Economics 421 - Econometrics

"Cereal Correlation "

This is from The Monkey Cage:

56% of women who consumed the most calories before conception gave birth to boys, compared with 45% of those who consumed the least. Of 132 individual foods tracked, breakfast cereal was the most significantly linked with baby boys.

That’s from a study by researchers at Exeter and Oxford, as per Melinda Beck’s write-up in the Wall Street Journal.

This made me wonder. After all, my brothers and I turned out to be, well, boys, and my mother never ever ate breakfast cereal. However, as a social scientist I recognize that correlational results admit of exceptions.

They also, as Beck notes, occasion doubt. One of the first things one is supposed to learn about “statistical significance” is that some results that appear to be real, aren’t. If you’re operating at the .05 significance level, then in the long run somewhere around 5% of the relationships that you accept as non-random should really be random. Those are “Type 1” errors — or are they “Type 2” errors? I could never keep those straight. (Andrew, though not not a frequentist, presumably can straighten me out here.) Anyway, these breakfast cereal results apparently have produced a minor kerfuffle among epidemiologists and statisticians, which you can read about in the Beck article. If nothing else, this episode provides a nice example for those who are teaching intro methods courses, and it also gives “Monkey Cage” readers an opportunity to admire the excellent pun I devised for the headline of this item. (Please hold your applause.)

The Relationship Between Input and Output Price Inflation

David Altig's post at macroblog on the relationship between shocks to the producer price index (PPI) and changes in the (CPI) piqued my interest [originally here]:

macroblog: The February PPI -- Hot Or Not?: ...A few years back, Jonathon Weinhagen took a look at what we think we know about the relationship between producer prices and broader measures of consumer prices. If terms like "VAR", "variance decompositions", and "impulse responses" mean something to you, you may want to take a look at his article, which appeared in the November 2002 edition of the Monthly Labor Review. If that doesn't sound too interesting to you, here is what Jonathon concluded:

Several authors have investigated the causal relationship between commodity prices and consumer inflation... The common finding in the majority of these studies was that the power of commodity prices to predict CPI inflation has diminished since the 1980s...

To take a quick look at this issue, I downloaded data on real GDP, the federal funds rate, the CPI for all items, the core CPI (less food and energy), the all item PPI, the crude goods PPI, the intermediate goods PPI, and the finished goods PPI from the St. Louis Fed web site (FRED). All data except the federal funds are logged, and the PPI and CPI indices are differenced to obtain inflation rates. Real GDP enters in levels, but using differences does not change the results meaningfully.

These data are used to estimate a VAR model. For those who are unfamiliar with these models, they are general reduced form models of the form:

where L is the number of lags; 2 lags are used here. These models are able, with some assumptions about the underlying structure that aren't apparent from these equations (on that issue, this uses a Choleski decomposition and the ordering is as shown), to show how each variable in the system responds to a shock to other variables. Various definitions of the CPI (all items and core) and the PPI (all items, crude, intermediate, and finished goods) are used. Here are the results showing how the CPI variously defined responds to shocks to each of the definitions of the PPI. The horizontal axis shows the number of quarters after the shock. The graphs are called impulse response functions:

The main result, at least in this particular specification of the empirical model, is that both core and overall inflation (as measured by changes in the CPI or core CPI) are least responsive to shocks to inflation in crude materials prices. In addition, the response of core inflation to shocks to input price inflation is more persistent than the response of overall inflation. The paper David cites notes differences in the results by sample period, and the results shown here are for the entire available sample, 1959:Q1 to 2005:Q4 with allowances for lags, so sub-sample results may show differences. This does, however, agree with the basic result from the paper that shocks to input prices at earlier stages in processing, in this case crude materials, have a smaller impact on output prices than shocks to prices at later stages of production.

Paul Krugman's Introduction to Keynes' General Theory

I thought some of you might want to read this. It's Paul Krugman's introduction to Keynes' General Theory of Employment, Interest, and Money:

Introduction by Paul Krugman to The General Theory of Employment, Interest, and Money, by John Maynard Keynes

SYNOPSIS:

Introduction

In the spring of 2005 a panel of “conservative scholars and policy leaders” was asked to identify the most dangerous books of the 19th and 20th centuries. You can get a sense of the panel’s leanings by the fact that both Charles Darwin and Betty Friedan ranked high on the list. But The General Theory of Employment, Interest, and Money did very well, too. In fact, John Maynard Keynes beat out V.I. Lenin and Frantz Fanon. Keynes, who declared in the book’s oft-quoted conclusion that “soon or late, it is ideas, not vested interests, which are dangerous for good or evil,” [384] would probably have been pleased.

