(BQ) Part 2 book Advanced macroeconomics has contents: Dynamic stochastic general equilibrium models of fluctuations, budget deficits and fiscal policy, unemployment, monetary policy, financial markets and financial crises.
Chapter DYNAMIC STOCHASTIC GENERAL-EQUILIBRIUM MODELS OF FLUCTUATIONS Our analysis of macroeconomic fluctuations in the previous two chapters has developed two very incomplete pieces In Chapter 5, we considered a full intertemporal macroeconomic model built from microeconomic foundations with explicit assumptions about the behavior of the underlying shocks The model generated quantitative predictions about fluctuations, and is therefore an example of a quantitative dynamic stochastic general-equilibrium, or DSGE, model The problem is that, as we saw in Section 5.10, the model appears to be an empirical failure For example, it rests on large aggregate technology shocks for which there is little evidence; its predictions about the effects of technology shocks and about business-cycle dynamics appear to be far from what we observe; and it implies that monetary disturbances not have real effects To address the real effects of monetary shocks, Chapter introduced nominal rigidity It established that barriers to price adjustment and other nominal frictions can cause monetary changes to have real effects, analyzed some of the determinants of the magnitude of those effects, and showed how nominal rigidity has important implications for the impacts of other disturbances But it did so at the cost of abandoning most of the richness of the model of Chapter Its models are largely static models with one-time shocks; and to the extent their focus is on quantitative predictions at all, it is only on addressing broad questions, notably whether plausibly small barriers to price adjustment can lead to plausibly large effects of monetary disturbances Researchers’ ultimate goal is to build a model of fluctuations that combines the strengths of the models of the previous two chapters This chapter starts down that path But we will not reach that goal The fundamental problem is that there is no agreement about what such a model should look like As we will see near the end of the chapter, the closest thing we have to a consensus starting point for a micro founded DSGE model with nominal rigidity has core implications that appear to be grossly counterfactual There are two possible ways to address this problem One is to modify the 309 310 Chapter DSGE MODELS OF FLUCTUATIONS baseline model But a vast array of modifications and extensions have been proposed, the extended models are often quite complicated, and there is a wide range of views about which modifications are most useful for understanding macroeconomic fluctuations The other possibility is to find a different baseline But that is just a research idea, not a concrete proposal for a model Because of these challenges, this chapter moves us only partway toward constructing a realistic DSGE model of fluctuations The bulk of the chapter extends the analysis of the microeconomic foundations of incomplete nominal flexibility to dynamic settings This material vividly illustrates the lack of consensus about how best to build a realistic dynamic model of fluctuations: counting generously, we will consider seven distinct models of dynamic price adjustment As we will see, the models often have sharply different implications for the macroeconomic consequences of microeconomic frictions in price adjustment This analysis shows the main issues in moving to dynamic models of price-setting and illustrates the list of ingredients to choose from, but it does not identify a specific ‘‘best practice’’ model The main nominal friction we considered in Chapter was a fixed cost of changing prices, or menu cost In considering dynamic models of price adjustment, it is therefore tempting to assume that the only nominal imperfection is that firms must pay a fixed cost each time they change their price There are two reasons not to make this the only case we consider, however First, it is complicated: analyzing models of dynamic optimization with fixed adjustment costs is technically challenging and only rarely leads to closed-form solutions Second, the vision of price-setters constantly monitoring their prices and standing ready to change them at any moment subject only to an unchanging fixed cost may be missing something important Many prices are reviewed on a predetermined schedule and are only rarely changed at other times For example, many wages are reviewed annually; some union contracts specify wages over a three-year period; and many companies issue catalogues with prices that are in effect for six months or a year Thus price changes are not purely state dependent (that is, triggered by developments within the economy, regardless of the time over which the developments have occurred); they are partly time dependent (that is, triggered by the passage of time) Because time-dependent models are easier, we will start with them Section 7.1 presents a common framework for all the models of this part of the chapter Sections 7.2 through 7.4 then consider three baseline models of time-dependent price adjustment: the Fischer, or Fischer-Phelps-Taylor, model (Fischer, 1977; Phelps and Taylor, 1977); the Taylor model (Taylor, 1979); and the Calvo model (Calvo, 1983) All three models posit that prices (or wages) are set by multiperiod contracts or commitments In each period, the contracts governing some fraction of prices expire and must be renewed; expiration is determined by the passage of time, not economic developments The central result of the models is that multiperiod contracts Chapter DSGE MODELS OF FLUCTUATIONS 311 lead to gradual adjustment of the price level to nominal disturbances As a result, aggregate demand disturbances have persistent real effects The Taylor and Calvo models differ from the Fischer model in one important respect The Fischer model assumes that prices are predetermined but not fixed That is, when a multiperiod contract sets prices for several periods, it can specify a different price for each period In the Taylor and Calvo models, in contrast, prices are fixed: a contract must specify the same price each period it is in effect The difference between the Taylor and Calvo models is smaller In the Taylor model, opportunities to change prices arrive deterministically, and each price is in effect for the same number of periods In the Calvo model, opportunities to change prices arrive randomly, and so the number of periods a price is in effect is stochastic In keeping with the assumption of time-dependence rather than state-dependence, the stochastic process governing price changes operates independently of other factors affecting the economy The qualitative implications of the Calvo model are the same as those of the Taylor model Its appeal is that it yields simpler inflation dynamics than the Taylor model, and so is easier to embed in larger models Section 7.5 then turns to two baseline models of state-dependent price adjustment, the Caplin-Spulber and Danziger-Golosov-Lucas models (Caplin and Spulber, 1987; Danziger, 1999; Golosov and Lucas, 2007) In both, the only barrier to price adjustment is a constant fixed cost There are two differences between the models First, money growth is always positive in the Caplin-Spulber model, while the version of the Danziger-GolosovLucas model we will consider assumes no trend money growth Second, the Caplin-Spulber model assumes no firm-specific shocks, while the DanzigerGolosov-Lucas model includes them Both models deliver strong results about the effects of monetary disturbances, but for very different reasons After Section 7.6 examines some empirical evidence, Section 7.7 considers two more models of dynamic price adjustment: the Calvo-withindexation model and the Mankiw Reis model (Mankiw and Reis, 2002; Christiano, Eichenbaum, and Evans, 2005) These models are more complicated than the models of the earlier sections, but appear to have more hope of fitting key facts about inflation dynamics The final sections begin to consider how dynamic models of price adjustment can be embedded in models of the business cycle Section 7.8 presents a complete DSGE model with nominal rigidity the canonical three-equation new Keynesian model of Clarida, Galí, and Gertler (2000) Unfortunately, as we will see, the model is much closer to the baseline real-business-cycle model than to our ultimate objective Like the baseline RBC model, it is elegant and tractable But also like the baseline RBC model, the evidence for its key ingredients is weak, and we will see in Section 7.9 that together the