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ContentsIntroduction.............................................................................................................................................. 1

Section 1: Descriptive Analysis ............................................................................................................... 2

1.1 Visual Analysis and Unit Root Tests ............................................................................................. 2

1.2 ARIMA Models ............................................................................................................................... 4

1.2.2: Box-Jenkins Identification ...................................................................................................... 4

1.2.2 Model Selection ...................................................................................................................... 7

1.2.3 Forecast Evaluation and Residual Diagnostics .................................................................... 11

Section 2: Robustness Check ............................................................................................................... 15

2.1 Pretesting .................................................................................................................................... 15

2.2 Correlations ................................................................................................................................. 18

References ............................................................................................................................................ 22



1

Introduction



2

Section 1: Descriptive Analysis

1.1 Visual Analysis and Unit Root Tests

Figure 1 displays the SAPU index in levels for the full sample; 1994m1 to 2014m6. Several features are

notable here. Firstly, there are several holes in

the data, starting from 2002m3 and ending in

2002m12. As discussed in McLean (2015:***)

these holes are due to a sudden drop in the

volume of news captured by SAMedia over this

period – the reason for this sudden sparseness

has not been ascertained. This data feature

effectively divides the index into two periods; the

first runs from 1994m1 to 2002m2, the second

from 2003m1 to 2014m6.

Secondly, the behaviour of the series appears to

differ markedly between these two sample

periods. As can be seen in Figure 2, the period

1994m1 to 2002m2 appears to be characterized

by a constant mean and variance. The series

does appear to exhibit some degree of cyclicality

over this period, but an Augmented Dickey-

Fuller (ADF) test indicates that we can reject the

hypothesis that this series is I(1) at the one

percent level of significance (the test was

specified with a constant; SIC automatic lag selection selected zero lags – see Table 1).

In contrast with Figure 2, a visual inspection of Figure 3 suggests that the mean and variance of the

data generating process (DGP) appears to increase as a function of time over the period 2003m1 to

2014m6. This portion of the index thus appears to be nonstationary. As is common practice, the

observed increase in the variance of SAPU is

addressed by taking the log of the series (****)

– as can be seen in Figure 4, this course of

action ostensibly reduces the high variance

observed in the latter half of the series. For this

reason, L_SAPU, the log transformed SAPU

index, is used throughout the remainder of this

section.

Regarding the apparent nonstationarity of theseries, Table 2 displays ADF test results for the

0

20

40

60

80

100

120

140

1994 1995 1996 1997 1998 1999 2000 2001

Figure 2: SAPU 1994m1 to 2002m2

0

50

100

150

200

250

300

1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

Figure 1: SAPU 1994m1 to 2014m6

0

50

100

150

200

250

300

2004 2006 2008 2010 2012 2014

Figrue 3: SAPU 2003m1 to 2014m6



3

L_SAPU 2003m1 to 2014m6 in levels. The test is specified with a constant and 3 lags. As indicated by

the p-value of 0.4011, we cannot reject the hypothesis that this portion of the series is characterized by

a unit root for any traditional level of significance. This test thus corroborates the hypothesis that the

series is nonstationary.

Regarding the nature of this apparent

nonstationarity, if one simply looks at the graph

of the series it is difficult to tell whether a trend

or a unit root accounts for the nonstationaity; the

series does appear to be characterized by a

slight degree of cyclicality, but it also appears to

trend upward quite consistently. ADF tests also

provide little guidance here: Table 3 shows that

for an ADF test on the level of the series

specified with a constant and a trend we can

reject the hypothesis that the series is nonstationary at the one percent level of significance; as can be

seen in Table 4, the same result is achieve for an ADF test on a constant and the first difference of the

series.

Table 1: ADF Test, 1994m1 to 2002m2 (Levels)

Null Hypothesis: SAPU has a unit root

Exogenous: Constant

Lag Length: 0 (Automatic - based on SIC, maxlag=11)

t-Statistic Prob.*

Augmented Dickey-Fuller test statistic: -5.577842 0.0000

Test critical values: 1% level -3.499167

5% level -2.891550

10% level -2.582846

*MacKinnon (1996) one-sided p-values.

