This paper discusses the different contemporaneous causal interpretations of Panel Vector Autoregressions (PVAR). I show that, under independence conditions, the interpretation of PVARs depends on the distribution of the causing variable, and can range from average treatment effects, to average causal responses, to a combination of the two.

If the researcher is willing to postulate a no residual autocorrelation assumption, and some units can be thought of as controls, PVAR can identify average treatment effects on the treated. This method complements the toolkits already present in the literature, such as staggered-DiD, or LP-DiD, as it formulates assumptions in the residuals, and not in the outcome variables. Such a method features a notable advantage: it allows units to be “sparsely” treated, capturing the impact of interventions on the innovation component of the outcome variables.

I provide two examples related to the evaluation of the effects of natural disasters economic activity at the weekly frequency in the US and at monthly frequency in the Euro Area.

Panel Vector Autoregressions are usually identified recursively, making it difficult to make

causal claims unless there is an underlying exogeneity assumption. However, little is said about contemporaneous causality. This paper proposes an identification scheme inspired from the VAR-IV literature to identify a PVAR. It discusses the identification, estimation, and inference of a PVAR identified using external instruments.

First, I introduce a form of LATE, defined as µ- LATE, which captures the local average

treatment effect emerging from a counterfactual generated through a continuous instrument but targeting a binary quantity. I show that under suitable conditions (independence, exclusion, monotonicity) PVARs which are identified using an external instrument estimate the µ−LATE.

Then, I discuss the best approaches to make inferential claims in PVARs. Through Monte

Carlo simulations, I show that the confidence set generated using the Anderson-Rubin statistic around the impulse response functions provides good coverage properties.

All the results are discussed using an application in which I instrument state level military

spending using the state’s fraction of total national military spending - a shift share instrument - to estimate the dynamic fiscal multiplier. I find that the state level fiscal multiplier is around 1.7 in the contemporaneous year and 1.5 in the year that follows, a result that is mainly driven by the large correlation between output and spending in the previous year.

This paper addresses the challenges of giving a causal interpretation to vector autoregressions (VARs). I show that under independence assumptions VARs can identify average treatment effects, average causal responses, or a mix of the two, depending on the distribution of the policy. But what about situations in which the economist cannot rely on independence assumptions? I propose an alternative method, defined as control-VAR, which uses control variables to estimate causal effects. Control-VAR can estimate average treatment effects on the treated for dummy policies or average causal responses over time  for continuous policies.

The advantages of control-based approaches are demonstrated by examining the impact of natural disasters on the US economy, using Germany as a control. Contrary to previous literature, the results indicate that natural disasters have a negative economic impact without any cyclical positive effect. These findings suggest that control-VARs provide a viable alternative to strict independence assumptions, offering more credible causal estimates and significant implications for policy design in response to natural disasters.