Welfare consequences of inconsistent monetary policy implementation in Vietnam

Abstract We develop a New Keynesian model featuring Calvo price setting and Calvo wage setting to quantify the welfare consequences of shifting trend inflation in Vietnam. To capture the characteristics of the Vietnamese economy, we use the Simulated Method of Moment and calibrate parameters jointly to match the important selected moments of Vietnamese data. The results show a severe consequence of a constant positive trend inflation and an exogenous shock to trend inflation, especially when a central bank sets a high level of inflation target. Among staggered price and wage contracts, the latter play a vital role in transmitting the adverse impacts of constant and shifting trend inflation into the economy. Based on our analyses, raising inflation targets would seem to be a bad policy prescription in Vietnam.


Introduction
Vietnam has experienced periods of unstable inflation in the past. In recent years, bad signals in the world market, such as an upsurge in the prices of commodity and petroleum, have raised concerns regarding potential substantial rises in future inflation in Vietnam. In addition, the implementation of Vietnamese monetary policies aiming to control these issues seems to be inconsistent and ineffective, which has partly contributed to a more substantial rise in inflation. All are expected to bring about serious consequences.
To model the substantial rise in inflation, many authors, such as Kozicki and Tinsley (2001), Ireland (2007), Cogley, Primiceri, and Sargent (2009) and Nakata (2014) have employed a highly persistent trend inflation process to depict slow changes in implicit inflation targets 1 set by a central bank. This adoption implies a lack of commitment to a fixed inflation target or a tendency of the central bank to let inflation rise. By using this idea, authors show the necessity for studies on shifting trend inflation 2 , for example, the study illustrating the implications for the term structure of interest rate by Kozicki and Tinsley (2001), that on the consequences for output and inflation by Ireland (2007), the research on implications for the predictability of inflation by Cogley et al. (2009), and the study on welfare consequences by Nakata (2014). However, the literature has mostly considered one form of rigiditiesthe sticky-price model with shifting trend inflation. Just recently, authors have considered other forms of rigidities to quantify welfare costs. In particular, Ascari, Phaneuf, and Sims (2018) incorporated staggered wages into the medium-scale model to quantify the welfare costs of constant trend inflation. They argue that constant trend inflation magnifies the inefficient utilization of labor, then produces more sizable welfare costs. Ha, Thanh, and Thang (2019) also emphasizes the important role of staggered wage contracts in transmitting the effects of trend inflation. However, the welfare consequences of shifting trend inflation, a salient property of developing countries, have not been fully exploited.
The present study fills the gap in the literature by exploiting the welfare costs of exogenous variation in trend inflation in Vietnam. In this paper, trend inflation is interpreted as a central bank's target inflation rate and we model it as a highly persistent AR (1) process. The focus is paid on the Vietnamese economy for the following reasons. First, the idea of shifting trend inflation is suitable for Vietnam because of its inconsistent and ineffective policy implementations during the 1996-2015 period. Table 1 reports changes in monetary policy targets as well as the difficulties in achieving them. Second, the actual data in Vietnam also indicate a time-varying and highly persistent property of trend inflation, especially during the financial crisis. Figure 1 clearly shows shifts in mean values or trend inflation (the red line) over time. To quantify the welfare consequences of shifting trend inflation, we first use a benchmark model -a standard New Keynesian model with Calvo price setting-to compare the welfare between an economy with zero and positive variance of shocks to trend inflation. Subsequently, additional analyses are conducted by considering a different price setting behavior to point out the welfare cost differences stemming from inefficient allocations of resources and physical adjustment costs; a higher-order approximation to check the accuracy of the second-order approximation; a robust check for parameters, and a model with both staggered price and wage contracts.
We model the characteristics of the Vietnamese economy by using the Simulated Method of Moment (SMM) for the quarterly data in Vietnam during the 1996Q1-2015Q4 period and make a robust check by calibrating the parameters jointly to match the important moments of the Vietnamese year data during the 2005-2016 period. The inconsistency of the time period stems from the unavailability of quarterly data for consumption and labor supply in Vietnam-these yearly data have only been available since 2005. Selected moments, closely related to dynamic behavior of consumption and labor supply, are important for welfare cost computations, which are the main exercise of the paper.
With these considerations, we show that the consequences of constant and shifting trend inflation are severe, especially when a central bank sets a high inflation target level. The evidence is more obvious if we adopt the model with staggered price and wage contracts. Among two channels, the staggered wage contracts play a crucial role in transmitting the impacts of constant and shifting trend inflation into the economy. Our conclusion in the case of developing country is aligned with Ascari et al. (2018), who conducted a similar exercise in the U.S. In the present study, we provide additional evidence for the role of staggered wage contracts in the welfare consequences of shifting trend inflation. The welfare consequences in Vietnam are more severe than those in developed countries due to parameter value differences.
The rest of this paper is organized as follows. We outline the literature review in Section 2 and the extended model is discussed in Section 3. Section 4 explains how to compute welfare and welfare costs. Estimated parameters are presented in Section 5 while Section 6 and Section 7 show the main results and results of further analyses. Some conclusions are provided in Section 8. 1997Q4 Figure 1. Vietnam CPI inflation: 1996Q1-2015Q4 (annualized quarter-to-quarter percent changes).
Source: GSO. The red lines are the average of inflation in different periods.

