Springtime for madcownomics

Should Creutzfeldt and Jakob get the Nobel prize in economics? Probably, except that they are dead, and did not really foresee how the mad cow disease would hit the economic sphere.
Under the impulse of Eurostat, European Countries are now supposed to include parallel activities — in particular drugs and prostitution — in their GDP computations. The pro argument is that these are mutually profitable transactions, and, as they are legal in some countries, it will facilitate cross-country comparisons. A similar adjustment takes place for owner-occupied housing, which contributes to GDP in the form of imputed rents. This allows to eliminate the bias that countries where renting dominates have an artificially greater GDP than those where owning dominates.

Where the mad cow disease strikes is here: How can the same government decide that an activity is illegal, ergo harmful, and at the same time include it in GDP, i.e. decree that it raises welfare? And, furthermore, if it is illegal, how are we supposed to measure it? And why should national accounts be harmonized between a country which thinks that drugs are bad and a country which thinks that drugs are good? [1]

Another pro argument, beyond ludicrous, is that those computations will mechanically reduce the debt/gdp and deficit/gdp ratios, making European countries look better in terms of “Maastricht”. Except that the reason why we divide debt or deficits by gdp is that we want to express them in relation to some measure of the tax base that will serve to pay back the debt. Including an illegal, and therefore untaxed activity is therefore absurd.

There is no limit to what can be included in GDP. When you watch TV, your TV is performing a service. The TV channels’ advertising revenues widely underestimate the value of this service (in fact they value a totally different service, the grabbing of your attention, which generally comes as a deduction of yoour own utility of watching TV). We could well impute the value of watching TV in GDP. There is no logical difference between doing this and imputing owner-occupied housing. In both cases we put a price on a service that people provide for themselves with the capital they own, so as to make it comparable to the same service sold on the market.

It turns out that each French person above 4 on average spends a daily 3 hours and 50 minutes in front of TV. Let’s make it 4 hours. We can value that on the basis of the price of movie theaters, which is something like 8 to 10 euros for a 2 hour sequence. As many people watch TV because they are not willing to pay that amount for what they see, we have a little bit of a truncation bias here, so let us divide this amount by 2. This eventually values the hour of TV watching at 2 euros per hour. Let us make these 4 hours 2 hours, because some people actually watch pay-tv, which is recorded in GDP. Putting these things together, the value of watching TV is evaluated at 2*2*365 = 1500 euros per year. There are some 60 million French people above 4. We should therefore raise French GDP by 90 billion euros, i.e. 4.5 points of GDP.

[1] In France and other places, the buying of sex is illegal, but the selling of sex is not. Similar absurdities prevail for drugs. For Marxists, feminists, and their ilk, there are no such things as good actions and bad actions; only good people and bad people. A voluntary transaction between a good person and a bad person is therefore good and bad at the same time. From there the Marxist/Feminist has two escape routes. He can claim, in an Orwellian fashion, that good = bad. Or, he can decide that good people are not endowed with free will, implying that the transaction is not voluntary. In the latter case, the life of the good people (women, the poor, etc) has to be regulated by the government. But, if good people have no free will, regulation can only be enforced by bad people…

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Famous hoaxes in economic theory: 1. The market for lemons is inefficient

