Monetary Policy When Preferences Are Quasi-Hyperbolic
What this paper finds — and why it matters
Layer 1: Overview
Research question and motivation: Experimental and survey evidence robustly documents “present bias” — people are more impatient over the short run than the long run, producing preference reversals inconsistent with standard exponential discounting. Dennis and Kirsanov ask how this behavioral feature, modeled as quasi-hyperbolic (quasi-geometric) discounting, changes the optimal conduct of monetary policy. Prior macro work on quasi-hyperbolic discounting concentrated on growth models, consumption/saving, and multiple equilibria; almost none examined monetary policy. The paper fills this gap.
Model setup: A nonlinear New Keynesian business-cycle model with monopolistically competitive firms that own capital, hire labor (Cobb-Douglas, alpha=0.33), and set prices subject to Rotemberg (1982) quadratic adjustment costs (omega=100, roughly a Calvo model with 1-year average price duration). Households consume a Dixit-Stiglitz bundle, supply labor, and save via one-period nominal bonds (zero net supply) and equities (fixed net supply of 1). Preferences are quasi-hyperbolic: the discount sequence is 1, betatheta, betatheta^2, … with theta in (0,1) the usual geometric factor and beta the present-bias factor (beta=1 restores geometric discounting; beta<1 is greater short-run impatience). Three shocks: technology, cost-push (elasticity/markup), and labor-supply. The central bank shares household momentary utility and sets the nominal bond return optimally under discretion (its discount factors gamma, xi may differ from household’s beta, theta); a Taylor-type rule is the comparison. The model is solved globally with Chebyshev polynomials and Gaussian cubature to obtain a unique interior solution to generalized Euler equations, avoiding log-linearization indeterminacy. A period is a quarter; theta=0.99, sigma=1 (log utility), Frisch elasticity nu=1, chi=1, depreciation delta=0.025, steady-state elasticity epsilon=11 (10% markup). The authors restrict attention to beta in [0.90, 1] because experimentally plausible values (beta around 0.60, per Meier-Sprenger 2015 and Wang-Rieger-Hens 2016, median ~0.60) generate implausible/extreme general-equilibrium outcomes.
Main quantitative findings (benchmark, central bank benevolent, beta=gamma): (1) Greater present bias lowers saving and capital accumulation. Lowering beta=gamma from 1.0 to 0.9 reduces output by about 10% (10.02%), with capital falling much more (24.55%), labor much less (1.84%), consumption 6.02%, and the real wage 7.77%; cutting beta to 0.7 cuts output ~30% (roughly linear). (2) Discretionary policy still produces positive average inflation (inflation bias), but the bias is SMALLER under present bias: average inflation falls from 2.553% (beta=1) to 2.362% (beta=0.9) under discretion, because firms, whose equity holders discount hyperbolically, spread costly price changes over time — present bias acts like greater price rigidity, so smaller inflation surprises suffice. (3) Asset returns balloon: a nonpecuniary return to capital (1-beta)/beta * KK(Z) appears, raising the total return on capital rcap and spilling into bonds. At beta=0.9 (discretion) the net real return on capital reaches 48.928% and the real interest rate 48.926% (annualized), versus ~4.0% at beta=1 — well above observed real rates, so experimentally-sized present bias is wildly counterfactual in general equilibrium. (4) The Taylor rule increasingly underperforms optimal discretion as households become more impatient (suboptimal-policy cost lambda_S rises with present bias). (5) Quasi-hyperbolic and geometric discounting are NOT equivalent because of the nonpecuniary (time-inconsistency) return to capital.
Policy implications: A benevolent central bank (sharing household preferences) keeps steady-state inflation under control across a wide range of discount factors. If instead the central bank does NOT adopt household time preferences and tries to discourage early consumption/delayed saving, it achieves only a marginal output gain at the cost of much higher average inflation. Conversely, delegating policy to a central banker who is MORE present-biased than households raises household welfare (akin to Rogoff’s conservative central banker), because it emphasizes the current-period cost of changing prices, lowering inflation volatility and average inflation toward zero.
