Monday, April 18, 2011

Laughing Our Way Out of a Recession

Don't ask me why, but the other day I was thinking about one of my all-time favourite opening sentences in an academic paper:

         "0.    Introduction.   Consider a light bulb."
         (Balkema and de Haan, 1974, p.792.)

It has a certain ring to it, doesn't it? It takes courage to begin a paper in that way. More courage than I have! From there, it was just a small leap to begin reminiscing about memorable light bulb jokes, but I'm not going to go down that track. Actually, I don't have a stock of econometrics jokes, though I recognize that many jokes are very "transportable" across professions. For instance, we could quite easily convert the line, "Once I couldn't even spell 'Engineer' - now I are one!", into something that hits a little closer to home, also beginning with an 'E'. But I digress!

In recent times there's been a lot of press relating to measuring 'happiness' (whatever that is), and to the idea that perhaps we should replace measures such as GDP with some sort of Gross National Happiness Index, at least for certain purposes. I'm not sure what I could possibly add to that discussion directly, but it got me thinking about how our mood is governed in part by the state of the economy, and that perhaps this is reflected in our use of humour to deal with both personal and economic depression.

A lot of cartoons that appear in newspapers and magazines relate, not too surprisingly, to political events and politicians. Political satire has always been popular. It's also the case that a decent number of these cartoons relate specifically to economic matters. Of course, I know that there is often an overlap between economics and politics. None the less, I think we'll all agree that we regularly see cartoons whose primary focus is some aspect of the economy.

Some of my favourite cartoons are those that appear in The New Yorker, a publication with an enviable history and reputation as an outlet for some of the best cartoonists we've seen in the past 85 years. This got me thinking: "I'll bet there's a relationship between the amount of attention that cartoonists pay to the economy, and the economic shape that we're in."

As usual, data are both the key and the problem. Fortunately, I own a copy of The Complete Cartoons of The New Yorker, which comes with two CD's containing all of the cartoons published by The New Yorker from its inception on 21 February 1925, to 16 February 2004. Not only is every single cartoon there, but there's also a searchable index. That index has a full written description of what one sees in every cartoon. Keep in mind that some cartoons have no caption at all - the picture says it all! So, a good written description is quite important if you're assembling an index.

Feeling a little lazy, I reluctantly deprived myself of the pleasant task of viewing all of the 68,647 cartoons individually, and then having to decide arbitrarily which ones were directed at The Economy. Instead, I took advantage of the searchable index. It worked like a charm!

So, now I had my data. The intensity of the 'economic cartoons' (as I'll call them, after Niño and Lesmes, 2009) is not simply the number that are published each year, but rather the contribution of this number to the total of all the cartoons in The New Yorker. The total number of cartoons in each issue has varied over the years. Also, we need to take account of the fact that the magazine began with 52 issues a year, but subsequently changed to its current number of 47 issues a year.

I decided to estimate an econometric model that 'explains' the percentage of The New Yorker cartoons that fall into the 'economic cartoons' category, on an annual basis. All of the data that I 'm going to be using are available in an Excel workbook on the Data page associated with this blog. My econometric analysis was undertaken, as usual, with EViews, and the associated workfile can be accessed from the Code page of the blog.

Given that the 2004 data for the cartoons were truncated in February, I worked with the figures from 1925 to 2003. Here's a histogram of the data I wanted to model:

The data values range from 0.3% to 4.8% p.a., with a mean of 2.2% and a standard deviation of 1.2%.

I'm not aware of any general economic theory of humour, so my modelling is going to be a bit ad hoc. There's a number of sociological and anthropological theories of humour, and if you think they may interest you, then you can dip into the piece by Alford & Alford (1981), or wade through Chapman and Foot (1976). However, these are not for me.

Despite the fact that there's much about jokes that really can't be quantified, there have been various attempts at statistical analyses of humour, ranging from Eysenck (1944) to Corduas et al. (2008). However, these are of little help here. After days of reading copious amounts of material from the linguistics and psycho-anthropological literatures, I arrived at the following working hypothesis:

The state of the economy and our need for a good laugh about it, move in opposite directions.

