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Expectations Formation and Optimal Taxation

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Luis E. Rojas (MOVE, UAB and Barcelona GSE)

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Expectations Formation and Optimal Taxation

  1. 1. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Expectations Formation and Optimal Taxation Research Overview Luis E. Rojas MOVE, UAB and Barcelona GSE October 2016, Barcelona GSE Trobada Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  2. 2. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Macroeconomics and Economics of Information Paper #1: “Optimal Redistribution With a Shadow Economy” Joint with P. Doligalski. 1. Information asymmetries - optimal taxation The government does not know the workers productivities (Optimal labor income taxation (Mirrlees 1971). Also, cannot observe shadow income. Workers with formal and shadow productivities decide where to work depending on the tax scheme. Subsidy eligibility can explain the large shadow economy in Colombia. Having a shadow economy may allow for a higher tax collection. Welfare Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  3. 3. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Macroeconomics and Economics of Information Paper #2: “Expectations Formation and Investment During Recessions” 1. Information asymmetries 2. Imperfect market knowledge Agents do not know the mapping from fundamentals to market outcomes. Conjecture the relationship and fit to observed data. Self-confirming equilibria (Sargent 2001). + Firms expectations about potential demand Firms have to decide whether or not to invest in the creation of a new good, having uncertainty about demand. Investment recovers slower than consumption. Corporate income tax deductions can be a better policy relative to investment subsidies. Policy Comparison Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  4. 4. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Macroeconomics and Economics of Information Paper #3: “Learning in Sovereign Debt Markets” 1. Information asymmetries 2. Imperfect market knowledge 3. Information asymmetries + Imperfect market knowledge Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  5. 5. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Sovereign debt Mostly bonds. Large asset class with many market participants. In 1950 it accounted for 22% of the market value of worldwide assets, and for 19% in 2010. Default is a recurrent feature More than 240 sovereign defaults occurred over the period 1824-2004. Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  6. 6. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Pricing of sovereign debt Default history matters. A default episode is typically followed by: 1) a raise in spreads and 2) a positive surplus for the lenders. 1. An increase of the haircut by one percentage point generates an increase of 4-5 basis points in spreads 4 to 7 years after the settlement. Cruces and Trebesch (2013) 2. Investors risk aversion and “objective” default probabilities are not enough to explain this feature. Benczur and Ilut (2016) Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  7. 7. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Pricing of sovereign debt Default history matters. A default episode is typically followed by: 1) a raise in spreads and 2) a positive surplus for the lenders. 1. An increase of the haircut by one percentage point generates an increase of 4-5 basis points in spreads 4 to 7 years after the settlement. Cruces and Trebesch (2013) 2. Investors risk aversion and “objective” default probabilities are not enough to explain this feature. Benczur and Ilut (2016) My hypothesis: Learning and overreaction. Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  8. 8. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Theory building blocks Sovereign debt model of incomplete markets (Arellano (2008),...) Internal Rationality (IR) (Adam and Marcet (2011), Adam, Marcet and Nicolini (2016)). Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  9. 9. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Theory building blocks Sovereign debt model of incomplete markets (Arellano (2008),...) Internal Rationality (IR) (Adam and Marcet (2011), Adam, Marcet and Nicolini (2016)). In RE there is an equilibrium mapping from fundamentals (debt, GDP) to default probabilities that creditors are assumed to know. In IR creditors beliefs are described by a joint distribution of fundamentals and default prob. Creditors learn about the default probability from experience. Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  10. 10. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Model: The government The government seeks to maximize ∞ t=0 βt E u(ct , gt ) where ct is private consumption and gt is the public provision of goods. The resource constraint of the government is gt + et − τyt ≤ qt (bt , yt )bt − bt−1 where et is an expenditure shock; yt is GDP and follows a Markov process; bt is sovereign debt issued at t; and qt (bt , yt ) is the market price of the bonds. Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  11. 11. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Model: The government The government seeks to maximize ∞ t=0 βt E u(ct , gt ) where ct is private consumption and gt is the public provision of goods. The resource constraint of the government is gt + et − τyt ≤ qt (bt , yt )bt − bt−1 where et is an expenditure shock; yt is GDP and follows a Markov process; bt is sovereign debt issued at t; and qt (bt , yt ) is the market price of the bonds. Default: Every period the government decides whether to repay or default. In case of default the government suffers a α loss of GDP every period until a settlement with the creditors is achieved.Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  12. 12. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Model: Creditors International creditors are risk neutral, competitive and have access to a risk free asset with gross return 1 + r. Let vt be the market value of the bonds maturing at t once the default decision is announced. The system of beliefs of the creditors is given by a probability measure P that specifies the joint distribution of {vt , yt , bt }∞ t=0. P is given as a primitive of the analysis and does not necessarily coincide with the equilibrium distribution of {vt , yt , bt }∞ t=0. Taking P as given the creditors maximize their utility, following the concept of Internal Rationality. Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  13. 13. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Pricing of debt The expected market value can be written as: EP t vt+1 = y∈Y EP t vt+1 yt+1 = y PP t yt+1 = y where EP t is the expectation operator with the probability measure P and conditional on the history {vs, ys, bs}t s=0 Assuming all investors have the same system of beliefs P we have that the non-arbitrage condition is: qt (bt , yt ) = y∈Y EP t vt+1 yt+1 = y PP t yt+1 = y 1 + r Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  14. 14. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Recovering the REE The Recursive Rational Expectations equilibrium corresponds to the particular case where EP t vt+1 yt+1 = y = µ(bt , y) PP t yt+1 = y = π y | y where µt (st−1, yt ) is the mean of repayment at t conditional on t − 1 states st−1 and contemporaneous income yt . Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  15. 15. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Subjective beliefs The system of subjective beliefs is characterized by the following: 1. Creditors believe that the process of vt when outstanding debt is b at the level of GDP y corresponds to: vt (b, y ) = mt (b, y ) + t (1) mt (b, y ) = mt−1(b, y ) + ut where t ∼ N(0, σ ) and ut ∼ N(0, σu) are independent from each other and also from { t , yt , bt }t s=0. 2. The subjective beliefs coincide with the objective transition probabilities PP t yt+1 = y = π y | y Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  16. 16. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Simulation Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  17. 17. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Model implications The other dimensions of the sovereign debt market to study are: Clusters of Default. If creditors learn about a group of countries: There is cyclical coordination in high debt exposure (loaded gun) A recession in one country can generate a joint recession. (trigger) Dynamic optimal contract. The learning procedure implements a spread pattern that resembles the optimal contract. Empirical validity: The reputational concerns of governments. Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  18. 18. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Roadmap Where am I heading to? A theory for policy implementation that acknowledges that agents will use their “limited” knowledge and experience to assess the effects of policy. Policy should be designed to anchor expectations and facilitate coordination on the intended outcome Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  19. 19. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Welfare with the shadow economy Back wf X is formal productivity of type X ∈ {L, H}. 0 ¯ws H wf H Shadow productivity of type H (ws H) ¯ws L wf L ShadowproductivityoftypeL(ws L) ↑positiveredistributiongain↑ ↑ positive efficiency gain ↑ Shadow economy improves welfare Shadow economy does not affect welfare Shadow economy hurts welfare Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  20. 20. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Comparison of policies Back c - cost of the investment; p probability of success πt profits; τ tax Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  21. 21. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Government problem Starting from the case where the sovereign is not in default in period t, the value functions have to satisfy: V (bt−1, yt , et , qt (b, y)) = max (dt ,gt ,bt )∈C(bt−1,yt ,et ,qt (b,y)) (1 − dt ) u(ct , gt ) + βE V(bt , yt+1, et+1, qt+1(b, y)) . . . +dt u(ct , gt ) + βE Vd ((1 + r)bt−1, yt+1, et+1, qt+1(b, y), yt ) where ct = (1 − τ) (yt − dt αyt ) and C(bt−1, yt , et , qt (b, y)) is the feasibility set. It is fully characterized by the constraints: gt + et ≤ τ (yt − dt αyt ) + (1 − dt ) (qt (bt , yt )bt − bt−1) dt ∈ {0, 1} Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  22. 22. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Government problem Now, considering the case where the government starts the period in default. Then we have that the value functions satisfy: Vd (bt−1, yt , et , qt (b, y), y∗) = max (dt ,gt ,bt )∈Cd (bt−1,yt ,et ,qt (b,y)) (1 − dt ) u(ct , gt ) + βE V(bt , yt+1, et+1, qt+1(b, y)) . . . +dt u(ct , gt ) + βE Vd ((1 + r)bt−1, yt+1, et+1, qt+1(b, y), y∗) where ct = (1 − τ) (yt − dt αyt ) and Cd (bt−1, yt , et , qt (b, y)) is the feasibility set in default. It is given by gt + et + (1 − dt ) (1 − ¯h)bt−1 − qt (bt , yt )bt ≤ τ (yt − dt αyt ) qt (bt , yt )bt ≤ (1 − ¯h)bt−1 Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  23. 23. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Recursive REE Recursive-REE A set of government policy functions for i) default d(s); ii) public goods provision g(s); iii) debt issuance b(s); and iv) a bond price menu q(b, y) such that: 1. Taking as given the bond price menu, the government policy functions d(s), g(s), b(s) and h(s) solve the government’s problem for every t. 2. The bond price menu q(b, y) satisfies the following condition q(b, y) = y ∈Y µ(b, y )π {y | y} 1 + r where µ(b, y) = e∈E 1 − ¯h d(st+1) f(e) 3. The probability measure P is equal to the distribution of { t , yt , bt }∞ t=0 implied by the policy functions and the process for the exogenous variables yt and et .Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  24. 24. Research Topics Learning in Sovereign Debt Markets Roadmap Extra Europe during the last recession: Too much debt? Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview
  25. 25. Research Topics Learning in Sovereign Debt Markets Roadmap Extra The market valuation of the debt. Luis E. Rojas (MOVE, UAB and Barcelona GSE ) Research Overview

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