4.2 The baseline model
4.2.9 Satellite models, model solution and fundamental shocks
For comparison purposes, I also consider three smaller satellite models. The first is a model without financial frictions between bankers and depositors, called the External Finance Premium (EFP) model. In the EFP model, entrepreneurs run capital utilization projects and pay dividends to thier shareholders while competitive bankers earn zero profit from financial intermediation. Technically, this satellite model is derived from the baseline model by: (1) dropping the moral hazard problem between bankers and shareholders, $t = 0; (2) deleting banking shareholder consumption from final private consumption, Cb,t= 0; (2) adjusting the lending rate on period t risky entrepreneurial loans after the realization of periodt+ 1 shocks in order to ensure that the bank receives a risk-free return,Re,t+1 =Rt; and (4) allowing riskless loans to be made at the risk-free rate,Rf,t=Rx,t=Rt andR∗m,t =R∗t. Thus I obtain an always binding constraint,
(4.53) Le,t=φb,tNb,t.
while the spread remains unchanged
(4.54) spre,t=
Rb,t
Rt
.
In this model, the banking sector raises non-friction deposits. Such a shadow banking sector, however, still has impact on the dynamics of the returns on entrepreneurial loans and the real economy due to the presence of credit supply data in my estimation exercise. In addition, the presence of a shadow banking sector will be helpful for comparing responses to the same shocks between the EFP model and other friction models with
$t>0.
By contrast, bankers manage the financial intermediary and pay dividends to their shareholders while competitive entrepreneurs earn zero profit from capital utilization in
the Incentive Compatibility Constraint (ICC) model. In this model, there are no frictions in the bank−entrepreneur relationship. Technically, this satellite model is extracted from the baseline model by: (1) dropping the costly state verification problem between bankers and entrepreneurs,µ= 0 andωt= 1; (2) deleting project shareholder consumption from final private consumption, Ce,t = 0; (3) assuming that entrepreneurial loans are state- contingent so that the interest rate on entrepreneurial loans equals the expected return on capital, Rb,t+1 = Re,t+1 = Rk,t+1; and (4) forcing the share of aggregate capital
purchase financed by entrepreneurial loans,ωK¯, to be the same as in the EFP model. I
define the weighted average lending-deposit spread as:
(4.55) sprb,t=
Rf,tLf,t+Rx,tLx,t+Rk,tLe,t
RtLt
,
and the zero profit condition of the entrepreneurial sector:
(4.56) Rk,t+1= Zk,t+1ut+1−Pi,t+1a(ut+1) + (1−δ)QK,t¯ +1 ωK¯QK,t¯ −(1−ωK¯)QK,t¯ +1 ωK¯QK,t¯ .
Entrepreneurs manage capital accumulation but accumulate no net worth and thus break even state by state in this model. However, the presence of such a passive entrepreneurial sector has impact on the dynamics of non-risky returns and real activities through the volatilities of the stock market index. Further, it helps in understanding how differently the economy responds to shocks once µ > 0 and ωt 6= 1 as in the baseline and EFP models.
In the absence of the financial sector, the structure of my baseline model collapses back to a pure trade open economy model − I call it Pure for short. To obtain this Pure model from the baseline model, I drop all equations that characterize the financial sector and add an intertemporal Euler equation corresponding to household capital ac- cumulation. It is of course also necessary to delete shareholder consumptions from final private consumption and monitoring costs from the resource constraint.
The two economies evolve along two stochastic growth paths in every model. There- fore, the overall solution across models involves the following steps. First, I transform the models into a stationary form. Specifically, real variables are detrended by the level of technology,{zt, zt∗}, and nominal variables are converted to real variables by deflating with the price index, {Pt, Pt∗}. Second, the models are written into a set of station- ary equilibrium conditions. Third, non-linear equilibrium conditions are log-linearized and solved using first-order approximation methods. Fourth, the log-linearized version of models is augmented by a set of measurement equations which link the observable variables in the dataset with the endogenous variables of the theoretical model.
The stochastic behavior of the system of linear rational expectations equations in the Baseline model is driven by 20 fundamental shocks: gz,t, t, λcm,t, λim,t, λx,t, λw,t,
εpc,t, bt, µt, ψt, εcom,t, p ∗
com,t, εt,π¯t, gt, θe,t, θb,t, $t, σe,t,z˜∗t for the Home economy and 12 fundamental shocks: g∗z,t, ∗t, λ∗p,t, bt∗, µ∗t, ε∗t,π¯t∗, gt∗, θ∗e,t, θb,t∗ , $∗t, σ∗e,t for the Foreign econ- omy, where ˜zt∗ = zt∗
trend levels of technology between the two economies. With two exceptions, I model the log-deviation of each shock from its steady state as a univariate first-order autore- gressive process. The autoregressive parameter of the inflation target shock,{ρπ¯, ρπ¯∗}is set at (0.975,0.975) in order to accommodate the downward inflation trend in the late part of the dataset. The two exceptions are the monetary policy shock,{εt, ε∗t}, and the consumption price inflation shock, επc,t, which are assumed to be white noise.