Monetary policy, informality and business cycle fluctuations in a developing economy vulnerable to external shocks.
Haider, Adnan ; Din, Musleh Ud ; Ghani, Ejaz 等
5. NUMERICAL SOLUTION AND CALIBRATION RESULTS
The model is solved numerically using the general methodology as
provided in Uhlig (1999), Klein (2000) and Sims (2002). In order to
obtain numerical solutions, it is required first to transform
model's complete set of non-linear equilibrium relations to its
log-linearised form. This is done by taking first order Taylor
approximations to each equilibrium condition around its steady state
path. A brief description of this approach along with log-linearised
equilibrium conditions are provided in Appendix-A. The numerical
solutions are then obtained by employing the method of undetermined
coefficients. This step considers the autoregressive shocks as key
exogenous processes. Our DSGE model consists of sixteen exogenous
shocks, among which nine are domestic and rest are propagated from
external sources. Based on the propagation mechanism of these shocks,
numerical algorithm computes model empirical moments, impulse responses
of endogenous variables to each exogenous process and variance
decomposition results. These results allow us to examine the empirical
fit of the model and to understand the behaviour of economy to various
structural shocks.
5.1. Model Parameterisation
Model parameterisation step requires assigning numbers to
structural parameters of the model.
We calibrate the model at quarterly frequency with the choice of
parameter values that are approximately consistent with key features of
developing economy in general and Pakistan's economy in particular.
Almost all parameter values used in this model have initially been
calibrated using partial estimation approach. The rest of few parameter
values whose data for estimation is unavailable, are then taken from the
existing DSGE/RBC literature on emerging market economies. The chosen
values of these parameters can be gleaned from personal introspection to
reflect strongly held beliefs about the validity of economic theories.
Therefore, the selection must reflect researcher confidence about the
likely location of structural parameter of the model. In our model,
there are forty-three structural and thirty-two shock related
parameters. The estimated values of structural parameters are given in
Table C1, whereas values to the shock related parameters are given in
Table C2 of Appendix C.
The first category of structural parameters is related to household
preferences. The parameter value of discount factor ([beta]) is taken as
0.991. This value is consistent with the quarterly estimates of discount
factor [beta] for Pakistan economy as given in Ahmed, et al. (2012).
This value is set in order to obtain historical mean of real interest
rate in the steady state. Ahmed, et al. (2012) estimates suggest that
the long run real interest rate is lower in most of developing
countries. Therefore, the selected parameter value of intertemporal
discount factor is quite useful for our model calibrations as our prime
concern is to replicate business cycle fluctuations of a developing
economy like Pakistan. The degree of external habit persistence (h) in
consumption is set as 0.36 [Haider and Khan (2008)]. This parameter
value implies that degree of habit persistence in consumption is quite
low as compared with advanced economies; see for instance, Lubik and
Schorfeide (2005). The semi-elasticity of money demand to interest rate
([mu]) is taken as -0.15 [Haider, et al. (2012)]. It shows that money
demand is less elastic with respect to nominal interest rate. The
relative weight in preferences assigned to real money balances
([[zeta].sub.M]) is 0.25 [Ahmad, et al. (2012)]. The parameter value of
wage elasticity of labour supply (ct/,) taken as 1.5. This value is
consistent with the estimates reported by Ahmad, et al. (2012) and Fagan
and Messina (2009). The share of core goods in the consumption basket of
household ([[alpha].sub.c]) is taken as 0.75. This value is computed
from Pakistan's Household Integrated Economic Survey (HIES),
2010-11. A similar estimated value is used by Batini (2010b) for Indian
case. This shows that subsistence level of consumption is high in most
of developing economies and people spend approximately 75 percent of
their budget on core-consumption related goods. The rest of share is
allocated to oil and energy related items. The elasticity of
intertemporal substitution between core and oil goods consumption bundle
is fixed at 0.35. This value is consistent with posterior estimates
given in An and Kang (2009) for the Korean and Medina and Soto (2007)
for Chilean economies.
The share of formal sector goods in the core consumption basket
([[upsilon].sub.c]) is set to be 0.55. The estimate is closer to value
given in Ahmad, et al. (2012) and Khan and Khan (2011). The elasticity
of substitution between formal and informal goods consumption bundle
([[phi].sub.c]) is taken as 0.70. This high value of substitution
elasticity shows significant share of informal goods consumption in the
core consumption bundle. The share of home goods in the formal
consumption basket ([[gamma].sub.c]) is fixed at 0.65. The corresponding
elasticity of substitution between home and foreign goods consumption
bundle ([[eta].sub.c]) is taken as 1.12. These parameter values are
consistent with the posterior estimates given in An and Kang (2009) and
Haider and Khan (2008). The share of formal labour in aggregate labour
supply ([[LAMBDA].sub.L]) is taken as 0.29. This value is consistent
with estimates used in Choudhri and Malik (2012) and Ahmad, et al.
(2012). (18) This is due to the fact that in developing countries about
70 percent of the non-agriculture labour is employed in the informal
sector. The corresponding elasticity of substitution between formal and
informal labour supply ([p.sub.L]) is fixed to be 2.00 and elasticity of
substitution between different labour skills in the formal sector
([[epsilon].sub.L]) is taken as 0.80. Ahmad, et al. (2012) has estimated
these values using labour force survey data from Pakistan.
The second category of parameters is related to aggregate
investment and production side of the economy. The share of home
investment in aggregate private investment ([gamma].sub.I]) is fixed at
0.52. The corresponding elasticity of substitution between home and
foreign private investment ([[eta].sub.I]) is taken as 1.20. These
parameter values are consistent with Medina and Soto (2007). Labour
share in formal sector production ([[eta].sub.H]) is fixed at 0.54. This
parameter value is taken from Bukhari and Khan (2008). The capital
depreciation rate ([delta]) is taken as 0.03. It implies capital
depreciates annually around 12 percent. Bukhari and Khan (2008), Haider
and Khan (2008) and Ahmad, et al. (2012) studies used a similar
estimates for depreciation rate for Pakistan economy. For simplicity,
the elasticity of substitution between differentiated formal
intermediate varieties ([[epsilon].sub.H]) is fixed at 1.00. Following,
Medina and Soto (2007) flat tax rate on both final home goods
([[tau].sub.H]) and final imported goods ([[tau].sub.F]) are fixed at
0.15. The share of nonoil factor inputs in the production of
intermediate formal sector varieties ([[alpha].sub.H]) is fixed 0.65 and
for intermediate informal sector varieties ([[alpha].sub.U]) at 0.75.
The corresponding elasticity of substitution between oil and other
factor of inputs in formal production ([[omega].sub.H]) is taken 0.85
and for factor of inputs in informal production ([[omega].sub.U]) at
0.95.
The third category of parameters is related to price setting
behaviour in both formal and informal sectors. Recent survey studies on
the frequency of price change in emerging market economies suggest that
prices are more flexible as compared with the developed countries [see
for instance, Choudhary, et al. (2011)]. In Calvo (1983) staggered
pricing sense, less degree of stickiness provide reasonable notion about
frequent price changes in developing economies. This means, probability
of not changing price is quite low in a given quarters. Therefore,
following survey estimates as given in Choudhary, et al. (2011), the
parameter values of degree of price stickiness for formal sector home
goods sold domestically ([[phi].sup.i.sub.H]) is fixed at 0.24 and for
formal sector home goods sold abroad ([MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII]) is at 0.64 respectively. On the other hand, the
degree of price stickiness for formal sector imported goods
([[phi].sup.i.sub.F]) is taken as 0.70. Finally, the degree of price
indexation to each category is adjusted to replicate flexible nature of
prices. These parameter values price stickiness along with the degree of
indexation are also consistent with the posterior estimates as given in
Haider and Khan (2008) for Pakistan and de-Castro, et al. (2011) for of
Brazilian case. (19) Choudhary, et al. (2011) survey finding also
suggest us to set degree of price stickiness for informal sector goods
([[phi].sup.i.sub.U]) at 0.21. The degree of price indexation for these
goods ([[chi].sub.U]) is fixed at 0.70.
The last category of structural parameters is associated with the
central bank reaction function. We have estimated these parameters which
satisfied optimal monetary policy criteria in a Ramsey policy sense. We
assume optimal monetary policy as a baseline case. The estimated optimal
parameter values suggest inflation coefficient ([[psi].sub.[pi]]) to be
fixed at 1.21, which is slightly low as compared with Taylor (1993)
suggestions for the US case. The optimal relative weight related to
changes in output growth ([[psi].sub.y]) is taken at 0.60 and to
exchange rate fluctuations ([[psi].sub.rer]) at 0.05. These estimated
values show that central bank in a developing economy also put
significant weights on growth and exchange rate stability objectives
along with inflation. Finally, the optimal weight associated with AR(1)
term of policy rate shows considerable inertia, which is around 63
percent. These parameter values for the baseline case are also
consistent with an empirical study by Ahmed and Malik (2011) for
Pakistan case. We have also used different parameter values of monetary
policy reactions function to evaluate alternative monetary policy
regimes in the context of developing countries.
The parameter values related to sixteen exogenous shocks are
reported in Table C2 of Appendix C. We have computed persistence level
and standard deviation corresponding to each shock. For the benchmark
developing economy, we have used data from Pakistan to estimate these
parameters. The results show that external shocks are more volatile as
compare with domestic one. Also, these shocks signify high persistence,
which suggests developing economies are more prone to shocks propagate
mainly from the external side of the economy. Finally, for model
calibrations, steady state values of key endogenous variables are given
in Table C3 of Appendix C. These values are calculated by taking long
term averages to each variable. For this purpose the data is taken from
Pakistan economy. However, estimates related to informal output is taken
from Gulzar, et al. (2010).
