The Effect of No Child Left Behind on the Percentage of Students Enrolled in Special Education Classes

I thought I'd use this post to discuss my other major research project that I have worked on throughout my college career. I also wrote this paper in my Junior year during my two semesters of econometrics. First off, it's probably good to go through a quick run down of what econometrics is. In a previous post, I said that I often refer to economics as a type of applied sociology. In a similar vein, I often describe econometrics as applied statistics. Just like any other scientists, economists attempt to answer questions using the Scientific Method. We form a hypothesis, test that hypothesis, draw conclusions, make adjustments, and repeat. Unlike most other sciences, however, it is often hard to develop controlled experiments to test economic theories. (Most people don't like it when you mess around with prices and incentives in the free market just to do some research). There is a branch of economics--experimental economics--that does just this in controlled settings, but this is a relatively small portion of the field. To get around these obstacles, economists use methods of statistics to control for observations and isolate variables in order to obtain ceteris paribus (all else equal) results. I'm actually taking a statistics class right now as part of my applied economics Masters program.

Anyway, about the research. The No Child Left Behind Act of 2001 (NCLB) was signed into law by President George W. Bush on January 8th, 2002. The purpose of this Act is "to close the achievement gap with accountability, flexibility, and choice, so that no child is left behind" (107th Congress, 2002). Part of NCLB was designed specifically with disabled students in mind. This legislation requires schools to administer state-wide standardized tests to their students in order to determine a "grade" for the school itself--to determine if each school has been accountable to its students. Each state is allowed to create its own tests, but each school must demonstrate "Adequate Yearly Progress" (AYP), else face decreased funding,  school restructuring, or mandatory school choice (I actually like the idea of school choice, but that's for another post).

The fundamental assumption of this legislation is that NCLB will force schools to increase teacher quality and accountability to students in order to achieve AYP, thereby decreasing the gap between low- and high-achieving students. As with most legislation, however, this Act creates incentives which may lead to some unintended consequences. For example, the calculus of school administrators will likely be changed by this legislation. Because schools, instead of students, bear more directly the cost of poor student achievement, school administrators are incentivized to "game the system" by placing marginally-performing students into special education classes. Although all students (including special education students) are required to take the state assessments, NCLB allows for accommodations--such as increased time--for students placed in these classes. By placing marginally performing students who would otherwise not be considered candidates for special education into these classes, the school is able to reduce the negative impact that these students will have on average regular-education scores, and perhaps boost the average scores of special education students.

Let's think of exactly why this might be. Consider a very simple example: a school with 10 students (Named A, B, C, D, E, F, G, H, I, and J...creative, huh?) taking a test, scored on a scale of 0 to 100. Further, let's say that the school is broken up into two classes: "Regular", consisting of A, B, C, D, E, F, and G; and "Special", consisting of H, I, and J. Let's say that the scores are as follows:

A: 100
B: 95
C: 90
D: 95
E: 65
F: 60
G: 55
H: 15
I: 20
J: 10

The average score of the "Regular" class is \[\frac{100+95+90+95+65+60+55}{7}=80\] The average score of the "Special" class is \[\frac{15+20+10}{3}=15\] If we just switch E, F, and G (who we might call "marginally performing students") over to the "Special" class and do nothing else, watch what happens. The new average score of the "Regular" class is \[\frac{100+95+90+95}{4}=95\] and the new average score of the "Special" class is \[\frac{65+60+55+15+20+10}{6}=37.5\] Just by regrouping the students (and without improving the quality of the teachers one bit) we have artificially raised the score of the "Regular" class by 15 points, and the score of the "Special" class by 22.5 points. Crazy, huh? Of course the overall average of the school will remain the same, but these classes would be reported separately with NCLB.

So we know that school administrators have the incentive to regroup students in these ways in order to artificially raise scores, but do they actually act on these incentives? This is where the econometrics comes in. I use a couple of different econometric models in my paper to try to answer this question. We don't have to go into the specifics of the models, but we should talk about their basic structure, and the data. My data range from 1996 to 2006, and include 20,624 school districts and all fifty states plus DC. Basically, the data can be broken up into two major time periods: preNCLB (1996 to 2000) and postNCLB (2001 to 2006). The dependent variable in all my models is %IEP, or the percentage of students (in a given school district or state) with Individualized Education Programs (IEPs) which are groups assigned to students in special education classes. My independent variables have to do with the time that an observation is taken. So the basic structure of all my models asks the question, "in a given year and in a given school district/state, what is the percentage of students in special ed?" We can track over time how this percentage changes, and discuss if it is reasonable to believe that any of that change can be attributed to NCLB.

If it is true that school administrators have acted on the incentives described above, we would expect there to be a sharp increase in the percentage of students in special education classes between the preNCLB period and the postNCLB period (around 2001). It turns out that some of my data show just that. If we regress %IEP on the individual years in my dataset, we can show how the percentage students in special education classes changes over time (with respect to my "base year" 1996). Below is a graph created from one of my regressions:

Now of course, this is not proof that school administrators are "gaming the system", but this is strong visual evidence in support of the hypothesis of my paper. Just as we move from the preNCLB period to the postNCLB period, there is a huge spike in the percentage of students enrolled in special education classes. There are a couple of other more technical tests that I run that provide me with even more evidence, but that is beyond the scope of this blog.

