bank runs liquidity costs and investment distortions abstract in this paper we extend the diamond and dybvig 1983 model of intermediation to study further the conditions under which bank runs can occur and to consider how private parties might adjust to the existence of bank run equilibria we provide weaker necessary conditions for runs we then characterize how banks respond to the possibility of runs in their design of deposit contracts and investment decisions banks might choose to offer contracts that prevent runs but under some conditions the second best contracts will involve accepting some risk of runs in order to achieve higher expected returns from their investments

terrorism and the fate of dictators the authors study the influence of domestic political dissent and violence on incumbent dictators and their regimes they argue that elite with an interest in preserving the regime hold dictators accountable when there is a significant increase in terrorism to pinpoint the accountability of dictators to elite who are strongly invested in the current regime the authors make a novel theoretical distinction between reshuffling coups that change the leader but leave the regime intact and regime change coups that completely change the set of elites atop the regime using a new data set that distinguishes between these two coup types the authors provide robust evidence that terrorism is a consistent predictor of reshuffling coups whereas forms of dissent that require broader public participation and support such as protests and insurgencies are associated with regime change coup attempts this article is the first to show that incumbent dictators are held accountable for terrorist campaigns that occur on their watch

equilibrium and government commitment abstract how should a government use the power to commit to ensure a desirable equilibrium outcome in this paper i show a misleading aspect of what has become a standard approach to this question and i propose an alternative i show that the complete description of an optimal indeed of any policy scheme requires outlining the consequences of paths that are often neglected the specification of policy along those paths is crucial in determining which schemes implement a unique equilibrium and which ones leave room for multiple equilibria that depend on the expectations of the private sector

banking panics information and rational expectations equilibrium this paper shows that bank runs can be modeled as an equilibrium phenomenon we demonstrate that some aspects of the intuitive story that bank runs start with fears of insolvency of banks can be rigorously modeled if individuals observe long lines at the bank they correctly infer that there is a possibility that the bank is about to fail and precipitate a bank run however bank runs occur even when no one has any adverse information extra market constraints such as suspension of convertibility can prevent bank runs and result in superior allocations banking panics were a recurrent phenomenon in the united states until the 1930s they have re emerged as a source of public concern and much theoretical research recently in this paper we provide an information theoretic rationale for bank runs the traditional story is that contagion is an important aspect of bank runs the idea seems to be that when the general public observes large withdrawals from the banking system fears of insolvency grow resulting in even larger withdrawals of deposits in our model some individuals withdraw because they get information that future returns are likely to be low uninformed individuals observing this also have an incentive to liquidate their investments in addition some individuals need to withdraw deposits for other than informationally based reasons thus if the random realization of such a group of individuals is unusually large then the uninformed individuals will be misled and will precipitate a run on the bank the technology is such that a large volume of withdrawals involves liquidation costs consequently runs on the bank do impose social costs a mechanism that may reduce these costs in our model is to suspend convertibility if withdrawals are high however those individuals who need to withdraw their assets for liquidity reasons are worse off ex post our model provides a rationalization for restrictions in demand deposits that were widespread prior to 1929 friedman and schwartz 7 suggest that restrictions of payments ensured

optimal fiscal policy under multiple equilibria abstract we study optimal fiscal policy in an economy where i search frictions create a coordination problem and generate multiple pareto ranked equilibria and ii the government finances the provision of a public good by taxing market activity the government must choose the tax rate before it knows which equilibrium will obtain and therefore an important part of the problem is determining how the policy will affect the equilibrium selection process we show that when the equilibrium selection rule is based on the concept of risk dominance higher tax rates make coordination on the pareto superior outcome less likely as a result taking equilibrium selection effects into account leads to a lower optimal tax rate

credible public policy abstract credible public policy is defined in a way that incorporates competitive equilibrium behavior for households and subgame perfect nash equilibrium behavior for the government it is shown that the set of all equilibrium outcome paths for credible policies can be constructed by using arguments analogous to those of abreu 1988 for repeated games the results are then extended to systems with state variables simple models of monetary policy and capital taxation are studied by way of example

