Auto regressive distributed lag model (ARDL) and its advantages

By Priya Chetty on February 16, 2018

Autoregressive Distributed Lag Models (ARDL) model plays a vital role when comes to 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 reflected 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.


The effect of a profit-making decision taken by an organization in a year may have an 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 behavioural consequences of a variable on other variables bring the role of a 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

Yt =f( Xt, Xt-1, Xt-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 a parsimonious infinite lag-distributed model. The term “autoregressive” shows that along with getting explained by the xt, yt also gets explained by its own lag also. Equation of ARDL(m,n) is as follows:

yt = β0 + β1yt-1 + …….+ βpyt-m + α0xt + α1xt-1 + α2xt-2 + ……… + αqxt-n + εt

Here, m and n are the numbers of years for lag, εt is the disturbance terms and βi’s are coefficients for short-run and αi’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 the 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

  • The absence of autocorrelation 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 a normal distribution.
  • Data should have stationary either on I(0) or I(1) or on both. In addition to this,  if any of the variables in the data has stationary at l(2), ARDL Model cannot run.

Priya is the co-founder and Managing Partner of Project Guru, a research and analytics firm based in Gurgaon. She is responsible for the human resource planning and operations functions. Her expertise in analytics has been used in a number of service-based industries like education and financial services.

Her foundational educational is from St. Xaviers High School (Mumbai). She also holds MBA degree in Marketing and Finance from the Indian Institute of Planning and Management, Delhi (2008).

Some of the notable projects she has worked on include:

  • Using systems thinking to improve sustainability in operations: A study carried out in Malaysia in partnership with Universiti Kuala Lumpur.
  • Assessing customer satisfaction with in-house doctors of Jiva Ayurveda (a project executed for the company)
  • Predicting the potential impact of green hydrogen microgirds (A project executed for the Government of South Africa)

She is a key contributor to the in-house research platform Knowledge Tank.

She currently holds over 300 citations from her contributions to the platform.

She has also been a guest speaker at various institutes such as JIMS (Delhi), BPIT (Delhi), and SVU (Tirupati).



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