Monetary policy, informality and business cycle fluctuations in a developing economy vulnerable to external shocks.

Haider, Adnan ; Din, Musleh Ud ; Ghani, Ejaz 等

1. INTRODUCTION

Modelling the sources of Business Cycle Fluctuations (BCF) (1) in an open economy Dynamic Stochastic General Equilibrium (DSGE) framework is a fascinating area of research. The main advantage of this framework over traditional modelling approach is due to an additional feature of micro-foundations in terms of welfare optimisation. This feature allows structural interpretation of deep parameters in a way that is less skeptical to Lucas critique [Lucas (1976)]. In DSGE modelling context, the sources of BCF are normally viewed as exogenous shocks, which have potential power to propagate the key endogenous variables within the system. This requires a careful identification, as the transmission of these shocks may emanate from internal side, such as, political instability; weak institutional quality in terms of low governance, or from external side, such as, natural disaster (like, earth quacks and floods); international oil and commodity prices; sudden stops in foreign capital inflows; changes in term of trade and exchange rate, or any combination of shocks from both sides. Also, the nature and magnitude of these shocks may vary, depending upon their variances and persistence levels.

After the seminal work of Kydland and Prescott (1982), a substantial body of research has been conducted to identity key possible sources of BCF and to understand propagation mechanisms of these exogenous shocks. But the earlier attempts have mainly focused on high-income countries, like US and Euro-Zone. But for developing courtiers, like Pakistan, small amount of efforts have been made to understand the dynamics of BCF. (2) Data limitations have often considered as root cause [Batini, et al. (2011a and 2011b)]. As, there is an inherent lack of microeconomic-based surveys and even high-frequency data on major macroeconomic variables is mostly unavailable [Ahmad, et al. (2012)].

Further, the structure of economy in developing countries is partially different as compared with the advanced countries, due to the existence of large informal sector. Structures of goods, labour and credit markets are quite different in formal and informal sector of economy due to variations in endowments and constraints of agents. When relative size of informal sector is small (as in developed economies) then ignoring informal sector may be plausible on the ground that it has very limited impact on aggregates. However, if informal sector represents a non-trivial [Schnieder, et al. (2010)] fraction of an economy as observed in many developing economies then neglecting informal sector in some micro-founded DSGE model may not be justified.

However, recent studies (3) come forward with some stylised-facts of BCF in developing countries. Table 1 provides a summary of business cycle statistics of various macroeconomic indicators in both absolute and relative terms. This table shows that: aggregate income is more volatile in developing countries as compared with developed countries, private consumption and investment relative to aggregate income are substantially more volatile, net exports is countercyclical with aggregate income and real interest rates. However, if we focus on Pakistan economy exclusively and compare its business cycle statistics with other developing countries, then we can observe that aggregate income is more volatile. This volatility is mainly triggered from net exports, which is a main component of aggregate demand. The remaining results are in line with business cycle statistics as we observed in rest of selected developing countries.

Based upon these facts, this study carries two dimensional motivation agenda. First, in developing economies, like Pakistan, with complex economic structures, one of the enduring research questions is to construct and calibrate a valid micro-founded DSGE model featured with nominal and real rigidities. This issue is really challengeable as such economic model which comprehensively explores the transmission mechanism of economic behaviours in the developing economies is scarcely available due to unavailability of high frequency data and because of a major share of the undocumented economy in the observed economic data. Furthermore, due to nature of small open emerging economy, BCF are mainly prone to external shocks, like international oil and commodity price shocks and sudden stops in capital inflows mainly in terms of foreign direct investment. This requires an intensive customisation of readily available DSGE models which are capable to answer these dynamics especially in the context of developing countries. Therefore, this study comes forward to meet these challenges by constructing a small open economy DSGE model feature with informal sectors vis-a-vis various external shocks.

More specifically, we develop a two-bloc DSGE model of a small open economy (SOE) interacting with the rest of the world. Alongside standard features of SOE, such as a combination of producer and local currency pricing for exporters, foreign capital inflow in terms of foreign direct investment and oil imports [see for instance, Batini et al. (2010a), Kolasa (2008), Medina and Soto (2007), Liu (2006), Gali and Monacelli (2005) and Lubik and Schorfheide (2005)], our model also incorporates informal sectors [while considering informal goods production and informal labour supply decisions by households, see for example, Ahmad, et al. (2012) and Batini, et al. (2011a)]. This intensifies the exposure of a SOE to internal and external shocks in a manner consistent with the stylised facts listed above. We then focus on optimal monetary policy analysis, by calibrating the model using data from Pakistan economy.

The rest of the essay is organised as follows: Section 2 provides a comprehensive literature review, Section 3 discusses some stylised-facts of Pakistan economy, Section 4 layout the structure of the model; Section 5 discusses empirical calibration results; and finally last section concludes.

2. LITERATURE REVIEW

DSGE modelling based on New-Keynesian (NK) framework (4) has emerged as a powerful tool to analyse various macroeconomic policies, which are essentially forward-looking in nature. The term DSGE was originally ascribed by Kydland and Prescott (1982) in their seminal work on Real Business Cycle (RBC) model. This modelling approach is based on classical-axioms of flexible prices and money neutrality. The initial contribution on RBC augments the neo-classical Ramsey-Cass-Koopmans growth model by introducing stochastic technology shocks. (5) Kydland and Prescott (1982), Altug (1989) and many of their followers, empirically show that such a modelling approach is capable of reproducing a number of stylised facts of the business cycle of US economy. Another reason of popularity of these models in the early 1990's that these are featured with solid micro-foundations of economic agents in terms of welfare optimisations, subject to various incentive constraints [for example, budget constraints, technological constraints]. (6) The agents-optimisation process implicitly considers Rational Expectation Hypothesis (REH).

These innovations give many advantages over the use of traditional Tinbergen (1953) type reduce-form macroeconomic models. Among them, the most important advantage is that the structural interpretations of deep parameters of RBC type models are less vulnerable to Lucas critique [Lucas (1976)]. The traditional macro-econometric models contained equations linking variables of interest of explanatory factors such as economic policy variables. One of the uses of these models is therefore to examine how a change in economic policy affects these variables of interest, other things being equal. However, in the RBC approach, since the equilibrium conditions for aggregate variables can be computed from the optimal individual behaviour of consumers and firms. Further, the REH enables this optimal behaviour of private agents to use available information rationally, so in this way they should respond to economic policy announcements by adjusting their supposedly actions. Therefore, results obtain from various policy simulations in those reduce-form models, which do not use REH are highly skeptical to Lucas critique. But, as RBC type models are based on optimising agents with REH, so structural parameters are invariant to Lucas-skepticism.

Despite these over-riding advantages, the RBC models had criticised in terms of the usefulness for monetary or fiscal policy simulations. This is because of the critical main assumption of classical dichotomy. This assumption assume that fluctuations of real quantities are caused by real shock only; that is, only stochastic technology or government spending shocks play their role. On the one hand, many researchers felt that the non-existence impact of monetary policy on business cycles is likely downplayed the role of market inefficiencies. On the other hand, the way in which the empirical fit of these models was measured came under strong criticism. (7) See for instance, Summers (1986), Cooley (1995), Rebelo (2005) and Romer (2011).

