Is it the “How” or the “When” that Matters in Fiscal Adjustments?

Abstract

Using data from 16 OECD countries from 1981 to 2014 we study the effects on output of fiscal adjustments as a function of the composition of the adjustment—that is, whether the adjustment is mostly based on spending cuts or on tax hikes—and of the state of the business cycle when the adjustment is implemented. We find that both the “how” and the “when” matter, but the heterogeneity related to the composition is more robust across different specifications. Adjustments based upon permanent spending cuts are consistently much less costly than those based upon permanent tax increases. Our results are generally not explained by different reactions of monetary policy. However, when the domestic central bank can set interest rates—that is outside of a currency union—it appears to be able to dampen the recessionary effects of consolidations implemented during a recession.

Appendices

Appendix 1: Predictability and Exogeneity

In a dynamic time-series model, estimation and simulation require, respectively, weak and strong exogeneity: these requirements are different from lack of predictability. To illustrate the point consider the following simplified model, which only includes the unanticipated component of fiscal plans:

$$\begin{aligned} \Delta y_{t}&= \beta _{0}+\beta _{1}e_{t}^{u}+\beta _{3}\Delta y_{t-1}+\beta _{4}\Delta \tau _{t-1}+\beta _{5}\Delta g_{t-1}+u_{1t}\\ e_{t}^{u}&= \gamma _{1}\Delta y_{t-1}+\gamma _{2}\Delta \tau _{t-1}+\gamma _{3}\Delta g_{t-1}+u_{2t}\\ \left( \begin{array}{c} u_{1t}\\ u_{2t} \end{array}\right)&\thicksim N\left[ \left( \begin{array}{c} 0\\ 0 \end{array}\right) ,\left( \begin{array}{cc} \sigma _{11} &{} \sigma _{12}\\ \sigma _{12} &{} \sigma _{22} \end{array}\right) \right] \end{aligned}$$

The condition required for $e_{t}^{u}$ to be weakly exogenous for the estimation of $\beta _{1}$ is $\sigma _{12}=0.$ This condition is independent of $\gamma _{1},\gamma _{2},\gamma _{3}.$ In other words, when weak exogeneity is satisfied, the existence of predictability does not affect the consistency of the estimate of $\beta _{1}.$ Moreover $\beta _{1}$ measures, by construction, the impact on $\Delta y_{t}$ of $u_{2t},$ i.e., of the part of $e_{t}^{u}$ that cannot be predicted by $\Delta y_{t-1}$, $\Delta \tau _{t-1}$ and $\Delta g_{t-1}$. In fact, by the partial regression theorem, estimating first $\overset{\wedge }{u_{2t}}=e_{t}^{u}-\overset{\wedge }{\gamma _{1}}\Delta y_{t-1}+\overset{\wedge }{\gamma _{2}}\Delta \tau _{t-1}+\overset{\wedge }{\gamma _{3}}\Delta g_{t-1}$ and then $\delta _{1}$, running $\Delta y_{t}=\delta _{0}+\delta _{1}\overset{\wedge }{u_{2t}}+v_{t}$, gives $\overset{\wedge }{\beta _{1}}=\overset{\wedge }{\delta _{1}}.$

Appendix 2: MA’s Versus VAR’s

The VAR model described in the text model (2) is not the way impulse response functions are constructed in the recent empirical literature. In the literature the effect of narratively identified shifts in fiscal variables relies either on estimates of a truncated MA representation or on linear projection methods. The reason for these choices is that in the presence of multiple nonlinearities the MA representation of a VAR is much heavier than in the linear case—which means it could only be estimated imposing restrictions that limit the relevance of such nonlinearities. Consider for instance the following model in which fiscal adjustment plans have heterogenous effects according to the state of the cycle, but the VAR dynamics does not depend on the state of the economy, that is, using the terminology in the text, $A_{i}^{E}=A_{i}^{R}$. Assume also that TB and EB plans have identical effects.³⁰

$$\begin{aligned} \mathbf {z}_{i,t}=A_{1}\mathbf {z}_{i,t-1}+(1-F(s_{i,t}))B_{1}e_{i,t}+F(s_{i,t})B_{2}e_{i,t}+\mathbf {u}_{i,t} \end{aligned}$$

(4)

where $\mathbf {z}_{i,t}$ is the vector containing output growth and the growth rates of taxes and spending, $e_{i,t}$ are, as in the main text, the narratively identified fiscal adjustments and $\mathbf {u}_{i,t}$ unobservable VAR innovations. From this VAR we would derive the following MA truncated representations:

$$\begin{aligned} \mathbf {z}_{i,t}=\underset{j=0}{\overset{k}{\sum }}A_{1}^{j}\left( (1-F(s_{i,t-j}))B_{1}e_{i,t-j}+F(s_{i,t-j})B_{2}e_{i,t-j}\right) +\underset{j=0}{\overset{k}{\sum }}A_{1}^{j}\mathbf {u}_{i,t-j}+A_{1}^{k+1}\mathbf {z}_{i,t-k-1} \end{aligned}$$

