Term Paper

Jack Adons

In coordination with Charlie Fay and Gideon Ikpegaogu

Professor Murray

ECON 255

April 7, 2015

TERM PAPER

INTRODUCTION

In a report titled “New Evidence on Deficits and Interest Rates,” Gregory

Hoelscher analyzed the general assumption that increased government borrowing causes

an increase in interest rates. Hoelscher acknowledged that a number of previously

published papers failed to provide evidence of a strong relationship between government

deficits and short-term interest rates. His research, however, dealt with the connection

between deficits and long-term interest rates. He uncovered strong evidence to support an

association between high deficits and high long-term interest rates. Hoelscher used data

from the period of 1953 to 1984. In order to better observe the relationship between

deficits and interest rates, the periods of data needed to be extended beyond that included

in Hoelscher’s report. In this paper, Hoelscher’s study is replicated as closely as possible

to include data from 1953 to 2013. Consequently, Hoelscher’s evidence was confirmed,

and further investigation was conducted to better understand the connection between

government borrowing and interest rates.

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The association between federal borrowing and interest rates has a crucial impact

on the government’s fiscal decisions on private spending and changes to aspects of the

deficits. The correlation between deficits and long-term interest rates concerns the

question of crowding out. Short-run indirect crowding out, an issue Hoelscher addressed,

is defined as a reduction in private spending caused by a rise in interest rates as a result of

an increase in federal borrowing and spending. When the government spending occurs in

a market of loanable funds, the demand for such funds rises, increasing the interest rates

as well. As a result, buyers would be driven away from private investment. A decrease in

investment would lower aggregate demand as well as the output of the economy.

Therefore, it is critical to analyze the affect deficits have on crowding out, as Hoelscher

does in his report.

However, the chief focus of the paper is on the link between the deficits and long-

term rates. Previous studies as noted in Hoelscher conveyed a fiscal and wealth impact of

bond-financed deficits on output and interest, with both effects contributing to higher

interest rates. The long-term rates are closely related to consumer and business spending

decisions. It was generally theorized by scholars that the long-term interest rate transmits

the effect of deficits to the real side of the economy. This is due to the fact that interest-

sensitive components of private spending were most sensitive to variability in long-term

interest rates.

Data used in this report was gathered from the DRI database and contained a

number of economically relevant variables. The EViews program was utilized to search

for variables that would represent best, the variables Hoelscher used in his analyses. In

the instance that the exact Hoelscher variable did not appear in the database,

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combinations of variables were utilized to reconstruct necessary variables. The variables

that were unavailable in the DRI database, such as expected rate of inflation, were

provided by outside sources.

THE VARIABLES

The research Hoelscher conducted utilized a number of variables for regression.

The first task of the assignment required the reconstruction of such variables using the

DRI database. Some of the variables did not exist directly in the database, so it was

necessary to combine variables to correspond to those appearing in Hoelscher’s

regressions. These variables included the expected inflation rate, p; the expected real

short-term interest rate, rs; the change in national income, y; a deficit variable, d;

government spending, GOVSP; transfer payments, TP; and the nominal one-year

Treasury bond rate, is.

In his report, Hoelscher described in detail first the deficit variables he used

represented by the letter d. Hoelscher noted in his paper that there was disagreement

about the proper measure of the government deficit. There was dispute concerning the

relation between inflation and real value of outstanding government debt. Another cause

of controversy was the uncertainty as to how to measure the impact of federal loan

guarantees and unfounded liabilities on the credit markets.

