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638 Chapter 15 Estimation of Dynamic Causal Effects

We begin our quantitative analysis of the relationship between orange juice
price and the weather by using a regression to estimate the amount by which
orange juice prices rise when the weather turns cold. The dependent variable is
the percentage change in the price over that month [%ChgPt, where %ChgPt =
100 * ∆ln(POt J) and POt J is the real price of orange juice]. The regressor is the
number of freezing degree days during that month (FDDt). This regression is
estimated using monthly data from January 1950 to December 2000 (as are all
regressions in this chapter), for a total of T = 612 observations:

%ChgPt = - 0.40 + 0.47 FDDt. (15.1)
(0.22) (0.13)

The standard errors reported in this section are not the usual OLS standard
errors, but rather are heteroskedasticity- and autocorrelation-consistent (HAC)
standard errors that are appropriate when the error term and regressors are auto-
correlated. HAC standard errors are discussed in Section 15.4, and for now they
are used without further explanation.

According to this regression, an additional freezing degree day during a month
increases the price of orange juice concentrate over that month by 0.47%. In a
month with 4 freezing degree days, such as November 1950, the price of orange
juice concentrate is estimated to have increased by 1.88% (4 * 0.47% = 1.88%),
relative to a month with no days below freezing.

Because the regression in Equation (15.1) includes only a contemporaneous
measure of the weather, it does not capture any lingering effects of the cold snap
on the orange juice price over the coming months. To capture these we need to
consider the effect on prices of both contemporaneous and lagged values of FDD,
which in turn can be done by augmenting the regression in Equation (15.1) with,
for example, lagged values of FDD over the previous 6 months:

%ChgPt = - 0.65 + 0.47 FDDt + 0.14 FDDt - 1 + 0.06 FDDt - 2
(0.23) (0.14) (0.08) (0.06)

+ 0.07 FDDt - 3 + 0.03 FDDt - 4 + 0.05 FDDt - 5 + 0.05 FDDt - 6. (15.2)
(0.05) (0.03) (0.03) (0.04)

Equation (15.2) is a distributed lag regression. The coefficient on FDDt in Equa-
tion (15.2) estimates the percentage increase in prices over the course of the
month in which the freeze occurs; an additional freezing degree day is estimated
to increase prices that month by 0.47%. The coefficient on the first lag of FDDt,
FDDt - 1, estimates the percentage increase in prices arising from a freezing degree