No Child Left Behind was designed to increase the math, reading, and writing skills of students throughout the United States, giving them greater preparation for life. The legislation is full of nothing but good intentions, but unfortunately also puts in place some perverse incentives that may have ended up hurting some students more than helping them. The legislation encourages school administrators to consider students more as "numbers" or "test scores"--assets or liabilities--than before the Act. This encourages them to decrease the "costs" imposed by these liabilities by regrouping marginally-performing students into special education classes, even though they would otherwise not have been considered in need of special education. This can hurt these marginally-performing students because they will not be in a setting appropriate to their needs, and it can also hurt students that should be in these special education classes, because some resources will be re-directed away from them, and towards these marginally-performing students.

Anyway, I hope this gave you something to think about. If you would like to see the full paper, shoot me an email at connor.cosenza@gmail.com

Have a magical day!

107^th Congress. (2002). No Child Left Behind Act of 2001. (PUBLIC LAW 107-110-JAN. 8, 2002). Washington, DC: U.S. Government Printing Office. <http://opi.mt.gov/PDF/FEDPrgms/USDOE/pl107110.pdf>.

The Opportunity Cost of Idle Time

I am a bit restless. I'm not a big fan of idle time. My family and close friends know this well. I'm not ADD, or ADHD, or anything like that. I just always have to be doing something. While trying to sleep, I'll frequently jump out of bed because a possible solution to a problem I've been working on will randomly pop into my head. While I'm sitting down drinking a beer, my mind will be racing, trying to plan out my day, prioritize the things I have to do, and figure out how I'm going to accomplish those things. Instead of listening to music while I run, I usually just let my mind wonder and try to use that time to tease out questions I've been pondering. I find it hard to just chill and zone out. I sometimes envy those that can, but I guess it's not all that bad.

This behavior is largely a result of my education in economics, which has altered my conception of time and its value. One of the most important concepts in economics is the idea of an opportunity cost. An opportunity cost, roughly defined, is the value of the next best alternative. It can take many different forms, and arise from many different situations. For an example, let's say that I am currently watching a game on TV (anyone who knows me, knows this is unlikely, but let's run with it). Further, suppose that if I had chosen not to watch the game, I would have instead gone to the theatre and seen a show (Les Misérables, perhaps?) . In this case, the opportunity cost of watching the game is the utility I would have gained had I gone to see Les Mis. Both the game and the show provide me with some degree of satisfaction, but I miss out on the satisfaction I would have obtained from watching Jean Valjean rise from beggar to bad ass because I decided to watch the game instead.

How about an example with numbers? (Feel free to skip this paragraph if you would like). What is the opportunity cost of seeking a degree at college? When you ask a question like that, you're asking, what would I be doing had I not been in college? Most people would say that they would be working. Let's say that Erin the economist is trying to decide whether or not she should go to college for another year (read: is the marginal benefit of going to college for another year greater than the marginal cost of going to college for another year?). Let's say that she currently has $10,000 stored away, and that tuition is $10,000 per year (she'll pay in cash). Also, let's say that if she decides to work, she believes that she can earn $30,000 during that time. Finally, let's say that if she does not go to college, she will put the $10,000 she has saved into a bank that earns 5.0% annually. Ok, so that's a lot of information, but let's try to figure out what the opportunity cost is of her going to college for this next year. In this example, there are actually two different opportunity costs. The first one is probably pretty obvious--it's the $30,000 she would have earned had she been working. There's one more, though. If she had not spent her money on tuition for that year, her next best alternative was putting it in a bank at 5.0% interest (I know, wishful thinking, right?). If she did this, then after the year ended, she would have $10,500 in her bank account. That extra $500 is the opportunity cost of paying tuition. Notice: this is not the cost of the tuition. This is the extra benefit she would have received had she not paid for school. So all in all, Erin's opportunity cost to going to college for another year is $30,500. I hope that made sense. Examples with numbers usually help me.

You can probably see where I'm going with this. Whenever I find that I am doing nothing, I am constantly asking myself what else I could be using my time for. How could I be spending these few minutes in a way that will give me more satisfaction? What could I be doing that is productive in some way? How can I utilize this time to best accomplish my goals? This is actually one of the major factors that lead me to start a blog. I found myself with a much lighter schedule that I am used to, and realized that I had a lot of idle time on my hands. As I talked about in my first post, there is definitely some benefit to having a blog, and each time I post, I gain a bit of additional, or "marginal" benefit. When I write down my thoughts, I consolidate what I think, and gain a better understanding of the world. Also, a lot of the jobs to which I am applying ask for a writing sample, and building up this arsenal is giving me fuel for those applications. So there is definitely some value to me in doing this. Another way to say that is that my opportunity cost of lounging around is the value I would have gained had I decided to sit at my computer and write a post.