All of the measures of the deficit were expressed in per capita 1972 dollars. The

first variable for the deficit that Hoelscher used was denoted as USDEF. This was defined

as the national income accounts version of the federal deficit. In the DRI database the

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variable ggfnet was discovered to be the national accounts version of the government

deficit. Because USDEF was measured as a per capita real value, it was necessary to

divide by the population, labeled gpop. Since ggfnet and gpog were measured in billions

and millions respectively the ratio was multiplied by 1000. Finally, it was multiplied by

the CPI-U from 1972 over the CPI-U from the corresponding year t, denoted pzunew in

the DRI database. This resulted in the following equation:

USDEF = [(ggfnet*1000)/(gpop)] * [(pzunew1972)/(pzunew)]

The second variable used to measure the government deficit was labeled

GOVDEF. Similar to USDEF, it was defined as the national income accounts version of

the federal deficit, however, GOVDEF also included borrowing from state and local

governments. In the DRI database the variable ggnet was discovered to be the sum of

both the state and local government deficits in addition to the federal deficit. Because

GOVDEF was measured as a per capita real value, it was necessary to divide by the

population, labeled gpop. Since ggnet and gpog were measured in billions and millions

respectively the ratio was multiplied by 1000. Finally, it was multiplied by the CPI-U

from 1972 over the CPI-U from the corresponding year t, denoted pzunew in the DRI

database. This resulted in the following equation:

GOVDEF = [(ggnet*1000)/(gpop)] * [(pzunew1972)/(pzunew)]

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The final variable Hoelscher utilized to measure the federal deficit was expressed

as CFD or the change in real par value of publically held federal debt. In the DRI

database the variable fbdp was discovered to be the federal debt securities held by the

public. Because CFD was measured as a per capita real value, it was necessary to divide

by the population, labeled gpop. Since fbdp and gpog were measured in billions and

millions respectively the ratio was multiplied by 1000. Finally, it was multiplied by the

CPI-U from 1972 over the CPI-U from the corresponding year t, denoted pzunew in the

DRI database. However, in order to achieve the change in real par value of publicly held

federal debts it was key to take the difference of the fbdp in per capita 1972 dollars from

one year and the fbdp in per capita 1972 dollars from the year previous. This resulted in

the following equation:

CFD = ([(fbdp*1000)/(gpop)] * [(pzunew1972)/(pzunew)]t) – ([(fbdp*1000)/(gpop)]

* [(pzunew1972)/(pzunew)]t-1)

The loanable funds model included a number of variables. Hoelscher denoted the

expected inflation rate as p. The DRI database did not include a variable that

corresponded well enough with Hoelscher’s version of p. Therefore, the variable

representative of p was obtained from the Livingston Survey.

Hoelscher labeled the expected real short-term interest rate as rs. It was defined as

the annual average rate on one-year Treasury bonds minus the expected rate of inflation.

In the DRI database the variable fygt1 was discovered to be the average annual rate on a

ten-year treasury bond. However, in order to obtain the expected short-term interest rate

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in real terms it was necessary to subtract the expected rate of inflation, p. The long-term

interest rate denoted, i (or fygt10 in the DRI database), was defined as the annual average

rate on ten-year Treasury bonds.

In addition, Hoelscher defined y as the change in national income or the change in

per capita GNP. In the DRI database the variable gnpq was discovered to be the gross

national product. Because y was measured as a per capita real value, it was necessary to

divide by the population, labeled gpop. Since gndp and gpog were measured in billions

and millions respectively the ratio was multiplied by 1000. Finally, it was multiplied by

the CPI-U from 1972 over the CPI-U from the corresponding year t, denoted pzunew in

the DRI database. Since y is the change in per capita GNP, the variable was expressed as

the following:

y = ([(gnpq*1000)/(gpop)] * [(pzunew1972)/(pzunew)])t - ([(gnpq*1000)/(gpop)] *

[(pzunew1972)/(pzunew)])t-1

The government spending from the National Income Accounts for all government

levels was represented in Hoelscher by GOVSP. In the DRI database the variable ggex

was discovered to be the federal spending in all levels of government. Because GOVSP

was measured as a per capita real value, it was necessary to divide by the population,

labeled gpop. Since ggex and gpog were measured in billions and millions respectively

the ratio was multiplied by 1000. Finally, it was multiplied by the CPI-U from 1972 over

the CPI-U from the corresponding year t, denoted pzunew in the DRI database. The result

was the following equation:

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GOVSP = [(ggex*1000)/(gpop)] * [(pzunew1972)/(pzunew)]

