Public debt and dynamic inefficiency

_ Hans-Werner Sinn, Dr. Sc., president, ifo Institute for Economic Research (1999-2016), member, advisory council, Federal Ministry for Economic Affairs and Energy (Germany); professor emeritus, Ludwig-Maximilian-University. Translation into English by Yuri Kofner. Munich, 3 September 2020.

The book by Carl Christian von Weizsäcker and Hagen Krämer (2019) deals with fundamental theoretical questions about the functioning of the capitalist market economy. The authors believe that the market economy suffers from an over-accumulation of capital because the marginal productivity of capital is permanently below the growth rate of this economy, and is even negative, and therefore needs a bloodletting in the form of a consumption surge, which can be brought about by the national debt. Society can increase its consumption not just once but permanently by consuming the superfluous part of the capital stock.

The Munchausen Effect

The possibility of a later increase in consumption through today’s consumption sounds absurd at first, but it is not. Every forest manager knows that. As much new wood grows back in the jungle as it dies, without humans getting anything from it. Keeping a jungle is economically inefficient. If you clear the forest, you can not only harvest wood once in the form of an initial felling, but you can then cut a certain amount of wood every year without further reducing the stock. In the case of a certain tree population, the current annual logging that is possible without a further decrease in the tree is maximum. There, the marginal productivity of the tree population with regard to annual logging is zero, while it becomes negative when the forest is overgrown.

What the wood stock is in forestry is the capital stock in the economy as a whole. It makes no sense to save so much capital that the marginal productivity of capital, r, becomes negative, because if you do that you can eat up part of the capital and then consume more in the long term. In other words: Firstly, you can omit replacement investments to compensate for the depreciation and prefer to produce consumer goods with the production factors saved in the process and, secondly, you can also produce more consumer goods afterwards for all eternity. A situation in which this is the case is what I call statically inefficient.

Almost more important than static inefficiency is dynamic inefficiency, the conditions of which Phelps (1961) and von Weizsäcker (1962) analyzed 60 years ago. Dynamic inefficiency occurs when r is permanently smaller than g, where g is a fixed, long-term possible growth rate of the national product and the capital stock, as it results from the population increase and from technical progress. The authors show that under this condition it is possible to increase the consumption of an economy by consuming the surplus capital stock not only initially, but permanently above the level that would otherwise have been reached. This Munchausen trick works even better in the growing economy than in the stationary one, because it is possible even with a positive marginal productivity of capital.

Only when so much capital is destroyed through consumption that marginal productivity exceeds the growth rate does the modified Münchhausen trick fail. Then the economy is dynamically efficient because any increase in consumption today implies a decrease in consumption in the future.

If the conditions exist for dynamically inefficient growth, then one can permanently increase economic consumption by increasing the national debt, because this can create a kind of chain letter between the generations. The only difference is that instead of asking for payment from the early players, government bonds are sold to the later players. Each generation of retirees sells securities through the state to the next generation of workers and receives money from them for their own consumption in old age. If every generation of retirees sells more paper than they bought themselves in their working life and than they would earn at market interest rates if they invested the money in the capital market, they make a profit. With this strategy, the stock of outstanding national debt grows at a rate that is above the interest rate, let’s say gS, with gS> r where r measures the market interest rate. The strategy can only work in the long term if gS ≤ g, because otherwise the young generation would eventually need more than the national product to acquire the newly issued government bonds. Overall, it is therefore necessary that g ≥ gS> r. If we equate the interest rate with the marginal productivity of capital, which is possible with some restrictions in the market economy, this is a method of using the Munchausen trick. The first generation of retirees to issue new government bonds has a particularly large profit in terms of size, but everyone else benefits too.

Piketty or von Weizsäcker?

As correct as the argument as such is, the crucial question is whether the economy without national debt is actually dynamically inefficient in the sense of r g in order to be able to show that, because of the reinvestment of interest income, the capital stock and thus the profit income is growing faster than the national income, so that the distribution is becoming more and more unequal.

The left love Piketty’s book because it gives them a rationale for growing wealth inequality. The left also love the theory of Carl-Christian von Weizsäcker because it gives them a reason for more government debt and more government spending. Unfortunately, they have to decide who they ultimately want to believe, because only one person can be right. Piketty is certainly not right, because even if you follow him and assume that r> g, his evidence is incorrect. The growth of profits and the capital stock is namely not r, but only s · r, where s is the profit-related savings rate of capitalists, and in the steady state it holds that 3 that s · r = g. In spite of r> g, profits do not grow faster than national product, and because that is the case, the distribution does not become more unequal, at least not because of the mechanism that Piketty claims. I don’t want to go into that further here, but refer to Sinn (2017b). Of course, it does not follow from this that Carl Christian von Weizsäcker and Hagen Krämer are right in their assumption that economic development is dynamic and statically inefficient, i.e. that r g, and not the other way around.

Now one can counter that the profit quota cannot be used because the profits are also explained by risk premiums. In truth, these are no investment income at all, because another production factor is working in the background, namely the willingness to take risks. If you subtract the risk premium from the profit ratio, the profit ratio adjusted in this way is perhaps smaller than the investment ratio.