To address inherent weaknesses in RBC models, later research, however included Keynesian short-run macroeconomic features (usually called nominal rigidities or gradual both of price and wage adjustment), such as Calvo (1983) type staggered pricing behaviour and Taylor (1980, 1998) type wage contracts. This provides plausible short-run dynamic of macroeconomic fluctuations with fully articulated description of the monetary-cum-fiscal policy transmission mechanisms [see, for instance, Christiano, et al. (2005) and Smets and Wouters (2003, 2005)]. Such new modelling framework labelled interchangeably as New-Neoclassical Synthesis (NNS) or New-Keynesian (NK) modelling paradigm. (8) Interestingly, the inclusion of NK ideas, into an otherwise RBC model, proved to be extremely successful in terms of reception by the economic profession as well as in terms of explanatory power of the empirical evidence. In particular, the introduction of nominal rigidities together with market imperfections sufficient to break the neutrality of money typical of RBC models, and hence it opened a new avenue for monetary policy analysis. Due to these reasons, the last decade shows a sharp interest in academics, international policy institutions and central banks in developing small-to-medium, even large-scale NK-DSGE models. (9)

The earlier attempts are based on the construction of closed economy NK-DSGE models [see, Christiano, et al. (2005), Smets and Wouters (2003, 2007) and the references within], with three main reduce-form equations: the New Keynesian Investment-Saving (NK1S) equation, the Hybrid New-Keyenesain Phillips Curve (NKPC) and the monetary policy rule [like, Taylor (1993, 1999) or McCullam (1988)]. But the later emphasis changed from NK Closed economy frameworks to NK Open economy Macroeconomics (NOEM). This approach is based on the seminal work of Obstfeld and Rogoff (1995) with open economy foundations as suggested in Mundell-Fleming framework [See for example, Adolfson, et al. (2007a, 2007b, 2008), Dib, et al. (2008), Justiniano and Preston (2004, 2005), Liu (2006), Gali and Monacelli (2005) and Lubik and Schorfheide (2005)].

The salient features of NOEM models are: optimisation-based dynamic generalequilibrium modelling, sticky prices and/or wages in, at least, some sectors of the economy, incorporating of stochastic shocks, and evaluation of monetary policies based on household welfare [Gali and Monacelli (2005), Monacelli (2005) and Lubik and Schorfheide (2003, 2005)], the persistence of real and nominal exchange rates [Chari et al, (2002, 2007)], exchange rate pass-through [Devereux and Engel (2002), Monacelli (2005) and Adolfson, et al. (2008)] and international oil price shocks [An and Kang (2009) and Medina and Soto (2005, 2006, 2007)]. More specifically, the model developed by Lubik and Schorfheide (2005) is a simplified and straightforward version of Kollmann (2001) and Gali and Monacelli (2005). Like its closed-economy counterpart, the model consists of an (open economy) forward looking IS curve and a NKPC type relationship which determine output and inflation by allowing for monopolistic competition and staggered re-optimisation in the import market as in Calvo-type staggered price setting respectively. The term of trade is introduced via the definition of the consumer price index (CPI) and under the assumption of purchasing-power parity (PPP). The exchange rate is derived from the uncovered interest rate parity condition. Monetary policy is described by a nominal interest rate rule and model is simulated by using Bayesian estimation approach.

Although, modern open economy NK-DSGE models fit the data well empirically and able to explain many policy related questions together with the propagation of exogenous shocks. But these models are essentially constructed for advanced (LIS or European) countries. But, in context of developing countries; however the objective (for example, empirical fit) cannot be achieved by simply replicating NK-DSGE models build for developed countries. As the structure of economy in developing countries is partially different as compared with the advanced countries, due to the existence of large informal sector. Structures of goods, labour and credit markets are quite different in formal and informal sector of economy due to variations in endowments and constraints of agents. When relative size of informal sector is small (as in developed economies) then ignoring informal sector may be plausible on the ground that it has very limited impact on aggregates. However, if informal sector represents a non-trivial [Schnieder (2010)] fraction of an economy as observed in many developing economies then neglecting informal sector in some micro-founded NK-DSGE model may not be justified. Keeping in view of potential implications of informal sectors, especially in the context of emerging market economies, new modelling research tries to extend NK-DSGE models with the dynamics of informality. Batini, et al. (2010b) provide a comprehensive survey of general equilibrium models with informal sectors. This survey covers issues ranging from definitional problems, attached with underground economy to DSGE models incorporating informality. With a focus on informal labour and credit markets, this survey emphasises the development of DSGE models for better understanding of costs, benefits and policy implications associated with informal sector. In a subsequent research, Batini, et al. (2011a) analyse costs and benefits of informality using a dynamic NK-DSGE model. In their model, formal sector is taxed, capital intensive, highly productive and has frictions in labour market. Informal sector, on the other hand, is untaxed, labour intensive, less productive and has frictionless labour market. Incidence of tax burdon only on formal sector and fluctuations stemming from tax financing are major costs whereas wage flexibility has been listed as benefit of informality. Policy experiments of tax smoothing lead this study to conclude that costs of informality are greater than its benefits.

Ahmad, et al. (2012) develop a closed economy DSGE model for Pakistan economy, where they incorporate informality in labour and product markets. This study finds that transmissions of productivity, fiscal and monetary policy shocks to informal sector are weak. In this way, informal sector damps the impact of shocks to economy. Gabriel et. al. (2010) constructs in a similar framework a closed economy NK-DSGE model for Indian economy and estimates it using Bayesian methods. This model has more features of liquidity constrained consumers, financial accelerator and informal sector in product and labour markets. This study step-by-step adds features of financial frictions and informal sector to a canonical dynamic New Keynesian model and concludes that addition of financial frictions and informal sector improves model fit in case of Indian economy.

Aruoba (2010) documents the association of institutions with informality, inflation and taxation using data set of 118 countries. This study finds better institutions are associated with low level of informality, high income taxation and low inflation taxation. On the other hand, poor institutions are associated with high level informality, low income taxation and high inflation taxation. After discussing these stylised facts from data, the study presents a general equilibrium model in which households optimally decides about quantum of informal activity for exogenous condition of institutions. Similarly governments optimally decide about their mix of income tax and inflation tax to finance their expenditures. The study claims this model does a reasonable job in explanation of cross differences in inflation, informal activity and taxation.

Ngalawa and Viegi (2010) develop a DSGE model to study inter-dependence of formal and informal financial sectors and impact of informal financial sector on overall economic activity and monetary policy in context of quasi emerging market economies. The model simulations reveal complementarity between the two financial sectors. Increase in formal credit causes a parallel increase in informal sector credit. In response to monetary policy shock, interest rates in the two sectors move in opposite directions; making the conduct of monetary policy hard in presence of large informal financial sectors.

Zenou (2007) develops two-sector general equilibrium model to study labour mobility between formal and informal labour markets under different labour policies. In the model design, formal labour market has search and matching frictions and informal labour market exhibits perfect competition. The study concludes that reduction in unemployment benefits or formal firms' entry cost causes increase in formal employment and an inverse impact on informal sector employment. Although not directly regulated, yet informal sector labour market is not independent of policies applicable on formal labour market due to interdependence of both markets.

Antunes and Cavalcanti (2007) study the impact of regulation costs and financial contract enforcement on size of informal economy and per capita GDP using a small open economy general equilibrium model. The study concludes that regulation costs are more important in accounting for informality. However, in a country where enforcement is very poor e.g. Peru, regulation costs and enforcement of financial contracts are equally important for explanation of informal sector. Regulation costs and enforcement are not much helpful for explaining income difference across countries.