The transfer payments from the National Income Accounts for all government

levels were symbolized in Hoelscher as TR. In the DRI database the variable ggt was

discovered to be the federal spending in all levels of government. Because TR was

measured as a per capita real value, it was necessary to divide by the population, labeled

gpop. Since ggt and gpog were measured in billions and millions respectively the ratio

was multiplied by 1000. Finally, it was multiplied by the CPI-U from 1972 over the CPI-

U from the corresponding year t, denoted pzunew in the DRI database. The result was the

following equation:

TR = [(ggt*1000)/(gpop)] * [(pzunew1972)/(pzunew)]

In Hoelscher the deficits are at times reported as percentages of the gross national

product. Consequently, each DRI database variable representative of the deficit (i.e.

ggfnet for USDEF, etc.) was divided by the GNP, and multiplied by 100 because it was

measured as a percentage. In the regressions these are labeled usdefg, govdefg and cfdg

respectively.

THE MODEL

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In his analyses, Hoelscher utilizes a loanable funds model to study the

relationship between deficits and long-term interest rates, as adapted from models used

by Sargent (1969) and Echols and Elliot (1976). The use of this model enabled Hoelscher

to analyze a variety of explanatory variables and observe their effects on long-term

interest rates. It originated from the need for economists to study interest rates instead of

the price of bonds. Therefore, this model is similar to a supply and demand diagram for

loanable funds in the economy where the x-axis is occupied by the quantity of bonds and

the y-axis is occupied by the interest rate. The point of intersection on the diagram, or

where the supply of loanable funds equals the demand for loanable funds, indicates the

interest rate. As a result, the equation (1) in Hoelscher is explained:

S(i, rs, p) – D(i, rs, p, y, d) = 0.

In this equation, the supply curve is determined by i, rs, and p, or 10-year

Treasury bond rates, expected real short-term interest rate, and the expected inflation rate.

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The demand curve is determined by the same components i, rs, p, in addition to y and d,

or the change in per capita GNP and some measure of the deficit. Hoelscher used the

equilibrium equation to solve for the long-term interest rate, denoted i, which produced a

reduced form function. An equation involving long-term interest rates equaled to the

outstanding variables included in the supply and demand functions apart of the

equilibrium equation can be observed:

i = α0 + α1p + α2rs + α3y + α4d.

As a result, Hoelscher was able to regress long-term interest rates on the

explanatory variables and display them in tables. These regressions determined the values

of the coefficients α0, α1, α2, α3, and α4, or the impact each independent variable had on

the dependent variable, 10-year Treasury bond rates. The correlation between long-term

interest rates and the variables could then be evaluated. In all of the regressions that

Hoelscher ran, he employed the Cochrane-Orcutt procedure to adjust for serial

correlation. Serial correlation is defined as a similarity between variables due to a time

lag between them.

The observed original Durbin-Watson statistic (1.614) signified that there did not

appear to be any serial correlation because its value was less than that of the critical value

(1.739). However, the concept of serial correlation could not be dismissed due to the

first-order autoregressive nature of the data. In addition, the t-statistic for rho that was

found in Table 1 to be .83, which was less than the critical value (1.96) at the 99 percent

significance level. Normally, this would indicate that the null hypothesis should not be

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rejected, however this could be inaccurate. The use of this estimation procedure

demonstrated that Hoelscher was concerned with similarities of observations within

variables from year to year.

THE REPLICATED TESTS

Replicated Table 1: Corc Estimates Of Ten-Year Bond Yield Determinants, 1953-84.

