16 © 2019 by the authors; licensee Asian Online Journal Publishing Group Asian Journal of Economics and Empirical Research Vol. 6, No. 1, 16-26, 2019 ISSN(E) 2409-2622/ ISSN(P) 2518-010X DOI: 10.20448/journal.501.2019.61.16.26 © 2019 by the authors; licensee Asian Online Journal Publishing Group Business Cycles and Financial Frictions under Money Growth Rule Wondemhunegn Ezezew Melesse1 1University of Gondar, Gondar, Ethiopia Abstract In the last few years, macroeconomic modeling has emphasized the role of credit market frictions in magnifying and transmitting nominal and real disturbances and their implication for macro-prudential policy design. In this paper, I construct a modest New Keynesian general equilibrium model with active banking sector. In this set-up, the financial sector interacts with the real side of the economy via firm balance sheet and bank capital conditions and through their impact on investment and production decisions. I rely on the financial accelerator mechanism due to Bernanke et al. (1999) and combine it with a bank capital channel as demonstrated by Aguiar and Drumond (2007). The resulting model is calibrated from the perspective of a low-income economy reflecting the existence of relatively high investment adjustment cost, strong fiscal dominance, and underdeveloped financial and capital markets. The main objective of this exercise is to see whether the financial accelerator mechanism documented under interest-rate-rule based simulations could be replicated under a situation where the central bank uses money growth rule in stabilizing the national economy. The findings are broadly consistent with previous studies that demonstrated stronger role for credit market imperfections in amplifying and propagating monetary policy shocks. Keywords: Financial frictions, Monetary policy transmission, Money growth rule, DSGE model, Calibration. JEL Classification: E30, E44 Citation | Wondemhunegn Ezezew Melesse (2019). Business Cycles and Financial Frictions under Money Growth Rule. Asian Journal of Economics and Empirical Research, 6(1): 16-26. History: Received: 22 October 2018 Revised: 16 November 2018 Accepted: 31 December 2018 Published: 18 January 2019 Licensed: This work is licensed under a Creative Commons Attribution 3.0 License Publisher: Asian Online Journal Publishing Group Funding: This study received no specific financial support. Competing Interests: The author declares that there are no conflicts of interests regarding the publication of this paper. Transparency: The author confirms that the manuscript is an honest, accurate, and transparent account of the study was reported; that no vital features of the study have been omitted; and that any discrepancies from the study as planned have been explained. Ethical: This study follows all ethical practices during writing. Contents 1. Introduction ...................................................................................................................................................................................... 17 2. Literature Review ............................................................................................................................................................................ 17 3. Model .................................................................................................................................................................................................. 19 4. Results and Discussion ................................................................................................................................................................... 23 5. Conclusion and Policy Implications ............................................................................................................................................. 25 References .............................................................................................................................................................................................. 25 Appendix ................................................................................................................................................................................................ 26 http://crossmark.crossref.org/dialog/?doi=10.20448/journal.501.2019.61.16.26&domain=pdf&date_stamp=2017-01-14 http://creativecommons.org/licenses/by/3.0/ http://creativecommons.org/licenses/by/3.0/ http://asianonlinejournals.com/index.php/AJEER/article/view/262 https://orcid.org/0000-0001-8762-3881 http://asianonlinejournals.com/index.php/AJEER/article/view/262 https://orcid.org/0000-0001-8762-3881 http://asianonlinejournals.com/index.php/AJEER/article/view/262 https://orcid.org/0000-0001-8762-3881 Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 17 © 2019 by the authors; licensee Asian Online Journal Publishing Group 1. Introduction Over the past few years, applied research has attached due emphasis to the explicit role of the financial sector in amplifying and propagating disturbances into the real economy. The financial crisis that broke out in 2007 has spurred a wide range of investigations into the importance of banking and financial activities in shaping business cycle fluctuations. Previously, economic thinking was widely influenced by the Modigliani-Miller (MM) principle in which financial structure was irrelevant for both banking and non-banking business funding considerations. As a result, it did not matter whether a firm financed its investment opportunities by issuing bonds (debt) or shares (equity) and the market valuation of the firm would be deemed independent of its capital structure. However, the MM hypothesis rests on numerous suspicious assumptions that are incompatible with empirical evidence. Some of those assumptions include absence of distortive taxation, symmetric distribution of information among transaction parties, efficient goods and financial markets, and zero bankruptcy costs. Since financial markets are perfect, there is no wedge between lending and borrowing rates, and in fact, there is no need for financial intermediaries as businesses can directly source their external funds from households. The MM principle, therefore, would rule out the monetary policy transmission aspects of bank asset and liability management as well as the effects of leverage ratio on