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680 Chapter 15 Estimation of Dynamic Causal Effects

Appendix

15.1 The Orange Juice Data Set

The orange juice price data are the frozen orange juice component of processed foods and
feeds group of the Producer Price Index (PPI), collected by the U.S. Bureau of Labor
Statistics (BLS series wpu02420301). The orange juice price series was divided by the over-
all PPI for finished goods to adjust for general price inflation. The freezing degree days
series was constructed from daily minimum temperatures recorded at Orlando-area air-
ports, obtained from the National Oceanic and Atmospheric Administration (NOAA) of
the U.S. Department of Commerce. The FDD series was constructed so that its timing and
the timing of the orange juice price data were approximately aligned. Specifically, the
frozen orange juice price data are collected by surveying a sample of producers in the
middle of every month, although the exact date varies from month to month. Accordingly,
the FDD series was constructed to be the number of freezing degree days from the 11th of
one month to the 10th of the next month; that is, FDD is the maximum of zero and 32 minus
the minimum daily temperature, summed over all days from the 11th to the 10th. Thus
%ChgPt for February is the percentage change in real orange juice prices from mid-
January to mid-February, and FDDt for February is the number of freezing degree days
from January 11 to February 10.

Appendix

15.2 The ADL Model and Generalized Least

Squares in Lag Operator Notation

This appendix presents the distributed lag model in lag operator notation, derives the ADL
and quasi-differenced representations of the distributed lag model, and discusses the condi-
tions under which the ADL model can have fewer parameters than the original distributed
lag model.

The Distributed Lag, ADL, and Quasi-Difference
Models, in Lag Operator Notation

As defined in Appendix 14.3, the lag operator, L, has the property that LjXt = Xt - j, and

the distributed lag b1Xt + b2Xt - 1 + g + br + 1Xt - r can be expressed as b(L)Xt, where
r 1Lj, L0
b(L) = g j = 0 bj + where = 1. Thus the distributed lag model in Key Concept 15.1

[Equation (15.4)] can be written in lag operator notation as