# Theoretical Framework

This section presents the theoretical model that allows us to derive the relevant hypothesis on the relationship between the current account and financial liberalization.

Our aim is to embed financial repression in a model of the current account that can explain the data well, yet is simple enough to derive intuitive theoretical predictions. Recent work by Bussiere et al. (2006), Gruber (2004), and Kano (2009) has shown that, augmented with either external/internal habits in consumption or a persistent world real interest rate, the intertemporal model of the current account (ICA), first presented in Sachs (1981), can give a good explanation of actual current account movements. Due to its simplicity and good empirical fit, we take this model as our basic building block. Conceptually, financial repression can affect macroeconomic variables in at least two ways. First, repression/ liberalization can affect the efficiency of transforming savings into productive investment (Goldsmith 1969) by either promoting or hindering competition in the banking system. Second, the volume of savings flowing into investment can either increase (Mckinnon 1973; Shaw 1973) or decrease (Devereux and Smith 1994; Jappelli and Pagano 1994) following liberalization. The former is likely to affect the price, while the latter the quantity, of capital available for investment. Since current account balances reflect quantities rather than prices, we focus on the second channel. While theoretically ambiguous, empirical evidence s upports the proposition that financial repression decreases savings through the liquidity constraints channel. Diaz-Alejandro (1985) points out that in developing countries, the volume of savings tends to fall following financial liberalization. Bayoumi (1993a, b) and Sarno and Taylor (1998) find that financial liberalization in the UK in the 1980s decreased liquidity constraints, leading to a decline in aggregate savings. Bayoumi and Koujianou (1989) and Jappelli and Pagano (1994) confirm this pattern across a range of industrialized countries. Bandiera et al. (2000) also find empirical support for the idea that financial repression affects savings via the liquidity-constraints channel in eight emerging market economies. Finally, using data for 72 countries, Lewis (1997) finds that consumers in countries with government restrictions on international transactions tend to act as if they are liquidity constrained. Note that in contrast to her work, we focus on government restrictions on domestic, rather than international, financial transactions. This breadth of evidence justifies our approach of introducing financial repression via liquidity constraints in the ICA model.

Bergin and Sheffrin (2000) and Ghosh (1995), among others, find no empirical support for the simple intertemporal current account model in most G7 countries. The literature has proposed three different modifications of the basic model to improve its empirical performance. Gruber (2004) introduced internal habit formation (where utility is a function of past individual consumption), Bussiere et al. (2006) used external habit formation (where utility is a function of past average consumption), and Nason and Rogers (2006) argued that a time-varying stochastic world interest rate would deliver a more realistic model. Recently, Kano (2009) has shown that the internal habits and time-varying world real interest rate approaches provide observationally equivalent predictions. We therefore add both external and internal habits and also add a liquidity constraint to the standard ICA model in order to model financial repression. We then show that our identification restrictions are robust to any possible parameterization of our model.

We consider a small open, endowment economy populated by a large number of households who maximize utility subject to a budget constraint. Output, investment, government expenditure, and lumpsum taxes are exogenous. The exogeneity assumption is a convenient s implification that is unlikely to hold empirically. However, since our main theoretical predictions follow directly from the Euler equation, they would most likely also hold in more complex DSGE models where all macroeconomic variables are endogenous. Unlike in those models, however, the fact that we can obtain an analytical solution, and that we do not need to resort to numerical methods, allows us to easily and transparently demonstrate that our predictions and, more importantly, identification restrictions are robust to all admissible parameter values. There are two types of households in the economy. One type of households is liquidity constrained in the sense that they do not have access to any savings technology. We will refer to them as non-Ricardian households. These households consume their exogenous net income (output) each period:

where *NO _{t}* =

*Y*is net output,

_{t}—I_{t}— G_{t}*Y*is output,

_{t}*I*is investment and

_{t}*G*is government spending, all expressed as per capita. The second type of household has access to incomplete international financial markets in which only non-contingent riskless bonds are traded. These households are characterized by their optimal behavior with respect to the intertemporal allocation of consumption. We will refer to this group of households as Ricardian throughout. We assume that non-Ricardian households make up a fraction of

_{t}*у ?*[0, 1] of the population with Ricardian households as the remainder. Hence, aggregate consumption is defined as

*C = rC*+(1

^{m}*-*y)cR.

