L26 - Cost of Adjustment

Question 1

What does the cost of adjustment model hypotheses?

Answer 1

if we are considering whether or not to change the Y variable when the X variable changes we need to take into account two types of costs:

1. The cost of being away from the equilibrium or desired value (Y*)
2. The cost of making changes to the value of Y

this is capture by the cost function C which is a weighted average of the squared deviation of Y from Y* and the change in Y

• The is a quadratic as they are easier to deal with, but also has some desirable properties from a theoretical point of view
  
  • in particular it penalises large deviation more than small deviations

Question 2

How do you get the partial adjustment model?

Answer 2

• θ –> weight on changes in weight
  
  • , if there was no cost of adjustment θ=0 and Y, would equal Y* in every time period

anything that has a lagged Y_t-1 in a model is called a partial adjustment model, as it shows that is it costly to adjust Y so it’s only partly done in the period

the being the value of θ the smaller the impact effect will be on Y –> (β/1 +θ) the larger the value of θ, the smaller the change on Y given a change in X

• the bigger value of θ (the larger cost of adjustment) the larger the coefficient of Y_t-1 –> as it tends to infinity it would tend to 1 –> meaning that if costs were really high you wouldn’t make any changes to Y

Question 3

What is the relationship between the impact effect and the long-run effect of a change in X?

Answer 3

• You can sub into the cost of adjustment model Y_t from the partial adjustment model to implement in the lagged variables

The weights will converge to 0 as I increases

The cumulative

Question 4

What is the Statistical implication of distributed lag models?

Answer 4

• sum of the errors equations is called an infinite moving average

Any finite autoregressive process can be written as an infinite moving average process in the errors

Beta < 1 –> so it converges

Question 5

In a distributed lag model, if the error is correlated with the lagged endogenous variable, what does this mean for the OLS estimator?

Answer 5

Question 6

When is a series non-stationary?

Answer 6

• if beta = 0 the variance express is not defined