Fiscal Consolidation and Inequality

Transcription

1 Fiscal Consolidation and Inequality Pedro Brinca Miguel Homem Ferreira Francesco Franco Hans A. Holter Laurence Malafry February 15, 2017 Abstract Following the Great Recession, many European countries implemented fiscal consolidation policies, aimed at reducing government debt. In a recent paper, Blanchard and Leigh (2013) show that these policies had significant negative effects on output for European economies and argue that the effects were generally miscalculated by the IMF. Other than the size of the fiscal consolidation they can, however, not find any factor that helps reducing the forecast error. Using the same data, we document a strong positive empirical relationship between higher income inequality and stronger recessive impacts of austerity across European countries. 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 and decreases the proportion of creditconstrained agents in the economy. Credit constrained agents have a higher marginal propensity to consume goods and leisure and their labor supply respond less in response to increases in taxes or decreases in government expenditures. This explains the relation between income inequality and impact of fiscal consolidation programs. Our model produces a cross-country pattern between inequality and the fiscal multipliers, resulting from consolidation, which is quite similar to that in the data. Keywords: Fiscal Consolidation, Income Inequality JEL Classification: E21; E62; H50 We thank Gauti Eggertsson and Robert Kirkby for helpful comments and suggestions. We also thank seminar participants at Nova SBE, University of Victoria-Wellington, Faculty of Economics University of Coimbra, Faculty of Economics University of Porto, Faculty of Economics University of Evora, School of Economics and Management University of Minho. 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 Homem 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 ; the Oslo Fiscal Studies Program. Nova School of Business and Economics, Universidade Nova de Lisboa Center for Economics and Finance at Universidade Porto Department of Economics, University of Oslo Department of Economics, Stockholm University 1

2 1 Introduction The 2008 financial crisis lead several European economies to adopt counter-cyclical fiscal policies. As a result large government deficits ensued - exceeding 10% in several European countries. This created an urgency for fiscal consolidation policies in order to counteract the rising trend of debt to GDP ratios and reduce budget deficits. The process of fiscal consolidation across European countries contributed to the upsurge of several questions in recent literature on the effects of fiscal consolidation. Is fiscal consolidation ultimately contractionary or expansionary? Do long-run benefits outweigh the short-run discomfort? What is the optimal strategy of fiscal consolidation? We relate to this literature by presenting evidence on a dimension that explains the heterogeneous response to fiscal consolidation across countries: income inequality. The fiscal impacts of these austerity policies were wrongly predicted by the International Monetary Fund (IMF). This fact is acknowledged by Blanchard and Leigh (2013), where the authors find evidence that the IMF underestimated the impacts of austerity across European countries, with stronger consolidation causing larger forecast errors. In Blanchard and Leigh (2014), the authors find that no significant alternative explanatory factors, such as precrisis debt levels or budget deficits, banking conditions, a country s external position, among others, help explain the forecast errors. We start by replicating the exercise conducted by Blanchard and Leigh (2013) with a focus on the explanatory power of income inequality. We find that in countries with higher income inequality, the forecast errors were larger thus amplifying the unanticipated recessive impacts of fiscal consolidation. We then follow Ilzetzki et al. (2013), who study the impacts of different factors on fiscal multipliers and find that countries with higher income inequality are associated with stronger declines in output following decreases in government consumption. In conclusion, we show both that income inequality is an important dimension that the IMF failed to take into account when anticipating the recessive impacts of fiscal consolidation and 1

3 that higher income inequality is associated with greater recessive responses to contractions in government consumption. In order to explore this relationship, we use an overlapping generations economy with uninsurable idiosyncratic risk as in Brinca et al. (2016). We calibrate the model to match several moments of the German economy and then simulate a reduction of 10 percentage points in the debt over GDP ratio, over a period of 50 years, financed by either a temporary decrease in government expenditures or a temporary increase in labor income taxation. The results from our simulations align with our empirical findings. Moreover, we find that it is the stochastic component of the income process that drives output s response to consolidation. To rationalize this result, start by noting that fiscal consolidation will shift resources from financing government debt to the productive side of the economy. The resulting increase in the capital stock will raise the marginal product of labor, wages and thus expected lifetime income. This will lead to a positive income effect leading agents to decrease their labor supply and output to fall in the short-run, despite the long run effects of consolidation on output being positive. An increase in income risk will lead to an increase in precautionary savings and a decrease in the share of agents with liquidity constraints. Since unconstrained agents have a more elastic labor supply response to the positive income effect from consolidation, labor supply will fall more when fewer agents are constrained. We assess the transmission mechanism first by simulating our benchmark model calibrated to Germany and decreasing the variance of ability and idiosyncratic risk one at a time. While the fiscal multiplier is not sensitive to changes in the variance of ability, it does respond to the variance of risk. The reasoning for this is that variance of ability does not impact the percentage of agents constrained in the economy, whereas decreasing the variance of risk from the benchmark value 0.44 to 0 raises the percentage of agents constrained from 3.44% to 34.94%, which diminishes the value of the multiplier, as the labor supply is less responsive the larger the percentage of constrained agents. In a multy-country exercise, we calibrate our model to 11 European economies, with 2

