Macroeconomics Theory II

Transcription

1 Macroeconomics Theory II Francesco Franco Nova SBE March 9, 216 Francesco Franco Macroeconomics Theory II 1/29

2 The Open Economy Two main paradigms Small Open Economy: the economy trades with the ROW but does not a ect the ROW. No strategic interactions. Two Countries Model: : the economy trades with the ROW and a ects the ROW. Strategic Interactions. Francesco Franco Macroeconomics Theory II 2/29

3 The Open Economy With many variants Price Setting decisions: producer currency pricing: PCP, local currency pricing: LCP International asset markets: complete markets, incomplete markets, imperfect substitution, financial autarky. Tradeables and NonTradeables. Exchange rate regime: flexible, fixed. Francesco Franco Macroeconomics Theory II 3/29

4 Benchmark SMOE Will intrododuce exchange rate. the terms of trade. exports, and imports. international financial markets. GDP deflator di erent from CPI. Francesco Franco Macroeconomics Theory II 4/29

5 Benchmark SMOE Gali-Monacelli 25 Many simplifying assumptions that hode many trade-o s (see: Corsetti, Dedola and Leduc 21), but useful as a benchmark. Francesco Franco Macroeconomics Theory II 5/29

6 Benchmark SMOE Gali-Monacelli 25 There is a continuum of countries indexed by i œ [, 1] of measure one. the problem facing households and firms located in one such economy (without an index) will be described in detail. Francesco Franco Macroeconomics Theory II 6/29

7 Households Utility The household seeks to maximize a standard constant elasticity of substitution where C t = E Œ ÿ s= s S U C 1 1 t+s 1 1 N1+ t+s 1 + T V, 5 6 (1 ) 1 (C H,t ) (C F,t ) 1 1. where C H,t is an index of consumption of domestic goods given by a constant elasticity of substitution aggregator C H,t = (C H,t (j)) 1 1 dj where j œ [, 1] denotes an individual good variety. Francesco Franco Macroeconomics Theory II 7/29

8 Households Foreign Goods Similarly C F,t is a consumption index of imported goods given by C F,t = (C i,t ) 1 1 di, where C i,t, is in turn, an index of the consumption of varieties of goods imported from country i, given by C i t = 5 1 (C i t(j)) 1 dj 6 1. Francesco Franco Macroeconomics Theory II 8/29

9 Nested indexes Parameters is the elasticity of substitution between varieties produced within a given country, is the elasticity between domestic and foreign goods, is the elasticity between goods produced in di erent foreign countries. indexes the degree of home bias, and can be interpreted as a measure of openness. Francesco Franco Macroeconomics Theory II 9/29

10 Budget Constraint Sticky wages Maximization of utility is subject to a sequence of budget constraints of the form 3 1 +B t+1 + P H,t (j)c H,t (j)dj B i,t+1 di Æ R t 1 B t P i,t (j)c i,t (j)djdi R i,t 1 B i,t+1 di+w t N t + t +T t Francesco Franco Macroeconomics Theory II 1/29

11 Optimal Expenditure allocation Intratemporal conditions The optimal allocation of any given expenditure within each category of goods yields the demand functions 1 2 PH,t (j) 1 2 Pi,t C H,t (j) = P CH,t H,t, C i,t = P CF F,t,t, C i,t (j) = 1 2 Pi,t (j) Ci,t P i,t and price indexes: Ë s P H,t = 1 P H,t(j) djè 1 1 1, Ë s È 1 P F,t = 1 P1 i,t di 1,P i,t = Ë s 1 Pi i,t (j)1 djè 1 1 Francesco Franco Macroeconomics Theory II 11/29

12 Optimal Expenditure allocation Intratemporal conditions The optimal allocation of expenditure in tradable goods between domestic and foreign implies C H,t = A Pt P H,t B (1 )C T,t, C F,t = A Pt P F,t B C T,t, r, where the latter is expressed in terms of consumption using the household s marginal valuation of income, where P t = Ë(1 )(P H,t ) 1 + (P F,t ) 1 È 1 1 is the CPI. Francesco Franco Macroeconomics Theory II 12/29

13 Exchange rates The Real Exchange Rate, and the Terms of Trade The real exchange rate is Q t = Pú t P t, where P ú t = Ë s È 1 1 Pi1 i,t di 1 and the terms of trade is where S i,t = P i,t /P H,t. S t = P F,t P H,t = S 1 1 i,t di, Francesco Franco Macroeconomics Theory II 13/29

14 Exchange rates The Nominal Exchange Rate Assume that the law of one price holds for individual goods at all times (both for importandexportprices),implying that P i,t (j) =E i,t P i i,t(j) for all i, j œ [, 1], wheree i,t is the bilateral nominal exchange rate: the price of country i s currency in terms of the domestic currency. Francesco Franco Macroeconomics Theory II 14/29

