We have found that the relationships between government spending and inflation are variable over time.1 How about another category of spending, that by consumers? This series studies that topic.
From image by Kris from Pixabay
Introduction
In this project, we examine the correlation between changes in consumer credit and changes in inflation as measured by the Consumer Price Index (CPI2). The Federal Reserve data for Household and Nonprofit Organizations credit (1951-2022)3 is the consumer credit data for this study. The U.S. government’s federal deficit spending is from the U.S. Treasury’s Historical debt outstanding.
The hypothesis we are testing is that inflation depends on consumer credit in a linear manner, expressed in the following equation:
I = mS + b
where
I = Change in CPI (the Consumer Price Index)
S = Change in Consumer Credit
The two constants, m and b, define the relationship of y, the dependent variable, to x, the independent variable. By writing the relationship in this way, we imply that CPI (y) depends on consumer credit (x). But this is a mere formality because the equation can be rearranged:
S = m’ I + b’
where
m’ = 1/m
b’ = -b/m
We could just as well write the equivalent equation implying that consumer credit depends on inflation without affecting results and conclusions.
Data
The data is organized similarly to the federal deficit spending and consumer inflation study.1 The inflation time series is divided into periods of inflationary surges, deflationary surges, and years when inflation/disinflation/deflation have trends with <4% change uninterrupted by countertrend moves >1.5%. The three types of inflationary periods from 1952-2022 are in Tables 1-3. For the definition of the various periods, see “Government Spending and Inflation: Reprise and Summary”.1
Table 1. Periods of Significant Increases of Inflation 1952-2022
Table 2. Periods of Significant Decreases of Inflation 1952-2022
Table 3. Periods without Significant Inflation Trends 1952-2022
Inflation Measured Quarterly
The definition of inflation above is done annually. Here we use inflation data reported quarterly, see Appendix 2. The previous work,4 using annual data, produces the inflation time series graph shown in Figure 1.
Figure 1. CPI Annual Inflation 1914-2022 with Significant Changes in Inflation Noted
(Each letter identifies the end of a significant move.)
The data in Figure 1 produced Tables 1-3.
Figure 2 shows the rolling four-quarter inflation using the quarterly data used in this study. This results in four times as many data points for 12 months of inflation over the same 109 years.
Figure 2. CPI Rolling Four Quarter Inflation 1914-2022
There is much more structure in Figure 2 than in Figure 1. This may reflect noise in the Figure 2 data or be real information. The only area where this question may have importance could be the three peaks from 3Q 1917 to 1Q 1920. In Figure 1, this time period shows only a single peak with a shoulder approaching 1920. Addressing this question has no bearing on the current study, which covers the 71 years 1952-2022.
Figure 3 displays the inflation data for the study period 1952-2022.
Figure 3. CPI Rolling Four Quarter Inflation 1952-2022 with Significant Changes in Inflation Noted
(Each letter identifies the end of a significant move. An * identifies the end of an insignificant time period.)
A summary of the data in Figure 3 is in Table 4.
Table 4. Timeline of Inflation Data 1952-2022
The quarterly data displays more information than the yearly data used previously.
- Table 4 has 8 periods with positive inflation surges for the 70-year period. The previous study defined only 5.
- There are 5 negative inflation surges in Table 4, one more than in the previous study.
- There are also 5 time periods with insignificant inflation changes in Table 4, while the previous study had only 3.
- Significant inflationary periods are identified here for 2006-08 and 2009-11 with the quarterly data. A significant deflationary period was identified for 2008-09.
- There were 3 1/2 years 1983-86 with no significant inflation changes that were not identified previously.
Note: 1999-2020 had been identified previously as a 22-year period with no significant inflationary trends. The quarterly data found two significant inflationary trends and one significant deflationary trend within the interval.
Using the quarterly data gives an apparently better resolution of inflationary and deflationary periods than was obtained with the annualized data. Whether or not this is useful remains to be seen with further analysis.
Comparing Household and Nonprofit Organization Credit Growth to Inflation
The determination of the credit growth rate by calendar year quarters is shown in Appendix 1. A table for comparing credit growth with inflation is constructed below from that growth rate data. For convenience, Household and Nonprofit Organization Credit is abbreviated HNO Credit below.
We use the Consumer Price Index (CPI) to calculate the inflation rate, as was done in the previous study of federal deficit spending.1 However, the data here for inflation growth is organized by calendar year quarters, as shown in Appendix 2.