4 different levels of variance of idiosyncratic risk. We find a positive correlation between income inequality and the fiscal multiplier. Moreover, we show that countries with higher variance of idiosyncratic risk have a smaller percentage of constrained agents and have larger multipliers, validating our mechanism. We then replicate the empirical exercise of Blanchard and Leigh (2014) expanded with income inequality using data from the model simulations for the 11 countries. We find that the simulations data replicate the empirical results, with income inequality amplifying the fiscal multipliers. The remainder of the paper is organized as follows: we begin by presenting some relevant literature in section 2. In Section 3 we assess the empirical relation between income inequality and fiscal multipliers. In Section 4 we describe the overlapping generation model, define the competitive equilibrium and explain the fiscal consolidation experiment. Section 5 describes the calibration of the model. In Section 6 we inspect the transmission mechanism, followed by the cross-country analysis in Section 7. In Section 8 we replicate the empirical exercise using data from the model simulations. In Section 9 we conclude. 2 Related literature The recent literature on fiscal consolidation has focuses much on it being contractionary or expansionary. On the one hand there are several contributions claiming fiscal consolidation to be contractionary. Guajardo et al. (2014) conclude that a 1% fiscal consolidation causes consumption to decline 0.75%, with the impact on GDP being smaller (0.62%). Yang et al. (2015) provide little support for the fiscal consolidation expansionary effects, attaining a contractionary effect on economic activity. Alesina et al. (2015) conclusions support previous findings, emphasizing that tax-based adjustments produce deep and long recessions. Pappa et al. (2015) assess the effects of the fiscal consolidation in welfare terms, finding evidence that fiscal consolidation causes welfare losses. The authors propose that this welfare loss could be partly compensated by decreasing tax evasion and corruption. 3

5 Winter et al. (2014) suggest that even though there are long-term welfare benefits of fiscal consolidation in the US, they do not outweigh the welfare costs of the transition to the new steady state. The authors also find evidence that inequality is a major driver of welfare effects. On the opposite hand there are contributions in the literature which present evidence of an expansionary effect of fiscal consolidation and welfare gains. Cogan et al. (2013) assess the impact of decreasing debt to GDP ratio, which yields both short and long term benefits. Our paper also relates to the recent literature on the optimal composition of fiscal policy. Romei (2015) addresses the issue of the optimal speed and composition of a fiscal consolidation, evaluating the impact of different speeds of adjustment and of variations in several fiscal instruments on aggregate welfare. Romei concludes that a fiscal consolidation should be done quickly and by cutting public expenditure. Ferriere and Navarro (2014) also propose a model where, in a context of heterogeneous households, an increase in government spending financed by an increase in tax progressivity gives rise to bigger fiscal multipliers than if financed by lump sum taxes. 3 Stylized Facts In this section we replicate Blanchard and Leigh (2013) and Ilzetzki et al. (2013) empirical exercises. With both exercises we present evidence that income inequality amplifies the fiscal multipliers. While the exercise of Blanchard and Leigh (2013) is more focused on the fiscal consolidation period in 2010 and 2011, which allow us to show that multipliers during that consolidation were affected by income inequality, Ilzetzki et al. (2013) exercise is more general and shows that on average over time income inequality affects fiscal multipliers. 3.1 Rational expectation model Blanchard and Leigh propose a standard rational expectation model specification to assess whether the IMF forecasters got fiscal multipliers wrong. The strategy consists on regressing 4

6 forecast errors for real GDP on forecast for fiscal consolidation. The specification tested by Blanchard and Leigh is the following Y i,t:t+1 Ê{ Y i,t:t+1 Ω t } = C + βê{f i,t:t+1 t Ω t } + ɛ i,t:t+1 (1) where C is the constant, Y i,t:t+1 is the cumulative year-on-year GDP growth rate in economy i in periods t and t+1 (years 2010 and 2011 respectively), and the forecast error is measured as Y i,t:t+1 Ê{ Y i,t:t+1 Ω t }, with Ê being the forecast given information Ω at time t. Ê{F i,t:t+1 t Ω t } denotes the planned cumulative change in the general government structural fiscal balance in percentage of potential GDP, and is used as a measure of discretionary fiscal policy. If β is different from zero, then either rational expectations do not hold in producing the forecast or the model misspecifies the effects of fiscal consolidation on GDP. Blanchard and Leigh find in their baseline specification that the multiplier is underestimated by 1. 1 Blanchard and Leigh also run the specification adding several controls that could plausibly have both affected the growth forecast error and been correlated with fiscal consolidation forecasts. The results are robust to controlling for almost any variable and no control is significant. Here we expand equation 1 to account for income inequality. Using the European Union Statistics on Income and Living Conditions (EU-SILC) dataset, we construct various measures of income inequality for the same 26 European economies used by Blanchard and Leigh. 2 The income inequality measures that we use are the 25% highest incomes over the bottom 25%, the highest over the lowest 20%, the top over the bottom 10%, top over bottom 5%, highest 1% over the lowest 1% and the income Gini coefficient. We use the inequality 1 Blanchard and Leigh also account for the fact that this result could have been driven by the fact that planned fiscal consolidations were smaller than actual consolidations. They show that this was not the case, as planned and actual consolidations have a match of almost 1 to 1. 2 The 26 economies used by Blanchard and Leigh were Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Germany, Denmark, Finland, France, Greece, Hungary, Ireland, Iceland, Italy, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovak Republic, Slovenia, Spain, Sweden, Switzerland, and the United Kingdom. 5

