redistributive fiscal policies and macroeconomics phân phối lại chính sách tài khóa vĩ mô

Essays on Redistributive Fiscal Policies and Macroeconomics by Mariano Eduardo Spector B.A Economics, Universidad Torcuato di Tella (2011) M.A Economics, Universidad Torcuato di Tella (2013) Submitted to the Department of Economics in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY June 2020 c 2020 Mariano Eduardo Spector Author Department of Economics May 15, 2020 Certified by Iván Werning Robert M Solow Professor of Economics Thesis Supervisor Certified by Daron Acemoglu Elizabeth and James Killian Professor of Economics Thesis Supervisor Accepted by Amy Finkelstein John & Jennie S MacDonald Professor of Economics Chairman, Departmental Committee on Graduate Studies Essays on Redistributive Fiscal Policies and Macroeconomics by Mariano Eduardo Spector Submitted to the Department of Economics on May 15, 2020, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract This thesis consists of three chapters Chapters and study redistributive fiscal policies Chapter analyzes the role of asymmetric information in frictional labor markets Fiscal stimulus during the Great Recession consisted mainly of transfers, rather than government purchases Chapter analyzes the role of marginal propensities to consume (MPCs) in shaping the effect of such policies I construct a continuous-time New Keynesian model with heterogeneous overlapping generations which allows for arbitrary MPC heterogeneity I characterize the output multipliers of fiscal transfers, and show that the role of MPCs is mainly to determine the timing of the fiscal stimulus The relation between this timing and the cumulative effect on output is, however, ambiguous Indeed, I show that transfers to low-MPC consumers may generate a higher cumulative effect on output From a normative perspective, however, there is no ambiguity: with larger differences in MPCs, optimal policy can obtain macro stabilization with smaller welfare losses In Chapter 2, I analyze redistributive policies when households are heterogeneous with respect to both their MPCs and their risk aversion I characterize transfer multipliers in a model in which capital is subject to uninsurable idiosyncratic risk Based on survey data, I assume that MPCs and risk aversion are positively correlated in the population A redistribution from low-MPC, low-risk aversion households to high-MPC, high-risk aversion households creates two opposing effects: a higher mean MPC tends to stimulate aggregate demand, but an increase in the mean risk aversion tends to depress asset prices, generating a negative income effect on consumption In Chapter 3, I study a frictional labor market with horizontally differentiated workers Firms have incomplete information about the skills of workers who apply to their vacancies Workers self-insure against unemployment risk by applying to jobs for which their skills are not well suited This decreases firms’ incentives to create vacancies by deteriorating the quality of the average applicant Workers thus impose a negative externality on each other, which makes the equilibrium inefficient However, although workers apply to too many jobs, I show that unemployment can be too low or too high Welfare-improving government policies are considered Thesis Supervisor: Iván Werning Title: Robert M Solow Professor of Economics Thesis Supervisor: Daron Acemoglu Title: Elizabeth and James Killian Professor of Economics Acknowledgments I am deeply indebted to my advisors, Iván Werning and Daron Acemoglu Through countless conversations over the years I have spent at MIT, they have