Driving economic fluctuations in Peru: the role of the terms of trade

Abstract

This paper uses a common trend model, following King et al. (Am Econ Rev 81:819–840, 1991), Mellander et al. (J Appl Econ 7(4):369–394, 1992), and Warne (A common trends model: identification, estimation and inference. Seminar Paper 555, Institute for International Economic Studies, Stockholm University, 1993), to evaluate, for 1994–2015, the role of the terms of trade vis-à-vis domestic productivity in explaining macroeconomic fluctuations in Peru. Our results show that Peru’s macroeconomic aggregates share two common trends: an external one, associated with the evolution of the terms of trade; and a domestic one, linked to the evolution of domestic productivity. The external common trend has a larger impact on private investment and public expenditure than on consumption and output, a result consistent with the role of investment in absorbing income volatility. The permanent terms of trade (foreign) shocks account for most of the volatility in output, consumption, private investment, and public expenditure. This result appears more pronounced as the time horizon approaches the long term.

Appendices

Appendix

Deriving identification restrictions in a model for a small open economy

In this Appendix we derive a set of equilibrium conditions for identifying the cointegration vectors used in the paper. These restrictions are obtained from a small open economy model where domestic firms export commodities and import investment and consumption goods. Public expenditure, financed with taxes and public debt, is used to provide firms with public goods. Households choose consumption paths optimally.

The commodity-producing sector

Output is produced using a constant-returns-to-scale production function that combines imported capital goods, $y_{ipri_{t}}$ and public goods, $y_{gpub_{t}}$, as follows:

$$\begin{aligned} y_{gdp_{t}}=A_{t}y_{ipri_{t}}^{\alpha }y_{gpub_{t}}^{1-\alpha }, \end{aligned}$$

(A.1)

where $0<\alpha <1$, represents the share of capital goods in domestic output, $A_{t}$ represents the domestic productivity, $y_{gdp_{t}}$ is domestic output, $y_{ipri_{t}}$ is private investment (which we assume as equivalent to capital imported goods), and $y_{gpub_{t}}$ are public goods provided by the government. The profit function of the typical firm is given by:

$$\begin{aligned} \pi _{t}=y_{td_{t}}y_{gdp_{t}}-y_{ipri_{t}}, \end{aligned}$$

(A.2)

where $y_{td_{t}}$ represents the terms of trade; i.e., the relative price of exports to imports. The efficiency condition that determines the optimal level of investment is given by the following condition, which equates the value of the marginal productivity of capital with its relative price (determined by the inverse of the terms of trade):

$$\begin{aligned} \alpha \frac{y_{gdp_{t}}}{y_{ipri_{t}}}=\left( y_{td_{t}}\right) ^{-1}. \end{aligned}$$

(A.3)

The amount of taxes that firms pay to the government is given by: $t_{t}=\tau \pi _{t}$, where $\tau$ represents the average tax rate. The remaining profits are distributed to domestic households.

Household decisions

Households face the following budget constraint:

$$\begin{aligned} y_{c_{t}}+s_{t}=\left( 1-\tau \right) \pi _{t}+s_{t-1}(1+r_{t-1}), \end{aligned}$$

(A.4)

where $y_{c_{t}}$ denotes consumption, $s_{t}$ represents household savings, and $r_{t}$ is the real interest rate that households receive for their savings. Assuming a typical isoelastic utility function, the Euler equation that determines the optimal path for savings is given by:

$$\begin{aligned} 1=E_{t}\left[ \left( \frac{y_{c_{t+1}}}{y_{c_{t}}}\right) ^{-\gamma }\left( 1+r_{t}\right) \right] , \end{aligned}$$

(A.5)

where $\gamma$ represents the risk aversion coefficient of the representative household.

The government budget constraint

The government faces a budget constraint given by:

$$\begin{aligned} y_{gpub_{t}}-\tau \pi _{t}=d_{t}-d_{t-1}-d_{t-1}r_{t-1}, \end{aligned}$$

(A.6)

where $d_{t}$ represents government debt.