15 New Conditions Log-linear equations Around a symmetric steady state S i,t = 1foralli œ [, 1] s t = 1 s i,t di The CPI p t =(1 ) p H,t + p F,t = p H,t + s t so that CPI inflation fi t = fi H,t + s t Francesco Franco Macroeconomics Theory II 15/29

16 New Conditions Log-linear equations Around a symmetric steady state E i,t = 1foralli œ [, 1] e t = 1 e i,t di The Foreign price level p F,t = e i,t + pi,t i di p F,t = e t + p ú t combining with terms of trade s t = e t + p ú t p H,t Francesco Franco Macroeconomics Theory II 16/29

17 New Conditions Log-linear equations Around a symmetric steady state Q i,t = 1foralli œ [, 1] q t = 1 q i,t di The Foreign price level q t = 1 q t =(1 ) s t 2 1e i,t + pi,t i p t di Francesco Franco Macroeconomics Theory II 17/29

18 Optimal Conditions Standard foc Intratemporal condition W t P t = C t N t and intertemporal condition I 3Ct+1 4 P t Q t = E t C t P t+1 J Francesco Franco Macroeconomics Theory II 18/29

19 Complete international Markets Full risk sharing The saving condition for securities traded internationally must hold for all economies, therefore YA B Z ] C i Q t = E t+1 P i t E i ^ t t [ \ C i t P i t+1 E i t+1 Equating the Q t and using the definition of the real exchange rate and an initial condition you get C t = Ë i C i tq 1 i,t the assumption of complete markets at the international level leads to a simple relationship linking domestic consumption with foreign consumption and the real exchange rate. Francesco Franco Macroeconomics Theory II 19/29

20 New Conditions Log-linear equations The risk sharin condition c t = c ú t + 1 q t where s 1 ci tdi = c ú t Francesco Franco Macroeconomics Theory II 2/29

21 Firms Standard New Keynesian model Continuum of firms,j œ [, 1], each producing a di erentiated good. Y t (j) =A t N t (j) Francesco Franco Macroeconomics Theory II 21/29

22 Firms Standard New Keynesian model The price of each good reset with a probability 1 p each period, which with the optimal pricing condition and the aggregate price dynamics gives but the marginal cost fi H,t = E t {fi H,t+1 } + mc t mc t = w t p H,t a t depends on domestic price not cpi. Francesco Franco Macroeconomics Theory II 22/29

23 Equilibrium Goods market clearing Market clearing in the tradable goods market requires that Y H,t (j) =C H,t (j)+ 1 C i H,t(j)di, holds in every period. Letting aggregate output be defined as 1 s 2 Y H,t 1 Y H,t(j) 1 dj 1 it follows that Y H,t = 3 PH,t P t (1 ) C t Qt i S i,t Si,t2 i C i t di. Francesco Franco Macroeconomics Theory II 23/29

24 New Conditions Log-linear equations The approximation around a symmetric steady state of the previous equation y t = c t + s t + y t = c t + Ê s t q t combining with risk sharing and s 1 y i tdi = y ú t with = 1+ (Ê 1) y t = y ú t + 1 s t Francesco Franco Macroeconomics Theory II 24/29

25 New Conditions Implications In this model the the marginal cost mc t =( + ) y t +( ) y ú t (1 + ) a t A change in domestic output has an e ect on marginal cost through its impact on employment (captured by f) and the terms of trade (captured by, which is a function of the degree of openness and the substitutability between domestic and foreign goods). World output, on the other hand, a ects marginal cost through its e ect on consumption (and, hence, the real wage as captured by ) and the terms of trade (captured by ). Francesco Franco Macroeconomics Theory II 25/29

26 New Conditions Implications In this model the the Euler y t = E t {y t+1 } 1 (i t E t {fi t+1 } fl) Ê E t{ s t+1 } y t = E t {y t+1 } 1 (i t E t {fi H,t+1 } fl)+ E t { y ú t+1} Francesco Franco Macroeconomics Theory II 26/29

27 Benchmark SOE NKM Three equations y t = E t { y t+1 } 1 (i t E t {fi H,t+1 } r n t ) fi H,t = E t {fi H,t+1 } + Ÿ y t r n t = fl (1 fl ) a t + + E t ) y ú t+1 * Francesco Franco Macroeconomics Theory II 27/29

28 Benchmark SOE NKM Policy Three di eren policies: i t = fl + fi fi H,t i t = fl + fi fi t e t = Francesco Franco Macroeconomics Theory II 28/29

29 IRFs Figure : Source: Gali-Monacelli 25 Francesco Franco Macroeconomics Theory II 29/29