Government The government faces an exogenous sequence {g t } t=0
|
|
- Ezra Sharp
- 5 years ago
- Views:
Transcription
1 Part 6 1. Borrowing Constraints II 1.1. Borrowing Constraints and the Ricardian Equivalence Equivalence between current taxes and current deficits? Basic paper on the Ricardian Equivalence: Barro, JPE, This material is from Sargent and Ljungqvist, Chapter 10. Wereturntotheanalysisofgovernmentintheeconomy,butherewerelaxthe assumption of a balanced budget. In this analysis we concentrate on lump-sum taxation, and here the notation will be τ t. (equivalent to φ t before). Government The government faces an exogenous sequence {g t } of real expenditures and has an initial debt b 0. The sequence of budget constraints for the government is g t + Rb t = τ t + b t+1, t 0, where R is the risk-free rate on a one-period bond. We impose the transversality condition lim t R t b t =0. A government policy is denoted by {g t,τ t,b t+1 }. There is no optimization problem for the government. The only requirements on this policy is that it satisfies the constraints. The intertemporal budget constraint of the government can be obtained by substituting the expressions for b t,t=1, 2,... from the constraints for periods t =1, 2,..., into the constraint for period 0. The resulting expression, using the transversality condition, is b 0 = 1 R R t (τ t g t ). Households The number of identical households in this economy is normalized to one. Each chooses {c t,a t+1 } so as to maximize P β t u(c t ), 0 <β<1,
2 where βr =1and u satisfies the standard conditions, and in particular lim c 0 u 0 (c) =, subject to c t + a t+1 = Ra t + y t τ t, t 0, a given value of initial assets a 0, an exogenous income sequence {y t }, P R t y t <, and a borrowing constraint yet to be chosen. To close the model we have two possibilities: (a) We can assume that this is a small open economy facing an international capital market, where borrowing and lending can be carried out at the rate R. In the world markets, the constraints on the government and household sector are the corresponding transversality conditions, which imply the natural borrowing constraints. (b) It can be a closed economy (or a large open economy), but then the assumption that R =1/β has to be changed. Let s adopt the Option (a) first, and later address Option (b). Definition of an equilibrium in this economy: Given b 0 and a 0, an equilibrium consists in a household plan {c t,a t+1 } and a government policy {g t,τ t,b t+1 } such that the intertemporal budget constraint of the government is satisfied, and, given P R t τ t, the household plan solves its optimization problem. The Ricardian Equivalence Proposition Assume that both households and the government are constrained by the corresponding ª transversality conditions. Given an initial condition (b 0,a 0 ), let c 0 t,a 0 t+1 and ª g 0 t,τ 0 t,b 0 t+1 be an equilibrium. Consider another tax policy satisfying R t τ 1 t = R t τ 0 t. The Ricardian Equivalence Proposition is that then, c 0 t,a 1 t+1ª and g 0 t,τ 1 t,b 1 t+1ª is also an equilibrium. (i.e., the two tax policies are equivalent.) 2
3 We can show that thee proposition holds as follows. Under the natural borrowing constraint, the households will choose the consumption plan subject to the intertemporal budget constraint a 0 = 1 R t (y t τ t )+ 1 R t c t, R R or, a 0 = 1 R t (c t y t )+ 1 R t τ t. R R Given that the consumption plan depends only on the present value of taxes, and that the alternative policy does not change it, the household does not change the consumption plan. Then, the budget constraints c t + a t+1 = Ra t + y t τ t, are used to construct the new a t+1 series, where a t+1 is adjusted minus-one to one with the new taxes. When τ 1 t >τ 0 t,a 1 t+1 <a 0 t+1bythesameamount,andthe opposite at times when taxes were reduced. The new sequence for government debt is constructed similarly. From g t + Rb t = τ t + b t+1, t 0, τ 1 t >τ 0 t,b 1 t+1 <b 0 t+1by the same amount, and vice-versa. Extensions of the basic setup We check in each of the following extensions whether the Ricardian Equivalence holds. 1. A closed economy (Option (b) above): In this case, the interest rates are not constant. Using the equilibrium condition in the financial market a t = b t, adding up the budget constraints of household and government c t + a t+1 = R t a t + y t τ t, g t + R t b t = τ t + b t+1, 3
4 yields y t = c t + g t. The Ricardian Equivalence proposition should be extended as follows. Given the initial conditions (b 0,a 0,R 0 ), let c 0 t,a 0 t+1,r 0 t+1ª and g 0 t,τ 0 t,b 0 t+1ª be an equilibrium. If we have another tax policy satisfying where à ty j=1 R 1 j! 1 τ 1 t = à ty j=1 R 0 j! 1 τ 0 j, j=1 0Y R j 1, then c 0 t,a 1 t+1,rt+1ª 0 and g 0 t,τ 1 t,bt+1ª 1 is also an equilib- rium. To show that the interest rate sequence is not altered we use the Euler equations: u 0 (c t )=βu 0 (c t+1 )R t+1, t 0. In the initial equilibrium, c 0 t = y t g 0 t, t 0 holds. The policy change does not alter this equation. Hence, interest rates do not change either. The Ricardian Equivalence holds. 2. Ad-hoc borrowing constraint. Back to the open economy (In the closed economy with a representative agent y t = c t + g t will always hold). If the condition a t 0 prevails (or other constraint tougher than the natural one), the Ricardian Equivalence will in general not hold. In this case, not only the present value of taxes matters, but also the current liquidity situation. If initially, the borrowing constraint holds, i.e., a 0 t+1 =0is the optimal choice, c 0 t = y t τ 0 t + Ra 0 t, τ 1 t >τ 0 t, requires that c 1 t <c 0 t. However, if the agent starts with positive assets, the Ricardian Equivalence will hold for tax changes which do not lead to a corner where a t+1 =0. 3. Finite horizon for the individual. 4
