Credit Accelerator Leads and Lags

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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 anti-cor­re­la­tion) shown in the fol­low­ing table:

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 lead-lag 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 lead-lag max­i­mized cor­re­la­tions were all sta­tis­ti­cal­ly sig­nif­i­cant. For the ear­li­er peri­od, we have:

And for the lat­er peri­od, we have:

Indeed, the lead-lag 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 non-neu­tral­i­ty of mon­ey in the short to medi­um term (10 to 20 years).

How­ev­er, the causal­i­ty of cred­it appears com­plex, not dis­play­ing the sim­ple time-invari­ant 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.