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Appendix A Role of Debt
I will discuss econometrically why it is important to include debt. The reason is simple, omitting debt may deliver biased estimates. The aim is to estimate the effect of fiscal adjustments on the output growth. As I discussed in Section 3, the records of the fiscal adjustments are identified in a way that they are exogenous to the business cycle. However, they depend on one key motivation. The motivation is to decrease the government’s deficit. Assume a simple model, with a focus just on output growth. Suppose that the true model is the following
I can reasonably assume that both β < 0 and γ < 0. The latter can be seen also from Figure 12 for the linear case, where the effect of fiscal consolidations has a recessionary effect on output growth. At the same time, I have that
where κ > 0, given the motivation of the fiscal adjustments. If I combine the two equations,
it is clear that if one considers just the fiscal adjustments, this would imply an overestimation of the effect
Appendix B Additional Figures and Checks
In this section I briefly discuss part of the preliminary tests regarding the narrative data and some of the building steps needed regarding my baseline model specification.
This paper was previously circulated under the title “Non-Linearities and Fiscal Policy”. I am grateful to my PhD supervisor Carlo Favero. In addition, I thank for their suggestions and advice Fabio Canova, Petros Dellaportas, Juan Dolado, Vitor Gaspar, Francesco Giavazzi, Luigi Iovino, Christophe Kamps, George Kapetanions, Ekaterini Kyriazidou, Paolo Mauro, Tommaso Monacelli, Evi Pappa, Catherine Pattillo, Luca Sala, Abdelhak Senhadji, Susan Yang, participants of the ECB Forum on Central Banking in Sintra, and seminar participants at Bocconi University, EUI, University of Amsterdam, Athens University of Economics and Business, ECB, Bank of Lithuania, ESRI, King’s College London, New Economic School, UCD, University of Leipzig, ADEMU group, and participants in the seminars of the Fiscal Affairs Department. I also acknowledge financial support from the ERC INDIMACRO project. The views expressed here are those of my own and do not necessarily represent those of the International Monetary Fund.
A fiscal consolidation is a mix of tax and government spending changes. Tax-based (expenditure-based) means that the total of adjustments is mainly based on tax increases (spending cuts).
In AG (2012) the identification of exogenous shifts in fiscal variables is obtained using the Blanchard-Perotti identification assumptions. This paper uses a narrative identification approach.
The challenge of the narrative data is that there is often a lack of information. Governments do not make legislative announcements on a frequent basis. This means that if ones takes the time series of announcements of a country, there is limited information, since there are many years that no announcement took place, hence there are many zeros in the data (see Figure 4). This phenomenon is even stronger when one accounts for the future implementation of fiscal changes, since in this case we would need to add an additional variable/ time series that it is going to include even less information affecting the degrees of freedom and the precision of the estimates. The exclusion of the future announcements does not create any bias, since in general most of the plans of announcements have a one year horizon (on average TB plans last around 1.5 years, and EB plans 1.8 years), which is the information that I include in my sample.
More precisely, government spending includes government final consumption, government investment, social security benefits and other current outlays.
I base the calibration of each country in years of extreme recessions, i.e. in years that all quarters where recorded as recessionary. However, since there are years that could be classified either as recessionary or expansionary because half of the quarters are recorded as being in recession, I use a random algorithm to also record some of these years and account for possible weak recessions. The shaded grey bars reported in Figure 5 include years both of extreme and weak recessions, in order to better understand the transition series.
With a small abuse of notation, i denotes both the interest rate and indexes the country under consideration. Nevertheless, no confusion should arise given that country-indexes always occur as subscripts.
I take the exponential of government spending (as a fraction to GDP) and government revenues (as a fraction to GDP), because these variables are in logarithms.
The effect on output has a further indirect effect on the primary balance, which arises from the automatic stabilizers. In addition, there is potentially a third channel through the interest rate payments. In my discussion, I will focus on the main effects of a. and b.
Of course, one could include an error term to account for measurement error, given the discrepancies that may arise as I discussed in the previous section and are observed in a couple of countries.
The linear model is a special case of STVAR for a value of γ = 0.
I elaborate more on this argument in the appendix by discussing the econometrics.
Econometrically, one could also examine whether the “when”, the “how”, or the “initial condition” is more relevant by testing different hypothesis.
Hypothesis Testing Cycle B1E = B1R; B2E = B2R Composition B1E = B2E; B1R = B2R Initial Condition
Applying this methodology in a linear VAR would produce standard impulse responses.
I report the 16–84% confidence intervals.
For my bootstrap, I re-sample the residuals of the estimated non-linear VAR (e.g. model 4) allowing for the correlation between the residuals of the different countries. This generates a set of observations for Y, F (z), Debt, which allows me to re-estimate my model and derive the GIRFs. I rely on 1000 iterations.
The combinations are: TB shock in recession (F(z) = 0.8) when debt is high (0.9); EB shock in recession (F(z) = 0.8) when debt is high ( 0.9 ); TB shock in expansion (F(z) = 0.2) when debt is high (0.9); EB shock in expansion (F(z) = 0.2) when debt is high (0.9); TB shock in recession (F(z) = 0.8) when debt is low ( 0.9 ); EB shock in recession (F(z) = 0.8) when debt is low (0.3); TB shock in expansion (F(z) = 0.2) when debt is low (0.3); TB shock in expansion (F(z) = 0.2) when debt is low (0.3). I set for each case the initial values for debt, the regime indicator, and all the related initial parameters.
I drop Japan from my study, since it is the only country in my sample with such high debt-ratios.
I do not depict the confidence intervals of the response of F(z) and debt. The reason is that they are pretty narrow and I prefer to keep the picture of the graph more clear given that there are many curves presented together.
Differently from AG, I allow for the endogenous transition from one regime to the other (F (z)). As it has been already stressed by Caggiano, Castelnuovo, Colombo and Nodari (2015), this is an important point to highlight. Therefore, I document the response of F (z) starting in recession versus the one starting in expansion.
One reason that I choose to present results for these values, is that these values are associated with the point of the tails of my sample distribution as depicted in Figure 3. In addition, the 90% value reflects the discussion of Reinhart and Rogoff (2010) and Herndon, Ash and Pollin (2014) regarding the evidence (or not) of a negative impact of growth when the level of debt ratio is above this threshold.
Ideally, one would construct a multiplier that would capture the direct effect of the shocks on gdp growth and the indirect coming from government revenues or government spending. However, since the shocks in our analysis are not pure shocks (i.e. they are a mix of spending and tax changes), this is not straightforward. In addition, given the number of non-linearities the resulted uncertainty levels can be really high, and therefore not making the results easy to understand or meaningful.