Over the past 70 years The General Theory has shaped the views even of those who haven’t heard of it, or who believe they disagree with it. A businessman who warns that falling confidence poses risks for the economy is a Keynesian, whether he knows it or not. A politician who promises that his tax cuts will create jobs by putting spending money in peoples’ pockets is a Keynesian, even if he claims to abhor the doctrine. Even self-proclaimed supply-side economists, who claim to have refuted Keynes, fall back on unmistakably Keynesian stories to explain why the economy turned down in a given year.

In this introduction I’ll address five issues concerning The General Theory. First is the book’s message – something that ought to be clear from the book itself, but which has often been obscured by those who project their fears or hopes onto Keynes. Second is the question of how Keynes did it: why did he succeed, where others had failed, in convincing the world to accept economic heresy? Third is the question of how much of The General Theory remains in today’s macroeconomics: are we all Keynesians now, or have we either superseded Keynes’s legacy, or, some say, betrayed it? Fourth is the question of what Keynes missed, and why. Finally, I’ll talk about how Keynes changed economics, and the world.

WSJ Econoblog: Stitching a New Safety Net

Andrew Samwick of Dartmouth (in 2003 and 2004, he served as the chief economist on the staff of the President's Council of Economic Advisers) and I just finished an Econoblog for the Wall Street Journal Online. The issue we were asked to address is:

WSJ Econoblog: Stitching a New Safety Net: For many years, workers could manage their medical expenses with employer-provided health insurance and Medicare and look forward to underwriting their golden years with payments from a defined-benefit pension and Social Security.

But the landscape of social insurance is shifting. Many large corporations are moving their employees from traditional pensions to riskier 401(k)s and asking workers to pay more out of their own pockets for health insurance. At the same time, Social Security and Medicare, the two venerable entitlement programs, are facing growing demographic strains as the vast baby boom generation reaches retirement age.

The Wall Street Journal Online asked economist bloggers Mark Thoma and Andrew Samwick to explore how we how arrived at this point and discuss what workers and retirees might expect in the future, as the composition of the social safety net continues to shift.

Here's the free link once again. And thanks to Andrew for an enjoyable discussion. [Originally posted here]

Technology and Class Attendance

I posted this on my blog today about posting class material on the web and how that impacts class attendance. I'd be curious to hear your comments (you might be interested in the comments people have left):

The Perils of Economic Forecasting

Here's something on economic forecasting that might be of interest:

Wall Street Journal Econoblog, The Perils of Forecasting: If economic forecasts are so often wrong, what value do they have? What's the real-word cost of a bad forecast? The Wall Street Journal Online asked bloggers James Hamilton and Kash Mansori to sort through the issues.

 

The Environmental Performance Index

In case this is of interest, this is from John Whitehead of the Environmental Economics blog. For some reason, they gave me keys to the door and I post stuff there once in awhile, though it's mostly just links to articles:

John Whitehead, Environmental Economics, How is the U.S. really doing on the 2006 Environmental Performance Index?: The U.S. ranks 28th in the world in achieving certain environmental goals according to the Environmental Performance Index produced by Yale and Columbia. Yesterday Mark Thoma linked to a NYTimes article which could be interpreted as implying that the U.S. should be doing better.

The analysis conducted in the reports puts the U.S. under the line. In other words, the U.S. is doing worse than expected given its income level. I wondered if this were true. Using a slightly more complicated analysis it appears that the U.S. is doing about as well as it should be doing.

First, the economic theory of achieving environmental goals considers the benefits and costs. One factor that affects the benefits of achieving environmental goals is income. Many economists believe, and have found in studies of individual and country-level demand for environmental quality, that the demand for environmental quality (i.e., benefits) increases with income. The costs of achieving environmental goals depends mostly on technology such as knowledge of the capital equipment needed to achieve environmental goals and policy instruments (e.g., marketable permits, command and control). Technology should be constant across countries.

