Simulations and experiments are reported for nonequilibrium steady-state assembly of small colloidal crystal clusters in rotating magnetic fields vs frequency and amplitude. High-dimensional trajectories of particle coordinates from image analysis of experiments and from Stokesian Dynamic computer simulations are fit to low-dimensional reaction coordinate based Fokker-Planck and Langevin equations.

The coefficients of these equations are effective energy and diffusivity landscapes that capture configuration-dependent energy and friction for nonequilibrium steady-state dynamics. Two reaction coordinates that capture condensation and anisotropy of dipolar chains folding into crystals are sufficient to capture high-dimensional experimental and simulated dynamics in terms of first passage time distributions. Our findings illustrate how field-mediated nonequilibrium steady-state colloidal assembly dynamics can be modeled to interpret and design pathways toward target microstructures and morphologies.

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We develop a three-location spatial applied general equilibrium model calibrated to the Tanzanian Social Accounting Matrix to examine the impact of various public investment programs on household welfare across this diverse geography in which production and consumption are locationally specific and transport costs support equilibrium price differences across locations.

Whether this nominal depreciation is also reflected in the real exchange rate depends on the speed of domestic price adjustment.

## Lysozyme in Water

The data reveal shocks to several of the variables in the mid—s Figure 1. This period was marked by turmoil associated with the transition to a multiparty democracy and the initiation of an economic reform program, including the floating of the exchange rate 8.

In addition, a variable has been introduced to capture the Balassa-Samuelson effect MacDonald and Ricci, and , and two variables have been added to capture the temporary misalignments induced by inconsistent macroeconomic policies. Hence, the empirical model for the ERER is.

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This analysis focuses on permanent changes in the explanatory variables that bring about changes in the long-run ERER. The ERER is associated with the fundamental variables in their steady state levels. Deviations of these variables from their respective steady state levels result in deviations from the ERER. This approach prevents the bias introduced by using the observed values to estimate the long-run cointegrating relationship between the real exchange rate and the fundamentals, as a temporary shock would have a permanent impact on the ERER.

In order to estimate the empirical model as shown in equation 14 , we first test for stationarity of the fundamental variables Table 1 , then for cointegration Table 2 , using the Johansen cointegration test Johansen, , and finally we proceed with the estimation procedure described in Appendix II. Using augmented Dickey-Fuller ADF statistics and selecting the number of lags based on the Schwarz information criterion, the results show that all explanatory variables are stationary in the first differences, as is the REER Table 1.

The first difference stationarity of the REER is consistent with other studies of the real exchange rate and renders the PPP, in its traditional form at least, less useful. In all model specifications tested by using the Johansen cointegration test, the null hypothesis of zero cointegrating equations can be rejected; in some cases there appear to be two cointegrating equations Table 2.

The likelihood ratio test indicates that ECM 2 is the most appropriate. Table 3 and 4 show the estimated elasticities of the ECMs: model 1, the specification closest to the theoretical model includes only the fundamental variables derived from the theoretical model; model 2, also captures the impact of the macroeconomic policy variables, and model 3, a parsimonious specification where the insignificant variables have been eliminated.

The results for the equilibrium real exchange rate for Malawi model 1 are given in its error-correction form in equation The detailed estimation results are given in Tables 3 and 4.

The coefficient before the term brackets is the speed-of-adjustment coefficient. The statistically significant short-term variables are listed after the term brackets. The resulting equation is as follows:.

## Vector Variational Inequalities and Vector Equilibria

The results of the estimation are consistent with the theoretical model. Public consumption, excluding wages and salaries, has a positive appreciating impact on the real exchange rate, indicating that most government spending in Malawi is directed toward nontradables. In contrast, the long-run impact of wages and salaries on the real exchange rate is negative, confirming that a larger wage bill in terms of GDP tends to put pressure on the external current account.

The terms of trade of goods are positively correlated with the real exchange rate, consistent with a possible wealth effect. The relatively high long term impact of GDP per capita is mitigated by a short term negative impact.

