2.5 Experiments and Simulations
2.5.2 Fiscal Shocks
In order to study what kind of fiscal shock has the strongest effect on total output, I conduct an experiment following closely the one pre- sented byFernández-Villaverde (2010)and in order to do so I consid- ering the same modellization of the fiscal side proposed in that paper. I study then the response at impact of total output, consumption and residential investment after a shock to government expenditure and to other 4 shocks to taxes, namely a tax on consumption, a tax on la- bor, a tax on debt and a tax on housing.24 It is not straightforward to
decide how to confront those different shocks. Indeed two kinds of problems emerge, the first one is if we should consider the effect on impact of the shock, or rather its medium term effect or its welfare related implications, that in this model, differently fromFernández- Villaverde (2010)are even more complicated because of the presence of two distinct classes of households. The second one is related to the problems in calibrating the shocks in a way that would allow one to compare them in the most informative way. These problems have been solved in the above mentioned paper by confronting the effect of the different shocks on impact and by calibrating the shocks in order to consider the same effect on the public balance as the one caused by an increase of one percent of public expenditure. That is also the approach I take in this study. More formally, this calibration is performed considering the following:
24Note that the original experiment byFernández-Villaverde (2010)is limited to output and as specified earlier it uses the financial accelerator related to firms net worth.
(2.42) 0.01ׯg =−∆τl,t×( ˜Nc,tw˜c,t + ˜Nd,tw˜d,t+Nc,twc,t+Nd,twd,t) ∆τl,t=−0.01 ¯ g ×( ˜Nc,tw˜c,t + ˜Nd,tw˜d,t+Nc,twc,t+Nd,twd,t)
where I use as an explicative example the way I calibrated the size of the shock on labor efforts. Namely, I impose that the variation in public expenditure, which puts a strain on government deficit equal to a one percent of the steady state value ofgis equal to an equivalent temporary increase in the budget given in this case by a reduction in labor taxes.25
Now, considering that the percent deviation of labor tax on im- pact is given byτˆl: (2.43) ˆ τl=log 1−τl 1−τ¯l
and that I want it to decrease it by the amount specified above, then: ˆ τl =log 1−τl−∆τl.t 1−τ¯l =log 1− ∆τl,t 1−τ¯l =log 1 + 0.01 1 1−τl,t ¯ g ×( ˜Nc,tw˜c,t + ˜Nd,tw˜d,t+Nc,twc,t+Nd,twd,t) !
I follow the same procedure to calibrate all other shocks and then examine the impulse response functions. The main result, which confirms the one ofFernández-Villaverde (2010)and that can be red from figure2.3, is that the fiscal shock that works better in increasing output on impact is an increase in government expenditure. Indeed, the multiplier of all other shocks is somewhat smaller than that im- plied by a positive increase ingt. While the overall effect is similar for
all kinds of shocks, there is a different response in residential invest- ment and aggregate consumption. What however emerges clearly 25Note that all the values considered in those computations are the steady state values.
2.5. Experiments and Simulations 85
from this analysis is that fiscal policy in presence of constrained agents, despite the source of the shock, crowds in residential investment and consumption and ultimately increases total output. The overall effect is stronger for the government expenditure shock, with a multiplier that is about0.5%larger with respect to all other shocks.
FIGURE2.3: Response to a1%increase in government expenditure
As highlighted in the fourth panel of figure 2.3, an important channel through which the model works is through the increase in inflation, this effect is stronger after a shock to government expendi- ture which directly increases aggregate demand. The mechanism I refer to is debt-deflation, which comes from Fisher’s account of the Great Depression and in the context of monetary policy has been already highlighted in different set-ups by (Bernanke, Gertler, and Gilchrist, 1999) and in a model similar to the one here presented by (Iacoviello, 2005). Indeed, debt in this model is nominal and an in- crease of inflation decreases its value.26 This works through the relax-
ation of borrowers budget constraint that goes in the same direction of an increase in house prices. Therefore, it boosts their consumption of non-durable goods and of housing.
Figure 2.4 shows the way the two distinct groups react to the shocks and helps shading some lights on the aggregate results. The 26The original analysis of Fisher was more focused on the effect of deflation on the magnification of debt.
figure highlights once again that households react differently to the shocks. A reduction in the tax rate on consumption has the second strongest effect on aggregate output and it works mainly through an increase in consumption. However, the incentive to consump- tion lowers investment with respect to a shock to government ex- penditure and is furthermore hindered by the presence of habits in consumption. The reduction of housing taxes has also expansionary effects, which differently from the previous shock rely more on the higher increase in housing consumption by borrowers. Interestingly enough, savers still reduce their housing consumption, due to the increase in real house prices, however their consumption of durable goods gets back to steady state far more quicker than in other shock exercises, and it overshoots dramatically after that. A reduction of taxes on savings increases savings by patient households. Indeed, that is reflected in figure 2.4 by the strong decline in housing con- sumption by them and by the opposite movement in the consump- tion of housing by borrowers. The two effects tend to compensate each other, while the effect on non-durable consumption is more lim- ited therefore the reduction of this tax rate is the least effective be- tween the ones analysed. Lastly, a reduction in the tax on labor does not manage to have effects on total output that are as stronger as in the case of government expenditure shock. One reason might be re- lated to the fact that this tax shock shifts households labor supply, therefore has limited effects on inflation.
This section highlights how different the reactions of the two groups of households are. However, the focus of the model is not on the wel- fare effect of fiscal shocks, for the analysis would also require to take a stance on the effect of government expenditure on the utility of households. This issue has not been tackled in this paper and since the empirical evidence on this topic is still mixed I omit any further discussion on the topic and leave it to future research.
2.5. Experiments and Simulations 87
FIGURE2.4: Response to a1%increase in government expenditure