Since one of the primary determinants of the demand for environmental quality varies across countries it is possible to estimate whether income is a determinant of how effective countries are at achieving environmental goals, measured by the EPI.

Fortunately, the EPI report includes an Excel file with all of the data necessary to estimate a simple model. I took the data and used regression analysis to estimate the effect of a country's per capita GDP (i.e., average income) on the EPI while holding constant the region of the world (i.e., Americas, European Union, etc). The EPI did not include these control variables. Here are the results:

EPI = 60.5 + .00215*(GDP/pop) - .00004*((GDP2/pop)/1000)

GDP/pop is GDP per capita and (GDP2/pop)/1000 is GDP squared divided by 1000. The regional effects are not shown but they indicate that the Americas has a higher EPI than the rest of the world. The independent variables (GDP, etc) explain about 75% of the variation in EPI, which is pretty good.

This model tells us that EPI increases with GDP but at a decreasing rate. In other words, the EPI is subject to diminishing returns. An country can improve its environmental performance with increasing gains in per capita GDP but these gains are smaller and smaller as GDP per capita increases.

One way of thinking about this model is as a production function. The input is income and the output is EPI. Plug in a country's GDP and region and the model will tell you how that country should be doing. Countries that have a positive difference between their EPI and the predicted EPI are doing better than expected. Countries that have a negative difference are doing worse than expected.

The U.S. ranks 28th in the world in EPI. The U.S. ranks 29th in the world. The U.S. EPI is 78.5 and the predicted EPI is 78.4514. The multiple regression model predicts the U.S. performance almost perfectly. The U.S. is achieving environmental goals about as well as expected given its GDP per capita.

Which countries are doing better than expected? They are all relatively poor:

 

	Country	EPI	Predicted EPI
1	Gabon	73.3	57.8956
2	Lebanon	76.7	61.7754
3	Malaysia	83.3	69.4951
4	Zimbabwe	63	50.621
5	Ghana	63.1	51.4095
6	Uganda	60.8	49.8188
7	Nepal	60.2	49.3573
8	Tanzania	59	48.1737
9	Sri Lanka	64.6	54.148
10	Benin	58.4	49.2083

Which countries are doing worse than expected? Again, they are all relatively poor:

	Country	EPI	Predicted EPI
124	Romania	56.9	66.6398
125	Turkmenistan	52.3	63.4779
126	Ethiopia	36.7	48.3823
127	Angola	39.3	51.0169
128	Mexico	64.8	77.2201
129	Mali	33.9	48.5901
130	Haiti	48.9	63.6234
131	Mauritania	32	50.4217
132	Chad	30.5	50.0206
133	Niger	25.7	48.5901

Of course, this isn't the whole story. There are a host of other variables that could potentially help explain the variation in the EPI. For example, increases in population density could limit the ability of countries  to achieve environmental goals. GDP could be high (or rising rapidly) because of sustainable factors (e.g., high labor productivity) or unsustainable factors (e.g., exploitation of natural resources). Maybe I'll think about this next week.

Also, I really should read the damn report and appendices before I naively plug the numbers into the computer and make them scream! Maybe next week.

And, feel free to make unreasonable demands for additional analysis!

One more thing: why didn't the authors of the EPI report do the multiple regression analysis?

New Support for Friedman's Plucking Model

[For those who might be interested ... originally posted here.]

Milton Friedman's "plucking model" is an interesting alternative to the natural rate of output view of the world. The typical view of business cycles is one where the economy varies around a trend value (the trend can vary over time also). Milton Friedman has a different story. In Friedman's model, output moves along a ceiling value, the full employment value, and is occasionally plucked downward through a negative demand shock. Quoting from the article below:

In 1964, Milton Friedman first suggested his “plucking model” (reprinted in 1969; revisited in 1993) as an asymmetric alternative to the self-generating, symmetric cyclical process often used to explain contractions and subsequent revivals. Friedman describes the plucking model of output as a string attached to a tilted, irregular board. When the string follows along the board it is at the ceiling of maximum feasible output, but the string is occasionally plucked down by a cyclical contraction.

