Journal Article•DOI•

Learning by Devaluating: A Supply-Side Effect of Competitive Devaluation

Juha Tervala¹•Institutions (1)

01 Dec 2011-Social Science Research Network-

TL;DR: In this article, the learning by doing (LBD) effect has substantial, both quantitative and qualitative, consequences for the international transmission of monetary policy, and it is shown that LBD increases the harmful effect of competitive devaluation on foreign output by 85-125%.

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Abstract: This study shows that the learning by doing (LBD) effect has substantial, both quantitative and qualitative, consequences for the international transmission of monetary policy. LDB implies that a country can increase its productivity-increasing skill level, at the expense of the neighbor, by competitive devaluation engineered through low interest rates. If measured by the cumulative change in output after 12 quarters, LBD increases the harmful effect of competitive devaluation on foreign output by 85–125%, when compared to the case without it. If LBD is sufficiently strong and the cross-country substitutability is high (low), it reverses the effect of monetary policy on foreign (domestic) welfare into negative (positive). Moreover, a combination of a high cross-country substitutability and a sufficiently strong LDB effect implies that competitive devaluation increases both domestic output and welfare, at the expense of foreign output and welfare.

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Summary (3 min read)

Jump to: [1 Introduction] – [2 Model] – [2.1.1 Preferences] – [2.1.2 Budget Constraints] – [2.2 Monetary Policy] – [2.3.1 Skill Level, Demand and Profits] – [2.3.2 Price Setting] – [2.4 Symmetric Equilibrium] – [3 Choice of Parameter Values] – [4.1 Method of Welfare Analysis] – [4.4 Sensitivity Analysis] and [5 Conclusions]

1 Introduction

During the recent global financial crisis, the U.S. Federal Reserve implemented expansionary monetary policy by lowering the short-term nominal interest rate to the zero-lower bound.
Porter (1990) argues that depreciations can be harmful, because an overvalued exchange rate can be better for productivity growth, by forcing higher productivity growth in the tradedgoods sector.
Moreover, they find that faster productivity growth is partly driven by the LBD effect.
They emphasise that the empirical labour economics literature has shown the following results:.
The LBD mechanism also has a qualitative implication for the welfare effects of monetary policy where the cross-country substitutability is low.

2 Model

I lay out a two-country open economy model.
Its innovation is the introduction of LBD into the production function, following the idea of Chang et al. (2002).
The world consists of two countries: home and foreign.
In the presentation of the model, I discuss only domestic equations, if the equations are symmetric across countries.

2.1.1 Preferences

The term is the elasticity of substitution between domestic and foreign goods, which is referred to as the cross-country substitutability.
These equations show that households allocate their total consumption between domestic and foreign goods, taking into account their relative prices and the cross-country substitutability.
All prices are expressed in local currency terms, although firms set their prices in the producer’s currency.
(5) The corresponding foreign indexes are defined in a similar way.
The purchasing power parity holds: *ttt PSP .

2.1.2 Budget Constraints

The foreign economy is identical to the domestic economy, with one notable exception: Foreign households can hold both domestic and foreign bonds; whereas domestic households can only hold domestic bond.
The use of the Taylor rule implies that the model must be stationary.
The log-linear version of UIP with a risk premium ( ) can be written as tttttt DSSEii ˆˆˆˆ) Equation (8) shows that the household has to pay a small cost if its bond holdings are not equal to their initial steady-state level (i.e., zero).
(12) Equations (9) and (10) are the Euler equations for optimal domestic and foreign consumption, respectively.

2.2 Monetary Policy

The central banks in both countries follow the log-linear Taylor rule with interest rate smoothing, as follows: titttt iyPi ,11321 ˆ)ˆ)(1(ˆ , (13) 6.
The empirical evidence supports the view that monetary policy shocks cause deviations from UIP (e.g., Faust and Roger, 2003; and Bluedorn and Bowdler, 2011).
The monetary policy rule shows that the inflation target is zero.
Therefore, the deviation of output from the initial steady state measures the output gap.
The central bank responds directly to the deviations of output from the initial level.

