[1] argued that the demand for real cash balances will drop as inflation develops. Earlier studies focus primarily on the impact of expected inflation on money demand during hyperinflation period. However, hyperinflations are extreme events, which lead to a small sample problem for sound estimation. The problem has been moderated by examining the money demand schedule at daily frequency such as [2] . But the data sets about the money demand at daily frequency are usually unavailable in most developing countries such as China. Another strand of research abandons Cagan’s framework and opts for money demand schedules that allow for money substitutes, where elasticity increases as inflation accelerates and extends the sample to include the lower inflation period. Advancing that line, [3] argued that Cagan’s hypothesis might also hold in the deflationary period in which the demand for money will be higher during such period. [4] investigated the money-prices relationship under low and high inflation regimes in Argentina. Other recent studies include [5] .

In 2009, the obvious behavior of the public’s purchase of real estate against future price increase makes the Chinese government explicitly express that inflation expectation should be efficiently managed for the first time. A number of studies have explored the relationship between inflation and inflation expectation in China. However, little research has explored above relationship in the perspective of the Cagan money demand. Recently [6] has investigated the money-supply effect of inflation expectation in China by the model combining Cagan model and Lucas microeconomic rational expectation equation. What’s more, most of these previous studies examine demand for money by a linear model from macro view. In this paper, we adopt a panel smooth transition regression (PSTR) approach to study the demand for money by firms in China. Our method complements previous studies in three directions. Firstly, it overcomes the problems resulting from the sample-splitting regressions. Secondly, it reduces the potential endogeneity bias [7] . Finally, it allows heterogeneity of money demand for individual firms.

[8] and [9] define the money demand model as

where, is the firm specific effects, and is the disturbance. is the money holdings of firm i at date t. is the volume of sales of firm i at date t, as a measure of the scale of activity. is the nominal opportunity cost of money and is the wage of the workers involved in the production of transaction services. represents a type of productivity parameter that can be considered as an indicator of the firm’s degree of financial sophistication. Since the variables might contain unit roots, we rewrite the above model as:

where, , , and are the corresponding first-difference of the log variables in Equation (1). captures that time fixed effect which controls for economy-wide changes in financial sophistication [9] . According to [8] , we expect that and. Our parameter of interest is. However, the sign of cannot be predetermined because not only measures the change of transaction costs, but also proxies for the inflation rate. If transaction costs dominate, a higher firm’s “shoe-leather costs” is expected to increase money holdings, which implies. When inflation drops to a level that does not materially enter into the decisions of firms, the above transaction-cost effect might dominate. [10] suggests an overwhelmingly negative effect of the inflation rate on money demand during periods of hyperinflation which might lead to a negative sign of coefficient on. However, due to the presence of opposing effects that might offset each other, it is not advisable to test for Cagan’s hypothesis by a linear model using the data which are not from hyperinflation period. Note that the higher inflation rate, the stronger the Cagan effect is. Therefore, a higher wage tends to result in a smaller coefficient on, which leads to nonlinearities of the demand for money.

Following [11] , we extend Equation (2) to a nonlinear panel smooth transition model:

where, the transition function is a continuous and bounded function of the transition variable. Following [7] , we use the following logistic transition function:

where, c denotes a location parameter, denotes a transition variable and parameter determines the shape of the transition function. The PSTR model has two major advantages over the linear model. First, it addresses the presence of the endogeneity that results from a two-way causal relationship between the variables and [7] . Second, it allows the parameters to be different at different inflation levels, as they are now functions of the wage variable. For instance, note that the wage coefficient for the i^th firm at time t is defined as:

Given the properties of the transition function, we have if or if. Consequently, the PSTR model allows us to evaluate the influence of the wage variables on money demand at different inflation-regimes. According to Cagan’s hypothesis, we expect.

There are a relatively limited number of studies addressing Cagan’s hypothesis on money demand in China. This paper attempts to fill this gap by adopting a panel smooth transition approach on the firm-level data. Our results support the presence of the Cagan effect in China. In addition, it is found that the higher the inflation rate is, the stronger the Cagan effect is. The policy implications are obvious. Firstly, central banks should be more concerned with inflation expectation than they have been in the past, for inflation may have a significantly greater acceleration in the high inflation period. Secondly, once inflation expectation zooms up, central banks need to pursue aggressive and nontraditional monetary policy to reestablish suitable price anticipations by the public.

We would like to thank the foundation from the National Natural Science Foundation of China (71201174 and 71002056) and Guangdong Natural Science Foundation (S2013010015019; 2014A030313577) for financial support of this research.