.0

.5

4.0

4.5

.0

.5

.0

2004 2006 2008 2010 2012 2014

Figure 4: L_SAPU 2003m1 to 2014m6

Table 2: ADF Test, 2003m1 to 2014m6 (Levels)Null Hypothesis: L_SAPU has a unit root

Exogenous: Constant


t-Statistic Prob.*

Augmented Dickey-Fuller test statistic -1.755684 0.4011


5% level -2.883073

10% level -2.578331




4

1.2 ARIMA Models

Given the findings discussed above, common practice dictates that SAPU is trend stationary (****).

However, economic reasoning might motivate us to treat the series as difference stationary. To

elaborate, one would not expect the DGP of the series to be characterized by a deterministic trend, but

rather by the stochastic development of social and political events. Thus, while a deterministic trend

might fit well with the SAPU sample observed over 2003m1 to 2014m6 in-sample, one would expect

that modelling SAPU with a deterministic trend would result in poor foresting and out-of-sample-fit. This

section tests this hypothesis by estimating and evaluating a battery of ARIMA(p,d,q) models.

1.2.2: Box Jenkins Identification

In following the Box-Jenkins (1976) estimation strategy, this process is initiated with a visual and

statistical inspection of the index, its autocorrelation function (ACF) and its partial autocorrelation

function (PACF). Table 5 presents descriptive statistics for L_SAPU (column 5.1) and two

transformations of L_SAPU: D(L_SAPU) (column 5.2) and DT(L_SAPU) (column 5.3), the first

difference of the log of SAPU and the detrended log of SAPU respectively. For D(L_SAPU) and

DT(L_SAPU), the Jarque-Bera statistic indicates that we can reject the hypothesis that these series are

normally distributed at the one percent level of significance. The third and fourth central moment provide

an indication of the source of this non-normality. The third central moment indicates that D(L_SAPU) is

Table 4: ADF Test, 2003m1 to 2014m6 (1st Difference)

Null Hypothesis: D(L_SAPU) has a unit root

Exogenous: Constant


t-Statistic Prob.*



5% level -2.883073

10% level -2.578331


Table 3: ADF Test, 2003m1 to 2014m6 (Levels)

Null Hypothesis: L_SAPU has a unit root

Exogenous: Constant, Linear Trend


t-Statistic Prob.*



5% level -3.442955

10% level -3.146165




5

skewed right and that DT(L_SAPU) is skewed

left; skewness is most pronounced in

DT(L_SAPU). The fourth central moment

indicates that both series are leptokurtic, with

D(L_SAPU) displaying fatter tails thanDT(L_SAPU). In sum, these test statistics

indicate that D(L_SAPU) and DT(L_SAPU) are

both characterized by a high proportion of data

residing in the tails of their respective

distributions, that D(L_SAPU) has a long right

tail, and that DT(L_SAPU) has a long left tail.

A visual inspection of these series provides an

indication of the source of the non-normality of

D(L_SAPU) and DT(L_SAPU). Referring back to

Figure 4, there appears to be a large downward

spike in the index at 2005m1 and 2003m2.

Column 5.1 in Table 5 indicates that L_SAPU has

an estimated standard deviation of approximately

0.42 and a mean of approximately 4.75;

observation 2005m1, which has a value of 3.26,

is 1.49 units below the mean of the series, and is

exactly one unit below observation 2004m12 and is 1.38 units below observation 2004m2; this

observation thus lies more than two standard deviations below the mean of the series and away from

its neighbouring observations. Similarly, observation 2003m2 (3.49 units) is 0.78 units (less than two

standard deviations) below observation 2003m1, and is 1.06 and 1.26 units below observation 2003m3

and the mean of L_SAPU respectively (both more than two standard deviations).

As can be seen in Figure 5 and Figure

6, differencing and detrending

L_SAPU further exacerbates the

irregularity of these observations,

particularly observation 2005m1.

Figure 5 shows that differencing

L_SAPU causes the deviation in

2005m1 to affect observation

2005m2; 2005m1, with a value of

-1.01, is just less than three standard

deviations below the mean of the

series, and 2005m2, with a value of1.38, is approximately four standard

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2004 2006 2008 2010 2012 2014

Figure 5: D(L_SAPU)

-1.2

-0.8

-0.4

0.0

0.4

0.8

2004 2006 2008 2010 2012 2014

Figure 6: DT(L_SAPU)

Table 5: Descriptive Statistics for L_SAPU Transformations

5.1 5.2 5.3

L_SAPU D(L_SAPU) DT(L_SAPU)

