Real-Business-Cycle-Theory | Macro Paper Warehouse

Deep Habits

Habit-formation models, internal or external, standardly assume households form habits over a single aggregate good, which means habits change macroeconomic propagation only through aggregate demand and possibly labour supply. This paper asks what changes if habits are instead formed variety by variety – over clothing, vacation destinations, music, cars – a specification the authors call “deep habits” and argue is the more compelling reading of the evidence, citing Houthakker and Taylor’s classic demand work and the marketing literature finding that brand choices depend on past brand choices. Two consequences follow. The demand side is unaffected: the consumption Euler equation is indistinguishable from the superficial-habit case, so existing Euler-equation estimates of habit strength carry over. The supply side changes fundamentally, because firms now recognise that today’s sales raise tomorrow’s demand through habit, making the pricing problem dynamic. Demand for an individual variety splits into a price-elastic term and a perfectly inelastic term coming from habitual consumption of that good, so the short-run price elasticity is a weighted average of the elasticity of substitution and zero – smaller than the elasticity of substitution, and rising when aggregate demand rises because the inelastic component shrinks in relative weight. Since the mark-up is inversely related to the elasticity, mark-ups fall in expansions: the “price-elasticity effect.” A second, “intertemporal” channel operates because firms invest in customer base by cutting mark-ups when the present value of future per-unit profits is high, which also makes the mark-up rise with the real interest rate. Together these deliver a central result – mark-ups are countercyclical in response to preference, government-spending and productivity shocks – which matters because ad hoc general equilibrium customer-market and switching-cost models had been criticised by Rotemberg and Woodford precisely for implying procyclical mark-ups; the authors’ answer is that once demand is derived from optimising households rather than assumed, the prediction reverses. Embedding the mechanism in a full real-business-cycle model with capital, labour supply and government, and estimating the habit parameters by nonlinear GMM on U.S. quarterly data for 1967:Q1-2003:Q1 (exploiting supply-side restrictions absent from Euler-equation-only estimation) gives a habit strength of 0.86, a habit-stock persistence of 0.85, an elasticity of substitution across varieties of 5.3 and a curvature parameter of 2, with the remaining calibration targets taken from Rotemberg and Woodford to make the comparison direct; the implied steady-state mark-up is 1.32, which the authors describe as “somewhat high,” against 1.23 in the no-deep-habit case. Quantitatively, a preference shock worth 1% of steady-state habit-adjusted consumption cuts the mark-up by about 0.4% and raises wages by about 0.3%, where under superficial or no habits wages fall. A 1% government-spending shock cuts mark-ups by about half a per cent, raises real wages, and – against the standard neoclassical prediction – raises private consumption, in line with evidence from Fatás-Mihov, Blanchard-Perotti and Galí-López-Salido-Vallés, though the authors are explicit that “the deep-habit model underpredicts the magnitude of the consumption increase.” The model’s conditional correlation between labour productivity and output is 0.33 under government-purchases shocks and 0.72 under preference shocks, against an unconditional figure of 0.34 reported by Cooley and Prescott, where the superficial-habit model gives -0.1 and -0.85. Three extensions separate the mechanisms: good-specific subsistence points isolate the price-elasticity effect and still give countercyclical mark-ups, but the movements are too small to deliver procyclical wages or procyclical consumption after a government-spending shock; relative deep habits isolate the intertemporal effect, whose sign then depends on whether a shock raises the habit-forming or the non-habit-forming component of demand; and internal deep habits make the monopolist’s pricing problem time inconsistent, a case the authors flag as “beyond the scope of this paper” and “perhaps, the most relevant next step in this research programme.”

