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ECON2006-E1
ECON2006-E1
The University of Nottingham
SCHOOL OF ECONOMICS
LEVEL 2 MODULE, SPRING SEMESTER 2022-23
ECON2006 APPLIED ECONOMETRICS II
Time allowed 1 hour and 30 minutes
Candidates may complete the front cover of their answer book and sign their desk card but
must NOT write anything else until the start of the examination period is announced
There are two Sections, A and B.
From Section A answer ALL questions.
From Section B answer TWO questions.
Section A accounts for 30%, Section B for 70% of the overall mark.
In Part A is multiple choice and each of the fifteen questions accounts for 2 marks.
In Part B individual questions have separately itemised parts (i.e. (a), (b), etc.)
and the marks for these parts are clearly indicated.
Only a calculator from APPROVED LIST A may be used in this examination.
Dictionaries are not allowed with one exception. Those whose first language is not English
may use a standard translation dictionary to translate between that language and English
provided that neither language is the subject of this examination. Subject specific translation
dictionaries are not permitted.
No electronic devices capable of storing and retrieving text, including electronic dictionaries,
may be used.
DO NOT turn examination paper over until instructed to do so
ADDITIONAL MATERIAL:
INFORMATION FOR INVIGILATORS:
Turn over
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Section A
Answer all of the following 15 multiple choice questions. For each question only one
answer is correct. Record your choice on your exam script, not on this question sheet.
Each question counts for 2 marks, the entire Section A accounts for 30 marks.
Time Series models
1. When we carry out forecasting, (a) we simply take the estimation equation we
obtained from our regression of the in-sample data, say, an ARDL(3,1), and plug
in the values for the x and y variables on the right hand side of the equation to
create a predicted value of y (a forecast) in the forecast sample. In this process of
computing the forecast (b) we ignore the standard errors from the original
ARDL(3,1) regression, but (c) we are able to compute a forecast interval using the
root mean squared error (RMSE) of the forecast.
a. The statement is correct.
b. Parts (b) and (c) of the statement are wrong.
c. Part (c) of the statement is wrong.
d. The statement is wrong in all three parts.
2. We use tools like the ACF (autocorrelation function) and the related PACF (partial
ACF) to learn about the dynamic structure of a variable (e.g. as the name suggests
whether it is ‘autocorrelated’) but we cannot use these to judge the dynamic
structure of a residual series.
a. This statement is wrong in its entirety.
b. Only the first part of the statement (‘learn about… of a variable’) is wrong.
c. Only the second part of the statement (‘cannot use… residual series’) is wrong.
d. Both parts of the statement are correct.
3. Which of the following is a distributed lag (DL) model of order 2
a. = + 1 + 2 +
b. = + + 1 +
c. = + 1 + 2 + 2 +
d. None of the above
4. The first difference of a variable series denotes the lagged value at time t-1
subtracted from the contemporaneous value at time t.
a. True
b. False
Continued overleaf
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5. Which formula is used to compute the long-run multiplier for the following dynamic
regression model:
= 1 + 2 + 1 + 2 + +
a. ( + )/(1 ( + ))
b. ( + )/(1 ( ))
c. ( + )/(1 ( ))
d. ( + )/(1 ( + ))
6. When we carry out a unit root test (e.g. a DF or ADF test), we can determine
whether a variable series is stationary or nonstationary. If the test cannot reject
the null that the series is nonstationary, we cannot tell whether it is I(1) or I(2)…
a. The statement is entirely wrong.
b. Only the second part of the statement (‘we cannot tell…’) is wrong.
c. … unless we conduct a unit root test of the variable series in first differences
(and, if need be, also second differences, etc, until we reject the null).
d. None of the above.
7. If two variables are cointegrated, this means that in the long-run they form a
stable equilibrium relationship, which we can represent with a constant parameter.
a. The statement is wrong, we do not have constant parameters due to
nonstationarity.
b. Since the underlying variables are nonstationary (e.g. random walks), we can
only interpret the sign of the cointegrating relationship, but not the magnitude.
c. Only the part of the statement about the ‘equilibrium relationship’ is correct.
d. The statement is correct.
8. When a time series regression model contains one or more lagged dependent
variable(s) and the residuals are serially correlated then OLS estimates…
a. … of all variables in the model will be biased.
b. … of only the lagged dependent variables in the model will be biased.
c. … of only the lagged dependent variables in the model will be unbiased.
d. … will be unbiased if we use Newey-West standard errors.
