生命与成长

NBER WORKING PAPER SERIES LIFE AND GROWTH Charles I. Jones Working Paper 17094 http://www.nber.org/papers/w17094 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 May 2011 This paper was previously circulated under the title "The Costs of Economic Growth.'' I am grateful to Raj Chetty, Bob Hall, Peter Howitt, Pete Klenow, Omar Licandro, David Romer, Michele Tertilt, Martin Weitzman and participants in seminars at Berkeley, the Federal Reserve Bank of San Francisco, an NBER EFG meeting, Stanford, UC Irvine, and UCSD for comments, and to the National Science Foundation for financial support. Arthur Chiang, William Vijverberg and Mu-Jeung Yang provided excellent research assistance. The views expressed herein are those of the author and do not necessarily reflect the views of the National Bureau of Economic Research. © 2011 by Charles I. Jones. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Life and Growth Charles I. Jones NBER Working Paper No. 17094 May 2011 JEL No. E0,I10,O3,O4 ABSTRACT Some technologies save lives — new vaccines, new surgical techniques, safer highways. Others threaten lives — pollution, nuclear accidents, global warming, the rapid global transmission of disease, and bioengineered viruses. How is growth theory altered when technologies involve life and death instead of just higher consumption? This paper shows that taking life into account has first-order consequences. Under standard preferences, the value of life may rise faster than consumption, leading society to value safety over consumption growth. As a result, the optimal rate of consumption growth may be substantially lower than what is feasible, in some cases falling all the way to zero. Charles I. Jones Graduate School of Business Stanford University 518 Memorial Way Stanford, CA 94305-4800 and NBER chad.jones@stanford.edu 2 CHARLES I. JONES Certain events quite within the realm of possibility, such as a major as- teroid collision, global bioterrorism, abrupt global warming — even cer- tain lab accidents— could have unimaginably terrible consequences up to and including the extinction of the human race... I am not a Green, an alarmist, an apocalyptic visionary, a catastrophist, a Chicken Little, a Luddite, an anticapitalist, or even a pessimist. But... I have come to believe that what I shall be calling the “catastrophic risks” are real and growing... —Richard A. Posner (2004, p. v) 1. Introduction In October 1962, the Cubanmissile crisis brought theworld to the brink of a nuclear holocaust. President John F. Kennedy put the chance of nuclear war at “somewhere betweenone out of three and even.” The historian Arthur Schlesinger, Jr., at the time an adviser of the President, later called this “themost dangerousmoment in human history.”1 What if a substantial fraction of the world’s population had been killed in a nuclear holocaust in the 1960s? In some sense, the overall cost of the technologi- cal innovations of the preceding 30 years would then seem to have outweighed the benefits. While nuclear devastation represents a vivid example of the potential costs of technological change, it is by no means unique. The benefits from the internal combustion engine must be weighed against the costs associated with pollution and global warming. Biomedical advances have improved health substantially but made possible weaponized anthrax and lab-enhanced viruses. The potential bene- fits of nanotechnology stand beside the threat that a self-replicating machine could someday spin out of control. Experimental physics has brought us x-ray lithogra- phy techniques and superconductor technologies but also the remote possibility of devastating accidents as we smash particles together at ever higher energies. These 1For these quotations, see (Rees, 2003, p. 26). LIFE AND GROWTH 3 and other technological dangers are detailed in a small but growing literature on so- called “existential risks”; Posner (2004) is likely themost familiar of these references, but see also Bostrom (2002), Joy (2000), Overbye (2008), and Rees (2003). Technologies need not pose risks to the existence of humanity in order to have costs worth considering. New technologies come with risks as well as benefits. A new pesticide may turn out to be harmful to children. New drugs may have unforeseen side effects. Marie Curie’s discovery of the new element radium led to many uses of the glow-in-the-dark material, including a medicinal additive to drinks and baths for supposed health benefits, wristwatches with luminous dials, and as makeup — at least until the dire health consequences of radioactivity were better understood. Other examples of new products that were intially thought to be safe or even healthy include thalidomide, lead paint, asbestos, and cigarettes. While some new technologies are dangerous, many others are devoted to sav- ing lives. Lichtenberg (2005), for example, estimates that new pharmaceuticals ac- counted for perhaps 40 percent of the rise in life expectancy between 1986 and 2000. MRI machines, better diagnostic equipment, and new surgical techniques as well as anti-lock brakes, airbags, and pollution scrubbers are all examples of life- saving technologies. How is growth theory altered when technologies involve life and death instead of just higher consumption? Consider what might be called a “Russian roulette” theory of economic growth. Suppose the overwhelming majority of new ideas are beneficial and lead to growth in consumption. However, there is a tiny chance that a new idea will be particu- larly dangerous and cause massive loss of life. Do discovery and economic growth continue forever in such a framework, or should society eventually decide that con- sumption is high enough and stop playing the game of Russian roulette? How is this conclusion affected if researchers can also develop life-saving technologies? The answers to these questions turn out to depend crucially on the shape of preferences. For a large class of conventional specifications, including log utility, safety eventually trumps economic growth. The optimal rate of growthmay be sub- stantially lower than what is feasible, in some cases falling all the way to zero. This project builds on a diverse collection of papers. Murphy and Topel (2003), 4 CHARLES I. JONES Nordhaus (2003), and Becker, Philipson and Soares (2005) emphasize a range of economic consequences of the high value attached to life. Murphy and Topel (2006) extend this work to show that the economic value of future innovations that reduce mortality is enormous. Weisbrod (1991) early on emphasized that the nature of health spending surely influences the direction and rate of technical change. Hall and Jones (2007) — building on Grossman (1972) and Ehrlich and Chuma (1990) — is a direct precursor to the present paper, in ways that will be discussed in detail below. Other related papers take these ideas in different directions. Acemoglu and Johnson (2007) estimate the causal impact of changes in life expectancy on income. Malani and Philipson (2011) provide a careful analysis of the differences between medical research and research in other sectors. The paper is organized as follows. Section 2 presents a simple model that il- lustrates the main results. The advantage of this initial framework is its simplic- ity, which makes the basic intuition of the results apparent. The disadvantage is that the tradeoff between growth and safety is a black box. Section 3 then devel- ops a rich idea-based endogenous growth model that permits a careful study of the mechanisms highlighted by the simple model. Section 4 discusses a range of em- pirical evidence that is helpful in judging the relevance of these results, and Section 5 concludes. 2. A Simple Model At some level, this paper is about speed limits. You can drive your car slowly and safely, or fast and recklessly. Similarly, a key decision the economy must make is to set a safety threshold: researchers can introduce many new ideas without regard to safety, or they can select a very tight safety threshold and introduce fewer ideas each year, potentially slowing growth. To develop this basic tradeoff, we begin with a simple two period OLG model. Suppose an individual’s expected lifetime utility is U = u(c0) + e −δ(g)u(c), c = c0(1 + g) (1) LIFE AND GROWTH 5 where c denotes consumption, g is the rate of consumption growth, and δ(g) is the mortality rate so e−δ(g) is the probability an individual is alive in the second period. A new cohort of young people is born each period, and everyone alive at a point in time has the same consumption— this generation’s c0(1+g) is the next generation’s c0. To capture the “slow and safely or fast and recklessly” insight, assume δ(g) is an increasing function of the underlying rate of economic growth. Faster growth raises the mortality rate. In the richer model in the next section, this “black box” linking growth andmortality will be developed withmuchmore care. Notice, however, that this approach incorporates the essential idea behind the Russian roulette example in the introduction. Each generation when young chooses the growth rate for the economy to max- imize their expected utility in equation (1). The growth rate balances the concerns for safety with the gains from higher consumption. The first order condition for this maximization problem can be expressed as u′(c)c0 = δ ′(g)u(c). (2) At the optimum, the marginal benefit from higher consumption growth, the left hand side, equals the marginal cost associated with a shorter life, the right hand side. This condition can be usefully rewritten as 1 + g = ηu,c δ′(g) (3) where ηu,c is the elasticity of u(c) with respect to c. To makemore progress, assume the following functional forms (we’ll generalize later): δ(g) = δg (4) u(c) = u¯+ c1−γ 1− γ . (5) Utility takes the familiar form that features a constant elasticity of marginal utility; 6 CHARLES I. JONES the important role of the constant u¯ will be discussedmomentarily. 