TANK meets Diaz-Alejandro
Household heterogeneity, non-homothetic preferences & policy design

The economy considered is populated by two type of households: Ricardian (”$R$”) households, which have access to different savings technologies, and Hand-to-Mouth (”$H$”) households which can not save and consequently consume the totality of their income. Parameter $\lambda^{R}\in\left(0,1\right)$ represents the share of Ricardian households in this economy.

The Ricardian household’s budget constraint is given by

where $K_{t}$ represents the stock of capital, $P^{k}_{t}$ is the price of capital, $D_{t}$ are holdings of domestic asset, $R_{d,t}$ and $R^{*}_{t}$ are the interest rate on domestic and foreign assets, $W_{t}$ is workers’ wage rate and $\Omega^{R}_{t}$ represents any profits from firms, commodity production and or net lump sum transfers from the government. Household’s optimality conditions can be characterized by its intra-temporal labor choice and three Euler equations with respect to capital, domestic asset and foreign assets

where $v_{t}$ is the Lagrange multiplier in the household’s time $t$ budget constraint and $R^{k}_{t+1}$ is the rate of return on capital given by

where $r_{t+1}$ is the real rental rate of capital.

Hand-to-mouth households are not able to smooth their consumption and, thus, consume their total income every period. The representative hand-to-mouth household’s budget constraint is given by

where $P^{H,C}_{t}$ is the price of this households consumption bundle, $W^{H}_{t}$ is the nominal wage of the hand-to-mouth households, and $\Omega^{H}_{t}$ represent net taxes/transfers from the government. Hence, this household’s optimality condition include the intra-temporal which relates labor and consumption

but no intertemporal optimality conditions.

Figure 3 shows how expenditure shares on the commodity good change as income levels increase when $\alpha_{Co}=0.5$. The solid magenta line shows that when $\phi_{Co}=0$, the preferences presented in Equation 3.1 collapse into the standard Cobb Douglas preferences, i.e., the expenditure share of the commodity good is equal to $\alpha_{Co}$. The dash and dot lines show the expenditure shares for the commodity (in red) and the non-commodity good (in blue) for a low but positive value of $\phi_{Co}$. Note that for low income levels the expenditure share in the commodity goods increase significantly (consequently the expenditure share in the non-commodity good decreases sharply). The skewness of expenditure share increases as $\phi_{Co}$ increases, as can be seen in the red and blue dashed lines in Figure 3.

Note that the domestic price of the commodity good is assumed to be equal to the international price $P^{Co}_{t}$ times the nominal exchange rate (which is the same assumption made for the domestic price of the imported goods in the rest of the model). This is not an innocuous assumption as it implies one-to-one exchange rate pass-through of the commodity good. In Appendix A.3 I study the dynamics of both international and Uruguay’s domestic food indexes and present evidence in support of this model assumption.

Finally, the non-commodity good is itself a CES aggregator of the homogeneous domestic final good and the homogeneous imported good, given by

where $C^{D}_{t}$ and $C^{F}_{t}$ represent the quantities consumed of the domestic and foreign final goods; $\varphi^{N}$ is a parameter that represents the relative importance of domestic goods in the non-commodity aggregator and $\epsilon$ is a parameter governing the elasticity of substitution across the two goods. This framework yields standard demand schedules given by

where $P^{N}_{t}$ is the price of the non-commodity consumption bundle, and $P^{F}_{t}$ is the price in foreign currency of the imported good.

This section describes the exporting side of the economy. In order to match the dynamics of a small open economy similar to those of Uruguay, exports are comprised of two distinct sub-sectors: a commodity sector and a non-commodity sector. On the one hand, the non-commodity good is produced using the domestic final good and exporters face a downward sloping demand curve which depend on a foreign demand shifter and the real exchange rate (in line with standard SOE-NK models). On the other hand, the commodity sector is characterized by stochastic processes which govern the international price of the good and the local endowment the commodity good.

Production of the non-commodity good is carried out through a one-to-one technology using domestic final goods as inputs. I assume that a perfectly competitive exporter purchases the domestic homogeneous good at price, $P_{t}$. It sells the good at dollar price, $P_{t}^{x}$, which translates into domestic currency units, $S_{t}P_{t}^{x}$. Note that competition implies that price, $S_{t}P_{t}^{x}$, equals marginal cost, $P_{t}$.

