Distributed Lag Model

Models that have the property of changing only at fixed interval of time and based on current values of variables on other current values of variables are called distributed lag model.

In economic studies some economic data are collected over uniform time interval such as a month or year.

This model consists of linear algebraic equations that represent continuous system but data are available at fixed points in time.

For example: Mathematical model of national economy

Let

C=consumption

I=investment

T=Taxes

G=government expenditures

Y=national income

Then,

C = 20 + 0.7(Y-T)

I = 2 + 0.1Y

T = 0.2Y

Y = C + I + G

All the equation are expressed in billions of rupees. This is static model and can be made dynamic by lagging all the variables as follows

C = 20 + 0.7(Y_-1 - T_-1)

I = 2 + 0.1Y_-1

T = 0.2Y_-1

Y = C_-1 + I_-1 + G_-1

Any variable that can be expressed in the form of its current value and one or more previous value is called lagging variable. And hence this model is given the name distributed lag model. the variable in a previous interval is denoted by attaching –n suffix to the variable. Where -n indicate the n^th interval.

Advantages of distributed lag model

·         Simple to understand and can be computed by hand, computers are extensively used to run them.

·         There is no need for special programming language to organize simulation task.