Transcript Document

Development Economics,
Part 2, First term 2012
Jean-Bernard CHATELAIN
Université Paris I Panthéon Sorbonne
Theoretical Insights: Growth
and Poverty traps
Eggertson: Why Iceland Starved.
Diamond: Collapse (Easter island et al.).
Fukuyama, Levy: Entry points for
development and political changes.
Econometrics explaining Growth
Growth and Finance, Growth and Aid
Beck: Survey on finance and development.
Arcand et al.: Too much finance
Burnside and Dollar: Aid Policies and
Growth
Doucouliagos Paldam: meta-analysis
Roodman: methodology of applied
econometrics of growth and aid.
Michigan University
Press (2005)
Iceland case /
Institutional Economics
(ISNIE, Ostrom).
Cf. to some extent,
Acemoglu on political
barriers to growth.
2 sectors model
L agriculture + L fishing = L(t).
Pre-industrial Malthusian Model of (cyclical)
Growth (cf. Galor’s papers) determines L(t).
Decreasing returns to scale for both
production functions F(L) and G(L): market
arbitrage and equilibrium:
F’(L agriculture) = (1 – t) G’(L fishing)
Questions: multifactor explanations of the
distorsion factor t during 900 years.
At least 4 actors
Internal: Landowners (Elite), Labor.
External: colonial power (Danmark),
competitors of Danmark.
Why the coalition among the elite remained
relatively stable, despite a relatively large
autonomy from Danmark, despite various
shocks, despite different coastal access to
fish?
Shocks
Climate shocks
Populations increases (starvation, migration)
Changes of colonial power / trade partners
Changes for Danmark the colonial power in
Europe (wars), relative weight of Iceland
policy in all policy matters.
Technological change for fishing and boats
(transportation costs) technology
Explain the distortion (t)
Price effects: tariffs on trade (what about the
domestic price?), transportation costs.
Quantity effects: constraints on trade
partners.
Regulatory constraints (quantity) on labor
sectoral mobility.
Determined from a political equilibrium
between the 4 actors.
Exhaustion of Key Necessary
Input(s)
Y = F (K1, K2, L)
Y=F(0, K2, L) = 0
Exhaustible ressources or
Over-exploited renewable ressources.
Consumption K1(t) > Quantity renewed K1(t)
(Energy, Food).
Explanation WHY K1 tends
towards zero
K1 turns to be a public good (« commons »).
External (climate) shocks, technology change
consuming more K1.
Knowledge: do not understand, do not believe.
Group think versus Dissent (value of dissent but
increases problems of coordination).
Action: problem of coordination, Differents costs in
the short run. (increases enemies, dissent/ lose
friends). Bottom up / Top down.
Fukuyama Levy
Four entry points for reforms against
poverty and political traps
1. Growth (just enough public governance)
2. State Building (tax system/ expenditures/
authority)
3. Political Institutions (rule of law, property
rights, democracy)
4. Civil Society Development (bottom up,
local and regional politics)
The Order of Reforms
and Local Constraints
The order of reform matters.
Their order is constrained by local, historical
and current constraints for the exit of poverty
traps.
External shocks matters (windows for
reforms).
Not all reforms are heading in the
development direction.
Finance and Growth,
Crisis and Political
Economy
Cf. « The failure of
financial
macroeconomics and
what to do about it »
EMBEDDED Macroeconomics:
« Banking Fragile by Political Design »
Political Economy:
Distribution conflicts,
Competing Jurisdictions
Microeconomics
of Financial
Regulation
Financial
Macroeconomics:
Monetary, MacroPrudential (Credit),
Budgetary
Policies, Growth
promoting Finance
Revising views
1. Allocation of capital between sectors (removing
barriers to entry due to credit rationing,
fostering creative destruction, risk sharing).
2. The fluctuations (risk increasing, crisis) channel
