Monetary Policy & Credit Easing pt. 7: R Econometrics Tests

In post 6 we introduced some econometrics code that will help those working with time-series to gain asymptoticly efficient results.  In this post we look at the different commands and libraries necessary for testing our assumptions and such.

Testing our Assumptions and Meeting the Gauss-Markov Theorem

In this section we will seek to test and verify the assumptions of the simple linear regression model.  These assumptions are laid out as follows and are extracted from Hill, Griffiths and Lim 2008:

SR1. The value of y, for each value of x, is
y= ß_{1}+ß_{2}x+µ
SR2. The expected value of the random error µ is
E(µ)=0
which is equivalent to assuming
E(y)= ß_{1}+ß_{2}x
SR3. The variance of the random error µ is
var(µ)=sigma^2 = var(y)
The random variables y and µ have the same variance because they differ only by a constant.
SR4. The covariance between any pair of random errors µ_{i} and µ_{j} is
cov(µ_{i}, µ_{j})=cov(y_{i},y_{j})=0
SR5. The variable x is not random and must take at least two different values.
SR6. The values of µ are normally distributed about their mean
µ ~ N(0, sigma^2)
if the y values are normally distributed and vice-versa 

Central to this topics objective is meeting the conditions set forth by the Gauss-Markov Theorem.  The Gauss-Markov Theorem states that if the error term is stationary and has no serial correlation, then the OLS parameter estimate is the Best Linear Unbiased Estimate or BLUE, which implies that all other linear unbiased estimates will have a larger variance. An estimator that has the smallest possible variance is called an "efficient" estimator.  In essence, the Gauss-Markov theorem states that the error term must have no structure; the residual levels must exhibit no trend and the variance must be constant through time.

When the error term in the regression does not satisfy the assumptions set forth by Gauss-Markov, OLS is still unbiased, but fails to be BLUE as it fails to give the most efficient parameter estimates. In this scenario, a strategy which transforms the regressions variables so that the error has no structure is in order. In time-series analysis, the problem of autocorrelation between the residual values is a common one.  There are several ways to approach the transformations necessary to ensure BLUE estimates, and the previous post used the following method to gain asymptotic efficiency and improve our estimates:

1. Estimate the OLS regression

2. Fit OLS residual to an AR(p) process using the Yule-Walker Method and find the value of p.

3.  Re-estimate model using Generalized Least Squares fit by Maximum Likelihood estimation, using the  estimated p from 2, as the order for your correlation residual term.

4. Fit the GLS estimated residuals to an AR(p) process and use the estimated p's as the final parameter estimates for the error term.  

What have we done?  First we have to find out what the error term autocorrelation process is. What order is p? In order to find this out we fit the OLS residuals to an AR(p) using the Yule-Walker method. Then we take the order p of our estimated error term and run a GLS regression with an AR(p) error term.  This will give us better estimates for our model.  Research has shown that GLS estimators are asymptotically more efficient than OLS estimates almost one-hundred percent of the time. If you notice in every single regression, the GLS estimator with a twice iterated AR(p) error terms consistently results in a lower standard deviation of the residual value. Therefore the model has gained efficiency which translates into improved confidence intervals.  Additionally, by fitting the GLS residuals to an AR(p) we remove any autocorrelation(or structure) that may have been present in the residual.  

Testing For Model Miss-specification and Omitted Variable Bias

The Ramsey RESET test (Regression Specification Error Test) is designed to detect omitted variable bias and incorrect functional form. Rejection of H_{0} implies that the original model is inadequate and can be improved.  A failure to reject H_{0} conveys that the test has not been able to detect any miss-specification.

Unfortunately our models of short-term risk premia over both estimation periods reject the null hypothesis, and thus suggest that a better model is out there somewhere.  Correcting for this functional miss-specification or omitted variable bias will not be pursued here, but we must keep in mind that our model can be improved upon and is thus not BLUE.  

In R you can run the Ramsey Reset test for standard lm functions using the library lmtest:

>library(lmtest)

> resettest(srp1.lm)

RESET test

data:  srp1.lm 

RESET = 9.7397, df1 = 2, df2 = 91, p-value = 0.0001469

For GLS objects however you'll need to do it manually and that procedure will not be outline here.  Although if you really want to know please feel free to email or leave a comment below.  

Addressing Multicollinearity

In the original formulation of the model there existed an independent variable called CreditMarketSupport, that was very similar to our FedBalance variable.  Both variables are percentages and shared the same numerator while also having very similar denominators.  As a result we had suffered from a condition called exact collinearity as the correlation between these two variables was nearly one.

> cor(FedBalance1,CreditMarketSupport1)

0.9994248

With exact collinearity we were unable to obtain a least squares estimate of our ß coefficients and these variables were behaving opposite of what we were expecting.  This violated one of our least squares assumptions SR5 which states that values of x_{ik} are not exact linear functions of the other explanatory variables.  To remedy this problem, we removed CreditMarketSupport from the models and we are able to achieve BLUE estimates.

 Suspected Endogeniety

In our estimation of long-term risk premia over the first time period we suspect endogeniety in the cyclical variable Output Gap.  In order to remedy this situation we replace it with an instrumental variable - the percentage change in S&P 500 and perform the Hausman Test which is laid out as follows:

H_{0}: delta = 0 (no correlation between x_{i} and µ_{i})

H_{1}: delta ≠ 0 (correlation between x_{i} and µ_{i})

When we perform the Hausman Test using S&P 500 as our instrumental variable our delta ≠ 0 and is statistically significant.  This means that our Output Gap variable is indeed endogenous and correlated with the residual term.  If you want to learn more about the Hausman Test and how to perform it in R please leave a comment or email me and i'll make sure to get the code over to you.  When we perform the Two Stage Least Squares Regression to correct for this not a single term is significant.  This can be reasonably be attributed to the problem of weak instruments.  The 2 Stage Least Squares Estimation is provided below. Since, the percentage change in the S&P500 was only correlated with the Output Gap 0.110954, there is strong reason to suspect that weak instruments are the source of the problem.  We will choose to not locate a proper instrumental variable to emulate the Output Gap, instead we will keep in mind that we have an endogenous variable when interpreting our coefficient estimates which will now end up being slightly biased. 

Below is how to perform a two-stage least squares regression in R when your replacing an endogenous variable with an exogenous one. First you'll need to load the library sem into R. In the below regression the first part includes all the variables from the original model and the second part lists all of our exogenous and instrumental variables which in this case is just the percentage change in the S&P 500.

> tSLRP1<-tsls(lrp1~yc1+CP1+FF1+default1+Support1+ER1+FedGDP1+FedBalance1+govcredit1+ForeignDebt1+UGAP1+OGAP1,~ yc1+CP1+FF1+default1+Support1+ER1+FedGDP1+FedBalance1+govcredit1+ForeignDebt1+sp500ch+OGAP1 )

> summary(tSLRP1)

 2SLS Estimates

Model Formula: lrp1 ~ yc1 + CP1 + FF1 + default1 + Support1 + ER1 + FedGDP1 + 

    FedBalance1 + govcredit1 + ForeignDebt1 + UGAP1 + OGAP1

Instruments: ~yc1 + CP1 + FF1 + default1 + Support1 + ER1 + FedGDP1 + FedBalance1 + 

    govcredit1 + ForeignDebt1 + sp500ch + OGAP1

Residuals:

   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 

 -9.030  -1.870   0.021   0.000   2.230   7.310 

             Estimate Std. Error  t value Pr(>|t|)

(Intercept)  -5.28137   44.06906 -0.11984   0.9049

yc1          -1.48564   10.60827 -0.14005   0.8889

CP1          -0.01584    0.09206 -0.17204   0.8638

FF1           0.20998    2.43849  0.08611   0.9316

default1     -7.16622   65.35728 -0.10965   0.9129

Support1      6.39893   47.72244  0.13409   0.8936

ER1           4.56290   35.91837  0.12704   0.8992

FedGDP1       1.86392    9.16081  0.20347   0.8392

FedBalance1   0.73087   12.96474  0.05637   0.9552

govcredit1    0.17051    0.89452  0.19062   0.8492

ForeignDebt1 -0.22396    1.41749 -0.15799   0.8748

UGAP1         4.55897   35.33446  0.12902   0.8976

OGAP1         0.01331    0.09347  0.14235   0.8871

Residual standard error: 3.3664 on 93 degrees of freedom

Notice that our model now doesn't have any significant terms.  This is why we will choose to ignore the endogeniety of our Output Gap and probably Unemployment Gap variables.  Correcting for endogeniety does more harm than good in this case.