The celebrated Akerlof paper on the market for lemons – i.e., used cars – analyzes a so-called market inefficiency due to the unobservability of product quality to the buyer. The argument runs as follows: Suppose people know the quality of their car and have the option of continuing to use it rather than sell it. Then the higher the market price, the higher the average quality of the cars sold on the market. Conversely, suppose the welfare of the buyers is increasing in quality and decreasing in price; then they are willing to pay a higher price for cars if the average quality of the cars sold in the market is greater. Thus the demand curve may be increasing in price over some range, and there may be multiple equilibria, or even no equilibrium at all. In particular, we may construct examples where a low-price, low-quality equilibrium is dominated by any other equilibrium with a higher price and a higher quality. For example, assume buyers are willing to purchase any number of cars if they know that their quality on average is greater than their price. The demand curve is such that quality equals price. At a high price, high quality equilibrium, more sellers sell their cars at a higher price. Sellers are strictly better-off than in the low price, low quality equilibrium. Buyers are indifferent, since in both cases they derive a zero surplus from transactions, as price equals quality. Consequently, the higher price equilibrium dominates the low price equilibrium.
Now, what is wrong with this argument?[1] Suppose the economy is in a low price, low quality equilibrium and that there exists a superior equilibrium that it could reach. Suppose people are rational, meaning they know the structure of the economy and in particular the probability distribution of car quality. Then a buyer (or an intermediary) can offer a price slightly lower than the superior equilibrium; almost all the sellers that sell their cars in that equilibrium, including of course those who are currently selling it in the inferior equilibrium, are going to propose their cars to this intermediary. The average quality will be the same as in the good equilibrium, and the buyer will obtain a positive surplus[2]. Clearly, this destroys the initial equilibrium.
The inferior equilibria are based on the assumption that market participants take prices as given and, consequently, the buyers cannot affect the quality of the cars they purchase. It is however not rational for market participants to hold such belief. I know that if I deviate by posting a higher price I will on average get offered higher quality cars. This error comes from a misunderstanding of the real meaning of price taking in Walrasian equilibrium. While this is spelled out mathematically as an assumption in the definition of an equilibrium, in logical terms price taking is not an assumption, it is a result. The actual economic assumption is perfect competition. Perfect competition means that a given firm, if it charges a higher price than the market one, will not sell any good. If it decides to charge a lower price, it will get the whole market. Therefore, if the firm underbids the market price, it is rational for it to pick a price arbitrarily close to it. [To prove this we need to first show that the market price is unique and below the monopoly price, which is true]. Therefore, everything takes place as if market participants took prices as given.
But the conclusion that perfect competition implies price taking no longer holds in markets where the characteristics of the good depend on the price, as is the case with the market for lemons. Instead of a single price, there is an equilibrium price schedule relating prices to the characteristics of the good, and perfect competition means that market participants cannot move this schedule. However they are perfectly free to move along it, which is what one does when offering a price higher than the low equilibrium one in the above example. There are a number of examples where inefficient outcomes do not survive if we view competition that way. Consider for example competition between swimming pools: a cheaper swimming pool will attract more clients and be more congested. Here again, the quality of the good depends on its price. Yet if market participants arbitrage correctly, they will internalize the correct trade-off between price and congestion, and this trade-off will be reflected in an equilibrium price schedule which will allocate people to swimming pools efficiently. The congestion problem is not an externality, as it is internalized by the owners of the pool. The congestion cost of more crowded swimming pools is exactly reflected in their lower price. Indeed nobody ever wrote a paper to show that the market for swimming pools is inefficient. Yet the market for lemons is essentially similar; what drives the action is the relationship between price and product characteristics, not imperfect information, which in this case is just a side show. What imperfect information implies is that the relevant welfare benchmark is a second best constrained optimum where the unobservability of car quality is taken into account.
This fallacy illustrates that mathematical assumptions are different from economic assumptions. There is more economics in a mathematically formulated model than what is just written in the mathematics. It is convenient to define walrasian equilibrium as a system where market participants take prices as given, but some economic reasoning has taken place before one decides to actually make this formal assumption.
One may argue that it is more difficult for the economy to reach the good equilibrium than to attain an efficient Walrasian equilibrium in an economy with observable goods characteristics. This is true. In the latter case, any situation which is not an equilibrium will entail an imbalance between supply and demand. Suppose the price is too high. What do sellers need to know in order to have an incentive to reduce their price? They need to know that they can get an arbitrarily large number of additional customers by charging a price arbitrarily smaller than the market one. That is, they need to know that competition is perfect. Any seller who is rationed and knows that will reduce his price. In the market for lemons case, in order to offer a price different from the “low equilibrium” one, the buyer needs to know the entire distribution of car quality, including those that are not currently for sale. Knowledge of the relationship between price and quality locally around the “low equilibrium” is not enough. If that situation is locally “stable”, meaning that a small increase in price will raise quality by less than the price, no buyer has an incentive to offer a price slightly higher than the equilibrium one. While in a Walrasian economy a disequilibrium with rationing is broken by a slight deviation, here the deviation must be large.
Indeed people need more information to reach the good equilibrium in the market for lemons than in a Walrasian market. But if the economy is stuck at a bad equilibrium because they do not have enough knowledge, we are in a case of cognitive failure, not market failure.[3] Note however that it is probably not difficult for the economy to learn the good equilibrium; all we need is a sufficient inflow of mutants who offer random prices and replicate if their strategies are successful. Clearly a mutant which offers a price in the vicinity of the good equilibrium price will do better than buyers in the bad equilibrium. Thus we can conjecture that the only evolutionary stable outcome is the good equilibrium.