Continued overleaf
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Limited Dependent Variable models
9. The marginal effects of x are constant across all values of x in a logit or probit
model but vary across x in a Linear Probability Model.
a. Only the second part of the statement (‘vary… Linear Probability Model’) is
correct.
b. Only the first part of the statement (‘constant… logit or probit model’) is
correct.
c. Both parts of the statement are wrong.
d. The statement is correct.
10. The -AAA- model by construction suffers from heteroskedastic residuals
whereas this is not the case for the -BBB- model. Fill in for -AAA- and -BBB-.
a. -AAA- is logit, -BBB- is linear probability
b. -AAA- is probit, -BBB- is logit
c. -AAA- is logit, -BBB- is probit
d. None of the above.
11. Since the probit and logit estimators are for nonlinear equations the ceteris
paribus assumption of standard multiple regression no longer applies.
a. False
b. True
Panel Data models
12. Below is a generic macro panel regression model for a dependent variable y and
an independent variable x. This equation represents…
= + +
′ +
a. a fixed effects ( ) model with additional year fixed effects
′
.
b. a random effects model.
c. a heterogeneous parameter model with a multifactor error structure.
d. None of the above.
13. In a simple pooled panel OLS model we do not capture the individual-level
effects and hence we know that by construction any individual-level effects are
uncorrelated with our regressors.
a. This statement is correct.
b. Only the first part (‘do not… individual effects’) of the statement is wrong.
c. Only the second part of the statement (‘know that… uncorrelated’) is wrong.
d. None of the above.
Continued overleaf
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14. Below we present some test output from Stata, related to an empirical model of
pupil test performance (dependent variable: the share of pupils in a Michigan
school district which pass a maths test) and various determinants.
—- Coefficients —-
| (b) (B) (b-B) sqrt(diag(V_b-V_B))
| fe_1 re_1 Difference Std. err.
————-+—————————————————————-
lnrexpp | 2.346264 4.834761 -2.488497 1.287811
lnravgsal | -.6153802 1.857593 -2.472973 .6410971
lunch | .0768641 -.315022 .3918861 .0390286
lnenrol | -1.183881 .3994717 -1.583352 .829609
y3 | 9.013511 9.332454 -.3189432 .0663922
y4 | 21.12335 21.11537 .0079759 .2888895
y5 | 21.71696 21.50314 .2138179 .3038124
y6 | 19.05486 18.8586 .1962638 .3328247
y7 | 33.86369 34.00986 -.1461733 .353021
——————————————————————————
b = Consistent under H0 and Ha; obtained from xtreg.
B = Inconsistent under Ha, efficient under H0; obtained from xtreg.
Test of H0: Difference in coefficients not systematic
chi2(9) = (b-B)'[(V_b-V_B)^(-1)](b-B)
= 114.09
Prob > chi2 = 0.0000
a. We are conducting a Hausman test which suggests the difference between RE
and FE results is not systematic.
b. We are conducting a Hausman test which suggests we should prefer the RE
model.
c. We are conducting a Hausman test which suggests the RE model is consistent
under the null.
d. None of the above.
15. Assume panel data for individuals (i) over several years (t). If individual-level
information on human capital (e.g. years of schooling) in a wage regression does
not vary over time (because individuals in this sample went to school first, then
joined the labour force but never returned to education) then we cannot estimate
the effect of human capital on wage if we adopt a random effects (RE) model.
a. True
b. False
END OF SECTION A
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Section B
Answer TWO of the THREE questions in this section. Each question counts for 35
marks (the breakdown within each question is clearly indicated), the entire Section B
accounts for 70 marks.
16. If there is a budget constraint, then the wealth and spending of a household
cannot permanently diverge. What holds for individual households, should also
hold for entire economies. In this question we examine this issue using quarterly
data from the United States for the period 1982-2019. Our analysis adopts current
asset value (w_curr) as our proxy for wealth alongside current consumption
(c_curr). In Figure 16.1 we chart the time series evolution of the two series over
the sample period. Figure 16.2 shows scatter plots of the levels of quarterly asset
value and wealth (left panel) as well as of the first difference of these variables
(right panel). Throughout this question, we adopt a 10% level of statistical
significance for any testing procedures.
