Regressions to determine coefficients in Effective Demand Equation

Effective Demand seeks to identify the end of a business expansion in the business cycle. This post will present a method to determine the coefficients in the effective demand equation to determine the effective demand limit upon the business cycle.

Defining the Top of the Business Cycle

In order to determine an equation to describe the top of a business cycle, we first need to identify the tops of a business cycle. I measure the business cycle by multiplying capacity utilization by (1 - unemployment rate). I call this composite measure T in the graph below. This measure gives a view into how capital and labor is being utilized throughout the business cycle.

The graph shows that the utilization of capital and labor rises and falls throughout the business cycle. I have connected the tops of the cycle with a yellow line. This yellow line will represent how the top potential of the business cycle has changed through time. The tops of business cycles are connected with a straight line. Whether the yellow line should dip below or hover above a straight line is not explored at this stage of the research. So the tops are connected with a straight line.

The effective demand equation will be determined by regressing variables against the yellow line. The idea is to develop an equation that will describe the behavior between T and effective demand at the top of the past business cycles since 1967.

Independent Variables to determine Effective Demand

In order to determine an equation for Effective Demand, we need to have independent variables to put into our regression. The dependent variable in the regression will be the yellow line connecting the tops of the "T" business cycle above.

Here is a list of the independent variables to be regressed. (All data is quarterly begining in 1967 because capacity utilization data began in 1967 according to data source, FRED.)

• Labor Share Index of National Income. (data) The labor share index as given by the US Bureau of Labor Statistics. Labor share will represent the final consumption power of society apart from the income of profits, which are left over after paying out labor income.
• Headline Inflation. (data) The CPI of all items. Inflation represents how prices cut into demand. A higher inflation will lower potential demand.
• Looseness or Tightness of the Federal Funds rate. A loose Fed rate will raise potential demand. This variable will be determined using the NGDP effective demand rule for monetary policy. This variable depends upon the coefficients used for the other independent variables, so there will be a series of iterations of the regression which change the other coefficients. The iterations will arrive at stable coefficients for all independent variables. (shown later) (Note: Core inflation is factored into the NGDP effective demand rule. See this post for its comparison to Headline inflation.)
• Looseness or Tightness of Long-term Interest rates. (data) The year-over-year change of the difference between the 10-year Treasury (constant maturity) minus the Fed rate. If the 10-year falls in relation to the Fed rate, then demand potential is raised.
• Population Growth rate. (data) The faster the population grows, the more demand potential would grow too.
• Yearly Change of Real GDP. (data from US Bureau of Economic Analysis, table 1.1.6) As real GDP grows, demand potential should fall. More products and services, all other variables equal, should lower demand potential resulting in less capital and labor utilized in businesses.
• Government Expenditures as a percentage of Real GDP. (data from US Bureau of Economic Analysis, table 1.1.6) The more the government spends, the more demand potential there should be.
• Net Exports as a percentage of Real GDP. (data from US Bureau of Economic Analysis, table 1.1.6) The more net exports are in relation to total production, the more demand potential there should be.
• Private Investment as a percentage of Real GDP. (data from US Bureau of Economic Analysis, table 1.1.6) The more private investment there is in relation to total production, the more demand potential there should be.

Iterations of Regressions to Determine the Coefficients

These independent variables are put into a regression. Estimated coefficients are used to start the iterations of the regression due to the variable (EDrule - Fed rate) needing a start. The starting estimated coefficients do not affect the ultimate result.

Effective Demand limit; Top potential of business cycle (yellow line in first graph) = 0.80*LSI - 1*CPIall + 1*(EDrule - Fed rate) - 1*(10year - Fed rate) + 1*popgrowth - 1*realGDPgrowth + 10*G/rGDP + 10*NX/rGDP + 10*I/rGDP

No residual factor is used in order to constrict the result to the variables chosen.

The initial estimation of this equation against the top demand potential (yellow line above) looks like this.

The first iteration of the regression gives these results.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0	#N/A	#N/A	#N/A	#N/A	#N/A
lsi	0.724	0.050	14.574	0.000	0.626	0.822
cpiall	-1.056	0.069	-15.302	0.000	-1.192	-0.920
ed-ff	86.338	5.589	15.449	0.000	75.312	97.364
10-ff	-0.656	0.088	-7.456	0.000	-0.829	-0.482
G	32.153	11.453	2.808	0.006	9.558	54.749
r growth	-0.483	0.082	-5.869	0.000	-0.645	-0.320
I	25.174	20.518	1.227	0.221	-15.307	65.654
nx	34.331	19.060	1.801	0.073	-3.274	71.935
pop	-2.080	0.969	-2.146	0.033	-3.992	-0.168

According to the P-values, Investment (I) and Net Exports (NX) are not significant enough to describe the effective demand limit by having values over 5%. The highest T stats point to labor share, headline inflation, monetary effects and real GDP growth as the most significant variables.