Anyway, I hope you found that interesting. Some people say that "time is money" but you could also say that "idle time is an opportunity". It's good to know what your opportunity costs are. Take some time to think about it.

Have a magical day!

Like Clockwork: Why People Love the Efficiency of the Marketplace

This is from a talk I gave a little over a year ago at an Adam Smith Conference hosted at Mercer University.

There is a wealth of literature dedicated to the so-called “Adam Smith Problem” which postulates that the Theory of Moral Sentiments is incompatible with the Inquiry into the Nature and Causes of the Wealth of Nations because the former is based in moral sympathy while the latter is based in self-interest. I would like to dissent from this view, and provide a possible way to bridge the gap between Adam Smith’s two most famous works. In The Theory of Moral Sentiments, Adam Smith explores the strong human propensity toward perfection. This drive towards perfection is one of the strongest forces that influence man. People are fascinated with trinkets and toys that work with the highest degree of precision. They are drawn to the impeccable consistency of such devises, and often admire them as much for their perfect execution as for the small conveniences they bring to the owner. In much the same way that people are drawn to these perfectly functioning gadgets, they are drawn to the mechanisms of the marketplace. These mechanisms can help to satiate a drive which Smith speaks of in the TMS—the need for people to understand and be understood by others. This drive presents a problem when people, in general, have vastly different, often irreconcilable, methods of valuation. One way to solve this problem is to make everyone speak the same language. Money, which objectively communicates subjective value, can be this common link. Through the perfectly harmonic forces of Supply and Demand, and with the language of the Market that is the money system, complete strangers can effectively communicate their desires and work for the happiness of each other. One way that the “Adam Smith Problem” can be solved is by realizing that people admire the beauty of the marketplace because it, without the supervision of any central power, works like clockwork.

In Part IV of The Theory of Moral Sentiments, Smith highlights the kinds of perfection that people seek in their lives. According to Smith, “The utility of any object…pleases the master by perpetually suggesting to him the pleasure or conveniency which it is fitted to promote” (TMS 179). This is an important distinction that Smith makes in Part IV: what pleases the master of an object is the suggestion of conveniency—not necessarily the conveniency itself. People marvel when an object seems perfectly fitted to its intended purpose—“that this fitness, this happy contrivance of any production of art, should often be more valued, than the very end for which it was intended” (TMS 179). Smith gives various examples of this. For instance, “a watch…that falls behind above two minutes in a day, is despised by one curious in watches. He sells it perhaps for a couple of guineas, and purchases another at fifty, which will not lose above a minute in a fortnight…But the person so nice with regard to this machine, will not always be found either more scrupulously punctual than other men, or more anxiously concerned upon any other account, to know precisely what time of day it is. What interests him is not so much the attainment of this piece of knowledge, as the perfection of the machine which serves to attain it” (TMS 180).

This same concept can be illustrated in the modern era—with me as a prime example. Since for the past couple years, I have been the proud owner of an iPhone 4S. The week before I got this smart phone, I told myself that I would never need a smart phone. I had an old fashioned cell phone, and that was perfectly fine by me. I was determined to not get sucked in to the smart phone craze. The week after I got it, however, I realized that I had, in fact, been completely sucked in—I could barely live without it. I am obsessed with this little thing. It can do just about anything. I can text, send emails, surf the web, watch videos, listen to music, catch the news, and call anyone I want—and it fits in my pocket! What an amazing machine! But why this obsession? Why do I feel so desperately attached to this device of which I had no earlier need? It’s because I’m fascinated with the beauty and simplicity with which it works. It would be no great hardship to wait until I get to my laptop to check my emails (or look at funny pictures on the internet) but the idea that I can do this whenever I want is awe-inducing. With only four buttons and a touch screen, I possess all knowledge known to man.

So how does my little iPhone obsession tie into Adam Smith? For that, we must inquire into the nature and causes of the wealth of nations. In Book I of this text, Smith lays out the basic laws of Supply and Demand. The consistency with which these forces work together to place goods in their most highly valued uses is just as awe-inducing as the capabilities of my phone—and unlike my phone, the forces of the marketplace need no central human force to perpetuate itself. Instead, it is through human interaction and the efficiency of the division of labor that it is possible to create something like an iPhone at a price that people can afford. People come together from all over the world to join perfectly the pieces of the puzzle necessary to produce a phone. Highly specialized people in extremely different areas of work are required to come together in a cohesive way to make one unique product. One needs miners to obtain the metals and other raw materials, plastics makers to form the casing, and glass makers for the screen. Then one needs engineers, electricians and programmers to make the phone run. After that, one needs artists and designers to make the phone visually, and audibly pleasing. Then one must employ social scientists to run beta tests on customers to make sure it is a product that people will actually want to buy. Then, one needs a full marketing team that is able to communicate to the entire consumer base that the product is ready for sale and worth purchasing. One needs sign producers, script writers, and actors to convey this message to the public. One needs truck drivers to bring the finished phones to all the stores, and finally retail workers to go through the transaction process with me so that at last I can have the whole world in my hands. This complex, even miraculous chain of events seems impossible, but somehow, all these strangers come together perfectly, like the components of a watch, to bring me this amazing device for a couple hundred bucks.