Whether the counter-argument works depends on whether the risk is proportional to the capital or can be manipulated separately. If it is proportional, for example because the willingness to take risks is linked to the existence of equity capital, the trick of deducting the risk premiums in order to mathematically press r below g cannot be used. Then the relevant r for the welfare consideration is the marginal productivity of capital including the risk associated with the use of capital. Admittedly, this is only one of the possibilities (Sinn, 1986).

The Niehans-Homburg argument

More important seems to me to be an argument that Jürg Niehans (1967) made. According to this, the present value of the rent of land, which tends to increase with general economic growth, would be infinitely large if the interest and thus the marginal productivity r of capital were permanently lower than the growth rate g. And since the present value of the land rent in the market economy corresponds to the land price, this price would then also be infinite. Homburg (1992) later incorporated this argument into an explicit growth model with a Cobb-Douglas production function, in which the soil is a factor of production and, under competitive conditions, absorbs a rent equal to a fixed share of the national product.

The Niehans-Homburg argument is important insofar as it excludes permanently inefficient economic growth, because with the constellation r g, which is also possible if r αB, so that the shot backfires. So the yields of land would be discounted at a rate less than r, and the explosion in land prices would start even earlier, limiting capital accumulation by way of a consumption surge. According to the Niehans-Homburg argument, the marginal productivity of productive capital would in the long run be at least αK – αB above the long-term stable growth rate g. The dynamic inefficiency that legitimizes more national debt could not exist a fortiori.

Something similar can be said of the argument that there are transaction costs in managing land. If the transaction costs are ongoing, they would formally act like αB and increase the discount rate for calculating the land price. However, there are also transaction costs in the management of real capital. They would appear analytically like αK in the above formulas and would lead to the same qualitative result, especially since αK> αB must be assumed because managing a company is many times more complicated than managing one that is equally expensive Soil inventory. So it cannot be said that the Niehans-Homburg argument can be refuted by referring to the probabilities of expropriation or transaction costs. The opposite is the case.

All of this shows that real estate wealth is a central regulator in the economy, which has long since achieved what the national debt could potentially achieve. That is no triviality, because in Germany around five sixths of the total real capital stock is real estate. One sixth consists only of equipment that economists normally put in their production function. Any surplus capital will be absorbed by real estate assets before there is a risk of returns that are smaller than the economy’s long-term growth rate, let alone those that are smaller than zero. One does not need the destruction of capital by way of the national debt to achieve a similar result.

Senseless empiricism, because r

But doesn’t the fact that we have zero and negative interest rates today, while we can expect a certain positive growth, support the assumption that a chain letter campaign such as that proposed by Weizsäcker would increase welfare? What are these fundamental theoretical considerations supposed to mean in empirical evidence so obvious at the moment?

However, this position seems to me to be far too superficial, because one can probably assume that the low interest rates are the result of monetary countermeasures against a financial crisis that has spread throughout the world for several years, and not permanent phenomena. The low interest rates are intended to save portfolios and banks by generating valuation gains on investments. They are also the result of a worldwide competition in devaluation, which the central banks have pursued through the low interest rates, with the aim of improving the sales opportunities of their own export industries. These are all artificial effects that have political-economic explanations and maintain valuation bubbles so that the Schumpeter-Marxian cleansing crisis does not have to take place. The result of these bubbles are returns from zombies artificially kept alive by monetary policy, which have little to do with an insufficient natural marginal productivity of capital in the market economy (Sinn, 2017a).

Above all, these are only temporary historical effects that say little about whether the condition r g by itself due to market processes. Such adaptation processes are, as the growth literature has shown many times, extremely slow. It can take half a century to walk most of the way to Steady State. Relevant models of the intertemporal general equilibrium with actors who take the well-being of their descendants into account in their consumption planning, as I formulated them myself in the 1970s and 1980s (Sinn, 1980, 1981, 1982), can last for many decades through an apparent violation the conditions of an efficient growth process, but are in truth dynamically efficient because they asymptotically control a steady state that is characterized by r> g. The steady state that the market economy achieves independently in these models is what the earlier central planning literature called the Modified Golden Rule. As is well known, this Modified Golden Rule alone can claim to be the end result of an intertemporal optimal growth path. In contrast, the simple golden rule lacks any normative force. It is nothing more, but also nothing less than a useful analytical boundary between efficient steady states and the inefficient steady states, from which Münchhausen experiments à la Weizsäcker can be carried out.

In concrete terms, this means that one cannot infer anything from a momentary observation of a low marginal productivity of capital that justifies the national debt. Even if the interest rate were the natural marginal productivity and would not be distorted by monetary policy due to political-economic effects, the expansion of the national debt could not be justified with the arguments of Weizsäcker if it is to be expected that interest rates will rise later and growth will weaken becomes.

In fact, there are indications that such a development can be expected in Germany. On the one hand, because of the pay-as-you-go system in pension insurance, the baby boomers will soon be consuming a lot of capital. On the other hand, for the same demographic reasons, growth in the German economy will only be very meager for the foreseeable future. In my opinion, it would therefore be a mistake, even dangerous, if one were to talk about permanent national debt today beyond the corona crisis. There are good reasons for a temporary increase in national debt in times of crisis, especially Musgrave’s inter-generation equity principle, which calls for an equal burden on all generations. The supposed improvement of all generations through the national debt in the sense of the Münchhausen argument, however, has no comparable basis. Unfortunately, it is too good to be true.


**Translated and republished without prior written consent. For educational purposes only.

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