Financial Frictions and the Credit Channel

File fa.mod

// New Keynesian model with a reduced-form financial accelerator:
// households and firms borrow at i + s, the spread s falls when borrower net worth nw rises
var y_gap pi i s nw v;
varexo eps_v;
parameters beta sigma kappa phi_pi phi_y chi rho_n rho_v;
beta = 0.99; sigma = 1; kappa = 0.1717; phi_pi = 1.5; phi_y = 0.125; chi = 0.05; rho_n = 0.9; rho_v = 0.5;
model(linear);
  pi = beta * pi(+1) + kappa * y_gap;
  y_gap = y_gap(+1) - (1 / sigma) * (i + s - pi(+1));     // spending depends on the borrowing rate
  s = -chi * nw;                                         // external finance premium
  nw = rho_n * nw(-1) + y_gap;                           // net worth accumulates profits
  i = phi_pi * pi + phi_y * y_gap + v;
  v = rho_v * v(-1) + eps_v;
end;
shocks; var eps_v; stderr 0.25; end;
stoch_simul(order=1, irf=20, noprint, nograph);

File ex9_1.m

dynare fa noclearall
fprintf('chi    output gap: impact   cum(0-19)   trough qtr   infl (ann.) impact   spread (ann.) peak\n');
for c = [0 0.05 0.1]
  set_param_value('chi', c);
  [info, oo_] = stoch_simul(M_, options_, oo_, {});
  ir = oo_.irfs; [mn, q] = min(ir.y_gap_eps_v);
  sp = 0; if isfield(ir, 's_eps_v'), sp = 4 * max(ir.s_eps_v); end
  fprintf('%4.2f        %7.3f      %7.3f        %2d            %7.3f             %6.3f\n', c, ...
          ir.y_gap_eps_v(1), sum(ir.y_gap_eps_v), q - 1, 4 * ir.pi_eps_v(1), sp);
end

Output:

chi    output gap: impact   cum(0-19)   trough qtr   infl (ann.) impact   spread (ann.) peak
0.00         -0.259       -0.518         0             -0.352              0.000
0.05         -0.263       -0.703         0             -0.504              0.084
0.10         -0.259       -0.852         0             -0.673              0.174

With \(\chi=0\) the model is the basic New Keynesian model and the output gap recovers as fast as the policy shock decays. With a financial accelerator, the tightening lowers output and profits, borrower net worth falls, and the external finance premium rises. The higher borrowing cost depresses spending further, so the cumulative output loss is 35–65% larger and the recovery slower, because net worth is rebuilt only gradually. Inflation falls more too. The impact response barely changes, because net worth is a stock that erodes over time. This captures the core BGG mechanism: credit conditions amplify and propagate shocks through balance sheets. It misses the explicit contract and default problem, the role of asset prices and leverage, and the possibility that shocks start in the financial sector itself (Gertler–Karadi, 2011) — as in 2008.

File ex9_2.m

D = readtable('us_monthly.csv'); S = readtable('mp_shocks_monthly.csv');
key = @(y, m) 12 * y + m;
[~, ia, ib] = intersect(key(D.year, D.month), key(S.year, S.month));
yr = D.year(ia); shock = S.jk_mp(ib);
series = {D.gs1(ia), D.baa(ia) - D.gs10(ia)}; names = {'1-year yield', 'Baa spread  '};
H = 24; T = numel(yr); B = zeros(2, H+1); SE = B;
for v = 1:2
  y = series{v}; dy = [NaN; diff(y)];
  for h = 0:H
    lhs = NaN(T, 1); lhs(1:T-h) = y(1+h:T) - [NaN; y(1:T-h-1)];
    X = [ones(T, 1) shock [NaN; dy(1:end-1)] [NaN(2,1); dy(1:end-2)] [NaN(3,1); dy(1:end-3)]];
    k = yr >= 1990 & yr <= 2019 & all(~isnan([lhs X]), 2);
    [b, se] = ols_nw(lhs(k), X(k, :), h + 1); B(v, h+1) = b(2); SE(v, h+1) = se(2);
  end
end
scale = 0.25 / B(1, 1);                       % shock size that raises the 1-year yield by 25 bp on impact
fprintf('scale: a shock of %.3f units raises the 1-year yield by 25 bp\n', scale);
fprintf('h (months)   %s\n', sprintf('%7d', [0 3 6 12 18 24]));
for v = 1:2
  fprintf('%s %s\n', names{v}, sprintf('%7.3f', scale * B(v, [0 3 6 12 18 24] + 1)));
  fprintf('   (s.e.)    %s\n', sprintf('%7.3f', abs(scale) * SE(v, [0 3 6 12 18 24] + 1)));
end

Output:

scale: a shock of 0.373 units raises the 1-year yield by 25 bp
h (months)         0      3      6     12     18     24
1-year yield   0.250  0.354  0.662  0.948  1.226  1.248
   (s.e.)      0.083  0.223  0.232  0.470  0.577  0.602
Baa spread    -0.010  0.192  0.114  0.124 -0.105  0.253
   (s.e.)      0.053  0.151  0.208  0.210  0.233  0.230

The 1-year yield rises by 25 bp by construction and keeps rising for about a year, although the later responses are imprecise. The raw Baa–Treasury spread shows no clear response: the point estimates are mostly positive but within one or two standard errors of zero. This is a useful negative result. Gertler and Karadi (2015) find a significant rise in the excess bond premium, a cleaner measure of credit risk premia built from bond-level data that removes expected default; the Baa index spread also moves with liquidity, duration and default expectations, which adds noise. The Jarociński–Karadi shocks separate pure policy surprises from central-bank information effects using the stock-market response, which removes one bias but not the noise. Detecting the financial-accelerator channel needs good measures of balance-sheet strength and risk premia, not just more precise shocks.