7 measures for the year of 2009, to prevent endogeneity problems. The specification that we estimate using the several measures of inequality is the following Y i,t:t+1 Ê{ Y i,t:t+1 Ω t } = C + βê{f i,t:t+1 t Ω t } + αi i,t + ɛ i,t:t+1 (2) where I i,t is the inequality measure for country i. Results presented in table 1 indicate that inequality was one variable that forecasters failed to take into consideration as the different measures of inequality are statistically significant and help to explain the forecast errors, with the R 2 increasing considerably when inequality is included. (1) (2) (3) (4) (5) (6) (7) VARIABLES Blanchard-Leigh inequality 4/1 inequality 5/1 inequality 10/1 inequality 95/1 inequality 100/2 inequality Gini β *** *** *** *** *** *** *** (0.255) (0.239) (0.235) (0.204) (0.246) (0.229) (0.242) α * * ** ** (0.474) (0.363) (0.130) (0.071) (0.030) (0.107) Constant 0.775* 4.135** 4.014** 2.888** 1.944* 2.438*** (0.383) (1.944) (1.742) (1.093) (1.004) (0.787) (3.171) Observations R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 1: GDP forecast errors and income inequality To test whether inequality helps to explain the fiscal multiplier we include in the regression an interaction between the planned fiscal consolidation and the inequality and estimate the following equation Y i,t:t+1 Ê{ Y i,t:t+1 Ω t } = C + βê{f i,t:t+1 t Ω t } + αi i,t 1:t + ιê{f i,t:t+1 t Ω t }I i,t 1:t + ɛ i,t:t+1 (3) Results in table 2 are illustrative of the role played by inequality in explaining the forecast error and the size of the fiscal multiplier. The interaction term is statistically significant and the negative sign of the coefficients suggest that the higher the inequality level and the 6

8 consolidation planned in country i the more forecasters underestimated the fiscal multipliers. In other words, income inequality amplified the fiscal multipliers during the consolidation. (1) (2) (3) (4) (5) (6) (7) VARIABLES Blanchard-Leigh inequality 4/1 inequality 5/1 inequality 10/1 inequality 95/1 inequality 100/2 inequality Gini β *** (0.255) (1.293) (1.086) (0.728) (0.610) (0.410) (2.523) α (0.570) (0.438) (0.150) (0.073) (0.031) (0.143) ι ** ** *** * * (0.292) (0.209) (0.081) (0.035) (0.009) (0.082) Constant 0.775* ** * (0.383) (2.367) (2.111) (1.203) (1.090) (0.842) (4.200) Observations R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 2: GDP forecast errors, income inequality and interaction To validate previous results, we reparametrize the previous specification and take the mean of the planned consolidation and of the inequality measure in the interaction term. Therefore, we estimate the following equation Y i,t:t+1 Ê{ Y i,t:t+1 Ω t } = C+βÊ{F i,t:t+1 t Ω t }+αi i,t 1:t +ι((ê{f i,t:t+1 t Ω t µ F })(I i,t 1:t µ I ))+ɛ i,t:t+1 where µ represent the mean of F and I. Results are presented in table 3 and validate the previous results in table 2 (1) (2) (3) (4) (5) (6) (7) VARIABLES Blanchard-Leigh inequality 4/1 inequality 5/1 inequality 10/1 inequality 95/1 inequality 100/2 inequality Gini β *** *** *** *** *** *** *** (0.255) (0.224) (0.218) (0.206) (0.191) (0.230) (0.256) α * (0.492) (0.379) (0.148) (0.064) (0.044) (0.123) ι ** ** *** * * (0.292) (0.209) (0.081) (0.035) (0.026) (0.082) Constant 0.775* ** (0.383) (2.078) (1.857) (1.193) (0.975) (0.999) (3.645) Observations R-squared Robust standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 3: GDP forecast errors, income inequality and interaction without the means (4) 7

9 3.2 SVAR In this section, we replicate Ilzetzki et al. (2013). Using their data for 44 countries we divide the countries into two groups, the countries with income Gini coefficient above and below the median. Then we run SVARs for each of the groups separately to measure if fiscal multipliers are different between the two groups. We find that for countries with income Gini coefficients above the average the fiscal multiplier is positive and statistically significant, while for the other group of countries the fiscal multiplier is not significantly different from zero. To measure the fiscal multipliers, we adopt Ilzetzki et al. (2013) methodology, who already followed this methodology from Blanchard and Perotti (2002). The relationship between the variables is defines as K AY nt = C k Y n,t k + u n,t (5) k=1 where Y nt is a vector containing the endogenous variables for country n in quarter t. The endogenous variables used by Ilzetzki et al. (2013) are government consumption, output, current account in percentage of GDP and the natural logarithm of the real effective exchange rate. C k is a vector specifying the effects between variables and the variables own lag effects. Given that A is not observable we cannot estimate this regression directly. So we need to pre-multiply everything by A 1. This way, using OLS we can recover the matrix P = A 1 C k and e n,t = A 1 u n,t. So we estimate the equation K Y nt = A 1 C k Y n,t k + A 1 u n,t (6) k=1 To be able to compute the fiscal multipliers we need more assumption on the A so that we can identify the innovations by solving e n,t = A 1 u n,t. We use the same assumption used by Blanchard and Perotti (2002), which is that government consumption cannot react to shocks in output within the same quarter, given that it is predetermined at the beginning of the year in the government budget. We also make assumptions on the ordering of the 8