5 The proposition is based on the assumption that T in P T R t τ t is the same for households and the government. If T h <T g then the policy change may not be neutral. Barro (1974) argued that planning horizons of households may practically be, if parents take into account the utility of their children, and use bequests B as a way to transferring resources to the next generation. If we define V (B t,y t ) as the maximized utility of a one-period-lived agent of generation t, given the bequest received and current exogenous income, then V (B t+1,y t+1 ) is the maximized utility of the next generation. When parents take into account the (discounted) welfare of their children, then their utility function is u(c t )+βv (B t+1,y t+1 ), 0 <β<1. By definition then, subject to V (B t,y t )=Max{u(c t )+βv (B t+1,y t+1 )}, c t + B t+1 y t τ t + RB t, and B t+1 0. Negative bequests are ruled out. In a recursive formulation, this problem is equivalent to the infinite-horizon version above with B t = a t, and the no-borrowing condition a t 0. Hence, the Ricardian Equivalence will hold only if bequests are positive, and the tax changes do not lead to the corner solution of no bequests. This issue can be analyzed more in detail in an overlapping-generations model, as in Barro (1974). 4. Distortionary taxes, uncertainty Borrowing constraints and labor supply Consider the problem of a household with the utility function P P βt c 1 σ t (1 n t ) 1 λ / (1 σ) if σ 6= 1, βt ln c t +ln(1 n t ) if σ =1. and the sequence of budget constraints R t b t + c t w t n t + b t+1, 5
6 where b t is the household s debt at the end of period t. Concavity of the utility function requires that (1 σ)(1 λ) is positive. Thehouseholdtakespricesasgiven. If the borrowing constraint is of the natural type, or, alternatively, the transversality condition holds, the intertemporal budget constraint is à ty! 1 à ty! 1 c t = w t n t R 0 b 0, with 0Y 1. R 1 τ The first-order conditions for utility maximization are c σ t (1 n t ) 1 λ = βc σ t+1 (1 n t+1 ) 1 λ R t+1, 1 λ c t = w t. 1 σ 1 n t The solution proceeds by solving the labor condition for n t and n t+1, substituting the expressions into both the Euler equation and the intertemporal budget constraint, in which now only consumption and wages appear. The remaining task is then the main one of determining the path for consumption. The point here: 1. If future wages increase, c t will jump upwards given the household s ability to borrow. 2. Then, for any given w t,higherc t should be accompanied by lower n t (wealth affect of a higher future wages). Let us introduce now the ad-hoc borrowing constraint b t+1 0. When the profile of future wages increases, if the borrowing constraint binds, c t cannot go up as in the previous case. 1. When the borrowing constraint binds, c t is lower than when borrowing is possible, and then n t will be higher. 2. When the borrowing constraint binds at least from the previous period, c t = w t n t. Substituting this into the labor supply condition yields µ 1 λ 1 σ wt n t 1 n t = w t 6 µ 1 λ 1 σ nt 1 n t =1.
7 Hours worked are constant, regardless of wage movements. Empirical implications of borrowing constraints for labor supply elasticity. 3. If the borrowing constraints binds this period, but did not bind last period, then c t = w t n t Rb t, b t < 0, µ 1 λ wt n t Rb t w t =. 1 σ 1 n t Higher future wage does not affect hours, but a current higher wage increases hours Borrowing constraints in general equilibrium For borrowing to take place in general equilibrium we need differenciated households. Here we assume different rates of time preference. Exogenous output Assume an economy with two groups of agents of the same size, which are identical in all respects, except that the rate of time preference of one group is higherthantherateoftimepreferenceoftheother. Theutilityfunctionofthe two groups are ˆβ t u(ĉ t ), β t u( c t ), where ˆβ < β, and u has the standard properties. Each household in both groups receive the same endowment y, andallstart period 0 with no assets, i.e., ˆb0 = b 0 =0. The budget constraints are, correspondingly, ĉ t y + ˆb t+1 R tˆbt, c t y + b t+1 R t bt. Equilibrium in this economy requires ĉ t + c t =2y ˆbt + b t =0. 7
8 n What is the equilibrium path R t+1, ĉ t, c t, ˆb t+1, b o t+1? n Definition: A competitive equilibrium consists of sequences of allocations ĉ t, c t, ˆb t+1, b o t+1 and returns {R t+1 } that solve the impatient and patient problems and all markets clear, i.e., ĉ t + c t =2y, ˆbt + b t =0, for all t 0. We turn now to compute and interpret this equilitbrium path. The intertemporal budget constraints for both households are where ĉ à t ty! = y 0Y =1. This implies that 1 à ty! = ĉ à t ty! = c à t ty!, c à t ty!. (1.1) To proceed we use the Euler equations, assuming that u(c) =lnc. The Euler equations for the two groups are Similarly, ĉ t = ˆβR t ĉ t 1, ĉ t = ˆβR tˆβrt 1 ĉ t 2,... ĉ t = ˆβ t à ty! ĉ 0. (1.2) à ty! c t = β t c 0. (1.3) 8
9 Using the Euler equations into (1.1): Ã ty! ˆβ t ĉ 0 Ã ty! = Ã ty! β t c 0 Ã ty! ˆβ t ĉ 0 = β t c 0 ĉ 0 = 1 ˆβ 1 β c 0 φ c 0. ˆβ < β φ>1 ĉ 0 > c 0. Using ĉ 0 = φ c 0 and the resource constraint for period 0 yields c 0 = 2 1+φ y<y ĉ 0 = 2φ 1+φ y>y. Hence, in period 0 the impatient borrows and the patient saves. The next step is to solve for the interest rates using the solution for the starting consumption levels, the Euler equations, and the resource constraints. Let s start with R 1. ĉ 1 = ˆβR 1 ĉ 0 = ˆβR 2φ 1 1+φ y, 2y ĉ 1 = βr 1 c 0 = βr φ y. Adding up the two equations and dividing by y yields µ 2φ 2=R 1 1+φ ˆβ φ β 1 R 1 = φ 1+φ ˆβ φ β. 9
10 Hence, the market discount rate is a weighted average of the two discount rates. To compute the future interest rates we need to show (left for the homework) that the interest discount factors are the following weighted averages of the two subjective discount factors: Ã ty! 1 = φ 1+φ ˆβ t φ β t, φ > 1. We can express this equation as ty = 1+φ φˆβ t t. (1.4) + β and given that ty t+1 = Y 1 R t+1, 1 = φˆβ t+1 + βt+1 R t+1 φˆβ t + β t = φˆβ t φˆβ t + β ˆβ β t t + φˆβ t t β. + β The market discount rate is always a weighted average of the two discount rates, but, given that ˆβ < β, the weight of the higher discount rate declines over time, and φˆβ t φ(ˆβ/ β) t lim t φˆβ t t =lim t + β φ(ˆβ/ β) t +1 =0. Hence, at the limit, the interest rate is set by the patient s rate of time preference. 1/R = β The profiles of consumption for the impatient and patient can be computed using the Euler equations in (1.2) and (1.3) and the discount factors in (1.4). It can be shown (left for the homework) that lim t ĉt =0, lim t c t =2y. 10
