A Statistical Analysis of Economic Interventionism

8/2/2019 A Statistical Analysis of Economic Interventionism

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A Statistical Analysis of Economic Interventionism

Kevin S. Hu, Ryan P. Furey, James P. Hogan, Felipe A.S. Da Cruz

May 2, 2012

1 Abstract

The purpose of this project is to bring to light a series of noteworthy and thought-provokingcorrelations. Inherent in this statistical analysis is the understanding that, although thecorrelations may be significant, one must be wary of the dangers of extrapolation associatedwith any analysis. With this said, this paper is intended to expand on the data associatedwith fiscal or monetary interventionism in the U.S. economy. This study has collected datafrom the U.S. Bureau of Labor Statistics and the Federal Reserve from 1960 to the present onrates of unemployment, consumer price index, inflation, GDP, money supply, money velocity,price level, GDP per capita, and labor force participation. From these sets of data one cantransform the variables necessary to run regression analyses, and it is this papers purpose

to do so in what was found to be a meaningful manner. From these regression analyses,resulting correlations, or lack thereof, have been expanded, and the resulting arguments thatcould possibly be created from the evidence found have been noted.


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2 Introduction

Many issues that plague societies around the world are a result of economic issues. Poverty,hunger and malnutrition, and even some wars are fought due to economic factors. As such,the study of economics is crucial for the advancement of societies everywhere.

Two poles have emerged in terms of government policy in economics - one characterizedas laissez-faire and the other as economic planning. Laissez-faire strategy, in which thegovernment plays no role in the economy, relies on the invisible hand that guides the economytoward the common good, as theorized by the father of capitalism, Adam Smith. However,this strategy does not always lead to the common good. What should the role of governmentbe in the economy?

There is wide agreement about the major goals of economic policy: high em-

ployment, stable prices, and rapid growth. There is less agreement that thesegoals are mutually compatible or, among those who regard them as incompatible,about the terms at which they can and should be substituted for one another.There is least agreement about the role that various instruments of policy canand should play in achieving the several goals.

- Milton Friedman

The question regarding the role of government in the economy is contentious - thus, how doeconomists determine the best course of action for the government? What science can beused?

Economics is, by nature, an observational science. It is impractical to actually experimenton societies, so economists are forced to rely on observed information to build models withwhich they propose to predict economic behavior. Statistical analysis can help determine thestrength of these models by measuring how closely the models fit observed data. This paperseeks to compare several theories of economic interventionism, and then to relate incomeinequality (commonly associated or even attributed to free markets and capitalism) withoverall and per-capita economic performance. To accomplish this, it analyzes data aboutthe U.S. economy from 1960 to the present.


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Contents

1 Abstract 1

2 Introduction 2

3 Theories of Economic Interventionism 4

3.1 The Exchange Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.2 Quantity Theory of Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3 Fiscal Theory of Price Level . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

3.3.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4 Inflation Rate as a Control for Unemployment 6

4.1 Phillips Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

4.2 New Phillips Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5 Income Inequality 75.1 Labor Force Participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5.1.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.1.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5.2 Economic performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.2.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

6 Conclusions and Discussion 9

7 References 10

A Appendices 11

A.1 Exchange Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11A.2 Quantity Theory of Money . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12A.3 Fiscal Theory of Price Level . . . . . . . . . . . . . . . . . . . . . . . . . . . 12A.4 Phillips Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13A.5 New Phillips Curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13A.6 Labor Force Participation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14A.7 Economic Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15


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3 Theories of Economic Interventionism

3.1 The Exchange Equation

An overarching tenet in economic policy is the exchange equation, which states:

M V = P Q,

where M represents the amount of money in circulation, V represents the transactionsvelocity of money, P represents the transactions price level, and Q represents economicoutput.

3.1.1 Methods

The Exchange Equation is identically true, but its validity can be tested regardless usingquarterly data from January 1st, 1960 to July 1st, 2011 (see pvmq.csv, columns m, v, p, andq). The data is readily available from the Federal Reserve Bank.

It is difficult to run a regression on the original Exchange Equation, but the equation canbe manipulated so that it is more linear:

M V = P Q log(M V) = log(P Q) log M + log V = log P + log Q.