10 variables (exchange rate follows current account, which in turn follows output). With all these assumptions, we can identify the impulse response functions to a primitive shock in government spending. Impulse response functions (in figure 1) are supportive of the empirical results we find when using the rational expectations model. Fiscal multipliers are bigger in countries with higher income inequality. For the group of countries with below the average income Gini coefficient results are not statistically different from zero. Figure 1: Impulse response functions of output to a 1% decrease in government consumption (95% error bands in gray) Findings from both empirical exercises are in accordance and show us that income inequality plays a role in explaining fiscal multipliers, particularly during the fiscal consolidation in European countries in 2010 and These findings motivate our study on explaining the role of income inequality in assessing the correct impact of a fiscal consolidation using a structural model. 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 similar to the life-cycle economy with heterogeneous agents and incomplete markets used by Brinca et al. (2016). 9

11 Technology There is a representative firm with production function defined by a Cobb-Douglas: Y t (K t, L t ) = K α t [L t ] 1 α (7) with K t being the capital input and L t the labor input in efficiency units. Capital evolution is given by K t+1 = (1 δ)k t + I t (8) with I t being gross investment, with capital depreciation rate δ. The firm hires labor and capital in each period to maximize profits: Π t = Y t w t L t (r t + δ)k t. (9) The factor prices, under a competitive equilibrium, will be equal to their marginal products given by: w t = Y t / L t = (1 α) ( Kt L t ) α (10) ( ) 1 α Lt r t = Y t / K t δ = α δ (11) K t Demographics Our economy is characterized by having J overlapping generations households. All households are born at age 20 and retire at age 65. Retired households face an age-dependent probability of dying, π(j) and at age 100 die with certainty. j denotes the household s age and goes from 1 (household s age 20) to 81 (household s age 100). A period in the model corresponds to 1 year, so an household has a total of 40 periods of active work life. We assume there is no population growth. The size of each new cohort is normalized to 1. Denoting the age-dependent survival probability ω(j) = 1 π(j), at any given period, the mass of alive retired agents of age j 65 still alive is equal to Ω j = q=j 1 q=65 ω(q), by the law of large 10

12 numbers. Besides age, households are heterogeneous across four other dimensions: idiosyncratic productivity, asset holdings, a subjective discount factor uniformly distributed across agents, assuming three distinct values β {β 1, β 2, β 3 } and in terms of ability, which is the starting level of productivity realized at birth. During active work-life an household must choose the amount of hours he wants to work, n, the amount to consume, c, and how much to save, k. Retired households have no labor supply dimension and receive a retirement benefit, Ψ t. We have no annuity markets in the model, so a percentage of households leave unintended bequests which are uniformly redistributed between the households that stay alive. Perhousehold bequest is denoted by Γ. Retired households utility is increasing in the bequest they leave when they die. Labor Income The wage of an individual depends on his/her own characteristics: age, j, permanent ability, a N(0, σa), 2 and idiosyncratic productivity shock or market luck, u, which follows an AR(1) process: u = ρu + ɛ, ɛ N(0, σɛ 2 ) (12) These characteristics will dictate the number of efficient units of labor the household is endowed with. Individual wage will also depend on the wage per efficiency unit of labor w. Thus, the individual i s wage is given by: w i (j, a, u) = we γ 1j+γ 2 j 2 +γ 3 j 3 +a+u (13) γ 1ι, γ 2ι and γ 3ι capture the age profile of wages. 11

13 Preferences The household s utility function, U(c, n), depends on consumption and work hours, n (0, 1], and is defined by: U(c, n) = c1 σ 1 σ χ n1+η 1 + η (14) Retired households gain utility from the bequest they will leave when they die: D(k) = ϕ log(k) (15) Government The government is characterized by running a balanced social security system. It taxes employees and the representative firm both at rate τ ss and pays retirement benefits, Ψ t. Besides this, the government taxes as well consumption, labor and capital income in order to finance public consumption of goods, G t, which enter in the utility function separably, public debt interest expenses, rb t, and lump sum redistribution, g t. We assume the government debt to output ratio, B Y = B t /Y t, is positive and kept constant over time. Tax rates on consumption, τ c, and on capital income, τ k, are flat. On the opposite, the labor income tax is non-linear and we use the functional form proposed in Benabou (2002) and used in Brinca et al. (2016): τ(y) = 1 θ 0 y θ 1 (16) with y being the pre-tax (labor) income, ya the after-tax income, and the level and progressivity of the tax is dictated by the parameters θ 0 and θ 1, respectively. 3. In a steady state, government revenues, denoted by R t and equal to the sum of revenues from labor, capital and consumption taxes, G t, g t and Ψ t remain proportional to output. Given the government s revenues from social security taxes denoted by R ss t, the government 3 See the appendix for a more detailed discussion of the properties of this tax function 12

