Friday, March 27, 2015

Forecasting long-term stock returns: the two-hour recipe (II)

Last week I started writing up a quick (?) methodology to forecast equity returns. Specifically, the question was
Forecast the real total return of U.S. equities over the next ten years. Show your work. Time: two hours.
I wrote down a decomposition of the total return into three components:

$$\frac{R_{t,t+k}}{(1+\widehat{\pi}_{t+1, t+k})^k} = \frac{V_{t+k}}{V_{t}} \frac{(1+g_F)^k} {(1+\widehat{\pi}_{t+1, t+k})^k} (1+\widehat{dy}_{t+1, t+k})^k$$

The three components are:

1) Income, which boils down to the geometric average of the dividend yield:
$$(1+\widehat{dy}_{t+1, t+k})^k$$
2) The 10-year change of a valuation ratio.
$$\frac{V_{t+k}}{V_{t}}$$
3) The real growth of the fundamental used in the construction of the valuation ratio.
$$\frac{(1+g_F)^k} {(1+\widehat{\pi}_{t+1, t+k})^k}$$
Since this is meant to be a quick estimation, I decided that I would use either the historical average or the ten-year rolling average of the relevant data to forecast each of the three components.

Pulling the Shiller long-term data set (xls) on stock prices, earnings, and dividends, I took the geometric average of the dividend yield between 2005 and 2014 as my forecast for the dividend yield over the next ten years: 2.0082%. So my forecast for \(\widehat{dy}_{t+1, t+10}\) is 0.02.

For the valuation ratio, we can calculate two from the Shiller dataset. The first one is the CAPE ("cyclically-adjusted" P/E ratio, or "Shiller's P/E"). A casual observation of the time series chart since 1880 suggests that the CAPE either experienced a shift sometime after the 1980s, or is experiencing upward drift. Today's CAPE (27.9) is significantly higher than the historical average (16.6) or the ten-year rolling average (22.6). We'll take those two values as alternative forecasts of the CAPE ten years from now. The historical CAPE implies that the ratio of valuation metrics, \(V_{t+k} / V_{t}\), is 0.595 (16.6 / 27.9). The ten-year rolling average CAPE implies a ratio of 0.81 (22.6 / 27.9).

The second valuation ratio we can compute from the Shiller dataset is the dividend yield (or rather, to fit the total return formula above, the price-to-dividend ratio):
Just like the CAPE, the price/dividend ratio seems to have experience either a shift or drift some time after the 1980s. Today's multiple (55.8) is close to the 10-year rolling average, but much higher than the historical average (27.9). As with the CAPE, we'll consider both to forecast the 10-year-ahead price/dividend ratio. Using the historical P/D, the ratio of valuation metrics, \(V_{t+k} / V_{t}\), is  0.50 (27.9 / 55.8), whereas using the 10-year rolling average, the ratio is  0.93 (51.9 / 55.8).

Growth of the fundamental

The third component of the total return is the real growth rate of the fundamental:
$$\frac{(1+g_F)^k} {(1+\widehat{\pi}_{t+1, t+k})^k}$$
Which fundamental we use is determined by the valuation ratio we pick. For the CAPE, the fundamental is the 10-year rolling average of earnings. For the price-dividend ratio, the fundamental is dividends.

The real growth rate of (the 10y average) of earnings has been 1.66% per annum. The rolling 10-year counterpart fluctuates quite a bit (even though this is the rolling average growth rate of a rolling average of earnings), and is now at 3.5%.

For real dividends, the historical (10-year rolling average) growth rate is 1.34% (5.1%).

Putting everything together

I have proposed two forecasts for each of two possible valuation ratios and their corresponding fundamentals, for a total of four forecasts (the income component is the same for all four).  The following table combines the forecast components of real returns to produce the total return forecast:


\(V_{t+k} / V_{t}\) \(g_F\) \((1+g_F)^k / (1+\pi)^k\) \(dy\) \((1+dy)^k\) \(R_{t,t+10} / (1+\pi)^k\)  Annual real return
CAPE (historical avg.)
0.595
0.0166
1.179
0.02
1.219
0.855
-1.55%
CAPE (10y rolling avg.)
0.81
0.035
1.411
0.02
1.219
1.393
3.37%
Dividend yield (historical avg.)
0.50
0.0134
1.142
0.02
1.219
0.696
-3.56%
Dividend yield (10y rolling avg.)
0.93
0.051
1.644
0.02
1.219
1.864
6.43%

The last column shows that the forecast real return, per year, varies from -3.6% to 6.4%.