Smith explains why societies tend to give rise to the division of labor. Different people from all over the world come together, each providing a small specialized service which highlights the special comparative advantage which that person possesses. By specializing and habituating one’s work, one can become highly efficient and differentiated from others, and therefore more highly valued. This increase in personal value incentivizes people to become even more specialized in their work to distinguish themselves as the most productive in their individualized line of work. Once people have honed these individual talents, they are able to exchange the result of their labor for a profit. The more highly specialized people are, the more productive they become, and the more they gain from their production. In this way, the tendency to become more and more efficient and productive is a self-perpetuating cycle.

Smith believes that this comes about due to a natural sociability in man. “This division of labour, from which so many advantages are derived, is not originally the effect of any human wisdom, which foresees and intends that general opulence to which it gives occasion. It is the necessary, though very slow and gradual consequence of a certain propensity in human nature which has in view no such extensive utility; the propensity to truck, barter, and exchange one thing for another” (WN 25). This same propensity of man is discussed in Smith’s Theory of Moral Sentiments, although the exchange is of emotions—not goods and services. In this text, Smith highlights that “we often derive sorrow from the sorrow of others” (TMS 9), but also that “nothing pleases us more than to observe in other men a fellow-feeling with all the emotions of our own breast; nor are we ever so much shocked as by the appearance of the contrary” (TMS 13).

Although emotions are the medium of exchange in The Theory of Moral Sentiments, Smith describes a very different currency in the Wealth of Nations. The latter also describes the social nature of man from a different perspective—analyzing the transactions of goods and services rather than the transactions of emotions. Even though they may sound terribly different, they actually share great similarity. Through the mutual sympathy that exists in human nature, people desire to communicate the subjective value of experiences using emotions just as they communicate the subjective value of goods and services using money in the marketplace. When a person shows happiness or sadness, he is expressing a sense of his idea of value. When one’s sport team wins, and a person feels happiness, the shared joy of others reinforces his sense of value in that victory and elevates his joy. When a loved-one dies, and a person feels sorrow, the sympathy of others validates the value of her loss and dampens her sorrow. The transactions of goods and services in the marketplace convey very similar information. The market allows people to communicate their subjective value judgments to everyone else. With the use of money and the price system, one can instantly know what the relative value is of a certain good or service as compared to all other goods and services. When given the price of an object, one can instantly place that object within one’s frame of reference in terms that one can understand. After having been told that my iPhone cost about two hundred dollars, I could place the iPhone within my frame of reference and understand what it was worth in my own subjective terms—about 10 dinner dates with my girlfriend (let’s just say I’m thrifty!) or 20 trips to the movie theatre, or 40 runs to McDonalds, or 80 loads of laundry.

We may solve the Adam Smith Problem if we appreciate that many of the same psychological mechanisms are at work in both The Theory of Moral Sentiments and the Wealth of Nations. People have a natural tendency to seek perfection—perfection in the objects they possess, perfection in communication and social interactions, and perfection in the proper allocation of resources. Humanity has learned that in order to approach perfection, people must work together within the marketplace. In order to produce anything of value, people are highly dependent on the specialized contributions of others. All people “truck, barter, and trade” within the marketplace, allowing humanity to exploit the comparative advantages of every individual.  Just as people trade sympathies of subjective value in the emotional marketplace, they trade goods and services of subjective value in the economic marketplace. Societies use money to objectively communicate subjective value judgments. Without any central oversight, these forces of the marketplace bring mankind as close as possible to awe-inducing, perfect efficiency. Through his writings, Smith attempts to communicate that the market is a beautiful structure of spontaneous order that really does work like clockwork.

Just some thoughts. I hope you enjoyed it.

Have a magical day!

Theatre and Economics: a Surprising Parallel

Throughout High School, I was a big part of my school's drama department. my school had a pretty big department, with an entire building set aside for its auditorium. I participated in five different productions every school year--two main stage productions that were open to anyone in the school, and three productions that were set aside just for members of the "Advanced Drama" class. It was a blast. I had so much fun. I have easily lost track of how many plays I have been a part of over my life time. I've played the full gambit of roles, ranging from Romeo to Bum Number 6 (really), and I think I was pretty good. Not the best, but not too shabby, either.

There are many reasons I love the theatre. Going to watch a play is always an experience. There is something very different about watching live people perform in front of you, as compared to watching a screen in a dark movie theater. Watching a movie is a bit more passive. It could be a beautiful romance, or an action packed thriller, but the audience is still relegated to observing something that was finished long before they sat down. In live theatre, however, the story is literally being retold every night to a new audience. Every night, the actors are interacting with the script, the audience is interacting with the actors. A person is running the lights, a different person is running the sound, a full crew team is working in the back to make sure every piece of the set and every prop is in exactly the right place at exactly the right time. And all of this happens in perfect synchronicity...well...maybe not exactly. One thing that I learned during my time in theatre is that no two nights are the same. A production is a living, breathing beast every time the curtain rises. There are so many things that could go wrong every night, but still for the most part, everything usually seems to work out. The show must go on, right?