The exported quantities of the sector are determined by the difference between the domestic production and the local consumption of the commodity good

In the parametrization of the model in Section 4.1, parameters are chosen such that the economy is a net-exporter of the commodity good both in steady state and for reasonable values of the stochastic processes in the economy.¹⁷¹⁷17In other words, parameters are chosen such that in both the non-stochastic steady state of the economy and under simulations the trade balance of the commodity good is positive.

In this economy government is comprised of two distinct policy makers. First, there is a monetary authority which sets a policy rule for the nominal interest rate. Second, there is a fiscal institution which carries out government expenditure of the domestic homogeneous final good.

The central bank sets the nominal interest rate every period following a standard Taylor rule of the form

where $R_{d,t}$ is the central bank’s risk-less interest rate, $\pi^{C,R}_{t}$ and $\pi^{C,H}_{t}$ are the Ricardian and Hand-to-mouth consumption basket inflation rates, $\bar{\pi}$ is the inflation target, $y_{t}=Y_{t}/A_{t}$ is final output scaled by technology, $\tilde{S}_{t}$ is the nominal exchange rate. and $\epsilon^{R}_{t}$ is an i.i.d. mean zero policy shock. I consider the Taylor rule described by Equation 3.3 as a benchmark and study alternatives in Section 5 where I study the design of optimal policies.

The fiscal authority follows a government expenditure rule every period. This rule is composed of an endogenous and exogenous block.

The first term on the RHS of Equation 16 is comprised of a constant or steady state value of government expenditure. The second term implies that government expenditure reacts to deviations of the commodity price from steady state values via a tax rate $\tau^{C}$.¹⁸¹⁸18This rule is similar to the one proposed by García-Cicco and Kawamura [2015]. However, I abstract from government debt for simplicity. I assume that taxes are levied lump-sum so that the resource constraint is satisfied every period. Consequently, I abstract from government debt issues.¹⁹¹⁹19See García-Cicco and Kawamura [2015] on fiscal expenditure optimal policy rules which take into account government debt explicitly. If $\tau^{C}<0$, then the government expenditure rule will decrease government expenditure and taxes during periods in which the total revenue of the commodity exporting sector are above their steady state values and increase it when commodity revenues fall. Given that commodity prices explain a large fraction of macroeconomic fluctuations (see Drechsel and Tenreyro [2018]), a rule parametrized to $\tau<0$ will take the form of a counter-cyclical government expenditure rule.

In this section I describe the parametrization of the model. In particular, I focus on discussing the choice of households’ and aggregate parameter values. This parametrization is the benchmark for the impulse response functions presented in Sections 4.2 and 4.3. Appendix C presents a full description of parameter values.

I begin by describing the parametrization of the Ricardian and Hand-to-mouth household’s parameters. Overall, the rationale behind the choice of households’ parameter is to simultaneously match statistics presented in Section 2: the share of Ricardian and Hand-to-mouth households, and heterogeneity in the share of consumption of commodity based nourishment goods without imposing unrealistic steady state values on models’ variables. Table 3 presents the benchmark numerical values and description of households’ key parameters.

The choice of the discount factor $\beta$ is consistent with a steady state interest rate of 5%, which is in line with EMBI spreads for Uruguay in the last two decades.²¹²¹21Furthermore, this value of $\beta$ is close to other values used in the literature, for instance higher than the value chosen in Garcia Cicco et al. [2012], but lower than the value used in Cubas et al. [2012]. The choice of a logarithmic utility function over consumption is in line with Cubas et al. [2012] and Camara et al. [2021]. The share of Ricardian households, $\lambda^{R}$, is set to 0.50. This motivation behind this value is twofold. Figure 1 in Section 2 the first bar graph in shows that around 50% of Uruguayan households have access to a bank account. However, the amount of savings and/or limits to overdrafts on these banks accounts is not clear. Thus, assuming 50% of Ricardian households is an upper bound on the share of agents with access to saving technologies. Additionally, 50% of Ricardian households is in line with other papers in the literature of TANK models in small open economies (see García-Cicco and Kawamura [2015] and Cugat et al. [2019]). I set the Frisch elasticity equal to 1, in line with Mendoza [2002]. The only parameter values which differ across households are $\chi_{R}$ and $\chi_{H}$ which are set to match steady state labor across the two type of households. Finally, I set $\alpha_{Co}$ equal to 0.25 and $\phi_{Co}$ equal to 0.45 such that in steady state commodity expenditure represent 33.69% and 48.43% of Ricardian and Hand-to-Mouth consumption, respectively (in line with the results presented in Table 2).