Wednesday, March 25, 2015

Links: Deep thoughts about macro models

1. Why do central banks use the New Keynesian model?, by Simon Wren-Lewis.
What is a NK model? It is a RBC model plus a microfounded model of price setting, and a nominal interest rate set by the central bank. Every NK model has its inner RBC model. You could reasonably say that these NK models were designed to help tell the central bank what interest rate to set. In the simplest case, this involves setting a nominal rate that achieves, or moves towards, the level of real interest rates that is assumed to occur in the inner RBC model: the natural real rate.
[...]
Why not just use the restricted RBC version of the NK model? Because the central bank sets a nominal rate, so it needs an estimate of what expected inflation is. It could get that from surveys, but it also wants to know how expected inflation will change if it changes its nominal rate.
[...]
To say that the RBC model assumes that agents set the appropriate market clearing prices describes an outcome, but not the mechanism by which it is achieved.
That may be fine - a perfectly acceptable simplification - if when we do think how price setters and the central bank interact, that is the outcome we generally converge towards. NK models suggest that most of the time that is true. This in turn means that the microfoundations of price setting in RBC models applied to a monetary economy rest on NK foundations. The RBC model assumes the real interest rate clears the goods market, and the NK model shows us why in a monetary economy that can happen (and occasionally why it does not).
2. A case where RBC works, by Noah Smith.

The Arezki et al. paper is a victory for that kind of simple RBC-type model. But it's a limited victory, since the fluctuations produced by oil news shocks don't look like most business cycles, and because simple models like this don't explain things like the Great Recession. 
[...]
...it's very interesting that simple RBC-type models should be so good at explaining something like an oil shock and so bad at explaining things like big recessions. This fact could lead economists toward something incredibly valuable: an understanding of the scope conditions of RBC-type models.
Scope conditions are the conditions under which a model works well. (**Physics analogy alert**) For example, we know that a model of frictionless motion works pretty well on an ice skating rink and pretty badly under the ocean. And we know exactly why. In decision theory, I personally think that experiments are starting to teach us the scope conditions of super-basic econ 101 demand theory: it works well for one-shot decisions, and not very well for dynamic situations with lots of uncertainty.
But for macro, it's inherently very hard to identify scope conditions, because there's so much going on at once that you can't get a clean comparison between the cases when a model works and the cases when it fails. 
[...]
Having a case where RBC models actually work helps us narrow down the list of possible reasons why they usually fail.
There will inevitably be many such differences, but they narrow down the types of models we want to consider. If a model fits the Great Recession but doesn't reduce to the Arezki et al. result when applied to an oil discovery shock, we should be skeptical that that is the right model of the Great Recession.
3. Rational expectations: retrospect and prospects (pdf). Transcript of a 2011 panel discussion with Michael Lovell, Robert Lucas, Dale Mortensen, Robert Shiller, and Neil Wallace.

Friday, March 20, 2015

Forecasting long-term stock returns: the two-hour recipe (I)

Suppose you are given the following task:
Forecast the real total return of U.S. equities over the next ten years. Show your work. Time: two hours.
This post describes how I would go about fulfilling this assignment.


The first thing is to define total return:
$$R_{t,t+k}=\frac{P_{t+k}}{P_{t}}\prod_{s=1}^{k}(1+dy_{t+s})$$
where \(R_{t,t+k}\) is the gross total return between year \(t\) and year \(t+k\), \(P_{t}\) is the price of the stock or index at time \(t\), and \(dy_{t}\) is the income yield at time \(t\). (The income from a stock is dividends plus net repurchases by the issuer.) You can get to that equation by "rolling over" the one-period total return, as I show below.

The total return can be further decomposed into more manageable bits. If you divide the price level by a "fundamental" \(F\):
$$R_{t,t+k}=\frac{(P_{t+k} / F_{t+k})}{(P_{t} / F_{t})} \frac{F_{t+k}}{F_{t}}\prod_{s=1}^{k}(1+dy_{t+s}) = \frac{V_{t+k}}{V_{t}} (1+g_F)^k (1+\widehat{dy}_{t+1, t+k})^k$$
Now the total return is a function of three things:

1) The change of a valuation ratio \(V\).

2) The growth of a fundamental \(F\): \(g_F\).

