Abstract
We analyze the conduct of fiscal policy in a financially integrated union in the presence of financial frictions. Frictions create a wedge between the return to investment and the union interest rate. This leads to an over-spending externality. While the social cost of spending is the return to investment, governments care mostly about the (depressed) interest rate they face. In other words, the crowding-out effects of public spending are partly “exported” to the rest of the union. We argue that it may be hard for the union to deal with this externality through the design of fiscal rules, which are bound to be shaped by the preferences of the median country and not by efficiency considerations. We also analyze how this overspending externality—and the union’s ability to deal with it effectively—changes when the union is financially integrated with the rest of the world. Finally, we extend our model by introducing a zero lower bound on interest rates and show that, if financial frictions are severe enough, the union is pushed into a liquidity trap and the direction of the spending externality is reversed. At such times, fiscal rules that are appropriate during normal times might backfire.
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Notes
Real short-term interest rates are computed from OECD (2020), by combining the series ‘Short-term interest rates’ and ‘Inflation (CPI)’. To compute the EA12 average, each country is weighted by its GDP in each year. The return to capital is constructed with data from the AMECO database, which provides aggregated measures for the EA12 countries. We divide the series ‘Net operating surplus: total economy’ by ‘Net-Capital Stock at 2015 prices: total economy’, where the latter is multiplied by ‘Price deflator gross fixed capital formation: total economy’. EA12 includes Austria, Belgium, Finland, France, Germany, Ireland, Italy, Luxembourg, Netherlands, Portugal, Spain, and Greece.
See for example Blanchard (2019). Note that one does not need to appeal to Keynesian arguments to argue this.
For evidence consistent with this view, see Farhi and Gourio (2019).
For evidence consistent with the relevance of such market frictions see Eggertsson et al. (2018), Farhi and Gourio (2019), and Faltermeier (2019). The former two show that market power plays a significant role in accounting for the spread, while the latter shows that financial frictions must also play a role.
Boehm (2020), for instance, estimates the fiscal multipliers of government consumption in the OECD to be around 0.8, and those of government investment to be practically zero.
See Beetsma and Giuliodori (2010) for a survey of this literature.
Devereux (1991), Epifani and Gancia (2009), and Hettig and Müller (2018) show that, when public spending improves countries’ terms of trade, global spending may be inefficiently high. The latter, like us, also find that the externality may switch signs when the interest rate is constrained by a lower bound.
The literature on “balanced budget rules”, for instance, emphasizes the benefits of limiting fiscal deficits in the presence of cross-border fiscal transfers (e.g. Bassetto and Sargent 2006; Azzimonti et al. 2016). In a similar vein, Gourinchas et al. (2018) analyze the cross-border spillovers that arise from fiscal transfers or inflationary bias within a monetary union.
With quasi-linear preferences, it is theoretically possible to have equilibria with corner solutions, i.e., such that \(c (\gamma ) =0\) for some \(\gamma \). We disregard these equilibria throughout and consider only equilibria such that \(c (\gamma ) >0\) for all \(\gamma \).
To provide a more formal justification for this constraint, assume that only a subset of individuals (“entrepreneurs”) with mass \(\varepsilon \) in each country can write contracts with savers and workers. Assume, moreover, that entrepreneurs can divert a fraction \(1 -\lambda \) of capital income ex post. It is straightforward to show that the financing that entrepreneurs obtain from savers cannot exceed
$$\begin{aligned} \frac{\lambda \cdot f^{ \prime } (k)}{R -\lambda \cdot f^{ \prime } (k)} \cdot \varepsilon \cdot \omega . \end{aligned}$$The case that we consider can be interpreted as the limit in which \(\varepsilon \rightarrow 0\), so that—to satisfy market clearing—the borrowing constraint is always binding and \(R \rightarrow \lambda \cdot f^{ \prime } (k)\).
The simplicity of Eq. (12) is in part due to some convenient assumptions. One should read this equation essentially as stating the optimal rule to allocate public and private capital from the perspective of the country. This rule says that the marginal product of public capital (which here is one!) times the marginal utility of public goods must equal the interest rate times the marginal utility of private goods (which here is one!).
This is because we are ignoring equilibria with corner solutions. See footnote 13.