11 zero, and the consumption of the saver increases over time, converging to total output. Thebehaviorofthedebtcanbecomputedasfollows: Ã ty! 1 ˆbt+1 = ˆb1 =ĉ 0 y,... Ã ty! ˆbt+1 =ĉ t y + R t (ĉ t 1 y)+r t 1 R t (ĉ t 2 y)... + (ĉ 0 y), Ã tx iy! 1 (ĉ i y). i=0 Using (1.4), solving the finite geometric sums, and rearranging, we get β ˆbt+1 = y ³ ³ φ(ˆβ/ β) t +1 1 β ³1 (ˆβ/ β) t+1. t, ˆb t+1 ˆb = β ³ 1 β y. Interpretation: Given that at the limit R =1/ β, this equation can be written as 1 ˆb = R 1 y. This is the natural borrowing constraint, i.e., the debt which leaves no consumption. The periodical interest payment is (R 1) = y. The transversality condition holds given that the debt converges to a constant, and the interest rate is positive. Imposing an ad-hoc borrowing constraint Assume now the borrowing constraint b t+1 0. This render the previous solution unfeasible. Conjecture: If the impatient doesn t have any assets, the equilibrium interest rates are now R t+1 =1/ β, t 0 11
12 Under this conjecture, R t+1 < 1/ˆβ, t 0, and hence the impatient would like to borrow permanently. However, given the borrowing constraint, ĉ t = y, t 0. The patient, in contrast, is not constrained, but because of the lack of saving or borrowing by the impatient, he becomes similar to the representative agent in a standard economy. With the logarithmic utility function, the Euler equation of the patient is c t+1 = βr t+1 c t. Equilibrium in the output market implies that c t = y for all t. Hence, 1= βr t+1, R t+1 =1/ β. The interest rate is set according to the patient, who is the only agent free to trade in the financial market. In the present case this equality holds immediately, and not asymptotically as in the previous case because b t 0. If b t φ>0, there would be a gradual convergence. The conjecture does represent an equilibrium because output and debt markets clear, and the first-order condition of the patient holds and the impatient does his best given the constraint. Two basic directions for extending this framework: 1. Adding leisure to the utility function, i.e., making income endogenous, and 2. Introducing capital accumulation (shortly discussed). 1. Endogenous labor Consider the same framework as above, but now the utility and production functions are: u(c t, 1 n t )=lnc t + ϕ ln(1 n t ), ϕ > 0, y t = wn t, w > 0. 12
13 The budget constraints are now ĉ t wˆn t + ˆb t+1 R tˆbt, c t wñ t + b t+1 R t bt. and the equilibrium conditions are ĉ t + c t = w(ˆn t +ñ t ), ˆbt + b t =0, t 0. TheEulerequationsarethesameaswheny t = y, but now there are additional conditions regarding the consumption-leisure choice: ϕĉ t 1 ˆn t = w wˆn t = w ϕĉ t, ϕ c t 1 ñ t = w wñ t = w ϕ c t. Case (a): Only the transversality condition applies. Substituting the conditions for labor into the budget constraints, to get rid of the n s, and rearranging, yields ĉ t = 1 ³ˆbt+1 R tˆbt + w c t = 1 ³ bt+1 R t bt + w. It is left as an exercise to show that the model can be solved similarly as in the case of exogenous output, and that consumption and leisure of the impatient go over time to zero. Hence, at the limit, the debt is b = w/(1/ β 1). For the patient, consumption and leisure at the limit are determined as follows: Ifthereisaninteriorsolution, w = c = w(1 + ñ ), ϕ c 1 ñ ñ = 1 ϕ, 13,
14 c = w(1 + 1 ϕ )= 2 w. This requires that ϕ<1. If ϕ 1, ñ =0, c = w. Case (b): The borrowing constraint b t+1 Ω, t 0, holds, and ˆb 0 = Ω, b0 = Ω. Assumption (i): Ω < w for all {R R t 1 t}. Note that the equilibrium sequence {R t } is perfectly foreseen at time 0. Conjecture: The equilibrium sequence of interest rates is R t = R =1/ β for all t 0. The key point here: This conjecture implies that the borrowing constraint on the impatient binds. The impatient wishes to borrow more at all times, but given the borrowing constraint, the consumption of these agents is ĉ t = wˆn t (R 1)Ω. Substituting this expression into the consumption-leisure condition we get w = ϕ [wˆn t (R 1)Ω] ˆn t = 1 1 ˆn t + ϕ (R 1) w Ω, ĉ t = 1 w 1 (R 1)Ω. Consumption and labor of the impatient are constant for all t 0, and the assumption Ω < w implies that ĉ R t 1 t > 0 and 0 < ˆn t < 1. The labor supply of the impatient has peculiar properties created by the wealth effect from interest rate payments which disappears when Ω =0. The interest payments have a positive effect, due to the liquidity constraint. The wage has a negative effect, given that as it increases, less effort is required to pay the interest. For the patient, the conjectured interest rates implies that c t is constant over time. The consumption and labor supply of the patient are then given by w = c = b t+1 R b t + wñ t, ϕ c 1 ñ t wñ t = w ϕ c. 14
15 Substituting the condition for labor into the budget constraint yields c = 1 ³ bt+1 R b t + w. Given that in equilibrium, b t+1 = b t = Ω, the budget constraint becomes c = 1 [w +(R 1)Ω]. Substituting this expression for consumption expression into the labor condition yields ñ t =1 ϕ c w ñ t = 1 ϕ (R 1)Ω. w Forthesaver,thewagehasapositiveeffect and the interest rate has a negative one. Note that the resource constraint ĉ t + c t = w(ˆn t +ñ t ) is also satisfied (Walras 2 Law). Total consumption is w, which is equal to total output. For an interior solution for the saver s labor, 1 ϕ (R 1)Ω 0. w With a borrowing constraint, the condition for an interior solution depends not only on ϕ, but also on R, w, Ω. (***) Summary: The conjecture we started from satisfies the equilibrium conditions. Additionally, given the starting point where the impatient s debt equals the constraint, the economy is from t =0onwards at a steady state with a binding borrowing constraint on the impatient. Variable productivity Using the previous case of a steady state with a binding borrowing constraint as a starting point, we consider now productivity varying around the level w. Specifically, assume the exogenous sequence {w t }, w t [w ε, w + ε], where ε is sufficiently small (in particular ε<w), so that the borrowing constraint on the impatient will always be binding. 15
