Interpreting Mixed Lag Coefficients in ARDL Models

Summary

The document raises a model-interpretation problem in an autoregressive distributed lag analysis of GDP and foreign direct investment. The author reports that selected lag coefficients have signs that change across quarters and asks whether this pattern indicates misspecification. Lag selection was based on information criteria, and the model reportedly showed no serial correlation and passed CUSUM stability checks. The included output gives coefficient estimates, standard errors, t-statistics, and p-values for several GDP terms.

The question also notes that FDI flows were not logged because the series contains negative observations. However, the document provides no accepted answer or analysis resolving the sign changes. The diagnostics cited address aspects of residual behavior and parameter stability, but do not by themselves establish that the specification is economically appropriate or that individual lag signs should be consistent. The excerpt is therefore useful as a prompt for econometric review, rather than as a complete method or conclusion; it supplies no broader robustness checks or interpretation of cumulative effects.

Key ideas

• Distributed lag coefficients can have mixed signs across different lag periods.
• Information-criterion lag selection does not alone determine whether a model is economically well specified.
• Passing serial-correlation and CUSUM tests does not explain every coefficient pattern.
• Negative values in FDI flows can prevent straightforward logarithmic transformation.
• The document presents a diagnostic question but does not provide a resolution.

Tags

# Autoregressive Distributed Lag Models (ARDL) results analysis


# Autoregressive Distributed Lag Models (ARDL) results analysis












When using autoregressive distributed lag models (ARDL), I usually get a counter-intuitive result for the selected lag.

For example, when examining the relationship between GDP and Foreign Direct Investment (FDI), I don't get consistency in the sign.

What does this really mean? Does this mean that I have a wrong model specification although lags are determined according to information criteria (using a quarterly frequency) or what? There is no serial correlation and the model passed the CUSUM test and CUSUM square test. This indicates stability in the estimation.

I want to add that I did not use the log of FDI flows as there are negative values in the time series.

Below is a snapshot of the estimation results.

```
variable    Coefficient Std. Error  t-Statistic     Prob.*  
LOGGDP     20945.17     31683.81    0.661068        0.5107
LOGGDP(-1)  -74547.39   39648.45    -1.880210       0.0641
LOGGDP(-2)  89724.73    33119.12    2.709152        0.0084
LOGGDP(-3)  -12340.11   35873.61    -0.343989       0.7319
LOGGDP(-4)  -55895.03   32666.16    -1.711099       0.0914
LOGGDP(-5)  50435.01    21241.29    2.374385        0.0202
```

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