Fiscal consolidation programs and income inequality

Fiscal consolidation programs and income inequality Pedro Brinca Miguel H. Ferreira Francesco Franco Hans A. Holter Laurence Malafry Working Paper # 617 2017 Fiscal Consolidation Programs and Income Inequality∗ Pedro Brinca ‡† Miguel H. Ferreira ‡Francesco Franco ‡ Hans A. Holter §Laurence Malafry ¶ November 15, 2017 Abstract Following the Great Recession, many European countries implemented fiscal consolidation policies aimed at reducing government debt. Using three independent data sources and three different empirical approaches, we document a strong positive relationship between higher income inequality and stronger recessive impacts of fiscal consolidation programs across time and place. To explain this finding, we develop a life-cycle, overlapping generations economy with uninsurable labor market risk. We calibrate our model to match key characteristics of a number of European economies, including the distribution of wages and wealth, social security, taxes and debt, and study the effects of fiscal consolidation programs. We find that higher income risk induces precautionary savings behavior, which decreases the proportion of credit-constrained agents in the economy. Credit-constrained agents have less elastic labor supply responses to fiscal consolidation achieved through either tax hikes or public spending cuts, and this explains the relationship between income inequality and the impact of fiscal consolidation programs. Our model produces a cross-country correlation between inequality and the fiscal consolidation multipliers, which is quite similar to that in the data. Keywords: Fiscal Consolidation, Income Inequality, Fiscal Multipliers, Public Debt, Income Risk JEL Classification: E21, E62, H31, H50 ∗We thank Anmol Bhandari, Michael Burda, Gauti Eggertsson, Mitchel Hoffman, Loukas Karabarbounis, Robert Kirkby, Dirk Krueger, Per Krusell, Ellen McGrattan, William Peterman, Ricardo Reis, Victor RiosRull, Marcelo Santos, Chima Simpson-Bell and Kjetil Storesletten for helpful comments and suggestions. We also thank seminar participants at Birbeck College, Humboldt University, IIES, New York University, University of Bergen, University of Minnesota, University of Oslo, University of Pennsylvania, University of Victoria-Wellington, and conference participants at the 2017 Junior Symposium of the Royal Economic Society, ADEMU, the 6th edition of Lubramacro, the 11th Meetings of the Portuguese Economic Journal, the 70th European Meetings of the Econometric Society, ASSET 2017 and the Spring Mid-West Macro Meeting 2017. Pedro Brinca is grateful for financial support from the Portuguese Science and Technology Foundation, grants number SFRH/BPD/99758/2014, UID/ECO/00124/2013 and UID/ECO/00145/2013. Miguel H. Ferreira is grateful for financial support from the Portuguese Science and Technology Foundation, grant number SFRH/BD/116360/2016. Hans A. Holter is grateful for financial support from the Research Council of Norway, Grant number 219616; the Oslo Fiscal Studies Program. †Center for Economics and Finance at Universidade of Porto ‡Nova School of Business and Economics, Universidade Nova de Lisboa §Department of Economics, University of Oslo ¶Department of Economics, Stockholm University 1 Introduction The 2008 financial crisis led several European economies to adopt counter-cyclical fiscal policy, often financed by debt. Government deficits exceeded 10% in many countries, and this created an urgency for fiscal consolidation policies as soon as times returned to normal. Many countries designed plans to reduce their debt through austerity, tax increases, or more commonly a combination of the two, see Blanchard and Leigh (2013), Alesina et al. (2015a). The process of fiscal consolidation across European countries, however, raised a number of important questions about the effects on the economy. Is debt consolidation ultimately contractionary or expansionary? How large are the effects and do they depend on the state of the economy? How does the impact of consolidation through austerity differ from the impact of consolidation through taxation? In this paper we contribute to this literature, both empirically and theoretically, by presenting evidence on a dimension that can help explain the heterogeneous responses to fiscal consolidation observed across countries: income inequality and in particular the role of uninsurable income risk. We begin by documenting a strong positive empirical relationship between higher income inequality and stronger recessive impacts of fiscal consolidation programs across time and place. We do this by using data and methods from three recent, state-of-the-art, empirical papers, which cover various countries and time periods and make use of different empirical approaches: i) Blanchard and Leigh (2013) ii) Alesina et al. (2015a) iii) Ilzetzki et al. (2013)1. Next we study the effects of fiscal consolidation programs, financed through both austerity and taxation, in a neoclassical macro model with heterogeneous agents and incomplete markets. We show that such a model is well-suited to explain the relationship between income inequality and the recessive effects of fiscal consolidation programs. The mechanism we propose works through idiosyncratic income risk. In economies with lower risk, there are more credit constrained households and households with low wealth levels, due to less pre1While the first two papers study fiscal consolidation programs in Europe, Ilzetzki et al. (2013) study government spending multipliers using a greater number of countries. We include this study for completeness. 1 cautionary saving. Importantly, these credit constrained households have less elastic labor supply responses to increases in taxes and decreases in government expenditures. Our empirical analysis begins with a replication of the recent studies by Blanchard and Leigh (2013) and Blanchard and Leigh (2014). These studies find that the International Monetary Fund (IMF) underestimated the impacts of fiscal consolidation across European countries, with stronger consolidation causing larger GDP forecast errors. In Blanchard and Leigh (2014), the authors find no other significant explanatory factors, such as pre-crisis debt levels2or budget deficits, banking conditions, or a country’s external position, among others, can help explain the forecast errors. In Section 3.1 we reproduce the exercise conducted by Blanchard and Leigh (2013), now augmented with different metrics of income inequality. We find that during the 2010 and 2011 consolidation in Europe the forecast errors are larger for countries with higher income inequality, implying that inequality amplified the recessive impacts of fiscal consolidation. A one standard deviation increase in income inequality, measured as Y10/Y90 3leads the IMF to underestimate the fiscal multiplier in a country by 66%. For a second independent analysis, we use the Alesina et al. (2015a) fiscal consolidation episodes dataset with data from 12 European countries over the period 2007-2013. Alesina et al. (2015a) expands the exogenous fiscal consolidation episodes dataset, known as IMF shocks, from Devries et al. (2011) who use Romer and Romer (2010) narrative approach to identify exogenous shifts in fiscal policy. Again we document the same strong amplifying effect of inequality on the recessive impacts of fiscal consolidation. A one standard deviation increase in inequality, measured as Y25/Y75, increases the fiscal multiplier by 240%. Our third empirical analysis replicates the paper by Ilzetzki et al. (2013). These authors use time series data from 44 countries (both rich and poor) and a SVAR approach to study the impacts of different country characteristics on fiscal multipliers. We find that countries 2In Section 8.1 we show that, in line with our proposed mechanism, household debt matters if an interaction term between debt and the planned fiscal consolidation is included in the regression. 