Cost of Business Cycles with Indivisibilities and Liquidity Constraints
📄 Summarized from the full manuscript · Human-reviewed for faithfulness before publication
In brief
A famous 1987 estimate put the cost of business cycles to US consumers at a trivial 0.1% of consumption -- but that estimate assumed people can perfectly insure themselves against job loss. This 1989 paper redoes the calculation for agents who can only self-insure by saving, and finds the cost jumps to four or five times as large once borrowing is ruled out. Oddly, letting people borrow again, even at an expensive rate, erases most of that extra cost -- showing that how, exactly, people are kept from insuring themselves matters enormously for how bad business cycles look.
What this paper finds — and why it matters
Imrohoroglu asks whether the small welfare cost of business cycles found by Lucas (1987) – who assumed individuals can perfectly insure against idiosyncratic risk – still holds once that perfect-insurance assumption is dropped. She builds two incomplete-markets economies populated by infinitely-lived agents who face a stochastic employment opportunity (work or receive lower home-production income) and can self-insure only through a non-interest-bearing storage technology, or, in a second version, through storage plus a technology that also allows borrowing at a rate that exceeds the lending rate; in both, the probability of obtaining work differs across “good times” and “bad times” to generate an aggregate business cycle calibrated to U.S. unemployment-rate and duration patterns. Comparing average utility across otherwise-matched economies with and without aggregate fluctuations, she finds that eliminating business cycles is worth a 0.3% increase in average consumption in the perfect-insurance benchmark (risk-aversion coefficient σ=6.2) but a 1.5% increase – five times larger – once agents are restricted to a storage-only technology with no borrowing; at lower risk aversion (σ=1.5) the cost estimate is still roughly four times larger under liquidity constraints than under perfect insurance. Surprisingly, allowing borrowing (even at a substantial 8-percentage-point spread over the lending rate) sharply reduces the cost of business cycles relative to the storage-only economy – by a factor of six at σ=1.5 – indicating that the specific form incomplete insurance takes matters a great deal for how large business-cycle costs appear to be, and that Lucas’s perfect-insurance benchmark is not obviously a safe approximation once liquidity constraints are present.
Summary of a classic paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.
Questions & answers
Q1. What question motivates the paper, and what specific prior result does it test?
The paper asks whether the magnitude of the welfare costs of business cycles found in economies with incomplete insurance markets differs significantly from the cost estimates obtained under the perfect-insurance assumption used by Lucas (1987), who found the cost of U.S. business cycles to be a remarkably small 0.1 percent of total consumption. Rather than generating incomplete insurance endogenously through moral hazard or private information (as in Green, Atkeson, or Townsend), Imrohoroglu follows Scheinkman and Weiss (1986) in imposing it exogenously, via restrictions on the agents’ set of feasible asset holdings – i.e., different specifications of liquidity constraints.
Q2. How are the model economies structured, and what generates the business cycle being studied?
Infinitely-lived agents maximize expected discounted utility over consumption, facing each period a two-state (employed/unemployed) idiosyncratic employment opportunity: if employed they produce y units of the consumption good, if not they produce θy units through home production (0 < θ < 1). Two environments are studied: one in which the only technology available to the consumer is non-interest-bearing storage (no borrowing), and one that adds an intermediation technology permitting borrowing, but at a rate above the lending rate. Within each environment, a “business cycle” economy (in which the probability of being offered work differs between good and bad aggregate states, calibrated to match the U.S. rate and duration of unemployment across peaks and troughs) is compared with a matched economy with the same average unemployment rate and average consumption but no aggregate state variation, isolating the pure effect of a fluctuating consumption stream from the level effect.
Q3. What is the paper’s central cost-of-business-cycles comparison, and what are the key numbers?