Results and Concluding Thoughts

As this paper hopefully shows, the Feds actions did directly impact the easing of broader credit conditions in the financial markets.  

Over our first estimation period from 1971 to 1997 we find that the Fed's support of Depository Institutions as a percentage of savings and time deposits is positively related to the short-term risk premia. Specifically we find that a 1 percentage point increase in Support leads to a 2.1 percent increase in short-term risk premia. This was as expected because Depository Institutions would only borrow from the Fed if no other options existed. We also find that a 1 percentage point increase in the federal funds rate leads to a .19 percentage increase in short-term risk premia.  This is consistent with our original hypothesis as an increased FF puts positive pressure on short-term rates like the 3 month commercial paper rate, thus resulting in an widened spread.  With respect to long-term risk premia, we find that a 1 percentage point increase in FF leads the long-term risk premia to decrease by .66 percentage points and a 1 percent increase in the federal funds rate leads to a .07 decrease in the long-term risk premia.

Over our second estimation period the composition of the Feds balance sheet is considered.  We see that the CCLF  did decrease short-term risk premiums, with every one percent increase translating to a decrease in short-term risk premia by .1145 percentage points.  Another important result is that Fed purchases of Agency Debt and Agency MBS did have a significant, although almost negligible effect on short-term risk premia.  One surprising result with the estimation of the long-term risk premia is that our Fed balance sheet size variable has a sign that is opposite of what we expected and its significance is particularly surprising.  This may be expected since this period is largely characterized by both a shrinking balance sheet and narrowing risk premia as investments were considered relatively safe.  However towards the end of the period risk premiums shot up and only after did the size of the balance sheet also increase, thus the sample period may place too much weight towards the beginning of the time period and not enough towards the end. This is a reasonable assumption given that our estimate of the balance sheet size showed a large negative impact on risk premia over our longer estimation period.  

A complete version of the paper can be located here.

Please people keep dancing and we'll delve further into some additional econometrics tests next week. 

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.

Monetary Policy & Credit Easing pt. 4: More Independent Variable Definitions

Support for Depositary Institutions

This variable will account for the Federal Reserves support of Depository Institutions through direct lending to these institutions.  Support will be measured by how much the Fed made up for any shortfalls in Depository Institutions main source of cash- time and savings deposits. Federal Reserve support for our first estimation period is operationalized as follows:

Support_{t}={TotalBorrowingFed^{DI}_{t}\ Total Time & Savings Deposits_{t}^{DI}}x 100

Where,
Support_{t}= Fed funds at depository institutions as a percentage of their main financing streams (total savings and time deposits) at time, t

TotalBorrowingFed^{DI}_{t}= Total Borrowings of Depository Institutions from the Federal Reserve (BORROW) at time, t

Total Time & Savings Deposits_{t}^{DI}= Total Time and Savings Deposits at All Depository Institutions (TOTTDP) at time, t

For our second estimation period from 4/1/01 to 4/1/11 we will use a different variable that excludes time-deposits as the series that we would ideally like to use above was discontinued in 2006.

Support_{t}={TotalBorrowingFed^{DI}_{t}\ Total Savings Deposits_{t}^{DI}}x 100

Where,
Support_{t}= Fed funds at depository institutions as a percentage of their main financing stream (total saving deposits) at time, t

TotalBorrowingFed^{DI}_{t}= Total Borrowings of Depository Institutions from the Federal Reserve (BORROW) at time, t

Total Savings Deposits_{t}^{DI}= Total Savings Deposits at all Depository Institutions (WSAVNS) at time, t

The expected beta coefficient should be positively related to short-term risk premia, as tighter credit conditions require Depository Institutions to go to the Fed for help.  Only after the risk-premia goes up and these institutions have no where else to go do they borrow from the Fed at the discount rate.

We expect the effect of lending support to depository institutions to be positively related to short-term risk premia, therefore:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

Furthermore, we expect Fed support to depository institutions to have a negative effect on long-term risk premia because of the expectations component.  As the Fed steps in with lending support, markets calm their fears about the future.  This is directly the opposite of short-term risk premia as the support in that situation is in direct response to the risk premia. Therefore,

H_{0}: ß ≥ 0 vs. H_{a}: ß < 0

Data Issues

The following time-series data were provided by FRED and the details are as follows:

(a) Total Borrowings of Depository Institutions from the Federal Reserve (BORROW), Monthly, Not Seasonally Adjusted, 1919-01-01 to 2011-10-01


(b) Total Savings Deposits at all Depository Institutions (WSAVNS), Weekly, Ending Monday, Not Seasonally Adjusted, 1980-11-03 to 2011-10-17


(c) Total Time and Savings Deposits at All Depository Institutions (DISCONTINUED SERIES) (TOTTDP), Monthly, Seasonally Adjusted, 1959-01-01 to 2006-02-01

The Federal Funds Rate

The motivation behind putting the Federal Funds rate into our regression model is simple.  This is the main policy tool that the Fed has used to manipulate short-term credit conditions and influence the rate of inflation.  The Fed controls this rate in hopes of influencing other rates such as the Prime Bank Loan Rate along with other short term credit instruments like Commercial Paper. Additionally, this variable is very easy to account for because it requires virtually zero manipulation.  Notationally we will define it in the following manner:

FF_{t}= Federal Funds rate at time, t

The expected beta coefficient should be positively related to the short-term risk premia and negatively related to long-term risk premia.  They theory is that by lowering the federal funds rate, or the rate at which banks lend to each other, the Fed is encouraging banks to lend and thus ease credit conditions.  When the Fed feels that tightening is appropriate, maybe the result of a jump in inflation expectations or an deep acceleration in the economy, they respond by raising the federal funds rate.  This tightens credit conditions and thus theoretically at least, should result in an increase in short-term risk premia. The opposite holds true for the federal funds rate effect on long-term risk premia.  Since long-term rates are a function of shorter-term rates, investors are inclined to sell Treasuries which decreases the spread between Aaa and 10 year nominal treasuries, therefore decreasing long-term risk premia.

For short-term risk premiums we expect the federal funds rate to be positively related:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

For long-term risk premiums we expect the federal funds rate to be negativity related:

H_{0}: ß ≥ 0 vs. H_{a}: ß < 0

Data Issues

We get the series for the federal funds rate from FRED and the details are as follows:

(a) Effective Federal Funds Rate (FF), Weekly, Ending Wednesday, 1954-07-07 to 2011-10-19

Interest Paid On Excess Reserves

This variable is also easy to account for because the introduction of interest paid on reserves has a direct impact on the physical quantity of excess reserves of depository institutions held at the Federal Reserve.  The motivation behind this variable is that banking institutions would not hold excess reserves with the Fed without some compensation i.e. that opportunity cost has to be greater than zero.  That is where the interest paid on excess reserves come in.  Without it there is an opportunity cost of letting the reserves sit with the fed instead of seeking more profitable safe havens for their cash. That is why we will be using the quantity of excess reserves as our explanatory variable and notationally defining it as follows:

ER_{t}= Excess Reserves of Depository Institutions at time, t

When the Fed initiated its policy of paying interest on reserves it created an incentive for banks to shore up their finances with the Fed.  It gave the Fed a way to conduct large scale asset purchases without suffering inflationary consequences. As long as the reserves are held with the Fed, they cannot be inflationary therefore an increase in excess reserves at the Fed is contractionary. Additionally, since the Fed had not initiated the policy of paying interest on reserves until October of 2008 there was no incentive for banks to hold any excess reserve balances before then. That is why our two estimation periods must have two different hypothesis tests for this variable:

For our estimation covering the 4/1/71 to 7/1/97 time period the interest paid on excess reserves policy was non-existent and therefore:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

In other words, we are looking to not reject the null hypothesis that beta is equal to zero.