3Ratio of top 10% income share over bottom 10% income share. 2 with higher income inequality experience significantly stronger declines in output following decreases in government consumption. To explain these empirical findings, we develop an overlapping generations economy with heterogeneous agents, exogenous credit constraints and uninsurable idiosyncratic risk, similar to that in Brinca et al. (2016b). We calibrate the model to match data from a number of European countries along dimensions such as the distribution of income and wealth, taxes, social security and debt level. Then we study how these economies respond to gradually reducing government debt, either by cutting government spending or by increasing labor income taxes. Output falls when debt reduction is financed through either a decrease in government spending or increased labor income taxes. In both cases, this is caused by a fall in labor supply. In the case of reduced government spending, the transmission mechanism works through a future income effect. As government debt is paid down, the capital stock and thus the marginal product of labor (wages) rise, and thus expected lifetime income increases. This will lead agents to enjoy more leisure and decrease their labor supply today, and output to fall in the short-run, despite the long run effects of consolidation on output being positive. Credit constrained agents and agents with low wealth levels do, however, have a lower marginal propensity to consume goods and leisure out of future income (for constrained agents the MPC to future income is zero4). Constrained agents do not consider changes to their lifetime budget, only changes to their budget in the current time period. Agents with low wealth levels are also less responsive to future income changes because they will be constrained in several future states of the world. Increases in expected future consumption and leisure levels will thus have a smaller effect on their labor supply today. In the case of consolidation through increased labor income taxes there will also be a negative income effect on labor supply today, through higher future wages and increased life-time income. For constrained agents, who do not consider their life-time budget but 4The fact that constrained agents also very slightly change their labor supply in our model simulations is due to general equilibrium effects (price changes) today. 3 only their budget today, the tax would instead cause a drop in available income in the shortrun, leading to a labor supply increase. However, the tax also induces a negative substitution effect on wages today, both for constrained and unconstrained agents. It turns out that all agents decrease their labor supply, but the response is weaker for constrained and low-wealth agents. When higher income inequality reflects higher uninsurable income risk, there exists a negative relationship between income inequality and the number of credit constrained agents. Greater risk leads to increased precautionary savings behavior, thus decreasing the share of agents with liquidity constraints and low wealth levels. Since unconstrained agents have more elastic labor supply responses to the positive lifetime-income effect from consolidation, labor supply and output will respond more strongly in economies with higher inequality. Through simulations in a benchmark economy, initially calibrated to Germany, we show that varying the level of idiosyncratic income risk strongly affects the fraction of credit constrained agents in the economy and the fiscal multiplier, both for consolidation through taxation and austerity. If we instead change inequality by changing the variance of initial conditions, prior to entering the labor market (permanent ability and the age-profile of wages in the model), there is very little effect on the fraction of credit constrained agents or on the fiscal multiplier. In a multi-country exercise, we calibrate our model to match a wide range of data and country-specific policies from 13 European economies, and find that our simulations reproduce the anticipated cross-country correlation between income inequality and fiscal multipliers. Moreover, we show that in our model, countries with higher idiosyncratic uninsurable labor income risk have a smaller percentage of constrained agents and have larger multipliers, confirming our analysis and mechanism for the benchmark model calibrated to Germany. We perform two empirical exercises to test the validity of the mechanism described above. First, in our calibrated model, higher levels of household debt are associated with a higher number of credit constrained households. This implies that countries with higher levels of 4 debt should have experienced less recessive impacts of fiscal consolidation programs. We show that such relationship exists in the data, by again performing a similar exercise to Blanchard and Leigh (2013). Second, the mechanism we propose implies that fiscal consolidations lead to decreases in labor supply, and that these are amplified by income inequality. We follow Alesina et al. (2015a) but now look at the impacts of fiscal consolidation and income inequality on hours worked. We find, precisely in line with our simulations, that fiscal consolidation programs have a negative impact on hours worked and that this impact is amplified by increases in income inequality. In Section 9, we conduct a final validity test of the mechanism by using our model. In the empirical analysis we make the case that the IMF forecasts did not properly take income inequality into account. In this section we show that using data from our model, obtained by simulating the observed fiscal consolidation shocks in the data, we get similar results to Blanchard and Leigh (2013) when we shut down all labor income risk in our model. The difference between the output drop that our calibrated model predicts both with and in the absence of risk (which is our proxy for the forecast error), is explained by the size of the fiscal shock and its interaction with the same income inequality metrics as in our replication of the Blanchard and Leigh (2013) experiment (found in Section 3.1). The resulting pattern of regression statistics are strikingly similar to Blanchard and Leigh (2013). The remainder of the paper is organized as follows: We begin by discussing some of the recent relevant literature in Section 2. In Section 3we assess the empirical relationship between income inequality and the fiscal multipliers associated with consolidation programs. In Section 4we describe the overlapping generations model, define the competitive equilibrium and explain the fiscal consolidation experiments. Section 5describes the calibration of the model. In Section 6we inspect the transmission mechanism, followed by the cross-country analysis in Section 7. In Section 8we empirically validate the mechanism and in Section 9 we replicate the Blanchard and Leigh (2014) exercise with model data. Section 10 concludes. 