Mean 4.746310 0.007362 1.03E-16

Median 4.693905 -0.012206 -0.008638

Maximum 5.644762 1.383108 0.612533

Minimum 3.255166 -1.006805 -1.142621

Std. Dev. 0.415366 0.345102 0.272905

Skewness -0.286317 0.357227 -0.592941

Kurtosis 3.365061 4.573799 4.478033

Jarque-Bera 2.651773 17.05243 20.64765

Probability 0.265567 0.000198 0.000033



6

deviations above the mean of the series. 2003m3 in

Figure 5 (with a value of 1.05) is also approximately

three standard deviations from the mean of the

series. These observations appear to account for the

rightward skewness and thick tails indicated in 5.2.For DT(L_SAPU), observations 2005m1 and

2003m2 are respectively 1.14 and 0.72 units (more

than three and more than two standard deviations)

below the mean of the series, thus accounting for the

leftward skewness and thick tails indicated in 5.3.

To account for the irregularity of these observations,

we restrict the sample to exclude all dates prior to

2003m3 and add dummy variables for observation

2005m1 and 2005m2 to D(L_SAPU) and a dummy variable for observation 2005m1 to DT(L_SAPU).

Table 6 shows descriptive statistics for the residuals of D(L_SAPU) regressed on a constant and these

dummies (6.1) and for DT(L_SAPU) inclusive of the 2005m1 dummy (6.2). For both series, the Jarque-

Bare statistic indicates that the hypothesis of normality cannot be rejected at any traditional level of

significance. All subsequent models presented in this section include the relevant dummy variables and

are estimated on samples which exclude 2003m2. This resolves the issue of outliers.

Turning now to the issue of lag length selection, Figure 7 and 8 respectively display the ACFs and

PACFs for L_SAPU, D(L_SAPU) and DT(L_SAPU). The ACF for L_SAPU shows a markedly slow linear

decay, a feature indicative of a unit root (Enders, 2010:73); however, the ACFs for D(L_SAPU) and

DT(L_SAPU) show that either approach removes this persistence, reducing the number of significant

Table 6: Accounting for Outliers

6.1 6.2

D(L_SAPU) DT(L_SAPU)

Mean -1.76E-17 2.35E-16

Median -0.008600 -0.015972

Maximum 0.695292 0.602350

Minimum -0.748037 -0.624201

Std. Dev. 0.294703 0.246021

Skewness -0.010816 -0.037858

Kurtosis 2.558378 2.755471

Jarque-Bera 1.091530 0.365859

Probability 0.579398 0.832827

-0,600

-0,400

-0,200

0,000

0,200

0,400

0,600

0,800

1 2 3 4 5 6 7 8 9 10

Figure 7: SAPU Autocorrelation Function

L_SAPU D(L_SAPU) DT(L_SAPU) Significance



7

lags to one in both cases. Turning to Figure 8, the PACF of D(L_SAPU) indicates that our ARIMA model

may need to contain as many as three lags, while the PACF of DT(L_SAPU) indicates that one lag may

be sufficient.

1.2.2 Model Selection

Given the ambiguity of these indicators, the model selection process employed here proceeds as

follows: Two sets of models are generated here; a set of ARIMA(p,1,q) models (i.e. a set with

D(L_SAPU) as the dependant variable) all specified with a constant, and a set of ARIMA(p,0,q) models

(i.e. a set with L_SAPU as the dependant variable) all specified with a constant and a linear time trend.

In consideration of the PACF of D(L_SAPU), models with up to three lags are considered; all models

are specified to contain either an AR or an MA term at every lag length lower than the model’s longest

lag. Carrying out the above yield two sets of fourteen models.

Estimation of these models is carried out over a sample period starting no earlier than 2003m5 and

running up to 2012m6. In addition to omitting the aforementioned outlier, the lower bound of each

estimate was selected so that all models are estimated on the same number of observations; this is

imperative, as it is under these conditions that the Akaike Information Criterion (AIC) and Schwartz

Bayesian Criterion (SBC) allow us to compare the goodness of fit for non-nested models (Enders,

2010:71). The upper bound was selected so as to conserve a sample period (2012m7 to 2014m6, 23

observations in total) for out-of-sample model evaluation.