More than anything else, though, my absolute favorite aspect of the theatre--whether I'm on stage or off--is the characters. My favorite type of show is one with a simple set, and minimal props or flashy lights, and instead has very in-depth character development. When watching a play, I love to try to figure out what a given character is going to do next. I love to see how an actor interprets a role. I love to see how different actors interpret the same role. When acting in a play, I love to become a character. I love to get inside his brain and really understand exactly why he makes the choices he does. I love to lose myself in his life and really know what make him tick. I move stage right, not because my director tells me to, but because I feel myself drawn in that direction. I break down, cry, and beat my breast, not because it says so in the stage directions, but because my world is falling apart. I do this because I really understand what he needs and what makes him move.

Right about now you're probably scratching your head in confusion, asking yourself what the hell this has to do with economics. Most people think of economics (often called the "dismal science") as only having to do with money and interest rates and GDP. Actually, it is much more than that. I think of economics as a behavioral science which uses the tools of statistics, calculus, and marginal analysis to figure out what makes people tick. I usually tell people that economics is sort of like applied sociology. Economists (microeconomists, at least) often find themselves wondering why people do the things that they do. Instead of just trying to guess at this question, though, we try to actually measure it. We use data sets, statistical analysis and theoretical and mathematical models to describe how people respond to the world around them. If prices rise, what do people do? If the government imposes a tax, how do people react? If a minimum wage is set, what is the result? How do school administrators respond to mandatory school testing? (Keep this last one in mind for a later post!).

I guess you could say that I use both theatre and economics to fulfill the same passion within myself--my passion for people. I find people to be very interesting. I love talking to them. I love learning their likes, their dislikes, their hopes and their dreams. I love to understand why people do the things that they do. I love to understand what makes them tick. The theatre gives me an artistic medium through which I can explore the emotions and inner workings of people. Economics gives me the tools to analyze people's actions, and come up with objective, scientific reasons why people act in the ways that they do.

Anyway, I hope that I have convinced you that, although you don't need a utility function to analyze a play, economics has a lot more in common with the theatre than most people think.

Have a magical day!

The Deceptive Unemployment Rate

So we hear a lot about the unemployment rate. It is one of the most widely used macroeconomic measurements. We all know that high unemployment rates are bad, and low unemployment rates are good. Simple enough, right? What exactly is the unemployment rate, though? It a percentage that represents the number of unemployed people divided by the number of people in the labor force, or \[Unemployment \; rate=\frac{number \; unemployed}{number \; in \; labor \; force}\] times 100, technically, if you want to express it as a percentage.

Now it's important to understand precisely the definitions of these terms. The labor force is defined as anyone who is able and willing to work. that last part is important. A person has to not only be of an appropriate age and be physically/mentally able to work. He or she must also be willing to work! (This will factor in later) Those that are considered "unemployed" must be a subset of the labor force. One is considered unemployed if he or she is willing an able to work, but is unable to find a job.

Now, with this in mind, what ways is it possible for the unemployment rate to be decreased? (that is what we want to happen, right?) Well, the most obvious way for this to happen is if a larger percentage of the labor force becomes employed. In terms of our equation, that would mean that, the size of the labor force held constant, people would simply leave the numerator, thereby decreasing the value of the expression as a whole. This is probably what we usually think about when we think of a decrease in the unemployment rate.

There is actually a second way to decrease the unemployment rate, though. Let's look really carefully at our definition of what the labor force is. Remember, those in the labor force must be both able and willing to work. Let's consider someone who has been searching for a job for a long time, and has given up hope. this is what we call a "discouraged worker". It is a person who is perfectly able to work, but has stopped actively searching for a job. This person will not be recognized as part of the labor force, and consequently, will not be recognized as an unemployed person. It is true that he or she is not employed, but to be unemployed one must be in the labor force. If this person becomes a discouraged worker and leaves the labor force, he or she will be removed from both the numerator and the denominator of our original equation. It turns out that this will also reduce the value of our expression. This means that if people just stop looking for work (meaning that no one new has started working) the unemployment rate will still decrease. Crazy, huh?

Now this is all well and good, but I actually didn't know that reducing a numerator and denominator by the same amount would always reduce the value of the a given (regular) fraction. I know this is a long-known mathematical fact, but I had never come across it, so I decided to prove it to myself. Let's try to do it.