Income and Wealth Heterogeneity in the Macroeconomy

In a calibrated stochastic growth model where a continuum of infinitely lived households face partially uninsurable employment risk and can self-insure only by holding aggregate capital, the macroeconomic aggregates turn out to be almost perfectly described by just two numbers — the mean of the wealth distribution and the aggregate productivity shock. The paper calls this approximate aggregation and states it carefully: “all aggregate variables — consumption, the capital stock, and relative prices — can be almost perfectly described as a function of two simple statistics,” so that “the distribution of aggregate wealth is almost completely irrelevant for how the aggregates behave in the equilibrium.” With a log-linear law of motion in the mean alone, the fitted rules are log k’ = 0.095 + 0.962 log k in good times and 0.085 + 0.965 log k in bad, both with R² = 0.999998 and regression-error standard deviations of 0.0028% and 0.0036%; price forecasts 25 years ahead have maximum errors under 0.1 percent. The mechanism is not that the distribution is stable — its standard deviation, skewness and kurtosis all “display substantial variation” — but that the marginal propensity to save is nearly independent of wealth except at the very bottom, and the agents whose propensities differ hold a negligible share of capital. The paper is equally clear that this benchmark fails as a model of inequality: the poorest 20 percent hold 9 percent of wealth against roughly zero in the data, the richest 5 percent hold 11 percent against roughly half, and the Gini is 0.25 against 0.79. The fix is a stochastic discount factor taking three values 0.9858, 0.9894 and 0.9930 with 50-year average duration at the extremes, read as imperfectly inherited patience; that model reproduces the data’s Gini (0.82 against 0.79) and its 11 percent of households with negative wealth, though it still understates the extreme upper tail. Approximate aggregation survives — R² = 0.999991 and 0.999985, with errors roughly twice as large. What does not survive is permanent-income behaviour: because impatient households face a large wedge between their discount rate and the market return, they consume hand-to-mouth, and while they “matter little for what happens to the evolution of economywide wealth,” their consumption is a large share of the total, pushing the aggregate consumption-output correlation to 0.825 against 0.691 in the complete-markets benchmark. Precautionary saving is small in the benchmark (0.6 percent of the capital stock) but rises to 6.7 percent with risk aversion of five. The methodological claim is stated as an enabling one — this “opens the possibility of characterizing a large class of new macroeconomic models in which heterogeneity in income and wealth plays a key role” — and the robustness claim is stated as an empirical regularity of their experiments, not a theorem: “it is extremely difficult to find exceptions to the approximate aggregation result,” while “like most numerical procedures, the present one does not provide bounds on how far the approximate equilibrium deviates from an exact equilibrium.”

Investment spikes: New facts and a general equilibrium exploration

The dispute the paper enters is whether the well-documented lumpiness of plant-level investment matters for aggregate dynamics. Caballero’s Handbook survey argued that “the changes in the degree of coordination of lumpy actions play an important role in shaping the dynamic behavior of aggregate investment”; Thomas (2002) built a general equilibrium model in which “the aggregate effects of lumpy investment are negligible,” because households’ consumption-smoothing offsets the lumpy investment demand – a result that led Prescott to conclude that “partial equilibrium reasoning to an inherently general equilibrium question cannot be trusted.” Gourio and Kashyap make three moves. The first is empirical. Using U.S. Annual Survey of Manufactures establishment tabulations for 1972-1998 and a Chilean plant census covering on average 1,780 plants per year for 1981-1999, capital-weighted throughout, they show that investment spikes (investment above 20 percent of beginning-of-period capital) account for about half of total investment in each country, and that variation in spike investment accounts for 97 percent of the variance of the aggregate investment rate in the U.S. and 86 percent in Chile. Decomposing spike investment into the amount invested per adjuster and the number of adjusters, they find the extensive margin dominates: it accounts for 0.87 of the variance in the U.S. and 0.925 in Chile. They also add the share of adjusters to a standard accelerator forecasting regression and find it enters with negative coefficients that are significant at the first and second lag in the U.S. and at the second lag in Chile – investment is depressed in the period after a surge, which is the sign a fixed-cost model predicts and the opposite of what would appear if the spike variable were merely proxying for productivity. The second move is to recalibrate Thomas’s model to match these facts. As originally calibrated it does not: spikes account for only about 62 percent of the variance of investment and the extensive margin for only 51 percent of the variance of spikes, against roughly 90 percent for both in the data. The critical change is the distribution of fixed costs. Thomas, following Caballero and Engel, uses a uniform distribution, under which moving more plants into action always means activating plants facing quite different costs; if instead the distribution is “compressed” so that many firms face nearly identical costs, moving many firms across the threshold is cheap and the extensive margin becomes powerful. Substituting a compressed distribution raises the extensive margin’s share to 92.6 percent and the variance share of spikes to 99.9 percent. The authors also argue Thomas’s calibration puts too little into adjustment costs – about one-fifth of one percent of investment spending, against Cooper and Haltiwanger’s estimate of roughly 7.5 percent, “roughly 40 times the size” – and too little curvature in the profit function, against a later literature estimating returns to scale between 0.5 and 0.7. Their preferred calibration raises the maximum fixed cost to 0.06 and sets returns to scale to 0.6. The third move is to re-run the irrelevance test. Under Thomas’s calibration the impact response of investment to a productivity shock is 99.8 percent of the frictionless RBC model’s; under theirs it is 89 percent, with a visible hump about twelve periods out. The larger divergence comes from a different experiment: perturbing the cross-sectional distribution of capital directly, as a temporary investment tax cut or an uncertainty shock would. There, Thomas’s model and the RBC model remain “essentially identical,” while the recalibrated model shows both a depressed investment response and a magnified echo when the recently-invested firms come back after 8 to 11 periods. The conclusion is carefully bounded: general equilibrium does attenuate the differences, and the authors agree with Thomas that GE and partial equilibrium can differ substantially – but “there is nothing generically related to DSGE models that guarantees that plant-level investment lumpiness is smoothed away,” and the stronger claim that GE makes fixed costs irrelevant “is premature.” They add that all their results use log utility, that their calibration “is not fully optimized,” and that “much more work needs to be done” on how such models should be estimated and calibrated.

