Extending the Harrod-Domar Model: Warranted Growth with Immigration, Natural Environmental Constraints, and Technological Change

Hendrik Vandenberg
University of Massachusetts
hvandenberg@umass.edu

Alfredo R. M. Rosete
Warren Wilson College
arosete@warren-wilson.edu

COPYRIGHT: American Review of Political Economy; the authors.

Introduction

Economists have differed sharply over how to deal with economic recessions and restore economic growth.  Following the 2007-2009 Great Recession, Post Keynesians advocated active expansionary fiscal policies supported by aggressive money creation by central bank in order to stimulate the growth of aggregate demand and thereby employment, while mainstream neoclassical economists advocated austerity policies to reduce government debt and spur private investment to achieve the same goals of higher employment and economic growth.  Despite these sharply different perspectives, virtually all economists are equally guilty of ignoring several very real barriers to economic growth that the traditional active or passive macroeconomic policies can overcome.  These barriers include the limited capacity of the natural environment to provide renewable natural resources, the obvious limits to exhaustible natural resources, the falling rate of population growth, and the political difficulties of compensating falling population growth through immigration.  Economists’ apparent ignorance of these barriers to growth reflect the disconnect between economists and the citizenry of most advanced countries, where global warming, environmental degradation, immigration, population aging, and birth control have become politically controversial issues.

Post Keynesians seem to be hampered by the predominantly demand-side bias of traditional Keynesian macroeconomic models.  Environmental constraints and population growth impact both aggregate demand and aggregate supply, so demand side policies, by themselves, cannot deal with unemployment because economic growth runs into supply-side barriers. Mainstream neoclassical economists, on the other hand, pay lip service to supply side issues, but their focus on “economic issues” results in their ignoring natural phenomena such as global warming and biodiversity, things to be treated as exogenous shocks rather than phenomena to be explained by economists.  Similarly, natural population growth is also almost always treated as an exogenous variable in mainstream macroeconomics, and the analysis of immigration has been left mostly to other fields such as sociology, anthropology, and political science.

This paper makes the case that, despite their continued emphasis on economic growth as the solution to macroeconomic problems such as unemployment, inequality, and poverty, Post Keynesians are actually better positioned than mainstream economists.  Specifically, we draw on the well-known Keynesian model developed by Roy Harrod (1939) and Evsey Domar, the  Harrod-Domar model, to bring immigration and environmental constraints directly into macroeconomic analysis.  This model was falsely discredited by mainstream economists back in the 1950s with the imposition of the one-sided Solow growth model in its place.  It is extraordinary that Keynesians did not defend the Harrod-Domar model, especially since its fall into obscurity meant Keynesian macroeconomics was left without a dynamic growth framework of analysis.  We argue here that it is high time to restore the Harrod-Domar model to the mainstream of macroeconomic analysis.

The organization of this paper is as follows: First, we introduce the Harrod-Domar model and highlight its important fundamental conclusions.  Then, we show how Harrod introduced population growth, and thus effectively immigration, into his model, as well as how the model incorporates environmental constraints.  We then discuss how the Harrod-Domar reveals practical paths forward for macroeconomic policymakers concerned with achieving full employment, including incentivating specific forms of technological change and managing employment creation in specific sectors.  We conclude with thoughts on future research.

The  Basic Harrod-Domar Model

Roy Harrod (1939) and Evsy Domar (1944) presented nearly identical dynamic models based on Keynes’ (1936) macroeconomic framework, which focused on determining an economy’s long-run growth path.  Their models are often jointly referred to as the Harrod-Domar model.  That two economists would independently produce the identical model was not surprising: their model is a logical extension of John Maynard Keynes’ (1936) macroeconomic model.  In analyzing how macroeconomic policy could restore full employment, Keynes had focused on investment as a major category of aggregate demand for the economy’s output, along with consumption demand and government demand.  Harrod and Domar noted, however, that in addition to contributing to aggregate demand for output today, investment also increased the economy’s potential output in the future.  Thus, dynamically over time investment has both demand side and supply side effects, and full employment can be maintained in the long run only if investment and the other sources of aggregate demand grow just fast enough to exactly absorb the increased output that the investment makes possible.  Harrod called this particular growth path the economy’s warranted growth, the path on which the economy’s circular flow remains in balance over time given its technological parameters and savings behavior.  If aggregate demand does not grow as fast as output capacity grows over time, unemployment will rise.

To make very clear the potential inconsistencies between investment’s effect on aggregate demand and its effect on the growth of the economy’s productive capacity, Harrod and Domar used an abbreviated version of Keynesian aggregate demand, namely that aggregate demand (YD) is split between two categories of commodities, consumption goods (C) and investment goods (I), or YD = C + I.  Also, they assumed a very simplistic process by which investment determined the economy’s output.  Specifically, the marginal product of capital is assumed to be constant; implicitly, capital does not suffer diminishing returns because unemployed labor is always available to accompany the increases in capital and keep factor inputs changing proportionately, and the capital-output ratio is a constant, or  K/YS =  γ.  A second assumption about capital is that there is no depreciation, which permits Harrod and Domar to represented investment with the change in the stock of capital, or I = ΔK, and aggregate supply, YS , can be written as YS = C + ΔK.  Finally, the Harrod-Domar model assumes that productive investment is always equal to saving, so

