Appendix 1. The Non-Stochastic Steady State.
Appendix 2. Solving the Model Using a Global Method.
Aiyagari, R., 1995), “Optimal Capital Income Taxation with Incomplete Markets, Borrowing Constraints, and Constant Discounting”, Journal of Political Economy, Vol. 103, No. 6, pp. 1158-1175
Aiyagari, R., Marcet A., Sargent, T.J., and Seppälä, J., 2002, “Optimal Taxation without State-Contingent Debt”, Journal of Political Economy, Vol. 110, No. 6, pp. 1220-1254.
Alesina, A. and Perotti, R., 1995, “The Political Economy of Budget Deficits”, IMF Staff Papers, No. 421 (Washington: International Monetary Fund).
Alesina, A. and Tabellini, G., 1990, “A Positive Theory of Fiscal Deficits and Government Debt”, Review of Economic Studies, Vol. 57, pp. 403-414.
Chari, V.V., Christiano, L.J. and Kehoe, P.J., 1994, “Optimal Fiscal Policy in a Business Cycle Model”, Journal of Political Economy, Vol. 102, No. 4, pp. 617-652.
Chari, V.V. and Kehoe, P.J., 1999, “Optimal Fiscal and Monetary Policy”, Chapter 26 in J.B. Taylor and M Woodford, eds., Handbook of Macroeconomics (North-Holland: Elsevier).
Chinn, M. and Frankel, J., 2003, “The Euro Area and World Interest Rates”, Working Paper, University of Wisconsin and Harvard University.
Engen, E. and Hubbard, R.G., 2004, “Federal Government Debts and Interest Rates”, Working Paper No. 10681 (Cambridge, Massachussets:National Bureau of Economic Research).
Gale, W.G. and Orszag, P.R., 2003, “Economic Effects of Sustained Budget Deficits”, National Tax Journal, Vol. 56, No. 3, pp. 463-485.
Grossman, H.I. and van Huyck, J.B., 1988, “Sovereign Debt as a Contingent Claim: Excusable Default, Repudiation, and Reputation”, American Economic Review, Vol. 78, No. 5, pp. 1088-1097.
King, R.G. and Rebelo, S.T., 1999, “Resuscitating Real Business Cycles”, Chapter 14 in J.B. Taylor and M. Woodford, eds., Handbook of Macroeconomics (North-Holland: Elsevier).
Laubach, T., 2003, “New Evidence on the Interest Rate Effects of Budget Deficits and Debt”, Federal Reserve Board of Governors, Finance and Economics Discussion Series, No. 2003-12.
Lucas, R.E. Jr. and Stokey, N., 1983, “Optimal Fiscal and Monetary Policy in an Economy without Capital”, Journal of Monetary Economics, Vol. 12, pp. 55-93.
Marcet, A. and Lorenzoni, G., 1999, “The Parameterized Expectations Approach: Some Practical Issues”, in: R. Marimon and A. Scott, eds., Computational Methods for the Study of Dynamic Economies (Oxford and New York: Oxford University Press).
Persson, T. and Svensson, L., 1989, “Why a Stubborn Conservative Would Run a Deficit: Policy with Time-Inconsistent Preferences”, Quarterly Journal of Economics, Vol. 104, pp. 325-346.
Persson, T. and Tabellini, G., 2004, “Constitutional Rules and Fiscal Policy Outcomes”, American Economic Review, Vol. 94, No. 1, pp. 25-45.
Reiter, M., 2005, “Solving Models of Optimal Monetary and Fiscal Policy by Projection Methods”, Working Paper, Universitat Pompeu Fabra.
Roubini, N. and Sachs, J.D., 1989, “Political and Economic Determinants of Budget Deficits in the Industrial Democracies”, European Economic Review, Vol. 33, pp. 903-938.
Schmitt-Grohé, S. and Uribe, M., 2004, “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function”, Journal of Economic Dynamics and Control, Vol. 28, pp. 755-775.
Shin, Y., 2005, “Ramsey Meets Bewley: Optimal Government Financing with Incomplete Markets”, Working Paper, University of Wisconsin.
Sleet, C. and Yeltekin, S., 2006, “Credibility and Endogenous Societal Discounting”, Review of Economic Dynamics, Vol. 9, pp. 410-437.
Woodford, M., 1999, “Commentary: How Should Monetary Policy Be Conducted in an Era of Price Stability?”, in: New Challenges for Monetary Policy: A Symposium Sponsored by the Federal Reserve Bank of Kansas City, Federal Reserve Bank of Kansas City.
Yaari, M.E., 1965, “Uncertain Lifetime, Life Insurance, and the Theory of the Consumer”, Review of Economic Studies, Vol. 32, pp. 137-150.
To make complete markets problems more interesting this is therefore typically ruled out through an ad-hoc restriction on the initial tax rate on debt.
See Sllet and Yeltekin (2005) and references therein.
This parameter depends on one’s benchmark value for the proportion of time spent working in steady state. King and Rebelo (1999), in a business cycle model without distorting taxes, set κ = 3.48, but values lower than 3 can also be justified on that basis.
As demonstrated in Appendix A, there is a possibility of two steady state values for labor and consumption. However, they are far apart and one of them is easy to rule out because it is clearly inferior in terms of welfare. This means that even for large fluctuations around the steady state, the use of a perturbation method that approximates the solution around the superior steady state remains appropriate.
Let the gross real interest rate be denoted by
The main merit of the quadratic adjustment cost formulation in (3) is clearly its analytical tractability. This allows us to remain consistent with the cited empirical evidence while focusing our main attention on the implications of short government planning horizons. In more elaborate models such as overlapping generations models based on Blanchard (1985) and Yaari (1965), a relationship such as (25) emerges endogenously.
Statistics computed for 24 developed countries excluding Belgium, Italy, and Japan. Source: OECD Factbook 2006: Economic, Environmental and Social Statistics.
Available at http://pythie.cepremap.cnrs.fr/mailman/listinfo/dynare.
All plots in Figure 4 show deviations from the original steady state, either in % or in percentage points.
It would be interesting to extend the model to one with capital, where such increases in the real interest rate would have more sizeable effects on output.
The latter may be the main reason why debt-to-GDP ratios in developing countries are often comparatively low, see Reinhart, Rogoff and Savastano (2003).
To obtain this ratio we compute the present discounted values of the increases in government spending and in labor income taxation at the steady state real interest rate. The remainder is accounted for by the difference between the present discounted values of primary surpluses evaluated at the steady state and at the actual real interest rates. This remainder is negative, because real interest rates rise during the transition.