Second, I describe the numerical values key model parameters that govern aggregate trade and policy rules, presented in Table 4. The first four parameters relate to the export of commodity and non-commodity goods

This parameter choice implies a steady state ratio of total exports to GDP of 33%, with 80% of exports being commodity goods in line with aggregate trade data. Additionally, the steady state price of the commodity good is set to 0.15, in line with firm-customs level data on export prices of commodity and non-commodity goods.²²²²22For more details on aggregate and firm-customs level data see Appendix A.2 for more details. The bottom five parameters of Table 4 govern the central bank’s Taylor rule. The inflation target is set to 5%, in the middle of the 3% to 7% inflation rate set by the Uruguayan Central Bank.²³²³23See https://www.bcu.gub.uy/Politica-Economica-y-Mercados/Paginas/Reportes-de-Politica-Monetaria.aspx. This value is in line with the value used in Cubas et al. [2012]. The numerical values of the Taylor rule’s reaction coefficients $\rho_{R},\phi_{\pi},\phi_{y},\phi_{s}$ are in line with the estimation results of Christiano et al. [2011] and Gonzalez-Rozada and Sola [2014]. In terms of fiscal policies, the value of parameter $\bar{g}$ is set to match a government expenditure to GDP ratio of 30% in line with data coming from the IMF’s WEO. For the benchmark exercises carried out in Sections 4.2 and 4.3 $\tau^{C}$ is set to zero.

Next, I describe the role of non-homothetic preferences over commodity goods in propagating two relevant exogenous shocks in small open economies: a foreign interest rate shock $R^{*}_{t}$ and a commodity price shock $P^{C}_{t}$. These exercises shed light on how changes in prices of key inputs of households’ consumption baskets have aggregate repercussions. In particular, I argue that higher degrees of non-homotheticity amplifies the macroeconomic impact of these shocks.

The rise in the foreign interest rate first impacts the small open economy through the uncovered interest rate parity condition. An increase of 60 annual basis points (see Panel 1.1) leads to a depreciation of the nominal exchange rate (see Panel 1.2). The exchange rate depreciation increases in the domestic currency price of both commodity and imported consumption goods, leading to a jump in the consumption bundle inflation rate of both households (see Panel 1.3). The central bank’s policy rate reacts to the exchange rate pass-through in prices by increasing the nominal policy rate $R_{d,t}$ (see Panel 2.1). While the initial depreciation boost exports and the production of the domestic final good $Y_{t}$ for the first two periods after the shock, the higher domestic rate leads to a persistent drop in $Y_{t}$ even 20 periods after the shock. The trade balance exhibits a similar pattern, with a sharp improvement in the first period which rapidly becomes a deficit, and later returns to its steady state value (see Panel 2.3). Ricardian and Hand-to-mouth households’ consumption exhibit a significant drop on impact (see Panels 3.1 and 3.2 respectively). However, Hand-to-mouth’s consumption a significantly greater initial drop and slower recovery. This slow recovery is primarily explained by the persistent drop in real wages measured in terms of the domestic final good (see Panel 3.3).

Next, I study the implications of non-homothetic preferences in the response of household specific variables to a foreign interest rate shocks $R^{*}_{t}$. Figure 5 shows the dynamics of household specific consumption, consumption price bundles and real wages for the benchmark model (blue solid line) and a parametrization homothetic preferences (magenta dotted line).

Non-homothetic preferences barely affect response of Ricardian consumption to a foreign interest rate shock $R^{*}_{t}$ (see Panel 2.1). However, non-homothetic preferences lead to a significantly greater and more persistent drop in Hand-to-Mouth consumption (see Panel 2.2). These greater initial drop in Hand-to-Mouth consumption in the model with non-homothetic preferences is partially explained by a greater drop in real wages, measured in terms of domestic final good. Notwithstanding, non-homothetic preferences impact households’ consumption primarily through price indexes. Panel 2.1 of Figure 5 shows that the relative price of the Ricardian consumption bundle with respect to the domestic final good hardly changes with respect to a homothetic exercise. However, Panel 2.2 shows that the increase in the relative price of Hand-to-mouth consumption bundle is five times greater with non-homothetic preferences compared to the homothetic exercise.

