Wednesday, May 14, 2008

Wages Aren't Everything

In today's online version of the Wall Street Journal, Thomas Frank (the author or "What's the Matter with Kansas") declares that we are in the midst of an economic catastrophe. The evidence? "Real hourly wages for most workers have risen only 1% since 1979." That sounds bad. And it's often cited as a seemingly powerful argument used against the New, global economy. Nobody questions the fact that the US has become more productive (see chart below, data from BLS). But if workers are not compensated for it, we have a problem.

How do we evaluate the validity of Frank's claim?

[Skip the bordered section if bored by math...]

Classical economics teaches us that the profit maximizing firm employs workers until the wage rate is equal to the marginal revenue product of labor (MRP,l). That is, a rational firm will hire labor until the extra revenue earned by an additional unit of labor is equal to its cost:


where P is price, L is labor and f represents the production function. Production functions map the output achieved given any mix of available inputs. The marginal physical product of labor, the additional output achieved with an another unit of labor, is given by df/dL.

Stating the decision rule for the for a profit maximizer mathematically (remember, the marginal revenue product of labor is equal to the wage rate):


Assuming a constant price, if productivity (df/dL) increases, the wage rate must also increase to maintain the equality.


So, we should be concerned if wages are stagnant while productivity is increasing. But wages don't tell the whole story. Employers provide a package of benefits to their employees, and these should not be left out of the discussion. Common benefits include those paid for health care, medicare, and social security.

Real compensation combines both real wages and real benefits, and represents the totality of employee earnings. [Tying up loose ends, we should redefine "w" in the section above to represent full compensation]. The following graph (data from BLS) displays the trend in real wages and real compensation. Both series are represented as indices, so even though real compensation is always greater than real wages, each series equals 100 in 2008.

The chart agrees that inflation adjusted wages have not increased over the last thirty years. On the other hand, real compensation has grown steadily over the same period. Further, the rate of increase is steeper since the late 1990's, the beginning of the New Economy. What does that mean? Basically that pundits who cite stagnant wage statistics are only telling part of the story. Is Frank sorry about the "economic catastrophe" thing?

It's true that employer provided benefits are not necessarily fungible; it's difficult to transform them into cash. However, they do represent an opportunity benefit--cash that would otherwise be spent on health care can be turned into a shiny new iPhone. While it's interesting that wages haven't increased over time, it's hardly grounds for alarmist predictions.

Unfortunately, Thomas Frank seems prone to those. Just read his book.

Copyright © 2008 TCE.

Friday, May 09, 2008

Intrade Prices & Barack Obama's Chances

A friend pointed me to a discussion at the about determining the political "momentum" of the presidential candidates. There, a poster suggested that a mathematical model be constructed in order to examine the factors associated with a politicians' likelihood to win the nomination. Fitting a smoothed trendline to polling data might allow us to consider the effects of certain events on a candidates' chances on the basis of temporal concurrence, but only roughly.

How can we isolate the effects of so many potential pieces of information? It's obvious that the likelihood of coming away the nominee is dependent on a candidate's primary wins, superdelegate count, popular vote total, as well as potentially scandalous news stories. Without controlling for each of these, it would be difficult to be confident that we're considering the true qualities associated with victory.

Fortunately, regression analysis allows us to do just that. If we can relate, say Barack Obama's chance to win the nomination with important causative factors like those mentioned above, we might be able to tell just how much the average primary win improves his probability of facing McCain in the fall, or how much the Reverend Wright controversy has affected him. But first, we have to collect the relevant data and build the model.

The Intrade prediction market allows traders to enter into futures contracts that consider the probability that Barack Obama will win the Democrat party's nomination. The price of the contract equates exactly with the market's belief that he will be the nominee, assuming that the market is efficient. By including the time series of price as the dependent variable in the regression analysis, we can estimate how the superdelegates or Reverend Wright have affected his chances.

y(t) = B*x(t) + u(t)

where y(t) is the price of Barack's contract (the market specified probability that he will win) at time t; x(t) is a matrix of exogenous (independent) variables that likely effect y(t), such as the number of superdelegates committed to either candidate, their popular vote totals, primary wins and news events; B is a vector of coefficients that relate x(t) to y(t); u(t) is a random error term that accounts for the "noise" in the futures price. Those terms in x(t) that correspond to statistically significant terms in B indicate that we can say with confidence that they had a meaningful impact on Barack's probability of winning. t=1 for 1/6/2008; the day after the Iowa caucus.

So. What are the results? Well...
Significant results are indicated by *'s. The more asterisks, the more confident we are that the independent variable affects the contract price. Generally, we consider significant only those variables that are significant at the 5% level (indicated by one *); we accept a 5% chance that the variables is in fact not significant, but that the coefficient was generated randomly. Two **'s indicate a high level of confidence (the 1% significance level).

