Econometrics Hoelscher Paper Final

Running Head: BREAKING DOWN DEFICITS AND INTEREST RATES 1

Breaking Down Deficits and Interest Rates:

A Comprehensive Analysis and Expansion of Hoelscher’s Theory

Daniel Willsey

Bates College Economics Department

December 8th, 2016


Breaking Down Deficits and Interest Rates: A Comprehensive Analysis and Expansion of

Hoelscher’s Theory

Introduction

Background

Economists have worked to support the theory that increases in government borrowing

are linked to increases in interest rates. A lot of these ideas revolve around the topic of

crowding out. Crowding out, defined as the stifling of private spending due to high government

expenditure, is important because it may be a large factor in the creation of deficits (R, 2015).

Past evidence contradicts this theory. When Mascaro and Meltzer did a study on interest rates,

they found that deficits did not have significant effects on interest rates in the short or long

term (Hoelscher, 1986). Additionally, Makin’s research studying short term interest rates

brought him to the conclusion that the deficit had little importance in predicting the effect.

Carrying on with this theme, further research done by economists such as Dewald, Motley,

Canto, Rapp, and Plosser all came to similar conclusions. Obviously, the evidence up to this

point strongly supports the idea that interest rates do not actually have any effect on

government deficits, despite initial theory. However, this is where Hoelscher’s research makes a

huge impact.

Hoelscher, like these other researchers, completed an analysis geared at finding the

supposed connection between long term interest rates and deficits in the period from 1953 -

1984 (Hoelscher, 1986). Unlike other economists, his approach will consider annual data and a

loanable funds framework to describe the interest rate determination process. Using this


strategy allows for government borrowing to be calculated as a direct factor in the calculation

of interest rates. As a result of this approach, Hoelscher is able to show that an analysis of

annual data represents a connection between deficits and increasing ten-year treasury bond

interest rates. Taking a step back, this specific paper will look to first replicate Hoelscher’s

process in proving this theory and then expand on his ideas. Expansion will include an analysis,

using Hoelscher’s method of not only the time period included in his study (1953 - 1984), but

also an analysis of the period from 1984 to 2013.

Following along with Hoelscher’s research has a few distinct purposes. First off,

replicating his study allows us to understand how and why he got the results that he did.

Originally, economists theorized that increases in government borrowing were a significant

contributing factor to long-term higher interest rate levels. This theory had been largely

accepted on a theoretical level. However, because this topic had been proven insignificant

numerous times in previous research, Hoelscher’s research was groundbreaking when he was

finally able to find evidence supporting it. Therefore, it makes sense to try to replicate the

results to determine whether they are valid. Additionally, replication of the research allows us

to understand why the utilization of this different technique has such different results from past

approaches.

An initial replication of the study will either yield significant or insignificant results,

testing whether Hoelscher’s analysis itself was correct. Then it is possible to see whether

Hoelscher’s results are applicable to more than just one time period. This is purposeful because

if it can be proven that Hoelscher’s techniques, when applied to different time periods are still

valid, it will be logical that his approach was correct. If it is not applicable to another time


period, there may be a flaw in his research. Such a flaw could consist of anything from a missing

variable, simultaneity bias, or even a large effect based on whatever significant world events

are occurring during the new period. By replicating his results, it is possible to gain a greater

knowledge of Hoelscher’s research and conclude whether his research is valid over longer time

periods.

Defining Variables

To follow Hoelscher’s method, the first task that needs to be completed is an analysis

and replication of the variables that he used to measure the deficit. Hoelscher uses three

variables to get different measures of the deficit. The first one is referred to as USDEF. USDEF as

defined by Hoelscher, is the national income accounts calculation of the federal deficit. This

measure is effectively trying to replicate the government's economic activity level. This variable

is measured in per capita 1972 dollars. Additionally, the variable is negatively correlated to

trends in the economic health of the United States. Our replication of this variable is as follows.

In the equation, ggsnet is equal to state and local government surplus or deficit,

gpop is the population of the united states in millions of people, and pzunew is the

consumer price index. Therefore, by taking the state and local government surplus and

deficit value and dividing it by the population of the United States, we get debt or surplus

per capita. By multiplying this number by - 1000, it is then possible to change our answer

from millions to billions. The value 41.81667 come from the CPI value in 1972. By dividing

41.81667 by the consumer price index we find the CPI value in 1972. This figure multiplied


by our per capita debt or surplus effectively gives us the government deficit levels in 1972

dollars.

The next variable that is necessary to define is what Hoelscher refers to as USDEF.

This variable is a broader measure of government deficit, including federal government

deficits as well as the state and local deficits included in the previous variable. According to

Hoelscher, this variable ends up being less volatile than USDEF and is in general a smaller

value. Our replication of the variable is as follows.

In the calculation of this variable, the only change was the addition of ggfnet which

is equal to the current federal government surplus or deficit. By adding this value to the

current state and local government surplus or deficit and keeping the rest of the variable

the same, the government deficit in 1972 dollars is calculated.

The third variable that Hoelscher discusses and defines is CFD. The CFD variable is

the third measure of the deficit that is used and is calculated by taking the depreciation in

the stock of publicly held bonds and subtracting from the money that the government is

borrowing. This calculation allows Hoelscher to calculate the change in real par values

when looking at the federal debt that is publicly held. Therefore, the CFD variable can show

that the source of government surpluses may be a result of inflation rates affecting the

value of bonds. The variable we generated to represent CFD is as follows.