implementing efficient allocations in a model of financial intermediation abstract in a finite trader version of the diamond and dybvig j polit econ 91 1983 401 model the ex ante efficient allocation is implementable by a direct mechanism i e each trader announces the type of his own ex post preference in which truthful revelation is the strictly dominant strategy for each trader when the model is modified by formalizing the sequential service constraint cf wallace fed reserve bank minneapolis quart rev 12 1988 3 the truth telling equilibrium implements the symmetric ex ante efficient allocation with respect to iterated elimination of strictly dominated strategies

bank runs and institutions the perils of intervention we study ex post efficient policy responses to a run on the banking system and the ex ante incentives these responses create we show that the efficient response to a run is typically not to freeze all remaining deposits since doing so imposes heavy costs on some individuals instead once a run is underway benevolent government institutions would allow additional deposit withdrawals placing further strain on the banking system when depositors anticipate these extra withdrawals their incentive to participate in the run increases in fact ex post efficient interventions can generate the conditions necessary for a self fulfilling run to occur jel g21 g8

bank runs and investment decisions revisited we examine how the possibility of a bank run affects the deposit contract offered and the investment decisions made by a competitive bank cooper and ross 1998 have shown that when the probability of a run is small the bank will offer a contract that admits a bank run equilibrium we show that in this case the bank will chose to hold an amount of liquid reserves exactly equal to what withdrawal demand will be if a run does not occur in other words precautionary or excess liquidity will not be held this result allows us to determine how the possibility of a bank run affects the level of illiquid investment chosen by a bank we show that when the cost of liquidating investment early is high the level of investment is decreasing in the probability of a run however when liquidation costs are moderate the level of investment is actually increasing in the probability of a run

sulfur dioxide control by electric utilities what are the gains from trade title iv of the 1990 clean air act amendments caaa established a market for transferable sulfur dioxide so2 emission allowances among electric utilities this market offers firms facing high marginal abatement costs the opportunity to purchase the right to emit so2 from firms with lower costs and this is expected to yield cost savings compared to a command and control approach to environmental regulation this paper uses econometrically estimated marginal abatement cost functions for power plants affected by title iv of the caaa to evaluate the performance of the so2 allowance market specifically we investigate whether the much heralded fall in the cost of abating so2 compared to original estimates can be attributed to allowance trading we demonstrate that for plants that use low sulfur coal to reduce so2 emissions technical change and the fall in prices of low sulfur coal have lowered marginal abatement cost curves by over 50 percent since 1985 the flexibility to take advantage of these chan

bayesian analysis of the two part model with endogeneity application to health care expenditure this paper studies the effect of managed care on medical expenditure using a model in which the insurance status is assumed to be endogenous insurance plan choice is modeled through the multinomial probit model the medical expenditure variable the outcome of interest has a significant proportion of zeros that are handled using the two part model extended to handle endogenous insurance the estimation approach is bayesian based on the gibbs sampler the model is applied to a sample of 20 460 individuals obtained from the medical expenditure panel survey the results provide substantial evidence of selectivity copyright 2006 john wiley sons ltd

collective moral hazard maturity mismatch and systemic bailouts the paper elicits a mechanism by which private leverage choices exhibit strategic complementarities through the reaction of monetary policy when everyone engages in maturity transformation authorities haver little choice but facilitating refinancing in turn refusing to adopt a risky balance sheet lowers the return on equity the key ingredient is that monetary policy is non targeted the ex post benefits from a monetary bailout accrue in proportion to the number amount of leverage while the distortion costs are to a large extent fixed this insight has important consequences first banks choose to correlate their risk exposures second private borrowers may deliberately choose to increase their interest rate sensitivity following bad news about future needs for liquidity third optimal monetary policy is time inconsistent fourth macro prudential supervision is called for we characterize the optimal regulation which takes the form of a minimum liquidity requirement coupled with monitoring of the quality of liquid assets we establish the robustness of our insights when the set of

a model of financial crises in emerging markets recent events in mexico asia russia and brazil have underscored that a satisfactory explanation of financial crises in emerging markets remains elusive not too long ago the prevailing view was that crises were the inevitable outcome of ongoing fiscal imbalances coupled with fixed exchange rates but this first generation view pioneered by krugman 1979 has fallen out of fashion because in many crises the crucial fiscal disequilibria were absent and as obstfeld 1994 has argued currency crises have sometimes occurred even though central banks had more than enough resources to prevent them witness much of europe in the early 1990s obstfeld put forward a second generation view in which central banks may decide to abandon an exchange rate peg when the unemployment costs of defending it become too large this new perspective implied that crises could be driven by self fulfilling expectations since the costs of defending the peg may themselves depend on anticipations that the peg will be maintained but obstfeld s emphasis on mounting unemployment and domestic recession while appropriate for the erm 1992 crisis was at odds with the facts in mexico in 1994 and east asia in 1997 asian

