Author:
(1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction


Methods


2.1 Statistical Methodology
2.2 US Time Series Data
2.3 Hyperinflation Model


Results


3.1 Characterisation of Price Inflation
3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923)
4. Discussion
5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix 4. Discussion The consumer price inflation model described is intended to investigate the consumer price index (CPI), over a period of years and not over a period of months, in order to investigate the longer-term relationships involved. In contrast, the hyperinflation model described is intended to investigate the increase in nominal prices, over a period of months, because of the accelerating nature of the decline in the purchasing power of the fiat currency being studied. Unlike in the case of hyperinflation, under “ordinary” circumstances, the growth in price inflation has a velocity, but the acceleration can be ignored because it is approximately constant, i.e., price inflation increases at an approximate constant rate with time. The hypothesis that the annual rate of growth in the US CPI is a function of the annual growth in the US broad money supply minus the annual growth in US real GDP minus the annual growth in US savings, over the time period 2001 to 2019, has been shown to be the case. However, an exact relationship required the use of a non-zero residual term, RES(t): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) − 𝑅𝐸𝑆(𝑡) This may be the case for a couple of reasons: (1) The measure of savings used was the estimated average annual American household savings [11]. While, this might be expected to be technically challenging to calculate accurately, it only pertains to households. It might be expected that in addition to average annual American household savings, there should also exist annual American non-household savings. Therefore, a limitation of this paper is that American household savings were used as a measure of overall savings in the US economy. (2) There may be an additional factor that needed to be included in the model, other than savings. Savings were included in the model because savings can be used, if required / desired to purchase goods and/or services, or not, as the case might be, and as a result might be expected to influence the CPI. An alternative approach might be to use another broad measure of the money supply that excludes savings. The model includes the terms, BMS and GDP. So also does the concept of the “velocity of money” [15], in which: "𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦" = 𝐺𝐷𝑃/𝑀𝑜𝑛𝑒𝑦 𝑆𝑢𝑝𝑝𝑙𝑦 This equation can be rearranged as follow: However, for the concept of the “velocity of money” to be relevant to this paper, it would need to be expressed in terms of its constant rate of change with time, as follows: Should the CPI model be valid (subject to the caveat discussed above in relation to savings) such that: 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) this would predict a few different economic scenarios: (1) When there is no (or very little) growth in GDP or savings (“stagflation scenario”): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) (2) When the growth in savings is sufficiently high, the growth in CPI could turn negative (“deflation scenario”). (3) When there is negative growth in GDP (“recession scenario”), the growth in CPI could be greater than the growth in BMS, should there be no “rebalancing” change in the growth of BMS. A mathematical statistical formulation of a hyperinflationary process has been provided and used to quantify the period of hyperinflation in the Weimar Republic from July 1922 until the end of November 1923. Why did this hyperinflationary happen and why was it allowed to occur by the Government and central bankers of the Weimar Republic? As outlined in [14], following World War 1 and the Treaty of Versailles (which came into effect on January 10, 1920), the strategy that Germany used to pay war reparations was the mass printing of bank notes to buy foreign currency, which was then used to pay reparations, but which also caused inflation of the paper mark. After Germany failed to pay France an instalment of reparations on time in late 1922, French and Belgian troops occupied the Ruhr valley, Germany's main industrial region, in January 1923. The German government's response was to order a policy of passive resistance in the Ruhr, akin to a general strike, to protest the occupation, while providing financial assistance to the striking workers by printing more and more banknotes, with the result that the paper mark became increasing worthless throughout 1923. The mathematical statistical formulation of a hyperinflationary process could be extended beyond two sequential exponential expansions to include any arbitrary number (n) of sequential exponential expansions. However, while this may have theoretical interest, it is not a phenomenon that has yet occurred in real-world economics, to the knowledge of the author. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Author: Author: (1) Laurence Francis Lacey, Lacey Solutions Ltd, Skerries, County Dublin, Ireland. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Editor's Note: This is Part 6 of 7 of a study on how changes in the money supply, economic growth, and savings levels affect inflation. Read the rest below. Table of Links Abstract and 1 Introduction Methods 2.1 Statistical Methodology 2.2 US Time Series Data 2.3 Hyperinflation Model Results 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References