5 2 Related Literature There has been a surge in the literature studying the impacts of fiscal consolidation programs. Guajardo et al. (2014) focus on short-term effects of fiscal consolidations on economic activity for a sample of OECD countries, using the narrative approach as in Romer and Romer (2010), finding that a 1% fiscal consolidation shock causes GDP to to decline by 0.62%; Yang et al. (2015) build a sample of fiscal adjustment episodes in OECD countries over the period from 1970 to 2009 and find a somewhat smaller recessive impact: a 1% fiscal consolidation shock leads to a 0.3% fall in output. Blanchard and Leigh (2013) and Blanchard and Leigh (2014) find a negative effect of fiscal consolidation programs on output and shows that this effect is underestimated by the IMF. The conclusions in Alesina et al. (2015b) support previous studies, emphasizing that tax-based consolidations produce deeper and longer recessions than spending based ones. Pappa et al. (2015) study the impact of fiscal consolidation episodes in an environment with corruption and tax evasion, and find evidence that fiscal consolidation causes large output and welfare losses. They find that much of the welfare loss is due to increases in taxes, which creates the incentives to produce in the less productive shadow sector. Dupaigne and F`eve (2016) focus on how the persistence of government spending can shape the short-run impacts on output through the response of private investment. More persistent government spending leads to greater fiscal multipliers. Our paper is also more broadly related to the large literature studying fiscal multipliers, i.e. the response of output to changes in fiscal policy, and in particular the literature focusing on how these responses depends on income and wealth inequality. Heathcote (2005) studies the effects of changes in the timing of income taxes and finds that tax cuts can have large real effects and that the magnitude of the effect depends crucially on the degree of market incompleteness. Hagedorn et al. (2016), in a New Keynesian model, present further evidence of the relevance of market incompleteness in determining the size of fiscal multipliers. Ferriere and Navarro (2016) provide empirical evidence showing that in the post-war U.S., fiscal expansions are only expansionary when financed by increases in tax progressivity. Like in 6 Brinca et al. (2016b), Ferriere and Navarro (2016) can replicate this empirical finding using a neoclassical framework. Brinca et al. (2016) provide empirical evidence that higher wealth inequality is associated with stronger impacts of increases in government expenditures and show that an overlapping generations model with uninsurable income risk calibrated to match key characteristics of a number of OECD countries, can replicate this empirical pattern. Krueger et al. (2016) assess how wealth, income and preference heterogeneity across households amplifies aggregate shocks. Krueger et al. (2016) conclude that, in an economy with the wealth distribution consistent with the data, the drop in aggregate consumption in response to a negative aggregate shock is 0.5 percentage points larger than in a representative household model. This is conditional on the economy featuring a sufficiently large share of agents with low wealth. Anderson et al. (2016) find that in the context of the U.S. economy, individuals respond differently to unanticipated fiscal shocks depending on age, income level, and education. The behavior of the wealthiest agents, in particular, is consistent with Ricardian equivalence but poor households show evidence of non-Ricardian behavior. Relatedly Carroll et al. (2014) measure marginal propensities to consume for a large panel of European countries, and then calibrate a model for each country using net wealth and liquid wealth. The authors find that the higher the proportion of financially constrained agents in an economy, the higher the consumption multiplier. Kaplan and Violante (2014) propose a model with two types of assets that provides a rationale for relatively wealthy agents’ choice of being credit constrained. In a context of portfolio optimization with one high-return illiquid asset and one low-return liquid asset, relatively wealthy individuals may end up credit constrained. Kaplan et al. (2014), using micro data from several countries, then argue that the percentage of financially constrained agents can be well above what is typically the outcome of models where very few agents have their wealth tied up in illiquid assets. Antunes and Ercolani (2016) also highlight the relevance of borrowing constraints for the dynamics of public debt. 7 the median, the recessive impacts of decreases in government consumption expenditures are stronger and statistically different from the impacts for the group of countries with income inequality metrics below the median. The objective is to estimate the following system of equations AYnt = K X k=1 CkYn,t−k+un,t (4) where Ynt is a vector containing the endogenous variables for country n in quarter t. The variables considered are the same as in Ilzetzki et al. (2013): government consumption, output, current account in percentage of GDP and the natural logarithm of the real effective exchange rate. Ckis a matrix of lag own and cross effects of variables on their current observations. Given that A is not observable we cannot estimate this regression directly. We need to pre-multiply everything by A−1and, using OLS, we can recover the matrix P=A−1Ckand en,t =A−1un,t. So we estimate the system Ynt = K X k=1 A−1CkYn,t−k+A−1un,t (5) To be able to estimate the effects of fiscal consolidation, we need more assumptions on A so that we can identify the innovations by solving en,t =A−1un,t. We use the same assumption used by Ilzetzki et al. (2013) and first introduced by Blanchard and Perotti (2002), to identify the responses of output to government consumption expenditures: government consumption cannot react to shocks in output within the same quarter. The plausibility of this assumption comes from the fact that the government’s budget is typically set on a yearly basis and can only react to changes in output with a lag. For the ordering of the remaining variables, we also follow Ilzetzki et al. (2013) and let the current account follow output and the real exchange rate follow the current account. Given this, we can identify the impulse responses to a primitive shock in government spending. In Figures 1,2and 3we plot the cumulative output multiplier to a government consumption shock, defined as: 14 cummulative multiplier G(T) = Pt=T t=0 1 (1+rm)t∆Yt Pt=T t=0 1 (1+rm)t∆Gt (6) rmis here the median interest rate in the data sample. The output multipliers shown in Figures 1,2and 3suggest that in countries with higher income inequality, contractions in government spending have a more recessive impact. Figure 1: Cumulative output multiplier, as defined in (6), to a government consumption shock (90% error bands in gray) Figure 2: Cumulative output multiplier, as defined in (6), to a government consumption shock (90% error bands in gray) 15 Figure 3: Cumulative output multiplier, as defined in (6), to a government consumption shock (90% error bands in gray) The empirical findings in Section 3together suggest that income inequality is a relevant dimension to take into account when studying the effects of fiscal policy. In particular, they suggest that higher inequality amplifies the recessive impacts of fiscal consolidation and decreases in government expenditures. In order to understand the mechanism through which income inequality may play such role, we build a structural model that is introduced in the next section. 