However, if countries do not consolidate the public budget according to the supranational rule, they have to pay a sanction if it is detected. Hence, the rule should mitigate the number of violating countries. The solution of the model is. This solution reveals, again, as long as debt accumulation free-riding incentive is greater than the sanction , countries prefer free-riding. Only sufficiently high sanctions, , or a high detection probability, , mitigate the problem.

Unfortunately, the enforcement of European law is rather weak and thus, , is low in reality [10] [11]. Moreover, the sanction scheme, , is ra- ther limited today as well 2. A more comprehensive modeling of the sanction scheme is. The sanction payment depends on a fixed rate and variable rate. The parameter depends on the number of breaching fiscal policies, , and is economically a marginal propensity of sanctions.

After subs- titution of Equation 2 in Equation 1 , I obtain. The differential Equation 3 is a so-called logistic-differential equation or Verhulst-Model. I obtain the solution of that differential equation through integration. Finally, I solve the equation for ,. This solution has the following boundaries for :. If supranational law is fully effective, i. However, if , i. Obviously, only fully effective supranational law mi- nimizes the number of breaching countries.

In other words, the smaller and the larger , the smaller the number of countries violating the rules. The term could be interpreted as a natural intake capacity of breaching countries in a monetary union. Next, I study monetary policy. The main instrument of a common central bank is the interest rate level. Importantly, in a monetary union the key interest rate is an average rate that should be appropriate for almost all member countries. But high domestic public deficits and debts indirectly affect increase the common interest rate.

Thus, there exists a fiscal policy spill-over to monetary policy through the interest rate channel. For sim- plicity, let me first abstract from the spill-over mechanism. I model the interest rate dynamics , again, through a differential equation. In addition, measures the target commitment of the central bank, i. The greater , the higher the interest rates and the lower inflation.

If the common central bank fully commits to the primary objective of price stability 3. Hence, in this case the parameter is dominating Equation 7. In the following, I define. Finally, represents a fixed punishment of the common central bank for the free-riding incentives of fiscal policies in a monetary union. Obviously, as already explained, a comprehensive model considers the fiscal spill-over me- chanism, too. Thus, depends on the number of breaching fiscal policies, such as. This group of countries lower the common interest rate. And depicts the effect of breaching unsound fiscal policies.

These countries endanger inflation in the whole monetary union. Thus, the common central bank has to increase the common rate for all member countries. Consequently, the benefits of domestic deficit spending pass through a higher interest rate to all member countries. Furthermore, I generalize. The incentive of free-riding is dependent on the interest rate level :. In the next section, I study the complete fiscal-mo- netary interaction.

Analyzing the complete dynamics of the fiscal-monetary-law interaction reveals new insights about the ne- cessary and sufficient conditions for a long-run stable and sustainable monetary union. Using Equations 3 and 7 together with conditions 8 and 9 , yields the following system:. To understand how the fiscal-monetary-law model evolves over the time, I first simplify the equations and assume.

This system has two possible solutions and :. The asymptotic stability or instability of the model can be studied. I define the function and cal- culate the eigenvalues. The function is,. Consequently, the eigenvalues of are computed by. This implies and. From an economic point of view , and thus and. The system is instable, if and. Hence, is an instable equilibrium.

To determine the eigenvalue for , I. The second solution of the model is instable again, due to and. But if , I obtain. Hence, there is the possibility of complex eigenvalues. This implies no real solution.

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Finally, I describe the solution behaviour of the model near a point , if the eigenvalues are complex. First, I rewrite the system as. Consequently, all solutions satisfy the implicit solution:. The integration constant can be calculated from the initial condition :. I suggest that satisfy a closed-form. For and trivial aggregation it results:. The second-order Taylor approximation of the solution in the environment of and yields , which is equivalent to:. This shows that that the specific solution solves the model for until an error term of order.

The model reveals an interesting economic interpretation for : the model has an equilibrium with a certain number of fiscal policies breaching the supranational deficit and debt rule as long as the supranational law and central bank are ineffective and do not intervene in case of fiscal policy violations. Finally, I study the full model of Equation 10 with. Again, I calculate the solutions and prove the stability of the associated equilibria. I obtain. For later computation purposes, I define and. The stability of the solutions are computed via the function.