2.3.1 Skill Level, Demand and Profits

Chang et al. (2002) assume that the skill level of the household depends on hours worked in the past, and that the skill level raises the effective unit of labour supplied by the household.
The stock of the skill level evolves according to the following log-linear equation: )(ˆˆˆ 1 zxx ttt , (14) where 10 and 0 are parameters.
The firm minimises its costs, )(zw tt , subject to the production function (15).

2.3.2 Price Setting

(19) Under flexible prices, the price is simply a mark-up over the marginal cost.
Equations (16) and (19) demonstrate that an increase in the skill level is like a productivity shock that reduces the price of the domestic good.
Following Calvo (1983), I introduce nominal rigidities by assuming that each firm may reset its price with a probability of 1 in each period, independently of other firms and time passed since the last price adjustment.

2.4 Symmetric Equilibrium

Every firm that changes its price in any given period chooses the same price and output.
The price setting framework means that each period, a fraction of 1 of firms sets a new price, while the remaining firms keep their price unchanged.
(24) Equation (23) is the Calvo-weighted price index of domestic goods.
The model is log-linearized around a symmetric steady state, where initial net foreign assets are zero ( 00D ) and the initial skill level is normalized to one ( 00x ).
The consolidated budget constraint, in the case of a symmetric equilibrium, implies that )(00 zyC .

3 Choice of Parameter Values

The rationale for the choice of parameter values is as follows: Periods are defined as quarters, therefore =0.99.
Gopinath and Rigobon (2008) find that the trade weighted median price duration is 10.6 months for U.S. imports and 12.8 months for U.S. exports.
Chang et al. (2002) use a Bayesian approach and micro level data to estimate these parameters.
Therefore, a unit increase in the number of hours worked today increases the skill level in the next period by 0.11 units, and the depreciation rate of the skill level is 20%.9.

4.1 Method of Welfare Analysis

The method used for welfare analysis is as follows: I first analyse the change in period-byperiod utility.
Then, I calculate the discounted present value (PDV) of the change in utility.
The PDV value of the change in utility is calculated as 8.
On the other hand, Sutherland (2006) argues that typical estimates for the average elasticity across all traded goods are in the range of 5 to 6.

4.4 Sensitivity Analysis

The next step is to assess how responsive the international effects of monetary policy are to changes in parameter values, which govern the strength )( and duration )( of LBD.
These imply a stronger effect of employment on the skill level, and a faster depreciation rate of the skill level.
Table 5 shows the cumulative change in output.
On one hand, the improvement in the foreign terms of trade implies that foreign consumption increases despite a fall in output.
Table 7 shows the effects of the new parameterisation on output when cross-country substitutability is 1.5.

5 Conclusions

This paper analyses the consequences of LBD for the international transmission of monetary policy.
This mechanism implies that demand-driven business cycles affect the supply side of the economy.
LBD implies that this, in turn, leads to an increase in the U.S. skill level, which not only lowers the relative price of U.S. goods even further, but also increases the supply of U.S. goods.
If the elasticity of substitution between U.S. and foreign goods is low, LBD reverses to positive the effect of U.S. interest rate reductions on U.S. welfare.
The United States can increase not only its output, but also its welfare at the expense of the rest of the world.

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Figures (12)

Table 6: Varying the Key Parameters: The Discounted Present Value of the Change in Utility When 6

Table 7: The Percentage Change in the Cumulative Change in Output Compared to the Case Without LDB When 5.1

Table 8: Varying the Key Parameters: Discounted Present Value of the Change in Utility When 5.1

Table 2: Discounted Present Value of the Changes in Utility When 6

Figure 1: Dynamic Effects of a Domestic Interest Rate Shock When 6

Figure 4: Effects of Varying Key Parameter Values When 6

Table 3: Cumulative Change in Output at Time Horizon k When 5.1

Figure 3: Dynamic Effects of a Domestic Interest Rate Shock When 5.1

Table 4: Discounted Present Value of the Changes in Utility When 5.1

Table 5: The Percentage Change in the Cumulative Change in Output Compared to the Case Without LDB When 6

Figure 2: Dynamic Effects of a Domestic Interest Rate Shock When 6

Table 1: Cumulative Change in Output at Time Horizon k When 6

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This study shows that the learning by doing ( LBD ) effect has substantial, both quantitative and qualitative, consequences for the international transmission of monetary policy.