In summary, the model’s benchmark parametrization leads to aggregate dynamics in line with other Two Agent New Keynesian models. The introduction of non-homothetic preferences amplifies the dynamics of both households’ consumption. The Hand-to-mouth household is particularly hit due to the drop in real wages and the lack of access to saving technologies. Moreover, non-homothetic preferences implies that as consumption decreases, a greater share of income is spent on the now more expensive commodity good (due to exchange rate pass-through). Thus, non-homothetic preferences amplify the drop in Hand-to-Mouth consumption.

The higher international prices for the commodity good impact the small open economy through two main channels: a transitory wealth effect and an increase in the price of households’ consumption bundle. A 5% international commodity price shock leads to a 1% increase in the domestic currency price of the commodity good (see Panel 1.1). The smaller impact on the domestic currency price of the commodity good is explained by the initial sharp appreciation of the nominal exchange rate (see Panel 2.1). However, the nominal appreciation is short-lived, leading to a mild depreciation in the following periods. The rise in the commodity price leads to an increase in the consumption bundle inflation rate (see Panel 1.3). The monetary authority reacts by increasing the nominal interest rate $R_{d,t}$ (see Panel 2.1). On the real side of the economy, the production of the domestic final good expands and the trade balance experiences a surplus (see Panels 2.2 and 2.3). On the one hand, Ricardian consumption experiences a initial drop and a mild expansion in subsequent periods, explained by consumption smoothing to a transitory wealth shock. On the other hand, the commodity price shock leads to a significant drop in Hand-to-Mouth consumption. Finally, Panel 3.3 shows that drop in Hand-to-Mouth consumption is at least partially explained by a drop in real wages measured in terms of the domestic final good.

Again, I analysis the implications of non-homothetic preferences in the response of household specific variables to a commodity price shock $P^{Co}_{t}$.

Figure 7 presents the dynamics for the benchmark parametrization (blue solid line) and for a homotheticity exercise (magenta dotted line). In line with the results presented for a foreign interest rate shock, non-homothetic preferences primarily affect households which do not have access to saving technologies. To see this, note that under the benchmark parametrization, Ricardian consumption experience a sharper drop on impact, but recovers faster than the case with homothetic preferences (see Panel 1.1). But non-homothetic preferences lead to a drop in Hand-to-Mouth consumption which is almost three times greater than in the homothetic exercise. The drop in Hand-to-Mouth consumption is driven by a significant fall in real wages, measured in domestic final goods, and a greater increase in the price of its consumption bundle.

In short, while the benchmark model parametrization leads to aggregate dynamics in line with a previous literature, non-homothetic preferences matter for household specific dynamics. While Ricardian households experience an increase in consumption after an increase in commodity prices, Hand-to-Mouth households experience a persistent drop in consumption. Moreover, I show that non-homothetic preferences amplify the negative impact of a commodity price shock on Hand-to-Mouth households. These results are in line with a literature which has highlighted how the commodity price boom in the 2000s negatively affected poor income households in Latin American (see Frenkel et al. [2016] for Argentina and Estrades and Terra [2012] for Uruguay) and African (Benson et al. [2008] for Uganda and Shimeles and Woldemichael [2013] for Ethiopia) countries. Thus, this framework highlights an underlying tension which arises in agricultural commodity exporting countries: an increase in commodity prices creates a positive wealth shock for the small open economy but negatively affects poor income countries which spend a significant share of their income in food and have no access to saving technologies.

In this section of the paper I show that in the structural framework presented in Section 3 monetary policy has a redistribution channel. More specifically, exogenous shocks in the domestic monetary policy rate produce opposite dynamics for the consumption of Ricardian and Hand-to-mouth households. Furthermore, I argue that the relative importance of this redistribution channel increases with the degree of non-homotheticity over the consumption of commodity goods. In order to show this, I carry out impulse response function exercises of a domestic monetary policy shock under different model parametrizations.

First, I study the dynamics of benchmark model after a domestic interest rate shock, presented in Figure 8.