Now apply to this framework the linear projection method. This would amount to deriving impulse responses for the relevant component of $\mathbf {z}_{i,t}$—say $\Delta y_{i,t}$—running the following set of regressions³¹:

$$\begin{aligned} \Delta y_{i,t+h}=\alpha _{i,h}+(1-F(s_{i,t}))\beta _{h,1}e_{i,t}+F(s_{i,t})\beta _{h,2}e_{i,t}+\Gamma _{h}\mathbf {z}_{i,t}+\epsilon _{i,t} \end{aligned}$$

(5)

Now compare this with the more general case in which the VAR dynamics is also affected by the state of the cycle—that is remove the restriction $A_{i}^{E}=A_{i}^{R},(i=1,2,3)$:

$$\begin{aligned} \mathbf {z}_{i,t}=(1-F(s_{i,t}))A_{1}\left( L,E\right) \mathbf {z}_{i,t-1}+F(s_{i,t})A_{1}\left( L,R\right) \mathbf {z}_{i,t-1}+(1-F(s_{i,t}))B_{1}e_{i,t}+F(s_{i,t})B_{2}e_{i,t}+\mathbf {u}_{i,t} \end{aligned}$$

In this case the truncated MA representation would be much more complicated than (5), as the response of $\mathbf {z}_{i,t+h}$ to $e_{i,t}$ would depend on all states of the economy between t and $t+h.$ Estimating the correct linear projection would no longer be feasible.

To further illustrate the point observe that the correct linear projection to estimate the effect of $e_{i,t}$ on $\Delta y_{i,t+1}$:

$$\begin{aligned} \Delta y_{i,t+1}&= \alpha _{i,1}+(1-F(s_{i,t+1}))F(s_{i,t})\beta _{1,1}e_{i,t}+(1-F(s_{i,t+1}))(1-F(s_{i,t}))\beta _{1,2}e_{i,t}\nonumber \\&+(F(s_{i,t+1}))F(s_{i,t})\beta _{1,3}e_{i,t}+(F(s_{i,t+1}))(1-F(s_{i,t}))\beta _{1,4}e_{i,t}\nonumber \\&+\Gamma _{h}\mathbf {z}_{i,t}+\epsilon _{i,t} \end{aligned}$$

(6)

is in general different from:

$$\begin{aligned} \Delta y_{i,t+1}=\alpha _{i,h}+(1-F(s_{i,t}))\beta _{1,1}e_{i,t}+F(s_{i,t})\beta _{1,2}e_{i,t}+\Gamma _{h}\mathbf {z}_{i,t}+\epsilon _{i,t} \end{aligned}$$

(7)

Note, in closing, that the cases in which the two representations coincide are very specific. Indeed, when (6) is the data generating process and (7) is estimated, the implied assumption is that the states $F(s_{i,t+1})=1$ and $F(s_{i,t+1})=0$ are observationally equivalent.

Summing up: if the data are generated by (6) the VAR representation is much more parsimonious than the linear projection which becomes practically not feasible unless very strong restrictions are imposed on the empirical model.

Table 12 Data sources

Appendix 3: Data Sources

See Table 12.

$\mathbf {gdpv,}$ $\mathbf {gdp}$::

OECD Economic Outlook n.97; for Ireland, IMF WEO April 2015;

$\mathbf {cgv}$::

OECD Economic Outlook n.97; for Ireland we used data from AMECO (final consumption expenditure of general government at current prices deflated in 2012 prices with the correspondent deflator series in the AMECO dataset—price deflator total final consumption expenditure of general government);

$\mathbf {igv}$::

OECD Economic Outlook n.97; for Austria missing data in the period 1978–1994; for Ireland, Italy, Portugal, Spain, we used data from AMECO (gross fixed capital formation at current prices: general government, deflated with correspondent deflator series in AMECO dataset—price deflator gross fixed capital formation: total economy); note that for Portugal and Ireland series are, respectively, in 2011 and 2012 prices;

$\mathbf {yrg}$::

OECD Economic Outlook n.98; for Australia in the period 1978–1988 and Ireland before 1990, Economic Outlook n.88;

$\mathbf {sspg}$::

OECD Economic Outlook n.98; for Australia in the period 1978–1988 and Ireland before 1990, Economic Outlook n.88;

$\mathbf {oco}$::

OECD Economic Outlook n.98; for Australia in the period 1978–1988 and Ireland before 1990, Economic Outlook n.88;

$\mathbf {popt}$::

OECD Historical Population Data and Projections (1950–2050).