For our second estimation covering the 4/1/01 to 4/1/11 time period the interest paid on excess reserves policy was in effect, if only for a short-time before the end of the sample and therefore:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

Data Issues

We get the series from FRED and the details are as follows:

(a) Excess Reserves of Depository Institutions (EXCRESNS), Monthly, Not Seasonally Adjusted, 1959-01-01 to 2011-09-01

Control Variables: Accounting For Factors Outside of Monetary Policy

We must account for changes in the risk premia that aren't necessarily related to monetary policy.  These include things like market fear, corporate default risk and controlling for changes due to underlying fundamentals like Corporate Profits After Tax.

The Yield Curve

The motivation behind including the yield curve is due to its known predictive power of economic growth and recessionary risk. As recessionary risk increase investors are more likely to put their funds into the safest assets with the highest return.  Historically, this involves the purchase of longer-term Treasuries as they have zero default risk.  When a bond is purchased its price goes up, and its effective yield decreases so the slope of the yield curve or the spread between the most liquid and shortest maturity bond and the most liquid, longest maturity bond decreases or flattens. As this slope flattens we expect risk premia to increase for longer maturity and less liquid debt instruments. As the yield curve flattens we expect T-bills to be sold and longer-term Treasuries to be purchased.  This puts upward pressure on T-bill rates, thus narrowing the spread between Commercial Paper and T-bills and reducing the short-term risk premia.
The yield curve as we define it is the spread between the 10-Year Nominal Treasury Note rate and the 3-Month Nominal Secondary Market Treasury Bill rate.  Notationally,

YC_{t}=GS10_{t} – TB3MS_{t}

Where,

YC_{t}= Yield curve at time, t

GS10_{t}= 10-Year Treasury Constant Maturity Rate at time, t

TB3MS_{t}= 3-Month Treasury Bill: Secondary Market Rate at time, t

The beta coefficient for both of our estimation periods is expected to be negatively related to long-term risk premia. Therefore:

H_{0}: ß ≥ 0 vs. H_{a}: ß ≤ 0

The beta coefficient for both of our estimation periods is expected to be positively related to short-term risk premia. Therefore:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

Data Issues

We get the two times-series data from FRED and the details are as follows:

(a) 10-Year Treasury Constant Maturity Rate (GS10), Monthly, 1953-04-01 to 2011-09-01


(b) 3-Month Treasury Bill: Secondary Market Rate (TB3MS), Monthly, 1934-01-01 to 2011-09-01

Stock Market Volatility

We will control for market fear by including a measure of stock market volatility into our regression model. We define volatility as follows:

 Volatility_{t}= CBOE DJIA Volatility Index (VXDCLS) at time, t

The motivation behind this control variable is that the returns from owning stocks become more volatile in times of fear. Thus the risk premia on assets that aren't risk free like corporate bonds may increase in response to this market volatility.

This variables is literally only relevant in the regression on long-term premiums for our second estimation period. We cannot reasonably assume it has any effect on short-term risk premia because stock market volatility signals the fear of financial markets which leads to flight to safety into longer term treasuries not short-term commercial paper. The reason is that an investor probably couldn't even have the capital to buy commercial paper to begin with and secondly when fear strikes investors tend to pour their capital into longer term treasuries because they can pick up some extra yield. This would widen the spread between Aaa and Treasuries thus increasing the risk premium.  Therefore we include this variable only in our second estimation and its only real effect will be on the long-term risk premia.

For the regression over our second estimation period, increased volatility is expected to increase the long-term risk premium:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

For the regression over our second estimation period, volatility is not expected to have an effect on short-term risk premia, therefore:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

In other words, we are looking to not reject the null hypothesis that $\beta$ is equal to zero.

Data Issues

We get the times-series data from FRED and the details are as follows:

(a) CBOE DJIA Volatility Index (VXDCLS), Daily, Close, 1997-10-07 to 2011-11-02

Corporate Bond Default Risk

It would be prudent to control for the perceived credit default risk of the corporate bonds market. To do this we use the spread between the AAA and BAA rates bonds which would theoretically correspond to increased compensation for the risk of a default. The reason being we want to see how much the Fed's actions influence the risk premia and factor out movements in the spread that may incorporate other things like flat out default risk. Ideally we would like to use a Credit Default Swap Index to control for default risk as it would help us control directly for default risk and not other things like liquidity risk, but given the sample length data limitations we are forced to stick with what we've got.

The control variable we use for corporate default risk is the spread between Moody's rated Baa's and Aaa's. This is used because data exists for the full length of our desired samples and therefore is operationalized as follows:

Default^{spread}_{t}=BAA_{t} – AAA_{t}

Where,

BAA_{t}= Moody's Seasoned Baa Corporate Bond Yield at time, t

AAA_{t}= Moody's Seasoned Aaa Corporate Bond Yield at time, t

The beta coefficient on our corporate default control variable is expected to be positive in our regression on long-term rates since an increase in the spread between BAA and AAA would indicate that these bonds expected default risk would increase:

H_{0}: ß ≤ 0 vs. H_{a}: ß > 0

In our regressions on short-term risk premia, the expected effect of this control variable is effectively zero as this variable deals with longer-term interest rates not exactly pertinent to short-term financing like commercial paper or Treasury Bills:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

In other words, we are looking to not reject the null hypothesis that $\beta$ is equal to zero.

Data Issues

For the AAA and BAA data we use FRED:

(a) Moody's Seasoned Aaa Corporate Bond Yield (AAA), Monthly, 1919-01-01 to 2011-09-01


(b) Moody's Seasoned Baa Corporate Bond Yield (BAA), Monthly, 1919-01-01 to 2011-09-01

Corporate Profits After Tax

As corporate profits after tax increase the risk premium on corporate bonds decrease.  This fundamentally negative relationship should be controlled for in our regression model.  Operationally, this is defined as:

CP_{t} = Corporate Profits After Tax at time, t

The beta coefficient on our CP control variable should be negatively related to our dependent variables.  This is because as corporate profits after tax increase the risk that they will renege on their debt obligations will decrease. This gives us the following test.

H_{0}: ß ≥ 0 vs. H_{a}: ß < 0

Data Issues

We get the times-series data from FRED and the details are as follows:

(a) Corporate Profits After Tax (CP), Quarterly, Seasonally Adjusted Annual Rate, 1947-01-01 to 2011-04-01

Keep dancin'

Steven J.

Monetary Policy & Credit Easing pt. 3: Accounting For The Composition of The Fed's Balance Sheet & Credit Easing

Credit Easing shifts the composition of the balance sheet away from default-free assets towards assets with credit risk. An example of Credit Easing which is pertinent to our testing the effects of monetary policy on commercial paper is the Commercial Paper Funding Facility. Implementation of this facility involved the U.S. central bank selling T-bills and purchasing commercial paper of similar maturity.  This shift in composition leaves the size and average maturity of bank assets on the Fed's balance sheet unchanged. When the Fed purchases an asset like commercial paper, it lowers the supply of this asset to private investors. This scarcity has the effect of boosting its price and pushing down its yield. In the absence of private demand for the risky asset, the Feds purchase makes credit available where no alternative existed. The composition effect will be captured by our second time period estimation (from 4/1/01 to 4/1/11) of Monetary Policy's effects as all of the credit easing policies employed by the Fed occurred over this time period. A little background on the implementation of these polices is introduced below.

