tend to make more money while ascending auctions tend to be more efficient. We re-examine these issues in an environment in which bidders are allowed to endogenously choose in which auction format to participate. Our findings are that more bidders choose to enter the ascending auction than the first price sealed bid auction and this extra entry is enough to make up the revenue difference between the formats. Consequently, we find that both formats raise approximately the same amount of revenue. They also generate efficiency levels and bidder earnings that are roughly equivalent across mechanisms though the earnings in the ascending might be slightly higher. In expected utility terms though, we find that the expected utility of entering a first price sealed bid auction is greater than entering an ascending for any risk averse bidder suggesting that we are seeing “overentry” into the ascending auctions

The Augmented Synthetic Control Method

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The "synthetic control" is a weighted average of control units that balances the treated unit's pre-treatment outcomes as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pre-treatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pre-treatment fit is infeasible. Analogous to bias correction for inexact matching, Augmented SCM uses an outcome model to estimate the bias due to imperfect pre-treatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package