ΔK = I = S = σYS ,                                                      (1)

where σ is the saving rate.  Since the model assumes that each additional unit of capital increases output by a fixed proportion and every increase in saving directly increases investment, an increase in saving must increase the rate of growth in output.  These assumptions about the supply side of the economy can be combined to give us

YS = (1/γ)K.                                                                (2)

This linear relationship leads to the Harrod-Domar model’s conclusion that the rate of growth in output is exactly proportional to the economy’s rate of saving.  If we now put equations (1) and (2) together, it follows that

ΔYS = (σ/γ)YS                                                             (3)

Dividing both sides of equation (3) by Y, a temptingly simple formula for the rate of output growth of the economy emerges, which we denote as GYs:

GYs  = ΔYS/YS  = σ/γ                                                 (4)

That is, the rate of growth of output, given the assumed savings rate and capital output ratio, is the constant ratio σ/γ.  Note that an increase in the rate of saving increases the warranted rate of economic growth, as does decline in the capital output ratio.

In order to determine whether a given rate of investment is compatible with long-run demand for goods and services, the demand effects of investment must be brought into the model.  This is what Harrod and Domar did, but this aspect of Harod’s and Domar’s models was ignored in the field of economic development.  Consumption goods demanded are equal to actual income not saved, or C = (1 − σ)Y.  The other component of demand, I, is not so easily determined.  Textbook versions of the Keynesian macroeconomic model usually assume that investment is an inverse function of the interest rate, which measures the opportunity cost of investment.  If S = I, then all income not spent on consumption is instead spent on investment, and aggregate demand equals aggregate supply.  However, in his General Theory of Employment, Interest, and Money, Keynes (1936) viewed investment as a much more complex function, driven by a great many variables, including volatile expectations of the future.  Keynes argued that the decision to invest was not the result of a precise decision process that compared future returns to the opportunity cost of investment.  In reality, no one has enough information about the future to perform such a deterministic exercise: “Only a little more than an expedition to the South Pole, is it [investment] based on exact calculation of benefits to come.”[i]  Rather, Keynes suggested that investment was driven by “animal spirits,” by which he meant the complex combination of confidence, optimism, and unsubstantiated faith in the future growth of the economy.  So how do investors make their decisions?  Keynes surmised that as long as most investors’ expectations were approximately validated, investment would continue to occur despite the lack of any “exact calculations of benefits to come.”  If a large proportion of investments fail to meet expectations, however, confidence in the “benefits to come” erodes and investment collapses. Harrod and Domar thus hypothesized that investment demand is a function of recent growth in the demand for output:

ID = b(ΔYD)                                                                   (5)

The variable b defines the relationship between the change in total actual output demanded, YD., and new investment I.  Hence, aggregate demand, C + I, is:

YD = (1 − σ)YS + b(ΔYD)                                              (6)

Suppose now that the economy starts out on the warranted growth path so that YD = YS.  For the economy to remain on the warranted growth path, first of all, equality between desired investment and actual savings must be maintained:

b(ΔYD) = σYS                                                                 (7)

This implies that after shifting b and Y to the other side of the equal sign and setting YD = YS, it becomes clear that under full employment the growth of demand is equal to

ΔYD/YS = ΔYD/YD = σ/b                                                (8)

Hence, in a state of full employment demand growth is equal to supply growth, given as ΔYS/YS = σ/γ in equation (9), only if

ΔYD/YD = σ/b = ΔYS/YS = σ/γ                                       (9)

Thus, a continuous growth path at full employment requires that b = γ.

The problem for macroeconomic stability is that, first, γ is not as constant as is often assumed, and, second, the parameter b is dependent on the volatile state of investor confidence, on Keynes’ animal spirits.  Suppose, realistically, that after many years of consistent growth during which b remained equal to γ because things generally turned out as expected and there were no diminishing returns to capital, a financial crisis suddenly causes investment to fall, which means that actual investment is less than the amount of savings available to fund investment, or

ID = b(ΔYD) <  σYS                                                            (10)

Aggregate demand does not rise enough for it to absorb the increased output created by last period’s investment, and investors’ “animal spirits” are not validated.  A further decline in desired investment is likely in the next period of time, and the demand for output will fall even more.  A cumulative downward spiral in aggregate demand results, unemployment grows, and economic growth declines.  Alternatively, if a sudden surge in optimism causes the demand for capital to rise above savings, then aggregate demand will exceed the economy’s production capacity, and an investment boom results.

The Harrod-Domar model has been described as a knife’s edge model: once the economy falls out of its full employment equilibrium, the economy spirals out of control.  This suggests that when the economy falls off the knife’s edge, there is a need for active economic policies that can raise or reduce aggregate demand in order to keep the growth in demand and the growth in the economy’s supply side more or less in line.[ii]

Examples of the Harrod-Domar Model’s Dynamics

Harrod specifically defined three different dynamic growth paths: the actual growth of output, which we designate as GY, the warranted growth rate, GW, and the natural growth rate, GN.  The warranted growth rate determines the growth path on which aggregate demand equals aggregate supply, or where the circular flow of the economy is in balance.  This path does not necessarily coincide with full employment of the labor force; it merely defines the economy’s sustainable level of output given the technical relationship between capital and output (the capital-output ratio), consumers’ propensity to save, and investors’ willingness to invest in new capital.  The Harrod-Domar model thus describes a dynamic path that, like Keynes static analysis, shows the economy can settle into an equilibrium that is characterized by permanently high unemployment.