Figure 16.1
Figure 16.2
Continued overleaf
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a. In time series econometrics we have a unique methodology for analysing a
long-run equilibrium relationship when we may be concerned that the
relationship in the data is merely spurious. Discuss the concept underlying this
methodology (how can Figure 16.2 speak to this ) and how spurious
regression can arise. [7 marks]
b. Table 16.1 reports results from some statistical tests carried out on the two
variables of interest, consumption and wealth. Describe the tests and their
rationale. What do you conclude for the time series properties of these
variables Can you deduce the order of integration from the test results
provided [8 marks]
c. We adopt the Engle-Granger two-step methodology to analyse whether
consumption and wealth exhibit a long-run equilibrium relationship. Describe in
detail what this methodology entails, including assumptions about the time
series properties of the variable series. [8 marks]
d. What do you make of the results presented in Table 16.2, panel (a) Next,
interpret, with reference to your above discussion of the methodology, the
results in Table 16.2, panel (b) – you can adopt a 10% level of statistical
significance for your econometric judgement. What do you conclude for the
long-run wealth-consumption relationship for the 1983-2019 period What
about the two sub-periods [12 marks]
Table 16.1
Variable p obs Test
Stat.
CV
(1%)
CV
(5%)
CV
(10%)
Consumption
Variable in levels 0 147 -3.444 -3.494 -2.887 -2.577
Variable in levels 6 147 -1.437 -3.494 -2.887 -2.577
Variable in first differences 0 146 -8.250 -3.494 -2.887 -2.577
Variable in first differences 6 146 -3.186 -3.494 -2.887 -2.577
Wealth (Asset value)
Variable in levels 0 147 -0.738 -3.494 -2.887 -2.577
Variable in levels 6 147 -0.718 -3.494 -2.887 -2.577
Variable in first differences 0 146 -10.160 -3.494 -2.887 -2.577
Variable in first differences 6 146 -3.775 -3.494 -2.887 -2.577
Notes: CV refers to the ‘critical value’ for the test carried out. ‘obs’ refers to the sample
size. Variables ‘in levels’ are those plotted in Figure 1, ‘first differences’ are self_xfffe_explanatory.
Continued overleaf
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Table 16.2
Panel (a) EG first stage (top to bottom: 1982-2019, 1982-2001, 2001-2019)
Source | SS df MS Number of obs = 147
————-+———————————- F(1, 145) = 6988.17
Model | 5.97845909 1 5.97845909 Prob > F = 0.0000
Residual | .124049085 145 .000855511 R-squared = 0.9797
————-+———————————- Adj R-squared = 0.9795
Total | 6.10250818 146 .041798001 Root MSE = .02925
——————————————————————————
c_curr | Coefficient Std. err. t P>|t| [95% conf. interval]
————-+—————————————————————-
w_curr | .6767463 .0080955 83.60 0.000 .6607458 .6927467
_cons | 2.068956 .0983716 21.03 0.000 1.874528 2.263383
——————————————————————————
Source | SS df MS Number of obs = 76
————-+———————————- F(1, 74) = 3648.56
Model | 1.17576827 1 1.17576827 Prob > F = 0.0000
Residual | .023846919 74 .000322256 R-squared = 0.9801
————-+———————————- Adj R-squared = 0.9799
Total | 1.19961519 75 .015994869 Root MSE = .01795
——————————————————————————
c_curr | Coefficient Std. err. t P>|t| [95% conf. interval]
————-+—————————————————————-
w_curr | .7059463 .0116872 60.40 0.000 .682659 .7292336
_cons | 1.716015 .1391237 12.33 0.000 1.438805 1.993225
——————————————————————————
Source | SS df MS Number of obs = 75
————-+———————————- F(1, 73) = 640.27
Model | .315223667 1 .315223667 Prob > F = 0.0000
Residual | .03594012 73 .00049233 R-squared = 0.8977
————-+———————————- Adj R-squared = 0.8963
Total | .351163787 74 .004745457 Root MSE = .02219
——————————————————————————
c_curr | Coefficient Std. err. t P>|t| [95% conf. interval]
————-+—————————————————————-
w_curr | .4729979 .018693 25.30 0.000 .4357429 .5102529
_cons | 4.60166 .2317862 19.85 0.000 4.139711 5.063609
——————————————————————————
Panel (b) EG second stage (1982-2019 and subsamples)
Consumption-Wealth obs Test
Stat.