on the future of macroeconomics a new monetarist perspective this article argues that a pressing goal for macroeconomics is to incorporate financial considerations but we need models with solid microfoundations in particular the use of assets in facilitating exchange as well as different credit or other financial arrangements should be outcomes of not inputs to theories as a preview i suggest that mainstream macro does a good job explaining many phenomena and a financial crisis does not disprove such theory but understanding crises requires better incorporating factors related to money credit banking and liquidity the approach called new monetarist economics can help a lot in this regard

how amsterdam got fiat money abstract a fiat money system was introduced in the seventeenth century by a prominent public bank of the time the bank of amsterdam employing data from the bank s archives we show that bank money became a more attractive transactions medium following a 1683 policy change which unbundled the bank s account balances from a right to redeem these balances in coin balances not matched by a redemption right became fiat this change also stabilized the value of bank money as a unit of account freed the bank from defensive open market operations and promoted seigniorage collection

the role of independence in the green lin diamond dybvig model abstract green and lin study a version of the diamond dybvig model with a finite number of agents independence independent determination of each agent s type and sequential service for special preferences they show that the ex ante first best allocation is the unique equilibrium outcome of the model with private information about types via a simple argument it is shown that uniqueness of the truth telling equilibrium holds for general preferences and in particular for a constrained efficient allocation whether first best or not the crucial assumption is independence

evolution coordination and banking panics abstract i study equilibrium selection by an evolutionary process in an environment with multiple equilibria one of which involves a banking panic the analysis is built on a repeated version of the diamond dybvig 1983 model the optimal equilibrium is uniquely selected if it is also risk dominant when there are multiple banks the probability of observing a panic increases as the size of the banks decreases local interaction generates contagion effects that allow a bank run to spread first among banks in the same geographic location and then throughout the population

banking crises and liquidity in a monetary economy abstract this study investigates banks liquidity provision using the lagos and wright model of monetary exchange with aggregate uncertainty we show that banks sometimes exhaust their cash reserves and fail to satisfy their depositors needs for consumption smoothing we also show that banking crises can be eliminated by a rate of return equalizing policy under perfect risk sharing but the first best outcome can be only achieved with the friedman rule these results cannot be obtained with other monetary models e g overlapping generations models we also derive a rich array of non trivial effects of inflation on equilibrium deposits the probability of banking crises and banks portfolios

banking panics and policy responses we study how banking panics unfold in av ersion of the diamond and dybvig 1983 model with limited commitment as is well known the banking authority could eliminate the possibility of a run on the banking system by committing to suspend payments to depositors if a run were to start once a run is under way however the banking authority will choose to reschedule rather than suspend payments we construct equilibria in which depositors run on the banking system with positive probability and we show that an equilibrium bank run in this setting is necessarily partial with only some depositors participating we also show that a run naturally occurs in waves with each wave of withdrawals prompting a further policy response from the banking authority the number of waves that occur in equilibrium is stochastic and can be arbitrarily large

a bank runs model with a continuum of types abstract we consider a bank runs model a la diamond and dybvig 1983 3 with a continuum of agent types indexed by the degree of patience much of our understanding based on the two type model must be modified the endogenous determination of a cutoff type is central to the analysis in the case where the bank can credibly commit to a contract the optimal contract results in socially excessive early withdrawals in every equilibrium of the post deposit subgame thus even at the best equilibrium the socially efficient outcome is not achieved and agents behavior exhibits features of a bank run in the case where commitment is not possible there are strictly more early withdrawals and strictly lower welfare than the full commitment equilibrium

a model of a systemic bank run abstract this paper provides a model of the view that the 2008 financial crisis is reminiscent of a bank run focussing on six stylized key features in particular core financial institutions have invested their funds in asset backed securities rather than committed to long term projects in distress these can potentially be sold to a large pool of outside investors at steep discounts i consider two different motives for outside investors and their interaction with banks trading asset backed securities uncertainty aversion versus adverse selection i shall argue that the version with uncertainty averse investors is more consistent with the stylized facts than the adverse selection perspective in the former the crisis deepens the larger the market share of distressed core banks while a run becomes less likely instead as a result in the adverse selection version therefore the outright purchase of troubled assets by the government at prices above current market prices may both alleviate the financial crises as well as provide tax payers with returns above those for safe securities