of Finance on Growth emphasized.
3. Control of capital flows and regulation fostering
financial stability?
4. Excess ressources into finance in developped
world (excess trades, excess labour due to
excess wages, too much risk-taking, excessive
rents)?
Applied Econometrics
Explaining Growth
Allegory
of
Truth:
in
L’iconologia, by Cesare Ripa,
wood engraving, from Cesare
d’Arpino, 1618.
Beautiful naked (simple) woman
Unvieled by Time
who holds:
the sun (light) or a mirror.
an open book (where is truth)
a palm (strength)
with Earth on her feet (over
earthly matters, in the sky).
Explaining growth
Many causal factors: up to 500 indicators for 50
effects explaining growth (some of the indicators
intend to measure the same effect).
Reverse causality: endogeneity, except for
geography and far in the past.
Outliers.
Poverty traps: thresholds, non linear effects.
For the country monograph to general effects and
policy?
Data: Cross sections; Historical
time series; Panel Data.
1. Historical time series: Maddison’s data set.
2. Cross section, Between (averages of cross
sections over time): look at time invariant
variables (initial GDP per head).
3. Panel data, fixed effects or first differences:
Excellent to eliminate endogeneity of
regressors with time invariant
country/individual unobservable charateristics:
cov(x(it),a(i)). Drawback: not suited for the
effect of in sample time-invariant regressors.
Dependant variable:
Growth versus cycles
Data availibility (1960s) varies for regressors.
Averages over arbitrary 5, 6,…, 10 years.
Trend versus cycles using filters (example
Hodrick Prescott).
Interaction between cycles of GDP/head and the
growth trend, long term effects of crisis?
Less Wrong?
The 12 labours of regression
1.
2.
3.
4.
5.
6.
7.
8.
Inference: statistical versus substantive significance,
Publication bias and multiple comparisons.
Multiple testing
Instrumental variables
Instrumental variables with GMM using panel data.
Power: minimal number N of observations
Maximal number k of regressors, contributions to R2.
Panel data: Within versus Between: time trends versus
endogeneity
9. Time invariant variables in panel data.
10. Outliers detection, residuals graphs, robust estimates; overfitting.
11. Quadratic and interaction terms
12. Spurious regressions and near multicolinearity.
1. Statistical significance
criterion
Abs(x-mean)<sigma=66% of shocks (normal)
Abs(x-mean)<1.96.sigma=95%
Statistical significance versus
substantive significance
Fisher p<0.05 (1925-1940) type I error only.
1 published result in 20 expected to be
wrong.
Gosset (Student), Egon Pearson and Jerzy
Neyman (1928, 1938), type I, type II error
Deirdre (ex Donald) McCloskey and
Stephen Ziliak (1980s to now).
Around 200 A.D.
Disagreement in
Wikipedia: « Statistical
Significance »
This article needs
attention from an
expert in statistics.
Please add a reason or a
talk parameter to this
template to explain the
issue with the article.
WikiProject Statistics or
the Statistics Portal may
be able to help recruit an
expert. (June 2012)
A response
Test a minimal « significant » size of the
effect and not its existence:
Change: H0: ρ=0 by: H0: ρ<ρ(min)
Select the threshold (ρ(min))
Using a loss function of 2 types of errors
Example follows:
Binary case: Power curve: % of True Positive (1-β)
function of % de False Positive (α) (Logit, Probit)
37
38
DECISION making knowing
proba of default: Loss function
LOSS FUNCTION of weighted sum of:
Type I Error: lend to a bankrupt firm next
period: loss of loan and interest.
Type II Error: do not lend to a profitable firm
next period: loss of profit.
LOSS=
LossGivenDefault * P(type I error) +
(r-r0)*P(type II error).
39
Choice of threshold s
minimizing the lender loss function
Min LOSS=LGD*P(P0/1)+(R-r0)*P(P1/0)
Loss given default LGD:
LGD=(%lost)*(1+r)*Loan > (R-r0)*Loan.
LGD*(1-y)+(R-r0)*x=L1 (given level of expected
losses).
y = 1 - L1/LGD + ((R-r0)/LGD)*x
ISO-LOSS LINES: upper ones with lower loss level
(intercept).
40
The straight lines are iso-profit lines defining the optimal cutoff s*
at the tangential point with the Power curve.
41
2. Publication bias
And Meta-Analysis
Veritas
Filia
Temporis
3. Multiple testing: test m several proxies
(corruption, governance indices) one after
the other in m different regressions.
i.e. running many (m) regressions
Remark: It is not a discussion of the number k of
t-test in a given multiple regression
including k regressors .
m=5 trials: one should
use the threshold:
p = 1% = 5%/(m=5)
Data fatigue
« In doing this paper of tremendous scope,
he had a great struggle with the data. He
won a few points, the data won a few points,
and I gather they are both exhausted.»
Nordhaus (1975). It was burdensome to run
regression in 1975.
The mining ratio in applied
macroeconomics (Paldam (2012))
The mining ratio is the number m of regressions made
for each published paper. The full m-set and m itself are
unknown except by the researcher. Meta-analysis study
the m’-set (m’<<m) of reported regressions in disclosed
grey literature (working papers) and published articles.
The costs of regression have fallen, and this has caused
the mining ratio to increase.
Paldam suggests two consequences: (1) It causes
publication biases to rise. (2) It contributes to the rapid
rise in the number and sophistication of econometric
tools, even when it appears that the marginal
productivity of new tools is falling.
The Aid-Growth Regressions
Rocket ?
« It is only by repeating
experiments that one
manage to succeed…
In other terms,…
the more you fail, the
more you have chances
that it works…»
The positive and necessary side of multiple testing:
exploratory data analysis (Tukey); « data mining ».
Along with serendipity, hypothesis changes:
« Randomness only helps prepared minds »
(Pasteur)
Data mining involves six common classes of tasks:
Anomaly detection (Outlier/change/deviation detection) – The identification
of unusual data records, that might be interesting or data errors and
require further investigation.
Association rule learning (Dependency modeling) – Searches for relationships
between variables. For example a supermarket might gather data on customer
purchasing habits. Using association rule learning, the supermarket can
determine which products are frequently bought together and use this
information for marketing purposes. This is sometimes referred to as market
basket analysis.
Clustering – is the task of discovering groups and structures in the data that are
in some way or another "similar", without using known structures in the data.
Classification – is the task of generalizing known structure to apply to new
data. For example, an e-mail program might attempt to classify an e-mail as
"legitimate" or as "spam".
Regression – Attempts to find a function which models the data with the least
error.
Summarization – providing a more compact representation of the data set,
including visualization and report generation.
4. Instrumental Variables:
« Imperfect IV »
E = disturbance
X1 = X1exo + X1endogène
But relative SHARE OF variance
UNKNOWN between the two parts.
Perfect IV: never really available.
Cor ( Z, X1exo ) = 1
(strong > weak)
Cor ( Z, e ) = 0
Often, very exogenous instruments are
weak and conversely = imperfect IV.
Near multicollinearity may corrupt Hausman
Test if uses another regressor as instrument
Y = a.x1 + b. x2 + e
First step: x2hat = a’ x1 + b’.z
Second step: Y = a(IV). x1 + b(IV). (x2hat).
If Near collinearity b(IV) >>>> b:
Hausman test confirms endogeneity and
b(IV) relevance.
Gonzalez (2005) Bank regulation and risk-taking