To be precise, the assumption that \(F ( \cdot )\) is continuous and differentiable ensures that in all votes the median voter is always arbitrarily close to \(\gamma _{M}\).
To see this, use Eqs. (32)–(33) to rewrite the utility function in Eq. (30) as follows:
$$\begin{aligned} U (\gamma ) =f \left( \omega -g^{U}\right) +\gamma _{A} -\gamma +\gamma \cdot \ln \left( \frac{\gamma }{\gamma _{A, 0}} \cdot g^{U}\right) . \end{aligned}$$Thus, \(U (\gamma )\) is increasing in \(g^{U}\) when \(g^{U}\) is low, but decreasing when \(g^{U}\) is large. The maximum or peak is given by:
$$\begin{aligned} f^{ \prime } \left( \omega -g^{U}\right) =\frac{\gamma }{g^{U}} . \end{aligned}$$Equation (32) shows that the tax rate that delivers this outcome is \(t =\frac{\gamma _{A}}{\gamma } \cdot \lambda ^{ -1}\).
If the union were large relative to the world, all the effects we discussed in previous sections would still apply. Spending would crowd out union capital, although less than one-to-one. Part of the crowding-out effect would be exported outside of the union. Also, the union would import crowding-out effects from the rest of the world. To determine the welfare effects of these “exports” and “imports” we would need to take a stand on how strong financial frictions are outside the union, and how policymaking is conducted there. These dimensions of the problem are certainly interesting and worth studying in future research.
Sufficient conditions for Eq. (36) to hold are that (i) \(R^{ *} <\lambda \cdot f^{ \prime } \left( \omega \right) \) ; and (ii) \(\lambda ^{ *}\) be low enough.
If \(R^{ *}\) lies outside of this range, public spending does not crowd out union investment. To see this, note that there are only two possibilities in any such equilibrium. First, \(R^{ *} =\lambda ^{ *} \cdot f^{ \prime } (k)\), in which case union firms borrow from the rest of the world at the margin. Second, \(R^{ *} =\lambda \cdot f^{ \prime } (k)\), in which case union savers lend to the rest of the world at the margin. In either case, the capital stock in the union is independent of public spending in the union.
From our discussion in Sect. (2.3), it makes no difference whether non-credible countries finance their spending through taxes or through domestic debt. To simplify the exposition, we assume throughout that they resort fully to domestic debt.
To see this, use Eqs. (47) to rewrite the utility function in Eq. (46) as follows:
$$\begin{aligned} U \left( \gamma ,1\right) =f \left( \omega -g_{0}\right) +\nu \cdot \gamma _{A ,0} -R^{ *} \cdot g (\gamma ,1) +\gamma \cdot \ln g (\gamma ,1) . \end{aligned}$$Thus, \(U \left( \gamma ,1\right) \) is maximized by setting t as high as possible to minimize the crowding-out effect of \(g_{0}\). Some readers may wonder why there are no terms-of-trade effects. In particular, credible countries are net creditors in the union and they are hurt when taxes on public spending reduce the union interest rate. This terms-of-trade effect, however, is offset by a positive redistribution effect, which arises because part of the union’s tax revenues is appropriated by credible countries.
To see this, use Eqs. (47) to rewrite the utility function in Eq. (46) as follows:
$$\begin{aligned} U \left( \gamma ,0\right) =f \left( \omega -g_{0}^{U}\right) +\nu \cdot \gamma _{A ,0} -\gamma +\gamma \cdot \ln \left( \frac{\gamma }{\nu \cdot \gamma _{A, 0}} \cdot g_{0}^{U}\right) . \end{aligned}$$Thus, \(U \left( \gamma ,0\right) \) is maximized by setting t to satisfy Eq. (48).
Thus, we focus throughout on the case in which the USM makes zero profits. Nothing substantial would change if the USM made profits by lending to non-credible governments at an interest rate \(R >R^{ *}\).
Even in this period, there is evidence of intermediation by banks located in credible euro area countries (i.e., “core” countries) between international financial markets and borrowers located in the rest of the euro area (i.e., “periphery” countries). See Hale and Obstfeld (2016).
