1. Monetary Policy and Inventory Investment
Louis J. Maccini Bartholomew Moore
Johns Hopkins University Fordham University
Huntley Schaller
Carleton University

2. Monetary policy changes short-term interest rates and these interest-rate changes affect aggregate expenditure.
The interest rate should affect inventories and inventory investment. Forty years of research did not find this empirical relationship.
The fall in inventory investment accounts for 80% of drop in Y in post-war US recessions [Blinder-Maccini, 1991]. Large % in most G7 countries [Ramey-West, 1999]
Understanding the relationship between interest rates and inventories is essential to our understanding of the monetary policy transmission mechanism

3. Puzzles
The mechanism puzzle. Monetary policy changes the interest rate and this should affect inventories (opportunity cost). In fact, VAR studies find that monetary policy shocks affect inventories. But 40 years of empirical literature on inventories has generally failed to find any significant effect of the interest rate on inventories?
The second puzzle is the sign puzzle. Contractionary monetary policy raises the interest rate. An increase in the interest rate should decrease inventories through the increase in opportunity cost. VAR studies find that the short-term effect of contractionary monetary policy is to increase inventories.
The third puzzle is the timing puzzle. Monetary policy induces transitory changes in the interest rate. The effect of monetary policy on the interest rate largely disappears within one year. But inventories begin to fall only after the transitory shock to the interest rate has largely dissipated.

5. Markov switching process for rt
Transition probabilities

6. Maccini, Moore, and Schaller (2004)
The real interest rate is a three-state Markov switching process. There are long periods of transitory variation around a persistent mean and occasional shifts in the mean.
Conventional tests, which focus on high-frequency movements, will have a hard time detecting a relationship between inventories and the real rate. This relationship can only be detected using low-frequency techniques.
Prediction that the stock of inventories is determined by and is confirmed by the data.

7. This paper
Having established a link between the real interest rate and inventories operating through and , we want to use this link to evaluate the effect of monetary policy on inventories.
Pure (or “narrow”) interest-rate effect: Higher interest rate makes it more costly to hold inventories.
Broad interest-rate effects: Higher interest rates affect sales and input prices both of which affect inventories.

8. The Model (briefly):
Firm minimizes
s.t.

9. Linearized Euler Equation
Decision Rule

10. GMM estimation of the Euler equation and ML estimation of decision rule (high frequency) fail to uncover a statistically significant effect of interest rates on inventories and so, fail to identify the relevant parameters.
Our strategy: 
Use Euler to derive cointegrating relationship (low frequency).  
Estimation of cointegrating regression allows us to infer the values of the structural parameters.
Using the structural parameters we can determine the values of the coefficients in the decision rule.
We can then simulate the behavior of inventories as implied by the decision rule.
We can simulate how inventories respond to a monetary policy shock.

11. Estimation and Calibration of structural parameters
Estimated Cointegrating Vector
Inventories, Sales, Observable Cost Shocks, and the Probabilities
Constant
Time X W
Levels
(2.82)
[.005]
41.767
(1.03)
[0.306]
0.237
(1.06)
[0.289]
(-4.34)
[0.000]
(1.73)
[0.085]
(-6.36)
DOLS estimates with (t-statistic) and [p-values].

12. Table 2: Parameters of the Cost Function, Baseline1
765.09
302,001
Table 4: Coefficients in the Decision Rule Values
0.965
0.008
-10.55
985.01
using mean values of N, X, and W and ergodic probabilities.
Identify monetary policy shocks using Bernanke-Mihov’s (1998) semi-structural VAR. Estimate response of and to a stimulative monetary policy shock

13. The response of and to a monetary policy shock.

14. Simulating the pure interest-rate effect of monetary policy on Nt.
Substitute the response of and into the decision rule to obtain the path of inventories.
Model X and W as exogeonous random walks. Standard deviations of from data.
Output from the inventory accumulation identity:
Examine and , averaging over a large # of repetitions

22. New Estimates of the Cointegrating Regression
Estimated Cointegrating Vector
Nondurable Manufacturing, 1959:1 to 1999:2
Inventories, Sales, Observable Cost Shocks, and the Probabilities
Constant
Time X W
Levels
(2.82)
[.005]
41.767
(1.03)
[0.306]
0.237
(1.06)
[0.289]
(-4.34)
[0.000]
(1.73)
[0.085]
(-6.36)
DOLS estimates with (t-statistic) and [p-values].
Estimated Cointegrating Vector
Total Manufacturing, 1959:1 to 2004:8
Log Inventories, Log Sales, Log Observable Cost Shocks, and the Probabilities
Constant
Time
Log X
Log W
Logs
1.596
(18.57)
0.000
(-37.81)
0.446
(5.00)
-0.990
(-6.25)
0.103
(11.25)
-0.027
(-3.673)
DOLS estimates with (t-statistic) .

23. Linearize Euler equation around what?