Implementation of Credit Easing and Large Scale Asset Purchases*

*This section draws heavily from Sack 2010

The Federal Reserve holds the assets it purchases in the open market in its System Open Market Account (SOMA).  Historically, SOMA holdings have consisted of nearly all Treasury securities, although small amounts of agency debt have been held. Purchases and sales of SOMA assets are called outright open market operations (OMOs).  Outright OMOs, in conjunction with repurchase agreements and reverse repurchase agreements, traditionally were used to alter the supply of bank reserves in order to influence the federal funds rate.  Most of the higher-frequency adjustments to reserve supply were accomplished through repurchase and reverse repurchase agreements, with outright OMOs conducted periodically to accommodate trend growth in reserve demand. OMOs were designed to have a minimal effect on the prices of securities included in its operations.  It is the Fed's way of not distorting prices on debt instruments and thus protecting its independence from political pressure.  To this end, OMOs tended to be small in relation to the markets for Treasury bills and Treasury coupon securities. Large Scale Asset Purchases, however aimed to have a noticeable impact on the interest rates being purchased as well as on other assets with similar characteristics. In order to lower market interest rates, Large Scale Asset Purchases were designed to be large relative to the markets for these assets.  As mentioned in Gagnon, Raskin, Remache and Sack 2010:

Between December 2008 and March 2010, the Federal Reserve will have purchased more than $1.7 trillion in assets. This represents 22 percent of the $7.7 trillion stock of longer-term agency debt, fixed-rate agency MBS, and Treasury securities outstanding at the beginning of the LSAPs.

In the following discussion of the independent variables selected to capture this effect please note that they are all defined as Federal Reserves holdings as a percentage of the total market value outstanding.  In this way we can quantify how much the Fed's holdings relative to the total market supply of these assets impacted market risk premia.

Large Scale Asset Purchases were focused on four main securities:

1. Agency Debt

2. Mortgage Backed Securities

3. Treasury Securities

4. Commercial Paper

Although we do not explicitly account for these Treasury Purchases, we rely on our main balance sheet variable to capture their effects. The first asset to account for which is especially pertinent to our short-term risk premia variable is commercial paper.

Commercial Paper

Accounting for commercial paper and the Commercial Paper Funding Facility LLC, we will use the Fed's holdings as a percentage of the total commercial paper outstanding. The Commercial Paper Funding Facility LLC, like all of the Fed's Credit Easing tools was only functional during our second estimation period  (4/1/01 to 4/1/11). That is why it will only be used as a variable over that estimation period. Operationally:

Commercial Paper^{Fed}_{t}={CPaper^{Fed}_{t}\ CPaper_{t}^{total}}x 100

Where,

Commercial Paper^{Fed}_{t}= the percentage of the total commercial paper outstanding the Fed owns at time, t

CPaper^{Fed}_{t}= Net Portfolio Holdings of Commercial Paper Funding Facility LLC (WACPFFL) at time, t

CPaper_{t}^{total}= Commercial Paper Outstanding (COMPOUT) at time, t

We expect this variable to be negatively related to short-term risk premia over our estimation period. The reason being that increased Fed support in this market should have directly reduced the spread between commercial paper and Treasury bills.  Especially if the Fed sold T-bills to purchase short-term commercial paper and asset backed commercial paper.  Therefore the following hypothesis test is appropriate:

H_{0}:ß ≥ 0 vs. H_{a}: ß < 0 

With respect to the long-term risk premia, we should expect this monetary policy action to have a negligible effect.  This is because this policy was aimed at impacting short-term commercial paper and not longer-term rates:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

Data Issues

The following data sets are pulled from FRED and their details are as follows:

(a) Assets - Net Portfolio Holdings of Commercial Paper Funding Facility LLC (DISCONTINUED SERIES) (WACPFFL), Weekly, As of Wednesday, Not Seasonally Adjusted, 2002-12-18 to 2010-08-25

(b) Commercial Paper Outstanding (COMPOUT), Weekly, Ending Wednesday, Seasonally Adjusted, 2001-01-03 to 2011-10-26

This required the following data transformation within FRED:

{(WACPFFL\1000)\ COMPOUT}x100

Mortgage-Backed Securities & Agency Debt

In order to account for the Feds holdings Agency Debt and Mortgage Backed Securities as a percentage of the total outstanding we use the following variable:

Agency Debt & MBS^{Fed}_{t} = {FADS^{Fed}_{t} + MBS^{Fed}_{t}\ DomesticFinancial_{t}^{Total}}x 100

Where, 

Agency Debt & MBS^{Fed}_{t}= Feds holdings of agency debt and Mortgage-Backed Securities as a percentage of the total outstanding at time, t

FADS^{Fed}_{t}= Fed's holdings of Federal Agency Debt Securities (WFEDSEC) at time, t

MBS^{Fed}_{t}= Fed's holdings of Mortgage-Backed Securities (WMBSEC) at time, t

DomesticFinancial_{t}^{Total}=  Domestic Financial Sectors holdings of Agency- and GSE-Backed Mortgage Pools (AGSEBMPTCMAHDFS) at time, t

This variable, theoretically should have almost no impact on both long-term and short-term risk premiums. The reason is Agency Debt and MBS are not highly correlated with either of our dependent variables, in fact it wasn't meant to impact these measures. It was however meant to influence 30 year mortgage rates which much research has shown it did in fact help ease.  We include this variable only because it was a major part of the Fed's credit easing policy and that future models with measures of housing affordability as their dependent variable would be able to use the variables listed in this paper to show Fed support of the housing market. 

The beta coefficient in front of this independent variable is therefore expected to have no significant relation to either long-term or short-term risk premiums as defined in this paper:

H_{0}: ß = 0 vs. H_{a}: ß ≠ 0

We fully expect to not reject the null hypothesis for both of our models.

Data Issues

The data for the above variables comes from the following financial time-series from FRED:

(a) Total Credit Market Assets Held by Domestic Financial Sectors - Agency- and GSE-Backed Mortgage Pools (AGSEBMPTCMAHDFS), Quarterly, End of Period, Not Seasonally Adjusted, 1949-10-01 to 2011-04-01

(b) Reserve Bank Credit - Securities Held Outright - Federal Agency Debt Securities (WFEDSEC), Weekly, Ending Wednesday, Not Seasonally Adjusted, 2002-12-18 to 2011-10-26

(c) Reserve Bank Credit - Securities Held Outright - Mortgage-Backed Securities (WMBSEC), Weekly, Ending Wednesday, Not Seasonally Adjusted, 2009-01-14 to 2011-10-26

Please keep dancing and wait for our next post which finishes defining our independent variables,

Steven J. 

Monetary Policy & Credit Easing pt. 2: Defining Our Variables

IN order to get a more complete picture of how monetary policy influences credit conditions we will estimate its effects on both long-term and short-term risk premia.  Our first dependent variable is the short-term risk premia and our second is the long-term risk premium. We will be testing the effects of monetary policy on both risk premias over two separate time periods. The first is from 4/1/71to 7/1/97 and the second is from 4/1/01 to 4/1/11.  We use two different time periods to more strongly capture the influence of the different monetary policy tools that were prevalent to each respective time period.  For example, the first time period was a time characterized by the Federal Reserve's indirect manipulation of the federal funds rate to influence other short-term rates like the prime bank loan rate and rates on short-term commercial paper.  In direct contrast, the second time periods estimation recognizes the Fed's manipulation of both the size and composition of its balance sheet as well as it's use of the federal funds rate to influence short-term market rates.

