where the levels of the first two entries are I(1) variables which will be cointegrated if t h e P P P c o n d i t i o n h o l d s w i t h c o i n t e g r a t i n g v e c t o r τ τ τ τ p p e q − + = * – t h i s i s , o f

course, the real exchange rate. Therefore, an investigation of the dynamic properties of this system would in principle require an impulse response analysis based on its vector error correction (VECM) representation. Notice that the last two variables in this

s y s t e m , t h e i n t e r e s t r a t e d i f f e r e n t i a l 1 * + τ i

− i_{τ +1 }

and VX_{τ }_{+1 }

, appear in the levels because

they are stationary. It is not common to have mixed orders of integration within the variables in a system, however, this poses no difficulty from a statistical point of view and the problem is well posed.

Because the rather short time-series dimension of our panel, we cannot use a system's estimator on (1) to obtain impulse responses because it requires estimation of many parameters and availability of degrees of freedom that are not simple at our disposal. Instead, we focus on the local projections of Jordà (2005, 2009) extended to the panel context. In particular, it is of interest to determine the response of the carry

trade (i.e. m _{j,τ +1 }

≡ ∆e_{j,τ }_{+1 }

+i

* j ,τ

− i _{j,τ }

) to fluctuations in the inflation differential, the

P P P c o n d i t i o n , t h e U I P c o n d i t i o n c a p t u r e d b y τ τ i i − * , a n d t h e v o l a t i l i t y τ V X . C h o n g ,

Jordà and Taylor (2009) show that this can be accomplished with the following series of fixed-effect panel regressions:

m_{j,τ +h }

∆ + = , e j h e h j τ β α

+ ( h π π β

* j ,τ

+ − ( ) , , q j h q j τ τ β π

− q) +

(2)

K

β ( h i i

* j ,τ

τ τ β , ) h v j V X i + + − ∑

τ γ , k j h k y ∆ −

+

u

_{j,τ }

k =1

for h =1,K, H . Specifically, Chong, Jordà and Taylor (2009) show that for the stationary variables, for example

LP(e_{τ+h }

v V X β τ = ) h ,

(3)

and similarly for i

* j ,τ

− i_{j,τ }

. However, the local projections due to a PPP shock are

LP(e_{τ +h }

q h h e q β β β π τ + + = ) ( ) h ,

(4)

10