Penn Wharton Budget Model: Dynamics

Transcription

1 Penn Wharton Budget Model: Dynamics Penn Wharton Budget Model September 8, /20

2 Dynamic Model Overview Dynamic general euilibrium OLG model with heterogeneity Idiosyncratic productivity risk distribution of earnings histories Detailed Social Security system, progressive taxes, immigration Evaluates unbalanced fiscal reform over long time horizons Considers open and closed economy frameworks 2/20

3 Household Labor Productivity(z) Deterministic dependence on age j Permanent shock drawn at birth Transitory and persistent (AR1) shocks Initial distribution of non-permanent shocks 3/20

4 Household Social Security and Beuests Social Security benefit ss(b) depends on average lifetime labor earnings b, issuance during retirement ages: j > Tr. Accidental beuests are collected by the government and redistributed evenly in lump-sum (be) among all living households 4/20

5 Investment Expensing Let = (1 eτ cap ), where e is the rate of investment expensing. Following Altig, Auerbach, Kotlikoff, Smetters, and Walliser (2001), a no-arbitrage condition on old capital relative to new capital implies the net return to capital is r K 1, where r K will be the gross rental rate of capital. 5/20

6 Household Taxation Personal Income Tax y pit = wzn1 {j Tr} + (1 φ ss )ss(b)1 {j>tr} + ( ) r K 1 φ K (1 θ) + (1 φ K )(r G 1) a (1) where wzn is labor income, (1 φ ss ) is the taxable share of Social Security benefits, φ K is the portfolio weight on physical capital, r G is the return on government debt, θ is the share of capital income subjected to the capital tax rate, and a is asset holdings. τ pit (y pit ) = ypit 0 ξ (y) dy (2) Tax function τ pit (y pit ) is cumulative tax liability from marginal tax rate function ξ (y). The function ξ (y) is a step-function (from TPC) which accounts for deductions and credits. 6/20

7 Household Taxation (cont.) Capital Tax r K 1 y cap = φ K θa (3) τ cap (y cap ) = τ cap y cap (4) Payroll Tax y ss = min{wzn, y taxmax } (5) τ ss (y ss ) = τ ss y ss (6) 7/20

8 Household Optimization: Working age Working-age household Bellman s euation: { (c γ (1 n) 1 γ ) 1 σ } V j (a, z, b) = max + s j+1 βe a,n 1 σ {z z}[v j+1 (a, z, b )] (7) subject to: ( c = wzn + [φ K 1 + r ) ] K (1 φ k )r G a b j+1 = 1 j τ pit (y pit ) τ cap (y cap ) τ ss (y ss ) a + be (8) ( ) (j 1)b j + min{wzn, y taxmax }, (9) where s j+1 is survival probability, (8) is the budget constraint, and (9) determines average earnings for SS benefit calculation. Households take φ K as exogenous. 8/20

9 Household Optimization: Retiree Retired household Bellman s euation: { (c γ (1) 1 γ ) 1 σ } V j (a, b) = max + s j+1 βv j+1 (a, b ) a 1 σ (10) subject to: ( c = ss(b) + [φ K 1 + r ) ] K (1 φ k )r G a τ pit (y pit ) τ cap (y cap ) a + be (11) b j+1 = b j. (12) 9/20

10 Production: Closed Economy Capital K euals aggregate savings A less government debt D in capital terms: K = A D. Output: Y = K α L 1 α, (13) where L is aggregate efficient labor. Firms problem: { K α L 1 α + (1 δ)k r K K wl }, (14) max K,L where δ is depreciation and r K is the rental rate of capital faced by firms. Firms gross interest rates and wages are determined according to: r K = 1 + αk α 1 L 1 α δ (15) w = (1 α)k α L α (16) 10/20