Koreshkova (2006) studies the consequences of tax-evading informal sector for budget financing that ultimately affects inflation. Using cross country data, the study shows that size of informal sector, financing of government expenditure through seigniorage and inflation are positively associated. After establishment of stylised facts, the study uses a two-sector general equilibrium model to analyse implications of informal sector for inflation. Cross country simulations of the model show that in presence of large informal sectors where taxes are not paid, financing of government expenditures through inflation tax is consistent with solution of Ramsay problem.

Conesa, et al. (2002) explains the negative relationship between participation rate and GDP fluctuation observed in cross country data through existence of informal sector. Using a dynamic general equilibrium model incorporating informal sector in labour and product markets, the study shows that agents switch between formal and informal sectors during productivity shocks. This transition enhances the impact of shocks on registered output and culminates into amplification of fluctuations.

3. PAKISTAN ECONOMY: SOME STYLISED-FACTS

The history of Pakistan economy has showing a high degree of political uncertainty. After every autocratic regime, economy rebounded in the troubling position by posing stagnant economic growth and unstable prices. In most of politically-elected regimes, Pakistan has experienced with high inflation rates, large budget deficits and low growth in private sector credit. These regimes also witnessed wobbly external sector along with large trade deficit and declining trend in capital inflows both in the form of foreign direct investments and portfolio investments, which indicates low level of confidence of foreign investors in the domestic economy. The most recent episode of alternative regimes, in Pakistan, is an obvious illustration of this belief. After having seven successful years (autocratic regime of General Pervaiz Musharaf especially from FY01 to FY08) of high growth, balanced fiscal and external position and high investments, the country suffered historic inflation, faltering economic growth, increase in twin deficit, record low investment and rapid accumulation of public debt that increases inter-temporal debt burden.

Table 2 portrays the performance of selected macroeconomic variables during current episode. Specifically, the consumer price inflation increased to around 19 percent during FY09 and remained persistent afterwards. The economy grew around 3 percent during the last four years as compared with over 7 percent average growth observed during autocratic regime. The interest rate increased in tandem to the overall inflation that has negative impact on investment. The impact of low investment is also reflected from the contraction of large scale manufacturing during the last few years. On external side, the trade deficit widened to historical high level of over 13 percent of GDP in FY08 and remained unabated afterwards. The current account deficit increased to unsustainable level of over 8 percent in FY08. All these developments are the manifestation of political uncertainty, deteriorating law and order situation, prolong power outages and severe energy shortages. As a consequence foreign investment dried up, which put unprecedented pressure on external accounts. The exchange rate depreciated significantly against US dollar and liquid foreign exchange reserves declined considerably due to high twin deficit. In addition, the role of external shocks in worsening of domestic economic situation cannot be disregarded. A significant rise in international commodity prices in 2008 has not only affected negatively Pakistan's trade balance but also seeped into domestic inflation. Moreover, oil imports contribute around 30 percent in Pakistan's total imports and increase in oil price in international market also put pressure on external account. Therefore, analysis of these shocks in shaping in domestic economic condition is central in DSGE modelling.

In this study we investigate the impact of various external shocks--like oil price, commodity price, Calvo shock (sudden stops)--vis-a-vis conventional domestic shocks--productivity shock, government spending shock, monetary policy shock. The significance of external shocks is evaluated in the perspective of the economic structure of Pakistan. Pakistan is a small open economy, where trade to GDP ratio stands at 40 percent--ranked third after Sri-Lanka and India in the region- but much lower than Malaysia and other South Asian countries (see, Figure 1). Importantly, textile and textile products contribute around 50 percent in overall Pakistan's exports. Pakistan is considered in top 10 textile exporting countries of the world and 4th largest producer of cotton yarn and cloths. In addition, Pakistan is also considered as 3rd largest player in Asia with a spinning capacity of 5 percent of total world production. Like other countries in the region, Pakistan also started to liberalise, though partially, its capital account during early 1990s. In term of financial openness, based on the sum of foreign direct investment (FDI) and portfolio equity investments (PI) as percent of the GDPs, Pakistan is ranked third after Malaysia and India while it is much ahead of Bangladesh and Sri Lanka (see Figure 1).

However, based on the average of South Asian countries and the world, Pakistan falls short in this respect. On the other hand, Pakistan's imports are largely dominated by petroleum and petroleum products, foods items and agriculture/chemical products. Therefore, any shocks to commodity and energy price in international market, have a likely impact on domestic imports. Anecdotal evidence suggests that the impact of such shocks is not only observes in overall external account but also emerges in domestic inflation. This evidence confirms in a recent study by Khan and Ahmad (2011) while analysing impulse responses in macroeconomic variables by introducing a positive oil price shock. They find that an increase in international oil prices not only put pressure on domestic currency to depreciate but also increases domestic inflation. Similarly, interest rate also tends to rise and domestic economy wanes (see Figure 2).

[FIGURE 2 OMITTED]

Being a small open economy, Pakistan received capital inflows largely in the shape of foreign remittance, foreign debt, portfolio and foreign direct investment. Importantly, Pakistan has received significantly large inflows of foreign capital during 2000s as compared with earlier decades. Until FY04, these inflows limited to unrequited transfers for instance, workers' remittance, grants and logistic supports. But large capital inflows took place during FY05 and onwards, when government adopted pro-cyclical policies by going sovereign, allowing institutions to generate funds from external sources, privatising more public sector enterprises and financial institutions and provide free access to foreign investors in domestic equity market, thus creating capital inflow bonanza. Importantly, widening current account deficit remained unnoticed during this period as healthy inflows not only financed burgeoning current account deficit, but also resulted in accumulation of foreign exchange reserves. However, this trend seems no longer continue during FY08 and beyond. Calvo and Reinhart (2000) has rightly pointed out that capital flow bonanzas should not be mistaken as blessings and great harm is done when policymakers and investors start treating the bonanza as a permanent phenomenon rather than a temporary shock.

[FIGURE 3 OMITTED]

The recent decline in foreign investment in Pakistan and then reversal of portfolio investments is an obvious illustration of Calvo shock (see Figure 3). Importantly, the origin of a capital account shock or sudden stop (SS) may be systemic and exogenous, for instance see Calvo, et al. (2004). The systemic sudden stop or 3S, initially triggered by factors, which is exogenous to a country, but then a weak economic fundamentals and financial shallowness exacerbate the situation and ultimately lead to "full-fledge SS" [Calvo, et al. (2008)]. Understanding these differences and carefully modelling the transmission mechanism of internal and external shocks is crucial to the design of stabilisation programmes and the conduct of economic policies.

Another important characteristic of Pakistan's economy is the existence of large informal sector. Although the size of informal sectors, in term of GDP, trenched during the last decades, nevertheless, it is still high in the region and as compared with other developing countries (see Table 3). As most of the economic activities in Pakistan, particularly agriculture, are undocumented that employed large portion of unskilled or partially skilled labour. Specifically, Pakistan's economy is considered agrarian economy in term of labour as around 70 percent of total work force is informally employed in this sector. In addition, in term of the size of informal sector as a percent of non-agriculture Pakistan stands out, among the competing countries, (see Figure 4). Specifically, this size of 70 percent is slightly lower than HIPIC countries (sub-Sahara region) but much higher compared with emerging Asian economies. Due to its large size, the importance of informal sector in designing of DSGE model cannot be ignored.

