We use a random forest model to classify firms’ financial constraints using only financial variables. Our methodology expands the range of classified firms compared to text-based measures while maintaining similar levels of informativeness. We construct two versions of our constraint measures, one using many firm characteristics and the other using a small set of more primitive characteristics. Using our measures, we find that institutional investors hold a lower percentage of shares in equity-focused constrained firms, while retail investors show a preference for them. Equity issuance and investment of constrained firms also increases during periods of high investor sentiment.

We show that a common component governs volatility dynamics across a wide range of traded equity factors. This “common factor volatility” (CFV) exists even among orthogonal factors. CFV occurs in both cash-flow and discount-rate components of factor returns and derives from market responses to fundamental news rather than underlying commonality in news volatility. Incorporating CFV improves factor volatility forecasts relative to models that include only own-factor volatility. CFV allows us to characterize stochastic discount factor (SDF) volatility dynamics in a very general sense and we show that many popular models imply SDFs with time-varying volatility that correlates strongly with CFV.

Pesaran, Shin, and Smith (2001) (PSS) proposed a bounds procedure for testing for the existence of long run cointegrating relationships between a unit root dependent variable ($y_{t}$) and a set of weakly exogenous regressors $\boldsymbol{x}_{t}$ when the analyst does not know whether the independent variables are stationary, unit root, or mutually cointegrated processes. This procedure recognizes the analyst’s uncertainty over the nature of the regressors but not the dependent variable. When the analyst is uncertain whether $y_{t}$ is a stationary or unit root process, the test statistics proposed by PSS are uninformative for inference on the existence of a long run relationship (LRR) between $y_{t}$ and $\boldsymbol{x}_{t}$. We propose the long run multiplier (LRM) test statistic as a means of testing for LRRs without knowing whether the series are stationary or unit roots. Using stochastic simulations, we demonstrate the behavior of the test statistic given uncertainty about the univariate dynamics of both $y_{t}$ and $\boldsymbol{x}_{t}$, illustrate the bounds of the test statistic, and generate small sample and approximate asymptotic critical values for the upper and lower bounds for a range of sample sizes and model specifications. We demonstrate the utility of the bounds framework for testing for LRRs in models of public policy mood and presidential success.