Monday, April 20, 2015

More deep thoughts about macro models

Jérémie Cohen-Setton at Bruegel does a great job, as usual, rounding up recent blog posts on a specific topic. This time: a critique of modern macro. Can the models built during the Great Moderation explain what happened after the Great Recession?

I would say that "raising the profile" of the financial sector within macro models helps--but I don't know whether a Copernican revolution is necessary. But, ultimately, we will always (literally, always) have to live with model uncertainty. Noah Smith makes this point well.

Thursday, April 16, 2015

Global financial stability: the IMF report

Financial stability has been a bubbling topic since 2008--although it never really stopped simmering since the emerging market crises of the 1990s. Over the past year or so, a dominant view seems to be forming that financial instability risks are rising, particularly among some emerging-market countries.

Here's a list of great articles or papers, and one oral presentation, on the topics of financial instability, financial crises, etc. I have perused recently:
Chapter 1 of the IMF's Global Financial Stability Report (pdf), published this week, warns of the main risks to global financial stability. Here's a summary of the report:

1. Financial stability risks have increased since October. Lower growth prospects and disinflation have prompted central banks to respond by loosening policy. The BoJ and the ECB are the most notorious examples, but other central banks have relaxed their monetary policy stances as well.

2. Emerging market financial stability risks have increased. Commodity price declines have hurt commodity exporters, while the corporate sector has increased its foreign currency indebtedness. Lower energy prices have impacted negatively firms in the energy sector. 

3. The fall in nominal yields, and flattening of the yield curve, are a threat to the life insurance and pension fund sectors, especially in Europe.

4. Monetary policy divergence has lead to a sharp increase in volatility in foreign exchange markets amid the appreciation of the U.S. dollar. Term premia are narrow in all three main currencies (dollar, euro, and yen). Asset valuations remain elevated, in part because of persistently loose monetary policy. Market volatility in general has increased.

5. Quantitative easing can boost inflation and growth, but it also encourages greater financial risk taking, so monitoring and addressing financial excesses is necessary. Additional policy measures are necessary to enhance the effectiveness of monetary accommodation.

The report also has special boxes for two sub topics:

  • The oil price fallout, explaining the channels through which the abrupt fall of oil prices could spawn financial vulnerabilities.
  • Russia's financial risks and potential spillovers.

Here are a few charts from the report that caught my attention. Having a good legal system helps a country de-leverage. According to the chart below, an index of the strength of the legal system explains 45% of the cross-sectional dispersion of de-leveraging:


An increasing number of short- and long-term European government bonds have a negative yield:


QE in the eurozone and Japan could lead to significant portfolio outflows. Eurozone investors might allocate up to €1.3 trillion abroad by the end of 2015, a good chunk of which would go to the U.S. Insurance companies and pension funds in Japan could invest as much as $559 billion, or 12.8% of GDP, in foreign assets by the end of 2017 (that's if announced policies are fully implemented and work to their fullest extent across the three reform arrows): 



Non-performing loans and write-offs are frighteningly high in the eurozone and Japan:


European life insurers are in the unsustainable business of writing long-term policies without assets of a correspondingly long duration, which has resulted in negative duration gaps. Moreover, many policies contain high return guarantees, which are unsustainable in a low-interest-rate environment. Insurers in Sweden and Germany have the largest mismatches: 


Despite the recent round of monetary policy easing in emerging markets, real rates are expected to rise in 2015 in almost all of them:


Debt of the non-financial (private and government) sector of emerging markets has increased dramatically since 2007:


A significant share of debt is owed by firms with poor interest-coverage ratios:


Friday, April 10, 2015

Global activity: mixed nowcasts

Fulcrum's nowcasting model shows that advanced economies have decelerated so far in 2015:


The slowdown is particularly persistent in the U.S., which is now estimated to be growing at 2% a year, half the pace of last fall:


China is growing at a fairly steady pace, and the eurozone's economy keeps picking up:



According to the Institute of International Finance's EM Coincident Indicator "EM GDP may have grown in 2015Q1 at its weakest pace since early 2009", or 1.8% q/q saar:


That's at odds, however, with the J.P. Morgan global composite output index, which picked up slightly from an average of 53.0 in Q4 (53.0) to 53.9 in Q1:


And, despite a plunge of the J.P. Morgan  U.S. composite in earlier months, output has rebounded of late:


And the HSBC emerging markets composite index looks fairly stable, not falling:



Thursday, April 2, 2015

Guest post: Are Australian investors (relatively) conservative?

Naomi Fink, CEO and founder of Europacifica Consulting, is my guest today, writing about the risk preferences of Australian investors.

In one of the preliminary documents leading to Australia’s Financial System Inquiry, authors speculated that the abundance of overseas financing for Australia might owe to a gap in risk preferences between domestic and foreign investors (no supporting evidence or parameter calibration was cited).

Anecdotally, yet consistent with this viewpoint, many players within the domestic financial sector tout about the supposed conservatism of Australian domestic investors.  But is there empirical evidence of such conservatism?

Firstly, following the argument made in passing in the preliminary FSI documents, if divergent risk preferences were the best explanation for Australia’s chronic current account deficits, they would explain Australia’s investment income deficit (the largest component of Australia’s external deficit), given the sensitivity of investment rather than trade to relative risk preferences.

The argument implies, first, that foreign investors should be categorically more risk-tolerant than Australians, who pay higher premiums to compensate for the higher risk of capital they export than what they receive on their lower-risk investments overseas.

The second implication of the argument is less obvious.  Risk preferences in financial economic models are typically parametric rather than variable. Extending this logic, Australia’s investment income deficit is the result of more consistently conservative attitudes among domestic investors in comparison to consistently risk-tolerant overseas counterparts.  This may seem to be splitting hairs, but the distinction is non-trivial.

Risk premiums may wax and wane alongside risk perception, while risk preferences among rational investors are typically more consistent over time.  But if this were so, we would expect to see behavioral evidence of consistently greater risk-aversion among Australian investors than their overseas counterparts.

We took it upon ourselves to perform our own stylised version of the missing calibration; a comparison of risk preferences among OECD countries (using equity market participation, per Vissing-Jorgenson (1997), Guiso (2002), and Guiso et al. (2008)).

This basic examination of parametric measures of relative risk tolerance undermines the hypothesis that Australian investors are relatively risk-averse.

Our results, shown in the chart below, not only argue against the notion that Australia is more risk-averse than the rest of the world: they show that Australia is one of the most risk-loving players in the OECD.  In this light, it is highly doubtful that relative risk preferences somehow structurally rationalize Australia’s income deficit.

Note: Arguments that Australia pays a higher premium on its debt because Australians are more risk-averse than the rest of the world fail to hold up to our calibration.
Source: Europacifica, OECD

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.