Notes:

[1] What follows is by no means a discovery. The formal treatment of the lemons problem in the textbook by Green, Whinston and Mas-Colell parallels the arguments made here. Yet the view that the market for lemons is inefficient pervades popular wisdom, partly because of the uncritical exposition in many undergraduate textbooks.
[2] In fact the average quality will also be slightly lower, but strictly greater than the price. This requires the good equilibrium to be “stable”, in the sense defined later in the text. It is possible to show that the highest price equilibrium is always stable.
[3] This critique does not apply to all markets with imperfect information. In a Rothschild-Stiglitz insurance market, the incentive compatible contract is subject to some pecuniary externality which may deliver an inefficient separating equilibrium. See Bisin and Gottardi, Journal of Political Economy, 2006.

Y=I+C+G, the unlikely identity, part II

I now turn to the discussion of G, the level of public expenditures. We recall that since GDP is the total value of the final goods produced, only expenditures on final goods should appear on the right-hand side of the identity. Yet, the government is a producer and does not spend anything on final goods. Therefore, G stands for government production, not government consumption. In other words, G is the total value of households’ consumption of publicly provided goods. The problem is that this value is not measured, because most of those goods are provided to the households for free, or for a price which does not reflect their hedonic value. For this reason we use government consumption as a proxy for government production. We measure the output of the government by its costs.

An immediate consequence is that, contrary to the private sector, productivity growth in the public sector will not be reflected in GDP. Suppose workers can either produce 1 unit of the private consumption good or a units of a public good. In equilibrium wages should be equal to 1. If H denotes the total provision of the public good, then public expenditure equals G=H/a. If the total labor force is equal to L, then L-H/a people work in the private sector and H/a people work in the public sector. Therefore, C=L-H/a and measured GDP equals Y=C+G=L-H/a+H/a=L. Total measured GDP is therefore independent of productivity in the public sector a. When it rises, if H is unchanged, more private goods are produced for the same level of public services; GDP should therefore go up. But national accountants wrongly consider that fewer public goods are produced when the public sector cuts costs, in a way which exactly offsets the contribution of higher private consumption.

In this example the economy is in a full employment equilibrium. How do things work in a Keynesian underemployment equilibrium? Here we have to distinguish between measured GDP (Y), total income (U), and actual GDP (Z). Assume a consumption function C = m(U-T)+b, where T is the level of taxes. Assue again unit wages, and a unit price of the consumption good. We have that U=C+H/a=C+G, which decomposes total income between that of private goods producers and that of public good producers. Consequently, Y=U: total income actually matches measured GDP*. Assuming a balanced budget, we have T=H/a. Therefore U=Y=H/a+b/(1-m).  Now measured GDP unambiguously falls when a goes up, as long as H goes up less than proportionally, i.e. as long as some downsizing takes place in government. Consumption is equal to b/(1-m), and therefore actual GDP is equal to Z=b/(1-m)+uH, where u is the appropriate hedonic price, or marginal utility, of public services. Actual GDP goes up as long as the public sector is downsized less than proportionally to the raise in public sector productivity.**

These examples suggest that the way we impute government services is far from innocent. At the end of the day, official GDP growth figures make the headlines. A politician would think twice about making the public sector more efficient, if this delivers negative news in the short run, and no measured effect in the long run. The conventional expenditure approach to GDP accounting embodies a built-in bias in favor of artificially growing the public sector by reducing its efficiency, which of course benefits some interest groups such as public sector unions. Ideology can pervade not only the way models are formulated, but the very measurement of our key concepts.

NB:* This is a tricky concept of income; if public expenditure does not measure the true value of public goods, part of the wages of civil servants should be interpreted as a transfer. U would then differ from the relevant concept of pre-tax, pre-transfer income. And U would be artificially boosted by just raising taxes and government wages. What is truly relevant here is rather disposable income U-T, which determines consumption.

** It is optimal in the short run to increase H proportionally to a, because the civil servants who are laid off do not find jobs in the private sector (due to wage and price rigidity). In this case, we have no change in measured GDP.

Y = I+C+G, the unlikely identity (part I)

The national income identity, Y=I+C+G, is the cornerstone of Keynesian macroeconomics. It decomposes GDP, Y,  between its main expenditure components, investment (I), consumption(C ), and government expenditures (G). It captures the essence of the Keynesian mantra, namely that in the short run, output fluctuations are driven by fluctuations in those demand components. Thus, recessions are triggered by a fall in consumer or investor confidence (animal spirits), and government  spending can be adjusted to counteract these sources of fluctuations and stabilize output.