provided mentorship, encouragement and support, and they have had a profound impact on my approach to economic questions I would also like to particularly thank Robert Townsend He has been extremely generous with his time and offered not just insightful observations about this dissertation but also guidance and support during my doctoral studies This dissertation has benefited as well from discussions with Ricardo Caballero, Marios Angeletos, Alp Simsek and Martín Beraja I am very thankful for their comments and suggestions, which have helped shape this thesis to its final form Special thanks also go to my professors at Universidad Torcuato di Tella, Andrés Neumeyer, Marzia Raybaudi, Leandro Arozamena, Andrea Rotnitzky, Emilio Espino, Martín Sola and Martín Besfamille, for their mentorship and encouragement to pursue this PhD I would also like to express my gratitude to my fellow MIT graduate students I have greatly enjoyed going through this journey together with my classmates of the 2014 Economics PhD cohort I have also been fortunate to share this experience with my fellow Di Tella graduates, Andrés Sarto, Nicolás Caramp and Juan Passadore This journey would not have been possible without the love and support of my family back home This thesis is dedicated to my parents, Jorge and Susy, and my brother, Javier JEL codes: E21, E32, E62 Contents Redistributive Fiscal Policy and Marginal Propensities to Consume 13 1.1 Introduction 13 1.2 A model of heterogeneous MPCs 19 1.3 Transfer multipliers 26 1.3.1 1.4 A neutrality result: one-time transfers in an infinitely lasting liquidity trap with fixed prices 27 1.3.2 Back to the general case 32 1.3.3 Discussion of assumptions 41 1.3.4 Transfer multipliers with particular monetary policy rules 44 Extensions 49 1.4.1 Government purchases multipliers 50 1.4.2 Redistributive effect of government policies 54 1.5 Welfare 55 1.6 A Bewley-Huggett-Aiyagari model 60 1.6.1 Calibration 62 1.6.2 Partial equilibrium response 63 1.6.3 Government expenditure financed with an up-front tax 64 1.6.4 Transfer multiplier 66 1.6.5 Endogenous interest rate 68 1.6.6 Sticky prices 72 1.7 Conclusion 73 1.8 Appendix 75 1.8.1 Proofs for Section 1.2 75 1.8.2 Proofs for Section 1.3 78 1.8.3 Proofs for Section 1.4 97 1.8.4 Proofs for Section 1.5 101 1.8.5 Proofs for Section 1.6 114 1.8.6 Optimal policy with rigid prices, infinite liquidity trap and exponential natural rate Redistributive Fiscal Policy and Heterogeneous Risk Aversion 116 123 2.1 Introduction 123 2.2 First approach: a two-period model 128 2.3 Empirical evidence 135 2.4 An infinite horizon model 2.5 141 141 2.4.1 Environment 2.4.2 Household’s problem 144 2.4.3 Aggregation 144 2.4.4 Government 145 2.4.5 Equilibrium 146 2.4.6 Law of motion of the wealth distribution 147 2.4.7 Returns to capital and an amplification mechanism 148 2.4.8 Steady state and log-linearization 149 Shocks to the the wealth distribution 150 2.5.1 Neoclassical regime 150 2.5.2 Exogenous risk-free rate 152 2.6 Welfare 156 2.7 Conclusion 158 2.8 Appendix 160 2.8.1 Extension: Taylor rule and Phillips Curve 160 2.8.2 Proofs for Section 2.2 163 2.8.3 Proofs for Section 2.4 166 10 which is equivalent to saying that El∗ [ω G (s)] = El∗ [ω N (s)] I want to prove that I can find τ1 that implements the efficient allocation From the value functions we have VF (s) = Y (s) − ω G (s) , ρ+δ VW (s) = ω N (s) + δVU ρ+δ and Therefore, the surplus from a match is S (s) = VW (s) + VF (s) − VU = Y (s) − ρVU wN (s) − wG (s) + ρ+δ ρ+δ Using the Nash bargaining condition (3.11) we find: ω G (s) = φY (s) + (1 − φ) [ρVU − (ω N (s) − ω G (s))] , ω N (s) = φτ − τ1 (φY (s) + (1 − φ) ρVU ) − φ + (1 − φ) (1 − τ ) − τ1 We need to show that we can choose expression for VU , τ1 so that it implements (l∗ , θ∗ ) Replacing in the we find (ρ + δ) b + 2lκθ1−α El ω N (s) ρVU = ρ + δ + 2lκθ1−α If the workers choose choosing τ0 l∗ , then ρVU is the same as if there were no taxes because we are so that net revenue from the tax schedule is zero bargaining threat point is the same, the submarket tightness 213 θ Therefore, since the Nash will by θ∗ The condition for workers to choose l∗ is VW (l∗ ; l∗ , θ∗ ) = VU (l∗ , θ∗ ) ω N (l∗ ) + δVU (l∗ , θ∗ ) = VU (l∗ , θ∗ ) ρ+δ ω N (l∗ ) = ρVU (l∗ , θ∗ ) Replacing the expression for ωN that we found above, with a bit of manipulation we can express this as a linear equation in τ 1, which always has a solution The last thing we need to show is that τ > 0, τ < We know if there were no taxes workers would want to choose an application rule higher than l , so that VWN o T axes (l∗ ; l∗ , θ∗ ) > VW (l∗ ; l∗ , θ∗ ) = VU (l∗ , θ∗ ) Since the worker who takes a job at distance l∗ is worse off with the taxes than without taxes, this must mean that this workers is a net payer of taxes, and since the tax schedule is affine this can only happen if the lump-sum component of the schedule takes money away from workers and the marginal component subsidizes them 3.8.3 Proofs for Section 3.5 TFP Let us show that ∂lCE (A) ∂A be equivalent to a drop in c, (3.17), let us take a given l, the function θF E (l, c), < By construction, the effect on so we can alternatively show that and see how an increase in θF E (l) of an increase in ∂c affects θ > A will Using equation That is, if we define we want to find the sign of the partial derivative with respect to Differentiating the equation, it is trivial that function c l ∂lCE (c) ∂θ FE (l,c) ∂c will be shifted downwards when c < c This means that the implicit increases (the shift is not necessarily parallel) Then, using the implicit function theorem in equation (3.18) (after replacing 214 θF E (l) into the equation), we find that ∂VU (lCE ,θ(lCE ,c)) ∂θ(lCE ,c) ρ ∂lCE (c) ∂θ ∂c = ∂VU (lCE ,θ(lCE ,c)) ∂θ(lCE ,c) CE ∂c Y (l ) − ρ ∂θ ∂l The numerator is clearly negative As for the denominator, while its sign is not obvious at first sight, we know that it has to be negative because the curve Y (l) − ρVU (l, θ (l)) only intersects the axis once from above (we are assuming uniqueness of the equilibrium) UI Benefits I first want to show lCE decreases with the UI benefits This is equivalent to showing that, if we parametrize the model by the home production b, then ∂lCE (b) ∂b < Recall that we had defined χ (l) ≡ Y (l) − b − − λ (l, θ (l, b)) (El [Y (s)] − Y (l)) , λ (l, θ (l, b)) and the competitive equilibrium is characterized by χ lCE = By the Implicit Function Theorem, ∂χ ∂lCE ∂b = − ∂χ ∂b ∂l We know that equilibrium, χ ∂χ(lCE ) ∂l < because we proved before that when we assume uniqueness of the only intersects the horizontal axis from above Therefore, sign ∂lCE ∂b = sign ∂χ ∂b If we compute the derivative, we get ∂χ 2lκφθ (l, b)1−2α − α ∂θα (l, b) = −1 − (El [Y (s)] − Y (l)) ∂b ρ+δ α ∂b 215 Recall that the free-entry condition (3.17) can be written as θα = El [Y (s)] − ρVU (l, θ, b) κ (1 − φ) , c ρ+δ so differentiating we get κ (1−φ) ∂(ρVU (l,θ,b)) c ∂θα ρ+δ ∂b =− κ (1−φ) ∂(ρV U (l,θ,b)) ∂b 1+ c α ρ+δ ∂θ Differentiating (3.16) we find that ∂ (ρVU (l, θ, b)) = λ (l, θ) , ∂b and ∂ (ρVU (l, θ, b)) ∂λ (l, θ) = (b − El [Y ]) α ∂θ ∂θα (ρ + δ) 2lκ 1−α θ1−2α φ α = (El [Y ] − b) ρ + δ + 2lκθ1−α φ Replacing all these expressions back into ∂χ , we obtain ∂b 1−2α 1−α κ (El [Y (s)] − Y (l)) 2lκφθ(l,b) (1 − φ) ρ+δ+2lκθ 