Consider a fraction \(\frac{x}{y}\) which represents the unemployment rate. To stay consistent with our earlier discussion, let's say that \(x\) represents the number of people unemployed and \(y\) represents the number of people in the labor force. Let us suppose that a certain number of people (let's say \(a\) people) become discouraged after not finding a job for a long time and decide to stop looking, and thereby leave the labor force. This means that the unemployment rate is now \[\frac{x-a}{y-a}\] What we have to do is figure out which is bigger, and which is smaller. Since we don't yet know, I will use a question mark in between the two sides until we can figure it out. Like this: \[\frac{x}{y}?\frac{x-a}{y-a}\] Well if we take this expression, and multiply the denominators on both sides of the expression we will get \[x(y-a)?y(x-a)\] Multiplying through, we get \[xy-xa?xy-ya\] We can then subtract \(xy\) from both sides of the equation and get \[-xa?-ya\] Then divide by \(-a\) to get \[x?y\] So what does this tell us? Well, we said that \(x\) represented the number of people unemployed, and \(y\) represented the number of people in the labor force, and we said earlier that the unemployed is a subset of the labor force, meaning that the number of people unemployed must be less than or equal to the number of people in the labor force. I think we can safely assume that this will be strictly less than, so this means that \[x < y\] Now all we have to do is get back to the original expression. No problem. Just do the opposite of everything we just did in reverse order. So we'll start by multiplying both sides by \(-a\). Don't forget to switch the direction of the inequality, since we are multiplying by a negative. \[-xa>-ya\] Next, add \(xy\) to both sides: \[xy-xa>xy-ya\] and factor out an \(x\) on the left side and a \(y\) on the right side: \[x(y-a)>y(x-a)\] Finally, divide by \(y\) and by \((y-a)\) to give our final expression: \[\frac{x}{y}>\frac{x-a}{y-a}\] And there you have it. If you decrease a fraction by the same amount in the numerator and the denominator, the original fraction will be greater than the new fraction (assuming that the numerator is smaller than the denominator).

So what is the moral of the story? Be careful when someone tells you with great joy that the unemployment rate has gone down. Such a decrease does not necessarily imply that more people are working. It might just as well mean that some people have given up and have stopped looking for work entirely--not exactly a reason for joy.

Now, once again, I know this is nothing new. I just didn't know it for sure myself until I sat down and proved it. I hope you enjoyed it as much as I did.

Have a magical day!

How Much Pollution Do We Want?

Below is a transcript of a lecture I was going to give with Ronnie Davis. Unfortunately, we never got the chance but I thought this would be a good place to share it. I hope you enjoy!

There is often much pressure put on the government to regulate corporations and society in general in the name of the preservation of our environment. It is somewhat taken for granted that the government knows exactly what society needs in order to conserve our resources. People assume that the government knows exactly what the correct amount of pollution is for the public. Now notice that I said the correct amount of pollution. Do we know what the correct amount of pollution is? Do you know what the correct amount of pollution is? I certainly don’t know what it is. Do you think that the correct amount of pollution is zero? That would be great, wouldn’t it? Zero pollution. We would have clean air, and clean water, and a quiet and serene world. We would also be free of cars, computers, mass-produced products, telephones, the mail system, and even candles and wood-burning stoves. Zero pollution is not the best level of pollution. So what is? How can we figure it out?

The answer lies in finding some way to measure what society wants, and what is most efficient for society. There are a few different methods that are available to measure what society wants. One of these methods is the political process. Society can vote on different candidates that have different platforms about the environment. One politician might advocate very heavy regulations, and another might advocate light regulations. One might want to focus his or her attentions on the pollution of cars, while the other wants to focus his or her attentions on the pollution produced by paper mills. Of course, the obvious downfall of this is that you cannot make everyone happy. Not everyone agrees on what the appropriate level of pollution is relative to the products and benefits we receive at the cost of that pollution. But that’s not that big of a problem. We always chose the best people to run the country, and every country always chooses the best leaders with the best policies that will regulate pollution in a way that the costs of pollution will exactly equal the benefits we derive from that pollution. The government always gets it right!! right? Right??? Well…maybe not. But if we can’t rely on the government to satisfy our desire to have just enough, but not too much pollution, then how can we ever achieve an efficient level of pollution?

Well that is the question. Another possible method of measuring what society wants is something called Free Market Environmentalism. Does that sound like an oxymoron? It does to a lot of people, but bear with me. So what is free market environmentalism? It is the idea that, when left to their own devices, actors in the free market can achieve an efficient balance between conservation, production, and pollution. It is the idea that there could be market-based solutions to the world’s problems related to excess pollution.