The set of ARIMA(p,1,q) models are displayed in Table 7.1 and Table 7.2, and the set of ARIMA(p,0,q)

models are displayed in Table 8.1 and Table 8.2. Statistical significance is indicated by asterisks: ***,

**, * indicate statistical significance at the one, five and ten percent level respectively. Notably, the

-0,600

-0,400

-0,200

0,000

0,200

0,400

0,600

0,800

1 2 3 4 5 6 7 8 9 10

Figure 8: SAPU Partial Autocorrelation Function

L_SAPU D(L_SAPU) DT(L_SAPU) Significance



8

highest adjusted R-squared (of 0.511053, column 7.9) achieved by the set of ARIMA(p,1,q) models is

less than the lowest adjusted R-squared (of 0.564614, column 8.2) achieved by the set of ARIMA(q,0,1)



9

Table 7.1: L_SAPU ARIMA(p,1,q) Modes (Specified with a Constant)

7.1 7.2 7.3 7.4 7.5 7.6 7.7

AR(1) -0.442928*** -0.563887*** -0.799862*** -0.657519***

AR(2) -0.300189*** -0.079993 -0.450292***

AR(3) -0.264077***

MA(1) -0.811335*** -0.773702*** -0.801019***

MA(2) -0.652691*** -0.179567*

MA(3)

R-Squared 0.378499 0.503519 0.440800 0.503985 0.505632 0.515960 0.483596

Adjusted R-Squared 0.360910 0.489467 0.419497 0.485089 0.486799 0.497521 0.458769

AIC 0.262895 0.038304 0.175446 0.055546 0.052221 0.031107 0.114011

SBC 0.361094 0.136503 0.298196 0.178295 0.174970 0.153856 0.261310

Table 7.2: L_SAPU ARIMA(p,1,q) Models (Specified with a Constant)

7.8 7.9 7.10 7.11 7.12 7.13 7.14

AR(1) -0.689573*** -0.759654*** -0.749900*** AR(2) -0.500107*** -0.133164 -0.093440 AR(3) 0.068400 -0.085062 -0.046456MA(1) -0.784627*** -0.764419*** -0.809714*** -0.754525***MA(2) -0.738372*** -0.094265 -0.170669* -0.651971***MA(3) -0.412994*** -0.243409*** -0.100864 -0.213780**

R-Squared 0.502941 0.533482 0.521552 0.523528 0.518376 0.509577 0.506587 Adjusted R-Squared 0.479044 0.511053 0.498549 0.500621 0.495221 0.485999 0.482865 AIC 0.075830 0.012419 0.037670 0.033530 0.044286 0.062389 0.068468SBC 0.223129 0.159718 0.184969 0.180829 0.191585 0.209688 0.215767



10

Table 8.1: L_SAPU ARIMA(p,0,q) Models (Specified with a Constant and a Linear Time Trend)

8.1 8.2 8.3 8.4 8.5 8.6 8.7

AR(1) 0.281013*** 0.249483** 0.250299** 0.233942** AR(2) 0.124413 0.190037* 0.098348 AR(3) 0.112301MA(1) 0.242873** 0.277499*** 0.265961***MA(2) 0.092901 0.144951MA(3)


Table 8.2: DT(L_SAPU) ARIMA(p,0,q)

Models (Specified with a Constant and a Linear Time Trend

8.8 8.9 8.10 8.11 8.12 8.13 8.14

AR(1) 0.239662** 0.242073** 0.247522** AR(2) 0.125431 0.189134* 0.182591* AR(3) 0.106804 0.125459 0.089720MA(1) 0.262686*** 0.275539*** 0.261801*** 0.256385**MA(2)

0.088107 0.146813 0.152479 0.076966MA(3) 0.009099 0.039288 0.041488 0.006766




11

models. This finding corroborates the first element of our hypothesis that models including a linear trend

will fit well in-sample. Note however that adjusted R-squared is not an appropriate criterion for

evaluating the relative goodness of fit for non-nested models (Wooldridge, *****); as mentioned above,

for this purpose we must refer to each model’s AIC and SBC score . Moreover, it is also necessary to

note that the AIC and SBC cannot be used to rank models between these groups, as they do not allowfor comparison across models with different transformations of the dependent variable (Burnham &

Anderson, 2002:80). Rather, the AIC and he SBC are used here to select the best models from within

each group respectively.