Table 5. HNO Credit Growth and Inflation (CPI), Coincident Data, 1952-2022*
Table 6. HNO Credit Growth and Inflation (CPI), HNO Leads by 3 Months, 1952-2022*
Table 7. HNO Credit Growth and Inflation (CPI), HNO Leads by 6 Months, 1952-2022*
Table 8. HNO Credit Growth and Inflation (CPI), HNO Leads by 9 Months, 1952-2022*
Table 9. HNO Credit Growth and Inflation (CPI), HNO Leads by 12 Months, 1952-2022*
Table 10. HNO Credit Growth and Inflation (CPI), HNO Leads by 18 Months, 1952-2022*
Table 11. HNO Credit Growth and Inflation (CPI), HNO Leads by 24 Months, 1952-2022*
Table 12. HNO Credit Growth and Inflation (CPI), HNO Lags by 3 Months, 1952-2022*
Table 13. HNO Credit Growth and Inflation (CPI), HNO Lags by 6 Months, 1952-2022*
Table 14. HNO Credit Growth and Inflation (CPI), HNO Lags by 9 Months, 1952-2022*
Table 15. HNO Credit Growth and Inflation (CPI), HNO Lags by 12 Months, 1952-2022*
Table 16. HNO Credit Growth and Inflation (CPI), HNO Lags by 18 Months, 1952-2022*
Table 17. HNO Credit Growth and Inflation (CPI), HNO Lags by 24 Months, 1952-2022*
Analysis
The first thing to notice about this data concerns the complete lack of patterned structure. Figure 4 shows that the timeline variations for HNO Credit and CPI Inflation show no consistent correlations. Over the long 71-year time frame, the two patterns seem to follow largely independent paths.
Figure 4.
A scatter plot of the quarterly data with coincident timelines for the two variables Figure 5) indicates negligible correlation ( R2 = 0.63%, R = 8%). This is found for a desirable oval football shape6 for the data points, so the result should be considered reliable.
Figure 5. Scatter Diagram for HNO Credit – CPI Inflation Data Pairs 1952-2022, Coincident Timelines
We see no potential for useful correlation analysis in the entire data set. Further work will study what happens with the analysis of shorter time periods within the 71-year time frame.
Conclusion
There are many more data points for the various time periods studied here with quarterly data compared to the previous study1 using annualized data. There are also more periods with significant inflation trends. The finer data granularity appears to contain more information than the previous data. It remains to be seen if that carries through to the analysis of correlation. In particular, we hope to indicate possible cause-and-effect relationships when the data timelines vary with respect to each other. That work will be addressed in the next phase of this project. We will look at correlations during the specific event periods for inflation (Table 4).
Appendix 1
The Household and Nonprofit Organization (HNO) Credit data is from the Fed database.3 The table below shows the conversion of the Fed data to growth rate by quarter.
Table A1. Growth Rate of HNO Credit 1952-2022* (Quarter-over-Quarter)
Appendix 2
The Consumer Price Index (CPI) data is from the Fed database.2 The table below shows the conversion of the Fed data to growth rate by quarter.
Table A2. Growth Rate of CPI 1913-2022* (Quarter-over-Quarter)
Footnotes
1. Lounsbury, John, “Government Spending and Inflation. Reprise and Summary”, EconCurrents, August 20, 2023. https://econcurrents.com/2023/08/20/government-spending-and-inflation-reprise-and-summary/.
2. Federal Reserve Economic Data, Consumer Price Index for All Urban Consumers: All Items in U.S. City Average, Index 1982-1984=100, Monthly, Not Seasonally Adjusted, https://fred.stlouisfed.org/graph/?id=CPIAUCNS.
3. Federal Reserve Economic Data, Households and Nonprofit Organizations; Consumer Credit; Liability, Level, HCCSDODNS, Last update June 8, 2023. https://fred.stlouisfed.org/series/HCCSDODNS.
4. Lounsbury, John, “Government Spending and Inflation. Part 10”, EconCurrents, August 20, 2023. https://econcurrents.com/2023/04/23/government-spending-and-inflation-part-10/.
5. United States Department of the Treasury, Historical Debt Outstanding, Last update October 4, 2022.
https://fiscaldata.treasury.gov/datasets/historical-debt-outstanding/historical-debt-outstanding
6. Freedman, David, Pisani, Robert, and Purves, Richard, Statistics, Fourth Edition, W.W. Norton & Company (New York) and Viva Books (New Delhi), 2009. See Chapters 8 & 9 for an explanation of how normal distributions relate to determining correlation coefficients. See p. 147 for a discussion of football-shaped scatter diagrams.