Layer 2: Deep Dive
What is the model’s solution strategy and why does it matter for the results?
The model is solved as a fully nonlinear global problem rather than log-linearized. The authors use Chebyshev polynomials (giving continuous decision rules and derivatives) and compute expectations via Gaussian cubature instead of finite-state Markov chains. They impose symmetry across households and firms in equilibrium (kt=Kt, ct=Ct, etc.; bonds in zero net supply Bt=0, stocks fixed St=1) and solve the interior solution to a system of generalized Euler equations, following Maliar and Maliar (2005). This matters because quasi-hyperbolic discounting creates strategic interaction between the household and its future self that can generate multiple equilibria (Krusell and Smith 2003); log-linearization can introduce indeterminacy (Maliar and Maliar 2006a). Allowing a large domain for wealth/capital is, per Cao and Werning (2018), key to ruling out local multiplicities. The result is a unique stable equilibrium.
What is the central economic mechanism through which present bias affects asset returns?
Equation (25): the total gross return on capital equals the pecuniary part (shadow rental rate rk + 1 - delta) PLUS a nonpecuniary part (1-beta)/beta * KK(Z), where KK(Z) is the derivative of next period’s capital decision rule with respect to current capital. This nonpecuniary term arises only under time inconsistency (it vanishes when beta=1): the firm/household uses capital accumulation to constrain its future self. Even small present bias makes this term large, raising rcap; because households arbitrage between stocks and bonds (bonds offer no nonpecuniary return), the real bond rate rises commensurately. This is why beta=0.9 pushes real rates to ~49% — counterfactual — and why the paper restricts to beta in [0.90,1].
Why does present bias REDUCE the discretionary inflation bias rather than raise it?
Quasi-hyperbolic discounting weights the cost of changing prices today more heavily than future price-change costs (since firms’ equity holders discount the future more). When shocks hit, firms make smaller price changes now and defer the rest, so present bias acts like an increase in price rigidity. The central bank then calculates that smaller inflation surprises are enough to boost output to the efficient level, so equilibrium average inflation falls (2.553% at beta=1 down to 2.362% at beta=0.9 under discretion). The structure of the policy trade-off (eq. 21) is unchanged by present bias; only the relative costs and benefits shift.
How do the three shocks differ in their interaction with present bias?
Technology shock (Fig 1): financial variables are affected most; relative to geometric baseline, consumption rises more and labor rises less, pushing real wages and real marginal costs up; the real and nominal interest rates rise by more due to increased demand for current consumption. Price-elasticity/cost-push shock (Fig 2): responses are generally more muted; labor rises less, consumption more, inflation falls by less (firms defer price changes); the real interest rate and nominal bond return are the most sensitive variables. Labor-supply shock (Fig 3): an adverse shock raises labor disutility, cutting labor, output, consumption, investment and capital while raising the real wage; inflation and real marginal costs are little affected, and policy eases (real and nominal rates fall); present bias mainly amplifies consumption/investment responses and raises impact responses, increasing unconditional volatility.
What welfare measures are used and how do they move with present bias?
Three consumption-equivalent costs: lambda_C (Lucas 1987 cost of business cycles), lambda_B (magnitude of the present bias), and lambda_S (cost of the suboptimal Taylor rule vs. optimal discretion). Greater present bias lowers the utility level U, raises lambda_C (e.g., 0.033 to 0.045 under discretion as beta=gamma goes 1.0 to 0.9), and raises lambda_B substantially (0 to 2.808). lambda_B rises much more than lambda_C, showing that discounting future consumption dominates cyclical-volatility effects. lambda_S also rises, meaning the Taylor rule becomes progressively more costly relative to discretion as households grow more impatient.
What does the comparison of quasi-hyperbolic vs. geometric discounting (Table 3) show?
