Subject Index

Contents

Subject Index#

Numerals are chapter numbers. Preface and Road Map name the front matter; App. 8 and App. 11 name the two chapter appendices. Entries that carry a numbered definition, proposition, or theorem link to it directly. Cross-references read see and see also.

A#

  • absolute continuity of alternative probability models — 8

  • act (decision theory) — 10

    • Anscombe-Aumann — 10

    • Savage — 10

  • additive functionalDefinition 4.1, 4

    • decomposition of — Proposition 4.1, 4

    • martingale component, construction — 4

    • exponential of — 8

    • stochastic volatility example — Example 4.1

  • additive martingale3, 4

  • admissibility of decision rules — 10

  • aggregate consumption, long-run risk in — 4, 11

  • ambiguity1, 10

    • aversion — 10

    • interval — Remark 8.8

    • distinguished from risk and misspecification — 10

  • aperiodicity2, Theorem 2.2

  • Arrow securities, recovering transition probabilities from — 8

  • asset pricing

    • cash flows — 8

    • conditional moment restrictions — Example 13.2

    • long-term risk-return tradeoff — 8

    • marginal valuations as — 12

B#

  • balanced growth, stochastic — 3

  • Bayes’ rule, posterior updating — 6, 10

  • Bayesian decision theory10

    • conditional problem — 10

    • robust — 10, 10

    • threshold rule for model selection — Remark 7.3

  • belief distortion8

    • bounds from asset prices — 8

    • subjective belief factor — 8

    • survey measurement of — 8

    • wedge — 8

  • beliefs of agents inside a model1, 8

  • Birkhoff’s theoremTheorem 1.2, 1

  • Borel set1

  • Brownian motion

    • drift distortion of — 11, 12

    • stochastic responses to — 5

C#

  • canonical construction of a probability space — 1

  • cash flows, valuation of stochastic — 8

    • cointegrated families of — 8

    • finite versus infinite value — 8

    • Gordon growth model, stochastic — 8

    • holding-period returns — 8

  • central limit theorem

  • certainty equivalent, risk-adjusted — 4, 11

  • Chernoff entropy7, 8

  • climate change, social cost of — 12

  • cointegration3

    • and long-term valuation — 8

    • cointegrating vector — 3

    • imposed on a VAR — 4

  • commitment, dynamic robust decision problem under — 10

  • conditional expectation

    • given invariant events — 1

    • as least squares projection — 1

    • operator \({\mathbb T}\)2

  • conjugate prior6

  • consumption, logarithm of — 4, 11

  • continuation value4, 11

    • continuous-time limit — 11

    • regime switching — 4

    • small-noise expansion — 11

  • counterfactuals, and structural models — 5, 8

  • co-states, relation to stochastic responses — 12

D#

  • decision rule10

    • threshold — 10

  • deep uncertainty10

  • detectability, statistical7, 8

  • divergence, statistical — 10

    • intertemporal — 8, 10

    • minimum divergence problem — 8

    • \(\phi\)-divergence — 10, 13

    • quadratic — 13

    • see also relative entropy

  • drift condition for stochastic stability — 2, 2

  • dynamic mode decomposition8

E#

F#

  • Feynman-Kac equation12

  • filtration1, 3

  • Fisher information7

    • nuisance parameters and — 7

  • forecasting

    • multiperiod, GMM — 13

    • convergence of multi-period — 2

G#

  • Gaussian, see normal distribution

  • generalized method of moments (GMM)13

    • continuously-updated estimator — 13

    • decomposing moment conditions — 13

    • efficiency bound — 13

    • indirect inference — 13

    • misspecification, quantifying — 13

    • moment matching — Example 13.1

    • selection matrices — 13

    • tests of overidentifying restrictions — 13

  • Gibbs sampling6

  • Gordin’s theoremProposition 3.2

  • Gordon growth model, stochastic — 8

  • growth

    • geometric — 8

    • regimes — 4, 6

H#

  • habit persistence11

  • Hamiltonian formulation — 12

  • Haussmann-Clark-Ocone representation5

  • hidden Markov model6

    • discrete hidden state — 6

    • parameters as invariant hidden states — 6

    • VAR regimes — 6

I#

  • identification

    • partial — 8, Remark 8.8

    • of shocks in a structural VAR — 6

  • impulse response function5

    • causal readings of — 5

    • local projections — 5

    • as limit of shock elasticities — Example 9.1

  • indirect inference13

  • information state vector7

  • innovation process, Kalman — 6

  • instrumental variables, nonlinear — Example 13.1

  • intertemporal elasticity of substitution11

    • differing from unity — 12

  • invariant event1

    • for a Markov process — 2

    • conditioning on — 1, 13

  • irreducibility2

  • Ito’s formula11

J#

  • Jensen’s inequality7, 8

  • jumps, Poisson — 12

    • intensities, distortion of — 12

K#

  • Kalman filter6

    • gain — 6

    • innovations representation — 6

    • Riccati recursion — 6

  • Kalman smoother6

  • Kullback-Leibler divergence, see relative entropy

L#

  • Law of Large Numbers1, Theorem 1.2

    • conditioned on invariant events — 1

    • and rational expectations — 1