ingredients make predictions about the macroeconomy that appear to be almost embarrassingly incorrect Section 7.10 therefore discusses elements of other DSGE models with monetary non-neutrality Because of the models’ 312 Chapter DSGE MODELS OF FLUCTUATIONS complexity and the lack of agreement about their key ingredients, however, it stops short of analyzing other fully specified models 7.1 Building Blocks of Dynamic New Keynesian Models Overview We will analyze the various models of dynamic price adjustment in a common framework The framework draws heavily on the model of exogenous nominal rigidity in Section 6.1 and the model of imperfect competition in Section 6.5 Time is discrete Each period, imperfectly competitive firms produce output using labor as their only input As in Section 6.5, the production function is one-for-one; thus aggregate output and aggregate labor input are equal The model omits government purchases and international trade; thus, as in the models of Chapter 6, aggregate consumption and aggregate output are equal Households maximize utility, taking the paths of the real wage and the real interest rate as given Firms, which are owned by the households, maximize the present discounted value of their profits, subject to constraints on their price-setting (which vary across the models we will consider) Finally, a central bank determines the path of the real interest rate through its conduct of monetary policy Households There is a fixed number of infinitely lived households that obtain utility from consumption and disutility from working The representative household’s objective function is ∞ β t [U (C t ) − V (L t )], < β < (7.1) t =0 As in Section 6.5, C is a consumption index that is a constant-elasticity-ofsubstitution combination of the household’s consumption of the individual goods, with elasticity of substitution η > We make our usual assumptions about the functional forms of U (•) and V(•):1 1−θ U (C t ) = V(L t ) = B γ Ct 1−θ γ Lt , , θ > 0, B > 0, γ > The reason for introducing B in (7.3) will be apparent below (7.2) (7.3) 7.1 Building Blocks of Dynamic New Keynesian Models 313 Let W denote the nominal wage and P denote the price level Formally, P is the price index corresponding to the consumption index, as in Section 6.5 Throughout this chapter, however, we use the approximation we used in the Lucas model in Section 6.9 that the log of the price index, which we will denote p, is simply the average of firms’ log prices An increase in labor supply in period t of amount dL increases the household’s real income by (Wt /Pt ) dL The first-order condition for labor supply in period t is therefore V (L t ) = U (C t ) Wt Pt (7.4) Because the production function is one-for-one and the only possible use of output is for consumption, in equilibrium C t and L t must both equal Yt Combining this fact with (7.4) tells us what the real wage must be given the level of output: Wt Pt = V (Yt ) U (Yt ) (7.5) Substituting the functional forms in (7.2) (7.3) into (7.5) and solving for the real wage yields Wt Pt θ + γ −1 = BYt (7.6) Equation (7.6) is similar to equation (6.58) in the model of Section 6.5 Since we are making the same assumptions about consumption as before, the new Keynesian IS curve holds in this model (see equation [6.8]): ln Yt = a + ln Yt +1 − rt θ (7.7) Firms Firm i produces output in period t according to the production function Yi t = L i t , and, as in Section 6.5, faces demand function Yi t = Yt (Pi t /Pt )−η The firm’s real profits in period t, R t , are revenues minus costs: Rt = = Yt Pi t Pt Yi t − Pi t Pt Wt Pt 1−η − Yi t Wt Pi t Pt Pt −η (7.8) Consider the problem of the firm setting its price in some period, which we normalize to period As emphasized above, we will consider various assumptions about price-setting, including ones that imply that the length 314 Chapter DSGE MODELS OF FLUCTUATIONS of time a given price is in effect is random Thus, let q t denote the probability that the price the firm sets in period zero is in effect in period t Since the firm’s profits accrue to the households, it values the profits according to the utility they provide to households The marginal utility of the representative household’s consumption in period t relative to period is β t U (C t )/U (C ); denote this quantity λ t The firm therefore chooses its price in period 0, P i , to maximize ∞ E t = q t λt R t ≡ A, where R t is the firm’s profits in period t if P i is still in effect Using equation (7.8) for R t , we can write A as ⎡ ⎤ ∞ 1−η −η Pi Wt Pi ⎦ q t λ t Yt − A= E⎣ Pt Pt Pt t =0 (7.9) ⎡ ⎤ =E⎣ ∞ η −1 q t λ t Yt Pt 1−η Pi −η − Wt P i ⎦ t =0 The production function implies that marginal cost is constant and equal to Wt , and the elasticity of demand for the firm’s good is constant Thus the price that maximizes profits in period t, which we denote P t∗ , is a constant times Wt (see equation [6.57]) Equivalently, Wt is a constant times P t∗ Thus we can write the expression in parentheses in (7.9) as a function of just P i and P t∗ As before, we will end up working with variables expressed in logs rather than levels Thus, rewrite (7.9) as ⎡ ⎤ A= E⎣ ∞ η −1 q t λ t Yt Pt F ( p i , pt∗ )⎦ , (7.10) t =0 where p i and p ∗t denote the logs of P i and P t∗ One can say relatively little about the P i that maximizes A in the general case Two assumptions allow us to make progress, however The first, and most important, is that inflation is low and that the economy is always close to its flexible-price equilibrium The other is that households’ discount factor, β, is close to These assumptions have two important implications η −1 is negligible relabout (7.10) The first is that the variation in λ t Yt Pt ative to the variation in q t and p ∗t The second is that F (•) can be well approximated by a second-order approximation around p i = p ∗t Period-t profits are maximized at p i = p ∗t ; thus at p i = p ∗t , ∂F ( p i , p ∗t )/∂p i is zero and 2 ∂ F ( p i , p ∗t )/∂ p i is negative It follows that F ( p i , p ∗t ) F ( p ∗t , p ∗t ) − K ( p i − p ∗t )2 , K > (7.11) These claims can be made precise with appropriate formalizations of the statements that inflation is small, the economy is near its flexible-price equilibrium, and β is close to 7.1 Building Blocks of Dynamic New Keynesian Models 315 This analysis implies that the problem of choosing Pi to maximize A can be simplified to the problem, ∞ q t E [( p i − p ∗t )2 ] pi t =0 (7.12) ∞ = ∗ ∗ q t {( p i − E [ p t ]) + Var ( p t )}, t= where we have used the facts that q t and pi are not uncertain and that the expectation of the square of a variable equals the square of its expectation plus its variance Finding the first-order condition for pi and rearranging gives us ∞ pi = ωt E [ p ∗t ], (7.13) t =0 where ωt ≡ q t / ∞ τ =0 q τ ωt is the probability that the price the firm sets in period will be in effect in period t divided by the expected number of periods the price will be in effect Thus it measures the importance of period t to the choice of pi Equation (7.13) states that the price firm i sets is a weighted average of the profit-maximizing prices during the time the price will be in effect In two of the models we will consider in this chapter (the Calvo model of Section 7.4 and the Christiano Eichenbaum Evans model of Section 7.7), prices are potentially in effect for many periods In these cases, the assumption that the firm values profits in all periods equally is problematic, and so it is natural to relax the assumption that the discount factor is close to The extension of (7.12) to a general discount factor is ∞ pi q t β t {( pi − E [ p ∗t ])2 + Var ( p ∗t )} (7.14) t=0 The resulting expression for the optimal pi analogous to (7.13) is ∞ pi = t=0 ~t E [ p ∗ ], ω t ~t ≡ ω β t qt ∞ τ =0 β τ qτ (7.15) Finally, it will often be useful to substitute for p ∗t in equation (7.13) (or [7.15]) A firm’s profit-maximizing real price, P ∗/P , is η/(η − 1) times the real wage, W/P And we know from equation (7.6) that wt equals pt + ln B + (θ + γ − 1)yt (where wt ≡ ln Wt and yt ≡ ln Yt ) Thus, the profitmaximizing price is p ∗ = p + ln[η/(η − 1)] + ln B + (θ + γ − 1)y (7.16) 316 Chapter DSGE MODELS OF FLUCTUATIONS Note that (7.16) is of the form p ∗ = p + c + φy, φ > 0, of the static model of Section 6.5 (see [6.60]) To simplify this, let m denote log nominal GDP, p + y, define φ ≡ θ +γ −1, and assume ln[η/(η−1)]+ln B = for simplicity.3 This yields p ∗t = φm t + (1 − φ)pt (7.17) Substituting this expression into (7.13) gives us ∞ pi = ωt E [φm t + (1 − φ)pt ] (7.18) t =0 ~ (see In the case of a general discount factor, the ω’s are replaced by the ω’s [7.15]) The Central Bank Equation (7.18) is the key