Figure 1

The Harrod-Domar model also derived a conclusion that differs from the static Keynesian model: instead of a stable unemployment equilibrium, in the dynamic Harrod-Domar model the economy’s equilibrium is unstable.  Under the assumption that the capital-output ratio is a fixed technological constant, the interaction between the actual and warranted rates of growth leads to the well-known “knife’s edge” phenomenon.  When the capital output ratio is greater than one, which evidence suggests is normally the case, then any demand shock leads to a greater increase in demand relative to output, and the economy is pushed off its warranted growth path to either spiral upwards into an inflationary boom or downwards into a deep depression.  The Harrod-Domar model thus suggested that the economy is inherently unstable, prone to long booms and busts.

Figure 2

The natural growth rate plays a secondary, but, as we argue, a serious long-run role in an economy’s long-run growth.  Simply put, Harrod’s natural growth rate represents an upper limit to the economy’s rate of growth, the “maximum rate of growth allowed by the increase in population, accumulation of capital, technological improvement, and the work/leisure preference schedule, supposing that there is full employment in some sense.”[iii]  This upper bound on the growth of the economy’s capacity to produce goods and services interacts with the warranted and actual growth paths in complex ways.

Figure 3

The natural growth path does not restrict output if the warranted and actual growth paths lie at or below the natural growth path.  In Figure 3, the three growth paths coincide, and so long as the economy is not bumped off the knife’s edge, growth continues along the natural growth path.

The economy can also continue growing on the knife’s edge along the warranted path if that path falls below the natural growth path, as in Figure 4.  In this case, there is continual excess capacity, as the savings and investment rates, conditioned by the technical fixed capital-output ratio, keep the economy on an unemployment growth path.  This is the dynamic version of Keynes’ static unemployment equilibrium.  Of course, there is no problem with constraints on growth due to a shortage of labor or a shortage of natural resources.

Figure 4

Then there is the possibility that some shock in output or some unexpected change in the capital output ratio pushes the economy off the knife’s edge.  For example, Figure 5 shows that the situation can worsen from that of Figure 4 if there is a sudden excess supply in the economy: the recline in aggregate demand causes a downward spiral in output that pushes unemployment even farther from full employment.

Figure 5

On the other hand, a sudden decrease in the capital output ratio of new investment, perhaps because of a poor investment or faulty business plan, or a sudden increase in aggregate demand, perhaps due to a sudden shift in optimism about future income or profitability, could push the actual rate of growth above the long run warranted growth path.  This triggers a boom spiral upward from the warranted growth path.  Of course, the booming economy will sooner or later bump into the natural growth path that constrains real economic activity, as shown in Figure 6.  Unemployment is eliminated, but at the cost of accelerating inflation in this case because the real level of output cannot exceed the natural growth path.

Figure 6

Just as in the static Keynesian model, active macroeconomic policy is called for to deal with unemployment or inflation.  In Figure 3, active monetary cum fiscal policy is called for in order to counter any deviations from the warranted growth path, and in Figure 4 active policy is needed to put the actual growth path on the natural growth path of full employment.  Such policies could target the savings rate, the investment rate or aggregate demand.  In Figure 5, the downward spiral must be reversed.  In Figure 6, the initial boom spiral may be welcomed, but as the economy approaches the natural growth path, active macroeconomic policy must be exercised to prevent an inflationary boom when the actual growth path reaches the natural growth path.

Figure 7

Finally, in the case where GW > GN  the constraints on growth will, sooner or later, prevent the economy from reaching the warranted growth path.  As shown in Figure 7, when the warranted growth path exceeds the natural growth path, policymakers are constrained from keeping the economy on its knife’s edge.  This implies the economy will persistently invests less than the savings rate underlying the warranted growth path requires, and the economy is continually tending toward depression.  It is not clear what the correct macroeconomic policy is in this case, because any attempt to push the economy toward the warranted growth path bumps into the natural growth path and triggers potentially accelerating inflation rather than faster real growth.  Interestingly, this scenario reminds us of the 1970s, when attempts to restore steady economic growth led to stop-go macroeconomic policies that reacted to the seemingly simultaneous increases in unemployment and inflation.

In short, the Harrod-Domar model suggests that macroeconomic policy must consider supply side variables such as environmental constraints, labor shortages, and technological progress.  Macroeconomic policies must, therefore, include incentives for innovation and direct regulations to shift technological change, a much more difficult task than even the macroeconomic policies economists have focused on for decades.  Note that Harrod and Domar show that the Keynesian framework can indeed deal with the supply side of the economy as well as the demand side, and, therefore, supply siders’ claims that the Keynesian model lacked a supply side were inaccurate.  In fact, the Harrod-Domar dynamic Keynesian framework seems to explain the 1970s quite well, contrary to mainstream economics’ common argument that Keynesian analysis became irrelevant in the 1970s.  Equally important, the Harrod-Domar model anticipated the limits to growth that we are facing today.