In the CFD variable we now use fbdp in addition to pzunew and gpop. The variable fbdp

is equivalent to the federal debt securities that are held in public hands. When describing the

variable, we can start by looking at the first set of parentheses. Like in the past two variables,

when this value is divided by the population it is converted into a per capita value. It is then

converted into the correct units by multiplying the equation by 1000. It was then multiplied by

the same conversion rate to get our answer into 1972 dollars using the consumer price index,

similar to the process previously used. This generates the equivalent of what Hoelscher refers

to as the real par value of publicly held debt. Within the first set of parentheses the subscript

“n” represents the current year. In the second set of parentheses, almost the same exact

calculation is done. However, the subscripts in this section “n-1” represents the current year

minus one. By subtracting the previous year from the current year, the difference between the

values is calculated. As a result, the change in the real par value of public debt is calculated.

Now that the three variables that calculate the value of the deficit have been formed,

the process of replicating Hoelscher’s original analysis can begin. First, the variables included in

these regressions must be defined. Hoelscher regresses his deficit calculator variables on i, the

interest rate over long periods of time; p, the expected inflation rate; rs, interest rate expected

over a short period y; the amount of change in gdp per capita; and d, standing for deficit

(Hoelscher, 1986). Expanding on Hoelchers definitions, these variables were formulated using

the data on hand to capture the same result. The variable I is reproduced using a variable called

fygt10 which stands for US treasury maturities on interest rates over ten year periods. P, like


Hoelscher’s definition, was defined as the expected inflation rate based on twelve month

forecasts. The rs variable was calculated as fygt1-p. In this case, fygt1 is equivalent to the

interest rates on US treasury cost maturities. From that, the variable p, which has been

previously defined, is subtracted. Subtracting the expected inflation rate gives us the correct

value for the expected interest rates. The calculation for the variable y is a bit more complex. It

is shown below.

In this variable, a similar procedure to the calculation of CFD is followed. However, in

this variable we now use gnyq which represents gross national income. Seen in the first set of

parentheses, gnyq divided by the general population and multiplied by 1000 as well as our

consumer price index value for 1972 has the effect of determining the per capita gross national

income in 1972 dollars. The second set of parentheses contain the same formulation of

variables as the first set apart from altered subscripts. The subscripts “n” and “n-1”, like in the

CFD variable denote the change in year from current to prior. Therefore, the first set of

parentheses represents the current year and the second set represents past year. By

subtracting this value the change in per capita gross national income is measured. The next

variable is d. As stated earlier, it represents the deficit. This variable is responsible for denoting

Hoelscher’s three different deficit variables in the analysis: USDEF, GOVDEF, and CFD.


i=α0+α1p+α2rs+α3y+α4d

In his paper, Hoelscher uses the above equation to estimate the long-term interest

rates (Hoelscher, 2016). Each coefficient in the model is positive.

Methodology Behind Regressions: Cochrane Orcutt and Durbin Watson

With the variables for the first table defined, the analysis can now be executed. Rather

than using ordinary least squares, Hoelscher uses the Cochrane-Orcutt model. Due to the

nature of interest rates, a variable that exist over time, past year shocks affect current year

outputs, resulting in serial correlation. Reviewing the stata tools used to complete this

regression helps to explain the methodology (Stata Manual). The “prais” estimator is used to

tell stata to use only consistent estimators of ρ; therefore, because OLS is not consistent in this

scenario, it cannot be used. “Twostep”, is entered to stop the regression after the previous

year, fixing the problem of past shocks affecting current years. Using the command “corc”,

specifies to stata that the Cochrane-Orcutt analysis should be used. Culmination of this process

solves the problem of serial correlation in the variables and an initial inconsistent estimation

using OLS.

The Durbin-Watson statistic is used as a test to see whether ρ, a value capable of

revealing serial correlation, is equal to 0. If ρ is in fact equal to 0, it can be said that there is no

serial correlation in the model. If ρ is not equal to 0, there is serial correlation in the model

(Murray, 2006). Looking at the Durbin-Watson statistic, a value between 0 and 4, it can be

tested at the five percent significance level that ρ is equal to 0. Generally speaking, values

greater then around 1 point to a failure at rejecting the null hypothesis that ρ is 0. Therefore,


no serial correlation would be evident in the model. Numbers approaching 0 for the Durbin-

Watson statistic point towards a rejection of the null hypothesis that ρ is equal to 0 as well as

serial correlation in the model. To conclude, using the Cochrane-Orcutt model as well as the

Durbin-Watson statistic allows for Hoelscher to generate values for his regressions and test

them for serial correlation.

Results

Hoelscher’s Initial Results

After conducting the regressions, the tables generated were closely correlated to the

tables that Hoelscher came up with. However, values vary slightly due to usage of a different

data set as well as slight differentiation between our variables and the ones used by Hoelscher.

Hoelscher Table 1.1 Corc Estimates of Ten-Year Treasury Bond Yield Determinants, 1953-84

Coefficient EstimatesDeficit Variable Constant P rs y d R2 D-W ρ

1. USDEF 1.2086 0.7455 0.7857 -0.0008 0.0081 0.9782 1.6143 0.1612(5.15) (15.96) (13.75) (-1.53) (6.85)

2. GOVDEF 1.2914 0.7615 0.7879 -0.0003 0.0074 0.982 1.7415 0.0697(5.72) (17.82) (14.52) (-0.53) (7.15)

3. CFD 1.4661 0.8697 0.8119 -0.0009 0.0069 0.9857 1.6989 0.0674(7.04) (28.15) (17.04) (-1.88) (8.39)

4. USDEF2 none 0.5245 0.6778 -0.001 0.0033 0.8118 1.5741 0.2123(6.31) (9.47) (-2.59) (2.56)

Table 1.1 is effectively showing the regression of the independent variables that

Hoelscher used for his regressions and presenting their output. To determine these values, a

Cochrane-Orcutt style regression is run to account for serial correlation. This analysis is aimed

to test whether Hoelscher’s hypothesis that deficits cause higher long term interest rates is true


(Hoelscher, 1986). Based on the results of this table, like Hoelscher, we can determine that

these results strongly support his hypothesis.