business investment choices. Theory and empirical regularities show that agency problems such as moral hazard and information asymmetry play a huge role in influencing access to credit and, therefore, the balance sheet structure of entrepreneurial firms, especially small and micro enterprises (SMEs). Stiglitz and Weiss (1981) have shown how existence of agency problems could generate credit rationing in which among observationally identical applicants some are offered credit and others are rejected. Thus applicants who are denied credit would not be able to get external funds even if they were willing to accept a higher interest rate than the one prevailing in the market or post more collateral than was required of eligible borrowers. Under such circumstances, banks would reconcile the supply of available funds with demand for credit not by raising the lending rate or demanding more collateral but by restricting the number of borrowers via rationing. Thus, downsized balance sheets reduce the banks‘ capacity to offer additional loans and lower debt-to-equity ratio incentivizes banks to minimize the variability of their portfolio. If this logic is operational, banks are willing to sacrifice more profits on [potentially] successful loan advancements by increasing screening and monitoring of loan applicants (Agur, 2010). One important force behind the screening and filtering barriers erected by lenders is that agency problems can operate through the size of the borrowing firm.1 Size can affect the capital structure of the firm because of the role of scale economies in reducing asymmetric information, degree of risk exposure, the extent of transaction costs, and access to market facilities. Smaller firms receive less capital or pay higher rates as it is relatively more expensive for them to solve informational problems with their potential creditors. This implies that the effect of size on financing structure should be more pronounced among start-ups as new firms are more information-wise dense than their established counterparts. Moreover, to the extent that firm size is inversely correlated with risk, bankruptcy costs, and market barriers, this would discourage smaller firms from accessing outside financing options. Consequently, in light of these frictions and imperfections, the capital structure of firms and financial intermediaries could be vastly different from the one predicted by the MM principle. Size is particularly relevant in the context of low income countries where small and micro enterprises (SMEs) have great potential in terms of employment creation as well as in their contribution to GDP but face significant barriers against access to finance.2 The World Bank report on small and micro enterprise financing in Ethiopia (World Bank, 2015) confirms this observation. The report shows that in both manufacturing and service sectors, job creation is higher among established and older firms than under young businesses, suggesting a lack of competitiveness and innovation in the private sector. The retail and service sectors were also more important than manufacturing in job creation and employment. Regarding financial constraints, the report indicates small firms struggle the most in getting access to credit, smaller and young firms are more likely to be rejected for a loan or a line of credit, and that SMEs are discouraged or willingly distance themselves from applying for loans due to prohibitive collateral requirements. The report also identifies a ‗missing link‘ in which small firms are disproportionately affected compared with micro, medium, and large enterprises.3 The main objective of this paper is to see whether the financial accelerator mechanism documented under interest-rate-rule based simulations could be replicated under a situation where the central bank uses money growth rule in stabilizing the national economy. The findings are broadly consistent with previous studies that demonstrated stronger role for credit market imperfections in amplifying and propagating monetary policy shocks. 2. Literature Review Despite their popularity as the workhorse for monetary policy scenario analysis, standard New Keynesian general equilibrium models had devoted insignificant role to financial market frictions in magnifying and driving macroeconomic volatility.4 These models replicate business cycle properties only with heavy reliance on extensive and persistent shocks whose existence cannot easily be verified and explained (Brázdik et al., 2012). In this paper, we introduce explicit roles for both business and financial market rigidities that facilitates the amplification and propagation of real and nominal shocks affecting the economy.5 As noted by Markovic (2006) we can identify between two distinct categories of modeling frameworks featuring financial market imperfections. The first category includes bank balance sheet models that emphasize the supply side aspects of financial markets such as bank balance sheet status. The second group focuses on corporate 1See Cassar (2004) for more detail on financing issues affecting business start-ups. Additionally, owner characteristics (level of education or experience), asset structure or collateral, legal organization (presence or absence of limited liability) and other factors can shape financing structure. 2For instance, under the five-year Growth and Transformation Plan (GTP), the government of Ethiopia recognized the industrial potential embedded in SMEs and it planned to generate more than 3 million jobs between 2010/11 and 2014/15,a goal which was realized by more than threefold by the end of July 2015. 3According to this report only 1.9 percent of small firms have loan or line of credit while the corresponding figures for micro, medium and large firms are 6, 20.5, 35.5 percent, respectively. 4 For instance, influential papers like Clarida, Gali and Gertler (1999). do not consider financial frictions at all in their New Keynesian models 5 See also Vousinas (2013) on the financial-real economy linkage. Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 18 © 2019 by the authors; licensee Asian Online Journal Publishing Group or business balance sheet conditions like the financial accelerator mechanism influencing firm net worth. While most of the literature has so far concentrated solely on the demand side, we also consider interaction with the supply side to account for frictions arising from banking and financial markets. On the demand side, Bernanke et al. (1989) and Bernanke et al. (1999) constitute the foundation by incorporating information asymmetry in credit markets as a source of agency costs influencing investment- spending behavior among firms. This link is particularly strong when the economy is stuck below its capacity. In recession, for instance, demand shortfall negatively affects revenue and consequently firm profit and equity6 fall substantially. The attendant increase in leverage ratio (or decrease in net worth) aggravates the already existent agency problem and creditors respond by raising the finance premium on their loans. The higher external financial premium reduces the demand for capital investment which, in turn, further undermines the net worth position and survivability of the firm. This self-reinforcing mechanism is known as the ―financial accelerator‖ and illustrates the pro-cyclical nature of adverse changes in business net worth and their impact on the ability of firms to access external funding opportunities. The financial accelerator principle implicitly assumes that producers can get unlimited amount of funding at the prevailing lending rate subject to the strength of their balance sheet structures (banks demand no guarantee that the loan be repaid in full). In this setting, the external risk premium only affects their capacity to borrow without facing the possibility of credit rationing or some other quantitative restrictions imposed by lenders. Kiyotaki and Moore (1997) consider collateral constraints that facilitate the magnification of business cycle volatility and persistence as a result of dynamic association between credit prices and quantities. In the past, the vast majority of the literature focused its attention on credit market imperfections affecting firms while the role of banking was understated or totally ignored. Incorporating the financial sector permits an important role for the supply side of the credit market by activating banks‘ liquidity and capital structures, which creates a two-way bridge between banking services and the broader non-financial economic activity. Consequently, introducing an active banking sector creates a double-agency-cost problem between banks and their shareholders on the one hand and between borrowers and creditors on the other.7 Heuvel (2002); Markovic (2006); Aguiar and Drumond (2007); Christensen and Dib (2008) and Dib (2010) among others, have rationalized how capital sufficiency regulations imply a breakdown of the Modigliani-Miller principle: the bank‘s credit supply policy is a function of its capital structure, lending opportunities, and market interest rates. For instance, a sharp fall in bank capital—from cancellation of large non-performing loans or other adverse shocks—will force the bank to reduce the supply of credit because of regulatory capital requirement or the punitive cost of attracting new capital. A similar argument can be deployed regarding the role of insufficient bank liquidity in amplifying tight monetary policy measures and other negative shocks affecting the broader economy. As emphasized byAguiar and Drumond (2007) the discussion on the importance of bank equity in business cycle fluctuations is relevant in view of the implementation of the Basel Capital Accords (the first in 1988/1992, the second in 2004, and the third motivated by the 2007 financial crisis and yet to be implemented). This series of international standards establishes the basis for a host of central banks and other regulatory authorities to make sure that commercial banks have adequate capital to weather individual and aggregate risks stemming from within and outside the financial system. By imposing risk and capital measurement and management requirements, such standards can influence bank credit offer and investment decisions: if a bank finds itself exposed to large outstanding risky loans, it will be required to increase its capital to avoid total collapse, and this should reduce lending to the wider economy. The cost of bank capital can be an important factor for the smooth operation of credit providers. Markovic (2006) identifies three key bank capital channels that cause a variation in the expected return and thus a variation in the cost of bank capital: 1) the default risk channel due to the possibility of banks defaulting on their capital. This channel is active in equilibrium and its strength is, in turn, a function of firms defaulting on bank loans 2) the adjustment cost channel which rests on the existence of information asymmetry between depository institutions/banks and their investors/shareholders, and the associated monetary cost necessary to minimize this asymmetry. If this channel is real, raising fresh capital is costly, as this would send a bad signal to potential investors about the financial conditions of the target bank. As a result, prospective investors would buy bank shares only after incurring search costs (costs involved in checking the health of specific banks) 3) the capital/equity loss channel works via existing shareholders‘ expectation of future bank losses. During recession, shareholders anticipate that in the future there will be a decline in the value of their bank capital. Thus, the higher the expected erosion in bank equity, the stronger the capital loss channel will be. On the empirical front, there have been numerous studies accentuating the significant role of the financial sector in intensifying and propagating the effects of adverse shocks affecting the economy. Fukunaga (2002) built upon the Bernanke et al. (1999) framework to develop a dynamic general equilibrium model calibrated to the Japanese economy. The model features a micro-financial contractual problem involving companies/borrowers and financial intermediaries/banks. Retailers are included to introduce inertia in the price setting process with the objective of providing room for monetary non-neutrality in the short run. Moreover, capital producers and government (fiscal and monetary sectors) are included. In this decentralized, rational-expectation-equilibrium- model economy, three sources of unanticipated shocks are considered: technology (total factor productivity), monetary and demand (exogenous fiscal expenditure). The results suggest, among other things, that tight monetary policy stance (negative shock) is followed by a decline in corporate investment, net worth, and demand for capital as a result of a rise in the external financial risk premium. This fall in investment is much deeper and more persistent in the model with financial accelerator than the one without credit market frictions. In addition to the net worth channel, demand-side financial imperfections have also been identified to originate from collateral constraints. Brzoza-Brzezina et al. (2010)8 compare the relative significance of the two channels in 6Throughout the discourse, I use net worth, equity and capital interchangably both in the context of bank and business balance sheets. 