Professor Paul Palley's
          Economics Seminars

Probability concepts are very relevant in our decision-making. We consider the probability of a stock price increasing before we buy a stock, the probability depending on our assumptions about the future course of the firm’s profitability and the strength of the broader market. We consider the probability that we will arrive at an important meeting on time when determining the time we should leave for that meeting. These forms of subjective probability can be fairly elusive to deal with, but are important components in our considerations towards making a decision.

Gambling games, on the other hand is an example where probability is clearly evident in our winning and losing. For example, we can very concretely determining the probability of winning the lottery. Suppose there are 42 numbers to select from, and you must pick 6 different numbers. What is the probability of selecting the right combination of numbers? Using the combinations formula (see the text for more about this) you can determine the number of correct combinations as follows;

C = 42!/(42-6)!6! = 5,245,786

The probability, then, of select the right six numbers is only 1/5,245,786 or .000000191. This is a very bad use of the $1 it costs to by the lottery ticket. You could do far better by putting it in the bank. Here is an interesting link related to these concepts (http://members.cox.net/mathmistakes/rawdata.htm).

Of course, Las Vegas understands probability very well. As a result, they profit and habitual gamblers lose.

 

 

 

 

 

 

Survey and research generates data, and the statistics or data derived can very effectively facilitate efforts to systematically analyze and interpret data and arrive at smart decisions. These decisions follow from statistical inference or the steps associated with hypothesis testing. This should support market research efforts, political polling, statistical quality control research, and many other functions. That being said, survey design and the questions used can influence outcomes, and unless the goal of your research effort is to skew the results of the research, this should be avoided. How can you make a smart and rational decision with poorly collected and analyzed data?

 

An example where survey design and the questions being asked has wildly affected survey results is research related to health reform in 2009. For example, different surveys have found different opinions related to the views of doctors on a public health insurance option. Here is a link to an article discussing this, particularly the importance of disclosing research methodology in order to clarify points (http://www.pollster.com/blogs/a_tale_of_two_doctor_polls.php). Here is a link to the New England Journal of Medicine for their information related to this (http://healthcarereform.nejm.org/?cat=72). This report from Kaiser Health News illustrates varying poll results as well (http://www.kaiserhealthnews.org/Daily-Reports/2009/September/29/Poll-and-politics-health.aspx). There have also been indications that how questions are worded affects survey results, and so does the order of the questions. This blog post from ABC News does a very good job of delineating the differences in these analyses and is a good resource for other issues (http://blogs.abcnews.com/thenumbers/2009/08/views-on-a-public-option-let-the-fur-fly.html). What we are seeing through this is that survey design, the wording of questions, order of the questions, and the population sampled all influence outcomes. The choices related to these in this case may be political, deliberate, or accidental. The point is that it is hard to make smart decisions through statistical inference based on poorly constructed and analyzed surveys, and poorly constructed reports.

 

There are many interesting blogs related to numbers, statistics, and data analysis that illustrate applications of data analysis and research, good and bad, or the proper use of numbers. One is through the Numbers Guy in the Wall Street Journal (http://blogs.wsj.com/numbersguy/). Freakonomics on the New York Times is a good resource for interesting uses and misuses of economics and statistics (http://freakonomics.blogs.nytimes.com/). Charles Blow, a columnist with the New York Times also focuses on statistics and the uses of statistics (http://blow.blogs.nytimes.com/). Another resource from Professor Andrew Gelman, Columbia University is (http://www.stat.columbia.edu/~gelman/blog/).

 

I hope you have fun with these and other resources, and think critically about the data and reports you read.

 

 

 

 

 

The recession of 2007 to 2009 and its impact on households, businesses, and government, indicates the importance of anticipating changes in the direction of the economy and having a model to facilitate this analysis. The following discussion details a proposed model that facilitates efforts to forecast real GDP and also an approach for monitoring changing economic conditions. The model is based on economic logic, and was developed using regression analysis. The independent or explanatory variables that will be focused on include new private housing unit permits, the bond market, and the stock market. The advantage associated with focusing on these is that they are actively monitored and reported on in the press and by analysts. In addition, professional forecasts and data sources are readily available that can be used to facilitate efforts to analyze changing economic conditions. Measures of risk are also identified that serve as very helpful indicators to also facilitate forecasting efforts.

 

The model is specified as follows;

 

Dependent Variable

RGDP – Real Gross Domestic Product (GDP) in a given quarter

 

Independent Variables

PERMIT –     new private housing units permits in a given quarter.

    RVARBOND – real or inflation adjusted variance between the Baa Corporate Bond yield and the 10-year Treasury in a given quarter.

RS&P500 –     the annual percent change in the real or inflation adjusted S&P 500 stock index in a given quarter.

RGDP_t-1 –     lagged dependent variable in a given quarter.