4. DESCRIPTION OF THEORETICAL MODEL

This section presents a multi-sector small open economy DSGE model for Pakistan. Following mainly Gali and Monacelli (2005), Smets and Wouters (2007), Medina and Soto (2007), Haider and Khan (2008), and Batini, et al. (2010a) the model structure begins with the world-economy as inhabited by a continuum of infinite-lived households, (indexed by j [member of] [0,1]) who take decisions on the consumption and saving, in a standard rational optimising manner. (10) They hold real and financial assets and earn income by providing labour to different types of firms working in formal and informal sectors.

There is a set of formal sector firms that produce differentiated varieties of intermediate tradable goods. These firms produce goods using labour, capital and oil as inputs. They have monopoly power over the varieties they produce and set prices in a staggered way. They sell their varieties to assemblers that sale a composite home good in the domestic and foreign markets. A second group of formal sector firms are importers that distribute domestically different varieties of foreign goods. These firms have monopoly power over the varieties they distribute, and also set prices in a Calvo (1983) type staggered fashion. A third group of firms is producing informal non-tradable intermediate goods. These firms do not pay any tax to government and relatively considered less productive as compared with formal sector firms. These firms produce varieties using labour and oil as inputs and have monopoly power over the goods they distribute, and also set prices in a similar staggered fashion.

Along with manufacturing of goods in both formal and informal sectors, agriculture production is also taking place. For simplicity, it is assumed that commodities produced in this sector are completely exported abroad. The formal sector firms have access to rent capital from capital leasing firms working domestically and abroad. The rest of the model assumes symmetric preferences and technologies, and allowing potentially rich exchange rate and current account dynamics. Government in this model deals with fiscal issues and central bank conducts monetary policy using interest rate as a policy instrument.

4.1. Households

The domestic economy is inhabited by a representative household who derives its utility from consumption, [C.sub.t], real money balances, [M.sub.t]/[P.sub.c,t], and leisure 1-[l.sub.t] Its life time preferences are described by an intertemporal utility function as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (1)

Where [beta] [member of] (0,1) is the intertemporal discount factor which describe rate of time preferences, E is expectation operator and [P.sub.c,t], is aggregate price index for core consumption bundle. In these preferences, we introduce external habit formation in consumption for the optimisation household as, [C.sub.t] = [C.sub.t](j) - [??] [C.sub.t-1] with degree of intensity (11) indexed by [??], where [C.sub.t-1], is the aggregate part of consumption index. The functional specification of utility function [u.sub.s] is given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In this specification, [[zeta].sub.C,t] consumption preference shock (a kind of taste shock), [mu] is the semi-elasticity of money demand to nominal interest rate, [[zeta].sub.M] is relative weight assign to real money balances, [[sigma].sub.L] is the inverse of wage elasticity of labour supply and [[zeta].sub.L,s] a labour supply shock. As usual, it is assumed that, [mu] < 0 and [[sigma].sub.L] > 1. It is also assume that [u.sub.s]([[??].sub.s], [M.sub.s](j)/[P.sub.C,s], 1 - [l.sub.s](j)) is an increasing function with diminishing returns in each of its arguments. The household does want to maximise its utility level subject to the following budget constraints at time t:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Where [Q.sub.t,t+1] is defined as a stochastic discount factor for assessing consumption streams (12) (or asset price kernel) with the property that the price in period t of any bond portfolio with random values. [D.sub.t] (denotes nominal payoffs from a portfolio of assets at time t - 1) in the following period is given by: [B.sub.t] = [E.sub.t][[Q.sub.t,t+1] [D.sub.t+i]]. (13) [W.sub.t] is the nominal wage for labour services provided to firms, [[epsilon].sub.t] is nominal exchange rate and [B.sup.*.sub.t], is foreign bond holdings with rate of return [i.sup.*.sub.t]. In this budget constraint, [THETA](.) = [THETA] is the premium that domestic household have to pay when they borrow from abroad. The premium is a function of the net foreign asset positions relative to gorss domestic product (GDP) and define as: [[beta].sub.ti] = [[epsilon].sub.t][B.sup.*.sub.t]/[P.sub.Y,t][Y.sub.t]. The premium function also satisfies two properties: [THETA](.) = [THETA] and ([THETA]' / [THETA])) [beta] = [rho]. Finally, [[tau].sub.P,t] is nominal transfer and [[tau].sub.P,t], is nominal lump-sum tax, which every household have to pay to government. The household optimisation process solves the following Langrangian function as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The solution to this problem yields the following first order conditons (FOCs):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The above FOCs can further simlify by solving them simultanously, and yield four important results, intertemporal Euler equation of consumption, real money demand equation, labour supply function and uncovered interest parity condition.

The Euler equation of conumption is given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

where, [E.sub.t][Q.sub.t,t+1] = 1/1 + [i.sub.i]

The real money demand function is given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

The labour supply function is given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (5)

Finally, the uncovered parity condition is given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Using the fact that: [E.sub.t][Q.sub.t,t+1] = [E.sub.t][Q.sup.*.sub.t,t+1][[epsilon].sub.t+1]/[[epsilon].sub.t], so it simplifies as:

(1 + [i.sub.t])/1 + [i.sup.*.sub.t])[THETA]([[beta].sub.t]) = [E.sub.t][[epsilon].sub.t+1]/[[epsilon].sub.t] ... ... ... ... ... ... (6)

This equation implies that the interest rate differential is related with expected future exchange rate depreciation and international risk premium, which defined as uncovered interest parity condition.

4.1.1 Household Consumption Decisions

The aggreagate consumption bundle, [C.sub.t], for the jth household is a composite of core consumption bundle, [Q.sub.z,t], and oil consumption, [C.sub.o,t]. Its composition is given by the constant elasticity of substitution (CES) aggregator:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (7)

Where, [[omega].sub.c] is the elasticity of intertemporal substitution between core consumption and oil consumption bundle. Larger the value of [[omega].sub.c] implies that goods are closer substitutes. [a.sub.c] measures the proportion (persentage share) of core goods in the consumption of households. If its value equals to one then it implies households only consume core goods and there is no oil consumption taking place. The representative household aims at maximising the utility from consumption of both goods by minimising the expenditure on these two varieties, while maintaing a certain target level of consumption. Solving this problem of optimal allocation of expenditure on core and oil goods yields the following demand functions for these goods.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (8)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (9)

Where [P.sub.z,t] and [P.sub.o,t] are prices of core and oil consumption bundles. [P.sub.c,t] is the aggregate consumer price index (CPI) and defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (10)

The core consumption goods are produced either in the formal sector or in undocumented (also known as: informal or hidden) sector. Therefore, the consumption of this bundle is determined by a CES index composed of formal sector goods, [C.sub.D,t], and informal goods, [C.sub.U,t], as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (11)

Where, [[phi].sub.c] is the elasticity of intertemporal substitution between formal goods consumption and informal goods consumption bundle. Larger the value of [[phi].sub.c] implies that goods are closer substitutes. [v.sub.c] measures the proportion (persentage share) of formal sector goods in the core consumption of households. As with the case of total consumption above, expenditure minimisation problem on the core consumption goods yeilds the following demand functions for the formal sector and informal sector goods.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (12)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (13)