Coefficient Estimates

Deficit variable Constant p rs y d R2 D-W rho

(t-stat)

USDEF 1.2 0.745 0.785 -0.000841 0.00807 0.978 1.61 0.161

(0.83)

GOVDEF 1.29 0.762 0.788 -0.000276 0.00744 0.9820 1.742 0.697

CFD 1.47 0.870 0.811 -0.000932 0.00691 0.9857 1.70 0.0674

USDEF --- 0.533 0.6868 -0.0010074 0.00386 0.8173 --- ---

Table 1 in Hoelscher described the regression results for estimating the long-term

interest rate equation using data from 1953-1984. The first three tests were run using a

Cochrane-Orcutt Two-Step procedure that adjusted for serial correlation. The ten-year

Treasury bond yield was regressed on the expected inflation, the expected real short-term

interest rate, the change in per capita GNP, and three separate deficit variables. The

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fourth line of Table 1 utilized the first difference estimation method with no constant. In

his report, Hoelscher cited that other studies recommended that time series regression

models be constructed with both levels and changes in levels of variables as a precaution

against spurious regression. Line 4 in Table 1 utilized this method to eliminate correlation

between a variable for a given year and the same variable from the year before.

The replicated version of Hoelscher’s Table 1 is observed above. The Cochrane-

Orcutt Two-Step procedure was again utilized to approximate the best linear unbiased

estimator of the model with first-order autoregressive disturbances. In order to replicate

Table 1 line 4 lag variables of one year were generated for each variable in the USDEF

regression. This lag variable was then included in generated variables that expressed the

change in one year from the previous year for each variable in the USDEF regression.

The coefficients produced in the replicated Table 1 closely resembled those

reported in Hoelscher, however, were not exact due to differences in data. Nonetheless, it

was possible to imply the same relationship between the explanatory variables and the

long-term interest rate as in Hoelscher. The estimated coefficients in all three regressions

had expected signs, and were all statistically significant at the at the 99 percent level,

except for the term y. This was the case because the p-value for each significant variable

was below .01. It was concluded that all the regressions fit the data very well and almost

all of the variation in ten-year Treasury bond rate had been explained. This was

determined because the values for R2 were .85 or greater, signifying a good fit.

Replicated Table 2: Additional Corc Estimates Of Ten-Year Treasury Bond Yield

Determinants, 1953-1984.

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Coefficient Estimates

Deficit variable Constant p rs y d R2 D-W rho

USDEF/GNP 1.05 0.785 0.804 -0.000584 0.456 0.973 1.60 0.149

CDF/GNP 1.22 0.888 0.828 -0.000792 0.397 0.979 1.57 0.151

It is often the case that deficits are recorded as a percentage of GNP as opposed to

a per capita basis. As a result, the regressions in Table 1 lines 1 and 3 were reconstructed.

The respective deficit variables were rescaled to be a percentage of GNP. Hoelscher

again regressed ten-year Treasury bond yield on the expected inflation, the expected real

short-term interest rate, the change in per capita GNP, and the rescaled deficit variables

and reported the results in Table 2 lines 2 and 4.

The replicated version of Table 2 lines 2 and 4 for years 1953-1984 was carried

out in similar fashion, but with different data. All three of the deficit variables maintained

positive and significant coefficients like Table 2 of Hoelscher. This indicated that deficits

are important regardless of the scaling mechanism used (population or GNP). The other

terms of the regression also maintained similar values to that in Hoelscher. However, the

sign for y became negative compared to the regressions ran by Hoelscher. Nonetheless,

the change and resulting effect on interest rates was small and insignificant.

Replicated Table 3: Corc Estimate Of Ten-Year Treasury Bond Yield Determinants With

Additional Regressors, 1953-1984.

Coefficient Estimates

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Deficit variable Constant p rs y d GOVSP TR R2 D-W rho

GOVDEF 0.803 0.521 0.791 -0.000578 0.00424 -0.000538 .0061604 0.985 1.67 0.103

It was noted in Hoelscher’s paper that some studies expressed concern about the

correlation between government deficits and government spending or transfer payments.

If this did exist, the coefficient on the deficit variables may have factored in the effects of

government spending and transfer payments and result in false estimates. Consequently,

he regressed long-term interest rates on previously used variables, with the addition of

GOVSP and TR variables. In Table 3 line 1, Hoelscher used the GOVDEF as the variable

for the deficit.

