Open Economy Macroeconomics: Theory, methods and applications

Transcription

1 Open Economy Macroeconomics: Theory, methods and applications Econ PhD, UC3M Lecture 9: Data and facts Hernán D. Seoane UC3M Spring, 2016

2 Today s lecture A look at the data Study what data says about open economies Stress 1: business cycle differences among developed and emerging economies Stress 2: private versus sovereign behavior Technical point: data treatment (log-linear, log-quadratic, HP filter, Band pass filter, growth rates, etc)

3 Today s lecture (cont.) A Mickey Mouse model Endowment small open economy Small open economy with capital RBC small open economy model

4 Today s lecture References This lecture is based on chapters 1 to 4 of Schmitt-Grohe and Uribe (2015) texbook

5 Detrending We focus in cyclical component We have to remove the trend or secular component from the raw data The cyclical component is going to be different depending on the assumptions about the trend y t = y c t + ys t

6 Detrending Log-quadratic trend y t denotes the log of real output (per capita) Assume: y t = a + bt + ct 2 + ɛ t Set y c t = ɛ t y s t = a + bt + ct2

7 Detrending Log-quadratic trend Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1

8 Detrending Log-quadratic trend Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1

9 Detrending Log-quadratic trend The cyclical component shows 3 cycles std(y c t ) = 10.7% corr(y c t, yc t 1 ) = 0.85

10 Detrending Log-quadratic trend 94 countries,at least 30 observations, worldwide Cross country average std(y t ) = 6.2% std(g t )/std(y t ) = 2.3 Government consumption is more than 2 times more volatile than output

11 Detrending Log-quadratic trend Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1

12 Detrending Log-quadratic trend Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1 ρ(y, tby) = 0.15 and ρ(y, g) = 0.02

13 Facts 1 High global volatility 2 High volatility of government consumption 3 Global rank of volatilities 4 Procyclical aggregate demand components 5 Countercyclical trade balance and the current account 6 Acyclical Government consumption to GDP 7 Persistence

14 Detrending Log-quadratic trend Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1

15 Facts 1 US is much less volatile than the rest of the world 2 std(c t )/std(y t ) = the role of durable goods 3 std(g t )/std(y t ) = government spending is strongly counter-cyclical 4 US is much less open than the rest of the world, (x + m)/y = 18%, while for the world is about twice as much 5 Conditional on income level

16 Detrending Log-quadratic trend Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1

17 Detrending Log-quadratic trend Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1 1 Conditional on country size

18 Facts Emerging Economies 1 Excess volatility of emerging and poor countries 2 Less consumption smoothing 3 Countercyclical trade balance increases with income 4 Countercyclical government spending increases with income

19 Detrending Hodrick-Prescott Filter (1987) Here, the trend and cyclical components are identified by solving a minimization problem min {y c t,y s t }T t=1 { T (y c t) 2 + λ t=1 } T 1 [( y s t+1 y s ) ( t y s t y s )] 2 t 1 t=2 Subject to y t = y c t + ys t

20 Detrending Hodrick-Prescott Filter (1987) Trade-off between minimizing the variance of the cyclical component and keeping the growth rate of the trend constant λ regulates this trade-off. The higher λ, the more we penalize changes in the growth rate of the trend component. If λ is infinite the resulting trend is linear Ravn and Uhlig (2001)

21 Detrending Hodrick-Prescott Filter (1987) Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1

22 Detrending Hodrick-Prescott Filter (1987) Figure: Source: Schmitt-Grohe and Uribe (2015) Ch1

23 Three Models 1 Cycles look very different 2 However, business cycle facts still hold 3 Other options: first differencing 4 However, business cycle facts still hold 5 Quarterly data too

24 Three Models 1 Small Open Economy Endowment model 2 Small Open Economy with Capital 3 Small Open Economy Real Business Cycle Model

25 SOE Endowment model E 0 t=0 β t u(c t ) d t d t 1 = rd t 1 + c t y t d t is the debt position (net) assumed in period t and due in t + 1 d t+j A no Ponzi condition lim E j 0 j (1+r) j The Lagrangian for this problem is L = E 0 t=0 β t {u(c t ) + λ t [d t d t 1 rd t 1 c t + y t ]}

26 SOE Endowment model Euler equation is u (c t ) = β(1 + r)e t [u (c t+1 )] with the standard interpretations: in the margin the household is indifferent between consuming in period t or saving the extra unit of consumption for period t + 1 The intertemporal budget constraint (1 + r)d t 1 = E t j=0 y t+j c t+j (1 + r) j

27 SOE Endowment model Note that the definition of the trade balance is tb t = y t c t The intertemporal budget constraint implies then that (1 + r)d t 1 = E t j=0 tb t+j (1 + r) j

28 SOE Endowment model Assume u(c t ) = 1 2 [c t c] 2 and β(1 + r) = 1 Euler equation is c t = E t [c t+1 ] Standard RW result Using the intertemporal budget constraint we can get c t = r (1 + r) E t j=0 y t+j (1 + r) j rd t 1 note that it depends on the the income process