First Dependent Variable: Short-term Risk Premium & Commercial Paper

Commercial Paper is an unsecured promissory note with a fixed maturity of 1 to 270 days. We will be focusing on 90 day Commercial Paper. Commercial Paper is a money-market security issued by large banks and corporations to get money to meet short term debt obligations, and is only backed by an issuing bank or corporation's promise to pay the face amount on the maturity date specified on the note. Since it is not backed by collateral, only firms with excellent credit ratings from a recognized rating agency will be able to sell their Commercial Paper at a reasonable price. Additionally, Commercial Paper rates increase with maturity so they also have a duration risk associated with the price they fetch in the market place. Since this type of security is typically considered pretty risk free and has virtually zero rollover risk its deviation from the three-month Treasury bill rate seems like an appropriate measure of the short-term risk premium.  The 3 Month T-bill is used as our risk-free asset because it is considered to have zero default risk and is highly liquid. Moreover, T-bills are used for short-term financing purposes which makes its use very similar to that of Commercial Paper. The short-term risk premium is thus operationalized as follows:

SR^{premium}_{t}= CP3M_{t} – TB3MS_{t}

Where,

SR^{premium}_{t} = Short-term Risk Premium at time, t

CP3M_{t}= 3-Month Commercial Paper Rate at time, t

TB3MS_{t}=3-Month Treasury Bill: Secondary Market Rate at time, t

Data Issues

For the 3-Month Treasury Bill series we use the following from FRED:

(a) 3-Month Treasury Bill: Secondary Market Rate (TB3MS), Monthly, 1934-01-01 to 2011-09-01

The 3-Month Commercial paper series is unfortunately not so easy to deal with.  For one the series stops in 1997 and breaks off into two separate time series:

(b) 3-Month Commercial Paper Rate (DISCONTINUED SERIES) (CP3M), Monthly, 1971-04-01 to 1997-08-01

The two separate series include the financial commercial paper rate and the non-financial commercial paper rate:


(c) 3-Month AA Financial Commercial Paper Rate (CPF3M), Monthly, 1997-01-01 to 2011-09-01


(d) 3-Month AA Nonfinancial Commercial Paper Rate (CPN3M), Monthly, 1997-01-01 to 2011-09-01

To reconcile these issues, we take the average of the two and use them for the estimation of the Fed's policies over the second time period.

Second Dependent Variable: Long-term Risk Premium For Corporate Debt

For our long-term risk premium we choose to employ the 10 year Treasury Note rate as our risk-free rate because it shares the full promise of repayment by the United States Government.  Moody's Aaa rated securities aren't so lucky and therefore carry a risk premium associated with them. Although, the risk-premium for longer-term securities includes several things that are more acute under stress than our counterpart short-term risk premium. These include a heightened duration risk, liquidity risk and default risk.  We would expect our estimation of monetary policy effects on this variable to be more accurate as it theoretically should fluctuate more in response to actions taken by the Federal Reserve. The long-term risk premium is defined as follows:

LR^{premium}_{t}= BAA_{t} – GS10_{t}

where,

LR^{premium}_{t} =Long-term Risk Premium at time, t

BAA_{t} =Moody's Seasoned Baa Corporate Bond Yield at time, t

GS10_{t} =10-Year Treasury Constant Maturity Rate at time, t

Data Issues

All of the data here comes from FRED and there series details are listed as follows:

(a) Moody's Seasoned Baa Corporate Bond Yield (BAA), Monthly, 1919-01-01 to 2011-09-01


(b) 10-Year Treasury Constant Maturity Rate (GS10), Monthly, 1953-04-01 to 2011-09-01

Independent Variables: The Federal Reserve's Monetary Policy Toolbox

Our independent variables seek to capture the many tools the Federal Reserve can and has employed throughout its history.  This includes capturing the effects of traditionally unorthodox tools such as the manipulation of both the size (known as quantitative easing) and the composition (known as credit easing) of the Fed's balance sheet as well as capturing the effect from our more well known tools like changing the federal funds rate.  We will also seek to determine the effects of interest paid on reserves.


Accounting For The Size Of The Fed's Balance Sheet & Quantitative Easing

Our first and in the authors opinion most important independent variable seeks to capture the Fed's balance sheet effects on risk premiums.  It will be defined as the Feds holdings of credit market assets as a percentage of the total amount of assets held.  The more the Fed supports credit markets the larger this percentage will be.  It captures the balance sheets size as a percentage of the total market balance sheet. It is available over both our sample time periods and is therefore of pinnacle convenience to our analysis.  One special component of the balance sheet has been the holding of Treasury Securities. Before November of 2008, the Federal Reserve maintained a relatively small portfolio of between $700 billion and $800 billion in Treasury securities- an amount largely determined by the volume of dollar currency that was in circulation. In late November 2008 the Federal Reserve announced that it would purchase up to $600 billion of agency debt and agency mortgage-backed securities (MBS). In March 2009, it enlarged the program to include cumulative purchases of up to $1.75 trillion of agency debt, agency MBS, and longer-term Treasury securities. As mentioned previously, the use of the balance sheet for financial easing was initiated because the Federal Reserves main policy instrument, the federal funds rate had effectively reached the zero lower bound in late 2008.

Operationally we define this variables as:

FedBalance^{size}_{t}={CreditAssets^{Fed}_{t}\ CreditAssets_{t}^{total}}x 100

where,

FedBalance^{size}_{t}= the percentage of the total credit market assets the Fed owns at time, t

CreditAssets^{Fed}_{t}= Total Credit Market Assets Held by Domestic Financial Sectors - Monetary Authority (MATCMAHDFS) at time, t

CreditAssets_{t}^{total}= Total Credit Market Assets Held (TCMAH) at time, t

This variable is the percentage of the total credit market assets that the Fed holds. Its coefficient is meant to be negative so that as it increases market interest rate risk premiums decrease. It accounts for the effects of the size of the Fed's balance sheet. We expect this variable to have a negative effect on both short-term and long-term risk premia and therefore:

H_{0}: ß ≥ 0 vs. H_{a}: ß ≤ 0

Data issues

The data for this variable is available for extraction from FRED and are detailed as follows:

(a) Total Credit Market Assets Held (TCMAH), Quarterly, End of Period, Not Seasonally Adjusted, 1949-10-01 to 2011-04-01


(b) Total Credit Market Assets Held by Domestic Financial Sectors - Monetary Authority (MATCMAHDFS), Quarterly, End of Period, Not Seasonally Adjusted, 1949-10-01 to 2011-04-01

Monetary Policy & Credit Easing pt. 1: Background & Theoretical Considerations

An Introduction & Literary Review

Monetary Policy in the United States has traditionally been set to meet two objectives as defined in Federal Reserve Act; price stability and maximum employment.  In order to meet these goals the Federal Reserve manipulates the federal funds rate (FF) through a process called Open Market Operations (OMOs).  Unfortunately, when a recession is brought about by financial crisis this tool lose its potency and the economy enters into a "Liquidity Trap".  In a liquidity trap the FF is effectively at zero, and additional support is necessary to blunt the fall in asset prices and reduce measures of heightened financial stress. The Federal Reserve has recently enlisted a range of tools that are meant to provide further accommodation when their primary tool, the FF hits the lower bound.  These include manipulation of both the size and composition of its balance sheet, informational easing and paying interest on excess reserves.  We seek to formally investigate how these tools impact two important measures of financial stress, the long-term and short-term risk premia. 