1−α ∂χ ρ+δ α c φ = −1 + 1−α 1−2α κ (ρ+δ) 2lκ θ φ (1−φ) ( ) ∂b α + c ρ+δ (El [Y ] − b) (ρ+δ+2lκθ1−α φ) = −1 + κ c (1 − φ) 2lκφθ(l,b)1−2α 1−α α (El [Y (s)]−Y (l)) ρ+δ ρ+δ+2lκθ1−α φ 2lκ 1−α θ1−2α φ (El [Y ]−b) α + κc (1 − φ) ρ+δ+2lκθ 1−α φ ρ+δ+2lκθ1−α φ Finally, note that equation (3.18) is equivalent to El [Y (s)] − Y (l) El [Y ] − b (El [Y ] − Y (l)) = (El [Y ] − b) ⇐⇒ = , λ (l, θ) ρ+δ ρ + δ + 2lκθ1−α φ so the second term of ∂χ ∂χ is lower than one and therefore ∂b ∂b < 0, which is what we wanted to prove Let us now consider the effect on θ While we are doing the same comparative statics exercise, I will write things a bit differently to make it easier to identify the sign of the 216 derivative Let us write the equilibrium equations (3.17),(3.18) respectively as h1 (l, θ) = (ρ + δ) θα + 2lκφθ − κ (1 − φ) El [Y − b] = c h2 (l, θ) = Y (l) − λ (l, θ) b − (1 − λ (l, θ)) El [Y ] = From the IFT, we get sign ∂θ ∂b = −sign   ∂h1 ∂l ∂h1 ∂b    ∂h2 ∂l ∂h2 ∂b  (it is quite straightforward to show that the condition , χ lCE < is equivalent to having the denominator in the IFT expression being positive) These derivatives are ∂h1 ∂l ∂h1 ∂b ∂h2 ∂l ∂h2 ∂b κ 2κφθl − (1 − φ) (Y (l) − El [Y ]) l c κ = (1 − φ) c = = Y (l) = −λ (l, θ) , so we get (with a bit of reordering of terms, and evaluating at b = 0, without loss of generality) that ∂h1 ∂l ∂h1 ∂b ∂h2 ∂l ∂h2 ∂b κ (1 − φ) [(−lY (l)) − λ (l, θ) (El [Y ] − Y (l))] − 2κφθlλ (l, θ) c   λ(l,θ) + (−lY (l)) − κ  − 2κφθlλ (l, θ) = (1 − φ)  l l n (x))−(−Y n (l))]dxds [(−Y c s −λ (l, θ) = l κ λ (l, θ) (1 − φ) (−lY (l)) − − 2κφθlλ (l, θ) c κ λ (l, θ) = (1 − φ) (−lY (l)) − − λ (l, θ) El [Y ] + λ (l, θ) (ρ + δ) θα c λ (l, θ) κ = (1 − φ) (−lY (l)) − − (El [Y ] − Y (l)) + λ (l, θ) (ρ + δ) θα , c > 217 where the last expression is positive, because given our assumption of concavity of El [Y ] − Y (l) difference satisfies 18 Y (s), the Y (l)(−l) El [Y ] − Y (l) < The proof that welfare is increasing in UI benefits near the competitive equilibrium with k=0 is almost trivial The change in welfare can be written as dY = where at lCE , θCE k = 0) ∂Y ∂θ dθ + (l,θ)=(lCE ,θCE ) ∂Y ∂l dl, (l,θ)=(lCE ,θCE ) is the competitive equilibrium without UI benefits (that is, I am evaluating Note that there is no partial derivative with respect to k because since UI benefits are a transfer, they are not directly welfare relevant, they are only relevant through their effect on (l, θ) Under the Hosios condition, we know that free entry is optimal for any given l ∂Y ∂θ (l,θ)=(lCE ,θCE ) ∂Y ∂l (l,θ)=(lCE ,θCE ) We know that 0 ∂ ρVU l,{θξ } ξ ∂θξ ξ∈R ∂θξ dξ ∂l ξ > ∂θξ  ∂θξ  dξ , Ξ ∈ R ∂l Then, we would get that ∂θΞ (l) ∂l < ∀Ξ, we obtain a contradiction, so this concludes the proof The last proof remaining is the case in which the noise disappears in the limit Reordering 221 the terms of the last expression as αθΞα−1 ∂θΞ (l) + κ (1−φ) ∂l c ρ+δ ∂ ρVU l, {θξ }ξ∈R ξ ∂θξ ∂El|ξ [Y (s)] ∂θξ dξ = , Ξ ∈ R ∂l ∂l We can think of this as a linear system that 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McKay and Reis (2016) and Oh and Reis (2012) focus on redistributive fiscal policies Auclert and Rognlie (2018) analyze the implications of changes in the wealth distribution for aggregate demand,... consists of three chapters Chapters and study redistributive fiscal policies Chapter analyzes the role of asymmetric information in frictional labor markets Fiscal stimulus during the Great Recession... Universidad Torcuato di Tella, Andrés Neumeyer, Marzia Raybaudi, Leandro Arozamena, Andrea Rotnitzky, Emilio Espino, Martín Sola and Martín Besfamille, for their mentorship and encouragement to pursue