Silviase/jgov_v1.4_full_ann huggingface dataset:
#### B.1.4 Capital Utilization Decision Equation

From (7):

$$ \hat{z}_{t}=\psi\left[\hat{r}_{t}^{k}-\frac{\bar{\tau}^{k}}{1-\bar{\tau}^{k}}(1+\hat{r}_{t}^{k})\hat{\tau}_{t}^{k}\right], $$

where ψ ≡ Ψ′(1)/ Ψ′′(1).

#### B.1.5 Capital Law of Motion

From (2):

$$ \hat{K}_{t}=(1-\delta)\hat{K}_{t-1}+\delta\hat{I}_{t}. $$

#### B.1.6 Real Wage Law of Motion

From (9):

$$ \begin{aligned}\hat{w}_{t}&=\frac{\beta}{1+\beta}E_{t}\hat{w}_{t+1}+\frac{1}{1+\beta}\hat{w}_{t-1}+\frac{\beta}{1+\beta}E\hat{\pi}_{t+1}\\&-\frac{1+\beta\gamma_{w}}{1+\beta}\hat{\pi}_{t}+\frac{\gamma_{w}}{1+\beta}\hat{\pi}_{t-1}-\frac{1}{1+\beta}\frac{\left(1-\beta\xi_{w}\right)\left(1-\xi_{w}\right)}{\left(1+\frac{\left(1+\lambda_{w}\right)\sigma_{l}}{\lambda_{w}}\right)\xi_{w}}\\&\times\left[\hat{w}_{t}-\sigma_{l}\hat{L}_{t}-\frac{\sigma_{c}}{1-h}\left(C_{t}^{R}-h C_{t-1}^{R}\right)-\hat{\varepsilon}_{t}^{l}-\eta_{t}^{w}-\frac{\bar{\tau}^{d}}{1-\bar{\tau}^{d}}\hat{\tau}_{t}^{d}-\frac{\bar{\tau}^{c}}{1+\bar{\tau}^{c}}\hat{\tau}_{t}^{c}\right],\end{aligned} $$

where

$$ \hat{\varepsilon}_{t}^{l}=\rho_{l}\hat{\varepsilon}_{t-1}^{l}+\eta_{t}^{l}. $$

### B.2 Non-Ricardian Households

From (8):

$$ \frac{\bar{C}^{N R}}{\bar{Y}}\left[\hat{C}^{N R}\left(1+\bar{\tau}^{c}\right)+\bar{\tau}^{c}\hat{\tau}_{t}^{c}\right]=\bar{w}\frac{\bar{L}}{\bar{Y}}\left[\left(1-\bar{\tau}^{d}\right)\left(\hat{w}_{t}+\hat{L}_{t}\right)-\bar{\tau}^{d}\hat{\tau}_{t}^{d}\right]. $$
### B.3 Firms

#### B.3.1 Marginal Cost

From (10):

$$ \widehat{m c}_{t}=\left(1-\alpha\right)\hat{w}_{t}+\alpha\hat{r}_{t}^{k}-\hat{\varepsilon}_{t}^{a}. $$

#### B.3.2 Labor Demand

From (11):

$$ \hat{L}_{t}=-\hat{w}_{t}+\hat{r}_{t}^{k}+\hat{z}_{t}+\hat{K}_{t-1}. $$

#### B.3.3 Profit Payment

From (12):

$$ \frac{\bar{D}}{\bar{P}\bar{Y}}\hat{d}_{t}=(1-\overline{m c})\hat{Y}_{t}-\overline{m c}\varphi\widehat{m c}_{t}. $$

#### B.3.4 Inflation Law of Motion

From (13):

$$ \begin{aligned}\hat{\pi}_{t}&=\frac{\beta}{1+\beta\gamma_{p}}E_{t}\hat{\pi}_{t+1}+\frac{\gamma_{p}}{1+\beta\gamma_{p}}\hat{\pi}_{t-1}\\&+\frac{1}{1+\beta\gamma_{p}}\frac{\left(1-\beta\xi_{p}\right)\left(1-\xi_{p}\right)}{\xi_{p}}\left[\alpha\hat{r}_{t}^{k}+(1-\alpha)\hat{w}_{t}-\hat{\varepsilon}_{t}^{a}+\eta_{t}^{p}\right],\end{aligned} $$

where

$$ \hat{\varepsilon}_{t}^{a}=\rho_{a}\hat{\varepsilon}_{t-1}^{a}+\eta_{t}^{a}. $$