Q₂ –    indicator variable for the second quarter of the year, accounting

    for seasonal variations in economic activity.

Q₃ –     indicator variable for the third quarter of the year, accounting for

    seasonal variations in economic activity.

Q₄ –     indicator variable for the fourth quarter of the year, accounting for

    seasonal variations in economic activity.

 

New private housing unit permits (PERMIT) is an important leading indicator as new permits trigger a lot of new economic activity. Housing permits lead to substantial development and construction activity. In addition, the relative strength in the housing market tends to indicate the perception of households related to the strength of the economy. The importance of this indicator has only been reinforced during the most recent period of economic growth, and even more during the recent economic recession.

 

Corporate bonds which are rated Baa are judged by Moody’s to be medium-grade obligations. Moody’s indicates that this means that they are neither highly protected nor poorly secured. Moody’s further judges that interest payments and principal security appear to be adequate for the present but certain protective elements may be lacking or may be characteristically unreliable over any great length of time. These corporate bonds do not have outstanding investment characteristics and reflect speculative characteristics as well. As a result, Moody’s Seasoned Baa Corporate Bond Yield is an indicator related to the relative risk of the current and future business climate. On the other hand, investments in 10-year Treasury are risk-free in that default is an impossibility, these bonds are held by very cautious long-term investors, and their yield is judged to indicate a risk-free rate of return other investments are judged against. As a result, the real or inflation adjusted variance between the Baa Corporate Bond yield and the 10-year Treasury (RVARBOND) in a given quarter is an indicator of business expectations. The bond market is indicating greater risk to the business climate and the economy when the difference between the Baa Corporate Bond yield and the 10-year Treasury increases.

 

The annual percent change for the most recent twelve moth period of the real or inflation adjusted S&P 500 stock index (RS&P500) is another indicator related to the perceived strength of the economy in the future. The stock market, over a ling period of time, is generally considered to be an important leading indicator in that it reflects expectations related to the future strength of the economy. It is true that in the short-term, the stock market can fluctuate seemingly randomly due to changes in market psychology and business and economic news. For this reason, forecasters look at long-term adjustments in the stock market as an economic indicator because over time the stock market better reflects the evaluation and analysis by investors of data related to future business conditions. The S&P 500 stock index is used because is represents a broad range of stocks.

 

The lagged dependent variable (RGDP_t-1) is included as an independent variable in order to resolve a potential statistical problem, positive first-order autocorrelation, a condition that is common in time series models. The consequence of this issue is that the validity of this model would be uncertain and the elasticities can not be accepted as reliable. In addition, it is logical that current levels of water use per account would in some degree depend on prior levels of water use per account

 

The forecasting model is;

 

RGDP = -18.7227 + 0.0588 PERMIT – 21.8687 RVARBOND + 1.3874 RS&P500 + 1.0024RGDP_t-1 + 22.7832Q₂ + 5.7021Q₃ + 12.7139Q₄

 

All coefficients have the expected signs. An increase in the number of new private housing unit permits should have a positive impact on the economy. On the other hand, an increase in the spread or difference between the real or inflation adjusted Baa Corporate Bond yield and the 10-year Treasury, should indicate a decline in the economy. In other words, the bond market indicating an increase in the relative risk associated with the business climate is an indicator that the economic growth is declining or will decline. It is logical that additional strength in the stock market indicates future strength in the economy. Two reasons can be presented for this. First, it means that the stock market is anticipating stronger economic growth. Second, the wealth affect will be at work in that higher stock prices lead to an increase in wealth and this facilitates additional spending and economic activity.

 

The following tables illustrate a comparison between actual changes in real GDP and predictions that would have been produced by the model for the period leading up to, and including, the current recession. We see that economic growth slowed significantly in the third quarter of 2008, and then real GDP declined after this point. The model would have also predicted the same outcomes, with some small differences in the rates of change. More interestingly, the model would have predicted much lower rates of growth during the periods of the second quarter of 2007 to the second quarter of 2008, signaling the underlying weakness of the real economy that we now accept as a fact. The recession actually is dated to have started in December 2007.