incentives: An international comparison of bank risk
Non performing loans
(bank level).
Explained by:
REG(high) « freedom in the banking sector in a
country» by Heritage foundation. Lots of freedom
0 (level 1 and 2), government intervention (level
3 and 4).
In the first stage for Q, only « tangible assets» is
absent in the second stage.
9 variables are common regressors in first stage
and second stage.
The parameters are multiplied by a factor 2 to 15
which changes of signs in the second stage with
respect to no IV.
Hausman test of b(IV)-b(nonIV) confirms IV,
researcher states best regression = IV
Before IV: shift to 1 in Reg(high) implies
+2.54 in non performing loans ratio (min=0,
median 0.9, mean 2.3, standard error 4.5,
max=39).
After IV: shift to 1 in Reg(high) implies
ceteris paribus -25 (10 x +2.54 with change
of sign) in non performing loans ratio, 5
times the standard error (>>>1% of shocks
of a normal distribution). Its stretches
credulity.
Now: before and after IV of Reg(high):
Parameter for Reg(high) shifts from +2.5 to
+9.9 or +15.4 using IV. This time the sign is
positive with IV.
Sign flips, very large parameters leading to
impossible ceteris paribus effects on the
dependent variable were downplayed: what
mattered was that the researcher « dealt
with endogeneity » and that « exogeneity is
strongly rejected ».
Instrument selection is very often
disguised « Multiple Testing » on x2hat
Researchers may try
many, many
instruments! Until:
Desired sign and
desired value of
parameter estimate
with statistical
significance and
distinct from OLS.
5. IV with GMM on panel data
Stata Xtabond2 by Roodman
Designed for a few periods T<10
Corrects the bias of the parameter of autoregressive y(i,t-1) bias, but this bias is quite
small as soon as T>10.
Too many instruments, J-test not selective:
Records of multiple testing for this method!
Instrument: X(i,t-2) counts for 1 for each
date of estimation (T=10, 8 instruments for
« one » lagged variable)
GMM-panel estimators are
very unusual IV estimators
Arellano and Bond (1991): First differences instrumented
by lagged levels.
Arellano and Bover (1995), Blundell and Bond (1998):
GMM system First differences instrumented by lagged
levels AND Level equation instrumented by first
differences.
Read: Roodman (2009):
“A Note on the Theme of Too Many Instruments”
Oxford Bulletin of Economics and Statistics
GMM-System: a few limits
1.Multiplies x 2 the number of instruments, and by much more the
number of combinations and trials and errors (multiple testing).
2.Levels have more variances than first differences: the level
equation performs better (in terms of « expected » coefficients).
The debate of using only levels instrumented by first differences
has never really occured.
3.Levels often INCLUDES TRENDS: method not robust to unit
roots and near-multicollinearity (explanatory variables with
common trends).
4.Levels (including trends) are weakly correlated with first
differences (wipes out trends): both GMM panel estimators are
weak instruments methods.
Sargan: do not conclude
the opposite (cf. Ph.D. candidate)
H0: b=0, researcher « happy » if reject the
null; Happy if p<0.05.
Sargan, J-test, Over-identifying restrictions
test:
H0: E(Z(it).e(it))=0, researcher « happy » if
does not reject the null,
Happy if p>0.05.
Selecting IV with GMM using the difference
of Sargan (JBC economics letters, 2007)
Upwards testing.
Begin with a small set of farthest lags as
instruments (m=k+1):
X(i,t-4).
Then add one by one X(i,t-3) or X(i,t-2)
which minimize the Sargan or maximise the
p-value.
Difference of sargan: H0: m are
exogenous is crucial for power.
J(m instruments): H0: m are exogenous
For a joined null H0’ AND the alternative:
J(m+1 instruments) – J(m instruments):
H0’: (m+1)th is exogenous; HA’ alternative: it
is not, with both H0’ and HA’
