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229-08-L03a - Econ 229 Notes Walsh Ch.4 P.1 Econ 229...

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Econ 229 Notes Walsh Ch.4 - P.1 Econ 229 – Handout on Walsh’s Ch.4 Main Points: • Intertemporal budget constraint with emphasize on money and seignorage. • Distinguish nominal, real, and growth-adjusted variables; identities and constraints. Budget accounting • Start with Walsh’s nominal budget identity (4.1): Outlays = Receipts plus debt issues. G t + i t " 1 # B T t " 1 = T t + RCB t + [ B T t " B T t " 1 ] - Walsh’s “total debt” is known in the U.S. as the Public Debt (end of period). T = Revenues from the private sector, excluding the central bank. - RCB = central bank transfer, in the literature often subsumed into total revenues. - Narrow interpretation: One period nominal debt with predetermined interest rate i t-1 . Broader: Any type debt with nominal return i; preferably t-dated. • Dynamics of total public debt: B T t = (1 + i t " 1 ) # B T t " 1 " [ T t + RCB t " G t ] - Exponential growth at the interest rate, unless reduced by a primary surplus.
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Econ 229 Notes Walsh Ch.4 - P.2 • Central bank budget identity (4.2): - Money creation plus interest on debt invested in bonds or transferred to Treasury [ H t " H t " 1 ] + i t " 1 # B M t " 1 = [ B M t " B M t " 1 ] + RCB t • Replace RCB in the budget identity: G t + i t " 1 # B T t " 1 = T t + [ H t " H t " 1 ] + i t " 1 # B M t " 1 " [ B M t " B M t " 1 ] + [ B T t " B T t " 1 ] - Define B t = B T t " B M t = Privately-held public debt Then G t + i t " 1 # B t " 1 = T t + [ H t " H t " 1 ] + [ B t " B t " 1 ] => [ B t + H t ] = [ B t " 1 + H t " 1 ] + i t " 1 # B t " 1 + [ G t " T t ] - Find: Public sector liabilities consist of privately-held public debt plus monetary base. Interest is paid only on the privately-held public debt; interest on central bank holdings are returned to the Treasury. • Useful practical approximation: - Suppose money is created trough open market operations and H is backed by bonds, then B t M " H t => B t + H t " B t T and RCB t " i t # 1 $ B M t # 1 " i t # 1 $ H t # 1 - Then: public debt is a good proxy for public-sector liabilities (much used). Added insight: the fiscal benefit of money is that the central bank’s interest income is returned to the budget. - However: Don’t use this for theoretical analysis. Not a good approximation when the CB has significant other assets (e.g., loans to banks).
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Econ 229 Notes Walsh Ch.4 - P.3 Accounting for growth • With inflation ( π ), a constant real debt implies a growing nominal debt.
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