 

                 Actual         Actual

Year (QTR)         Real GDP        12-Month % Change

2007 (1)         13,099.90         1.425%

2007 (2)         13,204.00         1.863%

2007 (3)         13,321.10         2.739%

2007 (4)         13,391.20         2.530%

2008 (1)         13,366.90         2.038%

2008 (2)         13,415.30         1.600%

2008 (3)         13,324.60         0.026%

2008 (4)         13,141.90         -1.862%

2009 (1)         12,925.40         -3.303%

2009 (2)         12,892.50         -3.897%

 

                 Predicted         Predicted

Year (QTR)         Real GDP        12-Month % Change

2007 (1)         13,143.14         2.242%

2007 (2)         13,204.40         1.310%

2007 (3)         13,273.49         1.730%

2007 (4)         13,371.51         2.363%

2008 (1)         13,384.23         1.834%

2008 (2)         13,377.40         1.310%

2008 (3)         13,382.77         0.823%

2008 (4)         13,210.92         -1.201%

2009 (1)         13,008.25         -2.809%

2009 (2)         12,843.60         -3.990%

 

A forecasting model is only as accurate as the analyst’s ability to estimate the future direction of the independent variables. This means that, in this case, it is necessary to monitor the strength of the real estate market, the corporate and U.S. Treasury bond markets, and the stock market. Resources that will be helpful with monitoring the national housing market includes; the National Association of Home Builders, Mortgage Bankers Association, and Freddie Mac. In addition, the National Association for Business Economics, Congressional Budget Office, Federal Reserve Bank of Philadelphia, Livingston Survey, and the Federal Reserve Bank of St. Louis Economic Research are all helpful resources for economic forecasts and data. Measures of risk in the financial markets will be helpful with assessing the current condition of the financial markets.

 

Measures of risk that can be monitored include; the 3-month Treasury bill rate; the three-month Libor; the CBOE Volatility (VIX) Index; inflation expectations. The safest investment is the 3-month Treasury bill. The financial markets signaled extreme distress as the 3-month Treasury bill rate approached 0.00% during the recent financial crisis. This sort of extreme movement in this rate indicates a flight from any sort of risk and indicates that financing any initiatives would be very problematic. The result will be adverse impacts on the stock market and a widening of the spread between the inflation adjusted Baa Corporate Bond yield and the 10-year Treasury yield. The three-month Libor is a measure of what banks pay each other to borrow for three months. This rate rose significantly in the months of September and October 2008 at the start of the recent financial crisis. The significant increase in the three-month Libor reflected risk, the perspective of banks that there was greater risk related to lending to one another. This is characteristic of a credit crunch, and when credit is choked off and lending between banks becomes constrained, the economy will decline. The CBOE Volatility (VIX) Index is a measure of volatility given by S&P 500 stock index options prices, and as a result illustrates the perspectives of those who speculate in the stock market. The volatility demonstrated by this index starting in September 2008 indicated real difficulty for firms seeking to raise funds in the equity markets, and constrains those who are more risk averse from investing in equities. As a result, it can be used as an indicator related to the future strength of the stock market. Finally, Inflation is associated with growing economies. Of course, the exceptionally high rates of inflation seen in the 1970s indicated significant stress on the economy. Very low rates of inflation can also be very problematic as it indicates lower rates of economic growth and potential difficulty for businesses seeking to prudently raise the prices of their products. The difference between the 10-Year Treasury Constant Maturity Rate and the 10-Year Treasury Inflation-Indexed Security is a very good indicator of the bond market’s expectations related to inflation.

 

What is indicated for the future? Assumptions consistent with current economic conditions, and reasonable assumptions about the future, point towards relatively slow economic growth in calendar year 2010, and stronger but still moderate economic growth in 2011. Assuming continued small improvements in the housing market, strengthening of the corporate bond market, relatively low rates of inflation, and marginal increases in the S&P 500 stock market index from here, point towards 1.8% growth in real GDP in 2010 and 2.6% growth in real GDP in 2011. The low level of growth in 2010 indicates a fragile economy. The moderate levels of growth expected for 2011 indicates an economy that has stabilized. Stronger growth after 2011 is logical. This indicates moderate increases in retail sales in 2010 and additional improvements after this. The potential does exist for stronger economic growth if the housing market improves faster and households feel increasing confidence about the future faster.

This column by Liaquat Ahamed, the author of a book I highly recommend, “Lords of Finance: The Bankers Who Broke the World“. It is very interesting. The focus here is on the international monetary system, specifically its reliance on the dollar as the reserve currency, and then depends on the United States running trade deficits in order to facilitate an increase in the supply of dollars around the world. This column does a very good job of articulating issues related to trade deficits, the accumulation of dollars by foreign central banks, and the low interest rates that result from investments by these banks in the bond market in the United States. It also describes how this helped lead to the very severe recession of 2007-2009.

 

Mr. Ahamed wrote, “So far we have avoided a repeat of the Great Depression. Countries have collectively pursued the right macroeconomic policies — protecting and recapitalizing their banking systems, cutting interest rates to the bone and letting budget deficits expand.” He then described potential problems and issues that need to be addressed following this recession. He concludes with, “Until we can reconcile the export ambitions of the Asian countries, particularly China, with the import capabilities of the rest of the world, and make the volume and value of reserves less dependent on the vagaries of macroeconomic policy in one country, the risk of a similar loss of faith in today’s international financial system remains.”

 

What do you think?