A Neoclassical Version of the Harrod-Domar Model

Sato’s (1964) specification of the Harrod-Domar framework includes a neoclassical production function in place of Harrod’s fixed proportions production function.  This specification addresses the mainstream criticism of the Harrod-Domar model, namely that its assumption of fixed factor proportions pre-determines the “knife’s edge” conclusion that the macroeconomy is dynamically unstable.[iv]  Under the neo- classical assumption of variable proportions, the economy is saved from the instability that characterized the model under the fixed proportions assumption of the Harrod-Domar model.  However, when Sato assumes realistic year-to-year levels of depreciation, private saving and investment relative to total capital stocks, public finance and public investment, shifts in the labor market, and technological change, he finds that it would take the economy a very long time, more or less one hundred years, to reach a full-employment natural growth path.  Sato (1964, p. 387) concludes: “The adjustment process in the dynamic model is so slow that fixed proportions may be a realistic assumption for practical purposes.”  Hence, Keynes’ famous statement that “in the long run we are all dead” remains a useful insight.

It is nevertheless informative to look at the long-run outcomes of the Harrod-Domar model with a neoclassical production function because it still highlights the interplay between the warranted and natural growth rates.  Sato presents three different qualitative outcomes, depending on the relationship between the warranted and natural growth paths.  For example, in the case where the warranted growth path coincides with the natural growth path, the long-run outcome is a stable growth path on which the warranted, natural, and actual growth rates become equal.  The logic of the continuously variable neoclassical production function that Sato (1964) introduces into the Harrod-Domar model permits us to conclude that, in this case where the warranted, actual, and natural growth rates coincide, the economy is characterized by full employment. Figure 3 again applies in this case.

If the actual growth path lies above the warranted growth path, but below the natural growth path, then the social, biological, and natural barriers to growth are not challenged.  In the not-so-short run, there would presumably be reserves of unemployed workers and other factors.  The short-run dynamic would ensure that the economy would, more often than not, expand its investment and output, and the economy would move persistently towards its natural growth path.  This is the fortunate case that laissez-faire proponents point to as justifying a passive policy response to unemployment.  Figure 6 has already illustrated this case above.

On the other hand, if the natural growth rate lies below the warranted rate, then long-run adjustment towards full employment will be more difficult: This is potentially an inflationary outcome, although the fact that actual growth is below the warranted growth rate implies that, in the short and medium term, the economy is likely to suffer from insufficient demand and, hence, a deflationary spiral in the direction of the natural growth path.  One could easily see the economy teetering between inflation and deflation, increasing employment and decreasing employment, and the severe confusion in policy determination similar to the 1970s.  In this case, traditional Keynesian measures to raise actual growth of output do not work.  Instead, measures must be taken to raise the natural growth path, perhaps by stimulating technological change, increasing labor force growth, or pursuing new sources of natural resources.  Of course, we have also witnessed common policy responses such as ignoring the long-run consequences of exploiting and depleting nature’s ecosystem, expanding the workweek and inducing people to work more than one job, and engaging in modern forms of imperialism to steal resources abroad.  Figure 8 illustrates such a shift in the natural growth path from GN to GN2.  After such a supply-side intervention actually raises the natural growth path above the warranted and actual growth paths, there will again be an underutilization of available resources and technologies.  In the spirit of the Harrod-Domar model, this case points to the need for a sophisticated and potentially very complex combination of demand-side and supply-side policies to maximize an economy’s sustainable growth.

Figure 8

Immigration

Our results suggest that, in the case where GN  < GW ,  a policy shift that raises the rate of immigration can help an economy stabilize and grow faster.  This can be seen in Figure 8, for example, where the economy’s natural growth path is raised from GN to GN2.  There is empirical research that confirms a positive relationship between immigration and economic growth.   For example, Coates and Gindling (2012) find that during the 1990s, U.S. rural counties whose populations were in decline grew faster when they received an influx of Hispanic migrants.  And, Boubtane et al. (2016), looking at data from 22 OECD countries spanning the years 1986-2006, conclude that, statistically, human capital from immigrants has a positive effect on GDP per-capita and GDP per worker.  But, these studies do not specify the exact causes of such a relationship.

On the other hand, an increase in the quantity of immigrant labor means there will tend to be less capital per unit of labor, and this may cause economic growth to slow down (Card, 2012). Indeed, Dolado et al. (1994) found that immigration had a negative impact on growth, although they also noted that this impact was half of what it would be for a comparable natural increase in the native population because immigrants added to the economy’s stock of human capital. Furthermore, the negative effect is temporary because, as Mendez et al. (2016), Duleep and Regets (1996), and Green and Worswick (2012) also find, immigrants quickly add to their human capital after they arrive in their destination.  Cipolla (1978) describes the Swiss clock and watch industry, in which immigration greatly affected technological development and subsequent economic growth.  Many early clock makers were French, but a large percentage of the early French clock makers, who were highly literate and often interested in various aspects of science, were also active in the Reformation movement.  When France expelled the Huguenots, as the French Protestants were called, a number of French clock makers went to Geneva, Switzerland.  According to Cipolla (p. 64), “to destroy or to build up the [clock] industry it was enough to dismiss or attract a few dozen craftsmen…..  The future Swiss watch industry was founded by “the inflow of a handful of refugees–to the injection of a small but precious amount of human skills.”