This shock leads to a persistent drop in the domestic currency commodity price (see Panel 1.1) explained by a persistent nominal exchange rate appreciation (see Panel 1.2). The drop in the domestic currency price of the commodity good leads to an overall initial fall in the consumption price bundle inflation (see Panel 1.3). Panel 2.1 exhibit the dynamics of the domestic monetary policy interest rate $R_{d,t}$. The significant drop in the domestic price of the commodity good leads to an initial and brief drop in $R_{d,t}$ which later reverts to a temporary increase. The higher interest rate lead to a drop in the production of the homogeneous final good (see Panel 2.2) and a deterioration of the trade balance (see Panel 2.3). Households’ consumption experience exactly opposite dynamics. On the one hand, the Ricardian household experience a hump-shaped decrease in consumption driven by inter-temporal consumption smoothing (see Panel 3.1). On the other hand, Hand-to-mouth households experience a significant increase in consumption (see Panel 3.2). This increase in $C^{H}_{t}$ is explained by both the decrease in the domestic price of commodity goods and an increase in real wages measured in terms of the homogeneous final good (see Panel 3.3). In summary, the structural framework presents aggregate dynamics in line with previous literature (exchange rate appreciation, fall in inflation, drop in economic output), but suggests households react differently to a hike in domestic interest rates.

Next, I study the role of non-homothetic preferences in explaining the opposing households’ consumption dynamics in response to a domestic monetary policy shock.

Figure 9 presents the dynamics for the benchmark parametrization (blue solid line) and for a homotheticity exercise (magenta dotted line). Note that non-homothetic preferences are not the driving force which explains the opposing consumption dynamics. The inter-temporal smoothing channel leads Ricardian households to reduce consumption under both exercises (see Panel 1.1). Hand-to-mouth households increase consumption (see Panel 1.2) due to the increase in real wages (see Panel 1.3) and the reduction in the consumption price bundle (see Panel 2.2). However, in line with the results presented in Section 4.2, non-homothetic preferences matter for the quantitative impact of a domestic monetary policy shock for Hand-to-mouth households. Panel 1.2 shows that the presence of non-homothetic preferences doubles the increase of Hand-to-mouth consumption, while a significantly smaller impact for Ricardian consumption (see Panel 1.1). The greater increase in $C^{H}_{t}$ is driven by an appreciably greater increase in real wages and significantly sharper decrease in the Hand-to-mouth consumption price index.²⁴²⁴24Note that non-homothetic preferences do not affect the Ricardian consumption price index as significantly as the Hand-to-mouth consumption price index

To summarize, the exercises presented in this section showed that under the present structural framework a domestic monetary policy shock impact households’ consumption with opposite signs. Hand-to-mouth households are benefited by the nominal exchange rate appreciation which reduces the domestic currency price of the consumption commodity good. Additionally, I showed that non-homothetic preferences matter for the quantitative impact of a domestic monetary policy shock on Hand-to-mouth households’ variables. These results suggest that monetary policy has a re-distributional channel, negatively affecting Ricardian households while benefiting Hand-to-mouth households.

Before carrying out the welfare analysis I show how different policy regimes shape aggregate and household specific dynamics in response to foreign interest rate shocks and commodity price shocks. This exercise sheds light on how households value different policy regimes. I consider both monetary and fiscal policy regimes.

The impact of monetary police regimes with less-flexible exchange rate regimes are in line with a previous literature. In response to a foreign interest rate shock, regimes with a less flexible nominal exchange rate (see Panel 1.2), the impact on consumer price inflation is lower or may even lead to deflation (see Panel 1.3). The policy rate $R_{d,t}$ shows a more persistent increase (see Panel 2.1). Note that the impact on the real interest rate (proxied by the difference between the dynamics shown in Panels 2.1 and 1.3) is appreciably greater in monetary policy regimes with less flexible nominal exchange rates. The higher domestic interest rate leads to greater drops in the production of the domestic final good (see Panel 2.2) and smaller trade balance surplus (see Panel 2.3).

Following the description of aggregate dynamics, I analyze household specific dynamics under a monetary policy regime with less flexible exchange rates. On the one hand, panel 3.1 shows that, compared to the benchmark parametrization, regimes with less flexible nominal exchange lead to a greater drop in Ricardian households’ consumption. This is driven by the greater response of the policy interest rate $R_{d,t}$ which leads to a higher inter-temporal motive. On the other hand, Panel 3.2 shows that Hand-to-mouth households’ consumption actually increases on impact under less flexible regimes. This initial increase is driven by a drop in the consumption price index (see Panel 1.3) and lower drop in real wages measured in the domestic final good (See Panel 3.3). However, this increase is short lived, and after 4 quarters consumption decreases and follows dynamics similar to the benchmark exercise. The opposing impact over households’ consumption dynamics under less flexible exchange rate regimes is in line with the results presented in Section 4.3. The benchmark exercise with a greater nominal depreciation and lower real interest rate leads to a lower impact on Ricardian households’ consumption and in the production of final goods. However, the less flexible regimes reduces the impact on Hand-to-mouth’s consumption price index which may even increase their total income (at least initially).