CV
(1%)
CV
(5%)
CV
(10%)
Half-life
Full Sample 1982-2019 147 -2.702 -3.973 -3.378 -3.074 9.5
Early Sample 1982-2001 76 -3.412 -4.046 -3.419 -3.101 5.1
Late Sample 2001-2019 75 -1.664 -4.049 -3.420 -3.102 10.0
END OF QUESTION 16
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17. In this question we study the effect of race on market outcomes. In a seminal
online experiment conducted in 2009, economists Jennifer Doleac and Luke Stein
(2013) advertised new Apple iPods [a digital personal stereo popular before the
launch of the iPhone] for sale through 329 local online market platforms across the
United States. They included a photograph of a hand holding the iPod for sale in
each advert, which enabled them to study the effect of being a black seller (i.e. an
advert including a photo of a dark-skinned hand holding the iPod) on the number
and magnitude of offers from potential buyers compared with that of a white seller
(light-skinned hand). They also studied the effect of being a white seller with a
tattoo (light-skinned hand featuring a wrist tattoo): it is hypothesised that
tattooed sellers are likely to be discriminated against for many of the same
reasons as black sellers. Just to be very clear: there were no black or white or
tattooed sellers; all iPods were sold by Doleac and Stein, who randomly varied the
photographs accompanying the adverts.
In the following we focus on the response characteristics of potential buyers who
got in touch with the seller by email: rather than questions related to the
economics of the sale (e.g. how much the potential buyer is offering) we examine
issues of underlying levels of respect or trust. The research question for this part
of the experiment is: Do black sellers experience different levels of respect or
trust
We investigate the following dependent variables:
Name: the potential buyer included or signed their name in the email;
Polite: the potential buyer was polite, using expressions like ‘please’, ‘thank you’ or
variations (‘pls’, ‘thx’) in the email;
Personal: the potential buyer included a personal story, presumably to appeal to
the seller’s sentiment and secure a lower price.
The two primary independent variables of interest are:
Black: a dummy variable equal to 1 if the hand shown in the advertisement was
dark-skinned and 0 otherwise;
Tattoo: a dummy variable equal to 1 if the hand shown in the advertisement was
light-skinned and tattooed and 0 otherwise;
From a host of additional controls we report below the following:
Christmas: a dummy variable equal to 1 if the advert was posted in the lead-up to
Christmas and 0 otherwise;
Valentine’s Day: a dummy variable equal to 1 if the advert was posted in the lead up to Valentine’s Day and 0 otherwise;
Median HH income (log): the average household income in the locality in logs of
$US 1,000;
% population White: the share of population in the locality who is White;
Poverty Rate: the share of the local population living in poverty.
Continued overleaf
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a. Table 17.1 columns (1) to (3) present results from three different models (one
for each of the three dependent variables) estimated using ordinary least
squares (OLS). Discuss the marginal effects from all three models, covering
statistical significance and economic interpretation. If some results are
surprising to you then you should remark on this. What do we learn from these
results to answer our research question [10 marks]
b. Discuss in detail what the advantages and problems of using OLS are instead of
Logit or Probit when analysing binary outcomes. In your discussion, touch upon
the scatter plots in Figure 17.1, which present predicted outcomes (y-axis,
here: the potential buyer uses their name in the email to the seller) plotted
against a number of the regressors. Are some advantages or problems
seemingly less significant in the current application [6 marks]
c. Table 17.1 columns (4) to (6) present raw estimates from a probit regression.
Interpret the results: what can you say about the statistical and economic
interpretation of these three models [6 marks]
d. Explain how ‘marginal effects’ are constructed for a least squares and a probit
estimator in a limited dependent variable model and the conceptual differences
between them. Distinguish between marginal effects for continuous and binary
independent variables. You can use primarily words but, if you wish, also
graphs and equations in your explanations. [6 marks]
e. In Table 17.2 we report a number of diagnostic test results for the OLS and
Probit models in columns (1) and (4) of Table 17.1. Which model would you
prefer on the basis of overall model success rate (correctly predicted
outcomes) Which would you prefer on the basis of model maximised
likelihood Finally, if you only cared about which of these two models best
predicts which potential buyer uses their name in the response email, which one
would you prefer [7 marks]
Figure 17.1
Notes: These scatter plots present the predictions from Model (1) in Table 17.1
(a dummy equal to 1 if the potential buyer used their own name in the email)
graphed against the dummy variables ‘Black’ and ‘Tattoo’ as well as the continuous
variable ‘Median HH income (logs)’. Each small circle represents the predictions for a
single individual.