7 This agency problem has two dimensions: moral hazard (when one agent--the bank--cannot without cost verify the intention, activity or action of another agent--the borrower) and adverse selection (when one agent has access to private information). 8 They also introduce a banking sector in both versions of frictions even though analyzing the impact of shocks emanating from the banking system is not their main objective. Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 19 © 2019 by the authors; licensee Asian Online Journal Publishing Group an extended medium scale New Keynesian model calibrated to the Polish economy. They compare the collateral constraint framework of Kiyotaki and Moore (1997) with the external finance premium setup of Carlstrom and Fuerst (1997) and Bernanke et al. (1999). They rely on business cycle accounting, moment matching, and impulse response analyses to see the qualitative and quantitative performance of the two models. Their results indicate that both models with financial frictions add volatility to the baseline New Keynesian framework, with the external finance premium showing significantly stronger internal propagation mechanism than its collateral constraint counterpart. In terms of business cycle accounting, they find superior performance of the models with financial frictions to the baseline specification, with the model under collateral constraint offering moments closely resembling those filtered from actual data. Recently, there have been growing tendencies to model banking activity as a potential source of economic fluctuations. For instance, Meh and Moran (2010) using a general equilibrium framework, show that bank capital can be an important channel for the transmission of shocks in view of moral hazard problems between banks and investors that provide funds. Other works emphasizing the role of bank balance sheets in intensifying and transmitting exogenous shocks include Gertler and Karadi (2011) and Hafstead and Smith (2012) among others. Though much of the focus has been on bank equity, there have been efforts to incorporate the importance of liquidity under a general equilibrium framework. This might involve assigning roles to interbank markets as in Carrera and Vega (2012) or studying the impact of reserve requirements as in Areosa and Coelho (2013). The vast majority of studies on financial market imperfections are devoted to advanced industrial economies and to some extent to emerging blocks while there appears to be scant interest in low-income countries, especially those in Sub-Saharan Africa. One contribution is by Babilla (2014) who uses a mix of calibration and Bayesian estimation of a modified small open dynamic stochastic general equilibrium model for the West African Economic and Monetary Union (WAEMU). The paper evaluates the effectiveness of bank lending channel in the propagation of monetary policy measures within a currency union where financial intermediation is dominated by oligopolistic banks. Consistent with the evidence for advanced and emerging countries, the paper finds that including financial market distortions improves the performance of the model. This paper relates to the works of Markovic (2006); Aguiar and Drumond (2007); Christensen and Dib (2008) by allowing interaction between the balance sheet structures of the corporate and banking sectors. The Bernanke et al. (1999) model of financial accelerator mechanism is augmented to accommodate distortions arising from credit suppliers. This way, a double-agency-cost problem is emphasized to capture the effects of information and moral hazard costs between banks and borrowers on one side and between banks and their shareholders on the other. It is assumed that banks mobilize funding by issuing shares to and collecting deposits from households. The household preference for liquidity determines the relative costs of banking finance through equity issuance and deposit mobilization. The rest of the paper has been structured as follows. Section 3 outlines the model followed by the presentation of calibration and simulation exercise in section 4. Section 5 concludes. 3. Model The model setup features standard elements in New Keynesian general equilibrium models augmented with financial frictions. The household sector makes consumption, labor supply and saving decisions. They use their savings to make deposits and/or buy shares in banks. Entrepreneurs rely on bank credit to purchase investment capital and combine it with hired worker to produce wholesale goods. The banks mobilize household resources in the form of deposits and equity and make loans to businesses/entrepreneurs. 