Hoelscher Table 2.1Additional Corc Estimates of Ten-Year Treasury Bond Yield Determinants, 1953-84


1. USDEF/GNP 1.0539 0.7854 0.8042 0.0029 0.4558 0.9731 1.6047 0.1492(4.1) (15.88) (12.69) (-0.63) (5.67)

2. GOVDEF/GNP 1.2028 0.7871 0.8065 0.0026 0.4214 0.9773 1.6891 0.081(4.83) (17.01) (13.43) (0.10) (6.03)

3. CFD/GNP 1.2247 0.8886 0.8278 0.0026 0.3972 0.979 1.5652 0.1505(5.28) (24.55) (14.96) (-1.13) (6.95)

Table two expands upon table one’s calculation by examining our deficit variables

(USDEF, GOVDEF, and CFD) and dividing them by gross national product.

USDEF/GNP= (−100 (ggsnet ))gnpq

GOVDEF/GNP= (−100 (ggsnet+ggfnet ))gnpq

CFD/GNP= ( fbdp¿¿ n∗100)−( fbdp¿¿n−1∗100)gnpq

¿¿

These variables are regressed on the same independent variables as in table 1.

Hoelscher provides reasoning for this analysis, describing that deficits are sometimes reported

as a percentage of GDP rather than simply on a per capita basis. Thus, dividing by gross

domestic product rescales the measures into a more relevant unit. Completing this secondary

analysis shows us similar values in terms of magnitude and direction to the ones found in table

1. Therefore, we find that deficits values are important in predicting long term interest rates

whether they are scaled by population or gross national product.


Expanding Hoelscher’s Results to the 1984-2013 period

Table 1.2Corc Estimates of Ten-Year Treasury Bond Yield Determinants, 1984-2013


1. USDEF 1.0057 1.2618 0.5217 0.0002 0.001 0.8022 0.9925 0.4976(1.3) (5.25) (4.88) (0.27) (1.38)

2. GOVDEF 0.9414 1.2738 0.5327 0.0003 0.0009 0.8018 0.9982 0.4954(1.16) (5.23) (4.75) (0.3) (1.3)

3. CFD 1.0205 1.2988 0.5233 0.0003 0.0009 0.8054 1.005 0.4933(1.36) (5.31) (4.91) (0.3) (1.42)

4. USDEF none 1.2448 .4271 .0005 .0018 .7249 2.4029 -.2732(5.17) (4.63) (0.73) (2.49)

Table 2.2Additional Corc Estimates of Ten-Year Treasury Bond Yield Determinants, 1984-2013

Coefficient EstimatesDeficit Variable Constant P rs Y d R2 D-W ρ

1. USDEF/GNP 0.967 1.251 0.5272 0.0031 0.1083 0.8057 0.9838 0.503(1.29) (5.32) (5.07) (0.34) (1.67)

2. GOVDEF/GNP 0.8718 1.2678 0.5426 0.0032 0.0997 0.8058 0.9902 0.5007(1.11) (5.34) (4.99) (0.38) (1.61)

3. CFD/GNP 0.9454 1.3024 0.5286 0.0032 0.0936 0.8104 1.0091 0.4916(1.27) (5.43) (5.04) (0.34) (1.61)

After an initial replication of Hoelscher’s data, we now move to an analysis of the period

of 1984-2013. These tables utilize the same independent variables and regression method used

in the original tables. Assuming Hoelscher’s techniques are valid, they should be able to be

applied to alternative time periods and have the original hypothesis maintain its standing.


Analysis of Hoelscher’s Table 4: A Breakdown of Time Frames

Hoelscher Table 4.1Corc Estimate Of Ten-Year Treasury Bond Yield Determinants For Sub-periods (Original)


1. 1953-66 1.9362 0.685 0.5342 -0.0009 0.0038 0.9044 1.6145 0.1872(6.96) (4.58) (4.93) (-1.52) (2.15)

2. 1967-84 1.6385 0.6803 0.808 -0.0008 0.0077 0.9581 1.5451 0.1865(2.66) (7.1) (10.96) (-0.92) (4.83)

3. 1953-84 1.2086 0.7455 0.7857 -0.0008 0.0081 0.9782 1.6143 0.1612(5.15) (15.96) (13.75) (-1.53) (6.85)

Hoelscher’s table 4.1 is a test on the temporal stability of two subperiods within his

initial time period. Hoelscher’s reasoning behind this breakdown lies in treasury bond rates.

1966, the divider between the two periods was chosen as it represents the first-time treasury

bond rates increased to a level above five percent (Hoelscher, 1986). The following years were

characterized by a positive trend reaching a high of around 14 percent in 1981. By using this

table, it is possible to explain the different variations for bond rates between individual periods.

Hoelscher’s table is replicated below.