5.2. Quantitative Assessment and Empirical Fitness of the Model
In this section, we try to assess the quantitative performance of
the model by drawing comparisons with quantitative features of the
business cycle statistics. The main purpose of this quantitative
.assessment is to test empirical fitness of the model. It examines,
whether a constructed DSGE model is really capable to replicate standard
features of business cycles which prevail in the developing economies,
like Pakistan. The standard RBC/DSGE literature tries to compare
statistical moments of the data from those generated by the model.
Therefore, following this approach, we focus on the model's
prediction with respect to the volatility of key macroeconomic
variables, relative volatility of these selected variables with respect
to formal sector output and the contemporaneous correlations of these
variables with each other. The results are reported in Table C4, C5 and
C6 of Appendix C.
The Table C4 shows the standard deviations for formal consumption,
informal consumption, formal sector output, informal sector output,
agriculture commodity output, formal sector inflation, informal sector
inflation, real exchange rate, aggregate labour, aggregate wages,
domestic investment, foreign investment, oil consumption, domestic
interest rate, government consumption and current account. The table
also provides results of relative standard deviations of these variables
with respect to formal sector output. The model matches the observed
volatility in formal sector consumption, informal sector consumption,
inflation in the formal and informal sector and aggregate output in the
Pakistan, which turns out to be high but not very different from the
volatility in these two key variables in other developing economies.
(20) It over predicts the volatility in few other endogenous variables,
like agriculture commodity output, domestic and foreign investments and
oil consumption. The predicted volatility of the domestic interest rates
and current account are slightly lower than observed in Pakistan but
higher than observed in the emerging countries and these are about equal
to the mean volatility for the panel of all selected countries as taken
in Aguiar and Gopinath (2007). The same is true for volatility of the
rest of the variables; the model's predicted value being higher
than Pakistan's and lower than in the other developing countries
but approximately equal to the average volatility for the complete set
of countries.
In terms of the relative standard deviations, the model predicts
higher volatility of formal and informal consumption relative to GDP.
This is a unique stylised business cycle fact of emerging counties and
the model is fairly capable to replicate this fact. However, it predicts
a higher volatility of domestic and foreign investment relative to
formal sector output than observed in Pakistan and other emerging
economies. As far as the relative volatility in rest of the selected
endogenous variables with output is concerned, this model underestimates
the results as compared to the data.
The Table C5 presents the contemporaneous correlation and Table C6
shows autocorrelations of all these sixteen variables. Among these
results, contemporaneous correlations of all endogenous variables with
respect to aggregate formal sector output have prime importance due to
theoretical moment matching concerns of the model. Autocorrelations
results indicate non-stationary behaviour of selected variables at
level. Our DSGE model does well in matching these correlations,
producing results with correct signs that lie between the observed
values for Pakistan and other emerging economies. Broadly speaking, the
model does quite well quantitatively, producing moments that are roughly
consistent with empirically observed counterparts in developing
economies in general and Pakistan economy in particular.
5.3. Impulse Responses
The impulse response functions compute dynamic responses of model
variables to the fundamental economic disturbances. These are plotted
against the number of quarters that have elapsed since the shock
occurred. (21) We have computed impulse-response of the key endogenous
variables to the sixteen exogenous shocks hitting the domestic economy,
under five different monetary policy regimes. These alternative regimes
are represented by conventional Taylor (1993) type interest rate rules
with various policy assumptions. (22) These assumptions vary with
respect to the different responsiveness of the central bank to its
various key objectives, like inflation, economic growth, interest rate
smoothing and exchange rate stability. However, among all these policy
specifications, price stability is taken as a primary objective of the
central bank.
The first specification named as baseline policy, which follows
optimal Ramsey policy rule defined in terms of welfare optimisation
criteria. We have calculated optimal reaction parameters using this
specification. The values are as follows: [[psi].sub.i], = 0.63,
[[psi].sub.[pi]] = 1.21, [[psi].sub.y] = 0.60 and [[psi].sub.rer] =
0.05. These relative weights associated with the baseline rule are
characterised by a moderate reaction to inflation, a stronger response
to changes in economic growth, a significant degree of interest rate
smoothing and a marginal reaction to exchange rate movements. The second
specification assumes considerable inertia in the policy rate and
central bank in this case only respond to inflation. However, the
responsiveness is less aggressive. The policy reaction parameters used
in this specification are: [[psi].sub.i], = 0.90, [[psi].sub.[pi]] =
1.01, [[psi].sub.y] = 0 and [[psi].sub.rer] = 0. The third specification
is similar to second one. However, in this case response of central bank
to inflation is more aggressive. The policy reaction parameters used in
this specification are: [[psi].sub.i] = 0.90, [[psi].sub.[pi]] = 1.65,
[[psi].sub.y] = 0 and [[psi].sub.rer] = 0. The forth specification
assumes considerable inertia in the policy rate and central bank in this
case respond to both inflation and output. However, the output response
is less aggressive. The policy reaction parameters used in this
specification are: [[psi].sub.i] = 0.90, [[psi].sub.[pi]] = 1.21,
[[psi].sub.y] = 0.53 and [[psi].sub.rer] = 0. Last specification of
monetary policy rule is similar to forth with a difference is that here
response to output is more aggressive. The policy reaction parameters
used in this specification are: [[psi].sub.i] = 0.90, [[psi].sub.[pi]]=
1.21, [[psi].sub.y] - 0.95 and [[psi].sub.rer] = 0. Based on these
alternative monetary policy specifications, we have simulated impulse
responses and results are displayed in Figures C1 -to- C16 of Appendix
C.
We start by illustrating the dynamic effects of an international
oil price shock on a number of endogenous variables. Figure C1 of
Appendix C represents the impulse responses to a unit positive
innovation in international oil price under the five alternative
monetary policy regimes. This shock has a first round impact on marginal
costs of formal and informal sector production. Therefore, inflation
rises in both these sectors. Due to increase in inflation, output and
consumption fall in each sector respectively and then converges to its
steady state level. On the household side, oil price increase creates a
negative income effect that reduces domestic consumption. As a result,
the demand for different types of goods in the consumption basket falls.
There is also a substitution effect that tends to increase the demand
for both formal and informal goods. However, since the degree of
substitution between oil and the other types of goods is low, this
effect does not counteract the negative income effect on the demand for
core goods. Moreover, this shock also pushes up the cost of formal and
informal sector firms producing these types of goods, and their prices
relative to the price of foreign goods increases. This shock also has a
negative impact on domestic and foreign investment. Exchange rate
depreciates in this case and this shock forces a further monetary
tightening in the policy interest rate. (23) We have also notice that
both monetary policy specifications generate a similar kind of
responses, unlike the specification with more aggressive reaction to
output, in which more adverse consequences in all endogenous variables
are being observed.
Next, we have computed dynamic impulse responses associated to unit
negative shock in domestic and foreign investment. On average, the
responsiveness of endogenous variables to these shocks under all policy
regimes is similar. However, in terms of magnitude, the negative shock
to foreign investment has more adverse consequences as compared with
domestic one. The results are displayed in Figure C2 and C3 of Appendix
C. Following these shocks, output drops and inflation rise up both in
formal and informal sectors. Exchange rate depreciates, as investment
goods are relatively more import intensive than other final goods. The
monetary policy response under most of regime specifications to these
shocks lead to a surge in the interest rate. Similar kinds of results
are associated with negative adjustment cost shock which is displayed in
Figure C4 of Appendix C. These results suggest implications associated
with the sudden stops in foreign capital inflows and their likely
adverse consequences on the key endogenous variables. Domestic economy
ends up with stagflation situation in the form of high inflation and a
reduction in output.
Figure C5 of Appendix C show impulse responses to a negative
foreign demand shock. Due to this shock, all domestic endogenous
variables behave according to the theory. A reduction in the foreign
demand leads to an increase in domestic formal sector inflation, a
tightening of monetary policy, and a fall in output, consumption and
employment. On the other hand a negative commodity price shock generates
an output contraction, a reduction in employment, and a surge in
inflation. This last effect is explained by the currency depreciation,
which increases imported inflation and makes capital goods expensive.
This creates a burden on marginal costs and it forces a reduction in
real wages. Finally, current account faces deficit position and interest
rate rises due to this shock. These results are displayed in Figure C6
of Appendix C.
The next figure plots the impulse responses to a positive import
price shock. The impact of this shock on the model endogenous variables
is quite similar with international oil price shock. In response to this
shock, domestic formal sector inflation increases, as higher import
prices pushing up the cost of production causes as a surge in domestic
inflation. Aggregate consumption decreases due to a foreign price surge
relative to domestic prices. The economic interpretation of this
reduction is that domestic agents substitute out of foreign produced
goods into home produced goods in response to positive import price
shock, which causes expenditure switching effect and hence leads to a
decline in the aggregate consumption. This shock also leads to exchange
rate depreciation and a reduction in output and all kind of investments.
The results associated with import price shock are displayed in Figure
C7 of Appendix C. Next, we have observed response of endogenous
variables due to a positive foreign interest rate shock. This shock
affects negatively investment decisions and it increases consumption of
foreign sector goods and leads to a reduction in aggregate output and in
employment. This shock also generates a real appreciation of the
currency and a reduction in foreign investment. Optimal monetary policy
response to this shock suggests an increase in the policy rate to boost
up foreign investment. The results of this shock are displayed in Figure
C8 of Appendix C. The next figure plots the impulse responses to a
positive foreign inflation shock. Due to this shock, consumption of
foreign sector goods decline whereas informal sector goods consumption
rises up. This is mainly due to increase in the price of imported items
which forces a substitution affect in the formal and informal
consumption goods. This shock helps the domestic economy by increasing
domestic and foreign investment. Monetary policy reaction is loose to
this shock by decreasing policy interest rate. The results are given in
Figure C9 of Appendix C.