Investment, Capacity Utilization, and the Real Business Cycle

In the real business cycle models of Kydland-Prescott and Long-Plosser, cycles come from shocks to the production function; this paper instead adopts Keynes’s view that it is shocks to the marginal efficiency of investment that drive output fluctuations, and asks whether such shocks can be made to work inside a neoclassical framework. The obstacle is well known and the authors state it up front: in a standard model an investment shock raises the return to investment, which induces intertemporal substitution that persuades people to work more now but also to consume less now, so consumption moves countercyclically; and because labour expands against a fixed capital stock, labour productivity falls. Both contradict the evidence. The paper’s answer is to make the rate at which installed capital is used a choice variable. Production depends on capital services – the capital stock times a utilization index – and higher utilization causes faster depreciation, which is Keynes’s own notion of user cost. The shock is a technological change that raises the productivity of newly produced capital goods only, entering as a multiplicative factor on gross investment in the capital accumulation equation and reaching output only after a time-to-build delay taken to be about a year. The mechanism then runs as follows. A positive shock lowers the replacement cost of old capital in terms of new, so it becomes optimal to run old capital harder and depreciate it off faster. Because capital and labour services are complements under constant returns, higher utilization raises the marginal product of labour, employment rises, and average labour productivity rises with it – all without relying on intertemporal substitution in labour supply, which the paper’s preference specification (utility in consumption less a convex function of labour effort) deliberately eliminates. The higher marginal product of labour also creates an intratemporal substitution away from leisure and toward consumption, which is what makes it possible for consumption and investment to rise together. The authors are explicit that the restriction to new capital is load-bearing: if the technological shift is applied to installed capital as well, the shock drops out of the utilization and labour conditions entirely, and “the positive effects of a technological shift on h, l, y, and productivity, in addition to the procyclical effect on consumption, are all lost.” Quantitatively, the model is parameterised annually (discount factor 0.96, capital share 0.29 from the average 1950-85 U.S. figure, labour supply elasticity 1.7, depreciation elasticity 1.42 chosen to deliver a steady-state depreciation rate of 0.1), solved exactly by computing the stationary joint distribution of capital and the two-state shock over a discretised state space, and calibrated so that it reproduces the standard deviation and first-order autocorrelation of detrended U.S. output for 1948-85 – and nothing else. It then reproduces qualitatively the relative volatilities of consumption, investment and hours, though it exaggerates them, and it ranks the persistence of consumption, productivity and investment correctly. Fit is better at a risk aversion of 2 than of 1: the correlation of consumption with output rises from 0.50 to 0.79 against an actual 0.74, and the standard deviation of investment falls from 14.7 to 11.6 percent against an actual 10.5. A notable auxiliary finding is that the required exogenous persistence is far lower than in conventional Solow-residual-driven models: the fitted annual autocorrelation of the shock is 0.47 or 0.51, against Hansen’s quarterly 0.95, which implies a four-quarter figure of 0.81. On shock size the authors concede no advantage – the ratio of shock to output standard deviation, 1.47, sits inside Hansen’s range of 1.3 to 1.7 – but argue that a shock of a given size is a weaker requirement here because it applies only to new capital goods. The paper’s own conclusion is hedged throughout: variable capacity utilization “may be important” and “may allow for a smaller burden to be placed on intertemporal substitution.”