For ease of evaluation, the four lowest (and thus best) AIC and SBC scores among each of the two sets

of models have been colour-coded: light blue is lowest, dark blue is second lowest, light gold is third

lowest, dark gold is fourth lowest. Of the ARIMA(p,1,q) models, the ARIMA(0,1,2) model in column 7.6

scores lowest in both AIC and SBC and is thus the strongest contender of this group; the ARIMA(1,1,2)

model (7.9) is also a strong contender, with the second lowest AIC score and the third lowest SBC

score. For the third ARIMA(p,1,q) contender, the ARIMA(0,1,1) model (7.2) is selected given that it

attains the second lowest SBC score; this statistic is unbiased in small samples (****), and thus 7.2 is

selected not only for the level of its SBC score but also for the reliability of this score vis-à-vis models

that achieved low AIC scores.

Among the ARIMA(p,0,q) models, the ARIMA(1,0,0) model (8.1) achieves the lowest SBC score and

the second lowest AIC score, and is thus selected. The ARIMA(0,0,1) model (8.2) performs poorly

relative to many of the other ARIMA(p,0,q) models with respects to its AIC score, but is selected on the

basis of its SBC score (which is second-lowest among this group of models). Finally, the ARIMA(1,0,1)

model (8.5), which achieved the lowest AIC score and the third lowest SBC score, is selected.

1.2.3 Forecast Evaluation and Residual Diagnostics

Table 9 presents forecast evaluation statistics for the six models selected above. Let us first consider

the root mean squared error (RMSE), the mean absolute error (MAE) and the mean absolute

percentage error (MAPE). The formulas for these statistics as calculated by EViews (EViews User’s

Guide Part II, “Basic Data Analysis”, 2015) are given as follows:

√ ∑ (∗ − )2ℎ+=+ [1]

∑ |∗ − |ℎ+=+ [2]

100 ∑ ∗ −

+

=+ /ℎ [3]



12

where the ∗ are the forecasted values of series, the are the actual values of the series, ℎ is the

number of observations that comprise the forecast period and is the final period of the sample used

for estimation. It can be deduced from the equations above that the RMSE and the MAE are invariant

to additive transformations to

{} and

{∗

} (the series of

and

∗ respectively) and are sensitive to

multiplicative transformations thereof;



13

Table 9: Forecast Evaluation Statistics

7.2 7.6 7.9 8.1 8.2 8.5

Root Mean Squared Error 0,233025 0,233939 0,232661 0,227842 0,222692 0,241225

Mean Absolute Error 0,174137 0,177961 0,175856 0,176699 0,170752 0,188668

Mean Abs, Percent Error 81,88688 114,4257 119,8167 3,423309 3,303542 3,657336

Theil Inequality Coefficient (UI) 0,490039 0,478561 0,497255 0,021892 0,02141 0,023171

Bias Proportion 0,038518 0,045005 0,006261 0,013418 0,021025 0,009302

Variance Proportion 0,179617 0,135159 0,191533 0,467837 0,513652 0,379572

Covariance Proportion 0,781866 0,819836 0,802206 0,518745 0,465323 0,611126

Theil Inequality Coefficient (UII) 0,819317 0,822532 0,818037 0,043657 0,042670 0,046221

Table 10: Residual Diagnostics

7.2 7.6 7.9 8.1 8.2 8.5

Jarque-Bera Test for Normality

Jarque-Bera Statistic 1,131019 0,703254 0,676746 0,980092 0,926902 0,667017

Prob, 0,568071 0,703542 0,712929 0,612598 0,629109 0,716406

Breusch-Godfry Serial Correlation Test, 4 Lags

F-statistic 0,471431 1,804706 0,406063 1,26157 2,001406 0,996703

Prob. 0,7566 0,1337 0,8039 0,29 0,0999 0,413

Obs*R-squared 1,956233 6,898901 1,59509 5,185523 8,004894 4,176669

Prob. 0,7438 0,1413 0,8097 0,2688 0,0914 0,3826

ARCH Heteroskedasticity Test, One Lag

F-statistic 0,105423 0,067843 0,157677 0,087633 0,055419 0,204926

Prob. 0,746 0,795 0,6921 0,7678 0,8143 0,6517

Obs*R-squared 0,107288 0,069067 0,160388 0,089198 0,056425 0,208357

Prob. 0,7433 0,7927 0,6888 0,7652 0,8122 0,6481



14

the opposite is true of the MAPE. However, none of these three statistics are comparable across

difference transformations of the dependent variable, as the series {} and {∆} do not generally

contain the same forecastable information (*****).