equation of the aggregate supply side of the model, and equation (7.7) describes aggregate demand for a given real interest rate It remains to describe the determination of the real interest rate To this, we need to bring monetary policy into the model One approach, along the lines of Section 6.4, is to assume that the central bank follows some rule for how it sets the real interest rate as a function of macroeconomic conditions This is the approach we will use in Section 7.8 and in much of Chapter 12 Our interest here, however, is in the aggregate supply side of the economy Thus, along the lines of what we did in Part B of Chapter 6, we will follow the simpler approach of taking the path of nominal GDP (that is, the path of m t ) as given We will then examine the behavior of the economy in response to various paths of nominal GDP, such as a one-time, permanent increase in its level or a permanent increase in its growth rate As described in Section 6.5, a simple interpretation of the assumption that the path of nominal GDP is given is that the central bank has a target path of nominal GDP and conducts monetary policy to achieve it This approach allows us to suppress not only the money market, but also the new Keynesian IS equation, (7.7) 7.2 Predetermined Prices: The Fischer Model We can now turn to specific models of dynamic price adjustment Before proceeding, however, it is important to emphasize that the issue we are interested in is incomplete adjustment of nominal prices and wages There are many reasons involving uncertainty, information and renegotiation costs, It was for this reason that we introduced B in (7.3) 7.2 Predetermined Prices: The Fischer Model 317 incentives, and so on that prices and wages may not adjust freely to equate supply and demand, or that firms may not change their prices and wages completely and immediately in response to shocks But simply introducing some departure from perfect markets is not enough to imply that nominal disturbances matter All the models of unemployment in Chapter 11, for example, are real models If one appends a monetary sector to those models without any further complications, the classical dichotomy continues to hold: monetary disturbances cause all nominal prices and wages to change, leaving the real equilibrium (with whatever non-Walrasian features it involves) unchanged Any microeconomic basis for failure of the classical dichotomy requires some kind of nominal imperfection Framework and Assumptions We begin with the Fischer model of staggered price adjustment.4 The model follows the framework of the previous section Price-setting is assumed to take a particular form, however: each price-setter sets prices every other period for the next two periods And as emphasized above, the model assumes that the price-setter can set different prices for the two periods That is, a firm setting its price in period sets one price for period and one price for period Since each price will be in effect for only one period, equation (7.13) implies that each price (in logs) equals the expectation as of period of the profit-maximizing price for that period In any given period, half of price-setters are setting their prices for the next two periods Thus at any point, half of the prices in effect are those set the previous period, and half are those set two periods ago No specific assumptions are made about the process followed by aggregate demand For example, information about m t may be revealed gradually in the periods leading up to t ; the expectation of m t as of period t − 1, E t −1 m t , may therefore differ from the expectation of m t the period before, E t −2 m t Solving the Model In any period, half of prices are ones set in the previous period, and half are ones set two periods ago Thus the average price is pt = 12 ( p1t + p 2t ), (7.19) The original versions of the Fischer and Taylor models focused on staggered adjustment of wages; prices were in principle flexible but were determined as markups over wages For simplicity, we assume instead that staggered adjustment applies directly to prices Staggered wage adjustment has qualitatively similar implications The key difference is that the microeconomic determinants of the parameter φ in the equation for desired prices, (7.17), are different under staggered wage adjustment (Huang and Liu, 2002) 318 Chapter DSGE MODELS OF FLUCTUATIONS where p1t denotes the price set for t by firms that set their prices in t − 1, and p 2t the price set for t by firms that set their prices in t − Our assumptions about pricing from the previous section imply that p1t equals the expectation as of period t − of p ∗t , and p2t equals the expectation as of t − of p ∗t Equation (7.17) therefore implies p1t = Et−1 [φm t + (1 − φ) pt ] = φ Et−1 m t + (1 − φ) 12 ( p1t + p2t ), p2t = Et−2 [φm t + (1 − φ) pt ] = φ Et−2 m t + (1 − φ) 12 (E t−2 p1t + p2t ), (7.20) (7.21) where E t−τ denotes expectations conditional on information available through period t − τ Equation (7.20) uses the fact that p2t is already determined when p1t is set, and thus is not uncertain Our goal is to find how the price level and output evolve over time, given the behavior of m To this, we begin by solving (7.20) for p1t ; this yields p1t = 2φ 1+φ Et−1 m t + 1−φ 1+φ p2t (7.22) Since the left- and right-hand sides of (7.22) are equal, the expectation as of t − of the two sides must be equal Thus, Et−2 p1t = 2φ 1+φ Et−2 m t + 1−φ 1+φ p2t , (7.23) where we have used the law of iterated projections to substitute Et−2 m t for Et−2 Et−1 m t We can substitute (7.23) into (7.21) to obtain p2t = φ Et−2 m t + (1 − φ) 2φ 1−φ Et−2 m t + p t + p2t 1+φ 1+φ (7.24) Solving this expression for p2t yields simply p2t = Et−2 m t (7.25) We can now combine the results and describe the equilibrium Substituting (7.25) into (7.22) and simplifying gives p1t = Et−2 m t + 2φ 1+φ (Et−1 m t − Et−2 m t ) (7.26) 768 Subject Index Financial-market imperfections (continued) and debt crises, 704–710 and long-run growth, 475 magnification effect, 473 in new Keynesian models, 362 and nominal frictions, 301–303 and real rigidity, 283 and short-run fluctuations, 475 tests on cash flow and investment, 475–479 Financial markets, 225, 302, 368, 395, 458, 508 agency costs, 463–472 cash flow and investment, 475–479 Diamond–Dybvig model, 491–501 excess volatility, 459, 479–487 financial accelerator, 459, 472–473 mispricing, 479–487 perfect, model of, 460–463 private marginal products in, 460 Financial system development, 460 Financing, 283, 470, 502 and cash flow, 475–479 costs of obtaining, 473 debt vs equity, 457 internal vs external, 475–479 outside, 464–465, 471, 475, 478 tax vs debt, 73, 196n, 668–670 Fire-sale contagion, 503–504, 506–507 First welfare theorem, 65 Fiscal crises; see Debt crises Fiscal policy, 627, 660–714; see also Budget deficits; Policymakers; Stabilization policy and consumption, 387 debt vs taxes, 668–676 deficit bias in, 578, 678–679, 695, 697 and dynamic inconsistency, 634n and government budget constraint, 662–669 in industrialized countries, 696–700 issues in macroeconomics, 660–661 in new Keynesian models, 363 Ricardian equivalence result, 669–673 short-run macroeconomic effects, 660–661 and social infrastructure, 163 stability of, 660, 710–711 and stabilization policy, 660 sustainable and unsustainable deficits, 666–669, 701–704 in United States, 661, 666–669, 696n, 701 and zero lower bound, 615 Fiscal reform, 223n and conditionality, 713 and crises, 696, 713 delays in, 680, 691–696 and hyperinflation, 651 Fischer model, 311–312, 316–320, 345–346, 365 Fisher effect, 582 Fisher identity, 580, 582, 654 ‘‘Five Papers in Fifteen Minutes,’’ 178 Fixed adjustment costs, 310, 449–453; see also Menu costs Fixed prices, 239–244, 320–326, 349 Fixed vs floating exchange rates, 224 Fluctuations, overview of, 188–192; see also Dynamic stochastic general-equilibrium models; Nominal adjustment, incomplete; Nominal rigidity; Real-business-cycle theory Forward guidance, 355, 626 Forward guidance puzzle, 354–359 Forward-looking interest-rate rules, 350, 354, 610–611 Forward-looking monetary policy model, 602–607 Forward-looking price-setting, 359 Fragile equilibria, 292 Frequency effect, 329, 330, 334 Frequency of price adjustment, 335–337, 349 Frictional unemployment, 558 Full-employment output, 259 Fully endogenous growth models, 114, 132–133, 135 Fully-funded social security, 96 Fundamental risk, 485–486, 516–517 G Game theory, 289–291 General Theory (Keynes), 245–247, 253 Geography, and cross-country income differences, 165, 168, 172–177 Golden-rule capital stock, 22, 64, 67, 88–89 Golden-rule level of education, 154n, 183 Golosov–Lucas model, 311, 331–335 