Where [P.sub.D,t] and [P.sub.U,t] are prices of formal and informal consumption bundles. [P.sub.z,t] is the aggregate price index of core consumption bundle and given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (14)

The formal sector consumption bundle is given by the following CES aggregator of home and foreign goods:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (15)

Where, [[eta].sub.c] is the elasticity of intertemporal substitution between home goods consumption and foreign goods consumption bundle. Larger the value of [[eta].sub.c]. implies that goods are closer substitutes. [[gamma].sub.c] measures the proportion (persentage share) of home goods in the formal goods consumption by the households. As with the case of core consumption above, expenditure minimisation problem on the core consumption goods yeilds the following demand functions for the home and foreign goods.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (16)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (17)

Where [P.sub.H,t] and [P.sub.F,t] are prices of home and foreign consumption bundles. [P.sub.D,t] is the aggregate price index of formal consumption goods and given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (18)

4.1.2. Household Labour Supply Decisions

In this model, a fraction [[DELTA].sub.L] of households provide labour to formal sector firms and rest of them, (1 - [[DELTA].sub.L]), provide labour to informal sector. The aggregate labour is given by the following CES aggregator of formal sector labour, [l.sub.D,t], and informal sector labour, [l.sub.U,t]

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (19)

Where, [P.sub.L] the inverse elasticity of intertemporal substitution between formal and informal sector labour. The household optimisation problem based on wage earnings, yeilds the following supply functions for the formal and informal labour:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (20)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (21)

Where [W.sub.D,t], and [W.sub.U,t], are nominal wages in the formal and informal sector respectively. [W.sub.t] is the aggregate wage index which is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (22)

The supply functions (20) and (21) show that supply of each type of labour depend on relative wage of respective labour and on aggregate labour supply. The simultaneous solution to above supply functions with aggregate wage index yield following real wage functions:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (23)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (24)

Following Ahmad, et al. (2012), we assume that formal labour is a composite of labour differentiated on basis of different levels of skill represented by s. Using this assumption, aggregate formal labour supply can taken as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (25)

Where, [[epsilon].sub.L] is the elasticity of substitution between different labour skills in the formal sector. Using this aggregator, it is easy to define aggregate wage in the formal sector as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (26)

This condition allows each household to have some market power to set wages on basis of its skill s. Therefore, household optimises following wage income function as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (27)

The solution to this problem yields the following wage markup condition:

[W.sub.D,t](s) = ([[epsilon].sub.L]/[[epsilon].sub.L] - 1)[W.sub.D,t] (28)

4.2. Capital Leasing Firm and Investment Decisions

There is a representative capital leasing firm that rents capital goods to formal sector firms producing intermediate varieties. Due to formal documentation and legal requirments, this firm does not intract with informal sector firms. It also decides how much capital to accumulate each period in the formal sector. New capital goods are assembled using a CES technology that combines home and foreign goods as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (29)

Where, [I.sub.D,t] is the total private investment in the formal sector, [[eta].sub.t] is the elasticity of intertemporal substitution between home and foreign investment goods and [[gamma].sub.t] measures the proportion (persentage share) of home goods in total foraml sector investment. The invesetment optimisation problem yeilds the following demand functions for the home and foreign goods:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (30)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (31)

Where, [[zeta].sub.I.sub.H,t] and [[zeta].sup.I.sub.F,t] are shocks to the domestic investment and foreign investment respectively, which are assumed to follow first-order autoregressive processes with IID-Normal error terms: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is the aggregate price index of total investment and given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (32)

As in Smets and Wouters (2003, 2007) and Christiano, et al. (2005) we introduce a delayed response of investment observed in the data. Capital leasing firm combine existing capital, [K.sub.D,t], leased from the entrepreneurs to transform an input [I.sub.D,t], gross investment, into new capital according to:

[K.sub.D,t+1] = [[zeta].sup.I.sub.t][I.sub.D,t]S([I.sub.D,t]/[I.sub.D,t-1]) + (1 - [delta])[K.sub.D,t] ... ... ... ... ... (34)

Where [I.sub.D,t], is gross formal sector investment, [delta] is the depreciation rate and the adjustment cost function S(*) is a positive function of changes in investment. S(*) equals zero in steady state with a constant investment level [S(1) = 0 and S(1 + [g.sub.y]) = 1]. In addition, we assume that the first derivative also equals zero around equilibrium, so that the adjustment costs will only depend on the second-order derivative (S'(.) = 0,S"(.) = -[[mu].sub.s] < 0) as in Christiano, et al. (2005). We also introduced a shock to the total investment, which is assumed to follow a first-order autoregressive process with an IID-Normal error term: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Formal sector firms choose the capital stock and investment in order to maximise their profit function. Let [Z.sub.t] is the rental price of capital. The representative formal sector firm must solve the following optimisation problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (33)

The first-order conditions result in the following two equations:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (35)

[Q.sub.t]/[P.sub.C,t] = [E.sub.t][[XI].sub.t,t+1]{[[Z.sub.t+1]/[P.sub.C,t+1]] + (1 - [delta]) [[Q.sub.t+1]/[P.sub.C,t+1]]} ... ... ... ... ... (36)

These equations samultanously determine the evolution of the shadow price of capital, [Q.sub.t] and real invesetmtent expenditure.

4.3. Domestic Formal Sector Production

In domestic formal sector, there are three types of firms: domestic formal sector retailers, intermediate goods producing firms and import goods retailers. Domestic formal sector retailers are net buyers of domestic intermediate varieties produced by domestic intermediate goods producing firms and assemble them as final home goods. These firms sell a quantity of formal home goods, in domestic formal goods market and also export remaining quantity abroad. Import goods retailers on the other hand purchase foreign goods at world market prices, and sell to domestic consumers. These firms charge a markup over their cost, which creates a wedge between domestic and import prices of foreign goods, when measure in the same currency.

4.3.1. Formal Sector Retailers

Retailers in the formal sector produce a quantity of home goods, [Y.sub.H,t] sold domestically and [Y.sup.*.sub.H,t] the quantity of goods sold abroad. These quantities of final goods are assembled using CES technology with a continuum of intermediate goods, [Y.sub.H,t] ([z.sub.H]) and [Y.sup.*.sub.H,t] ([z.sub.H]) respectively as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (37)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (38)

Where, [[member of].sub.H], is the elasticity of substitution between differentiated formal intermediate varieties. Under the assumption of perfectly competitive environment, the profit function for both quantities of final goods can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (39)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (40)

Where, [[tau].sub.H] is the flat tax rate on final goods, [P.sub.H,t] ([z.sub.H]) is the price of variety [Z.sub.H], when used to assemble home goods sold in the domestic market, and [Y.sup.*.sub.H,t] ([z.sub.H]) is the foreign currency price of this variety when used to assemble home good sold abroad. Formal sector retailers try to optimise their profit functions while taking decision on how much intermediate variety [Z.sub.H] to purchase given its price and demand elasticity. This optimisation problem yields the following demand functions for the particular intermediate variety [Z.sub.H] as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (41)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (42)

4.3.2. Intermediate Goods Production in the Formal Sector

In the formal sector, there is a set of monopolistic compretitive firms, which produce intermediate goods using labour, capital and oil as key inputs. These firms maximise profits by choosing the prices of their differetiated good subject to the corresponding demands and the available CES technology of the following type:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (43)