15

Section 2: Robustness Check

As a robustness check, McLean (2015) evaluates the relationship between the L_SAPU index and

L_SAVI (the log of the South African Volatility Index) over the period 2007m7 to 2012m11. The results

found here were mixed. Correlation between L_SAVI and L_SAPU was found to be negligible at 0.013,

but was also found to be much higher for the first differences of these series (0.177); this finding

suggests that there is non-negligible correlation between the changes in these indices (Mclean,

2015:14-15). Less positively, a simple regression of the L_SAVI on L_SAPU did not produce a

statistically significant coefficient, a result that is probably partially a product of the small sample of 65

observations used in these estimates, but which nevertheless bodes ill as a reflection of the robustness

of the index (McLean, 2015: 15).

In light of the opacity of this previous investigation, this section adds to McLean’s (2015) robustness

checks with an examination of the relationship between SAPU and an index (administered by the BER

(Bureau for Economic Research) and obtained from Quantec’s Easy Data (2015) database) which

tracks the percentage of a representative sample of manufacturing firms that cite the current political

climate as a constraint on production. This index is denoted here as MSPC.

Thinking about the data generating process underlying both of these indices leads to two testable

hypotheses. Firstly, the theoretical and empirical literature documenting the effects of policy uncertainty

on production suggest that policy uncertainty constrains production by increasing the option value of

future investment (Rodrik, 1991); thus, one would expect SAPU and MSPC to be positively correlated

and possibly cointegrated. Secondly, SAPU is arguably a direct measure of policy uncertainty, whileMSPC is a variable that should respond to policy uncertainty; thus one would expect SAPU to be weakly

exogenous with respects to MSPC.

2.1 Pretesting

Table 12 shows the ADF critical and test statistics for a variety of transformations on MSPC and under

a variety of specifications, broken into sample periods that correspond with the data availability of

SAPU. As indicated in 12.1 and 12.2 respectively, ADF tests conducted over the full sample, specified

with a constant or a constant and a deterministic trend, produce test statistics that are too high to reject

the hypothesis of a unit root; high p-values of 0.5963 and 0.8504 respectively make this rejection

uncontentious. Furthermore, under 12.3 it can be seen that for the first difference of MSPC (D_MSPC)

the hypothesis of a unit root can be rejected at the one percent level of significance; hence we can

conclude from these full sample tests that MSPC is difference stationary (i.e. is I(1)). With reference to

12.10, 12.11 and 12.12, the same conclusion may be drawn with regards to the log of MSPC (L_MSPC)

and for the first difference of the log of MSPC (DL_MSPC).

When MSPC is examined in sections corresponding the data availability of SAPU, tests for the level of

integration of the series produce results similar to those reported in Section 1 for SAPU in the

corresponding sample periods: For the period 1994Q1 to 2001Q4, MSPC and L_MSPC tests as I(0);



16

Table 12: ADF tests MSPC

1994Q1 to 2014Q2 1994Q1 to 2001Q4 2003Q1 to 2014Q2

12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9

Dependent Variable MSPC MSPC D(MSPC) MSPC MSPC D(MSPC) MSPC MSPC D(MSPC)

t-Statistic -1.363019 -1.411030 -13.40636 -5.061119 -5.382322 -9.542237 -0.944454 -3.641963 -9.035099

ADF Test critical values:

1% level -3.514426 -4.076860 -3.514426 -3.661661 -4.284580 -3.670170 -3.581152 -4.170583 -3.581152

5% level -2.898145 -3.466966 -2.898145 -2.960411 -3.562882 -2.963972 -2.926622 -3.510740 -2.92662210 % level -2.586351 -3.160198 -2.586351 -2.619160 -3.215267 -2.621007 -2.601424 -3.185512 -2.601424

Prob.* 0.5963 0.8504 0.0001 0.0003 0.0007 0.0000 0.7649 0.0371 0.0000

Exogenous: Constant Constant Constant Constant Constant Constant Constant Constant Constant

Trend Trend Trend

12.10 12.11 12.13 12.14 12.15 12.16 12.17 12.8 12.9

Dependent Variable L_MSPC L_MSPC D(L_MSPC) L_MSPC L_MSPC D(L_MSPC) L_MSPC L_MSPC D(L_MSPC)

t-Statistic -2.313132 -2.312348 -12.56348 -4.813128 -5.105216 -9.568363 -0.992759 -3.538037 -8.323042