Goods market imperfections, 251–253, 269–275 Goods-producer-surplus effect, 130 Government budget constraint, 662–669, 701, 714 Government debt; see Budget deficits; Fiscal policy; Policymakers Government default, 703, 705 Government purchases, 190, 197, 202, 206, 209, 243, 361, 368, 678, 690; see also Fiscal policy in Diamond model, 90–91 and distortionary taxes, 231, 674–675 and household budget constraint, 73, 670 predictable movements in, 677 Subject Index with price rigidity, 242, 244–253 in Ramsey–Cass–Koopmans model, 72–76, 93–94 in real-business-cycle models, 194–195, 207, 215–217 Government rent-seeking behavior, 118, 162–163, 165, 679 Great Depression, 172, 192, 227, 459, 506, 595–596, 615, 626, 630, 635 Great Inflation, 192, 639–642 Great Moderation, 192–193 Great Recession, 188–189, 192–193, 228, 513, 550, 596 Great reversal, 176 Grossman-Helpman model, 101, 116, 132 Growth accounting, 30–33, 49, 143–144, 149, 156, 174 Growth-accounting-style techniques, 32–33 Growth disasters and miracles, 7, 182–183 Growth drag, 41–42 Growth effects, 21, 131 Growth in Ramsey–Cass–Koopmans model, 92–93 Growth rate, 14, 16n, 21n, 27n, 45 H Habit formation, 361, 364, 398n, 399n, 417 Half-life, 27n Hamiltonian, 428–429, 454–456 present-value, 429n Harris–Todaro model, 575–576 Harrod-neutral technological progress, 10 Hazard rate, 533 Health care costs, 661–662 Hedging of risks, 390–391 Hicks-neutral technological progress, 10n, 13n High-powered money, 222, 303n, 588–589, 608, 615, 627, 644 Hodrick–Prescott filter, 218n Home bias, 391 Households, 209, 395, 616–617, 620; see also Consumption; Labor supply in baseline price rigidity model, 239–242 in Diamond model, 78–80 entry into economy, 51, 77n forward-looking behavior of, 67, 75–76 heterogeneity among, 463 in imperfect competition model, 269–272 infinitely lived, 50, 124–125, 195–196, 312–313 permanent-income hypothesis, 381–385 in Ramsey–Cass–Koopmans model, 51–53 in real-business-cycle models, 197–201 in Romer model, 123n, 124–127 769 ‘‘Housing bubble’’, 488 Housing market, 190, 455 Human capital, 2, 32, 122, 136, 186, 549 and cross-country income differences, 155–162, 180 and increasing returns, 186 physical capital effects on, 159 vs raw labor, 151 in Solow model, 150–155 sources of variation in, 158 Hybrid IS curve, 263 Hybrid Phillips curve, 261, 263, 339–341, 631 Hyperinflation, 301, 579, 582, 642–643, 647–651, 680, 691, 704 Hysteresis, 549–550 I Identity operator, 325 Idiosyncratic risk, 449, 475, 507 Immigrants, and wage differences, 158–159 Impatience, and consumption, 402, 404, 407 Imperfect competition; see Competition, imperfect Imperfections in financial markets, 458 Imperfect information, 283, 301, 678; see also Lucas imperfect-information model Implicit contracts, 545–546, 574–575 Implicit differentiation, 24n Inada conditions, 12, 17, 77, 87, 95 Incentive-compatible contracts, 574–575 Incentive contracts, for policymakers, 635n Income, permanent vs transitory, 370, 374 Income differences, cross-country, 149–187 and convergence, 33–37, 178–180 growth miracles and disasters, 7, 182–183 and investment choices, 29 and knowledge, 30, 33, 142–144, 147–148 overview of, 7–8, 149–150 and Solow model, 28–30, 150–155 Income effect, 80, 198, 203, 387, 564n Incomplete markets, 97–98, 398n Increasing returns to scale; see Returns to scale, increasing Indexation, 361, 367, 589 and employment movements, 306–307 lack of, with debt contracts, 301–302 new Keynesian Phillips curve with, 342–344 Indivisible labor, 229–230 Inertia, in deficits, 695–696 Inertia, inflationary, 261, 338–350, 360 Infinitely lived households, 50, 124–125, 195–196, 312–313 770 Subject Index Infinite output, in research and development model, 107n Inflation; see also Dynamic inconsistency; Interest-rate rules; Output-inflation tradeoff; Seignorage in AS-AD diagram, 263 and central bank independence, 637–639 core, 259–261 costs of, 588–591 and debt crises, 703 and deficit measurement, 663–665 and delegation, 636–639 dislike of, 590 and divine coincidence, 602–603 expected, 259, 261, 297, 360, 647, 653 expected vs actual, 631–633, 644 expected vs core, 261 in Great Inflation, 192, 639–642 implications for, 358–359 inertia in, 261, 338–341 lagged, 342–345, 597 low, monetary policy, 630–637 from money growth, 579–583 in new Keynesian Phillips curve, 329 optimal rate of, 591–593, 596, 632–633 and output, 299–300, 340 and policymaker reputation, 635–636 potential benefits of, 591–592 potential sources of, 579–580 and real money balances, 579–580 during recessions, 191 variability of, 589–590 Inflation bias, 578, 630 Inflation-indexed bonds, 587n Inflation inertia, 261, 338–350, 360 Inflation-output tradeoff; see Output-inflation tradeoff Inflation shocks, 352, 354 Inflation targeting, 223n, 600, 626, 629 in Krugman model, 623–625 Inflation-tax Laffer curve, 645–646 Inflation-tax revenues, 644 Information, imperfect; see Imperfect information Information-technology and productivity rebound, 32 Informationally insensitive assets, 497 Input-output linkages, 283 Insensitivity of profit function, 281–282, 284 Insider-outsider models, 547–550, 575 Inside the unit circle, 605 Instantaneous utility functions, 215, 218n, 230n, 369, 373, 386, 448 for constant-absolute-risk-aversion, 418 quadratic, 376, 378–379, 403–404 in Ramsey–Cass–Koopmans model, 52–53, 55 in real-business-cycle models, 196–197, 218n in Romer model, 124–125 in Shapiro–Stiglitz model, 532 Institutions, 162–164, 170–173, 176–177, 464 Instrumental variables, 165–169, 380, 405, 613–614 Intensive form of production function, 11–13 Interacted variables, 698 Interest factors, 705–709 Interest-rate rules in canonical new Keynesian model, 351, 354 design of, 609–613 estimation of, 613–615 in exogenous nominal rigidity model, 262, 265n forward-looking, 351, 354, 610–611 in monetary policy models, 600–601, 603–605 vs money-stock rules, 607–609 and natural rate of interest, 600–601 in new Keynesian models, 363 overview of, 607–609 Interest-rate spreads, 612 Interest-rate targeting, 655 Interest rates central bank control of, 304–305 and consumption, 385–389 and expectations, 583–587 and Federal Reserve policy, 224–226 forward guidance about real, 356–359 and investment, 438–439, 444–445 in IS curve, 262–263 and labor supply, 199 and lagged inflation, 597 and money growth changes, 580–582 natural, 600–601, 603–604, 610 and new Keynesian IS curve, 241, 242 nominal vs real, 224 in q theory model, 438–439 during recessions, 191 and saving, 385–389 short-term, 438, 583–587 in specific models, 52, 65n, 78–80, 86–87, 126, 597 as tax rate on money balances, 644n and technology shocks, 213–214 term structure of, 583–587, 653–654 zero lower bound on nominal, 305n, 591, 603n, 615–629, 655 Intergenerational links, 671 Subject Index Interindustry wage differences, 566–569 Intermediation, 363, 475, 479–480, 492, 703 Internal adjustment costs, 408, 423, 435n Internal habits, 417 Internal vs external financing, 475–479 International aid, 713 International borrowing, 704n Intertemporal elasticity of substitution, 52, 92, 215, 228, 386, 389 Intertemporal first-order condition, 210–211 Intertemporal substitution in labor supply, 198–199, 204, 214–215, 243 Intratemporal first-order condition, 208–209 Intrinsic bubbles, 415 Inventories, 190 Investment, 420–457; see also Financial-market imperfections; q theory model of investment actual vs break-even, 17, 19–23, 24n, 60 and capital income, 422 and cash flow, 475–479 and cost of capital, 421–423 and cross-country income differences, 29, 159–160 and financial-market imperfections, 302, 460, 472–473, 475–476, 478–480 with fixed adjustment costs, 451–453 and government purchases, 73 and inflation, 588–591 irreversible, 447–448 and kinked adjustment costs, 449–451 and saving rate, 18–19 and social infrastructure, 162–163 and stabilization policy, 595 and taxes, 93–94, 442–447, 455, 475 under uncertainty, 444–448, 452, 456 Investment adjustment costs, 423n Investment-output ratio, 160–161, 218 Investment tax credit, 422, 439–441 Irrational exuberance, 488 Irreversible investment, 447–448 IS curve, new Keynesian, 241–242, 262–263, 313, 350–354, 359, 361, 602, 604 continuous-time, 366 IS curve, traditional, 241, 263, 265, 597 IS-LM model, 242–243 IS-MP model, 262–264 J Job breakup rate, 533, 551, 557 Job creation and destruction, 559 Job-finding rate, 553, 556 Job selling, 542–543 771 K Keeping up with the Joneses, 371 Keynesian consumption function, 371–372 Keynesian models, 245–246, 371–372; see also Dynamic new Keynesian models Kinked adjustment costs, 449–453 ‘‘Kleptocracy’’, 163 Knowledge accumulation, 100, 108; see also Research and development model and allocation of