Question

Explain a typical dynamic lag equation, issues with it and possible solutions.

Answer 1

A distributed lag-model in which the effect of the regressor x on y occurs overtime rather then all at once.We can write he model as

  where u is a stationary error term.

This form is very similar to infinite moving average representation.The individual coefficients   are called lag weights and they collectively comprise lag distribution.

They define the pattern how x affects y over time.

We cannot estimate an infinite number of co-efficients. One practical method is to truncate the lag in to finite length q which is appropriate if the lag distribution is effectively 0 beyond q periods. Another approach is to use a functional form that allows the lag distribution to gradually become 0.

One of the most common problem to all distributed lag model is choice of lag length,whether to choose length q or choosing how many lag dependent variables to include.

In cross sectional models we often use economic methods to estimate marginal effects of an independent variable x on the dependent variable y holding all other independent variables constant. We assume that y does not depend on the future value of x, thus we exclude negative values of s. however it is theoritically possible to have ''negative lags'' on the right hand side. for example the people might change their behaviour now if change is going to happen in future.

Distributed lag models

To see the interpretation of of lag weights we see two cases,

1.Temporary change

2. Permanent change

1. Temporay change - suppose x increases temporarily by one unit in time period t, then returns to its original level for periods t+1 and all future periods.Then the path will look as illustrated in the figure below

2. permanent change - x increases by one unit in period t and remains higher in all periods after t then it was before t. this chnge is graped below