Show that the Koyck’s approach to estimating the distributed lag models helps in overcoming an ‘infinite series situation’.

Koyck's Approach to Estimating Distributed Lag Models

Distributed lag models (DLMs) are used to analyze the impact of a variable on another variable over time, considering the lagged effects of the variable. One challenge in estimating DLMs is dealing with the infinite series of lagged effects, which can make estimation complex. Koyck's approach offers a solution to this problem by transforming the infinite series into a finite geometric series, simplifying the estimation process.

1. Infinite Series Situation in Distributed Lag Models:

• In DLMs, the effect of a variable on another variable is assumed to extend over several time periods, resulting in a series of lagged effects that theoretically extends to infinity.
• Estimating such infinite series directly can be computationally intensive and may require assumptions about the decay pattern of the effects over time.

2. Koyck's Approach:

• Koyck's approach proposes a transformation of the infinite lagged effects into a finite geometric series, which is easier to estimate.
• The transformation involves assuming a geometric decay pattern for the lagged effects, where each successive effect is a constant fraction of the previous effect.

3. Simplification of the Model:

• By transforming the infinite series into a geometric series, Koyck's approach simplifies the DLM to a form that can be estimated using standard regression techniques.
• The transformed model includes only a few lagged terms, typically representing the initial effect and the subsequent decay pattern.

4. Overcoming the Infinite Series Situation:

• Koyck's approach effectively overcomes the infinite series situation by approximating the lagged effects with a finite number of terms.
• This approximation allows researchers to estimate the DLM without the need to specify the entire infinite series of lagged effects.

5. Conclusion:

• Koyck's approach provides a practical and manageable way to estimate distributed lag models by transforming the infinite lagged effects into a finite geometric series.
• By simplifying the estimation process, Koyck's approach makes it easier for researchers to analyze the dynamic effects of variables over time, overcoming the challenges posed by the infinite series situation in DLMs.