4 Model In this section, we describe the model we will use to study the effects of a fiscal consolidation in different countries. Our model is a relatively standard life-cycle economy with heterogeneous agents and incomplete markets. It is similar to the model in Brinca et al. (2016b), except that we have introduced a bequest motive to get a more realistic distribution of wealth over the life-cycle. Technology There is a representative firm, producing output with a Cobb-Douglas production function: Yt(Kt, Lt) = Kα t[Lt]1−α(7) 16 where Ktis the capital input and Ltthe labor input in efficiency units. The evolution of capital evolution is given by: Kt+1 = (1 −δ)Kt+It(8) where Itis gross investment and δthe capital depreciation rate. Each period, the firm hires labor and capital to maximize its profits: Πt=Yt−wtLt−(rt+δ)Kt.(9) In a competitive equilibrium, the factor prices will be equal to their marginal products given by: wt=∂Yt/∂Lt= (1 −α)Kt Ltα (10) rt=∂Yt/∂Kt−δ=αLt Kt1−α −δ(11) Demographics The economy is populated by Joverlapping generations of finitely lived households11. All households start life at age 20 and enter retirement at age 65. Let jdenote the household’s age. Retired households face an age-dependent probability of dying, π(j) and die for certain at age 100.12. A model period is 1 year, so there are a total of 40 model periods of active work life. We assume that the size of the population is fixed (there is no population growth). We normalize the size of each new cohort to 1. Using ω(j)=1−π(j) to denote the agedependent survival probability, by the law of large numbers the mass of retired agents of age j≥65 still alive at any given period is equal to Ωj=Qq=J−1 q=65 ω(q). In addition to age differences, households are heterogeneous with respect to asset holdings, idiosyncratic productivity, and their subjective discount factor, which for each household is constant over time but takes one out of the three values β∈ {β1, β2, β3}; the dis11Recent work by Peterman and Sager (2016) makes the case for having a life-cycle dimension when studying the impacts of government debt. 12This means that J= 81. 17 tribution of discount factors is uniformly distributed across agents in each cohort. Finally, they also differ in terms of a permanent ability component, i.e., they have a starting level of productivity that is realized at birth. Every period of active work-life they decide how many hours to work, n, how much to consume, c, and how much to save, k. Retired households make no labor supply decisions but receive a social security payment, Ψt. There are no annuity markets, so that a fraction of households leave unintended bequests which are redistributed in a lump-sum manner between the households that are currently alive. We use Γ to denote the per-household bequest. Retired households’ utility is increasing in the bequest they leave when they die. This helps us calibrate the asset holdings of old households. Labor Income The wage of an individual depends on his/her own characteristics: age, j, permanent ability, a∼N(0, σ2 a), and idiosyncratic productivity shock, u, which follows an AR(1) process: ut+1 =ρut+t+1,  ∼N(0, σ2 ) (12) These characteristics will dictate the number of efficient units of labor the household is endowed with. Individual wages will also depend on the wage per efficiency unit of labor w. Thus, individual i’s wage is given by: wi(j, a, u) = weγ1j+γ2j2+γ3j3+a+u(13) γ1ι,γ2ιand γ3ιcapture the age profile of wages. 18 Preferences The momentary utility function of a household, U(c, n), depends on consumption and work hours, n∈(0,1], and takes the following form: U(c, n) = c1−σ 1−σ−χn1+η 1 + η.(14) Retired households gain utility from the bequest they leave when they die: D(k) = ϕlog(k) (15) Government The government runs a balanced social security system where it taxes employees and the employer (the representative firm) at rates τss and ˜τss and pays benefits, Ψt, to retirees. The government also taxes consumption and labor and capital income to finance the expenditures on pure public consumption goods, Gt, which enter separably in the utility function, interest payments on the national debt, rBt, and a lump-sum redistribution, gt. We assume that there is some outstanding government debt and that government debt-to-output ratio, BY= Bt/Yt, does not change over time. Consumption and capital income are taxed at flat rates the τcand τk. To model the non-linear labor income tax, we use the functional form proposed in Benabou (2002) and recently used in Heathcote et al. (2017) and Holter et al. (2017): τ(y) = 1 −θ0y−θ1(16) where ydenotes pre-tax (labor) income and τ(y) the average tax rate given a pre-tax income of y. The parameters θ0and θ1govern the level and the progressivity of the tax code, respectively.13.Heathcote et al. (2017) argue that this function fits the U.S. data well. In a steady state, the ratio of government revenues to output will remain constant. Gt, 13A further discussion of the properties of this tax function is provided in the appendix 19 gt, and Ψtmust also remain proportional to output. Denoting the government’s revenues from labor, capital, and consumption taxes by Rtand the government’s revenues from social security taxes by Rss t, the government budget constraint in steady state takes the following form: g 45 + X j≥65 Ωj!=R−G−rB, (17) Ψ X j≥65 Ωj!=Rss.(18) Recursive Formulation of the Household Problem At any given time a household is characterized by (k, β, a, u, j), where kis the household’s savings, β∈β1, β2, β3, is the time discount factor, ais permanent ability, uis the idiosyncratic productivity shock, and jis the age of the household. We can formulate the household’s optimization problem over consumption, c, work hours, n, and future asset holdings, k0, recursively as follows: V(k, β, a, u, j) = max c,k0,n hU(c, n) + βEu0V(k0, β, a, u, j + 1)i s.t.: c(1 + τc) + k0= (k+ Γ) (1 + r(1 −τk)) + g+YL YL=nw (j, a, u) 1 + ˜τss 1−τss −τlnw (j, a, u) 1 + ˜τss  n∈[0,1], k0≥ −b, c > 0 (19) Here, YLis the household’s labor income after social security taxes and labor income taxes. τss and ˜τss are the social-security contributions paid by the employee and by the employer, respectively. The problem of a retired household, who has a probability π(j) of dying and 20 gains utility D(k0) from leaving a bequest, is: V(k, β,j) = max c,k0hU(c, n) + β(1 −π(j))V(k0, β, j + 1) + π(j)D(k0)i s.t.: c(1 + τc) + k0= (k+ Γ) (1 + r(1 −τk)) + g+Ψ, k0≥0, c > 0 (20) Stationary Recursive Competitive Equilibrium Let the measure of households with the corresponding characteristics be given by Φ(k, β, a, u, j). The stationary recursive competitive equilibrium is defined by: 1. Given the factor prices and the initial conditions the consumers’ optimization problem is solved by the value function V(k, β, a, u, j) and the policy functions, c(k, β, a, u, j), k0(k, β, a, u, j), and n(k, β, a, u, j). 