3) The (geometric) average of income yield: \(\widehat{dy}_{t+1,t+k}\)

The question asked to forecast the real return, but for that you just need to divide through by the inflation factor \((1+\widehat{\pi}_{t+1, t+k})^k\), where \(\widehat{\pi}_{t+1, t+k}\) is the geometric average of the inflation rate between \((t+1)\) and \((t+k)\):

$$\frac{R_{t,t+k}}{(1+\widehat{\pi}_{t+1, t+k})^k} = \frac{V_{t+k}}{V_{t}} \frac{(1+g_F)^k} {(1+\widehat{\pi}_{t+1, t+k})^k} (1+\widehat{dy}_{t+1, t+k})^k$$

The "fundamental" \(F\) that goes in the valuation ratio could be anything, but you should probably pick a variable such that:

1) The resulting valuation ratio is "mean reverting" (over the relevant forecasting horizon, in this case ten years), and

2) You can forecast the growth of the "fundamental." Once you pick a particular valuation ratio, you are also committing to forecasting the growth rate of its corresponding fundamental.

Several such valuation ratios have been proposed in the finance literature. I list them in the following table:

Valuation ratio (V) Fundamental (F)
Price/dividend Dividend
CAPE (a.k.a. Shiller's PE) Ten-year average of real earnings
q ratio Net worth of corporations at market value
Market capitalization / GDP GDP
Price/total income Total cash flow (dividend + net repurchases)

The last ratio, price/total income, is really just a generalized version of the price/dividend ratio. I expect the two to be highly correlated, but I'll keep both for now.

Next you need a forecasting strategy, i.e. you need to put values on \(V_{t+k}\), \(\frac{(1+g_F)^k} {(1+\widehat{\pi}_{t+1, t+k})^k}\), and \((1+\widehat{dy}_{t+1, t+k})^k\) You only have two hours to do this whole thing, so you can't do a lot.

Off the top of my head, I would say you can either:

1) Use historical averages, using the entire history of data available.
2) Use the historical averages from a recent subset of the data available.

The strategy should depend on (a) how long are your historical time series, and (b) whether you suspect structural changes that shifted those averages over time, or make them drift.

Where should you get the data for this exercise? A lot of people use the Shiller's time series that go back to 1870. You won't get q-ratios or total cash flow or total market capitalization from Shiller's spreadsheet, so you would be limited to the CAPE and the dividend yield as valuation ratios. For today that will suffice.

The income component

Let's start with the last component of the return, the dividend yield: \( (1+\widehat{dy}_{t+1, t+k})^k\).

A cursory inspection of the time series suggests the dividend yield has declined over its entire history, but it seems relatively stable since the late 1990s. I would then use the most recent ten years to forecast the dividend yield over the next ten.

The Shiller dataset is monthly. For each December, I take the 12-month trailing average of the dividend series (column C), and I divide it by the price (column B). That's my estimated dividend yield for the year ended in December. Next I calculate the geometric average of the dividend yield between 2005 and 2014, which is 2.0082%. So my forecast for \(\widehat{dy}_{t+1, t+10}\) is 0.02.

The valuation ratio

Next, the valuation ratio. Let's start with the CAPE (cyclically-adjusted PE ratio). The chart below shows that the historical average (in green, 16.6) is much below today's CAPE (27.85) and also below today's ten-year rolling average (in red, 22.6). It does seem like the CAPE shifted upward sometime in the 1980s or 1990s, but we don't know whether that shift is permanent. We can use both the historical average and the ten-year rolling average to come up with alternative forecasts of the CAPE ten years from now.

[I ran out of blogging time today! I will continue next time.]
........................................................................................................................................................
Derivation of the multi-period total return formula:

The one-period total return is given by
$$R_{t,t+1} = \frac{P_{t+1}+D_{t+1}}{P_{t}}$$
If you reinvest the income \(D_{t+1}\) into the stock, that will buy you \(D_{t+1} / P_{t+1} \) additional stock units, for a total return of
$$R_{t,t+1} = \frac{P_{t+1}(1+D_{t+1} / P_{t+1})}{P_{t}} = \frac{P_{t+1}(1+dy_{t+1})}{P_{t}}$$
Next period you do the same thing, reinvesting \(D_{t+2}\) at price \(P_{t+2}\), for a total return
$$R_{t,t+2} = \frac{P_{t+2}(1+dy_{t+1})(1+D_{t+2} / P_{t+2})}{P_{t}} = \frac{P_{t+2}(1+dy_{t+1})(1+dy_{t+2})}{P_{t}}$$
When you generalize to \(k\) periods you get
$$R_{t,t+k}=\frac{P_{t+k}}{P_{t}}\prod_{s=1}^{k}(1+dy_{t+s})$$

Friday, March 13, 2015

Five facts about productivity

Global labor productivity is not slowing down; but it is slowing down, in many countries.

I have been playing with the labor productivity statistics from the Conference Board's Total Economy Database. Labor productivity is defined as real, PPP-adjusted GDP per person employed --using Geary-Khamis purchasing power parities. (Output per hour would be better, but many developing countries don't have data on hours.)