The variables we use in the analysis are constructed as follows:

• GDP deflator

  $$\begin{aligned} pgdp_{i,t}=\frac{gdp_{i,t}}{gdpv_{i,t}} \end{aligned}$$

• Real per capita GDP growth

  $$\begin{aligned} {\Delta }y_{i,t}=100*\left[ \log \left( \frac{gdpv_{i,t}}{gdpv_{i,t-1}}\right) -\log \left( \frac{popt_{i,t}}{popt_{i,t-1}}\right) \right] \end{aligned}$$

• Percentage Change of Government Spending (as fraction of GDP)

  $$\begin{aligned} {\Delta }g_{i,t}=100*\left[ \frac{\left( igv_{i,t}+cgv_{i,t}\right) +\frac{oco_{i,t}+sspg_{i,t}}{pgdp_{i,t}}}{gdpv_{i,t}}-\frac{\left( igv_{i,t-1}+cgv_{i,t-1}\right) +\frac{oco_{i,t-1}+sspg_{i,t-1}}{pgdp_{i,t-1}}}{gdpv_{i,t-1}}\right] \end{aligned}$$

• Percentage Change of Government Revenues (as fraction of GDP)

  $$\begin{aligned} {\Delta }\tau _{i,t}=100*\left[ \frac{\frac{yrg_{i,t}}{pgdp_{i,t}}}{gdpv_{i,t}}-\frac{\frac{yrg_{i,t-1}}{pgdp_{i,t-1}}}{gdpv_{i,t-1}}\right] \end{aligned}$$

Appendix 4: Multipliers in the Alternative Specifications

See Tables 13, 14, 15.

Table 13 Output multipliers in the alternative specifications

Table 14 Output multipliers controlling for monetary policy and excluding zero lower bound observations

Table 15 Output multipliers under alternative specification of F(s)

Fig. 1

Evolution of $F\left( s\right)$ and Recessions. Note. The graph shows the evolution of F(s) for the countries in our sample and years of recession (years of negative growth per capita, shaded areas), 1981–2013

Fig. 2

Impulse responses from the model with heterogeneities between EB and TB plans and across states of the cycle. Note. The graph shows the response of VAR variables and F(s) to a deficit reduction plan of 1 percent of GDP. IRFs for tax-based shock starting in recession labeled with stars, for tax-based shock starting in expansion labeled with squares, for expenditure-based shock starting in recession labeled with circles and expenditure-based shock starting from expansion labeled with triangles. Dashed lines and shaded areas are for bootstrapped (1000 repetitions) 90 percent confidence intervals

Fig. 3

Impulse responses from the model with heterogeneity only across states of the cycle. Note. The graph shows the response of VAR variables and F(s) to a deficit reduction plan of 1 percent of GDP. IRFs for a plan starting in expansion labeled with circles, for a plan starting in recession labeled with triangles. Dashed lines and shaded areas are for bootstrapped (1000 repetitions) 90 percent confidence intervals

Fig. 4

Impulse responses from the model with heterogeneity only between EB and TB plans. Note. The graph shows the response of VAR variables to a deficit reduction plan of 1 percent of GDP. IRFs for tax-based shock labeled with circles, for expenditure-based shock labeled with triangles. Dashed lines and shaded areas are for bootstrapped (1000 repetitions) 90 percent confidence intervals

Fig. 5

Impulse responses from the model with heterogeneities between EB and TB plans and across states of the cycle, controlling for monetary policy. a Constrained Monetary Policy. b Unconstrained Monetary Policy. Note. The graph shows the response of VAR variables and F(s) to a deficit reduction plan of 1 percent of GDP in euro area countries—under a common monetary policy—panel (a), and in the other countries—where monetary policy is free to adjust—panel (b). IRFs for tax-based shock starting in recession labeled with stars, for tax-based shock starting in expansion labeled with squares, for expenditure-based shock starting in recession labeled with circles and expenditure-based shock starting from expansion labeled with triangles. Dashed lines and shaded areas are for bootstrapped (1000 repetitions) 90 percent confidence intervals

Fig. 6

Impulse responses from the model with heterogeneities between EB and TB plans and across states of the cycle, excluding episodes at the ZLB. Note. The graph shows the response of VAR variables and F(s) to a deficit reduction plan of 1 percent of GDP, from a model where we exclude episodes at the ZLB. IRFs for tax-based shock starting in recession labeled with stars, for tax-based shock starting in expansion labeled with squares, for expenditure-based shock starting in recession labeled with circles and expenditure-based shock starting from expansion labeled with triangles. Dashed lines and shaded areas are for bootstrapped (1000 repetitions) 90 percent confidence intervals

Fig. 7

Impulse responses from the model with heterogeneities between EB and TB plans and across states of the cycle, alternative specification of $F\left( s\right)$. Note. The graph shows the response of VAR variables to a deficit reduction plan of 1 percent of GDP, from a model where we use an alternative specification of F(s) depending on current output growth. IRFs for tax-based shock starting in recession labeled with stars, for tax-based shock starting in expansion labeled with squares, for expenditure-based shock starting in recession labeled with circles and expenditure-based shock starting from expansion labeled with triangles. Dashed lines and shaded areas are for bootstrapped (1000 repetitions) 90 percent confidence intervals. The cycle indicator is held fixed throughout the simulation horizon