It is worth noting that the standard conclusion that immigrants lower the marginal productivity of labor in the destination country (Borjas, 2003) was based on models that assumed constant levels of capital and technology.  Because an increase in the labor supply increases marginal productivity of capital, more capital will be accumulated. Immigration may, therefore, push the economy above the warranted growth path if it comprises a separate stimulus to investment.  Also, in line with the Harrod-Domar model’s fundamental recognition of an economy’s circular flow from supply to demand, Bodvarsson and Van den Berg (2006) and Bodvarsson, Lewer, and Van den Berg (2008) show that immigrants both supply labor and add to aggregate demand when they spend their earnings.  Re-estimating the 1980 Mariel Boat lift that brought over 100,000 Cuban immigrants to Miami over a period of a few months, Bodvarsson et al. (2008) use Card’s (1990) data to conclude that this labor demand effect offsets possible negative effects of immigration, and, in some case, even raises wages.  This demand effect is further supported by the work of Saiz (2007), and Chatterjee et al. (2011), who, respectively, find that immigration generates greater demand for housing, and immigrant home-buyers tend to have more equity in their housing purchases. It still may require policy intervention to keep the economy on the warranted growth path, however, because immigration’s impact on the marginal productivity of capital and the level of investment may not be perfectly balanced by immigrants’ impact on the demand for output.

Rosenberg (1994) linked immigration to a positive economies of scale effect.  He argues that the rapid economic growth of the United States in the 1800s was made possible by “rapid growth in demand and circumstances conducive to a high degree of product standardization…. Probably the most pervasive force of all was the extremely rapid rate of population growth…with immigration assuming a role of some significance in the 1840s.”[v]

Immigration also impacts technological change, which determines the position of the Harrod-Domar model’s natural growth path.  There is an ample literature on the relationship between immigration and technological change.  Schumpeter (1934) emphasized the role of immigrants in entrepreneurial activity.  Chiswick (2000) found that the self-selection of immigrants in terms of personal characteristics favorable to economic growth “the greater the out of pocket (direct) costs of migration and return migration, the greater the effect of ability on lowering the costs of migration, and the smaller are the wage differences by skill in the lower income origin than in the higher income destination.”[vi]  The fact that international migration is difficult and risky implies that immigrants are likely to be less risk averse and more adventuresome than the average person in their countries of origin.

Immigration is not a solution for global economic growth, however.  If countries receiving immigrants grow more rapidly, then source countries of immigration are likely to suffer a decline in economic growth.[vii]  Some researchers have suggested that growth declines can be avoided if emigrants eventually return to their homelands or their earnings remittances enable greater levels of investment than otherwise would occur in source countries.  The evidence on the growth effects of immigrant remittances is not very clear, however. Most studies of the use of remittances find that remittances are used for consumption, not investment.  But, remittance studies do not capture the multiplier effects.  Taylor’s (1999) summary of village studies in Kenya, West Java, Senegal, and Mexico concludes that multiplier effects are often small in local communities, with the countries’ urban areas receiving the greatest secondary boosts.  A comparison of Mexican families that receive remittances and those families that do not receive remittances by Germán Zárate-Hoyos (2001) shows that, all other things equal, “households receiving remittances devote a higher proportion of current expenditures to investment and savings than those households that do not receive remittances.”

A slowdown in economic growth in the source country can also be avoided if immigration opens channels for technology transfers from countries that are technological leaders, but immigration’s impact on technology transfers from developed to developing countries is theoretically ambiguous.  The conventional wisdom that talented, entrepreneurial, and educated people are needed to adapt and apply foreign technologies is strongly supported by the evidence, which means that a country’s capacity to absorb foreign technology will diminish if talented and entrepreneurial people immigrate elsewhere.  It is equally well known, however, that immigration can actually enhance international technology flows.  As Dustmann and  Kirchkamp (2002) and  Mesnard and Ravallion (2002) show, immigrants often maintain ties with their native countries, and these ties can serve to create channels through which technology can be transferred.  Agrawal, Cockburn, and McHale (2003) find that social capital, the subtle relationships among people that have been shown to facilitate the sharing of knowledge and technology, endures even after immigration separates people.  Specifically, their rigorous analysis of patent citations shows that former colleagues and associates that were separated by immigration continue to influence each others’ research disproportionately.  This effect is especially important for countries such as India, China, Taiwan, and others that have many university graduates living overseas.  Lundborg and Segerstrom (2002) found evidence suggesting that immigrants influenced home-country technological progress.  Also, the possibility of emigrating to a high income country raises the return to education in the source country, which increases the overall demand for education. [viii]

In terms of the Harrod-Domar model, it becomes possible to build immigration into a macroeconomic framework that looks at how immigration impacts the natural growth rate of the economy, as well as how immigrants affect the economy’s aggregate demand.  When the warranted rate of growth is lower than the natural growth rate, raising immigration will tend to generate unemployment unless the rate of investment is also increased.  On the other hand, when current levels of saving/investment keep the warranted growth rate above the natural growth rate, the economy will be recession-prone unless immigration can be increased in order to raise the natural growth path up to the warranted growth path.