conditional to H0: m are exogenous.
Upwards procedures are correct, downward
procedures may deliver inconsistent
outcome when H0 not true.
In Xtabond2
The difference of Sargan test of group1
added to group2 is given
But also the difference of Sargan test of
group2 added to group1 is given.
One of the 2 tests is likely to violate H0
which should be valid in the null H0’ and the
alternative HA’ = hence this test has little
power.
Why? Too many « heterogenous/exogeneity »
instruments in the group for J-test.
Difference of J test has the following tendency:
M=4 very exogenous set of instruments:
Only accept an additional instrument which
is very exogenous. (an elitist group selects a
high quality new member to remain at top).
m=7, includes 4 very exogenous and 3
poorly exogenous instruments, accept an
8th which is moderately exogenous: (a
mixed group improves with a medium quality
additional individual)
Diff of Sargan procedure:
depends on the starting set
Initial set of instruments: p-value = 80%
Ends final set at most to 65%
If initial set of instruments p-value is 20%,
takes all lags for all variables and ends to pvalue 5%.
Some samples are more restrictive for Jtest.
6. Sample size determination,
(Number of observations),
Statistical power
Determine sample size
Expect the magnitude of the effect (size of
the partial effect) on the dependent variable
Decide on power (up to 20%+5% errors):
(1-proba type II error)>80%
for proba type I < 5%.
Regression: rule of thumb:
N=10 per each additional covariate.
(N=100, k=10).
76
Adding heterogenous samples
to reach statistical significance?
Y= a x + b +e for N1=20 observations.
Y=0.x + b + e for N2=1000 observations
Statistical significance may be gained if the
mean point of sample 1 is different from the
mean point of sample 2.
To correct: add a dummy for sample 2.
To gain statistical significance: omit this
dummy.
Beware of spurious policy advice following
spurious inference when pooling heterogenous
individuals/countries
From the slide above, if statistical
significance is obtained for 2 groups
(because you omitted a dummy for group
2), you mayrecommend a costly
policy/treatment which is required for group
1 to be extended to group 2.
Researchers may believe that effects
applying to a larger population is a greater
contribution of them.
7. Number of useful covariates
k= 5 to 6
An interesting (not the only one) indicator:
the ordered contribution to differences of
R2(k+1) – R2(k) (remark: taken into account
downwards in t-test power analysis).
Wage equation, Within transformed (fixed
effect): T=7, N = 595 individuals
NT-N-k = 3561 = statistical significance too
easy to get!
The relative importance of
regressors
1. Ordered contributions is an indicator. But
some contributions may be very close so
that the order may overweight too much
differences.
2. Standardized parameters allows to
compare parameters between variables:
but when they exceed 1, it is a signal of
near-multicollinearity.
The relative importance of regressors, taking into
account the number of observations and the
standard error
1. Ordering variables by t-statistics (N is the
same) or p-value, with the *; **;***.
2. Compute the power or the proba of type II
error of the t-test for each regressor. In
this case, the last contribution to R2 given
by: R2 (final regression) – R2 (regression
omitting this variable) is one of the
component of the power of the t-test for
this variable in the multiple regression.
8. Panel Data:
Within versus Between
Orthogonal spaces:
70% Between: average over time of of cross
sections, dimension N = good for time
invariant inference. X(i.)
30% Within: deviation from this average,
NT-N, Regression on within transformed
variables X(it) – X(i.) = fixed effect models.
cov( x(it)-x(i.) , x(i.) ) = 0
Weakness of