resources, 114–121, 130–131 and basic scientific research, 116 and capital accumulation, 99, 120 and central questions of growth theory, 142–144 and cross-country income differences, 142–143, 149 dynamics of, 102–107 endogenous, 101–102, 109, 137–142 and ever-increasing growth, 106–107 over human history, 137–142 and learning-by-doing, 119–121, 135, 145 private incentives for, 116–118 in Romer model, 121n and talented individuals, 118–119 Knowledge; see also Research and development lags in diffusion of, 33, 143 production function for, 101 in real-business-cycle models, 199 in Solow model, 10, 13–14, 28–29, 151 k-percent rule, 607 Kremer model, 137–142 Krugman model, 615–625, 627, 656 L Labor-augmenting technological progress, 10, 13n Labor demand and employment movements, 520–521, 527–529, 546, 549–550, 567–569 fall in, 249, 521–522, 540, 545, 566 with flexible wages and competitive labor, 247–250 impact of shift in, 559–562 in real-business-cycle models, 2, 194, 228 in search and matching models, 3, 522, 551, 558–560 in Shapiro–Stiglitz model, 538–543 Labor-force attachment, 549–550 Labor market, 246, 279, 543; see also Contracting models; Contracts; Efficiency wages; Unemployment; Wages 772 Subject Index Labor market (continued) competitive, 247–249, 531 cyclical behavior of, 253–255, 520–521 dual, 542 economy-wide, 293 heterogeneity of, 551, 557 imperfections in, 249–250, 285–286 in insider-outsider model, 547–549 real rigidity in, 284–287 in search and matching models, 553 short-side rule, 304 turnover in, 538–539, 541, 558 and wage rigidities, 251–253, 545, 561 Labor mobility, 284, 544–545 Labor supply, 194 in dynamic new Keynesian models, 313 elasticity of, 301, 520, 546 and hours of work, 595 and hysteresis, 549 in imperfect competition model, 274 inelastic, 213–214, 278–279 intertemporal substitution in, 198–199, 204, 214–215 in Ramsey–Cass–Koopmans model, 51 raw labor vs human capital, 151 in real-business-cycle models, 194, 198–199, 201–206, 209 in research and development model, 101, 104–105 in Romer model, 123 in Shapiro–Stiglitz model, 538–539 in Solow model, 13–14 tradeoff with consumption, 201 Lag operators, 205n, 320, 324–326 Land, 11, 37–43, 137–138, 140, 147, 174–175 Law of iterated projections, 266, 318, 326n, 343, 404, 445 Layoffs, 541, 570–571 Leaders death of, and policy changes, 170–171, 223 differences in beliefs, 172 Learning-by-doing, 116, 119–121, 135, 145–146 Lehman Brothers, 459, 504, 509 Lender-of-last-resort policies, 499–500 Level effects, on balanced growth path, 21, 131 Life-cycle saving, 404n, 413 Limited liability, in debt markets, 302 Limited pledgeability, 515–516 Linear growth models, 107, 124, 126, 131, 348 Liquidity, concept of, 635 Liquidity constraints, 399, 402–404, 409n, 672, 682, 702 Liquidity crisis, 497–498, 635 Liquidity effect, 583 Liquidity trap, 305, 621, 656n; see also Zero nominal interest rate in Krugman model, 619–625 policies to raise expected inflation in, 625–627 policies to stimulate economy in, 627–628 LM curve, 243, 262 Logarithmic utility, 80, 81, 90, 91n, 127, 203, 691 in Cobb–Douglas production, 81–83 in Diamond model, 83–85, 95 in Ramsey–Cass–Koopmans model, 50, 92 in real-business-cycle models, 196–197, 203 in Romer model, 124 in Tabellini-Alesina model, 688–690 Log-linear approximation, 196n, 207–211, 237 Log-linearization, 207–208 Lognormal distribution, 210n, 481, 516 Long-term interest rates, 438–439, 583–587 Lucas asset-pricing model, 416 Lucas critique, 299–300 Lucas imperfect-information model, 293–303 Lucas supply curve, 296–297, 299, 329, 338–339, 593, 595, 631, 653 M Macroeconomic contagion, 503–504, 507 Macroeconomic crisis of 2008–; see Economic crisis of 2008– Macroeconomic effects of financial crises, 508–514 Maddison Project, 6n Malthusian determination of population, 138, 141, 142n Mankiw–Reis model, 311, 345–350, 367 Marginal disutility of work, 209, 230, 239, 545–547, 564 Marginal product of capital, 22, 25 in Diamond model, 78, 87 in learning-by-doing model, 145 private, 146 in q theory model, 426, 431, 435 in Ramsey–Cass–Koopmans model, 53 in simple investment model, 422–423 in Solow model, 12, 22, 25, 29 Marginal q, 430–431, 443 Marginal revenue-marginal cost diagram, 276–277, 282–284 Market beta, 396n Market-clearing condition, 462 Markup, 127, 245, 592 countercyclical, 249, 283, 286 Subject Index function, 251 in imperfect competition model, 274 by intermediaries, 362 over wages, 317n, 346 procyclical, 249n and real rigidity, 283–284 with wage rigidity, flexible prices, and imperfect goods, 251 Martingale, 377n Matching function, 552–553, 577 Maturity mismatch, 492 Mean-variance objective function, asset holdings with, 391–394 Measurement error, 35–36, 186 classical, 166 and convergence, 35, 49 and cross-country income differences, 166–167, 187 and interest-rate rules, 609–610 and q theory tests, 442–443 Median-voter theorem, 684–686 Medical costs, 666–668 Menu costs, 269, 276, 293, 310; see also Price adjustment defined, 268 and efficiency wages, 531 empirical evidence on, 337–338 with imperfect competition, 277–278, 284–287 models, 301 with multiple equilibria, 306 and profit function insensitivity, 281 and real rigidity, 279–286, 292 Method of undetermined coefficients, 208, 236n, 305, 320–323, 352–353 Minimum wage, 522n Mispricing of assets, 479–490, 506 Model-based risk, 486n Models, purpose of, 3–4, 15 Modern approach to labor market, 521–522, 550 Modified golden-rule capital stock, 67 Modigliani-Miller theorem, 457 Monetary conditions index, 611 Monetary disturbances, 238; see also Aggregate demand shocks in canonical new Keynesian model, 351–353 in Caplin–Spulber model, 335 in Danziger–Golosov–Lucas model, 332–334 with exogenous price rigidity, 242–243 and incentives for price adjustment, 277–279, 285–286 and inflation shocks, 352, 354 long-lasting effects of, 323–324 773 in Lucas model, 293, 295 and natural experiments, 222–224 and predetermined prices, 320, 345 with price rigidity, 242–243 in real-business-cycle models, 195, 220–226 and St Louis equation, 221–222 in Taylor model, 323 and vector autoregressions, 225–226 Monetary expansion, 224, 245, 583, 620, 623, 626n effects in Krugman model, 621–622 Monetary policy, 578–659; see also Dynamic inconsistency; Interest-rate rules; Policymakers; Stabilization policy backward-looking model, 596–601 in canonical new Keynesian model, 350–354, 360 central bank independence, 637–639 contractionary policy, 586–587 control of interest rates, 304–305 and delegation, 635–636, 638–639, 657 and exchange rates, 611, 628n and financial-market imperfections, 301–303, 458–460, 475–479 forecasts in, 611n forward-looking model, 602–607 and the Great Inflation, 192, 639–642 inflation bias in, 578, 630 inflation targeting, 223n, 600, 626, 629 k-percent rule, 607 low-inflation, 630–637 and Lucas critique, 299–300 and money growth effects, 580–582, 647–651 and natural experiments, 168–169, 223–226, 499n and natural-rate hypothesis, 257–258, 261, 642 in new Keynesian models, 312–316, 363 overview of, 578–579 and political business cycles, 658 and regime changes, 653 and reputation, 657 and rules, 608–609, 634 and seignorage, 578–579, 642–651, 659 and social welfare, 592–596 and St Louis equation, 222 super-inertial, 612 and term structure of interest rates, 583–587, 653–654 and uncertainty, 610, 655 and vector autoregressions, 225–226 and zero lower bound, 305n, 507, 591, 603n, 615–629, 655–656, 660 774 Subject Index Money in baseline price rigidity model, 239–240 high-powered, 303n, 588, 589, 615n, 644 vs interest-rate targeting, 655 and output, 220–226 in Samuelson overlapping-generations model, 97–98 as source of utility, 239–240 Money demand in baseline price rigidity model, 242 and future inflation, 648n, 5651n gradual adjustment of, 647–649 and inflation, 579–580 and seignorage, 643–645 and St Louis equation, 222 and vector autoregressions, 225 Money-financed tax cut, 628n Money growth and hyperinflation, 542–543, 647–651 inflation from, 579–582 and interest rates, 580–582 and real money balances, 581–583, 643–651, 652 and seignorage, 642–651, 659 Money-in-the-utility-function, 240n, 270 Money market, 262, 497, 504, 579 Money-output regressions, 225–226, 585 Money-stock rules, 607–609 Monopoly power, 121, 123, 126, 145, 163n Moral hazard, 302, 471 Mortgage-backed securities, 511–512 MP curve, 262–263, 265, 305 Multiple equilibria in coordination-failure models, 286–291 defined, 267 in Diamond model, 88–90 and economic crisis of 2008–, 585 in forward-looking monetary policy model, 605 with menu costs, 306 in model of debt crises, 707–709 punishment, 635n, 657–658 reaction function and, 288 real non-Walrasian theories, 291–292 