2.1. Exponential Growth: 0 < γ < 1 To begin, let’s assume γ < 1 and set u¯ = 0. In this case, the elasticity of utility with respect to consumption is ηu,c = 1− γ, so the solution for growth in (3) is g∗ = 1− γ δ − 1. (6) As long as δ is not too large, the model yields sustained positive growth over time. For example, if γ = 1/2 and δ = 1/10, then g∗ = 4 and 1 + g∗ = 5: consumption increases by a factor of 5 across each generation. This comes at the cost of a life expectancy that is less than the maximum, but such is the tradeoff inherent in this model. One can check that this conclusion is robust to letting u¯ 6= 0. In general, that will simply introduce transition dynamics into the model with γ < 1. The key elasticity ηu,c then converges to 1 − γ as consumption gets large, leading to balanced growth as an asymptotic result. 2.2. The End of Growth: γ > 1 What comes next may seem a bit surprising. We’ve already seen that this simple model can generate sustained rapid growth for a conventional form of preferences. What we show now is that in the case where γ is larger than one, themodel does not lead to sustained growth. Instead, concerns about safety lead growth to slow all the way to zero, at least eventually. In this case, the constant u¯ plays an essential role. In particular, notice that we’ve implicitly normalized the utility associated with “death” to be zero. For example, in (1), the individual gets u(c) if she lives and gets zero if she dies. But this means that u(c) must be greater than zero for life to be worth living. Otherwise, death is the optimal choice at each point in time. With γ > 1, however, c 1−γ 1−γ is less than zero. For example, this flow is −1/c for γ = 2. An obvious way to make our problem LIFE AND GROWTH 7 Figure 1: Flow Utility u(c) for γ > 1 u(c) = u¯ + c 1− γ 1−γ for γ > 1 Consumption, c Utility 0 u¯ Note: Flow utility is bounded for γ > 1. If u¯ = 0, then flow utility is negative and dying is preferred to living. interesting is to add a positive constant to flow utility. In this case, the flow utility function is shown in Figure 1. Notice that flow utility is bounded, and the value of u¯ provides the upper bound.2 Assuming γ > 1 and u¯ > 0, the first order condition in (3) can be written as (1 + g) ( u¯cγ−10 (1 + g) γ−1 + 1 1− γ ) = 1 δ . (7) The left-hand side of this expression is increasing in both c0 and in g. As the econ- omy gets richer over time and c0 rises, then, it must be the case that g declines in order to satisfy this first order condition. The optimal rate of economic growth slows along the transition path. In fact, one can see from this equation that consumption converges to a steady state with zero growth. According to the original first order condition in (3), the 2As the figure illustrates, there exists a value of consumption below which flow utility is still neg- ative. Below this level, individuals would prefer death to life, so they would randomize between zero consumption and some higher value; see Rosen (1988). This level is very low for plausible parameter values and can be ignored here. The role of the constant in flow utility is also discussed by Murphy and Topel (2003), Nordhaus (2003), Becker, Philipson and Soares (2005), and Hall and Jones (2007). 8 CHARLES I. JONES steady state must be characterized by η∗u,c = δ — that is, the point where the elas- ticity of the utility function with respect to consumption equals the mortality pa- rameter. More explicitly, setting g = 0 in (7) reveals that the steady state value of consumption is given by c∗ = ( 1 u¯ ( 1 δ + 1 γ − 1 )) 1 γ−1 . (8) Because growth falls all the way to zero, mortality declines to zero as well and life expectancy is maximized. To see the intuition for this result, recall the first order condition for growth: 1 + g = ηu,c/δ. When γ > 1 (or when flow utility is any bounded function), the marginal utility of consumption declines rapidly as the economy gets richer — that is, ηu,c declines. This leads the optimal rate of growth to decline and the economy to converge to a steady state level of consumption. A crucial implication of the bound on utility is that the marginal utility of con- sumption declines to zero rapidly. Consumption on any given day runs into sharp diminishing returns: think about the benefit of eating sushi for breakfast when you are already having it for lunch, dinner, and your midnight snack. Instead, obtain- ing extra days of life on which to enjoy your high consumption is a better way to increase utility. This point can also be made with algebra. Consider the following expression: u(ct) u′(ct)ct = 1 ηu,c = u¯cγ−1t + 1 1− γ . (9) The left side of this equation is based on the flow value of an additional period of life, u(c). We divide by the marginal utility of consumption to value this flow in units of consumption rather than in utils, so u(c)/u′(c) is something like the value of a period of life in dollars. Then, we consider this value of life as a ratio to actual consumption. The right side of this equation shows the value of life as a ratio to consumption under the assumed functional form for utility. Crucially, for γ > 1, the value of life LIFE AND GROWTH 9 rises faster than consumption. As the economy gets richer, concerns about safey become more important than consumption itself. This is the essential mechanism that leads the economy to tilt its allocation away from consumption growth and toward preserving life in the model. 2.3. Generalizing More generally, it should be clear from equations (9) and (3) that this steady-state result would obtain with any (well-behaved) bounded utility function: in that case, the elasticity of utility with respect to consumption falls to zero as consumption goes to infinity, so the condition ηu,c = δ delivers a steady state. Interestingly, this same result obtains with log utility. For γ = 1, we have u(c) = u¯ + log c, and therefore ηu,c = 1/u(c). The elasticity of utility still declines to zero as consumption gets arbitrarily large, leading to constant consumption in the long run, even though utility is unbounded. Alternatively, consider changing the mortality function. If we instead assume δ(g) = δgθ with θ > 1, then the simple model leads the growth rate to slow to zero, but only as consumption rises to infinity.3 The implication that consumption will be constant in the long run, then, seems to be somewhat fragile. The more robust prediction is that safety considerations may lead consumption growth to slow to zero. 2.4. Summary of the Simple Model This simplemodel is slightymore flexible than the “Russian roulette” example given in the introduction. Rather than choosing between stagnation and a fixed rate of growth with a small probability of death, the economy can vary the growth rate and the associated death rate smoothly. This death rate can be given two different in- terpretations. It may apply independently to each person in the population, so that 3The first order condition analogous to equation (3) becomes g θ−1(1 + g) = ηu,c δθ which implies that g → 0 only occurs as ηu,c → 0 when γ > 1. 10 CHARLES I. JONES e−δ(g) is the fraction of the population that survives to old age in each cohort. Alter- natively, it may represent an existential risk that applies to the entire economy. With γ < 1, the optimal tradeoff between growth and mortality leads to sus- tained exponential growth, albeit with some positive death rate. In the idiosyn- chratic interpretation of the death rate, life expectancy is simply less than its maxi- mum but the economy continues forever. In the existential risk interpretation, the economy grows exponentially until, with probability one, the existential risk is real- ized and the economy comes to an end. A very different result occurs when γ ≥ 1, or more generally when flow utility is bounded. In this case, themarginal utility of consumption in any period falls rapidly as individuals get richer. In contrast, each additional year of life delivers a positive and growing amount of utility. The result is an income effect that favors safety over growth. The growth rate of the economy eventually falls to zero, life expectancy rises to its maximum, and consumption may even settle down to a constant. In the exis- tential interpretation, the economy stops playing Russian roulette and, assuming it did not get unlucky before reaching the steady state, goes on forever. 3. Life and Growth in a Richer Setting The simple model in the previous section is elegant and delivers clean results for the interaction between safety and growth. However, the way in which faster growth raises mortality is mechanical, and it is simply assumed that the economy can pick whatever growth rate it desires. In this section, we address these concerns by adding safety considerations to a standard growthmodel based on the discovery of new ideas. The result deepens our understanding of the interactions between safety and growth. For example, in this richer model, concerns for safety can slow the rate of exponential growth from 4% to 1%, for example, but will never lead to a steady-state level of consumption. While supporting the basic spirit of the simple model, then, the richer model illustrates some important ways in which the simple model may be misleading. Themodel below canbe viewed as combining the “direction of technical change” LIFE AND GROWTH 11 work by Acemoglu (2002) with the health-spending model of Hall and Jones (2007). That is, we posit a sta