These insights on immigration are in line with recent research on the relationship between immigration and growth.  A common channel under which increased immigration can absorb investment is through the entry of skilled immigrants, who bring human capital into the economy.  However, even in the case where new immigrants have not acquired human capital, there is evidence to suggest that, eventually, their propensity to acquire human capital in the host country, and thus, contribute to growth.  This suggests that immigration policy should be lenient enough, unlike the contemporary discussions around “merit-based systems”.  In a situation where the natural growth rate is below the warranted growth rate, simulations by Sato (1964) suggest that convergence to the warranted growth rate can take a century or so. However empirical results suggest that acquisition of human capital on average takes about ten years. Thus, even family-based entry can help get the economy back on track.  Immigration policy, then, cannot be too restrictive if the objective is to stimulate economic growth.

Looking at both source and destination countries, immigration can also generate an increase in international inequality, as the high-income destination countries grow faster and become economically more stable, while the source countries fall into more frequent recessions and slower growth paths.  Immigration thus triggers yet another mechanism through which the Marxian center-periphery dependency relationship impedes poor country development.

Environmental Barriers to Growth

Also impacting the natural growth path of an economy is the finite capacity of the earth’s ecosystem to provide the vital services that humans depend on for survival.  The World Wildlife Fund (2014) estimates that humanity’s demand on the planet’s living resources now exceeds the planet’s regenerative capacity by 30 percent.  Liu et al. (2007, p. 1513) explain that the relationships between the economic and natural spheres are complex:

… couplings between human and natural systems vary across space, time, and organizational units.  They also exhibit nonlinear dynamics with thresholds, reciprocal feedback loops, time lags, resilience, heterogeneity, and surprises.  Furthermore, past couplings have legacy effects on present conditions and future possibilities.

The anthropogenic (human-made) natural phenomena of global warming, diminishing ecosystem services, and accelerated species losses that constitute our future barriers to economic growth.

The natural barriers to growth can be alleviated by increasing the rate of technological change, as Solow (1956) famously pointed out with his now-standard growth model.  However, in reality, many types of technological advances are continuously required to raise the ecosystem’s finite capacity to provide the exhaustible resources and renewable natural services that humanity depends on for its survival.  Technological progress was often nothing more than the development of new methods to more quickly use up the earth’s natural resources.  Dirty air, polluted rivers, exhausted soils, eroded farmland, deforested river basins, the surge in extinctions of animal species, and global warming are just a few of the many signs suggesting that the human population and its per capita production have expanded beyond the levels that the natural environment can sustain.  The economic growth made possible by technological change has also increased the rate of population growth as people live longer and produce more over the course of their lifetimes.  In short, the more intensively we use renewable resources, the more explicit and costly actions we must take to conserve the natural sphere and help nature replenish the resources we depend on for our social and economic existence.

The Harrod-Domar framework suggests that macroeconomic policymakers must consider the natural growth path of the economy when they formulate policy responses to economic conditions.  In the case of environmental constraints, Figures 4 and 6 illustrate cases in which macroeconomic policies to maintain full employment without inflation might include measures to change the economy’s rate of technological change in order to raise the natural growth path of the economy.  When the warranted growth path lies above the natural growth path, the short-term knife’s edge will more often put the economy on a downward actual growth path and instability is more prevalent over time.

Some economists, businesspeople, and policymakers argue that economic growth’s pressure on the earth’s resources will directly stimulate the technological changes necessary to mitigate the stresses.  However, experience clearly shows that existing markets in the economic sphere have not led to the development and application of all the new technologies and lifestyle changes necessary to avoid climate change and biodiversity losses.  Today, there simply are no markets whose prices accurately reflect true resource scarcities.

Conclusions and Implications

We have demonstrated that the Harrod-Domar model satisfies two criticisms directed at the Keynesian macroeconomic model by putting Keynes’ ideas into a dynamic framework with a clear supply side component.  Where the warranted growth rate represents an economy’s growth path on which aggregate demand and supply remain in balance, the  model’s natural growth rate reflects the supply of productive resources and the level of technology, the long-run limit to real output growth.  The interaction between the warranted and natural growth rates provides a useful perspective for policymaking in today’s environmentally-constrained global economy.  Also, since the growth of the labor force is built into the natural growth path, the model also helps to clarify policy choices in an economy impacted by immigration.

The point that stands out from using the Harrod-Domar model to frame economic policy is that supply-side policies must be developed along with the standard Keynesian demand side policies, and the interactions between the two require disaggregated policies to address specific types of investment, technological change, and demand.  That is, it is not generally possible to solve the unemployment problem by simply expanding aggregate demand.  Instead, macroeconomic policy calls for a complex combination of policies to invest in different forms of real and human capital, programs to develop and apply new technologies, as well as taxes and subsidies to keep fine tune aggregate demand to keep the economy on the short-run knife’s edge. Blunt policy tools will tend to leave the economy violating the very real environmental constraints on long-run growth, generating opposition to immigration, disadvantaging entire segments of the labor market, and increasing income inequalities.  Perhaps it is time to bring the Harrod-Domar model back into mainstream policy analysis.

References

Ajay Agrawal, Iain Cackburn, and John McHale (2003), “Gone But Not Forgotten: Labor Flows, Knowledge  Spillovers, and Enduring Social Capital,” NBER Working Paper No. w9950.

