Suicide and the Business Cycle
Here is a short summary of the lecture. The main goals of this lecture were to describe how we can measure the business cycle; to identify the costs of the business cycle and ask whether it is worthwhile to smooth the cycle; to narrow our focus to the issue of suicide by looking at possible economic models of suicide; to present a statistical method called logit regression; and to review a few empirical papers specifically dealing with suicide and unemployment.
We began the class by asking why it is reasonable to “assume the future will resemble the past”. This is called the problem of induction or the problem of Hume. It is the basis for all use of statistics in science and therefore it is a major philosophical problem. It always arises when we discuss the problem of causation. Usually students will answer this question by saying that we think that the future will be like the past because doing so has always proved to be useful in the past. This does not answer the question because it assumes that induction will remain useful in the future. It assumes what we are trying to establish. One of the students, Jan, made an insightful comment that if we don’t assume the future will be like the past, there will be too many alternative futures choose from. This is the logical attack on the problem of induction and is one of the few partially successful ways of answering the question. Essentially, we assume that the future will resemble the past because the alternative is chaos. Chaos means that we cannot plan. Our thoughts would also have to be chaotic too. Therefore, to be a human being requires that we assume the future will resemble the past. It follows that statistics and probability become useful for this reason. We cannot prove the world is orderly, but to assume otherwise is to assume chaos.
See the article on Hume in Wikipedia for the “problem of induction” by clicking on the following link
- Creating Business Cycle Data
Next, we described the business cycle.
The simplest way of describing or constructing this is to take the natural logarithm of real GDP and plot as a time series graph. We then subtract a deterministic linear trend from the log(GDP) series. This leaves us with the residual cycle which we take as the business cycle. Here is a graph of the cycle so constructed from the log of US GDP. Note how that it does a poor job in the 1960’s and after 2004. This always happens to the ends of our data sets. Usually the middle parts are more reliable.
Note also how that it is difficult to determine exactly when a recession began, ended, and how long it lasted.
There are other ways of constructing a business cycle from data on real GDP.
A popular method is the Hodrick-Prescott Filter
The follow function is minimized by choosing the changing trend.
where yt = log(real GDP) The variable λis usually taken to be 1600 for quarterly data. The business cycle can then be defined as
Cycle = yt - .
Gretl can be used to create an H-P decomposition of log real GDP. Here is what results when we plot the cycle using H-P’s methodology.
Note how that the 1960’s and post-2004 looks very different from the deterministic trend above. The H-P filter appears to produce a much better estimate of the business cycle.
Yet another way to create business cycle data is to use the Baxter-King Filter.
The basic idea is that a time series, such as the log of real GDP, can be written as a combination of sin and cos functions. Smooth trending data is mainly composed of low frequency-long, wavelength sin and cos functions. Cyclical time series are mainly composed of higher frequency, shorter wavelength sin and cos functions. Baxter and King proposed that one could obtain the business cycle by subtracting the long wavelength sin and cos components from the log GDP series. The very high components could be deducted also, since these changes too often to be business cycles. This would leave the medium length sin and cos components which would closely approximate the slowly changing economy.
GRETL can help us estimate the cycle using the B-K filter. When we use GRETL we get the following result.
Comparing the two filters shows that they have a sample correlation of 0.97
Thus, the two methods produce very close results. However, the correlation with the deterministic trend is much lower…roughly 0.60.
There are other ways of creating business cycle data.
The NBER, a private economic research center, has a celebrated business cycle dating committee which gives very precise estimates of the peaks and troughs of all business cycles. The NBER’s dating service is free and is used extensively by researchers.
Finally, it is possible to create a large scale econometric model and estimate the full employment level of national output. These potential output models are much harder to create but they have the advantage of being able to explain why the trend in GDP is changing. None of the other methods above can do this.
II. Costs of the Business Cycle
Next, we considered the question of what costs there are to the business cycle.
Oddly enough, it is not at all clear that the business cycle is something bad. Nor is it clear that we should attempt to reduce the fluctuation in output. That is, a case must be made for stabilization policy. The history of modern macroeconomics is a continuing fight over whether it is worthwhile to pursue stabilization policies such as monetary and fiscal policies. Franco Modigliani gives us a clear summary of this debate.