14 budget constraints is given by ( g 45 + ) Ω j = R G rb, (17) j 65 ( ) Ψ Ω j = R ss. (18) j 65 Time subscripts are suppressed, since they are not needed in steady state. Recursive Formulation of the Household Problem An household is characterized in any period by his savings k, the time discount factor β β 1, β 2, β 3, his permanent ability a, the idiosyncratic productivity shock u and his age j. We can formulate the working-age household s optimization problem over consumption, c, work hours, n, and future asset holdings, k, recursively: [ [ V (k, β, a, u, j) = max U (c, n) + βe u c,k V (k, β, a, u, j + 1) ]],n s.t.: c(1 + τ c ) + k = (k + Γ) (1 + r(1 τ k )) + g + Y L Y L = nw (j, a, u) 1 + τ ss ( ( )) nw (j, a, u) 1 τ ss τ l 1 + τ ss n [0, 1], k b, c > 0 (19) with Y L being household s labor income post social security taxes paid by the employee, τ ss, and payd by the employer, τ ss, and labor income taxes. The problem of a retired household, 13

15 who has a probability, π(j), of dying and gains utility from leaving a bequest, is: [ ] V (k, β,j) = max c,k U (c, n) + β(1 π(j))v (k, β, j + 1) + π(j)d(k ) s.t.: c(1 + τ c ) + k = (k + Γ) (1 + r(1 τ k )) + g + Ψ, k 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: Definition: 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), k (k, β, a, u, j), and n(k, β, a, u, j). 2. Markets clear: K + B = kdφ L = (n(k, β, a, u, j)) dφ cdφ + δk + G = K α L 1 α 3. The factor prices satisfy: ( ) α K w = (1 α) L ( ) α 1 K r = α δ L 14

16 4. The government budget balances: g ( ( ) ) nw(a, u, j) dφ + G + rb = τ k r(k + Γ) + τ c c + nτ l dφ 1 + τ ss 5. The social security system balances: ( ) Ψ dφ = τ ss + τ ss nwdφ j τ ss j<65 6. The assets of the dead are uniformly distributed among the living: Γ ω(j)dφ = (1 ω(j)) kdφ Fiscal Experiment and Transition The fiscal experiment that we analyze in this paper is a decrease of the debt to GDP ratio by 10 percentage points in 50 periods. The government decreases the government spending (G) or increases revenues (R), by increasing the labor tax τ l, so that at the end of 50 periods the debt to GDP ratio is 10 percentage points lower. After debt to GDP ratio is at the new steady state level the economy takes 50 periods to converge to the new steady state. In the context of this experiment a recursive competitive equilibrium is defined as: Definition: Given the initial capital stock, the initial distribution of households and initial taxes, respectively K 0, Φ 0 and {τ l, τ c, τ k, τ ss, τ ss } t= t=1, a competitive equilibrium is a sequence of individual functions for the household, {V t, c t, k t, n t } t= t=1, of production plans for the firm, {K t, L t } t= t=1, factor prices, {r t, w t } t= t=1, government transfers {g t, Ψ t, G t } t= t=1, government debt, {B t } t= t=1, inheritance from the dead, {Γ t } t= t=1, and of measures {Φ t } 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), 15

17 k (k, β, a, u, j), and n(k, β, a, u, j). 2. Markets clear: K + B = kdφ L = (n(k, β, a, u, j)) dφ cdφ + δk + G = K α L 1 α 3. The factor prices satisfy: ( ) α K w = (1 α) L ( ) α 1 K r = α δ L 4. The government budget balances: g ( ( ) ) nw(a, u, j) dφ + G + rb = τ k r(k + Γ) + τ c c + nτ l dφ 1 + τ ss 5. The social security system balances: ( ) Ψ dφ = τ ss + τ ss nwdφ j τ ss j<65 6. The assets of the dead are uniformly distributed among the living: Γ ω(j)dφ = (1 ω(j)) kdφ 7. Aggregate law of motion: Φ t+1 = Υ t (Φ t ) 16

18 5 Calibration Our benchmark model is calibrated to match moments of the German economy. The other countries calibration process is done using the same strategy. Certain parameters can be calibrated outside the model using direct empirical counterparts. We choose Germany as our benchmark since it is the largest economy in the European Union and the second economy with higher income inequality, measured by the variance of log wages, just behind France. Wages To estimate the wage profile through the life cycle (see equation 13), data from the Luxembourg Income and Wealth Study is used and for each country we run the following regression ln(w i ) = ln(w) + γ 1 j + γ 2 j 2 + γ 3 j 3 + ε i (21) with j being the age of individual i. Similar to what Brinca et al. (2016) have done, we use U.S.A data of the Panel Study of Income Dynamics (PSID) to eliminate the idiosyncratic wage shocks. Then we run regression (21) and save the residuals, ε it, which are used to estimate ρ and σ ɛ for the U.S. economy. We then assume σ a to be the same across countries and equal to the average value obtained if we would use the parameters governing the idiosyncratic productivity process estimated for the U.S. and if we would calibrate the σ a endogenously. With the σ a equal across countries, we calibrate the variance of the idiosyncratic shock endogenously. Preferences The Frisch elasticity of labor supply, η, has created a considerable debate in the literature. We decide to set it to 1.0, which is similar to Brinca et al. (2016). The other parameters ϕ, χ, β 1, β 2 and β 3, respectively the utility of leaving bequest, disutility of working more hours and the discount factors, are calibrated endogenously to match the share of wealth of 17

