Models for dynamic macroeconomics phần 1 doc

[...]... 13 4 13 6 13 8 13 9 14 0 14 1 14 4 14 7 14 8 15 1 15 2 15 3 15 6 15 7 15 8 16 0 16 3 16 7 16 8 17 0 17 1 17 1 17 2 18 0 18 0 18 2 18 5 18 8 18 9 19 1 19 2 19 5 19 9 19 9 203 xii DETAILED CONTENTS 5.5 Externalities and efficiency Appendix A5: Strategic Interactions and Multipliers Review Exercises Further Reading References 206 211 216 217 219 ANSWERS TO EXERCISES 2 21 INDEX 274 LIST OF FIGURES 1. 1 Precautionary savings 24 2 .1 Unit investment... FIGURES xiii 1 Dynamic Consumption Theory 1 1 5 7 9 11 13 13 15 19 22 22 25 29 31 35 36 41 43 45 1. 1 Permanent Income and Optimal Consumption 1. 1 .1 Optimal consumption dynamics 1. 1.2 Consumption level and dynamics 1. 1.3 Dynamics of income, consumption, and saving 1. 1.4 Consumption, saving, and current income 1. 2 Empirical Issues 1. 2 .1 Excess sensitivity of consumption to current income 1. 2.2 Relative... 5.2 .1 The structure of the economy 5.2.2 Optimal strategies and equilibria 5.2.3 Implications 5.3 Search Externalities in the Labor Market 5.3 .1 Frictional unemployment 5.3.2 The dynamics of unemployment 5.3.3 Job availability 5.3.4 Wage determination and the steady state 5.4 Dynamics 5.4 .1 Market tightness 5.4.2 The steady state and dynamics 11 0 11 4 11 5 11 7 11 9 12 2 12 5 12 7 12 8 12 9 13 0 13 2 13 4 13 6 13 8... to permanent income Unfolding the definition of human wealth Ht in (1. 16), we can write saving at t as s t = yt − = r 1+ r ∞ i =0 1 1 yt − − 1+ r 1+ r 1 1+r − ∞ =− i =1 1 1+ r i 1 1+r 2 − E t yt+i 1 1+r 1 1+r 2 E t yt +1 3 E t yt+2 + i E t yt+i , (1. 17) where yt+i = yt+i − yt+i 1 Equation (1. 17) sheds further light on the motivation for saving in this model: the consumer saves, accumulating financial... substituted into (1. 15) to obtain the effect on consumption c t +1 The revision in expectations of future incomes is given by E t +1 yt +1+ i − E t yt +1+ i = Îi εt +1 , ∀i ≥ 0 Substituting this expression into (1. 15) for each period t + 1 + i , we have r 1 1+r ∞ i =0 1 1+r i Î εt +1 i r = εt +1 1+r ∞ i =0 Î 1+ r i , (1. 19) and solving the summation, we get6 c t +1 = c t + r εt +1 , 1+ r −Î (1. 20) which directly... agent in t + 1, (E t +1 − E t )yt +1+ i ≡ E t +1 yt +1+ i − E t yt +1+ i is not zero for all i The evolution over time of consumption follows that of permanent income, so that we can write c t +1 1 = ct + r 1+ r = c t + ut +1 ∞ i =0 1 1+r i (E t +1 − E t )yt +1+ i (1. 15) It can be easily verified that the change of consumption between t and t + 1 cannot be foreseen as of time t (since it depends only on information... rule out, or limit, borrowing): 1 1+r ∞ i 1 1+r i =0 c t+i = 1 1+r ∞ 1 1+r i =0 i yt+i + At (1. 4) 1. 1 .1 OPTIMAL CONSUMPTION DYNAMICS Substituting the consumption level derived from the budget constraint (1. 2) into the utility function, we can write the consumer’s problem as ∞ i 1 1+Ò max Ut = E t i =0 u( (1 + r )At+i − At+i +1 + yt+i ) with respect to wealth At+i for i = 1, 2, , given initial wealth... period, we have P yt +1 = r (At +1 + Ht +1 ) (1. 13) P Taking the expectation at time t of yt +1 , subtracting the resulting expression from (1. 13), and noting that E t At +1 = At +1 from (1. 2), since realized income yt is included in the consumer’s information set at t, we get P P yt +1 − E t yt +1 = r (Ht +1 − E t Ht +1 ) (1. 14) Permanent income calculated at time t + 1, conditional on information available... expression in (1. 19) can be written εt +1 (r /1 + r )S∞ (Î /1 + r ) if we denote by S N (·) a geometric series with parameter ·, of order N Since S N (·) − ·S N (·) = (1 + · + ·2 + + · N ) − (· + ·2 + ·3 + + · N +1 ) = 1 + · N +1 , such a series takes values S N (·) = (1 + · N +1 )/ (1 − ·) and, as long as · < 1, converges to S∞ (·) = (1 − ·) 1 as N tends to infinity Using this formula in (1. 19) yields the... consumption 1. 2.3 Joint dynamics of income and saving 1. 3 The Role of Precautionary Saving 1. 3 .1 Microeconomic foundations 1. 3.2 Implications for the consumption function 1. 4 Consumption and Financial Returns 1. 4 .1 Empirical implications of the CCAPM 1. 4.2 Extension: the habit formation hypothesis Appendix A1: Dynamic Programming Review Exercises Further Reading References 2 Dynamic Models of Investment 2.1 . dynamics 5 1. 1.2 Consumption level and dynamics 7 1. 1.3 Dynamics of income, consumption, and saving 9 1. 1.4 Consumption, saving, and current income 11 1. 2 Empirical Issues 13 1. 2 .1 Excess sensitivity. CONTENTS xi 3.2 The Dynamics of Employment 11 0 3.3 Average Long-Run Effects 11 4 3.3 .1 Average employment 11 5 3.3.2 Average profits 11 7 3.4 Adjustment Costs and Labor Allocation 11 9 3.4 .1 Dynamic wage. borrowing): 1 1+r ∞  i=0  1 1+r  i c t+i = 1 1+r ∞  i=0  1 1+r  i y t+i + A t . (1. 4) 1. 1 .1. OPTIMAL CONSUMPTION DYNAMICS Substituting the consumption level derived from the budget constraint (1. 2) into