Coefficients listed in the replicated Table 3 line 1 were comparable to that of

Hoelscher’s. The replicated Table 3 line 1 and the Hoelscher Table 3 line 1 both indicated

that GOVSP was not significant, but the coefficient on TR was positive and significant.

However, GOVDEF also had a positive and significant effect on the long-term interest

rate. Therefore, Hoelscher was able to prove that the government deficit was not in

correlation with government spending or transfer payments, so it was likely that the

added variables did not change the significance of the deficit’s effect on long-term

interest rate.

Replicated Table 4: Corc Estimate Of Ten-Year Treasury Bond Yield Determinants For

Subperiods.

Coefficient Estimates

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Period Constant P rs y d R2 D-W rho

1953-66 1.93 0.685 0.534 -0.000863 0.00379 0.904 1.61 0.187

1967-84 1.63 0.680 0.808 -0.000753 0.00770 0.958 1.55 0.186

In Table 4 the long-term interest rate was regressed using USDEF for two sub

periods in order to test for temporal stability, or retesting. It was important to test this to

see if it explained variation in the ten-year Treasury bond rate for each sub period.

Hoelscher determined the cutoff for the sub periods by noting that after 1966, ten-year

Treasury bond rates rose above five percent and continued on a gradual increase for the

rest of the time period.

The replicated Table 4 displayed estimated coefficients and R2 values comparable

to that of Hoelscher. The USDEF measure is only used because the other two measures of

the deficit estimated similar results. In both tables USDEF exerted a positive and

significant effect on the long-term interest rate despite a lower deficit in the earlier

period. As Hoelscher expected, the coefficient estimates for the independent variables

varied more in the latter sub period. In fact, the coefficient on USDEF doubled.

Replicated Table 5: Illustration Of Estimated Effects Of Deficits On Long-Term Rate.

Variable Average (1980-84) Estimated Effect on i (basis point increase)

USDEF 249.8 202

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GOVDEF 240.0 179

CFD 117.3 81

Hoelscher created Table 5 lines 1-3 to add perspective on the varying estimated

magnitude of the deficit coefficient. He summarized the estimated effect that the average

annual deficit over the last five years of the period would have on the ten-year Treasury

bond rate. The deficits were averaged over a five-year period to smooth transitory effects

and measured in per capita 1972 dollars.

The deficit variables were summarized to observe the mean for each. This is

represented in the first column of replicated Table 5. In order to find the estimated effects

on I each average value was multiplied by the corresponding estimated coefficient from

Table 1 and then multiplied by 100 to be measured in basis points. According to

Hoelscher’s findings, USDEF was responsible for a 1.95 percent increase in the long-

term interest rate. The average values and resulting basis point increase in the replicated

Table 5 varied in comparison to Hoelscher. The USDEF and CFD values were smaller

than that recorded in Hoelscher, whereas the GOVDEF values were larger.

THE UPDATED TESTS

Further tests were run in order to re-estimate the relationships of variables using

data from 1953 to 2013. The regression commands for the 1953-1984 data were repeated

for the updated data, but for the period 1953-2013. In the process of expanding the data

through the year 2013 it was necessary to decide the best procedure for estimation. The

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options provided were OLS with ordinary standard errors, OLS with Newey-West

standard errors, or Cochrane-Orcutt. Because serial correlation was present in each of the

earlier regressions and therefore would no longer be BLUE, OLS with ordinary standard

errors was ruled out. The Newey-West procedure estimated coefficients with OLS with

heteroskedasticity and first-order auto regression robust standard errors. The Cochrane-

Orcutt procedure for iterated estimates is only robust for first-order auto regression

standard errors. However, both procedures produced similar coefficients when tested for

Table 1 line 1.

