This article will attempt to study NASA’s budget as a distribution to investigate changes in NASA’s budget from the years 1957-2014 using cutting-edge theories in political science such as measuring for leptokurtosis and applying a predictive distribution. Understanding NASA’s budget changes are the crucial first step in understanding how NASA’s budget may change and proponents of NASA might find whether NASA’s budget has been incremental or show punctuations very useful. This paper will use kurtosis mathematical methods and Robinson (2007) calculations for budget changes.
NASA’s budget has not been fully understood because NASA’s budget has not been a source of scrutiny in the academic literature. The history of studying budgets may be found in political science works such as Jones et al.  yet no one has indeed applied these frameworks to NASA’s budget.
Understanding NASA’s budget will be crucial first step in understanding NASA’s Congressional decision-making process. First, NASA’s empirical budget may be the output to which researchers can calculate back, apply theory, and map the decision-making process. This information will be crucial for proponents looking to get NASA’s budget changed for example.
1.1 Spaceflight in Literature
Prior studies of interest include Steinberg (2011) who studied affect of public opinion on NASA’s budget, finding support for space exploration negatively correlated with NASA budget increases, when properly measuring NASA’s budget as a percentage total of budget . The resulting negative correlation is likely not a relationship worth concern, it is likely that public opinion has no effect on NASA’s budget at all rather than public opinion having a negative effect on NASA spending.
Nadeau (2013) took this correlation a step further and sought predictors for public opinion support for a space exploration budget increase, finding white educated male baby boomers and those who have prior scientific knowledge and education are more likely to support an increase in the federal budget for space exploration. 
Nadeau (2013) improperly understood public opinion to have a desired effect on NASA budget spending changes. Instead, it is of note that of understanding that public opinion has a very negligible effect on spending in Washington due to spaceflight being such a negligible amount on overall US budget spending per a given year and taking up a small policy space on the overall US Federal agenda.
These studies do no address NASA’s budget as a source of investigation, and largely miss the point of spending as a variable to study. Spending is a result of a massive decision-making process and cannot be understood in terms of public opinion alone. Congress has a unique process for decision-making and without studying budget changes, it will be difficult to study the decision-making process.
1.2 Describing NASA’s budget
The first step to understanding NASA budget change is to effectively study NASA’s budget itself. If change is studied as a variable other predictors of change may be found to have an effect. Once these mechanisms are understood, proponents of NASA budget change (increases or decreases) may have what they need to pursue change at the federal level.
This study will continue upon prior studies, but in fact start with NASA’s budget as a distribution and analyze spending over time and apply cutting-edge theory in political science: Incrementalism and Punctuated Equilibrium Theory as a first step to determine ways in which NASA’s budget described.
1.3 Incrementalism and Punctuated Equilibrium Theory
Lindbloom (1959) and Wildavsky (1964) argue budgets are incremental, that is, exhibiting little change in allocation . This is largely due to organizational/institutional friction according to Jones, Sulkin, and Larsen (2003) due to opposing forces within the system working against each other for change, resulting in a zero directional output .
Budget allocations are predicted to exhibit little changes because of institutional friction and therefore spaceflight as a policy issue for example would see little change in budget because internal forces cancel out any positive or negative resulting change. The budget would then be incremental, having only small changes per year and never seeing larger changes or shifts in budget spending. After studies measured budget allocations and Incrementalist theory, it was shown budgets in fact are punctuated meaning they show larger changes as incrementalist theory would not have predicted. 
Jones (2009) found budget distributions actually follow an Empirical Law of Budget Distributions such that budgets are predicted to show larger changes, contrary to what was predicted by incrementalist theories of budget allocations.  Jones et al. (2003) modeled this distribution output and showed budgets exhibit signitures of Punctuated Equilibrium Thoery; the observed distribution exhibited leptokurtosis as illustrated with fat tails, sharp central peaks, weak shoulders.  This was contrary to Incrementalist theory and a new branch of political science was thought to understand why, if budgets are incremental, would exhibit large punctuations.
Punctuated Equilibrium results in punctuations in budget, and this is theorized to be because of the lack of policy reprioritizations that arise when government rethinks a policy issue and changes allocation of funding between issues. This would be shown with a decrease or increase in budget per year given policy issue type. A punctuated budget would predict both stability of incrementalism but with rare dramatic changes. The greatest differences between Incrementalist and Punctuated Equilibrium Theory are that in incrementalist theory changes are small and punctuated equilibrium theory means larger changes are to be expected.