What this idea hinges on is something called Property Rights. Ever heard of them? You probably have. It’s the concept of “mine”. It means that I own my property, and I can do whatever I want with my property so long as what I do does not infringe upon your property. So what can I not do with my property? I can’t use my property to steal your property. I can’t use my property to hurt you. I can’t use my property to deface of destroy anything that you own. So what can I do with my property? Well, I can dig a hole in my back yard and bury it and forget about it—that way no one can take it, so long as they don’t find it! But that doesn’t really allow me to use my property. It just allows me to have it and say that it is mine. What else can I do? I can use it! I can consume it in some way that gives me satisfaction. Use it in some way that makes me happy. For example, if I own a slice of pizza, and I am hungry, I’m probably going to eat it. That would probably make the most sense. But what if my property included an entire pizza pie? Well, if I’m really hungry, I guess I could eat that too. But what if I had TWO large pizza pies with extra cheese and pepperoni and mushrooms? I might eat some of it, but I probably can’t eat all of it at once. I’m going to eat a few slices, but then I’m going to save it! I’m going to put it in the refrigerator and save it for later that day (or breakfast tomorrow). Now why would I save my pizza instead of eating it all right now? Because I believe that the pizza will retain enough of its value in the future to warrant consumption at a later time.

Alright, so why are we talking about pizza? What does this have to do with the environment, and how does it inform how we can measure society’s demand for pollution and production? Well, according to free market environmentalists, what we really need in order to ensure an efficient level of pollution is well-defined property rights to natural resources. The argument is very similar to the one we just encountered about my pizzas. If someone (let’s say a fisherman) owns some natural resource (let’s say a pond with fish in it), then that fisherman has a very strong incentive to not “over-fish” the pond. Why? For the same reason I didn’t eat all my pizza in one sitting. The fisherman is not going to over-fish the pond because he believes that the fish in the pond, if allowed to reproduce, will create a perpetual stream of income in the future. If the fisherman decides that he wants to fish every single fish out of his pond, he can certainly do that (it’s his pond after all), but it wouldn’t be a very smart move, considering that he could use the pond, and those fish, in the future if he just cuts back on his fishing a little bit. This fisherman is what we call the “residual claimant”. After all is said and done, he owns the pond, and all the fish, and all the income that it generates. After he has fished all the fish he has decided to fish, sold or consumed them, and paid all his bills, he will either gain a profit, or incur a loss. As the residual claimant, he gets all the profit, or he incurs all the loss. The residual claimant of a natural resource has a very strong incentive to make sure that that resource remains profitable into the future so that he can continue to gain from it in future years.

Now let me paint you a different picture. Let’s say that a bunch of different fisherman all share this pond in common. There is Connor the fisherman, and Ronnie the fisherman, and Billy the fisherman and everybody shares the resources in the pond. Remember—sharing is caring!—they all decide individually how much each person wants to fish. Billy might fish a little, and Ronnie might fish a lot, and each person gets to keep and profit from anything he catches. So what’s going to happen to the fish in the pond? Well, let’s try to figure out who the residual claimant is to the pond. Is it Billy? Is it Ronnie? Is it Connor? Well…it’s actually none of them. No one really owns the pond, because there are not well-defined property rights to the pond. So does anyone have the incentive to conserve the fish in the pond? Does anyone have the incentive to make sure that there is a constant stream of profit coming out of the pond in future years? No! No one has the incentive to reign in the amount they fish because they are not guaranteed the residual claim to the offspring of the fish in future years. So what is the end result? The fish population in the pond is probably going to be completely depleted in a year or two. Think about it. If Connor, being a forward-thinking and rational human being, decides to only fish enough to make a little profit so that there will be plenty of fish in the pond for next year, what is going to happen? Ronnie is going to catch all the fish that Connor didn’t! So Connor’s going to end up with a smaller profit than he otherwise could have had, and he won’t have any profit next year because Ronnie and Billy all caught the extra fish! So if Connor truly is a rational human being, and he understands all of this he’s actually going to catch every damn fish that he can as soon as he can so that Ronnie and Billy can’t get them. To put it another way, I’m going to eat both pizzas right now. Why? Because if I don’t eat both pizzas right now, as soon as I can, Ronnie and Billy are going to eat them instead. I might have a belly-ache, but at least I got to consume my resources. We call this the “Tragedy of the Commons”.

So let’s get back to the government. What if the pond if publically owned? What if it is owned by the government? Then what is going to happen? Well let’s go through the same thought process. Who is the residual claimant if the government owns a natural resource? There isn’t one! Who owns the pond? The government owns the pond. Who owns the government? We own the government. So who owns the pond? We all own the pond. So does anyone have any incentive to conserve anything if anyone in the nation can come to the same pond and fish as much as they want? No. Of course not. There is no residual claimant, so there is no guarantee of profit in future years, so there is no incentive to conserve, and more importantly, there is a very strong incentive to consume as much as possible right now, because if I don’t catch as many fish as possible right now, I probably won’t be able to catch any extra tomorrow. I don’t benefit—in fact, I am worse off—if I decide to curtail my fishing and conserve the fish. The result: The Tragedy of the Commons! And a serious tragedy it is!

