This chapter highlights some key issues in the use of sign restrictions for the purpose of identifying shocks. It does so by examining two benchmark examples. In the first part, I discuss a generic example of demand and supply, seeking to identify a supply shock from price–quantity data. In the second part, I discuss a generic example of Bayesian vector autoregressions and the identification of a monetary supply shock. Along the way, I formulate some principles and present my view on some of the recent discussion and literature regarding sign restrictions.

INTRODUCTION

The approach of sign restrictions in time series analysis has generated an active literature, many successful applications, and a lively debate. The procedures are increasingly easy to use, with implementations in econometric software packages such as RATS or with ready-to-implement code in a variety of programming languages; see, e.g., Danne (2015) as one example. Let me say from the outset that I am very happy about that, including those contributions that have criticized my own work, sometimes sharply. Skepticism and critique is crucial for science to advance, so all power to them! That should not prevent me from critiquing back, of course, and that is partly what this chapter will be about. Debate is good.

While Leamer (1981) surely deserves being highlighted here, I believe that the literature pretty much started with Dwyer (1998), Faust (1998) and its discussion, Uhlig (1998), Canova and Pina (1999), Canova and de Nicolo (2002), as well as my “agnostic identification” paper Uhlig (2005b). This one was published quite a number of years after my discussion of the Faust paper, but that discussion shows that I had already developed my methodology then, and that imposing sign restrictions on impulse responses and not just on impact can add considerable bite. There are deep connections to the seemingly different literature on partial identification and estimation subject to inequality restrictions: rather than review that literature, let me just point the reader to the excellent discussions on this topic by Canay and Shaikh (2017) as well as by Ho and Rosen (2017), appearing elsewhere in this volume, or, say, Kline and Tamer (2016).