The following analysis supplements the previous chapters, which initially reviewed the NHTS datasets and then developed seasonally adjusted time series travel estimates. The econometric analysis to follow includes equation estimates for three modes of travel: air, highway, and rail passenger. Each equation will be reviewed for statistical qualities, followed by a discussion that will establish a relationship between travel by mode and the catastrophic events of 9/11.

The seasonally adjusted monthly travel data used in the econometric analysis spans the period of January 2000 through June 2003, and is identical to the data used in the time series analysis. The exponential weights for the dummy variable used in the VMT equation for the 5-month period from September 2001 to January 2002 are: 1.000, 0.6494, 0.4217, 0.2738, and 0.1778. These weights were approximated by applying a standard natural exponential curve to the data, which would result in a function ranging from 1.0 to 0. These 5 months were chosen based on their proximity to 9/11 and appeared to be the time frame when travel appeared to be most affected by 9/11. Other time periods were chosen and were not found to be statistically significant.

The economic data comes from the Economic Report of the President, which was obtained from the web.^{6} The fuel price data originates from the U.S. Department of Energy, Energy Information Administration. Revenue Passenger Miles per Departure data came from the Bureau of Transportation Statistics,

Office of Airline Information. Although the equations listed in the tables below contain only those variables that were statistically significant, several variables were tested, but did not meet the statistical significance tests at either the 5 or 10 percent probability levels. The variables that were excluded in the equations consisted of industrial production and wholesale and retail sales. However, all variables were tried in logarithmic and lagged conversions, and equation specifications were estimated in linear and nonlinear formats.

Travel was econometrically estimated for aviation, highway, and rail passenger modes from monthly data. Both linear and log specifications were tested with combinations of the following economic variables: unemployment, wholesale and retail sales, industrial production, income per driver, fuel prices by mode and fuel type or fuel cost per mile. Two types of dummy variables were used, a typical 0,1 value for September 2001 through February 2002, and another with an exponential decay curve. Corrective procedures were also implemented when needed, such as those associated with serial or time dependent correlation over several periods. Lagged variables through two time periods were also used, and in cases where serial correlation were present, AR(1) (auto-regressive terms of one period) were then included in the estimations. Other independent variables were also used, such as the airline revenue passenger miles per departure. In all, over 30 estimations per mode were attempted with varying combinations of variables and equation specifications.

The results of the aviation estimation (table 4) indicate that there was a statistically significant negative impact of 9/11 on air travel per person above age 16. Other relevant variables such as income per person above age 16, jet fuel price, and the unemployment rate were significant as well, with all variables statistically significant at the α = 0.01 level. All variables have the correct a priori mathematical sign. For example, income has a positive effect on travel, while both unemployment and jet fuel price negatively impact travel.

Overall, the statistical fit accounts for 51 percent of the variation from the dependent variable mean. The Durbin-Watson test is inconclusive for autocorrelation among error terms, so no adjustments were made to the original equation.

Where:

Income per population aged 16+ = income^{7 }per population aged 16+^{8} (in real 1996 dollars per population aged 16 and over)

Jet fuel price = kero-jet fuel price^{9} (1/10^{th }cent per bbl in nominal dollars)

Dummy 9/11 = dummy variable, where value equals 1 for September 2001 through February 2002

Unemployment = unemployment (percent)^{10 }

The highway vehicle-miles traveled (VMT) equation estimation (table 5) has an R-squared value of 74.8 percent, which is much higher than the aviation or rail equations. The premise for using the revenue-pas-senger miles variable (RPM_DEPART) was to capture the effect of travel declining as a result of 9/11, especially very short air ﬂights (100 miles or less), which may be leading to more highway travel. The RPM variable is significant at α = 0.05 level, while all other variables are significant at the α = 0.01 level. This indicates that there is a strong relationship between the events of 9/11 on highway travel. All of the variables also have the proper sign, such as when air travel declines, VMT increases, indicating that they are substitutes. Travel increases with rising income as well. The EXP_9/11 variable consists of a weighted dummy variable for 9/11, in which the weights decline exponentially over a 4-month period after 9/11. The exponential form of the dummy variable was found to be statistically significant, but the (0,1) dummy was not statistically significant. The original Durbin-Watson statistic tested positive for positive serial correlation (α = 0.01), so an adjustment was made to include an autoregressive (AR) period 1 error term variable.