11 Production: Open Economy International capital flows in and out of the economy, but labor is immobile. Let constant: ( r ss λ K 1 ss ) (1 τ ss cap), (17) denote the after-tax net capital return in the initial steady-state closed economy. We set λ as the international after-tax net capital return for the small open-economy. After change in policy, territorial capital tax capital flows until r K clears international capital markets by matching the international after-tax net return on capital: ( ) rk 1 (1 τ cap ) = λ, (18) where and τ cap represent the new transition path values. 11/20

12 Open Economy (cont.) Rearranging terms in (18) gives: r K 1 = λ (1 τ cap ) (19) Euation (15) implies a uniue capital-to-labor ratio κ = K L given in the firm s FOC: r K = 1 + ακ α 1 δ, (20) or euivalently: r K 1 = ακα 1 δ (21) (19) and (21) give: κ = [ ( )] 1 1 λ α 1 + δ α 1 τ cap (22) 12/20

13 Open Economy (cont.) κ in (22) then gives wages: w = (1 α)κ α (23) Agents optimize over the transition path given (20) and (23), which results in an aggregate efficient labor seuence, L. Then, the corresponding capital seuence is given by the product: K = κl (24) 13/20

14 Open Economy (cont.) Since the closed economy steady-state provides initial conditions for the open economy, we assume that initial foreign capital is zero. Define K domestic to be the aggregate capital holdings of households in the economy. Then, foreign capital is K foreign = K K domestic (25) 14/20

15 Capital Tax Revenue Because of territorial capital tax, must account for taxation of foreign capital. By assumption, capital tax share θ also applies to foreign capital. In other words, 1 θ of foreign capital income is not taxed in the US. Capital tax revenue from foreign capital is then: θ r K 1 K f. 15/20

16 Household Portfolio Weighted average of return on capital and government interest rate: φ K = K K + D (26) Open economy: portfolio allocation fixed at initial steady state shares of capital and debt. Closed economy: portfolio allocation determined in general euilibrium throughout transition path all debt is held by households. 16/20

17 Government Debt Seuence of government interest rates r g is exogenous. Government debt evolves according to: D + R = r g D + G, (27) where R is government revenue and G is government expenditures. R and G have explicit model components. For revenue, personal income taxes (PIT), capital taxes (CT) and payroll taxes (SSREV), and for expenditures, Social Security expenditures (SSEXP). We can expand (27) as follows: D + FIT + SSREV + CT + T = r g D + SSEXP + G (28) where G is the non-interest government budget surplus not accounted by the explicit model revenue and expenditure components and T is non-explicit tax revenue introduced only in counter-factual experiments (e.g., estate taxes, tariffs). 17/20

18 Simulating Debt Over the Transition Path Process of matching CBO debt projection: 1 Choose G to match CBO non-interest surplus in each year in the open economy. 2 Use CBO government interest rates to generate debt seuence (generates exactly the CBO debt projection). 3 Use resulting G from open economy (no macroeconomic feedback from debt) to construct government budget in closed economy. Key intuition: CBO debt projections correspond to our open economy (no feedback effects of debt). Baseline closed economy accounts for macroeconomic feedback from this debt seuence. 18/20

19 Reported Tax Revenue Aggregates Personal Income Tax is assessed on wage income and a portion of capital income: PIT BASE = wl + (1 θ) r K 1 K domestic, (29) where L is aggregate efficient labor. Capital Income is r K 1 K Portion taxed at PIT is (1 θ) r K 1 K. Portion taxed at the single capital tax rate is θ r K 1 K. Capital tax is from corporate tax, tax on dividends, tax on capital gains, etc. Complex tax structure Simplified into the PIT and single rate structure as above. PIT residential, single rate τ cap territorial 19/20

20 Reported Tax Revenue Aggregates (cont.) Since PIT is non-linear, it is not clear how to assign tax dollars from capital income portion: PIT REVENUE = τ pit (PIT BASE ) (30) We say taxes assigned by percent of income So CT is PIT CAP REV = (1 θ) r K 1 K domestic PIT REVENUE (31) PIT BASE CT REVENUE = τ cap θ r K 1 K + PIT CAP REV (32) 20/20