16 Additional assumptions: ii. Either w t > Ω for all t, or w t < Ω for all t, ii. w t w = w as t, iii. The economy at time 0 is at the steady state derived above. This requires that R 0 = R 1 = R =1/ β, (***) and w 0 = w 1 = w. Additional assumption: iv. Ω < wt, for all t 0. Note that all future values of w R t 1 t and R t are known at time 0. This replaces assumption (i). Under the assumption that the borrowing constraint on the impatient always binds, we generalize the solution of the model above by computing the equilibrium sequence {R t+1 }. The impatient s consumption and labor at any t 0 are given by ĉ t = w tˆn t (R t 1)Ω, w t = ϕ [w tˆn t (R t 1)Ω] 1 ˆn t, (R t 1)Ω, w t ĉ t = 1 w t 1 (R t 1)Ω. ˆn t = 1 + ϕ Note that assumption (iv) implies that ĉ t > 0 and 0 < ˆn t < 1. For the patient, the budget constraint and first-order conditions are c t = b t+1 R t bt + w t ñ t, c t+1 = c βr t+1, t w t = ϕ c t w t ñ t = w t ϕ c t. 1 ñ t Substituting the condition for labor into the budget constraint, to get rid of ñ t, yields c t = b t+1 R t bt + w t ϕ c t, c t = 1 ³ bt+1 R t bt + w t. 16
17 In equilibrium, b t+1 = b t = Ω, and hence this budget constraint becomes c t = 1 [(R t 1)Ω + w t ]. (1.5) Substituting (1.5) into the labor condition ñ t =1 ϕ ct w t ñ t = 1 ϕ (R t 1)Ω. w t yields We turn now to solve for the interest rate sequence. Using the patient s Euler equations and (1.5) for c t and c t+1 we get (R t+1 1)Ω + w t+1 (R t 1)Ω + w t = βr t+1. Tosolveforthecurrentinterestrate(R t+1 )weneedthevalueoflastperiod s interest rate and so on backwards. Given assumption (iii) that the economy in period 0 is at a steady state we should have (R 1 1)Ω + w 1 (R 0 1)Ω + w = βr 1 (R 1)Ω + w (R 1)Ω + w =1. Then, (R 2 1)Ω + w 2 (R 1)Ω + w = βr 2 R 2 = w 2 Ω β (w Ω), and so on for R 3,R 4... In general, R t is predetermined at time t and R t+1 = w t+1 Ω. β (w t Ω)+Ω ³ βrt 1 A current productivity shock reduces the interest rate and a future productivity shock increases it. Summary: 17
18 ˆn t = 1 + Ω ϕ (R t 1), w t (R t 1), w t ĉ t = 1 w t Ω 1 (R t 1), ñ t = 1 Ω ϕ c t = 1 w t + Ω 1 (R t 1). RBC with this structure. A productivity shock increases hours worked of high income people and reduce hours worked of low income people. Aggregate labor remains constant. Effects of relaxing the borrowing constraint, i.e., increasing Ω (still satisfying assumption iv Ω < w t R t 1 ). Who is worse off? Consider now a steady state with the natural borrowing constraint: Ω = w R 1. Thesolutioninthiscaseis ˆn t = 1 + ϕ w (R t 1) w t (R 1) 1 ñ t = 1 ϕ w (R t 1) w t (R 1) 1 ϕ ĉ t = 1 w t 1 (R t 1) (R 1) w 0 c t = 1 w t + 1 (R t 1) (R 1) w 2 w 2. Introducing capital accumulation The incorporation of a production technology operated with capital, but without exogenous labor, was addressed by Becker (QJE, 1980). He showed that at the limit only the most patient agent will hold all the capital, and hence, the marginal productivity of capital (the interest rate) will be equalized to his rate 18
19 of time preference. All the other agents will receive wages only. By not having leisure in the utility function, leisure is zero at all times. In this case however, as capital is the only asset which cannot be negative, the model is equivalent to one with the ad-hoc borrowing constraint of zero borrowing. Aiyagari (1994). Additional capital accumulation of capital due to a borrowing constraint. Precautionary saving. Krusell and Smith (JPE 1998) extended the Aiyagari model in two respects: i. Incorporated an aggregate productivity shock, so that they could study the precautionary savings over the business cycle, and more importantly, in the present context, ii. incorporated three levels of type preference, with a slow but stochastic evolution over time. Two main results here: First, agents who are currently impatient tend to be borrowing constrained, and hence consume their current income. This explains the excess sensitivity of consumption to income found in the data. Second, wealth distribution is much more unequal than when the only source of inequality are individual income shocks. The degree of inequality is governed primarily by the persistence in the rates of time preference. 19
The Real Business Cycle Model
The Real Business Cycle Model Macroeconomics II 2 The real business cycle model. Introduction This model explains the comovements in the fluctuations of aggregate economic variables around their trend.
More informationAdvanced Macroeconomics
Advanced Macroeconomics The Ramsey Model Micha l Brzoza-Brzezina/Marcin Kolasa Warsaw School of Economics Micha l Brzoza-Brzezina/Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 47 Introduction Authors:
More informationAdvanced Macroeconomics
Advanced Macroeconomics The Ramsey Model Marcin Kolasa Warsaw School of Economics Marcin Kolasa (WSE) Ad. Macro - Ramsey model 1 / 30 Introduction Authors: Frank Ramsey (1928), David Cass (1965) and Tjalling
More informationproblem. max Both k (0) and h (0) are given at time 0. (a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming
1. Endogenous Growth with Human Capital Consider the following endogenous growth model with both physical capital (k (t)) and human capital (h (t)) in continuous time. The representative household solves
More informationChapter 4. Applications/Variations
Chapter 4 Applications/Variations 149 4.1 Consumption Smoothing 4.1.1 The Intertemporal Budget Economic Growth: Lecture Notes For any given sequence of interest rates {R t } t=0, pick an arbitrary q 0
More information1 Bewley Economies with Aggregate Uncertainty
1 Bewley Economies with Aggregate Uncertainty Sofarwehaveassumedawayaggregatefluctuations (i.e., business cycles) in our description of the incomplete-markets economies with uninsurable idiosyncratic risk
More informationFoundations of Modern Macroeconomics Second Edition
Foundations of Modern Macroeconomics Second Edition Chapter 5: The government budget deficit Ben J. Heijdra Department of Economics & Econometrics University of Groningen 1 September 2009 Foundations of
More informationu(c t, x t+1 ) = c α t + x α t+1
Review Questions: Overlapping Generations Econ720. Fall 2017. Prof. Lutz Hendricks 1 A Savings Function Consider the standard two-period household problem. The household receives a wage w t when young
More informationComprehensive Exam. Macro Spring 2014 Retake. August 22, 2014
Comprehensive Exam Macro Spring 2014 Retake August 22, 2014 You have a total of 180 minutes to complete the exam. If a question seems ambiguous, state why, sharpen it up and answer the sharpened-up question.