Then a multiple regression on the data can determine whether a model of this form issignificant, with an R2 value close to 1 and an F-test p-value less than 0.01.

3.1.2 Results

Multiple linear regression produces the following equation:

log Q = 0.9257567 log P + 1.022252 log M + 1.132964 log V + 3.971635

P0.9257567Q = 103.971635M1.022252V1.132964.

This form matches that of the Exchange Equation, with factors due to specific measures used:for M, the M2 money supply; for V, the M2 money velocity; for P, the U.S. Consumer Price

Index (CPI); for Q, the U.S. real gross domestic product (real GDP). Moreover, this relationis extremely strong, with an R2 value of 0.998. An F-test returns a probability of virtuallyzero, suggesting that the model is strongly significant. The p-values associated with t-testson each of the individual variables also return probabilities of virtually zero.

The residuals show a clear pattern, failing a kurtosis test. Similarly, the test fails theBreusch-Pagan and Cook-Weisberg test for heteroskedasticity. On both tests, the p-valuesreturned by the tests are below 0.01, suggesting high statistical significance. However, sincethe exchange equation is identically true, the variables are deeply related, and there wasstrong multilinearity in the data. Thus the heteroskedasticity and kurtosis levels of themodel produced are not concerning.


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3.2 Quantity Theory of Money

The Quantity Theory of Money suggests that money supply and price level have a direct

proportional relationship. It is an extension of the Exchange Equation that is associatedwith the Monetarist school of economics.

3.2.1 Methods

If money supply and price level have a direct proportional relationship, a linear regressionon M and P should return a positively-sloped line with F-test p-value below 0.01 and anR2 value near 1. This analysis uses quarterly data from January 1st, 1960 to July 1st, 2011from the Federal Reserve Bank. If the F-test returns a p-value less than 0.01 and the t-testfor the significance of the independent variable also returns a p-value less than 0.01, it is a

strong suggestion that the model is accurate.

For P this analysis uses the CPI and for M this analysis uses the M2 money supply (seepvmq.csv, columns m and p).

3.2.2 Results

A single regression on M and P produces the model:

P = 0.0128719M + 18.44568.

The F-test and t-test both return p-values of virtually zero. Also, the R2 value is 0.9362,suggesting an extremely strong correlation. While the model fails our tests for heteroskedas-ticity, multilinearity again plays an important role.

The fact that a linear model with positive slope relates price level and money supply sostrongly suggests that for the past fifty years, in the U.S., the Quantity Theory of Moneyhas in fact been valid.

3.3 Fiscal Theory of Price Level

The Fiscal Theory of Price Level suggests that government fiscal policy affects inflation;namely, it suggests that government budgets must be balanced in order to stabilize inflation.As a heterodox economic theory, it is not widely accepted, although the Fiscal Theory ofPrice Level and the Quantity Theory of Money are not mutually exclusive.

3.3.1 Methods

If the Fiscal Theory of Price Level holds, there should be some correlation (positive ornegative) between government budget surplus/deficit and inflation. Therefore, this analy-


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sis examines the relationship between these variables (see pvmqyear.csv, columns pi anddeficit).

3.3.2 Results

According to the scattergram of inflation and surplus/deficit, there is no obvious relationshipamong the points. The regression model gives a p-value for the F-test of 0.4826, which isnot significantly significant; the R2 value is 0.0101, which suggests there is no correlationbetween the variables. Then for the past fifty years in the U.S., the Fiscal Theory of PriceLevel has not been valid.

4 Inflation Rate as a Control for Unemployment

In order to control the unemployment rate, governments often result to tactics that canchange the inflation rate (e.g. increasing/decreasing the money supply). Although thetheory is commonly disbelieved in modern economics, the theory of the Phillips Curve was animportant principle in traditional Keynesian economics. The Phillips Curve was a proposedinverse correlation between inflation and unemployment; historically, it sometimes held trueduring short periods of time, but was never showed to hold in the long term. Does it holdfor the recent American economy?

4.1 Phillips Curve

The Phillips Curve suggests that inflation and unemployment are inversely related. Its va-lidity can be tested for the recent American economy through determination of the accuracyof a model of this form.

