A number of blog members argued that my lead/lag analysis of the Credit Accelerator and economic and financial variables (unemployment, share and house price indices) appeared erroneous.
I am the first to admit that–though my mathematical modelling is strong–my statistical analysis is not up to the same level. I long ago reacted adversely to the practice of econometrics in economics, largely on the same grounds that led Ed Leamer to publish his famous paper “Let’s Take the Con out of Econometrics” (AER, March 1983), omitted variable bias, etc.
However this is one of those issues where someone with a strong statistical basis (as well as mathematical physics foundation) using standard statistical programs can do better than I did, so I passed the data on to “Lyonwiss”. Here are the results of his analysis–and here is the original data, should others wish to analyze it themselves.
Steve sent me his calculated data for “Credit Accelerator” (CA), “Unemployment Change”, “Real House Price Change” and “Share Price Change” (Change in % pa) for Australia and USA over 1993 to 2011 and asked me to check his calculated correlations of CA against the other variables. I confirmed his correlation calculations and proved that the correlations are all statistically significant (greater than 99.9% probability) over the period. For the period 1993–2011, I also confirmed that credit accelerator leads and lags (in months) the other variables for produce the maximum correlation (or anticorrelation) shown in the following table:
Country 
Unemployment 
House Price 
Share Price 

Australia Lead(+)/Lag() 
0 
10 
–8 

Australia Correlation 
–0.7768 
–0.3411 
0.7175 

USA Lead(+)/Lag() 
–5 
–9 
–11 

USA Correlation 
–0.8516 
0.7228 
0.5739 
Note that CA leads another variable by +x months, if the data for the other variable are lagged by x months, by shifting x months of data in the future to the present. Similarly CA lags another variable by –x months if the CA data is shifted x months from the future to the present.
The above table states that CA in the USA lags house price changes by 9 months and share price changes by 11 months. This roughly agrees with Figure 7 and 8 of Steve’s June 11 post, where both house price and share price changes dripped well before CA. The empirical data suggest that the CA is more likely to be a lagging variable rather than a leading one, as four cases out of six are lags, one leads, while one is contemporaneous.
Moreover, if we reject the stationary equilibrium world of neoclassical economics, the leadlag relationships are not expected to be stable. So, I divided Steve’s dataset into an earlier period 1993–2001 and a later period 2002–2011 and performed the same analysis for each period separately. The leadlag maximized correlations were all statistically significant. For the earlier period, we have:
Country 
Unemployment 
House Price 
Share Price 

Australia Lead(+)/Lag() 
0 
4 
4 

Australia Correlation 
–0.4097 
–0.5445 
–0.4636 

USA Lead(+)/Lag() 
12 
–15 
11 

USA Correlation 
–0.4405 
–0.3787 
0.4103 
And for the later period, we have:
Country 
Unemployment 
House Price 
Share Price 
Australia Lead(+)/Lag() 
0 
–4 
–8 
Australia Correlation 
–0.8706 
0.5057 
0.8007 
USA Lead(+)/Lag() 
–5 
–10 
–11 
USA Correlation 
–0.9029 
0.901 
0.6299 
Indeed, the leadlag relationships appear unstable, with four of the relationships changing from leads to lags or vice versa, from the earlier period to the later period. In the US CA remains a consistent lag versus real house price changes, while Australian CA changes remains contemporaneous relative to unemployment changes. (There are other suggestive observations, not mentioned here.)
The results are largely what I expected. The key result is that there are statistically significant relationships between CA and economic variables, suggesting the importance of private credit in the real economy and the nonneutrality of money in the short to medium term (10 to 20 years).
However, the causality of credit appears complex, not displaying the simple timeinvariant causality of physics. As Steve suggests in a complex system where there are nonlinear feedbacks rather than linear causation one expects leads and lags to alter over time.