On Why It is Important to Distinguish Between Consumption and Expenditures When Testing the Permanent Income Hypothesis

A central idea in modern macroeconomics is the permanent income hypothesis. The basic idea is as follows. Suppose that you could dichotomize your income into a permanent component and a temporary component. The permanent income hypothesis suggests that you would base your consumption decisions on the permanent component.

Why would people behave this way?

Well, individuals want to smooth the marginal utility of their consumption over time. To understand this, consider the following example. Suppose that you varied your consumption proportionately with your current income and that your income fluctuated significantly from year to year. This would imply that your consumption would be high in years when your income was high and low in years when your income was low. However, if consumption is subject to diminishing marginal utility, this would mean that the marginal utility of consumption in high income years is less than the marginal utility of consumption in low income years. So wouldn’t it be nice to take some consumption from your high income years (when the marginal utility is low) and transfer it to the low income years (when the marginal utility is high)? Yes, because your lifetime utility would be higher. Fortunately, you can do this by adjusting your savings behavior in response to temporary fluctuations in your income over time (note that this includes borrowing behavior, which is just negative savings).

So this sounds reasonable, but it is important to think about why the permanent income hypothesis might not hold.

Given our discussion, one obvious reason pops up. What if some fraction of consumers are subject to credit constraints (i.e. either limits or lack of access to borrowing). Individuals who face borrowing constraints might find themselves unable to borrow following a reduction in their income. If this is true, individuals might not always be able to smooth the marginal utility of their consumption over time.

Some have posited other, “behavioral” reasons why the permanent income hypothesis might not hold. For example, maybe people are myopic and don’t plan adequately for the future.

So how do we know if the permanent income hypothesis is a good guide in thinking about consumption decisions? Well, we have to go to the data.

Now suppose that you wanted to test the implications of the permanent income hypothesis. There are a number of ways you might do this. You might test the cross-sectional predictions of the model outlined by Milton Friedman. You might try to estimate consumption Euler equations with aggregate data. Or you might find identify periods of time in which people experience a significant decline in income and see what happens to their consumption behavior.

The evidence testing Friedman’s predictions with cross-sectional data seem to support the permanent income hypothesis. Estimates of the consumption Euler equation do not. (However, as John Seater points out, this is likely due to problems with aggregation and not the theory itself since aggregation imposes pretty strong implicit assumptions about households.) Finally, the work focusing on periods of significant declines in income seems to show a corresponding significant decline in consumption. It is this last bit of evidence that I want to discuss in more detail.

If you notice that consumption declines significantly after a person becomes unemployed or after they retire, this would seem to provide evidence against the permanent income hypothesis. The unemployed worker should be spending out of his savings or borrowing until he finds a new job. The retired person should have planned better for the future.

The problem with this assessment is that whether or not the permanent income hypothesis holds depends on consumption behavior. In reality, most of our data on consumption is typically consumption expenditures. It is important to understand the difference.

To understand why it is important to distinguish between consumption and expenditures, consider the following example. Suppose that I am interested in food consumption. How should I measure food consumption? I could measure food consumption by how much I spend on food. I could also measure food consumption by the number of calories I eat. This might not seem like an important difference, but it can be quite important.

Imagine that I can eat the same exact meal at home as I can at a restaurant. If I eat it at the restaurant, then my expenditures are equal to the market price of the meal. If I eat it at home, my expenditures are the cost of the ingredients. The latter should be less than the former. In addition, the degree to which the latter are less than the former will depend on how much time I spend shopping for the lowest prices of those ingredients. Nonetheless, despite the difference in expenditures, my food consumption is the same (by definition, it’s the same meal).

So why is this distinction important?

Think about people who become unemployed or people who retire. What they have in common is that they have more time than they had when they were working. The opportunity cost of their time has fallen. As a result, those who are unemployed and those who are retired are likely to spend more of their time cooking than they would if they were working. They are also likely to spend more time searching for better prices on the ingredients to make their meal than they would if they were working. The result is that the individual will spend more time on what economists call “home production” (and therefore home consumption) while reducing market expenditures.

This is important for the following reason. There is a difference between expenditures and consumption. Expenditures are simply the subset of consumption that occurs in a market setting.

So how significant is this distinction?

