Step 283: a central bank with an effective lower bound

Why. Step 282 ended with two price closures and no monetary policy. At the investment response estimated from OECD data, preservation is 49% when the price level is held and 11% when prices fall with the demand gap. "Held" assumed that something holds the price level. Here a central bank tries to do so, with an interest-rate rule that cannot go below zero.

The model is scripts/closure_model_v283.py, a copy of step 279; with the new options off it reproduces step 279 exactly (tested). The grid is scripts/monetary_v283.py, with output in data/processed/monetary_v283.json. All 432 cases use the revised specification with the symmetric demand closure: prices respond to the demand gap, and investment responds to Tobin's q. Illustrative; not a forecast.

The rule

• Policy rate. i_t = max(0, 0.7·i_(t−1) + 0.3·[3% + 1.5·π_(t−1) + 0.5·gap_(t−1)]). Here π is the

model's inflation, measured around its zero baseline, and gap is planned demand less capacity, as a share of output.

• What it moves:

- the government bond rate (the risk premium is added on top), with the public debt repricing a seventh a year, an average maturity of about seven years; - the firms' overdraft rate; - planned investment: planned I/K changes by −s·(i − 3%).

• The investment sensitivity s. Planned I/K is about 0.1 in the model. Each value of s corresponds to

a response of investment to a 1-point rate cut:

| s | Investment response to a 1-point cut | Source | |---:|---|---| | 0.15 | about +1.5% | US local projections with Romer–Romer shocks; the RBA's MARTIN model gives about 1.3% | | 0.6 (central) | about +6% | the direct loan-rate channel in German firm surveys (ifo), over two years | | 1.5 | about +15% | the total first-year effect of euro-area high-frequency shocks on corporate investment |

The model generates the demand feedback itself, so the direct channel is the central value.

Results

Each cell gives the number of the 432 cases in which both displaced cohorts are preserved, with fiscal crises in brackets. The rule is the central one; Phillips 0.5 as in step 279.

With a flatter Phillips curve (0.25), the central rule gives 290, 286, 248 and 207 cases. Without a central bank the same rows give 341, 326, 206 and 114.

Sensitivity of the rule, at s 0.6 and decay 1.27:

Without smoothing the rule is unstable where demand runs ahead: 53 runs stop at decay 0.

What it shows.

• A central bank narrows the uncertainty but does not remove it. Across the four investment worlds,

preservation without a central bank ranges from 11% to 88%. With the central rule it ranges from 30% to 69%.

• It costs something where demand runs ahead. When investment holds, inflation of about 3% a year used

to erode the public debt. The rule raises the rate against it, and preservation falls from 88% to 69%. Higher rates also raise interest payments to bond holders, which in this model is extra demand. With a weak investment channel this partly offsets the tightening.

• At the estimated slump the lower bound binds. The rate reaches zero in 85% of cases, and the price

level still falls, by a median of about 40% over 20 years. Preservation rises from 11% to 30%, not to the 49% that a held price level would give.

• What decides the slump case is how strongly investment responds to the rate. At the strong end

(s 1.5), preservation reaches 58%; at the weak end (0.15), 15%.

Correction to step 282. The statement "monetary policy that prevents falling prices keeps preservation at 49% instead of 11%" assumed that policy can hold the price level. With a lower bound at zero it cannot in most slump cases. With the central rule the figure is 30% (15%–58% by the investment sensitivity).

Limits

• A simple rule. It is annual, has one target and no forward guidance, quantitative easing or exchange

rate.

• Investment sensitivity is borrowed from studies of ordinary monetary shocks, not estimated for

Israel.

• The equity discount rate does not move with the policy rate. With present-value equity, moving it

one for one would triple Tobin's q at the bound.

• Interest income is spent like other income. Owners consume 90% of income, interest included, so

higher rates add demand. With a lower propensity to consume out of interest, tightening would bite harder.

• No fiscal–monetary coordination. The central bank does not buy government debt.