This article will attempt to plot NASA’s budget distribution along with a hypothetical distribution and apply Incrementalism and Punctuated Equilibrium theories to the budget distribution to analyze what type of distribution NASA budget allocation has fallen under. Secondly, this article will analyze changes in NASA’s budget and investigate where the changes have occurred and when. Lastly, this paper will discuss implications these findings may have on spaceflight.
II. Finding NASA’s budget distribution
We start with 66 observations (one per year of change), NASA’s budget as a percentage change per year over the course of NASA’s history, 1958-2014 as recorded by Policy Agendas Project, now Comparative Agendas Project. I use Policy Agendas Project (updated April 2016) because variables are coded as NASA’s budget rather than Comparative Agendas Project which codes the data under separate policy issues effectively not given NASA’s budget in relation to the total US federal budget. The coding is still consistent over time and effectively isolates NASA’s budget numerically. 
I measure percentage change not in Dollars, but as percent total value. I do this because of the zero-sum of attention per year (limited government funding, caps that force unequal allocation as government cannot attend to every issue by distributing money to it and certainly does not attend to every issue equally). This also helps set an even measure for the US federal budget spending outputs over time.) I use coded values that effectively measure NASA’s budget in entirety. There are 66 observations, one per year of NASA’s historical budget.
2.2 Measuring Kurtosis and Changes
Breunig and Jones (2011) effectively measured budget kurtosis using an L-moments test and K-S test using the observed distribution. We can effectively measure the level of kurtosis in the observed distribution by applying a series of tests, Kurtosis test, K-S test, and increasing tau4 value.  Once these tests are finished, it will be clear if the budget exhibits leptokurtosis as consistent with Punctuated Equilibrium Theory.
Another way to measure whether NASA’s observed budget will exhibit characteristics of Incrementalist or Punctuated Equilibrium theory are to measure the amount of changes in spending. If NASA’s observed budget was plotted against a normal budget and the budget were to be broken into different quadrants where the graph intersects such as Robinson (2007), the count of changes can effectively be measured and then compared to the normal gaussian distribution to see if there is a variance between counts. 
If the observed distribution is plotted against a normal distribution and plotted against a hypothetical distribution using the mean and variance of distribution, than cut points could be made as indicated by True et al.(2011). This was first done by Robinson (2007). The theory is Punctuated characteristics are an increase in the in the expected proportion of small changes, a decrease in the expected proportion of medium changes, and an increase in the expected proportion of large changes. 
3.1 Kurtosis Measurements
If starting at Table 1, it can be shown the discriptive statistics for NASA’s budget distribution output, showing a level of kurtosis given magnitude of the kurtosis, K-S Test, and lastly increasing tau value. The resultant table is conclusive with Punctuated Equilibrium theory such that the values show kurtosis in the distribution. Given test results it is clear the observed distribution of NASA budget changes exhibits characteristics of leptokurthic budget distribution signaling towards Punctuated Equilibrium theory of budget changes.
The second part of the analysis deals with investigating medium changes, and the observe distribution shows less medium changes that expected signifying punctuated characteristics. Given there are only 66 observations and not 1000, looking at large changes is negligible given it takes a significant number of observations for rare occurrences to occur. 
In conclusion, it is clear the observed distribution showed signatures of Punctuated Equilibrium theory, as indicated by the results of the first analysis as shown the descriptive statistics of Table 1. The observed distribution passes the litmus test of whether the distribution shows characteristics of leptokurtosis as predicted by Punctuated Equilibrium theory or a normal distribution as predicted by Incrementalism.
Given table 2, is it clear the budget when applied to the hypothetical distribution shows signs of Punctuated equilibrium theory as shown by the observed proportion of small changes greatly out predicts the hypothetical distribution and the predicted amount of medium changes is less than the amount of observed changes.
Further, it is of note the vast information this data presents and how predictors of budget change may find it as the crucial first step to understanding changes. NASA’s budget distribution exhibits characteristics of Punctuated Equilibrium, not Incrementalism. It is incorrect to describe NASA’s budget as Incremental despite the large numbers of small changes. This is simply not enough of a description. NASA’s budget also shows less medium changes than expected with Incrementalism and predicted by the normal distribution. This can still be because of internal forces cancelling out other forces resulting in small changes in the distribution and lack of medium ones.
What this information presents is that NASA’s budget is due for a large change eventually as predicted by the Law of Empirical budgets. NASA’s budget, given 1,000 observations, is likely to erupt in a large change and will not remain in stasis incrementalism forever. The data already with 66 observations show the budget is punctuated not incremental and therefore change is expected.
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VI. Graphs and Tables