The CBO's assumptions are fundamentally flawed

CBO assumption:

"When the federal government borrows, it increases the overall demand for funds, which generally raises the cost of borrowing and reduces lending to businesses and other entities; the eventual result would be a smaller stock of capital and lower output and income than would otherwise be the case, all else being equal. 

The large amount of debt might restrict policymakers’ ability to use tax and spending policies to respond to unexpected future challenges, such as economic downturns or financial crises. Continued growth in the debt might lead investors to doubt the government’s willingness or ability to pay its obligations, which would require the government to pay much higher interest rates on its borrowing."

The 1980s peak in interest rates came at a time when Gov debt/GDP was below 30%!

That assumption is false.  At that very least, low rates coincide with the private sector holding a greater % of government treasury securities relative to nominal gross domestic income (US Government Debt/NGDP). 

Here is a model/narrative to think about why this could be. 

When private investment spending slows or declines on aggregate, demand for private credit slows or declines as firms issue fewer liabilities (especially debt) to fund such expenditure.  A slowdown in spending reduces the demand for labor and overall employment.  Lower employment leads to greater social insurance spending by the government.  It also leads to lower tax receipts relative to a fully employed domestic economy as taxable transactions in the economy slow or fall.  An increasing in spending and a reduction in tax revenues very well may cause the government to run a budget deficit (or a larger deficit as was the case with the US after the financial crisis).  This means that treasury issuance will increase.  It's important to note that the cyclical component of the fiscal budget position is an outcome that endogenously results from the overall level of real economic activity which the government can influence, but not solely determine.  The above should also highlight how government debt held by the private sector will rise during periods when GDP remain depressed.  This causes the government debt/GDP ratio to rise.   

When the government runs a budget deficit, it issues treasuries and receives deposits in return.  The non-government sector also retains the deposits which the government recycles when it spends.  Therefore, when the government runs a larger deficit, the non-government sector of the economy runs a larger surplus as they are in possession of newly issued treasury securities.  As Gary Gorton has pointed out, treasury securities are a stabilizing force in the system as they provide collateral which the non-government sector can use to safely expand credit (via the repo market).  In doing so, spending and income growth are stabilized.  In a situation where the economy remains depressed, a reduction in government's budget deficit very well could cause the government's debt/GDP ratio to rise not fall as aggregate income (NGDP) slows or declines.  In order to allow this ratio to fall safely, the government must work to aid the private sector in generating stronger economic conditions. 

The federal budget deficit (blue) worsened as Nominal Gross Domestic Income (green) declined during the Great Recession.  The Fed responded by targeting a lower policy interest rate (red).  Thus, large deficits coincided with economic weakness and low interest rates.  The opposite occurs during expansions.

Moreover, the Fed has policy goals based on their duel mandate which have been assigned to them by Congress. 

Chicago Fed: The Federal Reserve's Dual Mandate

"The Board of Governors of the Federal Reserve System and the Federal Open Market Committee shall maintain long run growth of the monetary and credit aggregates commensurate with the economy's long run potential to increase production, so as to promote effectively the goals of maximum employment, stable prices and moderate long-term interest rates."

Fed Board of Governors: What are the Federal Reserve's objectives in conducting monetary policy?

"The Congress established the statutory objectives for monetary policy--maximum employment, stable prices, and moderate long-term interest rates--in the Federal Reserve Act."

Therefore, when the economy fails to produce maximum employment in the context of price stability, the Fed reacts by targeting a lower fed funds rate which reduces the cost of overnight borrowing between banks in the banking system.  To target a lower FF rate, the Fed conducts open market operations by buying (removing) treasury securities from the private sector in exchange for Fed reserves.  The Fed credits the banking system's reserve account at the Fed and the banking system credits the bank account of the member of the private sector that sold the treasury security. 

This is an asset swap where the Fed removes one government security (treasuries) for another (Fed reserves).  A lower FF rate reduces the interest costs within the banking system.  Therefore in a competitive banking system, banks will pass on these reduced costs by buying loans/bonds from the private sector at a reduced interest rate. 

​A lower FF rate and the removal of treasury securities affect long term interest rates in the follow ways:

Long-term interest rates are a series of future short-term rates

"The facts strike me as consistent with two different views. In one account, long rates are pinned by arbitrage to the expected path of short-rates plus a risk premium, and market participants have become increasingly certain that nominal interest rates will be very low for a very extended period. In a second account, important clienteles of investors do not consider money issued by the Fed and debt issued by the Treasury, particularly long-term debt, to be close substitutes. These investors have basically been starved of new Treasury supply, and so have bid up bond prices, in order to draw supply from the inventory of investors less wedded to maturity."

Thus, long term interest rates on treasury securities reflect the expected path of future short-term rates which the Fed anchors.  As the Fed responds to economic conditions via the dual mandate, the spread between nominal long term rates relative to short term rates reflects the market's expectations pertaining to the future state of the economy and nominal GDP. 

To conclude, when economic activity is weak and below potential, the government's debt to GDP will tend to rise while the Fed's policy interest rate target declines or remains depressed.  Low short term rates are a reflection/sign that the past policy mix has created the present conditions where nominal income/spending growth ​​is ​not high enough to support full employment or the Fed’s inflation target.  If the market expects that this weakness will persist where the current and expected policy response isn't sufficient enough to counter this, then long term interest rates on treasury securities will also fall or remain at the low levels which prevail today.  Thus, low and/or falling short and long term interest rates suggest that the policy mix (monetary, fiscal, and credit regulations) was and continues to be too tight. 

So no, a US government* debt/GDP ratio that is rising endogenously often coincides with falling interest rates on government treasury securities.  This is quite the opposite of the dangerous story being promoted by the CBO.

*It’s incredibly important to note that the above reflects conclusions which derive from the institutional design of the US monetary and financial system where the US government is a monetary sovereign.  The FOMC is beholden to the Congress in the way they conduct monetary policy (expand or contract their balance sheet).   

Suggested Reading:
Will the US soon have a budget surplus?
My comments on comments on the CBO report