So, here are some of the (measurable) factors that I thought might be important in determining the propensity for economic cartoons:

  • Business cycle: As measured by one or more of - Peak year; Trough year; time from Peak-to-Trough; time from Trough-to-Peak; months elapsed from Peak to start of year; months elapsed from Peak to mid-point of year.
  • Presidential Election year: Measured with a dummy variable.
  • Presidential Party: Measured with a dummy variable for Republican or Democrat.

My priors are: (1) when people realize that the economy has "peaked", and has turned down, they'll be glad of some light relief; and (2) the economy is going to get more attention from cartoonists in an election year. I'm going to claim that as a Canadian, I'm a priori ignorant about U.S. political parties. In any case, the 'party' dummy proved to be insignificant.

I'll  work with the logarithm of the percentage of 'economic cartoons'. When this series is plotted over time, with the NBER business cycle recessions shaded in, this is what we get:

This last time-series is stationary (according to the ADF and KPSS tests), and we see that there is a mild (but very imperfect) tendency for economic cartoons to become more prevalent during recessions.

I'm not pretending that the three factors noted above are the only ones that may be important. For example, we could take a look at who was the Cartoon Editor of The New Yorker in each year, and take account of their political leanings, if any; or their interest in economic affairs. Also, cartoonists know about comparative and absolute advantage, so different cartoonists specialize to some degree in different broad topics. I'm not taking account of those (and some other) things here, but I have some on-going research that attempts to do so. Here's just a really simple example of what emerged from my analysis.

Using a 'general-to-specific' modelling strategy, and applying the usual range of diagnostic tests, I arrived at the following estimated model (with Newey-West standard errors in parentheses):

log(RATIOt) = 0.167 + 0.270 PEAKt-1 + 0.401 PRESt                     
                    (0.126)  (0.160)               (0.164)
                     + 0.458 log(RATIOt-1) + residualt   ;  R2 = 0.271
                       (0.109)

To be specific, the variables in the model are:

RATIO =100*(No. of 'economic catoons' p.a.) / (Total no. of cartoons p.a.)
PEAK = 1, if the business cycle peaked that year; = 0, if it did not.
PRES = 1, if there was a Presidential Election that year; = 0, if there was not.

The one-year lag on the business cycle peak seems reasonable, given the delays involved in 'dating' these cycles; and my Presidential prior is fulfilled. Econometrically, this model appears to be quite well specified - the Breusch-Godfrey LM tests indicate that there is no serial correlation in the errors; and the Jarque-Bera test indicates that they are normally distributed (p = 0.49)

The Actual/Fitted/Residual plot looks like this:

Interpreting the estimated coefficients of the 'Peak' and 'Election dummy variables, and allowing properly for the log-linear form of the model, we see that: (1) if the business cycle peaked in the previous year, the percentage of cartoons that are 'economic' will be 29.3% higher than if it did not peak; and (2) if it is a Presidential election year then  this percentage will increase by 47.3%, relative to non-election years. (If you're not sure how these numbers were calculated, see my previous posting titled 'Dummies for Dummies'.)

I then used the model for some simple forecasting. I re-estimated the model using the shorter sample period, 1925 to 2000. The details are in the EViews file, but suffice to say that nothing really changed. This robustness in itself is of some comfort. I then produced both 'static' and dynamic' forecasts of the percentage of 'economic cartoons' (not the log of the percentage of such cartoons) for the years 2001 to 2003.  In the first forecast period static and dynamic forecasts are identical, by construction. After the first period, dynamic forecasts are generated by using the predicted value of log(RATIOt-1), rather than its observed value, in the forecasting equation. In real-life ex ante forecasting, this is what you would have to do. Here's how my forecasts compared with the actual data:

                Year        Actual          Static Forecast      Dynamic Forecast
                                 (%)                     (%)                          (%)
      
                2001         2.01                   1.89                        1.89
                2002         2.99                   2.10                        2.04
                2003         1.91                   1.99                        1.66

The forecasts are reasonable, but generally on the conservative side - especially the dynamic ones.