19 the population in the age cohort 75 to 80 from Luxembourg Income and Wealth Study 4, average yearly hours of work from OECD Economic Outlook and the capital to output ratio K/Y, from the Penn World Table 8.0. Taxes and Social Security As in Brinca et al. (2016) and as is described in Section 10.1, we use the Benabou (2002) labor income tax function (equation 16). Using the OECD data on the German labor income tax we estimate θ 0 and θ 1 for different family types. Then, to have a tax function for the single individual household in our model, we calculate the weighted average of both parameters using the weights of each family type on the overall population. 5 Table 8 in the Appendix presents our estimates of the two parameters for all countries. Following Brinca et al. (2016) and using the rate from the bracket covering most incomes, we assume a flat taxes equal to 21.0% and 20.6%, for the social security contributions for the employee, τ SS, and the employer, τ SS, respectively. We also set τ k = 23.3% and τ c = 15.5%. Parameters Calibrated Endogenously To calibrate the parameters that do not have any direct empirical counterparts, ϕ, β 1, β 2, β 3, b, χ and σ ɛ, we use the simulated method of moments so that we minimize the following loss function: L(ϕ, β 1, β 2, β 3, b, χ, σ ɛ ) = M m M d (22) with M m and M d being the moments in the data and in the model respectively. Given that we have seven parameters to calibrate endogenously we need seven data moments to have an exactly identified system. The seven moments we target in the data are the share of wealth of the households in the age cohort 75 to 80 year old, three wealth quartiles, the variance of log wages and capital to output ratio. All targeted moments are 4 Given that we only have data for the U.S. we assume the share of wealth for this age cohort to be equal across countries. 5 As we do not have detailed data for the weight of each family on the overall population for European countries we assume the USA family shares. 18

20 calibrated with less than 2% of error margin, as is displayed in Table 4. Table 5 presents the calibrated parameters Table 4: Calibration Fit Data Moment Description Source Data Value Model Value 75-80/all Share of wealth owned by households aged LWS K/Y Capital-output ratio PWT Var(ln w) Variance of log wages LIS n Fraction of hours worked OECD Q 25, Q 50, Q 75 Wealth Quartiles LWS , 0.027, , 0.026, Table 5: Parameters Calibrated Endogenously Parameter Value Description Preferences ϕ 3.6 Bequest utility β 1, β 2, β , 0.997, Discount factors χ Disutility of work Technology b 0.09 Borrowing limit σ ɛ Variance of risk 6 Inspecting the mechanism In our model output is driven by labor supply and most of the impact of the consolidation on output will come from the labor supply response to this shock. With the decrease in debt the capital labor ratio in the economy will increase, which will drive wages up, causing a positive and permanent income shock to the households. With this positive income shock, households will not need to work as much and will diminish their labor supply, leading to a fall in GDP. What we show in this section is that the correlation between income inequality and fiscal multipliers during a consolidation arrives due to differences in the idiosyncratic risk between countries and not through differences in the variance of the permanent ability. When the fiscal consolidation begins, the constrained agents will not react as much to the positive income shock given that they are constrained. An economy with high income inequality 19

21 arising from idiosyncratic productivity risk induces more precautionary saving behavior. Because households face a relatively higher probability of being hit with a negative shock, there is a lower percentage of constrained agents and consequently a higher decrease in labor supply in response to austerity, which translates in a larger multiplier. Alternatively, given that ability is permanent, the variance of ability will not affect the precautionary saving behavior of the agents, and therefore fiscal multipliers are not sensitive to income inequality arising from changes in the variance of ability. To illustrate the difference between changes in the variance of idiosyncratic risk and ability, and how they affect the consolidation multiplier, we decrease each aspect separately in our benchmark economy and evaluate the evolution of the consolidation multiplier. Variance of ability vs variance of risk We now focus on the two parameters that drive wage inequality in our model to further understand the role that the two play in explaining the correlation between wage inequality and fiscal multipliers during a consolidation. We show that the correlation between wage inequality and fiscal multipliers captured in the empirical section is explained by differences in idiosyncratic risk and not by the permanent ability. To validate our mechanism we run two different experiments: Decrease V ar(ln w) in the benchmark model calibrated to Germany, by decreasing the variance of ability to 0; Decrease V ar(ln w) in the benchmark model by decreasing the variance of the idiosyncratic risk to 0; We perform these two experiments both for the government spending and the labor tax consolidations. In both cases we adjust the gamma0 by a constant to guarantee that the average productivity stays unchanged. 20