Table 4.2 Alternate YearsCorc Estimate Of Ten-Year Treasury Bond Yield Determinants For Sub-periods (New Time Periods)


1. 1970-80 2.5354 0.5785 0.5359 -0.0012 0.0086 0.9891 1.5043 0.1004(5.97) (9.14) (6.6) (-2.33) (6.67)

2. 1981-90 -10.1856 3.4936 -0.4675 -0.0021 0.0208 0.987 2.3795 -0.2486(-2.85) (3.91) (-0.93) (-0.129) (3.54)

3. 1970-90 1.1097 0.7703 0.8028 0.0003 0.0068 0.9446 1.6932 0.0877(1.47) (7.71) (10.25) (0.33) (3.97)

To expand on Hoelscher’s usage of table 4.1 in the 1984-2013 period, it was divided into

sub-periods. This is represented in table 4.2. These dates were chosen through an analysis of


the federal funds rate graph. The peak for the period in question comes in 1981 with a value of

19.08 (“Effective Federal Funds Rate”). Utilizing this date allows for the individual analysis of the

data ten years to either side of this value. From the graph, it is apparent that there is a upward

trend from 1971 to 1981 and a downward trend from 1981 to 1990.

Analysis of Hoelscher’s table 5

Hoelscher Table 5.1Illustration of Estimated Effects of Deficits on Long Term-Term Rate 1980-1984

Average Value Estimated Effect on I (basis point inc)

1. USDEF 249.83 201.652. GOVDEF 240.03 178.6473. CFD 117.299 81.108

Looking at the data depicted in Hoelscher’s table 5 gives us a breakdown of the average

deficit value and is represented in 1972 dollars per capita. Analysis of the estimated effect

shows the percentage change in interest rates, depicted in basis points.

Table 5.2 Illustration of Estimated Effects of Deficits on Long Term-Term Rate 2009-2013

Average Value Estimated Effect on I (basis point inc)

1. USDEF 697.45 71.9212. GOVDEF 839.569 77.1823. CFD 639.408 59.849

A reproduction of table 5 was completed to show the change in values from the first

period, (1953-1984) to the second (1984-2013). Just as before, if Hoelscher’s ideas are valid, his

original results here are expected to be correlated with those found in the more recent period.

Initial analysis of the two tables points to little correlation between the two-time periods.


Table 10.1T Test

Ho: T1=T2 t CV(.95,29) DNR/RUSDEF 3.6543 2.0480 Reject

GOVDEF 3.7338 2.0480 RejectCFD 4.0320 2.0480 Reject

A two-sample t-test was run based on the null hypothesis that deficit means were equal.

It was found that it is necessary to reject this null hypothesis for all measured values of the

deficit variable. Therefore, there is a significant difference between deficit mean values for the

first and second periods.

Discussion

Discussion of Differences Between Time Periods in Table 1 and 2

Analysis of the recreations of Hoelscher’s tables 1 and 2, defined as tables 1.1 and 2.1 in

this paper, respectively, reflect the same result as was found when the original regressions

were done in Hoelscher’s work. As previously stated, the values calculated in our regressions

are similar, but not exactly the same as Hoelscher’s due to use of a different data set and

slightly different variables. A closer look at table 1.1 reveals that the R2 values are all above a

rounded value of .98 excluding the USDEF with no constant variable. These values show that

the independent variables in the regression are doing an excellent job of predicting the deficit

values. However, upon analysis of R2 values in table 1.2, a drop in values to around .80 for each

value is now seen. This significant drop shows that in this new period, there is an increased

amount of unexplained variance in the determination of the deficit. Because of this significant

drop, it is obvious that there are likely unaccounted for factors in play.


Next, the replication of Hoelscher’s second table and its corresponding second period

table are considered. In these two tables, table 2.1 and 2.2, the same trend is found in the

differences between time periods. Strong R2 values in the first period at around .97, (1953-

1984) are contrasted by weaker R2 values in the second time-period of around .80 (1984-2013).

Therefore, the correlation is not as strong between deficit and interest rates in the second

period.

To test for serial correlation in the model, the Durbin-Watson statistic is considered. It is

tested by using a k-value of 4, taking into account the number of regressors and an n equal to

29 for the first period and 31 for the second period. For the first table, the rejection region for

the statistic is below .921 and the failure to reject region is between 1.511 and 4. Any value

between these numbers would be in an unknown region. Because all the values in table 1.1 are

above 1.511, we fail to reject the hypothesis that row is equal to zero, showing that there is no

serial correlation. Looking at table 1.2, the rejection region, with an n of 31 is now less than .96

to reject and greater than 1.509 to fail to reject. Unfortunately, all the values except for the

second calculation of USDEF here are between this value. In this region, it is impossible to

determine whether there is serial correlation in the model. Rejection regions remaining the

same, in table 2.1, all the Durbin-Watson statistics show that ρ is equal to 0 and there is no

serial correlation. For table 2.2, the Durbin-Watson statistic values land in the uncertainty region

for all three deficit variables; therefore, there is no evidence to support or reject the null

hypothesis that ρ is equal to 0.


Discussion of Different Periods Between Tables 4.1 and 4.2

Moving on to a discussion of table 4.1 and 4.2, emphasis is placed on unravelling

differences between shorter time spans and variations in ten-year bond rates for the model.

Specifically looking at table 4.1, the first period, (1953-1966) shows the lowest R2 value at .90.

According to Hoelscher, rates were relatively stable during this period (Hoelscher, 1986). The

second period, (1966-1984) had a higher R2 at .96. Throughout this period, rates are said to be

increasing to a peak of 14% in 1981. Interestingly, the overall value for the entire period (1953-

1984) R2 value is even stronger at .98. Although all these values show strong correlations

between coefficients and deficit predictions, there is noticeable variation in coefficients (2

Hoelscher). Hoelscher explain these noting that there are not high degrees of freedom in the

model (Hoelscher, 1986). Therefore, he can conclude that the reason R2 values are the highest

for the overall period is due to overall stability in the model and a pooling of all relevant data.