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However, this could be more due to this variable capturing tobacco production, which represent about 80 percent of export earnings but less then 10 percent of GDP, than a strong Balassa-Samuel son effect. Moreover, investment is also positively correlated with the real exchange rate. However, when the macroeconomic policies are added to the model specification model 2 , the terms of trade are found not to be significant.

Finally, while the nominal depreciation associated with overly expansionary monetary policies has offset the effect on the domestic price level, overly expansionary fiscal policies were found to be not statistically significant. The finding that changes in net foreign assets were not significant might be due to the choice of this variables as proxy capital flows. One possible explanation might be that, while the data set starts in , tobacco export earnings and balance of payments assistance became a substantial part of net foreign assets only during the s.

It could also be that the terms of trade have an indirect impact through net foreign assets.

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As model 3 indicates, an increase in net foreign assets could indeed have a positive impact on the real exchange rate as long as terms of trade are omitted from the model specification. The long-run relationship between the equilibrium real exchange rate and the key explanatory variables can be summarized as follows Table 3 : A 1 percent increase in the level of government consumption as share of GDP, excluding wages and salaries, is associated with an appreciation of the REER of 0.

A 1 percent increase in the terms of trade of goods appears to be associated with an appreciation of the REER of about 0. When there is a gap between the value of the real exchange rate and its equilibrium level, the real exchange rate will tend to converge to its equilibrium level.

Depending on the cause of the gap, the adjustment requires that the real exchange rate either move progressively toward a new equilibrium level or return from its temporary deviation to the original equilibrium value. This study estimates that some 20 percent of the gap is eliminated every quarter, implying that, in the absence of further shocks, half of the gap would be eliminated within about 11 months.

As the Malawi kwacha was pegged to a basket of seven major currencies until February , this led to an overvalued real exchange rate Reserve Bank of Malawi, Following the flotation of the exchange rate and the sharp depreciation of the nominal exchange rate, the REER became undervalued. The paper shows that the ERER in Malawi is determined by standard fundamental variables, as well as by monetary policies. Government consumption, excluding wages and salaries, has a positive impact on the real exchange rate, consistent with most government spending being directed toward nontradables.

In contrast, the long-run impact of wages and salaries on the real exchange rate is negative, indicating that a larger wage bill in terms of GDP tends to put pressure on the external current account.

The terms of trade of goods appear to be positively correlated with the real exchange rate, confirming the impact of the wealth effect. Also real per capita growth and investment are positively correlated with the real exchange rate. Finally, a loose monetary policy is associated with a depreciating real exchange rate.

The results also indicate a rapid adjustment of any deviation of the real exchange rate from its equilibrium value. The paper shows that, in the absence of further shocks, about half the gap between the actual value of the REER and its equilibrium values could be eliminated within about 11 months. Sources: IFS ; and staff estimates.

Source: National Statistical Office, Malawi. Source: IFS. Source: National Statistical Office, Malawi; and staff estimates. This paper relies on an econometric technique developed by Gonzalo and Granger to decompose the observed real exchange rate RER into a transitory and a permanent component. The estimated ERER is taken to be the permanent component, while the transitory component reflects deviations from equilibrium.

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In order to understand the link between equilibrium and cointegration, it is useful to depart from the theory of purchasing power parity PPP , which implies a constant value of ERER. However, if the RER contains a unit root i. The failure of PPP to hold does not necessarily imply that no equilibrium exists, but rather that the equilibrium may be time varying. Thus, cointegration among a set of variables allows for the presence of a time-varying equilibrium and presents a very desirable property: it allows for the decomposition of the relationship among the variables into two components.

The permanent component, which would be I 1 , describes the long-run properties of the relationship among the variables and can be identified with a time-varying equilibrium path; a transitory component, which would be I 0 , corresponding to deviations over time from the permanent component and would represent departures of the fundamentals from their steady state values. Gonzalo and Granger propose a way of solving the econometric problem so that the permanent equilibrium component of the key endogenous variable, the real exchange rate, can be constructed by means of the permanent components, rather than by the actual values of the fundamental determinants.

The first restriction implies that the changes in the transitory component will not have an effect on the long-run values of the variables. The second restriction makes the permanent component observable and assumes that the contemporaneous observations contain all the information necessary to extract the permanent component.