Within-Fixed effects
It eliminates cov (x(it) , a(i) ) BUT:
Common trends remains even with T<10:
spurious regressions, trend driven nearmulticollinearity.
Try also first differences (but smaller
variance)
BUT ALSO: large share of variance
(between variance) unexplained.
Specification minimizing the gap Within versus
Between (sub-correlation matrix W = B)
Minimize Panel Hausman Test statistics
while selecting regressors for the null:
H0: b(within)=b(between)
If not rejected:
1.Within regression with trends not spurious
(same results in between/cross section).
2.Between not facing endogeneity Ex(it)a(i)=0
3.Between variance (often 70%) explained.
Baltagi Griffin (1983), N=18, T=19,
Complete Analysis of Variance of
y=log(gasoline/head) explained by:
Between y(i.), dof=N-k-1
Beta
(t-stat,
Dof=15)
Within y(it) – y(i.), dof=NT-N-k-1
Diff-R2
ordered
%
x 83.3% Beta
of var(y) (t-stat,
Dof=321)
Diff-R2
ordered
%
x 17.7%
of var(y)
Log(car/N)
0.63
(7.15)
79,9
66,5
0.61
(55.79)
91.7
16.2
Log(pgas/p)
-0.29
(-2.01)
+4,2
+3,5
-0.35
(-7.47)
+1,2
+0.2
Intercept
0.77
(0.92)
None
R2
=84.1
=70.0
=92,9
=16.4
+1-R2
+15.9
+13.3
+7,1
+1.3
Within transformed variables correlation with year trend:
For the dependent variable: r = 91.5; for log(car/N), r = 0.86
9. Time invariant using panel
data
Orthogonal spaces:
Between: average over time of of cross
sections, dimension N << NT – N
Valid space for inference of time invariant
Z(i) via cancelling out of individual
disturbances.
Regression in each between or
within subspace.
Time Invariant
Y(it) = b X(it) + c Z(i) + a(i) + e(it)
If a(i) random individual effect
If cov ( X(it) , a(i) ) non zero (endogeneity)
Then use: within = fixed effects.
But Z(i) – Z(i.) = 0, eliminates time invariant
Between: cov (Z(i), a(i) ) non zero possible.
Y(i.) = b X(i.) + c Z(i) + a(i) + e(i.)
Time Invariant – Mundlak
Pretest (JBC)
Y(it) = b X(it) + (bw-bb) X(i.)
+ c Z(i) + a(i) + e(it)
If H0: bw-bb=0 not rejected, X(i.) is
exogenous with respect to a(i).
Could be a valid « internal » instrument in
the Hausman Taylor estimator with time
invariant variables (but Weak ???)
10. Outliers – Graphs for detecting residuals patterns.
Anscombe quartet:
all summary statistics identical including t-stats.
Property
Value
Mean of x in each
9 (exact)
case
Variance of x in
each case
11 (exact)
Mean of y in each 7.50 (to 2 decimal
case
places)
Variance of y in
each case
4.122 or 4.127 (to
3 decimal places)
Correlation
between x and y
in each case
0.816 (to 3
decimal places)
Linear regression
line in each case
y = 3.00 + 0.500x
(to 2 and 3
decimal places,
respectively)
INFLUENCE: Studentized residuals over 1.96
DFBetas (for each observation i)
both divided by a standard error
for each observation (i)
Burnside Dollar DFbeta
What to do with studentized
residuals? Robust estimates
99
Over fitting = too many estimated parameters k
in order to capture outliers, high R2 in the
estimation or learning sample, large prediction
errors in a validation sample (« out of estimation
sample » prediction).
100
11. Quadratic term/ interaction
term: graphs Arcand et al.
No statistically significant
effect during crisis. (only
when confidence interval
strictly below or higher
than zero). Never
interpret coefficients
ceteris paribus
a X + b X*X =
(a + b X) * X
aX+bY*X+cY
= (a + b Y) * X + c Y
12. Correlation matrix inspection: Omitted variable bias
is bad except when adding highly collinear covariate or
« classical suppressor »
Y= a1. x1 + a2 . x2 + e
If corr (y , x1) below 0.1 in absolute value
(« classical suppressor »):
If possible, omit x1 in the regression.
If corr (x1, x2) higher that 0.85 in absolute
value: if possible, omit x1 OR x2 in the
regression.
Ordinary least squares estimators
Yule (1898)
With standardized variables (mean = 0, standard
error = 1), we get:

