Explain instrumental variables with an example

Question

Explain instrumental variables in simple terms and provide a concrete example.

Codemia · Accepted Answer

In this scenario, we want to analyze the impact of a new trading algorithm on the trading volume at Optiver. The analytical question we need to address is: **Does the new trading algorithm cause an increase in trading volume, or is the observed change simply due to other factors?** To explore this, we would need data on trading volumes before and after implementing the algorithm, as well as data on potential confounding variables such as market conditions, investor sentiment, and trading activity of competitors.

To isolate the effect of the new trading algorithm, we can use **instrumental variables (IV)**. An instrumental variable is a third variable that is correlated with the independent variable (the new algorithm) but is not directly related to the dependent variable (trading volume) except through the independent variable. In this case, we could use the implementation date of the algorithm as an instrument, assuming that the timing of algorithm deployment is not associated with other market changes. We can employ two-stage least squares (2SLS) regression to estimate the causal effect of the algorithm on trading volume.

Suppose we gather data over two months: One month prior to the algorithm launch (Volume Before = 1000 units) and one month after (Volume After = 1500 units). Using 2SLS, we can run our first stage regression, where we regress the new trading algorithm implementation on the instrument (implementation date). Then, in the second stage, we regress trading volume on the predicted values from the first stage. If the coefficient from the second stage indicates an increase of 200 units (e.g., Volume After - Volume Before = 1500 - 1000), we interpret this as the causal impact, suggesting that the new algorithm resulted in a net increase in trading volume.

The results from the 2SLS regression suggest that the new trading algorithm causally increased the trading volume by 200 units. This interpretation implies that the algorithm is effective in driving trading activity, independent of confounding factors like market conditions since we controlled for them using the instrumental variable. Therefore, it is reasonable for Optiver to consider scaling up the use of this algorithm across other trading strategies.

Common pitfalls in using instrumental variables include selecting an invalid instrument that is correlated with the error term in the regression model, leading to biased results. Additionally, not accounting for other confounding variables can distort the estimated effect. For instance, if market volatility increased coinciding with the algorithm's launch, and this volatility was not controlled for, our estimates may misattribute changes in trading volume to the new algorithm rather than market conditions. It's crucial to rigorously validate the instrument's assumptions before drawing conclusions.

Explain instrumental variables with an example

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