3.1. Entrepreneurs Every period the entrepreneur purchases the required capital stock which will be combined with labor to produce goods the next period. Thus, at time t entrepreneur j purchases homogenous capital for use at t+1, 1 j tK  . The return to capital is affected by both systemic risk and risk that is specific to the firm. The ex-post gross return on capital for firm j is 1 1 j K t tR   , where 1 j t  is an idiosyncratic shock specific to firm j‘s return and 1 K tR is the ex post aggregate return to capital. The idiosyncratic disturbance ( )j is independently and identically distributed both across entrepreneurs and over time, with a continuous and once-differentiable cumulative distribution function (c.d.f), ( )F  , over a non-negative support, and with expected value equal to unity. Entrepreneur j enters next period with net worth 1 j tN  which complements borrowed funds for the purchase of 1 j tK  . The borrowed money finances the difference between the total capital expenditure and own funds (net worth) and is equal to 1 1 1 j j j t t t tL QK N    , where tQ is the unit price of capital in period t. Each entrepreneur signs a credit contract with a bank which demands a required rate of return on lending between t and t+1, 1 F tR . This arrangement reflects an agency problem due to asymmetric information between the bank and the entrepreneur. This implies that only the borrower can without incurring costs observe the return of the project. The financial contract is designed to minimize the expected agency cost. As popularized by Bernanke et al. (1999) this gives rise to a costly state verification (CSV) problem, in which the lending bank must incur monitoring and supervision costs in order to know the actual performance of the borrower‘s project. We assume this monitoring cost is equal a fraction  of the realized gross return of the entrepreneur‘s capital: 1 1 1, j K j t t t tR QK     where 0 1  . Neither the bank nor the entrepreneur knows the idiosyncratic disturbance 1 j t  prior to the investment decision. That is both capital expenditure and the credit contract are established before the realization of the shock specific to the borrower. Once the investment project has been installed, the bank can observe the random shock but only after incurring monetary costs. Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 20 © 2019 by the authors; licensee Asian Online Journal Publishing Group Given 1 j t tQ K  , 1 j tL  , and 1 K tR , the optimal contract is characterized by a gross non-default loan rate , 1 j tZ  , and a cut-off 1 j t  , such that, if 1 1 j j t t   , the borrower pays the lender the amount 1 1 1 j K j t t t tR QK    and keeps the residual value 1 1 1 1( ) .j j K j t t t t tR QK     That is, 1 j t  is defined by: 1 1 1 1 j K j j t t t t t tR QK Z L     (1) If 1 1 j j t t   , the borrower receives nothing, while the bank monitors the borrower and receives 1 1 1(1 ) j K j t t t tR QK     . In equilibrium, the contractual arrangement ensures that the lender gets an expected gross return on the loan equal to the required return: 1 1 1 1 1 1 1 1 1 1 0 (1 ( )]Z (1 ) ( ) ( ), j tj i j j K j F j j t t t t t t t t t t tF L R Q K f d R Q K N                     (2a) where ( )f  is the probability density function (p.d.f) of  . Combining Equation (1) with Equation (2a) yields the following expression:  1 1 1 1 1 1 1 1 1 0 [1 ( )] (1 ) ( ) ( ) j tj j j K j F j j t t t t t t t t tF f d R K R Q K N                     (2b) Expanding the expression within the parenthesis on the left hand side of Equation (2b) we can define the share of income going to the lender ( ( ) ) and the residual amount to the entrepreneur ( ( ) ): 1 1 1 1 1 1 0 0 ( ) ( ) [1 ( )] ( ) ( ) j j t tj j j j t t t tF f d f d                           Thus the optimal financial contract involves maximizing the profit share of the entrepreneur subject to the lender resource constraint discussed previously: 1 1 1 1, [1 ( )](1 R )(lev 1) max 1 t t K t t t t F tlev E R           (2c) s.t. 1 1 1 1 [ ( ) ( )](1 R )(1 lev ) 1 K t t t t tF t lev R              where 1 1 1 t t t t t Q K N lev N      . Bernanke et al. (1999) have demonstrated that the lender‘s expected return is maximized at a unique interior point 1 j t  , * 1 j t  , and the equilibrium is characterized by 1 j t  always being below * 1 j t  . As a result, the possibility of equilibrium under credit rationing is not considered and the creditor‘s expected return is always increasing in 1 j t  . Denoting the expected discounted return to capital by the ratio, 1 1 ( )K t t F t E R R   , if this ratio exceeds unity, the first order conditions of the contracting problem produces the following relationship between 1 1 j t t j t Q K N   and the expected return to capital: 1 1 1 1 ( )j K t t t t j F t t Q K E R N R           , (3) where (.) 0  and (.) 0  . This implies that the entrepreneur incurs capital expenditures that are proportional to their net worth, with a proportionality factor that is positively correlated with the expected return to capital. Thus the probability of default should fall with a rise in the discounted return to capital. The decline in the specter of bankruptcy enables the firm to take on more loans and expand its operation. However, future default costs rise with the leverage ratio and this limits the ability of borrowers to expand investments indefinitely. Reformulating the preceding relationship in aggregated form (over firms) we get: 1 1 1 1 ( ) , K t t t t F t t Q K E R N R           (4) where 1tK  represents the aggregate stock of capital bought by all entrepreneurial firms at time t, and 1tN  is their aggregate equity or net worth. 1 1 1 1 ( ) , K t t t t F t t E R Q K R N            (5) where (.) is increasing in 1 1 t t t Q K N   for 1 1t t tN Q K  . Consequently, in equilibrium, the expected discounted return to capital, 1 1 ( )K t t F t E R R   , evolves inversely with the volume of capital expenditure financed by the firms‘ net Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 21 © 2019 by the authors; licensee Asian Online Journal Publishing Group worth. 1 1 ( )K t t F t E R R   is what has been referred to as external finance premium in Bernanke et al. (1999) faced by entrepreneurs. 3.1.1. Entrepreneurial Net Worth Entrepreneurs build their net worth based on accumulated retained earnings from past capital investments and wage compensation from supplying labor. As a technical requirement, we allow entrepreneurs to start with some net worth to begin their operations. Moreover, we assume that the fraction of the population who are entrepreneurs remains constant over time: in every period the number of firms entering the market is equal to the number of firms going out of the market. Let tV be the entrepreneurs‘ total net worth accumulated from business operations, then normalizing the entrepreneurial work hour to unity we have: 1 e t t tN V W   (6) where e tW captures the wage income to entrepreneurs and  is the chance that the specific entrepreneur survives to the next period. To rule out the possibility that firms build sufficient net worth to be fully self financed, we assume that those firms are active for finite horizons. Note the equilibrium value of tV can be cast as a function of the variables from the financial contract as: 1 1 1( ) ( ) ,K F K t t t t t t t t t t tV R Q K R Q K N R Q K        (7) where 1( ) K t t t tR Q K   represent the total default monitoring costs and 0 ( ) ( ) . t j t t f d        Equations (6) and (7) indicate that the net worth of firms is influenced by their earnings net of interest expenses to the bankers. Entrepreneurs that exit from the market in period t are not allowed to purchase capital and simply consume their residual equity (1 ) tV : (1 )e t tC V  , (8) where e tC is the total consumption of entrepreneurs that exit from the market. 