29 SOE Endowment model r Note, (1+r) E t j=0 1 = 1 (1+r) j Consumption is a weighted average of your expected lifetime stream of endowments Endowments are exogenous d t 1 is predetermined c t = r (1 + r) E t j=0 y t+j (1 + r) j rd t 1 is a closed form solution of c t Define y p t = r (1+r) E t j=0 y t+j (1+r) j

30 SOE Endowment model Plugging the closed form solution to c t in the budget constraint, we get d t d t 1 = y p t y t is a closed form solution of debt An expression for the current account ca t = tb t rd t 1 Combining it with the sequential budget constraint ca t = (d t d t 1 ) The current account equals the change in the net foreign asset position (a deficit in the current account is associated with an increase in foreign debt)

31 SOE Endowment model we can also write ca t = y t y p t you run a current account surplus when income is larger than your permanent income E t y t+j = ρ j y t Also tb t = y t y p t rd t 1

32 SOE Endowment model Recall that we assume endowment follows a mean reverting AR(1) process E t y t+j = ρ j y t Here c t = r (1 + r ρ) y t rd t 1 Consumption responds positively to income, but not 1 to 1 Recall: tb t = y t c t Recall: ca t = rd t 1 + tb t or ca t = (d t d t 1 )

33 SOE Endowment model you can build the path of sovereign debt d t = d t 1 1 ρ (1 + r ρ) y t There is a unit root for the international assets The trade balance tb t = rd t 1 + ca t = 1 ρ (1 + r ρ) y t 1 ρ (1 + r ρ) y t A positive shock to output have a permanent effect on foreign debt and a permanent deterioration on the trade balance

34 SOE Endowment model: stationary shock Endowment Consumption Trade Balance and the Current Account Foreign Debt ca1 tb1

35 SOE Endowment model If ρ 1, you tend to consume all the increase in endowment No changes in your debt position, trade balance or current account

36 SOE Endowment model Problem, current account is pro-cyclical (it improves during expansions) Trade balance is procyclical In the data it is the opposite What happens with permament shocks? y t = y t y t 1 and y t = ρ y t 1 + ɛ t

37 SOE Endowment model Implies ca t = E t j=1 y t+j (1 + r) j ca equals expected output fall. In we expect output to fall, ca is positive because we are saving (accumulating assets) for future consumption smoothing Given that E t y t+j = ρ j y t ca t = ρ 1 + r ρ y t

38 SOE Endowment model: Nonstationary shock Output Consumption

39 SOE Endowment model Consumption responds on impact more than output The difference is financed with foreign debt Implies that current account deteriorates Trade balance also deteriorates This is more in line with the data

40 SOE Endowment model Testing the model A testable implication of the model Let x = [ y t ca t ca t = Estimate the following VAR ] j=1 E t y t+j (1 + r) j x t = Dx t 1 + ɛ t Under y t univariate AR(1), the VAR representation exists

41 SOE Endowment model Testing the model Use H t to denote the information contained in vector x t, then E t [x t+j H t ] = D j x t Using this representation [ E t [ y t+j H t ] j=1 (1 + r) j = [1 0] I D ] [ 1 D 1 + r 1 + r y t ca t ] Use [ F = [1 0] I D ] 1 D 1 + r 1 + r

42 SOE Endowment model Testing the model Now, suppose you run 2 separate regressions on the right and left hand sides of ca t = j=1 E t y t+j (1 + r) j The coefficients for the regressors for the left hand side should be [0 1] The coefficients for the regressors for the right hand side should be F The model implies the constraint than F = [0 1] Nason and Rogers (2006) test this implications using Canadian data

43 SOE Endowment model 1 The data rejects this cross-equation restriction 2 This suggests we should start looking for other model 3 How do things change when we endogenize output 4 Introduce capital... why capital? 5 If investment is procyclical, this will contribute to a countercyclical trade balance

44 Capital and open economy E 0 t=0 β t u(c t ) c t + i t + (1 + r)d t 1 = y t + d t y t = θ t F(k t ) k t+1 = k t + i t lim j d t+j (1 + r) j 0 And the no Ponzi game constraint

45 Capital and open economy Optimality conditions u (c t ) = λ t λ t = β(1 + r)λ t+1 λ t = βλ t+1 [1 + θ t+1 F (k t+1 )] c t + k t+1 k t + (1 + r)d t 1 = d t + θ t F(k t )

46 Capital and open economy Set β(1 + r) = 1 c t + rd t 1 = c t = c t+1 r = θ t+1 F (k t+1 ) r θ t+j F(k t+j ) k t+j+1 + k t+j (1 + r) j=0 (1 + r) j Implies k t+1 = κ ( θt+1 r ) ; κ > 0

47 Capital and open economy Steady state equilibrium Let s look at the steady state equilibrium Until t = 1 the technology θ t is fixed at θ Agent s expect θ t to remain at this level However, in this period θ t = θ > θ for all t 0 Recall that k was constant at k, now ( ) ( θ θ ) k = κ < κ = k r r So, investment jumps only for one period

