Appendix: Model Setup
We nest traditional short-run restrictions and use the long-run properties of the model to introduce cointegrating relationships so that we identify exogenous fiscal shocks (Pagan and Pesaran, 2008). Further, we follow Favero and Giavazzi (2007) which extends the Blanchard and Perotti (2002) and Perotti (2004) SVAR to account for government’s budget constraint.
We typically consider the following SVAR model in which the public debt ratio (dt) enters as exogenous:5
The debt ratio, in turn, is determined in the government budget constraint from :
Where, following Blanchard and Perroti (2002), the vector of endogenous variables Yt = [gt, tt, yt, reert, it] includes government spending (gt) defined as the sum of government consumption and investment (excluding interest payment), net revenue (excluding interest receipt on government debt) (tt), real output (yt), real effective exchange rate (reert), and the yield on government securities (it).
Identification is achieved with assumptions about policy decision lags and estimated elasticity through cointegrating properties. As defined in Banchard and Perotti (2002) and in Perotti (2004), observed fiscal policy reactions (expenditure and tax):
is function of (i) automatic response of spending/tax to output, exchange rate, and financial shocks; (ii) systematic discretionary response of fiscal policy to macroeconomic system; and (iii) random discretionary fiscal policy shocks. The relation between the structural shocks and the innovation is thus given by:
Or in matrix format  is: A0et = Bεt
From , a just identification of  would require
1. We make the assumptions that:
on the ground that interest payments on government debt are excluded from the definition of expenditure and tax that enter the model. Furthermore, the contemporaneous impact of interest rate on tax is generally likely to be small or close to zero (in practice).6
2. Next, we consider that the interest rate on government depends on fiscal stance and exchange rate, but (contemporaneously less on output.; thus:
3. We now need (at least) 2 restrictions. Notice that most studies using high frequency data, have assumed that either (αg,y = 0) expenditure or (αt,y = 0) tax do not respond to the economic activity within a quarter. Such assumption may not hold for annual data. One can rule out this constraint by dwelling on the statistical properties of the cointegration analysis. Suppose that there is at least one cointegration relation (which is likely to be the case, given that, by construction, all system variables enter in level and generally follow I(1) processes), then one could either estimate the automatic response of tax to change in economic environment or exchange rate movement or the automatic response of government spending to economic or exchange rate shocks.
Assuming that there is evidence of (at least) one cointegrating vector7, then the structural VECM counterpart of the baseline model  is:
where a = A0α where α is the loading parameter.8
Now let’s assume that such cointegration is found between government spending, output growth, and exchange rate, then the remaining two coefficients can be obtained by:9
Hence, the corresponding SVECM representation of the baseline model is:
And its associated error correction terms with parameters to achieve, at least, a just-identified system is:
With this estimation, all fiscal shocks are identified and the matrix A0 can be fully estimated.
Blanchard, Olivier and Roberto Perotti, 2002, “An Empirical Characterization Of The Dynamic Effects Of Changes In Government Spending And Taxes On Output,” The Quarterly Journal of Economics, 117(4), pages 1329-1368.
Estevão, Marcello and Samake, Issouf, 2012, “Fiscal Multipliers and Debt Feedback in Central America” IMF Working Paper (forthcoming), Washington D.C.
Favero, Carlo and Francesco Giavazzi, 2010, “Reconciling VAR-based and Narrative Measures of the Tax-Multiplier,” CEPR Discussion Papers 7769.
Ilzetzki, Ethan, Enrique G. Mendoza and Carlos A. Végh, 2010, “How Big (Small?) are Fiscal Multipliers?” CEP Discussion Papers DP1016, Centre for Economic Performance, LSE.
Kaminsky, Graciella, Carmen Reinhart and Carlos A. Végh, 2004, “When It Rains It Pours: Procyclical Capital Flows and Macroeconomic Policies” in NBER Macroeconomics Annual, edited by Mark Gertler and Kenneth Rogoff, Cambridge, MA: MIT Press.
Perotti, Roberto, 2004, “Estimating the effects of fiscal policy in OECD countries,” WorkingPapers 276, IGIER Bocconi University.
Romer, C. D., and D. H. Romer, 2007a, “The Macroeconomic Effects of Tax Changes: Estimated Based on a New Measure of Fiscal Shocks,” NBER Working Paper No. 13264. 1, 26.
Prepared by Issouf Samake.
Contrary to a number of studies on Latin American countries which focus on clusters, the proposed model is tailored for each country to account for their idiosyncratic factors (on monetary, exchange rate, trade, and fiscal policies) as well as vulnerabilities and structural breaks.
Recently, Ilzetzki (2011) found that government expenditure is more potent in expanding output in high-income countries than in developing countries. On tax, he found that tax multiplier is virtually zero in most countries. However, the exception was developing countries where the tax multipliers range from 0.3 on impact to close to 0.8 in the long-run. See also Ilzetzki, Mendoza, and Végh (2010), IMF (2010), and Perotti (2004 and 2011).
Note, however, that in 2007, the salaries of teachers and service staff from autonomous colleges were reclassified (mostly capital spending) from municipalities to the central government budget (as current spending).
A pitfall of using standard VAR (or VECM) is the lack of power to measure foreseen changes in fiscal policy (Ramey, 2007; Romer and Romer, 2007).
However, the assumption that tax is inelastic to interest rate change is controversial given that income tax-base includes interest income as well as dividends, which co-move negatively with interest rate.
The SVECM representation also hold with mix of I(0) and I(1) system variables. We assume shocks are either temporary or persistent.
The β’yt-1 is estimated e β’yg,t-1 = yg,t-1 - αg,yyGDP,t-1 - αg,reryrer,t-1 = ECMt-1
Typically, this would imply that