The tested causal hypothesis is whether change in Consumer Spending causes Unemployment [rate] or vice versa... This presentation details the steps to demonstrate causality using Granger Causality, Path Analysis, and narrative tests.

1.  Consumer Spending causing Unemployment?... Guy Lion January 2010

5. Granger Causality

7. Granger Causality – The Basics Here, the change in Consumer Spending would be variable A. And, the Unemployment rate would be variable B.

8. Granger Causality – the whole picture

9. Correlations with quarterly lags The correlations tables with quarterly lags from 1 quarter to 8 quarters indicate where the causality between the two variables appears more pronounced. In terms of direction (sign), we get far more logical results when we focus on quarterly change in Consumer Spending causing Unemployment [rate] on the right rather than the reverse on the left. When we cut the data since 1990 instead of since 1970, we get stronger correlations. As shown, the more meaningful correlations are in the highlighted yellow zone. And, the strongest (negative) correlation is for change in Consumer Spending impacting the Unemployment rate level with a three quarter lag. So, that’s the relationship we will study. Note the variables are seasonally adjusted. Thus, the lag 4 quarter has no competitive advantage over any other lags.

10. Granger Causality test (data since 1990) This is a very successful Granger Causality outcome as it demonstrates the direction of the Granger causality is clearly  Consumer Spending -> Unemployment and not the reverse. The P value (unpaired t test) of only 11.0% confirmed the (squared) residuals were materially lower for the Test model vs the Base case model. When the causality direction was reversed (Unemployment ->  Consumer Spending), the P value jumped to 89.8% suggesting that any difference in (squared) residuals between the Base case Model and Test Model was pretty much due to randomness.

11. Granger Causality test (data since 1970) We did the exact same exercise using now data since 1970. Surprisingly, the results were nearly as strong as when using the data since 1990 that showed stronger absolute correlation. I suspect that the results using data since 1970 were nearly equally good because even though the difference in absolute correlations (whether A causes B or B causes A) was very small; the difference in actual correlations (including the sign) was nearly as high for the 1970 data than for the 1990 data. Also, the 1970 data had a larger sample which reduces the standard errors, boosts the t Stats, and lowers P values everything else being equal.

13. Path Analysis

14. Path Analysis: Direct and Indirect Effects The Correlation of the independent variable can be decomposed into its Direct Effect and Indirect Effect on the dependent variable. The Indirect Effect is derived from intermediary variables in between the independent and dependent one. The Causal Effect is the sum of the mentioned Effects and should equal the Correlation.

15. Path Analysis – Correlation Table (data since 1990) This is Path Analysis starting point. You start with a correlation matrix of all variables. Next, you develop a diagram with the independent variable at the left, intermediary variables in the middle, and the dependent variable in the right. You then embed all the relevant correlations from the table into the diagram. The correlation between Consumer Spending (CS lag 0) and Unemployment lag 3 (U lag 3) (highlighted in yellow) is the relation we tested with Granger Causality. We are looking at the impact of Consumer Spending on all four Unemployment variables (lag 0, lag 1, lag 2, and lag 3). In this case, we treat U lag 0, U lag 1, and U lag 2 as intermediary variable. In turn, those three variables have an impact on U lag 3. This latter impact is just serial or autocorrelation.

16. Path Analysis With standardized variables within a single relationship the Correlation is equal to the Slope. In view of the above, the correlations between the independent variable and the intermediary variables are equal to regression coefficients or path coefficients as they are called in Path Analysis.

17. Path Analysis – Path Coefficients The path coefficients between the independent variable (CS lag 0) and the intermediary variables (U lag 0, U lag 1, U lag 2) do not need to be calculated because given that the variables are standardized the slope or path coefficients are equal to the original correlations. We just need to calculate the path coefficients highlighted in yellow. And, those are the regression coefficients shown above generated by a linear regression model including all variables with Unemployment lag 3 quarters as the dependent variable.

18. Direct & Indirect Effects Note that the sum of the direct (-0.06) and indirect effects (-0.56) = -0.62 which is exactly the same as the original correlation between change in Consumer Spending and Unemployment rate lag 3 (quarters).