In particular, in Figure 11 I compare the benchmark dynamics presented in Figure 6 with two fiscal regimes depending on the value of $\tau^{C}$ in Equation 16: (i) a pro-cyclical regime with $\tau^{C}=1$ (dotted magenta line) in which government expenditure increases in response to an increase in the commodity price; (ii) a counter-cyclical regime with $\tau^{C}=-1$ (dashed red line) in which government expenditure decreases in response to an increase in the commodity price.

First, a pro-cyclical (counter cyclical) fiscal regime exacerbates (reduces) the aggregate impact of a commodity price shock, compared to the benchmark exercise. For instance, a pro-cyclical fiscal rule leads to a greater impact in consumer price in inflation (see Panel 1.3), and consequently a greater reaction of the domestic monetary interest rate (see Panel 2.1). Furthermore, the pro-cyclical rule increases aggregate demand leading to higher production of domestic final goods (see Panel 2.2). These exacerbation of aggregate dynamics can also be observed in the a greater trade balance surplus and a sharper drop in real wages measured in terms of the domestic final good (see Panels 2.3 and 3.3 respectively).

Second, I show that the pro-cyclical (counter-cyclical) fiscal regime also exacerbates (reduces) the impact of a commodity price shock on households’ consumption dynamics. Panel 3.1 shows that the pro-cyclical regime leads to greater Ricardian consumption, while Panel 3.2 shows that this regime leads to a greater drop in Hand-to-mouth consumption. This greater drop is explained by the aforementioned greater consumer price inflation and the sharper drop in real wages.

In summary, a pro-cyclical fiscal policy regimes in response to commodity prices shocks amplifies the dynamics found under the benchmark parametrization presented in Section. A counter-cyclical fiscal policy rule has the opposite effect, reducing the impact of a commodity price shocks. This result implies significant differences for the households in this economy. On the one hand, Ricardian households experience an even greater increase in consumption under a pro-cyclical rule compared to the benchmark scenario. On the other hand, Hand-to-mouth households experience an even greater drop in consumption under a pro-cyclical expenditure rule compared to the benchmark scenario. Consequently, households’ consumption dynamics differ across fiscal policy rules, as is the case for monetary policy regimes.

This section of the paper presents a normative analysis of households’ welfare under the different policy regimes described in previous sections. To do so, I choose the value of $\eta=\{\phi_{s},\tau^{C}\}$ which maximizes

for $j=\{H,R\}$. I approximate the value of this expected utility using a second order Taylor approximation around the non-stochastic steady state, following Schmitt-Grohé and Uribe [2007]. Furthermore, I compute both the mean and standard deviation of households’ consumption and labor across different values of $\eta$ to shed light on the household specific preferences over policy regimes.²⁵²⁵25To carry out the computation of the optimal policy exercise I impose bounds on parameter values. In particular, I set $\tau^{C}\in[0,1]$, which implies I consider fiscal policies anywhere between the full pro-cyclical and complete counter-cyclical cases. These bounds are in line with the optimal policy exercise carried out by García-Cicco and Kawamura [2015]. In the case of $\phi_{s}$, I only set a lower bound of 0.0002. This is due to a second order approximation solution to the model fails the Blanchard-Kahn conditions for values under this lower bound. I show that both Ricardian and Hand-to-mouth’s welfare is maximized at values of $\phi_{s}$ above this lower bound. I take this result as evidence that imposing a lower bound on $\phi_{s}$ does not drive the results of this normative analysis. Finally, I carry out the same optimal policy analysis shutting down non-homothetic preferences, i.e., setting $\phi_{Co}$ equal to zero.

The results of the optimal policy regimes are presented in Table 5. The main message of this table is that Ricardian and Hand-to-mouth households have opposing preferences over policy regimes. The former prefer regimes with strongly pro-cyclical fiscal policy and relatively more free floating exchange rate regimes, while the latter prefer counter-cyclical fiscal policy and a monetary policy regimes which exhibit “fear-of-floating”. The first panel shows the results for Ricardian households. For both the case with non-homothetic preferences and the case with homothetic preferences, Ricardian households prefer a pro-cyclical fiscal policy. The optimal combination of policy regimes reduce both the volatility of consumption and labor, while simultaneously increasing the mean consumption stream and decreasing average labor (compared to the benchmark case with an acyclical fiscal policy regime and a freely floating exchange rate regime).