More informationFoundations of Modern Macroeconomics B. J. Heijdra & F. van der Ploeg Chapter 6: The Government Budget Deficit
Foundations of Modern Macroeconomics: Chapter 6 1 Foundations of Modern Macroeconomics B. J. Heijdra & F. van der Ploeg Chapter 6: The Government Budget Deficit Foundations of Modern Macroeconomics: Chapter
More informationMacroeconomics Qualifying Examination
Macroeconomics Qualifying Examination August 2015 Department of Economics UNC Chapel Hill Instructions: This examination consists of 4 questions. Answer all questions. If you believe a question is ambiguously
More informationThe representative agent model
Chapter 3 The representative agent model 3.1 Optimal growth In this course we re looking at three types of model: 1. Descriptive growth model (Solow model): mechanical, shows the implications of a given
More informationSuggested Solutions to Homework #3 Econ 511b (Part I), Spring 2004
Suggested Solutions to Homework #3 Econ 5b (Part I), Spring 2004. Consider an exchange economy with two (types of) consumers. Type-A consumers comprise fraction λ of the economy s population and type-b
More informationMacroeconomic Theory II Homework 2 - Solution
Macroeconomic Theory II Homework 2 - Solution Professor Gianluca Violante, TA: Diego Daruich New York University Spring 204 Problem The household has preferences over the stochastic processes of a single
More informationNeoclassical Business Cycle Model
Neoclassical Business Cycle Model Prof. Eric Sims University of Notre Dame Fall 2015 1 / 36 Production Economy Last time: studied equilibrium in an endowment economy Now: study equilibrium in an economy
More informationDynamic stochastic general equilibrium models. December 4, 2007
Dynamic stochastic general equilibrium models December 4, 2007 Dynamic stochastic general equilibrium models Random shocks to generate trajectories that look like the observed national accounts. Rational
More information1 With state-contingent debt
STOCKHOLM DOCTORAL PROGRAM IN ECONOMICS Helshögskolan i Stockholm Stockholms universitet Paul Klein Email: paul.klein@iies.su.se URL: http://paulklein.se/makro2.html Macroeconomics II Spring 2010 Lecture
More informationLecture 6: Discrete-Time Dynamic Optimization
Lecture 6: Discrete-Time Dynamic Optimization Yulei Luo Economics, HKU November 13, 2017 Luo, Y. (Economics, HKU) ECON0703: ME November 13, 2017 1 / 43 The Nature of Optimal Control In static optimization,
More informationDynamic Optimization Using Lagrange Multipliers
Dynamic Optimization Using Lagrange Multipliers Barbara Annicchiarico barbara.annicchiarico@uniroma2.it Università degli Studi di Roma "Tor Vergata" Presentation #2 Deterministic Infinite-Horizon Ramsey
More informationIn the Ramsey model we maximized the utility U = u[c(t)]e nt e t dt. Now
PERMANENT INCOME AND OPTIMAL CONSUMPTION On the previous notes we saw how permanent income hypothesis can solve the Consumption Puzzle. Now we use this hypothesis, together with assumption of rational
More informationslides chapter 3 an open economy with capital
slides chapter 3 an open economy with capital Princeton University Press, 2017 Motivation In this chaper we introduce production and physical capital accumulation. Doing so will allow us to address two
More informationSmall Open Economy RBC Model Uribe, Chapter 4
Small Open Economy RBC Model Uribe, Chapter 4 1 Basic Model 1.1 Uzawa Utility E 0 t=0 θ t U (c t, h t ) θ 0 = 1 θ t+1 = β (c t, h t ) θ t ; β c < 0; β h > 0. Time-varying discount factor With a constant
More informationNotes on Alvarez and Jermann, "Efficiency, Equilibrium, and Asset Pricing with Risk of Default," Econometrica 2000
Notes on Alvarez Jermann, "Efficiency, Equilibrium, Asset Pricing with Risk of Default," Econometrica 2000 Jonathan Heathcote November 1st 2005 1 Model Consider a pure exchange economy with I agents one
More informationPermanent Income Hypothesis Intro to the Ramsey Model
Consumption and Savings Permanent Income Hypothesis Intro to the Ramsey Model Lecture 10 Topics in Macroeconomics November 6, 2007 Lecture 10 1/18 Topics in Macroeconomics Consumption and Savings Outline
More informationA simple macro dynamic model with endogenous saving rate: the representative agent model
A simple macro dynamic model with endogenous saving rate: the representative agent model Virginia Sánchez-Marcos Macroeconomics, MIE-UNICAN Macroeconomics (MIE-UNICAN) A simple macro dynamic model with
More informationPractice Questions for Mid-Term I. Question 1: Consider the Cobb-Douglas production function in intensive form:
Practice Questions for Mid-Term I Question 1: Consider the Cobb-Douglas production function in intensive form: y f(k) = k α ; α (0, 1) (1) where y and k are output per worker and capital per worker respectively.
More informationHOMEWORK #3 This homework assignment is due at NOON on Friday, November 17 in Marnix Amand s mailbox.
Econ 50a second half) Yale University Fall 2006 Prof. Tony Smith HOMEWORK #3 This homework assignment is due at NOON on Friday, November 7 in Marnix Amand s mailbox.. This problem introduces wealth inequality
More informationProblem 1 (30 points)
Problem (30 points) Prof. Robert King Consider an economy in which there is one period and there are many, identical households. Each household derives utility from consumption (c), leisure (l) and a public
More informationEquilibrium in a Production Economy
Equilibrium in a Production Economy Prof. Eric Sims University of Notre Dame Fall 2012 Sims (ND) Equilibrium in a Production Economy Fall 2012 1 / 23 Production Economy Last time: studied equilibrium in
More informationMacroeconomic Theory and Analysis Suggested Solution for Midterm 1
Macroeconomic Theory and Analysis Suggested Solution for Midterm February 25, 2007 Problem : Pareto Optimality The planner solves the following problem: u(c ) + u(c 2 ) + v(l ) + v(l 2 ) () {c,c 2,l,l
More informationRedistributive Taxation in a Partial-Insurance Economy
Redistributive Taxation in a Partial-Insurance Economy Jonathan Heathcote Federal Reserve Bank of Minneapolis and CEPR Kjetil Storesletten Federal Reserve Bank of Minneapolis and CEPR Gianluca Violante
More informationRamsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path
Ramsey Cass Koopmans Model (1): Setup of the Model and Competitive Equilibrium Path Ryoji Ohdoi Dept. of Industrial Engineering and Economics, Tokyo Tech This lecture note is mainly based on Ch. 8 of Acemoglu
More informationMonetary Economics: Solutions Problem Set 1
Monetary Economics: Solutions Problem Set 1 December 14, 2006 Exercise 1 A Households Households maximise their intertemporal utility function by optimally choosing consumption, savings, and the mix of
More informationEconomic Growth: Lecture 8, Overlapping Generations
14.452 Economic Growth: Lecture 8, Overlapping Generations Daron Acemoglu MIT November 20, 2018 Daron Acemoglu (MIT) Economic Growth Lecture 8 November 20, 2018 1 / 46 Growth with Overlapping Generations
More informationUncertainty Per Krusell & D. Krueger Lecture Notes Chapter 6
1 Uncertainty Per Krusell & D. Krueger Lecture Notes Chapter 6 1 A Two-Period Example Suppose the economy lasts only two periods, t =0, 1. The uncertainty arises in the income (wage) of period 1. Not that
More informationMacroeconomics Theory II
Macroeconomics Theory II Francesco Franco FEUNL February 2016 Francesco Franco (FEUNL) Macroeconomics Theory II February 2016 1 / 18 Road Map Research question: we want to understand businesses cycles.
