Friday, December 30, 2011

Monetary Policy & Credit Easing pt. 5: Explanatory Variables Continued...

Capturing Treasury Supply Effects

WE will need to account for things other than the Fed that influenced risk premia as they relate to Treasury supply. The following three variables are meant to accomplish such a thing:

1. Federal Reserves holdings of total public debt as a percentage of GDP

2. Total government holdings of domestic credit market debt as a percentage of the total

3. Foreign holdings of government debt as a percentage of total public debt

1. Fed's holdings of total public debt as a percentage of GDP

Federal Reserve holdings of total public debt as a percentage of GDP is important because it controls for how much Federal Government support the Fed is accounting for.  It is especially pertinent to our second estimation as the Feds holdings of total public debt relative to GDP increased sharply.  Operationally, we define this variable as:

FedGDP_{t}= {GovDebt_{t}^{Fed}\ GDP_{t}}x 100

Where,

GovDebt_{t}^{Fed}=Federal Debt Held by Federal Reserve Banks (FDHBFRBN) at time, t

GDP_{t} = Gross Domestic Product, 1 Decimal (GDP) at time, t

We expect that this variable will move in line with both short-term and long-term risk premiums. Therefore:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

Data Issues

The time-series necessary for this variable is provided by FRED and the details are as listed:

(a) Federal Debt Held by Federal Reserve Banks (FDHBFRBN), Quarterly, End of Period, Not Seasonally Adjusted, 1970-01-01 to 2011-0
(b) Gross Domestic Product, 1 Decimal (GDP), Quarterly, Seasonally Adjusted Annual Rate, 1947-01-01 to 2011-07-01

2. Government Holdings Of Domestic Credit Market Debt As A Percentage Of The Total

It would be wise to include a variable that account for fiscal policies support of the financial markets.  This we can define as Federal Government holdings of credit market assets as a percentage of the total outstanding. To account for total government support of the financial markets we will use the following variable: govcredit.

govcredit_{t}={ CAssets_{t}^{Gov}\ CAssets_{t}^{Total} }x 100

Where,

CAssets_{t}^{Gov} = Total Credit Market Assets Held by Domestic Nonfiancial Sectors - Federal Government (FGTCMAHDNS) at time, t

CAssets_{t}^{Total} = Total Credit Market Assets Held by Domestic Nonfiancial Sectors (TCMAHDNS) at time, $t$

We expect that this variable will reduce both short-term and long-term risk premiums. Therefore:

H0: ß ≥ 0 vs. Ha: ß < 0

Data Issues

The time-series necessary for this variable is provided by FRED and the details are as listed:

(a) Total Credit Market Assets Held by Domestic Nonfiancial Sectors - Federal Government (FGTCMAHDNS), Quarterly, End of Period, Not Seasonally Adjusted, 1949-10-01 to 2011-04-01
(b) Total Credit Market Assets Held by Domestic Nonfiancial Sectors (TCMAHDNS), Quarterly, End of Period, Not Seasonally Adjusted, 1949-10-01 to 2011-04-01

3. Foreign Holdings of Federal Debt As A Percentage Of The Total

This variable labeled ForeignDebt_{t} seeks to capture the impact that foreign holdings of United States government debt have on both short-term and long-term risk premia.  Theory would suggest that as foreign holdings go up risk-premia would go down. Operationally this variable is defined as follows:

ForeignDebt_{t} = {GovDebt_{t}^{Foreign}\ total public debt_{t}} x 100

Where,

GovDebt_{t}^{Foreign}= Federal Debt Held by Foreign & International Investors (FDHBFIN) at time, t

total public debt_{t}= Federal Government Debt: Total Public Debt (GFDEBTN) at time, t

Our ß coefficient on this variable is expected to be negative for both short-term and long-term risk premia and therefore:

H_{0}: ß ≥ 0 vs. H_{a}: ß < 0


Data Issues

The following data comes from FRED and the details are as follows:

(a) Federal Debt Held by Foreign & International Investors (FDHBFIN), Quarterly, End of Period, Not Seasonally Adjusted, 1970-01-01 to 2011-04-01
(b) Federal Government Debt: Total Public Debt (GFDEBTN), Quarterly, End of Period, Not Seasonally Adjusted, 1966-01-01 to 2011-04-01

Accounting For Cyclicality

We include two variables to help account for cyclicality in the overall economy.  Both are relevant as the Fed uses these variables in its decision making process.  For example in setting the federal funds rate, the Fed is said to have used a Taylor Rule that incorporated both the output gap and unemployment gap in its objective function.  Thus incorporating these variables may present a problem of endogeneity over a short-part of our sample(like when a taylor-rule was said to be used), but these effects we will choose to ignore.  The two cyclical variables we shall use are the output gap and the unemployment gap. The output gap is defined,

OGAP_{t}= Potential GDP_{t} – GDP_{t} at time, t

Where,

Potential GDP_{t}=Nominal Potential Gross Domestic Product (NGDPPOT) at time, t

GDP_{t}=Gross Domestic Product, 1 Decimal (GDP) at time, t

Our unemployment gap is defined in a similar fashion:

UGAP_{t}= NROU_{t} – UNRATE_{t} at time, t

Where,

NROU_{t}= Natural Rate of Unemployment (NROU) at time, t

UNRATE_{t}= Civilian Unemployment Rate (UNRATE) at time, t

Theoretically we assume that over the long-run as both of these variables increase the long-term risk premia increase.  Over the short-run regressions we would expect these variables to have almost no significant effect as that time period is cluttered with many short-term things impacting risk-premia. Additionally for the short-term risk premia we would expect either a negative relationship or no relationship.  This is because many things that impact the long-term risk premia one way have an opposite sign with respect to the short-term risk premia.

Data Issues
The data for these cyclical variables is provided by FRED and their details are laid out as follows:

(a) Civilian Unemployment Rate (UNRATE), Monthly, Seasonally Adjusted, 1948-01-01 to 2011-10-01 
(b) Natural Rate of Unemployment (NROU), Quarterly, 1949-01-01 to 2021-10-01 
(c) Nominal Potential Gross Domestic Product (NGDPPOT), Quarterly, 1949-01-01 to 2021-10-01 
(d) Gross Domestic Product, 1 Decimal (GDP), Quarterly, Seasonally Adjusted Annual Rate, 1947-01-01 to 2011- 07-01

The next post gets into the R analysis and lays out our model in full.

1 comment:

  1. I would like to know who in the world is buying all the debt being issued by the Government.

    ReplyDelete