Methods and Problems in Business Cycle Theory

This 1980 essay by Robert Lucas, prepared for an American Enterprise Institute seminar on rational expectations, opens by proposing that economic theories be understood not as claims about how actual economies behave but as explicit instructions for constructing fully articulated, artificial “analogue” model economies whose behavior can be tested against data and against each other, so that a genuinely useful model will necessarily be abstract and unrealistic on its face. From this vantage point, Lucas retraces the history of business cycle theory: Wesley Mitchell’s early twentieth-century statistical documentation of recurring co-movements among economic series; Keynes’s Treatise on Money and General Theory, which Lucas reads as intelligent but technically under-equipped attempts to combine a quantity-theoretic view of nominal prices with real-side determination of output; and the postwar “neoclassical synthesis” of Samuelson, Hicks, Modigliani, and Patinkin, which grafted a Samuelson-style theory of disequilibrium price dynamics – prices and quantities adjusting toward a static general-equilibrium core in response to “excess demands” – onto that equilibrium core, gaining its ability to mimic Keynesian business cycles from added free parameters governing the speed of that adjustment. Lucas argues this synthesis was disturbed from the late 1960s by Milton Friedman’s natural-rate hypothesis and Edmund Phelps’s search for microeconomic foundations of wage and price setting, both of which implied no long-run trade-off between inflation and unemployment, and that John Muth’s rational-expectations hypothesis subsequently proved essential, and subversive, once economists tried to formalize how expectations should be modeled under that hypothesis. In parallel, Lucas traces a purely technical development in general equilibrium theory – Hicks’s reinterpretation of dynamic choice as choice over dated goods, and Arrow and Debreu’s further extension of commodities to be indexed by the state of nature in which they are delivered – which let uncertainty be incorporated into competitive equilibrium theory without any disequilibrium-adjustment apparatus, and which underlies both rational expectations and a new class of “equilibrium models of the business cycle” that treat prices and quantities as always market-clearing. Using an extended example contrasting the unpredictability of an isolated animal’s behavior with the predictability that competitive interaction restores to group outcomes, Lucas argues that competitive-equilibrium models of wage and employment determination can in principle match the fit of Phillips-curve-style models while relying only on parameters describing preferences and technology, rather than an added, empirically opaque parameter describing the speed of an auctioneer’s wage adjustment. He concludes that the discipline’s task is to build policy-evaluation model economies whose deep parameters are estimated from individual and cross-sectional behavior rather than fitted to aggregate time series, and that this is best understood as a continuation, not a rejection, of the same practical compromise between ambition and available technique that produced the neoclassical synthesis itself.

