Economic theory posits that the effect of the deficit on long-term interest rates is an important channel through which the deficit affects the real sector of the economy. The dynamics of the relationship between the deficit and long-term interest rates is essentially an empirical question, which this paper attempts to address. I measure the expected deficit as the CBO's projected deficit 5 years ahead as a ratio of potential GDP.

A review of the literature by Seater (1993) finds support for the Ricardian equivalence hypothesis, which implies that federal debt does not affect interest rates. First, the non-linearity in the impact of the expected deficit on interest rates has not been addressed in the literature to the best of my knowledge. The imposition of the variable 𝑒𝑝𝑡 in the regression (and in the VAR) is due to a different restriction.

In the full sample, a percentage point increase in the projected GDP deficit ratio raises 5-year-ahead interest rates by 16 basis points. Similarly, in the full sample, a percentage point increase in the projected GDP deficit ratio raises interest rates 10 years ahead of 5 years by 18 basis points. To investigate the nature of the impact on future interest rates of the expected deficit, I now perform a Threshold VAR, so that I can introduce richer dynamics between the variables.

The specifications of the VAR threshold and impulse responses are discussed in the next section.

## Threshold VAR

Not only is Hansen's method more robust to a small sample size, the asymptotic theory developed by Hansen helps construct a confidence interval around the estimated threshold value, which Tsay's test does not take into account. An important difference between my specifications and those used in the literature is that I do not introduce such an additional variable, but instead restrict one of the endogenous variables of the VAR (projected deficit) to the threshold variable. Although introducing a measure of the output gap as a threshold variable would be quite simple, the nature of the question I am asking makes such a measure problematic.

When I ran the asymptotic test in the single equation framework of the type in Equation 5, I also found no nonlinear effect of the expected output gap on future long-term interest rates. In my version of the threshold VAR, 𝑥𝑡 = [𝑅𝑟𝑡, 𝑑𝑡, 𝑦𝑡], where all the variables are those used in the single equation regression except 𝑅𝑟𝑡, which is the real 5-year interest rate minus expected long-term inflation the nominal. Again, the expected nature of the variables is implicit in the notation, as explained in section 3.

I present my main results in the form of impulse response functions (henceforth IRFs) estimated in the usual way. In a 'low' deficit regime, the effect is a small drop in the real interest rate of 3 basis points, which returns to pre-innovation levels within 6 months. One way to interpret the results of my VAR threshold is to think of the novelty of the projected deficit variable as a revision of the market's expectations of the future deficit independent of the CBO forecast.

The friend's Smyce can also be thought of as private CBO information that becomes public. In a regime where economic agents already expect the deficit to be high in the future, any revision of such projections is likely to have a large and significant impact on future real interest rates (agents expect interest rates to in the future to be high). To see how robust my results are to the nature of the data as well as the single equation regression and Threshold VAR specifications, I run the entire exercise using an alternative measure of the equity premium and using additional data on government spending projections and projection error in my VAR.

The results of such exercises are qualitatively and quantitatively similar to what I present in my main results, both in the single equation Threshold Estimation Model and in the VAR. I also test the sensitivity of my result in the single equation to the threshold value of deficit/GDP that is estimated. The VAR impulse responses are also robust to different ordering of the variables in the Cholesky ordering as long as I order slower moving variables last11.

## Conclusion

The VAR structure, while imposing minimal if theoretical limits on dynamics, controls for the fact that part of the projected deficit will have to include future interest payments and GDP growth rates. However, this effect is positive and significant (both economically and statistically) in the "high regime", when the economy expects the future deficit to be higher than a certain threshold (deficit-to-GDP ratio of 1.8). The size of the impact is 30 basis points for a one percentage point increase in the expected deficit/GDP ratio.

I use the estimated threshold value of deficit and use a threshold VAR to examine the dynamics of the impact of a structural shock on deficit expectations at long-term rates. The result of this paper suggests that any such revision will have a significant impact on future interest rates (thus future investment, consumption and saving) in a scenario where deficit expectations are already high. This evidence is not only interesting for policymakers in designing debt stabilization strategies, but it can also help reconcile conflicting predictions about the effects of deficits on interest rates across different types of macroeconomic models.

A new implication of my result is that it may be worthwhile for policymakers to include the management of deficit expectations in their policymaking framework. This will be particularly effective in a scenario of high deficit expectations, where an upward revision (“bad news”) of deficit projections has the potential to raise interest rates in the future. An Empirical Characterization of the Dynamic Effects of Changes in Government Expenditures and Taxes on Output', Quarterly Journal of Economics.

The impact of budget deficit forecasts on interest rates in the United States and other G-7 countries, Working Paper, Federal Reserve Board. Budget Deficits, National Savings, And Interest Rates', working paper, Tax Policy Center and Brookings Institution. New Evidence on the Interest Rate Effects of Budget Deficits and Debt', Journal Of The European Economic Association.

Estimating the threshold in the regression using the 5-year forward interest rate and the 5-year 10-year interest rate as the dependent variable. 90% F Test for the presence of the Threshold effect of the expected deficit in 5-year forward interest rates. For forward 5-year interest rates, the bootstrapped P-value for the F sequence greater than the 95% critical is 0.052; therefore the line almost touches the 95% critical line, but crosses the 90% critical line.

95% F Test for the presence of Threshold effect of expected deficit in 5-year interest rates in 10 years. The average of one-year forward rates 5-9 years ahead, calculated from the zero-coupon yield curve sampled on the last trading day of the CBO publication month. Average of forward one-year rates 5-14 years ahead, calculated from the zero-coupon yield curve sampled on the last trading day of the CBO publication month.

Equity premium: Calculated as the dividend component of national income, expressed as a percentage of the market value of corporate equity held (directly or indirectly) by households.