bank runs as an equilibrium phenomenon a standard demand deposit contract in which individuals are entitled to their full deposit at any time provided the bank is solvent is analyzed in a context in which there are no exogenous events on which agents condition their behavior and a unique equilibrium involving a bank run with positive probability is shown to exist

market uncertainty correlated and sunspot equilibria in imperfectly competitive economies first version received june 1988 final version accepted november 1990 eds an imperfectly competitive economy is very prone to market uncertainty including uncertainty about the liquidity or thickness of markets we show in particular that there exist stochastic equilibrium outcomes in nonstochastic market games if and only if the endowments are not pareto optimal we also provide a link between extrinsic uncertainty arising in games e g correlated equilibria and extrinsic uncertainty in market economies e g sunspot equilibria a correlated equilibria to the market game is either a sunspot equilibrium or a non sunspot equilibrium to the related securities games but the converse is not true in general

bailout uncertainty in a microfounded general equilibrium model of the financial system abstract this paper develops a micro founded general equilibrium model of the financial system composed of ultimate borrowers ultimate lenders and financial intermediaries the model is used to investigate the impact of uncertainty about the likelihood of governmental bailouts on leverage interest rates the volume of defaults and the real economy the distinction between risk and uncertainty is implemented by applying the multiple priors framework to beliefs about the probability of bailout results of the analysis include i an unanticipated increase in bailout uncertainty raises interest rates the volume of defaults in both the real and financial sectors and may lead to a total drying up of credit markets ii lower exante bailout uncertainty is conducive to higher leverage which in turn raises moral hazard and makes the economy more vulnerable to expost increases in bailout uncertainty iii bailout uncertainty affects the likelihood of bubbles the amplitude of booms and busts as well as the banking and the credit spreads iv higher bailout uncertainty is associated with higher returns variability in diversified portfolios and higher systemic risks v pre crisis expansionary monetary policy reinforces those effects by inducing higher aggregate leverage levels vi the larger the change in bailout uncertainty and the change in aversion to this uncertainty the stronger the pre crisis buildup and the deeper the ensuing crisis a central policy implication of the analysis is that the vaguest is bailout policy prior to a crisis the lower is the magnitude of investments destroyed or missed due to errors in evaluating bailout and other intervention policies on the other hand the clearer is bailout policy upon the eruption of a crisis the smaller the contraction of credit and the destruction of investment activity

bank suspension of convertibility abstract a banking panic occurs when depositors at all banks seek a large reduction in their deposit holdings suspension of convertibility of demand deposits into currency was the banking system s response to a banking panic when depositors are incompletely informed about the state of bank investments a panic can occur when depositors expect capital losses conditional on having observed noisy indicators of the state of bank investments banks with superior information about the investments can signal to depositors by suspending convertibility that continuation of the long term investments is mutually beneficial

international coordination of fiscal policy in limiting economies we examine the limiting behavior of cooperative and noncooperative fiscal policies as countries market power goes to zero we show that these policies converge if countries raise revenues through lump sum taxation however if there are unremovable domestic distortions such as distorting taxes there can be gains to coordination even when a single country s policy cannot affect world prices these results differ from the received wisdom in the optimal tariff literature the key distinction is that contrary to the tariff literature the spending decisions of governments are explicitly modeled

interest rates and financial fragility abstract how do the interest rates banks earn on their assets affect the susceptibility of the banking system to a self fulfilling run by depositors i study this question in a version of the model of diamond and dybvig 1983 with limited commitment and a non trivial portfolio choice i show that the relationship between these interest rates and financial fragility is often non monotone for example a small increase in the return on illiquid investment or a small increase in the term premium may raise banks susceptibility to a run while a larger increase would make the banking system more stable the same is true for changes in short term rates holding the longer term rates fixed i provide a precise characterization of these comparative statics of financial fragility