Friedman found evidence for the Plucking Model of aggregate fluctuations in a 1993 paper in Economic Inquiry. One reason I've always liked this paper is that Friedman first wrote it in 1964. He then waited for almost twenty years for new data to arrive and retested his model using only the new data. In macroeconomics, we often encounter a problem in testing theoretical models. We know what the data look like and what facts need to be explained by our models. Is it sensible to build a model to fit the data and then use that data to test it to see if it fits? Of course the model will fit the data, it was built to do so. Friedman avoided that problem since he had no way of knowing if the next twenty years of data would fit the model or not. It did. I was at an SF Fed Conference when he gave the 1993 paper and it was a fun and convincing presentation. Here's a recent paper on this topic that supports the plucking framework (thanks Paul):

Asymmetry in the Business Cycle: New Support for Friedman's Plucking Model, Tara M. Sinclair, George Washington University, December 16, 2005, SSRN: Abstract This paper presents an asymmetric correlated unobserved components model of US GDP. The asymmetry is captured using a version of Friedman's plucking model that suggests that output may be occasionally "plucked" away from a ceiling of maximum feasible output by temporary asymmetric shocks. The estimates suggest that US GDP can be usefully decomposed into a permanent component, a symmetric transitory component, and an additional occasional asymmetric transitory shock. The innovations to the permanent component and the symmetric transitory component are found to be significantly negatively correlated, but the occasional asymmetric transitory shock appears to be uncorrelated with the permanent and symmetric transitory innovations. These results are robust to including a structural break to capture the productivity slowdown of 1973 and to changes in the time frame under analysis. The results suggest that both permanent movements and occasional exogenous asymmetric transitory shocks are important for explaining post-war recessions in the US.

Let me try, within my limited artistic ability, to illustrate further. If you haven't seen a plucking model, here's a graph to illustrate (see Piger and Morley and Kim and Nelson for evidence supporting the plucking model and figures illustrating the plucking and natural rate characterizations of the data). The "plucks" are the deviations of the red line from blue line representing the ceiling/trend:

Notice that the size of the downturn from the ceiling from  a→b (due to the "pluck") is predictive of the size of the upturn from b→c that follows taking account of the slope of the trend. I didn't show it, but in this model the size of the boom, the movement from b→c, does not predict the size of the subsequent contraction. This is the evidence that Friedman originally used to support the plucking model. In a natural rate model, there is no reason to expect such a correlation. Here's an example natural rate model:

Here, the size of the downturn a→b does not predict the size of the subsequent boom b→c. Friedman found the size of a→b predicts b→c supporting the plucking model over the natural rate model.

Household Debt Payments and Unemployment

This is something I posted on my blog tonight.  Fun with regressions:

Here is a graph of household debt service payments as a percent of disposable personal income from 1980Q1-2005Q3, the latest period for which consistent data exist (total financial obligations show a similar pattern):

I wanted to see how the debt load related to economic downturns, so the shaded areas are NBER dated recessions. It's hard to see a strong association between the recessions and changes in debt. The next graph plots the same series along with the negative of the unemployment rate. The association appears much stronger:

To see if regression confirms the association, I ran OLS on

           %Debt_t = β₀ + β₁%Debt_t-1 + β₂%Debt_t-2 + β₃UN_t + e_t

and it does (debt data described here). The coefficient on UN is significant at the 5% level:

     Linear Regression - Estimation by Least Squares
     Dep Var PERCENTDEBT
     Quarterly Data:  1980:03 To 2005:03
     Usable Observations             101
     Degrees of Freedom               97
     Durbin-Watson Statistic    2.014351

     Variable        Coeff          T-Stat     Signif
     ***************************************************
        β0        0.468304856      1.49629   0.13782438
        β1        1.125298228     11.06370   0.00000000
        β2       -0.150035410     -1.48249   0.14145135
        β3       -0.024721984     -2.01484   0.04668936

As you interpret the second graph, remember that it's the negative of the unemployment rate. Thus, when the blue line is rising, unemployment is falling. In the regression results the actual unemployment rate, not the negative of it, is used. This is a fairly broad brush and it may hide detail such as differences by income class, and omitted variables are a concern, but in general these data and this model suggest unemployment and the debt percentage are negatively related.