Time to Build and Aggregate Fluctuations

This 1982 Econometrica paper by Finn Kydland and Edward Prescott builds an equilibrium growth model, fitted to post-war U.S. quarterly data, in which business-cycle fluctuations arise from technology shocks propagating through two departures from the standard growth model: a time-to-build technology, in which new productive capital requires multiple periods (calibrated to four quarters) of construction and only finished capital counts as productive, and a non-time-separable utility function in which current leisure’s marginal value depends on a distributed lag of past leisure choices, admitting substantially greater intertemporal substitution of leisure than a standard time-separable specification. The technology shock is decomposed into a highly persistent (autoregressive, calibrated at 0.95 per quarter) permanent component and a transitory component, both observed only through a noisy indicator at the time labor-supply and new-investment decisions are made, so the model incorporates a signal-extraction problem alongside its intertemporal optimization. Because there are no externalities, the authors compute the competitive equilibrium as the solution to a representative-household planning problem, approximated by a quadratic objective and linear constraints around the model’s deterministic steady state so that equilibrium decision rules are linear and second moments can be computed analytically; nearly all parameters are calibrated from steady-state national-accounts ratios and evidence from other applied literatures (e.g., surveyed construction lags of about two years) rather than formally estimated, leaving a small number of free parameters chosen to match the model’s simulated second moments to Hodrick-Prescott-filtered U.S. data for 1950:1-1979:2. The fitted model reproduces, surprisingly well given its simplicity, the U.S. economy’s pattern of output autocorrelation over six lags, the relative volatility ranking across output components (investment about three times as volatile as output, consumption about half as volatile), the strong procyclicality of consumption and hours, and the fact that cyclical output variation comes mainly from variation in hours worked rather than in labor productivity. The paper directly tests time-to-build against the leading alternative propagation mechanism, a quadratic adjustment-cost technology, and finds that even a small adjustment cost badly distorts the model’s implied comovements – making output driven mainly by productivity rather than hours, and making consumption too volatile and investment too smooth relative to the data – concluding that adjustment costs “were not a substitute for the time-to-build assumption in explaining the data.”

Time to Plan and Aggregate Fluctuations

Studies of major capital projects report two facts about investment gestation: projects take longer than a quarter to complete, and they open with a lengthy planning phase – drawing plans, arranging finance, obtaining permits – during which the direct resource cost is small relative to the project total. Kydland and Prescott’s Time to Build built the first fact into a macro model; this paper argues the second is the one that matters quantitatively, and that the first “per se has relatively modest implications for business cycle dynamics.” The authors take Christiano and Eichenbaum’s divisible-labour model with technology and government consumption shocks and compare three investment technologies: one-period completion; Kydland and Prescott’s four-period gestation with resource weights of 0.25 in each quarter (time to build); and the same four-period gestation reweighted to 0.01, 0.33, 0.33, 0.33 so that the first quarter consumes almost nothing (time to plan). The empirical basis is explicit – in Mayer’s (1960) data projects took 22 months on average with the first 7 months a preconstruction planning phase, and Krainer (1968) finds that in all 25 projects he studies less than 5 percent of total cost was incurred in the first three months, and in 18 of them less than 2.5 percent. The mechanism the planning phase supplies is a delay in the response of hours worked. In a standard model a positive technology shock makes households work harder to accumulate the investable resources needed to exploit the higher return on investment; with a planning phase there is little to do with those resources in the period of the shock, so hours worked actually falls a little, investment barely moves, and much of the extra output is simply consumed. That delay in hours translates into a delay in output, and produces three matches to U.S. quarterly data for 1947:1-1995:1. First, persistence: the first-order autocorrelation of U.S. GDP growth is 0.37 (standard error 0.07), the one-period and four-period even-weight models produce essentially zero even though the exogenous technology growth rate is serially uncorrelated, and the time-to-plan model produces 0.36. Second, the timing of productivity and hours: because hours are damped on impact while productivity jumps, productivity comes to lead hours worked, and the contemporaneous hours-productivity correlation falls from roughly 0.90 in the other two models to 0.28 – the U.S. figure being near zero with a significantly positive correlation between productivity and future hours. Third, investment now lags output, which is counterfactual for aggregate investment but matches the behaviour of business investment in structures and equipment, the components for which a planning period is most plausible. The authors are careful about what does not work: consumption leads the cycle and is far too volatile in the time-to-plan model, both counterfactual, and they attribute this to the level of aggregation rather than to the mechanism, conjecturing that a model separating business structures from residential investment and household durables would fix it. Adding government consumption shocks – which in their specification are temporary – cuts persistence rather than raising it, because with no investment margin available hours must rise sharply to absorb the shock; it also reduces the excess volatility of consumption, and contributes almost nothing to output volatility. They describe the work as “primarily as preliminary and, we hope, suggestive.”