Equity Markets and Economic Development: What Do We Know

The sensitivity of equity market i to the foreign news factors is measured by the parameters
β_{iUS,t -1} and β_iREG,t-1 . These risk parameters are time-varying and modeled as follows:

^βiUS,t-1 = p1ii * XiUS,t-1 ^{+ q}iXiW t-1 * WUS,t-1

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^βREG,t-1 = p2,i * XiRlEJG,t-1 ⁺ qi^XiW,t-1 * ^WUS,t-1

Where W_US,t-1 represents the US market capitalisation relative to the world market
capitalisation at time t - 1. X_iUS,t-1 , X _{iREG,t -1} and X_iW,t-1 are information variables that
capture the covariance risk of market iwith the US and the region, respectively³. ε_i,t
represents the unexpected portion of local market returns. It is driven not only by shocks from
the local market, but also by two foreign shocks originating in the U.S. and the region, that is,

^εi,t ^{= β}iUS,t-1 ^*eUS,t-1 ^{+ β}iREG,t -1 ^*eREG,t-1 ^{+ e}i,t

Where e_i,t represents the idiosyncratic shock on any market i (including the US and world
portfolio). It follows a normal distribution such as e_i,t ~ N (0,σ2_it). The U.S. and regional
markets models are special cases of (1)-(2). For the U.S. market (with i = us ),
p_1,US = p_2,US = q_US = 0 . For the regional market, (with i = reg ), p_2,REG = q_REG = 0. US and
regional dollar excess returns can thus be expressed as:

^RUS,t ^{= γ}US ^ZUS,t -1 ^{+ ε}US,t

(4)
^RR.EG,t = ^γREGZREG,t-1 ^{+ β}reg,US,t-1 * ^μUS,t-1 ^{+ ε}REG,t

³ In the empirical model, these include the proportions of bilateral trade (Xus+Mus)/E(X+M),
(Xreg+Mreg)/E(X+M) and (X+M)/GDP, respectively.

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