The derivative yields. The point is non-stationary because. The second solution is non- stationary because. The point is unstable, if or asymptotically stable,. The point has positive values, i. As long as , the point is asymptotically stable. That means for. Economically, it implies a certain number of fiscal policies violating the supranational deficit and debt rule. The following expressions summarize the results, for :. The first constellation becomes a reality if free-rider incentives are small and the number of dis- ciplined fiscal policies are great.

The next proposition reveals an answer to the following question: Is a supranational central bank sufficient to constrain the number of fiscal policies violating the supranational debt rule in a monetary union? Proposition 1 The number of fiscal policies in violation with a debt rule is always positive in a mo- netary union, as long as , , and are non-zero.

The proof of this proposition follows from Equation First, the constellation is eco-.

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Any- way, even in this case the number of breaching fiscal policies converge to a positive fixed ratio. For the second constellation and is always positive, too. Our third contribution is normative. Finally, in case of ZLB, we show that. Indeed, because of.

As a result, for our calibrated policy objectives, the optimal coordinated spending policy when monetary policy hit the zero lower bound in would have been to increase public spending by 0. Outside the ZLB, if. We find that. The effects. Regarding the first two axes, the effects of fiscal.

In a standard New Keynesian framework with independent. Coenen et al. Similarly, using a world economy model. However, for strongly integrated economies,. Indeed, in a monetary union, fiscal. This stems from the fact that cuts in public spending are more. They also find that the. More generally, and beyond the scope. Likewise, Furceri and. All in all, these papers clearly posit the existence of spillovers in a monetary union. As such, those spillovers need to be taken into account when designing consolidation or stimulus programs.

Our paper directly follows this literature and takes a broader normative approach to. Campagne and Poissonnier a on the basis. Designed to be as parsimonious as possible, 1. In each region, firms and households. Both firms and households, as well as production. Firms produce partially substitutable goods with a standard constant return to scale production.

TFP is exogenous and growing at the same pace in both regions. To keep the labor market framework simple, there is no unemployment and labor only adjusts at the intensive margin. In addition, following Gali et al. This distinction enables to replicate credible private consumption behaviors. Therefore, a fraction of households, Ricardian households,. In each region, the government behaves according to a standard budget rule where public consumption ensures the convergence of the public debt to GDP ratio towards its steady state level.

The central bank sets the nominal interest rate common to both regions through a Taylor rule Taylor, , where it reacts to current consumer. Financial frictions,. However, to ensure the convergence. Those spreads are calibrated to. Lastly, structural and policy shocks are introduced. Specific to each region, structural shocks. Also, specific to each region,.

In the estimating step of the model,. Fiscal Authorities. Structural and non-structural parameters. Tax rates on consumption and labor are deterministic and arbitrarily chosen by the government. This choice is consistent with a low variability of apparent tax rates in the data over the calibration period. In the absence of public production or employment in the present model, all dimensions of public expenditures are encompassed through public consumption, which endogenously reacts to economic developments. A noteworthy assumption is that public consumption is fully domestic.

In addition,. We discuss the impact of this simplification. Lastly, government behavior is modeled through a budget rule inspired on Corsetti et al. This rule is such that each regional government follows a convergence criterion derived. It adjusts. G and pa denotes the steady state level of each variable. All in all, the government is budget constrained by:. In addition, Rt denotes the gross nominal. Greece, Spain, Italy and Portugal. Northern countries are those with lower inflation and thus. Germany and the Netherlands.

The calibration is constructed to stay close to. National Accounting data following a methodology similar to Campagne and Poissonnier a. In a second step, remaining parameters. Parameters for inflation, TFP growth and technology are imposed to be equal across regions. As explained in Campagne and Poissonnier a , these restrictions are necessary for the mathematical existence of a steady state solution.

As for the fiscal policy block, the government. Tax rates are calibrated using the implicit tax rates by economic function. We also assume that public bonds are considered safe by all agents. This assumption seems reasonable to us since as we simulate the. Note that in the long run our model represents a closed monetary union and the choice of a public debt to GDP target implies that the sum of public. In the model, this large net external debt is arbitrarily attributed within our regions, and the private assets to GDP ratios will.