Literature review
A log-linearization around the zero inflation steady state is the popular approach in the existing literature 3 . The approach is convenient because it can produce a simple and tractable model but wash out some implications of the microfoundations 4 and can lead to misleading conclusions. Realizing the limitations, Ascari (2004) and Bakhshia, Khanb, Burriel-Llombartc, and Rudolf (2007) make substantial changes in the short-term and long-term properties of model based on the Calvo staggered price model with trend inflation. In particular, Ascari (2004) studies the impulse response of output to the money-growth shock with various levels of trend inflation to analyse the effects of trend inflation on output persistence, while the effects of non-zero inflation on the slope of the NKPC are investigated by Bakhshia et al. (2007). The early contribution of Ascari (2004) and Bakhshia et al. (2007) are building blocks in the literature for the latter researchers to exploit diverse implications of non-zero and then shifting trend inflation. Regarding welfare analysis, this paper is related to two strands of the literature. First, it is related to the literature on non-zero trend inflation. The plurality of models has so far adopted the sticky-price model with positive trend inflation, such as Ascari,(2004), Amano, Ambler, and Rebei (2007), Ascari and Ropele (2009), and Coibion and Gorodnichenko (2011). These papers show that a less-than-4-percent trend inflation rate has a minor impact on the economy. In particular, Ascari (2004) finds that an additional steady-state output loss of 0.5 percent is created when increasing trend inflation from 2 to 4 percent, while the compensation-equivalent welfare loss is less than one percent, as found in Amano, Moran, Murchison, and Rennison (2009). By contrast, Ascari et al. (2018) study a medium-scale model with staggered prices and staggered wages to show significant welfare costs of constant trend inflation. They also emphasize the role of staggered wage contracts on these costs.
The other strand is related to the model with shifting trend inflation. By employing the second perturbation approximation method suggested by Kim, Kim, Sims, and Schaumburg (2008), Nakata (2014) attempts to quantify the welfare consequences of shifting trend inflation. In his model, he argues that the negative impacts of exogenous variations in trend inflation are transmitted into the economy solely by the staggered price contracts. With this consideration, he shows the trivial welfare costs of shifting trend inflation. In this study, we follow an approach similar to that used in Nakata (2014) to measure the welfare consequences of shifting trend inflation. However, we incorporate an additional channel that trend inflation distorts the relative allocation of labors across households through a staggered wage contract, as discussed by Erceg, Henderson, and Levin (2000), thus causing changes in welfare. By matching the important moments of Vietnam, we argue the welfare consequences of inconsistent policy implementation for the case of developing countries.
Previously, many authors argue that raising inflation targets would seem to be a bad policy prescription. On the policy front, the significant welfare costs of trend inflation present a warning against policy proposals requiring central banks to raise their inflation targets. This policy implication is aligned with those of Ascari and Sbordone (2014) and Ascari et al. (2018). However, these results might conflict with the fact that central banks target a positive level of inflation, around 2 percent per year. The discussion against targeting a zero or a low rate of inflation is the Zero Lower Bound (ZLB, henceforth) constraint. In particular, Summers (1991) discusses that with a very low average inflation rate, the central banks might encounter limitations of conducting an effective stabilization policy since this policy requires nonnegative real interest rates and nominal rates. The need for a negative real rate of interest when there exists the zero lower bound would be accommodated by an inflation target ranged from 1 to 3 percent as argued by Summers (1991) and Fischer (1996). Krugman (1998) raises a similar point when he argues that an inflation target of 4 percent for several years in Japan is necessary to generate the negative real rates and curb deflation.
In recent years, economists have emphasized on the likelihood and consequences of hitting the ZLB, for example, Reifschneider and Williams (2000), Schmitt-Grohe and Uribe (2011), and Coibion, Gorodnichenko, and Wieland (2012). They argue that raising the inflation targets could reduce the costs related to the ZLB as well as the probability of hitting the ZLB. Moreover, the literature has so far advocated a higher inflation target, which is realized by a temporary increase in expected inflation instead of a permanent increase in the long-run inflation objective. To generate the expectation of higher inflation, the key is the commitment to a history-dependent policy as argued by Eggertsson and Woodford (2003), Coibion et al. (2012), and Ascari and Sbordone (2014). The commitment to the future policy can decrease the current real interest rate and provide economic stimulus. Without the commitment to a history-dependent policy, it would be more likely to emphasize the costs of positive trend inflation.