I smoothed the time series, country by country, using the Hodrick-Prescott filter (smoothing parameter = 100). The last data point available in the dataset is for 2013, but the last data point I use is 2010, to mitigate the end-point problem of one-sided filters such as Hodrick-Prescott.

The impression I have received lately is that productivity has stagnated or declined, but all the evidence seems to come from the U.S. or Western Europe. So the first thing I wanted to know is: Has labor productivity growth, for the world as a whole, declined?

This chart reveals Fact #1: World productivity growth has not slowed down significantly. Actually, average productivity growth was faster in 2000-2010 than in 1990-2000, although year-to-year growth seems to have plateaued in the second half of 2000-2010.

The chart shows the year-to-year growth of labor productivity growth. Each regional composite is constructed as the weighted average of country productivity growth, using the levels of real, total GDP as weights.

But both within developed markets and emerging markets output per worker is not growing as much as it used to. Among rich countries the deceleration is noticeable to the naked eye since the early 2000s, whereas in poorer nations the slowdown started in the mid-2000s.

This (superficial) paradox is possible, of course, because the share of emerging markets in world output has risen. So, Fact #2: World productivity growth has managed to stay constant through the 2000s because more and more output comes from emerging economies, where the level of productivity growth is higher

Next I compare the growth of productivity of two adjacent decades: 1990-2000 and 2000-2010. This map shows the change of (the geometric average of) productivity growth from one decade to the next. Green means an acceleration of productivity. The more intense the shade of green, the larger the increase of productivity growth. Shades of orange and red indicate a decrease of productivity growth. (Click here to see a bigger map, with values.)

The map shows the change in average productivity growth, by country, from 1990-2000 to 2000-2010. Source: Total Economy Database, author's calculations, http://gunnmap.herokuapp.com/.
The time series are here:

The chart shows the year-to-year growth of labor productivity growth. Each regional composite is constructed as the weighted average of country productivity growth, using as weights the levels of real, total GDP.

The chart shows the year-to-year growth of labor productivity growth. Each regional composite is constructed as the weighted average of country productivity growth, using as weights the levels of real, total GDP.
The map and the time series reveal the (largely expected) Fact #3: From one decade to the next, productivity accelerated in every major emerging region, and slowed down in every major advanced region

The Asiaphoria paper by Lant Pritchett and Larry Summers  made a lot of noise a while ago. In it the authors show that growth is not persistent in the long run: higher-than-average GDP growth in one decade tends to be followed by lower-than-average growth in the next. I wanted to know whether, from a casual observation of the data, that finding holds true for labor productivity, over the past two decades. On the following chart, the vertical (horizontal) axis shows the difference between country-specific productivity growth and the world productivity growth in 2000-2010 (1990-2000).

The chart shows, in the vertical axis, the difference between a country average productivity growth in 2000-2010 and the world average productivity growth in the same period. The readings along the horizontal axis are analogously defined. 

There is no correlation. If a country's productivity grows faster than the global average in one decade, that tells us nothing about excess productivity the next decade. If, instead, we look at excess productivity within advanced and emerging economies, the picture changes a little:



The chart shows, in the vertical axis, the difference between a country average productivity growth in 2000-2010 and the average productivity growth among advanced economies, in the same period. The readings along the horizontal axis are analogously defined. 

The chart shows, in the vertical axis, the difference between a country average productivity growth in 2000-2010 and the average productivity growth among developing economies, in the same period. The readings along the horizontal axis are analogously defined.
Productivity growth is in fact persistent within advanced economies, but there is no sign of persistence or reversion to the mean within emerging economies.

And so we have Fact #4: Within emerging economies, there is no significant persistence or reversion-to-trend of productivity growth in the long run. Within advanced economies, there is some evidence of persistent productivity growth.

Finally, I wanted to see if there appears to be unconditional convergence in productivity. This chart shows the average growth of productivity in 1990-2010 vs. the level of productivity in 1990. Unconditionally on stage of development, there is little relationship between level of productivity and subsequent productivity growth. But there are differences conditional on stage of development.

The chart shows, in the vertical axis, the average productivity growth in 1990-2010. The horizontal axis displays the log of the level of productivity in 1990. 

The chart shows, in the vertical axis, the average productivity growth in 1990-2010. The horizontal axis displays the log of the level of productivity in 1990. 

The chart shows, in the vertical axis, the average productivity growth in 1990-2010. The horizontal axis displays the log of the level of productivity in 1990. 
And that leads me to Fact #5: Within advanced economies there seems to be productivity convergence over the period 1990-2010. That's not the case, however, for developing economies.