So the best and most efficient way to conserve natural resources is to have well-defined, enforceable property rights over those resources. This way, goods will be produced, and fish will be caught, and pollution will be generated, only so long as it is profitable to do so. The problem with this approach is in how to define these property rights. Property rights of some natural resources are really hard to define, and even harder to enforce. Air comes to mind. How do we define property rights over the air? Well it is really hard to. Especially because air blows around, and by the time you complain about my factory polluting your air, you’re going to have a really hard time pinning that pollution down on anyone in particular. Who are you going to sue for infringing your rights to clean air? Is the hassle worth it to you? This is such a problem because it is so easy for businesses to “externalize” the cost of pollution onto the public. The trick to solving this problem is to get the businesses to “internalize” the cost of pollution, so that it will factor into their income statement. There are some solutions that have been explored. Most of them do require some government regulation, but in a much different way than the EPA passing arbitrary regulations directly on businesses. A possible solution is called “Cap-and-Trade”. With Cap-and-Trade, the government “Caps” the amount of a certain pollutant that can be released into the atmosphere, and then the government issues a certain number of pollutant vouchers to businesses which can either use them (by polluting) or sell them (Trade) to other firms. In this way, pretty efficient outcomes can be achieved because those firms that are more profitable, and are more able to bear the burden of these internalized costs of pollution will be able to produce (and pollute) more, while those that are less profitable (and probably less efficient) will either produce less or end up going out of business. The main problem now becomes figuring out just how high that “cap” should be set. There is no getting around the need for the government in this sense, but over time (a long time, perhaps) it is reasonable to believe that the government can find a relatively efficient cap on pollution.

So what have we learned today? Property Rights, Property Rights, Property Rights! If you own something, you have the incentive to take care of it and make sure it retains its value for the future. If you are the residual claimant of a resource, you are able to capture all of the profits generated from the use of that resource, and therefore have a strong incentive to conserve that resource for future use. If there is not a residual claimant to a resource, then there is no incentive for anyone to conserve anything, because resources not used today will simply be resource that are used today by someone else. The result of this is the Tragedy of the Commons. If the government owns a resource, everybody owns the resource, and then there is definitely no residual claimant. In this case, it is very likely that that resource will be fully depleted very quickly. Finally, we learned that in order to define some property rights, it may be necessary to utilize the government in a limited sense—just enough to pick a level of overall pollution, and then allow the market to sort out how much each individual is going to be allowed to pollute. Overall, it is important to realize that the government is not a panacea to all our problems. The government’s solutions are usually not the most efficient, and are usually unrepresentative of a large portion of the nation. Using the free market, and sometimes the government in a limited sense, we can most accurately measure just how much pollution we really want.

Sorry that was a bit long, but if you stuck with it, I hope you liked it!

Have a magical day!

My Opinion on the Minimum Wage

I came across an article today that I posted on my Facebook entitled A Modest Proposal to Ban Volunteering, by A. Barton Hinkle. This was a sarcastic article which pretended to take the side that "If people aren't allowed to work for $7.24 an hour, even if they want to, then they darn well shouldn't be allowed to work for $0 an hour either." The article points out the arbitrary distinction that people make between volunteerism and all other types of work. It's okay to do work for nothing, but as soon as you get paid at all, your paycheck must immediately jump from $0.00 to $7.25. Why the jump? why $7.25? Why not $7.24? To me, it seems very arbitrary and artificial.

This article stirred up a bit of discussion among my friends, and I thought it would be a nice way to introduce my opinion about the minimum wage. I'm sure most people have heard the argument that the minimum wage raises unemployment, but let's flesh out exactly why this is so, and why the minimum wage can harm the very people that it attempts to help. Let's say that I am unskilled, and attempting to find employment. I am hired by some company, and am paid the federally mandated minimum wage of $7.25 per hour. Since I am unskilled, let's say that I am only able to gain the company $5.00 per hour. This means that for every hour that I work, the company which I am supposed to be helping to remain profitable is actually losing $2.25. If I work 40 hours a week, for a year and do not noticeably improve, I will have lost my company about $4,680.00. Not exactly chump change. No business owner in his or her right mind would keep me on. Sooner or later, the company is going to cut its losses and fire me. If I am not able to increase my skill level very quickly, this will happen every place I go within a relatively short period of time. Anywhere I go, I will be fired, because I will always be detrimental to my company.

If, on the other hand, there was no minimum wage, I would be able to accept a wage of $5.00 per hour and work to improve without the imminent threat of termination. As time goes on, and I raise my skill level, I would be able to credibly ask for a higher and higher wage, and seek other employment if I do not get the wage I desire. If I never get to work in any one place for an extended period of time because my skill set is not adequate for $7.25 per hour, I will never be able to improve my work and I will never be able to credibly request higher wages. The truth is, I am better off working for $5.00 per hour than not working at all because the minimum wage shut me out of long-term employment.

Often, people are afraid to do away with regulations that have been in place for a long time because these regulations feel safe. We often see the government as a benevolent force that protects us from harm and unfairness. I don't wish to say that the government is evil, or that the people in the government do not have good intentions. I only wish that people would take into consideration the unintended consequences of many well-intentioned government policies.

Either way, something to think about. I hope that I gave you a new way to look at the topic.

Have a magical day!

In case you wanted to read the the article alluded to above:
http://reason.com/archives/2014/05/26/a-modest-proposal-to-ban-volunteering