After 6 iterations, the results look like this.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0	#N/A	#N/A	#N/A	#N/A	#N/A
lsi	0.69316	0.04859	14.26542	1.41E-31	0.597294	0.789026
cpiall	-1.13543	0.071273	-15.9306	1.79E-36	-1.27605	-0.99481
ed-ff	87.10909	5.554219	15.68341	9.45E-36	76.15095	98.06723
10-ff	-0.44419	0.083452	-5.32273	2.95E-07	-0.60884	-0.27955
G	43.9263	11.15365	3.93829	0.000116	21.92082	65.93178
r growth	-0.19435	0.079358	-2.44901	0.015262	-0.35092	-0.03778
I	29.42429	20.27896	1.450976	0.148489	-10.5849	69.43348
nx	47.67543	18.85586	2.528415	0.012298	10.47395	84.87692
pop	-2.97525	0.96935	-3.06932	0.00247	-4.88772	-1.06278

Now the only independent variable with a P-value too high for significance is Investment (I). Investment will be dropped from the regression. Then the regression iterations will be run over again.

Here is how the coefficients change over the 6 iterations giving two examples. All coefficients trend toward a stable value.

Second Run of Regression Iterations without Investment

After 6 iterations of the regression without investment, the results look like this.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0	#N/A	#N/A	#N/A	#N/A	#N/A
lsi	0.759053	0.018787	40.40267	1.01E-93	0.721988	0.796118
cpiall	-1.13232	0.071133	-15.9182	1.68E-36	-1.27265	-0.99198
ed-ff	88.26595	5.387935	16.38215	7.43E-38	77.63626	98.89565
10-ff	-0.46773	0.081525	-5.73728	3.87E-08	-0.62857	-0.30689
G	29.49403	5.457594	5.404218	1.99E-07	18.72691	40.26115
r growth	-0.12814	0.06538	-1.95997	0.051502	-0.25713	0.000844
nx	27.20015	12.30226	2.210989	0.028262	2.929399	51.4709
pop	-2.77093	0.955917	-2.89871	0.0042	-4.65683	-0.88503

The variable pushing the limits of significance for a P-value is real GDP growth. The regression iterations will be run again without real GDP growth.

Third Run of Regression Iterations without Real GDP Growth

After 6 iterations of the regression without real GDP growth, the results look like this.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0	#N/A	#N/A	#N/A	#N/A	#N/A
lsi	0.758384	0.018787	40.3675	5.85E-94	0.721321	0.795447
cpiall	-1.09859	0.068206	-16.1069	4.08E-37	-1.23315	-0.96404
ed-ff	87.68955	5.366844	16.33913	8.52E-38	77.10184	98.27726
10-ff	-0.39175	0.071212	-5.50122	1.24E-07	-0.53224	-0.25127
G	28.0139	5.426011	5.162891	6.22E-07	17.30947	38.71834
nx	26.34758	12.29211	2.143454	0.033376	2.097702	50.59745
pop	-2.85751	0.95646	-2.98759	0.003191	-4.74442	-0.97061

The variable with less significance for a P-value when compared to the other variables is Net Exports/rGDP. The regression iterations will be run again without Net Exports/rGDP.

Third Run of Regression Iterations without Net Exports/rGDP

After 6 iterations of the regression without Net Exports/rGDP, the results look like this.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0	#N/A	#N/A	#N/A	#N/A	#N/A
lsi	0.729557	0.012576	58.01381	1.7E-121	0.704748	0.754365
cpiall	-1.02953	0.059659	-17.2568	1.54E-40	-1.14722	-0.91184
ed-ff	86.61256	5.30586	16.32394	8.11E-38	76.14552	97.07959
10-ff	-0.37225	0.070746	-5.26183	3.88E-07	-0.51182	-0.23269
G	33.8623	4.607057	7.350093	5.99E-12	24.77381	42.95078
pop	-2.03106	0.866964	-2.34273	0.020195	-3.74135	-0.32077

The variable with less significance for a P-value when compared to the other variables is population growth. The regression iterations will be run again without population growth.