2. Markets clear: K+B=ZkdΦ L=Z(n(k, β, a, u, j)) dΦ ZcdΦ + δK +G=KαL1−α 3. The factor prices satisfy: w= (1 −α)K Lα r=αK Lα−1 −δ 21 4. The government budget balances: gZdΦ + G+rB =Z τkr(k+ Γ) + τcc+nτlnw(a, u, j) 1 + ˜τss !dΦ 5. The social security system balances: ΨZj≥65 dΦ = ˜τss +τss 1 + ˜τss Zj<65 nwdΦ! 6. The assets of the dead are uniformly distributed among the living: ΓZω(j)dΦ = Z(1 −ω(j)) kdΦ Fiscal Experiment and Transition The fiscal experiments that we analyze in this paper is 50 periods of reduction in government debt, B, either financed through a decrease in government spending, G, by 0.2% of benchmark GDP14, or an increase in the labor income tax τl, by 0.1% for all agents. The economy is initially in a steady state and the 50 periods of fiscal consolidation is unanticipated until it is announced15. After the 50 periods either the government spending or the labor tax go back to the initial level. The lumpsum transfer, gis set to clear the government budget, and we assume that the economy takes an additional 50 periods to converge to the new steady state equilibrium, with lower debt to GDP ratio. To save space, the definition of a transition equilibrium after the fiscal experiment is stated in Appendix 11.2. The key change compared to the steady state is that the dynamicprogramming problem of households need another state variable: time, t, capturing all the changes in policy and price variables relevant in this maximization problem. The numerical solution of the model necessitates guessing on paths for all the variables that will depend 14The total revenue available for debt repayment over the 50-year period is thus 10% of benchmark GDP 15In Section 3.2, we found that unanticipated but not anticipated fiscal consolidations have a statistically significant negative effect on output. 22 on time and then solving this maximization problem backward, after which the guess is updated; the method is similar to that used in Brinca et al. (2016b) and Krusell and Smith (1999). Definition of the Fiscal Multiplier in the Context of a Fiscal Consolidation Shock In the experiment with debt reduction financed by a reduction in G, we define the impact multiplier as: impact multiplier G =∆Y0 ∆G0 (21) where ∆Y0is the change in output from period 0 to period 1 and ∆G0is the change in government spending from period 0 to period 1. The cumulative multiplier at time Tis defined as: cummulative multiplier G(T) = Pt=T t=0 Πs=t s=0 1 (1+rs)∆Yt Pt=T t=0 Πs=t s=0 1 (1+rs)∆Gt (22) where ∆Ytis the change in output from period 0 to period tand ∆G0is the change in government spending from period 0 to period tWhen the consolidation is financed through an increase in the labor income tax, τl, we define the impact multiplier as: impact multiplier τl=∆Y0 ∆R0 (23) where ∆Y0is the change in output from period 0 to period 1 and ∆R0is the change in government revenue from period 0 to period 1. Government spending, Gand lumpsum redistribution, g, are kept constant during this consolidation. For the tax-based consolidation we define the cumulative multiplier as: 23 6.1 Illustrating the Mechanism: Comparing Fiscal Consolidation in Germany and the Czech Republic To illustrate the impact of differences in inequality, we first compare the effects of consolidation in Germany and in the Czech Republic, two European countries on the opposite side of the spectrum in terms of wage inequality. Germany with the second highest variance of log wages, 0.354, and Czech Republic with the lowest value, 0.174. These two countries differ along several dimensions, but the reason why we choose Germany and Czech Republic is due to their differences in wage inequality, idiosyncratic risk and the percentage of constrained agents. In the Czech Republic the calibrated variance of the idiosyncratic risk is 0.145 and the percentage of constrained agents is 7.39%, while Germany has a higher variance of risk, 0.439, and a lower percentage of constrained agents, 3.41%. We find what our mechanism suggests that the output multiplier following the unanticipated fiscal consolidation shock is larger in Germany than in Czech Republic. Figure 6: Labor tax consolidation: Output cumulative multiplier (left panel) and Labor Supply cumulative multiplier (right panel) in the first three periods in Germany (dashed line) and Czech Republic (solid line) In Figures 6and 7we plot the cumulative output multiplier and labor supply response to labor tax and government spending consolidations respectively, for the two countries. Both the labor supply responses and the output multipliers are significantly larger in the German economy, where wage inequality is higher. As Germany has a smaller share of constrained and low-wealth agents, the output drop is more pronounced. One should also note that the consolidation through increased labor income taxes causes deeper recessions than the 30 Figure 7: Government spending consolidation: Output cumulative multiplier (left panel) and Labor Supply cumulative multiplier (right panel) in the first three periods in Germany (dashed line) and Czech Republic (solid line) consolidation financed by a reduction in government spending. This is consistent with the results by Alesina et al. (2017). 6.2 Inequality: Variance of Risk vs. Variance of Ability vs. Age Profiles Next, we perform three experiments in our German benchmark economy to verify the mechanism described above. We focus on understanding the role of the different parameters that drive wage inequality in our model, σ,σa, and γ1,γ2,γ3. These parameters govern the variance of idiosyncratic wage shocks, the variance of permanent ability and the shape of the age-progile of wages. We find that the correlation between wage inequality and fiscal multipliers that we documented in the empirical section can only be explained by differences in idiosyncratic risk and not by predetermined differences in ability or in the age-profile of wages. We perform three different experiments: 1. We gradually change V ar(ln w) from in the benchmark model by changing the variance of the innovations to the stochastic income process, σ2 , from low to high. 2. We gradually change V ar(ln w) in the benchmark model calibrated to Germany, by changing the variance of ability, σ2 a, from low to high. 3. We gradually change V ar(ln w) in the benchmark model calibrated to Germany, by multiplying the age-profile of wages, governed by γ1,γ2,γ3, by a Scalar, going from low to high. 31 In all cases we adjust γ0by a constant to guarantee that average productivity in the economy stays unchanged. Then for each value of σu,σaand the Scalar we perform our two fiscal consolidation experiments: i) consolidation through government spending and ii) consolidation through the labor income tax. Figure 8: Impact multiplier for the labor tax consolidation in the benchmark model for Germany when changing the variance of risk (left panel), the variance of ability (middle panel), and the age profile of wages (right panel). In Figure 8we plot the impact multiplier in the experiment with fiscal consolidation through labor income taxes for different values of σ,σaand the Scalar. In the left panel we observe that the fiscal multiplier is very sensitive to changes in income risk. When we change the variance of the innovations to the idiosyncratic shock, , from 0 to 0.45 the impact multiplier falls from about -1.40 to -1.95. In the middle and right panels we observe that it is relatively inelastic with respect to changes in ability and the steepness of the age-profile of wages19. Figure 9: Impact multiplier for the consolidation through government spending in the German benchmark economy when changing the variance of risk (left panel), the variance of ability (middle panel), and the age profile of wages (right panel). 19Germany has one of the steepest age-profiles in our sample of countries. We therefore let the scalar go from 0 to 1, capture the effect of going from a steep age-profile to a completely flat age-profile. 