1% level -3.513344 -4.075340 -3.514426 -3.661661 -4.284580 -3.670170 -3.581152 -4.170583 -3.581152

5% level -2.897678 -3.466248 -2.898145 -2.960411 -3.562882 -2.963972 -2.926622 -3.510740 -2.926622

10 % level -2.586103 -3.159780 -2.586351 -2.619160 -3.215267 -2.621007 -2.601424 -3.185512 -2.601424

Prob.* 0.1704 0.4224 0.0001 0.0005 0.0013 0.0000 0.7482 0.0470 0.0000

Exogenous: Constant Constant Constant Constant Constant Constant Constant Constant Constant

Trend Trend Trend



17

for the period 2003Q1 to 2014Q2, MSPC and L_MSPC test as trend stationary at the five percent level

of significance.

Table 13 shows the results of a similarly implemented battery of ADF tests for a variety of

transformations of SAPU; as in Section 1, full sample tests are omitted here due to the discontinuity in

the data from 2002Q1 to 2002Q4. For the period 2003Q1 to 2014Q2 the results in Table 13 are similar

to those presented in Section 1: 13.4 and 13.10 indicate that we cannot reject the hypothesis that SAPU

and L_SAPU are nonstationary, while the rejection of the hypothesis in 13.5 and 13.11 suggest that the

data is trend stationary. For 1994Q1 to 2001Q4, the results obtained for SAPU differ importantly from

those obtained for the series’ monthly counterpart: for this period and at this data frequency, the

hypothesis that the series is non-stationary cannot be rejected at the ten percent level for SAPU and

L_SAPU; the rejection of the null hypothesis obtained in 13.2 and 13.5 thus suggest that this portion of

the series is trend stationary.

Table 13: ADF Tests SAPU (Quarterly)

1994Q1 to 2001Q4 2003Q1 to 2014Q2

13.1 13.2 13.3 13.4 13.5 13.6

Dependent Variable SAPU SAPU D(SAPU) SAPU SAPU D(SAPU)t-Statistic -2.592892 -3.791835 -5.627037 -2.424996 -3.959771 -8.359628


1% level -3.689194 -4.323979 -3.711457 -3.581152 -4.170583 -3.581152

5% level -2.971853 -3.580623 -2.981038 -2.926622 -3.510740 -2.926622

10 % level -2.625121 -3.225334 -2.629906 -2.601424 -3.185512 -2.601424

Prob.* 0.1063 0.0323 0.0001 0.1407 0.0172 0.0000

Exogenous: Constant Constant Constant Constant Constant Constant

Trend Trend

13.7 13.8 13.9 13.10 13.11 13.12

Dependent Variable L_SAPU L_SAPU D(L_SAPU) L_SAPU L_SAPU D(L_SAPU)

t-Statistic -2.432925 -5.319496 -4.917714 -1.313868 -3.931164 -9.590602


1% level -3.661661 -4.394309 -3.752946 -3.588509 -4.175640 -3.588509

5% level -2.960411 -3.612199 -2.998064 -2.929734 -3.513075 -2.929734

10 % level -2.619160 -3.243079 -2.638752 -2.603064 -3.186854 -2.603064

Prob.* 0.1414 0.0013 0.0007 0.6149 0.0186 0.0000

Exogenous Constant Constant Constant Constant Constant Constant

Trend Trend



18

2.2 Correlations

Though it is not robust to sources of endogeneity, the correlation structure between variables can

provide valuable insight regarding the relationship between them. Table 14 displays the correlation

coefficients for the SAPU and MSPC in levels, first differences, log levels and for the first differences of

the log levels of these series. Columns corresponds to lags, leads or contemporaneous value of SAPU

or its transformation (the relevant transformation of SAPU and MSPC for each row is indicated in the

left hand column); a positive (negative) number indicates that the reported correlation is between MSPC

and a lead (lag) of SAPU (or transformations thereof). For convenience, positive correlations are

highlighted in yellow, negative correlations are highlighted in blue.

As can be seen in Table 14 below, correlation between MSPC and SAPU for the period 1994Q1 to

2001Q4 (14.1) is positive for contemporaneous values of SAPU, as well as for its first and second lag.