deposit insurance and risk taking we review the theory of deposit insurance highlighting the underlying assumptions that were not satisfied during the recent financial crisis and that may have led to serious policy mistakes in theoretical models deposit insurance is mostly seen as an equilibrium selection device to avoid panic based runs in such a context it is not drawn on and is thus costless and fully credible however if bank runs are linked to a fall in asset values providing deposit insurance can be very costly and as the case of ireland has shown can even threaten sovereign solvency this perspective indicates a need for new research on the relation between bank failures deposit insurance schemes sovereign default and currency depreciation and for reforms of deposit insurance schemes copyright 2011 oxford university press

run equilibria in the green lin model of financial intermediation abstract we study the green lin model of financial intermediation e j green p lin implementing efficient allocations in a model of financial intermediation j econ theory 109 2003 1 23 under a more general specification of the distribution of types across agents we derive the efficient allocation in closed form we show that in some cases the intermediary cannot uniquely implement the efficient allocation using a direct revelation mechanism in these cases the mechanism also admits an equilibrium in which some but not all agents run on the intermediary and withdraw their funds regardless of their true liquidity needs in other words self fulfilling runs can arise in a generalized green lin model and these runs are necessarily partial with only some agents participating

inequality and financial fragility abstract i study how the distribution of wealth influences the government s response to systemic banking crises and shapes financial fragility distributional concerns tend to make full government guarantees of deposits credible for relatively poor individuals but not for wealthier individuals as a result wealthier individuals have a stronger incentive to panic and in equilibrium the institutions in which they invest are endogenously more likely to experience runs and receive partial bailouts even under utilitarian government moreover the shape of the wealth distribution affects the level of financial fragility recognizing this fact may alter the government s desire to redistribute wealth ex ante

regime and leader instability under two forms of military rule the finding that military regimes are more fragile than other authoritarian regimes represents one of the few stylized facts in comparative politics however the existing literature contains subst

economic growth liquidity and bank runs abstract we construct an endogenous growth model in which bank runs occur with positive probability in equilibrium in this setting a bank run has a permanent effect on the levels of the capital stock and of output in addition the possibility of a run changes the portfolio choices of depositors and of banks and thereby affects the long run growth rate these facts imply that both the occurrence of a run and the mere possibility of runs in a given period have a large impact on all future periods a bank run in our model is triggered by sunspots and we consider two different equilibrium selection rules in the first a run occurs with a fixed exogenous probability while in the second the probability of a run is influenced by banks portfolio choices we show that when the choices of an individual bank affect the probability of a run on that bank the economy both grows faster and experiences fewer runs

on freezing depositor funds at financially distressed banks an experimental analysis this article reports an experiment conducted to evaluate the effects of alterations in the terms of repayments to depositors following a liquidity suspension as well as the effect of alterations in the publicity of information about withdrawal behavior on the fragility of distressed banks results indicate that a tough renegotiation stance of protecting depositors who maintain their money in the bank can quite effectively promote stability information provided to depositors regarding past withdrawal behavior weakens the effectiveness of a tough renegotiation policy but reduces fragility somewhat for a more lenient rescheduling condition

experimental evidence of bank runs as pure coordination failures abstract we investigate how coordination requirement measured by the coordination parameter affects the occurrence of miscoordination based bank runs in controlled laboratory environments we identify an indeterminacy region of the coordination parameter such that games with the parameter within the region have varying coordination outcomes and exhibit persistent path dependence experimental economies with the parameter above below the region stay close or converge to the run non run equilibrium switches between the two equilibria occur even with fixed economic fundamentals the experimental results are well accounted for by a version of the evolutionary algorithm that uses experimentation rates estimated from the experimental data

current federal reserve policy under the lens of economic history a review essay this review essay reviews the volume edited by owen humpage current federal reserve policy under the lens of economic history essays to commemorate the federal reserve system s centennial and provides a broader perspective on central banking issues the papers in the humpage volume address various aspects of central banking history money and private banking with a focus on putting recent fed policies in perspective the topics covered include the role of the central bank as lender of last resort the effects of open market operations versus central bank lending central bank independence the political economy of monetary unions financial crises the effects of unconventional monetary policies commodity monies and the canadian financial system as a natural experiment

on the calculation of marginal effects in the bivariate probit model abstract we examine the effects of marginal changes in continuous variables on the joint conditional and marginal probabilities involved in the bivariate probit model and contrast them with the univariate probit case we provide an empirical application using canadian data

