Lucas Cost of Business Cycles

where {displaystyle r} is the real return (after-tax) on invested capital (the real interest rate), ρ {displaystyle rho } is the subjective rate of time preference (which measures impatience), and g {displaystyle g} is the annual growth rate of consumption. r {displaystyle r} is generally estimated to be about 5% (0.05) and the annual growth rate of consumption is about 2% (0.02). Then, the upper limit of the cost of fluctuations occurs when θ {displaystyle theta } is the highest, which is the case in this case when ρ = 0 {displaystyle rho =0}. This implies that the highest possible degree of risk aversion Assuming that business cycles represent random shocks around a trend growth path, Robert Lucas has argued that the cost of business cycles is extremely low,[1][2] and that, as a result, the emphasis by academic economists and policymakers on economic stabilization policies rather than long-term growth is shifted. [3] [4] Lucas himself, having already calculated these costs in 1987, based his own macroeconomic research program on the study of short-term fluctuations. [ref. needed] Nobel laureate Robert Lucas proposed measuring the cost of business cycles as the percentage increase in consumption needed to make a representative consumer indifferent between a smooth, non-fluctuating consumption trend and a trend subject to business cycles. Lucas (Models of Business Cycles, Basil Blackwell, New York, 1987) argues that the gain from eliminating global fluctuations is insignificant. However, a number of researchers have modified their assumptions about preferences, finding that the gain from eliminating business cycles is potentially very large. This paper estimates the welfare costs of business cycles by taking into account the potential temporal inseparability of preferences, where the choice of preference parameters is disciplined by requiring preferences to match the fluctuations observed in a general equilibrium model of business cycles. Estimates of inseparability parameters differ considerably from those used elsewhere, resulting in low welfare costs of business cycles. which, in turn, in combination with the above estimates, results in fluctuation costs, as Lucas` conclusion is controversial.

Keynesian economists, in particular, generally argue that business cycles should not be understood as fluctuations above and below a trend. Instead, they argue that booms are times when the economy approaches its potential output trend, and recessions are times when the economy is well below trend, so there is a large output gap. [4] [5] From this point of view, the social costs of business cycles are higher, because a cyclical economy suffers not only from more variable consumption, but also, on average, from lower consumption. In macroeconomics, the cost of business cycles is the decline in social welfare, if any, caused by cyclical fluctuations. where λ {displaystyle lambda } is the cost of fluctuations (the percentage of average annual consumption that a person would be willing to pay to eliminate all fluctuations in consumption), σ {displaystyle sigma } is the standard deviation of the natural logarithm of consumption, and θ {displaystyle theta} measures the degree of risk aversion. [6] In a survey of the impact of the equity premium, Simon Grant and John Quiggin note that «high-risk costs mean that recessions are extremely destructive.» [9] Robert Lucas` basic formula for welfare costs of business cycles is given by (see mathematical derivation below): The implication is that if the calculation is correct and appropriate, the ups and downs of business cycles, recessions and booms are of little importance to individual and perhaps social well-being. It is the long-term trend of economic growth that is crucial. As an example, consider the case of the log utility (see below), where θ = 1 {displaystyle theta = 1}.

In other words, eliminating all fluctuations in a person`s consumption trajectory (i.e. completely eliminating the business cycle) is worth only 1/20 of 1% of average annual consumption. For example, a person who consumes an average of $50,000 worth of goods per year would be willing to pay only $25 to eliminate fluctuations in consumption. where σ {displaystyle sigma } is the standard deviation of the natural logarithm of consumption and ε {displaystyle epsilon } is a random shock assumed to be logarithmically distributed normally, such that the mean of l n ( ε t ) {displaystyle ln(epsilon _{t})} is zero, implying that the expected value of e − 1 2 σ 2 ε t {displaystyle e^{-{frac {1}{2}}sigma ^{2}}epsilon _{t}} is 1 (i.e. On average, volatile consumption corresponds to a certain consumption). In this case, λ {displaystyle lambda} is the «compensation parameter», which measures the percentage by which the average consumption must be increased so that the consumer is indifferent between the particular consumption path and the volatile path. λ {displaystyle lambda } are the cost of fluctuations. where A {displaystyle A} is the initial consumption and g {displaystyle g} is the consumption growth rate (none of these parameters are important for the cost of fluctuations in the base model, so they can be normalized to 1 and 0, respectively). If we look at two consumption trajectories, each with the same trend and initial level of consumption – and therefore the same level of consumption per period on average – but with different volatility, then, according to economic theory, the least volatile consumption path is preferred to the most volatile.

This is due to the risk aversion of individual agents. One way to calculate how costly this greater volatility is in terms of individual (or, under some restrictive conditions, social) well-being is to ask what percentage of their average annual consumption an individual would be willing to sacrifice to eliminate this volatility altogether. Another way to express this is to ask to what extent an individual with a smooth consumption trajectory would need to be compensated in terms of average consumption to accept the volatile path instead of the one without volatility. The resulting amount of compensation, expressed as a percentage of average annual consumption, corresponds to the cost of fluctuations calculated by Lucas.