Wednesday, March 4, 2015

Inflation round-up

The Reserve Bank of India is officially an inflation targeter. The agreement between the Ministry of Finance and the RBI was signed on February 20, and published a few days ago. The target is to "bring inflation below 6 per cent" by January 2016. For financial year 2016-17 and subsequent years the target will be 4±2%, so the acceptable inflation band will be 2%-6%. That would represent a significant reduction from the typical inflation rates in India since 2008.

RBI governor Raghuram Rajan has de facto followed an inflation target since the start of 2014, but the monetary policy framework was not official. Prior to inflation targeting, the RBI's policy target can be described as flexible, as it included, besides inflation, the rupee exchange rate and banking sector stability.

Amol Agrawal, at Mostly Economics, doesn't like the agreement.

------------------------------

Eurozone inflation expectations are sinking, say researchers at the New York Fed. Survey-based inflation expectations have been falling at the one, two, and five-year horizons. They're particularly worried that the whole distribution of inflation expectations is shifting down, not just the median, or the lower percentiles.

A report by Generali, however, shows that inflation expectations measured by inflation swaps have picked up during 2015.

------------------------------

Inflation, relatively: The following map shows inflation relative to each country's own history (the 10-year z-score), as of 2014-Q4. Despite abundant talk of Russian inflation, prices are increasing slightly more than they have, on average, over the past ten years, adjusted for standard deviation (z score of 0.13).

The highest inflation rates, relative to their own medium-term experiences, are for Argentina, Bolivia, Venezuela, Japan, and Gabon. The lowest inflation rates, relative to their own experiences, are in Greece, United Kingdom, Hungary, and Poland, in that order.

The eurozone is pretty green (meaning low inflation), but if you squint you'll notice that Sweden and Switzerland are experiencing relatively less deflation than their European neighbors. Even the U.S. is deviating more from its own history than Switzerland.

One-year inflation rate, 2014-Q4, 10-year z-score, relative to own country's history. Source: FactSet data, gunnmap.herokuapp.com, author's elaboration.


Friday, February 27, 2015

Sundry links

No time for writing this week, so I'm listing blog posts and articles that caught my eye recently:

1. Liftoff levers. John Cochrane is doing a fantastic job explaining how the Fed's reverse repo operations are supposed to work. Start with this post, and then read this other one.

2. A "new" working paper, by Katharina Knoll, Mortiz Schularick, and Thomas Steger, looks at global house prices in the really long run (1870-2012). From the abstract:
...house prices in most industrial economies stayed constant in real terms from the 19th to the mid-20th century, but rose sharply in recent decades. Land prices, not construction costs, hold the key to understanding the trajectory of house prices in the long-run. Residential land prices have surged in the second half of the 20th century, but did not increase meaningfully before. We argue that before World War II dramatic reductions in transport costs expanded the supply of land and suppressed land prices. Since the mid-20th century, comparably large land-augmenting reductions in transport costs no longer occurred. Increased regulations on land use further inhibited the utilization of additional land...
3. An Icelander goes to Cyprus and tells us why Cypriots keep cash worth 6% of GDP under the mattress.--Sigrún Davíðsdótti at A Fistful of Euros.

4. China's monetary and exchange rate framework under pressure.

           4.1 Huge FX inflows turn into small outflows, and the PBoC switches from draining renminbis to injecting them. To keep base money growing, the central bank has introduced new tools. By Gabriel Wildau for the Financial Times.

           4.2 Time to ditch the renminbi-dollar peg? The Chinese currency has depreciated and is hitting the central bank's target band.

           4.3 On the internationalization of the RMB, a colleague forwards several papers and reports
                 Paths to a reserve currency, at the Asian Development Bank Institute.
                 The rise of the redback, by HSBC.
                 Yuan is fifth world's payments currency, at the WSJ.
               
An important event to keep in mind is that the IMF is reviewing the SDR basket in 2015. China is under pressure to step up the internationalization of the renminbi, ahead of the basket review.