There have been a slew of recent studies which seek to estimate the effects of Large Scale Asset Purchases (LSAP's) on Treasury Rates. Using an event-study methodology that exploits both daily and intra-day data, Krishnamurthy and Vissing-Jorgensen 2011 estimate the effects of both Quantitative Easing 1 and 2.  They find a large and significant drop in nominal interest rates on long-term safe assets (Treasuries, Agency bonds, and highly-rated corporate bonds).  

Sack, Gagnon, Raskin and Remache 2011 estimate the effects of large-scale asset purchases on the 10-year term preimium.  They use both an event-study methodology and a Dynamic OLS regression with Newey-West standard errors. They present evidence that the purchases led to economically meaningful and long-lasting reductions in longer-term interest rates on a range of securities, including securities that were not included in the purchase programs. Importantly, they find that these reductions in interest rates primarily reflect lower risk premiums, including term premiums, rather than lower expectations of future short-term interest rates.  

In 1966 Franco Modigliani and Richard Sutch wrote a seminal piece on Monetary Policy titled ``Innovations in Interest Rate Policy." In the paper the authors estimate the effects of ``Operation Twist", a policy by the Federal Reserve and the Kennedy Administration aimed at affecting the term structure of the yield curve.  In summary they find that the targeting of longer maturities has a rather minimum effect on the spread between short-term and long-term government debt securities.    

Bernanke, Reinhart and Sack 2004, estimate the effects of ``non-standard policies" when the Federal Funds Rate hits the lower bound.  They find that the communications policy can be used to effectively lower long-term yields when short-term interest rates are trapped at zero. They also find evidence supporting the view that asset purchases in large volume by a central bank would be able to affect the price or yield of the targeted asset.  This research was most likely the basis for the Feds actions taken over the course of the latest U.S. financial crises.  

Theoretical Model, Assumptions & Further Details

A risk premium is the amount a debt issuer has to pay in order to borrow above the interest rates on the safest of assets for a given maturity, m. By comparing interest rates on debt with the same maturity we are able to isolate the part of the spread that stems from duration risk from the other factors that influence the risk of default.  Additionally, by using only nominal debt instruments we remove elements in the spread that stem from inflation compensation.  

Risk premiums are thus defined as follows:

r_{m}^{premium} = r^{RR}_{m} - r^{Rf}_{m} 

Where,

 r_{m}^{premium} = Risk Premium for time till maturity, m

r^{RR}_{m}= Risky interest rate on nominal debt, for time till maturity, m

 r^{Rf}_{m} = Risk free interest rate for nominal debt, for time till maturity, m

In order to see what factors influence r_{m}^{premium} we have to analyze what moves the interest paid on the risk free interest rate, r^{Rf}_{m}, which is usually defined as some sort of United States Government debt, and the interest rate that carries risk, r^{RR}_{m}.  

Uncertainty and financial stress go hand in hand as  well documented in Charles P. Kindleberger's "Manias, Panics and Financial Crisis".  Historically during periods of high uncertainty, asset prices fluctuate wildly as more cautious investors cling to the safest assets (known as flight to safety) and the more bold investors bargain shop. Investors sell assets that carry r^{RR}_{m} and purchase those that carry r^{Rf}_{m}.  This causes the r_{m}^{premium} to increase dramatically and it becomes relatively more expensive for firms to access the capital markets to meet their funding needs.  There is a shortage of credit or credit crunch as debt issuers struggle to find buyers of their debt. 

In expansionary times the two interest rates that determine the risk premium move towards each other thus decreasing the risk premia.  Investors feel more confident and become hungry for yield, this leads to movement away from the risk-less lower interest carrying assets into riskier assets with a higher yield.  This pushes down the yield on the riskier assets and pushes the yield on the riskless assets up, thus making the return on these assets similar.   

Room For Policy

During periods of financial stress the Federal Reserve can reduce the risk premia and thus ease credit conditions by moving either r^{Rf}_{m} or r^{RR}_{m}.  The Fed has relied on the "portfolio balance channel" in order to reduce the financial stress felt by credit worthy firms.  As the Fed purchases Treasuries, yield hungry and  "crowded out" investors may purchase assets with similar credit ratings (like bonds with a AAA rating) in order to capture that increased yield differential thus lowing the yield on these assets.  

Brian P. Sack, Executive Vice President of the Federal Reserve, provided a great description of the Portfolio Balance Channel in a 2010 speech given at the CFA Institute Fixed Income Management Conference:

Under that view (portfolio balance channel view), our (the Fed) asset holdings keep longer-term interest rates lower than otherwise by reducing the aggregate amount of risk that the private markets have to bear. In particular, by purchasing longer-term securities, the Federal Reserve removes duration risk from the market, which should help to reduce the term premium that investors demand for holding longer-term securities. That effect should in turn boost other asset prices, as those investors displaced by the Fed’s purchases would likely seek to hold alternative types of securities.

All other things being equal the risk premia should decrease because the U.S. Treasury market is the most liquid market on earth. So the decrease in Treasury yields should be less than that of the less-liquid and risk-bearing assets.  

The Fed can also influence the risk premia by purchasing the risk bearing asset directly.  Examples of this include its implementation of the Commercial Paper Funding Facility (CCFF) and Agency Mortgage-Backed Securities Purchase Program (ABMBSPP).

Credit Easing is another channel the Federal Reserve has looked to exploit. Credit Easing policies involve changing the composition of the Fed's Balance Sheet from risk-less assets to riskier ones, all while keeping its size constant. Operationally it involves selling risk-free assets like 3 month T-bills to finance the purchase of risk-bearing assets like 3 month Commercial Paper. These assets have the same maturity m and the goal of the operation is accomplished as it circumvents the need to reduce the size of balance sheet. These policies lead to lower risk premiums as they increase the rate r^{Rf}_{m} on the risk-free asset being sold and decrease the r^{RR}_{m}, or interest rate on the risky asset being bought in the risk-free assets place.  This leads to additional easing as investors feel more certain that the market value of these assets will be supported by the Fed's holdings.  Removing the uncertainty leads to these riskier assets being transformed into less risky ones, thus increasing the appeal for them in periods of tumultuous financial stress.

In the next post we will delve into defining our dependent variables which seek to explicitly capture in risk premia while also looking at a few of our independent variables.  

Please people keep dancing into the new year,

Steven J.

Monetary Policy and Credit Easing

Here at the dancing economist, we wish to educate our followers on the finer points of economics and this includes econometrics and using R. R as mentioned previously is a free statistical software that enables regular people like us to do high end economics research. Recently, I wrote a paper on how the Federal Reserves actions have impacted both short-term and long-term risk premiums. In the next few blog posts I will be posting sections of the paper along with the R code necessary to perform the statistical analysis involved. One interesting result is that the Feds balance sheet although not previously manipulated was heavily involved in reducing long-term risk premia over the period from 1971 to 1997. The methodology in the paper involved performing a Generalized Least Squares procedure and accounting for residual correlation to achieve the assumptions as stated by the Gauss-Markov Theorem. More will follow,


Keep Dancing,

Steven J.

Paying Interest On Excess Reserves: From Theory To Practice

What is paying interest on excess reserves? It's a tool that the Fed created and has been using since October 1, 2008 to keep inflation in check.  The interest on excess reserves is the rate that the Fed pays depository institutions to keep excess reserves with the Fed.  The theory goes that by holding interest on excess reserves above the federal funds rate, there is an opportunity cost that is created which is the difference between the two interest rates.  FRED allows you to see this theory work in practice:

Notice that interest paid on excess reserves (the blue diamond line) has been at .25% and how an increase (decrease) in effective federal funds rate (red line) relative to interest on reserves leads to decreasing opportunity cost (increasing opportunity cost) associated with holding those excess reserves.  We have been observing that a decrease in the effective fed funds rate (relative to interest on excess reserves) leads to increased holdings of excess reserves (green line).  Many economists believe (including myself) that this Federal Reserve tool has been a main reason for inflation being subdued. 