The impulse responses associated with negative transitory and
permanent productivity shocks and negative agriculture commodity
production shock are displayed respectively in Figures C10, C11 and C12
of Appendix C. The productivity shocks have a negative impact on formal
and informal sector output. These shocks also imply an immediate surge
in inflation, as they increase marginal costs of production. However, in
response to the permanent productivity shock, inflation rises
significantly above its steady state after some periods. The monetary
authority tights its policy rate in response to the surge in inflation.
For both shocks, employment initially rises because the reduction of
aggregate demand associated with the monetary contraction. . The
negative transitory technology shock tends to depreciate the real
exchange rate, however the negative permanent productivity shock leads
to a real appreciation of the currency, explained by the monetary policy
tightening that follows some periods after the shock to curb inflation.
Similar results have been observed for the case of agriculture commodity
production shock. The preference shock on the other hand increases
formal and informal sector goods consumption. Due to rise in consumption
demand forces inflation to rise up. The optimal monetary policy response
to this shock suggests a further tightening of policy interest rates. We
have also observed impulse responses to positive domestic labour supply
shock. Due to this shock, output initially rises and then after one
quarter it declines from its steady state. The later decrease in output
shows that agent's substitution between working and leisure
dominates the lower cost of production that arises from the increase in
labour supply. The results associated with these shocks are displayed
respectively in Figures C13 and C14 of Appendix C.
Next figure shows the impulse response to a positive interest rate
shock. This shock can be thought of a contractionary monetary policy
shock. Following an unanticipated surge in the policy interest rate, a
decline in inflation and output is observed both in formal and informal
sectors. On the other hand, exchange rate depreciates due to this shock
before returning to its equilibrium level. This shock also reduces
domestic and foreign investment by increasing cost of business and there
is a fall in the aggregate employment. We have also notice that both
monetary policy specifications generate a similar kind of responses,
unlike the specification with less aggressive reaction to inflation, in
which more contraction in most of endogenous variables are being
observed. These results are displayed in Figure C15 of Appendix C. The
last figure shows impulse responses to positive shock to government
spending. This shock forces domestic policy interest rate to rise which
creates a burden on formal sector firms to invest in private capital. It
results in a crowding-out effect on domestic vis-a-vis foreign
investments. This shock also lowers aggregate wage and increase
employment at a cost of inflation. This shock produces current account
deficit and exchange rate depreciates before returning to its steady
state level. We have also observed that baseline monetary policy yields
more optimal responses as computed with other alternative policy regimes
in terms of contraction in key endogenous variables. These results are
displayed in Figure C16 of Appendix C.
5.4. Variance Decompositions
In the previous subsection, we carefully analysed and understand
the transmission mechanisms of exogenous shocks and corresponding
responsiveness of key endogenous variables to each shock. We also
observed that these shocks propagate from domestic and external sources.
Now question arises, how much do these shocks contribute both as a group
and individually to economic fluctuations in a representative emerging
market economy? It depends not just on the magnitude of the response
when a shock of a given size occurs, but also how often and, on average,
what size of shocks hit the domestic economy. This problem can be
tackled by considering a famous empirical technique known as variance
decompositions, which compute the percentage of the forecast error
variances at various forecast horizons that are attributable to each of
the individual shocks or a group of shocks. We focus here on a medium
term horizon which defined three years of time interval. The results are
reported in Table C7 of Appendix C.
We have observed that external shocks explain around 50 percent of
the fluctuations in consumption of formal sector goods. Whereas,
consumption of informal sector goods is mainly explained by domestic
shocks which uncover 73 percent of its fluctuations. Similar results can
be observed with respect to domestic formal and informal sector output.
External shock mostly explain forecast error in formal sector output,
which is around 52.3 percent, whereas fluctuation in informal sector
output is mainly explained by domestic shocks. In contrast with these
results, however, business cycle fluctuations in both formal and
informal sector inflation are mainly determined by domestic shocks which
cover around 70 percent of total variations. Fluctuations in real
exchange rate and oil consumption are mainly explained by external
shocks whereas, the rest of endogenous variables are hit by shocks
propagated from domestic sources. Finally, we notice that domestic
shocks are relatively more important in explaining movements in
variables over longer horizons whereas, short run fluctuations are
mainly determined from external shocks.
5.5. Performance of Alternative Monetary Policy Rules under
Learning
This section evaluates the performance of baseline optimal monetary
policy rule with four alternative rules incorporating different
responses to inflation, changes in economic growth, interest rate
smoothing and exchange rate fluctuations. We evaluate performance of
these rules with two approaches: first conventional welfare loss
criterion based on quadratic approximation of household utility, and
secondly, through monetary policy learning in terms of analysing
conditions of expectational stability (E-stability) and In-determinacy.
(24)
Table C8 of Appendix C reports the welfare losses associated with
the five monetary policy rules analysed in the previous section:
baseline policy, less aggressive anti-inflation policy, more aggressive
anti-inflation policy, less aggressive reaction to output and more
aggressive reaction to output. There are five panels in this table. The
first panel reports welfare losses in the case of our baseline
parameterisation, while the remaining four panels display the effects of
alternative specifications. Correspond to each panel, we have reported
volatility associated with each endogenous variables. Along with
volatility results, we have also reported welfare loss results
associated to formal and informal sectors. Among these calibration
results, baseline policy out performs all other regime specifications.
It produces less volatility in endogenous variables and yield minimum
welfare loss both in formal and informal sectors. Finally, we have also
observed that more-aggressive anti-inflation policy yield second best
results. The implied welfare losses in this case are quantitatively
small as compared with all other policy regimes.
Next, we follow Bullard and Mitra (2002, 2007) to assess optimal
monetary policy through learning in terms of E-stability and
In-determinacy conditions. Since it is hard to derive clear analytical
results due to complex open economy DSGE model with formal and informal
sectors, we present a numerical simulation on a calibrated version of
our economy and check the determinacy area. We consider four alternative
cases: (i) less inertia in monetary policy and no reaction to exchange
rate, (ii) more inertia in monetary policy but no reaction to exchange
rate, (iii) less inertia in monetary policy with reaction to exchange
rate, and (iv) more inertia in monetary policy with reaction to exchange
rate. For each case, along with all possible values of pair
([[psi].sub.[pi]], [[psi].sub.y]), our numerical routine (25) checks the
Eigen-values of complete model solution to determine whether all the
eigenvalues have real part less than unity. Regions where the solution
is determinate (and thus E-stable) are shown in dark green colour
format. Regions where at least one eigenvalue have a real part greater
than unity are white, i.e. the solution is indeterminate. The resulting
graphs are displayed in Figure C17 to C20 of Appendix C.
From these results, we have noted several policy implications. The
first implication is associated with Taylor Principle. This means that
each case must ensure that model E-stability and equilibrium determinacy
are possible only when central bank sets relative weight to inflation,
which is greater or equal to one. The likelihood of in-determinacy is
maximum in the first case. This means a policy with less inertia in
policy rate along with zero-reaction to exchange rate is not optimal.
The second case also generates E-instability area, even in a case, where
central bank follows Taylor principle. Third and forth policy
combinations produce relatively more desirable results. These cases
ensure more likelihood of determinacy and E-stability. However, results
of first monetary policy evaluation criteria based on society welfare
loss meet with the third specification of monetary policy learning in
terms of E-stability and determinacy. It indicates that central bank in
emerging market economy must follow Taylor Principle and put some with
on exchange rate fluctuations even, there is less inertia in the policy
interest rate.
6. CONCLUDING REMARKS
In this paper, we develop a two-bloc open economy DSGE model
interacting with the rest of the world. Alongside standard features of
emerging economies, such as a combination of producer and local currency
pricing for exporters, foreign capital inflow in terms of foreign direct
investment and oil imports, our model also incorporates informal labour
and production sectors. This intensifies the exposure of a developing
economy to internal and external shocks in a manner consistent with the
stylised facts of business cycle fluctuations. More specifically, we
have considered nine domestic and seven external shocks. In the presence
of these shocks, our model reasonably captures the likely responses of
key endogenous variables, which are consistent with the existing
empirical literature available for developing countries. We also
evaluate the performance of the model by other conventional measures in
terms of theoretical moments matching, like, standard deviations,
contemporaneous correlations, auto-correlations etc. Broadly speaking,
our model comprehensively matches patterns of business cycle statistics
consistent with the empirical facts from emerging market economies. We
then focus on optimal monetary policy analysis by evaluating alternative
interest rate rules and calibrating the model using data from Pakistan
economy as benchmark emerging economy case. The learning and determinacy
analysis suggest monetary authority in developing economies to follow
Taylor principle and to put some weight on exchange rate fluctuations,
even if there is relatively less inertia in the setting of policy
interest rate. Finally, for the future research, this model can be
extended by incorporating banking and non-banking financial sectors to
understand dynamics associated with fiscal borrowing from the banking
system, and its likely consequences on monetary expansion and inflation.
This helps to explain fiscal dominance issue, which is also an important
feature of developing economies in large.
APPENDEX-A
Log-Linearisation and Canonical Representation of the Model
This section proceeds by a model solution methodology with the
log-linearisation and canonical representation of the model along with
its foreign sector counterpart. In order to solve the model, we first
state the first order nonlinear dynamic system that characterises the
competitive equilibrium. In order to calculate the steady state we
transform the system equations into their deterministic steady state
representation and solve using numerical methods. Then we log-linearise
around the deterministic steady state where [[??].sub.t] =
ln([x.sub.t])- ln([bar.x]). At this stage the system is expressed in
terms of relative deviations from the steady state. After solving the
model using the method of Klein (2000) (26) we obtain matrices M and H
which generate the dynamic solution by iterating on the following two
equations:
[Y.sub.t] = [HX.sub.t]
[X.sub.t+1] = [MX.sub.t] + R[[eta].sub.t+1]
Where [Y.sub.t] is a vector composed by control, co-state and flow
variables, [X.sub.t] is a vector of endogenous and exogenous states, H
characterises the policy function and M the state transition matrix.
