*2.3. Fiscal Policy*

The governmen<sup>t</sup> budget constraint is given by:

$$R\_t^{-1}B\_{t+1} = B\_t + P\_t \left[ G\_t - \tau \mathbf{Y}\_t - T\_t \right] \tag{13}$$

where (*τ*) and (*Tt*) denote distortionary and lump-sum taxes, respectively. Moreover, (*Bt*) indicates the one-period nominal discount bonds.

We analyse two different cases: firstly, we focus on the model with total governmen<sup>t</sup> spending; secondly, we disentangle public expenditure into civilian and military components.

#### 2.3.1. Total Government Spending

In the model with aggregated public expenditure, total governmen<sup>t</sup> spending is treated as an exogenous *AR*(1) process:

$$\log\left(G\_{t}\right) = \rho^{\stackrel{\circ}{G}} \log\left(G\_{t-1}\right) + \epsilon\_{t}^{\stackrel{\circ}{G}} \tag{14}$$
 
$$\text{where: } \epsilon\_{t}^{\stackrel{\circ}{G}} \sim N\left(0, \sigma\_{\stackrel{\circ}{G}}^{2}\right)$$

where *ρG* indicates the persistence of total governmen<sup>t</sup> spending and  *<sup>G</sup> t* is an i.i.d. distributed error term that captures the shock volatility.

#### 2.3.2. Non-Military and Military Expenditures

In the model with disaggregated components of public expenditure, we adopt the additive principle where total governmen<sup>t</sup> spending can be seen as the sum of its different components. Thus, governmen<sup>t</sup> spending is divided into civilian sector spending (*NMt*) and military sector spending (*Mt*):

$$G\_t = NM\_t + M\_t \tag{15}$$

We assume that civilian and military expenditure levels are independent and exogenous *AR*(1) processes:

∼

*N*

0,

*M*

$$\log\left(NM\_{l}\right) = \rho^{NM}\log\left(NM\_{t-1}\right) + \epsilon\_{l}^{NM}\,,\tag{16}$$

$$\text{where: }\epsilon\_{l}^{NM} \sim N\left(0, \sigma\_{NM}^{2}\right)$$

$$\begin{aligned} \text{where: } & \varepsilon\_{\text{f}}^{NM} \sim N\left(0, \sigma\_{\text{NM}}^2\right) \\ \log\left(M\_{\text{f}}\right) &= \rho^M \log\left(M\_{\text{f}-1}\right) + \epsilon\_{\text{f}}^M, \\ \text{where: } & \varepsilon\_{\text{f}}^M \sim N\left(0, \sigma\_M^2\right) \end{aligned} \tag{17}$$

where *ρNM* and *ρ<sup>M</sup>* are, respectively, the persistence parameters of the civilian and military shocks, while  *NM t*and  *<sup>M</sup> t*are, respectively, the stochastic civilian and military terms that are i.i.d. distributed.

#### 2.3.3. Financing Mechanism of Public Expenditure

The governmen<sup>t</sup> primary deficit is defined as:

where:

*t*

$$D\_t = G\_t - \tau Y\_t - T\_t \tag{18}$$

Equation (18) simply means that governmen<sup>t</sup> primary deficit is the total non-interest spending less revenues. Moreover, we assume that the governmen<sup>t</sup> incurs a structural deficit (*Ds*,*<sup>t</sup>*), which is given by the changes in the primary deficit adjusted by automatic responses of tax revenues resulting from deviations on output from its steady state value (*Y*):

$$D\_{\mathbb{S},l} = D\_l + \tau \left( \mathbb{Y}\_l - \mathbb{Y} \right) = G\_l - T\_l - \tau \mathbb{Y} \tag{19}$$

We assume that the structural deficit is adjusted according to the following log-linearized rule:

$$d\_{s,t} = \eta d\_{s,t-1} + \phi\_{\mathbb{S}} G\_Y g\_t \tag{20}$$

This type of rule is in line with those used by Bohn (1998) and Galí and Perotti (2003). The parameter *η* captures the possibility that budget decisions are autocorrelated. The parameters *φg* measure the response of structural deficit to changes in governmen<sup>t</sup> spending.

#### *2.4. Monetary Policy*

We assume that the monetary authority sets the nominal interest according to the following log-linearized monetary policy reaction function:

$$r\_t = \rho^R r\_{t-1} + \left(1 - \rho^R\right) \left\{\pi\_l + r\_\pi \left(\pi\_{t-1} - \pi\_t\right) + r\_y \left(y\_t - y\right)\right\} + \epsilon\_t^R \tag{21}$$

where *ρR* is an interest rate smoothing parameter, whereas *πt* denotes the inflation rate. Equation (21) implies that the central bank responds to deviations of lagged inflation from an inflation objective and to an output gap defined as the difference between actual and steady state output (Rabanal and Rubio-Ramírez 2001).

Our monetary policy rule assumes two exogenous shocks: The first is a shock to the inflation objective (*π*¯*t*), which is assumed to follow a first order autoregressive process:

$$\log\left(\bar{\pi}\_{t}\right) = \rho^{\mathcal{T}} \log\left(\bar{\pi}\_{t-1}\right) + \mathfrak{e}\_{t}^{\mathcal{T}} \tag{22}$$

$$\text{where: } \mathfrak{e}\_t^\mathfrak{n} \sim \mathcal{N}\left(0, \sigma\_\pi^2\right) \tag{23}$$

The second shock is a temporary i.i.d. monetary policy shock  *Rt*∼ *N* 0, *<sup>σ</sup>*2*R*.

#### *2.5. General Equilibrium and Aggregation*

The final goods market clearing condition is given by:

$$Y\_t = \mathcal{C}\_t + \mathcal{G}\_t \tag{24}$$

that is production equals demand by total household consumption and total governmen<sup>t</sup> spending. The aggregate consumption is given by:

$$\mathcal{C}\_t = \lambda \mathcal{C}\_{N,t} + (1 - \lambda)\mathcal{C}\_{A,t} \tag{25}$$

The equilibrium in the labour market is given by:

$$N\_l = \lambda N\_{N,t} + (1 - \lambda) \, N\_{A,t} \tag{26}$$

that is the wage level is such that demand by firms for labour equals total labour supply. Finally, the equilibrium in the share market is given by:

$$B\_{t+1} = \left(1 - \lambda\right) B\_{A, t+1} \tag{27}$$

that is households hold all outstanding equity shares and all governmen<sup>t</sup> debt is held by asset holders.

#### **3. Estimating the Model**

In this section, we focus on the estimated results of our model. We start by describing the data, then we discuss the assumptions on the prior distributions of the parameters estimated with Bayesian techniques. Finally, we present the posterior estimates of such parameters.