It turns out that this distinction is quite important. Mark Aguiar and Erik Hurst have a paper in the Journal of Political Economy that uses a cool data set that consists of food diaries of U.S. households. What the paper shows is that neither the quality nor quantity of food intake by retired households decline after retirement. In addition, they find that the food intake of unemployed workers does decline, but only as much as one would predict from the decline in permanent income typical of being displaced for some period of time from one’s job. In other words, if one considers the role of home production, then the evidence of a significant decline in expenditures following retirement or job displacement should not be interpreted as evidence against the permanent income hypothesis. Relying on expenditure data to measure consumption might cause one to incorrectly reject the permanent income hypothesis.

What does this mean for economists and their models?

First, as more and more micro-level data becomes available, it is important to consider whether one has the correct measure of the variable of interest before embarking on hypothesis testing. Second, this result seems to imply that if you are going to take a model to the data and you use standard measures of consumption expenditures, the model should include home production in the household decision. Otherwise, what the researcher is calling consumption and how consumption is calculated are not consistent.

Are Helicopter Drops a Fiscal Operation?

This is meant to be a quick note on what I think is a common misconception about helicopter drops. I am not advocating that the Federal Reserve or any other central bank undertake the actions I am going to describe nor do I care about whether it is legal for the Federal Reserve or any other central bank. All I am concerned with is helicopter drops on a theoretical level. With that being said, let me get to what I believe is a misconception.

First, some context. Typically, when the Federal Reserve wants to increase the money supply, they buy assets on the open market in exchange for bank reserves. These are called open market operations. One potential problem is that the Federal Reserve is typically purchasing short-term government debt. When short term nominal interest rates are near the zero lower bound, many believe that open market operations are impotent since the central bank is exchanging one asset that does not bear interest for another asset that does not bear interest. Banks are indifferent between the two. The exchange has no meaningful effect on economic activity.

Given this problem, some have advocated a “helicopter drop” of money. Typically, they don’t mean an actual helicopter flies overhead dropping currency from the sky. What they are referring to is something like the following. Suppose that the U.S. Treasury sends a check to everyone in the United States for $100 and issues bonds to pay for it. The Federal Reserve then buys all of these bonds and holds them to maturity. This is effectively a money-financed tax rebate. Thus, it resembles a helicopter drop because everyone gets $100, which was paid for by an expansion of the money supply. However, many people are quick to point out that this is actually a fiscal operation. The U.S. government is giving everyone a check and the Federal Reserve is simply monetizing the debt.

But are helicopter drops really a fiscal operation? Certainly if we think about helicopter drops as I have described them above, it is correct to note that such action requires monetary-fiscal cooperation. However, let’s consider an alternative scenario.

The Federal Reserve has a balance sheet just like any other bank. The Fed classifies things on their balance sheet into 3 categories:

1. Assets. Assets include loans to banks, securities held, foreign currency, gold certificates, SDRs, etc.
2. Liabilities. Liabilities include currency in circulation, bank reserves, repurchase agreements, etc.
3. Capital.

The balance sheet constraint is given as

Assets = Liabilities + Capital

Let’s consider how things change on the balance sheet. Suppose that the Fed took large losses on the Maiden Lane securities purchased during the financial crisis. What would happen? Well, the value of the Fed’s assets would decline. However, the liabilities owed by the Fed would not change. Thus, for the balance sheet to remain in balance, the value of the Fed’s capital would have to decline.

So imagine the following scenario. We all wake up one morning to discover that actual helicopters are lifting off from the rooftops of regional Federal Reserve banks. The helicopters fly through each region dropping currency from the sky. People walk out of their homes and businesses and see money raining down upon them. They quickly scoop up the money and shovel it into their pockets. It is a literal helicopter drop of money!

But how can this be? How could the central bank do such a thing?

If the central bank were to do such a thing, think about what would happen to its balance sheet. Currency in circulation increases thereby increasing Fed liabilities. However, asset values are still the same. So capital declines. (The latest Fed balance sheet suggests that the Fed has $10 billion in surplus capital. This would decline dollar-for-dollar with the increase in the supply of currency.)