Model
The model is populated by four classes of agents: the household indexed by j 2 ½0, 1; the final-goods producing firms; a continuum of intermediate-goods producing firms indexed by i 2 ½0, 1; and the government.

The household
In the benchmark model, households maximize their expected discounted present value of future period utility with respect to a given budget constraint. Their period utility function can be separated into two components: consumption ðC t Þ and working hours ðH t Þ as given where b and c denotes the discount factor and the habit formation parameter, which are restricted as 0<b<1, 0 c<1: t is the inverse Frisch elasticity of labor supply. The flow budget constraint is represented as Equation (2) shows the different sources of households' income. Households earn W t h t ðiÞ by providing h t ðiÞ units of labor to each intermediate-goods producing firm i 2 ½0, 1 at the beginning of each period. They also receive a nominal profit, D t , because they own the intermediate goods, and receive the lump-sum government transfer, T t . They then decide to use their income in different ways. During each period t, households purchase consumption goods, C t , from the final-goods producing firms at the nominal price, P t . They also purchase the one-period bond, B t , from the intermediate-goods producers at the price 1=R t as a saving. Therefore, households choose labor supply, h t , bond holding, B t , and consumption, C t , to maximize the lifetime utility, subject to the budget constraints.

The Final-Goods producing firm
Final-goods producing firms maximize profits by using constant-return-to-scale technology. In order to manufacture Y t units of final products, they employ Y t ðiÞ units of intermediate goods sold at a nominal price P t ðiÞ as follows where h p is the price elasticity of demand for intermediate goods. The profit maximization problem of the final-goods producing firms is given as The first-order condition for the final-goods producing firms problem is given as Since the competitive final-goods firms have zero profit in the equilibrium, the final good price, therefore, can be rewritten as