More informationDynamic Optimization: An Introduction
Dynamic Optimization An Introduction M. C. Sunny Wong University of San Francisco University of Houston, June 20, 2014 Outline 1 Background What is Optimization? EITM: The Importance of Optimization 2
More informationSTATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics
STATE UNIVERSITY OF NEW YORK AT ALBANY Department of Economics Ph. D. Comprehensive Examination: Macroeconomics Fall, 202 Answer Key to Section 2 Questions Section. (Suggested Time: 45 Minutes) For 3 of
More informationSession 4: Money. Jean Imbs. November 2010
Session 4: Jean November 2010 I So far, focused on real economy. Real quantities consumed, produced, invested. No money, no nominal in uences. I Now, introduce nominal dimension in the economy. First and
More informationMacroeconomic Theory and Analysis V Suggested Solutions for the First Midterm. max
Macroeconomic Theory and Analysis V31.0013 Suggested Solutions for the First Midterm Question 1. Welfare Theorems (a) There are two households that maximize max i,g 1 + g 2 ) {c i,l i} (1) st : c i w(1
More information1 Two elementary results on aggregation of technologies and preferences
1 Two elementary results on aggregation of technologies and preferences In what follows we ll discuss aggregation. What do we mean with this term? We say that an economy admits aggregation if the behavior
More informationLecture 3: Dynamics of small open economies
Lecture 3: Dynamics of small open economies Open economy macroeconomics, Fall 2006 Ida Wolden Bache September 5, 2006 Dynamics of small open economies Required readings: OR chapter 2. 2.3 Supplementary
More informationA suggested solution to the problem set at the re-exam in Advanced Macroeconomics. February 15, 2016
Christian Groth A suggested solution to the problem set at the re-exam in Advanced Macroeconomics February 15, 216 (3-hours closed book exam) 1 As formulated in the course description, a score of 12 is
More information(a) Write down the Hamilton-Jacobi-Bellman (HJB) Equation in the dynamic programming
1. Government Purchases and Endogenous Growth Consider the following endogenous growth model with government purchases (G) in continuous time. Government purchases enhance production, and the production
More informationLecture 15. Dynamic Stochastic General Equilibrium Model. Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017
Lecture 15 Dynamic Stochastic General Equilibrium Model Randall Romero Aguilar, PhD I Semestre 2017 Last updated: July 3, 2017 Universidad de Costa Rica EC3201 - Teoría Macroeconómica 2 Table of contents
More informationECOM 009 Macroeconomics B. Lecture 2
ECOM 009 Macroeconomics B Lecture 2 Giulio Fella c Giulio Fella, 2014 ECOM 009 Macroeconomics B - Lecture 2 40/197 Aim of consumption theory Consumption theory aims at explaining consumption/saving decisions
More information1. Money in the utility function (start)
Monetary Economics: Macro Aspects, 1/3 2012 Henrik Jensen Department of Economics University of Copenhagen 1. Money in the utility function (start) a. The basic money-in-the-utility function model b. Optimal
More informationLecture 2. (1) Permanent Income Hypothesis (2) Precautionary Savings. Erick Sager. February 6, 2018
Lecture 2 (1) Permanent Income Hypothesis (2) Precautionary Savings Erick Sager February 6, 2018 Econ 606: Adv. Topics in Macroeconomics Johns Hopkins University, Spring 2018 Erick Sager Lecture 2 (2/6/18)
More informationTA Sessions in Macroeconomic Theory I. Diogo Baerlocher
TA Sessions in Macroeconomic Theory I Diogo Baerlocher Fall 206 TA SESSION Contents. Constrained Optimization 2. Robinson Crusoe 2. Constrained Optimization The general problem of constrained optimization
More information1 The Basic RBC Model
IHS 2016, Macroeconomics III Michael Reiter Ch. 1: Notes on RBC Model 1 1 The Basic RBC Model 1.1 Description of Model Variables y z k L c I w r output level of technology (exogenous) capital at end of
More informationOnline Appendix for Investment Hangover and the Great Recession
ONLINE APPENDIX INVESTMENT HANGOVER A1 Online Appendix for Investment Hangover and the Great Recession By MATTHEW ROGNLIE, ANDREI SHLEIFER, AND ALP SIMSEK APPENDIX A: CALIBRATION This appendix describes
More informationSimple New Keynesian Model without Capital
Simple New Keynesian Model without Capital Lawrence J. Christiano January 5, 2018 Objective Review the foundations of the basic New Keynesian model without capital. Clarify the role of money supply/demand.