Where:

RPM per departure = Revenue passenger miles^{11} per departure

Exponential Dummy 9/11 = exponentially weighted dummy variable, where value exponentially decays through 4 time periods.

AR(1) = Auto-regressive error terms of time period one^{12 }

Only the logarithmic equation specification (table 6) was found to be statistically acceptable, in terms of fit and statistical significance. Notice that the equation has no 9/11 variable, because it was found to not be statistically significant in all combinations of log and linear specifications as well as combinations of all variables. Both the log of the time period lag of one for the dependent variable and the log of the income per driver were found to be statistically significant. Each variable has the proper positive sign indicating that rail passenger travel rises as a result of the effects of the previous time period and the effects of increases in income per driver. The Durbin-Watson statistic revealed no serial correlation.

Often an evaluation of econometric equations includes comparisons to other estimates using the estimated coefficients to develop economic elasticities. Demand elasticities measure the degree, in percentage change, to which one economic variable changes based on the percentage change of another economic variable. Table 7 shows a comparison between demand elasticities from the BTS study versus Carol Dahl’s compilation of various model elasticities.^{13} All of the BTS elasticities were calculated at the mean and are very close or within the range of Carol Dahl’s findings, possibly with the exception of the aviation income elasticity, which appears to be larger than the higher range of the estimates (Dahl, 1995). It should also be noted that Dahl’s elasticities are measured with respect to transportation fuel consumption and are not as specific to a particular mode as the BTS study. Therefore, the elasticities should be judged in a more general manner than viewed as exact comparisons by mode.

The results indicate that there is a strong statistical relationship between the events of 9/11 and aviation and highway travel, but not rail revenue passenger miles. Given that the 9/11 dummy variables are statistically significant, it can be concluded that the negative effect of 9/11 on travel declines in a more arithmetic fashion for air travel over a 6 month period, in which there is a decline in the intercept. Similarly, highway travel has a tendency to decline in a more exponential pattern over a 4-month period. These conclusions do not attempt to determine when travel will return to a more normal historical level, but rather only the declining portion of the travel. Furthermore, it can be concluded that there is a statistically significant substitution relationship between air travel and highway travel, although the cross elasticity is small at -0.041. This cross elasticity was derived from the air travel coefficient and indicates that for each 100 percent drop in air travel, highway travel will increase at approximately 4.1 percent.

The conclusions of this study do not equate to assuming that future catastrophic events would yield the same results because the degree of damage and the impending effect on behavior may not be the same for future events. The severity of catastrophic events and their impact on future behavior is not easily quantifiable, and yet is essential for future analysis of catastrophic events. Hopefully future research and analysis will lead to some kind of indicator of the degree of severity of catastrophes.

^{6}http://www.gpoaccess.gov/eop/

^{7 }U.S. Department of Commerce, Bureau of Economic Analysis, table 2.6, Personal Income and Its Disposition, Monthly, seasonally adjusted, www.bea.gov.

^{8} Economic Report of the President, Table B–35, Civilian population and labor force, 1929–2001, monthly data seasonally adjusted, 2004.

^{9} U.S. Department of Energy, Energy Information, State Energy Price and Expenditure Report, 2004. http://www.eia.doe.gov.

^{10 }U.S. Department of Labor, Bureau of Labor Statistics, Unemployment Rate, seasonally adjusted, LNS14000000, www.bls.gov.

^{11 }U.S. Department of Transportation, Research and Innovative Technology Administration (RITA), Bureau of Transportation Statistics, Transportation Services Index (TSI), http://www.bts.gov/xml/tsi/src/index.xml and National Transportation Statistics, http://www.bts.gov/publications/national_transportation_statistics/2005/index.html, 2005.

^{12} See William Greene, *Econometric Analysis*, 2003.

^{13} Carol Dahl, Professor, Director of CSM/IFP Joint International Degree Program in Petroleum Economics and Management, Colorado School of Mines, Golden, Colorado. Dahl has compiled demand equation elasticities for 20 authors, many with multiple estimations over time. They are categorized according to equation specifications and type of data used. Elasticities are derived from equation coefficients in the form of a percentage change in demand for a percentage change in price or income.