Observing table 4.2, an opposite effect from table 4.1 is found. The R2 values for the

shorter periods (1970-1981 and 1981-1990) are stronger than the value for the overall period

(1970-1990). Because the data was chosen with a peak value during the year 1981, the trend in

data for the first period is increasing while the trend in the data for the second period is

decreasing (“Effective Federal Funds Rate”). Having the maximum value in the middle of the

time period means that the overall regression is trying to account for two completely different

trends, thus weakening the R2 values. For each subperiod, the regression only takes into

account a one-way trend. This makes the linear estimators more accurate, resulting in a larger

R2 value.


Discussion of the Importance of Table 5.1

Continuing with the discussion of our results, table 5.1’s importance is broken down.

These tables can be considered the most important piece to proving Hoelscher’s hypothesis.

The main point of this table is to show the average deficit value for USDEF, GOVDEF, and CFD,

as well as to calculate the average value of deficit on estimated interest rates. Results found in

this table are like Hoelscher’s, proving that his process was closely replicated. Looking at the

data, there is a large positive effect on interest rates when the deficits are high, confirming

Hoelscher’s original hypothesis that increasing deficits result in higher long term interest rates.

Hoelscher states that deficits are created through the short-term debt because of huge

government spending (Hoelscher, 1986). High spending by the government needs to be

compensated for by increasing interest rates. However, interest rates are raised artificially high,

absorbing lending capacity of smaller borrowers because of cost prohibitive borrowing levels.

What has been explained here is the crowding out effect. This supports Hoelscher’s hypothesis

because independent borrowers are forced to move into shorter term markets because of the

financial burden associated with bigger investments. Because of this effect, the economy is

hindered. To restart the economy, the government is left trying to spend more money and must

gain funding in the long term by increasing interest rates.

The data in the table supports this idea. GOVDEF has a significantly higher average debt

then CFD. This means that there is far more government spending then private spending in this

scenario. In line with Hoelscher’s theory, it makes sense that if the crowding out theory holds

true, the public should have a lower deficit due to less investment.


Shifting attention to table 5.2, the opposite effect is found, contradicting Hoelscher’s

predictions. Deficit means in table 5.2 are visibly larger then means reported in table 5.1.

However, when looking at estimated effect, values for each deficit measure significantly

decrease. Per Hoelscher’s hypothesis, with such an increase in overall deficit the estimated

effects on interest rates should be increasing. However, this is not the case. A closer look at the

GOVDEF and CFD variables support the opposition to this hypothesis in terms of the crowding

out effect. Although both deficit variables increase in table 5.2, percentage wise CFD is now a

much greater portion of USDEF. If crowding out was the case, private investment should not be

catching up to government spending. Small investments should have been “crowded out” by

high government spending; therefore, increasing interest rates. With the contradictory drop in

rates seen in the time change, investments now increased with easier accessibility to short term

markets.

A t-test was conducted in table 10.1 to test whether the means for each period were

significantly different from one another. It was found that this null hypothesis is rejected for all

three variables. Knowing that deficits significantly increased confirms the problem in the

estimated effects. Because these basis point values decreased rather than increased, the

opposite effect from Hoelscher’s paper is found. Increasing deficits did not cause an increase in

long term interest rates. It is now imperative to analyze possible problems with Hoelscher’s

model to determine what may have caused the reversal of this effect. To do this, omitted

variables and world events were analyzed to determine some of the variations found.


Analysis and Discussion of Omitted Variables

Purpose for the selection of these three specific Variables

Based on the findings that Hoelscher’s original hypothesis is not applicable to the

second period, the question of “why” becomes relevant. To attempt to solve this problem,

thought was put into coming up with different ideas that could result in the change from

deficits being positively correlated to long term interest rates and the new found negative

correlation. Broadly speaking, these changes could be a result of effects such as world events,

simultaneity bias, or omitted variables. Narrowing down the options, three omitted variables

that were deemed most likely to have significant effects on interest rates were chosen: federal

reserve data, foreign direct investment, and the S&P 500. Data for these three different

variables was then factored in individually to our regressions to determine each of their effects.

Federal Funds Rate

Federal reserve data was the first omitted variable to be analyzed. The federal funds

rate was initially chosen as a good variable to look at because of several factors. First off,

because the FED is a measure of the overnight funds rate, it should have a direct positive

correlation to interest rates in general. Therefore, it is logical that because the rate is applicable

to current financial institutions trading large sums of money, there would be direct correlation

to increases in long term interest rates. Additionally, when looking at a graph of the federal

funds rate for the years 1953-2013, there is an obvious trendline break in the year 1981

(“Effective Federal Funds Rate”). This max point corresponds very closely with the break


between the two-time periods in question. The first period, (1953-1984) shows a distinct

upward trend while the second period, (1984-2013) shows a distinct downward trend.

Table 6 FEDFederal Reserve Data Effects on Conducted Regressions

Coefficient EstimatesDeficit Variable Constant P rs y d FED R2 D-W ρ

USDEF 1955-84 0.956 1.063 1.073 -0.001 0.006 -0.011 0.975 1.496 0.233(3.05) (4.55) (5.04) (-1.41) (3.75) (-1.39)

USDEF 1984-2013 1.105 2.063 1.380 0.000 0.001 -0.036 0.869 1.053 0.473(1.71) (6.32) (4.7) (-0.19) (0.99) (-3.06)

GOVDEF 55-84 1.044 1.054 1.056 0.000 0.006 -0.010 0.979 1.626 0.154(3.29) (4.56) (4.94) (-0.66) (3.93) (-1.29)