More informationLecture notes on modern growth theory
Lecture notes on modern growth theory Part 2 Mario Tirelli Very preliminary material Not to be circulated without the permission of the author October 25, 2017 Contents 1. Introduction 1 2. Optimal economic
More informationA Theory of Optimal Inheritance Taxation
A Theory of Optimal Inheritance Taxation Thomas Piketty, Paris School of Economics Emmanuel Saez, UC Berkeley July 2013 1 1. MOTIVATION Controversy about proper level of inheritance taxation 1) Public
More informationDYNAMIC LECTURE 5: DISCRETE TIME INTERTEMPORAL OPTIMIZATION
DYNAMIC LECTURE 5: DISCRETE TIME INTERTEMPORAL OPTIMIZATION UNIVERSITY OF MARYLAND: ECON 600. Alternative Methods of Discrete Time Intertemporal Optimization We will start by solving a discrete time intertemporal
More informationGraduate Macroeconomics 2 Problem set Solutions
Graduate Macroeconomics 2 Problem set 10. - Solutions Question 1 1. AUTARKY Autarky implies that the agents do not have access to credit or insurance markets. This implies that you cannot trade across
More informationPseudo-Wealth and Consumption Fluctuations
Pseudo-Wealth and Consumption Fluctuations Banque de France Martin Guzman (Columbia-UBA) Joseph Stiglitz (Columbia) April 4, 2017 Motivation 1 Analytical puzzle from the perspective of DSGE models: Physical
More informationLecture 2 The Centralized Economy: Basic features
Lecture 2 The Centralized Economy: Basic features Leopold von Thadden University of Mainz and ECB (on leave) Advanced Macroeconomics, Winter Term 2013 1 / 41 I Motivation This Lecture introduces the basic
More informationGraduate Macroeconomics - Econ 551
Graduate Macroeconomics - Econ 551 Tack Yun Indiana University Seoul National University Spring Semester January 2013 T. Yun (SNU) Macroeconomics 1/07/2013 1 / 32 Business Cycle Models for Emerging-Market
More informationSimple New Keynesian Model without Capital
Simple New Keynesian Model without Capital Lawrence J. Christiano March, 28 Objective Review the foundations of the basic New Keynesian model without capital. Clarify the role of money supply/demand. Derive
More informationMultiple Interior Steady States in the Ramsey Model with Elastic Labor Supply
Multiple Interior Steady States in the Ramsey Model with Elastic Labor Supply Takashi Kamihigashi March 18, 2014 Abstract In this paper we show that multiple interior steady states are possible in the
More informationInternet Appendix for: Social Risk, Fiscal Risk, and the Portfolio of Government Programs
Internet Appendix for: Social Risk, Fiscal Risk, and the Portfolio of Government Programs Samuel G Hanson David S Scharfstein Adi Sunderam Harvard University June 018 Contents A Programs that impact the
More informationPart A: Answer question A1 (required), plus either question A2 or A3.
Ph.D. Core Exam -- Macroeconomics 5 January 2015 -- 8:00 am to 3:00 pm Part A: Answer question A1 (required), plus either question A2 or A3. A1 (required): Ending Quantitative Easing Now that the U.S.
More informationECON 5118 Macroeconomic Theory
ECON 5118 Macroeconomic Theory Winter 013 Test 1 February 1, 013 Answer ALL Questions Time Allowed: 1 hour 0 min Attention: Please write your answers on the answer book provided Use the right-side pages
More informationMacroeconomics Qualifying Examination
Macroeconomics Qualifying Examination January 2016 Department of Economics UNC Chapel Hill Instructions: This examination consists of 3 questions. Answer all questions. If you believe a question is ambiguously
More informationSlides II - Dynamic Programming
Slides II - Dynamic Programming Julio Garín University of Georgia Macroeconomic Theory II (Ph.D.) Spring 2017 Macroeconomic Theory II Slides II - Dynamic Programming Spring 2017 1 / 32 Outline 1. Lagrangian
More information14.06 Lecture Notes Intermediate Macroeconomics. George-Marios Angeletos MIT Department of Economics
14.06 Lecture Notes Intermediate Macroeconomics George-Marios Angeletos MIT Department of Economics Spring 2004 Chapter 3 The Neoclassical Growth Model In the Solow model, agents in the economy (or the
More informationHandout: Competitive Equilibrium
1 Competitive equilibrium Handout: Competitive Equilibrium Definition 1. A competitive equilibrium is a set of endogenous variables (Ĉ, N s, N d, T, π, ŵ), such that given the exogenous variables (G, z,
More informationCompetitive Equilibrium and the Welfare Theorems
Competitive Equilibrium and the Welfare Theorems Craig Burnside Duke University September 2010 Craig Burnside (Duke University) Competitive Equilibrium September 2010 1 / 32 Competitive Equilibrium and
More information2. What is the fraction of aggregate savings due to the precautionary motive? (These two questions are analyzed in the paper by Ayiagari)
University of Minnesota 8107 Macroeconomic Theory, Spring 2012, Mini 1 Fabrizio Perri Stationary equilibria in economies with Idiosyncratic Risk and Incomplete Markets We are now at the point in which
More informationMacro I - Practice Problems - Growth Models
Macro I - Practice Problems - Growth Models. Consider the infinitely-lived agent version of the growth model with valued leisure. Suppose that the government uses proportional taxes (τ c, τ n, τ k ) on
More informationIncomplete Markets, Heterogeneity and Macroeconomic Dynamics
Incomplete Markets, Heterogeneity and Macroeconomic Dynamics Bruce Preston and Mauro Roca Presented by Yuki Ikeda February 2009 Preston and Roca (presenter: Yuki Ikeda) 02/03 1 / 20 Introduction Stochastic
More informationLecture 2. (1) Aggregation (2) Permanent Income Hypothesis. Erick Sager. September 14, 2015
Lecture 2 (1) Aggregation (2) Permanent Income Hypothesis Erick Sager September 14, 2015 Econ 605: Adv. Topics in Macroeconomics Johns Hopkins University, Fall 2015 Erick Sager Lecture 2 (9/14/15) 1 /
More informationThe New Keynesian Model: Introduction
The New Keynesian Model: Introduction Vivaldo M. Mendes ISCTE Lisbon University Institute 13 November 2017 (Vivaldo M. Mendes) The New Keynesian Model: Introduction 13 November 2013 1 / 39 Summary 1 What
More informationECON 582: The Neoclassical Growth Model (Chapter 8, Acemoglu)
ECON 582: The Neoclassical Growth Model (Chapter 8, Acemoglu) Instructor: Dmytro Hryshko 1 / 21 Consider the neoclassical economy without population growth and technological progress. The optimal growth
More informationDynamic Problem Set 1 Solutions
Dynamic Problem Set 1 Solutions Jonathan Kreamer July 15, 2011 Question 1 Consider the following multi-period optimal storage problem: An economic agent imizes: c t} T β t u(c t ) (1) subject to the period-by-period
More informationPublic Economics Ben Heijdra Chapter 3: Taxation and Intertemporal Choice