[[eta].sub.t+1] is an innovation vector and R is a matrix composed of
zeros, ones or a parameter instead of a one. This matrix determines
which variables are hit by the shock and in what magnitude. Given a set
of values of the parameters of the model, this state space
representation will help us to compute the relevant statistics of the
model such as the spectrum of the data, the likelihood function, among
others.
Log-linearised Equilibrium Relations
The small open economy model consists of the following
log-linearised equations for endogenous variables and equations for the
exogenous processes expressed in terms of AR(1) processes.
* Household's aggregate consumption:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.01)
* Household's real demand for money:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.02)
* Aggregate labour supply:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.03)
* Supply of Documented and Undocumented labour:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.04)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.05)
* Composite wage index:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.06)
Where,
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.07)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.08)
* Uncovered interest parity condition:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.09)
* Aggregate consumption bundles:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.10)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.11)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.12)
* Core consumption bundles:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.13)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.14)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.15)
* Consumption bundles of Documented goods:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.16)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.17)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.18)
* Equation of motion of capital stock:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.19)
* Investment goods bundles of documented sector:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.20)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.21)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (s-22)
* Supply and demand for investment goods in documented sector:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.23)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.24)
* FOCs for cost minimisation and marginal cost (Formal Sector):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.25)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S-26)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.27)
* FOCs for cost minimisation and marginal cost (Informal Sector):
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.28)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.29)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.30)
New-Keynesian Phillips Curve for domestic formal-sector goods
consumed at home:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.31)
New-Keynesian Phillips Curve for domestically produced
formal-sector exported goods consumed at abroad:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.32)
New-Keynesian Phillips Curve for the imported goods:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.33)
New-Keynesian Phillips Curve for domestic Informal-sector goods
consumed at home:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.34)
The foreign demand for domestically produced goods:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.35)
Law of one price of commodity-goods:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.36)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.37)
Law of motion of relative prices:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.38)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.39)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.40)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.41)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.42)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.43)
Evaluation of Government Consumption:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.44)
Choice of Fiscal Policy instrument:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.45)
Evaluation of Fiscal net asset position:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.46)
Monetary policy rule:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.47)
Where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is real
rate of interest.
The total aggregate demand for domestically produced goods in the
formal-sector is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.48)
The total aggregate demand for domestically produced goods in the
Informal-sector is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.49)
The total supply for domestically produced goods in the
formal-sector is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.50)
The total supply for domestically produced goods in the
Informal-sector is:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.51)
Real formal-sector GDP:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.52)
Real informal-sector GDP:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.53)
Balance of payments:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.54)
Real exports and corresponding price-deflator:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.55)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.56)
Real imports and corresponding price-deflator:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.57)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.58)
List of Exogenous Shocks:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (S.59)
Where, [[??].sub.t] vector of 16 exogenous shocks and
[[??].sub.[xi],t] is a vector of iid processes.
APPENDIX B
Determinacy and E-Stability Conditions under Monetary Policy
Learning
This section provides technical details about determinacy and
expectational-stability (E-Stability) conditions under learning of
alternative monetary policy rules. A more general discussion can be
found in Evans and Honkapohja (2001) and Bullard and Mitra (2002, 2007).
The fundamental notion of determinacy encapsulate under a necessary and
sufficient condition which ensure equilibrium to exist. This condition
for the uniqueness of such a solution in a system with no pre-determined
variables is that correct number of eigenvalues lie inside the unit
circle. This idea was initially highlighted by Blanchard and Kahn (1980)
and later extended by McCallum (1983), Farmer (1992) and Klien (2000)
for more general cases. Here we elaborate Blachard and Kahn (1980)
method which is more feasible for model determinacy solution.
B1: Conditions of Determinacy/Local-Indeterminacy:
Consider a model given by the general form:
[[PHI].sub.1] [E.sub.t] ([Y.sub.t+1] = [[PHI].sub.2] [E.sub.t]
([Y.sub.t]) + [[THETA].sub.1] [[eta].sub.t]
Where, [Y.sub.t] is a vector of endogenous variables,
[[PHI].sub.1], [[PHI].sub.2] and [[THETA].sub.1], are matrices of
coefficients and [[eta].sub.t], is a vector of exogenous variables which
is assumed to follow a stationary VAR. If [[PHI].sub.1] is invertible,
then we can write the system as:
[E.sub.t] ([Y.sub.t+1]) = [[PHI].sup.-1.sub.1] [[PHI].sub.2]
[E.sub.t] ([Y.sub.t]) + [[PHI].sup.-1.sub.1] [[THETA].sub.1]
[[eta].sub.1]
Let us assume: [PHI] = [[PHI].sup.-1.sub.1] [[PHI].sub.2] and
[THETA] = [[PHI].sup.-1.sub.1] [[THETA].sub.1], then the above system
can re-written
as:
[E.sub.t]([Y.sub.t+1]) = [PHI] [E.sub.t] ([Y.sub.t]) +
[[THETA][eta],
Using the notion of Jordan-decomposition, we can write matrix [PHI]
as: [PHI] = A[LAMBDA][A.sup.-1], where A is the matrix of eigenvectors
of [PHI] and A is the diagonal matrix of eigenvalues. Since vector
[Y.sub.t] may contain backward and forward looking variables, so we can
easily make a partition of [Y.sub.t] into two sub vectors such that
[YB.sub.t], is a vector of backward looking variables and [YF.sub.t], is
a vector of forward looking variables. Therefore, we can write as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Under these settings, we can express the whole system into its
decomposition form
as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
If we pre-multiply both sides by [MATHEMATICAL EXPRESSION NOT
REPRODUCIBLE IN ASCII], then we get the following
result as:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Thus we can easily separate each equation as:
[KB.sub.t+1] = [conjunction] [KB.sub.t] + [[GAMMA].sub.1]
[[eta].sub.t]
[E.sub.t] ([KF.sub.t+1]) = [[LAMBDA].sub.2] [KF.sub.1] +
[[GAMMA].sub.2] [[eta].sub.t]
Based upon above decomposed system into two separate equations,
Blachard and Kahn (1980) provide general determinacy conditions as:
Condition (a): if [absolute value of diag([[LAMBDA].sub.1])]
<< 1 and [absolute value of diag([[conjunction].sub.2])] >>
1 both condition true, then the system has a unique solution (Unique
Equilibria)
Condition (b): if [absolute value of diag([[LAMBDA].sub.1])]
<< 1 holds but [absolute value of diag([[conjunction].sub.2])]
>> 1 does not hold, then the system has many solutions (Multiple
Equilibria)
Condition (c): if [absolute value of diag([[LAMBDA].sub.2])]
>> 1 holds but [absolute value of diag([[LAMBDA].sub.1])] <<
1 does not hold, then the system has no solution. (In-determinacy)
These joint determinacy conditions guide us that, while both
eigenvalues of matrix A can be shown to be real and positive, the
largest is always greater than one. As a result there exists a continuum
of solutions in a neighbourhood of (0, 0) that satisfy the equilibrium
conditions (local indeterminacy) and one cannot rule out the possibility
of equilibria displaying fluctuations driven by self-fulfilling
revisions in expectations. (27) Gali and Monacili (2005) have argued
that these conditions can help to understand various combinations of
alternative monetary policy rules. Their results shown that any kind of
indeterminacy problem can be avoided, and the uniqueness of the
equilibrium allocation restored, by having the central bank follow a
rule which would imply that the interest rate should respond to
inflation and/or the output gap, if these variables to deviate from
their (zero) target values. It requires a credible threat by the central
bank to vary the interest rate sufficiently in response to any
deviations of these variables from target; yet, the very existence of
that threat makes its effective application unnecessary.
In a more general case with complex model structure, Blanchard and
Kahn (1980) conditions guide to categorise determinacy and indeterminacy
regions numerically using any weighting scheme of generalised
Taylor-type monetary policy rule. (28)
B2: Conditions of E-Stability under Learning
This section briefly describes learning framework of alternative
monetary policy rules. Using this framework, we also discuss
expectational stability (E-stability) conditions as proposed by Evans
and Honkapohja (2001). Under learning, the agents do not have rational
expectations, instead they form their expected values with adaptive
learning rules which are updated as data is produced by the system. The
fundamental idea is that at each period private agents possess the
Perceived Law of Motion (PLM) whose form is similar to the Minimum-State
Variable (MSV) solutions. Since the agents do not know the parameter
values of the system, they use a kind of recursive least square updating
rule, which is conditional upon E-stability. According to Evan and
Honkapohja (2001) and Bullard and Mitra (2002), this E-stability is a
notional time concept correspond to stability under real time adaptive
learning under general conditions. According to them, under E-stability,
recursive least square learning solution is locally convergent to
rational expectation equilibrium. They have also argued that under weak
assumptions, if rational expectation equilibrium is not E-stable, then
the probability of convergence of the recursive least squares solution
to rational expectation equilibrium is zero.
