1. Introduction At the start of most beginning economics courses we learn the economics is a science aimed toward answering the following questions: 1.What does society produce with its resources? 2.How does society perform this production? 3.Who receives the results? We can thus look at history as many economic questions and answers. This search leads to another, perhaps more important question: “Who is best suited to answer these questions?

2. Introduction “Who is best suited to answer these questions?” It has been argued that those who go into government honestly, and altruistically, think that they should answer the questions for others. If this is the case, it follows that those in government will think it best that they stay in government and that society would be better off if government answered more of the economic questions. Conclusion: The Government will grow over time.

3. Introduction Problem 1: To test this conclusion, we can look at the size of the Government in the United States. Size of Government: The number of economic questions answered by the Government/total number of economic questions. Extremes: Anarchy and Marxist Communism – Government does not answer any economic questions. Soviet Communism and social planning– Government answers all (or most) economic questions. All other societies lie between the two extremes. If we look at each dollar of expenditure as a tool used in a modern economy toward these answers, an apt measure of government size is: Size of Government: G/GDP

4. Size of the Government: G/GDP The above chart shows government expenditure as a portion of GDP. Note that it is relatively flat.

5. Size of the Government: G/GDP Possible problems: The chart on the previous slide was generated using data directly from the NIPA tables. Other sources show government spending as a portion of GDP rising sharply. It is likely that the discrepancy is caused by prices. For example, government expenditures are valued at cost, while consumption expenditures are valued through the market. Size of the Government: G/GDP One issue: Why not include transfer payments? Transfer payments are ambiguous in this context because they are the result of government deciding that one person is better off with someone else’s money. Still, the use of that money in the end is still decided by a person, and not the government. We include only those purchases made in the end by Government.

6. Modeling G/GDP: Trend The red series includes WWII. It trends downward slightly. The blue series excludes WWII and we can see that it trends upward. Thus, using this series, and excluding WWII, we can see that government does tend to grow over time. Using other sources, the government clearly grows over time.

7. Modeling G/GDP: Cycles Problem 2: In most economic texts, government spending is considered exogenous. That is, that it is not predicted by the particular model. Is it appropriate to consider the size of government to be independent of any large force (such as unemployment, etc.)? To approach this question we need to look closely at the characteristics of the series itself and its relationship to other variables.

8. Modeling G/GDP: Cycles For simplicity, we approached this task without WWII, creating the following series.

9. Modeling G/GDP: Cycles Autocorrelation and partial-autocorrelation functions Comments: Note that the series is highly correlated to itself at lag 1, indicating that it will be properly modeled with an AR(1) process.

10. Modeling G/GDP: Cycles Unit Root Test The Dickey Fuller Test tests whether or not the time series being examined is stationary or evolutionary. The ADF statistic is not significant at the 99% level. Due to this evidence that it is evolutionary, the series was pre-whitened by taking a logarithmic transformation to remove the trend in variance, and then first- differenced to remove the trend in the mean.

11. Modeling G/GDP: Cycles The above chart shows the resulting series, which appears to have lost most of its structure.

12. Modeling G/GDP: Cycles Unit Root Test: Proportional Changes This Dickey-Fuller test gives evidence that the time series is now stationary as seen by its ADF statistic being significant at the 99% level.

13. Modeling G/GDP: Cycles Autocorrelation and partial-autocorrelation functions Comments: Note that the series is still highly correlated to itself at lag 1, and there is some correlation at lag 5, indicating an ARMA 1,5 model.

14. Modeling G/GDP: Cycles We can quickly reduce the residuals to white noise with an ARMA model. Below is the actual and fitted graph for an AR(1), MA(5) model, followed by the ACF and PACF of the residuals.

15. Modeling G/GDP: Cycles Comments: We can see now that the residuals do not have any structure. The P- values and the Q-statistics are all well above the 5% level.

16. Modeling G/GDP with the Unemployment Rate One possible explanation for movement in the government’s share of the economy may be found in employment variables. The basic intuition behind this is that the government will try to stimulate the economy using fiscal policy. Thus government spending will grow with unemployment while other GDP component shrink. To test this, we look to see if the unemployment rate can explain a significant portion of the movement of government spending.