3.2. Banks In our model economy, the financial industry is dominated by banks which function by mobilizing household funds and extending loans to entrepreneurial firms. In Bernanke et al. (1999) banks are only intermediaries and their operation is totally insulated from aggregate risk or whatever risk they face is diversified away. In our approach, for simplicity, lenders are exempt from exogenous reserve requirement, but must satisfy a risk-based capital requirement imposed by the regulatory regime. It is presumed that banks are the sole business entities that issue equity which rests on households‘ willingness and ability to hold capital in addition to deposits. The asset side of the bank balance sheet reveals not just loans to entrepreneurs, but also short term treasury securities. The debt instruments have zero weight in the risk-based capital assessment as they entail no risk (the fiscal sector is assumed not to default on its obligations). A special characteristic feature of banks concerns the facility necessary to monitor and supervise the activities of borrowers. Households—who are the major bank shareholders—lack this facility and delegate the responsibility of monitoring to banks, which grapple with the costly state verification problem described previously. Under such arrangements, each bank does not enjoy any bargaining advantage. In other words, the banks operate in a perfectly competitive environment and obtain zero profit in the long run as entry and exit are totally unregulated. The banks problem involves:   1 1 1 1 1 1 1 1 1 1 1 1 , , , max ( ) t t t t F D S t t t t t t t t t S D B L R L R B R D E R S               s.t. 1 1 1 1t t t tL B D S      (9) 1 1 _t t S del k L    (10) where 0 _ 1del k  is the exogenous capital adequacy ratio. Equations (9) and (10) specify the bank balance sheet constraint and the regulatory capital requirement, respectively. Moreover, 1 1 1 1, , ,andt t t tL B D S    denote, respectively, the loan advancement, purchase of treasury securities, deposit collection and equity issuance by banks between periods t and t+1; while 1 1 1 1, , ,andF D S t t t t tR R R E R    represent the required gross real rate of return on loans; the gross real rate of return on treasury securities; the gross real rate of return on deposits; and the expected gross real rate of return on bank equity—in the same order. Notice that 1 F tR differs from the non-default lending rate, 1tZ  . The difference arises from the possibility of entrepreneurs getting bankrupt--default on their loans—and the attendant monitoring costs which are reflected in 1 F tR . In addition, while the other rates of return are known in advance in period t, the rate of return on equity, 1 S t tE R  , is uncertain and depends on the realization of the state of the economy at t+1. Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 22 © 2019 by the authors; licensee Asian Online Journal Publishing Group Under binding bank capital requirement, 1 1 _t t S del k L    , the first order conditions9 of the admissible solution of the bank‘s maximization problem are: 1 1 D t tR R  (11) 1 1 1(1 _ ) _ ( )F S t t t tR del k R del kE R     (12) These conditions illustrate that with binding minimum capital threshold, the required rate of return on lending is a weighted average of the rate of return on deposits and the expected rate of return on bank equity. Thus, we have significant departure from the Bernanke et al. (1999) framework where the required rate of return on lending equals the riskless/deposit rate. 3.2.1. Return on Capital The exogenous regulatory capital requirement entails that the bank must maintain a level of equity which amounts to _del k times the volume of total loan advancement. The supply of credit is therefore financed by a combination of bank equity and deposits mobilized from households, who allocate their savings between these financial instruments. The relative ease of using deposits for liquidity services and the riskless rate associated with them establishes a spread vis-à-vis the rate of return on bank capital, that is, 1 1 S D t t tE R R  . Moreover, we assume that the real rate of return on physical and bank capital is the same: 1 1 S K t t t tE R E R  (13) The interpretation of (13) is that even if entrepreneurs are the only investors in physical capital, households would demand the same expected rate of return on both physical and bank capital if they were to make capital expenditures. Thus, Equation (13) represents a no-arbitrage condition as physical and bank capital provide no liquidity services and their returns are exposed to the same systemic risk. 3.2.2. Capital Producers In this section we integrate the optimal financial contract signed in a partial equilibrium setting into New Keynesian general equilibrium framework. Capital producers buy final investment goods ti from retailers and transform them using existing capital to generate new capital stock. Investment decisions are subject to quadratic adjustment costs. The inclusion of such costs induces volatility of entrepreneurial net worth and bank capital via the variability of the price of capital. We assume that capital producers deploy a linear technology and choose the level of investment spending to maximize profits subject to adjustment costs: 2 q,i max 2 k t t t t t t t I K Q I I K K              (14) where tQ is the real price of capital while ,q ik and  are parameters capturing the degree of adjustment cost and depreciation of capital, respectively. The optimization problem gives rise to the following first order condition: .1 t t q ik t I Q K           (15) Notice that the higher the value of ,q ik , the higher the volatility of the price of capital. Setting this parameter to zero entails a constant price of capital equal to unity. The law of motion for the aggregate capital stock in the economy is evolves according to: 1 (1 )t t tK I K    (16) 3.3. Production by Entrepreneurs Entrepreneurial firms rely on bank loans to supplement their net worth in the purchase of capital goods. They combine the purchased capital with hired labor to produce wholesale goods which they sell at nominal marginal cost in perfectly competitive markets. Only households and entrepreneurs are employed by the firm as bankers are assumed to be insignificant fraction of the labor force. The firm uses constant returns to scale Cobb-Douglas production technology: 11[( ) ( ) ]k kh e t t t t tY AK H H   (17) where 0 1k  is the capital share in aggregate output; 1( ) ( )h e t tH H  is total labor supply with h tH and e tH indicating the work hours of households and entrepreneurs, respectively.  