the volatility proxy VX . The analysis considers the following three linear models: (1) the model that relies on lagged exchange rates and the inflation and interest rate differentials, labeled VAR; (2) a model that extends the VAR model to include the PPP condition labeled VECM; and (3) a model that extends VECM with lagged values of VX labeled VECM+X. These three models will be pitched against the ubiquitous random walk model investigated in the celebrated Meese and Rogoff (1983) paper. Full sample, monthly panel estimates of these models with three-month holding periods are reported in table 3.

Table 4 – Tests of Nonlinearity

## Specification of the auxiliary regression:

(e_{j,t − }e_{j,t−3 }

) = α _{j + ρ(ej,t−3 }

− e_{j,t−6 }

) + γ_{π (π }

* t−3

− pi_{j,t−3 }

) + γ _{q (q j,t }

− q) +

4

∑ h i β

* t−3

− i_{j,t−3 }

h

4

∑ + h V X δ

h j ,t −3

+

u

_{j,t }

h =1

h −1

fixed-effects, panel-estimation.

## Nonlinearity hypothesis:

( a ) 0 4 1 = = = β β L

( b ) 0 4 1 = = = δ δ L

( c ) 0 4 1 4 1 = = = = = = δ δ β β L L

## Summary of results:

## Hypothesis

(a) Nonlinearity in i

* t−3

− i_{j,t−3 }

(b)

Nonlinearity in VX

_{j,t−3 }(c)

Nonlinearity in both

F(3,826)

16.62

[p-value]

[0.0000]

F(3,826)

0.61

[p-value]

[0.6090]

F-test

## Value

F(6,826)

9.43

[p-value]

[0.0000]

19