What this implies is that a central bank could (in theory) conduct a helicopter drop by effectively reducing its net worth. In the future, the Federal Reserve could restore its capital by reinvesting its earnings into new assets. Thus, the helicopter drop is a form of direct transfer to the public that is paid for by the Fed’s future earnings.

[Now, some of you might be saying, “Ah ha! If the Fed is retaining earnings these are earnings that would have otherwise gone to the Treasury and so it is still a fiscal operation.” I would argue that (a) this is semantics, and (b) there is no reason to believe this is true. The Fed, for example, could simply have used those earnings to furnish new offices at the Board and all of the regional banks — in that case it would be a transfer of wealth from the staff to the general public.]

Money and Banking

You might be able to teach an entire course on the microeconomics of money and banking based on the following thought experiment.

Imagine the following scenario. I want to start a business, but I need to borrow $10,000 to get started. You offer to provide me with that $10,000. However, since you won’t get to consume using that $10,000 and you won’t get to invest that $10,000 in anything else you require that I pay you some interest. I give you a piece of paper that promises to pay you back, with interest, at some future date in time. Intrinsically, that piece of paper that I have given you is worthless. It is just a piece of paper. However, if that piece of paper represents a legally binding agreement, then we call that piece of paper a bond. You are willing to accept that piece of paper from me because you anticipate that I am going to do something productive with your money. In the event that I don’t, you will be entitled to the assets of my business. So, the value of the bond is the expected value of the bond over the duration of the loan plus the value of the option to seize my assets in the event that I cannot/do not pay you back. Now, of course, there is some chance that between now and when I have promised to pay you back you will want to spend money. As a result, a market emerges that allows you to sell this piece of paper to other people.

Now imagine the following alternative scenario. Suppose that you want to save, but you don’t want to deal with trying to figure out how to invest that savings. Fortunately, we have a mutual friend who likes to do this sort of thing. So you give your $10,000 to our friend and he promises to give you your money back plus some interest payment. I also make a visit to our mutual friend, but I ask him to borrow $10,000. He agrees to lend me $10,000, but I have to pay him back with interest (slightly higher than what he is offering you). Since our mutual friend knows that you might need cash for unexpected expenditures in the future, he promises to give you the right to show up and demand your $10,000 (or some fraction thereof) at any moment you want. Thus, to our mutual friend, the value of the loan is the expected value of the loan over the duration agreed upon plus the expected value of the option to seize my assets in the event that I cannot/do not pay him back. The value of the contract for you is the expected value of the loan that you have given our mutual friend plus the value of the option to get your $10,000 back whenever you want plus the value of the option to seize the assets of our mutual friend in the event that the value of his assets decline below what he owes you.

What is the difference between these two scenarios?

Some would say that in the latter scenario the problem is that our mutual friend is offering to give you dollars that he himself does not have to give. Thus, he is “creating dollars out of thin air.” In fact, if he doesn’t have actual dollars, he might give you a piece of paper that promises to give you those dollars in the future. If you are able to trade these pieces of paper in exchange for goods and services, it would appear as though our mutual friend has really created money out of thin air. But has he really? Or is he merely allowing you to transfer some fraction of what he owes you to another individual?

Why might people be willing to accept these pieces of paper printed by our mutual friend and use them in transactions?

Replace “$10,000” with “7.5 ounces of gold.” Do your answers to these questions change?

Reasoning from Interest Rates

A quick note…

We can think of long-term yields as consisting of two components, the average expected future short-term rate and the term premium. However, it is important to note that the average expected future short-term rate itself is a function of the rate of time preference, expectations of future growth, and expectations of inflation. Also, the term premium is a function of duration risk, a liquidity premium, and a safety premium.

So suppose that you see long-term yields change, what can you learn about the stance of monetary policy?

October Surprises

I recently talked with Jim Tankersley of the Washington Post about October surprises.

What Are Real Business Cycles?

The real business cycle model is often described as the core of modern business cycle research. What this means is that other business cycle models have the RBC model as a special case (i.e. strip away all of the frictions from your model and its an RBC model). The idea that the RBC model is the core of modern business cycle research is somewhat tautological since the RBC model is just a neoclassical model without any frictions. Thus, if we start with a model with frictions and take those frictions away, we have a frictionless model.

