How much fiscal space do emerging market economies have to maintain expansive fiscal policies? This is a key question given the observed increase in public debt since 2007. To answer this question we estimate a debt limit for emerging market economies, from which the public debt to GDP ratio would have an explosive trajectory, in the spirit of Ghosh, Kim, Mendoza, Ostry and Qureshi (2013). For this, we estimate the determinants of the public debt ratio dynamics, the primary balance and the effective cost of debt, for 26 emerging market economies during the 2000-2015 period. We propose an alternative measure, the stochastic debt limit, which takes into account the uncertainty and sensitivity of the debt limit to macroeconomic and financial conditions. The main results are: i) There is evidence of “fiscal fatigue”, namely the loss of control of the debt growth via fiscal adjustments as the debt ratio increases; ii) the debt ratio is an important determinant of the effective cost of public debt; and iii) the debt limit as traditional measured (deterministic) is between 68-97 percentage points of GDP, and between 5-89 percentage points for the stochastic case, which gives evidence of limited fiscal space for the majority of the economies analyzed.