### B.4 Fiscal and Monetary Authorities

#### B.4.1 Fiscal Policy Rules

From (14)-(18):
$$ \frac{\bar{G}}{\bar{Y}}\hat{G}_{t}+\frac{\bar{B}}{\bar{P}\bar{Y}}\left(\hat{b}_{t-1}-\hat{\pi}_{t}\right)=\bar{\tau}^{c}\frac{\bar{C}}{\bar{Y}}\left(\hat{\tau}_{t}^{c}+\hat{C}_{t}\right)+\bar{\tau}^{d}\bar{w}\frac{\bar{L}}{\bar{Y}}\left(\hat{\tau}_{t}^{d}+\hat{w}_{t}+\hat{L}_{t}\right)+\bar{\tau}^{k}\bar{r}^{k}\frac{\bar{K}}{\bar{Y}}\left(\hat{\tau}_{t}^{k}+\hat{r}_{t}^{k}+\hat{z}_{t}+\hat{K}_{t-1}\right) $$

$$ +\bar{\tau}^{k}\frac{\bar{D}}{\bar{P}\bar{Y}}\left(\hat{\tau}_{t}^{k}+\hat{d}_{t}\right)+\beta\frac{\bar{B}}{\bar{P}\bar{Y}}\left(\hat{b}_{t}-\hat{R}_{t}\right), $$

$$ \hat{\tau}_{t}^{c}=\rho_{t c}\hat{\tau}_{t-1}^{c}+\left(1-\rho_{t c}\right)\phi_{t c b}(\hat{b}_{t-1}-\hat{Y}_{t-1})+\eta_{t}^{t c}, $$

$$ \hat{\tau}_{t}^{d}=\rho_{t d}\hat{\tau}_{t-1}^{d}+\left(1-\rho_{t d}\right)\phi_{t d b}(\hat{b}_{t-1}-\hat{Y}_{t-1})+\eta_{t}^{t d}, $$

$$ \hat{\tau}_{t}^{k}=\rho_{t k}\hat{\tau}_{t-1}^{k}+\left(1-\rho_{t k}\right)\phi_{t k b}(\hat{b}_{t-1}-\hat{Y}_{t-1})+\eta_{t}^{t k}, $$

$$ \hat{G}_{t}=\rho_{g}\hat{G}_{t-1}+\left(1-\rho_{g}\right)\phi_{g y}\hat{Y}_{t-1}+\eta_{t}^{g}. $$

#### B.4.2 Monetary Policy Rule

From (19):

$$ \hat{R}_{t}=\rho_{r}\hat{R}_{t-1}+\left(1-\rho_{r}\right)\phi_{r\pi}\hat{\pi}_{t-1}+\left(1-\rho_{r}\right)\phi_{r y}\hat{Y}_{t}+\eta_{t}^{R}. $$

### B.5 Aggregation and Market Clearing

#### B.5.1 Goods Market Equilibrium Condition

From (20):

$$ \frac{\bar{C}}{\bar{Y}}\hat{C}_{t}=\left(1-\omega\right)\frac{\bar{C}^{R}}{\bar{Y}}\hat{C}_{t}^{R}+\omega\frac{\bar{C}^{N R}}{\bar{Y}}\hat{C}_{t}^{N R}. $$

From (22):

$$ \hat{Y}_{t}=\frac{\bar{C}}{\bar{Y}}\hat{C}_{t}+\delta\frac{\bar{K}}{\bar{Y}}\hat{I}_{t}+\frac{\bar{G}}{\bar{Y}}\hat{G}_{t}+\left(1-\bar{\tau}_{t}^{k}\right)\bar{r}_{t}^{k}\frac{\bar{K}}{\bar{Y}}\hat{z}_{t}. $$
#### B.5.2 Aggregate Production Equation

From (21):

$$ \hat{Y}_{t}=\varphi\left(\hat{\varepsilon}_{t}^{a}+\alpha\hat{z}_{t}+\alpha\hat{K}_{t-1}+\left(1-\alpha\right)\hat{L}_{t}\right), $$

where $ \varphi \equiv 1 + \Phi / \bar{Y} $
Table 1: Prior and posterior distributions of the parameters (a)