5. Dani Rodrik summarizes the results of his latest paper on de-industrialization.

Premature deindustrialization is not good news for developing nations. It blocks off the main avenue of rapid economic convergence in low‐income settings, the shift of workers from the countryside to urban factories where their productivity tends to be much higher.
Industrialization contributes to growth both because of this reallocation effect and because manufacturing tends to experience relatively stronger productivity growth over the medium to longer term. In fact, organized, formal manufacturing appears to exhibit unconditional convergence (Rodrik 2013), which makes it special and an engine of growth. Since low‐income countries tend to start with small manufacturing sectors, the dynamic within manufacturing initially plays a small role, overshadowed by the reallocation effect. But over time, the within‐manufacturing effect becomes a more potent force as the manufacturing sector becomes larger.Premature deindustrialization throws sand in the wheels of both engines (Rodrik 2013, 2014).
The consequences are already visible in the developing world. In Latin America, as manufacturing has shrunk informality has grown and economy‐wide productivity has suffered. In Africa, urban migrants are crowding into petty services instead of manufacturing, and despite growing Chinese investment there are as yet few signs of a real resurgence in industry. Where growth occurs, it is driven largely by capital inflows, transfers, or commodity booms, raising questions about its sustainability.  
In the absence of sizable manufacturing industries, these economies will need to discover new growth models. One possibility is services‐led growth. Many services, such as IT and finance, are high productivity and tradable, and could play the escalator role that manufacturing has traditionally played. However, these service industries are typically highly skill‐intensive, and do not have the capacity to absorb – as manufacturing did – the type of labor that low‐ and middle‐income economies have in abundance. The bulk of other services suffer from two shortcomings. Either they are technologically not very dynamic. Or they are non‐tradable, which means that their ability to expand rapidly is constrained by incomes (and hence productivity) in the rest of the economy.

I couldn't help but tie Rodrik's paper to that other paper by Pritchett and Summers, the one about regression to the mean of long-term growth rates. Growth is far from a uniform process. It tends to happen in fits and starts. Those who are projecting high growth rates of developing economies, based on past high growth rates, which in turn hinged on industralization, are probably going to be disappointed.

6. The translation industry.The Economist opines that translation is very hard for machines. Humans will need to stay involved, but technology will improve productivity.

A different question: Do improvements in translation bode well for language diversity in the world? How about the language learning industry? I see this as a race between technologies that allow machines to translate better, and technologies that allow humans to learn languages faster. The machines are winning, by a long shot. We're clearly on a path to better simultaneous translation capabilities. Soon we'll be able to listen to anything, anywhere in our native tongue, in real time. That means humans won't have to know more than one language. Learning languages will become a hobby, like dancing. (Sorry, parents, but you're wasting your money on Mandarin lessons.)

As for language diversity, I think a more important force than technology is urbanization. The lion's share of the world's languages are spoken by small, rural communities in developing countries. Urbanization increases the usefulness of majority languages, killing the minority languages. And urbanization will happen faster than the spread of cheap, simultaneous translation technology. At some point, however, the trend towards fewer and fewer languages will slow down, as simultaneous translation becomes pervasive.

Friday, February 20, 2015

Is aging deflationary?

Hideki Konishi, Kozo Ueda, and Mitsuru Katagiri presented a few months ago a paper titled "Aging and deflation from a fiscal perspective." Here are the slides.

The authors build a model that combines overlapping generations, the fiscal theory of price determination, and political considerations to analyze how the price level changes with fertility and longevity.

The simplified version of the model, in section two of the paper, assumes that taxes are exogenous. This simple version, nevertheless, is enough to produce a key result:
"Aging is deflationary when caused by an increase in longevity, but inflationary when caused by a decline in birth rate." 
The reason is political considerations:
"If the birth rate declines, the resultant contraction in the tax base reduces the fiscal surplus. The government is then inclined to maintain its solvency partly by generating inflation at the cost of the older generation's well-being and partly by making the younger generation pay more taxes. In contrast, if the life expectancy increases and older persons survive longer than expected, they might face a shortage of savings for their retirement period. The government then, led by the strengthened political influence of the older generation, attempts to suppress inflation and increase the real value of the government bonds held by the older generation."
Japan has experienced both unexpected declines in fertility and unexpected increases in longevity. The deflationary effect of higher longevity, however, dominated. The authors' simulations of the model show that Japan's aging depressed inflation by 0.6 percentage points annually.

Another key result, which comes from the fiscal theory of price determination, is that our children don't pay for our deficits. The government debt at the beginning of each period is fixed in nominal terms. Today's price level changes to equate the real value of today's debt with the present value of future deficits.

A corollary of this result is that tomorrow's fiscal policy is not constrained by today's level of debt or fiscal policy. Governments are unencumbered by the deficits of their predecessors in office.

A second corollary of the fiscal independence result is that governments don't have an incentive to strategically accumulate debt. In some political economy models of fiscal policy, a government can tie the hands of a successor it dislikes, by raising debt. If the price level, however, adjusts every year to fulfill the government's inter-temporal budget constraint, strategic debt accumulation doesn't happen.

I thought this paper was a refreshing way of looking at the link between deflation and aging.

+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

[The following list was edited on March 17, 2015.]

Other recent papers (post 2000) about this topic, in chronological order:

Fair, R. C. and K. Dominguez (1991), “Effects of the changing U.S. age distribution on macroeconomic equations”, American Economic Review, 81(5), pp 1276–94.