32 The experiment with consolidation through government spending generates similar results. In the left panel of Figure 9, we observe that as we change the variance of the innovations to the idiosyncratic shock, governed by σ, from 0 to 0.45 the impact multiplier increases from about 0.41 to 0.47. In the middle and the right panels of the figure we observe that the changes in the multiplier induced by changing the variance of ability and the steepness of the age-profile of wages are small. We conclude that only through changes in income risk can we generate a positive relationship between the impact of fiscal consolidation programs and income inequality. The analysis in Figures 8and 9covers changes in risk that go from zero to the highest value obtained in our calibration of the model to 13 different European countries. In our calibration exercise, the lowest value of the variance of risk was obtained for Greece and equal to 0.12 and the highest was equal to 0.5, for France. One should note that the relative magnitude of changes in the multiplier induced by changing the risk is larger for tax-based than for spending-based consolidation. Going from the lowest to the highest level of risk, implies a 30% increase in the impact multiplier for the tax-based consolidation and an 8% increase in the impact multiplier for the spending-based consolidation. As mentioned before it is worth noting that the actual consolidations studied in Section 3include both changes in taxes and spending. In Figure 10 we verify our hypothesis about the relationship between income risk and the fiscal consolidation multipliers stemming from the fact that economies with higher income risk have a lower share of credit-constrained agents. In the left panel of the figure we document a strong, negative relationship between the variance of risk and the proportion of credit constrained agents in the economy. In the middle panel we see that changing the variance of ability does not affect the share of agents with liquidity constraints, as we anticipated. A steeper age-profile of wages leads to more liquidity-constrained agents (as one would expect20) but the effect is very weak compared to the impact of income risk. 20With a steeper age profile agents will save less early in the life-cycle. 33 Figure 10: Share of credit-constrained agents in the German benchmark economy when changing the variance of risk (left panel), the variance of ability (middle panel), and the age profile of wages (right panel). In Figure 11 we illustrate the relationship between the share of agents with liquidity constraints and the impact multiplier, for both spending-based and tax-based fiscal consolidation, as we change income risk. We observe that there is a strong negative relationship between the share of credit constrained agents and the fiscal consolidation multipliers. Figure 11: Impact multiplier for the G-consolidation (left panel) and for the τl-consolidation (right panel) plotted against the share of credit-constrained agents in the German benchmark economy, when decreasing the variance of risk. Finally, as a last robustness test to verify that the relationship between inequality and fiscal multipliers comes from the variance of risk we conduct the following experiment: we keep wage inequality constant by choosing different combinations of risk and ability, going from one extreme, where all wage inequality (except from the age-profile) is due to the variance of risk, to the other extreme, where wage inequality is fully explained by variance of ability. Figure 16 in the Appendix shows that the multiplier is largest when all inequality is explained by income risk and smallest when all inequality is explained by the variance of 34 ability, for both tax-based and expenditure-based consolidations. 7 Cross-country Analysis In the previous Section we demonstrated that our model is able to reproduce the empirical relationship between income inequality and fiscal multipliers, through variation in income risk. In this Section we perform a cross-country analysis to show that this mechanism is strong enough to matter empirically. We calibrate our model to match a wide range of different country characteristics, where, in addition to the distributions of income and wealth, we match data on taxes, social security and government debt. We show that even when introducing substantial country heterogeneity, we are able to reproduce the crosscountry relationship between both taxand spending-based fiscal consolidation and income inequality. The model is calibrated to 13 European countries21 using country-specific age-profiles of wages, keeping the variance of the permanent ability fixed and changing the variance of the idiosyncratic shock to match the variance of log wages in the data. Tables 10 and 14 summarize the wealth distribution, the other country specific data used to calibrate the model, and the country specific parameters estimated outside of the model. Table 15 summarizes the country specific parameters estimated through the simulated method of moments, as described in Section 5. Parameters kept constant for all the countries, are summarized in Table 16. Figure 12 reveals that our model is able to reproduce the cross-country empirical relationship between income inequality and the impacts of fiscal consolidation: countries with higher inequality experience larger output drops on impact, both for tax and spending based consolidations. These effects are large and economically meaningful, in particular for tax-based 21For this exercise we use only countries which actually went through fiscal consolidation processes after 2009. Compared to Blanchard and Leigh (2013), we are forced to exclude Belgium, Cyprus, Denmark, Ireland, Malta, Norway, Poland, Romania and Slovenia due to data limitations. The results in Section 3.1 are, however, robust to considering only these 13 countries. See Table 12 in Appendix. 35 consolidations. Using the coefficient found when regressing the multiplier on income inequality, we find that the response between the country with the lowest income inequality (Czech Republic) and the highest (France) leads to a 90% increase in the tax-based multiplier. One should also note that tax-based consolidations in general produce deeper recessions across countries than spending based consolidations. Figure 12: Impact multiplier and Var(ln(w)). On the left panel we have the cross-country data for a consolidation done by decreasing G (correlation coefficient 0.35 , p-val 0.25 ), while on the right panel we have the cross-country data for a consolidation done by increasing the labor tax (correlation coefficient -0.60 , p-val 0.03 ). In the previous section we argued that the mechanism through which higher income risk translates into larger multipliers is through changes in the share of credit-constrained agents. In Figure 13 this relation is documented for the 13 economies for which we calibrate the model. Countries with a higher standard deviation of the innovations to idiosyncratic income risk, σ, have a smaller share of constrained agents. As argued before, the labor supply of constrained agents is less elastic with respect to the fiscal shock, and the larger the percentage of constrained agents the smaller the multiplier. In Figure 14 this relationship is documented for the cross country analysis. Countries with a larger share of liquidity constrained agents experience a smaller output drop for both spendingand tax-based consolidations. 