17. Modeling G/GDP with the Unemployment Rate Unemployment Rate

18. Modeling G/GDP with the Unemployment Rate Granger Causality The Granger Causality test above gives some evidence that there is a causal relationship from the unemployment rate (unrate) to the proportional changes to the government’s share of the economy (dlngovshare). This leads to the following model form: DLNGOVSHARE = h(z)*DLNUNRATE + error In other words, the fractional change in government share is some function of lagged values of the fractional change in unemployment rate, plus the usual error term. The unemployment rate will be transformed to log differences for easy interpretation.

19. Modeling G/GDP with the Unemployment Rate Unemployment Rate: Proportional Changes Form

20. Modeling G/GDP with the Unemployment Rate Correlogram of dlnUnRate Date: 06/01/04 Time: 14:16 Sample: 1948:1 2004:1 Included observations: 224 AutocorrelationPartial Correlation AC PAC Q-Stat Prob *|. | 1-0.091 1.89440.169.|* |.|. |20.0710.0633.04550.218 ****|. | 3-0.471-0.46553.8640.|. | *|. |4-0.011-0.10553.890.|. | 50.0120.06253.9250.|. | **|. |60.01-0.2653.9470.|. | *|. |70.011-0.08553.9740.|. | 80.0030.05553.9760.|. | **|. |9-0.025-0.1954.1290.|. | *|. |10-0.018-0.10454.2090

21. Modeling G/GDP with the Unemployment Rate ARMA Model for the Unemployment Rate in Proportional Changes

22. Modeling G/GDP with the Unemployment Rate Correlogram of the Residuals of the ARMA model Date: 06/01/04 Time: 14:25 Sample: 1949:1 2004:1 Included observations: 221 Q-statistic probabilities adjusted for 2 ARMA term(s) AutocorrelationPartial Correlation AC PAC Q-Stat Prob *|. | 1-0.132 3.8966.|. | 20.0190.0023.9769.|. | 30.0210.0244.07640.043 *|. | 4-0.105-0.16.55680.038.|. | 50.024-0.0036.69230.082.|. | 60.0120.0186.72640.151 *|. | 7-0.067-0.0627.75320.17.|. | 80.009-0.0197.77110.255.|. | 9-0.024-0.0227.90230.341.|. | *|. |10-0.056-0.068.63940.374.|. | 11-0.013-0.0438.68170.467.|. | 12-0.002-0.0088.68320.562.|. | 13-0.017-0.0218.75220.645.|. | 14-0.012-0.0348.78690.721

23. Modeling G/GDP with the Unemployment Rate Derivation of the Distributed Lag Model  w(t) Using the derived AR(3) and MA(6) error structure from the DLNUNRATE time series, it is possible to transform the original model (see “Proposed Model Form”) so that that the DLNUNRATE term is approximately orthogonalized ( N un (t) is used to represent this new term). Since all terms in the original equation must undergo the same transformation, a new dependent variable is derived, which is referred to as w(t). In similar fashion, the transformed error term is now referred to as residw(t). The exact procedure is as follows: The Coefficients of the Zs (the lag operators) are the Betas from the ARMA(3,6) DLUNRATE model. w = (dlngovshare +.0749958*dlngovshare(-3)) / (dlngovshare- 0.567410*dlngovshare(-6))

24. Modeling G/GDP with the Unemployment Rate Cross Correlation of W(t) and ResUnrate There is clearly significant correlations at lag 2 and lag 5.

25. Modeling G/GDP with the Unemployment Rate Estimation of the distributed lag model While this model performs well, it produces residuals with significant structure as seen by the low p-values on the correlogram Q-statistics. The ACF highlights lag 3 and 9 as candidates for AR processes. Estimation of the above model with added AR(3) and AR(9) terms produces significant coefficients and residuals without structure. They are not normal, however.

26. Modeling G/GDP with the Unemployment Rate Squared Residuals: Episodic Variance. The residuals are not normal because the variance is non-constant, as seen by the following chart of the squared residuals. The problem can be solved using an ARCH model.

27. Modeling G/GDP with the Unemployment Rate ARCH model:

28. Modeling G/GDP with the Unemployment Rate Forecasts 2 period forecast results

29. Modeling G/GDP with the Unemployment Rate Forecasts Slight increase in government share. Overall, the forecast is relatively “stable.”

30. Modeling G/GDP with the Unemployment Rate Conclusions Theoretically, government share should increase over time. Forecasts predict a slight increase in government share over time. Government share is not an exogenous variable (Econ 208). Rather, it is influenced by other factors such as the unemployment rate.