f refers to the fiscal position.<sup>3</sup> Our measure of the fiscal position is the government debt-to-GDP ratio. While the literature has used a variety of measures, our choice is in line with theoretical models, where government debt is the modal state variable (as discussed below).<sup>4</sup> Since measures of the fiscal position are endogenous and move in tandem with the business cycle, we take lagged moving averages of our fiscal measures to control for business cycle effects.<sup>5</sup> The matrices determine the effects of structural shocks on the dynamics of endogenous variables in the VAR system. By conditioning the law of motion of the coefficients in ll these matrices on the fiscal position, as in Equation (2), we are allowing those effects to depend AA , ll= 1, ... , LL on the fiscal position. This scheme allows us to calculate impulse responses and hence estimates of fiscal multipliers conditional on a specific fiscal position.

As standard in the literature, we compute the cumulative fiscal multiplier at horizon T as the discounted cumulative change in output until horizon , as the discounted cumulative government consumption increases by one unit. That is, TT M ∑t <u>0</u> ∆g <u>g</u> , (3) ∑TT ∆g t= (1+rr)<sup>−tt</sup> tt TT llM ggllMMr (TT) = tt=0(1+rr)<sup>−tt</sup> tt where denotes the interest rate. We utilize the median short-term rate in the sample. From (3), the impact multiplier is obtained by setting rr and the long-run multiplier by setting T at an arbitrarily large number, which is taken to be (5 years). To calculate the fiscal multiplier using the coefficient estimates from the IPVAR, we first cumulate the discounted TT= 0 impulses of output and government consumption at different horizons and compute the ratio of TT= 20 the two impulses. That ratio is then multiplied by the average government consumption-to-GDP ratio in the sample to yield multipliers. Since the conditional multipliers are estimated from the panel of countries, they reflect an average estimate across those countries included in the panel. Thus, we use the average government consumption-to-GDP ratio in the sample to calculate the multipliers rather than country-specific government consumption-to-GDP ratios.

Equations (1) and (2) jointly denote the IPVAR system that is estimated with ordinary least squares (OLS) applied separately to each equation.<sup>6</sup> This yields model coefficients that depend on the fiscal position such that a given level of the fiscal position maps out to a set of model coefficients. For presenting the results, we evaluate model coefficients at specific values of the fiscal position which are mostly taken to be the 10<sup>th</sup> and 90<sup>th</sup> percentiles within the sample. Confidence bands are calculated by bootstrapping over 300 iterations. We report median estimates, along with the 16 - 84 percent confidence bands.

> 3 Including the fiscal position in the law of motion in Equation (2) is tantamount to having interaction terms with the fiscal position in the regressors of Equation (1). For this reason, we do not separately include the fiscal position as an endogenous variable in the IPVAR.

> 4 For instance, while Riera-Crichton, Vegh, and Vuletin (2015) condition multipliers on fiscal balances, Auerbach and Gorodnichenko (2013), Ilzetzki, Mendoza, and Vegh (2013), and Nickel and Tudyka (2014) condition on government debt.

> 5 In particular, we take the 5-quarter moving average of the fiscal position, and then lag it by 2 quarters. Given the average length of the business cycle, this effectively allows us to abstract from changes in the fiscal state that may potentially be contaminated by cyclical movements. We allay any residual endogeneity concerns by jointly conditioning on the fiscal position and the phase of the business cycle below.

> 6 Because the error terms are uncorrelated across equations by construction, estimating the IPVAR equation by equation does not result in loss of efficiency. See Towbin and Weber (2013) for a discussion.

4