The lower bound on the real interest rate is typically justified as an implication of two assumptions. (i) There is an upper bound on inflation that arises either from nominal rigidities or from the central bank’s commitment to price stability. As a result, there is an upper bound on the difference between nominal and real interest rates. (ii) The central bank is the only producer of money, and it sets the nominal interest rate by trading money for nominal bonds. As a result, the nominal interest rate cannot be negative, since otherwise the demand for money would be infinite and the central bank would go bankrupt. (See Krugman 1998, Eggertsson and Woodford 2003, 2004).
The zero lower bound usually applies to the nominal interest rate. To save on notation, we assume that inflation is zero so the zero lower bound applies to the real interest rate as well. Nothing would change if the lower bound were different from zero.
During liquidity traps there is rationing since, at prevailing prices, all savers would like to produce and sell all their potential output \(\bar{\omega }\). We focus throughout on symmetric equilibria in which all savers in the union produce and sell the same fraction of potential output \(\omega /\bar{\omega }\).
These critical values are obtained by combining the decentralized equilibrium condition \(\gamma _{A}/\hat{g} =\lambda \cdot f^{ \prime } \left( \bar{\omega } -\hat{g}\right) \) and the optimality condition \(\gamma _{A}/\hat{g} =f^{ \prime } \left( \bar{\omega } -\hat{g}\right) \) with the zero lower bound condition \(\lambda \cdot f^{ \prime } \left( \bar{\omega } -\hat{g}\right) =R =1\). Since \(\hat{g} (\lambda )\) is decreasing in \(\lambda \), \(\hat{g} \left( 0\right) =\bar{\omega }\), and \(\hat{g} \left( 1\right) =\bar{\omega } -f^{ \prime -1} \left( 1\right) \), there is exactly one solution to both equations if \(\bar{\omega } \in \left[ \gamma _{A} ,\gamma _{A} +f^{ \prime -1} \left( 1\right) \right] \).
To show this, note that when the economy is in a liquidity trap, welfare can be expressed as
$$\begin{aligned} U (\gamma ) =f (f^{ \prime -1} (1)) +\gamma _{A} -\gamma +\gamma \cdot \ln \left( \frac{\gamma }{\gamma _{A}} \cdot g\right) \text {,} \end{aligned}$$which is monotonically increasing in g. So all countries, regardless of \(\gamma \), benefit from an increase in g in liquidity traps. So no country would favor a tax that is so high (or a subsidy that is so low) that \(g <\hat{g}\).
To derive Eq. (56), simply note that the analysis is exactly as in Sect. 3.2 when the economy is outside the liquidity trap. Hence, the equilibrium tax is as in Eq. (34). When the economy is inside the liquidity trap, the capital stock is fixed at \(f^{ \prime -1} (\lambda ^{ -1})\). Thus, the welfare of an individual country can be expressed as
$$\begin{aligned} U (\gamma ) =f (f^{ \prime -1} (\lambda ^{ -1})) +\gamma _{A} -\gamma +\gamma \cdot \ln \left( \frac{\gamma }{\gamma _{A}} \cdot g\right) . \end{aligned}$$The welfare of all countries, including the median, is thus monotonically increasing in g when the economy is in a liquidity trap. The median country will thus never choose a tax rate higher than \(\frac{\gamma _{A}}{\hat{g} (\lambda )}\), as this would imply that \(g <\hat{g}\).
This is consistent with Benguria and Taylor (2020) who show that, historically, financial crises have been accompanied by shortfalls in aggregate demand.
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We thank Philippe Martin, Linda Tesar, and participants at the IMFís 20th Jacques Polak Annual Research Conference and LBS seminar for their comments. Broner and Martin acknowledge financial support from the Spanish Ministry of Economy and Competitiveness (ECO2016-79823-P). Broner, Martin and Ventura acknowledge support from the Spanish Ministry of Economy and Competitiveness through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000915-S), and the Generalitat de Catalunya through the SGR Programme (2017-SGR-1393) and CERCA Programme. In addition, both Martin and Ventura acknowledge financial support from the European Research Council (ERC) under the EU Seventh Framework Programme (FP7/2007-2013), Consolidator Grant (615651-MacroColl) and European Union's Horizon 2020 research and innovation program, Advanced Grant (693512-GEPPS) respectively. Janko Heineken and Carl-Wolfram Horn provided excellent research assistance. The views presented here are those of the authors and not of the European Central Bank.