is the fraction of work hours provided by households. Finally, the demand for capital must satisfy the following condition for the expected return on capital: , 1 1 1 (1 )k t tK t t t MP Q E R Q            (18) 3.4. Retailers Retailers are included to generate inertia in the price setting schedule. They are monopolistic firms that set their prices in a staggered fashion due to Calvo (1983). In each period, a random fraction 1  ( [0,1]  ) of firms 9 The complete set of first order conditions is available from the author upon request. Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 23 © 2019 by the authors; licensee Asian Online Journal Publishing Group adjust their prices optimally. The remaining fraction,  , are assumed to follow an adjustment process that exploits indexation of current prices to inflation in the previous period: 1 2 (j) P ( )I t t t t t P P j P            (19) Denoting the price level that the optimizing firm chooses in each period by tP , the aggregate price level in the domestic economy evolves according to the pricing rule: 1 1 1 1 1 1 2 (1 ) t t t t t P P P P P                            (20a) Or 2 1 1(1 )( )t t t tp p        (20b) Those optimizing firms that are able to adjust their prices in the current period will choose tP in such a way as to maximize the present discounted sum of future streams of profits subject to the sequence of demand constraints for household and residual government consumption:      , 0 max t j n t j t j H t t j P j Q Y P MC       (21) Subject to  t t j t j t t j P Y C G P             where n t jMC  is the nominal marginal cost while j t t jE  is the effective stochastic discount factor that considers the fact that firms have a 1  provability of being able to reset their prices in each period. 3.5. Households The economy is inhabited by an infinitely lived forward looking representative household. The household engages in key economic decisions that involve labor supply, consumption, and saving. The typical household has the opportunity to allocate its savings between riskless deposits ( tD ) and risky equity investment ( tS ) offered by banks, which offer expected returns of 1 D tR and 1 S tR , respectively. The maximization problem of the typical household is: 1 1 1 1 1 0, , , ( ) max 1 1 1 t t t t h j t t t jC N D S C D H                        s.t. 1 1 h h D S t t t t t t t t t t tC D S T W H R D R S        (22) where  is the subjective discount rate,  is the inter-temporal elasticity of substitution (same for both consumption and deposit demand),  is the inverse elasticity of labor supply; h tH captures the number of hours worked, h tW is the hourly household real wage rate, tT is tax expense, t is the dividend receipts, tC denotes the real composite consumption index of home produced goods and services. 4. Results and Discussion 4.1. Calibration The quarterly business bankruptcy rate is set to 0.0075 based on the International Development Research Centre (IDRC) survey results which report an annual 3 per cent business discontinuance rate for Ethiopia. The loan monitoring cost is fixed at 0.12 as in Bernanke et al. (1999). The fraction of entrepreneurs who survive to the next period is assumed to be 97 percent. These values suggest a steady state leverage ratio of 1.932, an annual external finance premium of 200 basis points, and an elasticity of external finance premium to leverage ratio of 0.041. Based on these values and choosing a value of 1.01 for the quarterly gross risk-free rate, we get a quarterly gross return on capital equal to 1.0157 and a quarterly gross bank financing cost of 1.0107. See Appendix A for the complete list of parameters and their definition. Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 24 © 2019 by the authors; licensee Asian Online Journal Publishing Group 4.2. Simulation Results Figure-1. Impulse Response to Monetary Policy Shock with Financial Frictions (solid line) and without Financial Frictions (dotted line) Source: (Author‘s own simulation results) Figure 1 shows the relative responses of selected endogenous variables to a one-off quarterly monetary policy shock equal to 0.05 standard deviation applied under money growth rule. It is clear that the results are significantly different for the two models. In the model with financial distortions, unexpected increase in the policy rate lifts the cost of raising fresh capital for financial intermediaries which they translate into higher external premium for loan applicants. By contrast, when the role of frictions is switched off, there is no difference among the policy rate, the required rate of return on bank loans, and the rate of return on equity investment. This is summarized by the flat impulse response of the external finance premium. Consistent with conventional empirical evidence, monetary tightening is accompanied by a decline in inflation, output, consumption, investment, and asset prices. But the degree of contraction is deeper and more persistent in the model where supply and demand side financial market imperfections have been considered. These results are broadly in line with previous findings that include Markovic (2006); Aguiar and Drumond (2007) and Zhang (2009) that found unanticipated monetary shocks are amplified and propagated much more strongly with double agency cost problems in the financial markets. Figure-2. Impulse Responses of Output and Inflation under Interest Rate (dotted) and Money Growth (solid) Rules (Source: Author‘s own simulation