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640 Chapter 15 Estimation of Dynamic Causal Effects

group would apply no such random changes; for both groups, economic activity (for
example, GDP) would be measured over the next few years. But what if we are
interested in estimating this effect for a specific country, say the United States?
Then this experiment would entail having different “clones” of the United States
as subjects and assigning some clone economies to the treatment group and some
to the control group. Obviously, this “parallel universes” experiment is infeasible.

Instead, in time series data it is useful to think of a randomized controlled
experiment consisting of the same subject (e.g., the U.S. economy) being given dif-
ferent treatments (randomly chosen changes in interest rates) at different points in
time (the 1970s, the 1980s, and so forth). In this framework, the single subject at
different times plays the role of both treatment and control group: Sometimes the
Fed changes the interest rate, while at other times it does not. Because data are
collected over time, it is possible to estimate the dynamic causal effect, that is, the
time path of the effect on the outcome of interest of the treatment. For example, a
surprise increase in the short-term interest rate of two percentage points, sustained
for one quarter, might initially have a negligible effect on output; after two quarters
GDP growth might slow, with the greatest slowdown after 121 years; then over the
next 2 years, GDP growth might return to normal. This time path of causal effects
is the dynamic causal effect on GDP growth of a surprise change in the interest rate.

As a second example, consider the causal effect on orange juice price changes
of a freezing degree day. It is possible to imagine a variety of hypothetical experi-
ments, each yielding a different causal effect. One experiment would be to change
the weather in the Florida orange groves, holding weather constant elsewhere—for
example, holding weather constant in the Texas grapefruit groves and in other
citrus fruit regions. This experiment would measure a partial effect, holding other
weather constant. A second experiment might change the weather in all the
regions, where the “treatment” is application of overall weather patterns. If
weather is correlated across regions for competing crops, then these two dynamic
causal effects differ. In this chapter, we consider the causal effect in the latter
experiment, that is, the causal effect of applying general weather patterns. This
corresponds to measuring the dynamic effect on prices of a change in Florida
weather, not holding weather constant in other agricultural regions.

Dynamic effects and the distributed lag model. Because dynamic effects neces-
sarily occur over time, the econometric model used to estimate dynamic causal
effects needs to incorporate lags. To do so, Yt can be expressed as a distributed
lag of current and r past values of Xt:

Yt = b0 + b1Xt + b2Xt - 1 + b3Xt - 2 + g + br + 1Xt - r + ut, (15.3)