Chapter

Appendix

Author(s):
International Monetary Fund. Western Hemisphere Dept.
Published Date:
April 2007
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Modeling the Impact of External Shocks on Latin America

Section III in this Regional Economic Outlook—as well as the confidence intervals around the central forecast shown in section II—is based on a multivariate autoregressive model that relates growth outcomes in Latin America to a variety of economic variables. Specifically, the analysis employs a “Bayesian Vector-Autoregression” model for Latin American growth. This can be written as

In equation (1), xt stands for an nx1 vector of macroeconomic variables including growth, G(L) denotes a 'lag polynomial of order p” (a shorthand for the fact that several lags of xt were included in the model) and ηt an nx1 vector of identically independently distributed error terms. Finally, ψ is a vector of steady state values describing the levels to which the variables converge in the long run. This model is specified in terms of deviations from the steady state (see Villani, 2005), for details, thereby allowing the researcher to specify an informative prior distribution for the steady-state values. In this way, knowledge about policy frameworks and economic structure that affect the long-run behavior of the n variables—which may not be fully reflected in their realizations in the estimation sample, such as views about long-run potential growth—can be reflected in the estimation. Using Bayes' law, this information is then combined with the data to estimate a “posterior” distribution of Ψ.1

The framework described by (1) was used to estimate two different models. In the first, xt was set as follows:

Some steady-state priors followed standard conventions, for example, U.S. inflation and short-term nominal interest rates were centered on 2 and 4 percent, respectively (see table). Steady-state priors for world and U.S. growth were based on medium-term WEO projections; while the steady-state prior for Latin American growth, centered on 4.25 percent, was based on econometric studies of long-run growth in Latin America (see Loayza, Fajnzylber, and Calderon, 2005; and Zettelmeyer, 2006 for an overview). The table shows that post and prior distributions are generally close, indicating that the assumed prior intervals were judged reasonable by the data. Importantly, it was confirmed that the dynamics of the model were not affected by the steady-state priors chosen (”non-informative” or “diffuse” priors, which give the data a free hand in estimating the steady state parameters, produced similar results). Hence, the assumed steady state priors do not prejudge the model's short-run forecasts.

When estimating the model, exogeneity of the world/U.S. variables with respect to the Latin American variables was assumed, and shocks were orthogonalized using a standard recursive ordering: world (or U.S.) growth was ordered first (i.e. assumed to be contemporaneously unaffected by the other variables), followed by the remaining variables in the order listed in equation (2).

Model Variables: Steady State Prior and Posterior Distributions(In units of the variables shown: 95 percent probability intervals) 1/
priorposterior 2/
World growth(3.75, 4.75)(3.4, 4.1)
U.S. growth(2.0, 4.0)(2.8, 3.9)
U.S. inflation(1.0, 3.0)(2.0, 2.8)
U.S. T-Bill rate(3.0, 5.0)(3.5, 5.0)
U.S. HY spread(3.0, 6.0)(3.8, 5.9)
Commodity prices(-2.0, 4.0)(-1.4, 4.4)
LA6 growth(3.5, 5.0)(3.4, 4.8)
Latin EMBI spread(2.0, 5.0)(2.1, 4.9)

As usual, the properties of the estimated models can be summarized using variance decompositions, which summarize the relative contribution of various shocks to the variation of the endogenous variables at different time horizons, and impulse response functions, which show how a variable responds to a particular shock (see Ôsterholm and Zettelmeyer, 2007), for a full set of impulse responses and variance decompositions:

Variance decompositions suggest that about 52 percent of the medium-term variance of Latin American GDP growth is explained by external factors: approximately 12 percent by world growth shocks, 6 percent by commodity prices, and a remarkable 34 percent by U.S. financial conditions (the combined influence of U.S. short-term interest rates and the U.S. high yield bond spread). If the model with U.S. growth and inflation is used, the influence of external factors rises to about 57 percent, of which 16 percent corresponds to U.S. growth and 5 percent to commodity prices. U.S. financial conditions account for 27 percent of the variance in this model; this rises to 36 percent if the contribution of U.S. inflation is included in this category.

Impulse responses give a direct answer to the question of how growth in Latin America has tended to react to external shocks, taking account not only the direct effects of shocks, but also the effects through the reactions of other endogenous variables. The figures show the growth response (with growth expressed as the percentage change in GDP with respect to the same quarter of the preceding year) to a one-standard-deviation shock in the variable indicated in the title; this shock turns out to be about 0.28 percentage point for world growth, 5 percent for commodity prices, 90 basis points for the U.S. high yield bond spread, and 115 basis points for the Latin EMBI. Hence:

Response of LA6 Growth with Respect to One Standard Deviation External Shocks

  • Increases in world growth are passed on to Latin America about one-for-one: a 0.3 percent world growth shock leads to an increase in (four-quarter) Latin American growth by about 0.4 percentage point after four quarters. This is similar to the impulse response of world growth with respect to its own shock (not shown) which also reaches a maximum of about 0.4 in the fourth quarter after the shock.

  • A standard deviation commodity shock—which in this sample is a change of almos 5 percent in a quarter, illustrating how volatile Latin American commodity prices have been—leads to a change in four-quarter Latin American growth of about percentage point after two quarters.

  • A 90-basis-point rise in the U.S. high yield bond spread, interpreted as reflecting a retreat of investors from risk, leads to a decline of four-quarter growth in Latin America by about 0.9 percentage point after three quarters.

  • Finally, a 115-basis point rise in the Latin EMBI is associated with drop in four-quarter growth by 0.5 percent after four quarters.

LA6 Growth Response with respect to U.S. Growth Shock

The alternative model, which includes U.S. growth and inflation instead of world growth, has very similar effects for the commodities and EMBI shocks, while the reaction to a shock to the U.S. high yield bond spread is slightly more muted, with LA6 growth increasing by only about 0.8 percentage point after three quarters. The reaction to a U.S. growth shock is faster and slightly larger (it is also more precisely estimated, in the sense that the standard error bands are tighter). The figure describes the reaction to a 0.48 percent increase in U.S. growth (U.S. growth being more volatile than world growth); this is shown to lead to an increase of 4-quarter Latin American growth by about 0.6 point. Since the U.S. growth shock eventually leads to a total increase in U.S. growth of about 0.55 percentage point after three quarters (not shown), this implies that the overall average reaction of Latin American growth to U.S. growth is a little over one-for-one.

For the parameters governing the dynamics of the model around the steady state, a slightly modified “Minnesota prior” (Litterman, 1986) was used. This involves setting the prior mean on the first own lag to 0.9 for variables that are modeled in levels, and to 0 on all coefficients for variables that are modeled in first differences (see Ósterholm and Zettelmeyer, 2007, for details on the modeling approach).

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