To explain this framework, we consider a model of the form:
[Y.sub.t] = A + [BE.sub.t] ([Y.sub.t+1] + [CY.sub.t-1] +
D[[eta].sub.1]
[[eta].sub.t] = [rho][[eta].sub.t-1] + [[epsilon].sub.t]
Where, [Y.sub.t] is a vector of endogenous variables, A, B, C and D
are matrices of coefficients and [[eta].sub.t], is a vector of exogenous
variables which is assumed to follow a stationary VAR. Given this
general form with C [not equal to] 0, an MSV rational expectational
equilibrium takes the following form: (29)
[Y.sub.t] = [bar.a] + [bar.b][Y.sub.t-1] + [bar.c][[eta].sub.t],
Where, [bar.a], [bar.b] and [bar.c] are conformable and are to be
calculated by the method of undermined coefficients. In order to define
E-stability, we consider PLM of the same form of the MSV as:
[Y'.sub.t] = a + b[Y.sub.t-1] + c[[eta].sub.t]
Evan and Honkapohja (2001) and Bullard and Mitra (2002) analyse
different information assumption about how agents update their PLM. The
first assumption treats expectations as determined before the current
values of endogenous variables are to be realised. Under this
assumption, the next period expectation is:
E([Y.sub.t+1]) = a + b(a + b[Y.sub.t-1]] + c[[eta].sub.t]) +
c[[eta].sub.t],
By substituting it into original model form, we can compute Actual
Law of Motion (ALM) as:
[Y.sub.t] = A + (B(I + b))a + ([Bb.sup.2] + C)[Y.sub.t-1] (B(bc + c
[rho]) + D)[[eta].sub.t],
To analyse the E-stability conditions, we have to check the
stability of the mapping T from the PLM to ALM:
T(a, b, c) = (A + (B(I + b))a, [Bb.sup.2] + C, B(bc + c[rho]) + D)
Using this mapping we can easily define principle of E-stability,
which comes from analysing the following matrix of differential
equation:
d/d[tau](a,b,c) = T(a,b,c) - (a,b,c)
Using this differential equation, Evan and Honkapohja (2001) and
Bullard and Mitra (2002) have shown three equilibrium conditions, which
are:
(a) [DT.sub.a] = B(1 + [bar.b])
(b) [DT.sub.b] = [bar.b] [cross product] B + I [cross product]
B[bar.b]
(c) [DT.sub.c] = [rho]' [cross product] B + I B[bar.b]
The rational expectational equilibrium ([bar.a], [bar.b], [bar.c])
is E-stable or learnable if all real parts of the eigenvalues of
[DT.sub.a], [DT.sub.b] and [DT.sub.c] are lower than 1. The solution is
E-unstable, if any of them have real part higher than 1. Alternatively,
E-stability holds, if all eigenvalues of DTa -1, DTb -1 and DTC -1 have
negative real parts. Bullard and Mitra (2002) have shown that these
E-stability conditions actually govern stability under adaptive learning
and therefore, really helpful to understand behaviour of alternative
monetary policy rules in more complex set of DSGE models.
APPENDEX-C
MODEL CALIBRATION RESULTS
[FIGURE C1 OMITTED]
[FIGURE C2 OMITTED]
[FIGURE C3 OMITTED]
[FIGURE C4 OMITTED]
[FIGURE C5 OMITTED]
[FIGURE C6 OMITTED]
[FIGURE C7 OMITTED]
[FIGURE C8 OMITTED]
[FIGURE C9 OMITTED]
[FIGURE C10 OMITTED]
[FIGURE C11 OMITTED]
[FIGURE C12 OMITTED]
[FIGURE C13 OMITTED]
[FIGURE C14 OMITTED]
[FIGURE C15 OMITTED]
[FIGURE C16 OMITTED]
[FIGURE C17 OMITTED]
[FIGURE C18 OMITTED]
[FIGURE C19 OMITTED]
[FIGURE C20 OMITTED]
Table C1
Key Structural Parameter Values for Model
Calibrations (on Quarterly Basis)
Parameters Description Value
[beta] Subjective discount factor 0.99
h Degree of habit formation 0.36
[[zeta].sub.M] Relative weight in preferences assigned 0.25
to real money balances
[mu] Semi-elasticity of money demand to -0.15
interest rate
[[sigma].sub.L] Inverse of wage elasticity of labour 1.50
supply
[[alpha].sub.c] Share of core goods in the consumption 0.75
basket
[[omega].sub.c] Elasticity of substitution between core 0.35
and oil goods consumption bundle
[[upsilon].sub.c] Share of formal sector goods in the core 0.55
consumption basket
[[phi].sub.c] Elasticity of substitution between fonnal 0.70
and informal goods consumption bundle
[[gamma].sub.c] Share of home goods in the formal 0.65
consumption basket
[[eta].sub.c] Elasticity of substitution between home 1.12
and foreign goods consumption bundle
[[LAMBDA].sub.L] Share of formal labour in aggregate 0.29
labour supply
[[??].sub.L] Elasticity of substitution between formal 2.00
and informal labour
[member of L] Elasticity of substitution between 0.80
different labour skills in the formal
sector
[[gamma].sub.1] Share of home investment in aggregate 0.52
private investment
[[eta].sub.1] Elasticity of substitution between home 1.02
and foreign private investment
[member of H] Capital depreciation rate 0.03
[[tau].sub.H] Elasticity of substitution between 1.00
differentiated fonnal intermediate
varieties
[[alpha].sub.M] Flat tax rate on final home goods 0.15
[[omega].sub.M] Share of non-oil factor inputs in the 0.65
production of intermediate formal sector
varieties
[[eta].sub.M] Elasticity of substitution between oil 0.85
and other factor of inputs in formal
production
[member of F] Labour share in formal sector production 0.54
function
[[tau].sub.F] Elasticity of substitution between 1.25
differentiated formal intermediate
imported varieties
[member of U] Flat tax rate on final imported goods 0.15
[[alpha].sub.u] Elasticity of substitution between 0.78
differentiated informal intermediate
varieties
[[omega].sub.u] Share of non-oil factor inputs in the 0.75
production of intermediate informal
sector varieties
[[phi].sup.i.sub.H] Elasticity of substitution between oil 0.95
and other factor of inputs in informal
production
[[chi].sub.H] Calvo degree of price rigidity in formal 0.24
sector home goods
[[phi].sup.i] Indexation of price of formal sector home 0.65
goods
H * Calvo degree of foreign price rigidity in 0.64
formal sector home goods
[chi] * H Indexation of foreign price of formal 0.55
sector home goods
[[phi].sup.i.sub.F] Calvo degree of price rigidity in formal 0.70
sector imported goods
[[chi].sub.F] Indexation of price of formal sector 0.45
imported goods
[[phi].sup.i.sub.U] Calvo degree of price rigidity in 0.21
informal sector home goods
[[chi].sub.U] Indexation of price of informal sector 0.70
home goods
[[phi].sub.i] Relative weight of interest rate inertia 0.63
in monetary policy rule
[[phi].sub.[pi]] Relative weight of inflation in monetary 1.21
policy rule
[[phi].sub.y] Relative weight of output in monetary 0.60
policy rule
[[phi].sub.rer] Relative weight of real exchange rate in 0.05
monetary policy rule
[[gamma].sub.c] Share of government consumption of home 0.75
goods in aggregate government consumption
[[eta].sub.c] Elasticity of substitution between 1.50
government consumption of home and
foreign goods
[zeta] * Share of domestic intermediate goods in 0.04
the consumption basket of foreign agents
[eta] * Price elasticity of the foreign demand of 0.78
domestic goods
Table C2
Data for Benchmark Model Calibrations
(Shock Process Paramters)
Persistence Volatility
in Shocks in Shocks
([[rho] ([[sigma]
Exogenous Shocks .sub.xi]) .sub.xi])
Transitory negative productivity shock 0.86 0.05
in formal sector
Negative agriculture commodity production 0.75 1.45
shock
Negative foreign commodity price shock 0.89 1.82
Negative foreign demand shock 0.65 3.55
Positive foreign interest rate shock 0.55 0.37
Positive foreign inflation price shock 0.81 0.27
Domestic tight monetary policy shock 0.31 0.03
Domestic labour supply shock 0.85 1.02
Positive preference shock 0.81 2.51
Domestic fiscal policy shock 0.78 0.15
Negative investment adjustment cost shock 0.35 4.02
Negative domestic investment shock 0.65 4.55
Negative foreign investment shock 0.68 4.58
Positive import price shock 0.89 4.16
Positive international oil price shock 0.95 6.25
Permanent negative productivity shock 0.92 0.04
Table C3
Data for Benchmark Model Calibrations
(Annualised Steady State Values)
Steady State
Variables Values
Formal sector output growth 5.0%
Informal sector output growth 3.5%
Formal sector overall inflation 7%
Informal sector inflation 9%
Current account to GDP ratio 2.5%
Formal sector consumption to Output ratio 70%
Informal sector consumption to informal output ratio 75%
Domestic private investment to output ratio 12%
Foreign private investment to output ratio 9%
Table C4
Standard Deviations and Relative Volatility with Output
(Calibration results from Baseline version of the Model)
Relative S.D with
Variables S.D Formal Output
Formal Consumption 5.365 1.109
Informal Consumption 9.316 1.926
Formal Sector Output 4.837 --
Informal Sector Output 4.811 0.995
Agriculture Commodity Output 7.269 1.503
Inflation in Formal Sector 1.376 0.284
Inflation in Informal Sector 2.18 0.451
Real Exchange Rate 5.718 1.182
Aggregate Labour 6.071 1.255
Aggregate Wages 4.792 0.991
Domestic Investment 20.219 4.180
Foreign Investment 24.992 5.167
Oil Consumption 17.269 3.570
Domestic Interest Rate 0.554 0.115
Government Consumption 9.414 1.946
Current Account 2.816 0.582
Table C5
Pairwise Correlation Matrix
(Calibration Results from Baseline Version of the Model)
Var. Var. Var. Var. Var. Var. Var. Var.