Empire State Manufacturing Survey for June: Slightly Better?

Each month the Federal Reserve Bank of New York releases the Empire State Manufacturing Survey (ESMS) which tracks manufacturing activity in New York.  Although this particular survey does not necessarily shake markets up, the nice people at the Federal Reserve like to look at the ESMS because it provides hints on the forthcoming (and highly influential) Institute for Supply Management (ISM) Manufacturing Index (for a quick refresher).  It is designed to gauge the present condition of New York's manufacturing industries, as well as what company execs believe they will do in the next six months.
Positive index number indicates that more respondents believe that the index will move higher than lower.  A negative index number tells us that more respondents were expecting that variable to decrease than increase.

Things to notice when looking at the Empire State Manufacturing Survey:

1. General Business Conditions Index- where a positive index number is a sign that factory activity is strengthening. This index edged up slightly from 19.11 in May to 19.57 in June. 

2. New Orders Diffusion Index- where a jump in new orders is a good sign that factories will keep on producing.  We see a nice increase in new orders with the index rising from 14.3 in May to 17.53 in June. 

3. Unfilled Orders- which measures how overburdened (or under burdened) manufacturers are.  The larger the index number the more businesses may want to spend to expand production capacity to satisfy customers with snappier deliveries.  We have seen a nice improvement here as this index went from -7.89 in May to -1.23 in June.

4. Prices Paid- because the first signs of inflation appears here as factories ultimately pass higher costs onto consumers.  Keep in mind that the Fed monitors this section closely (price stability is part of the Federal Reserve's dual mandate).  Inflation does not seem to be as eminent on the horizon as it was last month but input prices are still expected to increase as this index moved from 44.74 in May to 27.16  in June.

5. Prices Received- as these help to forecast changes in corporate earnings. There is little change here as the index moved slightly downward from 5.26 to 4.94. 

6. Number of Employees- which is the earliest indicator available on labor conditions for the month.  This is where you preview changes in manufacturing jobs that could be seen in the official employment situation report.  Unfortunately we don't see the enthusiasm we saw last month in this indicator as it contracted from 22.37 in May to 12.38 in June.  This means that more firms this month than last month will be looking at lowering their number of employees and reducing their search for new hires.

From the NY Fed:

"The Empire State Manufacturing Survey indicates that conditions for New York manufacturers improved in June. The general business conditions index edged up from its May level to 19.6, extending its string of positive readings to eleven months. The new orders and shipments indexes were also positive and higher than their May levels. The inventories index remained near zero for a second straight month, indicating that inventory levels were little changed."

You know what's not going to occur this June 23rd?

An increase in the Federal Funds rate by the Federal Open Market Committee (FOMC).

Follow around the Federal Reserve's Board of Governors and you get a sense that the Fed is making it blatently clear.  From Chairman Bernanke's testimony to Congress:

"The latest economic projections of Federal Reserve Governors and Reserve Bank presidents, which were made near the end of April, anticipate that real gross domestic product (GDP) will grow in the neighborhood of 3-1/2 percent over the course of 2010 as a whole and at a somewhat faster pace next year.  This pace of growth, were it to be realized, would probably be associated with only a slow reduction in the unemployment rate over time. In this environment, inflation is likely to remain subdued. "

To begin with let us think about what the Fed is mandated by law to do (for a wonderful speech by Frederic S. Mishkin on this):

"to promote effectively the goals of maximum employment, stable prices, and moderate long-term interest rates"

This being said with the employment numbers so weak (with initial claims for unemployment insurance still around 456,000) and inflation not even poking its nasty head up to say hello, there is no way (by law) that the Federal Reserve will raise the Federal Funds rate.  With long-term inflation expectations stable and a struggling labor market why in the world would the Fed raise the interest rate?

Maybe, some should argue, that the zero bound interest rate will cause global imbalances elsewhere as investors search for the greatest yield.  This may lead to a rush of credit to fuel the next great bubble.  This leads me down the road to a third possible mandate: Financial Stability.  Financial stability is one thing, maximum employment and stable prices are certainly another.  The traditional monetary policy interest rate policy is way too blunt to deal with asset price bubbles and other threats to our economy.  So to deal with this problem, lets create a new mandate for the Fed.  Clearly I am not the first person to reach this conclusion- having first read something about this back in November of 2009:

"When it comes to redesigning monetary policy, there is disagreement as to how this might best be accomplished. Wharton finance and economics professor Franklin Allen believes more checks and balances could be built into the Federal Reserve system. “We need to have a third mandate - - a financial stability mandate,” he said."

An adaptive financial stability mandate would give the Fed power to monitor developments in the financial world and allow it to 'quickly' propose regulation to make the growth more balanced.  I know this sounds a little far fetched but why not?  If mortgage origination was such a rampant free for all, then why not have the Fed be alerted of the developments?  The Fed could theoretically be allowed to step in to find gaps in the regulation and the private sector could help:

 "A dynamic regulatory regime is most likely to be realized if it receives non-governmental perspectives on these changes. In addition to disclosing more data to investors and counterparties, exposing supervisory practices and policies to external assessment in a structured way can improve supervision. Such exposure could, for example, reduce the chances of regulators converging around a conventional wisdom that overlooks anomalous data."

If the Fed is allowed to extend credit to failing firms then it should be allowed to adaptively regulate those same firms.  For more on financial regulation, Daniel K.Tarullo of the Federal Reserves seems to be on the front lines.

Why I Keep The Beige Book Under My Pillow. . .

It gives me vivid dreams of whats to come in the economy and I like that, also it matches the color of my pillow case. The Beige Book is a summation of the 12 regional Federal Reserve Banks on whats currently occurring. It's a snapshot of the economy which is released 8 times a year, generally two weeks before the Fed's FOMC meetings. If you want to have some sort of a clue as to what the Fed will recommend at the next FOMC meeting then read the Beige Book and the Fed's speeches. The Beige Book is based on interviews with local business people and academics from each of the 12 regions. A look inside this report (The WSJ econ blog has its own tidbits here) reveals that economic activity has continued to improve but growth is at a "modest" pace.

Home sales and construction picked up till the end of the Home Buyers Tax Credit which expired on April 30th, and coincidentally in May these areas have been reported as slowing. Lower rents have pointed as a reason for increasing leasing activity in New York, Philadelphia, Richmond, Kansas City, Dallas, and San Francisco. One noteworthy extract is that some districts cited concerns over the potential impact of the European fiscal crises on financial and business conditions. These districts reported a corresponding increase in uncertainty and financial market volatility.

A look at Cleveland's report (since Cincinnati is a local branch) reveals that demand by business for new loans remains weak sauce. However, some bankers commented that the lending environment is starting to grow more competitive. This is generally consistent with yesterdays release of the Small Business Optimism Index . On a positive note, a large majority of the contacts reported that inventories are now well balanced which reflects increased demand. Furthermore, the number of respondents who plan on additional spending during the second half of 2010 has increased "substantially" since the last report.

For some Gulf oil spill action, the Atlanta Feds district said that contacts indicated the potential impact on the tourism industry along the coast line of Louisiana, Mississippi, Alabama, and western Florida could be substantial:

"In some cases, vacation lodging cancellations have been replaced by bookings for clean up crews, laborers, and the National Guard."

