This paper utilizes a Granger (1969) causality test to address the sequencing of group registrations and bill introductions previously investigated by Lowery et al. (2004). In a time-series, bivariate framework, one variable is said to Granger cause a second variable if including the lagged values of the first variable improves a forecast of the second variable that is built using its lagged values. In other words, does the history of the first variable help
8Running the Zhao, Lynch, and Chen (2010) version of a Sobel mediation test, shows that it is a com-
plimentary mediation. Thea*b pathway is significant and 0.59 of the direct effect of lagged lobbying on contemporary bills is mediated.
Table 3: Levin, Lin, and Chu (2002): Unit Root Test
Test Test statistics p
States Bills 54.5 1.0
Groups 141.4 1.0
Congress Bills -0.72 0.23
Groups -0.67 0.25
H0: All panels contain unit roots,Ha: Some panels are stationary.
predict the values of the second? An advantage of a Granger test is that it can also test the inverse relationship. A second advantage is that it can identify the two-sided relationship that the previous model was unable to properly observe.
The dataset being used for this test has many cross-sections, but very few time periods, so it actually resembles panel data more than a traditional time-series cross-sectional framework. Dumitrescu and Hurlin (2012) adapt the Granger framework for this situation, and can even increase the efficiency of the test by using both the variation across cases, as well as over- time variation within the cases to increase the degrees of freedom (Hoffmann et al., 2005). The first task is conducting a unit root test to determine if the data is stationary. This dataset has 750 panels and 5 periods. Table 3 shows that it is not possible to rule out that either time series has a unit root, or may be non-stationary. The Congress data has more time periods, but has similar unit-root concerns. However, Herrerias, Joyeux, and Girardin (2013) note in their study with a similar 10 year dataset, that this test is unreliable with such a short time series. But to quell this concern they run the model with differences instead of levels (counts). I follow their lead and use the logarithm (plus one, to account for policy areas without any bills or groups) for both quantities.
The equation for the Granger test in the states is as follows. For each policyp,
yp,s,t=αp,s+ K ∑ k=1 γp,s(k)yi,t−k+ K ∑ k=1 βp,s(k)xi,t−k+εp,s,t (3.2)
where s is the state, t is the number of time periods, in this case five. K is the number of lags, and α are fixed effects. This model is run for restricted and unrestricted versions. In the restricted version, values of β are held equal to zero. The unrestricted version has no such constraints. The Wald test to determine the Granger causality is:9
F1=
(RSS2−RSS1)/N p RSS1/[N T −N(1 +p)−p]
(3.3)
Results
The first row of Table 4 shows that in Congress, groups Granger cause the logged number of bills at a conventional level of significance, but not the inverse. The third row shows the same result with the 50 states pooled together with a one-year lag. The results are not as strong in either direction using a two-year lag. This results imply that changes in the number of groups registered to lobby in a given sector: say insurance companies in Indiana, will affect the number of bills introduced in the following session. However, more bills being introduced in the current session may affect how many groups register in that current session, it will not affect how many groups register in the following session.
9Dumitrescu and Hurlin (2012) note that an F-test of the key coefficient being equal to zero is functionally
Table 4: Do bills cause groups or do groups cause bills?
Groups → Bills Bills→ Groups
Venue Years Lags F-stat p-value F-stat p-value
U.S. Congress 1999-2014 1 3.05 (0.08)* 0.39 (0.53)
2 1.59 (0.21) 0.36 (0.55)
States 2007-2014 1 4.58 (0.03)** 2.13 (0.15)
2 2.68 (0.10) 0.66 (0.42)
Policy/state fixed effects. P-values in parentheses. **p <0.05, *p <0.10
Table 5: Where do groups set the agenda? 2007-2014 Groups → Bills Bills →Groups
Venue Lags F-stat p-value F-stat p-value
Low 1 2.55 (0.11) 4.51 (0.03)* 2 0.04 (0.85) 0.04 (0.85) Medium 1 2.47 (0.11) 2.37 (0.13) 2 15.36 (0.00)* 1.50 (0.22) High 1 0.36 (0.55) 0.01 (0.99) 2 2.03 (0.16) 0.15 (0.70)
Policy/state fixed effects. P-values in parentheses. *p <0.05
Hood, Kidd, and Morris (2008) note another advantage of this approach in panel data is being able to examine heterogeneous effects between the panels. In Table 5, the Granger test is run for states broken into three groups by their professionalization: there are 16 states in the low category10, 17 states in medium11, and 17 states in the highest category.12 Conducting the test in this fashion provides an opportunity to revisit the chapter’s third hypothesis. It shows that in the states with low-professionalization, bills are able to Granger cause the number of group registrations. This is in line with the hypothesized mechanism that group registration behavior is more inelastic in states with higher policy capacity.
10Low: AL, AR, GA, ID, KS, KY, ME, MT, ND, NH, NM, SD, UT, VT, WV, WY. 11
Med: CT, DE, IA, IN, LA, MN, MS, NC, NE, NV, OK, OR, RI, SC, TN, TX, VA.