Public Economics: Chapter 3 1 Public Economics Ben Heijdra Chapter 3: Taxation and Intertemporal Choice Aims of this topic Public Economics: Chapter 3 2 To introduce and study the basic Fisherian model
More informationEconomic Growth: Lectures 5-7, Neoclassical Growth
14.452 Economic Growth: Lectures 5-7, Neoclassical Growth Daron Acemoglu MIT November 7, 9 and 14, 2017. Daron Acemoglu (MIT) Economic Growth Lectures 5-7 November 7, 9 and 14, 2017. 1 / 83 Introduction
More informationEconomic Growth: Lecture 7, Overlapping Generations
14.452 Economic Growth: Lecture 7, Overlapping Generations Daron Acemoglu MIT November 17, 2009. Daron Acemoglu (MIT) Economic Growth Lecture 7 November 17, 2009. 1 / 54 Growth with Overlapping Generations
More informationRedistribution and Fiscal Policy. Juan F. Rubio-Ramirez. Working Paper a February Working Paper Series
Redistribution and Fiscal Policy Juan F. Rubio-Ramirez Working Paper 2002-32a February 2003 Working Paper Series Federal Reserve Bank of Atlanta Working Paper 2002-32a February 2003 Redistribution and
More informationLecture 6: Competitive Equilibrium in the Growth Model (II)
Lecture 6: Competitive Equilibrium in the Growth Model (II) ECO 503: Macroeconomic Theory I Benjamin Moll Princeton University Fall 204 /6 Plan of Lecture Sequence of markets CE 2 The growth model and
More informationNeoclassical Growth Model: I
Neoclassical Growth Model: I Mark Huggett 2 2 Georgetown October, 2017 Growth Model: Introduction Neoclassical Growth Model is the workhorse model in macroeconomics. It comes in two main varieties: infinitely-lived
More informationUNIVERSITY OF WISCONSIN DEPARTMENT OF ECONOMICS MACROECONOMICS THEORY Preliminary Exam August 1, :00 am - 2:00 pm
UNIVERSITY OF WISCONSIN DEPARTMENT OF ECONOMICS MACROECONOMICS THEORY Preliminary Exam August 1, 2017 9:00 am - 2:00 pm INSTRUCTIONS Please place a completed label (from the label sheet provided) on the
More informationMacroeconomics Theory II
Macroeconomics Theory II Francesco Franco FEUNL February 2011 Francesco Franco Macroeconomics Theory II 1/34 The log-linear plain vanilla RBC and ν(σ n )= ĉ t = Y C ẑt +(1 α) Y C ˆn t + K βc ˆk t 1 + K
More informationReal Business Cycle Model (RBC)
Real Business Cycle Model (RBC) Seyed Ali Madanizadeh November 2013 RBC Model Lucas 1980: One of the functions of theoretical economics is to provide fully articulated, artificial economic systems that
More informationFoundation of (virtually) all DSGE models (e.g., RBC model) is Solow growth model
THE BASELINE RBC MODEL: THEORY AND COMPUTATION FEBRUARY, 202 STYLIZED MACRO FACTS Foundation of (virtually all DSGE models (e.g., RBC model is Solow growth model So want/need/desire business-cycle models
More informationThe Ramsey Model. (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 2013)
The Ramsey Model (Lecture Note, Advanced Macroeconomics, Thomas Steger, SS 213) 1 Introduction The Ramsey model (or neoclassical growth model) is one of the prototype models in dynamic macroeconomics.
More informationEquilibrium Conditions and Algorithm for Numerical Solution of Kaplan, Moll and Violante (2017) HANK Model.
Equilibrium Conditions and Algorithm for Numerical Solution of Kaplan, Moll and Violante (2017) HANK Model. January 8, 2018 1 Introduction This document describes the equilibrium conditions of Kaplan,
More informationCapital Structure and Investment Dynamics with Fire Sales
Capital Structure and Investment Dynamics with Fire Sales Douglas Gale Piero Gottardi NYU April 23, 2013 Douglas Gale, Piero Gottardi (NYU) Capital Structure April 23, 2013 1 / 55 Introduction Corporate
More informationLecture 2 The Centralized Economy
Lecture 2 The Centralized Economy Economics 5118 Macroeconomic Theory Kam Yu Winter 2013 Outline 1 Introduction 2 The Basic DGE Closed Economy 3 Golden Rule Solution 4 Optimal Solution The Euler Equation
More informationOn the existence, efficiency and bubbles of a Ramsey equilibrium with endogenous labor supply and borrowing constraints
On the existence, efficiency and bubbles of a Ramsey equilibrium with endogenous labor supply and borrowing constraints Robert Becker, Stefano Bosi, Cuong Le Van and Thomas Seegmuller September 22, 2011
More informationSimple Consumption / Savings Problems (based on Ljungqvist & Sargent, Ch 16, 17) Jonathan Heathcote. updated, March The household s problem X
Simple Consumption / Savings Problems (based on Ljungqvist & Sargent, Ch 16, 17) subject to for all t Jonathan Heathcote updated, March 2006 1. The household s problem max E β t u (c t ) t=0 c t + a t+1
More informationA Modern Equilibrium Model. Jesús Fernández-Villaverde University of Pennsylvania
A Modern Equilibrium Model Jesús Fernández-Villaverde University of Pennsylvania 1 Household Problem Preferences: max E X β t t=0 c 1 σ t 1 σ ψ l1+γ t 1+γ Budget constraint: c t + k t+1 = w t l t + r t
More informationNegative Income Taxes, Inequality and Poverty
Negative Income Taxes, Inequality and Poverty Constantine Angyridis Brennan S. Thompson Department of Economics Ryerson University July 8, 2011 Overview We use a dynamic heterogeneous agents general equilibrium
More information"0". Doing the stuff on SVARs from the February 28 slides
Monetary Policy, 7/3 2018 Henrik Jensen Department of Economics University of Copenhagen "0". Doing the stuff on SVARs from the February 28 slides 1. Money in the utility function (start) a. The basic
More information1 Overlapping Generations
1 Overlapping Generations 1.1 Motivation So far: infinitely-lived consumer. Now, assume that people live finite lives. Purpose of lecture: Analyze a model which is of interest in its own right (and which
More informationIndeterminacy with No-Income-Effect Preferences and Sector-Specific Externalities
Indeterminacy with No-Income-Effect Preferences and Sector-Specific Externalities Jang-Ting Guo University of California, Riverside Sharon G. Harrison Barnard College, Columbia University July 9, 2008
More informationEco504 Spring 2009 C. Sims MID-TERM EXAM
Eco504 Spring 2009 C. Sims MID-TERM EXAM This is a 90-minute exam. Answer all three questions, each of which is worth 30 points. You can get partial credit for partial answers. Do not spend disproportionate
More informationGrowth Theory: Review
Growth Theory: Review Lecture 1.1, Exogenous Growth Topics in Growth, Part 2 June 11, 2007 Lecture 1.1, Exogenous Growth 1/76 Topics in Growth, Part 2 Growth Accounting: Objective and Technical Framework
More informationDynamic (Stochastic) General Equilibrium and Growth
Dynamic (Stochastic) General Equilibrium and Growth Martin Ellison Nuffi eld College Michaelmas Term 2018 Martin Ellison (Nuffi eld) D(S)GE and Growth Michaelmas Term 2018 1 / 43 Macroeconomics is Dynamic
More information