The purpose of the original RBC models was not necessarily to argue that these models represented an accurate portrayal of the business cycle, but rather to see how much of the business cycle could be explained without the appeal to frictions. The basic idea is that there could be shocks to tastes and/or technology and that these changes could cause fluctuations in economic activity. Furthermore, since the RBC model was a frictionless model, any such fluctuations would be efficient. This conclusion was important. We typically think of recessions as being inefficient and costly. If this is true, countercyclical policy could be welfare-increasing. However, if the world can be adequately explained by the RBC model, then economic fluctuations represent efficient responses to unexpected changes in tastes and technology. There is no role for countercyclical policy.

There were two critical responses to RBC models. The first criticism was that the model was too simple. The crux of this argument is that if one estimated changes in total factor productivity (TFP; technology in the RBC model) using something like the Solow residual and plugged this into the model, one might be misled into thinking the model had greater predictive power than it did in reality. The basic idea is that the Solow residual is, as the name implies, a residual. Thus, this measure of TFP only captured fluctuations in output that were not explained by changes in labor and capital. Since there are a lot of things besides technology that might effect output other than labor and capital, this might not be a good measure of TFP and might result in attributing a greater percentage of fluctuations to TFP than was true of the actual data generating process.

The second critical response was largely to ridicule and make fun of the model. For example, Franco Modigliani once quipped that RBC-type models were akin to assuming that business cycles were mass outbreaks of laziness. Others would criticize the theory by stating that recessions must be periods of time when society collectively forgets how to use technology. And recently, Paul Romer has suggested that technology shocks be relabeled as phlogiston shocks.

These latter criticisms are certainly witty and no doubt the source of laughter in seminar rooms. Unfortunately, these latter criticisms obscure the more important criticisms. More importantly, however, they represent a misunderstanding of what the RBC model is about. As a result, I would like to provide an interpretation of the RBC model and then discuss more substantive criticisms.

The idea behind the real business cycle model is that fluctuations in aggregate productivity are the cause of economic fluctuations. If all firms are identical, then any decline in aggregate productivity must be a decline in the productivity of all the individual firms. But why would firms become less productive? To me, this seems to be the wrong way to interpret the model. My preferred interpretation is as follows. Suppose that you have a bunch of different firms producing different goods and these firms have different levels of productivity. In this case, an aggregate productivity shock is simply the reallocation from high productivity firms to low productivity firms or vice versa. As long as we think of all markets as being competitive, then the RBC model is just a reduced form version of what I’ve just described. In other words, the RBC model essentially suggests that fluctuations in the economy are driven by the reallocation of inputs between firms with different levels of productivity, but since markets are efficient we don’t need to get into the weeds of this reallocation in the model and can simply focus our attention on a representative firm and aggregate productivity.

I think that my interpretation is important for a couple of reasons. First, it suggests that while “forgetting how to use technology” might get chuckles in the seminar room, it is not particularly useful for thinking about productivity shocks. Second, and more importantly, this interpretation allows for further analysis. For example, how often do we see such reallocation between high productivity firms and low productivity firms? How well do such reallocations line up with business cycles in the data? What are the sources of reallocation? For example, if the reallocation is due to changes in demographics and/or preferences, then these reallocations could be interpreted as efficient responses to structural changes in the economy and be seen as efficient. However, if these reallocations are caused by changes in relative prices due to, say, monetary policy, then the welfare and policy implications are much different.

Thus, to me, rather than denigrate RBC theory, what we should do is try to disaggregate productivity, determine what causes reallocation, and try to assess whether this is an efficient reallocation or should really be considered misallocation. The good news is that economists are already doing this (here and here, for example). Unfortunately, you hear more sneering and name-calling in popular discussions than you do about this interesting and important work.

Finally, I should note that I think one of the reasons that the real business cycle model has been such a point of controversy is that it implies that recessions are efficient responses to fluctuations in productivity and counter-cyclical policy is unnecessary. This notion violates the prior beliefs of a great number of economists. As a result, I think that many of these economists are therefore willing to dismiss RBC out of hand. Nonetheless, while I myself am not inclined to think that recessions are simply efficient responses to taste and technology changes, I do think that this starting point is useful as a thought exercise. Using an RBC model as a starting point to thinking about recessions forces one to think about the potential sources of inefficiencies, how to test the magnitude of such effects, and the appropriate policy response. The better we are able to disaggregate fluctuations in productivity, the more we should be able to learn about fluctuations in aggregate productivity and the more we might be able to learn about the driving forces of recessions.