I once naively thought that this identity decomposed total spending between the spending levels of the three “institutional sectors” (households, firms and government), and at the same time stated that spending must be equal to output (and simultaneously to total income).

In fact, things are not so simple. GDP is defined as the total value of all the final goods produced on a given territory in any given period. If the left-hand side of the national income identity is the production of final goods, its left-hand side should consist of the expenditure on final goods.  But neither firms nor the government purchase any final goods. They both are producers of goods and services and by definition only purchase intermediate goods. Only households purchase final goods. Adding government purchases and firms’ investment spending to consumer spending  therefore seems inconsistent with the definition of GDP. It looks like instead we should have Y=C in a closed economy and Y = C+X-M in an open economy, where X=exports and M=imports.

Therefore, there is more than meets the eye in this identity, and while there are some good reasons why G and I are there, the way they are included in the right-hand side is not exempt from ideology.

Let us start with investment, I. When one decomposes GDP between industries, one is careful in avoiding double-counting of economic activity,  by valuing the contribution of a firm to GDP, not by its total sales, but by its value added, defined as sales minus the cost of intermediate inputs. Yet, when we add  I on the right-hand side of the national income identity, we are guilty of such double-counting.

Consider the following simple example: Robinson Crusoe lives for two periods. In period one, he gathers two coconuts on a tree. He eats one of them and plants the other one in the ground. In period 2, this coconut has grown into a tree, which produces one coconut, that Robinson gathers and eats (I assume the preceding period’s tree no longer exists in period 2). Clearly, Robinson has eaten  one coconut in each period.  For all practical purposes, the total cumulated output of this economy over the two periods is two coconuts. Yet, conventional GDP accounting states that in period 1, GDP is equal to two coconuts, with I=1 and C=1, and in period 2, GDP is equal to 1 coconut, with I=0 and C=1. Even though Robinson has eaten two coconuts over his lifetime, conventional GDP accounting considers that this economy has produced 3 coconuts over that period. There is double counting of the coconut which has been planted in period 1.

Interestingly, if that same coconut had delivered its tree in period 1, it would have been treated as an intermediate input instead of investment, and the double counting would have been avoided. Similarly, if, instead of being planted in the ground, the coconut had been stored between period 1 and period 2, it would have been counted as inventory, and double-counting would also have been avoided, as inventory depletion comes in deduction of total GDP. In such a case one would have Y=2, with C=1 and I=1 in period 1, and Y=0, with C=1 and I=-1, in period 2 (inventories are one component of investment, and in this example, investment is only made of inventories, while in the preceding example, investment consists of fixed capital formation—the period 2  tree).

It is curious that double counting is avoided for the inventory part of investment, but  not for equipment and structures. This is in fact acknowledged in national accounting, the “G” in GDP means “gross”, that is, gross of capital depreciation. If one were subtracting capital depreciation from GDP, thus computing Net Domestic Product (NDP), one would avoid double-counting: over time, any additional unit of capital would end up been fully depreciated, and therefore fully deducted from GDP. In the Robinson Crusoe example, the tree planted in period 1 should be fully depreciated in period 2, because it is no longer used thereafter. Therefore, NDP is equal to 2 in period 1 and to 0 in period 2. The accounting is identical to the case where the coconut is stored instead of planted.

Despite that NDP is a more correct measure than GDP, all the debate and policy analysis is cast in terms of GDP.  This is not without consequences.  NDP is substantially below GDP. With a typical capital output ratio equal to 3, and a typical deprecation rate of 6 % per year, NDP is 18 % below GDP. Focusing on GDP substantially biases the comparison between countries that invest a lot, like China or Singapore, with those that invest little, like the United States. A country with an investment/gdp ratio of 50 % (the current Chinese level) will settle at a steady-state capital/output ratio as high as 8, meaning that its NDP will be only half its GDP (It will likely be “dynamically inefficient”, i.e. could consume more forever by just decumulating capital). Also, the structure of economic fluctuations will change. If investment booms are protracted, GDP will look more volatile than NDP. If they are short-lived, NDP will be more volatile than GDP.