Continued overleaf
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Table 17.1
[1] [2] [3] [4] [5] [6]
Estimator OLS OLS OLS Probit Probit Probit
Dep. variable Name Polite Personal Name Polite Personal
Black -0.074 -0.024 0.012 -0.206 -0.066 0.123
[2.54]** [0.82] [0.98] [2.57]** [0.85] [0.97]
Tattoo -0.079 -0.039 0.008 -0.218 -0.105 0.075
[2.48]** [1.22] [0.57] [2.48]** [1.24] [0.52]
Christmas 0.033 0.052 0.010 0.087 0.135 0.109
[0.66] [1.01] [0.58] [0.65] [1.03] [0.70]
Valentine’s -0.107 -0.079 -0.016 -0.317 -0.225 -0.215
Day [2.87]*** [2.04]** [0.90] [2.73]*** [2.02]** [0.86]
Median HH 0.063 0.332 0.117 0.181 0.881 1.253
income (log) [0.55] [2.93]*** [2.58]** [0.58] [2.90]*** [2.99]***
% population 0.001 0.003 0.001 0.002 0.008 0.009
White [0.69] [3.17]*** [1.95]* [0.68] [3.13]*** [1.99]**
Poverty rate 0.003 0.015 0.003 0.008 0.039 0.035
[0.64] [3.32] [1.89]* [0.65] [3.31]*** [2.06]**
Observations 2,547 2,547 2,547 2,547 2,547 2,547
Outcome = 1 36.7% 39.5% 4.5% 36.7% 39.5% 4.5%
Notes: We present estimates (slope coefficients and, in square brackets, absolute t statistics) from OLS and Probit regressions for three different dependent variables as
described in the text. A constant term and a host of other control variables are
included in each model but not reported here. The final row of the table indicates how
frequently the dependent variable of the respective model is equal to 1. *, ** and
*** indicate statistical significance at the 10%, 5% and 1% level.
Table 17.2 Diagnostic Results
Notes: These are diagnostic results for the models for ‘name’ in columns (1) and (4)
of Table 17.1, where the former is for an LPM and the latter for a probit model. Max
LL* is the maximised log likelihood.
END OF QUESTION 17
[1] [4]
Dichotomised predicted outcomes ( )
Data ( ) 0 1 0 1
0 1,527 83 1,522 88
1 873 64 871 66
Max LL* -1687.2 -1607.8
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18. In this question we study the returns to R&D (research and development)
investment in a ‘Griliches knowledge production function’. Griliches’ (1979) work
introduced R&D stock as additional input into a standard log-linear Cobb-Douglas
production function and this approach has proven very popular: in this setup the
coefficient on log R&D stock can be interpreted as the percentage return to R&D
investment. A related literature, following the work by Grossman and Helpman
(1991) and Coe and Helpman (1995), studies ‘knowledge spillovers’ (e.g. how R&D
investment in the transport equipment sector also fosters growth in the machinery
and equipment sector). Curiously these two strands of literature for a long time
developed in isolation (and ignorance) of each other. More recently, researchers
have asked whether we can ignore knowledge spillovers when estimating the
returns to R&D, and it is this question we investigate in the following.
Our sample is made up of twelve manufacturing sectors (from ‘Food and
Beverages’ to ‘Transport Equipment’ production) in ten advanced OECD countries
over the 1980 to 2005 period. The unit of analysis is the country-sector: to avoid
confusion we use the single subscript i for the country-sector. Our dependent
variable is real value added of country-sector i at time t, ln ( ), conventional
inputs are capital and labour, measured as real capital stock (accumulated gross
fixed capital formation), ln( ), and total hours worked, ln ( ). Our primary
variable of interest is the real R&D stock, ln( ) – as can be seen, all these
variables are in logarithms.
In the first part of the question, (a) to (c), we focus on the returns to R&D, i.e. the
statistical significance and magnitude of the R&D stock coefficient. Only part (d)
uses tools from macro panel econometrics.
a. Discuss the general advantages and potential disadvantages of panel data over
single cross-section data. [9 marks]
b. Write down an empirical model for ln ( ) with the above regressors (labour,
capital, R&D) paying close attention to the subscripts and notation in general:
(i) for a pooled OLS model with year fixed effects, and
(ii) for a country-sector fixed effects model with additional year fixed effects.