GOVDEF 84-2013 1.076 2.076 1.390 0.000 0.001 -0.037 0.869 1.060 0.469(1.58) (6.34) (4.71) (-0.18) (0.88) (-3.06)

CFD 1955-1984 1.148 1.172 1.106 -0.001 0.005 -0.011 0.982 1.475 0.215(4.08) (6.85) (6.57) (-1.88) (5.09) (-1.79)

CFD 1984-2013 1.074 2.096 1.387 0.000 0.001 -0.036 0.872 1.063 0.468(1.71) (6.47) (4.75) (-0.15) (1.14) (-3.1)

USDEF, no con 55-84 - 0.8727 0.9389 -0.0008 0.0016 -0.01101 0.8442 1.5206 0.2821

(4.91) (6.93) (-2.19) (1.17) (-2.23)USDEF, no con 84-2013 - 1.7978 1.2646 0.0001 0.0007 -0.03546 0.7951 1.9817 -0.0390

(6.97) (5.2) (0.18) (0.96) (-3.65)

Table 6 depicts our new regression values factoring in the federal reserve data. To

determine the significant changes between this table and the originals, table 1.1 and 1.2, the R2

values are looked at. It was found that for the initial period, the R2 values remained at a

relatively stable value. However, for the second period, R2 values for USDEF, GOVDEF, and CFD

all increased by a significant account. It is also important to look at the coefficient on d, the

deficit variable. Larger coefficients should lead to higher t-values and thus, significant results.

Comparing original values for d and the values after the addition of FED shows that there was

either small decreases or no change in the value. These results show that the correlation

between independent variables better matched the model then without the FED variable.


Federal Direct Investment

The second variable that was deemed a strong possibility for an omitted variable was

the foreign direct investment rate of the United States government. Foreign direct investment

is generally defined as the amount of money that one country invests into another. Our data

specifically is showing that the amount of money coming in from foreign countries investing in

the United States, less military spending. There is an inherent connection between foreign

investment and domestic interest rates. Foreign direct investment has gradually increased since

the 1950’s; however, starting in the late 1970’s the rate began to increase at an increasingly

positive rate (“Rest of the world; foreign direct investment in U.S.”). Over this period, the

federal deficit has also continually increased. High investment from outside countries has the

same crowding out effect that Hoelscher discusses. Smaller corporations and investors will no

longer have the capability to borrow as the interest rate rises. Taking this variable into account

represents another possible reason for the positive correlation between deficits and interest

rates.

Table 7 FDIForeign Direct Investment Effect on Conducted Regressions

Coefficient EstimatesDeficit Variable Constant P rs y d FDI R2 D-W ρ

USDEF 61-84 1.1568 0.7385 0.7965 -0.0007 0.0081 0.000003 0.9748 1.6185 0.1579(1.8) (10.93) (10.7) (-0.92) (4.58) (0.07)

USDEF 84-2013 2.9643 1.0196 0.4196 0.0002 0.0017 -0.00002 0.9351 1.4234 0.2435(3.98) (5.42) (4.42) (0.23) (2.96) (-3.9)

GOVDEF 61-84 1.0990 0.7603 0.7888 -0.0001 0.0072 0.00002 0.9777 1.6820 0.1139(1.81) (12.31) (10.87) (-0.14) (4.88) (0.35)

GOVDEF 84-2013 2.8094 1.0486 0.4433 0.0003 0.0016 -0.00002 0.9370 1.4636 0.2297(3.82) (5.68) (4.52) (0.36) (2.97) (-3.97)

CFD 61-84 1.2386 0.8749 0.8108 -0.0007 0.0066 0.00001 0.9810 1.6621 0.0844(2.16) (18.11) (11.67) (-1.07) (5.43) (0.33)

CFD 84-2013 2.8294 1.1097 0.4175 0.0003 0.0015 -0.00002 0.9426 1.5741 0.1791(3.93) (6.23) (4.37) (0.41) (2.93) (-3.83)

USDEF, no con 55-84 - 0.5808 0.7308 -0.0008 0.0033 0.00003 0.8177 1.5733 0.2500(5.17) (8.04) (-1.44) (1.91) (0.89)

USDEF, no con 84-2013 - 1.2530 0.4191 0.0005 0.0021 -0.00001 0.7508 2.4258 -0.3785

(5.27) (4.67) (0.66) (2.86) (-1.09)


Examination of the R2 values for this table shows similar results to what was found for

the FED variable. Values for the first period were only marginally different from the original R2

value from table 1.1; however, when examining the later period, values once again show

significant increases, showing a stronger fit of our data to the regression line. When looking at

the d coefficients for FDI compared to the ones generated from Hoelscher’s original analysis, it

is found that all the values for the first period remain almost constant. However, all the

coefficients for the second period decrease except for USDEF. This change is unexpected; it

would be hypothesized that these values should all increase with the entrance of the FDI

variable into the regressions. Because the decrease is small, it is not necessarily a hindrance to

our original predictions. Further analysis later in the will help to embellish these results.

The S&P 500

The third variable chosen was the S&P 500. The S&P 500 is a list of large stock holding

companies. As a result, it was deemed likely that because this variable is a measure of the

overall health of the economy, it could be used as an explanator to some of the change that

was seen between the two-time periods in the regressions. Rationale here is that with low

deficits comes increases in overall market health. Increasing market health is directly correlated

with increasing investments into markets and thus, lower interest rates. Therefore, it was

hypothesized that increasing S&P 500 values when deficits are low should be positively linked

to interest rates.