Where, [A.sub.H,t] is the exogenous level of technology available to all firms, [H.sub.H,t] ([z.sub.H]) is a composite of labour and capital inputs used in the production process and [O.sub.H,t], ([z.sub.H]) is the amount of oil input used in production of intermediate vareites. In this technology, [[omega].sub.H] is the elasticity of intertemporal substitution between oil and other factor of inputs. Larger the value of [[omega].sub.H] implies that oil and other factor of imputs are closer substitutes. [a.sub.H] measures the proportion (persentage share) of non-oil factor inputs in the production of intermediate varieties. The composite of labour and capital is given by the following Cobb-Douglas technology:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (44)

Where, [l.sub.D,t]([z.sub.H]) is the amount of domestic formal labour being used in the formal sector production and [K.sub.D,t] ([z.sub.H]) is the amount of physical capital rented from capital leasing firm. In this Cobb-Douglas technology, [[eta].sub.H] represents labour share and [T.sub.D,t] represents stochastic trend in the labour productivity and it evolves according to the follwing expression:

[T.sub.D,t]/[T.sub.D,t-1] = [[zeta].sub.DT,t] ... ... ... ... ... ... ... (45)

The aggregate technology shock in CES technology (43) and formal sector labour productivity shock in Codd-Douglas technology (44) are defined in the following manner:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII])

Where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], are stochastic respective iid innovations and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are respective persistence levels. Following, Calvo (1983) staggered-price setting is assumed. This means that domestic formal sector differentiating goods are defined subject to Calvo-type price-setting. In this setup, at each period, only 1 - [[phi].sup.i.sub.H] fraction of randomly selected domestic firms set prices optimally for domestic market and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] fraction of randomly selected domestic firms set prices optimally for foreign market, while remaining firms keep their prices unchanged. (14) As a result the average duration of a price contract is given by 1/(1-[[phi].sup.i.sub.H]) for domestic market and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] for foreign market. This implies that if a firm does not receive a signal, it revises its price following a simple rule that weights past inflation and the inflation target set by the central bank. (15) Therefore, when a firm receives a signal to adjust its price for domestic formal market then it solves the following optimisation problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (46)

Subject to demand constraint (41) and updating rule for prices, [[GAMMA].sup.i.sub.H,t]. Similarly, when a firm receives a signal to adjust its price for foreign market then it solves the following optimisation problem:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (47)

Subject to demand constraint (41) and updating rule for prices, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. In above expressions (46) and (47), [MC.sub.H,t+i] is the nominal marginal cost which is defined as follow:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (48)

Given this price structure, the optimal path for inflation is given by a New-Keynesian Phillips Curve with indexation.

4.3.3. Import Goods Retailers in the Formal Sector

In the formal sector, there is a set of competitive assemblers that use a CES technology to combine a continuum of differentiated imported varieties to produce final foreign good, [Y.sub.F,i].

The CES aggregator is given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (49)

Where, [[member of].sub.F], is the elasticity of substitution between differentiated formal intermediate imported varieties. Under the assumption of perfectly competitive environment, the profit function for imported final goods can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (50)

Where, [[tau].sub.F] is the flat tax rate on imported final goods, [P.sub.F,t]([Z.sub.F]) is the price of variety [Z.sub.F], when used to assemble imported goods sold in the domestic market. Formal sector import retailers try to optimise their profit functions while taking decision on how much intermediate imported variety [Z.sub.F] to purchase given its price and demand elasticity. This optimisation problem yields the following demand function for imported variety [Z.sub.F] as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (51)

Following Gali and Monacelli (2005) and Monacelli (2005), it is assumed that the law-of-one price (LOP) holds at the wholesale level for imports. But, endogenous fluctuations from purchasing power parity (PPP) in the short run arise due to the existence of monopolistically competitive intermediate variety importers. Since, they keep domestic import prices over and above the marginal cost. As a result, the LOP fails to hold at the retail level for domestic imports. Importers purchase foreign goods at world-market prices [P.sup.*.sub.F,t]([z.sub.F]) so that the law of one price holds at the border. These purchased foreign goods are then sell to domestic consumers and a mark-up is charged over their cost, which creates a wedge between domestic and import prices of foreign goods when measured in the same currency. (16) Now following a similar staggered-pricing argument (46) as defined in the case of domestic formal sector producer, the optimal price setting behaviour for the domestic monopolistically competitive importer could be defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (52)

Importing firms try to optimise (52) subject to demand constraint (51) and use updating rule for prices [[GAMMA].sup.i.sub.F,t].

4.4. Domestic Informal Sector Production

In this model setup, it is assume that along with domestic formal sector, informal production is also taking place. There are two types of firms: domestic informal sector retailers and informal intermediate goods producing firms. The informal retailers are working in a symmetric fashion to the formal sector retailers. The only two exceptions distinguish their role from formal to informal that these retailers pay no taxes and can only use intermediate varieties produced in the informal intermediate goods producing sector.

4.4.1. Informal Sector Retailers

Retailers in the informal sector produce a quantity of goods, [Y.sub.U,t] which is completely consumed domestically. This quantity of informal final goods is assembled using CES technology with a continuum of informal intermediate varieties, [Y.sub.U,t] ([z.sub.U]) as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (53)

Where, [[member of].sub.U], is the elasticity of substitution between differentiated informal intermediate varieties. Under the assumption of perfectly competitive environment, the profit function of final informal goods producing retailer can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (54)

Where, [P.sub.U,t] ([z.sub.U]) is the price of variety [Z.sub.U], when used to assemble informal goods sold in the domestic informal market. Informal sector retailers try to optimise their profit functions while taking decision on how much intermediate variety [Z.sub.U] to purchase given its price and demand elasticity. This optimisation problem yields the following demand function for the intermediate variety [Z.sub.U] as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (55)

4.4.2. Intermediate Goods Production in the Informal Sector

Similar to formal sector, there is a set of monopolistic compretitive informal firms, which produce intermediate goods using labour and oil as key inputs. However, these firms have no access to rent capital as an input of production. These firms maximise profits by choosing the prices of their differetiated good subject to the corresponding demands and the available CES technology of the following type:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (56)

Where, [A.sub.U] is the constant exogenous level of technology available to all informal sector firms. It is also assumed that these firms are less productive as compared with formal sector firms. In the production technology of these firms, [V.sub.U,t], ([z.sub.U]) is a composite of labour input only and [O.sub.U,t], ([z.sub.U]) is the amount of oil input used in production of intermediate informal vareites. Furthermore, [[omega].sub.U] is taken as the elasticity of intertemporal substitution between oil and other factor of inputs. Larger the value of [[omega].sub.U] implies that oil and other factor of imputs are closer substitutes, [a.sub.U] measures the proportion (persentage share) of non-oil factor inputs in the production of intermediate informal varieties. The labour composit is given by the following form:

[V.sub.U,t] ([z.sub.U]) = [[T.sub.U,t][l.sub.U,t]([z.sub.U]) (57)

Where, [l.sub.U,t] ([z.sub.U]) is the amount of domestic informal labour being used in the informal sector production. In this composite technology, [T.sub.U,t] represents stochastic trend in the informal labour productivity and it evolves according to the following expression:

[T.sub.U,t]/[Tu.sub.U,t-1] = [[zeta].sub.UT,t] (58)