Comparing quasi-hyperbolic (beta=gamma=0.99, theta=0.99) to a geometric model (beta=1, theta=0.992) calibrated to be comparable: the geometric model produces LOWER average capital, labor, output, consumption, investment, and real wage. Under quasi-hyperbolic discounting, household ownership of capital generates a nonpecuniary return that compensates for the lower rental rate and encourages higher saving, so the capital stock is larger even though the marginal product and rental rate of capital are lower. The two are genuinely non-equivalent because of the time-inconsistency-driven nonpecuniary return. Welfare cost of business cycles is higher under geometric than quasi-hyperbolic discounting and higher under the Taylor rule than optimal discretion; to be compensated for the Taylor rule’s suboptimality households would require a permanent consumption increase of 0.07% (geometric) or 0.10% (quasi-hyperbolic).
What is the policy-delegation result and its scope condition?
In Section 6 the central bank’s discount factor gamma is allowed to differ from the household’s beta. Allowing the central bank to be MORE present-biased than households (lower gamma) raises household welfare: welfare is higher in column (2) (gamma=0.9, beta=1) than column (1) (both =1), and higher in column (3) (both=0.9) than column (4) (beta=0.9, gamma=1). The mechanism is that a more present-biased central banker emphasizes the current-period cost of changing prices — like greater price rigidity or a conservative (Rogoff 1985) central banker — yielding less volatile and lower average inflation (e.g., inflation drops to 0.699% in column 2). Effects on real variables are small; effects on nominal variables are larger and quantitatively significant. This parallels Dennis (2014), where distorting the discretionary central bank’s objective (risk-sensitivity) improved welfare. Scope: this holds because policy is conducted under discretion, which is suboptimal; under commitment the delegation logic would differ.
Where does present bias enter, and not enter, the equilibrium conditions?
It does NOT enter the household’s intratemporal labor-leisure condition (eq. 7) or the firm’s static conditions defining the rental rate and real wage (eqs. 12-13). It enters the bond and stock Euler equations (eqs. 8-9) and the Phillips curve (eq. 11) only by changing how next period is discounted (via beta*theta). Most importantly, it enters the firm’s capital-accumulation Euler equation (eq. 10) in TWO ways: changing the discount rate AND adding the nonpecuniary term (1-beta)*KK(Z), which disappears when beta=1. The Phillips curve’s structure is otherwise unaffected because, in the symmetric equilibrium, all firms set the same price so the relative price equals one.
What robustness/extensions are considered?
Capital ownership: the main analysis has firms own capital, but Online Appendices 1-2 show households-own-capital (rented competitively) is equivalent even under quasi-hyperbolic discounting. Geometric-discounting benchmark is explored fully in Online Appendix 4. Numerical accuracy (consumption-Euler residuals) is reported in the appendix. The authors also vary the markup elasticity epsilon and note that values of 6 or 21 gave implausible steady-state inflation, so they use epsilon=11. They report results across beta=gamma of 1.00, 0.99, 0.95, 0.90 under both discretion and the Taylor rule.
How does this paper differ from the closest prior work?
Graham and Snower (2013) study a sticky-WAGE NK model where households prefer positive inflation because it erodes real wages over time, overturning the Friedman rule. This paper uses sticky PRICES (Rotemberg), firm-owned capital, and finds present bias LOWERS average inflation under optimal discretion. Maeda (2018) extends Krusell-Smith to a cash-in-advance monetary economy and recovers the Friedman rule via cash constraints. Most prior quasi-hyperbolic macro work (Krusell-Smith 2003, Maliar-Maliar, Krusell-Kuruscu-Smith 2002) focused on growth, consumption/saving, multiplicity, or income distribution — not monetary policy. This paper is distinctive in focusing on optimal discretionary monetary policy, quantifying the inflation bias, and identifying the asset-return implications and the welfare case for delegating to a present-biased central banker.