Fourth Run of Regression Iterations without Population Growth

After 6 iterations of the regression without population growth, the results look like this.

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	0	#N/A	#N/A	#N/A	#N/A	#N/A
lsi	0.713623	0.009986	71.45959	3.2E-138	0.693923	0.733323
cpiall	-1.01453	0.059451	-17.0648	4.71E-40	-1.1318	-0.89725
ed-ff	85.47596	5.282628	16.18057	1.85E-37	75.05511	95.8968
10-ff	-0.37906	0.070897	-5.3467	2.58E-07	-0.51892	-0.23921
G	32.05953	4.617768	6.942646	6.07E-11	22.95023	41.16883

The P-values all show high significance.

Evaluating the Final Equation for Effective Demand

Using the coefficients in the last regression run, the effective demand equation looks like this.

Effective Demand limit; Top potential of business cycle (yellow line in first graph) = 0.714*LSI - 1.015*CPIall + 0.855*(EDrule - Fed rate) - 0.379*(10year - Fed rate) + 0.32*G/rGDP

and plots like this.

In this above graph, the effective demand limit (orange line) is currently rising. Towards the end of 2014, there was concern about the economy. The stock market had a correction. Then the price of oil started to fall and the 10-year long-term rates started to fall. The combination of those two made effective demand start to rise. The economy and the stock markets have been rising upon this resuscitation of effective demand.

The resulting Effective Demand rule rate is now compared to the Fed rate. When the Fed rate (red line) is below the blue line, the Fed rate is looser than the effective demand limit would prescribe.

Concluding thoughts

The resulting equation could be used as a guide to assess when the end of the business cycle might occur. Still, the economic environment must be evaluated because the effective demand limit may just slow down utilization of capital and labor instead of lead it into recession. The research into effective demand continues.

The effective demand blog here has spent almost 2 years using labor share as the only variable for effective demand. The P-value of the above regression results show that labor share has the highest significance for the effective demand limit. So the principles developed over the last two years are not lost. They have paved the way to a better understanding of the current equation.

Real GDP growth may still have a significant influence. If I add real GDP growth with a coefficient of 0.40, the plot matches up better to the peaks, for example in the late 1960's, 1980, 1984 and 2005. This addition also shows how close T and effective demand came together before the stock market correction in the 3rd quarter of 2014. I want to put the graph here for reference.

Comments

[JimH]

Edward,

You had me worried until I read this article several times. I have almost no understanding of the statistics which you are using. You cite the P factor and with your context, I assume that the item with the lowest P factor is the most relevant.

It appears that you are still looking at labor share as the most important factor in causing our current economic problems. I have serious doubts about the other factors. The other factors which you cite here seem to be only secondary.

Population increases may well work to lift an economy but only if the economy needs more labor. That certainly is not true of the US while we are importing as much as we are. The problem is not that we don't have enough labor it is that we have moved too much production overseas.

We should expect cpiall to stall as consumers have less and less income to spend on discretionary purchases. Speculators fear the FED will raise interest rates. As bubbles caused by loose money collapse, prices should fall. (Think oil prices, as oil prices rose for no good reason from 2003 to 2008 then fell before returning to unreasonable highs.) We are getting back to the essentials of supply and demand.

But the FED is only responding to the reality of the economy.

Long term interest rates are also responding to the economy and its future prospects.

I assume that G is government spending and obviously that is limited by revenue and a willingness to borrow ever more money. This is obviously responding to the private economy.

I can see that all those other factors do affect the economy and thus do add or subtract from the effect of low labor share. Thus your graphs can not completely match the real world without them. But I still view them as a distraction.

My view is that consumers can not spend what they do not have and producers will not produce what they can not sell. That is our problem, stated as briefly as I can. Any explanation which wanders very far from that is flawed.

We will either deal with our primary problem or we will twist in the breeze as economists and politicians wander thru the maze of other possibilities.

[Edward Lambert]

Hi Jim,
According to the statistics, labor share is still the most significant variable to determine effective demand. When labor share moves, all other variables are dragged along with it.
I have more to publish on this. Yet, from what I see, monetary policy is going to great lengths to try to battle the drop in labor share. Japan too... These great lengths produce some uncertainty in the business world. The uncertainty does hinder business expansion and investment in productive capacity.
But a proper look at effective demand should include all the factors with a significant impact.