Appendix Abstract and 1 Introduction Abstract and 1 Introduction Methods Methods Methods 2.1 Statistical Methodology 2.1 Statistical Methodology 2.2 US Time Series Data 2.2 US Time Series Data 2.3 Hyperinflation Model 2.3 Hyperinflation Model Results Results Results 3.1 Characterisation of Price Inflation 3.1 Characterisation of Price Inflation 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 3.2 Characterisation of Hyperinflation in the Weimar Republic (1922 to 1923) 4. Discussion 4. Discussion 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix 5. Conclusion, Supplementary materials, Acknowledgements, and References Appendix Appendix 4. Discussion The consumer price inflation model described is intended to investigate the consumer price index (CPI), over a period of years and not over a period of months, in order to investigate the longer-term relationships involved. In contrast, the hyperinflation model described is intended to investigate the increase in nominal prices, over a period of months, because of the accelerating nature of the decline in the purchasing power of the fiat currency being studied. Unlike in the case of hyperinflation, under “ordinary” circumstances, the growth in price inflation has a velocity, but the acceleration can be ignored because it is approximately constant, i.e., price inflation increases at an approximate constant rate with time. The hypothesis that the annual rate of growth in the US CPI is a function of the annual growth in the US broad money supply minus the annual growth in US real GDP minus the annual growth in US savings, over the time period 2001 to 2019, has been shown to be the case. However, an exact relationship required the use of a non-zero residual term, RES(t): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) − 𝑅𝐸𝑆(𝑡) This may be the case for a couple of reasons: (1) The measure of savings used was the estimated average annual American household savings [11]. While, this might be expected to be technically challenging to calculate accurately, it only pertains to households. It might be expected that in addition to average annual American household savings, there should also exist annual American non-household savings. Therefore, a limitation of this paper is that American household savings were used as a measure of overall savings in the US economy. (2) There may be an additional factor that needed to be included in the model, other than savings. Savings were included in the model because savings can be used, if required / desired to purchase goods and/or services, or not, as the case might be, and as a result might be expected to influence the CPI. An alternative approach might be to use another broad measure of the money supply that excludes savings. The model includes the terms, BMS and GDP. So also does the concept of the “velocity of money” [15], in which: "𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑜𝑓 𝑚𝑜𝑛𝑒𝑦" = 𝐺𝐷𝑃/𝑀𝑜𝑛𝑒𝑦 𝑆𝑢𝑝𝑝𝑙𝑦 This equation can be rearranged as follow: However, for the concept of the “velocity of money” to be relevant to this paper, it would need to be expressed in terms of its constant rate of change with time, as follows: Should the CPI model be valid (subject to the caveat discussed above in relation to savings) such that: 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) − 𝑣𝐺𝐷𝑃(𝑡) − 𝑣𝑆𝐴𝑉(𝑡) this would predict a few different economic scenarios: (1) When there is no (or very little) growth in GDP or savings (“stagflation scenario”): 𝑣𝐶𝑃𝐼(𝑡) = 𝑣𝐵𝑀𝑆(𝑡) (2) When the growth in savings is sufficiently high, the growth in CPI could turn negative (“deflation scenario”). (3) When there is negative growth in GDP (“recession scenario”), the growth in CPI could be greater than the growth in BMS, should there be no “rebalancing” change in the growth of BMS. A mathematical statistical formulation of a hyperinflationary process has been provided and used to quantify the period of hyperinflation in the Weimar Republic from July 1922 until the end of November 1923. Why did this hyperinflationary happen and why was it allowed to occur by the Government and central bankers of the Weimar Republic? As outlined in [14], following World War 1 and the Treaty of Versailles (which came into effect on January 10, 1920), the strategy that Germany used to pay war reparations was the mass printing of bank notes to buy foreign currency, which was then used to pay reparations, but which also caused inflation of the paper mark. After Germany failed to pay France an instalment of reparations on time in late 1922, French and Belgian troops occupied the Ruhr valley, Germany's main industrial region, in January 1923. The German government's response was to order a policy of passive resistance in the Ruhr, akin to a general strike, to protest the occupation, while providing financial assistance to the striking workers by printing more and more banknotes, with the result that the paper mark became increasing worthless throughout 1923. The mathematical statistical formulation of a hyperinflationary process could be extended beyond two sequential exponential expansions to include any arbitrary number (n) of sequential exponential expansions. However, while this may have theoretical interest, it is not a phenomenon that has yet occurred in real-world economics, to the knowledge of the author. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. This paper is available on arxiv under CC BY-NC-ND 4.0 DEED license. available on arxiv

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