In practice, the first order. Baseline shocks. We argue that fiscal shocks starting in. Using Eurostat quarterly data on consumption, investment, output, public debt, inflation and. This approximation. Appendix 2 shows a measure of fit for each variable,. The best fit is obtained with. Underlying structural shocks, their estimated. The financial crisis impact is best characterized. Figure I shows the trajectory under the shocks previously estimated, as well as the point at which the model enters the ZLB, denoted by the.

Under that baseline scenario, output. Public deficits are. Capital returns and interest rates are. Fiscal multipliers. The channels through which fiscal policy. A stimulus package directly boosts domestic demand, with a positive effect on the output of the domestic economy region. It also tends to have inflationary effects in. Observed and simulated data at steady state.

S1 correspond to the whole domestic economy, S2 to the rest of the world and S13 to the public sector. This hike will decrease aggregate demand in both the domestic and foreign economies resp. On the other hand, the. Table 2 Key structural parameters calibration. Papers cited for calibration are given as an example of a paper close to the median of our literature review. Parameters name are those in Campagne and Poissonnier The positive effect on domestic demand region A also increases foreign exports, leading to positive spillovers. The net effect on foreign. As detailed in Campagne and Poissonnier b for the purely linear case, those multipliers compare with those.

First, as expected, in the case of stimulus packages big enough to immediately lift the Euro Area out of the ZLB, the marginal effect of the last unit spent or raised is constant. In the case of spending shocks, the impact multiplier is around 1. The effect on foreign output, yet relatively small, goes opposite to domestic consolidation or expansion in. Spillovers on foreign. This results from the fact that VAT.

However, over three years, spillovers are weaker than for public spending cuts and even slightly negative. Second, at the ZLB, the marginal effect of fiscal. Spending cuts tend to have an increasing. In the case of VAT shocks, the effect is even stronger. Cooperative governments. As mentioned earlier, those public spending multipliers rely on the simplifying assumption that public consumption gathers the whole public spending while in the current context of low TFP growth in the euro area, international institutions advise changes in the composition of public spending in order to favor public investment and support potential growth.

In the long run, public investment shocks are indeed expected to have higher multipliers than public consumption. However, in the short run, fiscal multipliers tend. In particular,. Policy coordination. Policy objective. However, the realism. Following the crisis,. This suggests. Our goal is to analyze how governments in each region could have decided to accelerate or reduce the pace of debt convergence by implementing additional fiscal policies when.

For illustrative and simplification. The trajectories correspond to the simulation around the steady state using estimated structural shocks. Reading note: at the beginning of , activity declined by 0. Simulations with the Meleze model. We assume governments maximize an objective function or minimize a loss function. We consider a static game, meaning that the government decides in. However, the definition of such preferences is a difficult task and relates to the construction of an adequate objective function for the fiscal.

We argue that a reasonable objective function needs to comply with a few constraints or expected properties: i it increases with activity, ii it decreases with the public. The third property relates to the fact that governments will not seek to boost activity by such an amount that the debt will explode, and vice versa.

The fourth property ensures that the further a deviation from the steady state, the costlier it is. Three propagation channels for spillovers of fiscal policy. Namely, in the absence of shocks, we assume that governments will hold to the budget rule and choose to maintain a debt to GDP ratio at its target. Optimal Policy. Therefore, there is. Outside the ZLB, and following consolidation package in the North, expansionary monetary policy will have positive effects. However negative spillovers will prevail at the ZLB and regional objectives will converge. The optimal amount of coordination will thus differ whether monetary policy can or cannot react.

As in Mendoza et al. We also assume than. Each regional government chooses its instrument value so as to maximize the objective functions V i as defined earlier. Given the. North region.

### Services on Demand

Each of these cooperative equilibria is said to. Although each decision maker will have an idiosyncratic incentive to deviate from the coordinated policy, we assume that they expect that themselves deviating will result in the other decision maker also deviating. Both decision. Note that for all the following figures, shocks. Strategic vs cooperative game. Those first figures can be analyzed along three dimensions:.