36 Figure 13: Percentage of agents constrained in the y-axis and variance of idiosyncratic risk on the x axis. Correlation coefficient of -0.73 and p-value of 0.00 Figure 14: Impact multiplier and percentage of agents constrained. On the left panel we have the cross-country data for a consolidation done by decreasing G (correlation coefficient -0.68 , p-val 0.01 ), while on the right panel we have the cross-country data for a consolidation done by increasing the labor tax (correlation coefficient 0.55 , p-val 0.06 ) 8 Empirical Validation of the Mechanism In Section 3we established that income inequality amplifies the recessive effects of fiscal consolidations. In Section 6we study a mechanism that leads to this amplification effect: 37 labor supply responds stronger in countries with higher income inequality, leading to a larger output drop. In this section we present two pieces of empirical evidence that supports our mechanism. First, we use the fact that household debt and the share of credit-constrained agents are strongly correlated in our benchmark economy. If our mechanism is correct, the output drop in response to fiscal consolidations should be smaller in countries with higher household debt because they have more constrained agents. We expand the Blanchard and Leigh (2014) regression with an interaction term between household debt and the planned fiscal consolidation and find exactly this: household debt diminishes the recessive effects of fiscal consolidation. The larger the household debt, the smaller the forecast error. Then, to test how income inequality affects the labor supply response to fiscal consolidation programs, we use the Alesina et al. (2015a) dataset but instead of considering GDP growth rates as our dependent variable, we use annual hours worked per capita. We find that for countries with higher income inequality, labor supply is more responsive to fiscal consolidation programs, just as our mechanism suggests. 8.1 Household Debt Blanchard and Leigh (2014) test whether pre-crisis household debt was one of the dimensions the IMF did not take properly into consideration when forecasting the GDP growth rates. Like all the other variables they test, they find that debt does not affect the forecast error. However, our mechanism suggests that debt should have affected the recessive impacts of fiscal consolidation programs. Decreasing risk, induces less precautionary savings, which results in higher household debt and consequently in a higher share of credit-constrained agents, as can be seen in Figure 15. Higher household debt should, according to our model, translate into smaller multipliers. To test whether household debt helps to explain the impacts of fiscal consolidation programs, besides extending Equation (1) with pre-crisis household debt, as already done by Blanchard and Leigh (2014), we also include an interaction term between planned fiscal 38 Figure 15: The fraction of liquidity constrained agents (y-axis) and household debt level (x-axis), when changing the level of idiosyncratic risk in the German benchmark economy. consolidation and pre-crisis household debt. The equation that we estimate is: ∆Yi,t:t+1 −ˆ E{∆Yi,t:t+1|Ωt}=α+βˆ E{Fi,t:t+1|t|Ωt}+γHDi,t−1+ ι(( ˆ E{Fi,t:t+1|t|Ωt})(HDi,t−1−µHD)) + i,t:t+1 (27) HDi,t−1is here pre-crisis household debt in country i, measured as total financial liabilities in percent of household disposable income. We use pre-crisis household debt so that it is exogenous to the fiscal shocks and to the output variation. Once again, we reparametrize the interaction term. The results in Table 5are consistent with our mechanism. The interaction term is positive and statistically significant. Moreover, the R2is substantially higher than in the specification without the interaction term, and the coefficient associated with the planned consolidation is more negative and statistically different from the specification without the interaction. This suggests that during the consolidations in the European countries in 2010 and 2011, higher pre-crisis household debt contributed to diminish the recessive effects of fiscal consolidation programs, just as our mechanism suggests. Increasing pre-crisis household debt by one standard deviation decreases the recessive impacts of fiscal consolidation by 52%. 39 Brinca, P., Chari, V. V., Kehoe, P. J., and McGrattan, E. (2016a). Accounting for business cycles. Handbook of Macroeconomics, 2:1013–1063. Brinca, P., Holter, H. A., Krusell, P., and Malafry, L. (2016b). Fiscal multipliers in the 21st century. Journal of Monetary Economics, 77:53–69. Carroll, C. 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Krueger, D., Mitman, K., and Perri, F. (2016). Macroeconomics and household heterogeneity. Handbook of Macroeconomics, 2:843–921. Krusell, P. and Smith, A. (1999). On the welfare effects of eliminating business cycles. Review of Economic Dynamics, 2(1):245–272. Pappa, E., Sajedi, R., and Vella, E. (2015). Fiscal consolidation with tax evasion and corruption. Journal of International Economics, 96:S56–S75. Peterman, W. and Sager, E. (2016). Optimal public debt with life cycles motives. Working Paper. Romer, C. D. and Romer, D. H. (2010). The macroeconomic effects of tax changes: estimates based on a new measure of fiscal shocks. American Economic Review, 100(3):763–801. Stierli, M., Shorrocks, A., Davies, J. B., Lluberas, R., and Koutsoukis, A. (2014). Global wealth report 2014. Zurich: Credit Suisse Research Institute (CSRI). Trabandt, M. and Uhlig, H. (2011). The laffer curve revisited. Journal of Monetary Economics, 58(4):305–327. 47 Yang, W., Fidrmuc, J., and Ghosh, S. (2015). Macroeconomic effects of fiscal adjustment: A tale of two approaches. Journal of International Money and Finance, 57:31–60. 48 11 Appendix 11.1 Tax Function 26 Given the tax function ya =θ0y1−θ1 which we employ, the average tax rate is defined as ya = (1 −τ(y))y and thus θ0y1−θ1= (1 −τ(y))y and thus 1−τ(y) = θ0y−θ1 τ(y) = 1 −θ0y−θ1 T(y) = τ(y)y=y−θ0y1−θ1 T0(y) = 1 −(1 −θ1)θ0y−θ1 Thus the tax wedge for any two incomes (y1, y2) is given by 1−1−τ(y2) 1−τ(y1)= 1 −y2 y1−θ1 (29) and therefore independent of the scaling parameter θ0.Thus by construction one can raise average taxes by lowering θ0and not change the progressivity of the tax code, since (as 26This appendix is borrowed from Holter et al. (2017) 49 long as tax progressivity is defined by the tax wedges) the progressivity of the tax code27 is uniquely determined by the parameter θ1. 11.2 Definition of a Transition Equilibrium after the Unanticipated Fiscal Consolidation Shock We define a recursive competitive equilibrium along the transition between steady states as follows: Given the initial capital stock, the initial distribution of households and initial taxes, respectively K0, Φ0and {τl, τc, τk, τss,˜τss}t=∞ t=1 , a competitive equilibrium is a sequence of individual functions for the household, {Vt, ct, k0 t, nt}t=∞ t=1 , of production plans for the firm, {Kt, Lt}t=∞ t=1 , factor prices, {rt, wt}t=∞ t=1 , government transfers {gt,Ψt, Gt}t=∞ t=1 , government debt, {Bt}t=∞ t=1 , inheritance from the dead, {Γt}t=∞ t=1 , and of measures {Φt}t=∞ t=1 , such that for all t: 1. Given the factor prices and the initial conditions the consumers’ optimization problem is solved by the value function V(k, β, a, u, j) and the policy functions, c(k, β, a, u, j), k0(k, β, a, u, j), and n(k, β, a, u, j). 2. Markets clear: Kt+1 +Bt=ZktdΦt Lt=Z(nt(kt, β, a, u, j)) dΦt ZctdΦt+Kt+1 +Gt= (1 −δ)Kt+Kα tL1−α t 27Note that 1−τ(y) = 1−T0(y) 1−θ1 >1−T0(y) and thus as long as θ1∈(0,1) we have that T0(y)> τ(y) and thus marginal tax rates are higher than average tax rates for all income levels. 