Baumol, William J., Sue Anne Batey Blackman, and Edward N. Wolff (1989), Productivity and American Leadership: The Long View, Cambridge, MA: MIT Press.

Beine, M., F. Docquier, and F. Rapoport (2003), “Brain Drain and Growth in LDCs: Winners and Losers,” IZA Discussion Paper, IZA, Bonn, Germany.

Bodvarsson, Orn, and Van Den Berg, Hendrik (2006), “Does Immigration Affect Labor Demand? Model and Test,” in S. Polachek, C. Chiswick, and H. Rapoport (eds.), Research in Labor Economics (Vol. 24), New York: Elsevier.

Bodvarsson, Orn, Joshua Lewer, and Hendrik Van den Berg (2008), “Measuring Immigration’s Effects on Labor Demand: A Reexamination of the Mariel Boatlift,” Labour Economics 15(4):560-574.

Borjas, George (1995), “The Economic Benefits from Immigration,” Journal of Economic Perspectives 9(1):3-22.

Boubtane, E., Dumont, J. C., & Rault, C. (2016). Immigration and economic growth in the OECD countries 1986–2006. Oxford Economic Papers, 68(2), 340-360.

Card, David (1990), “The Impact of the Mariel Boatlife on the Miami Labor Market,” Industrial & Labor Relations Review 81:292-296.

Card, D. (2012). Comment: The elusive search for negative wage impacts of immigration. Journal of the European Economic Association, 10(1), 211-215.

Chatterjee, S., & Zahirovic-Herbert, V. (2011). Homeownership and Housing Equity: An Examination of Native-Immigrant Differences in Housing Wealth. International Advances in Economic Research, 17(2), 211-223.

Cipolla, Carlo M. (1978), Clocks and Culture, 1300-1700, New York, NY: W.W. Norton.

Coates, D., & Gindling, T. H. (2013). Is Hispanic Population Dispersion into Rural Counties Contributing to Local Economic Growth? Contemporary Economic Policy, 31(4), 649-668.

Costanza, Robert, et al. (1997), “The Value of the World=s Ecosystem Services and Natural Capital,” Nature 387:253–260.

Daly, Herman (1998), ”Uneconomic Growth,” Clemens Lecture 11, Saint John’s University, October 25.

Daly, Herman (2014), From Uneconomic Growth to a Steady-State Economy, Northampton, MA: Edward Elgar.

Diamond, Jared (2005), Collapse: How Societies Choose to Fail or Succeed, New York: Penguin Books.

Dolado et al.  (1994)

Domar, Evsey (1946), “Capital Expansion, Rate of Growth, and Employment,” Econometrica 14:137–147.

Duleep, H. and Regets, M. (1997), “Are Lower Immigrant Earnings at Entry Associated with Faster Growth? A Review,” Washington, DC: The Urban Institute.

Dustmann, C., and O. Kirchkamp (2002), “The Optimal Migration Duration and Activity Choice after Remigration,” Journal of Development Economics, Vol. 67(2), pp. 351-372;

Easterly, William (1999), “The Ghost of Financing Gap: How the Harrod-Domar Model Still Haunts Development Economics,” Journal of Development Economics 60(2): 423–438.

Easterly, William, and Ross Levine (2001), “It’s Not Factor Accumulation: Stylized Facts and Growth Models,” The World Bank Economic Review 15(2):177–219.

Ehrlich, Paul (1968), The Population Bomb, New York: Ballantine Books.

Ehrlich, Paul (1972), in Sue Titus Reid and David L. Lyon (eds.), Population Crisis — An Interdisciplinary Perspective, Glenview, Illinois: Foresman.

Green, D. A., & Worswick, C. (2012). “Immigrant earnings profiles in the presence of human capital investment: Measuring cohort and macro effects”. Labour Economics, 19(2), 241-259.

Hahn, Frank (1960), “The Stability of Growth Equilibrium,” Quarterly Journal of Economics 74.

Haque, N.U., and S.-J. Kim (1995), “Human Capital flight: Impact of Migration on Income and Growth, IMF Staff Papers, Vol. 42(3), pp. 577-607.

Harrod, Roy F. (1939), “An Essay in Dynamic Theory,” The Economic Journal 49:14–33.

Hill, Peter J. (1971), “The Economic Impact of Immigration into the United States,” Journal of Economic History, Vol. 31(1), pp. 260-263

Intergovernmental Panel on Climate Change (2007), IPCC Report on Global Warming, Geneva: United Nations.

Intergovernmental Panel on Climate Change (2014), Climate Change 2014: Synthesis Report, Geneva: United Nations.

Kempf, Hervé (2007), How the Rich Are Destroying the Earth, White River Junction, VT: Chelsea Green Publishing Co., p. xiii.

Krautkraemer, Jeffrey (1998), “Nonrenewable Resource Scarcity,” Journal of Economic Literature 36(4):2065–2107

Keynes, John Maynard (1936), The General Theory of Employment, Interest, and Money, New York: MacMillan.

Liu, Jiangguo et al. (2007), “Complexity of Coupled Human and Natural Systems,” Science 317(September):1513–1516.

Lobell, David, Woldram Schlenker, and Justin Costa-Roberts (2011), “Climate Trends and Global Crop Production Since 1980,” Science, online May 5, 2011.