For a given action of a foreign government,. How does that optimal domestic strategy. What is the combination of shocks that maximizes. Consider spending shocks from the point of view of the North region top left panel. This choice i. Squares are best responses. Moreover, the.

Therefore, a domestic consolidation package would become costlier to the North.

## Fiscal policy coordination in a monetary union at the zero lower bound - Persée

This global maximum is out of the range of allowed. A symmetric behavior is observed for the South region. Consequently, the uncoordinated equilibrium is to increase spending by. VAT shocks, the form of the best responses of.

North and South region are similar: due to the. Now, superposing both best responses, Figure V. Panels on the left display the average objective of the entire monetary union when each region are weighed according to their population share, and compares it to the strategic interaction. In both case public spending or. VAT shock , the optimal and strategic equilibria. Given the level of output. The panels on the right show that for regions weights that are close to the population share, the cooperative. By comparison, Figure VI shows the same graphs, with the same calibration but in the case where monetary policy is never constrained by the ZLB.

In that case, spillovers are smaller or. Indeed, when foreign actions by the other government. Moreover, when spillovers. Given negative spillovers of fiscal expansion in one region. Coordination would therefore lead to more consolidation by both regions than their. Stated in terms of our. All in all, both regions will be better off at.

Second, spillover effects from fiscal policy. Increasing with the size of fiscal consolidation. Outside the ZLB, there are gains from fiscal. At the ZLB however, national objectives tend to be closely related and there are fewer gains from consolidation. The existence of a ZLB and consequently. However, as the recovery strengthens in the Euro Area, and as the normalization of monetary policy is closing in, divergence across national objectives will gradually increase, as well as gains from cooperation. This sets path for future research on the means. Within the scope of the current paper, future work will focus on the study of more detailed.

One main limit of our analysis is the fact that most structural parameters are calibrated.

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This could be improved,. Lastly, going beyond the retrospective analysis of the crisis and going forward, in the latest environment of low growth, focusing on. As international organizations are now calling for more public investment expenditure, distinguishing between public consumption and investment in the present model will be. Abiad, M. The macroeconomic effects of public investment: Evidence from advanced economies.

Annicchiarico, B. Structural reforms and the potential effects on the. Italian economy. Journal of Policy Modeling, 35 1 , 88— Auray, S. Bayoumi, T. Benefits and Spillovers of Greater Competition in. Europe: A Macroeconomic Assessment. Cacciatore, M. Reforms in Labour and Product Markets. Calvo, G. Journal of Monetary Economics, 12 3 , — Campagne, B. Christiano, L. Journal of Political Economy, 1 , 78— Nominal Rigidities and the Dynamic Effects.

Journal of Political Economy, 1 , 1— Clinton, K. European Economic Review, 55 1 , — Coenen, G. Effects of Fiscal Stimulus in Structural Models. American Economic Journal: Macroeconomics,. Journal of Economic Dynamics and Control, 32 8 , — Economic Modelling, 25 5 , — Corsetti, G.

International Journal of Central Banking, 60 March : 05— Cwik, T. Keynesian government spending multipliers and spillovers in the euro area. Economic Policy, 26 67 , — European Commission Economic Papers. Eggertsson, G. Can structural reforms help Europe? Journal of Monetary Economics, 61, 2— Fiscal consolidation. Journal of Economic Dynamics and Control, 37 2 , — Farhi, E. Chapter 31 — Fiscal. Multipliers: Liquidity Traps and Currency Unions. In Handbook of Macroeconomics Vol. Forni, L. Macroeconomic Effects of Greater Competition in the.

Service Sector: the Case of Italy. Furceri, D. The Effects. Monetary policy, inflation, and the. Princeton: Princeton. Understanding the Effects of Government Spending. Journal of the European Economic Association, 5 1 , — Guerrieri, L. OccBin: A toolkit for solving dynamic models with occasionally binding constraints easily.

Journal of Monetary Economics,. Fiscal consolidations and spillovers in the Euro area periphery and core. Kaplan, G. Brookings Papers on Economic Activity, 0: 0 77— King, R. Mendoza, E. Saving Europe? Cambridge, MA.