The Intermediate-Goods producing firm
A continuum of intermediate-goods producing firms, indexed by i 2 [0 1], hire h t ðiÞ units of labor from households to produce Y t units of intermediate goods (i) during the period t. They employ constant-returns-to-scale technology, which can be written as: The logarithm of aggregate technology shock, Z t , follows a stationary stochastic process: where Z t is the serially uncorrelated innovation, which has a normal distribution with mean zero and standard deviation r Z . We assume that the intermediate-goods producers set nominal prices as in a staggered Calvo price fashion. According to Calvo (1983), a fixed fraction, g p , of firms, which cannot re-optimize their nominal prices, still set their prices according to the indexation rule. The way those firms reset their prices is given as: where v p and l p are a degree of price indexation and the relative weight on lagged inflation, respectively. The inflation, p t , is defined as P t P tÀ1 and p t is interpreted as the central bank's inflation target. The fraction (1Àg p ) of firms, on the other hand, are able to set their price. They maximize the present value of future profits by choosing the price P Ã such that where p tþsÀ1 ¼ P tþ2 P tþ1 ::: P tþs P tþsÀ1 if s ¼ 1,2,3, … , k t is the same as the Lagrangian multiplier on the household's budget constraints, and W t denotes the nominal wage.

Monetary policy
The authority sets the short-term nominal interest rates following a Taylor rule. In particular, the rule allows for interest rate smoothing and interest rate responses to deviations of inflation from the central bank's inflation target and deviations of output from the steady state: where R, y are the steady state of R t and Y t , respectively. The parameter q R illustrates the degree of interest rate smoothing. R t is an i.i.d. monetary policy shock.
The evolution of trend inflation is described as a persistent AR(1) process as: where q p denotes the degree of shock persistence and p t is a standard normally distributed shock that is independent of time.

Fiscal policy
The public spending is given by where g t is an exogenous disturbance following the stochastic process where 1À1 g ð Þ represents the steady-state value of government spending relative to output.

Market clearing condition
The market clearing condition in the labor market, the goods market and the bond can be expressed in turn as

Welfare and welfare cost computation
Following Nakata (2014), we also use the perturbation method to compute the approximation to the policy functions around the deterministic steady-state, and use these to compute the welfare. We decompose the welfare into the three different components as given below: and Muð xÞ and Nuð xÞ are vectors that contain the first and second derivative of u(.) evaluated at x, which are the deterministic steady state of x t . Three components consist of: the deterministic component, , and the volatility component, U v ¼ P 1 t¼0 b t Nuð xÞE½ðx t À xÞ ðx t À xÞ: Then the welfare cost can be computed as: where C A, t , H A, t are consumption and labor supply in the economy with r p >0 and C B, t , H B, t , are consumption and labor supply in the economy with r p ¼ 0:

Data
The system involves three observable variables, including output growth ðg y t Þ, inflation ðp t Þ and short-term nominal interest rate ðr t Þ: This study uses quarterly Vietnamese data collected from 1996Q1 to 2015Q4. The raw data are taken from the database available at the General Statistics Office of Vietnam (GSO) and the International Financial Statistics (IFS). Seasonally-adjusted figures for real GDP, which are converted to GDP per capital by dividing by the total population, serves as a measure of output growth. Quarterly changes in seasonally-adjusted figures for Consumer Price Index and quarterly lending rate yield the measure of inflation and nominal interest rate, respectively. Regarding the yearly data, we collect figures for the private consumption, the number of employment and the government expenditure during the 2005-2016 period. All data are de-trended prior to the estimation of the model.