results) Source: (Author‘s own simulation results) Asian Journal of Economics and Empirical Research, 2019, 6(1): 16-26 25 © 2019 by the authors; licensee Asian Online Journal Publishing Group The next task is to see if previous findings under Taylor based rules could be quantitatively any different from those under money growth rule. Figure 2 presents the responses of output and inflation to shocks under alternative monetary policy regimes. The qualitative aspects of the results are more or less preserved. For instance, monetary policy tightening (a rise in the policy rate or a fall in money supply) leads to noticeable reduction in output and inflation while improvement in factor productivity boosts production and eases upward pressure on price changes. Increased fiscal intervention also expands output under both monetary policy rules. However, the effects of a rise in public expenditure on inflation clearly depend on the operational instrument deployed by the central bank. When the monetary authority sticks to an interest rate rule, increased government borrowing feeds into higher inflation. But under money growth rule expanded fiscal activism results in a decline in inflation in the first few quarters. To the extent that the output effect of a fiscal stimulus is more persistent, the money growth rule contributes to a fall in price changes in the immediate short run perhaps reflecting delayed effects of fiscal policy due to, say, the low velocity of money in developing economies such as Ethiopia. Over all, the model with money growth rule generates qualitatively similar results as those which employ interest rate rules (Markovic, 2006; Aguiar and Drumond, 2007; Zhang, 2009). 4.3. Sensitivity Check A common challenge when using DSGE models is the so called ―parameter bifurcation problem‖—the observation that changing parameter values a little leads to considerable change in the impulse response of endogenous variables. It is impractical to verify the sensitivity of these responses to changes in the value of every parameter. However, given the objective this paper, I tried to evaluate how sensitive the results are to variations in the values of policy parameters in the central bank money growth reaction function rule. The impulse response functions were generally stable both qualitatively and quantitatively to such small changes in the values of the parameters in the monetary policy rule. 5. Conclusion and Policy Implications In the last few years, macroeconomic modeling has emphasized the role of credit market frictions in magnifying and transmitting nominal and real disturbances and their implication for macro-prudential policy design. In this chapter, we construct a medium-size small New Keynesian general equilibrium model with active banking sector. In this set-up, the financial sector interacts with the real side of the economy via firm balance sheet and bank capital conditions and their impact on investment and production decisions. We rely on the financial accelerator mechanism due to Bernanke et al. (1999) and combine it with a bank capital channel as demonstrated by Aguiar and Drumond (2007). We calibrate the resulting model from the perspective of a low income economy reflecting the existence of relatively high investment adjustment cost, strong fiscal dominance, and underdeveloped financial and capital markets where the central bank uses money growth in stabilizing the national economy. The findings are broadly consistent with previous studies that demonstrated stronger role for credit market imperfections in amplifying and propagating monetary policy shocks. While most studies assume an interest feedback rule to capture the behavior of monetary authorities, we rely on a money growth rule to adapt to the dominant policy practice in low income economies. It is interesting that in our model the interaction of corporate and bank balance sheets generates similar results as those which employ interest rate rules (Markovic, 2006; Zhang, 2009; Agur, 2010) for instance). The policy implication of this result is particularly relevant in low income countries where small and fragile firms face very high external finance premium. With little or no net worth to post as collateral, these firms often have to pay above market rates on small loans obtained from banks and microfinance institutions. Even though adding a default premium on poor borrowers makes perfect financial sense, it creates a kind of self-fulfilling prophesy where the higher lending rate undermines the ability of the poor borrower to start and operate profitable projects. 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Parameter definitions and values Parameter Description Value β Subjective discount factor 0.98 Central bank weight attached to inflation gap 1 Central bank weight attached to output 0.11 i Interest semi-elasticity 0.0035 θ Calvo price rigidity 0.75 Money growth rate smoothening/persistence 0.8 AR Coefficient for each exogenous process 0.8 1/σ Inverse elasticity of inter-temporal substitution 1/3 φ Inverse elasticity of labor supply 4 v Elasticity of external premium with respect to leverage 0.041 ,q ik Sensitivity of price of capital to the investment-capital ratio 0.5 δ Capital depreciation rate 0.025 Steady state gross return on entrepreneurial project 1.0157 Steady state cost of raising funds by lender 1.0107 r Steady state deposit/riskless rate 1.01 K/N Steady State leverage ratio 1.932 Y/N Steady State output net worth ratio 0.2383 MP_K Steady state marginal product of capital 0.0407 Del_K Exogenous capital requirement ratio 0.12 C/D Steady state consumption-deposit ratio 0.22  Capital share in production 0.3 (1 )  Fraction of labor supplied by households 0.693 (1 )(1 )  Fraction of labor supplied by entrepreneurs 0.007 MC Steady state gross cost mark up 1.1 μ Loan monitoring cost 0.12 γ Business survival rate 0.97  Steady state profit division parameter 0.4805 ( )F  Quarterly business bankruptcy rate 0.0075 I/Y Steady State ratio of Investment to GDP 0.18 C/Y Steady State ratio of Consumption to GDP 0.60 G/Y Steady State ratio of Public spending to GDP 0.22 Asian Online Journal Publishing Group is not responsible or answerable for any loss, damage or liability, etc. caused in relation to/arising out of the use of the content. 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