To better understand the intuition behind Ricardian households’ preferences over policy regimes, Figure 12 shows the mean and standard deviation of Ricardian consumption streams as a function of $\eta$.

The first panel shows that pro-cyclical fiscal rules lead to higher mean Ricardian consumption streams, compared to acyclical or counter-cyclical rules. Also, for a given fiscal rule, higher exchange rate rigidity decreases mean consumption streams. The second panel shows that pro-cyclical fiscal rules increases the volatility of consumption streams compared to acyclical or counter-cyclical rules. Interestingly, the exchange rate rigidity has a non-monotonic relationship . For a given fiscal policy rule, an increase in exchange rate rigidity initially reduces consumption volatility, but after some intermediate level, further increasing $\phi_{s}$ leads to greater volatility. Consequently, the Ricardian households’ optimal set of policy regimes is the fiscal policy which maximizes mean consumption streams. This fiscal policy rule is accompanied of a low-degree of exchange rate rigidity which reduces overall consumption volatility, albeit sacrificing a small degree of mean consumption stream.

Next, I turn to the analysis of optimal policy regimes from the perspective of the Hand-to-mouth households, shown in the second panel of Table 5. Contrary to Ricardian households, Hand-to-mouth households prefer counter-cyclical fiscal policies for both the non-homothetic and homothetic cases. Furthermore, Hand-to-mouth households with and without non-homothetic preferences have preference towards “dirty-float” exchange rate regimes. This set of optimal policy regimes lead to a significant reduction in Hand-to-mouth consumption and labor compared to the benchmark parametrization (see columns 4 and 5 respectively). Additionally, the optimal policy regime leads to a significant increase in the mean consumption stream and a decrease in mean labor compared to the benchmark parametrization.

Once more, to shed light on the Hand-to-mouth households’ preferences over policy regimes, Figure 13 shows the mean and standard deviation of consumption streams as a function of $\eta$. The first panel shows that the mean $C^{H}$ is decreasing with the level of fiscal pro-cyclicality.

Also, for a given fiscal policy rule, the relationship between exchange rate rigidity and mean consumption stream is U-shaped. Initial increases in exchange rate rigidity increases mean consumption streams. After certain value of $\phi_{s}$, further increasing exchange rate rigidity decreases mean consumption streams. However, the decreasing segment of the “U” is significantly less steep than the increasing segment. A similar pattern is exhibited by the standard deviation of Hand-to-mouth consumption, with volatility increasing with the degree of fiscal pro-cyclicality. For a given fiscal policy rule exchange rate rigidity has an inverted U-shape impact on consumption volatility. Again, the second segment of the “U” is appreciably less steep than for the Ricardian households’ case. Consequently, Hand-to-mouth household’s optimal policy regime implies counter-cyclical and high-degree of exchange rate rigidity. Finally, while Hand-to-mouth preferences over policy regimes are aligned with and without non-homothetic preferences, the gain in utility from the changes in mean consumption and mean labor streams of moving to the optimal policy regime is three times greater in the case with non-homothetic preferences. This is not the case for Ricardian households, in line with the results presented in Section 4 which show that non-homothetic preferences only significantly amplify the response of Hand-to-mouth households’ consumption.

In summary, the normative analysis carried out in this section leads to the conclusion that in the current structural framework households have opposing preferences over both fiscal and monetary policy regimes. This result presents policy makers with a challenge on which policy regime to put in place. Even more, the preference of Hand-to-mouth for monetary policy regimes with significant exchange rate rigidity is a rationalization for Central Bankers’ “Fear-of-floating” found in the data (see Calvo and Reinhart [2002]). This preference over “dirty float” exchange rate regimes is based on the impact of exchange rate movements have on Hand-to-mouth households’ consumption and labor. Given that non-homothetic preferences exacerbate the impact of exogenous shocks on Hand-to-mouth households’ variables, as seen in Sections 4.2 and 4.3, it is not surprising that the benefits of “dirty float” regimes are increasing in the degree of non-homothetic preferences.