Explain any specific features of these models in words. [8 marks]
c. Interpret the results in Table 18.1 columns (1) to (4) with regards to (i) the
sum of the three technology parameters, (ii) the returns to R&D investment,
and (iii) common suggestion that the capital coefficient should be ‘around 0.3’ –
see Table notes for pointers. Economic and statistical interpretation! [8 marks]
d. The models in columns (5) and (6) of Table 18.1 present average estimates
from heterogeneous panel estimators: the Pesaran and Smith (1995) MG and
the Pesaran (2006) CCEMG. Discuss which assumptions made in regression
models (1) to (4) are relaxed in these empirical implementations. Which of
models (5) and (6) can flexibly capture spillovers or common shocks Which of
the six models is your preferred model and why What do the empirical results
for this preferred model imply for the returns to R&D investment [10 marks]
Continued overleaf
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Table 18.1
(1) (2) (3) (4) (5) (6)
Estimator POLS FD-OLS RE FE MG CCEMG
Dep. Var. Real Value Added in logs
Labour 0.464 0.634 0.520 0.608 0.568 0.599
in logs [40.72]*** [18.01]*** [6.56]*** [18.41]*** [6.57]*** [9.00]***
Real capital 0.465 0.274 0.459 0.487 0.117 0.244
stock in logs [37.59]*** [3.66]*** [4.84]*** [10.60]*** [0.96] [1.70]*
Real R&D 0.096 0.050 0.083 0.063 -0.058 0.035
stock in logs [22.80]*** [1.88]* [3.16]*** [4.42]*** [0.73] [0.44]
Country- 0.022
Sector trend [2.97]***
Constant 1.080 0.859 0.274 4.468 1.240
[18.79]*** [2.29]** [0.72] [5.63]*** [0.54]
Observations 2,637 2,518 2,637 2,637 2,637 2,637
# of Countries 10 10 10 10 10 10
# of Sectors 12 12 12 12 12 12
Sum of Coeff. 1.025 0.958 1.062 1.158 0.627 0.878
CRS (p) 0.000 0.647 0.026 0.001 0.000 0.468
Residual tests
CD test (p) 0.116 0.208 0.264 0.143 0.000 0.505
Order of Int. I(1) I(1) I(1) I(1) I(0) I(0)
Year dummies yes yes yes yes no n/a
CS dummies no n/a yes yes yes yes
Heterog. no no no no yes yes
CSD addr. no no no no no yes
Notes:
Estimators – We report pooled and mean group estimates for a range of estimators as indicated: POLS – pooled
panel OLS; FD-OLS – pooled panel OLS with all variables in first differences; RE and FE are random and fixed
effects estimators; MG is the Pesaran and Smith (1995) mean group estimator; CCEMG is the Pesaran (2006)
Common correlated effects mean group estimator. C-S trend is a linear trend for each country-sector.
Specifications – CS dummies refers to ‘country-sector fixed effects’, which in our context are the ‘individual fixed
effects’. Year dummies are time fixed effects. ‘n/a’ is for ‘not applicable’ – here this is to mean that while the FD
and the CCEMG do not have year dummies these are ‘accounted for’. ‘Heterog.’ refers to heterogeneous parameter
models. ‘CSD addr.’ indicates whether the estimator explicitly accounts for cross-section dependence.
Interpretation – We interpret the three input estimates (for labour, capital and R&D stock) as technology
parameters which should sum to 1 if production follows ‘constant returns to scale’ (CRS) – if the sum is less
(more) than 1 we observe decreasing (increasing) returns to scale. Most theoretical models find it difficult to
justify decreasing returns to scale. The row ‘CRS (p-value)’ reports the p-value for a test with the null of constant
returns for each model. The R&D stock coefficients can also be interpreted as a ‘return’ to investment in innovation
(multiply by 100 to obtain percentage returns, like a savings rate or interest rate).
Test results – The ‘CD test’ is the Pesaran (2015) test for cross-section dependence, we report p-values; the
‘Order of Int.’ is a qualitative judgement of the residual time series properties, based on a range of panel unit root
tests, including Pesaran (2007). The CRS test is covered above.
Other – Values in square brackets are absolute t-statistics. Estimates in columns (5) and (6) are unweighted
averages of the country-sector-specific results, their t-statistics are based on standard errors computed nonparametrically (following Pesaran, 2006). *, ** and *** indicate statistical significance at the 1, 5 and 10 percent
level – we take the 10% level as the relevant significance level for all estimates and tests.
END