This indicated that both procedures would be appropriate to utilize because both

adjusted for the presence of serial correlation. The Cochrane-Orcutt for iterated estimates

or Cochrane-Orcutt One-Step was chosen as the procedure for estimation. The observed

original Durbin-Watson statistic (.89) signified that there did not appear to be any serial

correlation because its value was less than that of the critical value (1.727). However, the

concept of serial correlation could not be dismissed due to the first-order autoregressive

nature of the data. This was concluded by the fact that the transformed Durbin-Watson

statistic (1.964) was greater than the critical value, and therefore the null hypothesis of no

serial correlation was rejected. In addition, the t-statistic for rho that was found in Table 1

to be 4.98, which was greater than the critical value (2.00) at the 99 percent significance

level. Consequently, this would indicate that the null hypothesis of zero serial correlation

should be rejected. The Newey-West standard errors were consistent, but bias because the

standard errors were changed. Thus, the Cochrane-Orcutt procedure for iterated estimates

was the best linear unbiased estimator. Though this method discards the first observation

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compared to the Prais-Winsten procedure, it was utilized in order to remain as close to

Hoelscher as possible. The updated versions for each table are listed below.

Updated Table 1: Corc Estimates Of Ten-Year Bond Yield Determinants, 1953-2013.

Coefficient Estimates

Deficit variable Constant p rs y d R2 D-W rho

(t-sta)

USDEF 2.7 0.626 0.597 -0.000283 0.00144 0.698 0.896 0.872

(4.98)

GOVDEF 2.68 0.627 0.604 -0.000228 0.00137 0.698 0.929 0.880

CFD 2.75 0.667 0.694 -0.000274 0.00121 0.702 0.907 0.861

USDEF --- 0.585 0.575 -0.000284 0.00133 0.672 --- ---

Updated Table 2: Additional Corc Estimates Of Ten-Year Treasury Bond Yield

Determinants, 1953-2013.

Coefficient Estimates

Deficit variable Constant p rs y d R2 D-W rho

USDEF/GNP 2.60 0.646 0.611 -0.000355 0.133 0.713 0.926 0.851

CDF/GNP 2.42 0.732 0.632 -0.000337 0.126 0.733 0.981 0.816

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Updated Table 3: Corc Estimate Of Ten-Year Treasury Bond Yield Determinants With

Additional Regressors, 1953-2013.

Deficit variable Constant p rs y d GOVSP TR R2 D-W rho

GOVDEF 7.72 0.609 0.618 -0.000132 0.00191 -0.00280 .002621 0.715 0.919 0.874

Coefficient Estimates

Updated Table 4: Corc Estimate Of Ten-Year Treasury Bond Yield Determinants For

Subperiods.

Coefficient Estimates

Period Constant P rs y d R2 D-W rho

1953-66 2.92 0.469 0.438 -0.000454 0.00295 0.965 1.61 0.899

1967-84 1.76 0.672 0.815 -0.000814 0.00726 0.943 1.55 0.332

1985-1998 2.18 0.877 0.448 0.000566 0.00398 0.968 2.45 -0.337

1999-2013 9.85 -2.23 0.473 -0.00296 -0.00288 0.952 2.05 -0.462

Updated Table 5: Illustration Of Estimated Effects Of Deficits On Long-Term Rate.

Variable Average Estimated Effect on i (basis point increase)

USDEF 697.4 100

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GOVDEF 839.6 115

CFD 639.4 77.27

In order to evaluate the updated results, it was necessary to observe the

coefficients on the deficit variable in the regressions. In addition, it was sensible to

compare the replicated and updated Table 5 to see the effect of deficits in the final years

of the data between both versions. Finally, the R2 values were discerned with expanded

years relative to Hoelscher.

The coefficient of an independent variable infers the extent and method to which

the independent variable relates to the dependent variable. The independent deficit

variables included were USDEF, GOVDEF, CFD, USDEF / GNP, and CFD / GNP and

were regressed with a dependent variable i. Paralleled with Hoelscher, the deficit

variables were consistently positive and significant as indicated by their p-values, except

for USDEF in Table 4 for sub period 1999-2013. Because the data was extended to 2013,

two more sub periods had to be created. The positive relationship between government

deficits and long-term interest rates is indicated nonetheless. This meant that government

borrowing increased as the ten-year Treasury bond rate went up. The negative coefficient

of USDEF in Table 4 was most likely explained by the presence of enormous debt in the

economic recession during the sub period 2009 to 2013.