Modern macroeconomics began with the publishing of J.M. Keynes’ General Theory and J.R. Hicks’ explanation of Keynes. The worldwide Great Depression made it obvious that simply allowing the economy to self-correct was unacceptable. Active steps must be taken to force the economy to recover. Keynesian theory emphasized fiscal policy. During the 1960’s P. Samuelson and Modigliani modified and extended this Keynesian theory to better fit with standard economic notions, and this was called the Neoclassical Synthesis. Both Samuelson and Modigliani believed that there was still a role for government in reducing the severity of the business cycle and even in pre-empting such recessions. At the same time, M. Friedman was asserting that it was inadvisable for the government to attempt to pre-empt economic downturns and that such policies would lead to accelerating inflation over time. Lowering the inflation rate in the future could be extremely costly with rising unemployment. Instead, the government should take a very predictable monetary policy (a fixed money growth policy, if possible), hold down inflation, and not engage in wasteful and disruptive spending. With the growth in inflation during the 1970s and with the apparent failure of social welfare programs in the US, Friedman’s ideas became more and more acceptable. The 1980’s witnessed a further extension of Friedman’s ideas with the rational expectations revolution. It was shown that any attempt by the government to force the economy to recover would be foreseen by the public and the public would adjust to this making the policies completely ineffective. The very costly recessions of 1982 and later 1990 made the rational expectations revolution seem wrongheaded. Many economists have come to believe that there remains a short run tradeoff between inflation and unemployment. To stabilize the economy forces us to choose in the short run between low inflation and low unemployment.
While economists have emphasized the costs of recession in terms of unemployment and lost output and erratic consumption, sociologists and historians have rightly looked at a more general concept of social cost.
The broader aspects of social costs include –
(1)higher rates of suicide
(2)higher rates of crime and homicide
(3)higher rates of divorce
(4)higher rates of stress-based illness including heart attacks
(5)high risks that lower the incentive to invest
(6)higher rates of population movements and immigration
(7)dead weight losses due to uncertainties over the short run behavior of the economy
A complete study of each of these and their relations to the business cycle would take a whole semester. Instead we will concentrate on determining how that higher unemployment affects rates of suicide.
III Economic Models of Suicide
Economic models of suicide are all based on the concept of rational choice. People kill themselves because it is rational for them to do so. Rational means that people weigh up the costs and benefits from suicide and then make their decision based on that. In fact, all people-all the time must decide whether they will remain alive or not. If we are careless, it is easy to be injured. But how careful should we be? This is an economic decision since it requires us to take conscious action and spend resources to keep ourselves safe. Willful suicide can be seen as a conscious act in the face of a future devoid of utility.
By contrast, suicide can be seen alternatively as an impulsive act, done without clear judgment and on the basis of distorted views of one’s present circumstances and future opportunities. The influence of alcohol, drugs, extreme illness, or medication can make normal utility calculations very distorted. If this is present, then economic models cannot help us understand much of the tragic nature of suicide.
Economic models can be classified into about five different types:
(1)loss of income or assets models
(2)unemployment models
(3)supply and demand models
(4)signaling models
(5)afterlife models
The first of these emphasizes the fact that people become depressed whenever they suffer a loss of income or a loss of assets. The simple view of this is a stockholder who jumps out of a window after seeing his portfolio collapse in value. The natural response to this is to create programs that help to support income.
The second of these models emphasizes the pain of losing one’s job. The loss of self-esteem, the feelings of intense embarrassment, and all the attendant social pressures lead to despair and to thoughts of suicide.
The third of these models is unusual since it considers suicide an act that must be produced. It requires both a motive and a means. If barriers are erected that increase the cost of committing suicide, then suicide can be reduced. For example, it may be well for government to restrict the sale of sleeping pills if this opens the way to a quick and painless means of suicide.
The fourth type of model is the signaling model. This model emphasizes the idea of attempted suicide as a means of signaling concerned other parties of the depression one is feeling. This model is reasonable if one accepts that utilities can be interlocking. That is, if one’s utility is dependent on another’s utility then one may try to elicit care from others by attempting to harm oneself. This model does well explaining female suicide since generally speaking females attempt suicide more often than males. However, male suicide is generally more effective since more males die from suicide than females.
