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Chapter

15 Estimation of Dynamic Causal Effects

I n the 1983 movie Trading Places, the characters played by Dan Aykroyd and Eddie
Murphy used inside information on how well Florida oranges had fared over the
winter to make millions in the orange juice concentrate futures market, a market for
contracts to buy or sell large quantities of orange juice concentrate at a specified
price on a future date. In real life, traders in orange juice futures in fact do pay close
attention to the weather in Florida: Freezes in Florida kill Florida oranges, the source
of almost all frozen orange juice concentrate made in the United States, so its sup-
ply falls and the price rises. But precisely how much does the price rise when the
weather in Florida turns sour? Does the price rise all at once, or are there delays; if
so, for how long? These are questions that real-life traders in orange juice futures
need to answer if they want to succeed.

This chapter takes up the problem of estimating the effect on Y now and in the
future of a change in X, that is, the dynamic causal effect on Y of a change in X.
What, for example, is the effect on the path of orange juice prices over time of a
freezing spell in Florida? The starting point for modeling and estimating dynamic
causal effects is the so-called distributed lag regression model, in which Yt is
expressed as a function of current and past values of Xt. Section 15.1 introduces
the distributed lag model in the context of estimating the effect of cold weather in
Florida on the price of orange juice concentrate over time. Section 15.2 takes a
closer look at what, precisely, is meant by a dynamic causal effect.

One way to estimate dynamic causal effects is to estimate the coefficients of
the distributed lag regression model using OLS. As discussed in Section 15.3, this
estimator is consistent if the regression error has a conditional mean of zero given
current and past values of X, a condition that (as in Chapter 12) is referred to as exo-
geneity. Because the omitted determinants of Yt are correlated over time—that is,
because they are serially correlated—the error term in the distributed lag model
can be serially correlated. This possibility in turn requires “heteroskedasticity- and
autocorrelation-consistent” (HAC) standard errors, the topic of Section 15.4.

A second way to estimate dynamic causal effects, discussed in Section 15.5, is to
model the serial correlation in the error term as an autoregression and then to use
this autoregressive model to derive an autoregressive distributed lag (ADL) model.
Alternatively, the coefficients of the original distributed lag model can be estimated

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