The difference between the Hoelscher and updated Table 5 was another indicator

of how the deficit variable affected the long-term interest rates. In addition, changes

beginning from the years of Hoelscher to the years of the updated data could be viewed.

The average value and estimated effects on i in basis point increase varied from that in

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Hoelscher. The average values for each deficit variable in the 2009-2013 period were

sizably larger than those in the 1980-1984 period. The estimated effects on i in terms of

basis point increase also differed from Hoelscher’s results. Unlike the average value, the

estimated effects on i were significantly smaller than that given by Hoelscher. The huge

increase in government deficits since the period used in Hoelscher produced decreased

deficit coefficients. However, the coefficients remained significant.

The last signal of difference between Hoelscher’s tables and the expanded tables

was the R2 value. The values corresponding to regressions for 1953 to 2013 were smaller

than those estimated by Hoelscher for 1953-1984. The R2 values for 1953 to 2013 were

large enough to conclude that the regression was a good fit of the data, however, not as

well as Hoelscher. This was due to a greater variability and range in values for the deficit,

as they have risen substantially since 1984. Therefore, the replicated and updated data

confirmed Hoelscher’s analyses that long-term interest rates increase as the government

deficit increases.

THE ADDITIONAL TESTS

In order to grasp the relationship between government deficits and long-term

interest rates further, additional tests were run. In order to better understand the

movement of long-term interest rates, variables were substituted and added into

regressions previously tested. This was similar to the procedure Hoelscher took in

creating Table 3 line 1. The condition of the U.S. economy has a major influence on

long-term interest rates. As the economy grows, consumers have jobs and savings to lend

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through banks; however, they must borrow for large capital items, such as a home. The

rise of interest rates performs as a ration for funds available, as the resulting increase in

demand for funds occurs. The opposite is true for a decrease in demand for funds. As a

result, data was collected from the Federal Reserve Bank of St. Louis FRED database on

the All-Transactions House Price Index for the United States for the years 1975 through

2013. This data was estimated using sales prices and appraisal data. Data did not exist

previous to the year 1975. The variable that represented this data was named house and

was measured with 1975 as the base year.

In addition to the condition of the economy, the dollar is a highly influential

factor of long-term interest rates. As the main currency in international trade and foreign

exchange markets, orderly fluctuations of the dollar are essential for stability. Major or

volatile exchange rate movements could force the United States Federal Reserve to affect

long-term interest rates and other monetary policy. As a result, data was collected from

the Federal Reserve Bank of St. Louis FRED database on the Real Trade Weighted U.S.

Dollar Index against multiple major currencies that circulate widely outside the United

States. Major currencies index included the Euro Zone, Canada, Japan, United Kingdom,

Switzerland, Australia, and Sweden. Data did not exist previous to the year 1975. The

variable that represented this data was named dollar and was measured with 1975 as the

base year.

The loanable funds model was again utilized to regress ten-year Treasury bond

rates. The dependent variable was regressed on the expected rate of inflation, the real

short-term interest rate, the house price index, the U.S. dollar price index and GOVDEF.

The GOVDEF deficit variable was utilized because it was the broadest measure, although

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the two other measures would presumably provide similar results. Also, it should be

noted that house was substituted in for y. The change in national income is a factor that

expressed the condition of the U.S. economy. However, in all of the previous regressions,

the coefficients on y were found to be insignificant. As a result, the house is utilized as an

alternative measure of the U.S. economy.

The increased variability in the Table 1 for the period 1953 to 2013 compared to

the 1953-1984 period of Hoelscher is expressed by the decreased R2 value. Since 1984,

more determinants of long-term interest rates have existed than just the four independent

variables originally used. This implied that the model utilized in Table 1 for the period

1953 to 2013 experienced some level of omitted variable bias. As a result, the dollar

variable was added to the regression to better explain how long-term interest rates move

in a more developed economy. Even though the R2 value decreased between the periods,

it was still important to add an explanatory variable to see if the absence of this variable

would affect the accuracy of the other coefficients estimated in the model.