Parameters	Prior	Posterior
Distribution	Mean	S. D.	Mean	90% interval
h	consumption habit	beta	0.7	0.1	0.465	[0.313, 0.622]
σc	consumption utility	gamma	1.5	0.2	1.620	[1.283, 1.954]
σl	labor utility	gamma	2	0.375	2.113	[1.472, 2.736]
φ	fixed cost	gamma	1.45	0.25	1.904	[1.529, 2.312]
ψ	capital util. adj. cost	gamma	0.2	0.075	0.416	[0.290, 0.536]
ξw	Calvo wages	beta	0.75	0.15	0.824	[0.762, 0.887]
ξp	Calvo prices	beta	0.75	0.15	0.432	[0.323, 0.543]
γw	indexation wages	beta	0.75	0.15	0.211	[0.096, 0.325]
γp	indexation prices	beta	0.75	0.15	0.595	[0.308, 0.887]
ω	non-ricardian share	beta	0.35	0.05	0.248	[0.183, 0.310]
ρr	interest rate AR coeff.	beta	0.8	0.1	0.934	[0.904, 0.959]
φrπ	interest rate inflation coeff.	normal	1.7	0.1	1.533	[1.363, 1.705]
φry	interest rate output gap coeff.	normal	0.125	0.05	0.254	[0.189, 0.318]
ρg	gov. exp. AR coeff.	beta	0.8	0.1	0.736	[0.644, 0.832]
φgy	gov. exp. output gap coeff.	normal	0.1	0.05	0.068	[-0.016, 0.152]
ρtc	cons. tax AR coeff.	beta	0.8	0.1	0.507	[0.350, 0.668]
φtcb	cons. tax debt coeff.	normal	0.1	0.05	0.013	[-0.016, 0.041]
ρtd	labor tax AR coeff.	beta	0.8	0.1	0.568	[0.417, 0.718]
φtdb	labor tax debt coeff.	normal	0.1	0.05	0.005	[-0.029, 0.044]
ρtk	capital tax AR coeff.	beta	0.8	0.1	0.655	[0.547, 0.761]
φtkb	capital tax debt coeff.	normal	0.1	0.05	0.123	[0.055, 0.190]
ρa	persistence of productivity shock	beta	0.8	0.1	0.518	[0.383, 0.654]
ρb	persistence of preference shock	beta	0.8	0.1	0.431	[0.250, 0.619]
ρl	persistence of labor supply shock	beta	0.8	0.1	0.257	[0.157, 0.353]
ρi	persistence of inv. adj. cost shock	beta	0.8	0.1	0.800	[0.652, 0.960]
Table 2: Prior and posterior distributions of the parameters (b)

S. D. of Shocks	Prior	Posterior
Distribution	Mean	S. D.	Mean	90% interval
$ \eta^{a} $	productivity shock	inv. gamma	0.4	2	0.788	[0.679, 0.892]
$ \eta^{b} $	preference shock	inv. gamma	0.2	2	4.652	[3.128, 6.116]
$ \eta^{i} $	inv. adj. cost shock	inv. gamma	0.1	2	0.078	[0.023, 0.139]
$ \eta^{l} $	labor supply shock	inv. gamma	1	2	169.6	[54.19, 282.4]
$ \eta^{q} $	external finance premium shock	inv. gamma	0.4	2	1.968	[1.653, 2.280]
$ \eta^{w} $	wage markup shock	inv. gamma	0.25	2	0.231	[0.056, 0.432]
$ \eta^{p} $	price markup shock	inv. gamma	0.15	2	2.215	[1.436, 2.979]
$ \eta^{r} $	interest rate shock	inv. gamma	0.1	2	0.224	[0.180, 0.267]
$ \eta^{g} $	government spending shock	inv. gamma	0.3	2	1.220	[1.057, 1.379]
$ \eta^{tc} $	cons. tax shock	inv. gamma	0.1	2	0.643	[0.551, 0.732]
$ \eta^{td} $	labor tax shock	inv. gamma	0.1	2	0.676	[0.581, 0.767]
$ \eta^{tk} $	capital tax shock	inv. gamma	0.4	2	4.805	[3.625, 5.969]