Lundberg, Per, and Paul S. Segerstrom (2002), “The Growth and Welfare Effects of International Mass Migration,” Journal of International Economics, Vol. 56, pp. 177-204.

Manacorda, M., Manning, A., & Wadsworth, J. (2012). The impact of immigration on the structure of wages: theory and evidence from Britain. Journal of the European Economic Association, 10(1), 120-151.

Marx, Karl (1959[1894]), Capital, Vol. III, New York: International Publishers.

Méndez, F., Sepúlveda, F., & Valdés, N. (2016). Legalization and human capital accumulation. Journal of Population Economics, 29(3), 721-756.

Millennium Ecosystem Assessment (2005), “Living Beyond our Means: Natural Assets and Human Well-Being,” Statement from the Board, Washington DC: World Resources Institute.

Miyagiwa, K. (1991), “Scale Economies in Education and the Brain Drain Problem, International Economic Review, Vol. 32(3), pp. 743-759.

Mokyr, Joel (1990), The Lever of Riches, New York: Oxford University Press.

Mountford, A. (1997), “Can a Brain Drain Be Good for Growth in the Source Economy?”, Journal of Development Economics, Vol. 58(2), pp. 287-303;

Ottaviano, G. and Peri, G. (2005), “Rethinking the Gains from Immigration: Theory and Evidence from the U.S.,” NBER Working Paper 11672.

Ottaviano, G. I., & Peri, G. (2012). Rethinking the effect of immigration on wages. Journal of the European economic association, 10(1), 152-197.

Rosenberg, Nathan (1994), Exploring the Black Box, Technology, Economics, and History, Cambridge, U.K.: Cambridge University Press,

Saiz, A. (2007), “Immigration and Housing Rents in American Cities,” Journal of Urban Economics 61:345-371.

Sato, Ryuzo (1964), “The Harrod-Domar Model vs the Neoclassical Growth Model,” The Economic Journal 74(294):380-387.

Schumpeter, Joseph (1934), The Theory of Economic Development, Cambridge, Massachusetts: Harvard University Press.

Solow, Robert (1956), “A Contribution to the Theory of Economic Growth,” Quarterly Journal of Economics 70(1):65–94.

Stark, O., C. Helmenstein, and A. Prskawetz (1998), “Human capital Depletion, Human Capital Formation, and Migration: A Blessing or a ‘Curse’?” Economics Letters, Vol. 60(3), pp. 363-367

Stern, Nicholas (2007), The Economics of Climate Change, Cambridge, U.K.: Cambridge University Press.

Swan, T. W. (1956), “Economic Growth and Capital Accumulation,” Economic Record 32(63):334-361.

Tainter, Joseph (2000), “Problem Solving: Complexity, History, and Sustainability,” Population and Environment 22(1):3-41.

Taylor, John.E. (1999), “The New Economics of Labor Migration and the Role of Remittances in the Migration Process,” Migration and Development, Vol. 37(1).

United Nations Population Fund (2010), The State of World Population 2010, New York: UNFPA; available at www.unfpa.org.

United Nations Population Fund (2010), The State of World Population 2010, New York: UNFPA; available at www.unfpa.org.

Veblen, Thorstein (1899), The Theory of the Leisure Class, New York: Modern Library.

Vidal, J-P (1998), “The Effect of Emigration on Human capital Formation,” Journal of Population Economics, Vol. 11(4), pp. 589-600

Wackernagel, Mathis, et al. (2002), “Tracking the Ecological Overshoot of the Human Economy,” Proceedings of the National Academy of Sciences 99:9266–9271.

Wilson, Edward O. (2002), The Future of Life, New York: Alfred A Knopf, Inc.

World Wildlife Fund (2014), Living Planet Report 2014, Gland, Switzerland: World Wildlife Fund for Nature.

Wong, K-Y, and C.K. Yip (1999), Education, Economic Growth, and the Brain Drain, Journal of Economic Dynamics and Control, Vol. 23(5-6), pp. 699-726.

Zárate-Hoyos, Germán  (2001), “The Case for a Remittance Policy in Mexico,” paper presented at the Pacific Coast Council on Latin Americn Studies Conference, April 5-7, 2001, Tijuana, Baja California, Mexico.

Endnotes

[i] John Maynard Keynes (1936), p. 162.

[ii] The recognition that in the short run a fall in investment generates a larger decrease in demand than it does in supply had been described earlier by J.M. Clark in the U.S. and Albert Aftalon in France, and in the literature on business cycles it was known as the acceleration principle.

[iii] Harrod (1939), p. 273.

[iv] The fixed factor proportions assumption was addressed by many papers in the 1950s and 1960s; see, for example, Solow (1956), Swan (1956), and Hahn (1960).

[v] Nathan Rosenberg (1994), p. 113.

[vi] Barry R. Chiswick (2000), “Are Immigrants favorably Self-Selected? An economic Analysis,” IZA Discussion Paper No. 131, March, 2000.

[vii] Miyagiwa (1991), Haque and Kim (1995), and Wong and Yip (1999).

[viii] See, for example, Mountford (1997), Stark, Helmenstein, and Prskawetz (1998), Vidal (1998), and Beine, Docquier, and Rapoport (2003).