48 Capital and open economy Steady state equilibrium Output increases because of the increase in productivity Later, it increases once more because of the increase in the capital stock We can plug these dynamics in the budget constraint

49 Capital and open economy Steady state equilibrium Figure: Source: Schmitt-Grohe and Uribe (2015) Ch3

50 Capital and open economy A permanent shock Note that k 0 = k as it was chosen in t = 1, but k 1 increases This implies that i 0 = k 1 k 0 = k k. Plug it here c 0 = rd + r (1 + r) [θ F(k) k + k] + 1 (1 + r) θ F(k ) or, given that all future consumption is constant c = rd + θ F(k) + 1 { θ [F(k ) F(k)] r(k k) } 1 + r

51 Capital and open economy A permanent shock or c = rd + θ F(k) + 1 { θ [F(k ) F(k)] θ F (k )(k k)] } 1 + r Given that F is strictly concave and k > k, the bracket is positive ( F(k ) F(k) k k > F (k )) Then c > rd + θ F(k) > rd + θf(k) = c

52 Capital and open economy A permanent shock It can be shown that consumption increases more than output in period 0 Intuition, output will continue to grow after 0 because of the response of capital Households increase borrowing Trade balance deteriorates to finance the extra investment and the extra consumption The current account also deteriorates and after period 1 it goes back to 0 this result is different from the endowment economy, with a permanent shock trade balance used to remain unchanged, but here deteriorates on impact

53 Capital and open economy A temporary shock Suppose that now, unexpectedly θ increases but only for 1 period; i.e. purely temporal change Investment does not respond. We will only have high technology for 1 period, but capital is fixed in that period Output then only changes because of the productivity change, and only for that first period y 0 = y 1 + (θ θ)f( k) Here y 1 = ĀF( k). Remember that consumption was equal to (before the shock) c 1 = rd + θf( k)

54 Capital and open economy A temporary shock Now you can show that c 0 = c 1 + r 1 + r (y 0 y 1 ) Implications of the permanent income hypothesis are that consumption responds only partially (you only consume the returns of extra income, and reinvest the rest) savings increases, so trade balance has to improve tb 0 tb 1 = (y 0 y 1 ) (c 0 c 1 ) = r (A Ā)F( k) > 0 persistence of the shock affects the countercyclicality of the trade balance

55 Capital and open economy Adjustment costs usually the open economy model needs to assume adjustment costs on capital, otherwise the growth rate of investment is counterfactually large during the period of the shock (1 + r)d t 1 = d t + θ t F(k t ) c t i t 1 i 2 t 2 k t Investment does not respond Output then only changes because of the productivity change, and only for that first period Implications of the permanent income hypothesis are that consumption responds only partially savings increases, so trade balance has to improve

56 Capital and open economy E 0 t=0 β t u(c t ) (1 + r)d t 1 = d t + y t c t i t 1 i 2 t 2 k t y t = θ t F(k t ) k t+1 = k t + i t lim j d t+j (1 + r) j 0 And the no Ponzi game constraint

57 Capital and open economy Optimality conditions. Denote β t λ t the Lagrange multiplier on the budget constraint and β t λ t q t the Lagrange multiplier on the law of motion of capital { [ ]} L = β t u(c t ) + λ t θ t F(k t ) + d t (1 + r)d t 1 c t i t 1 i 2 t + q t (k t + i t k 2 k t+1 ) t=0 t which gives the following FOCs λ t q t = βλ t+1 [ 1 + i t k t = q t q t+1 + θ t+1 F (k t+1 ) ( ) ] 2 it+1 k t+1

58 Capital and open economy Keep assuming that β(1 + r) = 1 This implies that c t = c t+1 and λ t is constant c t = rb t 1 + r (1 + r) c t = c t+1 j=0 θ t+j F(k t+j ) i t+j 1 2 (1 + r) j i 2 t+j k t+j

59 Capital and open economy 1 + i t k t = q t ( it+1 ) 2 + q t+1 (1 + r)q t = θ t+1 F (k t+1 ) k t+1 i t = k t+1 k t Here q t is the Tobin s q: 1 + i t k t = q t implies that the marginal cost of producing 1 unit of capital equals the marginal revenue of selling it the following equation is an arbitrage condition that compares the return of that unit of capital (sold) in bonds, and the returns on keeping the unit of capital and using it for production

60 Capital and open economy Working out the FOC, you can obtain a dynamic system for capital and q k t+1 = q t k t q t = θ t+1f (q t k t ) + (q t+1 1) 2 /2 + q t r

61 Capital and open economy Figure: Source: Schmitt-Grohe and Uribe (2015) Ch3

62 Capital and open economy A permanent shock The locus KK does not change QQ shifts up capital increases permanently but the price does not change in the long run now capital adjusts slowly, before without adjustment costs the capital stock goes to the steady state level immediately Then the trade balance is less responsive to productivity shocks

63 Capital and open economy 1 Proposition 1: The more persistence the productivity shock, the more likely is the trade balance to deteriorate after a productivity shocks 2 Proposition 2: the higher adjustment costs of capital, the less likely the trade balance is going to deteriorate after a productivity shock