specialists refer to this phenomenon as the “overfitting problem” and have
come up with several ways to deal with it.
First, since simpler models tend to work better for out of sample forecasts,
machine learning experts have come up with various ways to penalize models
for excessive complexity. In the machine learning world, this is known as
“regularization” and we will describe some examples below. Economists tend
to prefer simpler models for the same reason, but have not been as explicit
about quantifying complexity costs.
Second, it is conventional to divide the data into separate sets for the
purpose of training, testing and validation. You use the training data to
estimate a model, the validation data to choose your model, and the testing
data to evaluate how well your chosen model performs. (Often validation
and testing sets are combined.)
Third, if we have an explicit numeric measure of model complexity, we
can view it as a parameter that can be ”tuned” to produce the best out of
sample predictions. The standard way to choose a good value for such a
tuning parameter is to use k-fold cross validation.
1. Divide the data into k roughly equal subsets (folds) and label them by
s = 1, . . . , k. Start with subset s = 1.
2. Pick a value for the tuning parameter.
3. Fit your model using the k − 1 subsets other than subset s.
4. Predict for subset s and measure the associated loss.
5. Stop if s = k, otherwise increment s by 1 and go to step 2.
Common choices for k are 10, 5, and the sample size minus 1 (“leave
one out”). After cross validation, you end up with k values of the tuning
parameter and the associated loss which you can then examine to choose
an appropriate value for the tuning parameter. Even if there is no tuning
7
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