Similar to previously run regressions, the Cochrane-Orcutt procedure for iterated

estimates was utilized to adjust for serial correlation. The observed original Durbin-

Watson statistic (1.443) signified that there did not appear to be any serial correlation

because its value was less than that of the critical value (1.786). However, the concept of

serial correlation could not be dismissed due to the first-order autoregressive nature of the

data. This was concluded by the fact that the transformed Durbin-Watson statistic (1.98)

was greater than the critical value, and therefore the null hypothesis of no serial

correlation was rejected. The equation for the expected long-term interest rate when

regressed to substitute house for y, and include dollar is listed below:

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For 1975-2013: i = 1.230549 + .6492327p + .6869269rs – .0046901house

+ .031041dollar + .0017428GOVDEF

It can be observed that the coefficients on house and dollar were both statistically

significant due to very small p-values. The coefficient on house was negative, denoting

an inverse relationship between long-term interest rates and housing prices. Based on the

coefficient, a one-unit increase in the housing price index causes a .00469 percent

decrease in the long-term interest rate. This is a sensible conclusion because as housing

prices increase the demand for homes fall. In order to counter the decrease in demand, the

Federal Reserve would decrease interest rates in order to incentivize saving and

investment.

The coefficient on dollar was positive, denoting a direct relationship between

long-term interest rates and the exchange rate of the U.S. dollar. Based on the coefficient,

a one-unit increase in the housing price index caused a .031 percent increase in the long-

term interest rate. Again this is a sensible conclusion because as the exchange rate for the

U.S. dollar increase, the demand for loanable funds by foreign investment increases. In

order to cope with the increased demand, the Federal Reserve would raise interest rates to

discourage saving in U.S. banks.

The high computed R2 value of .9418 indicted that the substitution of house for y,

and the addition of dollar created a better fitting model than that in Table 1 and Table 3

line 1 for period 1953-2013. This was visible through the increase in the R2 term, and

consequently, the omitted variable bias present was reduced.

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Additional Table 5: Illustration Of Estimated Effects Of New Variables On Long-Term

Rate.

Variable Average Estimated Effect on i (basis point increase)

House 333.141 -156.2465

Dollar 97.3275 302.1143

GOVDEF 185.492

6

32.32765

In addition to regressing long-term interest rates on certain variables, the average

values and estimated effects on i, were discovered for each new variable. The results

were listed in the above table in order to discern the magnitude to which the new

variables effected i. The magnitude of the impact of housing prices and the dollar on the

ten-year Treasury bond rate could be compared to the magnitude of the impact of the

deficit on the ten-year Treasury bond rate. The magnitude of the estimated effect on i for

house and dollar were both greater than the value found for the deficit. As a result, we

can conclude that both housing prices and the exchange rate of the dollar have more of an

impact on long-term interest rates than any measure of the deficit. This was a significant

result to consider when looking back on Hoelscher’s research. It questioned the use of the

deficit in Hoelscher to determine the movements of ten-year Treasury bond rates.

CONCLUSION

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The empirical evidence of Hoelscher was ultimately confirmed by replicated and

updated regressions. Confirmation was given to the theoretical prediction that deficits

cause long-term interest rates to rise. In addition, the regression results indicated that the

relationship between government deficit and ten-year Treasury bond rates were strong,

robust and very significant for given periods.

The additional analyses carried out provided significant results that in turn

questioned the use of deficit in Hoelscher to determine the movement of long-term

interest rates. Because the effect of housing prices and the U.S. dollar exchange rate had

on i was of greater magnitude than the defict, it was concluded that Hoelscher chose not

to include the most impactful variables to regress against the ten-year Treasury bond rate.

However, this could mean that the housing price and exchange rate are more important

determinants today, than they were during the period of Hoelscher’s study. Further

analyses could be done to investigate deeper, the association of housing prices and

exchange rates on long-term interest rates versus the correlation of the deficit on long-

term interest rates.

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