The dual-axis line plot visualizes the relationship between manufacturing employment (MANEMP) and labor productivity over time.

• Manufacturing Employment (blue line, left axis): The plot shows a clear downward trend in manufacturing employment, particularly after 2000. This decline is consistent with the hypothesis that technological advances and automation have led to job displacement in the manufacturing sector.

• Labor Productivity (orange line, right axis): Meanwhile, labor productivity has seen a steady rise over the same period, indicating that fewer workers are needed as productivity improves. This increase in productivity aligns with the rise in automation, where machines and technology enhance output while reducing the need for human labor.

The plot supports Hypothesis 8, suggesting that as automation increases, employment in the manufacturing sector declines, while labor productivity continues to rise.

Interpretation of FEVD Results:

Employment_diff_2:

• The first row (0) shows that initially, 100% of the variance in the employment series is explained by itself.
• Over time (from lag 1 to lag 9), the contribution of labor productivity (productivity_diff_2) to the variance in employment increases, though the majority of the variance is still explained by the employment series itself.

Productivity_diff_2:

• Initially (at lag 0), around 76.2% of the variance in productivity is explained by itself, and 23.8% is explained by employment.
• As time progresses, the percentage of variance explained by productivity itself decreases slightly, while the contribution from employment stabilizes around 31% after several lags.

Key Takeaways:

• The FEVD analysis shows that both variables have a significant influence on each other, especially in the case of productivity_diff_2, where employment_diff_2 consistently explains a notable portion of the variance.
• Over time, labor productivity becomes increasingly influenced by changes in employment, as shown by the rising contribution from employment_diff_2 in the productivity_diff_2 decomposition.

The paired t-test result shows a very small p-value (1.114557731297368e-29), which is much smaller than the typical significance level of 0.05. This means that we can reject the null hypothesis and conclude that there is a significant difference between manufacturing employment and labor productivity over time.

Interpretation of the Results:

Equation for employment_diff_2:

• The coefficients for L1.productivity_diff_2 (lag 1) and L2.productivity_diff_2 (lag 2) are statistically significant (p < 0.05), indicating that changes in manufacturing labor productivity at lag 1 and lag 2 are likely influencing changes in employment.
• The coefficient for L2.productivity_diff_2 is positive and significant, suggesting that an increase in productivity at lag 2 is associated with an increase in employment.

Equation for productivity_diff_2:

• The coefficient for L1.employment_diff_2 (lag 1) is statistically significant (p < 0.05), suggesting that changes in employment at lag 1 are influencing changes in labor productivity.
• The coefficient for L2.employment_diff_2 is also significant, indicating that changes in employment at lag 2 influence changes in productivity.

The calculated correlation coefficient is approximately -0.955. This strong negative correlation suggests that as manufacturing labor productivity (MFGOPH) increases, manufacturing employment (MANEMP) tends to decrease. This supports your hypothesis that manufacturing employment has a negative correlation with automation indices over time, as indicated by labor productivity. The stronger the productivity growth, the more significant the decrease in employment, likely due to technological advancements and automation in the sector.

The p-values from the Augmented Dickey-Fuller (ADF) test for both manufacturing employment and manufacturing labor productivity are greater than 0.05, which indicates that neither of these series is stationary. Non-stationary data can lead to misleading results in time series analysis because it can introduce trends, seasonality, and other time-dependent structures that violate the assumptions of many statistical models.

Based on the results of the Granger causality test:

For lag 1:

The p-values are slightly above 0.05 for the F-test and the chi-squared test, meaning there’s weak evidence against the null hypothesis, but it’s not strong enough to conclude causality at a 5% significance level.

For lag 2:

The p-values are mostly below 0.05, suggesting that manufacturing labor productivity (MFGOPH) Granger-causes manufacturing employment at this lag.

For lag 3:

Similarly, the p-values are below 0.05, further supporting the idea that there is Granger causality at this lag.

For lag 4:

The p-values are again above 0.05, suggesting no evidence of Granger causality at this lag.