Tech. Note: Which U.S. Administration is Fiscally Responsible?

(1) s_t = α + Βb_t-1 + γg_t + e_t, where e_t~i.i.d.

Where s, b and g are the share of primary surplus to GDP, the share of government debt to GDP, output gap, respectively.  Primary surplus is defined as government tax revenues net of government spending, and it is equal to government deficit excluding the debt service component.  Output gap is deviation of real GDP from its potential.  Sustainability requires Β>0: as debt accumulates, the government has to generate a primary surplus.  It can do this either by reducing the spending or increasing taxes or both.  This is a partial equilibrium model that ignores the secondary effects of a change in debt and deficit on interest rates and the feedback to the government budget.  The impact of business cycles is proxied by the variable gap.  When GDP rises above its potential, primary surplus is expected to rise, γ>0.

In order to introduce the political economy dimension in our analysis we include two multiplicative dummy variables on the coefficients of debt/GDP and output gap.  DUM_D represents the years with a Democratic President Administration (DP Administration) and  DUM_R = 1 – DUM_D the years with a Republican President Administration (RP Administration).  The model then becomes:

(2) s_t = α₀ + Β₁DUM_Db_t-1 + Β₂(1-DUM_D)b_t-1 + γ₁DUM_Dg_t + γ₂(1-DUM_D)g_t + ε_t

Data and Methodology

All data come from Bureau of Economic Analysis except potential GDP that is from CBO and are from 1976 to 2017 and is annual.  We divide the sample into two, democrats and republicans.  Each subsample consists of the years during which the president from one of the parties is in power.   covers the years 1966-68, 1977-1980, 1993-2000, 2009-2016 and  the years 1969-76, 1981-92, 2001-08, 2017.  We first test the stationarity of each variable.  Tests reject non stationarity of all the first differenced series at the 5% confidence level (10% level for debt/GDP) suggesting that they are integrated of order one.  To control for the impact of recessions on the estimation, we generate a dummy variable, recess, where we indicate with 1 each NBER recession period from peak to through and include it as an exogenous variable into the estimation equation. 

The VAR lag order selection criteria (Table 1, top panel), such as Likelihood Ratio, FPE, and Akaike information criteria indicate that 4 lags are optimal.  Since for small samples AIC is more appropriate, we select 4 lags.  Both the Trace test and the maximum Eigenvalue test in the Johansen Full Information Maximum Likelihood (FIML)test suggests one cointegrating equation for three model assumptions concerning deterministic trends (Table 1, lower panel).  We select the more flexible model that allows for linear deterministic trend in the data and no intercept in the VAR, which is also supported by Schwarz criteria. 

Next, we proceed to build a Vector Error Correction Model (VECM) with 3 lags determined optimally as described above:

(3) Δy_t = -Πy_t-1 + ∑_i=1 Φ_jΔy_t-i + u_i,

where y_t = [s_t, b_t-1, g_t]’, Π = (I-∑_i=1A_i) and Φ_i = -∑_i=1A_j = -A(L).

We present below the impulse responses (IRs) for 10 periods.

Results

Table 2 presents the long-run cointegration relations under the two administrations.  An increase in the debt/GDP ratio generates a primary surplus in the economy, irrespective of the political party in the administration, indicating that the US government is overall fiscally responsible and does not let debt accumulate without reacting to it.  This suggests that the US debt is sustainable.  As expected, an increase in output gap, i.e. a rise of GDP above its potential is associated with an increase in the primary surplus, under both administrations, spurred by higher tax revenues.  However, quantitatively both estimates are starkly different under both administrations.  When the debt/GDP ratio goes up, over the long run, DP Administrations generate a primary surplus that is twice larger than that of a RP Administration to pay the debt back, suggesting that unsustainability of debt is likely to become a bigger issue under the latter.  Similarly, a positive output gap creates a larger surplus under a DP Administration than RP one.

Do these results also hold in the short run?  To answer this question, we now turn to impulse response functions.  Table 3 (Figure 3 in the text) illustrates the response of the primary surplus to one percent change in the innovation of the lagged debt/GDP ratio.  Here also the short-run results are consistent with the long-run results.  When debt rises by 1% a democratic administration starts generating a surplus immediately following the year when debt rises and starts reducing it.  It continues doing so every period and at the end of the 8^th year, it accumulates 1.59% surplus, more than   A Republican President Administration, however, allows the primary deficit to continue throughout the fourth year, turns the budget into a surplus only after a large lag and at the end of the eighth year accumulates a surplus of only 0.36%. 

In practice, once recovery takes place, with a virtuous cycle the primary surplus continues to rise independent of government’s reaction and reins in debt accumulation, as can be seen from the full-sample reaction function (Figure 3, left panel).  Although the impact of the business cycle is controlled for, as mentioned above, this is a partial equilibrium model and ignores other channels through which debt and deficit interact with each other, such as change in the cost of borrowing, external and internal factors.  Yet, it also isolates the reaction of the government under various administrations, which the raw data hint at in Figures 1 and 2.

Table 1: Lag and Rank Order Selection

Lag order

Rank Order

*Critical Values based on MacKinnon-Haug-Michelis (1999).

Table 2 : Cointegrating Equations

5% t-statistics are in parentheses.

Table 3 Impulse Response of primary surplus to a 1% change in debt/GDP

[1] See Bohn 1995, and Uctum at al. 2006, Polito and Wickens 2012 for literature review and application.

References

Bohn, H. 1995. The sustainability of public deficits in a stochastic economy.  Journal of Money, Credit and Banking 27, 257-271.

Polito, V. and Wickens, M. 2012. A model based indicator of the fiscal stance. European Economic Review 56, 526-551.

Uctum, M. Thurston, T. and Uctum, R. 2006. Public debt, the unit root hypothesis and structural breaks: a multi-country analysis.