For risk aversion σ=6.2, the perfect-insurance economy’s cost of eliminating business cycles is 0.3% of average consumption (about $25.50 per person per year on a $2 trillion 1983 U.S. consumption base), but with only a storage technology available the cost rises to 1.5% of consumption – five times larger ($128 per person, $30 billion economy-wide per year). For the lower risk-aversion case σ=1.5, the storage-only cost estimate (0.3%) is four times the perfect-insurance estimate (0.08%). The paper interprets this as showing that liquidity constraints, modeled as the unavailability of borrowing, substantially raise the measured welfare cost of fluctuations relative to the perfect-insurance benchmark.
Q4. What happens to the cost estimate once borrowing is allowed, and why does the paper call this result unexpected?
When borrowing is permitted (at σ=1.5), the cost of business cycles falls to just 0.05% of average consumption – a sixfold reduction from the storage-only estimate – even though the borrowing rate in this economy exceeds the lending rate by 8 percentage points. The author explicitly flags this as an unanticipated finding: despite a substantial intermediation cost (the spread between borrowing and lending rates), access to even limited borrowing (average equilibrium borrowing is modest relative to total saving) does far more to attenuate the welfare cost of aggregate fluctuations than the storage-only comparison would have suggested, implying that the specific form of market incompleteness assumed matters a great deal for the size of the estimated cost.
Q5. How sensitive are the findings to the risk-aversion parameter and the time discount factor?
Increasing the coefficient of relative risk aversion from 1.5 to 6.2 increases average precautionary asset holdings in the storage-only economy by a factor of 2.6, confirming that more risk-averse agents self-insure more; doubling the unemployment compensation replacement rate (from one-fourth to one-half of market income) roughly halves average asset holdings. Varying the subjective discount factor β to imply steady-state annual real interest rates of 6% versus 2% (versus the baseline’s implied rate) changes the σ=6.2 storage-only cost estimate only modestly, from 1.5% to 1.6% and 1.3% of consumption respectively – the paper reports this sensitivity as small.
Q6. What computational approach does the paper use to solve these incomplete-markets economies, and why does that matter for the paper’s contribution?
Because the economies have no closed-form solution, the paper discretizes the state space (asset holdings and employment state) and the control space and computes equilibrium value functions and decision rules numerically, then determines the invariant distribution of agents across states to obtain the statistical properties (including average utility) of each economy’s equilibrium stochastic process. The paper frames its methodological contribution partly as developing these computational tools for comparing economies with different incomplete-insurance structures, a toolkit the author’s companion/related work (cited as Imrohoroglu 1989a, 1989b) and the 1992 Hansen-Imrohoroglu unemployment-insurance paper both build on.
Key terms in this paper
Definitions below follow the paper's own usage.
- Cost of business cycles (compensating-consumption measure)
- following Lucas (1987), the percentage increase in average consumption that would leave an agent in the economy with aggregate fluctuations just as well off, in expected-utility terms, as an otherwise-identical agent in a matched economy with no aggregate fluctuations but the same average consumption and unemployment rate; the paper's basic unit of comparison across the perfect-insurance, storage-only, and intermediation environments.
- Liquidity constraint (storage-only technology)
- the restriction, imposed exogenously rather than derived from moral hazard or asymmetric information, that consumers can only self-insure against idiosyncratic employment risk by accumulating a non-interest-bearing storage asset, with no access to borrowing; the paper's main vehicle for generating incomplete insurance markets, following Scheinkman and Weiss (1986).
- Intermediation technology
- an extension of the storage-only environment in which consumers can also borrow, but at an interest rate that exceeds the lending/storage rate (an 8-percentage-point spread in the paper's calibration); the paper's unexpected finding is that even limited access to this costly borrowing sharply lowers the measured cost of business cycles relative to the storage-only case.
- Home production (unemployment state)
- the θy units of the consumption good an agent produces while not given the stochastic opportunity to work in the market sector (0 < θ < 1), serving as the model's analogue of unemployment compensation / non-market income and a key determinant, alongside the asset-holding technology, of how much consumption volatility an unemployed spell actually generates.