Leads of SAPU are found to be negatively correlated with MSPC, but these correlations are of a

negligible magnitude. This correlation structure is consistent with the above-stated hypotheses that

SAPU and MSPC should be positively correlated and that SAPU should be seen to drive the variation

in MSPC. However, this result is somewhat reversed for L_MSPC and L_SAPU: here, leads of L_SAPU

are found to be positively correlated with L_MSPC, and lags of L_SAPU are negligibly negatively

correlated with L_MSPC, suggesting that it is L_MSPC that drives L_SAPU. Furthermore, for D(MSPC)

Table 14: Correlations for Leads and Lags of SAPU

14.1: 1994Q1 to 2001Q4

+2 +1 0 -1 -2

MSPC and SAPU -0,0073 -0,0141 0,1821 0,2347 0,2393

D(MSPC) and D(SAPU) 0,1435 -0,1465 0,1907 0,0236 0,0526

L_MSPC and L_SAPU 0,3056 0,2607 0,2506 -0,0400 -0,0789

D(L_MSPC) and D(L_SAPU) -0,0014 -0,1424 0,2917 -0,0257 0,1232

14.2: 2003Q1 to 2014Q2

+2 +1 0 -1 -2

MSPC and SAPU 0,7687 0,8255 0,8853 0,9050 0,8844

D(MSPC) and D(SAPU) -0,1361 -0,0691 0,2428 0,1166 0,0842

L_MSPC and L_SAPU 0,7987 0,8424 0,8771 0,8817 0,8661

D(L_MSPC) and D(L_SAPU) 0,0527 0,0230 0,2459 -0,0380 -0,1001



19

and D(SAPU) and for D(L_MSPC) and

D(L_SAPU), the correlation structure for lags

and leads of SAPU breaks down into obscure

patterns. However, there remains the positive

finding that for all transformations of the dataSAPU and MSPC are contemporaneously

positively correlated; this is the least one

would expect if these two series contain

information derived from the same underlying

source.

Referring now to 14.2, the correlation structure

between SAPU and MSPC is very pronounced

in the period 2003Q1 TO 2014Q2, with

positive correlations ranging from a low of

0,7687 at two leads of SAPU, up to a high of

0,9050 at one lag of SAPU; similarly

pronounced correlations are also evident for

L_SAPU and L_MSPC. Little of a conclusive

nature can be drawn from this association

given the indications of nonstationarity that

characterize this section of the data (as

discussed in Section 2.1), but nevertheless

this result is very encouraging. To put this

finding into perspective, Baker, Bloom and

Davis (2013:18), in checking the robustness of

their United States policy uncertainty index

(USPU), found that the VIX and USPU shared

a contemporaneous correlation of 0.578. For

a more direct check of the efficacy of their

methodology, Baker, Bloom and Davis(2013:18) also construct a news-based equity

market uncertainty (EMU) index and find that it exhibits a contemporaneous correlation of 0.733 with

the VIX. Though Baker, Bloom and Davis (2013) do not report on the stationarity of these series, a

visual inspection of them (see Baker, Bloom and Davis (2013:46)) suggests that they are also

nonstationary. Given this context, the findings presented here, which indicate a greater

contemporaneous correlation between SAPU (L_SAPU) and MSPC (L_MSPC) than was found

between the VIX and Baker, Bloom and Davis’ (2013) EMU index, should be regarded as strong

evidence of the reliability of SAPU as a measure of policy uncertainty.

2

3

4

5

6

7

94 96 98 00 02 04 06 08 10 12 14

L_SAPU L_MSPC

Figure 9: L_SAPU and L_MSPC 1994Q1 to 2014Q2

-1.6

-1.2

-0.8

-0.4

0.0

0.4

0.8

1994 1995 1996 1997 1998 1999 2000 2001

L_SAPU L_MSPC

Figure 10: L_SAPU and L_MSPC 1994Q1 to 2001Q4 (Demeaned)

-1.2

-0.8

-0.4

0.0

0.4

0.8

03 04 05 06 07 08 09 10 11 12 13 14

L_SAPU L_MSPC

Figure 11: L_SAPU and L_MSPC 2003Q1 to 2014Q2 (Demeaned)



20



21



References

Bonate, P. 2006 Pharmacokinetic-Pharmacodynamic Modeling and Simulation. New York: Springer

Science & Business Media, Inc.

Burnham, K.P. & Anderson, D.R. 2002. Model Selection and Multimodel Inference: A Practical

Information-Theoretic Approach. New York: Springer Inc.

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