If one cares about final goods, why take investment into account at all? Indeed, one could just ignore it entirely and focus on consumption. Consumption is much less volatile than investment, which drives most fluctuations in GDP.  Macroeconomics would be little news if one looked at consumption instead of GDP.  Furthermore, consumption is all that matters for the people (it is what enters into the “utility function”).  In other words, the theoretical case for focusing on consumption is much stronger than for GDP. Since, empirically, consumption is so smooth, the gains from stabilizing it are very small.

Of course, the reason why people decided to add investment on the RHS of the national account identity, is that when there is an investment slump, people lose their jobs – resources seem to be underutilized, which is the reason why one worries about economic fluctuations in the first place. However, this is no excuse to double-count the contribution of the workers producing the investment goods.

From a pure accounting perspective, the issue is the following: To what time period should we allocate economic activity, when the cost and benefit sides of that activity occur at different dates? Shall we consider that Robinson’s investment increases GDP at the time the tree is planted, versus the time when the coconut produced by the tree is eaten? While NDP takes the first route, consumption takes the second one.

It seems that if we care about the welfare flow of the population, we should look at consumption. If we care about the level of economic activity, NDP looks more appropriate. Here, however, we run into another inconsistency.

Let us go back to our example and assume that the tree planted by Robinson now delivers two coconuts in period 2. Furthermore, let us assume that the only effort provided by Robinson is in planting coconuts – no effort is needed to gather them. In period 1, we still have Y=2, I=1 and C=1. In period 2, we now have Y=2, I=0 and C=2. GDP is equal to 2 in each period, while NDP is equal to 2 in period 1 and to 1 in period 2. This one coconut produced in period 2, is the return to “capital”, i.e. the tree, net of its own depreciation. Given that Robinson Crusoe does not plant any tree in period 2, he does nothing at all in that period – the return to labor is zero.  We consider that there is economic activity in period 2, because the tree delivers some coconuts. Yet this tree is there just because Robinson planted it in period 1. The true cause of the tree’s presence is Robinson’s planting activity in period 1. Why do we then allocate the net return of capital to period 2 instead of period 1? Surely this cannot be because that coconut is consumed in period  2; if we cared about that we would just look at Robinson’s consumption flow, not at domestic product.  Or is it because that coconut is produced in period 2? So is the coconut which was deducted for depreciation; after all there are two coconuts available for consumption in period 2. Shall we, then, restore GDP and forget about NDP? Then we start double-counting again. Or shall we deduct the tree’s depreciation in period 1 rather than period 2? This gets us back to looking at consumption rather than domestic product.

The example illustrates that, since capital is just past frozen labor, we may allocate its net return at any given date to the period when the investment activity which generated this capital took place.  In the preceding example, this new notion of domestic product would be equal to 3 in the first period and to 0 in the second period.  This method has the Marxist flavor of computing the labor-value of capital at any given date, and allocating it to the date when the capital was produced.  Let us call this the “labor value” domestic product (LVDP).

Only labor income at date t contributes to LVDP at that same date.  Capital income is allocated to the preceding date when the corresponding investment took place. It is reasonable to use the discount rate between the two periods to convert this capital income. It is then easy to see that the contribution of investment to LVDP at date t is simply equal to the present discounted value of the income flows generated by that investment – or, equivalently, the market value of that investment. If financial markets work well, the net marginal product of capital will be equal to the discount rate, and the market value of investment will accordingly equal to the total investment cost (things would be more complicated if there were installation costs to capital). Thus, to compute LVDP, we should just add total labor income to total investment. Calling Z the LVDP, we get

Z = wL + I

In a steady state, assuming for simplicity no economic growth, we would have I=d.K, where d is the depreciation rate of capital. Total GDP is equal to Y=wL+mK, where m is the marginal productivity of capital, also equal to d+r, where r is the real interest rate. Therefore, in steady state, we have that

Z = Y – rK

If r>0, then Z<Y, because LVDP recognizes that the benefits of investment accrue later and therefore should be discounted. If r=0, though, we are at a “golden rule” steady state and GDP and LVDP coincide. Note that LVDP coincides with GDP, not with NDP. This is because LVDP recognizes that preventing capital from depreciating today brings useful future benefits in terms of consumption.

If r>0, we in fact get that LVDP is greater than GDP in steady state. In such a case, the economy is dynamically inefficient. It accumulates too much capital. In a dynamically inefficient economy, the notion of LVDP becomes dubious because investments are imputed at their market value, but the private discount rate is not efficient in such an economy.