Balance of payment equation

To derive the balance of payments condition for a small open economy, we apply Walras’ Law and aggregate all the budget constraints in the economy, that is, Eqs. (A.4) and (A.6), respectively:

$$\begin{aligned}&y_{c_{t}}+s_{t} =\left( 1-\tau \right) \pi _{t}+s_{t-1}(1+r_{t-1}), \\&y_{gpub_{t}}-\tau \pi _{t} =d_{t}-d_{t-1}-d_{t-1}r_{t-1}. \end{aligned}$$

Then we obtain:

$$\begin{aligned} y_{c_{t}}+y_{gpub_{t}}+s_{t}=\pi _{t}+\Delta \left( d_{t}-s_{t}\right) -\left( d_{t-1}-s_{t-1}\right) r_{t-1}. \end{aligned}$$

(A.7)

Furthermore, by replacing the definitions of profits (A.2), we obtain:

$$\begin{aligned} y_{c_{t}}+y_{gpub_{t}}+y_{ipri_{t}}=y_{td_{t}}y_{gdp_{t}}+\Delta \left( d_{t}-s_{t}\right) -\left( d_{t-1}-s_{t-1}\right) r_{t-1}. \end{aligned}$$

(A.8)

The final set of equations

We use the following set of key equations to derive the identification restrictions for the common trend model estimated in this paper:

$$\begin{aligned} \alpha y_{td_{t}}y_{gdp_{t}}= & {} y_{ipri_{t}}, \end{aligned}$$

(A.9)

$$\begin{aligned} \frac{y_{gpub_{t}}}{y_{td_{t}}y_{gdp_{t}}}-\tau= & {} \frac{ d_{t}-d_{t-1}-d_{t}r_{t-1}}{y_{td_{t}}y_{gdp_{t}}}, \end{aligned}$$

(A.10)

$$\begin{aligned} \frac{\left( y_{c_{t}}+y_{gpub_{t}}+y_{ipri_{t}}\right) }{ y_{td_{t}}y_{gdp_{t}}}-1= & {} \frac{\Delta \left( d_{t}-s_{t}\right) -\left( d_{t-1}-s_{t-1}\right) r_{t-1}}{y_{td_{t}}y_{gdp_{t}}}. \end{aligned}$$

(A.11)

The first equation is the optimal condition for private investment, which establishes that the value of the marginal product of capital is equal to the inverse of the terms of trade. The second equation is the government deficit as percentage of GDP, and the third equation is the trade deficit as percentage of GDP.

Imposing the conditions that the fiscal deficit and the trade balance, as proportion of GDP, are stationary, and taking logarithms to the efficiency condition for private investment, we obtain the first cointegration relationship in the model:

$$\begin{aligned} \ln y_{ipri_{t}}-\ln \alpha -\ln y_{gdp_{t}}-\ln y_{td_{t}}\sim I(0). \end{aligned}$$

(A.12)

The second condition implies that the $\frac{y_{gpub_{t}}}{ y_{td_{t}}y_{gdp_{t}}}$ ratio is stationary in the long run, which implies (after taking logarithms) that:

$$\begin{aligned} \ln y_{gpub_{t}}-\ln y_{td_{t}}-\ln y_{gdp_{t}}\sim I(0). \end{aligned}$$

(A.13)

Similarly, if the two previous conditions are satisfied, we obtain that $\frac{y_{c_{t}}}{y_{td_{t}}y_{gdp_{t}}}$ is also stationary, which (after taking logarithms) implies that:

$$\begin{aligned} \ln y_{c_{t}}-\ln y_{gdp_{t}}-\ln y_{td_{t}}\sim I(0). \end{aligned}$$

(A.14)

Therefore, equations (A.12), (A.13) and (A.14) represent the theoretical support for the three cointegrating vectors used in the paper.