22 Figure 2: Impact multiplier for the labor tax consolidation in the benchmark model for Germany and when shutting down the variance of ability (left panel) and variance of risk (right panel). In figure 2 it can be seen the variations induced in the labor tax consolidation multiplier from variations in the ability variance and the risk variance. The fiscal multipliers are not sensitive to variations in ability, although it is to variations in the variance of risk. Moreover, when decreasing the variance of risk the multiplier diminishes in absolutes terms, in accordance with the empirical findings. The government spending consolidation generates similar results. As can be seen in figure 3 the variations induced in the multiplier from variations in the ability variance produce the opposite results to the empirical findings. On the opposite side, when decreasing the variance of risk, which diminishes the wage inequality, the multipliers is reduced. What justifies the different response of fiscal multiplier to changes in the variance of ability and in the variance of risk is the impact that these two parameters have on the percentage of constrained agents. While reducing the variance of ability does not affect the precautionary saving behavior of the agents, as ability is a permanent shock, shrinking the variance of risk diminishes the probability of agents being hit with a negative shock, which causes agents to save less and be less afraid of being constrained. The relation between variances of ability and risk and the percentage of credit constrained agents can be seen in 21

23 Figure 3: Impact multiplier for the government spending consolidation in the benchmark model for Germany and when shutting down the variance of ability (left panel) and variance of risk (right panel). figure 4. In figure 5 it can be seen the relation between fiscal multiplier and the percentage of constrained agents, when changing the variance of risk, which illustrates the mechanism described before: credit constrained agents have a less elastic response to the positive income shock. So, the larger the percentage of credit constrained agents in the economy the smaller the labor supply response and consequently the smaller the GDP fall. 7 Cross country analysis In the previous section we show that our model is capable of reproducing the empirical relation between income inequality and fiscal multipliers. Moreover, we show that the transmission mechanism that explains this relation happens through the households idiosyncratic productivity shock and not through permanent ability. In this section we calibrate the model to 11 European countries 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. Besides, we calibrate the model to match equally the share of wealth owned by households aged 22

24 Figure 4: Percentage of agents constrained in the benchmark model for Germany and when shutting down the variance of ability (left panel) and variance of risk (right panel). Figure 5: Impact multiplier of the G consolidation (left panel) and of the τ l consolidation (right panel) and the percentage of agents constrained in the benchmark model for Germany and when shutting down the variance of risk. 23

25 Figure 6: 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 0.28, p-val 0.42), while on the right panel we have the cross-country data for a consolidation done by increasing the labor tax (correlation coefficient -0.45, p-val 0.16). 75 to 80, distribution of wealth, hours worked and capital output ratio. We also match country specific characteristics such as taxes. Tables 9 and 10 summarize the wealth distribution, the country specific data that we use to calibrate the model as well as country specific parameters estimated outside of the model. Table 11 summarizes the country specific parameters estimated through simulated method of moments as described in section 5. Parameters kept constant for all the countries, such as the variance of ability, are summarized in table 12. In figure 6 we have on the y-axis the impact multipliers of the consolidation through G on the left panel and through τ l on the right panel, and on the x-axis the variance of log wages, the measure used in our model to match income inequality in the data. It can be seen that the higher the income inequality the larger the multiplier in absolute value for both types of consolidations. The multipliers range from 0.37 for Finland to 0.51 for Greece in the G consolidation and from -1 for Greece to -2.2 for Sweden in the labor tax consolidation. To check if the transmission mechanism from the previous section still holds in the cross- 24

26 country analysis we first verify if the relation between variance of idiosyncratic risk and percentage of agents constrained continues to be negative, with higher variance of risk inducing a precautionary saving behavior, decreasing the percentage of agents constrained. In figure?? it can be seen that this relation still holds, with the correlation coefficient between variance of idiosyncratic risk and percentage of agents being -0.86, with the p-value being In the previous section, we established that labor supply of constrained agents is less elastic to the fiscal shock, and so, the larger the percentage of agents constrained the smaller the multiplier. So, if the mechanism still holds, countries with larger percentage of agents constrained should have smaller multipliers in absolute value. In figure 8 it can be seen the relation between the percentage of constrained agents and the impact multiplier of both the consolidation through a decrease in G (left panel) and through an increase in labor tax (right panel). The mechanism still holds, with countries with larger percentage of agents constrained experiencing a smaller fall in output. It can also be noticed that consolidation through an increase in the labor tax produces deeper recessions across countries. This is not surprising, given that a temporary increase in the labor tax is equivalent to an increase in the cost of working, causing households to diminish even more their labor supply and producing deeper recessions. 8 Replication of the empirical exercise In section 3.1 we replicate Blanchard and Leigh (2014) rational expectation model and we show that income inequality was one variable that the IMF failed to consider when predicting the fiscal multipliers for the consolidations across European countries. In sections 6 and 7 we show that it is the stochastic component of the income process that has an impact on the response of output to the consolidation. To replicate the empirical exercise from section 3.1 using data from the simulations to different countries we need to create the forecast for the output response to the fiscal 25