Table 8 S&P 500S&P 500 Data Effects on Conducted Regressions

Coefficient EstimatesDeficit Variable Constant P rs y d SP R2 D-W ρ

USDEF 53-84 0.7349 0.7142 0.7355 -0.0010 0.0062 0.00177 0.9788 1.5393 0.1998(2) (14.36) (11.46) (-1.82) (3.93) (1.68)

USDEF 84-2013 4.5242 0.6732 0.4881 0.0008 0.0001 -0.00030 0.9359 1.4246 0.2313(4.12) (2.72) (5.32) (1.05) (0.13) (-3.86)

GOVDEF 53-84 0.8049 0.7203 0.7303 -0.0006 0.0058 0.00185 0.9820 1.6203 0.1376(2.35) (15.07) (11.7) (-1.2) (4.42) (1.89)

GOVDEF 84-2013 4.5144 0.6745 0.4895 0.0008 0.0001 -0.00030 0.9357 1.4269 0.2325(4.05) (2.71) (5.08) (1.05) (0.14) (-3.89)

CFD 53-84 1.0891 0.8213 0.7630 -0.0011 0.0058 0.00135 0.9860 1.6648 0.0994(3.36) (18.3) (13.16) (-2.18) (5.51) (1.5)

CFD 84-2013 4.4462 0.6863 0.4972 0.0009 0.0002 -0.00029 0.9380 1.4617 0.2203(4.08) (2.74) (5.52) (1.09) (0.32) (-3.81)

USDEF, no con 55-84 - 0.5530 0.6914 -0.0010 0.0024 0.00136 0.8205 1.5783 0.2132

(6.38) (9.56) (-2.52) (1.66) (1.1)USDEF, no con 84-2013 - 1.1820 0.4404 0.0007 0.0016 -0.00006 0.7290 2.4021 -0.2867

(4.18) (4.49) (0.83) (1.94) (-0.45)

For the S&P 500 variable, it was found that although the R2 values increased, showing a

better fit of the data because of the new variable, coefficients were now significant and

negative for the S&P variables. Furthermore, the variables for d all decreased in the second

period and had strong t-values. This represents the opposite effect of what was initially

hypothesized for this variable. Therefore, a negative correlation between increasing deficits and

the S&P 500 values is apparent. The problem may be that deficits are low in the first period but

not decreasing. Rather, the value of the deficit is growing. Therefore, because the deficits are

growing, the overall economic state would be decreasing and stock markets would be doing

poorly. Thus, it is apparent that bigger deficits are correlated with declines in the stock market,

explaining the negative coefficients.


Table 9Impact of R2 Values Resulting from New Variables

Omitted VariablesDates FED* FDI** S&P 500USDEF 55-84 -0.003 -0.0034 0.0006USDEF 84-2013 0.0667 0.1329 0.1337GOVDEF 55-84 -0.0031 -0.0043 0GOVDEF 84-2013 0.0672 0.1352 0.1339CFD 55-84 -0.0039 -0.0047 0.0003CFD 84-2013 0.0669 0.1372 0.1326USDEF, no con 55-84 0.0324 0.0059 0.0087USDEF, no con 84-2013 0.0702 0.0259 0.0051*FED data was not available before 1955, this change is reflected in the table**For FDI, the Years are Adjusted to 1961-1984 Due to Limited Data

To get a better sense for the effect of the addition of the three new variables, table 9

was created. It shows the different effects of the new variables on R2 values for each period.

Therefore, it is easy to tell how much better our regressions are getting at fitting the data. The

overall trend shows us that with the addition of FED and FDI in the first period, R2 values drop

by a small increment. However, a decently sized increase is seen for FED and FDI in the second

period. This effect shows that these two variables did an excellent job of pushing the model to a

better overall fitment of the data. The S&P 500 variable had the same effect; however, for each

deficit variable there was either no change or an increase in R2, once again showing that the

addition of the new variable led to better fitted values.

Discussion of New Variables and their Estimated Effect on Interest Rates

Table 5.3 With FED Estimated Effects of Deficits on Long Term-Term Rate

1980-1984 2009-2013Average Value Estimated Effect on i

(basis point inc)Average Value Estimated Effect on i

(basis point inc)1. USDEF 249.8 157.0 697.4 44.82. GOVDEF 240.0 142.0 839.6 45.43. CFD 117.3 64.2 639.4 41.5


The FED variable was taken and broken down into tables to get at the estimated effect

of the average values of each deficit variable. Just as before, evaluating table 5.3 is extremely

important. It allows us to see what the difference in estimated effect is between periods. From

the table, it is apparent that although average deficit values all increase, respective estimated

effects on interest rates also decrease. Like the initial findings between tables 5.1 and 5.2, these

results still contradict Hoelscher’s initial hypothesis that increasing deficits lead to increased

interest rates.

Table 5.4 With FDIEstimated Effects of Deficits on Long Term-Term Rate

1980-1984 2009-2013Average Value Estimated Effect on i

(basis point inc)Average Value Estimated Effect on i


Next, the FDI variable was broken down into tables to get at the estimated effect of the

average values of each deficit variable. In this table, all results found apart from the CFD

variable, still oppose Hoelscher’s initial hypothesis.

Table 5.5 With SPEstimated Effects of Deficits on Long Term-Term Rate

1980-1984 2009-2013Average Value Estimated Effect on I

(basis point inc)Average Value Estimated Effect on I


In table 5.5, Hoelscher’s findings are once again not supported. It is evident here, like

with the other variables that the effect they had on estimated effect of interest rates was not


substantial enough alone to alter the data to a point that would support Hoelscher’s initial

findings.