The fifth and final model is the most controversial. It assumes that some people may believe that utility does not stop at death. That is, there is an afterlife and utility associated with it. Moreover, one’s actions now may influence the reward one gets in the afterlife. This type of model can be used to explain the phenomenon of suicide bombing.
- Data and Empirical Studies
There are many data sets on suicide. The two major types of data which we have are time series data and cross sectional data.
What are the stylized facts regarding suicide?
First, the time series data showing the suicide rate in the US is much lower now than during the early part of the century. This is shown in the graph below
Note how that the rate hits a high of 19 suicides per 100,000 people right during the start of the Great Depression and remains high until the start of World War II. After 1970 we have the graph on the next page. The two graphs are not completely comparable since the definition of suicide is different. The general trends remain true.
The suicide rate began a steep fall beginning in 1990. One possible reason for this is the widespread use of anti-depressant drugs like Prozac.
If we try to correlate the suicide rate with the unemployment rate we get the following for the period 1900 - 1970:
Correlation Coefficients, using the observations 1900 - 1970
5% critical value (two-tailed) = 0.2335 for n = 71
suicide un
1.0000 0.5438 suicide
1.0000 un
and for the period 1960 – 2002
Correlation Coefficients, using the observations 1960 - 2002
5% critical value (two-tailed) = 0.3008 for n = 43
suicide u
1.0000 0.2522 suicide
1.0000 u
Clearly there is a much stronger association between suicide and unemployment in the period 1900 – 1970. The influence of the Great Depression is important here.
We can also consider some other countries.
Most countries show a falling suicide rate. But, Japan has experienced a stupendous rise in male suicide. The movement in suicide in Japan is closely correlated with the Japanese unemployment rate.
Note how that female suicide rates are stable or falling in Japan. Note also how that the unemployment rate and the male suicide rate are very closely related.
To understand many of the empirical works on suicide and unemployment, we must first study the method of logit regression.
Suppose that we let Yt be a binary qualitative dependent variable where Yt = 1 if the person commits suicide and Yt = 0 is the person does not commit suicide. We also let Xt = 1 if the person is unemployed and Xt = 0 if the person is employed. Suppose we survey 10 people and collect this data on each person. We then create a table like the one below.
We next assume that the probability of Yt = 1 (i.e., person commits suicide) given Xt= 1 (i.e., that the person is unemployed) is equal to P, which means that the probability of not committing suicide given Xt= 1 is (1 – P). The “odds” of committing suicide given Xt= 1 is therefore P/(1-P). Now, suppose we assume this “odds” is a log-linear function of Xt. This means that
where is a Normally distributed random variable.
DATA
Person = t Suicide = Yt Unemployment = Xt
1 0 0
2 1 1
3 1 0
4 0 0
5 0 1
6 0 0
7 0 0
8 0 1
9 1 1
10 0 0
Therefore, when Xt = 1 we know P/(1-P) = eα+βand also when Xt = 0 then
P /(1-P) = eα. Thus, the “odds ratio” is defined as
This shows that to compute the “odds ratio” we first estimate the regression
And get the estimate. We then proceed to compute the odds ratio .
The odds ratio shows how much more probable suicide is for the unemployed than for the employed. In other words, if the odds ratio is 3.5, then the probability of suicide for the unemployed is 3.5 times larger than for employed persons. We often hear such statistics on the news. For example, we often hear that smokers are 5 or 10 times more likely to suffer cancer than-smokers. This means the odds ratio is 5 or 10.
GRETL can help us compute logit regressions.
After reading in the data above, we use the set logit program.
We then enter the variables into the logit window.
After clicking on OK we have the following output.
The odds ratio can be computed from this output as follows.
ODDS RATIO = e1.60944= 5.0
The most impressive study on suicide and unemployment was done by Blakely et al and consisted of detailed data on 1.65 million men and women.
Note the OR (odds ratios) in the above table. It shows that for people 25-44 years of age, being unemployed raises the probability of suicide by roughly 2 and 1/2 times. The result does not hold up for women who are older than 45 years of age. The 95% CI in the table above refers to the 95% confidence interval for the Odd Ratio.
Similar results hold in UK studies. In summary, we find that unemployment is definitely associated with suicide. It remains unclear whether it is unemployment which causes suicides or whether suicide predisposes people to unemployment.