50 3. The factor prices satisfy: wt= (1 −α)Kt Ltα rt=αKt Ltα−1 −δ 4. The government budget balances: gtZdΦt+Gt+rtBt=Z τkrt(kt+ Γt) + τcct+ntτlntwt(a, u, j) 1 + ˜τss !dΦt+ (Bt+1 −Bt) 5. The social security system balances: ΨtZj≥65 dΦt=˜τss +τss 1 + ˜τss Zj<65 ntwtdΦt! 6. The assets of the dead are uniformly distributed among the living: ΓtZω(j)dΦt=Z(1 −ω(j)) ktdΦt 7. Aggregate law of motion: Φt+1 =Υt(Φt) 11.3 Description of Data used in Sections 3,8, and 9 The data series used in Sections 3.1 and 3.2 for the inequality measures are from the European Union Statistics on Income and Living Conditions (EU-SILC). The EU-SILC is a survey aiming at collecting cross-sectional and longitudinal microdata on income, poverty, social exclusion and living-conditions. Data collected is based on a nationally representative probability sample of the population residing in private households within the country. Cross-sectional data series used is gross income - total monetary and non-monetary income received by the household before deduction of taxes. 51 The growth forecast error and planned fiscal consolidation series are taken from Blanchard and Leigh (2014), who use data from the IMF’s WEO database. The forecasts used were made for the European Economies in early 2010. The growth forecast error consist on the difference between actual cumulative growth in 2010-11 and the IMF forecast prepared for the April 2010 WEO. The planned fiscal consolidation is the IMF forecast of the cumulative changes of structural fiscal balance as percent of potential GDP, also prepared for the April 2010 WEO. The household debt variable used in Section 6also comes from Blanchard and Leigh (2014), who take it from the dataset of the April 2012 WEO chapter on household debt. Household debt consists on total financial liabilities in percent of household disposable income. The data series used in Section 3.3 are taken from Ilzetzki et al. (2013). The data series consist of quarterly observations (not interpolated) on real government consumption, GDP, the ratio of current account to GDP, and the real effective exchange rate for 44 countries, roughly balanced between developed and developing economies (see Table 9for the list of included countries). Nominal series are deflated using a GDP deflator when available (and CPI when not). Consumption, GDP, and exchange rate variables are transformed by taking natural logarithms. These series are de-seasonalized and analyzed as deviations from their quadratic trend given they exhibit strong seasonality and are non-stationary. Data in Table 9comes from the World Bank’s World Development Indicators for the years of 2009 for Botswana and Malaysia, 2010 for Australia, Canada and Israel, 2011 for Germany and South Africa, 2012 for Belgium, Bulgaria, Croatia, Czech Republic, Denmark, Estonia, Finland, France, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Mexico, Netherlands, Norway, Portugal, Slovakia, Slovenia, Spain, Sweden and United Kingdom, and 2013 for all the other countries. 52 Table 9: Income Inequality measures for 44 Selected Countries Country Income Gini Y20/Y80 Y10/Y90 Argentina 0.42 9.8 19.1 Australia 0.35 5.9 10.2 Belgium 0.28 4.2 6.7 Botswana 0.61 23.1 45.0 Brazil 0.53 17.4 41.8 Bulgaria 0.36 6.9 13.7 Canada 0.34 5.8 9.5 Chile 0.51 12.3 24.4 Colombia 0.54 17.1 38.1 Croatia 0.33 5.7 9.6 Czech Republic 0.26 3.8 5.7 Denmark 0.29 4.4 8.4 Ecuador 0.47 11.5 22.8 El Salvador 0.43 9.1 16.4 Estonia 0.33 5.7 10.1 Finland 0.28 3.9 5.7 France 0.33 5.3 8.6 Germany 0.30 4.6 7.0 Greece 0.37 7.6 15.7 Hungary 0.31 4.9 8.0 Iceland 0.27 4.0 6.0 Ireland 0.33 5.3 8.3 Israel 0.43 10.3 18.4 Italy 0.35 6.7 13.8 Latvia 0.36 6.7 12.1 Lithuania 0.35 6.5 11.7 Malaysia 0.46 11.2 19.2 Mexico 0.48 11.0 20.5 Netherlands 0.28 4.2 6.6 Norway 0.26 3.8 5.8 Peru 0.45 11.3 22.3 Poland 0.33 5.2 7.8 Portugal 0.36 6.6 12.6 Romania 0.28 4.1 6.0 Slovakia 0.26 4.1 6.6 Slovenia 0.26 3.7 5.7 South Africa 0.63 27.6 57.0 Spain 0.36 7.2 15.2 Sweden 0.27 4.2 6.7 Thailand 0.38 6.5 10.1 Turkey 0.40 8.0 13.9 United Kingdom 0.33 5.4 8.5 United States 0.41 9.1 17.8 Uruguay 0.42 9.3 16.3 Sample median 0.35 6.5 10.9 53 11.4 Eurosystem Household Finance and Consumption Survey - Summary Wealth Statistics Table 10 presents the cumulative wealth distributions for the countries in the Eurosystem Household Finance and Consumption Survey. We include four additional countries’ wealth distributions, from the Luxembourg Wealth Study’s compilation of various household wealth surveys. Table 10: Cumulative Distribution of Net Wealth 25% 50% 75% HFCS samplea Austria -1.0 2.2 18.6 France 0.1 5.4 26.2 Germany -0.4 2.7 17.9 Greece 1.1 12.5 36.7 Italy 0.9 10.2 32.4 Netherlands -2.5 5.0 30.3 Portugal 0.6 8.2 26.6 Slovakia 5.5 20.7 45.0 Spain 1.7 12.9 34.2 Other sourcesb Czech Republicc0.4 6.1 22.1 Iceland 0.5 7.7 27.6 Sweden -9.9 -7.8 11.5 UK -0.7 5.4 27.0 aCumulative distribution of net wealth (survey variable designation: DN3001) for a selection of countries from the first wave of the ECB’s HFCS. bSourced from Luxembourg Wealth Study’s most recent entry for each respective country (survey variable designation: nw1). cSourced from the Stierli et al. (2014). We use 2009 data provided by the authors. 54 11.5 Additional Figures and Tables Table 11: Blanchard and Leigh (2013) Regressions with GDP as the Dependent Variable Coefficients Blanchard-Leigh Y25/Y75 Y20/Y80 Y10/Y90 Y5/Y95 Y2/Y98 Income Gini β-1.556*** -1.116** -1.078** -0.901** -0.901** -1.026*** -1.696*** (0.467) (0.441) (0.436) (0.379) (0.339) (0.339) (0.406) γ-0.402 -0.302 -0.170 -0.039 0.019 0.286 (0.578) (0.444) (0.191) (0.053) (0.050) (0.169) ι-0.405 -0.365 -0.229* -0.116*** -0.098** -0.000 (0.388) (0.304) (0.113) (0.036) (0.035) (0.115) Constant 3.763*** 6.545* 6.335* 6.264** 4.938*** 3.612*** -6.990 (0.576) (3.760) (3.493) (2.578) (1.302) (1.057) (6.402) Observations 26 26 26 26 26 26 26 R-squared 0.465 0.533 0.544 0.607 0.634 0.587 0.542 a*** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. bThe table displays the results from estimating the regression in (1) with GDP as the dependent variable. cY25/Y75, Y20/Y80, Y10/Y90, Y5/Y95 and Y2/Y98 represent the share of income of the top 25%, 20%, 10%, 5% and 2% divided by the share of the bottom 25%, 20%, 10%, 5% and 2%. Table 12: Blanchard and Leigh (2013) Regressions for the Countries in Section 7 (1) (2) (3) (4) (5) (6) (7) Coefficients Blanchard-Leigh Y25/Y75 Y20/Y80 Y10/Y90 Y5/Y95 Y2/Y98 Income Gini β-1.430*** -1.161*** -1.170*** -1.204*** -1.286*** -1.259*** -1.378*** (0.182) (0.131) (0.134) (0.172) (0.164) (0.176) (0.204) γ-0.490 -0.303 -0.033 0.031 0.048 0.365** (0.750) (0.534) (0.165) (0.034) (0.046) (0.120) ι-0.122 -0.119 -0.073 -0.039* -0.040** -0.053 (0.187) (0.134) (0.047) (0.017) (0.017) (0.063) Constant 1.207* 4.304 3.553 1.712 0.616 0.228 -12.831** (0.567) (5.167) (4.552) (2.709) (1.233) (0.840) (4.458) Observations 13 13 13 13 13 13 13 R-squared 0.715 0.755 0.750 0.736 0.736 0.748 0.919 a*** p<0.01, ** p<0.05, * p<0.1. Robust standard errors in parentheses. bThe table displays the results from estimating the regression in (1) just for the countries in Section 7. These are the countries for which we have enough data to calibrate the model. cY25/Y75, Y20/Y80, Y10/Y90, Y5/Y95 and Y2/Y98 represent the share of income of the top 25%, 20%, 10%, 5% and 2% divided by the share of the bottom 25%, 20%, 10%, 5% and 2%. 55