    • what it can and cannot disclose — 1

  • Law of Iterated Expectations2, 3

  • least squares

    • as conditional expectation — 1

    • estimating a VAR — 1

  • likelihood function, distinguished from prior — 10

  • likelihood ratio process7, 7

  • limiting empirical measure1

  • local projection5

  • long-run risk4, 10, 11

  • long memory3

  • Lyapunov equation, discrete — 2

M#

  • Malliavin calculus5

  • marginal valuation12

    • decomposition by horizon — 12

    • decomposition by state variable — 12

    • robust — 12

    • with jumps — 12

  • Markov chain, finite-state — Example 2.2, 2

  • Markov process2

    • constituents — 2

    • stationary distribution — Definition 2.1

    • transition distribution — 2

  • martingale

    • additive — 3, 4

    • convergence theorem — 8, 10

    • multiplicative — 7, 8

    • extraction of — 4, 4

  • measure-preserving transformation1, Theorem 1.1

  • misspecification, model — 10

    • bounding expectations under — 13

    • distinguished from risk and ambiguity — 10

    • quantifying, in GMM — 13

    • robust control and — 10, 11

  • mixture of normals6, 6

  • model selection7, 10

  • moment restrictions

  • moving-average representationExample 1.8, 3

    • continuous-time counterpart — 5

    • non-invertible — Example 6.1

  • multiplicative functionalDefinition 8.1, 8

    • factorization of — Theorem 8.1, 8

    • perturbation of — 9

    • three primitive types — 8

    • worked example — 8

  • multiplicative martingaleDefinition 7.1

  • Murphy’s law, stochastic version — 11

N#

  • Negishi weights11

  • normal distribution, multivariate — 2, 6

  • nuisance parameters7, 13

O#

  • Ornstein-Uhlenbeck process5

  • overidentifying restrictions, tests of — 13

P#

  • periodicity of a Markov process — 2

  • permanent income model4

  • permanent shock3, 4

    • inferred from asset prices — 8

    • identification of — 4

  • Perron-Frobenius theory8

  • perturbation methods4, 11

    • small-noise expansion — 11

    • order zero, one, two — 11, App. 11

  • pessimism parameter — 8, 11

  • planner’s problem11, 11

  • prior probability distribution1, 10

    • conjugate — 6

    • improper — 6

    • robustness to — 10

    • worst-case — 10

  • probability space1

  • proportional risk premium8, 9

Q#

  • quadratic approximation of state dynamics — 4

R#

  • Radon-Nikodym derivative8

  • rational expectations1, 8

    • econometrics — 8

    • as a consistency requirement — 8

    • communism of beliefs — 8

  • recursive utility4, 11

    • continuous-time limit — 11

    • homogeneous of degree one — 11

    • robustness interpretation — 11

  • regime switching4, 6

  • relative entropy10, 11

    • discounted — 10

    • continuous-time counterpart — 11

    • in GMM — 13

    • penalizing belief distortion — 8

  • resolvent operator2

  • risk

    • distinguished from uncertainty — 1, 10

    • function (Wald) — 10

    • long-run — 4, 11

  • risk aversion, separated from intertemporal substitution — 11

  • risk-return tradeoff, long-term — 8

  • robust control10, 11

  • Ross recovery8

S#

  • score processDefinition 7.2, 7

  • self-confirming equilibrium1

  • semigroup of operators — 8

  • shadow price4, 11

  • shock elasticity, see elasticity, shock

  • skip sampling2

  • smooth ambiguity preferences10

  • social cost of carbon12

  • social value of research and development12

  • spectral density estimation13

  • state vector2

  • statistical modelDefinition 1.6, 1

    • learning which one applies — 6, 7

    • as ergodic building block — 1

    • partially specified — 13

  • stationary distributionDefinition 2.1, 2

  • stationary increments3

    • Markovian — 4

  • stationary stochastic process1

  • stochastic discount factor4, 11

    • approximation — 11

    • martingale component of — 8, 8

  • stochastic response5, 5

    • to initial shocks — 5

    • relation to shock elasticities — 9

    • in marginal valuation — 12

  • stochastic stabilityDefinition 8.2, 8

  • stochastic volatilityExample 4.1, Example 8.7

  • strong contractionDefinition 2.6, 2

  • structural model5, 1

  • structural vector autoregression5, 6

  • submartingaleProposition 7.2

  • supermartingaleProposition 7.2

  • survey forecasts8

T#

  • term structure of interest rates8

  • time reversibility2

  • transient state1, 2

  • transition distribution2

  • trend, in a stationary-increment process — 3

  • Type I and Type II error10

U#

  • uncertainty

    • deep — 10

    • Knightian — 1, 10

    • prices — 11

    • quantification — 10

  • unit eigenvalue2

V#

  • variance multiplier11

  • variational preferences10

  • variational process, see stochastic response

  • vector autoregressionExample 2.1, 2

    • ergodic — 2

    • estimating — 1, 6

    • infinite past — 2

    • martingale increment of — 4

    • multiplicative functional built from — Example 8.6

    • regimes — 6

    • stationary but not ergodic — 2

W#

  • worst-case

    • density — 10

    • prior — 10