Simulated method of moment estimates
Following Ruge-Murcia (2012), the present study uses the Simulated Method of Moment (SMM). By using this method, we minimize the weighted distance between the empirical moments and the moments computed from the artificial data.
The model parameters are separated into two subsets. The first subset includes fixed parameters that are fixed prior to the estimation Table 2 shows the parameter values of this subset. We set the discount factor (b) and the inverse Frisch elasticity of labor supply (t) to 0.99 and 3.00, respectively. Regarding the production sector, the degree of indexation (v) and the weight on lagged inflation (l) are set to 0.00 and 1.00, as argued by Cogley and Sbordone (2008) 5 . The elasticity of the substitution parameter for differentiated intermediate goods is set to 10. We also set the probability of not being able to optimize (g p ) to 0.65 and then we let this value change to observe differences in welfare consequences. The share of government expenditure to output is set to its respective sample mean.
The second subset includes the remaining parameters for the persistence level and volatility level of monetary shock (q R and r R ), technology shock (q Z and r Z ), and shock to trend inflation (q p and r p ), the Taylor coefficients on inflation (/ p ) and output growth (/ y ). Table 3 reports the SMM estimated parameters based on the second-order approximate solution for the Vietnamese data. The null hypothesis that each estimated parameter does not differ from zero is statistically rejected at 5 percent significance level. Regarding a shock to trend inflation, although previous work, such as Ascari and Sbordone (2014), Cogley et al. (2009), Fuhrer andMoore (1995) and Fuhrer (2010) holds the consensus on the high persistence of trend inflation, its exact magnitude still remains debated, especially considering the time-varying trend inflation in developing countries. Table 3 shows that the persistence of trend inflation is close to 0.995 and statistically significant at 5 percent.
Regarding the coefficients of Taylor rule, this study shows a fairly high persistence of monetary shock. Furthermore, the obtained parameters imply that the central bank responds considerably to the inflation gap, but weakly to the output gap. These results are consistent with Hieu (2012). Moreover, the monetary shock volatility is smaller than that of the shock to trend inflation ( Figure 2).

SMM impulse responses
The top panel of Figure 2 shows a decrease in consumption and labor supply in response to a one-standard deviation increase in the monetary policy shock. Moreover, reductions in both output and inflation are also attributed to the monetary policy shock, as expected by the theory in the bottom panel of Figure 2. A higher magnitude of change, such as a two-standard deviation increase in exogenous  Taylor coefficient on the output gap 0.5000 Ã 0.0001 Note: S.E. is a standard error. The superscripts Ã denote that for the null hypothesis the true parameter value is zero and rejected at the 5 percent significance levels. Source: Authors' calculation.
monetary policy shock, signifies changes in the respective macroeconomic variables. The converse happens when considering a negative exogenous shock.
It is essential to analyze the consequences of inconsistent policy implementation for the shock to trend inflation. The top panel of Figure 3 provides some implications to explain how the shock to trend inflation leads to welfare distortions. In particular, a one-standard deviation increase in exogenous shock to trend inflation leads to a decrease in consumption but a rise in labor supply. These opposite trends tend to expand over time. In addition, we also investigate the macroeconomic effects of exogenous shock to trend inflation in the bottom panel of Figure 3. A diminishing of output growth and a rise in inflation are explicit consequences of the shock to trend inflation. From the results, it can be seen that  ignoring the positive constant and time-varying property of trend inflation may lead to serious consequences.

Welfare and welfare cost results
This study firstly conducts exercises to observe the welfare effects of exogenous shock to trend inflation 6 . Moreover, we perform additional analyses to make some robust checks of some issues, such as a different price setting behavior, the accuracy of the second-order approximation, alternative parameters, and different nominal rigidities.  Table 4 compares the economy with a 0-annualized-percent level and a 6-annualizedpercent level of trend inflation. When a central bank changes its inflation targets from 0 percent to 6 percent, it leads to a high welfare cost (3.14%) compared to the results in Lucas's study. The results suggest that the sudden change in inflation targets might cause severe welfare consequences in developing countries like Vietnam. A welfare cost due to a higher level of trend inflation mainly stems from changes in the level component (from -0.25 to -4.94), while changes in the deterministic component and volatility component are negligible(from -211.06 and -1.50 to -212.11 and -2.16, respectively). The economic properties reflected by the steady-state values, mean values, and volatility values of consumption and labor supply in Table 4 provide explanations for welfare differences between two economies. A reduction in the steady-state and mean values and a rise in the volatility values of consumption and leisure are sources of welfare distortions when a central bank sets up a constant positive level of trend inflation. The results are aligned with those of Amano et al. (2007) and Nakata (2014). The top panel of Figure 4 represents changes in welfare costs with respect to a rise in the trend inflation level and the bottom panel provides reasons to explain these changes. A given amount of rise in trend inflation causes welfare costs to grow non-linearly.