The regression results seem to make sense; at least they exhibit the proper signs. As expected, Obama's wins (significant at the 10.8% level), his popular votes, and the interaction between them (interpreted as the extra effect of winning large states) positively affect his chances to win. On other hand, Clinton's wins, her popular votes, and their interaction adversely affected his Intrade price.

Interestingly, we may interpret the share price one-to-one with percentage points in the probability that Obama will be the nominee. So we can quantify the results: the coefficient of 3.48 on Obama's wins relates that each primary win boosts his probability of winning the nomination by about 3.5%. Of course, the average Clinton win reduces the probability that he will face McCain by almost 5%.

I made a few other assumptions about the nature of the news events and debates. Each Reverend Wright incident (when the comments broke, and when he reiterated them in front of the Press Club) was assumed to last for 5 days, about the length of a news cycle. The impact of Barack's response and the debates was assumed to last for 3 days. These values can (and probably should) be changed to maximize the likelihood of observing the price data, but I included them as structural assumptions for simplicity. No other news events (Hillary'"misremembering" the warzone evasion) were considered.

If we accept those assumptions, we can further quantify the impact of the Reverend Wright controversy on Obama's chances. According to the table, both instances were detrimental to Obama's probability of winning, by 7% and 5%, respectively. Interestingly, the results indicate that Obama's Philadelphia speech, in which he refused to "disown" the Reverend served in fact to reduce his share price. Although widely lauded by the media, my results show that the speech may have lowered the likelihood that he will take the nomination.

So, the results seem interesting. But how realistic are they? Well, in order to gauge that, I found that model explained almost 94% of the variation in the share price, an acceptable proportion for time series work. Further, I was pleased to see that the estimated coefficients did a reasonable job predicting the contract price, as related by the chart below. In other words, the red line (prediction) resembles the blue line (price) effectively:

So, what can we take away? If the objective is to quantify the effect of various exogenous (independent) variables on the probability that a candidate will be elected, we should consider using econometrics rather than simply attempting to calculate derivatives of the trend line in opinion polling. For one, we can check how well our models measure up to the empirical data. Additionally, we can estimate the relevant parameters while controlling for the effects of multiple, simultaneous influences.

1. It is important to verify that the relationship between the time series variables is stationary. That is, two series may not be related to one another (say U.S. GDP and the total number of homeruns hit in Japanese baseball). However, since both are increasing over time, we may find a significant relationship between them if we simply regress one on the other. If we have stationarity in the relationship (i.e., if the residual does not have a unit root), then we don't have to worry about this problem. I verified that the relationship between the price of Barack's contract and the explanatory variables used in estimation is indeed stationary, by computing the post-estimation residuals and performing an augmented Dickey-Fuller test.

2. Intrade prices were used to represent the probability that Obama will win rather than opinion polls, since futures prices are real choices in a market (revealed preference), versus simply stated preferences.

Copyright © 2008 TCE.

Monday, May 05, 2008

Uncle Sam's Gas Tax

Two candidates for president in 2008 have recently expressed a desire to temporarily remove the federal gasoline tax, which currently stands at ~$0.18 per gallon. Doesn't sound too bad, does it? We all dislike paying paying more than we have to. And make no mistake, that's the side effect of taxes. However, why is it that many economists have publicly denounced the idea?

Are they:
(a) Generally misanthropes that enjoy human suffering
(b) Unhappy that John Mccain doesn't have a plan to pay for it (Hillary's notion)
(c) Upset that snap bracelets went out of style
(d) Concerned that the supply of refined gasoline is inelastic

Answer: Possibly (a) but definitely (d)

When the supply for a good is inelastic, the quantity supplied by producers does not change very much for a given change in price. If we imagine that the gasoline market is perfectly inelastic, and that producers cannot supply more gasoline even if they wanted to, then removing the tax on gasoline would not result in a concurrent price reduction. Why?

Because we know that at its current price, the total amount of gasoline available is consumed. Even if more consumers wanted to buy gas during the tax moratorium, they would not be able to since the current price of gas rations the amount available, i.e., shortages would result from a price reduction. The producers response? Keep prices stable. They would reap the welfare gains of the tax suspension. And this is not necessarily bad, as long as we can find a way to fund our highway construction. Ugh, earmarks. Ahem.

However, no price reduction is a worst case scenario. It is likely that the supply of gasoline is less than perfectly inelastic, and that the demand for gasoline is also somewhat inelastic. In that case, a gas tax results in a dead weight loss. Its' suspension benefits society overall, but again helps producers more than consumers (which is only fair since they bear the incidence of a tax in this situation). See the following graph...

is the net result? If the 18 cent gas tax is removed, consumers may realize a 9-12 cent per gallon price decrease, according to Jeffrey Perloff at UCB. Better than nothing, but not much to look at. Certainly not enough to make a big deal about.

Copyright © 2008 TCE.