self enforcing democracy author s fearon james abstract if democracy is to have any of the good effects said to justify it it must be self enforcing those who control the government must want to hold regular competitive elections for the highest offices and all parties must be willing to comply with the results i consider a model in which citizens can always protest or rebel against the current ruler but can unseat the ruler only if enough people rebel when individuals privately observe a signal of the government s performance e g their own welfare they face a difficult problem of how to coordinate to pose a credible threat of rebellion necessary to keep the ruler from stealing further if the signals are noisy inefficient rebellions must occur in equilibrium to keep the ruler honest allowing for the possibility of elections makes for equilibria that eliminate both problems the convention of holding elections at particular times provides a public signal for coordinating rebellion in the event that elections are suspended of blatantly rigged the electoral results themselves aggregate private information about the ruler s performance providing the ruler an incentive to stick to the terms int he case of noisy signals of government performance the electoral results act as a cheap talk signal that allows the public to commit to rebel if a losing ruler does not step down avoiding the need for costly rebellions these arguments pose an explanation for self enforcing democracy whereas the several models in the literature do not because they do not explain why anyone would want to use elections to allocate power

equilibrium bank runs we analyze a banking system in which the class of feasible deposit contracts or mechanisms is broad the mechanisms must satisfy a sequential service constraint but partial or full suspension of convertibility is allowed consumers must be willing to deposit ex ante we show by examples that under the so called optimal contract the postdeposit game can have a run equilibrium given a propensity to run triggered by sunspots the optimal contract for the full predeposit game can be consistent with runs that occur with positive probability thus the diamond dybvig framework can explain bank runs as emerging in equilibrium under the optimal deposit contract

regime type the fate of leaders and war we propose and test a formal model of war and domestic politics building on recent evidence on the relationship between regime type the effect of war on the probability of losing office and the consequences of losing office the less the outcome of international interaction affects a leader s tenure and the less punitive are the consequences of losing office the more a leader is willing to make concessions to strike a peaceful bargain we demonstrate that our theory successfully predicts war involvement among nondemocratic regime types moreover our theory offers an intuitive explanation for the democratic peace compared to nondemocratic leaders the tenure of democratic leaders depends relatively little on the war outcome and democratic leaders fare relatively well after losing office thus democratic leaders should be more willing and able to avoid war especially with other democrats

destructive effects of constructive ambiguity in risky times unclear bailout policy underinvestment and calls for greater responsibility by bankers are some of the observations from the recent financial crisis the paper explains underinvestment as an inefficient equilibrium under ambiguous bailout policy agents suffer from a lack of information about the insolvency resolution methods the beliefs of bankers regarding whether an insolvent bank is liquidated may differ from those of depositors even if bankers and depositors possess absolutely symmetric information about the economy this disrupts the flow of funds through the banking channel if the investment climate is characterized by high aggregate risk the paper suggests policy implications aimed at a reduction of the anxiety of agents and at aligning their beliefs to restore efficiency

bailouts and financial fragility how does the belief that policymakers will bail out investors in the event of a crisis affect the allocation of resources and the stability of the financial system i study this question in a model of financial intermediation with limited commitment when a crisis occurs the efficient policy response is to use public resources to augment the private consumption of those investors facing losses the anticipation of such a bailout distorts ex ante incentives leading intermediaries to choose arrangements with excessive illiquidity and thereby increasing financial fragility prohibiting bailouts is not necessarily desirable however it induces intermediaries to become too liquid from a social point of view and may in addition leave the economy more susceptible to a crisis a policy of taxing short term liabilities in contrast can correct the incentive problem while improving financial stability

run proof banking without suspension or deposit insurance abstract in a model of banking with asymmetric information among depositors and multiple sources of aggregate risk i show that a demand deposit arrangement with state contingent deposit payments and a priority of claims provision on final date resources is almost best under this arrangement intermediaries infer the realization of aggregate risk and of a privately observed signal on the outcome of the risky technology from depositors withdrawal choices and panics as well as information based runs are averted neither suspension provisions nor deposit insurance are necessary for an efficient run proof banking system furthermore intermediation provides information production services that a credit market does not necessarily provide

marginal effects of a bivariate binary choice model this paper discusses the copula based approach of a bivariate binary choice model we derive the marginal effects of explanatory variables on an outcome of interest both direct and indirect in the model we also show that the signs of the marginal effects are determined by the signs of the coefficient parameters a real data application is provided