It is assumed that informal labour is less productive ([T.sub.U,t] < [T.sub.D,t]) and labour productivity shock [[??].sub.UT,t] is defined as: [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], where, [[xi].sub.UT,t] is stochastic iid innovations and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is respective persistence levels. Similar to formal sector firms, it is also assumed that informal sector firms set prices according to Calvo (1983) staggered-price setting scheme. This implies that at each period, only 1 - [[phi].sup.i.sub.U] fraction of randomly selected domestic informal sector firms set prices optimally for domestic informal market, while remaining informal sector firms keep their prices unchanged. As a result the average duration of a price contract is given by 1/(1 - [[phi].sup.i.sub.U]) for domestic informal market. This implies that if any informal sector firm does not receive a signal, it revises its price following a simple rule that weights past inflation and the inflation target set by the central bank. Therefore, when this firm receives a signal to adjust its price for domestic formal market then it solves the following optimisation problem as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (59)

Subject to demand constraint (55) and updating rule for prices, [[GAMMA].sup.i.sub.U,t] In this expression, M[C.sub.U,t+i] is the nominal marginal cost which is defined as following:

M[C.sub.U,t] = [W.sub.U,t] [l.sub.U,t]([Z.sub.U]) + [P.sub.O,t][O.sub.U,t]([z.sub.U])/[[gamma].sub.U,t]([z.sub.u]) ... (60)

Given this price structure for informal firms, the optimal path for inflation is given by a New-Keynesian Phillips Curve with indexation.

4.5. Agriculture Commodity Producing Sector

In this model, aggriculture production is also taking palce along with the manufacturing of formal and inforaml goods. It is assumed that there is sigle firm produces a quantity of homogenous aggriculture commodities that is completely exported abraod. Production technology evolves with the same stochastic trend as other aggregate variables and requires no inputs as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (61)

Where, [[gamma].sub.S,t] is total aggriculture output, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] is stochastic iid technology and [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] represents persistence of shock in aggriculture output. As there is no factor input in this production process, so an increase in aggriculture commodity production implies directly an increase in domestic output. This increase in production can be taken as a windfall gain. It also may increase exports, if no counteracting effect on home goods exports dominates. We would expect that, as with any increase of technological frontier of tradable goods, a boom in this sector would induce an exchange rate appreciation. Lastely, it is also assumed that aggriculture production is positively related with informal labour productivity indirectly through prduction pssibility frontier.

4.6. Monetary Policy

It is assumed that monetary authority follows Taylor-type reaction functions. Since the basic objective of the central bank is to stabilise both output and inflation. So in order to specify this reaction function, it needs to adjust nominal interest rate in response to deviations of inflation, a measure of output and exchange rate depreciation from their targets. Following Clarida, Gali and Gertler (2001) and Gali and Monacili (2005), simple open economy version of reaction function is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (68)

Where, [[pi].sub.C,t] = ([P.sub.C,t] - 1)/[P.sub.C,t-1] i is total consumer price index and [r.sub.t], = (1 + [I.sub.i])/(1 [[pi].sub.C,t]). The parameter [[psi].sub.i] is the degree of interest rate smoothing and (1 - [[psi].sub.i],) [[psi].sub.y], (1 - [[psi].sub.i]) [[psi].sub.[pi]], and (1 - [[psi].sub.i]) [[psi].sub.rer] are relative weights on output, inflation and real exchange rate respectively. [[xi].sub.m,t] is iid-innovation, defined as a monetary policy shock.

4.7. Fiscal Policy

In this model setup, government finances its expenditures by seigniorage (printing money, [M.sub.t] - [M.sub.t-1]) and imposing lump-sum tax [[tau].sub.P,t] on households and flat taxes on final goods produced in the domestic formal sector as, [[tau].sub.H][P.sub.H,t], [Y.sub.H,t] and on imported goods from abroad as, [[tau].sub.F] [P.sub.F,t] [Y.sub.F,t]. These expenditures are consisting of spending on goods and services, [P.sub.G,t] [G.sub.t] and making lump-sum transfers to households, [TR.sub.t]. The deficit in any case is finance using foreign bonds [[epsilon].sub.t][B.sup.*.sub.G,t] and domestic bonds, [B.sub.Gt], on which it pays interest back as well. Therefore, the government's budget constraint can be written as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (62)

We assume that the basket consumed by the government includes both home, [G.sub.H,t] and foreign goods, [G.sub.F,t] Its composition is given by the constant elasticity of substitution (CES) aggregator:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (63)

Where, [[eta].sub.G] is the elasticity of intertemporal substitution between home and foeign consumption good. Larger the value of [[eta].sub.G] implies that goods are closer substitutes, [[gamma].sub.G] measures the proportion (percentage share) of home good in government consumption goods. If its value equals to one then it implies government only consume home good and there is no foreign good consumption taking place. The government decides the composition of its consumption basket by minimising its cost. Solving the cost optimisaiton problem of optimal allocation of government expenditure yields the following demand functions:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (64)

Where, the deflator of government expenditure is given by:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (65)

Finally, it is assumed that government follows a simple structral fiscal balance rule according to which government aggregate expenditure as percent of GDP evolves as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (66)

Where, [[xi].sub.G,t], is exogenous government spending shock defined as a autoregressive of order one process with iid innovation.

4.8. Foreign Sector Economy

Agents in the foreign sector economy demand both the agriculture commodity goods and formal sector home goods. The demand for the agriculture commodity good is assumed to be completely elastic at the international price, [P.sup.*.sub.S,t] if the law of one price

holds for this good, then its domestic-currency price can be defined by:

[P.sub.S,t] = [[epsilon].sub.t][P.sup.*.sub.S,t] (69)

Similar to pricing assumption of agriculture commodities in the international market, we assumed that demand for oil commodity is completely elastic at the international price, [P.sup.*.sub.O,t] and if the law of one price holds then the oil price in domestic currency is given as:

[P.sub.O,t] = [[epsilon].sub.t][P.sup.*.sub.O,t] (70)

The real exchange rate is defined as the product of nominal exchange rate, [[epsilon].sub.t] with relative price of a foreign price index, [P.sup.*.sub.t], and the price of the consumption bundle in the domestic economy, [P.sub.C,t]:

[RER.sub.t] = [[epsilon].sub.t][P.sup.*.sub.t]/[P.sub.C,t] (71)

As usual the foreign price index is not necessarily equal to the price of imported goods. However, under the assumption of long-run relationship, we can write as:

[P.sup.*.sub.F,t] = [P.sup.*.sub.t][[??].sup.*.sub.F,t] (72)

Where, [[??].sup.*.sub.F,t] is a stationary transitory shock to the relative price of imports abroad. This shock may be related to changes in the relative productivity across sector in the foreign economy. Foreign demand for home goods depends on the relative price of this type of goods abroad and the total foreign aggregate demand:

[Y.sup.*.sub.H,t] = [[??].sup.*] ([P.sup.*.sub.H,t]/[P.sup.*.sub.t])-[[eta].sup.*] [Y.sup.*.sub.t] (73)

Where, [[??].sup.*] corresponds to the share of domestic intermediate goods in the consumption basket of foreign agents, [[eta].sup.*] is the price elasticity of the demand and [Y.sup.*.sub.t], the foreign output. This demand can be obtained from a CES utility function with an elasticity of substitution across varieties equal to that parameter.