The effects of the changing U.S. age distribution on various macroeconomic equations are examined in this paper. The equations include consumption, money demand, housing investment, and labor force participation equations. Seven age groups are analyzed: 16-19, 20-24, 25-29, 30-39, 40- 54, 55-64, and 65+. There seems to be enough variance in the age distribution data to allow reasonably precise estimates of the effects of a number of age categories on the macro variables. The results show that, other things being equal, age groups 30-39 and 40-54 consume less than average, invest less in housing than average, and demand more money than average. Age group 55-64 consumes more and demands more money. If these estimates are right, they imply, other things being equal, that consumption and housing investment will be negatively affected in the future as more and more baby boomers enter the 30-54 age group. The demand for money will be positively affected. If, as Easterlin argues, the average wage that an age group faces is negatively affected by the percent of the population in that group, then the labor force participation rate of a group should depend on the relative size of the group. If the substitution effect dominates, people in a large group should work less than average, and if the income effect dominates, they should work more than average. The results indicate that the substitution effect dominates for women 25-54 and that the income effect dominates for men 25-54.


Lindh, T. and B. Malmberg (1998), “Age structure and inflation: A Wicksellian interpretation of the OECD data”, Journal of Economic Behavior and Organization, 36(1), pp 19-37.

Wicksell's cumulative inflation process is founded on the separation of investment and saving decisions. The demographic age structure influences the aggregate of both these decisions, and therefore should be one of the determinants behind the inflation processes. We study annual OECD data 1960–1994 using age variables to explain inflation. Panel estimations of a reduced form inflation-age model show a robust correlation consistent with the hypothesis that increases in the population of net savers dampen inflation while especially the younger retirees fan inflation as they start consuming out of accumulated pension claims. This pattern is expected from life-cycle saving but could also be due to age effects on budget deficits or on money demand. Our results are potentially important for inflation forecasts and monetary policy.


Lindh, T. and B. Malmberg (2000), “Can age structure forecast inflation trends?”, Journal of Economics and Business, 52, pp 31–49.

The demographic age structure influences the aggregate of individual economic decisions. Standard macroeconomic models imply that inflation pressure will covary with the age distribution unless accommodated by monetary policy. We estimate the relation between inflation and age structure on annual OECD data 1960–1994 for 20 countries. The result is an age pattern of inflation effects consistent with the hypothesis that increases in the population of net savers dampen inflation, whereas especially the younger retirees fan inflation as they start consuming out of accumulated pension claims. This can be explained, for example, with life-cycle saving behavior combined with a cumulative process of inflation, but other mechanisms are also consistent with the results. In any case, the results suggest that demographic projections may be useful for long- and medium-term inflation forecasts. Forecasts from our panel model catch the general downward trend in OECD inflation in the 1990s. However, useful forecasts for individual countries need to incorporate more country-specific information.


Bullard J., C. Garriga and C. J. Walker (2012), “Demographics, Redistribution, and Optimal Inflation,” Federal Reserve Bank of St. Louis Review, November/December 2012, 94(6), pp. 419–39.

The authors study the interaction among population demographics, the desire for intergenerational redistribution of resources in the economy, and the optimal inflation rate in a deterministic life cycle economy with capital. Young cohorts initially have no assets and wages are the main source of income; these cohorts prefer relatively low real interest rates, relatively high wages, and relatively high rates of inflation. Older cohorts work less and prefer higher rates of return from their savings, relatively low wages, and relatively low inflation. In the absence of intergenerational redistribution through lump-sum taxes and transfers, the constrained efficient competitive equilibrium requires optimal distortions on relative prices. The authors’ model allows the social planner to use inflation/deflation to try to achieve the optimal distortions. In the model economy, changes in the population structure are interpreted as the ability of a particular cohort to influence the redistributive policy. When older cohorts have more influence on the redistributive policy, the economy has a relatively low steady-state level of capital and a relatively low steady-state rate of inflation. The opposite happens when young cohorts have more control of policy. These results suggest that aging population structures, such as those in Japan, may contribute to observed low rates of inflation or even deflation.


Anderson, D., D. Botman and B. Hunt (2014), ”Is Japan’s Population Aging Deflationary?” IMF Working Paper 14/139, August.

Japan has the most rapidly aging population in the world. This affects growth and fiscal sustainability, but the potential impact on inflation has been studied less. We use the IMF’s Global Integrated Fiscal and Monetary Model (GIMF) and find substantial deflationary pressures from aging, mainly from declining growth and falling land prices. Dissaving by the elderly makes matters worse as it leads to real exchange rate appreciation from the repatriation of foreign assets. The deflationary effects from aging are magnified by the large fiscal consolidation need. Many of these factors will beset other advanced countries as well, but we find that deflation risk from aging is not inevitable as ambitious structural reforms and an aggressive monetary policy reaction can provide the offset.