4.1.1 Methods

Let inflation be represented by the variable and let the unemployment rate be representedby the variable rU. If the Phillips Curve is indeed accurate, for some constant c:

rU = c = cr1

U .

Thus a regression of against r1U will determine if the Phillips Curve matches the data havefrom the previous fifty years in the U.S. (see pvmq.csv, columns pi and ue). The variable can be generated based on monthly relative changes in CPI.


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4.1.2 Results

The data does contain an outlier with < 0.02; once this outlier is removed, the model is

still relatively inconsequential, with the t-test returning a p-value of 0.8896, which definitelyis statistically insignificant. The R2 value is 0.0001, suggesting almost no correlation betweeninflation and the unemployment rate. Thus, the Phillips Curve has not been accurate forthe U.S. in the past fifty years.

This may largely be a result of the 1970s, an example of rampant stagflation, with highunemployment and high inflation caused largely by supply shocks such as the 1973 OilCrisis.

4.2 New Phillips Curve

The New Phillips Curve is a theory suggesting that the change in inflation is negativelycorrelated with unemployment; it was a derivative of the original Phillips Curve proposedafter the original theory fell into disuse.

4.2.1 Methods

A regression of the change in inflation against unemployment rates can determine whetheror not a negative correlation exists, and if so, how powerful the correlation is (see pvmq.csv,columns dpi, and ue). If the t-test returns a p-value greater than 0.05, the model is signifi-

cantly insignificant, and the correlation is weak, if existent.

4.2.2 Results

The model that determined has a p-value for the t-test of 0.9847, suggesting the insignificanceof the model and the weakness of the correlation. The R2 value is virtually zero, suggestingthe correlation essentially does not exist. The New Phillips Curve has thus been inaccuratefor the U.S. in the past fifty years.

5 Income Inequality

Income inequality is commonly measured by the Gini coefficient - a higher Gini coefficientimplies higher inequality.

5.1 Labor Force Participation

After the 2008 financial crisis, analysts were concerned that although the economy has beenrecovering in terms of the unemployment rate, the labor force participation rate has de-


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creased, suggesting that perhaps the unemployment rate has at least partially decreased asa result of the formerly unemployed leaving the labor force, discouraged from seeking jobs.An interesting problem is to determine the relation between income inequality and the labor

force participation rate.

5.1.1 Methods

Regression of the Gini coefficient and the labor force participation rate, if it results in ap-value for the F-test that is less than 0.01, produces a significant model. Also, the RamseyRegression Equation Speficiation Error Test (Ramsey RESET) determines if the model ispolynomial as opposed to simply linear.

The data used in the analysis is annual data from the Federal Reserve Bank for the U.S. in

the past fifty years (see pvmqyear.csv, columns gini and participation).

5.1.2 Results

Although the linear regression returns a p-value for the F-test of virtually zero, the modelcan be improved as a quadratic model, as suggested by the Ramsey RESET, which returns ap-value of virtually zero. If we let G represent the Gini coefficient and represent the laborforce participation rate, the quadratic model that is generated is:

G = 0.00142612 0.1682947 + 5.3205.

This is clearly not a model that can be extrapolated from, since 0 G 1; however, itaccurately models the data from the previous fifty years. The p-value is still virtually zero.The Ramsey RESET returns a statistically insignificant p-value of 0.0651.

Since this model is monotonically increasing over our data domain, it suggests that the Ginicoefficient and labor force participation rate are positively correlated. This is particularlyinteresting as it suggests that when more people enter the labor force, income inequalityactually increases, although this is a correlative and not a causative relation.

5.2 Economic performance

It is also interesting to determine the relation between income inequality and economic per-formance. Does income inequality preclude economic growth? Are they reconcilable?

5.2.1 Methods

Two measures of economic growth that can be analyzed are real GDP and real GDP percapita. Regression on each with the Gini coefficient can determine whether or not a positive


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or negative correlation exists. Again, the Ramsey RESET can be used to determine if themodel is polynomial.

The data used is from the same source as above (see pvmqyear.csv, columns gini, q, andgdppc).