 12 
1  1
  
   1  r 2  r
23
23 
 13 
 r23  r12 
1  r12  r13r23 
  



2 
1  r13  1  r23  r13  r12r23 
A sign reversal or sign flip is more frequent
when including a highly correlated regressor
(high r23). Example: from bivariate x1/x2
to trivariate regression x1/x2 and x3
1
12  r12
 0  r12  0
2

r12  r13r23  1
12.3 
 0, r12  0  0  r12  r13r23
2
1  r23  2

Quadratic or Interaction terms:
How the statistical significance target
leads to spurious effects
(example: growth, aid*policy and aid2*policy)
x1  12aid . policy  13aid 2 . policy  1.23
x1  r12 .aid . policy  13 (aid 2 . policy  0.92aid . policy )  1.23
x1  r12 .aid . policy  13aid . policy .(aid  0.92)  1.23
1

R   r12
r
 13
r12  0.06  0.1
1
r23
r13  0.13 

r23  0.92  0.85 

1

* Statistically significant at the 5% level, N=275
observations; Burnside Dollar (2000)
PIF(1.2)= 0.20/0.095 = 2.13
PIF(1.3)= -0.019/0.0046 = -4.15 (opposite sign)
r12 = 0.13 test r12=0 not rejected
r13 = 0.06 test r13=0 not rejected
r23= 0.92
The (Un-)stability of conditional
independance
Regression
includes x3
Does not reject
β12=0
Reject β12=0
Does not
reject r12=0
Reject r12=0
No effect
Type I
discordance
Type II
discordance
(spurious)
Effect
Statistical significance is easy to obtain when r12
and r13 close to zero and r23 >0.85
r12  f (r13 ), r23  0.95, N  102
Critical regions in the graph
Critical region (reject the null) of t test in trivariate
regression: Inside blue ellipse: feasible value of
correlations coefficients ou Outside the red one.
Critical regions of t-tests in bivariate (simple)
regression: outside the central horizontal and
verticals strips limited by red line.
In the central small square, statistical significance
is reached with trivariate regression except on the
diagonal. By contrast, it is rejected in both
bivariate regressions (x1 with x2 or x1 with x3).
Nowadays, textbooks claim
« Near-multicollinearity is only a problem
when statistical significance is lost
(estimated standard errors are too large). »
Frisch (1933), Tinbergen (1939) and Tobin
(1950): even though it is statistically
significant, one of the near-multicollinear
variable should be omitted or its parameter
constrained.
x1 = 0 x2 + ε1.2
x2 = 0,99 x3 + ε2.3
x1 = 0,14107 x3+ ε1.3
R2 = 0 %
R2 = 0,992 = 98 %
R2 = 2 %
x1 = -7,0181 x2 + 7,0889 x3 + ε1.23
x1 = 0.x2 + 7,0889.(x3 – 0,99 x2) + ε1.23
= ε2.3 (var (ε2.3)=0.02)
R2 = – 7,0181. r12 + 7,0889 . r13
= – 7,0181. 0 + 7,0889. 0,14107 = 100 %
Estimators for the variance and the
t-value



2
2
ˆ
  ˆ1 2 
1
1  R1.23 1  r23

1




2  
 ˆ ˆ 
1
1

r
N

2


23
 13 
 t ˆ1 2 
 r12  r13r23 
N

2
 


 t ˆ 
2
2
r

r
r
1

R
1

r
13
12
23 

 13 
1.23
23



Roodman graph: residuals =
intermediate orthogonalization
Residuals:
e= Aid - a Aid*Tropical + b
Are almost identical to
dummies for Jordan Egypt
and Syria observations.
Residuals: orthogonal to the
regressors subspace.
Three equivalent regressions:
Interaction term (1), with orthogonal regressors (2)
which suggests outlier driven (3).
(1) Growth = b1*aid + b2* aid*tropical area
With statistically significant parameters.
(2) Growth= (b3 close to 0)*aid
+ b4*(aid-a.aid*tropical)
(3) Growth = b5*dummy (Egypt)+b6*dummy(Syria)
+b7*dummy (Jordan)
Publication bias: Journals publish (1): « interaction terms »
general result and never (3): a few outliers exist.
The orthogonal residuals for a regression
between highly correlated variables has indeed a
small variance (RMSE). Used as a regressor
explaining another dependent variable, his
parameter (with its standard error at the
denominator) will mechanically be very high and
with a high sensitivity to outliers.
cov x1 , x3  0,99 x2 
 x1 
 1
2
 x3  0,99 x2 
 x3  0,99 x2 

1
1 r
2
23

1
1  0,99
2
 7,0889
Spurious regression with nearmulticollinearity: X2 has no effect on X1
X3 is highly correlated Very interesting because:
with X2:
X4 unobserved
common cause to X3
and X2
X3=X2(t-1)
X3 as a statistically
significant « control
variable »
Dynamical model
X3=X2 square,
X3= X2 cube
Non-linear model.
X3=X2 * X4
Interaction term
Complementarity
13. Conclusion: Non Spurious Robust Statistics and
Science without Authority Support: Semmelweiss, 1847.
Veritas Filia Temporis: Pasteur confirmed 40 years after
http://www.deirdremccloskey.org/
http://sites.roosevelt.edu/sziliak/
http://www.mostlyharmlesseconometrics.com/
http://www.econ.vt.edu/faculty/2008vitas_research/Spanos/Spano
s%20Research.html
Time invariant variables in panel data:
http://hal-paris1.archivesouvertes.fr/docs/00/49/20/39/PDF/Chatelain_Ralf_Time_Invariant
_Panel.pdf
Exogenous Instruments selection with Panel-GMM:
http://halshs.archives-ouvertes.fr/docs/00/11/72/94/PDF/elinst3.pdf
Spurious regressions with near-multicollinearity:
http://mpra.ub.uni-muenchen.de/42533/1/MPRA_paper_42533.pdf
The good, the bad and the ugly: avoiding the pitfalls of IV
estimation (Murray), 2006.