**Table 2:** Externally Calibrated Parameters

|Parameters|Description||Value||
|---|---|---|---|---|
|_β_|Time discount factor||0.95||
|_ψd_|Central interest elasticity||0.03||
|_ψb_|Local interest elasticity||0.03||
|_μ_|Unconstrained region’s Pareto weight||0.80||
|_B_<sup>_o_</sup>|Constrained region’s debt limit||0.04||
|||1988|1996|2006|
|_e_|Total government revenue|0.3117|0.3835|0.4041|
|_f_|Local government revenue|0.0430|0.0638|0.1327|
| ̄_T_|Lower bound on uniform transfer|0.032|0.07|0.0485|

Note: Revenue and transfer statistics are normalized by national GDP.

In general, changing the values of _μ_ and _B_<sup>_o_</sup> does not significantly affect the quantitative results once the other parameters of the model are also re-calibrated. As a robustness check, in Section 4.3.3, we present an alternate classification of constrained regions and the corresponding set of _μ_ and _B_<sup>_o_</sup> , which yield similar quantitative results.

**Time discount (** _β_ **) and interest rate schedules (** _R_ ( _·_ ), _S_ ( _·_ ) **).** The annual time discount rate _β_ is set at 0.95. We use log utility functions. The exogenous interest rate schedules for local (unconstrained and constrained) and central debt are defined à la Schmitt-Grohe and Uribe (2003):

and satisfy Assumption 2. Grande et al. (2013) estimate that a 1-percentage-point increase in public debt-to-GDP ratio corresponds to a 3-basis-point increase in interest rates among OECD countries during 1995–2011. Based on this estimate, we set the elasticity parameter for central debt _ψd_ = 0.03. There is no consensus on the interest rate elasticity of local debt, and so in the baseline, we set _ψb_ equal to _ψd_ . In Section 4.3.2, we use alternative values of _ψb_ and _ψd_ for sensitivity analysis.

**Revenue (** _e_ , _f_ **) and transfer (** _T_<sup> ̄</sup> **).** Data on government revenue, inter-governmental transfer, and central and local (regional) government debt come from Eyraud and Lusinyan (2013) and IMF’s Government Finance Statistics (GFS), and are normalized by trend national GDP. The lower bound _T_  ̄ on uniform transfer is not directly observable in the data. Sorribas-Navarro (2011) documents that over 1987–1996, about 85% of central-to-regional transfers (grants) in Spain were non-discretionary (formula-based), and this ratio fell to 81% during 2002–2006. This non-discretionary transfer corresponds to the uniform transfer _T_<sup>_u_</sup> in our model. Because _T_<sup>_u_</sup> = _T_<sup> ̄</sup> (Proposition 1), _T_<sup> ̄</sup> is then calculated as the product of the total central-to-regional transfer from the data and the share of nondiscretionary transfers reported by Sorribas-Navarro (2011).<sup>37</sup>

> 37In the data, a government’s fiscal balances (flow) do not necessarily match the change in debt (stock). For example, the central government’s budget equation (in nominal terms) _transfer + other non-interest expenditure + interest expense = revenue + change in debt_ does not hold in the data. One reason for this statistical discrepancy is that we use gross debt instead of net debt to calculate _change in debt_ , as is customary in the literature, due to the lack of accurate public asset data.

26