5.2.2 Results

A linear regression of real GDP with Gini coefficient returns a p-value of virtually zero, butthe Ramsey RESET suggests (p = 0.0041) that the model should instead be quadratic, forwhich we find the equation:

Q = 569696G2 359637.9G + 60117.64

with a p-value of virtually zero and a Ramsey RESET p-value of 0.0879, which is statisticallyinsignificant at an -level threshold of 0.05.

This suggests that as income inequality increases, real GDP increases as well; this is acorrelative and not a causative relationship.

A linear regression of real GDP per capita with Gini coefficient returns a p-value of virtuallyzero, and the Ramsey RESET suggests that the model is indeed linear. Then the modelis:

Qpc = 268937.2G 72955.25

with a Ramsey RESET p-value of 0.1328, which is statistically insignificant.

This suggests that as income inequality increases, real GDP per capita increases as well;however, again, it must be emphasized that this is a correlative and not a causative relation-ship.

Overall these results suggest that income inequality is quite strongly positively correlatedwith economic performance and average standards of living.

6 Conclusions and Discussion

Based on data from the past fifty years in the United States, the Exchange Equation hasheld, as has its derivative, the Quantity Theory of Money. However, the Fiscal Theory ofthe Price Level, the Phillips Curve, and the New Phillips Curve all appear to be obsolete.Also, income inequality and economic growth, two concepts that are contentious in theethics of economics, seem to be negatively correlated. To determine these results, we usedmultilinear regressions on the raw data itself, or if necessary, on manipulations of the datathat were mathematically necessary. In general, the results were quite stark - either themodels were extremely accurate (with a p-value less than 0.01) or were extremely inaccurate(with a p-value greater than 0.05), so the results would still hold given any sensible -levelof significance.


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A division of CPI by a factor of 100.9257567, multiplication of M2 money supply by a factorof 101.022252, or multiplication of M2 money velocity by a factor of 101.132964 would result ina multiplication of real GDP by a factor of 10.

For each additional dollar in the M2 money supply, CPI increases by 0 .0128719, indexed to2005.

For each additional increase of 0.01 in the Gini coefficient, GDP per capita increases by2689.37 USD.

Similar simplistic slope statements cannot be stated for the relation between GDP and theGini coefficient or between the Gini coefficient and the labor force participation rate, as bothmodels are quadratic. Both models are, however, positive correlations.

While statistical analysis of several economic quantities yields, as described above, severalinteresting results, it is important to note that regression analysis determines the strengthof correlations, not of causations. This is a particularly dangerous difference in economicdata; for example, since real GDP has increased over time in general, any other variable thatincreases over time will be somewhat correlated with real GDP, although the growth ratesmust be similar in order for linear models or quadratic models to match.

Thus it is not correct to conclude that income inequality causes economic growth; nor is itcorrect to conclude that economic growth causes income inequality. The analysis only demon-strates that income inequality and economic performance tend to grow together and fall to-gether - the economic variables are intricately and complexly related to each other throughmeans that even multipolynomial regression cannot describe with great confidence.

This study adds fuel to the fire for the controversy regarding the role of government inthe economy. It shows that government action can affect price levels and economic output,and that income inequality, commonly associated with the free market, can lead to highereconomic growth. Future studies that could test the veracity of these conclusions as well asbroaden their implications to the rest of the world include similar studies in other countries(e.g. China, Japan, and the Euro zone), as well as studies with more historic data.

7 References

StataCorp (2010). StataSE (Version 11) [Computer software]. College Station, TX:StataCorp LP

Economic Research - St. Louis Fed. Economic Research. Web. 02 May 2012.

{

U.S. Bureau of Labor Statistics. U.S. Bureau of Labor Statistics. U.S. Bureau ofLabor Statistics. Web. 02 May 2012.


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A Appendices

A.1 Exchange Equation


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A.2 Quantity Theory of Money

A.3 Fiscal Theory of Price Level


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A.4 Phillips Curve

A.5 New Phillips Curve


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A.6 Labor Force Participation


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A.7 Economic Performance


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A Statistical Analysis of Economic Interventionism

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