Multiplier-accelerator, 304 Multisector models, 230 Mutual fund separation theorem, 394–395 Mutual funds closed-end, 489–491 open-end, 490n N Nash bargaining, 552, 554–555 Nash equilibrium, 278, 289–290, 307, 495–496, 714 National Bureau of Economic Research (NBER), 188n Natural experiments, 168–169, 223–226, 499n Natural-rate hypothesis, 257–258, 261, 642 Natural rate of interest, 600, 603–604, 612 Natural rate of output, 259, 610, 641–642 Natural rate of unemployment, 257–258, 304, 549, 564 Natural resources, 11, 37–45, 168 New growth theory; see Human capital; Income differences, cross-country; Knowledge accumulation; Research and development model New Keynesian IS curve, 241–242, 262–263, 313, 350–354, 359, 361, 602, 604 continuous-time, 356 New Keynesian models; see Dynamic new Keynesian models New Keynesian Phillips curve in canonical new Keynesian model, 350–351, 360 continuous-time, 356–357 and costs of disinflation, 354 derivation of, 327–328 in forward guidance puzzle, 354 in forward-looking monetary policy model, 602–604, 606 forward-looking price-setting in, 359 implications of, 354 with indexation, 342–344, 360, 367 and inflation, 357 and inflation inertia, 338–341, 360 and long-run output-inflation tradeoff, 630n in new Keynesian models, 360 with partial indexation, 367 with wage inflation, 360 New political economy, 678–680 Newly industrializing countries (NICs), 32 No-bubbles condition, 415 Noise traders, 481, 484n, 485, 490, 518 risk, 484, 516–517 Nominal adjustment, incomplete, 268–308; see also Dynamic stochastic general-equilibrium models; Lucas imperfect-information model; Price adjustment baseline imperfect competition model, 269–275 in debt markets, 301–302 Subject Index incentives for, 276–279, 284–286 liquidity effect, 583 Nominal imperfection, 195, 238, 268, 282, 293, 301–303, 310, 317 Nominal prices/wages, 316–317, 330, 338, 345, 350, 364 Nominal rigidity, 309, 327, 354; see also Price rigidity in DSGE models, 311 exogenous, 239–267 overview of, 238–239 in real-business-cycle models, 195, 229, 232–233 and small barriers to price adjustment, 277–278, 285n Nonexpected utility, 398n, 399n Nonrivalry of knowledge, 115, 129, 142 Nonstationarity vs stationarity, 132–134 Nontradable consumption goods, 160–161 No-Ponzi-game condition, 54–56, 240 No-shirking condition, 536–543 Numerical methods, 408, 413, 418–419 O Observational equivalence, 308 Oil prices, 258, 478, 697 Okun’s law, 191 Olivera-Tanzi effect, 647n Omitted-variable bias, 165–166, 170, 699 Open-end mutual funds, 490n Open-market operations, 224, 585, 625–628 Option value to waiting, 447 Output-inflation tradeoff, 634n, 643 accelerationist Phillips curve, 260–262, 329, 338–340, 593, 597 and backward-looking monetary policy model, 596–599 expectations-augmented Phillips curve, 259–261, 297 failure of Phillips curve, 258 and forward-looking monetary policy model, 606–607 and the Great Inflation, 640–641 hybrid Phillips curve, 261, 339–341 and hyperinflation, 642 and inflation bias, 578, 630 in Lucas model, 299 and natural-rate hypothesis, 257–258 and new Keynesian Phillips curve, 630n Phillips curve, 256 Output taxation, 231 Overidentifying restrictions, 381n 775 Overlapping-generations models, 9, 50, 55n, 77n, 96–98; see also Diamond model P Panel Study of Income Dynamics (PSID), 253–254, 382 Paradox of toil, 656n Pareto efficiency and budget deficits, 702 in specific models, 65, 87–90, 117n, 202, 204, 289–291 Partial vs general equilibrium models, 232–233 Partial-equilibrium search, 576 Patent laws, 115 Pay-as-you-go social security, 96, 666 Pecuniary externalities, 65n, 117n Penn World Tables, 7n, 157 Perfect competition; see Competition, perfect Perfect financial markets model, 458–463, 472, 474–475 Permanent income, 370, 375 Permanent-income hypothesis, 399n, 674 consumption behavior and, 382, 384–385 derivation of, 369–371 and excess smoothness of consumption, 379n, 414 failures of, 398–399 household data, 381–385 implications of, 371–373 and random-walk hypothesis, 377 and Ricardian equivalence, 671–673 Persson–Svensson model, 680–682, 713 Phase diagrams, 18, 94, 106, 113, 431, 447 with kinked adjustment costs, 449–450 in q theory model, 432–433, 436–437, 439–441 in Ramsey–Cass–Koopmans model, 61–62, 67, 71 in research and development model, 103–105, 107–110 in Solow model, 17 sustainable vs unsustainable seignorage, 649–650 with uncertainty, 446–448 Phillips curve; see also New Keynesian Phillips curve; Output-inflation tradeoff accelerationist, 260, 329, 338–340, 355, 593, 595, 597, 655 expectations-augmented, 259–261, 296 failure of, 258 history of, 256 hybrid, 261, 263, 339–341, 631 776 Subject Index Phillips curve (continued) and Lucas critique, 299–300 and natural-rate hypothesis, 257–258, 261 and productivity growth, 304 Pigovian tax, 44, 505 Poisson processes, 327–328, 342, 346, 532–533 Policies vs institutions, 150, 162–165, 167, 169–173, 182 Policy rules, 263, 265, 300, 363, 600, 609–611, 640, 653; see also Interest-rate rules Policymakers, 45, 145, 256–257, 299–300, 363, 578, 582, 588, 592, 596, 629; see also Fiscal policy; Monetary policy; Stabilization policy commitment by, 630–634, 687 delegation to, 636–639 disagreements among, 662–664 discretion of, 630–633 and economic crisis of 2008–, 585 incentive contracts for, 635n incomplete knowledge of, 679 independence of, 637–639 inflation choices of, 606–607, 630–634, 636–638 known inefficient outcomes, 680–681 liberal vs conservative, 681 and maximization of social welfare, 363 and preferences, 683–685, 688 reasons for accumulating debt, 681–682 and reputation, 635, 657 rules vs discretion, 634–635 and statistical relationships, 300 and the Great Inflation, 639–642 Political business cycles, 658 Political-economy theories of budget deficits, 678–681, 697 Political participation, 688 Political power, 171n, 697–700 Political Risk Services, 167 Pollution, 37, 43–45 Ponzi games/scheme, 54, 55n, 408, 409n, 617, 665–666 Population exogenous growth of, 13–14, 51, 77, 102, 196 and long-run economic growth, 104, 106, 108–109, 112, 120, 129, 136–142 Malthusian determination of, 138, 141, 142n in specific regions, 140 and technological change, 137–142 turnover in, 76, 671 over very long run, 137–142 Potential output, 259, 262 Precautionary saving, 389n, 399–402, 404, 418, 672, 711 dynamic-programming analysis of, 407–413 Predetermined prices, 311, 316–320, 345–346, 497; see also Fischer model; Mankiw–Reis model Present-value Hamiltonian, 429n Presidential political systems, 699 Price adjustment, 2, 276n, 279n, 281, 283, 286, 292, 309, 311, 324, 331, 350, 596; see also Inflation; Menu costs; State-dependent price adjustment; Time-dependent price adjustment of assets, 416 barriers to, 277 in Calvo model, 326–329 in canonical new Keynesian model, 350–351 in Caplin–Spulber model, 330–331 in Christiano–Eichenbaum–Evans model, 342–345 costs of, 337 and costs of inflation, 588–589 in Danziger–Golosov–Lucas model, 331–334 in dynamic new Keynesian models, 312–314 in Fischer model, 316–320, 365 and fixed prices, 320–326 frequency of, 335–337, 349 imperfect competition model, 269–275 and imperfect information, 293–294 incentives for in contracting models, 547 and efficiency wages, 527, 530–532 and real rigidity, 279–286 and small frictions, 276–279 incomplete, 324 and inflation inertia, 338–341 in Mankiw–Reis model, 345–350 microeconomic evidence on, 335–338 and monetary policy, 225 real non-Walrasian theories, 286–289 and real rigidity, 284–287 and sales, 336 synchronized, 365–366 and taxes, 443 in Taylor model, 320–326 Price indexes, 271, 274, 294, 313, 335, 642 limitations of, 6n Price-level inertia, 323 Price-level paths, 625, 629 Prices of assets; see Asset prices Price-price Phillips curve, 304 Price rigidity; see Nominal rigidity; Price adjustment Subject Index Price-setters in Calvo model, 326–329 in Caplin–Spulber model, 330–331 in Danziger–Golosov–Lucas model, 331–334 in Fischer model, 316–320 in imperfect competition model, 269–275 incentive to obtain information, 301 in Mankiw–Reis model, 345–350 and small barriers to adjustment, 277–278 and sticky information, 346 in Taylor model, 320–326 Pricing kernel, 395 Primary deficit, 663 Primary jobs, 542 Private incentives for innovation, 116–118 Private vs social returns; see Social infrastructure Production functions; see also Cobb–Douglas production function aggregation over firms, 91 in baseline real-business-cycle model, 195 in Diamond model, 78 in dynamic new Keynesian models, 310 Ethier, 122–124 for human capital, 151 Inada conditions, 12, 17 intensive form of, 11–13 for knowledge, 100–102, 110 and learning-by-doing, 119–121 in Ramsey–Cass–Koopmans model, 51 in real-business-cycle