Forthcoming Publications

Blogging has been a bit light around here. In lieu of a blog post, here are a few papers of mine have recently been accepted for publication that might be of interest to regular readers:

1. “Money, Liquidity, and the Structure of Production” (with Alexander Salter), Journal of Economic Dynamics and Control. This paper is a little bit of Hayek, Hirshleifer, Tobin, and Dixit all rolled into one. Here is the abstract:

We use a model in which media of exchange are essential to examine the role of liquidity and monetary policy on production and investment decisions in which time is an important element. Specifically, we consider the effects of monetary policy on the length of production time and entry and exit decisions for firms. We show that higher rates of inflation cause households to substitute away from money balances and increase the allocation of bonds in their portfolio thereby causing a decline in the real interest rate. The decline in the real interest rate causes the period of production to increase and the productivity thresholds for entry and exit to decline. This implies that when the real interest rate declines, prospective firms are more likely to enter the market and existing firms are more likely to stay in the market. Finally, we present reduced form empirical evidence consistent with the predictions of the model.

2. “An Evaluation of Friedman’s Monetary Instability Hypothesis“, Southern Economic Journal. This paper examines two elements of Milton Friedman’s work within the context of a relatively standard structural model. The first element is the idea that deviations between the money supply and money demand are a significant source of business cycle fluctuations. The second element is the idea that shocks to the money supply are much more empirically significant that shocks to money demand. Here is the abstract:

In this paper, I examine what I call Milton Friedman’s Monetary Instability Hypothesis. Drawing on Friedman’s work, I argue that there are two main components to this view. The first component is the idea that deviations between the public’s demand for money and the supply of money are an important source of economic fluctuations. The second component of this view is that these deviations are primarily caused by fluctuations in the supply of money rather than the demand for money. Each of these components can be tested independently. To do so, I estimate an otherwise standard New Keynesian model, amended to include a money demand function consistent with Friedman’s work and a money growth rule, for a period from 1875-1963. This structural model allows me to separately identify shocks to the money supply and shocks to money demand. I then use variance decompositions to assess the relative importance of shocks to the supply and demand for money. I find that shocks to the monetary base can account for up to 28% of the fluctuations in output whereas money demand shocks can account for less than 1% of such fluctuations. This provides support for Friedman’s view.

3. “Interest Rates and Investment Coordination Failures“, Review of Austrian Economics. This paper examines the role of interest rates in influencing both production time and entry decisions of firms. The paper therefore examines coordination problems similar to those emphasized in the Austrian business cycle theory and the business cycle theory of Fischer Black. I show that in low interest rate environments firms are more likely to preempt the entry of their competitors at lower levels of demand than when interest rates are high. When firms enter simultaneously at these levels of demand, it is a coordination failure. Low interest rates also produce changes in the length of production that are consistent with the ABCT. This provides some support for business cycle theories such as the ABCT, which have been criticized as violating the assumption of rational expectations.

The theory of capital developed by Bohm-Bawerk and Wicksell emphasized the roundabout nature of the production process. The basic insight is that production necessarily involves time. One element of the production process is to determine the period of production, or the length of time from the start of production to its completion. Bohm-Bawerk and Wicksell emphasized the role of the interest rate in determining the period of production. In this paper, I develop an option games model of the decision to invest. Two firms have an opportunity to enter a market, but production takes time. Firms face a two-dimensional decision. Along one dimension, they determine the period of production and the prospective profit therefrom. Along another dimension, they determine whether or not they want to enter the market given the amount of time it will take to start generating revenue from production. Within this option games approach, the period of production can be understood as an endogenous time-to-build and I argue that this framework provides a tool for evaluating the claims of Bohm-Bawerk and Wicksell against the backdrop of competition and uncertainty. I evaluate the period of production decision and the option to enter decision when the real interest rate changes. I show that investment coordination failures are more likely to occur at lower levels of profitability when real interest rates are low. I conclude by discussing the implications of low interest rates for boom-bust investment cycles.