The cost of price dispersion
The Calvo mechanism creates a price dispersion term, which generates a wedge between output and hours to cause welfare distortions. The wedge, however, is sensitive to trend inflation, i.e. it induces differences when trend inflation is positive and disappears when trend inflation is zero. In this section, we argue that positive trend inflation affects the steady-state price dispersion to create the cost of price dispersion. The steady state of price dispersion is represented as follows: It can be seen that the steady-state price dispersion increases corresponding to an increase in g, h, and p t whereas a reduction of price indexation ðvÞ leads to an improvement of price dispersion. More intuitively, if the price is entirely flexible ðg ¼ 0Þ, there is no price dispersion, sð p t Þ ¼ 1: On the other hand, a greater level of substitution elasticity leads to a growth in price, due to more inefficient allocations among firms. More importantly, a rise in constant positive trend inflation drives the steady-state price dispersion up by inducing a gap between the price set by re-setting firms and the average price level, and this results in an inefficiency loss in aggregate production. Finally, a decrease in steady-state price dispersion can be explained by price indexation since it implies that non-optimizing firms can catch up with price changes by optimizing firms. Hence, a greater price indexation causes price to be less dispersed at any inflation rate.
Following Damjanovic and Nolan (2010) and Ascari and Sbordone (2014), this study also measures the cost of price dispersion, expressed asz t ¼ z t s t , which is a measure of effective aggregate productivity and maps a percentage increase in price dispersion into an equivalent percentage. Figure 5 illustrates that trend inflation leads directly to a reduction in effective aggregate productivity. Furthermore, a rise in price stickiness and elasticity of substitution or a fall in price indexation causes effective aggregate productivity to diminish. This is due to the way in which these parameters impact the steady-state price dispersion, as discussed above. These effects, then, are magnified when trend inflation reaches a higher level. In short, trend inflation can impact the cost of price dispersion in both direct and indirect ways.

Determinacy regions
In this section, the paper examines the effects of changes in trend inflation on the ability of the monetary authority to guarantee a determinacy region and macroeconomic stability. As argued by Woodford (2003), a given increase in inflation, intuitively, requires a greater proportional rise in the nominal interest rate, inducing a rise in the real interest rate. As a result, a drop in output is recorded via the Euler equation to curb the initial growth of inflation via the NKPC. Figure 6 illustrates the determinacy region in the space of the policy parameters ð/ y , / p Þ: The left-hand side to the right-hand side of the top panel of Figure 6 correspond to changes in the determinacy region when trend inflation is 0, 4, and 8 percent. The bottom panel represents changes in the determinacy region when trend inflation increases.
For the interest rate rule, the determinacy region narrows rapidly with a rise in trend inflation. Visually, the determinacy region shrinks because the two lines governing the generalized principles rotate when trend inflation increases. Hence, a weaker policy toward output gap and a stronger policy toward inflation are required simultaneously to guarantee the determinacy region. Consistent with previous studies, for example, Ascari and Ropele (2009) and Ascari and Sbordone (2014), the monetary policies that respond more to deviations of inflation from the target and less to the output gap are preferred in order to ensure the determinacy region in the higher inflation rate regime. Table 5 compares the economy with zero variance of shocks to trend inflation and the economy with positive variance of shocks to trend inflation. In both economies, we set a positive level of trend inflation but this exercise differs from the previous one by assuming the time-varying variance of trend inflation. The results show a lower welfare in the economy with shifting trend inflation compared to the economy with constant trend inflation. The welfare differences come mainly from a reduction in the level and volatility component, whereas the deterministic component remains unchanged. In this exercise, we also report changes in the properties of economies to explain the sources of the welfare costs of shifting trend inflation. Both mean consumption and leisure tend to decrease, while the economy becomes more volatile, reflected by its higher volatility levels due to a positive variance in shocks to trend inflation. The welfare cost is 0.13%, which is slightly larger than the result of Nakata (2014), who performed the same exercise to explain the persistently high inflation during the Great Inflation period in the U.S. In his study, Nakata also performs the sensitivity analysis to show that the welfare costs of trend inflation are contingent on the values of relevant parameters, such as the degree of price indexation, the frequency of price adjustment, the level of trend inflation and the persistence and variance level of shocks to trend inflation. Because we employ SMM for the Vietnamese data to obtain the different parameter values, these partly explain the welfare cost differences between our study and Nakata's.

