The estimation of the structural model, controlling for expansion and recession, yields the following table which shows significant differences in some estimated elasticities between the two models (expansion versus recession). We also observe that some signs are inverted from positive to negative, or vice versa, between two situations in the equation of interest rate and private investment. This shows that some behaviours are changing over the business cycle, which may explain the differences in fiscal multipliers between periods of expansion and recession.
Model’s estimation controlling for expansion | Model’s estimation controlling for recession |
\({r}_{t}=\underset{(.256)}{.129}{y}_{t}+{\underset{(.287)}{.311}{\pi }_{t}+e}_{1t}\) \({d}_{t}=\underset{(.174)}{-1.05}{y}_{t}\underset{(.355)}{-1.12}{\pi }_{t}\underset{(.087)}{-.308}{r}_{t}+{e}_{2t}\) \({y}_{t}=\underset{(.018)}{.167}{i}_{t}+\underset{(.029)}{.209}{\pi }_{t}-\underset{(.020)}{.017}{r}_{t}+{e}_{4t}\) \({\pi }_{t}=\underset{(.030)}{-.024}{r}_{t}\underset{(.021)}{-.005}{i}_{t}+{e}_{5t}\) \({i}_{t}=\underset{(.605)}{-.636}{y}_{t}\underset{\left(2.07\right)}{-2.13}{r}_{t}+{e}_{6t}\) \({g}_{t}={e}_{3t}\) | \({r}_{t}=-\underset{(.192)}{.071}{y}_{t}+{\underset{(.279)}{.383}{\pi }_{t}+e}_{1t}\) \({d}_{t}=\underset{(.181)}{-.639}{y}_{t}\underset{(.354)}{-1.20}{\pi }_{t}\underset{(.088)}{-.269}{r}_{t}+{e}_{2t}\) \({y}_{t}=\underset{(.021)}{.163}{i}_{t}+\underset{(.032)}{.245}{\pi }_{t}-\underset{(.024)}{.016}{r}_{t}+{e}_{4t}\) \({\pi }_{t}=\underset{(.031)}{-.022}{r}_{t}\underset{(.021)}{-.009}{i}_{t}+{e}_{5t}\) \({i}_{t}=\underset{(.368)}{.378}{y}_{t}\underset{\left(1.25\right)}{-1.15}{r}_{t}+{e}_{6t}\) \({g}_{t}={e}_{3t}\) |
(…) are standard errors |
Next, we produce the impulse response functions to structural shocks of the interest rate (shock1), public debt variable (shock2), private investment (shock3) and public expenditure (shock6) for the variables of, output, investment, inflation, interest rate and debt. We produce these IRFs for eight cases: two controlling for the business cycle periods (expansion versus recession), two controlling for debt ratio movements (accumulation versus reduction) and four cases controlling jointly for the business cycle and debt movements (expansion and debt accumulation/reduction and recession and debt accumulation/reduction). These outputs are displayed in Appendix (Figs. 1.a to 1.h).
To shed more light on the effects of fiscal variables on output, inflation, and private investment, we prefer to focus on the corresponding IRFs, which we reproduce in this section. For the effects of the innovations of public debt (shock2) on output, private investment and inflation, Fig. 2 shows clearly in the first row corresponding to the expansion model’s IRFs that public debt increase has a deflationary effect on the other variables by reducing economic growth, especially through crowding out private investment in the United States and inducing an increase in government expenditure. However, in times of recession (the second row of Fig. 2), an increase in public debt is likely to increase growth by stimulating private investment and inflation while keeping the interest rate reduced in the second quarter and pushing up government expenditures. We also observe that the effects are generally delayed by one quarter and are at their peaks in the second or third quarter, while fading away at the fourth or sixth quarter, except for inflation, which has a long-term persistence.
Figure 2. Responses to a structural shock of the government public debt ratio (shock2) in times of expansion
(first row of charts) and recession (second row of charts)
For the effects of the structural innovations of total government expenditure (shock6, in Fig. 3) in periods of expansion and recession, we note that the effect is immediate and high (in the first quarter), especially for the response of GDP, private investment and the public debt ratio. The effects of government expenditure are generally independent of the business cycle effects, except for the inflation variable being reduced in times of expansion and pushed up in times of recession. For the periods of expansion and recession as well, an increase in government expenditure is likely to immediately increase the output and then reduce the public debt ratio, while inducing an increase in the interest rate, especially in the second quarter, to counter the inflationary effects, albeit less important, in times of recession. However, this reduction of the public debt ratio could be a consequence of an algebraic computation of the increase of GDP being the denominator of the debt ratio variable. An important point is that all the responses are very short-lived (the effects occur and fade way within the first year), except for the reaction of the prices. In concordance with the public debt and government expenditure effects, we can conclude that expenditure multipliers are mainly weakened in times of expansion and increased in times of recession by the effects of the public debt that crowd out the private agent decisions of investing, while the effects of fiscal policy are positive and short-lived, independent of the business cycle.
Figure 3. Responses to a structural shock of government expenditure (shock6) in times of expansion
(first row of charts) and recession (second row of charts)
For the effects of debt movements (Figs. 4 and 5), we observe almost the same findings about the reactions of the variables as those observed for the business cycle, except for prices (inflation and interest rates). A structural innovation of the public debt ratio is likely to reduce output by crowding out investment and may have a deflationary effect when debt is accumulated. However, in times of decumulating public debt, the effects of the public debt increase on output, investment and prices are positive (Fig. 4). For the effects of government expenditure, they are positive on output and investment, while reducing public debt. The prices’ reactions are slightly different for debt accumulation and debt reduction cases.
Figure 4. Responses to a structural shock of the public debt ratio (shock2) in periods of debt accumulation
(first row of charts) and debt contraction (second row of charts)
of debt accumulation (first row of charts) and debt contraction (second row of charts)
For the effects of the business cycle and debt movements, we produce the four cases (Figs. 6 to 9). A structural innovation of the debt in periods of debt accumulation and expansion decreases simultaneously the GDP, investment and prices (inflation and interest rate), while increasing government expenditure (first row of the panel in Fig. 6). For periods of debt accumulation in recession (second row of Fig. 6), the effects are opposite (positive) on the first three variables, while the reaction of the interest rate and government expenditure have almost the same shape as in the first case. For the effects of government expenditure (Fig. 7), they are short-lived and almost the same, independent of the two considered cases.
For the government debt reduction case (Fig. 8), jointly with the business cycle, unlike the case where debt is accumulated, the responses to the public debt structural shock are slightly different over the business cycle for private investment and interest rate, while they seem to behave the same way for the other variables, between the two situations. In particular, the output, investment and inflation are positively affected in the first year with persistent effects for inflation. For the response to a structural shock of the public expenditure in debt reduction and the business cycle (Fig. 9), the effect is almost the same as with debt accumulation (Fig. 7).
The constructed SVAR model, containing fiscal and monetary variables, sought to explain why the fiscal multipliers are weaker in expansion than in recession. In times of high public debt, and particularly expansion, an increase in public debt ratio crowds out private investment, hence reducing output. By contrast, the government expenditure effects on output are all positive in the short term, independent of the public debt development and the business cycle.