Are stationarity and cointegration restrictions really necessary for the intertemporal budget constraint

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Fiscal Fatigue, Fiscal Space and Debt Sustainability in Advanced Economies (2013, unknown): “…proportion of lagged debt, then a sufficient condition for this stricter definition is that the responsiveness of the primary balance be greater 3 Bohn (2007) shows that satisfying the government budget constraint requires only that there exist some (arbitrarily high but finite) degree of…”
THE IDENTIFICATION OF FISCAL AND MONETARY POLICY IN A STRUCTURAL VAR (2009, background): “More recently Bohn (2007) has shown that cointegration is a sufficient but not necessary condition for fiscal sustainability. ables and the external sector in consists of international output, export prices, import prices and the trade weighted index reflecting the small open economy assumption.”
What is a Sustainable Public Debt (2015, unknown): “IGBC tests that discount future primary balances at the risk-free rates are mispecified, because the correct discount factors are determined by the state-contingent equilibriun pricing kernel (Bohn, 1995).”
A Modern History of Fiscal Prudence and Profligacy (2013, background): “…data for the United 2 Other tests based on the univariate time-series behavior of the debt-to-GDP ratio have fallen by the wayside, because of the difficulties in detecting mean-reversion as the debt-to-GDP ratio is bounced around by various shocks (see Bohn, 1998, 2007, and citations therein).”