01 02 03 04 05 06 07 08
Var.01 1.00 -- -- -- -- -- -- --
Var.02 0.20 1.00 -- -- -- -- -- --
Var.03 0.74 0.39 1.00 -- -- -- -- --
Var.04 0.16 0.13 0.33 1.00 -- -- -- --
Var.05 0.02 0.02 0.06 0.00 1.00 -- -- --
Var.06 -0.02 -0.31 -0.23 0.09 0.05 1.00 -- --
Var.07 0.01 -0.25 -0.07 0.03 0.03 0.85 1.00 --
Var.08 0.28 0.07 0.42 -0.08 -0.02 -0.39 -0.15 1.00
Var.09 0.31 0.36 0.49 0.39 0.07 0.39 0.23 -0.05
Var.10 0.30 0.62 0.45 -0.01 -0.01 -0.67 -0.44 0.32
Var.11 0.18 0.55 0.70 0.05 0.03 -0.22 -0.06 0.13
Var.12 -0.02 0.72 0.47 0.06 0.03 -0.30 -0.14 0.08
Var.13 0.46 0.40 0.36 0.07 0.01 -0.18 -0.13 0.04
Var.14 -0.13 0.01 0.03 0.29 0.17 0.10 0.05 -0.12
Var.15 -0.41 -0.37 -0.64 -0.32 0.04 0.22 0.16 -0.25
Var.16 -0.13 -0.38 -0.38 0.31 0.07 -0.11 -0.35 -0.08
Var. Var. Var. Var. Var. Var. Var. Var.
09 10 11 12 13 14 15 16
Var.01 -- -- -- -- -- -- -- --
Var.02 -- -- -- -- -- -- -- --
Var.03 -- -- -- -- -- -- -- --
Var.04 -- -- -- -- -- -- -- --
Var.05 -- -- -- -- -- -- -- --
Var.06 -- -- -- -- -- -- -- --
Var.07 -- -- -- -- -- -- -- --
Var.08 -- -- -- -- -- -- -- --
Var.09 1.00 -- -- -- -- -- -- --
Var.10 -0.25 1.00 -- -- -- -- -- --
Var.11 0.54 0.36 1.00 -- -- -- -- --
Var.12 0.41 0.45 0.87 1.00 -- -- -- --
Var.13 0.20 0.48 0.25 0.24 1.00 -- -- --
Var.14 0.19 -0.12 0.09 0.05 -0.04 1.00 -- --
Var.15 -0.47 -0.22 -0.66 -0.54 -0.29 -0.14 1.00 --
Var.16 -0.32 -0.19 -0.67 -0.68 -0.11 0.07 0.24 1.00
Table Note:
Var.01 Formal Consumption
Var.02 Informal Consumption
Var.03 Formal Sector Output
Var.04 Informal Sector Output
Var.05 Agriculture Commodity Output
Var.06 Inflation in Formal Sector
Var.07 Inflation in Informal Sector
Var.08 Real Exchange Rate
Var.09 Aggregate Labour
Var.10 Aggregate Wages
Var.11 Domestic Investment
Var.12 Foreign Investment
Var.13 Oil Consumption
Var.14 Domestic Interest Rate
Var.15 Government Consumption
Var.16 Current Account
Table C6
A utocorrelations
(Calibration Results from Baseline Version of the Model)
Lag Lag Lag Lag Lag
Order 1 Order 2 Order 3 Order 4 Order 5
Formal Consumption 0.9428 0.8856 0.8282 0.7708 0.7143
Informal Consumption 0.9613 0.8998 0.8262 0.7480 0.6704
Formal Sector Output 0.9007 0.8222 0.7553 0.6948 0.6379
Informal Sector 0.6700 0.4489 0.3008 0.2015 0.1350
Output
Agriculture Commodity 0.7700 0.5929 0.4565 0.3515 0.2707
Output
Inflation in Formal 0.8690 0.7124 0.5828 0.4849 0.4136
Sector
Inflation in Informal 0.7727 0.5205 0.3270 0.1933 0.1052
Sector
Real Exchange Rate 0.8996 0.8120 0.7336 0.6617 0.5951
Aggregate Labour 0.7864 0.6464 0.5500 0.4779 0.4199
Aggregate Wages 0.9893 0.9693 0.9436 0.9149 0.8848
Domestic Investment 0.9071 0.8155 0.7264 0.6395 0.5550
Foreign Investment 0.9401 0.8657 0.7821 0.6937 0.6039
Oil Consumption 0.9687 0.9380 0.9079 0.8786 0.8501
Domestic Interest 0.5795 0.3564 0.2368 0.1702 0.1309
Rate
Government 0.9103 0.8358 0.7701 0.7097 0.6528
Consumption
Current Account 0.7950 0.6284 0.4894 0.3724 0.2734
Table C7
Variance Decomposition
(Calibration Results from Baseline Version of the Model)
Variables Shocks S.01 S.02 S.03 S.04 S.05 S.06
Formal
Consumption 9.11 0.68 6.27 5.49 2.67 0.35
Informal
Consumption 3.77 0.09 7.63 2.49 8.72 1.34
Formal Sector
Output 14.02 1.22 10.25 13.75 4.85 0.45
Informal Sector
Output 3.31 0.09 7.22 2.01 8.32 2.85
Agriculture
Commodity
Output 13.69 0.73 9.87 13.41 4.40 2.85
Inflation in
Formal Sector 1943 0.37 0.59 1.34 6.84 1.07
Inflation in
Informal Sector 3.90 0.21 0.92 0.57 11.33 2.07
Real Exchange
Rate 6.33 0.21 3.27 0.83 24.19 4.67
Aggregate
Labour 24.76 111 1.49 16.90 3.39 0.27
Aggregate
Wages 14.36 0.10 9.27 0.71 4.51 0.79
Domestic
Investment 4.81 0.54 8.21 2.74 16.34 1.75
Foreign
Investment 0.83 0.31 8.01 1.96 17.17 2.03
Oil
Consumption 0.45 0.04 1.28 0.64 1.20 0.20
Domestic
Interest Rate 1.82 4.46 0.80 12.82 4.62 0.94
Government
Consumption 8.16 0.51 32.46 11.78 4.20 0.62
Current Account 1.46 0.92 2.93 12.31 13.54 3.90
Variables Shocks S.07 S.08 S.09 S.10 S.11 S.12
Formal
Consumption 3.32 0.13 24.59 0.05 8.00 3.53
Informal
Consumption 0.27 0.02 10.54 0.01 2.08 55.86
Formal Sector
Output 3.76 0.18 1.43 0.17 18.18 8.06
Informal Sector
Output 2.63 0.02 10.16 0.01 1.60 56.04
Agriculture
Commodity
Output 2.63 0.18 0.94 0.17 17.90 7.65
Inflation in
Formal Sector 2.36 0.13 5.17 0.03 3.28 48.29
Inflation in
Informal Sector 2.38 0.04 2.05 0.01 3.92 64.21
Real Exchange
Rate 4.57 0.10 0.24 0.01 9.44 30.05
Aggregate
Labour 4.57 0.20 2.84 0.24 15.73 10.26
Aggregate
Wages 0.95 0.18 1.26 0.01 1.06 43.20
Domestic
Investment 1.35 0.04 1.89 0.00 20.88 25.22
Foreign
Investment 048 0.00 0.98 0.00 12.99 45.27
Oil
Consumption 0.03 0.00 2.73 0.00 0.08 0.47
Domestic
Interest Rate 45.69 0.01 1.47 0.24 15.41 0.74
Government
Consumption 2.23 0.09 1.48 1.03 14.20 11.97
Current Account 1.51 0.01 1.20 0.01 21.49 31.16
Variables\ Domestic
Shocks S.13 S.14 S.15 S.16 Contribution
Formal
Consumption 9.14 23.42 2.59 0.68 50.1%
Informal
Consumption 4.62 1.29 1.04 0.22 72.9%
Formal Sector
Output 4.48 10.07 8.43 0.70 47.7%
Informal Sector
Output 4.17 0.80 0.55 0.22 74.1%
Agriculture
Commodity
Output 4.03 9.69 8.03 3.87 47.8%
Inflation in
Formal Sector 3.24 7.45 0.33 0.10 79.2%
Inflation in
Informal Sector 1.42 6.82 0.10 0.05 76.8%
Real Exchange
Rate 0.77 15.19 0.04 0.09 51.0%
Aggregate
Labour 1.22 4.14 12.36 0.49 60.2%
Aggregate
Wages 17.10 6.22 0.10 0.17 61.3%
Domestic
Investment 2.33 1.94 11.36 0.59 55.3%
Foreign
Investment 1.86 3.51 0.01 4.59 65.5%
Oil
Consumption 92.09 0.45 0.28 0.06 3.9%
Domestic
Interest Rate 0.34 5.99 0.75 3.91 73.8%
Government
Consumption 4.30 4.23 0.33 2.42 42.1%
Current Account 0.45 1.75 0.40 6.94 64.7%
Variables\ Foreign
Shocks Contribution
Formal
Consumption 49.9%
Informal
Consumption 27.1%
Formal Sector
Output 52.3%
Informal Sector
Output 25.9%
Agriculture
Commodity
Output 52.2%
Inflation in
Formal Sector 20.8%
Inflation in
Informal Sector 23.2%
Real Exchange
Rate 49.0%
Aggregate
Labour 39.8%
Aggregate
Wages 38.7%
Domestic
Investment 44.7%
Foreign
Investment 34.6%
Oil
Consumption 96.1%
Domestic
Interest Rate 26.3%
Government
Consumption 57.9%
Current Account 35.3%
Table Note:
Shock.01 transitory negative productivity shock in formal sector
Shock.02 negative agriculture commodity production shock
Shock.03 negative foreign commodity price shock
Shock.04 negative foreign demand shock
Shock.05 positive foreign interest rate shock
Shock.06 positive foreign inflation price shock
Shock.07 domestic tight monetary policy shock
Shock.08 domestic labour supply shock
Shock.09 positive preference shock
Shock.10 domestic fiscal policy shock
Shock.11 negative investment adjustment cost shock
Shock.12 negative domestic investment shock
Shock.13 negative foreign investment shock
Shock.14 positive import price shock
Shock.15 positive international oil price shock
Shock.16 permanent negative productivity shock
Table C8
Performance of Alternative Monetary Policy Specifications
Less More
Aggressive Aggressive
Baseline Anti-inflation Anti-inflation
Variables Policy *, (1) policy *, (2) policy *, (3)
Formal Consumption 5.365 12.698 7.119
Informal Consumption 9.316 12.021 9.239
Formal Sector Output 4.837 12.820 7.221
Informal Sector 4.811 4.653 4.276
Output
Agriculture Commodity 7.269 7.031 6.964
Output
Inflation in Formal 1.376 4.614 1.297
Sector
Inflation in Informal 2.180 5.832 2.199
Sector
Real Exchange Rate 5.718 14.781 8.826
Aggregate Labour 6.071 18.411 8.191
Aggregate Wages 4.792 10.067 4.429
Domestic Investment 20.219 34.319 24.414
Foreign Investment 24.992 30.922 26.923
Oil Consumption 17.269 17.234 17.365
Domestic Interest 0.554 0.878 0.618
Rate
Government 9.414 19.601 12.298
Consumption
Current Account 2.816 4.309 3.192
Welfare Loss -22.156 -174.546 -43.848
(Formal Sector)
Welfare Loss -54.948 -393.238 -55.905
(Informal Sector)
Policy with Policy with More
Less Aggressive Aggressive
Reaction to Reaction to
Variables Output *, (4) Output *, (5)
Formal Consumption 8.970 8.353
Informal Consumption 9.876 9.865
Formal Sector Output 9.033 7.627
Informal Sector 5.102 4.418
Output
Agriculture Commodity 7.208 7.011
Output
Inflation in Formal 2.269 2.264
Sector
Inflation in Informal 3.292 3.211
Sector
Real Exchange Rate 10.761 9.582
Aggregate Labour 11.637 9.367
Aggregate Wages 6.161 5.832
Domestic Investment 27.225 20.926
Foreign Investment 27.869 24.096
Oil Consumption 17.360 17.283
Domestic Interest 0.699 0.565
Rate
Government 14.616 11.823
Consumption
Current Account 3.504 2.818
Welfare Loss -210.115 -149.063
(Formal Sector)
Welfare Loss -125.291 -119.230
(Informal Sector)
Table Note:
*/ Corresponding to each policy rule specification, percent
standard deviations are given for each variable.