27 Figure 7: Percentage of agents constrained in the y-axis and variance of idiosyncratic risk on the x axis. Correlation coefficient of and p-value of 0.00 Figure 8: 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 -0.56, p-val 0.08), 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 0.09) 26

28 shock. Our forecast will be given by the output response when we shut down the stochastic component of the income process. In the empirical exercise we establish that IMF did not take income inequality into account when predicting the output response to the consolidation. So, to do our forecast, we shut down the stochastic component of the income process, that is the component of the income process that we find to matter in explaining the output response to the fiscal shock. Then, our forecast error for each country is the difference between the output response in the benchmark case and the output response when we shut down the idiosyncratic risk. In figure?? it can be seen the growth forecast errors of simulations for the consolidation done by decreasing government spending and the different income inequality measures that we use in section 3.1. The correlation coefficients between the growth forecast errors and the different measures of income inequality all present the right sign: the larger the income inequality the more negative the growth forecast error, meaning that the multiplier was more underestimated in countries with larger income inequality. Moreover, the coefficients are all statistically significant, exception for the correlation with the income Gini coefficient. In figure?? it can be seen the same correlation between the different income inequality measures and the growth forecast errors for the consolidation done by increasing the labor tax. The same correlation is seen, with income inequality amplifying the growth forecast error. In table 6 it can be seen the results of equation 3 for the G consolidation using the data from the model simulations. Notice, that as in table 2, the coefficients for the interaction between the different measures of income inequality and the fiscal consolidation are statistically significant and indicate that the fiscal multiplier is amplified by income inequality. In table 7 it can be found the results for equation 3, but now for the labor tax consolidation. Once again, the coefficients associated with the interaction are statistically significant and indicate that the fiscal multiplier is amplified by income inequality. 27

29 Figure 9: Different measures of income inequality in the x-axis and growth forecast errors for the G consolidation experiment in the y-axis. (1) (2) (3) (4) (5) (6) (7) VARIABLES Blanchard-Leigh inequality 4/1 inequality 5/1 inequality 10/1 inequality 95/1 inequality 100/2 inequality gini G consolidation * 0.090* 0.074* 0.065* 0.064** (0.014) (0.045) (0.041) (0.034) (0.030) (0.026) (0.261) Inequality ** ** ** ** ** (0.251) (0.203) (0.119) (0.079) (0.052) (0.048) Interaction * * * * ** (1.255) (1.013) (0.590) (0.391) (0.253) (0.398) Constant * 0.020* 0.016* 0.014* 0.014** (0.003) (0.009) (0.009) (0.007) (0.006) (0.006) (0.032) Observations R-squared Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 6: GDP forecast errors for the G consolidation and income inequality 28

30 Figure 10: Different measures of income inequality in the x-axis and growth forecast errors for the τ l consolidation experiment in the y-axis. (1) (2) (3) (4) (5) (6) (7) VARIABLES Blanchard-Leigh inequality 4/1 inequality 5/1 inequality 10/1 inequality 95/1 inequality 100/2 inequality gini τ l consolidation (0.127) (0.375) (0.342) (0.279) (0.244) (0.234) (2.467) Inequality * * ** * * (1.085) (0.878) (0.516) (0.345) (0.249) (0.238) Interaction * 6.832* 4.800* (10.944) (8.837) (5.165) (3.441) (2.465) (3.783) Constant * (0.012) (0.040) (0.036) (0.030) (0.027) (0.026) (0.156) Observations R-squared Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1 Table 7: GDP forecast errors for the τ l consolidation and income inequality 29

31 9 Conclusion In this paper, we provide empirical evidence that income inequality is an important factor for studying the impacts of fiscal consolidation and that it was a relevant dimension that the IMF did not take into account, leading to large and unanticipated recessive impacts of fiscal consolidation efforts in European economies, in the aftermath of the great Recession. To explain this finding, we develop a life-cycle, overlapping generations economy with uninsurable labor market risk. Results from simulating a decrease of 10 percentage points of the debt to GDP ratio in our model are in accordance with the empirical findings. Moreover, we find that the component of the wage process that explains the amplification effect that income inequality has on the fiscal multipliers is the stochastic one. The reasoning for this is that while the percentage of agents constrained in the economy is sensitive to the variance of the idiosyncratic risk, it is not to the permanent ability shock. In the scenario where there is no risk, agents will have a less precautionary saving behavior and the percentage of credit constrained agents in the economy will raise. A decrease of government debt raises the amount of productive capital in the economy, which leads to a permanent positive income shock causing labor supply to fall. In the scenario with no risk and more credit constrained agents, the labor supply will be less elastic to the fiscal shock and consequently the output response to the shock will be smaller. We assess our mechanism in a cross-country exercise. We calibrate our model to match several moments from 11 European economies. We find that countries with lower variance of idiosyncratic risk have a larger percentage of credit constrained agents and consequently the multiplier in these countries is smaller. Moreover, we are able to replicate the empirical exercise results using data from the model simulations, despite having only 11 observations. In the paper, we analyze a debt reduction by either a decrease in government spending or an increase in the labor tax. Our findings suggest that labor tax consolidations produce deeper recessions than government spending consolidations. A raise in labor tax discourages agents from working, causing a larger fall in labor supply, which translates into larger 30