AD and money 1: BC’s model and some data

In a paper from fall 2013 Bernardo and Campiglio (BC) presents a neat macro model for AD including endogenous money, and also puts some constructive input to the 2012 debate between Krugman and Keen. BC claim that one important difference is AD ex post and ex ante, which spontaneously feels like an interesting take.

The basics of BC’s model is similar to the endogenous money (Keen) position (all math copied from BC): Aggregate demand equals income (Y) + net change in stock of debt:


where d is net change in stock of debt (interesting measure of debt is total stock of loans held by the non-financial private sector?). Bank’s have to decide how much credit to create, satisfying a portion of the demand for loans from households and firms. This credit creation (CC):


where β  (number between 0, 1) depicts rate of approval of the demand for loans, a proxy for the confidence level for the banking system. Net credit creation at time t (NCCt) is CCt minus repayment of present stock of debts (DRt). As NCC increases the total stock of debt, the flows of repayment also increases, making the flows converge to the same value as CC, causing NCC to converge to 0 in the long run, and the growth of Y to phase out.

BC argues that the common (Krugman’s position in 2012) definition of AD (where the stock of loans is ignored) is an ex-post phenomenon, realized expenditure. The model in BC (similiar to Keen and other post-keynesians) is AD ex-ante, which also take into account “planned” expenditure, such as:


where ct is planned (p) aggregate consumption at time t, which is the same as realized consumption at time t+1. I is (planned) aggregate investment (in the same time period), making


Private banks have 2 assets: reserves at the central bank and loans. And one liability: the total amount of deposits, which is held by households, firms and gilt sellers. As credit is created by banks, private banks requests increased reserves from the central bank. The central bank alters the amount of reserves and gilts according to the demand from private banks. Stock of reserves (R):


where r is reserve ratio (required/voluntary proportion of deposits that banks back with central bank reserves). To get balance between assets and liabilities, the central bank buys/sells same amount of bonds (B) in the secondary market:


The secondary market are represented by gilt sellers, from which the central bank buys the necessary amount of gilts. “In real economic systems, this role is typically played by pension funds”. Assume an infinite amount of gilts.

Risk for unstable dynamics in the long run

By putting this and more together to a complete model, BC discusses three different scenarios. Scenario 1, “Convergence to stationary state”: Private debt, income and planned expenditure is increasing at a decreasing rate, as describe in diagram 1. As the stock of private loans increases, flows of repayment also increases, converging to the same value as credit creation, thus making credit creation and income growth to phase out in the long run.

(blue = income; green = planned expenditure; red = net credit creation)


Copied from Bernardo and Campiglio

Scenario 2, “Recession to stationary state”: NCC is negative but as the stock of loans decreases, so does the repayment of loans. Pictured through simulation by BC
(blue = income; green = planned expenditure; red = net credit creation)


Copied from Bernardo and Campiglio

In BC’s third scenario the economy is growing along a balanced growth path (BGP): income, planned expenditure and credit creation growhs exponentially. For BGP in the long rund, firm’s propensity to invest or the banking confidence level need to be high enough. The loans-to-output ratio along BGP (l*) is a function of, among other things, firms propensity to invest.

Some data

BC develops the model further, making a stock-flow-consistent model and discusses how different events might affect outcome, such as shifting psychology, interest rates etc. But already on this basic level it is interesting to make a simple comparison between the theoretical scenarios and public data. Results are mixed but promising, not the least considering that my comparison below is so simply made  (not saying that makes it a proof or anything). Not 100% sure on nominal/real; total/per capita; change measured in money/percent; choice of deflator etc.

1. For some countries and time periods, data seems similar to the theoretical scenarios

Private sector stock of loan as % of GDP have been increasing for a long time in a lot of countries, such as the US:


Source: BIS; AMECO; own calculations

For some time periods, development seems somewhat similar to scenario 1 above. Maybe during the years from 1970 until today in the US: GDP and BC’s definition of AD (=GDP + change in loans) (left axis), and private stock of loans have been increasing at a somewhat decreasing rate (right axis).


Or maybe it should be real values. Real values show similar results for the same years in US as pictured above, but maybe even more so for the period 1960-1980.


Source: BIS; AMECO; own calculations
NFC = Non-financial corporations. Housh. = households.

BC’s theoretical scenario 2 showed decreasing income and loans. This is an overall unusual phenomenon in the OECD countries since WW2. One exception might be Japan and their lost decade(s), during the 90’s and 00’s. Just as Richard Koo argues in his most readworthy book The Holy Grail of Macroeconomics, one important factor behind the Japanese stagnation seems to be private companies deleveraging, depicted below. Credit was first increasing at a decreasing rate and then decreasing at a decreasing rate (moving upwards in the diagram from the late 90’s). GDP first stagnated and then decreased. AD seems to have been gradually decreasing since early 90’s. Nominal values. Real values show somewhat different results for GDP, b/c of deflation and so forth, but still indicates a similiar development.


Source: BIS; AMECO; own calculations

2. If private loans can affect AD, and AD is an important factor for employment and unemployment…

AD and loans seems to correlate with employment and unemployment (contrary to the common story about the long term NAIRU). Except for Keen (his book and a blog example here), interesting results have also been presented by Jauch and Watzka, Mian and Sufi and others. Data for the US pictured here: correlation btw % change in loans and % change in number of people employed. Real values of loans, to get a measure for purchasing power.


Source: BIS; AMECO; own calculations. Loans deflated using Consumer Price Index.

And there seems to be a relative strong correlation btw change in unemployment (% points) and change in the stock of private loans:


Source: BIS; AMECO; own calculations. Loans deflated against Consumer Price Index

Correlation is no proof, but it seems to fit the Minskian story very well. Have anyone not believing in “endogenous money” or similar ideas commented this kind of correlation? Think I’ve only seen theoretical responses.


2 thoughts on “AD and money 1: BC’s model and some data

  1. One thing worth looking at might be papers from Fed anti-creditists like Lacker or (the extremely smart & convincing) Robert Hetzel (both Richmond Fed iirc).

    I’d link to Hetzels best paper but I’m on my phone.


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