(1/) Baseline policy: [[psi].sub.i], = 0.63; [[psi].sub.[pi]] =
1.21; [[psi].sub.y] = 0.60 and [[psi].sub.rer] = 0.05
(2/) Less aggressive anti-inflation policy: [[psi].sub.i] = 0.90;
[[psi].sub.[pi]] = 1.01; [[psi].sub.y] = 0 and [[psi].sub.rer] = 0
(3/) More aggressive anti-inflation policy: [[psi].sub.i] = 0.90;
[[psi].sub.[pi]] = 1.65; [[psi].sub.y] = 0 and [[psi].sub.rer] = 0
(4/) Policy with less aggressive reaction to output: [[psi].sub.i]
= 0.90; [[psi].sub.[pi]] = 1.21; [[psi].sub.y] = 0.53 and
[[psi].sub.rer] = 0
(5/) Policy with more aggressive reaction to output: [[psi].sub.i]
= 0.90; [[psi].sub.[pi]] = 1.21; [[psi].sub.y] = 0.95 and
[[psi].sub.rer] = 0
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(1) According to Frisch's view on business cycle, a BCF is the
cyclical change in the macroeconomic indicator around its trend. See for
instance, Frisch (1933), Lucas (1977), Blanchard and Watson (1986) and
Bormotov (2009).
(2) Haider and Khan (2008), Ahmad, et al. (2012) and Choudhri and
Malik (2012) are few notable examples.
(3) See for instance, Batini, et al. (2011a. 2011b), Agenor and
Montiel (2010), Aguiar anf Gopinath (2007), Neumeyer and Perri (2005),
Agenor, et al. (2000).
(4) In macroeconomic literature, the terms
"new-Keynesian" or "new-neoclassical synthesis" are
being used synonymously; see, Clarida, Gali, and Gertler (1999), Gali
and Gertler (2007), Goodfriend (2007), Goodfriend and King (1997),
Mankiw (2006) and Ronter (1993, 2011).
(5) This approach is inspired with Frisch's view of the
business cycles [Frisch (1933)].
(6) Specifically, RBC type models deals infinitely-lived
representative agents, whose objective is to maximise its utility by
choosing an optimal path for consumption, real money balances and
leisure, as well as a representative firm whose objective, is to
maximise profits.
(7) The failure of these models to replicate some of the empirical
regularities such as liquidity effects, co-movement of productivity and
employment or the co-movement of real wages and output [Kremer, et at.
(2006)].
(8) Romer (1993) and Goodfriend and King (1997) are in the view
that such combined modelling framework is the result of a synthesis of
real business cycle (RBC) theory and New Keynesian theory.
(9) Some well-known NK-DSGE models developed by most of the central
banks and international policy institutions as noted by Tovar (2008)
are: (a) Bank of Canada (TotEM), (b) Bank of England (BEQM), (c) Central
bank of Brazil (SAMBA), (d) Central bank of Chile (MAS), (e) Central
bank of Peru (MEGA-D), (f) European Central bank (NAWM), (g) Norges Bank
(NEMO), (h) Sveriges Riksbank (RAMSES), (i) US Federal Reserve (SIGMA)
and (j) IMF (GEM and GIMF).
(10) Each household lives in one of two countries, individual
defined on the interval, y [member of] [0, n] lives in the home-country,
and remaining on the interval j [member of] [0, n] lives in the
foreign-country. The value of n measures the relative size of the
home-country.
(11) It also shows habit persistence parameter to reproduce
observed output, rages from 0 [less than or equal to] h [less than or
equal to] 1.
(12) In terms of this discount factor, the riskless short term
nominal interest rate [R.sub.t] corresponds to the solution to the
equation: 1/(1 + [i.sub.t]) = [E.sub.t]([Q.sub.t,t+1]),
(13) [Q.sub.t,t+1] remains a stochastic variable at time t, and
[E.sub.t] denotes expectations conditional upon the state of the world
at time t.
(14) [[phi].sup.i.sub.H] firms adjust prices according to steady
state inflation rate [pi]. This notion introduces inflation persistence
by allowing for price indexation to previous inflation.
(15) The degree of price stickiness is assumed to be same as the
fraction of past inflation indexation. The reason of this crude
assumption is that it validates a basic rationale of Phillips curve.
"In the long-run Phillips Curve is vertical", see for
instance, Gali and Gertler (1999).
(16) If PPP holds, then l.o.p gap implies that pass-through from
exchange rate movements to the domestic currency prices of imports is
imperfect as importers adjust their pricing behaviour to extract optimal
revenue from consumers. See for instance, Monacelli (2005).
(17) A second-order log-linear approximation to the function
([U.sub.t]) around its steady state ([bar.U]) is given by:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In general
[[??].sub.t] = [U.sub.t] - [bar.U] is deviation of ([U.sub.t]) around
its steady state ([bar.U]) and [??], = log([U.sub.t]/[bar.U]) is
log-deviation of ([U.sub.t]) around its steady state ([bar.U]), then
second order approximation can be obtained as: [[??].sub.t] =
[bar.U]([[??].sub.t] + 1/2 [[??].sup.2.sub.t]) +
O([parallel][a.sup.3][parallel]).
(18) Ahmad, et al. (2012) calculate this parameter value by taking
average of ratios of number of people employed in the formal sector to
total number of people employed in the non-agricultural sector during
1990-1991 to 2008-2009. The labour force data used in the calculation of
these ratios is taken from various issues of the Labour Force Surveys,
Pakistan Bureau of Statistics.
(19) These low parameter values shows the less proportion of firms
that do not re-optimise their prices in a given quarters. Furthermore,
these staggered price coefficients also imply that the average duration
of price contracts is around one to two quarters for domestic firms.
This duration is calculated as: 1/(1-[phi]).
(20) See for instance, Aguiar and Gopinath (2007) for a comparison
with other emerging countries.
(21) The impulse responses to a one unit increase in the various
structural shocks are calculated using 10,000 Monte-Carlo simulations.
These simulations are performed using MATLAB version 2010b.
(22) The fundamental reason to consider alternative monetary policy
regimes based on Taylor type rule is due to the fact that monetary
policy in most of the emerging countries switched from the traditional
monetary aggregation rule to the interest rate rule in the late 1990s
[Alba, et al. (2012)]. The current monetary policy practice in such
economies to achieve the objective of price stability no longer involve
setting quantitative target for any nominal variable--for example, broad
money growth or exchange rate-as an intermediate target [Hussain
(2012)].
(23) These results are similar with a recent empirical study by
Khan and Ahmed (2011) for the case of Pakistan.
(24) A brief discussion on monetary policy learning is given in
Appendix B.
(25) These numerical routines are implemented by using Global
Sensitivity Analysis toolkit, available with Dynare 4.3.
(26) Any other method can also be used to solve the log-linear
approximation to the rational expectations solution, e.g., Sims (2002).
(27) This is also known as: stationary sunspot fluctuation.
(28) This is especially under such cases where analytical solution
is not possible.
(29) See, McCallum (1983) for more details on this solution form.
Adnan Haider <ahaider@iba.edu.pk> is Assistant Professor,
Department of Economics and Finance, Institute of Business
Administration, Karachi. Musleh ud Din <muslehuddin@pide.org.pk>
is Acting ViceChancellor, Pakistan Institute of Development Economics,
Islamabad. Ejaz Ghani <ejaz@pide.org.pk> is Dean, Department of
Economics, Pakistan Institute of Development Economics, Islamabad.
