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How can you choose the best lag length for a macroeconometric model?

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Choosing the best lag length for a macroeconometric model is a crucial step in ensuring the validity and accuracy of your results. A lag is the number of time periods that you include in your model as explanatory variables. For example, if you want to estimate the impact of inflation on GDP growth, you may use lagged values of inflation as well as current and future values. But how do you decide how many lags to use? In this article, we will explain some of the methods and criteria that you can apply to select the optimal lag length for your macroeconometric model.

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William Peters

Macro data, analytics and visualisations

1 Why lag length matters

The lag length of your model affects several aspects of your analysis, such as the degrees of freedom, the multicollinearity, the serial correlation, and the model fit. If you use too few lags, you may omit relevant information and introduce bias and inconsistency in your estimates. If you use too many lags, you may waste degrees of freedom, increase the variance of your estimates, and create multicollinearity problems. Moreover, the lag length can influence the diagnostic tests for serial correlation, heteroskedasticity, and cointegration, which are essential to check the validity of your model assumptions. Therefore, choosing the best lag length is a trade-off between capturing the dynamic relationships among the variables and minimizing the potential problems.

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William Peters

Macro data, analytics and visualisations
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Leading indicators are a great source of information for understanding business cycles, economic performance and future growth opportunities. However, not all leading indicators have the same amount of foresight. Some typical leading indicators are PMIs on industrial production, the stock market on the economy, and credit card transaction statistics on retail trade data. It can be expected that surveys on companies early on in the supply chain (like PMIs) might lead events later in the business cycle, such as consumer spending. Getting this lag length correct is important for understanding the economy, in order to make better investment decisions.

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2 How to choose lag length

There are two main approaches to choose the lag length of a macroeconometric model: the general-to-specific approach and the information criteria approach. The general-to-specific approach starts with a large number of lags and then eliminates the insignificant ones using t-tests or F-tests. The information criteria approach uses a set of criteria that measure the trade-off between the model fit and the number of parameters. Some of the most common information criteria are the Akaike information criterion (AIC), the Bayesian information criterion (BIC), and the Hannan-Quinn criterion (HQC). The lower the value of the criterion, the better the lag length.

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William Peters

Macro data, analytics and visualisations
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There are several ways to choose lag length. The simplest being simple correlograms between an independent and dependent variable. One of the most common examples of this is using PMI data with a 3 month lag against industrial production. The next level up is using VAR or VECM models which might use Akaike method to select lags. This favors a simple model over a more complicated one, but still accounts for a good model fit. Machine learning techniques like Artificial Neural Networks train and test large data sets with non-linear relationships, allowing for improvements over multiple interations. With these more modern techniques having the perfect lead/lag length is less important than having a relationship to start with.

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3 How to apply information criteria

To apply the information criteria approach, you need to estimate your model with different lag lengths and compare the values of the criteria. The optimal lag length is the one that minimizes the chosen criterion. For example, if you use the AIC, you would select the lag length that has the lowest AIC value among all the alternatives. You can also use more than one criterion and see if they agree on the same lag length. However, sometimes the criteria may give conflicting results, in which case you may need to use some judgment or other criteria to make the final decision.

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4 How to use software tools

One of the advantages of using the information criteria approach is that you can easily implement it using software tools. Most statistical and econometric software packages have built-in functions or commands that allow you to estimate your model with different lag lengths and automatically calculate the values of the information criteria. For example, in R, you can use the VARselect() function from the vars package to select the optimal lag length for a vector autoregressive (VAR) model based on the AIC, BIC, or HQC. In Stata, you can use the varsoc command to do the same.

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William Peters

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Some modern software now allows forecasters to automatically train, test and weight time series forecasts. Macrobond will run Akaike Hannan Quinn, Schwarz and Final prediction error information criterion as part of it's VAR analysis. Indicio will go a step further and build 25 time series models at once - from classical VAR, to Bayesian, to ML models. The user can then simply analyse the residuals, coefficients and tables, make necessary adjustments to training and testing periods and then select the best fit.

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5 How to interpret the results

Once you have chosen the best lag length for your model, you should interpret the results carefully and critically. You should not rely solely on the information criteria, but also check the economic and statistical significance of your estimates, the diagnostic tests for your model assumptions, and the forecasting performance of your model. You should also be aware of the limitations and uncertainties of your choice, such as the sensitivity of the criteria to the sample size, the model specification, and the data frequency. You should also report and justify your choice of lag length and the criteria used in your research paper or report.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you choose the best lag length for a macroeconometric model?

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6

1 Why lag length matters

2 How to choose lag length

3 How to apply information criteria

4 How to use software tools

5 How to interpret the results

6 Here’s what else to consider

Economics

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How can you choose the best lag length for a macroeconometric model?

1

2

3

4

5

6

1 Why lag length matters

2 How to choose lag length

3 How to apply information criteria

4 How to use software tools

5 How to interpret the results

6 Here’s what else to consider

Economics

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