Yoon, J.-W., J. Kim and J. Lee (2014), “Impact of Demographic Changes on Inflation and the Macroeconomy” IMF Working Paper 14/210 November.

The ongoing demographic changes will bring about a substantial shift in the size and the age composition of the population, which will have significant impact on the global economy. Despite potentially grave consequences, demographic changes usually do not take center stage in many macroeconomic policy discussions or debates. This paper illustrates how demographic variables move over time and analyzes how they influence macroeconomic variables such as economic growth, inflation, savings and investment, and fiscal balances, from an empirical perspective. Based on empirical findings—particularly regarding inflation—we discuss their implications on macroeconomic policies, including monetary policy. We also highlight the need to consider the interactions between population dynamics and macroeconomic variables in macroeconomic policy decisions.


Juselius, M. and Takáts, E. (2015), “Can Demography Affect Inflation and Monetary Policy?” BIS Working Paper 485, February.

Several countries are concurrently experiencing historically low inflation rates and ageing populations. Is there a connection, as recently suggested by some senior central bankers? We undertake a comprehensive test of this hypothesis in a panel of 22 countries over the 1955-2010 period. We find a stable and significant correlation between demography and low-frequency inflation. In particular, a larger share of dependents (ie young and old) is correlated with higher inflation, while a larger share of working age cohorts is correlated with lower inflation. The results are robust to different country samples, time periods, control variables and estimation techniques. We also find a significant, albeit unstable, relationship between demography and monetary policy.

Friday, February 13, 2015

Leveraging, deleveraging, and assets

The world might not be "deleveraging," but I wouldn't know just by looking at the debt-to-GDP ratio.

The latest update to the McKinsey Global Institute's "Debt and deleveraging" report says that
...debt continues to grow. In fact, rather than reducing indebtedness, or deleveraging, all major economies today have higher levels of borrowing relative to GDP than they did in 2007. Global debt in these years has grown by $57 trillion, raising the ratio of debt to GDP by 17 percentage points.
What does a debt-to-GDP ratio of, say, 286% mean? It means that if a country devoted all its income to paying down debt, it would take 2.86 years, at today's income level, to pay it all off. And if the ratio rises to 300% next year, it means the country's debts grew faster than its income.

At first consideration it makes sense to normalize debt levels across countries and over time using GDP. Bigger and wealthier nations should be able to support more debt than smaller or poorer ones. And if income grows over time, a country should have the capacity to borrow more.

The proceeds from borrowing, however, are (often) not consumed, but rather used to buy assets. And if you have more assets you should be able to bear more debt too.

Suppose you make $200k this year. You buy a house that costs $500k, making a $100k downpayment, and getting a $400k mortgage. You have no other assets or debt. Your debt-to-income ratio in year 1 is 2 ($400k / $200k).

Next year you make $200k again, save $100k, and buy another $500k house, with a $400k mortgage and $100 downpayment. The principal on the first mortgage is still $400k. Now your debt-to-income ratio is 4 ($800k / $200k). Your "leverage" is going up fast!

If you measure leverage a different way, however, you will see that debt is not going up at all. Continuing with the example above, the debt-to-equity ratio is 4 at the end of year 1 ($400 / $100), and still 4 at the end of year 2 ($800 / $200). Leverage is stable.

You could question whether servicing an $800k debt is a sane financial decision for somebody with a stagnant $200k income. But a broad discussion about "leverage" shouldn't leave the two houses out of the equation.

"Leverage," measured by the conventional debt-to-GDP ratio, has been going up in a number of countries for decades:








Other than Japan, debt-to-GDP has been generally going up in the long run.

You might think that the world has been on a multi-decade borrowing binge that will be, eventually, corrected. But while we wait for the Big Crash, we could entertain another possibility: the economy's balance sheet is just growing faster than income is.

I don't mean to say there's nothing to worry about. I have no clue whether national assets or equity have gone up in most countries, or whether the increase in the value of assets or equity matches the rise in debt. Besides, asset values can fall just as quickly as they rise. And, crucially, one needs to consider the distribution of assets and debt within the economy to make any assessment of "stability," "risk," or "sustainability."

Nonetheless, looking at rising debt-to-GDP ratios and concluding, as McKinsey does, that leverage is going up, which "poses new risks to financial stability and may undermine global economic growth," is quite a leap, to the say the least. A more complete assessment of "leverage" would be welcome.

P.S. Antonio Fatás has similar concerns about the McKinsey report.