Table 5.6Change in Expected Effect on Interest Rates

Difference in 5 year Subperiods USDEF GOVDEF CFD

1. Original Analysis -1.2973 -1.0147 -0.21262. FED -1.1217 -0.9656 -0.22643. FDI -0.8384 -0.3506 0.18034. SP -1.4901 -1.3187 -0.0001

Expanding on our findings in the tables 5.3, 5.4, and 5.5 is extremely important.

Although values for the second period of the analysis did change, in most cases they were not

significant enough to show that Hoelscher’s original hypothesis of a positive correlation

between increasing deficits and interest rates was true. However, table 5.6 shows a visual

representation of how interest rates were affected by the three introduced variables, the FED,

FDI, and the S&P 500.

The values were generated by subtracting the estimated effect of the second period by

the estimated effect of the first period for each deficit variable, the original regression, and

each omitted variable. Then each value was divided by 100 to convert them from basis points

into percentages. When comparing our three deficit variables, (USDEF, GOVDEF, and CFD) to

the original value, it is possible to determine what effect each variable had on interest rates.

When the omitted variable regression values get closer to 0, a trend more similar to the

direction of what Hoelscher hypothesis was is seen. When they stray farther away from 0 then

the original value, it can be concluded that the effect on interest rates is getting farther away

from what Hoelscher would have hypothesized. If the numbers became greater than 0, it could


be concluded that Hoelscher’s hypothesis was now confirmed for the second period. Using this

method, it is easy to see which direction these new variables shift the expected interest rates

from the original regressions. Here a few very interesting effects of the data are found.

Looking at the FED variable, all percentages move towards zero except for CFD. These

findings show us that the FED variable was to some extent successful at shifting the findings of

our original regression to match Hoelscher’s findings. Additionally, this coincides with what

would be expected of the FED variable. Because the FED is inversely correlated with interest

rates and its values are known to be decreasing during this period, a movement towards

increasing interest rates is expected (“Effective Federal Funds Rate”). Movement in this

direction pushes values towards what Hoelscher would have expected. When considering the

FDI variable, the findings are even more significant. Values for GOVDEF and USDEF both move

towards 0, however, our CFD even becomes a positive value. These results are expected

because of the positive correlation between FDI and interest rates. CFD, at .1803, a positive

value, coincides directly with what Hoelscher would expect. An increase in the deficit in this

case, has led to an increase in interest rate values in terms of the par value of publicly held

debt. These findings can be explained with crowding out, foreign direct investment have been

continuously increasing for the second period. This trend along with the recession in 2008, led

to a huge spike in interest rates. During this period publicly held debt massively increased as is

typical in a recession. Therefore, when the economy crashed, the only money received was

from foreign investments, this explains why high deficits for this variable are contributing to

high interest rates for the public; therefore, explaining our positive value. Last, values for the

S&P 500 for USDEF and GOVDEF moved farther away from 0 and the original analysis value.


Therefore, this data coincides with the negative correlation between our increasing S&P 500

data and decreasing estimated effects of interest rates. Looking at these values shows what

amount of change was made in the second period by adding in the three omitted variables.

Conclusion

The main purpose of replicating Hoelscher’s study was to replicate his model and apply

it to a more recent period, 1984-2013. After this replication was complete, the two periods

were analyzed to determine whether Hoelscher’s hypothesis that increased deficits are

positively correlated to increased interest rates remained valid. Because it was found that this

hypothesis no longer held for the new period, ideas on how to explain this change were

formulated. It was decided that three omitted variables, the federal funds rate, foreign direct

investment, and the S&P 500, would be applied to the model to alleviate some of the change in

findings. It was found that adding foreign direct investment to the model had the greatest

effect on moving findings towards what Hoelscher would have expected. In fact, for the CFD

variable, Hoelscher’s findings were now supported in the second period. To expand on this

study, additional omitted variables could be considered as well as more world events. It was

concluded that the values generated made up for some amount of variation in the model;

however, Hoelscher’s hypothesis that higher deficits lead to increased interest rates could not

be definitively proven for the second period.


References

Board of Governors of the Federal Reserve System (US), Effective Federal Funds Rate

[FEDFUNDS], retrieved from FRED, Federal Reserve Bank of St. Louis;

https://fred.stlouisfed.org/series/FEDFUNDS, December 8, 2016.1

Board of Governors of the Federal Reserve System (US), Rest of the world; foreign direct

investment in U.S.; asset, Level [ROWFDNQ027S], retrieved from FRED, Federal Reserve

Bank of St. Louis; https://fred.stlouisfed.org/series/ROWFDNQ027S, December 8, 2016.

Hoelscher, G. (1986). New Evidence on Deficits and Interest Rates. Journal of Money, Credit and

Banking, 18(1), 1-15. doi:10.2307/1992316

Murray, M. P. 2006. Econometrics: A Modern Introduction. Boston: Pearson Addison Wesley,

2006. Print.

R. (2015). Crowding Out Effect. Retrieved December 09, 2016, from

http://www.investopedia.com/terms/c/crowdingouteffect.asp

Stata Manual. (n.d.). Retrieved November/December, 2016, from

http://www.stata.com/manuals13/tsprais.pdf

S&P 500 - 90 Year Historical Chart. (n.d.). Retrieved December 09, 2016, from

http://www.macrotrends.net/2324/sp-500-historical-chart-data

1 All members of this group, Chris Koziel, Rob Flynn, and I, worked extremely well together on the project. Meetings almost

always consisted of all three group members and all three members participated significantly. Working with Rob and Chris was an

excellent experience. Their inputs and work ethic over the past few weeks have significantly contributed to the writings of this

paper. Additionally, a special thank you would like to be given to Professor Michael P. Murray for his assistance with this project.

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Econometrics Hoelscher Paper Final