models, 195, 202, 204 in research and development model, 100–102, 110 in Romer model, 124 in Samuelson model, 96 in Solow model, 10–13, 29n, 150–151 Productivity growth, 8, 32, 668 impact on Phillips curve, 304 rebound in, in research and development, 129 slowdown in, 6, 92, 191 Profit functions, 279, 436–437, 562 in contracting models, 543 insensitivity of, 281 in Romer model, 127–128 in search and matching models, 561 Profitability, 478 effects of changes in, 435–438 uncertainty, effects of, 444–446 Property rights, 37, 115, 119, 142 Proportional output taxation, 231 Proportional representation, 699 777 PSID (Panel Study of Income Dynamics), 253–254, 382 Punishment equilibria, 635n, 657–658 Q q theory model of investment, 424–453 with constant returns in adjustment, 430n, 456 with kinked and fixed adjustment costs, 449–453, 456 and money demand, 648n and taxes, 439–441, 455 and uncertainty, 444–449, 456 q (value of capital), 426–427, 430–431, 433, 441–444 Quadratic adjustment costs, 430 Quadratic utility, 378, 390, 395–396, 399–400, 403–404, 448, 450–451 Quality-ladder models, 132 Quantitative easing, 627–628 R Ramsey–Cass–Koopmans model, 14–15, 50–76, 92, 125, 149, 617, 669 vs baseline real-business-cycle model, 195–197, 199–200 capital taxation in, 93–94 closed-form solution for, 93 vs Diamond model, 50, 76, 78, 83, 87–88 government purchases in, 72–76 vs research and development model, 104 and Ricardian equivalence result, 669–670 social planner’s problem, 65, 454 vs Solow model, 50, 66–67, 72 technology, 50–51 Random walk, 299, 320, 377, 413–414, 488, 600, 676 Random-walk hypothesis, 320, 376–377, 379–385 Random walk with drift, 299, 414 ‘‘Rater pays’’ model, 507 Rational expectations, 295, 479, 481, 491, 653–655 Rational political business cycles, 658–659 Raw labor vs human capital, 151 Reaction function, 287–289, 291–292 Real-business-cycle theory, 188–237 with additive technology shocks, 235 evaluation of models, 220, 227–230 monetary disturbances in, 220–226 overview of, 193–195, 232–233 with taste shocks, 235, 298 technology shocks, 194, 202, 206, 209, 211–215, 227–228, 472, 521 778 Subject Index Reallocations, productivity and, 33 Real non-Walrasian theories, 291–292 Real rigidity, 280, 337, 473 in Calvo model, 329 in Fischer model, 322 in Mankiw–Reis model, 345, 347 and multiple equilibria, 287, 289 overview of, 279–281 and real non-Walrasian theories, 291–292 and small barriers to price adjustment, 285n sources of, 282–285 in Taylor model, 323 Real-wage function, 250, 285 Recessions; see also Economic crisis of 2008–; Great Depression and consumption variability, 594 short-lived, 373n and socially optimal output, 274–275 and tax-smoothing, 677 in United States, 188–191 wage rigidity during, 569, 571 welfare effects of, 274–275, 592–596 Regime changes, 653–654 Renegotiation-proof contracts, 467n Rent-seeking, 118–119, 162–163 Reputation, and dynamic inconsistency, 635–636, 657 Research and development; see also Knowledge determinants of, 114–121 externalities from, 118, 125, 130 free-entry condition in, 125 macroeconomic fluctuations, 364–365 production function for, 100–102 and returns to scale, 101, 107–108, 110 Research and development effect, 117, 125, 130 Research and development model, 100–114, 135, 142–144, 148 Reserve Primary Fund, 504 Retail deposits, 509–510 Returns to scale constant in adjustment costs, 451, 456 in q theory model, 429–430, 441 in research and development model, 101, 107–108, 110 in Romer model, 121n in search and matching models, 553 in simple investment model, 424 in Solow model, 10–11 diminishing and entrepreneurial activity, 118–119 and lack of growth, 136 in q theory model, 429 in research and development model, 101, 107–108, 110 and entrepreneurial activity, 118–119 increasing and human capital, 185 in research and development model, 101, 107–108, 110 in Romer model, 121n in knowledge production, 101, 107–108, 110 to produced factors, 107–108, 110, 114 Ricardian equivalence, 661, 669–673 costs of deficits and, 701 and precautionary saving, 672, 711 in Tabellini–Alesina model, 681–682 and welfare costs of deficits, 701–702 Rigidity; see Nominal rigidity; Price rigidity; Real rigidity Risk aversion in contracting models, 541 in debt markets, 301 and equity-premium puzzle, 397–398 and precautionary saving, 400–401 and stabilization policy, 594–596 Riskless debt, 463 Risky assets, and consumption, 389–398, 458, 462 Risky projects, and investment, 475, 448–449 Rival goods, 115 Romer model, 99, 101, 116, 121–132, 145–146 Rule-of-thumb consumption behavior, 406, 702 Runs, and economic crisis of 2008–, 504–505, 585, 627, 660 S Saddle path, 64–65, 69–71, 74–75, 434–437, 440, 446–447, 449–450 Safe assets, 392, 394–395 St Louis equation, 221–222 Sale prices, 336–337 Sample-selection bias, 34–35 Samuelson overlapping-generations model, 97–98 Saving; see also Consumption buffer-stock, 398–399, 404n, 672 in Diamond model, 77, 85–88, 90–91 and discount rate, 402, 404 as future consumption, 370–371 and interest rates, 385–389 life-cycle, 404n, 407 and liquidity constraints, 402–404 over long horizons, 387–389 precautionary, 399–402, 407–413, 418, 672, 711 Subject Index in Ramsey–Cass–Koopmans model, 66, 92–93 and relative consumption, 371 Saving rate and capital-output ratio, 160–161 in Diamond model, 50, 80, 82, 85–86 endogenous, 9, 50 and externalities from capital, 174 and investment rate, 19–21 and learning-by-doing, 120 and long-run growth, 113, 120, 136 in Ramsey–Cass–Koopmans model, 50, 66 in real-business-cycle models, 203, 206 in research and development model, 102 in Solow model, 9, 15, 18–23, 66, 152, 153 Scale effects, 107–108, 113–114, 136 Scientific research, 116, 144 Search and matching frictions, 284, 551, 558–559 Search and matching models, 521–522, 550–558, 560n, 562, 576–577 Secondary jobs, 542 Sector-specific shocks, 230–231, 591, 703 Seignorage, 578–579, 642–651, 659, 680 Selection effect, 329, 331–335 Self-fulfilling prophecies, 87, 267, 288, 604–605, 709; see also Multiple equilibria Semi-endogenous growth models, 113, 131, 133, 136, 146 Sentiment shocks, 483–485, 490–491 Sequential service constraint, 495 Settler colonies vs extractive states, 176–177 Severe punishment, 658 Shapiro–Stiglitz model, 532–543, 552, 554, 570, 573 Sharpe ratio, 395 Shoe-leather costs, 589 Short-side rule, 304 Short-term debt, 509–510 Short-term interest rates, 438, 583–587, 628, 629 Signal extraction, 296 Signal-to-noise ratio, 296 Single-peaked preferences, 684 Slavery and colonialism, 176 Smets–Wouters model, 360 Social cost of carbon, 44 Social infrastructure, 150, 162–178, 183, 186 Social planner, 65, 88, 454, 493–494 Social security, 96, 661–662, 668 Social welfare; see Welfare (social) Solow model, 6–49 vs Diamond model, 50, 83, 85, 87 779 discrete-time version of, 95 with human capital, 150–155 microeconomic foundations for, 95 vs Ramsey–Cass–Koopmans model, 50, 66–69, 72 vs research and development model, 104 speed of convergence in, 26–27, 72 Solow residual, 31, 218, 227–228 Solvency crisis, 498 Sovereign debt crises, 696, 703–710, 713 Ss policy, 330, 332, 335 Stabilization policy; see also Fiscal policy; Monetary policy; Policymakers in backward-looking monetary policy model, 598–599 case for, 593–596 and fiscal policy, 660–661 and imperfect information, 300 and inflation, 588–592 and output, 592–593 overview of, 578 Staggered price adjustment; see also Caplin–Spulber model; Fischer model; Mankiw–Reis model; Taylor model Calvo model, 329 Christiano–Eichenbaum–Evans model, 311, 342–345, 360 instability of, 365 Mankiw–Reis model, 311, 345–350, 367 Staggered wage adjustment, 317n State-dependent price adjustment Caplin–Spulber model, 311, 331–332, 335, 366 Danziger–Golosov–Lucas model, 311, 331–335 defined, 310 with positive and negative inflation, 366 shortcomings of, 336 State variable, 102, 428 Stationarity vs nonstationarity, 132–134 Stein’s law, 702 Sticky information; see Mankiw–Reis model Stimulative fiscal policy, 627, 660–661 Stochastic discount factor, 395, 459, 472, 489 Stock-price movements, 379–380, 491 Straight-line depreciation, 453 Strategic debt accumulation, 681–691, 697, 711–712 Structural VARs, 225–226 Substitution effect in consumption under certainty, 387 in Diamond model, 80 in real-business-cycle models, 198, 203 Sufficient statistics, 429 780 Subject Index Sunspot equilibria, 87, 267, 288, 604–605, 608; see also Multiple equilibria Super-inertial monetary policy, 612 Supply shocks; see Aggregate supply shocks Suspension of payments, 498 Symmetric adjustment costs, 445–446 Symmetric equilibrium, 273 Synchronized price-setting, 365–366 T Tabellini–Alesina model, 681–691, 700, 712–713 Tail