A different price setting: Rotemberg quadratic price adjustment costs
This section investigates whether the aforementioned conclusions still hold with an alternative price friction. For comparison purposes, we quantify the welfare costs of constant and shifting trend inflation in the Rotemberg pricing model. As in Nakata (2014), this analysis helps us to point out the differences in the welfare costs of inflation stemming from the price dispersion, causing the inefficient allocation of resources and those stemming from the physical adjustment cost of changing prices. An intermediate-goods producing firm (i) selects the prices to maximize the expected discounted future profits as follows: subject to the quadratic price adjustment cost, AC t ðiÞ, which is given as: where / is the parameter capturing the price adjustment cost. In this Rotemberg model, we need to calibrate / such that the slope of the Phillips curve is the same as those in the Calvo pricing model at zero trend inflation. By mapping / in the Rotemberg model to g in the Calvo model, these two models imply an identical form for the first-order approximated Phillips curve. Under the Calvo pricing with zero trend inflation, the first-order approximation Phillips curve is presented as: whereN t ¼p t Àvlp tÀ1 andp ¼ ln p t p t À Á : Under the Rotemberg pricing with zero trend inflation, the first-order approximation Phillips curve is given aŝ Therefore, / needs to be set as: Accordingly, the values of / are [33,48,70,107] with respect to g ¼ ½0:6, 0:65, 0:7, 0:75: Table 6 reports the welfare costs of constant and shifting trend inflation in the Rotermberg model. An increase in trend inflation leads to a rise in the price adjustment costs, then an asymmetric change in consumption and labor supply decisions. Although conclusions in the two models are the same, the welfare consequences due to constant and shifting trend inflation in the Calvo model are slightly larger than those in the Rotemberg model.

A third-order approximation
In the following exercise, we conduct a robust check of the accuracy of the secondorder approximation by solving the model with a third-order approximation. We extend the method of Kim et al. (2008) to quantify a third-order welfare. The results do not indicate a significant quantitative difference between the second-order and third-order welfare costs 7 (0.13 percent versus 0.16 percent). By performing the higher-order approximation, we have some evidence to confirm our results on welfare costs. The third-order in the exercise, however, is computationally expensive, thus not convenient for further analyses.

A robust check of parameters
To conduct a robust check of parameters, we use an alternative set of parameters that are obtained from simulating the model to match the important moments of data. We select four moments: the output volatility (r Y) ; the consumption volatility(r C ); the labor supply volatility (r H ); and the correlation between consumption and output (corr(Y, C)). We choose these moments because they are closely related to the behavior of consumption and labor supply, which serve for welfare consequence analysis 8 . To obtain the information of these moments, we employ HP-filtered Vietnamese yearly data for output, consumption, and labor supply during the 2005-2016 period 9 instead of quarterly data for output growth, inflation, and short-term interest rate as previously. Table 7 reports the calibrated parameters. Table 8 compares the moments created by the calibrated model with the moments computed by the data. In general, the calibrated model is remarkably good at matching the selected moments, thus can provide an adequate laboratory for subsequent welfare analysis. Table 9 represents the welfare costs and dynamic properties of the economy due to constant and shifting trend inflation. In general, all conclusions in the previous exercise remain the same. However, welfare costs of constant and shifting trend inflation from using the recalibrated parameters are larger. These results might suggest that the changes in implicit inflation targets set by a central bank might be a serious problem in the case of developing countries like Vietnam.

