# Auto regressive distributed lag model (ARDL) and its advantages

Autoregressive Distributed Lag Models (ARDL) model plays a vital role when comes a need to analyze an economic scenario. In an economy, change in any economic variables may bring change in another economic variable beyond time. This change in a variable is not what reflects immediately, but it distributes over future periods. Not only macroeconomic variables, but other variables such as loss or profit earned by a firm in a year can also affect the brand image of an organization over the period.

For instance:effect of a profit making decision taken by an organization in a year may have influence on the profit and brand image of an organization in the time t along with future periods such as t + 1, t + 2 and so on. Thus, the long and short run behavioral consequences of a variable on other variable bring the role of distributed lag model in the scenario.

The below function represents the lag effect of a variable on other variables and its own lags as well

Y_{t }=f( X_{t}, X_{t-1}, X_{t-2,……) }, where, t-i represents the number of lags.

In order to determine, the dynamic influence of a variable on other variables, there occurs multiple distributed lag models such as polynomial, geometric and other distributed lag models in econometrics.

However, the ARDL model addresses the distributed lag problem more efficiently than these models.

## ARDL model

An ARDL (Autoregressive-distributed lag) is parsimonious infinite lag distributed model. The term “autoregressive” shows that along with getting explained by the x_{t}’ , y_{t }also gets explained by its own lag also. Equation of ARDL(m,n) is as follows:

y_{t} = β_{0} + β_{1}y_{t-1} + …….+ βpy_{t-m} + α_{0}x_{t} + α_{1}x_{t-1} + α_{2}x_{t-2} + ……… + α_{q}x_{t-n} + ε_{t}

Here, m and n are the number of years for lag, ε_{t }is the disturbance terms and β_{i}’s are coefficients for short-run and α_{i}’s are coefficients for long-run relationship.

## Lacks in distributed lag models other than ARDL

Collinearity emerges as a major issue while dealing with any econometrics model. The finite distributed lag model requires dealing with the collinearity issue by choosing an optimal lag length. The polynomial distributed lag (PDL) removes the collinearity by making the lag weights lie on its curve.

In the infinite lag model, there are infinite numbers of parameters to estimate which is complex to solve. This model solves the issue of specifying a certain length of lags. On contrary, it requires imposing a structure on the lag lengths by making the model non-linear. In addition to this, the Geometric model works as an infinite lag distributed model. This model puts the successive lag weights in this model to decline geometrically.

On the other hand, the ARDL model addresses the issue of collinearity by allowing the lag of the dependent variable in the model with other independent variables and their lags.

## Assumptions for ARDL Model

- Absence of auto correlation is the very first requirement of ARDL. The model requires that the error terms should have no autocorrelation with each other.
- There should not occur any heteroscedasticity in the data. In simple terms, the variance and mean should remain constant throughout the model.
- The data should follow normal distribution.
- Data should have stationary either on I(0) or I(1) or on both. In addition to this, if any of the variable in the data has stationary at l(2), ARDL Model cannot run.

## Discuss