I'm not suggesting that you should bet the bank on this little model. However, if you enjoy first-class cartoons about about economic affairs, or the state of the economy, perhaps a good time to purchase a copy of The New Yorker is just after the economy has peaked - especially if it's a Presidential election year.

Then just let the good times roll!


Note: The links to the following references will be helpful only if your computer's IP address gives you access to the electronic versions of the publications in question. That's why a written References section is provided.

References
Alford, F.and R. Alford (1981). A holo-cultural study of humor. Ethos, 9, 149-164.

Balkema,  A. and L. de Haan (1974). Residual life at great age. Annals of Probability, 2, 792-804.

Chapman, A. and H. Foot, eds. (1976). Humour and Laughter: Theory, Research, and Applications. Wiley, London.

Corduas, M., S. Attardo and A. Eggleston (2008). The distribution of humor in literary texts is not random: A statistical analysis. Language and Literature, 17, 253-270.

Eysenck, H. J. (1944). National differences in 'sense of humor': Three experimental and statistical studies. Journal of Personality, 13, 37-54.

Mankoff, R., ed. (2004). The Complete Cartoons of The New Yorker. Black Dog and Leventhal, New York.

Niño, J. V. and P. R. Lesmes (2009). Cartoons and economics: General analysis based on Colombian economic cartoons. Working paper, Faculty of Economics, University of Rosario.


© 2011, David E. Giles

4 comments:

  1. Hi Prof, could I ask, for in-sample forecasting, is static forecasting supposed to be more accurate/better than dynamic forecasting?

    ReplyDelete
    Replies
    1. Within sample, the static "forecast" just equals the usual "fitted" values. If there are lagged values of the dependent variable entering as regressors, then there becomes a distinction between "static" and "dynamic" forecasts. The latter are constructed using the predicted lagged values of y as inputs into the forecasts, rather the actual lagged values. Because it's the actual values that were used to estimate the, usually (but not necessarily) the static forecasts will generally be more accurate (in a mean-square sense)than the dynamic forecasts, within-sample.

      For out-of-sample "ex ante" forecasting (the real world), you HAVE to use dynamic forecasts, at least if you are forecasting (p+1) or more periods beyond the sample, where p is the max. lag of the dependent variable appearing as a regressor. This is because you won't know the actual values of the regressors.

      For out-of-sample "ex post" forecasting, where you have "held back" some sample observations, not used them estimation, but then use them for predicting as a diagnostic check on the model, you can construct either static or dynamic forecasts. Generally, dynamic forecasting constitutes a more tougher "test" of the model.

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  2. Thanks Prof for your explanation. I ran the equation "spot spot(-1)" in Eviews to simulate random walk, where spot represents oil price. I used % of correct signs to compare my forecasts with the actual change in price so as to test for the accuracy for the model. What's peculiar is that the dynamic forecasts has higher % correct signs than static forecasting's. Do you think it's pure coincidence or?

    If my equation is "y = y(-1) + x(-2)", hold-out period from say 2005-2010 and I would like to conduct "ex-post" out-of-sample dynamic forecasting for 2010-2012. Apparently EViews require me to have the values of x till 2012. Is that saying if I am "ex ante" dynamic forecasting, I would need to have expected future values of x?

    Appreciate your help.

    ReplyDelete
    Replies
    1. Ex ante forecasting is like real life. You can only proceed if you know the values of the regressors in the forecast period. This is the case for ANY regession model. With large forecasting models, the modellers either "assume" likely values for the X variables in the forecast, to use them as inputs into the forecasting equation (using the estimated coefficients, of course); or else they SEPARATELY forecast the X variables first - e.g. using ARIMA models - and use this information when forecasting using the original equation.

      Delete