risks, 44 Talented individuals, 116, 118–119 Tanzi effect, 647n Taste shocks, 235, 294, 298 Tax cuts, 670, 672 of 2008 and 2009, 670 expectations of, 678 and zero lower bound, 628n Tax revenues, 231, 668, 676, 706, 709 Tax-smoothing, 661, 673–678, 701–702, 711 Taxes in baseline real-business-cycle model, 196 vs budget deficits, 668–673 and capital, 93–94, 422, 677 and consumption, 385, 389 and costs of inflation, 588–589 distortionary, 231, 673–678, 682, 701, 712 expected vs unexpected changes in, 94 and inflation, 644 and investment, 93–94, 442–448, 455, 475 in model of sovereign debt crises, 705–709 non-lump-sum, 711 on pollution, 43 in Ramsey–Cass–Koopmans model, 73 and social infrastructure, 163 Tax vs debt financing, 73, 196n, 669–671, 677, 680n, 682, 706 Taylor model, 320–326 continuous-time version of, 366–367 vs other models, 311, 326, 331 overview of, 310–311 synchronized price-setting in, 365–366 Taylor rules, 609–611, 641; see also Interest-rate rules Taylor-series approximations, 4, 26, 27n, 69, 207–211, 396 Technological change; see also Knowledge accumulation capital-augmenting, 10n, 13n embodied, 48–49 endogenous, 9, 104, 137–138 Harrod-neutral, 10 Hicks-neutral, 10n, 13n labor-augmenting, 10, 13n and learning-by-doing, 119–121 in medicine, 667 vs natural resource limitations, 40–42 and population growth, 137–142 in research and development model, 100 in Romer model, 131–132 as worldwide phenomenon, 140 Technology; see Knowledge; Knowledge accumulation; Research and development Technology shocks, 194, 202, 206, 209, 211–215, 227–228, 235, 472, 521 Term premium, 584, 587n Term structure of interest rates, 583–587, 653–654 Thick-market effects, 283, 307, 553 Time-averaging problem, 413–414 Time-dependent price adjustment Calvo model, 310–311, 326–329, 331, 342–343, 366 Christiano–Eichenbaum–Evans model, 311, 315, 342–346, 347n, 349–350, 360 defined, 310 Fischer model, 310–311, 316–320, 331, 345, 365 fixed vs predetermined prices, 311 Mankiw–Reis model, 311, 345–350, 367 shortcomings of, 336, 349–350 Taylor model, 310–311, 320–326, 331, 365–367 Time-inconsistent preferences, 407, 418 Tobin’s q, 429–431, 441–444 Tradable consumption goods, 161 Trade balances, and debt crises, 703 Traditional approach to labor market, 521–522 Traditional IS curve, 241, 263, 265, 597 Transactions demand for money, 240n, 303 Transfer payments, 662, 674n, 677n Transition dynamics, 121–122, 131 Transitory consumption, 374–375 Transitory income, 370, 373–375 Transversality condition, 428–429, 434, 454 Trend stationarity, 133–135 Tropical countries, poverty in, 172–177 t-statistic vs confidence intervals, 134, 255, 384 Two-sided Ss policy, 332 Two-stage least squares, 165; see also Instrumental variables Subject Index U Unbalanced price-setting, 365 Uncertainty consumption under, 199–201, 376–378, 399–402 and dynamic efficiency, 666n and fiscal policy, 668 and household optimization, 199–200 investment under, 444–449, 452, 457 and monetary policy, 655 and price-setting, 316 tax-smoothing under, 676 Underemployment, 289, 545 Underlying (core) inflation, 259–261 Underwriters Laboratories, 507 Undetermined coefficients, method of; see Method of undetermined coefficients Unemployment, 520–577; see also Labor market contracting models, 522, 543–550, 564–566, 574–575 and cyclical real wage, 253–255 determinants of, 520 and economic crisis of 2008–, 660 and efficiency wages, 523–532, 572 equilibrium level of, 530, 538–541 in Europe, 549–550 and fair wage-effort hypothesis, 573–574 frictional, 558 Harris–Todaro model, 575–576 insider-outsider models, 547–550, 575 and interindustry wage differences, 566–569 key issues, 520–522 long-term, 558 natural rate of, 257, 304, 549, 564 and Okun’s law, 191 during recessions, 190–191 search and matching models, 550–557 from sector-specific shocks, 230–231 Shapiro–Stiglitz model, 532–543, 552, 554, 570, 573 and wage rigidities, 569–571 and welfare, 562–564 Unemployment benefits, 550 Unemployment-inflation tradeoff; see Output-inflation tradeoff Unfunded liabilities, 664, 666 Unified growth theory, 142n Uninsurable idiosyncratic risk, 231, 408 Union contracts, 310, 565–567 Union wage premium, 572 Unit circle, 605 United Kingdom 781 Great Inflation in, 639–640 inflation-indexed bonds in, 587n tax financing in, 701 United States budget deficits in, 666–671, 678 business-cycle history, 192–193 compensation in finance in, 460 data for calibration of model, 218–219 fiscal policy in, 606, 666–669, 691, 696n, 701 future government spending in, 681 Great Inflation in, 639–640 historical movement of money, 222–223 income stationarity in, 133 inflation-indexed bonds, 587n recessions in, 189–193 tax cuts, 670 User cost of capital, 421–423, 431, 453–454 Utility functions; see also Instantaneous utility functions constant-absolute-risk-aversion, 418 constant-relative-risk-aversion, 52–53, 77, 92, 239, 386, 396 logarithmic, 52, 79, 81–83, 92, 95, 124, 196–197, 203, 689–691 money in, 240, 270 quadratic, 376, 378, 390, 399–400, 403–404 Utility, nonexpected, 398n, 399n V Vacancy-filling rate, 553–556, 562 Value function, 236, 409–411, 534–536, 554–555 Value-function iteration, 410–411 Vector autoregressions (VARs), 225–226 Verification costs, in asymmetric information model, 465–471 Volcker disinflation, 192, 193, 223, 589 Voters and Condorcet paradox, 712 puzzle of participation, 687–688 in Tabellini–Alesina model, 684–685, 687–688, 712–713 W Wage contracts, 545–546, 565 Wage inflation, 256, 259n, 360–361 Wage-price Phillips curve, 304 Wage rigidity in Fischer and Taylor models, 317n with flexible prices and competitive goods, 246 with flexible prices and imperfect goods, 251–253 782 Subject Index Wage rigidity (continued) and inflation, 591 and labor market shifts, 521 in search and matching models, 561 and small barriers to wage adjustment, 285n survey evidence on, 569–571 and wage contracts, 545, 564–566 Wages; see also Efficiency wages; Price adjustment; Unemployment and aggregate demand, 521 cuts in, 530–532, 570–571 cyclical behavior of, 191, 247n, 249, 251, 253–255, 520–521 and education, 152 and fairness, 523, 543, 570–571, 573–574 and government purchases, 216–217 and human capital, 159–160 and incentives for price adjustment, 279, 284–286, 521, 527, 530–532, 546 and inflation, 256–258, 591 in insider-outsider model, 547–550, 575 interindustry differences in, 566–569 and labor supply, 520 posted, 557 in Ramsey–Cass–Koopmans model, 53, 65n in real-business-cycle models, 198–199, 206, 209 during recessions, 191 reservation, 531n in Romer model, 127 in search and matching models, 551–552, 555, 557, 561 setting, 549–550, 569–571 and signing of new contracts, 564–566 staggered adjustment of, 317n subsidies, 541 and technology shocks, 209, 213 and unions, 572 Wage-wage Phillips curve, 304 Waiting, option value to, 447 Walrasian model, 193–195, 224, 231–232, 238, 292 War of attrition, 691 Wartime government purchases, 190n, 677 Weak governments, and budget deficits, 697–700 Wealth redistribution, 302, 702, 704 Welfare (social) and booms and recessions, 274–275, 592–595 and budget deficits, 701–702, 713 and consumption variability, 594–595 in Diamond model, 88–89, 96 and inflation, 588–592 and long-run growth, 6–8 in Ramsey–Cass–Koopmans model, 65–66, 454 and stabilization policy, 592–596 and unemployment, 562–564 and variability in hours of work, 595 White-noise disturbances, 132, 197, 205, 299, 320, 351–352, 598, 602, 606 Whites vs blacks, consumption of, 372–373, 375 Wholesale short-term debt, 509–510 Workers; see also Labor market; Unemployment abilities of, 158–159, 523, 549, 567–568 in Alesina–Drazen model, 692–696 heterogeneity of, 521, 551, 557 immigration of, 158 insiders and outsiders, 547 long-term relationships with employers, 542–543 monitoring of, 524 perceptions of fairness, 523, 543, 570–571, 573–574 and students, 153–155 wealth redistribution from, 702 Work-sharing vs layoffs, 541 World War II, 179, 182, 192, 701 Y Y=AK models, 107, 121 Z Zero-coupon bonds, 583–584 Zero lower bound on nominal interest rates, 305, 507, 591, 603n, 615–629, 655–656 ... Et 2 p1t = 2 1+φ Et 2 m t + 1−φ 1+φ p2t , (7 .23 ) where we have used the law of iterated projections to substitute Et 2 m t for Et 2 Et−1 m t We can substitute (7 .23 ) into (7 .21 ) to obtain p2t... (7 .25 ) into (7 .22 ) and simplifying gives p1t = Et 2 m t + 2 1+φ (Et−1 m t − Et 2 m t ) (7 .26 ) 7 .2 Predetermined Prices: The Fischer Model 319 Finally, substituting equations (7 .25 ) and (7 .26 )... into (7 .21 ) to obtain p2t = φ Et 2 m t + (1 − φ) 2 1−φ Et 2 m t + p t + p2t 1+φ 1+φ (7 .24 ) Solving this expression for p2t yields simply p2t = Et 2 m t (7 .25 ) We can now combine the results