Table 1
Stylised Facts about Business Cycles: A Comparison of Developed
and Developing Countries
Business Cycle Statistics
[sigma](Y) [sigma](C)/ [sigma](I)
Countries [sigma](Y) [sigma](Y)
Pakistan * 4.48 1.20 2.76
Developing Economies ** 2.74 1.46 3.91
Argentina 3.68 1.38 2.53
Brazil 1.98 2.01 3.08
Ecuador 2.44 2.39 5.56
Israel 1.95 1.60 3.42
Korea 2.51 1.23 2.50
Malaysia 3.10 1.70 4.82
Mexico 2.48 1.24 4.05
Peru 3.68 0.92 2.37
Philippines 3.00 0.62 4.66
Slovak Republic 1.24 2.04 7.77
South Africa 1.62 1.61 3.87
Thailand 4.35 1.09 3.49
Turkey 3.57 1.09 2.71
Developed Economies ** 1.34 0.94 3.41
Business Cycle Statistics
[sigma](NX)/ [rho]([Y.sub.t], [rho](C,Y)
Countries [sigma](Y) [Y.sub.t-1])
Pakistan * 4.26 0.60 0.92
Developing Economies ** 3.22 0.76 0.72
Argentina 2.56 0.85 0.90
Brazil 2.61 0.65 0.41
Ecuador 5.68 0.82 0.73
Israel 2.12 0.50 0.45
Korea 2.32 0.78 0.85
Malaysia 5.30 0.85 0.76
Mexico 2.19 0.82 0.92
Peru 1.25 0.64 0.78
Philippines 3.21 0.87 0.59
Slovak Republic 4.29 0.66 0.42
South Africa 2.46 0.88 0.72
Thailand 4.58 0.89 0.92
Turkey 3.23 0.67 0.89
Developed Economies ** 1.02 0.75 0.66
Business Cycle Statistics
[rho](I,Y) [rho](NX,Y)
Countries
Pakistan * 0.52 -0.38
Developing Economies ** 0.77 -0.51
Argentina 0.96 -0.70
Brazil 0.62 0.01
Ecuador 0.89 -0.79
Israel 0.49 0.12
Korea 0.78 -0.61
Malaysia 0.86 -0.74
Mexico 0.91 -0.74
Peru 0.85 -0.24
Philippines 0.76 -0.41
Slovak Republic 0.46 -0.44
South Africa 0.75 -0.54
Thailand 0.91 -0.83
Turkey 0.83 -0.69
Developed Economies ** 0.67 -0.17
* Author's personal estimates based on Pakistan data [1951-2011],
** Based on Aguiar and Gopinath (2007).
Table 2
Key Pakistani Macroeconomic Indicators, FY08-FY11
2008
Q1 Q2 Q3 Q4
Inflation (a) 7.43 7.60 8.91 12.00
International Oil Prices (b) 73.57 87.62 95.47 121.11
Growth Rate (c) 3.7
Growth Rate of IPLSM (d) 7.13 2.33 5.65 1.24
Interest Rate (e) 9.83 10.00 10.33 11.83
(8.96) (9.10) (9.37) (10.33)
Fiscal Balances (f) -7.83
(-2.69)
Domestic Debt (g) 2.70 2.87 3.03 3.27
(33.01)
Current Account Balance (h) -2225 -3827 -3636 -4181
(-8.75)
Trade Balance (i) -1.25 -1.94 -2.28 -1.77
(-13.20)
External Debt (j) 44.87
(28.32)
International Reserves (k) 16.24 16.07 14.02 11.77
(7.43)
Real Exchange Rate (l) 97.21 96.32 94.46 93.57
(0.31) (-0.49) (-2.03) (-2.21)
2009
Q1 Q2 Q3 Q4
Inflation (a) 15.64 18.42 19.44 17.03
International Oil Prices (b) 115.47 56.09 44.21 59.17
Growth Rate (c) 1.7
Growth Rate of IPLSM (d) -5.72 -3.48 -12.06 -9.70
Interest Rate (e) 13.00 14.33 15.00 14.00
(12.37) (13.36) (12.65) (12.94)
Fiscal Balances (f) -5.61
(-0.19)
Domestic Debt (g) 3.42 3.57 3.75 3.85
(31.88)
Current Account Balance (h) -4213 -3625 -545 -878
(-6.01)
Trade Balance (i) -1.90 -1.41 -1.05 -1.31
(-11.12)
External Debt (j) 51 .06
(33.15)
International Reserves (k) 9.70 8.84 10.81 12.16
(7.91)
Real Exchange Rate (l) 91.02 94.74 96.72 95.30
(-6.37) (-1.64) (2.38) (1.85)
2010
Q1 Q2 Q3 Q4
Inflation (a) 13.80 11.01 9.68 10.10
International Oil Prices (b) 68.22 75.51 77.05 78.14
Growth Rate (c) 3.8
Growth Rate of IPLSM (d) -0.80 4.02 8.41 5.39
Interest Rate (e) 13.33 12.67 12.50 12.50
(12.10) (12.33) (12.05) (12.04)
Fiscal Balances (f) -6.60
(-1.90)
Domestic Debt (g) 4.01 4.30 4.49 4.89
(33.09)
Current Account Balance (h) -981 -1589 -536 -840
(-2.35)
Trade Balance (i) -1.12 -1.39 -0.93 -1.58
(-9.19)
External Debt (j) 54.78
(32.67)
International Reserves (k) 14.04 15.09 15.06 16.07
(9.74)
Real Exchange Rate (l) 93.25 92.18 95.46 100.49
(2.45) (-2.71) (-1.29) (5.44)
2011
Q1 Q2 Q3 Q4
Inflation (a) 11.26 12.94 13.50 13.66
International Oil Prices (b) 75.50 85.44 99.68 110.12
Growth Rate (c) 2.4 -0.45
Growth Rate of IPLSM (d) -1.13 1.51 4.34
Interest Rate (e) 13.00 13.83 14.00 14.00
(12.43) (12.95) (13.46) (13.31)
Fiscal Balances (f) -6.98
(-2.90)
Domestic Debt (g) 5.19 5.50 5.59 6.23
(34.82)
Current Account Balance (h) -597 483 52 604
(0.27)
Trade Balance (i) -0.82 -0.57 -0.97 -1.44
(-7.79)
External Debt (j) 59.12
(29.56)
International Reserves (k) 16.65 17.31 18.17 18.31
(9.27)
Real Exchange Rate (l) 101.41 101.74 102.08 101.34
(8.76) (10.37) (6 94) (0.84)
Source: State Bank of Pakistan.
Note: The Annual/Quarterly observations mentioned here correspond
to the fiscal years; for example, 2008 is FY08.
(a) Annual average growth rate of consumer price index (CPI),
(b) International Oil Prices (US$ per Barrel).
(c) Annual percentage change in real gross domestic product (GDP).
(d) YoY percentage change in Industrial production of Large Scale
Manufacturing.
(e) SBP Discount rate; figures in parenthesis are 6-month T-bill
rate.
(f) Budget Balance as percent GDP; figures in parenthesis are
primary balance as percent GDP.
(g) Domestic debt in billion of rupees;, figures in parenthesis are
public debt as percent of GDP.
(h) Current Account Balance in Million of Dollars; figures in
parenthesis are current account as percent of GDP.
(i) Trade Balance in Million of Dollars; figures in parenthesis are
trade balance as percent of GDP.
(j) External debt billion of dollars; figures in parenthesis are
external debt as percent of GDP .
(k) International reserves in billions of dollars; figures in
parenthesis are international reserves as percent GDP.
(l) Real effective exchange rate (REER; a rise in the index
indicates appreciation of rupee); figures in parenthesis are
percentage App/Depr.
Table 3
Size of Informal Economy (as percent of Formal GDP)
Malaysia * Sri Lanka * Egypt * Turkey *
1999 32.2 45.2 35.5 32.7
2000 31.1 44.6 35.1 32.1
2001 31.6 44.6 35.2 32.9
2002 31.5 44.1 35.7 32
2003 31.2 43.8 35.4 31.2
2004 30.7 43.9 35.0 30.4
2005 30.4 43.4 34.8 29.6
2006 30.0 42.9 34.1 29.5
2007 29.6 42.2 33.1 29.1
2008 -- -- -- --
2009 -- -- -- --
2010 -- -- -- --
Average 30.9 43.9 34.9 31.1
India * Pakistan ** Bangladesh *
1999 23.3 33.8 36
2000 23.1 40.2 35.6
2001 22.9 39.4 35.5
2002 22.7 37.6 35.7
2003 22.2 35.5 35.6
2004 21.9 33.6 35.5
2005 21.4 33.2 35.1
2006 21 34.0 34.5
2007 20.7 35.0 34.1
2008 -- 31.3 --
2009 -- 27.4 --
2010 -- 28.7 --
Average 22.1 35.8 35.3
* Based on Schneider, et al. (2010).
** Based on Gulzar, et al. (2010)
Fig. 1 Average Degree of Openness [FY01-FY11]
Trade Openness Financial Openness
Malaysia 1.96 2.97
Sri Lanka 0.68 0.42
Egypt 0.56 0.84
Turkey 0.49 1.31
India 0.42 2.82
Pakistan 0.4 2.14
Bangladesh 0.39 0.87
Data Source: International Financial Statistics, IMF Database.
Note: Trade Openness: = (Exports + Imports)/GDP;
Financial Openness: = (Foreign Direct Investment
+ Portfolio Investment)/GDP.
Note: Table made from bar graph.
Fig. 4. Informal Employment (as % of Non-agricultural Employment)
Malaysia 17.40%
Sri Lanka 50.50%
Egypt 51.20%
Turkey 30.60%
India 68.80%
Pakistan 70.00%
Bangladesh 48.03%
Sub-Saharan Region 72.60%
Latin American Region 55.80%
Note: Table made from bar graph.