Model expansion
In the literature, Ascari et al. (2018) show the more sizable welfare costs of constant trend inflation in the medium-scale DSGE model, incorporating both staggered price and wage contracts. In this section, we examine whether staggered wage contracts are an important channel through which shifting trend inflation distorts the economic welfare more significantly in Vietnam. We follow Erceg et al. (2000) to expand the benchmark model by assuming that there is a fraction, g w , of households who cannot freely set their wages but still can update their wages as follows: The remaining fraction of households can choose an optimal wage by maximizing subject to the labor demand function: Table 12 in Appendix A lists all the calibrated parameters that we use for welfare cost computation in this exercise. In this exercise, we assume a fair probability of non-optimization for prices and wages so that g p and g w , are calibrated at 0.69. In the exercise of quantifying the welfare costs of trend inflation, Ascari et al. (2018) also set similar values for these parameters. We also assume a fair degree of price and wage indexation (0.5).

Results
This section first represents the welfare costs of shifting trend inflation in the model with nominal price and wage rigidities (General Case). Subsequently, we consider two special cases: Case 1 -the model with staggered price contracts and completely flexible wages (g p >0, g w ¼ 0); and Case 2 -the model with completely flexible prices and staggered wage contracts (g p ¼ 0, g w >0), to analyse which channel is the most important for the transfer of the impacts of constant and shifting trend inflation. Table 11 reports the welfare consequences of constant and shifting trend inflation. Regarding the costs of constant trend inflation, they are roughly 2.73%. In addition, the welfare costs in the staggered price model (g p >0, g w ¼ 0) are highly trivial, compared to the staggered wage model(g p ¼ 0, g w >0). By adopting the similar model with staggered price contracts, Ascari (2004), Amano et al. (2009), andNakata (2014) also show the modest cost of constant trend inflation. The greater cost in the model with staggered wage contracts suggests that the staggered wage mechanism plays a vital role in transmitting the impacts of varying trend inflation levels into the economy. This argument is consistent with those of Ascari et al. (2018).
Regarding the welfare costs of shifting trend inflation, we provide striking results in this analysis. The welfare costs of shifting trend inflation in the model with staggered price and wage contracts are fairly high (0.25%). Comparing two special cases, the welfare costs of shifting trend inflation in the model with staggered wage contracts are remarkably higher than those in the model with staggered price contracts. The results reporting modest costs of shifting trend inflation in the model with nominal price rigidities are consistent with Nakata (2014). Our study emphasizes the role of staggered wage channel, through which exogenous variations in trend inflation significantly distort welfare.

Conclusions
This paper made its key contribution by exploiting the welfare consequences of shifting trend inflation, a salient property of developing countries like Vietnam, by building a New Keynesian model featuring a Calvo price setting. We used the Simulated Method  of Moment proposed by Ruge-Murcia (2012) to jointly calibrate parameters to match important moments of the Vietnamese data. Additional analyses such as the different price setting behavior, the higher order of approximation, the other parameter set, and the role of staggered wage contracts were performed to conduct robust checks on our arguments. Our results show that the consequences of constant positive trend inflation and shocks to trend inflation are severe, especially when trend inflation is high. Among the two channels, staggered wage contracts play a vital role in transmitting the adverse impacts of constant and shifting trend inflation in a developing economy.
The results of this study have crucial implications for both policy makers and economists. Based on the preceding analyses, raising inflation targets would seem to be a bad policy prescription. On the policy front, the significant welfare costs of constant positive and shifting trend inflation present a warning against policy proposals requiring central banks to raise their inflation targets.

Notes Funding
This work was supported by National Foundation for Science and Technology Development (NAFOSTED) of Vietnam [grant number: 502.01-2019.309].