Natural Rate of Interest and the New Keynesians

What is the natural rate of interest? The natural rate is the equilibrium real interest rate consistent with price stability. The natural rate is an idea that originated with Knut Wicksell in 1896 and has been made use of by more recent studies of monetary policy like Michael Woodfords' mind bending Interest and Prices: Foundations of a Theory of Monetary Policy. Unfortunately for everyone the natural rate cannot actually be observed which makes it pretty unpractical in terms of actual monetary policy, but it can still be used as a nice theoretical tool to help explain output fluctuations. The New Keynesian natural rate is an equilibrium rate consistent with period-by-period price stability as opposed to a deviation towards a longer term trend. Some New Keynesian models emphasize the "real rate gap"-which is the difference between the actual short-term real interest rate and the natural rate- as a principle source of Aggregate Demand driven imbalances. When output is equal to natural GDP, the natural rate is equal to the equilibrium real interest rate. This implies that real rigidities that prevent GDP from approaching natural GDP also prevent the real rate from approaching the natural rate.

A typical New Keynesian model has firms engaged in Monopolistic Competition and prices are assumed to be sticky. This leads to the horizontal short-run aggregate supply curve so output is demand determined. Household's and firms are assumed to act rationally, which implies they form expectations rationally. Consumption and investment decisions cause output to be affected by the private sectors expectations of future interest rates and future values of the natural rate. This framework is in equilibrium when current and expected real rate gaps are zero, GDP and natural GDP are equal and the price level has no tendency to change. The only reason i like the idea of a natural rate of interest is because it can be used to explain how imperfections in the financial markets can impact the real economy. Various market imperfections (including risk premia and credit rationing due to asymmetric information, incomplete indexation, and expectational errors by market participants) cause the real rate to deviate from the natural rate leading to a misallocation of credit.

Success of the Fed's Currency Swap Program

The Federal Reserve Bank of Cleveland's Credit Easing Policy Tools have all the graphs and download friendly data sets on the Fed's discretionary policy actions. This rather neat tool allows us to see the effects of the Fed's currency swap program on the LIBOR-OIS spread. To address international funding pressures the Federal Reserve introduced reciprocal currency arrangements with other Central Banks. One recent finding suggests that dollar funding pressures have tended to moderate following large increases in dollars lent under the new swap line program. Additionally, in a process called "informational easing" swap line announcements have been associated with improved conditions (i.e. lowering of the basis) in these markets. As the graph shows the most recent spike in the LIBOR on May 19th caused only a small withdrawal of funds. The successful use of these currency swaps to calm market fears and help meet global demand for dollars should be taken seriously as this is one tool that could prove invaluable for the Fed.

The dangers of financial liberalization

The WSJ Economics blog recently highlighted a paper written by Ke Tang at Renmin University in China and Wei Xiong at Princeton University about how commodity prices are becoming increasingly more correlated with stock prices. This finding has to do with it becoming easier for investors to move in and out of commodities markets. Greater financial liberalization will mean increased volatility within a market as the prices of commodities will now be based more off of market sentiment, animal spirits and speculation rather than actual supply and demand and mark-up. There are also implications for monetary policy because a spike in investor optimism (pessimism) will cause input prices to increase (decrease) leading to greater uncertainty as to the direction of inflationary expectations. Fluctuations in stock prices have important household and firm wealth effects and similarly fluctuations in commodities may lead to the destruction of many firms balance sheets.

We can see this with a simple example:
“Company A” in Michigan's Upper Peninsula deals with the mining and production of copper and "company B" makes copper tubing. B buys copper from A at a set market price "P". Then say there is an unrelated debt crisis in the euro-zone that shakes up investor confidence in everything from bond markets, stock markets and commodities so that a sudden drop in the price of copper worldwide occurs. Company B who now has to pay the original market price P finds that they also have to charge less for their copper tubing. This is because the tubing price is based off of the current market price per pound plus some service markup. Not only did company B already order this copper from company A at price P but now they have to charge less than it cost them to purchase it thus leading to a potentially crippling loss.

I guess the lesson here is that without stable expectations we may suffer from further bankruptcies. One of the reasons that the Fed controls the price level so well is that they convince people that the price level will change by a set amount. Unfortunately it is extremely unrealistic to create a Fed for the stock market or commodities markets to ensure slow and rising asset inflation. Instead we have a bunch of profit seeking investors searching for the greatest yield. Goods and services are determined by supply and demand and the rest of the mark-up comes from expected inflation. When something get financially liberalized its price is no longer a function of the market conditions (supply/demand/mark-up) it becomes a function of continuously changing expectations.

A further example may help illustrate my point. Assume tv's get financially liberalized and people sell and buy tv's based off their expectations about others demand for tv's. We would see drastic changes in tv prices that would not necessarily reflect supply and demand as a dramatic fall or rise in the price of tv's would put electronics stores out of business or in business. Waves of optimism and pessimism might impact their prices while not necessarily reflecting the true cost of production and mark-up.

For the opposite view...

After writing the previous post on why budget deficits are a negative thing for the economy I stumbled upon an article that justified them. The Levy Economics Institute of Bard College recently released a Public Policy Brief on why we should stop worrying about U.S. Government deficits. The authors Yeva Nersisyan and L. Randall Wray point out that a budget deficit is just a transfer from the government to the private sector and that surpluses are the exact opposite net transfers from the private to government sector.
Furthermore, they dispute the often heard claim that deficit spending today burdens our grandchildren:

"in reality we leave them with government bonds that represent net financial assets and wealth. If the decision is made to raise taxes and retire the bonds in, say, 2050, the extra taxes are matched by payments made directly to bondholders in 2050”

Today's deficit leads to debt that must be retired later, and future tax increases that are supposed to service tomorrow's debt represent a redistribution from taxpayers to bondholders. Although this may be undesirable given that bondholders are wealthier than tax payers, but if one takes into account the U.S. progressive tax system it may just represent a transfer from taxpayers back to taxpayers. This is a reasonable perspective given that we as public bondholders get repaid even if it is a discriminating redistribution of income taxes back to rich people who could afford the bonds from poor people may not hold any bonds.

A government deficit is a transfer of income from the government to the private sector in the form of non-government income.

"A government deficit generates a net injection of disposable income into the private sector that increases saving and wealth, which can be held either in the form of government liabilities (cash or Treasuries) or noninterest-earning bank liabilities (bank deposits). If the nonbank public prefers bank deposits, then banks will hold an equivalent quantity of reserves, cash, and Treasuries (government IOUs), distributed according to bank preferences."

A surplus has the opposite effect as increased tax revenue from the private sector lead to a reduction in wealth and in order to maintain the same standard of living the private non-government sector has to borrow more.

"A government budget surplus has exactly the opposite effect on private sector income and wealth: it’s a net leakage of disposable income from the nongovernment sector that reduces net saving and wealth by the same amount. When the government takes more from the public in taxes than it gives in spending, it initially results in a net debit of bank reserves and a reduction in outstanding cash balances."

One important argument made is that the largest part of the current deficit results from automatic stabilizers like transfer payments and unemployment benefits. The flipside to increased unemployment benefits as the economy goes through a contraction is their tendency to fall back down as the economy recovers. As the leading driver of the deficit they are also the main reason for the reduction in the debt/gdp ratio as the economy expands. Along with increased unemployment, tax revenues that fall during the recession pick up during the expansionary phase.

In defense of Obama's stimulus:

"These automatic stabilizers, not the bailouts or stimulus package, are the reason why the U.S. economy has not been in a free fall comparable to that of the Great Depression. When the economy slowed, the budget automatically went into a deficit, placing a floor under aggregate demand."

After reading this article, one highly theoretical argument that I can make is that if the United States was forced to monetize part of the debt it could raise interest on reserves to soak up any additional liquidity created in the system. This would represent a massive transfer of Government debt from the Treasury to the Fed in the form of excess reserves. The excess reserves could then be manipulated with the appropriate raising and lowering of the interest paid on reserves relative to the federal funds rate. This is quite an exciting premise that represents an internal transfer of funds by the U.S. Government that would keep inflation expectations stable while also calming the fears of deficit hawks.