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15.2 Dynamic Causal Effects 639

day in the preceding month, the coefficient on the second lag estimates the effect
of a freezing degree day 2 months ago, and so forth. Equivalently, the coefficient
on the first lag of FDD estimates the effect of a unit increase in FDD 1 month
after the freeze occurs. Thus the estimated coefficients in Equation (15.2) are
estimates of the effect of a unit increase in FDDt on current and future values of
%ChgP; that is, they are estimates of the dynamic effect of FDDt on %ChgPt. For
example, the 4 freezing degree days in November 1950 are estimated to have
increased orange juice prices by 1.88% during November 1950, by an additional
0.56% ( = 4 * 0.14) in December 1950, by an additional 0.24% ( = 4 * 0.06) in
January 1951, and so forth.

15.2 Dynamic Causal Effects

Before learning more about the tools for estimating dynamic causal effects, we
should spend a moment thinking about what, precisely, is meant by a dynamic
causal effect. Having a clear idea about what a dynamic causal effect is leads to a
clearer understanding of the conditions under which it can be estimated.

Causal Effects and Time Series Data

Section 1.2 defined a causal effect as the outcome of an ideal randomized con-
trolled experiment: When a horticulturalist randomly applies fertilizer to some
tomato plots but not others and then measures the yield, the expected difference
in yield between the fertilized and unfertilized plots is the causal effect on tomato
yield of the fertilizer. This concept of an experiment, however, is one in which
there are multiple subjects (multiple tomato plots or multiple people), so the data
are either cross-sectional (the tomato yield at the end of the harvest) or panel data
(individual incomes before and after an experimental job training program). By
having multiple subjects, it is possible to have both treatment and control groups
and thereby to estimate the causal effect of the treatment.

In time series applications, this definition of causal effects in terms of an ideal
randomized controlled experiment needs to be modified. To be concrete, consider
an important problem of macroeconomics: estimating the effect of an unanticipated
change in the short-term interest rate on the current and future economic activity
in a given country, as measured by GDP. Taken literally, the randomized controlled
experiment of Section 1.2 would entail randomly assigning different economies to
treatment and control groups. The central banks in the treatment group would
apply the treatment of a random interest rate change, while those in the control