4.9. Aggregate Equilibrium

Using the above model setup, we can drive general equilibrium dynamics around their steady-state level. The general equilibrium is achieved from goods market equilibrium and labour market equilibrium. The goods market equilibrium derived from aggregate demand side forces and labour market equilibrium dynamics emerge from aggregate supply side forces. So, the general equilibrium of the whole model is achieved from these market equilibrium and key equilibrium results are given as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (74)

Where the aggregate resource constraint of the formal sector is defined as:

[Y.sub.H,t] = [C.sub.H,t] + [I.sub.H,t] + [G.sub.H,t] (75)

The above aggregate equilibrium implies that total labour demand by intermediate varieties producers in the formal sector must be equal to labour supply implied in this sector. Since, economy is interacting with the rest of the world, therefore foreign demand for home goods depends on the relative price of these formal sector goods abroad and the total foreign aggregate demand is defined as:

[Y.sup.*.sub.H,t] = [[??].sup.*]([P.sup.*.sub.H,t]/[P.sup.*.sub.t])-[[eta].sup.*][Y.sup.*.sub.t] (76)

Where [[??].sup.*] is taken as the share of domestic intermediate formal sector goods, used in the consumption basket of foreign agents, [[eta].sup.*] is the price elasticity of the export demand function and [Y.sup.*.sub.t] is the aggregate foreign output. Under certain assumption, this demand can be deriveed from a CES utility function with an elasticity of substitution across intermediate arieties equal to that parameter. Similar to formal sector aggregate equilibrium conditions as jointly defined in (77) and (75), the equilibrium informal sector equates informal output to informal consumption.

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (77)

This equilibrium also implies that total labour demand by intermediate varieties producers in the informal sector must be equal to labour supply implied in this sector. Therefore, the aggregate resource constraint of informal sector is given as:

[Y.sub.U,t] = [C.sub.U,t] (78)

The joint combination of goods market equilibrium conditions, the budget constraint of the government and the aggregate budget constraint of households, it is easy to obtain an expression for the aggregate accumulation of international bonds:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (79)

This expression also shows net foreign asset position of the external sector of the economy. Corresponding to this expression with price deflator to each aggregate demand component the total GDP at current prices can be defined as the following relation:

[P.sub.Y,t], [Y.sub.t] = [P.sub.C,t] [C.sub.t] + [P.sub.G,t][G.sub.t] + [P.sub.I,t][I.sub.t] + [P.sub.X,t][X.sub.t] - [P.sub.M,t][M.sub.t] ... (80)

Finally, the total value of nominal exports and the total value of nominal imports are given by:

[P.sub.X,t][X.sub.t] = [[epsilon].sub.t] ([P.sup.*.sub.H,t][Y.sup.*.sub.F,t] + [P.sub.s,t][Y.sub.s,t]) (81)

[P.sub.M,t][M.sub.t] = [[epsilon].sub.t] ([P.sup.*.sub.F,t][Y.sub.F,t] + [P.sup.*.sub.O,t]([C.sub.O,t] + [O.sub.H,t] + [O.sub.U,t])) ... (82)

Where, aggregate resource constraint in terms of [Y.sub.F,t], can be defined as:

[Y.sub.F,t] = [C.sub.F,t] + [I.sub.F,t] + [G.sub.F,t] (83)

4.10. Alternative Monetary Policy Rules and Welfare

We analyse the likely impact of alternative monetary policy rules based on social welfare loss function minimisation. Among various monetary policy regimes, the optimal monetary policy or Ramsey policy rule is defined by maximising the intertemporal household welfare ([U.sub.t]) subject to a set of non-linear structural constraints of the model. To be more precise, a Ramsey equilibrium is a competitive equilibrium such that:

(i) Given a sequence of shocks, prices, policy instrument and quantities [P.sub.t]; [R.sub.t]; [Q.sup.[infinity].sub.tt=0] maximises the representative agent lifetime utility, [U.sub.t].

(ii) [r.sub.t] > 0.

In order to analyse essentially the macroeconomic stabilisation properties of the monetary policy, we assume subsidies on labour and goods markets are offsetting first order distortions. In that case, the flexible price equilibrium is Pareto optimal. The Ramsey policy problem is written using an infinite horizon Lagrangian:

F = [U.sub.t] + [E.sub.t][[lambda].sub.r] [J.summation over (j=0)] [[beta].sup.j] ... (84)

Where,

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

In above Lagrangian function, [[lambda].sub.r] is the weight associated to the cost on interest rate fluctuations. We introduce an interest rate objective in this problem in order to make the Ramsey policy operational. Following, Woodford (2004), Gali (2008) and Walsh (2010) we will take second order approximation of the agents lifetime expected utility function through Taylor's series. (17) In this framework the central bank tries to maximise the social welfare when there is a trade-off between the aggregate consumer price inflation and the changes in output.

First we can write the approximate utility of consumption as:

log(C.sub.t] - [??][C.sub.t-1]) = (1 - [??])[bar.C] + ([[??].sub.t] - [??][[??].sub.t-1]) (85)

We can also write the disutility of labour about its flexible price equilibrium as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (86)

Where, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Using these results with optimisation condition, we can write the second order approximation to the small open economy's utility function as follows:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (87)

Taking unconditional mean and letting [beta] [right arrow] 1, the expected welfare loss of any policy that deviated from Ramsey policy can be written in terms of variances of inflation and output gap as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (88)

Gali and Monacelli (2005) and Alba, et al. (2012) studies argued that that using this social welfare maximisation criteria along with the assumptions of purchasing power parity and uncovered interest parity, the combined effects of market power and terms of trade distortions could be offset so that under flexible price equilibrium. In this framework, domestic inflation targeting is the optimal monetary policy. However, apart from domestic inflation targeting in a strict sense, central banks in most of emerging market economies, put weight to some other secondary objectives of monetary policy, like economic growth stability and smoothing of exchange rate fluctuations. Therefore, optimal monetary policy in such developing economies is one produce minimum welfare loss of the central bank. Therefore, the optimal monetary policy rule under Ramsey policy framework is characterised as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (89)

This framework measures welfare loss as a second order approximation to the utility loss of the domestic consumer resulting from deviations from optimal monetary policy. Following, Lucas (1987) and Woodford (2004), alternative monetary policies regimes are specified in the context of a simple DSGE model and the welfare losses are compared to draw policy implications. In this paper, we have also considered four alternative monetary policy regimes along with optimal monetary policy rule. The first alternative policy regime is considered as less aggressive anti-inflation policy. This regime put less weight to inflation and assigned zero weight to both changes in output and exchange rates fluctuations. The policy rule associated with this regime can be defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (90)

The second alternative monetary policy regime is considered as more aggressive anti-inflation policy. This regime put relatively more weight to inflation and assigned zero weight to both changes in output and exchange rates fluctuations. The policy rule associated with this regime can be defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (91)

The third alternative monetary policy regime is taken in which central bank put less weight to changes in output together with price stability objective. However, this regime assigns zero weight to exchange rates fluctuations. The policy rule associated with this regime can be defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (92)

The forth alternative monetary policy regime is taken in which central bank put more weight to changes in output together with price stability objective. Similar to previous alternative regimes, this policy rule assign zero weight to exchange rates fluctuations. The policy rule associated with this regime can be defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (93)