The state-space models contain two equations: one state equation and one signal equation. The state equation reflects the
state of the dynamic system at a certain moment under the
effect of state variables and the signal equation (or measurement equation) connects the state vector of unobserved
variables with output variables EFit at some time. When the
dynamic system is expressed in state-space form, important
algorithms with Kalman filtering as the core can be applied to
it. The essence of a Kalman filter is to reconstruct the state vector of the system based upon the measurements.
The signal equation can be written as:
EFit =[ 1 1 1][ ] ωit νit εit ( 4)
The state equation is:
=+ [ [ [ ] ] ] ωit ωit ωit– 1 νit νit νit– 1 εit εit εit– 1 [ [ ] ] 11 0001 λν0001 ( 5)
I use monthly CPI-scaled equity flows for each emerging
market and choose Maximum Likelihood as the estimation
method for a recursive Kalman filter. Specific to each emerging
country, I have attempted the possibilities within the framework of general state-space models and choose the appropriate
model according to the R 2 criteria. The model for South Korea,
Brazil, Malaysia, People’s Republic of China, and Indonesia is
as follows: EFt=ωt+𝜈t+εt; ωt=ωt- 1+δt ;t=λ1𝜈t- 1+ξt. The state-space
model for Argentina and Chile can be written as EFt=ωt+𝜈t+εt;
ωt=ωt- 1+δt; 𝜈t=λ1𝜈t- 1+λ2𝜈t- 2+ξt. For Taiwan Republic of China,
the best specification is: EFt=ωt+𝜈t; ωt=ωt- 1+δt; 𝜈t=λ1𝜈t- 1+ξt.
The model I select for India, Philippines, and Thailand is:
EFt=ωt+𝜈t+ εt; ωt=γ+ωt- 1+δt; 𝜈t=λ1𝜈t- 1+ξt. Equity flows of Mexico
can be decomposed using the following model: EFt=ωt+ εt;
ωt=ωt- 1+δt . Q-ratios in table 1 measure the relative importance
of the temporary and permanent components of equity flows,
which are defined as:
Q-ratio(ωit)= σiδ max(σiδ, σiξ, σiε), Q-ratio(𝜈it)= σiξ max(σiδ, σiξ, σiε),
Q-ratio(ωit) is expected to be equal to 1 if the variation of
equity flows is mainly derived from the dynamics of the permanent component. Q-ratio(𝜈it) or Q-ratio (εit) is supposed to be
equal to 1 if most variation of equity flows can be explained by
the temporary component. For details of state-space models
and the Kalman filter, refer to Sarno and Taylor (1999a,b) and
Fuertes et al. (2016).
Rodrik, D. 1998. “Who Needs Capital-Account Convertibility?” In: Should
the IMF Pursue Capital-Account Convertibility? Essays in International
Finance 207 (May). Princeton, NJ: Princeton University Press: 55–65.
Rodrik, D., and A. Subramanian. 2009. Why Did Financial Globalizations
Disappoint? IMF Staff Paper 56, no. 1: 112–38. Washington, DC: International Monetary Fund.
Sarno, L., and M. P. Taylor. 1999a. Hot Money, Accounting Labels and the
Permanence of Capital Flows to Developing Countries: An Empirical
Investigation. Journal of Development Economics 59, no. 2 (August):
———. 1999b. Moral Hazard, Asset Price Bubbles, Capital Flows, and the
East Asian Crisis: The First Tests. Journal of International Money and
Finance 18, no. 4 (August): 637–657.
Stulz, R. M. 2005. The Limits of Financial Globalization. Journal of
Finance 60, no. 4 (August): 1,595–1,638.
Taylor, M. P., and L. Sarno. 1997. Capital Flows to Developing Countries:
Long- and Short-Term Determinants. World Bank Economic Review 11,
no. 3 (September): 451–470.
Yan, C. 2015. Foreign Investors in Emerging Equity Markets: Currency
Effect Perspective. Journal of Investment Consulting 16, no. 1: 43–72.
Yan, C., K. Phylaktis, and A-M. Fuertes. 2016. On Cross-Border Bank
Credit and the U.S. Financial Crisis Transmission to Equity Markets.
Journal of International Money and Finance 69 (December): 108–134.
State-space models (or unobserved components models) have
been used widely to estimate unobserved time variables such
as rational expectation, permanent income, measurement error,
etc. Using the recursive Kalman filter algorithm, these models
incorporate unobserved variables (state variables) into observable models and eventually receive the estimated result. Here,
state-space models enable us to measure unobserved hot
money via decomposing the observable equity flows. The
unobserved components model can be written as follows:
EFit = ωit + 𝜈it + εit ( 1)
where εt~i.i.d.N (0,σ 2 ε.i), i = 1, 2,…, N are countries, and t = 1, 2,…, T
EFit denotes the observed equity flows from the United States
to a given emerging market i at time t, ωit is the unobserved
permanent component of the equity flows that is considered
to be a random-walk process, and υit + εit is the unobserved
temporary component that is dominated by an appropriate
function, an order-two auto-regressive process to be exact.
The random disturbance in the system is also a set of time-dependent variables, which is represented by a white noise εit.
The general form of the permanent component is
ωit = γ + ωit- 1 + δit , δt~i.i.d.N(0, σ 2 iδ) ( 2)
where γ is the drift and δit is a white noise part.
The general form for the temporary component is
𝜈it = λ1𝜈it- 1 + λ2𝜈it- 2 + ξit ( 3)
where ξit ~i.i.d.N (0, σ 2 iξ ) and coefficients satisfy:
|λ1+λ2|< 1 , |λ1-λ2| < 1 ,- 1<λ2< 1.