The representative Ricardian household solves the following utility maximization problem:

where *в **E* {0, 1} is the discount factor and *C ^{f}* consumption at time t, and

*C*

_{t}__{j}is past consumption.

*B*+ j is the net stock of international bonds held by the Ricardian agent at the end of time t, which are reimbursed at the world real interest rate

_{t}*r.*Households choose

*Cf*and

*B*+

_{t}_{j}to maximize discounted lifetime consumption subject to the budget constraint and a no-Ponzi condition. We assume 0 <

*h*< 1, which implies that Ricardian households may be habit forming with respect to consumption. We explore both the possibility of external and internal habit formation in consumption. As a result, utility is increasing in consumption expenditure that exceeds the depreciated value of last period’s average consumption in the economy (in the case of external habits) or the depreciated value of the household’s lagged consumption, with

*h*being the rate of depreciation. The utility function takes a log form throughout to facilitate algebraic calculations. The first-order necessary conditions of this optimization problem comprise the budget constraint (8.2), the transver- sality condition (8.3) and the following Euler equation:

Iterating the budget constraint and imposing the no-Ponzi condition yields the intertemporal budget constraint of the Ricardian agent:

In order to derive an analytical solution to the present value of the current account, we take linear approximations of both the budget constraint (8.5) and the Euler equation (8.4). Following the approach in Kano (2008), one can show after a fair amount of algebra (see Appendix at the end of the chapter) that

Let *c* , *b ^{G}* ,

*b*,

^{P}*ц*and $ denote the unconditional means of the consumption to net output ratio, the net foreign private asset to net output ratio, the net foreign public asset to net output ratio, the log of the gross world real interest rate and the growth rate of net output and consumption, respectively. Let us define

*X*, where

_{t}= X_{t}- X*X*is the steady-state value of variable

*X.*Taking a first-order Taylor expansion of (8.6) around the steady state yields the following expression:

where *к* = exp ($*—*ц). In words, this is the linearized budget constraint. At this point further assumptions have to be made to solve the model. The literature has proposed three different simplifications to solve the model. The first option is to assume that the world real interest rate is constant and that Ricardian consumers display external habit formation (i.e., the argument of the utility function is *C ^{R} *

*-*

*hC*where

_{t-l}*C*denotes average consumption in the economy). The second option is to assume a constant world real interest rate and internal habit formation by Ricardian consumers (i.e., the argument of the utility function is

*C*

^{R}*-*

*hC*

^{R}_J*).*Finally, one can assume a stochastic world real interest rate and the absence of habit formation (h = 0 in our model). Kano (2009) shows that these last two frictions imply observationally equivalent data- generating processes. Although it is difficult to know in practice which model is underlying the data-generating process, it can be shown that our identification assumptions are robust to any of these specific modeling choices. This exercise, together with the detailed derivation of current account reaction functions, is relegated to the Appendix. Our exposition here focuses on the case of a constant world real interest rate and external habit formation. Under these assumptions the current account reaction function is described by

where f is an expectational error, defined as

*f _{t} = ^{h}* l

^{1 -}y)

^{2}E

^{- E}t-*1*){

^{ln}

*C*-4

^{R}t+i^{and}

*ca*. Th

_{t}=^{is theor}y

i=i *NO _{t}*

suggests that in the absence of liquidity constraints, the current account under external habit formation is a function of the lagged current account and a weighted average of current and future net output changes. In this case the model becomes virtually identical to Gruber (2004). As habits become stronger, the importance of both the lagged current account to net output ratio increases, the first term in (8.8), and the weight of expected future net output growth (second term) increases. Liquidity constraints play two roles in the current account reaction function (Eq. 8.8). First, as a larger fraction of households is liquidity constrained, the importance of net output shocks diminishes since fewer households are able to smooth such shocks by borrowing and lending internationally. With external habits, the consumption decisions of Ricardian agents depend on the past average consumption in the economy. Given that past average consumption is also affected by the presence of liquidity constraints, but Ricardian agents do not internalize this, the coefficient on the lagged current account term becomes a function of both habits and the fraction of liquidity-constrained consumers. With external habits, therefore, the speed of current account adjustment also becomes a function of the liquidity constraint. In the Appendix we show that the predictions obtained from a model with internal habits are identical with respect to the size effect, but the lagged current account term is not a function of liquidity constraints anymore since only individual, as opposed to average, past consumption is relevant to Ricardian consumers’ consumption decision in that framework.