The credit crisis that began in 2007 served as the trigger for one of the most serious recessions since the Great Depression. We all know that numerous companies were severely impacted by the recession, especially those whose businesses are especially cyclical (e.g., automobile, steel, etc.). What is less well known is that many state and local governments (municipalities) have also been seriously impacted by the recession. Declining economic activity tends to simultaneously reduce tax revenues and increase expenditures as more citizens are forced to rely on the social safety net.

In the early 1990s, some well-regarded financial engineers proposed that cyclically impacted corporations and municipalities could hedge their "macroeconomic risks" by engaging in macroeconomic derivatives (such as swaps or options). A macroeconomic swap would be a swap in which one leg pays a fixed rate of interest and the other leg pays a floating rate of interest tied to some "macroeconomic index" (such as the growth rate of GDP or an inflation rate such as the CPI). Macroeconomic derivatives are often embedded in other instruments. For example, the U.S. Treasury department's TIPS (Treasury Inflation Protected Securities) contain embedded inflation swaps. In the early 2000s, Goldman Sachs and Deutsche Bank teamed up to offer macroeconomic derivatives (which they called economic derivatives) to their clients. These were structured in much the same way the financial engineers had suggested ten years earlier.

Now suppose that you run a risk management consultancy firm and you have been hired by a mid-sized municipality to help them avoid future economically-induced fiscal crises. Specifically, the municipality wants to determine to what extent their cash flows are impacted by changes in regional inflation-adjusted GDP growth rates and then to hedge that risk. To help them, you have obtained quarterly inflation-adjusted regional GDP data from Bureau of Economic Analysis (BEA). BEA reports that for the past 40 quarters real GDP for the region has grown at about 2 percent on an annualized basis. You have also obtained, from your client (the municipality), inflation-adjusted revenue and expenditure data for the past 40 calendar quarters (not annualized). You need to determine by how much a change in annualized GDP quarterly growth rates will impact the municipality's quarterly net cash flows. Net cash flow is defined as the difference between the municipality's gross revenue and gross expenditures. This data is in the spreadsheet.

You should:

1. Are the parameters of the equation statistically significant at 5%? At 1%?

Quarter 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 annualized GDP growth rate % 2.20366 1.42981 4.03151 3.17109 2.20170 1.84874 5.57684 5.51188 4.91021 1.25852 1.26613 5.31170 3.07300 4.39021 3.17530 2.07842 3.38717 3.09552 3.06665 3.03434 3.12437 2.29554 2.09879 3.97218 1.52284 0.24247 2.17267 (0.63995) 2.58036 1.27183 (1.19737) 0.48518 (1.02822) 1.32837 3.08778 2.82230 4.27398 3.53091 3.09967 3.43398 in millions in millions Quarterly Revenue Quarterly Expenditures 111.66456 116.02655 112.26292 116.85823 123.56972 109.52809 118.46415 114.84887 109.53796 116.23801 111.68625 115.20062 126.08466 107.77336 128.64243 108.69670 121.56798 111.11335 102.95193 116.93421 105.88752 112.88753 124.82363 115.39704 118.81607 110.03874 121.58414 109.57530 120.53679 111.55644 114.32824 113.77150 113.92076 112.88821 121.04717 111.99817 121.36847 110.14525 119.37140 111.50880 112.13879 113.58584 107.83114 116.00611 115.86219 112.48733 123.55634 107.97472 107.51314 118.49560 104.44569 120.15441 111.02172 113.37364 86.62401 118.98728 113.12635 113.29117 108.08772 117.29220 98.56697 122.26152 99.02059 121.81462 96.00006 122. 13690 104.90961 114.77858 124.17482 109.82724 123.99908 112.25505 127.77929 107.17163 120.12803 109.16230 104.81654 120.01055 115.37592 116.45015 Quarter 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 annualized GDP growth rate % 2.20366 1.42981 4.03151 3.17109 2.20170 1.84874 5.57684 5.51188 4.91021 1.25852 1.26613 5.31170 3.07300 4.39021 3.17530 2.07842 3.38717 3.09552 3.06665 3.03434 3.12437 2.29554 2.09879 3.97218 1.52284 0.24247 2.17267 (0.63995) 2.58036 1.27183 (1.19737) 0.48518 (1.02822) 1.32837 3.08778 2.82230 4.27398 3.53091 3.09967 3.43398 in millions in millions Quarterly Revenue Quarterly Expenditures 111.66456 116.02655 112.26292 116.85823 123.56972 109.52809 118.46415 114.84887 109.53796 116.23801 111.68625 115.20062 126.08466 107.77336 128.64243 108.69670 121.56798 111.11335 102.95193 116.93421 105.88752 112.88753 124.82363 115.39704 118.81607 110.03874 121.58414 109.57530 120.53679 111.55644 114.32824 113.77150 113.92076 112.88821 121.04717 111.99817 121.36847 110.14525 119.37140 111.50880 112.13879 113.58584 107.83114 116.00611 115.86219 112.48733 123.55634 107.97472 107.51314 118.49560 104.44569 120.15441 111.02172 113.37364 86.62401 118.98728 113.12635 113.29117 108.08772 117.29220 98.56697 122.26152 99.02059 121.81462 96.00006 122. 13690 104.90961 114.77858 124.17482 109.82724 123.99908 112.25505 127.77929 107.17163 120.12803 109.16230 104.81654 120.01055 115.37592 116.45015